{"http:\/\/dx.doi.org\/10.14288\/1.0085503":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Science, Faculty of","type":"literal","lang":"en"},{"value":"Physics and Astronomy, Department of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Rixon, Scott John","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2009-12-02T01:04:04Z","type":"literal","lang":"en"},{"value":"2004","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#relatedDegree":[{"value":"Doctor of Philosophy - PhD","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeGrantor":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"Spectra of zirconium monocarbide (ZrC), zirconium methylidyne (ZrCH) and\r\nlanthanum imide (LaNH) are reported for the first time. All species have been produced under\r\njet-cooled conditions by reaction of gaseous metal atoms with methane or ammonia and\r\nexamined via laser-induced fluorescence.\r\n\r\nZrC has several electronic states below 2500 cm-\u00b9 : \u03a7\u00b3\u03a3\u207a and three \u00b9\u03a3\u207a states, which\r\nappear to represent all possible arrangements of two electrons in the nearly degenerate 11\u03c3 and\r\n12 \u03c3 orbitals (from Zr 5s\u03c3 + C 2p\u03c3). For \u03a7\u00b3\u03a3\u207a (r\u2080 = 1.807 \u00c5), the small spin-spin constant (\u03bb\u2080\r\n= 0.514 cm-\u00b9) and large Fermi contact parameter of \u2079\u00b9Zr\u00b9\u00b2C (I[sub zr] = 5\/2) indicate the\r\nconfiguration (11\u03c3)\u00b9(12\u03c3)\u00b9 . The tightly bound a\u00b9\u03a3\u207a state (T\u2080 = 187.83 cm-\u00b9, r\u2080 = 1.739 \u00c5) has\r\nthe configuration (11\u03c3)\u00b2, while anomalous vibrational intervals and \u00b9\u00b2C \/ \u00b9\u00b3C isotope shifts of\r\nthe other two states reveal their isosymmetry. This orbital scheme also accounts for the\r\ncomplex structure above 16000 cm-\u00b9; identical, strongly interacting manifolds result from\r\npromoting either a electron to the same orbital.\r\n\r\nZrCH has a \u00b2\u041f - \u03a7\u00b2\u03a3\u207a electronic system in the visible region analogous to that seen for\r\nisoelectronic ZrN, but they otherwise share little similarity. For \u03a7\u00b2\u03a3\u207a, high-resolution\r\nrotational analyses give r 0 bond lengths, while dispersed fluorescence has characterised its\r\nvibrational structure. Conversely, many details remain unclear for the excited state. \r\n\r\nUpper\r\nstate P = \u039b+l+\u03a3 values and Zr isotope shifts have been obtained for many subbands of ZrCH\r\nand ZrCD; \u00b9\u00b2C \/ \u00b9\u00b3C shifts have also been determined for some ZrCH bands. Unexpectedly\r\nsmall values of the spin-orbit constant and Zr-C stretching frequency, and the large Renner-\r\nTeller splitting in the 010-000 band are believed to be due to strong vibronic coupling with \u00b2\u03a3\r\nand \u00b2\u0394 states.\r\nThe electronic structure of LaNH is similar to isoelectronic LaO, with the added\r\ncomplication of vibronic coupling between the \u00c3\u00b2\u041f and B\u00b2\u03a3\u207a states. This is apparent from\r\nanomalies in the B\u00b2\u03a3\u207a - \u03a7\u00b2\u03a3\u207a hyperfine intensity profiles (I [sub La] = 7\/2), the Hund's case (a)\r\ncoupled B\u00b2\u03a3\u207a (0\u03c5\u20820) level structure and the large B\u00b2\u03a3\u207a state bending frequency.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/16115?expand=metadata","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/extent":[{"value":"17019791 bytes","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/elements\/1.1\/format":[{"value":"application\/pdf","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"HIGH RESOLUTION ELECTRONIC SPECTRA OF SOME NEW TRANSITION METAL-BEARING MOLECULES by SCOTT JOHN RIXON B. Sc., Memorial University of Newfoundland, 1993 M . Sc., University of Victoria, 1996 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (DEPARTMENT OF PHYSICS A N D ASTRONOMY) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A July 2004 \u00a9 SCOTT JOHN RIXON, 2004 11 Abstract Spectra of zirconium monocarbide (ZrC), zirconium methylidyne (ZrCH) and lanthanum imide (LaNH) are reported for the first time. Al l species have been produced under jet-cooled conditions by reaction of gaseous metal atoms with methane or ammonia and examined via laser-induced fluorescence. ZrC has several electronic states below 2500 c m - 1 : X 3 2 + and three l2Z+ states, which appear to represent all possible arrangements of two electrons in the nearly degenerate 11a and 12a orbitals (from Zr 55a + C 2pa). For X 3 \u00a3 + (r 0 = 1.807 A), the small spin-spin constant (Xq = 0.514 cm - 1 ) and large Fermi contact parameter of 9 1 Z r 1 2 C ( I Z r = 5\/2) indicate the configuration (1 la) 1(12a) 1. The tightly bound al~L+ state (T 0 = 187.83 cm\" 1, r 0 = 1.739 A) has the configuration (11a)2, while anomalous vibrational intervals and 1 2 C \/ 1 3 C isotope shifts of the other two states reveal their isosymmetry. This orbital scheme also accounts for the complex structure above 16000 c m - 1 ; identical, strongly interacting manifolds result from promoting either a electron to the same orbital. Z rCH has a 2n - X 2 Z + electronic system in the visible region analogous to that seen for isoelectronic ZrN, but they otherwise share little similarity. For X 2 E + , high-resolution rotational analyses give r 0 bond lengths, while dispersed fluorescence has characterised its vibrational structure. Conversely, many details remain unclear for the excited state. Upper state P = A+f+S values and Zr isotope shifts have been obtained for many subbands of ZrCH and ZrCD; 1 2 C \/ 1 3 C shifts have also been determined for some ZrCH bands. Unexpectedly small values of the spin-orbit constant and Zr -C stretching frequency, and the large Renner-Teller splitting in the 010-000 band are believed to be due to strong vibronic coupling with 2 E and 2 A states. The electronic structure of LaNH is similar to isoelectronic LaO, with the added complication of vibronic coupling between the A 2 n and B 2 E + states. This is apparent from anomalies in the B 2 X + - X 2 E + hyperfine intensity profiles (JL a = 7\/2), the Hund's case (a) coupled B 2 E + (0u 2 0) level structure and the large B 2 2 + state bending frequency. Ill Table of Contents Abstract 1 1 Table of Contents iii List of Tables ix List of Figures xiv List of Commonly Used Abbreviations, Acronyms and Symbols xviii Acknowledgements xxiii Chapter 1 Introduction 1 Chapter 2 Theoretical Background 3 2.1 Introduction 3 2.2 The Molecular Hamiltonian and the Born-Oppenheimer Approximation 3 2.2(a) The Born-Oppenheimer Approximation 3 2.2(b) Vibronic Coupling 6 (i) Selection rules for the Renner-Teller effect 6 2.3 Nuclear Part of the Molecular Hamiltonian 9 2.3(a) The Separation of Vibration and Rotation 9 2.3(b) Molecular Vibration 11 (i) Diatomic molecules 11 (ii) Polyatomic molecules 12 2.4 Angular Momentum and Spherical Tensor Operators 13 2.4(a) Introduction 13 2.4(b) Properties of Angular Momentum Operators 13 2.4(c) Addition of Angular Momenta: The Wigner 3-, 6- and 9-j Symbols 15 (i) The Wigner 3-j symbol 15 Table of Contents iv (ii) The Wigner 6-j symbol 15 (iii) The Wigner 9-j symbol 16 2.4(d) Coordinate Rotations: The Wigner Rotation Matrix 17 2.4(e) Spherical Tensor Operators 18 (i) Definition of a spherical tensor 18 (ii) Compound spherical tensor operators 19 (iii) The Wigner-Eckart Theorem 19 2.5 The Effective Molecular Hamiltonian 23 2.5(a) The Rotational Hamiltonian .23 2.5(b) The Fine Structure Hamiltonian . .25 (i) The spin-orbit Hamiltonian 25 (ii) The spin-rotation Hamiltonian 27 (iii) The spin-spin Hamiltonian 28 2.5(c) The Hyperfine Hamiltonian 29 (i) Magnetic hyperfine structure 30 (ii) Electric quadrupole hyperfine structure 33 2.6 Hund's Coupling Cases and Hamiltonian Matrix Elements 34 2.6(a) Hund's Coupling Cases 34 (i) Hund's case (a) 35 (ii) Hund's case (b) 36 (iii) Hund's case (c) 37 (iv) Modified Hund's cases: nuclear spin effects 37 2.6(b) Matrix Elements of the Hamiltonian 40 (i) Hamiltonian matrix elements evaluated in a Hund's case (ap) basis 40 (ii) Hamiltonian matrix elements of a 2 2 state evaluated in a Table of Contents v Hund's case (bp\u00a7) basis 47 2.7 Symmetry, Parity and A-type Doubling 49 2.7(a) Symmetry Properties of Linear Molecules and e\/\/*Parity Labels 49 2.7(b) A-type Doubling in Degenerate Electronic States 51 2.7(c) Effect of A-type Doubling on Hyperfine Structure 53 2.8 Selection Rules and Intensities 53 2.9 Fitting of Data and the Hellmann-Feynman Theorem 58 2.9(a) Method of Combination Differences 58 2.9(b) Non-linear Iterative Least Squares Fitting via the Hellmann-Feynman Theorem 58 Chapter 3 The Electronic Spectrum of Zirconium Monocarbide, ZrC, in the 16000 - 19000 cm- 1 Region: Analysis of Singlet and Triplet Structure 61 3.1 Introduction 61 3.2 Experimental Apparatus and Techniques 62 3.2(a) Overview 62 3.2(b) Preparation of ZrC in a Free Jet Expansion 62 (i) The vacuum chamber 62 (ii) The ablation laser 64 (iii) The gas handling system 64 (iv) The \"Smalley\" expansion source 65 3.2(c) The Two Probe Laser Systems 67 (i) The pulsed dye laser 67 (ii) The cw ring dye laser 68 3.2(d) Signal Detection and Data Acquisition 70 3.2(e) Description of the Experiments 71 (i) Wavelength-selected fluorescence (WSF) 71 Table of Contents vi (ii) Dispersed fluorescence (DF) 74 3.2(f) Calibration of WSF Spectra 75 3.3 The Visible Spectrum of Zirconium Monocarbide, ZrC 77 3.3(a) Motivation 77 3.3(b) Review of Relevant Literature 79 3.3(c) Description of the Spectrum 82 3.3(d) The Low-lying Electronic States of ZrC: X 3 E + , a 1 !* b 1 ^ and c 1 ^ 92 (i) Vibrational analysis of the low-lying electronic states of ZrC 92 (ii) Rotational analysis of the X 3 E + and a1!;4\" states of ZrC 101 (iii) Internal hyperfine perturbations in the X 3 2 + , v = 0 state of 9 1 Z r C 107 (iv) Discussion: A molecular orbital model of ZrC 122 3.3(e) Electronic States of ZrC in the 16000-19000 cm\" 1 Region 130 (i) T h e P 6 . 2 ] 3 I L - X 3 \u00a3 + ( 0 , 0 ) band 130 (ii) Higher-lying levels of ZrC 140 3.4 Conclusions 149 Chapter 4 Laser Spectroscopy of Zirconium Methylidyne: The ZrCH, ZrCD and Z r 1 3 C H Isotopomers 151 4.1 Background 151 4.2 Experiment 154 4.3 The Visible Spectrum of Zirconium Methylidyne 156 4.3(a) Description of the Spectrum 156 4.3(b) The X 2 E+ State 159 (i) Vibrational analysis 159 (ii) Rotational analysis 172 4.3(c) Levels of the A 2 n State in the 15100-15800 cm\" 1 Region 179 Table of Contents vii (i) Assignment of the A 2 n 1 \/ 2 and A 2 n 3 \/ 2 , v = 0 levels 179 (ii) Remaining levels up to 15800 c m - 1 : Vibrational structure of the A 2 n state 186 4.3(d) Levels above 15800 cm\" 1 194 (i) The 15800-16250 cn r 1 region 194 (ii) Evidence for the B 2 Z + state: the 16547 cm\" 1 band 196 4.4 Conclusions 200 Chapter 5 Laser Spectroscopy of Lanthanum Imide (LaNH and LaND) 202 5.1 Background 202 5.1 (a) Introduction 202 5.1(b) Electronic Structures of ScO, ScNH, YO, Y N H , LaO, LaS and LaNH 202 5.2 Experiment 204 5.3 Description of the WSF Spectrum 205 5.4 The X 2 E + State of LaNH and LaND 210 5.4(a) Vibrational Analysis 210 5.4(b) Rotational, Fine and Hyperfine Structure of v = 0 Level 213 5.4(c) The o 2 = 1 Level of the Ground State of L a N H 223 5.5 The Excited Electronic States, A 2 n and B 2 E+ 226 5.5(a) The A2Ur State 226 5.5(b) The B 2 Z + State 229 (i) Pure bending vibrational structure of the B 2 S + state 231 (ii) Anomalous intensity patterns in B 2 2 + - X 2 2 + system bands 234 5.6 Conclusions 241 Bibliography 242 Appendix I Rotational assignments and line measurements of triplet bands of ZrC 257 Appendix II Rotational assignments and line measurements of singlet bands of ZrC 317 Table of Contents viii Appendix III Hyperfine assignments and line measurements of triplet bands of 9 1 Z r C . . . . 322 Appendix IV Rotational assignments and line measurements of bands of Z rCH 325 Appendix V Rotational assignments and line measurements of bands of ZrCD 338 Appendix VI Hyperfine and rotational assignments and line measurements of B 2 S+ - X 2 E + system bands of LaNH and LaND 351 ix List of Tables 3.1 Comparison of ground state symmetries of some transition metal-containing monocarbides and their isoelectronic mononitrides 82 3.2 Low-lying vibrational levels of ZrC identified by dispersed fluorescence 95 3.3 Rotational and fine structure Hamiltonian matrix elements for a 3 E + state 102 3.4 ZrC, X 3 E + : Rotational, fine structure and vibrational constants 103 3.5 ZrC, a1^4\": Rotational constants of v = 0 level 106 3.6 9 0 Z r C , X 3 2 + , u = 1: Rotational and fine structure constants 106 3.7 Nonvanishing hyperfine Hamiltonian matrix elements for a 3 Z + state 114 3.8 9 1 Z r C , X 3 Z + , v = 0: Rotational, fine and hyperfine constants 117 3.9 Manifolds of electronic states arising from various two-electron configurations . . . 125 3.10 ZrC, [16.2]3ni, u = 0: Effective rotational and fine structure constants 137 3.11 Constants from the attempted deperturbation of the nearly degenerate Q. = Oe and 1 levels of 9 0 Z r C mear 17833 cm\" 1 147 4.1 Measurements of assigned excited vibrational levels in the X 2 Z + ground states of ZrCH, ZrCD and Z r 1 3 C H 170 4.2 Molecular constants and structure of the X 2 S + , v = 0 levels of various isotopomers of zirconium methylidyne 175 4.3 Comparison of spin-rotation constants for X 2 2 + states of various isovalent species 177 4.4 Some fine structure constants of several molecules isovalent to Z rCH 182 4.5 Calculated and observed isotope shifts of co3 for various states of ZrCH(D) 192 4.6 Rotational linestrengths for Q' - Q\" = 1\/2 - 1\/2 transitions 199 5.1 Characteristic molecular constants of some isovalent Group 3 molecules 203 5.2 Measurements of assigned excited vibrational levels in the X 2 S + ground states of LaNH and LaND 212 5.3 Hamiltonian matrix elements for a 2\u00a3 +(bps> I = 7\/2) electronic state 215 List of Tables x 5.4 Molecular constants and structure of the X 2 \u00a3 + , v = 0 levels of L a N H and LaND . 2 2 1 5.5 Bond lengths of the Group 3 monoxides, monosulphides and imides 223 5.6 Molecular constants of the X 2 E + , v2 = 1 level of L a N H 226 5.7 Molecular constants of the B 2 S + states of LaNH and LaND 231 5.8 Molecular constants of the o 2 = 1 and 2 levels of the B 2 S + state of L a N H 234 A I . l Rotational assignments and line measurements of the 16028\/61 c m - 1 band of ZrC 258 AI.2 Rotational assignments and line measurements of the 16178 c m - 1 band of ZrC . . . 259 AI.3 Rotational assignments and line measurements of the 16306 c m - 1 band of ZrC . . . 261 AI.4 Rotational assignments and line measurements of the 16488\/502 c m - 1 band of ZrC : 263 AI.5 Rotational assignments and line measurements of the hot 16626 c m - 1 band of ZrC 265 AI.6 Rotational assignments and line measurements of the 16643 c m - 1 band of ZrC . . . 266 AI.7 Rotational assignments and line measurements of the 16655\/80 c m - 1 band of ZrC 267 AI.8 Rotational assignments and line measurements of the hot 16655\/58 c m - 1 band of ZrC 269 AI.9 Rotational assignments and line measurements of the 16681 c m - 1 band of ZrC . . . 269 ALIO Rotational assignments and line measurements of the 16694 c m - 1 band of ZrC . . . 271 A L U Rotational assignments and line measurements of the 16702 c m - 1 band of ZrC . . . 273 AI.12 Rotational assignments and line measurements of the 16910 c m - 1 band of ZrC . . . 275 AI.13 Rotational assignments and line measurements of the 16911 c m - 1 band of ZrC . . . 277 AI.14 Rotational assignments and line measurements of the 16935\/41 c m - 1 band of ZrC 278 A I . l 5 Rotational assignments and line measurements of the 17089 c m - 1 band of ZrC . . . 280 A l . 16 Rotational assignments and line measurements of the 17112 c m - 1 band of ZrC . . . 281 A I . l 7 Rotational assignments and line measurements of the 17342 c m - 1 band of ZrC . . . 283 A l . 18 Rotational assignments and line measurements of the hot 17458 c m - 1 band of List of Tables xi ZrC 285 A l . 19 Rotational assignments and line measurements of the 17494\/506 c m - 1 band of ZrC 286 AI.20 Rotational assignments and line measurements of the 17535\/38 c m - 1 band of ZrC 288 AI.21 Rotational assignments and line measurements of the 17673 c m - 1 band of ZrC . . . 290 AI.22 Rotational assignments and line measurements of the 17689 c m - 1 band of ZrC . . . 292 AI.23 Rotational assignments and line measurements of the 17690\/700 c m - 1 band of ZrC 294 AI.24 Rotational assignments and line measurements of the 17815 c m - 1 band of ZrC . . . 296 AI.25 Rotational assignments and line measurements of the 17832 c m - 1 band of ZrC . . . 298 AI.26 Rotational assignments and line measurements of the 17833 c m - 1 band of ZrC . . . 300 AI.27 Rotational assignments and line measurements of the 17908 c m - 1 band of ZrC . . . 300 AI.28 Rotational assignments and line measurements of the 17912 c m - 1 band of ZrC . . . 302 AI.29 Rotational assignments and line measurements of the 18093 c m - 1 band of ZrC . . . 304 AI.30 Rotational assignments and line measurements of the hot 18101 c m - 1 band of ZrC , 304 AI.31 Rotational assignments and line measurements of the 18107 c m - 1 band of ZrC . . . 305 AI.32 Rotational assignments and line measurements of the 18159\/82 c m - 1 band of ZrC 307 AI.33 Rotational assignments and line measurements of the 18169 c m - 1 band of ZrC . . . 308 AI.34 Rotational assignments and line measurements of the 18338 c m - 1 band of ZrC . . . 309 AI.35 Rotational assignments and line measurements of the 18467\/79 c m - 1 band of ZrC 311 AI.36 Rotational assignments and line measurements of the 18569 c m - 1 band of ZrC . . . 313 AI.37 Rotational assignments and line measurements of the 18616 c m - 1 band of ZrC . . . 314 AI.38 Rotational assignments and line measurements of the 18981 c m - 1 band ofZrC . . . 315 AII . l Rotational assignments and line measurements of the 17485 c m - 1 band of ZrC . . . 318 AII.2 Rotational assignments and line measurements of the 17501 c m - 1 band of ZrC . . . 318 A l l . 3 Rotational assignments and line measurements of the 17502 and 17584 c m - 1 bands of List of Tables xii ZrC 319 AII.4 Rotational assignments and line measurements of the 17720 c m - 1 band of ZrC . . . 320 AII.5 Rotational assignments and line measurements of the 17724 c m - 1 band of ZrC . . . 320 AIL 6 Rotational assignments and line measurements of the 17975 c m - 1 band of ZrC . . . 321 AIII. 1 Hyperfine and rotational assignments and line measurements of the 16488\/502 c m - 1 band of 9 ' Z r C 323 AIII.2 Hyperfine and rotational assignments and line measurements of the 17089 c m - 1 band of 9 ' Z r C 323 AIII. 3 Hyperfine and rotational assignments and line measurements of the 17342 c m - 1 band of 9 ' Z r C 324 A I V . l Rotational assignments and line measurements of the 15179 c m - 1 band of Z r C H . .326 AIV.2 Rotational assignments and line measurements of the 15428 c m - 1 band of ZrCH . .327 AIV.3 Rotational assignments and line measurements of the 15621 c m - 1 band of ZrCH . .328 AIV.4 Rotational assignments and line measurements of the 15680 c m - ' band of ZrCH . .329 AIV.5 Rotational assignments and line measurements of the 15705 c m - ' band of Z r C H . .330 AIV.6 Rotational assignments and line measurements of the 15988 c m - ' band of Z r C H . .331 AIV.7 Rotational assignments and line measurements of the 16112 c m - ' band of Z r C H . .333 AIV.8 Rotational assignments and line measurements of the 16529 c m - ' band of Z r C H . .334 AIV.9 Rotational assignments and line measurements of the 16548 c m - 1 band of Z r C H . .335 AIV.10 Rotational assignments and line measurements of the 16661 c m - ' band of Z r C H . .336 A V . l Rotational assignments and line measurements of the 15189 c m - ' band of ZrCD . .339 AV.2 Rotational assignments and line measurements of the 15441 c m - 1 band of ZrCD . .340 AV.3 Rotational assignments and line measurements of the 15576 c m - ' band of ZrCD . .341 AV.4 Rotational assignments and line measurements of the 15623 c m - ' band of ZrCD . .342 AV.5 Rotational assignments and line measurements of the 15851 c m - ' band of ZrCD . .343 AV.6 Rotational assignments and line measurements of the 15941 c m - ' band of ZrCD . .344 AV.7 Rotational assignments and line measurements of the 16007 c m - ' band of ZrCD . .345 List of Tables xiii AV.8 Rotational assignments and line measurements of the 16022 c m - 1 band of ZrCD . . 346 AV.9 Rotational assignments and line measurements of the 16057 c m - 1 band of ZrCD . .347 A V . 10 Rotational assignments and line measurements of the 16437 c m - 1 band of ZrCD . . 349 AVI . 1 Hyperfine and rotational assignments and line measurements of the B2S+(000, 2 Z + ) - X2Z+(000,2S+) band of LaNH near 15198 cm\" 1 352 AVI.2 Hyperfine and rotational assignments and line measurements of the B 2 \u00a3+(001, 2E+) - X 2 S + (000, 2 2 + ) band of LaNH near 15889 c i r r 1 353 AVI . 3 Hyperfine and rotational assignments and line measurements of the B 2Z+(02\u00b00, 2 S + ) - X 2 Z + ( 0 0 0 , 2Z+) band of LaNH near 16412 cm\" 1 358 AVI . 4 Rotational assignments and line measurements of the B^+fOliO, 2n3\/2) - X 2S+(000, 2E +) band of LaNH near 15803 cm- 1 359 AVI. 5 Rotational assignments and line measurements of the B2??(p\\lG, 2n1\/2) - X 2 S + (000, 2 \u00a3 + ) band of L a N H near 15821 cm\" 1 360 AVI . 6 Rotational assignments and line measurements of the B 2 Z+(02 2 0 , 2 A 5 \/ 2 ) -X 2 I+(000, 2 S + ) band of LaNH near 15961 crrr 1 360 AVI . 7 Rotational assignments and line measurements of the B^+fO^O, 2 A 3 \/ 2 ) -X 2S+(000, 2 E + ) band of LaNH near 15989 cm\" 1 361 AVI . 8 Hyperfine assignments and line measurements of the B^E+YOliO, 2n3\/2) - X 2 I + ( 0 0 0 , 2 E + ) band of LaNH near 15803 cm\" 1 362 AVI . 9 Hyperfine assignments and line measurements of the B 2S +(0110, 2n 1 \/ 2) - X 2 I + ( 0 0 0 , 2 2 + ) band of LaNH near 15821 c n r 1 363 AVI . 10 Hyperfine assignments and line measurements of the B2E+(000, 2 Z + ) - X 2S +(000, 2Z+) band of LaND near 15160 c n r 1 . 363 xiv List of Figures 2.1 Mechanism of vibronic coupling between a II electronic state and a higher-lying I electronic state 8 3.1 Schematic diagram of experimental apparatus 63 3.2 Top face and side views of the \"Smalley\" source 66 3.3 Proposed structures of the metallo-carbohedrene M g C 1 2 78 3.4 Stick spectrum of 9 0 Z r C WSF bands 84 3.5 A portion of the [16.2]3n2 - X 3 I + (0,0) band of ZrC 86 3.6 High-resolution spectrum of the [17.67]Q=1 - alI+ band of ZrC 87 3.7 Effect of 1 2 C -> 1 3 C substitution on the 17908 c m - 1 WSF band of Z r 1 2 C and on the DF of its upper state 89 3.8 DF from the 17908 cm\" 1 level of Z r 1 2 C and its Z r 1 3 C counterpart 91 3.9 Dispersed fluorescence (DF) spectrum of the [16.2]3n2, v = 0 level of ZrC 93 3.10 DF spectra from the upper states of the 18512 c m - 1 band of Z r 1 2 C and the corresponding 18467 c m - 1 band of Z r 1 3 C 94 3.11 Vibrational structure of low-lying electronic states of Z r 1 2 C and Z r 1 3 C 96 3.12 Rotational structure of fluorescence from an Q. = 1 state to various electronic states . . 98 3.13 Rotationally resolved DF features from the 18512 c m - 1 band of ZrC 99 3.14 Electron spin structure of the X 3 E+, o = 0 level of 9 0 Z r C 104 3.15 Hyperfine structure of the S,(0) line of the 17342 c m ' 1 band of 9 1 Z r C 108 3.16 A portion of the 17342 c m - 1 band of ZrC 109 3.17 Hyperfine structure in 9 1 Z r C : the Si(5) line of the 17342 c m - 1 band and the P 3(5) line of the 16502 cm ' 1 band 110 3.18 Internal hyperfine perturbations in the Si(2) and Si (4) lines of the 17342 c m - 1 band of 9 1 Z r C I l l 3.19 Electron spin and hyperfine structure of the X 3 S + , v = 0 level of 9 1 Z r C 118 List of Figures xv 3.20 Enlarged portions of Fig. 3.19 119 3.21 Q-form head of the 16488 crrr 1 band of 9 1 Z r C 121 3.22 The P 2(4) line of the 16502 cm\" 1 band of 9 1 Z r C 123 3.23 Calculated hyperfine energy level patterns for the F 2 and F 3 electron spin components of the X 3 \u00a3+, v = 0 level of 9 1 Z r C from N = 11 - 34 124 3.24 M O diagrams and low-lying electronic states of ZrC and Y N 128 3.25 Vibrational levels of 9 0 Z r C identified in the 16000-19000 cm\" 1 region 131 3.26 WSF spectrum of the [16.2]3TL - X 3 S + (0,0) group of ZrC bands recorded at low resolution 132 3.27 Ri branch head of the [16.2]3n1 - X 3 S + (0,0) band of ZrC at high-resolution 134 3.28 DF spectrum of the [16.2]3n,, u = 0 level of ZrC 136 3.29 Reduced rotational energies of the Q = Oe and Q = 2 spin-orbit components of the [16.2]3nr,u = 01evelof 9 0 ZrC 139 3.30 Calculated v = 1 - 5 levels and A E ( 9 0 Z r C - 9 4 Z r C ) isotope shifts of the [16.2] 3IT(a) state of 9 0 Z r C 141 3.31 Reduced rotational energies of the 16681 c m - 1 group of levels of 9 0 Z r C , 9 2 Z r C and 9 4 Z r C 143 3.32 Anomalous D-type splitting of the Q = 1 level of 9 0 Z r C at 16681 cm- 1 144 3.33 Reduced rotational energies of selected 9 0 Z r C levels 146 3.34 Attempted deperturbation of the nearly degenerate Q = Oe and 1 levels of 9 0 Z r C near 17833 cm\" 1 148 4.1 Stick spectrum of 9 0 Z r C H and 9 0 Z r C D WSF bands 158 4.2 DF spectra of the A 2 T I 1 \/ 2 , u = 0 levels of ZrCH at 15179 c n r 1 and ZrCD at 15189 cm- 1 161 4.3 DF spectra of the 15988 c m - 1 level of ZrCH and the corresponding 15980 crrr 1 level of Z r 1 3 C H 163 4.4 DF spectrum of the 16461 cm\" 1 level of ZrCH 164 List of Figures xvi 4.5 DF spectra of the 15705 cm- 1 level of ZrCH 166 4.6 DF spectrum from the 16680 cm\" 1 level of Z rCH 167 4.7 DF spectra from various levels of ZrCH and ZrCD 169 4.8 Ground state vibrational levels of ZrCH, ZrCD and Z r 1 3 C H 171 4.9 Low-N lines in the 1\/2P branch of the 15179 cm\" 1 band of Z r C H 173 4.10 Stick spectrum of cold WSF bands of 9 0 Z r C H and 9 0 Z r C D in the 15100-15800 c m - 1 region 180 4.11 A-type doubling in the 15179 cm\" 1 level of 9 0 Z r C H 181 4.12 Reduced rotational energies of the 15179 and 15428 cm- 1 levels of 9 0 Z r C H 181 4.13 DF spectra of the 15428 cm- 1 level of Z rCH and the 15441 cm\" 1 level of ZrCD . . . 184 4.14 Vibronic energy levels of a linear triatomic molecule in a 2Ilr electronic state for u 2 = 0, 1, 2 and 3 188 4.15 DF spectra from the 15680 cm- 1 level of ZrCH and the 15576 cm\" 1 level of ZrCD 190 4.16 DF spectra from the 15621 cm- 1 level of ZrCH and the 15623 era\"1 level of ZrCD 193 4.17 ZrCH(D) bands in the 15800-16250 c m ' 1 region 195 4.18 A portion of the high-resolution spectrum of the 16548 c m - 1 band of Z rCH 197 5.1 Portions of the B 2\u00a3+(001) - X 2 \u00a3 + (000) band of L a N H 207 5.2 Hyperfine structure of the 1\/2P4(13) line of the B 2 S + (001)- X 2 I + (000) band of LaNH 209 5.3 DF spectra of the B 2 S + , n = 0 levels of LaNH at 15198 cm\" 1 and LaND at 15157 cm\" 1 211 5.4 Ground state ( X 2 Z + ) vibrational levels of LaNH and LaND 214 5.5 Hyperfine energy level pattern for N = 18 of the ground state of L a N H 216 5.6 Hyperfine structure of the rj = 0 level of the X 2 L + state of LaNH 220 5.7 The B 2Z+(02 20, 2 A 3 \/ 2 ) - X2Z+(0110, 2n(b)) hot band of L a N H 224 5.8 Excitation spectra of LaNH and LaND observed below 15000 c m - 1 228 5.9 Excitation spectra of LaNH and LaND observed above 15000 c m - 1 230 List of Figures xvn 5.10 The Av2 = +1 sequence of the B 2 E+ - X 2 E + system of LaNH 232 5.11 Results of hyperfine intensity profile calculations for the 1\/2P4(13) line in Fig. 5.2 236 5.12 Hyperfine intensities calculated for 1\/2P(1) F - G\" features in P = 1\/2 - 1\/2 transitions of the B - X system of LaNH 237 5.13 Effect of relative phase on calculated rotational profiles for a P = 1\/2 - 1\/2 transition 239 5.14 High-resolution spectrum of the B2Z+(01 *0, 2n1\/2) - X 2 \u00a3 + (00\u00b00 , 2 2 + ) band of L a N H 240 XV111 List of Commonly Used Abbreviations, Acronyms and Symbols A spin-orbit (or spin-vibration) parameter <xe vibration-rotation constant of a diatomic molecule vibration-rotation constant of a polyatomic molecule with respect to vibration Vj a nuclear spin-electron orbit hyperfine parameter B rotational constant B magnetic field b nuclear spin-electron coupling hyperfine parameter b F Fermi contact hyperfine parameter B O A Born-Oppenheimer Approximation c hyperfine dipolar coupling parameter c speed of light d hyperfine parity doubling parameter D centrifugal distortion parameter DF dispersed fluorescence <D Wigner rotation matrix element h Kronecker delta function 5(x) Dirac delta function e magnitude of electron charge * M o s t b o l d f a c e q u a n t i t i e s t h a t r e p r e s e n t a n a n g u l a r m o m e n t u m h a v e b o t h s p a c e - f i x e d a n d m o l e c u l e - f i x e d c o m p o n e n t s w r i t t e n i n r e g u l a r t y p e f a c e a n d d e n o t e d b y X , Y a n d Z a n d x , y a n d z s u b s c r i p t s r e s p e c t i v e l y , a n d a c o r r e s p o n d i n g q u a n t u m n u m b e r w r i t t e n i d e n t i c a l l y i n r e g u l a r t y p e f a c e ; t h e s e a r e o m i t t e d f r o m t h i s l i s t f o r b r e v i t y . L i k e w i s e o m i t t e d a r e s y m b o l s d e n o t i n g c e n t r i f u g a l d i s t o r t i o n c o r r e c t i o n s t o v a r i o u s m o l e c u l a r c o n s t a n t s ; t h e s e a r e u s u a l l y d e n o t e d b y t h e s a m e s y m b o l a s f o r t h e c o r r e c t e d c o n s t a n t w i t h a n a d d e d D s u b s c r i p t . F o r s y m b o l s w i t h m o r e t h a n o n e m e a n i n g , t h e m e a n i n g s a r e g i v e n i n d e c r e a s i n g f r e q u e n c y o f u s e i n t h i s t h e s i s . List of Commonly Used Abbreviations, Acronyms and Symbols xix E energy E * space-fixed inversion operator E electric field e e-type parity label eQq 0 hyperfine electric quadrupole coupling parameter 8ijk Levi-Civita symbol F total angular momentum including nuclear spin F Wilson's force field matrix Fi ith electron spin component of a rotational energy level Fi(J) rotational term energy of Fj \/ \/-type parity label Coriolis coupling constant G(n) vibrational term energy A G u+l\/2 energy interval between vibrational levels o and VJ+1 G pseudospin angular momentum (sum of I and S) G Wilson's inverse reduced mass matrix Se electron g-factor, 2.0023... \u00a722 anharmonicity constant corresponding to vibrational angular momentum S N nuclear spin g-factor Y spin-rotation operator r generic irreducible representation H Hamiltonian (total energy) operator h Frosch and Foley hyperfine parameter h Planck's constant hfs hyperfine structure List of Commonly Used Abbreviations, Acronyms and Symbols xx I moment of inertia I nuclear spin IHP internal hyperfine perturbation J total angular momentum excluding nuclear spin j generic angular momentum j \u00b1 ladder operator j x \u00b1 i) y of j k rank of a tensor k Boltzmann constant K rank of a compound tensor t (or I) vibrational angular momentum 1 single electron orbital angular momentum L total electron orbital angular momentum LTF laser-induced fluorescence X effective spin-spin coupling parameter XgQ second order spin-orbit coupling parameter A,\u00a7R true (first order) spin-spin coupling parameter A projection of L onto linear molecular axis nig electron mass M L magnetic quantum number corresponding to angular momentum quantum number L M n nuclear mass p reduced mass of diatomic molecule p dipole moment operator P B Bohr magneton P N nuclear magneton N rotational angular momentum including electron orbital angular momentum List of Commonly Used Abbreviations, Acronyms and Symbols xxi Vj ith vibrational mode (polyatomic) o A-type doubling parameter for 2S+ln electronic state, S = 1, 3\/2, 2, ... p A-type doubling parameter for 2S+ln electronic state, S = 1\/2, 1, 3\/2, ... q A-type doubling parameter for 2S+ln electronic state, S = 0, 1\/2, 1, ... q e set of electron coordinates Q n set of nuclear coordinates, OR nth vibrational normal coordinate r e (A-B) equilibrium bond length between atoms A and B R end-over-end molecular rotational angular momentum R2PI resonant two-photon ionisation p 2 ratio of reduced masses of diatomic isotopomers S electron spin angular momentum s single electron spin angular momentum ov(xz) operator for reflexion in xz plane \u00a3 projection of S onto linear molecular axis T k spherical tensor of rank k T e electronic term energy T e total electron kinetic energy operator T e v electronic plus vibrational term energy T n total nuclear kinetic energy operator T temperature v vibrational quantum number (diatomic molecule) Uj quantum number of ith vibrational mode (polyatomic molecule) v velocity cpn nuclear part of molecular eigenfiinction \\|\/e electronic part of molecular eigenfiinction List of Commonly Used Abbreviations, Acronyms and Symbols *F total molecular wavefunction WSF wavelength-selected fluorescence Xy vibrational anharmonicity constant (polyatomic molecule) yjjk vibrational anharmonicity constant (polyatomic molecule) co e vibrational frequency (diatomic molecule) <Dj frequency of ith vibrational mode (polyatomic molecule) co e x e vibrational anharmonicity constant (diatomic molecule) co e y e vibrational anharmonicity constant (diatomic molecule) Q, projection of J onto linear molecular axis XXlll Acknowledgements In a letter to Robert Hooke, Isaac Newton once commented that he was able to see farther by standing on the shoulders of giants. It remains to be seen how the results of this dissertation will be viewed in four hundred years; nevertheless, I, too, must thank a number of giants who have allowed me to see farther. First among them is my research supervisor, Prof. Anthony Merer. I consider it a privilege to have pursued molecular spectroscopic research in the laboratory of one of its foremost practitioners, and have learned a great deal from him. For this, and for continued financial support for the duration of my studies, I thank him. This thesis marks the end of an era; as the final graduate student to earn a Ph. D. under his guidance, I would like to take this opportunity to wish him many happy years of retirement. I am also grateful to Prof. Irving Ozier. I thank him for undertaking many administrative responsibilities, which allowed me, as a physics student, the opportunity to pursue my research interests in the Department of Chemistry. I would also like to acknowledge him for our countless lunchtime conversations on many wide and varied topics, ranging from the Lions' Grey Cup hopes to matters more scientific. Last, but not least, I would also like to acknowledge his generous donation of a sample of 1 3 CH4, which generated much useful data in the studies of ZrC and ZrCH reported herein. I would also like to thank Prof. Michael Gerry and all the members of the microwave team, past and present, whose time at U B C overlapped with mine. There are too many to name individually, but over the years, they have been a great source of advice, constructive criticism and muscle power in helping move those plasma tubes between floors, and have my gratitude. Several post-doctoral fellows and research associates have been among my contemporaries in the Merer lab and also deserve my thanks (in chronological order): Dr. David A. Gillett, Dr. James R. D. Peers, Dr. K. (\"Peggy\") Athanassenas, Dr. Shuenn-Jiun (\"S-T') Tang, Dr. Gretchen Rothschopf and Dr. Pradyot K. Chowdhury. I would also like to acknowledge Chris T. Kingston, who, for the duration of my time here, was my only fellow Acknowledgements xxiv Ph.D. student in the lab and a source of many discussions. Summer undergraduate students were always a welcome addition to the Merer lab; I would like to thank Ms. Francesca Setiadi, Ms. Vivian Yip and Ms. Connie Aw, all of whom offered valuable assistance in sundry tasks. I wish them every success in their future endeavours. Several support staff members at U B C also deserve my thanks. Mr. Chris P. Chan left the Merer lab much too soon, only months after I had arrived; nevertheless, a great deal of the electronics in the lab, used routinely in my experiments, were of his construction. I would also like to thank, from the electronics shop, Martin Carlisle, Dave Bains and Jason Gozjolko, all of whom coped with various electronic and computer maladies. Al l of the members of the mechanical shop were helpful in nursing various malfunctioning apparatus back to health and occasionally lathing away those nuisance oxide coatings from my zirconium and lanthanum rods. Various office staff in both the Chemistry and Physics & Astronomy Departments, in particular, Tony Walters and his predecessor Janet Johnson, were also supportive in smoothing out many of the wrinkles associated with my departmental duality. The Merer lab was home to several visiting scientists in recent years, from all of whom I have benefited greatly. Dr. Leah C. O'Brien of Southern Illinois University at Edwardsville afforded me my first opportunity at international travel by inviting me to Kitt Peak National Observatory in Arizona to assist in some of her experiments. Dr. Dennis J. Clouthier of the University of Kentucky was a valuable mentor in the lab and was instrumental in setting up the pulsed dye amplifier system. Dr. Allan G. Adam of the University of New Brunswick (Fredericton) also deserves acknowledgement; the installation of a transmission grating to remove A S E from the pulsed dye laser system was done at his suggestion. Without it, the projects reported in this thesis would have been nearly impossible to pursue. Finally, Dr. Thomas D. Varberg of Macalester College (St. Paul, MN) was of considerable help in the early stages of the LaNH project; his vision at near infrared wavelengths is far superior to my own! Other research colleagues from outside U B C have also been helpful. I would like to Acknowledgements xxv acknowledge Dr. Timothy C. Steimle of the University of Arizona for his interest in the LaNH project, which led his research group to undertake Stark spectroscopic experiments on this molecule. I also thank him for pointing out the utility of pyrromethene 556 laser dye; the performance improvement over other dyes in the same region was quite immense and doubtless improved the data quality accordingly. I would also like to thank Dr. Michael D. Morse of the University of Utah for his cordial e-mail correspondences and for forwarding portions of the Ph. D. thesis of his former student, Ryan S. DaBell. Finally, I would like to thank the many friends I have made in Vancouver over the years who helped make the time outside the lab just as enjoyable as the time inside. With memories of Christmas skits, Blenheim parties, Lions games at B C Place, concerts, and soccer and curling matches (before the leg injuries exacted their toll!), my U B C years will always be remembered with fondness. You can't spell loveliness without lines. 1 Chapter 1 Introduction While the ability of a molecule to emit and absorb discrete frequencies of electromagnetic radiation in a specific pattern, known as a spectrum, was recognised over a century ago, the classical Newtonian mechanics of that time could not account for such spectra. Only with the advent of quantum mechanics in the 1920s did satisfactory accounts begin to emerge; the quantum mechanical theory interprets the discrete nature of molecular spectra as radiative transitions between discrete energy levels. Substantial insights into the structural and bonding properties of the carrier molecules of these spectra were quickly achieved, thus pioneering the field of molecular spectroscopy that still flourishes almost a century later. Molecules, composed of atoms with electrons and nuclei, have several internal motions through which they store discrete amounts of energy; some examples can be outlined. The orbiting motion of the electrons around the nuclei gives rise to an electronic state; infinitely many bound electronic states of various energies can be realised depending on the details of this electron motion. The nuclei may also vibrate relative to one another; for each electronic state, a series of discrete vibrational energy levels results. One may further consider rotation of the entire molecular frame; consequently, each vibrational energy level subdivides into a set of rotational energy levels. Chapter 2 develops these ideas in more complete detail. A molecular spectrum can be defined, for purposes of this thesis, as a collection of radiative transitions between its various energy levels and classified by the type of transitions comprising it. Each type often appears in a specific region of the electromagnetic spectrum. Electronic spectra arise from transitions between electronic states and often, but not always, occur in the visible region; they are also called optical spectra. An infrared spectrum can arise from transitions between vibrational levels of the same electronic state. Transitions can also Chapter 1 Introduction 2 occur between rotational levels of the same vibrational level of the same electronic state; these are often called microwave spectra because they were first studied in detail in the microwave region. In this thesis, only electronic spectra have been studied; three molecules have been examined for the first time. All of them have the general form MR, where M and R respectively represent a transition metal (TM) atom and a monatomic or diatomic non-metal ligand. Such molecules enjoy a wide range of application in several fields of research. For example, TMs with several open shell d electrons are prominent constituents of catalytic cycles, in which intermediate M R species often form. Spectroscopic analyses of these can identify their properties and help advance understanding of these catalytic processes. MR-type molecules are also known to exist in the atmospheres of cooler (-2000-3000 K) stars. While this knowledge has advanced the understanding of stellar evolution, the identification of such stellar atmospheric constituents has only been possible by comparing stellar spectra with carefully recorded and analysed laboratory spectra. This thesis is organised as follows. Chapter 2 discusses the theoretical background required in analysing the data presented in the three following chapters. Chapter 3 describes the experimental apparatus and the procedures used to acquire spectral data. It also presents results from a study of the electronic spectrum of zirconium monocarbide (ZrC); singlet and triplet electronic states were identified in this work. This molecule was serendipitously discovered during studies of zirconium methylidyne (ZrCH). The latter species is the latest of several transition metal methylidynes first studied by the Merer lab; it is discussed in Chapter 4. Finally, Chapter 5 presents the analysis of the visible and near-infrared systems of another triatomic molecule, lanthanum imide (LaNH). Each polyatomic species shows, in its spectrum, evidence for strong interactions between its observed excited states. Chapter 2 Theoretical Background 3 2.1 Introduction This chapter reviews the theory used to analyse the data presented in Chapters 3-5. Section 2.2 presents the Schrbdinger wave equation of the molecule and the Born-Oppenheimer Approximation that separates its electronic and nuclear motion; vibronic coupling is also examined. Separation of nuclear motion into vibration and rotation is discussed in Section 2.3. Angular momentum and spherical tensor operators, in terms of which the Hamiltonian operator for the total energy of the molecule can be written, are described in Section 2.4; Section 2.5 identifies various terms of the effective Hamiltonian. Hund's coupling cases and their use in evaluating Hamiltonian matrix elements are discussed in Section 2.6. A-type doubling and its effect on hyperfine structure are reviewed in Section 2.7, and Section 2.8 evaluates the matrix elements of the dipole moment operator; these lead to transition intensity formulae and selection rules. Finally, use of the Hellmann-Feynman Theorem in the fitting of the data in Chapters 3-5 is discussed in Section 2.9. 2.2 The Molecular Hamiltonian and the Born-Oppenheimer Approximation 2.2(a) The Born-Oppenheimer Approximation Experimentally, one finds that a molecule cannot have an arbitrary amount of energy; rather, it possesses a set of quantised energy levels. The energies of these levels are determined by solving the Schrbdinger wave equation # - | \u00a5 > = E | \u00a5 > , [2.1] where Jfis the Hamiltonian (total energy) operator, E is one of the aforementioned energy levels or eigenvalues, and is an eigenfiinction corresponding to E, written in Dirac notation. Chapter 2 Theoretical Background 4 To develop Eq. [2.1] further, the following notation is used. In general, quantities pertaining to electrons are written in lower case with an e subscript, while those for nuclei appear in upper case with an n subscript. Thus, m e , q e and p e will refer to the mass, Cartesian co-ordinates and conjugate linear momentum of an electron, while the corresponding nuclear properties will be M n , Q n and P n . The symbol V ( q e , Q n ) will denote the total electrostatic energy of the molecule, i.e., the sum of all pairwise Coulombic interactions among the entire collection of electrons and nuclei, including all electron-electron repulsions, all nuclear-nuclear repulsions and all electron-nuclear attractions. With these definitions: 2 7 ^ I P e + X ^ + V ( q e , Q n ) 2 m e r n 2 M n | \u00a5 > = E | \u00a5 > . [2.2] Eq. [2.2] neglects contributions due to electron spin and nuclear spin; these are discussed in Section 2.5. The first summation on the left, taken over all electrons, represents the total electron kinetic energy operator T e of the molecule. Likewise, the second summation represents the total nuclear kinetic energy operator T n . Since Eq. [2.2] cannot be solved analytically, approximations must be introduced. Because electrons are much lighter than nuclei, they move much more rapidly within the molecule. Born and Oppenheimer (1) argued that the electrons thus adapt themselves instantaneously to a given nuclear configuration, and that Eq. [2.2] can be solved for a fixed configuration Q n . This is the essence of the Born-Oppenheimer Approximation (henceforth abbreviated as BOA), which allows the electron and nuclear motions to be treated independently. The total wavefunction |SP> of the molecule can then be written as a summation of functions, each a product of an electronic part, IVeOle'Qn)) > a n c * a nuclear part, l < P n ( Q n ) > : l ^ ) = Z | v i \/ 1 e ( q e , Q n ) > | c p 1 n ( Q n ) > - [2.3] i This summation is taken over all eigenfunctions IVefae'Qn)) o r * m e electronic Hamiltonian, Chapter 2 Theoretical Background % = ^ - Z P e + V ( q e , Q n ) , 2m f [2.4] *e e whose eigenvalues are E e ( Q n ) . |y e (q e ,Qn)> c a n b e called a fixed-nuclei electronic eigenfunction because the total molecular Hamiltonian Hreduces to J{Q if the nuclei are fixed at some configuration Q n . In the remainder of this section, the coordinates q e and Q n are suppressed for brevity. Substituting Eqs. [2.3] and [2.4] into the Schrodinger equation, 6 n 2 M n ZlVe>l<Pn> =EX|v(\/ e>|cPn>-[2.5] Since P\u201e acts on both |\\|\/e) and |cp^>, the product rule is required: Pn IVe>l<Pn> = (Pnlvi\u00bblq>n> + 2 (P n |v|\/e>)(Pn |(pn>) + l^X^n l<Pn\u00bb\u2022 Using this expression and the fact that #g|v|\/e) = Eg | \\ | \/ e ) , Eq. [2.5] becomes: EEi| V i>|q>i,> + Z ^ r [ ( P n | v i ' e \u00bb + 2(PnlM\/e\u00bbPn+|v|\/e>Pn]l<Pn> i i,n ^ M n = E\u00a3ivL>i<pii>. i Premultiplying by (\\|\/g | and using its orthonormality properties, this becomes [2.6] [2.7] Ee1cp n >+I i,n <V|\/e|PnlVe>+iVe|PnlVe>Pn 2 M r i 2 , \u201e k A + I ^ ^ = E | < p n > . [2-8] n 2 M n If the second term on the left is neglected, ^ n l c p \u201e > = Z % ^ + E e k | cp n >=E| (pk > ; n 2 M n [2.9] where Hn can be regarded as the nuclear Hamiltonian operator, and a wave equation for the nuclei moving in a potential Eg results. Thus, if the fixed-nuclei electronic eigenfunctions |vj\/g > are known, the total eigenfunction \\^) can be expanded as in Eq. [2.3] with |cpk> given by Eq. [2.9], provided the first summation on the left of Eq. [2.8] is negligible. Of the two terms in this summation, the first is essentially the matrix element of the nuclear kinetic energy operator T n taken between a pair of distinct electronic eigenstates. This depends on nuclear mass and leads to a small isotope-dependent correction to the potential curve Eg (mainly about 5 c m - 1 or less) that is largely negligible. The second is usually more Chapter 2 Theoretical Background 6 significant, particularly in the case of polyatomic molecules, and is discussed below. 2.2(b) Vibronic Coupling The second summand in the neglected term of Eq. [2.8] contains the matrix element |Pn|v|\/g>, which introduces an interaction between the electronic eigenstates |v|\/g) and |\\|\/e> via the nuclear momentum operator P n = -in d\/dQn. This term, the neglect of which essentially amounts to the BOA, represents a coupling between the vibrational and electronic motions of these electronic states and is therefore called vibronic coupling. While this approximation is valid for well-separated electronic states, non-negligible effects can arise under certain conditions for close-lying electronic states. In such cases, the total molecular wavefunction IT) can no longer be written as in Eq. [2.3]. In linear molecules, the only type studied in this thesis, vibronic coupling is referred to as the Renner-Teller effect (2). Conditions for this effect are now described. 2.2(b)(i) Selection rules for the Renner-Teller effect This derivation of the selection rules for the Renner-Teller effect is restricted to linear triatomic molecules. Vibronic coupling of and ) requires that the matrix element M v c = |Pn|\\)\/e) be non-vanishing. Discrete group theory gives the required condition: r ( M v c ) = r ( | V J \u00bb \u00ae r (Q n ) \u00ae r a y i \u00bb => r T S . [2.10] T(a) is the irreducible representation (or symmetry species) of a in the point group of the molecule, and T T \u00a7 refers to the totally symmetric representation of this point group. The symmetry of M v c is given by the direct product of the symmetries of the two electronic states and that of the operator coupling them; T(Q n ) = T(P n) since Q n and P n form a coordinate and linear momentum conjugate pair. An equivalent statement of Eq. [2.10] is that the direct product of r(|\\j\/e )) and r(|\\|\/e>) must contain T(Q n ) (where Q n is taken as a vibrational normal coordinate): r ( | v ^ \u00bb \u00ae r ( |v | \/ i\u00bb => r(Q n ) . [2.ii] Chapter 2 Theoretical Background 7 Linear triatomic molecules of the form A B C belong to the C ^ point group. These have three vibrational normal modes: two totally symmetric stretches, denoted by V i (o + ) and v 3 (o + ) , and one degenerate bending vibration, denoted by v2(7t). The Renner-Teller selection rule for the a + vibrations is that the two electronic states must have the same symmetry, but only the case of the bending (n) vibration is relevant to this thesis. Its selection rule can be stated arithmetically since the irreducible representation of the electronic state identifies its electron orbital angular momentum projection quantum number A and v2(7t) carries one unit of vibrational angular momentum: | A k - A i | = 1. [2.12] In other words, electronic states whose A values differ by one unit can vibronically couple through the bending vibration. This vibronic coupling can drastically affect the bending vibrational energy level manifolds of both states. As an example, Fig. 2.1 shows potentials for two electronic states of IT and E + symmetry, with the latter being more energetic. These are plotted as functions of the bending normal coordinate Q 2 (coordinates Qi and Q 3 are fixed). Renner-Teller coupling between them steepens the S + potential, thus increasing its bending frequency from the unperturbed value (the A' designation refers to the electronic symmetry in the Cs point group of the bent molecule). The situation is slightly different for the II state, whose orbital degeneracy is now lifted, creating separate A' and A\" states in the bent geometry. The A\" component is essentially unperturbed by the vibronic coupling and is shown displaced slightly above for clarity. Only the A' component is shifted downward by the higher-lying 2 + (A') state. The weak coupling depicted in the figure reduces the bending vibrational frequency of the n(A') potential. Sufficiently strong coupling can force this potential into a double minimum shape; the resultant non-linear equilibrium geometry effects a partial reordering of the bending vibrational energy levels, as discussed by Jungen et al. (3-6). Chapter 2 Theoretical Background Figure 2.1 Mechanism of vibronic coupling between a II electronic state and a higher-lying S electronic state. Dashed curves denote the unperturbed bending potentials; the coupling connects the A' component (C s geometry) of the orbitally degenerate IT state and the E (A) state and increases the bending frequency of the latter. The A\" component of the IT state is not affected by the perturbation and is shown displaced slightly above for clarity. Chapter 2 Theoretical Background 9 Two good examples of molecules with vibronically coupled electronic states are Y O H (7) and LaNH; Chapter 5 of this thesis discusses the latter of these. 2.3 Nuclear Fart of the Molecular Hamiltonian 2.3(a) The Separation of Vibration and Rotation In Section 2.2(a), the electronic and nuclear motions of the molecule were separated using the BOA. Hn specifies approximately the nuclear motion: where the potential E e ( Q n ) depends on the nuclear configuration and is an eigenvalue of 9fe. The next step is to separate the vibrational and rotational motions of the nuclei; this has been done by Wilson et al. (8) and Margenau and Murphy (9) as follows. Since no potential energy is associated with the rotational motion, the separation of vibration and rotation amounts to a separation of the kinetic energy term of Eq. [2.13]. This is more easily done if the momentum representation of this equation is replaced with a coordinate representation, although care must be taken in the choice of coordinate system. In particular, each coordinate should be defined using either space-fixed axes, with respect to which the molecule rotates, or molecule-fixed axes, which rotate in space with the molecule. The quantities required to separate the vibration and rotation are the following: R, the position vector of the centre of mass of the molecule in space-fixed axes, r{, the position vector of the z'th atom in molecule-fixed axes, a;, the equilibrium position of the z'th atom in molecule-fixed axes and dj, the displacement of the z'th atom from equilibrium in molecule-fixed axes, such that dj = rj - aj. The velocity Vj of the z'th atom (of mass mj), measured in the space-fixed frame, is simply the velocity of the centre of mass of the molecule, R , plus the velocity of the atom relative to this * n = Z n n + E e ( Q n ) , [2.13] Chapter 2 Theoretical Background 10 centre of mass, r; (the overdots indicate temporal differentiation): Vi=R + ri . [2.14] The velocity rj, measured in the molecule-fixed frame, is simply dj, but the rotation of this frame, at an angular velocity co (referred to the space-fixed axes), means that r j ^ d i + w x r ; [2.15] in the space-fixed frame. By definition, the molecular kinetic energy is T = | Z m i v i v i , [2.16] i Using Eqs. [2.14] and [2.15]: T = y \u00a3 m i ( R + d i +ojxrj)-(R + di + coxrj). [2.17] i The summation can be expanded and then simplified with the Eckart conditions (10) \u00a3 1 ^ 1 4 = 0 [2.18a] i and \u00a3 m i ( a i x d i ) = 0, [2.18b] i which stipulate that the origin of the molecule-fixed axes be the molecular centre of mass, and that the molecule has no net angular momentum in its equilibrium configuration, measured in the molecule-fixed axis system. When this is done, the result is 2T = R - R X m j +Xmi(\u00bbxn)-(G) x ri) + Z m i d i \u2022 dj + 2co\u2022 Z m i ( d i x d i ) t 2 1 9 J i i i i The four terms on the right are readily interpreted physically. The first one represents translational energy of the molecular frame, which can be ignored for molecules in free space. The second term corresponds to rotational energy, while the third can be regarded as the vibrational kinetic energy. The final term represents a Coriolis coupling of vibration and rotation that involves the vibrational angular momentum; as a result, the rotational and vibrational motions cannot strictly be completely separated. However, this Coriolis interaction is often negligible, so that rotational and vibrational energies determined from independent Chapter 2 Theoretical Background 11 quantum mechanical analyses can be added to yield the total nuclear kinetic energy to an adequate level of approximation. Townes and Schawlow (11) have discussed the general problem of determining the rotational energy levels of a molecule, which can be readily solved with the use of angular momentum and spherical tensor operators. These are considered in Section 2.4, after which the rotational Hamiltonian is discussed in detail in Section 2.5(a). The rest of this section deals with vibrational structure. 2.3(b) Molecular Vibration The solution of the Schrbdinger equation for the vibrational energy levels and eigenfunctions of a molecule has been discussed by Pauling and Wilson (12) and Dunham (13); the results are summarised by Herzberg (14, 15) and will be recapitulated here for diatomic and polyatomic molecules. 2.3(b)(i) Diatomic molecules The diatomic molecule has only one vibrational quantum number u = 0, 1, 2, ... ; its energy levels G(u) correspond to those of an anharmonic oscillator: G(u) = (Be(u +1) - co ex e(u +1) 2 + coeye(u +1) 3 + \u2022 \u2022 \u2022. [2.20] In this equation a > e = - . \u00a3 [2.21] c \\ p is the classical harmonic vibrational frequency measured in c m - 1 units, where c is the speed of light, k is the force constant of the bond and u = JHlE2_ [2.22] mj + m 2 is the reduced mass of the molecule; n^ and m 2 are its nuclear masses. Vibrational constants co'e, (o'qXq and \u00ae'eyle for another isotopomer of the molecule are related to those of the reference isotopomer by (13): Chapter 2 Theoretical Background 12 G>e=P<\u00b0e> [2.23a] C0ex'e =p 2 co e x e [2.23b] and co ey e = p 3 \u00a9 e y e , [2.23c] where p 2 = p \/p ' [2.24] is the reduced mass ratio of the two isotopomers. The anharmonicity constants, \u00a9 e x e and coeye, are generally much smaller than a>e. If these are neglected, then the wavefunctions associated with the eigenvalues G(o) of Eq. [2.20], are = N B exp( - l o x ^ H ^ c V a x ) , [2.25] where the normal coordinate x = ^\/p ( r - r e ) is the mass-weighted change in bond length from its equilibrium value, a = 27tca>e\/h and N v = \/\u2022^2vv\\ is a normalisation factor. a H 1 ) (Vax) is the nth degree Hermite polynomial, which has u nodes 2.3(b)(ii) Polyatomic molecules Non-linear (linear) polyatomic molecules with N atoms have 3N - 6 (3N - 5) normal modes of vibration, each with its own vibrational quantum number Oj. The vibrational structure can be approximated as a superposition of slightly anharmonic oscillators, so the vibrational energy G(u iv j 2 - ) can be written as an expression similar to Eq. [2.20] summed over all the vibrational modes of the molecule, with additional anharmonic terms to account for interactions between various vibrational modes: G(n,n 2- \u2022 \u2022) = Y>i(Ui +1) + 2>ij(Ui + \u00a3)0>j + ^ ) i j * i + Z yijkO>i+i)0>j+i)0)k+i) + - - t 2 - 2 6 ] k>j>i An alternative definition of G ^ O j \u2022\u2022\u2022) sets the zero-point energy at zero: G ( o 1 o 2 - ) = Z Q ) i 1 ) i + Z x i j , } i v j + Z yijkUiOjO k+--- t 2 - 2 7 ] i j>i k>j>i In the harmonic approximation, the eigenfunctions ^PYx^x^ \u2022\u2022\u2022) corresponding to G ( o i 0 2 - ) Chapter 2 Theoretical Background 13 are written as a product of the single oscillator eigenfunctions from Eq. [2.25]: ^ U l x a ) 2 - ) = n ^ D i ( x i ) ' p - 2 8 ] i although in this case, the normal coordinates Xj no longer relate simply to the corresponding geometrical structural parameters (i.e., bond lengths and bond angles). Moreover, the vibrational frequencies of polyatomic molecules have more complicated isotopic scaling relations than those of diatomic species; they involve the use of Wilson's matrices for the inverse reduced mass G and force field F and require knowledge of not only all vibrational frequencies of the molecule but also all structural parameters. Assumptions about the force constants of the various bonds are sometimes necessary. The treatment essentially determines the force constants of one isotopomer and assumes they are isotopically invariant to estimate vibrational frequencies of other isotopomers. Further discussion appears in Wilson et al. (8). 2.4 Angular Momentum and Spherical Tensor Operators 2.4(a) Introduction This section describes various aspects of angular momentum and spherical tensor operators, the Wigner 3-j, 6-j and 9-j symbols, the Wigner rotation matrix, the Wigner-Eckart Theorem and their applications. Much of this discussion can be found in Edmonds (16) and Zare (17). 2.4(b) Properties of Angular Momentum Operators An angular momentum operator is defined as a quantum mechanical operator J whose Cartesian components, Jx, Jy a n < ^ Jz> \u00b0bey J i J j - J j J ^ \/ h X s i j k J k , [2.29] k where 8p, the Levi-Civita symbol, equals +1 (-1) if ijk is a cyclic (anticyclic) permutation of X Y Z , and vanishes if any index is repeated. The quantity on the left side of Eq. [2.29] is called the commutator of Jj and J; and is usually written as [Jj, J;]; Jj and J; are said to commute if their Chapter 2 Theoretical Background 14 commutator vanishes. While no component of J commutes with any other component, it can be shown that each component Jj commutes with J 2 , i.e., [J 2 , Jj] = 0, i = X , Y o r Z . [2.30] With this result, simultaneous eigenfunctions of J 2 and one of Jx, J Y o r c a n D e f \u00b0 u n d- Jz is usually chosen because of its simple differential form in spherical polar coordinates, and the eigenfunctions are written as |JM>, where J and M are the quantum numbers respectively associated with J 2 and J^. Using only Eq. [2.30] and the commutation relations of Eq. [2.29], the eigenvalues of | JM> with respect to both J 2 and can be determined. The derivation can be found in several textbooks (see, for example, Zare (17) and Sakurai (18)); the results are J 2 |JM> =h2J(J+l)|JM> [2.31a] and J Z |JM> =hM|JM>. [2.31b] J is a non-negative integer or half-integer that specifies the total angular momentum; M , the projection quantum number, can assume any one of the 2J + 1 values ranging from - J to J in steps of one. If needed, T x | J M ) and Jy |JM) are easily obtained in terms of the ladder operators: J \u00b1 = J X \u00b1 \/ J Y , [2.32] which transform |JM) into a multiple of | J M \u00b11): L J J M ) = hVj(J + l ) - M ( M + l ) | J M \u00b1 l > . [2.33] The following matrix elements are easily obtained from Eqs. [2.31] and [2.33] < T M | J 2 1JM > = J (J +1) 5 J J . 5 M M - , [2.34a] < J ' M ' | J Z | J M > = M 6 J J . 5 M M . [2.34b] and < J' M ' | J \u00b1 | J M > = V \u00b1 ( J , M ) S J J . 5 M , M \u00b1 1 , [2.34c] where V \u00b1(a,b) =Va(a + l ) - b ( b \u00b1 l ) ; [2.34d] in Eq. [2.34d], a is generally an angular momentum quantum number with a projection Chapter 2 Theoretical Background 15 quantum number b. The Kronecker delta symbol, Sy, equals unity if i = j and vanishes otherwise; for convenience, units for which h = 1 have been introduced. The phase convention of Zare (17), for which the matrix elements of Jx are real and positive, has been adopted in Eq. [2.34]. 2.4(c) Addition of Angular Momenta: The Wigner 3-, 6- And 9-j Symbols 2.4(c)(i) The Wigner 3-j symbol The coupling of two angular momenta jj and j 2 to form a sum J can be represented by two different but equivalent types of wavefunctions. The first, called the coupled representation, have the form | J i J 2 J M ) (sometimes abbreviated as |JM)); these are simultaneous eigenfunctions of the four mutually commuting operators jj , j 2 , J = G l + J2) and J z =Jiz+J2Z- The alternative uncoupled representation | j i m i ; j 2 m 2 ) = | j i t t i i ) | j 2 m 2 > are simultaneous eigenfunctions of jj , j i z , j 2 and j 2 Z . These two equivalent representations are related by a unitary transformation |JM>= S l J i m i ; J 2 m 2 > < J i m i ; J 2 m 2 l J M > \u00bb P - 3 5 ] m]m 2 where J is one of + j 2 , j i + j 2 - 1, ... , | j i - j 2 | , and M = mi + m 2 . The Clebsch-Gordan coefficients ( j i m i ; j 2 m 2 | J M ) , easily calculated from these restrictions and the use of the ladder operators J\u00b1 = j ] \u00b1 + j 2 \u00b1 , appear in the literature, but are more usefully recast in terms of the Wigner 3-j symbol (17): < j 1 m 1 ; j 2 m 2 | JM> = ( - l ) J i - j 2 + M V 2 j T T f J l J 2 [ ) . [2.36] ^m, m 2 -M) This is advantageous because the Wigner 3-j symbols have higher symmetry; the most common ones are widely available in closed algebraic form. Eq. [2.35] can be rewritten: f : : t A |JM>= X ( - 1 ) J 1 _ J 2 + M V 2 J + 1 JI J2 J mj m 2 - M j 1 m 1 ; j 2 m 2 > . [2.37] 2.4(c)(ii) The Wigner 6-j symbol The wavefunctions for the sum J = + j 2 + J3 of three angular momenta can be formed Chapter 2 Theoretical Background 16 by adding the momenta in two stages using 3-j symbols in each step as discussed above, but this cannot be done uniquely. Any two of them can be combined into an intermediate angular momentum (j 1 2, J23 or j i 2 , with obvious definitions) to which the third can be added. The three coupling schemes are equivalent and related by unitary transformations of the type IGl h) J12 J3 J M > = S< Jl 0 2 J3) J23 M I Ox h) Jl2 J3 JM>I Jl 0 2 J3) J23 M > \u2022 [ 2- 3 8l J23 The recoupling coefficient <ji (J2 J3)J23 M lOi J2)Jl2 J3 J M ) c a n D e written as a product of four 3-j symbols, but is more commonly expressed in terms of the Wigner 6-j symbol: fj l J2 J12]_ ( - l ) J l + J 2 + J 3 + J <JlC2 J3)J23 M I G l J2)J12 J3 M > - [2.39] U3 J J23J V(2J12 +1X2J23 +1) Like the 3-j symbol, the 6-j symbol has many symmetry properties and has been evaluated algebraically for the most commonly encountered cases. 2.4(c)(iii) The Wigner 9-j symbol The logical extension of the preceding discussion is the recoupling of four or more angular momenta; the number of possible coupling schemes increases quickly with the number of angular momenta added. If there are four angular momenta, the Wigner 9-j symbol is used to relate one coupling scheme to another. The transformation in atoms from Russell-Saunders (LS) coupling to jj-coupling is a typical example. The two schemes are 11 + 12 = L ;s ! + s2 = S ; L + S = J [2.40a] and li + s 1 =j 1 ; li + s2 = j 2 ; J i + J 2 = J> t 2 - 4 0 b ] and the transformation between them is l ( l l S i ) J i ( l 2 S 2 ) j 2 J > - Z l ( l i l 2 ) L ( S l s 2 ) S J > LS :V(2L + l)(2S + l)(2j 1+l)(2j 2+l) h 12' L Jsi s 2 S ; [2.41] J l J2 J . the quantity in braces is a Wigner 9-j symbol, usually evaluated as a sum of products of three 6-j symbols or of six 3-j symbols. Chapter 2 Theoretical Background 17 2.4(d) Coordinate Rotations: The Wigner Rotation Matrix To describe the coupling of an angular momentum defined in a rotating reference frame (such as that of a freely rotating molecule) to another defined in a space-fixed frame, one must be transformed into the reference frame of the other. Great care is required to do this because of the anomalous commutation relations discussed by Van Vleck (19): if well-defined space-fixed components of an angular momentum operator obey Eq. [2.29], then its components referred to the rotating molecular frame do not obey Eq. [2.29]. Rather, they obey JiJj - Jj Jj = - i h \u00a3 e i j k J k . [2.42] k This \"anomalous sign of i\" means that care must be taken in evaluating the matrix elements of such operators. This can be done by defining the operators in a space-fixed frame and transforming them back to the molecule-fixed frame by a coordinate rotation. If J k is an angular momentum Cartesian component, the rotation operator R k(a) = exp(-\/a J k) [2.43] describes a rotation about the k axis by an angle a. According to results derived by Euler in the 18th century, there exist three angles a, P and y such that three such rotations can bring the space-fixed axes into coincidence with the molecule-fixed axes as follows: R(aPy) = exp(-\/a J z ) exp(-z' P J Y ) exp(-\/'y J z ) . [2.44] Al l rotations are taken about the original space-fixed axes, and a, P and y, the Euler angles, are referred to these. The rotation operator R(aPy) transforms the angular momentum eigenfiinction |JM) defined in the space-fixed system into a mixture of |JM'> eigenfunctions defined in the molecule-fixed system: R(aPy)|JM> = \u00a3 \u00a9 ^ M ( a p Y ) | JM'> \u2022 t 2 - 4 5 ! M ' The coefficients ( D ^ ' M ^ P Y ) are the matrix elements of R(aPy): ^ M ( a P Y ) = < J M ' | R | J M > ; [2.46] Chapter 2 Theoretical Background 18 these have a number of useful properties. The complex conjugate of an element is \u00a9 \u00a3 K ( a p Y ) = ( - l ) M - K \u00a9 J_M _ K ( a p y ) [2.47] It can be shown that the angular momentum wavefunction for a symmetric top molecule is |JKM>= E \u00b1 l [2.48] V 8tc2 where, in this case, M and K are the angular momentum projection quantum numbers in the molecule- and space-fixed frames respectively; a> refers to the set of Euler angles. Another useful property, of which use is made later, relates the integral of a product of three (D functions to a product of Wigner 3-j symbols: V l ^ M ^ K ' ^ ^ ^ ^ K ^ d C D = ( - I ) \u2122 8tc2 k 0 f J' k V - M ' P V - K ' P K > . [2.49] 2.4(e) Spherical Tensor Operators 2.4(e)(i) Definition of a spherical tensor An irreducible spherical tensor of rank k is defined as a set of 2k+l quantities, denoted by Tq where q = - k , -k+1 , ... ,k , which transform under a coordinate rotation according to R ^ R - V ) = X \u00a9 q \\ ( ( D ) T q k . . [2.50] q' This equation states that coordinate rotation by the set of Euler angles o transforms the k k spherical tensor component T q into a linear combination of the 2k + 1 components T q ' , with Wigner rotation matrix elements as expansion coefficients. Operators of rank zero, such as the Hamiltonian operator, are referred to as scalar operators because they are invariant under rotation. Racah's original definition (20) of the spherical tensor operator is based on the commutation relations of its components with those of the angular momentum operator J: [J Z >T q k ] = qT q k [2.51a] and [ J \u00b1 , T k ] = Vk(k + l ) - q ( q \u00b1 l ) T q < \u00b1 1 . [2.51b] From this definition, it follows that J itself is a first rank spherical tensor operator, whose Chapter 2 Theoretical Background 19 spherical components can be expressed in terms of the Cartesian components: To(J) = J z [2.52a] and Tl 1 (J)= + - ^ J \u00b1 - + - ^ ( J X \u00b1 \/ J Y ) . [2.52b] 2.4(e)(ii) Compound spherical tensor operators Since all first rank spherical tensors have the form of Eq. [2.52], the rules governing the addition of angular momenta apply to the construction of compound spherical tensor operators. For example, a kth rank compound tensor operator acting on a coupled system can be formed from two single spherical tensor operators: T^ x ( l ) of rank k i , which acts on the first part of the coupled system, and T^ 2(2) of rank k 2 , which acts on the second part. The spherical components of this compound tensor, denoted by [T k l(l)<8>T k2 (2)]q, can be written in terms of T ^ Q ) and T k2(2) by analogy with Eq. [2.37]: [ T k l ( l ) \u00ae T k 2 ( 2 ) ] k = X ( - l ) k l _ k 2 + q V 2 k + l Qi92 % k 2 k ^ T k 1 ( 1 ) T k 2 ( 2 ) [ 2 5 3 ] ^qi q2 ~v If two tensors of equal rank k couple to form a zero rank tensor (i.e., a scalar), this reduces to [ T k ( l ) \u00ae T k (2) ]\u00b0 = -^Lx(-l)q T k ( l ) T ^ ( 2 ) , [2.54] V 2k +1 q where the summation on the right represents the conventional scalar (dot) product. 2.4(e)(iii) The Wigner-Eckart Theorem The expression of operators as spherical tensors is advantageous because the Wigner-Eckart Theorem, proved in many angular momentum textbooks, can be used to evaluate their matrix elements in the basis of angular momentum eigenfunctions | r | JM). The theorem states that < n T M ' | T k h J M > =(-1)J'-M( J ' k J \\ r i ' J ' | |T k | | r , J> , [2-55] where r| represents the remaining quantum numbers of the system of interest. The Wigner-Eckart Theorem factorises the matrix element of Tq into two terms: the first depends on the Chapter 2 Theoretical Background 20 projection quantum numbers M and therefore on the geometry of the system, while the other, the reduced or \"double bar\" matrix element, is independent of such details and represents its physical properties. The Wigner-Eckart Theorem is typically applied by first determining independently a simple <r|TM'|Tq |r|JM> element and then solving Eq. [2.55] for the reduced element, after which the same equation is used to evaluate elements for other M values. This section concludes with some important reduced matrix elements often used in molecular spectroscopy. Reduced matrix element of the angular momentum operator The first element of interest is the double-bar element <J'||T1(J)|| J > . The matrix element for T-(J) = J z follows from Eq. [2.34b]: <J'M|T<5(J)|JM> = <J'M|J Z |JM> = M 5 j r . [2.56] The left side can be rewritten using the Wigner-Eckart Theorem: ( \" ^ ( L \\ A J r V , | |T 1 ( J ) | | J>=M5 J J , [2.57] ^ - M 0 MJ and the required 3-j symbol can be substituted: < J | | T 1 ( J ) | | J > =5JJVJ(J+1)(2J+1) . [2-58] Reduced matrix element of the (D functions Another reduced matrix element of interest is that of (D^ (co), which projects internal (molecule-fixed, corresponding to the q subscript) angular momenta expressed in space-fixed coordinates (corresponding to p) back into the molecule-fixed reference frame. The Wigner-Eckart theorem can be applied to \u00a9pq^*(o) matrix elements evaluated in the basis of symmetric top eigenfunctions: <J 'K 1 M , |\u00a9 p ( q ) *(co) |JKM>=(-l )J ' -M( T k J W ' | | \u00a9 \u00ab 1 | J K > , [2.59] where the dot subscript on the right means that the value of p need not be specified since the matrix element has been reduced with respect to its space-fixed components. The left side of Chapter 2 Theoretical Background 21 this equation can be recast by substituting Eq. [2.48] for the symmetric top eigenfunctions: ( r K ' M l ^ ^ a O I J K M ) - V ( 2 J + 1 ) f J ' + 1 ) J < i , ( \u00bb ) < > ) \u00a9 < & ) d \u00ab > P.\u00ab>l 8 7 T The integral is given by Eq. [2.49]. Eliminating < J T C M ' I ^ ^ Q ^ J K M ) between the resulting equation and Eq. [2.59] leads to an expression for the reduced matrix element: < J ' K ' 1 1 0 . ^ * 1 1 J K > = (-1)J'-K' V(2J + 1)(2J'+1) r T I k J [2.61] - K ' q K Reduced matrix elements of compound tensor operators in a coupled basis From the Wigner-Eckart Theorem, the matrix elements of a compound spherical tensor XQ (1 ,2) = [ T K i ( 1 ) \u00ae T K 2 ( 2 ) ] Q evaluated in the coupled basis | j i j 2 J M > are as follows: <Jl ' J2 , J 'M l |X^( l ,2) | j 1 j 2 JM> (-l)J' ' - M ' J' K J <Jl'J2'J , | |XK(l,2)||j 1j 2J>. [2.62] -M* Q M , Evaluation of the reduced matrix element requires conversion from a coupled to an uncoupled basis, several applications of the Wigner-Eckart Theorem and various properties of the Wigner symbols. Details of the derivation are available in several sources (16, 17, 21); the result is: <Jl , J2'J ' | |X K ( l ,2) | | j 1 j 2 J> = <Ji1|Tki (1)|| J iXJ2 ' l |T k 2 (2)|| j 2> Jl Jl k l )2 J2 k 2 T J K x > \/(2J+l)(2J ,+l)(2K+l) [2.63] Eq. [2.63] applies to any compound spherical tensor operator X of any rank K, but is rarely required in spectroscopy since such operators appearing in the Hamiltonian are scalar (i.e., K = 0), in which case the 9-j symbol in Eq. [2.63] collapses to a multiple of a 6-j symbol. A frequently encountered special case of Eq. [2.63] is that of a scalar product of two tensor operators of the same rank, T k ( l ) -T k (2) = X ( - i ) q T q (1)T^(2), identified inEq. [2.54]. q Its matrix element evaluated in the coupled basis is Chapter 2 Theoretical Background 22 < T i , j 1 ' j 2 7 ' M 1 T k ( l ) - T k ( 2 ) | T 1 j J 2 J M > = ( - l ) J i + J 2 , + J 5 J J . 5 M M , j ^ J. 2 J l l l k J l J2j x EOYJl 'H T k ( l ) II T,\"JiXr,\"J2'll T k (2 ) || T, j 2 > , [2.64] where r| represents the remaining quantum numbers of the system. Two other special cases of Eq. [2.63] can be identified. The first of these entails a single operator acting on only one part of a coupled basis, in which either T k l (1) or T k 2 (2) can be regarded as the zeroth rank identity operator. If the latter, then j 2 ' = j 2 k 2 = 0, K = k] and Eq. [2.63] reduces to <Jl ,J2J , | |T k l(l)IIJlJ2J> = (_l)Ji'+J2+J+ki^ ( 2J + i)( 2J'+l) j J ; ' J ' ^ W l l T ^ O H J i ) . [2.65a] U J l klJ Alternatively taking T k l (1) as the identity operator, j , ' =ji k x = 0 and K = k 2 so that <JlJ2 , J , | |T k 2(2) | | j 1 j 2 J> = ( - l ) J i + J 2 + J ' + k 2 ^ ( 2 J + l)(2J'+l) \\]] J , J l j<j2 , | |T k 2 (2) | | j 2 >. [2.65b] [ J J2 k 2 j Of particular note here is that the phases in Eqs. [2.65a] and [2.65b] are not the same, i.e., the order of the coupling of jj and j 2 governs the sign of the reduced matrix elements. The other special case of Eq. [2.63] is that for which both parts of the compound tensor X Q (1 ,2 ) act on the same system. In this instance, the reduced element of Eq. [2.63] becomes <r i , J1 |X K | hJ> = (- l ) K + >J 'V2KTTxj k . 1 k? 1^ ri\"j\"l J J J J x <r|']'l|T k l | |Ti\"j\"><Ti\"j , , | |T k2 |h j> . [2.66] Finally, a mechanism is required to transform spherical tensor operators between space-fixed and molecule-fixed coordinate systems. To express the molecule-fixed components T q in terms of space-fixed components Tp , the following transformation is used: Tqk = I \u00a9 p k q ( < \u00b0 ) T p k - t 2 - 6 T l P The inverse transformation is found by multiplying Eq. [2.67] by <D^ (\u00a9), summing over q Chapter 2 Theoretical Background 23 and using orthogonality properties of the Wigner rotation matrix elements. The result is: Tp =Z<Z)pT(ffi)Tq-q Eq. [2.68] is required when evaluating matrix elements for an internal operator written in a space-fixed axis system; it projects the operator into the molecule-fixed axis system. The reduced matrix elements for (D^*((o) are also required in such evaluation; they are given by an extension of Eq. [2.61]. Eqs. [2.58], [2.61], [2.64], [2.65], [2.66] and [2.68] are some of the most useful for evaluating Hamiltonian matrix elements. The individual terms of the Hamiltonian are presented in the next section; their matrix elements are evaluated in Section 2.6(b). 2.5 The Effective Molecular Hamiltonian 2.5(a) The Rotational Hamiltonian The Hamiltonian operator for a rigid rotating molecule can be written as R 2 R 2 T J 2 n g l d 2I X 2I y 2I Z where R x , R y and R z are the Cartesian components of the rotational angular momentum R, taken along the principal axes of the molecule, and I x , I y and I z are the corresponding principal moments of inertia, given by I i = Z m j r j i ' i = x>y>z> [2-70] j where nij and are respectively the mass and distance of the jth atom from the i axis. This thesis is concerned only with linear molecules, for which R is perpendicular to the molecular, i.e., z axis. Rotations about the z axis cannot be distinguished in this case, so R z = 0 [2.71] and I x = Iy = I. [2.72] For diatomic and linear triatomic molecules, the moment of inertia I can be expressed in terms of the bond length(s) of the molecule. For diatomics: Chapter 2 Theoretical Background 24 I = UJ-2, [2.73] where r is the bond length and p is the reduced mass from Eq. [2.22]. For linear triatomics: j = m 1m 2r 1 2 2 + mim 3 ( r 1 2 + r 2 3 ) 2 + m 2 m 3 r 2 3 [ 2 ? 4 ] mi + m 2 + m 3 where the subscript 2 denotes the central atom of the molecule and ry denotes the bond length between atoms i and j . In each case Eq. [2.69] simplifies to R ? + R ? R 2 Eq. [2.75] does not accurately specify the rotational Hamiltonian for a real molecule because with rotation of the molecule, centrifugal forces increase I; a more complete treatment yields (14, 15): Hroi = B R 2 - D R 4 . [2.76] In this expression D, the centrifugal distortion constant, is typically about 10 6 times less than B. An accurate estimate of D is made from the Kratzer relations (14, 15): 4 B 3 D = ^ - , [2.77a] or D = 4 B 3 (fl r 2 \\ Z2_L + 223_ 2 2 [2.77b] These expressions apply to diatomic and linear triatomic molecules respectively. In Eq. [2.77b], the \u00a3 2 i parameters describe the Coriolis coupling of the bending vibration with the 2 2 4 two stretching vibrations, and are normalised such that C 2 i + C 2 3 = 1- The R dependence of the distortion term comes from the general prescription for evaluating the centrifugal distortion correction of any term in the Hamiltonian: Xd = \\ C [ # R 2 + R 2 # ] = \\ C[H ,R2]+, [2.78] where C is the experimentally determinable constant and the anticommutator form [x, y ] + retains the Hermicity of 7^, as required of any Hamiltonian operator. R in Eq. [2.76] is one of many angular momenta that occur in a molecule; others Chapter 2 Theoretical Background 25 discussed in later sections include the electron orbital angular momentum L and the electron spin angular momentum S. The sum of these is J, the total angular momentum neglecting nuclear spin: J - R + L + S, [2.79] which leads to the form of R required in Section 2.6(b) for the evaluation of the matrix elements of Kro{. R = J - L - S . [2.80] 2.5(b) The Fine Structure Hamiltonian Electron spin contributions to the Hamiltonian have thus far been ignored. Spin arises in quantum mechanical systems as a relativistic effect; it is an intrinsic angular momentum of electrons (and many nuclei) with no classical analogue. Like other angular momenta, it produces a magnetic moment, [2.81] n directly proportional to itself. In this expression, g e is the relativistic gyromagnetic ratio or \"g-factor\", approximately equal to 2.0023, p B = eh\/2me is the Bohr magneton, the unit of electron magnetic moment, and s is the spin angular momentum of magnitude ^\/s(s +1) h where s = 1\/2. A minus sign appears in Eq. [2.81] because the electron is negatively charged; ji s and s point in opposite directions. Four important effects arise if the total spin angular momentum S is nonzero. A nonzero nuclear spin angular momentum, if present, can couple with the electron spin angular momentum; this represents one of a class of several nuclear spin effects collectively referred to as hyperfine structure. The hyperfine Hamiltonian is discussed in Section 2.5(c). The other three effects, referred to as fine structure, are now examined. 2.5(b)(i) The spin-orbit Hamiltonian The positively charged nuclei of the molecule produce an electric field through which Chapter 2 Theoretical Background 26 the electrons travel. This orbital motion generates a magnetic field; using Maxwell's equations of electromagnetic theory to describe the interaction of the electron spin magnetic moment with this magnetic field (22), the following Hamiltonian can be obtained: f \"\\ \u201e .. 1 ^ dV g e p B v 1 dV g e ^ B y 1 9 Z-i . 'en' Se ^ i 2 2hc m e e,nren V^ren j hc^ e,nren V\u00b0^ren J (renXVn)-Se- [2.82] Some of the quantities have already been defined; others require clarification: r e n denotes the displacement from a nucleus to an electron, V denotes the potential of the nuclei, I e n is the electron orbital angular momentum around a nucleus, and s e is the electron spin. The expression is summed over all electrons and nuclei in the molecule. The second term in this expression is #~sr, the spin-rotation interaction; it is discussed in Section 2.5(b)(ii). The first term is Jfso, the spin-orbit interaction, which describes the interaction of the electron orbital and spin angular momenta. A form of the spin-orbit Hamiltonian can be derived by considering the form of the potential V , which must take electron-electron repulsions into account. Van Vleck (19) has shown that the screening effect of these repulsions can be approximated adequately by a Coulombic potential that treats each nucleus n as an effective point charge Zn( eg)e: V = Z \" ( e \u00a3 \u00b0 e . [2.83] 47ts 0r e n With this potential and the definition of pg, the first term of Eq. [2.82] becomes: 43 v-> 2 2 1 Anz^h c e,n ren By defining the microscopic spin-orbit parameter a e according to s 4 T Z \u2014 P . \u00bb 5 1 47180 ft c n ren the spin-orbit Hamiltonian becomes e which is often approximated macroscopically as Chapter 2 Theoretical Background 27 #so = A L - S , [2.87] where A is the macroscopic spin-orbit coupling constant and L and S are respectively the total electron orbital and spin angular momenta: e and S = \u00a3 s e . t 2 - 8 8 b ] e Eq. [2.87] is normally sufficient to describe isolated, unperturbed electronic states, while Eq. [2.86] is required to model interactions between electronic states of different S or A. 2.5(b)(ii) The spin-rotation Hamiltonian The microscopic form of the spin-rotation Hamiltonian Hsx was given in the previous section as the second term in Eq. [2.82]: f ^ geHB sr 2 he e,n ren dV V^ren j ( r e n x v n ) - S e . [2.89] As with the spin-orbit Hamiltonian, the effective potential of Eq. [2.83] can be substituted. In addition, the nuclear velocity v n is given by v n = w x r n = (Ico) x r n \/ I = Rx r n \/ I , [2.90] where o> is the rotational angular velocity of the (linear) molecule, and R and I are the rotational angular momentum and moment of inertia as given in Section 2.5(a). With these modifications, ^ - - J ^ Z ^ I ' - x ( * \u00ab \u201e ) ] - , . . [2.9!] 47is0^c Ie,n r e n This can be written as a sum of two terms by using the triple cross product identity A x ( B x C ) = (C-A)B-(B-A)C. [2.92] Rewritten in this fashion, the second resulting term of Eq. [2.91] operates between different electronic states and is generally much smaller than the first; it is usually omitted. Therefore \u00ab - s r = - ^ Z ^ f I ( r \u201e r e n ) R S e . [2.93] 47t8Q c^ Ie,n r e n Chapter 2 Theoretical Background 28 This can be simplified in a manner analogous to the microscopic spin-orbit Hamiltonian of Eq. [2.86]; by defining b e = - ^ B i _ I ^ f - ( r n . r e n ) , [2.94] 47CS()ftc I n r e n Eq. [2.93] can be written as * s r=Xb e R-s e , [2.95] e whose approximate macroscopic form is #sr = y R - S , [2.96] where S is as defined in Eq. [2.88b]. This represents in effect an interaction of the rotational and total electron spin angular momenta with coupling constant y. This direct spin-rotation parameter is often dominated by a larger indirect spin-rotation coupling that arises from off-diagonal matrix elements of the spin-orbit Hamiltonian. Using second order perturbation theory, Henderson has shown (23) that this contribution has the same form as the direct spin-rotation coupling of Eq. [2.89]. Consequently, the experimentally determined y parameter is actually an inseparable sum of the direct spin-rotation constant of Eq. [2.96], renamed y S R , and the second-order contribution y s o : y = YSR + YSfJ [2.97] where y s o is usually the dominant contribution in all but the lightest molecules. 2.5(b)(iii) The spin-spin Hamiltonian The final contribution to the fine structure Hamiltonian arises from the interaction of the spin magnetic moment of each electron with the magnetic field produced by the remaining electron spins. This spin-spin interaction is . . r Si Sj 3 (S J -i-jiXsj -i-ji) ^ = _ 8 ^ Z | ^ ( o ) | 2 s i _ S j + g e2 p i 3n i>j n i>j r3. v5. Ji Ji [2.98] Some identification of parameters is necessary. The Sj denote the various electron spins, rjj denotes the distance between the ith and jth electrons and \\|\/j(0) refers to the wavefunction of Chapter 2 Theoretical Background 29 the jth electron evaluated at the location of the ith electron. In the first term of Eq. [2.98], |v|\/j(0)|2 is the probability that electrons j and i have the same coordinates; this term is thus constant and can be absorbed into the Born-Oppenheimer potential. The second term has the same form as the classical Hamiltonian for the interaction between dipoles; it is called the dipolar electron spin-spin interaction. It is usually written in the following macroscopic form as a direct spin-spin coupling: S z denotes the molecule-fixed projection of the total spin S and X is the electron spin-spin interaction parameter. Just as off-diagonal matrix elements of the spin-orbit Hamiltonian introduce an indirect second-order correction to the direct spin-rotation interaction of Eq. [2.96], they also introduce a second-order correction to the direct spin-spin Hamiltonian. As discussed by Levy (24) and Lefebvre-Brion and Field (25), the form of this correction is identical to the direct spin-spin Hamiltonian, so that the experimentally determinable spin-spin constant X has a form analogous toEq. [2.97]: where X s s represents the direct contribution of Eq. [2.98] and X s o represents the indirect contribution that arises from second-order spin-orbit interactions. Once again, the latter, when present, is usually the dominant contribution to the experimental value of X. 2.5(c) The Hyperfine Hamiltonian Like electrons, the protons and neutrons that comprise nuclei each possess an intrinsic one-half unit of spin angular momentum. The interaction of these spins within a nucleus results in a total nuclear spin I, whose quantum number I (not to be confused with the moment of inertia I introduced in Section 2.5(a)) is restricted to nonnegative multiples of one-half and is, for the purposes of this thesis, constant for a given nucleus. This nuclear spin, like the electron ^ s s _ 3^(3S 2 - S 2 ) ; [2.99] [2.100] Chapter 2 Theoretical Background 30 spin, possesses a magnetic moment that is free to interact with those associated with other angular momenta in the molecule. Accordingly, the molecular energy levels are split into magnetic hyperfine structure components. Nuclei with I > 1 have anisotropic charge distributions; the resultant electric quadrupole moments contribute additional complexity in the form of electric quadrupole hyperfine structure. Both phenomena, discussed below in further detail, are called hyperfine effects because the energy corrections they introduce are typically very small; in electronic spectra, their effects are discernible only at very high resolution. 2.5(c)(i) Magnetic hyperfine structure In the 1950s, Frosch and Foley (26) recognised the correspondence of the magnetic moments of the nuclear and electron spins, and thereby formulated the first general theory for the magnetic hyperfine structure of linear molecules. Their formalism was thus essentially identical to that presented above for the electron spin Hamiltonian, with the nuclear spin magnetic moment replacing that of the electron. As was the case for electron spin, several interactions of the nuclear spin magnetic moment can be identified, namely: (1) the spin magnetic moments of the electrons, (2) the orbital magnetic moments of the electrons, (3) the rotational magnetic moment of the molecule and (4) the spin magnetic moments of other nuclei. The last of these four interactions is far too weak to detect in electronic spectra and will not be considered here; only the remaining three are examined. The appropriate Hamiltonian in each case can be derived from the formalism of Section 2.5(b) by simply replacing the various electron parameters with those for the relevant nuclei. An additional hyperfine effect similar to A-type doubling of rotational structure is discussed in Section 2.7(c). Nuclear spin-electron spin interaction The Hamiltonian for the nuclear spin-electron spin interaction has the same form as Eq. Chapter 2 Theoretical Background 31 [2.98], except that one of the two electron spin magnetic moments is replaced by a nuclear magnetic moment g n ^ N 1 Hi h [2.101] where g n is the g-factor of the nucleus, p^ = eh\/2m p is the nuclear magneton and m p is the proton mass; the minus sign of Eq. [2.81] no longer appears since the nucleus is positively charged. With this change, the nuclear spin-electron spin Hamiltonian is % = M M \u00a3 g J v , e ( 0 ) f , n . s < 3h e , n g e W N h2 e , n ^ n s e 3 ( I n \u2022 r e n ) (s e \u2022 r e n ) [2.102] ' e n ' e n Once again, two terms arise as in Eq. [2.98], but in this case the first term is not a constant; it represents the Fermi contact interaction between the electron and the nucleus when the electron is in an orbital with non-vanishing amplitude at the nucleus. This occurs only when an unpaired electron occupies a molecular orbital with atomic s character. The second term is analogous to that of Eq. [2.98] and represents the dipolar interaction between the magnetic moments of the nuclear and electron spins. If, as is the case for all molecules studied in this thesis, only one nucleus has a large magnetic moment, no summation over n is needed. In addition, the Fermi contact parameter, bT 8 7 1 g e P - B U N g n \u2022 r m | 2 J F , e - \u2014 I V e C\u00b0) I 3 h2 can be introduced, so that Eq. [2.102] becomes fllS=X>F>eI.se - X g e g n f W N h2 I s e 3 ( I r e ) (s e - r e ) [2.103] [2.104] Nuclear spin-electron orbital angular momentum interaction Once again, the treatment follows that of the electron spin-electron orbital angular momentum interaction, with nuclear spin parameters replacing those of the electron spin. The Hamiltonian is given by Chapter 2 Theoretical Background 32 ^ = Z ^ M - | - | ^ I - ' e = Z a e I - l e ; [2-105] e 2hc m e dV where only one nuclear spin is assumed and the middle part of the equation defines a e. Nuclear spin-rotation interaction The nuclear spin-rotation interaction can be derived in similar fashion to the electron spin-rotation interaction, giving n w l dV ^ I n J = Z ^ n I n - J = C l I - J . [2.106] V r V U 1 n In the term following the first equals sign, the quantity I is the moment of inertia, not to be confused with the nuclear spin I. The last term applies if only one nuclear spin is present; J is used instead of R because the effect of the nuclear spin interaction with the electron spin and orbit angular momenta have already been considered in the preceding discussion. This very weak interaction is generally not significant for electronic spectra; it was not observed in the present work and will not be discussed further. The total magnetic hyperfine Hamiltonian Like the nuclear spin-rotation interaction, the other terms in the magnetic hyperfine Hamiltonian are usually expressed in terms of macroscopic hyperfine parameters: # m a g h f = a I - L + bI-S + cI z S z . [2.107] In Eq. [2.107], only the diagonal part of the dipolar nuclear spin-electron spin Hamiltonian is taken. The hyperfine parameters are the nuclear spin-electron orbit constant a= [2.108] the Fermi contact parameter b F = 8 7 L g e g n W N | v ) \/ ( 0 ) | 2 [ 2 1 0 9 ] 3 ti and the dipolar parameter \u201e _ 3 g e g n p B H N \/3cos 9-1 x m i n i 2 h2 \\ r 3 } - [ 2 1 1 0 ] Chapter 2 Theoretical Background 33 InEq. [2.107], b = b F - ^ c . [2.111] Of these constants, a, b and c are the experimentally determinable parameters. The constant b F is more fundamental than b because it gives the value of the electronic wavefiinction at the location of the spinning nucleus, but it can only be determined indirectly from Eq: [2.111]. 2.5(c)(ii) Electric quadrupole hyperfine structure While magnetic hyperfine effects are generally important only for open shell electronic states, another type of hyperfine effect arises even for closed shell electronic states, if an I > 1 nucleus is present. The anisotropic charge distribution in such a nucleus creates an electric quadrupole moment that interacts with the electric field gradient of the electron charge distribution. This effect, called the electric quadrupole hyperfine interaction, is the first non-vanishing term in the multipole expansion of the nuclear-electron Coulombic interaction. Many early workers (27-33) have examined the theory of electric quadrupole hyperfine structure for various types of molecules; Bardeen and Townes (34) offered the first general formalism. The electric quadrupole hyperfine Hamiltonian HQ can be expressed macroscopically as the scalar product of two second rank tensors: # Q = - T 2 ( V E ) - T 2 ( Q ) , [2.112] namely, the electric field gradient and the nuclear quadrupole tensor. By convention, the nuclear quadrupole moment operator eQ is given by e Q = Z q n r n ( 3 c o s 2 e n - l ) . [2.113] n The summation is over all nucleons, each with a charge q n and spherical polar coordinates r n and 6 n as measured from the nuclear centre. The corresponding nuclear quadrupole moment Q is defined by e Q = < L M I = I | Q | L M I = I > , [2.114] where I and M T are the quantum numbers for the nuclear spin and its axial projection. Q cannot Chapter 2 Theoretical Background 34 be measured independently from molecular spectra; the experimentally determinable parameters that specify the strength of the quadrupole interaction in linear molecules are the products eQqo and eQq2- As explained below in Section 2.6(b)(1), only the former is needed in this thesis. By convention, the value of qo is specified by the axial component of the electric field gradient (or equivalently, the negative Laplacian of the potential) evaluated at the quadrupolar nucleus: q 0 = <J, M j = J | ( - V E ) z 0 | J , M j = J> = <J, M j = J | (d2V\/dz2)0 \\ J , M j = J) . [2.115] 2.6 Hund's Coupling Cases and Hamiltonian Matrix Elements The formulation of the Hamiltonian Jfis the first step in determining the energy level structure for a molecular electronic state of interest. The next step is the evaluation of the matrix elements of 9f, followed by the diagonalisation of the resulting matrix to yield the energy eigenvalues of the state. Always implicit in this step is the representation, or choice of basis functions used to evaluate the matrix elements; since the eigenvalues are invariant to the representation, any valid, convenient basis set can be used. In part (a) of this section, the most commonly used basis sets are discussed. Part (b) evaluates the matrix elements using two of these representations. 2.6(a) Hund's Coupling Cases In 1926, Hund (35) considered four coupling situations that could arise for different strengths of the couplings between the rotation and electron angular momenta, which subsequently became known as Hund's coupling cases (a), (b), (c) and (d). Shortly thereafter, Mulliken (36) proposed a fifth coupling case that he labelled Hund's case (e). None of these considered the various types of nuclear spin angular momentum interactions because hyperfine effects had rarely been observed at that time, but the first three cases, the only ones used to describe the present data, were later so extended by Frosch and Foley (26) and Townes and Chapter 2 Theoretical Background 35 Schawlow (11). These three schemes and their extensions for nuclear spin are now discussed. The Hund's coupling cases are choices of basis functions that generate a convenient representation of the Hamiltonian matrix, usually the one that is either the most nearly diagonal or the one for which the matrix elements are algebraically simplest. The starting point is the spin-orbit and rotational Hamiltonian, #- = A L - S + J3R2, [2:116] where R = J - L - S. Expanding B R 2 gives 3f = B ( J 2 + L 2 + S2) + (A+2B) L S - 2B J L - 2B J S, [2.117] The choice of basis is made according to which of the final three terms in Eq. [2.117] is dominant over the other two in the state of interest. 2.6(a)(i) Hund's case (a) Hund's case (a) is an uncoupled representation, for which the electron orbital and spin angular momenta L and S are separately quantised along the molecular z-axis, with projections A and 2 respectively. Its basis functions are written | n A ; S E ; J Q > , [2.118] where n refers to the radial part of the electronic wavefiinction. This ket denotes independent electron orbital and spin factors, |(L) A) and | SS>, where L is written in parentheses since it is strictly not a good quantum number; since there is no molecular rotation about the z-axis, the projection Q. of the total angular momentum J (exclusive of nuclear spin) onto this axis comes from electrons only: \u00a32 = A + Z. [2.119] The possible values of A and S are A = 0 , \u00b1 l , \u00b1 2 , \u00b1 3 , ... , [2.120a] and 2 = +S, +S-1, +S-2, ... -S ; [2.120b] the A values correspond respectively to the irreducible representations (symmetries) E, n, A, O, Chapter 2 Theoretical Background 36 ..., of the electronic wavefunction in the C ^ y point group of the molecule. The various quantum numbers are usually assembled into the term symbols 2 S + 1 A Q ; the quantity 2S+1 is called the spin multiplicity and Q. is given by Eq. [2.119]. A superscript of either + or -denotes the Kronig symmetry for Z states (not to be confused with the quantum number \u00a3 of Eqs. [2.119] and [2.120b]), i.e., whether the electronic part of the molecular wavefunction remains unchanged or reverses sign upon reflexion in the molecular plane. Hund's case (a) is the most diagonal representation if L and S are moderately coupled through the spin-orbit operator (A+2B) L-S, with much smaller couplings from the last two operators in Eq. [2.117]. This coupling mixes case (a) basis functions for which A A = - A S , so that A and S are strictly no longer good quantum numbers, but can usually be approximated as such; their sum \u00a31 always remains good if the L-S coupling is sufficiently strong. Very large L-S coupling thoroughly mixes various A (and various Z ) , so that Hund's case (c), described below, applies. Even if the electronic state of interest does not conform closely to Hund's case (a) coupling, it is often the best choice of basis for data fitting purposes because its matrix elements are algebraically simplest. Since the projection of J is characterised by \u00a32, the quantum number J is restricted: J = |Q| , + | Q | + 2, ... . [2.121] 2.6(a)(ii) Hund's case (b) Hund's case (b) applies if the -2B J-S term in Eq. [2.117] dominates the two preceding it. Since this interaction increases with rotation while (A+2B) L-S is independent thereof, in principle this will always occur at sufficiently high J values; this process is called \"spin-uncoupling\". In case (b), the vector sum of R and L is called N: N = R + L. [2.122] Since R is perpendicular to the molecular axis, A can be regarded as the projection quantum number of both L and N. By analogy with Eq. [2.121], N is bounded below by | A | : Chapter 2 Theoretical Background 37 N = | A | , | A | + 1, | A | + 2, ... . [2.123] The total angular momentum J (exclusive of nuclear spin) is then J = N + S. [2.124] Thus if orbital angular momentum effects are negligible, the rotational energy is B R 2 ~ B N 2 = B(J - S) 2 = B t J 2 + S 2) - 2B J S, [2.125] The appropriate basis functions, when the effects of the - 2B J-S term dominate, represent the vector coupling of N and S as per Eq. [2.124], and follow from Eq. [2.37]: O S N ^  v n - z - A |r|A;SZ;jn>. [2.126] |n ;NASJ> = Q V 2 N + l | The symbol 2 S + 1 A , identical to the case (a) notation but with the superfluous Q. subscript removed, denotes an electronic state for which Hund's case (b) applies. 2.6(a)(iii) Hund's case (c) As explained earlier, Hund's case (c) applies if the spin-orbit coupling of L and S through the operator (A+2B)L-S is so strong that the projections A and \u00a3 lose their meanings. The vector coupling in this case is J a = L + S, [2.127] and the basis functions are simply \\r\\; J a\u00a32 ; JI2), where Q is the projection of both J and J a . This situation often occurs in the electronic states of molecules containing heavy atoms, even in states with nominal Z symmetry. In Hund's case (c) coupling a 2 Z \u00b1 state becomes a n i i = 1\/2 state without a Kronig symmetry, and a state becomes three case (c) states, one each with Q. - 0 + , 1 + and 1~ (although the last two are normally regarded as a single CI = 1 state). The rotational energy level patterns are essentially the same for case (a) and case (c). The allowed J values follow Eq. [2.121] and (for Q > 0) are doubly degenerate in the absence of A - or D-type doubling effects. 2.6(a)(iv) Modified Hund's cases: nuclear spin effects Frosch and Foley (26) and Townes and Schawlow (11) were the first to extend Hund's Chapter 2 Theoretical Background 38 coupling cases to account for nuclear spin effects. In their work, Hund's coupling cases (a), (b) and (c) are sub-classified depending on whether the nuclear spin angular momentum I is coupled more strongly to the molecular axis or to another angular momentum within the molecule. The appropriate coupling case is modified by a subscript; in the former case, a is used, while the latter uses a P subscript. In practice, the former situation is never encountered since the nuclear spin magnetic moment is so small compared to those of the other angular momenta that their interactions are too weak to couple I to the molecular axis; only cases (ap), (bp) and (cp) are generally observed. Hund's case (ap) is a simple extension of case (a), in which the nuclear spin couples to the total angular momentum excluding nuclear spin, J, to form the total angular momentum F. This coupling scheme can be written as J = R + L + S ; F = J + I. [2.128] The total angular momentum quantum number F has the 2 \u2022 min(J,I) + 1 allowed values F = J + I, J + I - l , ... , | J - I | [2.129] (where min(a,b) is the lesser of a and b), and the appropriate basis functions are written as | n A ; S 2 ; . [2.130] Hund's case (bp) is further subclassified by an extra subscript of N , J or S according to which of the corresponding angular momenta is most strongly coupled to the nuclear spin I. The coupling to I of N is generally much weaker than that of J or S; no examples of case (bpN) coupling appear in the literature and it will not be discussed here. Of the remaining pair, case (bpj) is the more commonly encountered; it is a simple extension of case (b) analogous to case (ap). Once again, the total angular momentum excluding nuclear spin, J, couples with the nuclear spin I to form the total angular momentum F; the coupling scheme for this case is: N = R + L ; J = N + S ; F = J + I. [2.131] Hund's case (bpj) basis functions are written in the form Chapter 2 Theoretical Background 39 | T | ; N A S J I F > . [2.132] The other coupling case, called Hund's case (bps), occurs if the interaction between the nuclear and electron spins {i.e., the Fermi contact interaction) is the largest electron spin interaction term in the Hamiltonian. Under these circumstances, the coupling of I and S forms a resultant angular momentum G that is sometimes called the pseudospin. Its quantum number G takes the values G = I + S , I + S - 1 , ... , 11 \u2014 S |, [2.133] in accord with the usual rules of vector coupling. G in turn couples with N to form the total angular momentum F ; the coupling scheme can be written as N = R + L ; G = I + S ; F = G + N , [2.134] This represents a less common coupling scheme for which J is not a good quantum number. Hund's case (bps) basis functions are written in the form |nA;(IS)GNF>; [2.135] in analogy with Eq. [2.129], the values of F range from | N - G | to N + G. Of the electronic states reported in the literature that follow Hund's case (bps) coupling, the vast majority have 2 Z symmetry, for which spin-spin and spin-orbit couplings do not occur. These couplings can be present for states of other symmetry and, if so, are usually much larger than the Fermi contact interaction. The only other electron spin interaction that appears in 2 S states is the spin-rotation interaction, which increases with rotation. In principle, every electronic state that begins in Hund's case (bps) coupling at low N eventually reaches a sufficiently high N value at which the spin-rotation interaction overtakes the (constant) Fermi contact interaction and a Hund's case (bpj) description becomes more appropriate. This is similar to the spin-uncoupling phenomenon, in which case (a) coupling converts to case (b) at high rotation. Finally, Hund's case (cp) is also possible. This extension of Hund's case (c) is Chapter 2 Theoretical Background 40 analogous to the extension of Hund's case (a) to Hund's case (ap). Once again, the total angular momentum F is formed from a coupling of J and I; the basis functions are written as |r,; J a Q;Jf i IF> . 2.6(b) Matrix Elements of the Hamiltonian Various contributions to the molecular Hamiltonian were identified in Section 2.5. This section presents the evaluation of their matrix elements using Hund's case (ap) and (bp\u00a7) basis sets; the latter are for a 2 2 state, the only type for which these are needed in this thesis. 2.6(b)(i) Hamiltonian matrix elements evaluated in a Hund's case (ap) basis The total molecular Hamiltonian operator can be written as X = e^v + r^ot + ^so + s^r + ^ss + ^mhfs + ^Q + ^ld- t 2 1 3 6 ] The terms on the right of Eq. [2.136] are the operators for, respectively, the electronic-vibrational energy, the rotation, the spin-orbit interaction, the spin-rotation interaction, the spin-spin interaction, the magnetic hyperfine structure, the electric quadrupole hyperfine structure and the A-doubling interaction. The final term has not yet been discussed; this is done in Section 2.7. The electronic-vibrational Hamiltonian needs little discussion since in any rotational basis it merely contributes the vibrational energy T v for its electronic state of energy T e ; thus < A ; S S ; J O I F | ^ e v | A ; S E ; JQIF) = T e + T v = T e v , [2.137] where r\\ is suppressed since only matrix elements within an electronic state are considered in this discussion. The remaining matrix elements are now evaluated. Some are independent of I and F; for brevity, these are suppressed from the basis functions for such elements. The rotational Hamiltonian: the B 1 } term The rotational Hamiltonian of a linear molecule is given by Eq. [2.76]; with R written in terms of J, L and S, Hm = B v (J - L - S) 2 - Dy (J - L - S)4 [2.138] Chapter 2 Theoretical Background 41 where the x> subscripts of the rotational and distortion constants specify the vibrational level of interest. The first term can be expanded: By (J - L - S)2 = B v (J 2 + L 2 + S 2 - 2 J-S + 2 L-S - 2 J-L). [2.139] The x and y components of the L operator connect electronic states with different A values; their effects are neglected here and incorporated into the A-type doubling operator. Thus, if the centrifugal distortion term is ignored for the moment, the rotational Hamiltonian becomes #-rot = Bv [(J2 + L 2 - J 2 - S 2 - (J+S_ + J_S+)], [2.140] where -Bv (J+S_ + JLS+) is the aforementioned spin-uncoupling operator. This form of the rotational Hamiltonian is useful because the Hund's case (a) basis functions \\r\\ A ; SZ ; Jfi} are eigenfunctions of J 2 , J z , S2, S z and L z , and the matrix elements can be evaluated using Eq. [2.34]: < A ; S Z ; J Q | # r o t | A ; S Z ; j n > = BV[J(J+1) + S (S +1) - Q 2 - Z 2 ] , [2.141a] and < A ; S Z ; JQ|#\" r o t | A ; S Z \u00b1 1 ; JO\u00b1l>= -BvV\u00b1(J,n)V\u00b1(S,i:), [2.141b] where V\u00b1(a,b) is given by Eq. [2.34d]. The off-diagonal matrix elements are derived with the implicit understanding that the ladder operators J \u00b1 behave like J+ because of the anomalous commutation rules for angular momentum operators in a molecule-fixed axis system. The rotational constant Bv strictly does not correspond to the inertial moment at the absolute minimum of the potential surface (i.e., at equilibrium) of the electronic state of interest, but represents instead an effective value for the vibrational level u. Rotational constants from at least two vibrational levels must be experimentally determined to extract the equilibrium moment of inertia. B^ is usually expressed as a power series in (UJ +-|): B v = B e -Xa i (v J i +l) + ..-. [2.142] i The summation is over all the vibrational modes; B e is the equilibrium rotational constant and the O j parameters are the vibration-rotation interaction constants. For a diatomic molecule, B e Chapter 2 Theoretical Background 42 corresponds to the equilibrium bond length r e; when written in c m - 1 units, B - h e 2 2 ' 87c cpr e [2.143] where p is the reduced mass of the molecule. For jet-cooled spectra of the type reported in this thesis, the v = 0 level of the ground state is usually the only one significantly populated, and the rotational constants of higher vibrational levels cannot be determined; in this case, r e is approximated by r 0 , corresponding to B 0 . Diatomic molecules have only one vibration-rotation interaction constant, called a e . The Pekeris relation (37) gives an approximate value of a e: where coe and coexe are the vibrational constants of Eq. [2.20]. For polyatomic species, the extraction of geometrical structural parameters from rotational constants is not always trivial. For a linear triatomic molecule, for example, the equilibrium constant B e depends on both bond lengths. These are usually determined by isotopic substitution; rotational constants are independently measured for the A B C and A B C isotopomers. In the BOA, the equilibrium bond lengths r e (A-B) and r e (B-C) are independent of isotopomer, so the B e (ABC) and B e ( A B C ) values can be used to give these. If only the zero-point vibrational level constants, B 0 , can be determined, then an r 0 structure emerges. As with diatomic molecules, this only approximates the equilibrium (re) structure, even more so since r 0 (B-C) differs for A B C and ABC ' . The Laurie correction (38) offers an improvement, the difference in r 0 (B-C) for the diatomic species BC and B C , if known independently, can approximate the corresponding difference in A B C and A B C and improve the r 0 values extracted from the B 0 constants. Centrifugal distortion: the D v term The matrix elements of the distortion term need not be given here; they can be found simply by squaring the coefficient matrix of the Bv term and reversing its sign. The centrifugal [2.144] Chapter 2 Theoretical Background 43 distortion constant D v , like the rotational constant B^, can be expressed as a rapidly converging power series in (u, + ): Do = D e + \u00a3 B i O > i + i ) + - - [2.145] i In the Kratzer relations of Eq. [2.77], the B and D constants are strictly the equilibrium constants of Eqs. [2.142] and [2.145], although the 04 and pj are sufficiently small compared to B e and D e that their zero-point counterparts are often used in Eq. [2.77] to good approximation. Eq. [2.78] gives the centrifugal distortion correction to any rotational operator in terms of the operator itself, so that the matrix elements of the centrifugal distortion corrections can be determined by straightforward matrix algebra. For brevity, therefore, such matrix elements will not be derived here, although they are quoted as needed in subsequent chapters. Also, for convenience, a subscript v identifying the vibrational level of interest has been suppressed from all determinable parameters in the matrix elements below. The spin-orbit Hamiltonian The spin-orbit Hamiltonian of Eq. [2.87] can be expanded into Cartesian components: Xso = A [ L Z S Z + \\ (L + S_ + LJS+)], [2.146] with diagonal elements <A; S E ; J\u00a32 | Jfs0 | A ; SE; J\u00a32> = A A E , [2.147] Matrix elements with A A = - A E = \u00b11 exist for this operator, but were not used in this thesis. The spin-rotation Hamiltonian The spin-rotation Hamiltonian of Eq. [2.96] must be expressed in terms of the J , L and S angular momenta for evaluation of its matrix elements in a Hund's case (a) basis: Hsr = y ( J - L - S) \u2022 S = y[S2Z - S 2 +^(J+S_ + J_S +)], [2.148] where terms involving the x and y components of L have been neglected in the expression after the second equals sign. Thus <A;SE ;JQ|#- s r |A ;SE ;J f i> = y [E 2 -S (S+ l ) ] [2.149a] Chapter 2 Theoretical Background 44 and < A ; S \u00a3 ; J Q | # s r | A ; S E \u00b1 1 ; JO+l ) = ^yV \u00b1(J,\u00a32)V \u00b1(S,S). [2.149b] The spin-spin Hamiltonian The spin-spin Hamiltonian of Eq. [2.99] has only diagonal elements when evaluated in a Hund's case (a) basis, and is only required for states of at least triplet multiplicity: < A ; S E ; J Q | ^ S S | A ; S E ; JQ> = \u00a7 X [3Z 2 - S(S+1YJ. [2.150] The magnetic hyperfine Hamiltonian The magnetic hyperfine Hamiltonian, Eq. [2.107], can be written in spherical tensor form: *mag.hf = a H O D \u2022 T l (L) + b Tl(I)\u2022 Tl(S) + cTj(I)T 0(S). [2.151] This formalism provides the simplest means of evaluating the matrix elements of ^niag.hf- The derivations are somewhat lengthy; only those for the second term are presented here. The operator TL(T) \u2022 TL(S) is a scalar product of two commuting first rank tensor operators; therefore, its matrix elements follow from Eq. [2.64]: < A ; SE ; JOTE | T^I) \u2022 T^S) | A ; SE' ; J'QTF > \u2022 ( - t ^ J ^ A ^ ^ I I T ^ A ^ m X ! , , ^ , , ! ! ) . [ 2 , 5 2 , Reduced matrix elements for T^I) and T*(S) appear in this equation. The former is given by Eq. [2.58]. The latter requires projection of T^S) from space- to molecule-fixed axes; from Eq. [2.68] (the p subscript is suppressed since only the reduced element of T^S) is needed): Tl(S)=X\u00a9 ( q 1 ) *(\u00bb)T q 1 (S). [2.153] q Therefore < A ; S E ; JO || T :(S) || A ; SE*; J'O') = \u00a3 < S E | T<J(S) | SZ'XJn || \u00a9 . ^ \" ( ( D ) II J'Q'> . [2.154] q The Wigner-Eckart Theorem and Eq. [2.67] are needed to evaluate the two matrix elements. The final result reads: Chapter 2 Theoretical Background ( A ; SE ; J O J F I ^ O Q - T ^ I A ; SE' ; J'QTF) 45 (_l)J'+J+I+F-n ^ s (S + 1)(2S +1) 1(1 + 1)(2I + 1)(2J + 1)(2J' +1) f S 1 S'N F J i (-i) s-s E q E' [2.155] - Q q OJ The evaluation of the matrix elements for the other two terms in Eq. [2.151] follows similar methods. The symmetry properties of the 3- and 6-j symbols determine the selection rules on J, Q. and E for the three terms; only four non-vanishing elements exist for -T^iag.hf <A ; SE ; JQTF | XmagM | A ; SE ; JDJF) _ hQR(J) and 2J(J + 1) ' <A ; S E ; JOJF | ^ m a g M \\ A ; S E ; J - l , O I F ) = hVj 2 -Q 2 P(J)Q(J) 2 j V 4 J 2 - l < T i A ; S E ; J Q I F | ^ m a g h f | nA ; SE + 1; JQ + 1,IF> _ bR(J)V \u00b1(J,Q)V \u00b1(S,Z) 4J(J + 1) < A ; S E ; J Q I F | ^ m a g h f | A ; SE \u00b1 1 ; J -1 ,Q\u00b11,IF> _ _ bV(j+n)(j+n-i)p(j)Q(j)v\u00b1(s,\u00a3) 4 j V 4 J 2 - l [2.156a] [2.156b] [2.156c] [2.156d] In Eq. [2.156], h, sometimes called the Frosch and Foley parameter (not to be confused with Planck's constant), is a linear combination of the hyperfine parameters in Eq. [2.151]: h = a A + (b + c)E, [2.157] and the functions P, Q and R are given by [2.158a] [2.158b] [2.158c] P(J) = V(J-I + F)(F + J + I + 1): Q(J) = V(J + I - F X F - J + I + 1), and R(J) = F(F+1)-1(1+1)-J(J+1). The electric quadrupole hyperfine Hamiltonian The evaluation of the matrix elements of the quadrupole Hamiltonian in Eq. [2.112] Chapter 2 Theoretical Background 4 6 follows from Eq. [ 2 . 6 4 ] by taking = J, j 2 = I and J = F: < A ; S E ; J O T F | ^ Q | A';S\u00a3;J'fl 'IF> = ( _ 1 ) J + I + F J F ^' j|<A;jn||-T2(yE)||A';J'n'>ai|T2(Q)||I). [ 2 . 1 5 9 ] The field gradient tensor must be projected into molecule-fixed axes using Eq. [ 2 . 6 8 ] : T2(VE) = X < D ( q 2 ) V ) T q 2 ( V E ) ; [ 2 . 1 6 0 ] q the dot subscript is used since the value of p need not be specified for the reduced element in Eq. [ 2 . 1 5 9 ] , which is now < A ; j n | | - T 2 ( V E ) | | A ^ m > = \u00a3 < ^ q K-i\/^VaJ+^r+i) q J' 2 J - f l ' q Q <A' | | -T a 2 (VE) | |A>. [ 2 . 1 6 1 ] Eq. [ 2 . 6 7 ] has been used in the second step for the evaluation of the reduced Wigner rotation matrix elements. In this thesis, only states with A = 0 , i.e., E states, had observable quadrupolar hyperfine structure, for which the only non-vanishing field gradient matrix element has q = 0 . Thus from Eq. [ 2 . 1 1 5 ] , and the relation TQ (VE)=^(VE) Z : <A;Jfl| | - T 2 ( V E ) | | A ; J'Q> = lq0(-l)J'-QV(2J + l)(2J'+l) J' 2 J fl 0 fl [ 2 . 1 6 2 ] The evaluation of (I ||T ( Q ) | | I) requires the Wigner-Eckart Theorem, which can be applied to the M T = I component of the unreduced element, whose value is taken from Eq. [ 2 . 1 1 4 ] : e Q = < L M T = I | 2 T 0 2 ( Q ) | I , M T = I> = 2 I 2 I - I 0 I <I||T2(Q)||I>. [ 2 . 1 6 3 ] Thus, <I||TZ(Q)||I> = i e Q I 2 I [ 2 . 1 6 4 ] and the conversion to spherical tensor components again introduces a factor of y . Eqs. [ 2 . 1 6 0 ] - [ 2 . 1 6 4 ] , taken together, give the quadrupole matrix elements as ( A ; S E ; J Q I F | # Q | A ; S E ; J 'O IF> = \\ e Q q 0 ( - 1 ) J + J ' + I + F _ Q V ( 2 J + 1 ) (2J '+1) fF y i]f r 2 J Y I 2 r- 1 2 I J \u2022 n o n - i o i [ 2 . 1 6 5 ] Chapter 2 Theoretical Background 47 This matrix element has selection rules | A J | = 0, 1 and 2; written explicitly: < A ; S Z ; J O J F | # Q | A ; S S ; J O J F > = e Q q 0 [ 3 n 2 - J ( J + l)]{3R(J)[R(J) + l ] - 4 J ( J + l)I(I + l)} 81(21 -1) J (J +1)(2 J -1)(2 J + 3) <A;SS; jn iF |^Q |A;SE;J - l ,OJF> [2.166b] [2.166c] = 3QeQq 0 [R(J)+J + l ]Vj 2 -Q 2 P(J)Q(J) 8 J (J -1) (J +1) I (21 - 1)V4J2 -1 and <A;S\u00a3 ; JQIF |#Q |A;SS;J-2 ,OIF> _ 3 eQqp yj [ J 2 - Q 2 ] [ ( J - 1 ) 2 -\"a 2] P(J) Q (J)P(J -1) Q (J -1) 161 (21 -1) J (J -1) (2 J -1) V(2 J - 3)(2 J +1) where P(J), Q(J) and R(J) are given by Eq. [2.158]. 2.6(b)(ii) Hamiltonian matrix elements of a 2 \u00a3 state evaluated in a Hund's case (bps) basis Problems associated with eigenvalue sorting occasionally necessitated evaluation of the Hamiltonian matrix elements in an alternative basis set. For example, the close conformity of the 2 Z + ground state of LaNH to Hund's case (bp\u00a7) required use of this basis set; the resulting matrix elements are now presented, for which the following coupling has been taken: G = I + S ; F = N + G. [2.167] For a 2 S state, several terms can be omitted from the Hamiltonian. The spin-spin interaction term only applies for states of at least triplet multiplicity; the coupling terms for the electron spin-orbit and nuclear spin-electron orbit interactions vanish since A = 0. For the same reason, N can be used in place of R. The following Hamiltonian remains: X = B N 2 - D N 4 + y H ( N ) \u2022 T!(S) + b F T^I) \u2022 T^S) + i c { 3 T \u201e ( I ) T u ( S ) - T 1 ( I ) \u2022 Ti(S)} - T 2 ( V E ) - T 2 ( Q ) . [2.168] The rotational Hamiltonian The rotation and distortion terms are diagonal in all quantum numbers: < N ( I S ) G F | B N 2 - D N 4 |N(IS)GF> = BN(N+1)-D[N(N+1)] 2 . [2.169] Chapter 2 Theoretical Background 48 Determination of the remaining matrix elements requires the spherical tensor formalism. The spin-rotation Hamiltonian The spin-rotation Hamiltonian y T ^ N ) \u2022 T^S) is the scalar product of two commuting first rank tensors in the coupled basis N + G = F. Eq. [2.64] applies: {F G' N ' l : \\ 1 N GJ x<N'||T 1(N)||N><(IS)G ,F||T 1(S)||(IS)GF> [2.170] The first reduced matrix element, for T^N) , is given by Eq. [2.58]. The second one involves an operator acting on the second half of a coupled basis, so from Eq. [2.65b]: <(IS)G'F||T 1(S)||(IS)GF> K S || T^S) || S> S G' II = (_i)I+S+G'+l ^ S(s + !)(2S + 1)(2G + 1)(2G'+1) | Q g ^ [2.171] where Eq. [2.58] has been used once again. Combining Eqs. [2.170] and [2.171]: < N 1 (IS) G F | y T 1 (N) \u2022 T 1 (S) | N(IS) G F > x ^ N ( N + 1)(2N +1) S (S + 1)(2S + 1)(2G + 1)(2G'+1) . [2.172] The magnetic and electric quadrupole hyperfine Hamiltonian The evaluation of the hyperfine matrix elements is similar to that of the spin-rotation Hamiltonian; only the results are shown here. The Fermi contact term, like the rotational term, is diagonal in all quantum numbers: < N 1 (IS) GF | b F Tl(I) \u2022 TL(S)\\N(IS) GF> = b F (-1 )I+S+G^(T + i)(2I +1)S(S + 1)(2S +1) | ^ ^ g | . [2.173] The dipolar term is much more complicated, with off-diagonal elements in both N and G: Chapter 2 Theoretical Background < N ' ( I S ) G ' F | \\c{3T<J(I)TQ1 ( S ) -T l(l) \u2022 T ^ S ) } | N ( I S ) G F > Vjo c ( _ 1 ) N + N ' + G ' + F ^ \/ l ( l + i)(2I + 1)S(S + 1)(2S +1) ' N ' 2 N x ^ \/(2N + 1)(2N'+1)(2G + 1)(2G'+1) [F G' N ' 2 N G v o 0 o y I I 1 S S 1 G' G 2 Finally, the electric quadrupole term is < ISP (IS)G' F | T 2 ( V E ) \u2022 T 2 (Q) | N(IS) GF> = l e Q q 0 ( - l ) ' N ' 2 N 0 0 0 N+N'+I+S+G+G'+F I 2 I - I 0 I V ( 2 N + 1)(2N'+1)(2G + 1)(2G'+1) F G* N ' H l G Si 2 N G l l G * I 2 |\" The exact algebraic forms of these matrix elements will be tabulated in Chapter 5. 49 [2.174] [2.175] 2.7 Symmetry, Parity and A-type Doubling 2.7(a) Symmetry Properties of Linear Molecules and e\/f Parity Labels The molecules investigated in this thesis are either linear triatomics of the form A B C , or simply diatomic. Both types belong to the C ^ point group since they have C ^ rotational symmetry about the molecular axis, as well as an infinite number of o v reflexion symmetry planes containing the molecule. The effect of this operator on the total molecular wavefunction or portions thereof leads to various symmetries by which the wavefunction can be classified. If the molecular plane is taken to be xz, then the effect of the reflexion operator, ov(xz) on the molecule- and space-fixed coordinates of the various electrons and nuclei can be written as follows (16): o v(xz) (X j, yh Z j ) = (x i ; - y i ; z4), [2.176a] and a v (xz)(Xi, Y i , Z i ) = ( - X i , - Y i , - Z i ) . [2.176b] The molecule-fixed ov(xz) operator and the space-fixed inversion operator, E*, have the same effect on space-fixed coordinates: Chapter 2 Theoretical Background 50 E * ( X i 3 Y i ; Zj) = (-Xj, - Y i ; -Zi) . [2.176c] Lefebvre-Brion and Field (25) and Larsson (39) have examined the effects of these operators on the | T | A ) , |SS) and | J Q > functions that comprise the Hund's case (a) basis functions: E * | J Q > = ( - 1 ) J - ^ | J - Q > , [2.177a] E * | S \u00a3 > = (-1)S-2|S-Z>, [2.177b] ov(xz)|SZ> = ( - l ^ i s - S ) [2.177c] and c v(xz)|nA> = ( -1) A + S | n - A > , [2.177d] where s = 1 for Ir states and vanishes otherwise. While none of the functions in Eq. [2.177] are eigenfunctions of the operators acting on them, it is clear that the eigenvalues of both operators must be \u00b11 since two applications of each one must yield the original function. Two linearly independent eigenfunctions can be constructed for each operator by taking a linear combination of the relevant basis function in Eq. [2.177] and another one identical except with the signs of its projection quantum numbers reversed; this is often called a Wang transformation. The normalised eigenfunctions for E * are | V | \/ ^ T I | A | ; S | I | ; J | Q | > = ^ { | q A ; S Z ; J T 2 > \u00b1 | n - A ; S - 2 ; J - Q > } , [2.178a] so that E * | V | \/ \u00b1 ; T 1 | A | ; S | S | ; J | 0 | > = \u00b1 ( - l )J -S+s | v \u00b1 ; T i |A | ;S |Z | ;J |n |> , [2.178b] with s defined as in Eq. [2.177]. Similarly, a Wang transformation of the electron orbital portion |qA) yields the following eigenfunctions of ov(xz): | y ; ; r , | A | > = ^ { J n A ) \u00b1 | n - A > } . [2.179a] From this definition of |\\|\/* ,r\\ | A | ) : o v (xz) |yt ;r) | A | > = \u00b1(- l )A + s | V \u00b1 ;r, | A | > [2.179b] The ly* ; T J | A | ; S | Z | ; J | Q | ) eigenfiinction of E* given by Eq. [2.178a] has a definite rotational parity eigenvalue of \u00b1 ( - l ) J - S + s that alternates with J for a given set of |A|, |E| and \\Q\\ values. A more convenient notation, originally proposed by Kopp and Hougen (40) and Brown Chapter 2 Theoretical Background 51 et al. (41), denotes a J level of rotational parity ( -1 ) J _ \u00b0 or - ( - 1 ) J _ \u00b0 with an e or \/ parity label respectively, where a = or 0 for states of even or odd spin multiplicity. When |Q| or |A| are nonzero, the rotational levels are doubly degenerate in the absence of interactions with other electronic states; the degenerate pairs consist of an e parity and an \/ parity level. For \u00a3 (A = 0) electronic states, the rotational levels of a given electron spin component all have the same elf parity, which depends in a complicated way on the spin and Kronig symmetry of the state. To be exact, e and \/ are merely labels rather than true parities, and the AJ = \u00b11 matrix elements of the hyperfine operators connect e levels with\/levels. The invariance of the Hamiltonian under all symmetry operations requires conservation of elf parity for all interactions between two electronic states for which J is a good quantum number. In particular, interactions between the nondegenerate J levels of a \u00a3 state and the degenerate J levels of a n state can perturb only those n levels with the same elf parity as the corresponding \u00a3 levels. This degeneracy lifting, known as A-type doubling, occurs in degenerate states (FL, A, etc.); it is discussed in Section 2.7(b). Both | r | A ; S \u00a3 ; J Q ) and ly* ; r | |A | ;S |\u00a3 | ; J |Q | ) are considered Hund's case (a) basis functions; they are distinguished respectively as signed basis functions (since A, \u00a3 and D. all carry signs) and e\/f parity or simply parity basis functions, for which only the absolute values of A, \u00a3 and Q. are significant. 2.7(b) A-type Doubling in Degenerate Electronic States Within the limit of the BOA, electronic states with A ^ 0 are orbitally degenerate, although strictly speaking, the interaction of molecular rotation and electronic motion removes this degeneracy. This effect, which introduces a splitting between energy levels differing only in elf parity, is known as A-type doubling or simply A-doubling; it originates from interactions of the |+A> and | - A ) components of the state with a comparatively distant \u00a3 (nondegenerate) state or states via the following Hamiltonian: Chapter 2 Theoretical Background 52 # i d = -2B J-L+Zailj-Sj, [2.180] i Even though this interaction occurs between different electronic states, it can be expressed equivalently as a direct coupling of the two A components of the state of interest (42), and can therefore be considered a |2A|th order effect. This effective Hamiltonian and its matrix elements have been examined for n and A states (43, 44); only the former, by far the more commonly encountered type of A-doubling, is considered here. Brown and Merer (43) have proposed the following effective Hamiltonian for the A-doubling of a n state that conforms to Hund's case (a) coupling: #id = \\(P + P + q) (S+ + S 2 . ) - \\(v + 2q)(J +S + + J_S_) + | q ( J 2 + J 2 ) , [2.181] where the angular momentum operators have their usual meaning (e.g., S \u00b1 = S x \u00b1 z'Sy) and are defined in molecule-fixed axes. The A-doubling parameters o, p and q are experimentally determinable only in the combinations (o + p + q), (p + 2q) and q that appear as coefficients in Eq. [2.181]; they can be derived algebraically via second order perturbation theory applied to the matrix elements of the Jf^ in Eq. [2.180]. This approach leads to complicated expressions identical to those listed by Brown and Merer (43); they will not be presented here. The formalism of Section 2.4(b), and Eq. [2.34c] in particular, can be used to evaluate the matrix elements of the effective for a n state in a signed case (a) basis set | A = \u00b1 1 ; SS; J\u00a32), although allowance must be made for the anomalous sign of i since molecule-fixed axes are used in Eq. [2.181]. The matrix elements are all diagonal in J and S with A A = \u00b12: < T l ; S Z \u00b1 2 ; J Q | # - l d | \u00b1 1 ; S I ; J Q > = \\(o + p + q)V \u00b1 (S, 2)V\u00b1(S, 2\u00b11), [2.182a] < T 1 ; S I \u00b1 1 ; J Q + 1 | # - U | \u00b1 1 ; S Z ; J Q > = - \u00b1 ( p + 2q)V \u00b1(S, S )V T ( J ,Q) [2.182b] and <+l ;SE; JQ+2\\J{LD | \u00b1 1 ; S 2 ; J Q > = | q V+(J,Q) V+(J,Q+1), [2.182c] where V\u00b1(a,b) is given by Eq. [2.34d]. Chapter 2 Theoretical Background 53 2.7(c) Effect of A-type Doubling on Hyperfine Structure A hyperfine interaction similar to the (o + p + q) term in the A-doubling Hamiltonian is important for n electronic states. Its Hamiltonian is generally written as (26, 45, 46): #idhfs= id[exp(2z(p)LS_ + exp(-2\/(p)I+S+], [2.183] where (p is the azimuthal angle about the molecular axis, and the spin ladder operators have their usual meanings. The nonvanishing matrix elements of this operator are off-diagonal in A when evaluated in a signed case (a) basis | A ; SS; J\u00a32IF): <A\u00b12; SE + l ; JQ\u00b11,IF | 7\/\" l d h f s | A ; SE ; J\u00a3HF> _ dR(J)V \u00b1 (J ,Q)V T (S,E) 4J(J + 1) and <A\u00b12; SE + l ; J-1,Q\u00b1 1,D717f l d h f s | A ; S E ; JQU7> [2.184a] _ _ dV(J + Q)(J + 0 - l )P(J )Q(J)V \u00b1 (S ,E) [ 2 1 g 4 b ] 4jV4J 2 - l where P(J), Q(J) and R(J) are given by Eq.- [2.158]. The determinable hyperfine doubling parameter d has a microscopic form similar to those of the other magnetic hyperfine parameters, a, b and c: d _ 3 g e g n p B p N \/ s i n 2 9 \\ [2 185] 2 h2 \\ r 3 \/ ' The selection rules for the A-doubling of the hyperfine structure are not exactly the same as for those of the A-doubling of the rotational structure, so that the two effects are not completely analogous; for example, only the latter appears for lU states. In fact, hyperfine A-doubling is important only for the Q = 1\/2 components of even-multiplicity n states, since these are the only states for which the Wang-transformed matrix elements of 7\/Jd nf s appear on the main diagonal of the Hamiltonian matrix when written in the elf parity case (a) basis. 2.8 Selection Rules and Intensities For the purposes of this thesis, a molecular spectrum can be loosely defined as a Chapter 2 Theoretical Background 54 collection of radiative transitions, or spectral lines (either absorptions or emissions of photons), between the eigenstates of the molecule; these spectral lines occur at discrete frequencies where E' and E\" are the energies of respectively the upper and lower eigenstates connected by the transition, and all quantities are in c m - 1 units. The discussion so far has addressed only the determination of the energy eigenstates producing the spectrum. This section considers the theory that governs (a) whether a radiative transition can occur between two energy eigenstates (i.e., the selection rules), and (b) if so, its relative intensity. Two factors determine the relative intensity of a spectral line. One of these is the population of each level between which the transition occurs. The high-resolution data collected in the present work are- essentially absorption spectra of highly cooled molecules for which the upper level population is zero; only the lower state population need be considered here. The molecules were prepared at thermal equilibrium, so the Boltzmann population distribution Nj applies: where gj and Ej are respectively the degeneracy and energy of the jth eigenstate, k is the Boltzmann constant and T is the temperature of the molecules associated with a specific degree of freedom. The apparatus described in Section 3.2 was designed to cool all degrees of freedom in the prepared molecules; usually, only the lowest 20 or so rotational levels of the ground state zero-point vibrational level were appreciably populated. Data from excited low-lying vibrational levels and electronic states were also occasionally obtained; this is discussed in the later chapters. The other factor governing the relative intensity of a spectral line is the matrix element of the interaction operator that mediates the transition. For this thesis, the only such operator O of concern is the interaction of the electric field E of the radiation with the electric dipole v = F - E\", [2.186] Nj oc g j exp[ -Ej \/ kT ], [2.187] Chapter 2 Theoretical Background 55 moment of the molecule: O = - M . E = -Tl( | i)-Tl(E) = - S H ^ T ^ - T i p C E ) . [2.188] P The matrix elements of this interaction must be evaluated between the two states of interest. If both states follow Hund's case (ap) coupling, they can be written in the following form: <TV;miFMF' l 0 | r|; JOIFM F> = - \u00a3 ( - i ) P T l p ( E ) <T|'; J 'Q'IF'Mp'l T^p) | r,; JDJFMF>, [2.189] P where |r|) = | u ; A S \u00a3 ) represents the vibrational and electronic parts of the total wavefunction. Neither of the states need necessarily follow Hund's case (ap) coupling, since the eigenvectors of the Hamiltonian for each state can always be expanded as a sum of such basis functions. The Wigner-Eckart Theorem can be applied to the dipole moment matrix element to remove its M F dependence: < r | ' ; m i F M y i Tpfji) | rj; JQIFM F> = ( _ 1 ) F ' - M F { F 1 F 1<TI';PO'IPIITV) II TI; jmF>. [2.190] ^ - M F p M F J The 3-j symbol yields the selection rule AF = 0, \u00b11, but can otherwise be ignored; its M F dependence is irrelevant since no external fields were used in this thesis. Only the reduced element of the dipole moment, hereafter called (Tl(\\i)), is of concern. TA(u) must be projected back into the molecular frame with the Wigner rotation matrix: Tl(u) = X C ^ T l f u ) = S S \u00a9 . ^ h \" ; J\"fi\"IF'><ri\";rn\"IF\u00bb| T ^ u ) , [2.191] q q \" where the double primed terms comprise the identity operator. The (D.^ operator is diagonal in r|, since it only operates on the | JO> part of the wavefunction; conversely, T q(p) operates only on | ri) and is diagonal in the remaining parameters. Thus <Tl(u)> = X<miF|| \u00a9 ( Q 1 }* || JOJFXTYU TjOi) |h>, [2.192] q where ( T I ' I I Tq(n) ||rj) is called the transition moment, hereafter referred to as Rq. Chapter 2 Theoretical Background 56 Since (D.^* acts on only the first part of the J + I = F coupled basis, its matrix element can be simplified using Eq. [2.65a], and the resulting reduced element is given by Eq. [2.67]: <j,n,iF,ll\u00a9.(q1)*l|jaiF> = ^ly+I+F+l >\/(2F + 1)(2F'+1) j ^ ' j j j a ' Q I I ^ I I J Q ) = (-l)2J'+I+F-0'+l ^ (2F + 1)(2F'+1)(2J + 1)(2J'+1) Jr F \\\\f r I r X [ F J q CI\/ The spectral line strength S(J'fiTF'; JQTF) is proportional to K T 1 ^ ) ) ! 2 : S(J'QTF'; JQ.W) oc (2J+1)(2J'+1)(2F+1)(2F*+1) 1 [2.193] | J ' F ' II f T I F J I Rr [2.194] - O' q O y This expression must be weighted by the Boltzmann distribution from Eq. [2.187] to describe the intensity of an observed spectrum. The selection rules for J, Q. and F can be read immediately from Eq. [2.194] using symmetry properties of 3- and 6-j symbols: AJ = J ' - J = 0, \u00b11, [2.195a] AQ = n'-Q = 0 ,\u00b1 l , [2.195b] and AF = F ' - F = 0 ,\u00b11 ; [2.195c] the last of these was already obtained from Eq. [2.190]. Selection rules for the remaining good quantum numbers require consideration of the transition moment Rq. The wavefunction |r|> can be factored by the B O A into electronic and vibrational terms, of which the dipole moment operator acts on only the former: Rq= <ir||TjG0||Ti> = <e'|Tj(u)|e> <u'|u>, [2.196] where (e'| Tq(u)|e) is called the electronic transition moment and (v'\\v) is the well-known Franck-Condon overlap integral (47). The only restriction on Ao = v'-v is that the resulting (U'|D) be nonvanishing. Herzberg Chapter 2 Theoretical Background 57 (14) describes sufficient conditions for this situation in diatomic molecules in terms of the change in bond length, Ar e , between the states of the transition. If an electronic band system has very small Ar e , then Au = 0 bands are by far the most intense. A band system with moderate Ar e distributes its transition moment among bands of various Au with an intensity maximum at some Au * 0. Finally, a system with very large A r e distributes its transition moment among bands over an even larger range of An, with no sharp intensity maximum. For polyatomic molecules, similar arguments relate the various geometrical parameter changes to the Arjj at which the most intense bands appear (48). Selection rules for <e'|Tq(u.) |e) are derived with group theory arguments similar to those applied in Section 2.2(b)(i) to the Renner-Teller effect. The aforementioned dipole moment operator, defined in the molecule-fixed system, acts upon only the orbital part of the electronic wavefunction and has \u00a3 + or Tl symmetry in CooV. Selection rules for S, \u00a3 and A follow immediately: AS = S ' - S = 0, [2.197a] AX = r - 2 = 0, [2.197b] and AA = A' - A = 0, \u00b11. [2.197c] A A = 0 transitions are said to be parallel, those with A A = \u00b11, perpendicular. Selection rules for the rotational parity can also be considered. The space-fixed dipole moment operator transforms as Ir (or TL) in linear molecules, so only levels of opposite rotational parity combine; this is expressed symbolically as + <\u2014>_ ) + <-A-+ ,_<- \/ - \u2022_ . [2.198] In terms of elf parity, these rules become (41) e <\u2014\u2022 e and f<\u2014> f for AJ = \u00b11 [2.199a] and e<\u2014>\/forAJ = 0. [2.199b] Chapter 2 Theoretical Background 58 2.9 Fitting of Data and the Hellmann-Feynman Theorem 2.9(a) Method of Combination Differences In fitting the spectral data to determine molecular constants, either one of two avenues can be pursued. One involves the direct fitting of observed spectral line measurements. For the present work, this method is not favoured because in most cases the upper states of the observed bands are too strongly perturbed to model by a simple Hamiltonian matrix, even though one ordinarily exists for the lower (usually ground) state. An alternative method, the use of combination differences, overcomes this difficulty. Two spectral lines with different lower levels of energies E a \" and E b \" from the same electronic state, but the same upper level with energy E c ' , have measurements v c a = E c ' - E a \" [2.200a] and v c b = E c * - E b \" . [2.200b] The combination difference A v a b = v c b - v c a = E a \" - E b \" [2.200c] between these line measurements depends only on the lower state (in principle, combination differences can also be formed for the upper state). A fit of only lower state combination differences overcomes the perturbative difficulties described above. Redundancies are also easily removed; all bands with the same lower state have the same set of combination differences, so duplicate measurements can be averaged before fitting. This lower (ground) state combination difference technique was the first step in the rotational analysis of most of the molecules in the present work. 2.9(b) Non-linear Iterative Least Squares Fitting via the Hellmann-Feynman Theorem If matrix diagonalisation is needed to determine the energy levels of a molecule, the least squares optimisation of the fitting parameters becomes non-linear. In this case, the calculation of the derivatives dE^\/dX^ is best performed using the Hellmann-Feynman Chapter 2 Theoretical Background 59 Theorem (49, 50): [2.201] U T ^ U In this expression, J\u20ac is the Hamiltonian matrix expressed as a function of the molecular constants X k , Ej are its eigenvalues, U is the unitary matrix of column eigenvectors that diagonalises JT, and U is the transpose of U . This theorem is useful because the Hamiltonian matrix is usually a linear function of the molecular constants even though its eigenvalues need not be: #-=XXp#p, [2.202] P where the #\"p are the matrices of the Hamiltonian operators corresponding to the molecular constants X p . This linearity allows the following iterative scheme for the determination of the X p molecular constants (25). An initial estimate Xp0-* of the X p parameters is used to diagonalise the Hamiltonian and determine both U and the eigenvalues E , . From Eq. [2.201], SEj \/ 5 X p is now completely specified since the Hamiltonian derivatives on the right are simply #\"p, from Eq. [2.202]. The residuals AE, are simply the difference between E \u00b0 b s , the energies observed from the data, and the calculated E j . The X ^ estimates can be improved by adding the approximate correction A X p given by AEi = Z D i p A X p , [2.203a] P where D i p = a E j \/ d X p [2.203b] are the known eigenvalue derivatives. Eq. [2.203a] can be rewritten in matrix\/vector notation AE = D A X [2.204a] and solved for A X : A X = (DTBO-iDTAE. [2.204b] Al l quantities on the right side of this equation are known since they are based on the X*-0-* Chapter 2 Theoretical Background 60 estimates of the molecular constants. The correction A X thus found is added to X*-0-* for new estimates of X , and the process of determining A X is repeated until the root-mean-square (rms) of AE converges to a minimum value and successive estimates of X are essentially identical. In practice, this convergence is very rapid; usually no more than two or three iterations are required if the parameters to which the data are most sensitive are reasonably estimated. The standard deviation (AE) T (AE) [ 2 2 Q 5 ] \\ N - m measures the fit quality, where N - m is number of degrees of freedom of the fit (number of data points minus number of fitted parameters). An acceptable fit has o approximately equal to the measurement uncertainty of the input data. The uncertainties in the fitted parameters are the square roots of the diagonal matrix elements of the variance-covariance matrix 0 : 0 = a2(DTT))-1. [2.206] The correlation matrix 0 Cij= , ' J , [2.207] whose elements range from -1 to +1, measures the extent to which the fitted parameters depend on one another. |Cy| values approaching unity indicate strong correlation between Xj and X J ; only their sum or some other specific combination can be measured accurately from the data. A Fortran programme performed the above non-linear least squares iterative procedure, taking as input initial estimates of the various parameters and the available spectral data with their relevant quantum number assignments. To determine the eigenvalue residuals AE correctly at each iteration of the routine, great care was required to ensure quantum numbers were properly assigned to the nearly degenerate energy eigenvalues determined by each diagonalisation; as noted in Section 2.6(b), this occasionally influenced the choice of basis set (i.e., Hund's coupling case) in which the Hamiltonian matrix elements were evaluated. 61 Chapter 3 The Electronic Spectrum of Zirconium Monocarbide, ZrC, in the 16000 -19000 cm-1 Region: Analysis of Singlet and Triplet Structure1 3.1 Introduction Diatomics, the simplest molecules, have interested spectroscopists since the dawn of quantum mechanics in the 1920s. While the last 75 or so years have seen the identification and systematic study of a large number of such molecules, initial data for many species, particularly those containing transition metals (TMs), have only appeared in the last twenty years or so. Among the reasons for this is the sheer complexity of their spectra. Their abundant unpaired d electrons cause not only their familiar catalytic behaviour, but also a high density of electronic states with large electron spin and orbital angular momenta, even for diatomics. Transitions between such states are often complicated, with many branches in each vibrational band. Some TMs have several isotopes, often with nonzero nuclear spins, further complicating their spectra with isotopic and hyperfine structure. Historically, the highly refractory nature of TMs and their compounds required high temperature sources (such as a King furnace) to prepare them in gaseous form. Under such conditions, the lowest rotational levels, which carry information about the symmetries of the states, are scarcely populated, yielding spectra dominated by mostly redundant lines of high rotational quantum number. Analysis was therefore slow and laborious. Advances in the last twenty years have simplified matters. The development of laser ablation and supersonic jet expansion methods have allowed preparation of sample molecules usually just in their electronic ground states, and at low rotational temperatures. State lA portion of this chapter has been refereed and accepted for publication: Rixon, S. J., Chowdhury, P. K . and Merer, A . J. (2004). \"Nuclear Hyperfine Structure in the X 3 S + State of 9 1 Z r C \" , Journal of Molecular Spectroscopy (in press). Chapter 3 Visible Spectrum of ZrC 62 assignments in these much simpler, colder spectra are relatively straightforward. The concurrent availability of high-resolution tuneable lasers has made recording of electronic spectra with resolved isotope and hyperfine structure virtually routine. Finally, modern computers have automated the data acquisition process, and permit calculation of complicated energy level patterns by numerical diagonalisation of the relevant Hamiltonian matrices. The rest of this chapter presents the analysis of the electronic spectrum of zirconium monocarbide, ZrC. Section 3.2 describes the apparatus and procedures used to acquire the spectra. This section also applies to similar studies of ZrCH and LaNH presented respectively in Chapters 4 and 5; only major differences in technique are discussed therein. The first part of Section 3.3 provides motivation for the study of ZrC and reviews some relevant literature; three further subsections give an overview of the ZrC spectrum and details of the low-lying and higher electronic states. Conclusions are given in Section 3.4. 3.2 Experimental Apparatus and Techniques 3.2(a) Overview The main component of the apparatus is a diffusion pumped vacuum chamber, in which a free jet expansion containing ZrC is prepared by reaction of laser-ablated zirconium atoms with a small amount of methane diluted in helium. A tuneable laser excites the ZrC molecules; the resulting laser induced fluorescence (LIF) is digitally recorded on a PC. Fig. 3.1 shows a schematic diagram of the apparatus. The remainder of the section gives details. 3.2(b) Preparation of ZrC in a Free Jet Expansion 3.2(b)(i) The vacuum chamber The free jet expansion occurs in a stainless steel vacuum chamber about 40 cm (length) x 40 cm (width) x 30 cm (height) in size. A rotary pump (Edwards, model E2M40) and a Roots blower (Edwards, model EH500A) provide backing for a water-cooled diffusion pump Chapter 3 Visible Spectrum of ZrC 63 delay generator 3.2(d) Tuneable bandpass (33 A or less) Vacuum Chamber 3.2(b)(1) 355 nm N d : Y A G 3.2(b)(ii) 50 psi gas line| 3.2(b)(iii) low-resolution probe laser < Av = 0.1 c m - 1 355\/532 nm Pulsed laser 3.2(Q(i) N d : Y A G 3.2(c)(1) high-resolution A probe laser 308 nm XeCl 4.2 A relative calibration P D A 4.2 A 750 M H z etalon 3.2(f) A Av = 500 kHz 514.5 nm cw dye laser 3.2(c)(ii) A r + laser 3.2(c)(ii) Figure 3.1 Schematic diagram of experimental apparatus. The number given with each component identifies the section of text where it is described. Chapter 3 Visible Spectrum of ZrC 64 (Balzers, model DIF 320) mounted underneath the chamber. A pneumatic valve (Parker Hannifin Corp., Skinner Electric Valve Div., model TJ4S) opens and closes the diffusion pump to the chamber; the chamber pressure is about 2X10 - 6 torr at stagnation and about one to two orders of magnitude higher during free jet expansion. Several windows allow laser beams and fluorescence signals to enter and exit the chamber. A quartz window on one side of the chamber admits the U V ablation laser beam. The probe lasers, described in Section 3.2(c), enter through another window mounted at Brewster's angle (to minimise reflexion losses) near the ablation window; an identical exit window on the other side of the chamber assists in their alignment. The LIF signal is collected through a window on the top of the chamber. An additional large window (20 cm diameter) facing the free jet expansion allows viewing inside the chamber while it is under vacuum. 3.2(b)(ii) The ablation laser ZrC molecules were prepared by the reaction of gaseous zirconium atoms and methane in an environment of helium. The metal atoms are ablated from the surface of a Zr rod (Goodfellow, 5 mm diameter x 100 mm length, 99.8% purity) by pulses of 355 nm radiation from a N d : Y A G laser (Lumonics, model HY400) operating at 15 Hz. Second harmonic generation via a KD*P (potassium dideuterium phosphate) crystal partially converts its 1064 nm fundamental to 532 nm. A C D * A (caesium dideuterium arsenate) crystal combines these two beams via sum-frequency generation to produce a frequency-tripled 355 nm beam, which is tightly focussed by a 50 cm focal length quartz lens onto the rod surface. The ablation process requires a minimum threshold of laser power, but since higher powers contribute considerable noise to the ZrC LIF signal, the ablation power was kept just above threshold. 3.2(b)(iii) The gas handling system The helium\/methane gas mixture flowed into the chamber through a 0.5 mm pulsed nozzle (General Valve Corporation, series 9). A custom-built power supply allows user control Chapter 3 Visible Spectrum of ZrC 65 over the duty cycle (about 0.2%). Soot, presumably from backflow of Z r \/ C H 4 reaction products, accumulates inside the nozzle after a few days of operation and degrades the ZrC signal; this necessitates periodic cleaning. Gas mixtures were prepared in a stainless steel cylindrical \"bomb\", 30 cm long x 10 cm diameter, connected to the nozzle via P V C tubing. Typically, the bomb was filled to 250 psi; a regulator placed beyond it maintained the nozzle at a constant pressure (usually 50 psi). The bomb was connected in parallel with the same rotary pump and Roots blower that backs the diffusion pump, allowing ready evacuation as needed; the pneumatic valve was closed at these times to prevent backflow into the reaction chamber through the parallel link. Closing a manually operated valve located between the diffusion pump and the backing pumps also helped to counter this problem. The ZrC signal was essentially constant for methane concentrations in helium in the range 1-8% (by pressure); however, to quench production of ZrCH (see Chapter 4), ZrC experiments normally used a 1% methane concentration. Some spectra were also taken with C D 4 and 1 3 CH4, in order to confirm the carriers and vibrational assignments of certain bands. 3.2(b)(iv) The \"Smalley\" expansion source In a \"Smalley source\" a gas expands adiabatically from a pressure of several atmospheres to the vacuum of the apparatus. The rotational and vibrational kinetic energy of the molecules converts almost entirely to translational energy, and they emerge as a narrow cone-shaped gas flow, with very low rotational temperature. Collisions between molecules no longer occur, effectively stabilising reactive species such as ZrC. In the present experiments a probe laser beam crosses the expansion about 5 cm downstream from the nozzle, and the resulting fluorescence is collected, again at right angles, from the centre of the cone. Fig. 3.2 shows the Smalley source used in the experiments. The pulsed gas nozzle is attached to a baseplate; gas from the nozzle enters at point C (Fig. 3.2(b)). The gas then flows Chapter 3 Visible Spectrum of ZrC 66 (a) (b) D 1 7 mm A (J c 7 cm 2 cm Figure 3.2 Top face (a) and side (b) views of the \"Smalley\" source located inside the vacuum chamber. The Nd: Y A G laser enters through aperture A and ablates the rotating Zr rod placed in aperture B . The resulting gas phase metal atoms react with a methane\/helium gas mixture admitted through aperture C; ZrC molecules enter the chamber via aperture D. Dimensions shown are approximate. Chapter 3 Visible Spectrum of ZrC 67 through a small channel and over the Zr rod, which is mounted vertically in hole B , at the point where the ablation laser beam strikes it, having come in through the 1 mm diameter hole A. The ablation beam, the gas flow and the rod axis are mutually perpendicular. The metal atoms and methane react as the mixture flows toward point D, from which it expands into the vacuum chamber. Soot accumulation inside the source, as in the nozzle, necessitates periodic cleaning. Two factors maintain the ZrC signal steadily with time. One is a fresh rod surface. To this end, a Motor Mike (Oriel Corp., model 18040), secured to one end of the rod by a small rubber tube, effects a screwing motion of the rod. Adjustable micro-switches set the range of translation, and a custom-built power supply controls the angular speed and direction of the Motor Mike. Over time, the laser cuts a thread into the rod, which can be removed with a lathe. The other is precession-free rotation of the rod about its axis; otherwise, the focus of the ablation laser spot and the signal vary with rod rotation. To achieve this, the diameters of the rod and of the rod aperture of the Smalley source were matched as closely as possible; the rod was further secured by several turns of Teflon tape wrapped around its non-ablated portions. 3.2(c) The Two Probe Laser Systems 3.2(c)(i) The pulsed dye laser For the low- to medium-resolution wavelength-selected fluorescence (WSF) and dispersed fluorescence (DF) spectra described in Section 3.2(g), a pulsed dye laser (Lumonics, model HD500) probed the ZrC species. Two identical such lasers are available; one is pumped by the 532 nm harmonic of a N d : Y A G laser (Lumonics, FTY400) virtually identical to the ablation laser, the other by the 355 nm harmonic. The 532 and 355 nm harmonics are both vertically polarised and exit the N d : Y A G laser head from different apertures, so that switching between the two prealigned dye lasers reduces to a simple tuning of the pump laser crystals. Each pulsed dye laser has a reflexion grating (1800 or 2400 groove\/mm) and tuning mirror assembly, two dye cells (an oscillator and an amplifier), a water-cooled circulator to Chapter 3 Visible Spectrum of ZrC 68 distribute dye in series to the two cells, and a wavelength scanning control touchpad. The pump laser excites the dye in the oscillator cell and induces isotropic, broadband spontaneous emission, some of which falls on the grating at grazing incidence and is dispersed toward the tuning mirror. Fluorescence at a wavelength determined by the orientation of this mirror (as specified by the touchpad) retroreflects to the oscillator cell and initiates stimulated emission, i.e., laser radiation. Rotation of the mirror scans this wavelength. The dye laser radiation, like that of the pump laser, is vertically polarised. The amplifier cell, about 40 cm beyond the oscillator, strengthens the laser signal with further N d : Y A G pumping, although the spontaneous emission from the oscillator cell is also amplified at this stage. Typically, this amplified spontaneous emission (ASE) amounts to at least 10-15% of the total output, as determined from power measurements with the reflexion grating blocked and unblocked. A transmission grating (1016 groove\/mm) placed downstream mostly removes the A S E from its first order laser radiation output. A 386 computer is available to interface with either pulsed dye laser; commercial software from Stanford Research Systems (SRS) allows computer control of laser scanning and digital recording of spectra. Sample linewidths are limited to 0.1 c m - 1 by the oscillator output; power broadening from the amplifier stage further increases this linewidth. 3.2(c)(ii) The cw ring dye laser The strong bands of ZrC were studied at high resolution with a continuous wave (cw) tuneable ring dye laser (Coherent, model 899-21) pumped by an argon ion laser (Coherent, Innova Sabre). In the visible region, where the ZrC bands lie, the ring laser gain medium is an organic dye, but for work in the near IR a Ti: sapphire crystal is also available. In \"dye mode\", either the 488.0 nm or 514.5 nm line of the A r + laser excites fluorescence from the organic dye in a ring-shaped optical cavity. Tuning elements in the cavity select one of the cavity modes and provide frequency tuning. The concept of all these tuning elements is the same: tilting it Chapter 3 Visible Spectrum of ZrC 69 about an axis perpendicular to the optical path tunes the cavity length slightly; this in turn tunes the frequency of the selected cavity mode. The cavity modes of the ring laser are less than 300 M H z apart, but it is possible to select just one of them by the use of a three element system. A \"thick etalon\", consisting of two triangular prisms whose separation can be varied piezo-electrically, and whose free spectral range is about 10 GHz, transmits a \"comb\" of frequencies separated by 10 GHz; its finesse is high enough that only one cavity mode of the laser resonator is transmitted at each interval of 10 GHz. A \"thin etalon\" with a free spectral range of 220 GHz, in series with it, then restricts the transmission to single cavity modes separated by 220 GHz; the point is that a single etalon with such a free spectral range would need an extremely high finesse to distinguish individual cavity modes, which is difficult to attain with wide wavelength coverage. Finally a Lyot filter (a birefringent crystal quartz plate that transmits light at a wavelength governed by the tilt of the crystal axis relative to the axis of polarisation) with a transmission bandwidth of about 300 GHz, selects just one out of the \"comb\" of cavity modes separated by 220 GHz that was transmitted by the two etalons. An additional quartz plate mounted inside the cavity at Brewster's angle can be tilted to tune the cavity length very slightly and the cavity mode frequencies accordingly. Electronic adjustment of the etalon tilts maintains transmission of the changing frequency of the chosen cavity mode. The ring laser has a linewidth of about 500 kHz, but residual Doppler broadening from the cone-shaped free jet expansion limits sample linewidths to about 150 M H z (0.0050 cm - 1 ) . Since the photon flux of the ring laser is much less than that of the pulsed dye laser, only the strongest bands of ZrC were recorded with it. A pulsed dye amplifier, which increases the photon flux at the expense of a modest increase in laser linewidth, allows recording of weaker bands, but this system was not used for ZrC. It is described in Chapter 4, which reports on the study of ZrCH. Chapter 3 Visible Spectrum of ZrC 70 3.2(d) Signal Detection and Data Acquisition A spatial filter consisting of an iris placed between a pair of confocal convex lenses (each of focal length \/ = 5 cm) collects laser-induced fluorescence (LIF) from the target molecules at right angles to both the probe laser beam and the free jet expansion. Optimising the height of this filter above the centre of the free jet expansion and its iris diameter reduces the spectral linewidths from 250 to 150 MHz. Various attempts to enhance the LIF signal were made, either by reflecting the probe laser beam back through the chamber or by placing a concave mirror underneath the jet expansion to collect light travelling in the opposite direction; these gave only modest improvements at the expense of considerable trouble and were therefore abandoned. The LIF signal from the spatial filter passes through a window at the top of the chamber, is steered horizontally by a 45\u00b0 mirror and focussed onto the entrance slit of a 0.75 m monochromator (Spex, model 1702). With its 1200 groove\/mm grating, the monochromator has a first order dispersion of 1.1 nm\/mm; with fully open slits (3 mm), this corresponds to a band pass of 40 c m - 1 at 900 nm or 120 c m - 1 at 500 nm, the shortest wavelength used in the ZrC experiments. An uv-blocking optical filter (Corning 3-73) removes stray ablation laser radiation (355 nm) that would otherwise be transmitted in second order at 710 nm. The LIF signal is collected by a Hamamatsu, model R943 photomultiplier tube (PMT), housed in a Pelletier cooling unit (Products For Research, model TE104RF), and held at between 900 and 1600 V by a Keithley, model 237 power supply depending on the strength of the detected LIF signal. The current from the PMT is amplified by a custom-built unit (gain = 880) and sent to a boxcar integrator (SRS, model SR250). Typically, the signals from thirty ablation shots are averaged using a gate width of approximately 1 ps for low-resolution experiments; this is increased to 5 ps for high-resolution experiments. A digital oscilloscope (Tektronix, TDS 340A) connected in parallel with the boxcar Chapter 3 Visible Spectrum of ZrC 71 integrator displays the intensity and timing of the LIF signal relative to the integration gate. This is important for optimising the boxcar settings and for maximising the LIF signal strength. The integrated voltage is sent to a display module (SRS, model SR280) and then to a PC via a computer interface (SRS, model SR245). A digital delay generator (SRS, model DG535) controls the event timing. It delivers trigger pulses at 15 Hz to the gas nozzle, to the ablation laser and, when in use, to the pulsed probe laser. Typical delay settings for the various pulses are as follows: the reference pulse triggers the nozzle, the ablation laser is triggered 200 ps later and the pulsed probe laser is triggered 35 ps before the ablation laser. This implies that the probe laser pulse arrives in the chamber before the free jet expansion, but the timings specified by the delay generator are not absolute since they do not account for non-electronic factors such as the mechanical delay in the opening of the gas nozzle and the time taken for the gas to travel through the apparatus. 3.2(e) Description of the Experiments The scanning capabilities of the probe lasers and the monochromator allow two types of experiments described below: wavelength-selected fluorescence and dispersed fluorescence. 3.2(e)(i) Wavelength-selected fluorescence (WSF) In this thesis, the term wavelength-selected fluorescence (WSF) describes the detection of laser-induced fluorescence (LIF) at only one wavelength (chosen with the monochromator) that is offset from that of the probe laser by an amount corresponding to a known (usually vibrational) interval of molecular energy. Thus, as the probe laser scans, the monochromator also scans to maintain this offset. This detection technique has two benefits: it suppresses scattered probe laser light, and since the energy interval is unique to the carrier molecules (notwithstanding coincidental near-degeneracies), the monochromator simultaneously acts as a molecule-selective filter. This latter point is important because impurity molecules are often present in the free jet expansion and can produce their own L U signals; the WSF spectrum Chapter 3 Visible Spectrum of ZrC 72 becomes contaminated if these are not separated from the target signal. Moreover, this technique allows concurrent recording of spectra from whatever isotopomers of the target molecule are abundant in the free jet expansion, provided the isotopic variation of a characteristic energy interval is smaller than the bandpass of the monochromator (which is usually the case for the type of molecules studied in this thesis). This is useful because isotopic data can provide checks on the validity of the analysis. Clearly, WSF experiments on a new molecule of unknown vibrational frequencies are not always trivial to undertake; they must be done using an estimated frequency or with the monochromator tracking the laser frequency itself. This produces a noisy spectrum containing resonance fluorescence from all the different molecules present. If the spectra of the other likely species present are known, strong bands of a new molecule can often be recognised without much difficulty; its characteristic frequencies can then be determined by dispersed fluorescence, as described below. However, it is entirely possible to generate simultaneously new spectra from two previously uncharacterised molecules. The two molecules discussed in this chapter and the next one, ZrC and ZrCH, present a good example of this more challenging scenario (see, for example, Fig. 4.6). The monochromator wavelength can be fixed at the target LIF frequency during a high-resolution cw ring laser scans since the 1 c m - 1 maximum range covered is much less than the 40-120 c m - 1 bandpass of the monochromator (vide supra); it need only be updated at 5 to 10 c m - 1 intervals of the cw laser frequency. In pulsed laser work, however, survey WSF scans typically cover 8 nm, far exceeding the monochromator bandpass, so that the monochromator wavelength must be scanned to preserve molecule selectivity. Although the probe laser can scan linearly in wavenumber or wavelength, the monochromator scans linearly in wavelength only. Only linear wavelength scanning of both pieces of apparatus is practical. Clearly, equal scan rates for the laser wavelength, X L , and the monochromator Chapter 3 Visible Spectrum of ZrC 73 wavelength, XM, cannot maintain a constant frequency difference between them over an entire scan; exact coincidence can occur only once in this case. As an example, the detection of ZrC in the 580-588 nm range, monitoring LIF at the X 3 E + , o = 0-1 interval of 880 cm\" 1 below the laser, may be considered. Initially the monochromator is set 880 c m - 1 to the red of 580 nm, i.e., at 611.20 nm (ignoring the vacuum correction for discussion purposes). When the laser has reached 588 nm, the monochromator, scanning at the same wavelength rate, will have reached 619.20 nm, offset 856.9 c m - 1 in frequency from 588 nm. Since the v 3 vibration of ZrCH lies at 863 c m - 1 , the monochromator now detects ZrCH rather than ZrC. This effect can be reduced by scanning the monochromator so that the desired 880 c m - 1 offset occurs at the centre of the scan, but another impurity species endangers the molecule-specificity in this case. ZrO is especially troublesome in ZrC work because its extremely strong triplet manifold spectrum lies in the same wavelength region; \"hot\" bands with large v\" readily appear under jet-cooled conditions, even without an added oxygen precursor. Although the first vibrational interval, AGy2, of its low-lying a 3 A state is 932 c m - 1 (1), the intervals decrease with vibration such that the v = 3-4 interval is only 912 c m - 1 . ZrO impurity bands are often seen in spectra recorded in this fashion. A refinement is possible, however, if the laser and monochromator are scanned at slightly different rates. While the monochromator scans only at certain fixed rates, s^, the laser scan rate, sL, is arbitrary and may be chosen to produce equal frequency offsets at the beginning and end of a scan. For the above example, the maximum variation in monochromator offset is less than 1 c m - 1 . Straightforward algebra gives the required S L . If the laser scan range is X - L to XL+AA, (in nm) and the monochromator offset by Av (in cm - 1 ) , then S L and Sjyj (both in nm\/s), are related by [3.1] s L = 1 0 _ 7SM AX 10' XL + AX -1 - Av ' l O 7 Av Chapter 3 Visible Spectrum of ZrC 74 For the example chosen, if s^ = 0.02 nm\/s, SL = 0.01799 nm\/s to four significant figures. The small deviation in Av over the course of the scan, never more than 1 c m - 1 from the desired 880 c m - 1 value, allows for a much narrower slitwidth (say, 1 mm) and the removal of almost all impurity features. WSF scans so recorded take about 10% longer than normal to complete but the ability to maintain Av within a very small tolerance greatly outweighs this disadvantage. 3.2(e)(ii) Dispersed fluorescence (DF) In a dispersed fluorescence (DF) experiment, the pulsed probe laser is tuned to a known absorption wavelength A,L of the molecule, and the monochromator wavelength XM is scanned. The resulting spectrum displays LIF intensity as a function of A,M . At the outset of a DF scan, the lower state of the absorption band is generally unknown, so the start value of Xjyj is chosen to allow for LIF features that may lie up to 1000 c m - 1 to the blue of X.L. Such features may appear for a \"hot\" absorption band, i.e., one whose lower state is not the ground vibrational level, as emission to lower-lying levels. Scans typically ranged over 200 nm at 0.2 nm\/s with averaging of LIF signals from thirty ablation pulses. DF spectra represent state-selected emission spectra from the upper levels of the various absorption bands. Since the relative intensity patterns follow the Franck-Condon principle, they potentially indicate the vibrational assignments of the upper states, although these are not always easy to extract. The energy displacements of the peaks from the laser wavelength give the positions of the low-lying vibrational and electronic levels of the molecule. Obviously the narrower the monochromator slit, the narrower the DF features, so that DF spectra should be taken with the narrowest slits compatible with intensity considerations. Typically a 1 mm slit is used, though for very strong bands this can be reduced. The DF spectra cannot be easily calibrated with external wavelength standards; instead this is done approximately by linear interpolation between the start and end wavelengths of the Chapter 3 Visible Spectrum of ZrC 75 scan, using the position of the very intense Rayleigh scattering peak at X L t 0 allow for any possible offset. Accurate measurement of this peak requires care that it not saturate the PMT; the vertically polarised pulsed dye laser output is easily attenuated with a polarisation filter. While XM is within 4 nm of X L , the filter is placed in the laser beam with its transmission axis tilted sufficiently from the vertical to produce a sharp unsaturated Rayleigh peak. Occasionally in the present work, no such attenuation was required, particularly in the red region of the visible, in accord with the well-known v 4 proportionality of Rayleigh scattering intensity. The absolute error in this calibration is quite small for low-lying vibrational levels, where it can be checked from the positions of hot bands measured to cw laser accuracy, but rises with vibrational energy because it is not easy to synchronise the scanning of the monochromator to the data acquisition exactly. At 3000 c m - 1 the uncertainty is probably \u00b110 cm - 1 . Nevertheless the reproducibility of the measurements is generally better than this, with the limiting factor being the widths of the LIF features. 3.2(f) Calibration of W S F Spectra For both low- and high-resolution WSF spectra, calibration against secondary wavelength standards is provided by atomic spectra recorded optogalvanically. A low reflectivity beamsplitter directs a small portion of the probe laser beam to a uranium hollow cathode lamp filled with either argon or neon (Cathodeon, model 3UAXU). For low-resolution experiments, the U\/Ar lamp is used and generally only the Ar lines are of sufficient strength to record. A custom-built amplifier (gain = 1000) collects the optogalvanic signal from the hollow cathode lamp and delivers it to a boxcar integrator identical to the one described previously. Air wavelengths of argon with an uncertainty of about \u00b10.005 nm are taken from Norlen (2). For high-resolution experiments, either the U\/Ar or U\/Ne lamp is used, but only the uranium lines, which are much narrower than the inert gas lines, are used in the calibration Chapter 3 Visible Spectrum of ZrC 76 process. A chopper and lock-in amplifier (Princeton Applied Research, model 128, or SRS, model SR510) are required to observe the uranium lines; the reference signal is detected by a photodiode (Pomona Electronics, model 2397) from a cw diode laser. Wavenumbers of the uranium lines, quoted to nine significant figures, are available from the Fourier transform measurements of Palmer et al. (3). Further calibration is recorded by directing a small portion of the ring laser output through an I 2 cell. A PMT, powered by a voltage supply (Fluke, model 4313) of typically about 650 V , detects fluorescence. The resulting current flows to a custom-built amplifier and is digitally recorded. Since the relative accuracy of the I 2 wavenumbers listed by Gerstenkorn and Luc (4) is only \u00b10.002 cm - 1 , this spectrum is used only to help establish proper overlap of consecutive cw laser scans. The uranium lines used for calibrating high-resolution WSF spectra are typically spaced about 5 c m - 1 apart, while the molecular lines are generally far more closely spaced. To interpolate between the uranium lines, a small portion of the cw ring laser output is sent through a confocal Fabry-Perot etalon (Burleigh, model CF100) that is locked to a frequency stabilized He-Ne laser (Spectra Physics model 117A). An evacuated, temperature-controlled housing isolates the etalon from variations in laboratory pressure and temperature, allowing for very trouble-free locking of the etalon to the laser. The free spectral range of the etalon is always in the range 0.024973 \u00b1 0.000001 c m - 1 . Transmission maxima from the ring laser are detected by a photodiode (Pomona Electronics, model 2397) and recorded simultaneously with the other calibration spectra. This etalon system was developed by the Merer group in the late 1980s; a paper by Adam et al. (5) offers further details on its operation. In all, four spectra are simultaneously recorded during high-resolution WSF experiments: (a) the sample spectrum, (b) the I 2 spectrum which, together with readings from a Burleigh WA20-VIS wavemeter, ensures proper concatenation of adjacent scans, (c) the Chapter 3 Visible Spectrum of ZrC 11 optogalvanic spectrum of the U\/Ar or U\/Ne hollow cathode lamp and (d) the spectrum of interpolation markers from the etalon. Using the latter two, calibration of sample spectra proceeds in two steps. In the first step, each etalon marker is assigned a relative order number n and the measurement of each uranium line in units of n is determined. The wavenumber v of each uranium line is then fitted by least squares to a polynomial in n; a simple linear fit with the coefficient of n given by the free spectral range of the etalon usually suffices. In the second step, each spectral line is measured in units of n and its wavenumber is determined from the polynomial. In this manner, strong unblended spectral lines over some 250 c m - 1 can be measured to nine significant figures with a relative precision of about 10 MHz. Care must be taken with the line shapes of the uranium calibration lines; incorrect settings on the lock-in amplifier can lead to unsymmetrical profiles and absolute calibration shifts. 3.3 The Visible Spectrum of Zirconium Monocarbide, ZrC 3.3(a) Motivation As discussed in Chapter 1, TM-containing molecules often appear as atmospheric constituents of cooler stars containing recycled supernova material. Well-known examples include ZrO (6, 7), TiO (7, 8), V O (7,8), ZrS (7, 9) and FeH (9). The strength of ZrO and ZrS features in the spectra of cool stars makes ZrC a plausible atmospheric constituent of carbon-rich stars and thus worthy of spectroscopic study. Further motivation stems from the 1992 discovery, via mass spectrometry, of the exceptionally stable M 8 C 1 2 family of metallo-carbohedrenes, or \"metcars\", for M = Ti, Zr, V and H f (10, 11). Fig. 3.3(a) shows the cage structure originally proposed to account for their stability (10). Each equivalent M atom lies at one of eight cube vertices; the twelve C atoms lie in pairs atop each of the six cube faces. Later ab initio (12-15) and experimental (16, 17) work (a) (b) Figure 3.3 Proposed structures of the metallo-carbohedrene M g C 1 2 (C atoms, open circles; M atoms, filled circles). The cube-based (broken lines) structure (a) was first proposed to account for its stability; structure (b) is currently more accepted. In (b) the inner metal atoms M 1 form a tetrahedron (heavy solid lines) that is capped (broken lines) by the four outer metal atoms M\u00b0; each M\u00b0 is bridged to each of the others (light solid lines) by a C 2 dimer. Chapter 3 Visible Spectrum of ZrC 79 suggested the alternative structure of Fig. 3.3(b), for which only four metal atoms of type M 1 or M\u00b0 are equivalent. The M ' form a regular tetrahedron (heavy lines), with an M\u00b0 capping each of its faces to form four additional tetrahedra with r ^ i - M 1 ) ^ r(Mi-M\u00b0); the M\u00b0 are bridged by C 2 dimers. An understanding of the properties of these metcars requires some knowledge of the TM-carbon bond, which gas phase spectroscopic studies of the smaller diatomic metal carbide species can offer. The literature review below shows the scarcity of such data before the discovery of metcars; for ZrC in particular, the void remained until the present work. This lack of prior data, especially for its ground state, makes ZrC interesting in its own right. Spectroscopic analyses of a wide range of T M monocarbides (18-54), reviewed below, suggest that TMs bond to carbon quite differently than to either nitrogen or oxygen. However, the behaviour of zirconium in this regard was unknown, since ZrC had never been studied. 3.3(b) Review of Relevant Literature Although there are no previous studies on ZrC, either experimental or theoretical, other T M monocarbides have received considerable attention (18-55). Three experimental papers on the isoelectronic Y N molecule have also appeared (56-58). This review describes just the more detailed experimental work, with only occasional reference to ab initio calculations. References to much of the theoretical research are given in the experimental papers. Scullman and co-workers were the first to study spectra of T M monocarbides; they examined electronic data on PtC (18-21), RhC (22-24), IrC (25, 26) and RuC (27, 28) in the mid-1960s and early 1970s. The samples were prepared at high rotational temperatures in a King furnace, which impeded definitive symmetry assignments in some of the spectra; later work with jet-cooled sources resolved some of these difficulties (vide infra). No further spectroscopic studies of T M monocarbides were undertaken until after the discovery of metcars; in 1994, Simard et al. (29) reported the first spectrum of Y C . A ground state of 4n, was assigned, from the electron configuration (10a)2(llo)1(12a)1(57c)3, in accord Chapter 3 Visible Spectrum of ZrC 80 with earlier ab initio calculations of Shim et al. (55). This result contrasted with the (10o)2(57t)4(lla)1 2 E + ground state symmetry that would be expected for a T M monoxide with the same number of electrons (59), showing clearly the profound effect of the different ionisation potentials (IPs) of carbon and oxygen on the nature of the bonding. Such considerations have stimulated a great deal of subsequent research on other T M monocarbides. Many papers, both extending the analyses of the Scullman group and describing new molecules, have appeared in rapid succession since the Y C study (30-54). The Morse group at the University of Utah has been at the forefront of these advances, applying laser ablation and jet-cooling techniques to prepare samples of FeC (30), MoC (31, 32), RuC (32, 33), PdC (32, 34), WC (35) and NiC (36). These six species were investigated primarily via resonant two-photon ionisation (R2PI); as the name implies, the molecule of interest is ionised by two sequential single photon absorptions. A tuneable dye laser supplies the first photon to promote the molecule to an excited state; the second photon, from a fixed wavelength laser, promptly ionises it from the intermediate state. As the first laser scans, a mass spectrometer detects ions produced by the second laser; the resulting signal mimics the absorption spectrum of the neutral species corresponding to the first photon. Dispersed fluorescence spectra similar to those described in Section 3.2(e)(ii) above were also recorded for MoC, PdC and RuC (32), providing rich insights into their low-lying vibrational and electronic structures. While Scullman could not determine any symmetries for the electronic states of RuC (27, 28), R2PI studies of supersonically cooled samples of this species by the Morse group showed unambiguously that its ground state is A \u00a3 + (33). Further unpublished R2PI data by the Morse group on V C , CrC and TiC are mentioned in their work on FeC (30); the latter molecule was first studied by Balfour et al. (37). Several recent studies of FeC in the microwave, infrared and visible regions by various workers (38-43) have made it the most widely Chapter 3 Visible Spectrum of ZrC 81 investigated of all T M monocarbides. Other groups have also studied T M carbides. The Ziurys group at the University of Arizona has recorded pure rotational spectra in the mm-wave region for NiC and CoC (44) as well as FeC (38, 43); for these studies the molecules were prepared in a high-temperature Broida-type oven by reacting the relevant metal vapour with methane. The Steimle group at Arizona State University has recorded both Stark and field-free high-resolution electronic spectra to provide, for the first time, electric dipole moment measurements in various electronic states of FeC (42), IrC (45), RuC (46, 47) and PtC (48, 49), as well as hyperfine analyses of these species, where appropriate (45, 46, 49, 50). Additional data on other T M monocarbides have also appeared since 1994. Two LIF studies of CoC have been published, the first by Barnes et al. (51) in the 12800 - 14700 c m - 1 region and the second by Adam and Peers (52) in the 14000 - 19100 c m - 1 region. A report by Simard et al. (53) on the electronic spectrum of NbC represents the only gas phase work on this species, while Balfour et al. (54) have reinvestigated RhC using jet-cooled LIF spectroscopy; they revised the symmetries of some of the states observed by the Scullman group (22-24) and identified some further states. The above discussion identifies all the gas phase spectroscopic studies of T M monocarbides published to date; with the current study of ZrC, AgC is now the only non-radioactive 4d T M monocarbide for which no gas phase spectrum has been reported. As expected from the results on Y C (vide supra), it has emerged that the ground states of the T M monocarbides are not necessarily the same as those of the isoelectronic T M mononitrides; Table 3.1 lists several examples. The differences follow from the difference in IPs of nitrogen (14.5 V) and carbon (11.3 V). Al l the metals in the molecules of Table 3.1 have IPs in the range 6.5 to 8.0 V, so that the valence atomic orbitals of carbon are more nearly degenerate with those of the metal. This rearranges the energy order of the valence molecular orbitals Chapter 3 Visible Spectrum of ZrC 82 (MOs) compared to the corresponding mononitrides and alters the most energetically favourable electron configuration and ground state symmetry of the molecule. Table 3.1 Comparison of ground state (GS) symmetries of some transition metal-containing monocarbides and their isoelectronic mononitrides Monocarbide GS Reference(s) Isoelectronic G S Reference NbC 2 A r 53 ZrN 2X+ 60 MoC 3 Z - 31 NbN 3Ar 61 CoC 2Z+ 51,52 FeN 2 A ; - 62 ZrC 3 \u00a3+ present work Y N lZ+ 56 The molecule described in this chapter, ZrC, is the latest such example: whereas prior work on isoelectronic Y N (56-58) establishes a 1 S + ground state, this state is found to lie 188 c m - 1 above the X 3 E + state in ZrC. The latter is shown to arise from the configuration (10a)2(57t)4(lla)1(12a)1; adapting the proposed M O scheme of ZrC to Y N , its ground state comes from the closed shell configuration (10a)2(57i)4(l l a ) 2 . 3.3(c) Description of the Spectrum Survey wavelength-selected fluorescence (WSF) spectra of ZrC have been recorded over the 16000-19000 c m - 1 region using normal isotopic methane (99% 1 2 C H 4 ) . These were recorded by monitoring fluorescence at four intervals of energy below the probe laser. Two of them, the v = 0-1 and 0-2 vibrational intervals of the X 3 S + ground state, are about 885 and 1755 c m - 1 . The al2Z+ state, which lies just 188 c m - 1 above X 3 S + , has very nearly the same vibrational intervals; this state was assigned from dispersed fluorescence and high-resolution WSF data discussed later in this Chapter. Since both states are populated in the free jet expansion, monitoring one of these two vibrational intervals generates the sum of the absorption spectra of the two spin manifolds, and it is not initially obvious at low resolution Chapter 3 Visible Spectrum of ZrC 82 (MOs) compared to the corresponding mononitrides and alters the most energetically favourable electron configuration and ground state symmetry of the molecule. Table 3.1 Comparison of ground state (GS) symmetries of some transition-metal containing monocarbides and their isoelectronic mononitrides Monocarbide GS Reference(s) Isoelectronic Reference v ' monomtnde NbC 2 \\ 53 ZrN 2 E + 60 MoC 3 Z - 31 NbN 3 A r 61 CoC 2 Z + 51, 52 FeN 2 A ; - 62 ZrC 3 E + present work Y N 12+ 56 -The molecule described in this chapter, ZrC, is the latest such example: whereas prior work on isoelectronic Y N (56-58) establishes a 1 Z + ground state, this state is found to lie 188 c m - 1 above the X 3 E + state in ZrC. The latter is shown to arise from the configuration (10o)2(57i)4(lla)1(12a)1; adapting the proposed M O scheme of ZrC to Y N , its ground state comes from the closed shell configuration (10o)2(57c)4(l l a ) 2 . 3.3(c) Description of the Spectrum Survey wavelength-selected fluorescence (WSF) spectra of ZrC have been recorded over the 16000-19000 c m - 1 region using normal isotopic methane (99% 1 2 C H 4 ) . These were recorded by monitoring fluorescence at four intervals of energy below the probe laser. Two of them, the v = 0-1 and 0-2 vibrational intervals of the X 3 E + ground state, are about 885 and 1755 c m - 1 . The a.lIf state, which lies just 188 c m - 1 above X 3 E + , has very nearly the same vibrational intervals; this state was assigned from dispersed fluorescence and high-resolution WSF data discussed later in this Chapter. Since both states are populated in the free jet expansion, monitoring one of these two vibrational intervals generates the sum of the absorption spectra of the two spin manifolds, and it is not initially obvious at low resolution Chapter 3 Visible Spectrum of ZrC 83 from which lower state a given band originates. To identify spin-contaminated excited states that connect to both X 3 E + and a 1 ^ , WSF scans monitoring two other intervals were also recorded. Levels that connect to the v = 0 levels of both states were identified by maintaining the monochromator 188 c m - 1 below the laser, while those that connect to X 3 Z + , VJ = 1 and alI+, v = 0 were monitored by maintaining the monochromator 692 c m - 1 below the laser. For these scans, the detection scheme unambiguously defines the lower state symmetry of any observed band. The resolution in the spectra generated from these four scans is about 15 cm - 1 , so neither rotational structure, nor structure from the naturally occurring isotopes of Zr ( 9 0 Zr, 51.45%; 9 1 Z r , 11.22%; 9 2 Z r , 17.15%; 9 4 Z r , 17.38% and 9 6 Z r , 2.80%), could be discerned; about 40 well-separated band heads appear. Dispersed fluorescence (DF) spectra have been collected for nearly all of them. A limited supply of 1 3 C H 4 was available to record a few key features of Z r 1 3 C at low resolution. Since the ZrC molecules were jet-cooled, only upper state vibrational progressions should appear in the WSF spectra, but these are not obvious at low resolution. Ffigh-resolution data, recorded for almost every band in the survey spectrum, show that many features in the survey data that are apparently single actually contain structure from two or more close-lying vibrational levels. In all, 56 bands have been identified, although few unambiguous D' assignments were possible. Fig. 3.4 gives a stick spectrum of the positions and relative intensities of these bands for the most abundant isotopomer, 9 0 Z r C ; corresponding bands of 9 2 Z r C and 9 4 Z r C are observed for all but the weakest of these. The bands have rotational envelopes that span typically about 50 c m - 1 and often have considerable overlap. The right inset of Fig. 3.4, near 16650 c m - 1 , shows nine bands that lie within 90 c m - 1 of one another. The strongly perturbed rotational structure in this region is discussed in Section 3.3(e)(ii). 19000 18500 18000 17500 laser wavenumber \/ cm\" 17000 1 .90 16500 16000 Figure 3.4 Stick spectrum of ZrC WSF bands. The plot indicates the location of the band head and its intensity as measured from its 3 + \u2022 1 + 3 + maximal fluorescence wavelength. Bands arising from X I , o = 0, a S , u = 0 and X E , u = 1 (marked by asterisks) appear in the spectrum. The band density is high in some areas, with eight or nine bands occasionally appearing within 100 cm - 1 , as shown in the insets (both have the same intensity scale). oo 4^ Chapter 3 Visible Spectrum of ZrC 85 A few isolated features of 9 6 Z r C were identified in the strongest bands, but no detailed assignments were attempted. While 9 1 Z r C might seem sufficiently abundant for its lines to be assigned easily, the spinning 9 1 Z r nucleus (I = 5\/2) distributes the rotational linestrength among six or more hyperfine components, each about as strong as a 9 6 Z r C line. Nevertheless, some 9 1 Z r hyperfine structure could be assigned in a few of the strongest bands, allowing a hyperfine analysis of the ground state. These results are presented in Section 3.3(d)(iii). The high resolution data show that the vast majority of the absorption bands come from the same 3 Z lower level, which is assumed to be the ground state v = 0 level because of the jet cooling; such bands are considered \"cold\". One of these appears near 16306 c m - 1 , a portion of which is shown in Fig. 3.5. The various branches in this band can be classified by their value of J '-N\", which ranges from +2 (\"S-form\") to -2 (\"O-form\"); there are nine of them: one S-, two R-, three Q-, two P- and one O-form. Subscripts of 1, 2 or 3 indicate whether the branch involves the F ^ J = N+l), F 2 (J = N) or F 3 ( J = N - l ) electron spin component of the 3 Z state. The first line of each branch has J' = 2; the structure is that of a 3 n 2 - 3 S transition. Rotational lines from the 9 0 Z r C , 9 2 Z r C and 9 4 Z r C isotopomers have been assigned in this band; only the 9 0 Z r C features have been labelled for clarity. Five weak \"hot\" bands from the X 3 Z , v = 1 level have also been observed (for 9 0 Z r C only). The vibrational assignment is clear because each of these has the same upper state combination differences as another band from X 3 E , v = 0 that appears about 880 c m - 1 above it; the rotational analyses of these two levels, discussed in Section 3.3(d)(ii), are consistent with their vibrational assignments. Further excitation bands in the high-resolution spectrum originate from a single vibrational level of the aforementioned aAS state. Fig. 3.6 shows a typical example of these bands. The rotational structure of this band is much simpler than the previous one in Fig. 3.5. Only three branches, labelled R, Q and P, appear; respectively, these have AJ = +1, 0 and -1 , Q 2 (N) Ql(N) 2 Q 3 (N) 2 R 2 (N) Ri(N) 13 3 + spin splitting of N=5 in X Z 14 15 9 16305.5 16305.0 16304.5 laser wavenumber \/ cm -1 16304.0 16303.5 3 3 + 90 Figure 3.5 A portion of the [16.2] Yl2 - X I -(\u00b0>0) band of ZrC. Lines from five of the nine branches are labelled for ZrC; unlabelled lines are from 9 2 Z r C and 9 4 Z r C . The Q-form branches connect to all three spin components of the ground state, as shown for N = 5. 00 R(J) 4 5 Q(J) 8 P(J) 2 4 10 12i 4^  ikJ \u2122lilnrr | TO* s a. o TO *P TO TO 17488 17486 17484 17482 -1 17480 17478 laser wavenumber \/ cm 1 + - 9 0 92 Figure 3.6 High-resolution spectrum of the [17.67]Q=1 - a \u00a3 band of ZrC. For clarity, only lines of ZrC are labelled. The ZrC and 9 4 Z r C R heads lie near 17484.47 and 17481.07 c m - 1 . Unlabelled lines above the 9 2 Z r C band head originate from the much weaker [17.69]Q=1-a 1Z +band. 00 Chapter 3 Visible Spectrum of ZrC 88 and first lines with J\" = 0, 1 and 2, indicating an Q = 1 - 0 (or LIJ - iE) transition. Once again, only lines from the most abundant 9 0 Z r C isotopomer are labelled for clarity. Most of the bands of the type shown in Fig. 3.6 have upper levels that also connect to X 3 \u00a3 , v = 0; the resulting bands appear about 188 c m - 1 to the blue. Two important conclusions follow from the rotational analyses of bands that connect to these two lower levels. One is that the X 3 Z and al2Z states have the same Kronig symmetry. This is apparent by observing, for example, that the R 2 (N) - P 2 (N) upper state combination differences of the \"triplet\" bands match the R(J) - P(J) differences of the \"singlet\" bands. From the proposed molecular orbital scheme discussed later in the Chapter, this symmetry is positive. The second conclusion is that the a^ 4 \" level observed in absorption has u = 0, which follows from its very small observed A E ( 9 0 Z r C - 9 4 Z r C ) = 0.068 cm\" 1 isotope shift (referred to the X 3 E+, v = 0 level). Since the vibrational frequencies of the X 3 Z + and &l2Z+ states are both about 900 cm - 1 , this shift would be at least 2 c m - 1 in magnitude for an excited vibrational level. The vibrational assignment is further substantiated by the observed carbon isotope shift of the X 3 S + , v = 0 - alIf, u = 0 interval observed in dispersed fluorescence. An example is shown in Fig. 3.7. Trace (a) in this figure shows a low-resolution WSF spectrum of Z r 1 2 C , recorded by monitoring fluorescence 188 c m - 1 below the probe laser. Ffigh-resolution data of the 17908 c m - 1 band (marked by. a heavy vertical line) show that it is excited from X 3 S + , v = 0. The DF spectrum observed from its upper state appears in trace (b); three features appear below the laser peak. The corresponding data for Z r 1 3 C are shown in traces (c) and (d). The WSF band shifts 26 c m - 1 to the red, to 17882 cm - 1 . In the DF spectrum, the 188 c m - 1 interval is essentially unchanged, which indicates that the two peaks have the same u; i.e., v = 0 for both peaks as shown in the figure. If a vibrational frequency of 880 c m - 1 is assumed, the isotope shift for i> = 1 predicted from the scaling factor p = [ p ( 9 0 Z r 1 2 C ) \/ p ( 9 0 Z r 1 3 C ) ] 1 \/ 2 = 0.9654 (to T i i i i | i i i i | i i i i 1 1 1 r 1 1 1 1 1 1 1 r 17900 17850 17800 0 -500 -1000 laser wavenumber \/ c m - 1 displacement from laser \/ c m - 1 12 13 \u20141 12 Figure 3.7 Effect of C substitution on the 17908 cm WSF band of Zr C and on the DF of its upper state. Laser pumping of 1 the band marked by a vertical line in WSF trace (a) gives the DF trace (b). Traces (c) and (d) are the corresponding Zr C data. For both WSF scans, LIF to the a1!4\", u = 0 level lying 188 c m - 1 above X 3 I + , o = 0 in both species was monitored. The isotope shifts of the various levels in traces (b) and (d) confirm the vibrational assignments in trace (b). Chapter 3 Visible Spectrum of ZrC 90 four significant figures, using the most abundant of the five naturally occurring isotopes of zirconium) is about -30 c m - 1 . This is in excellent agreement with the observed -29 c m - 1 shifts of the other two peaks. The different relative intensities of these three peaks, for Z r 1 2 C and Z r 1 3 C , reflect the isotopic dependence of the spin mixing in the excited triplet states of the absorption bands; the singlet peaks are relatively weak for Z r 1 2 C , while all three peaks are about equally intense for Z r 1 3 C . At high resolution, the rotational structure of the Z r 1 2 C absorption band shows strong absorption to a nominally 3 n 2 upper state level accompanied by weaker absorption to a lU level less than 5 c m - 1 higher, induced by weak mixing with the 3 n 2 level. This mixing also induces weak singlet DF features as the 3 n 2 level is pumped. No high-resolution data were recorded for the corresponding absorption band of Z r 1 3 C , but its 3 TI 2 and lIl levels must be essentially degenerate and thoroughly mixed, since the singlet and triplet features in the DF spectrum are equally intense. Vibrational features from both spin manifolds are observed in other DF spectra of both Z r 1 2 C and Z r 1 3 C , indicating a strongly mixed set of excited states, consistent with the confused appearance of the WSF spectrum and a very complicated electronic structure. It is clear from the DF data in Fig. 3.7 that the 17908 (17882) cm- 1 level of Z r 1 2 C (Zr 1 3 C) can be populated by excitation from a 1 2 + , u = 0. The DF spectra generated in this fashion are shown in Fig. 3.8. Aside from the laser scatter peak, the appearance of a DF spectrum is independent of the upper state population mechanism, so these spectra are the same as those in Fig. 3.7. The electronic interval is preserved and the shifts and relative intensities of the v = 1 peaks are essentially the same. The sharp features at the red ends of the WSF spectra in parts (a) and (c) of Fig 3.7 are worth mentioning. These are the a 3 P 0 \u2014\u00bb z 3 S f and a 3 P 2 \u2014\u00bb z 3 S \u00b0 atomic zirconium lines, lying at 17788.1 and 17777.3 c m - 1 respectively (63); they appear in the WSF spectra because of a Chapter 3 Visible Spectrum of ZrC 91 u = 0 u = 0 1 1 1 X 3 E + Z r 1 2 C 0 -500 -1000 displacement from laser \/ c m - 1 Figure 3.8 DF from (a) the 17908 cm 1 level of Z r 1 2 C and (b) its Z r 1 3 C counterpart. These levels are the same as those in Fig. 3.11(b) and (d) respectively; the only difference is that here, 1 + 3 + they are populated by absorption from a Z , u = 0 instead of X S , u = 0. As expected, the two spectra for each isotopomer are essentially identical aside from laser scatter effects. Chapter 3 Visible Spectrum of ZrC 92 coincidental degeneracy between the energy intervals of Zr and ZrC. The metastable a 3 P state has an unusual spin-orbit structure: the J = 0, 1 and 2 energies are respectively 4186.1, 4376.3 and 4196.9 c m - 1 , so that the \"central\" J = 1 component appears about 185 c m - 1 above the other two nearly degenerate components. For this reason, WSF scans that monitor fluorescence 188 c m - 1 to the red of the laser, such as those in parts (a) and (c) or Fig. 3.8, also detect Zr lines from either a 3 P 0 or a 3 P 2 if selection rules also allow fluorescence to the a3J*i level. Indeed, many Zr lines were observed in such WSF survey scans spanning 15000 - 19000 c m - 1 . This also necessitated, for each DF spectrum containing a peak displaced about 185 c m - 1 in either direction from its corresponding laser absorption, careful checking against known Zr lines to verify the carrier of this peak. Two other accidental degeneracies generate Zr lines in WSF scans that monitor the 692 c m - 1 interval between a^\"1\", v = 0 and X 3 E + , v = 1. The a5Fi level of Zr lies at 4870.5 cm - 1 , or about 680 c m - 1 above the metastable a 3 P 0 2 levels discussed above. Also, the a 3 F ground state of Zr has J = 2 and 4 levels that lie about 670 c m - 1 apart; J = 3 excited states can connect to both of them, generating impurity features in the DF spectra. This again required careful scrutiny to avoid confusion by atomic features. The rest of Section 3.3 is divided into two parts that discuss the low- and higher-lying electronic states of ZrC observed in the present work. 3.3(d) The Low-lying Electronic States of ZrC: X 3 E + , a JL:+, b 1 ^ and c1^ 3.3(d)(i) Vibrational analysis of the low-lying electronic states of ZrC DF spectra were recorded for nearly every feature observed in the survey WSF spectrum. Two of these were given in Fig. 3.7 and 3.8. Further examples are shown in Figs. 3.9 and 3.10. The DF spectrum in Fig. 3.9, from the upper state of the \"triplet\" excitation band shown in Fig. 3.5, is very simple; it contains only a single series of peaks corresponding to the u = 1, 2 and 3 levels of the ground state. The DF spectra shown in Fig. 3.10 are among the X 3 E + , u = 0 Attenuated pump laser scatter G(u)= 880 1753 2615 cm -500 -1000 -1500 -2000 -2500 Displacement from laser \/ cm -1 Figure 3.9 Dispersed fluorescence (DF) spectrum of the [16.2]3n2, u = 0 level of ZrC. The level is populated by pumping from u of the ground state; fluorescence to u = 1, 2 and 3 is clearly observed. J Chapter 3 Visible Spectrum of ZrC 94 ( a ) Z r 1 2 C u = 1 u = 0 1 2 3 i i 1 1 X 3 S + a 1 ^ - i \u2014 i \u2014 | \u2014 i \u2014 i \u2014 i \u2014 i \u2014 | \u2014 i \u2014 i \u2014 i \u2014 i \u2014 | \u2014 i \u2014 i - - | 1 1 1 1 1 1 1 1 r i 1 r-( b ) Z r 1 3 C \u2014 i \u2014 i -\u20221500 -i 1 r--2000 -1 -500 -1000 -2500 -3000 displacement from laser \/ cm Figure 3.10 DF spectra from the upper states of the (a) 18512 c m - 1 band of Z r 1 2 C and the (b) \u20141 13 corresponding 18467 cm band of Zr C. Tie lines between traces join corresponding features. No LIF to X \u00a3 , u = 0 occurs; two peaks in each trace (marked with asterisks) that do not belong to X 3 Z + or a*E + are assigned to the b X E + and c 1 S + states. See text for details. Chapter 3 Visible Spectrum of ZrC 95 most complicated. These are from the upper levels of a Z r 1 2 C band at 18512 c m - 1 and its Z r 1 3 C counterpart at 18467 c m - 1 ; these display even more features, which are assigned to two further low-lying electronic states, bl2Z+ and c1!\"1\", as discussed in more detail below. Table 3.2 Low-lying vibrational levels of ZrC identified by dispersed fluorescence3 Vibrational Energy \/ cm assignmentb Zrl2C Z r l 3 C X 3 E+, u = 0 0 0 a 1 ^ , v = 0 188(16) 187(13) X 3 E+, v = 1 880(11) 851(6) a A Z + , u = 1 1078(14) 1049(11) X 3 Z+, v = 2 1753(11) 1691(14) b!E+ 1846(15) 1802(11) a 1 2 + , v = 2 1944(14) 1907 c 1 E + 2463(12) 2409(3) X 3 Z+, u = 3 2615(6) 2528(18) a 1 ^ , v = 3 2792(14) 2775(10) b ! Z + 2888 X 3 E+, v = 4 3470(3) a 1 ^ , u = 4 3599 b 1 ^ 3735(22) 3684 X 3 Z + , rj = 5 4316 Quoted uncertainties are three times the standard deviation of the given weighted mean of all measurements; energies quoted without uncertainties were measured only once from data. bAssignments of some of the higher-lying singlet levels are tentative due to strong mixing of the a J S + , b : E + and c 1 ^ states and are only intended to represent the dominant character of the level. For all DF scans, careful measurements were made of both the displacement of each peak from the laser scatter and its signal to noise ratio (S\/N). For each low-lying vibrational level, an average of all the independent displacement measurements, weighted by their S\/N, was determined. Table 3.2 lists these mean values and their uncertainties, taken as three standard deviations of the mean; an energy level diagram is shown in Fig. 3.11. The energies quoted for the a 1! 4\", u = 0 and X 3 E + , v = 1 levels agree well with those obtained for 9 0 Z r C from the rotational analyses described in Section 3.3(d)(ii). The ground state vibrational intervals A G u + i \/ 2 = G(u+1) - G(o) decrease approximately Chapter 3 Visible Spectrum of ZrC 96 E\/10 3 cm 1 4 H 2 H 0 J S55 (-87) 3_ 862 (-63) 2_ 4_ 807 (-17) 3 850 (-37) 2_ 864 (-29) 1 1 (-51) 3735 2888 (-54) 2463 (-44) 1846 b 1 S + and cL2Z+ u = 0 890 ^ ^ - T 0 = 188cm- 1 X 3 E + a 1!* 12 13 Figure 3.11 Vibrational structure of low-lying electronic states of Zr CandZr C. The anomalous C -> C shifts (in parentheses in cm where known) suggest strongly mixed a 1 S + , b*E + and c 1 S + states. Energies are given instead of u for the levels at the far right. Chapter 3 Visible Spectrum of ZrC 97 linearly, as predicted by Eq. [2.20]; fitting them to this equation gives coe = 888.84(83) and coexe = 4.22(41) c m - 1 . The 1 2 C \u2014> 1 3 C shifts, about -29 c m - 1 per vibrational quantum, also scale linearly with u. The vibrational structure of the a^2Z+ state, however, has somewhat anomalous behaviour. The carbon isotope shifts for u = 0 and 1, already observed from Figs. 3.7 and 3.8, are reasonable, but deviate greatly from linearity thereafter. The vibrational quanta decrease with v, but not as smoothly as in the ground state, indicating the presence of strong perturbations. The source of these perturbations may be the four relatively poorly characterised levels in the rightmost column of Fig. 3.11, which must all therefore have the same symmetry as the a1^4\" state. The lowest of these, at 1846 c m - 1 , clearly represents a level of a third electronic state, which can be labelled b 1 !^ . The next one, at 2463 c m - 1 , seems too low to be its next vibrational level and is probably from a fourth electronic state, c^\"1\". The 2888 c m - 1 level is a more satisfactory candidate for the next level of bl2Z+. No u's are given since the states are too strongly mixed to have good vibrational quantum numbers. The supersonic jet-cooling precluded absorption spectra from these higher levels. However, the 1846 c m - 1 peak in the DF spectrum of the 18512 c m - 1 band (which appears at 1846 - 188 = 1658 c m - 1 in Fig. 3.10(a)) is strong enough to be recorded at higher resolution by using narrower monochromator slits and with the laser tuned to single unblended lines in the tail of the 18512 c m - 1 band. The hypothetical examples of Fig. 3.12 show how this technique reveals the electronic symmetry assignment of the peak simply from the number of rotational features that appear if a positive or negative parity level is populated. For example, only for Z states do the number of features produced change with upper state parity. Fig. 3.13 shows the results of exciting the Q(9) and P(10) lines of the 18512 c m - 1 band, which populate, respectively, the J' = 9 + and 9~ levels. Trace (a) in the figure is the emission pattern to X 3 Z + , v = 2 given by the Q(9) line. Q = 1, J = 9 N 10 + 9 -N 1 0 \u00b1 : 9+: 8 \u00b1 : N 10+-9 - \" 8+-N 11 -10 + 9 -8 + 7 - E F2(J=N>; F3(J=N-1), F,(J=N+1) 1 0 - \u2022 9 + 8 -N 11 +z 1 0 - = 9+ = 8 - z 7+ E F2(J=N), F3(J=N-1), F1(J=N+1) =ff= I U> s TO TO TO 1 s -(a) (b) Figure 3.12 Rotational structure of fluorescence from an Q = 1 state to various electronic states. The J = 9 upper level is pumped by one of the two absorptions at the far left. The stick spectra in row (a) are fluorescence from J = 9~ to the electronic state given directly above in the figure. Those in row (b) represent fluorescence from J = 9 + . Fine structure within each N is unresolved for the S states. The uniqueness of these five patterns indicates the lower state symmetry of the fluorescence. Chapter 3 Visible Spectrum of ZrC 99 i 1 1 1 \u2022 i 1 i 30 20 10 0 -10 -20 -30 relative wavenumber \/ c m - 1 Figure 3.13 Rotationally resolved DF features from the 18512 cm 1 band of ZrC. Trace (a) 3 + is the X S , u = 2 feature generated by pumping the Q(9) line of the laser band. The three peaks expected from Fig. 3.12 appear. Traces (b) and (c) are of the strong feature in Fig. 3.10 marked by an asterisk; these are obtained by pumping Q(9) and P(10) respectively of the laser band. The appearance of one and two peaks in these traces indicates 1 E + lower state symmetry. Chapter 3 Visible Spectrum of ZrC 100 This shows that the experiment can resolve rotational features, although with difficulty because of the weakness of the band and the comparatively low J value. The number of features that appear (three, labelled as S-, Q- and O-form lines) is significant. By comparison with row (b) in Fig. 3.12, this shows that the X 3 \u00a3 + and a1!\"*\" states have the same Kronig symmetry (two features would have appeared if the states had opposite symmetries). The absolute symmetries are not established though, because reversing all of the rotational parities in the figure reverses the Kronig symmetries of all the S states while conserving the energy level patterns. The absolute (positive) symmetry derives from the interpretation of the ground state rotational and hyperfine analyses discussed in Section 3.3(d)(iv). Trace (b), also from Q(9), shows that the emission from J' = 9 + to the 1846 c m - 1 level consists of a single rotational feature. Trace (c) also shows emission to the 1846 c m - 1 level, but from J' = 9~ (by pumping P(10)). The appearance of one and two peaks in these traces, respectively, though very weak, gives further confirmation of the bl2Z+ symmetry. Unfortunately, experiments of this type were not possible for the three higher levels, for intensity reasons, but the irregular 1 3 C isotope shifts are consistent with strong homogeneous perturbations between the a, b and c states, suggesting the same symmetry for all three. The 1 3 C shifts for the vibrational levels of the X 3 S + state are about -30 c m - 1 per quantum, as expected for a vibrational frequency of 880 cm - 1 . The al2Z+ state has an almost identical AGj\/2, so its 1 3 C shifts should be similar. The 1 3 C shifts for v = 2 and b : Z + , v = 0 sum to -81 c m - 1 , somewhat higher in magnitude than the -60 c m - 1 value expected for a total of two quanta in states whose average vibrational frequency is about 880 c m - 1 . This suggests that the observed levels are strongly mixed and that at least one of them has a vibrational frequency much higher than 880 c m - 1 . Consistent with this, the centrifugal distortion constant from the rotational analysis of the a!S +, v = 0 level, discussed in Section 3.3(d)(ii) below, shows that the unperturbed Chapter 3 Visible Spectrum of ZrC 101 vibrational frequency of the al~Z+ state is about 930 c m - 1 , much larger than the observed A G 1 ( \/ 2 value. It can be argued that the lower of the two levels near 1900 c m - 1 must have more al~L+, u = 2 character because of its larger carbon shift. This may be true; the assignment in Fig. 3.11 has been made only so that A G 3 \/ 2 for the al~Z+ state is close to the 850 c m - 1 value extrapolated from the o>e and A G i \/ 2 values. 3.3(d)(ii) Rotational analysis of the X 3 L + and a 1 !^ states of ZrC As discussed above, 56 vibronic transitions of ZrC have been identified from the high-resolution WSF spectra, most of which are \"cold\", i.e., with X 3 \u00a3 + , v = 0 lower states. Seven electronically \"hot\" bands, originating from al2Z+, v = 0, and five vibrationally \"hot\" bands, originating from X 3 2 + , v = 1, have been observed; the upper states of most of these hot bands also appear in cold bands. Over 8500 rotational lines have been assigned for 9 0 Z r C , 9 2 Z r C and 9 4 Z r C , the three most abundant isotopomers, though only unblended and well-measured lines were used for the data analysis (the assignments and measurements of these lines are listed in Appendices I and II). A systematic approach, making maximal use of this vast quantity of data and taking full advantage of all upper state linkages among the observed bands, has given accurate least squares rotational constants for the X 3 Z + , v = 0 and 1 and al2Z+, v = 0 levels. A description of this procedure, which makes extensive use of spreadsheets for the tedious arithmetic, now follows. Data fitting procedure Data from the three principal isotopomers, 9 0 Z r C , 9 2 Z r C and 9 4 Z r C , have been fitted independently. Initially, all possible combination differences for the X 3 Z + , v \u2014 0 level were extracted from the data as explained in Section 2.9(b). Some combination differences have been measured many times, since there are many available cold bands. Averages of these values were fitted by least squares using the standard Hamiltonian for a 3 S + state; Table 3.3 presents its matrix elements evaluated using Hund's case (a) unsigned (i.e., elf parity) basis Chapter 3 Visible Spectrum of ZrC 102 functions. Combination differences with only one available measurement were deweighted or discarded according to the quality of their fit. The rotational constants obtained from these fits were then used to calculate the X 3 2 + , o = 0 rotational energies. Table 3.3 Rotational and fine structure Hamiltonian matrix elements for a 3 E + state, evaluated using Hund's case (a) elf parity basis functions, where A = 0 and x = J(J+1) |J, Q=l+) |J, O = 0> |J,Q=l-> <J, 1 + | B x - y + 27J3 -D(x2 + 4x) -2 V x [B -y \/2 - 2D(x+l)] 0 < J, 01 B(x+2) - 2y - 4 X \/ 3 - D ( x 2 + 8x + 4) 0 < J, 1-1 symmetric Bx - y + 21\/3 - D x 2 Least squares fitting for the al~L+, v = 0 level followed, using data from the electronically \"hot\" bands for which corresponding \"cold\" bands had been analysed. The upper state rotational energies of the cold bands were found by adding the X 3 Z + , v = 0 rotational energies to the line measurements, and averaging where appropriate. The line measurements from the electronically hot bands were subtracted from the upper state energies, again averaging as appropriate, to determine the rotational energies of the a 1 ^ , v = 0 level. Rotational constants for this level were determined from a least squares fit of the rotational energies to the standard llf rotational energy expression: FV(J) = Tv + VCJ+l) - IV^J+l) 2 . [3.2] Five weak absorption bands from the X 3 S + , v = 1 level of 9 0 Z r C were also assigned in the high-resolution data; corresponding cold bands appeared for all of these. Rotational energies of the 9 0 Z r C , X 3 Z + , v = 1 level were thus evaluated, with appropriate averaging, in similar fashion to those of a1!\"1\", o = 0. These were also fitted to the matrix in Table 3.3, except that the vibrational energy Tj was added to the diagonal elements. Results of the fits The high-resolution data set for the most abundant isotopomer, 9 0 Z r C , contains over Chapter 3 Visible Spectrum of ZrC 103 4000 combination differences from the X 3 E + , v = 0 level; after averaging, about 200 unique values remain. The rotational constants obtained from them by least squares are given in Table 3.4; the uncertainties quoted are three standard deviations in units of the last quoted significant figure. Centrifugal distortion parameters yrj and XQ, initially included in the fit, were not kept because they were poorly determined and reduced the rms error only marginally. The vibrational constants determined from the A G v + i \/ 2 intervals for v = 0 - 4 are also given. Table 3.4 ZrC, X 3 Z + : Rotational, fine structure and vibrational constants3 9 \u00b0ZrC 9 2 Z r C (calc.)b 9 2 Z r C 9 4 Z r C (calc.)b 9 4 Z r C p 2 = p\/p ; 0.9974374 0.9949822 B 0 0.4878743(29) 0.4866241 0.4866219(41) 0.4854253 0.4854289(39) 107D0 5.860(55) 5.830 5.66(11) 5.784 5.76(10) Yo --0.0228714(42) -0.0228128 -0.0228109(65) -0.0227563 -0.0227539(62) *0 0.513958(79) 0.513958 0.51390(10) 0.513958 0.513911(99) r 0 \/ A 1.8065904(54) 1.8065904 1.8065935(76) 1.8065904 1.8065847(73) rms 0.0002428 0.0002792 0.0002686 4041 \/ 199 2025 \/ 178 1946\/ 178 N d 1 N max 28 22 21 Vibrational constants: oo e = 888.84(83), o o ^ = 4.22(41) a A l l constants in c m - 1 units except as indicated, with 3 a errors in parentheses bValues isotopically scaled from 9 0 Z r C constants cNumber of total and average combination differences used in least squares fit dHighest value of quantum number N appearing in data set Fig. 3.14 shows how the spin structure of the X 3 S + , v = 0 level of 9 0 Z r C varies with the rotational quantum number N . The quantity plotted is the calculated energy from the fit, less the purely rotational energy B 0N(N+1) - D 0[N(N+1)] 2. The separation of the Fi(J = N + 1) and F 3 ( J = N - 1) spin components approaches 2yN at high N ; F 3 lies above F j because y < 0. The F 2 (J = N) component lies above the mean of the other two by an amount asymptotic to X. Of particular note is the crossing of the F i and F 3 curves at N = 2, where the energy levels lie only 0.0071 c m - 1 apart. Another crossing occurs between the F 2 and F 3 components Chapter 3 Visible Spectrum of ZrC 104 Figure 3.14 Electron spin structure of the X S , u = 0 level of ZrC. The quantities plotted are the eigenvalues of the matrix in Table 3.3 calculated using the least squares molecular 2 2 constants of Table 3.4, less the purely rotational energy E r o t = B 0N(N+1) - D 0 N (N+l) . The F 3 curve crosses the F 1 and F 2 curves at N = 2 and 23 respectively. Chapter 3 Visible Spectrum of ZrC 105 near N = 23. These are not avoided crossings since the J values in each case differ for the two curves and the Hamiltonian matrix is diagonal in J. However, avoided crossings do occur here for the 9 1 Z r C species since 9 1 Z r has a non-zero nuclear spin, I = 5\/2; matrix elements of the hyperfine Hamiltonian off-diagonal in J exist. These internal hyperfine perturbations in the ground state of 9 1 Z r C are discussed in Section 3.3(d)(iii). Constants for the less abundant 9 2 Z r C and 9 4 Z r C species are included in Table 3.4. For comparison, isotopically scaled values, calculated from the 9 0 Z r C constants with B* = p 2 B, D ' = p 4 D, yl = p 2y and X1 = X, are also given. In virtually all cases the observed and calculated values agree to within the quoted uncertainties; the only exception is the D 0 constant of 9 2 Z r C . The isotopic scaling applies strictly only to equilibrium constants, but this should not be a major factor since D 0 must be very similar to D e . It is more likely due to the nature of the data. The coefficient multiplying D 0 in the energy level expression is N 2(N+1) 2 , so the uncertainty in D 0 depends strongly on N m a x , the highest value of N available in the data. From Table 3.4, N m a x ( 9 2 Z r C ) is somewhat less than N m a x ( 9 0 Z r C ) ; presumably the observed value of D 0 ( 9 2 Z r C ) would agree better with the isotopically scaled value if higher-N data were available. Also, the calculated values have uncertainties about equal to those of the observed values of 9 0 Z r C , so the ranges of calculated and observed values overlap significantly. Table 3.5 lists the constants of the v = 0 levels of 9 0 Z r C , 9 2 Z r C and 9 4 Z r C determined by least squares. Again, those of 9 2 Z r C and 9 4 Z r C agree with the values isotopically scaled from 9 0 Z r C . It is instructive to estimate coe for the al2Z+ state from these constants using the Kratzer relation. Only for 9 0 Z r C are both B 0 and D 0 determined to sufficient accuracy for this purpose; from these, the vibrational frequency is about 930 cm - 1 . The vibrational frequency can also be estimated from the observed A E ( 9 0 Z r - 9 4 Zr ) isotope shift of the, a^If, v = 0 level and the known co e (X 3 2 + ) value, and a similar result is obtained. Since the A G 1 \/ 2 = 890 c m - 1 value is much smaller, the alIf state must be highly anharmonic, Chapter 3 Visible Spectrum of ZrC 106 even in the absence of the perturbations discussed above in Section 3.3(d)(i). The estimated value of coexe for this state is 20 c m - 1 . Table 3.5 ZrC, a.lZ+: Rotational constantsa of v = 0 level 90ZrC 9 2 Z r C (calc.)b 9 2 Z r C 9 4 Z r C (calc.)b 9 4 Z r C p 2 = p\/p' 0.9974374 0.9949822 187.83053(42) 187.79451(49) 187.76263(60) B 0.526267(10) 0.524918 0.524924(17) 0.523626 0.523641(23) 10 7D 6.78(45) 6.75 7.50(113) 6.71 7.52(170) r\/A 1.739445(17) 1.739445 1.739434(28) 1.739445 1.739419(38) rms 0.0003070 0.0002733 0.0002631 #d 145 \/ 17 87\/13 74\/12 N e 1 > max 17 12 11 a A l l constants in cm 1 units except as indicated, with 3 a errors in parentheses bValues isotopically scaled from 9 0 Z r C constants cMeasured with respect to fictitious F 2(N=0) level of X 3 E + , u = 0 dNumber of total and averaged term values used in least squares fit eHighest value of quantum number N appearing in data set Table 3.6 9 0 Z r C , X 3 \u00a3 + , v = 1: Rotational and fine structure constants* J C 880.40170(29) B 0.4851992(67) 10 7D 5.97(29) y -0.023682(25) X 0.51475(25) r\/A 1.811564(13) rms 0.0003217 #c 184\/40 N c 1 ^ max 16 a A l l constants in c m - 1 units except as indicated, with 3 a errors in parentheses Equilibrium constants: B e = 0.4892119(55), a e = 0.0026751(73), r^A = 1.804119(10) These have the same meaning as in Table 3.5. Table 3.6 lists constants for the X 3 E + , o = 1 level of 9 0 Z r C . The equilibrium values B e , a e and r e can be determined from the constants for X 3 \u00a3 + , v = 0 and 1. With the coe and B e Chapter 3 Visible Spectrum of ZrC 107 values from Tables 3.4 and 3.6 respectively, the Kratzer estimate for the distortion parameter is 5.928(11) x 10 - 7 c m - 1 , consistent with the D 0 and D i values observed for 9 0 Z r C . 3.3(d)(iii) Internal hyperfine perturbations in the X 3 L + , v = 0 state of 9 l Z r C Description of the hyperfine patterns Hyperfine features of the minor isotopomer 9 1 Z r C (11.22% natural abundance) were assigned in a few of the strongest bands. To improve their signal-to-noise, some of them were rescanned at a slower speed and with greater signal averaging. Fig. 3.15 shows one such scan, recorded for the Si(N=0) rotational line of the Q' = 2 - X 3 S + band near 17342 cm\" 1. The lower level of an Si(0) line has J = 1 and therefore consists of 2J + 1 = 3 hyperfine components with total angular momenta F = 3\/2, 5\/2 and 7\/2. The upper level, with J = 2, has 5 hyperfine components with F = 1\/2, 3\/2, 5\/2, 7\/2 and 9\/2. Al l nine hyperfine transitions expected from the AF = 0, \u00b11 selection rules are observed and assigned in the figure, although one of these is blended with a 9 2 Z r C line. The hyperfine structure in each of the upper and lower states follows a Lande-type pattern, for which the spacing of adjacent levels, F and F+l, goes as F+l (64). The high density of rotational and isotope structure in the centres of the bands mostly blends the 9 1 Z r C hyperfine patterns beyond recognition. To some extent the well resolved spectrum of Fig. 3.15 is a lucky accident, because Si(0) lies fortuitously in the gap between the R i and R 2 heads of 9 2 Z r C . This is illustrated by Fig. 3.16, which shows the surrounding region under normal scanning conditions (i.e., faster and with less averaging); had Si(0) appeared only slightly to either side, much information would have been lost. It is usually only in the S branches, where the line density is sparsest, that the hyperfine patterns can be clearly identified. Further examples of 9 1 Z r C hyperfine structure appear in Figs. 3.17 and 3.18. The Si(5) line of the 17342 c m - 1 band is shown in the top trace of Fig. 3.17. In this case, the six r-type (AF = +1) \"main\" components, with F\" = 7\/2 through 17\/2, give a clear Lande-type pattern; Figure 3.15 Hyperfine structure of the S^O) line of the 17342 cm 1 (Q' = 2 - X 3 E + , u = 0) band of 9 1 Z r C . Al l nine components save q(7\/2) are resolved. o -1 r~ - i 1 1 r-17343.6 -1 r~ I U> a: TO TO TO 17344.2 17344.0 Figure 3.16 A portion of the 17342 cm 1 band of ZrC. Nine asterisks mark the fortuitously located hyperfine components of the 17343.8 laser wavenumber \/ cm\" 17343.4 .91 SjfO) line of ZrC shown in Figure 3.15. o Chapter 3 Visible Spectrum of ZrC 110 c--3\/2 5\/2 Figure 3.17 Hyperfine structure in 9 1 Z r C : the S1(5) line of the 17342 cm 1 band (fi' = 2) (top -1 trace) and the P 3(5) line of the 16502 cm band (Q! = 0) (bottom trace). The F assignments 3 + increase in opposite directions because at N = 5, the X \u00a3 hypermultiplets are inverted for the F, electron spin component and regular for F 3 . Both traces have the same dispersion. Chapter 3 Visible Spectrum of ZrC 111 r(F) 15\/2 13\/2 11\/2 9\/2 7\/2 5\/2 Figure 3.18 Internal hyperfine perturbations in the S,(2) (top trace) and S,(4) (bottom trace) \u20141 91 lines of the 17342 cm band (fl' = 2) of ZrC. F 3 \" features are induced by the perturbations as labelled on each trace; the heavy tie lines join the features with coupled F , \" and F 3 \" lower levels. Both traces have the same dispersion. Chapter 3 Visible Spectrum of ZrC 112 since the line has J\" = 6 and AJ = +1, the p- and q-type \"satellites\", with AF = -1 and 0 respectively, are too weak to appear. In a Hund's case (b) coupled 3 E + state, the hyperfine width of the F^ electron spin component barely changes with N (64); for this reason the hyperfine widths of the Si(0) and Si(5) lines of Figs. 3.15 and 3.17, about 0.2 c m - 1 , are nearly the same. The lower trace of Fig. 3.17 shows the six main (p-type) hyperfine components of the P 3(5) line of the 3TIo e - X 3 S + band near 16502 cm - 1 ; the sense of the Lande-type pattern is reversed compared to the lines, consistent with the opposite energy order of the hyperfine components in the F j and F 3 components of a 3 S + state. The top trace of Fig. 3.18 shows the hyperfine structure of the Si(2) line of the 17342 c m - 1 band. This is very different from the previous patterns; there is no obvious Lande pattern, so the F assignments are obfuscated. The reason is that an internal hyperfine perturbation (IHP) in the N \" = 2 level confuses the hyperfine pattern, causing shifts and splittings in the structure. Such perturbations are well documented for high multiplicity 2 electronic states, having previously been analysed in various states of 5 l V O ( C 4 E - and X 4 2 _ , I = 7\/2) (65, 66), 5 5 M n O ( X 6 S + , I = 5\/2) (67, 68), 5 5 M n S ( X 6 2 + ) (69), 5 5 M n H (X 7E+) (70, 71), 5 5 M n F (a 5S +) (72) and 5 1 V S (C 4 E\") (73). On the other hand, states with other symmetries, even 3 E states, rarely exhibit IHPs because they seldom satisfy the conditions described in the next paragraph required to produce them. Ubachs et al. (74) have observed an IHP in the A 2 A state of C H ( I H = 1\/2); it is the only known A ^ 0 state for which this phenomenon occurs and arises from its small spin-orbit coupling. Ahmed et al. (75), in their analysis of the a 3 2 + - X 1 S + system of 6 3 C u F (I =3\/2), cited irregular rotational structure in the F 2 electron spin component near J = 50 as evidence for an IHP in a 3 S + . Unfortunately the resolution of the data was too low to verify this hypothesis directly from hfs. Brazier et al. (76) later analysed the hfs of this system, but at a much lower rotational temperature; they could only verify the IHP indirectly by extrapolating the fit of their Chapter 3 Visible Spectrum of ZrC 113 colder data. The corresponding state of CuBr also almost certainly exhibits an DTP, but the currently available data (77) are again incomplete and inconclusive. To the author's knowledge, the HTP in the ground state of 9 1 Z r C reported here is the first to be directly observed and analysed for a 3 Z state. An HTP is an interaction that occurs among electron spin components of an electronic state with the same value of N but different values of J. If these happen to lie at similar energies because of the specific values of the rotational and spin parameters, the nearly-degenerate hyperfine levels then interact strongly via the matrix elements of the hyperfine Hamiltonian that are diagonal in N and F, but off-diagonal in J. The electron spin structure of the X 3 2 + state of 9 0 Z r C is illustrated in Fig. 3.14; a similar pattern occurs for 9 l Z r C , so this figure can be used to understand its level structure as well. 9 0 Z r C has no IHPs because I( 9 0Zr) = 0, but these occur for 9 1 Z r C because I( 9 1Zr) = 5\/2. The perturbations are observed in the data only if the hyperfine structures of the Fj and F 3 electron spin components overlap, i.e., only for N = 2, 3 and 4. The anomalous patterns in Fig. 3.18 reflect what happens for N = 2 and 4. The Si(0) line of Fig. 3.15 is unperturbed because the N \" = 0 level has only one spin component, F i ( J = 1). The Si(5) line in Fig. 3.17 is also unperturbed because at N = 5 the and F 3 spin components are too distant for their hyperfine manifolds to overlap. Unfortunately the perturbed part of the Si(3) line of this band is blended with stronger lines of other isotopomers, but Si(4) lies in the clear, as shown in the bottom trace of Fig. 3.18; its F\" = 5\/2 component is doubled. The full explanation is given in the next Sections. Suffice to say here that at N = 4, the high energy end of the F i hyperfine manifold slightly overlaps the low energy end of the F 3 hyperfine manifold, so that only the F\" = 5\/2 hyperfine components of the two manifolds lie close enough in energy to interact significantly. Matrix elements of the hyperfine Hamiltonian The rotational and fine structure Hamiltonian matrix elements required in the analysis Chapter 3 Visible Spectrum of ZrC 114 appear in Table 3.3. The hyperfine Hamiltonian matrix elements are given in Table 3.7, evaluated in a Hund's case (ap) parity basis. The various terms can be identified by the hyperfine parameters they contain: the Fermi contact parameter, b, the dipolar electron spin-nuclear spin constant, c, and the electric quadrupole parameter eQqQ. The matrix elements are diagonal in F; the basis functions are | JO*) , where | Or) means 2 _ 1 \/ 2 [ | fl = +1) \u00b1 | fl - -1) ], or | fl = 0) and the final \u00b1 symbol refers to the parity; the matrix elements have been evaluated using those from Section 2.6(b)(i), for which signed basis functions were used. Table 3.7 Nonvanishing hyperfine Hamiltonian matrix elements for a 3 2 + state, evaluated using Hund's case (ap) parity basis functions. The symbols are defined in the text. <J1+I <J0 <J 1 i <J-1 1+| <J-i o <J-11-<J-2 1+ <J-2 0 <J-2 1-J O = l+> a J e J h J , l J f l = 0) C J bj gj ^ ,0 J Q = l-> a J e J l T , i The functions aj, etc., in the matrix elements of Table 3.7 are as follows: a J (b + c)R(J) 2x + eQq 0 (3 - x){3R(J)[R(J) +1] - 4x1(1 +1)} 8xI(I- l)(2J-l)(2J + 3) bj = - eQq 0 3R(J)[R(J) + 1]-4x1(1 + 1) 81(1 -1)(2J - 1)(2J + 3) C j = jbR(J)\/V^, e J \u20221P(J)Q(J) 2J>\/4J2 -1 (b + c) + eQq 0 (R(J) + J + l) 41(21 -1)(J 2 -1) [3.3] [3.4] [3.5] [3.6] Chapter 3 Visible Spectrum of ZrC 115 fj 2bP(J)Q(J)Vx\" [3.7] W4J 2 -1 gj = -bP(J)Q(J)Vj(J^l) [3.8] 2jV4J 2 -1 and h J Q 3 e Q q 0 A \/ ( J - l ) 2 - Q^-y\/j2 - Q 2 P(J)Q(J)P(J-1)Q(J-1) [3.9] 161(21 -1)J(2 J - 1)^\/(21+ 1)(2J-3) where x = J(J+1) and the functions P(J), Q(J) and R(J) are given by Eq. [2.164]. The size of the matrix depends on the total angular momentum F for F < 7\/2; these cases are discussed below. For F > 7\/2, the matrix is of order (2I+1)(2S+1) = 18, although judicious choice of the basis functions | J, \u00a32*) labelling its rows and columns can block-diagonalise it into two matrices half as large. One can be obtained using the functions |F + 5\/2,l +>, | F + 5\/2,0>, |F + 3\/2,r>- | F + l \/ 2 , l + >, | F + l\/2,0>, | F - 1 \/ 2 , T > , IF \u20143\/2, l+>, IF \u20143\/2, 0) and | F - 5 \/ 2 , 1 \" ) . The other matrix can be formed from the remaining nine basis functions: |F + 5\/2,l\">, | F + 3 \/2 , l + >, |F + 3\/2,0>, |F + 1\/2,1\">, | F - l \/ 2 , l + > , | F - l \/ 2 , 0 ) , | F - 3 \/ 2 , T > , | F - 5 \/ 2 , l + ) and | F - 5 \/ 2 , 0) . It is clear from Tables 3.3 and 3.7 that none of the first nine basis functions connect with any of the latter nine, so two 9 x 9 submatrices result; these have well-defined rotational parities of ( - 1 ) F + 1 \/ 2 and - ( - 1 ) F + 1 \/ 2 respectively. For a S + state in case (b) coupling, the two matrices correlate to even or odd values of N , respectively. For example, if F = 7\/2, the values of J in the basis functions range from 1 to 6, but the first matrix gives eigenvalues corresponding to N = 0, 2, 4 and 6 (\"low-N\"), with positive rotational parity, while the eigenvalues of the second matrix correspond to N = 1, 3, 5 and 7 (\"high-N\"), with negative rotational parity. For F = 1\/2, 3\/2 and 5\/2 the orders of the matrices are 3, 6 and 8 respectively. The matrices for F = 1\/2 and 3\/2 are obtained from the general 9 x 9 matrices by retaining only the upper left 3 x 3 and 6 x 6 blocks respectively. If F = 5\/2, the two matrices have the same form as for F > 7\/2, except that the non-existent basis functions | F - 5 \/ 2,1 +) and | F - 5 \/ 2,1~) Chapter 3 Visible Spectrum of ZrC 116 are deleted to give a pair of 8 x 8 matrices. Because the spin-spin parameter X is quite small, a Hund's case (bpj) basis would give an almost diagonal matrix for the rotation and the electron spin effects. This is advantageous when IHPs cause problems with eigenvalue sorting for purposes of iterative least squares fitting, but comes at the expense of considerably greater algebraic complexity of the matrix elements. Case (bpj) offers no particular advantage here since the IHPs are localised for the available data; a case (ap) basis was adequate. The low-N IHPs found in ZrC have A N = 0, AF = 0 and AJ = \u00b12. Initially the AJ = \u00b12 perturbations were thought to require a term in the Hamiltonian with matrix elements of this type, namely the electric quadrupole interaction, but the mechanism is actually more subtle. Although the Fj(J = N+l) and F 3 ( J = N - l ) electron spin components for a given N value differ in J by two units, they both interact with the F 2 level (J = N) through AJ = \u00b11 matrix elements of the Fermi contact interaction. Since the Fermi contact interaction is by far the largest of the hyperfine interactions in the X 3 E + state of ZrC, and the F 2 level lies only 0.5 c m - 1 above the Fj and F 3 levels, the IHP arises in second order. The perturbing levels (from Fj and F 3 electron spin components) have no direct interaction; rather, they interact indirectly through a nearby third level (from F 2 ) . Nevertheless, the effects are non-negligible, as can be seen in Fig. 3.18. This mechanism is equivalent to that proposed by Launila and Simard (72) to describe similar perturbations in the a 5 S + state of MnF. Data fitting procedure and results Compared to the more abundant 9 0 Z r C , 9 2 Z r C and 9 4 Z r C species, only a small number of rotational lines were recorded and assigned for 9 1 Z r C . The assignments and measurements of these are given in Appendix III. No ground state rotational combination differences could be identified from them; the only available combination differences were between hyperfine components of the same N level. For least squares fitting, it was thus necessary to fix the non-Chapter 3 Visible Spectrum of ZrC 117 hyperfine parameters of 9 1 Z r C to values isotopically scaled and averaged, with appropriate weighting, from those of 9 0 Z r C , 9 2 Z r C and 9 4 Z r C given in Table 3.4. The available data gave 37 hyperfine combination differences from rotational levels with N < 9; the hyperfine constants obtained from them by least squares are listed in Table 3.8. Only the Fermi contact parameter, b, and the dipolar parameter, c, were determinable. As described above, the quadrupole parameter eQqo was initially believed responsible for the observed AJ = \u00b12 perturbations, but this hypothesis was rejected since it is too small to determine from the data. The significance of the b and c parameters is discussed in Section 3.3(d)(iv) in connection with the electron configuration of the ground state. Table 3.8 9 1 Z r C , X 3 Z+, u = 0: Rotational, fine and hyperfine constants3 B 0.4872417[20]b 10 7D 5.809[44]b y -0.0228406[31]b 0.513928[53]b b -0.03133(15) c -0.00123(37) rms 0.0004312 #c 37 N d 9 a A l l constants in c m - 1 units except as indicated, with 3 a errors in parentheses b Fixed value calculated as weighted mean of isotopically scaled constants of 9 0 Z r C , 9 2 Z r C and 9 4 Z r C ; uncertainty given in brackets is based on propagation of uncertainties in these observed values cNumber of combination differences used in least squares fit dHighest value of quantum number N appearing in data set The hyperfine structure of the X 3 E + , v = 0 level of 9 1 Z r C is plotted against N in Fig. 3.19; as in Fig. 3.14, subtraction of the rotational energy magnifies the details. Enlargements of two interesting regions are given in Fig. 3.20. The level patterns corresponding to the fflPs of Fig. 3.18 are shown in the top half of Fig. 3.20. Because of the different range of F values in the F L and F 3 electron spin components (from F = N+7\/2 to F = N-3\/2 and from F = N+3\/2 to F Chapter 3 Visible Spectrum of ZrC 118 0.4 0.2 -\\ 0.0 i -0.2 -\\ -0.4 -0.6 F 2 ( J = N) N - l ) F 1 ( J = N+1) F=N+5\/2 F=N+3\/2 F=N+l\/2 F=N-l \/2 F=N-3\/2 F=N-5\/2 F=N-7\/2 F=N-3\/2 F=N-l \/2 F=N+l\/2 F=N+3\/2 F=N+5\/2 F=N+7\/2 0 10 N 3 + 91 Figure 3.19 Electron spin and hyperfine structure of the X E , u = 0 level of ZrC. The quantities plotted are the eigenvalues of the matrix in Table 3.7 calculated using the least squares fitted constants in Table 3.8, less the purely rotational energy E r o t defined as in Fig. 3.14. In the N = 2 - 4 range, internal hyperfine perturbations produce avoided crossings in the four hyperfine components of F 1 and F 3 for which AF = 0. Larger plots of the boxed regions appear in Fig. 3.20. Chapter 3 Visible Spectrum of ZrC 119 0.0 -0.1 a w2 -0.2 i -0.3 H N = 1 0.39 7 0.38 a o w2 0.37 i m 0.36 0.35 N = 3 i 7 8 F=N+3\/2 F=N+l\/2 F=N-l \/2 F=N-3\/2 F=N-5\/2 F=N-7\/2 F=N-3\/2 F=N-l \/2 F=N+l\/2 F=N+3\/2 F=N+5\/2 F=N+7\/2 F=N-l \/2 F=N+l\/2 F=N-3\/2 F=N-5\/2 F=N+3\/2 \u2014 F=N+5\/2 Figure 3.20 Enlarged portions of Fig. 3.19. Top panel: Internal hyperfine perturbations in the 3 + 91 X S , u = 0 level of ZrC. The J values of the Fj and F 3 electron spin components differ by two units, so only four of the six hyperfine components are mutually perturbed in each of F L and F 3 . Bottom panel: unusual structure of the F 2 electron spin component. The six hyperfine components sort into pairs with the same |F - N | value. See text for details. Chapter 3 Visible Spectrum of ZrC 120 = N-7\/2 respectively), only four of the six hyperfine series interact. The avoided crossing in the F = N+3\/2 series (if regarded as continuous rather than quantised) occurs almost exactly at the N = 2 level, which explains the doubled F\" = 7\/2 component of Si(2) in Fig. 3.18. Similarly the avoided crossing in the F = N-3\/2 series occurs almost exactly at N = 4, for which N - 3\/2 is the lowest value of F for the F] spin component; as a result Si(4) shown in Fig. 3.18 has its F\" = 5\/2 component doubled. The avoided crossings in the F = N+l\/2 and F = N - l \/ 2 hyperfine series occur near N = 3, but not close enough to disrupt its hyperfine pattern significantly, or to induce obvious extra lines. As described above, the Si(3) line of the 17342 c m - 1 band is too severely blended to give any useful information. The DHPs are clearest in the S-form branches, because for these, only the Fj electron spin component carries zero-order oscillator strength. This means that for these branches, IHPs due to levels from the F 3 electron spin component induce obvious splittings and shifts. In the Q branches, by contrast, the effect of the IHPs is less obvious because all three electron spin components carry their own oscillator strength, even in the absence of the IHP. Fig. 3.21 illustrates this point for the Q branches of the 16488 c m - 1 band (the lines of the more abundant isotopomers, saturated in the figure, are fairly sparse, so that the 9 1 Z r C lines are, for once, mostly quite well resolved). The Qi(2) and Q 3(2) lines, for example, are affected by the same perturbation that induces extra features in the Si(2) line of Fig. 3.18, but it is not obvious at first glance that anything is irregular about them. The hyperfine structure of the F 2 electron spin component is plotted against N in the bottom half of Fig. 3.20. Somewhat surprisingly, the hyperfine energies are not proportional to F(F+1), as might be expected for magnetic hyperfine interactions. Instead the trend with increasing N is towards a pattern of three doubly-degenerate pairs, with F = N\u00b15\/2, F = N\u00b13\/2 and F = N\u00b1l\/2. This is a direct reflexion of the fact that the F 2 levels are mixed through the Fermi contact interaction with the Fj and F 3 levels, and can be regarded as a partial transition \u20141 91 3 + Figure 3.21 Q-form head of the 16488 cm band of ZrC (Q.' = Of- X \u00a3 ). Al l three ground state electron spin components carry their own hyperfine linestrength, but pairs of Q x and Q 3 lines with the same N and F are shifted apart by the AJ = 2 internal hyperfine perturbation; the two lines marked by asterisks are an example of this, for which N = 2 and F = 7\/2. Filled (open) circles 90 92 94 mark unblended (blended) lines. Saturated lines are from the more abundant ZrC, ZrC and ZrC species. Chapter 3 Visible Spectrum of ZrC 122 to Hund's case (bps) coupling. In this limit the dominant spin effect is the Fermi contact interaction, bl-S, which couples the electron and nuclear spins, S and I, to form a resultant G. In the present instance S = 1 and I = 5\/2, so the possible values of G are 7\/2, 5\/2 and 3\/2; since the spin energies are proportional to G(G+1), there will be three groups of levels. The double degeneracy results (78) from the specific forms of the matrix elements of the electron spin-spin interaction in case (bps) coupling. Fig. 3.22 shows the P 2(4) line of the 16502 c m - 1 band. At this low N value the grouping of the hyperfine components into three pairs is not complete: the two highest-F components are clearly resolved, while comparison with the calculated structure in Fig. 3.20 shows that the other four components are blended into the strong feature on the low frequency side of the line. The IHPs shown in Figs. 3.19 and 3.20 follow the selection rule AJ = \u00b1 2, and may be classed as \"second order\" since the coupled levels do not interact directly but are both coupled to a nearby third level through AJ = \u00b1 1 matrix elements of the Fermi contact operator. A \"first order\" DTP, for which the hyperfine levels belonging to two electron spin components interact directly through the AJ = \u00b11 matrix elements, occurs near N = 23 in the X 3 S + state of 9 1 Z r C . It was not observed in the present work due to the low abundance of 9 1 Z r C and the jet-cooling, but the calculated hyperfine level pattern is noteworthy; it is shown in Fig. 3.23. In this case the F 2 and F 3 electron spin components cross through each other, with internal perturbations affecting five of the six hyperfine series for each component. The F = N+5\/2 series of the F 2 component and the F = N-7\/2 series of the F 3 component pass through the perturbation region unscathed. The reason is that the ranges of F values in the two interacting electron spin components differ by one unit; therefore the highest- and lowest-F series only occur once in the group of levels, and are unaffected since there is nothing to perturb them. 3.3(d)(iv) Discussion: A molecular orbital model for ZrC Tables 3.2, 3.4, 3.5, 3.6 and 3.8 summarise all the data currently available for the four Figure 3.22 The P 2(4) line of the 16502 cm 1 band of 9 1 Z r C (OJ = Oe - X 3 S + ) . A head is formed by the F levels of the ground state F 2 electron spin component; the total hyperfine width (0.035 cm - 1 ) is much less than in Fj (0.168 cm - 1 ) or F 3 (0.125 cm 1 ) . 0.6 S o I 0.4 0.2 0.0 i F N + 5\/2 N + 3\/2 N + 1\/2 N - 1\/2 N - 3 \/ 2 N - 5 \/ 2 N - 7 \/ 2 F 2 (J = N) F 3 (J = N - l ) 10 15 20 25 30 35 N Figure 3.23 Calculated hyperfine energy level patterns for the F 2 and F 3 electron spin components of the X 3 L + , u = 0 level of 9 1 Z r C for N = 11 - 34. The plot is similar to Fig. 3.14, with E r o t identically defined. Levels with a common F - N value are joined by a curve; those with intermediate F - N values appear twice and have avoided crossings (internal hyperfine perturbations) near N = 20; the F - N = -7\/2 and +5\/2 curves appear only once each and are therefore unperturbed. to Chapter 3 Visible Spectrum of ZrC 125 low-lying electronic states of ZrC. Taken together, they allow a satisfactory molecular orbital (MO) scheme to be devised for this molecule. The starting point is the identification of the ground state as 3 \u00a3 + rather than 3 Z~, which follows from its very small electron spin-spin interaction parameter, X. Table 3.9 Manifolds of electronic states arising from various two-electron configurations Configuration Electronic states ca' \u2022 3E+ nii 3E+, 12- 3S- l A , 3 \\ 55' 3s+, 12-, 3 z - i r , 3 r r Tl2 3 s - l A 52 3E- i r If electron configurations with only two valence electrons are considered, 3 Z states arise if the two electrons have the same orbital angular momentum projection quantum number X, e.g., cc', mi, 88', n2 or 8 2 (Table 3.9 lists the set of electronic states arising from each of these). Except for the cc' configuration, the 3E states are always accompanied by states of opposite Kronig symmetry (for example, 3 2 r and 1 S + ) , between which strong spin-orbit interactions always occur (79). The result is that the \u00a31 = 0 and 1 components of a non-rotating 3 S state coming from one of these configurations may be separated by about 30-100 c m - 1 in a molecule containing a 3d or 4d transition metal atom. An example is the n2 X 3 \u00a3~ state of NiO (59), where interaction with the isoconfigurational 1E+ state pushes the Q = 0 component 52 c m - 1 below Q = 1. An even more extreme example, admittedly from a 5d system, is the 8 2 X 3 S _ state of ReN, where the separation is no less than 2630 c m - 1 (80-82). Similar arguments apply to 3E states from configurations with four or more valence electrons (79), so that no generality is lost here. The \u00a32 = 1 - 0 separation is, strictly speaking, a second-order spin-orbit interaction, but Chapter 3 Visible Spectrum of ZrC 126 is indistinguishable from the electron spin-spin interaction if the state is described by an effective Hamiltonian, since it has the same quantum number dependence. As a result, the electron spin-spin interaction parameter, X, includes the second-order spin-orbit interaction, and in fact is dominated by it in molecules containing heavier atoms. In a 3 2 state, the Q. = 1 component is defined as lying above the Q = 0 component by an amount 2X, so that values of X of the order of 15-50 c m - 1 can be expected for 3d and 4d systems. However, as previously indicated, this does not apply to the configuration aa', for which no spin-orbit interaction occurs; in this case the value of X more nearly represents the true spin-spin interaction, with at most higher order spin-orbit effects, and should not exceed 1 c m - 1 . The very small observed value, X = 0.514 c m - 1 , is therefore clear proof that the 3 E ground state of ZrC comes from the configuration aa', and must be a 3 Z + state. In fact, for the ground states of two-electron systems, 3 E + states are rare compared to 3 S _ states because stringent conditions are needed for them: there must be two o-type valence orbitals present, and they must lie close enough in energy that the exchange interaction of the aa' configuration places the 3 E + state below the closed shell l2Z+ (a 2) electronic state. Of all diatomic molecules studied so far, only ZrC appears to meet these conditions, although the isovalent TiC molecule, currently under study in the Morse laboratory, represents another possible example. At this time it is not clear whether its ground state is 3 2 + or lIf (30), although the complexity of the moderately resolved jet-cooled absorption data suggest its ground state is also 3 2 + (83, 84). The comparatively large Fermi contact parameter, bp = b + c\/3 = -0.03174(19) cm - 1 , further confirms the Kronig symmetry because it indicates the presence of an unpaired electron in a molecular orbital (MO) derived from the Zr 55a atomic orbital, which, from Table 3.9, can only be the case for the aa' configuration. Its value can be estimated from Ho 47ihc ' l > V 2 S y xgg#B^{^5 2 s(0)} . [3.10] Chapter 3 Visible Spectrum of ZrC 127 The ab initio value ( ^ ( O ) ) = 5.283 a ^ 3 (85) and the IUPAC recommended value for the magnetic moment of the 9 1 Z r nucleus (86) give b F = 0.00318625 x \u2014 x (1\/2) x V 3 J \u20221.30362 x 5.283 = -0.03677 cm\" 1. [3.11] 5\/2 J 1 1 This value, about 16% larger than the experimental value, indicates that the ab initio value of (Y 5 2 s (0)) is too large, as has generally been found for such Hartree-Fock calculations. The bp value for the 9 1 Z r atom is -0.0446 c m - 1 (87); the value for ZrC is about 83% of this, indicating that one of the a MOs is predominantly Zr(5s) in character. At this stage an M O diagram can be drawn for the ground state of ZrC, based on that for the diatomic 3d oxides (59); this is shown in Fig. 3.24(a). The a and a' orbitals (1 l a and 12c in the figure) are constructed from the Zr 5so and C 2po atomic orbitals; each holds one electron, giving the configuration (\\\\d)\\\\2ti)^. With the electron configuration of the ground state established, those of the other low-lying states may be considered. It is tempting to regard the a}l+ state as being isoconfigurational to the ground state, but the considerably different r 0 bond lengths of the two states do not support this conjecture. More reasonably, the much shorter bond length of al2Z+ suggests that it originates from the 11a 2 closed shell configuration. The proximity of the differently configured X 3 2 + (aa ' ) and a 1 S + (a 2 ) electronic states, less than 200 c m - 1 apart, indicates that the a and a' MOs must be very similar in energy. This implies that the two 1 E + states from the aa' and a' 2 configurations should also lie very low in the ZrC manifold, so that only slightly above the ground state there should be three close-lying 1 E + states, among which mutual homogeneous perturbations can occur. This is precisely the case (see Section 3.3(d)(i)), and supports the assignment of the b 1 ^ and c1!\"*\" states in the third column of Fig. 3.11. The only arrangement of the MOs consistent with all of the experimental facts is that shown in Fig. 3.24(a). Because there are no low-lying Tl or A states, the two a MOs, 1 l a and (a) Zr (4d25s2) 4d 5s 4do 4d% 4db 5sa 11a 13a 671 25 12CT 4-2p% 2pa 4 H H 5 ^ 2sa 10a\u2014It ^ C (2s22p2) 2p 2s (c) (4c?15s2) 4d 5s 4da 4dn 4dh 5sa 13a 671 25 12a 10a 2\/771 2pa l l a \\ \u2014 4 > -M M 15n 2scs N (2s22p3) 2E. 2s | U> TO TO TO (b) 12a 11a 12a lie* TQ\/ cm 2463 1846 188 b 1 S + a 1 S + ( r 0 = 1.74 A) X 3 S + ( r 0 = 1.81 A) (d) 12a z 11a 12a TQ \/ cm -1 3883 2496 B 1 I + (not yet observed) L L 3^+ A T ( r e = 1.82 A) a J I ( r 0 = 1.87 A) X : I + (r = 1.80 A) Figure 3.24 M O diagrams and low-lying electronic states of ZrC (parts a and b) and Y N (parts c and d). The difference in ligand IPs leads to different ground states for the isoelectronic ZrC and Y N species. Spectroscopic data for Y N are taken from Refs. 55 - 57, all ZrC data are from the present work. to 00 Chapter 3 Visible Spectrum of ZrC 129 12o, must lie between the nonbonding 25 and the bonding 5JI MOs. In part (b) of the figure the three electron configurations responsible for the four low-lying 2 states are illustrated; the 3 E + ground state comes from the configuration (10a)2(57i)4(llo)1(12a)1 and the &*2Z+ state from (10a)2(57t)4(llc)2. The bl2Z+ and c 1 ^ states originate from the (lQa)2(5ji)*(Ua)l(12c)1 and (10a)2(5jt)4(12a)2 configurations, but which is which cannot be determined without bond length measurements. The perturbations apparent in Fig. 3.11 indicate extensive mixing of the three electronic states. As discussed in Section 3.3(b), the ground state of the isoelectronic species Y N is known to be lZ+ (56-58), so that its M O scheme is clearly different. Its ground state must come from the configuration (10c) 2(5u) 4(l l a ) 2 , while the low-lying 3 E + state at 2496 c m - 1 (58) must be the analogue of the ground state of ZrC. A second singlet state at 3883 cm - 1 , A ! Z + (56), must correspond to either blZ+ or clIf in ZrC, but obviously it cannot yet be decided which. Fig. 3.24(c) shows how the M O diagram must be modified for Y N , and the resulting set of low-lying states, of which three have been observed (56-58), are shown in Fig. 3.24(d). The basic difference is that the nitrogen has a higher IP than carbon, so that the N atomic orbitals lie lower in the diagram than those of C; the 11a and 12a MOs are more separated in Y N than in ZrC. The ground state equilibrium bond length of Y N (1.80405 A) (56) is nearly identical to that of ZrC (1.80412 A), although a more insightful comparison would be with the analogous a^lf state of ZrC, which has a much shorter bond length of r 0 = 1.7394 A. The better energy match of the metal 5sc and ligand 2pa atomic orbitals in ZrC stabilises the 11a orbital with greater bonding character. The same reasoning should apply to the bond lengths of the ground state of ZrC and the analogous a 3 S + state of Y N . The latter, r e ~ 1.87(8) A, has been measured from medium resolution dispersed fluorescence data (58); its uncertainty is too large to draw definitive conclusions, but its support of the above argument does appear promising. Higher Chapter 3 Visible Spectrum of ZrC 130 resolution data of this state would be helpful. Based on the proximity of the 11a and 12a orbitals in ZrC, the complexity of the WSF spectrum in the 16000-19000 c m - 1 region can be understood. Any promotion of the 11a electron produces a manifold of electronic states that will be accompanied by an identical, nearly degenerate, manifold arising from an equivalent promotion of the 12a electron. Strong interactions occur between the two manifolds, producing the unusually disorganised spectrum described in Section 3.3(c). 3.3(e) Electronic States of Z r C in the 16000-19000 cm\" 1 Region Rotational analyses have been carried out at high resolution for 56 bands in the 16000 -19000 c m - 1 region. The first lines of the branches and the upper state H-doubling patterns give unambiguous Q! assignments of 0+e, 0~f 1 or 2. Most of the bands arise from the v = 0 level of the X 3 \u00a3 + state, though a few come from X 3 E + , v = 1 and alIf, v = 0. Fig. 3.25 plots the observed upper state vibrational energies; they are grouped into columns by their Q. values. The partitioning of the \u00a3 2 = 1 levels into 3TTi and lTL states is somewhat arbitrary as they are all to some extent mixtures of the two; the symmetry label indicates the dominant character of the level. The isotope shifts, A E ( 9 0 Z r C - 9 4 ZrC) , given in parentheses, are the shifts in the band origins of the transitions from the X 3 E + , v - 0 level; for those few upper levels that do not combine with this level, the shifts are referred to the alE+, u = 0 level. The upper state levels are readily divided into two categories: (a) the four lowest levels between 16000 and 16400 era\"1, comprising the upper state of the [16.2]3TL, - X 3 I + (0,0) band, which are relatively well-understood, and (b) the remaining levels between 16400 and 19000 c m - 1 , whose properties are obscured by severe perturbations. 3.3(e)(i) The [16 .2 ] 3 H r - X 3 E + (0,0) band Fig. 3.26 shows the four absorption bands in the 16000-16400 c m - 1 region as they Chapter 3 Visible Spectrum of ZrC E \/ c m - 1 19000 18500 18000 17500 17000 16500 16000 (5.7) (5.8) (9.1) (3.6) (3_pl (2.3) (-0.1) u = 0 (10-5) (5.4) (2.9) -(9.7)= (2.7) (103) (4.5) i l l ) (6.6) i !p\\4) (1.2) (-0.2) u = 0 (13.6) n = 2(3n2) Q = l(3Ul and 1!!) (6.8) (3.9) (15.9) (11.9) (6.9) (1.5) 0 2 ) u = 0 131 (7.5) (4.5) (18-3) (6.1) (103) (9.3) (3.2) u = 0 (-0.1) Q-Oe (3n0e) Q = o\/(3n0\/) Figure 3.25 Vibrational levels of 9 0 Z r C identified in the 16000 - 19000 cm Region. Where available, isotope shifts A E ( 9 0 Z r C - 9 4 ZrC)\/cm~ 1 are given in parentheses and show few obvious trends. The levels appear with high density and mostly follow Hund's case (c) coupling, 3 1 with predominantly Tl and n parentage; nearly all of them are globally perturbed. Q \u2022 = 2 Q ' = 1 Si' = Of i 1 1 1 1 1 1 1 1 < 1 1 ' 1 1 r 16300 16200 16100 16000 laser wavenumber \/ c m - 1 3 3 + Figure 3.26 WSF spectrum of the [16.2] TLr - X I (0,0) group of ZrC bands recorded at low resolution. Portions of the Q' = 2 and 1 bands, recorded at high resolution, appear in Figs. 3.5 and 3.27 respectively. Of all the observed bands, these are the only four for which unambiguous u' assignments can be made. Two ZrCH features near 16200 c m - 1 and a Zr atomic line near 16090 c m - 1 also appear; these are marked with asterisks. Chapter 3 Visible Spectrum of ZrC 133 appear at low resolution. They arise from the X 3 \u00a3 + , u = 0 level and are the lowest energy bands found in the search region (15000-19000 cm - 1 ) for their D! values. Some minor perturbations are present, but these are only apparent at high resolution. A detail of the high-resolution spectrum of the Q! = 2 band was shown in Fig. 3.5. Fig. 3.27 shows the rotational structure of the R-form head of the Q.' = 1 band as seen at high resolution. F T \" and F 2 \" spin components might be expected to appear in this R-form structure on the basis of the AJ and parity selection rules. However, it is well known that of the nine branches in a 3Ui - 3 \u00a3 + band that satisfy these rules, the three involving the F 2 \" spin component are vanishingly weak if the upper state has sufficiently large spin-orbit coupling (88), as is the case here. Accordingly, only F i \" components appear in the R-form head of this band, although other Q' = 1 cold bands in the spectrum exhibit F 2 \" branches; the relative strength of these branches is regarded as a measure of the extent of upper state 3Ui ~ lU mixing. The 9 0 Z r \/ 9 2 Z r \/ 9 4 Z r isotope structure of this R-form branch is also shown in the figure. The Av( 9 0 Zr - 9 4 Z r ) isotope shift of this band, and of the others, where known, is very small and negative (approximately -0.20 cm - 1 ) . The spacing of the four bands in Fig. 3.26, their similar isotope structures and their Q' ordering with increasing energy indicate that they are the Hund's case (a) spin-orbit components of the [16.2]3n>. - X 3 Z + (0,0) band, where the upper state is labelled using the convention of Linton et al. (89). The upper state A-doubling parameter (o + p + q) (90) of the Q' = 0 level, corresponding to half the T y - T e splitting at zero rotation, is very large, at about -16 c m - 1 . Moreover, while the intensity of the 3 I % - X 3 \u00a3 + band is similar to those of 3 n x - X 3 E + and 3 n 2 - X 3 S + , the 3 IIo e - X 3 E + band is much weaker. Both observations indicate that the 3IIo level interacts with a \u00a3 electronic state, although no such states were identified above the four low-lying \u00a3 + states previously discussed. 16182.2 16182.0 16181.8 16181.6 16181.4 laser wavenumber \/ c m - 1 Figure 3.27 R } branch head of the [16.2] - X E (0,0) band of ZrC at high resolution. Diagonal tie lines join corresponding features of 9 0 Z r C , 9 2 Z r C and 9 4 Z r C , as shown for the N = 3 lines. Some lines are blended because the isotope shift is coincidentally equal either to the branch spacing or to the separation of lines on the outgoing and returning arms of the branch. \u00a3 Chapter 3 Visible Spectrum of ZrC 135 The Q.' = 2 band, shown in Fig. 3.5, has an R-form head at N \" = 6, indicating a moderate increase in bond length on excitation. The same conclusion follows from the steadily decreasing intensity pattern in the DF spectrum of the upper level of this band (see Fig. 3.9). Moreover, the lack of a local minimum in this pattern indicates a nodeless upper state vibrational wavefunction, i.e., v' = 0, as already concluded from the Av( 9 0 Zr - 9 4 Z r ) isotope shift. The DF spectra for the two Q! = 0 bands behave likewise, while that for the Q' = 1 band, shown in Fig. 3.28, shows additional features corresponding to the low-lying states discussed in Section 3.3(d). These weak features indicate that the Q' = 1 level, though nominally 3 I I 1 , must also have a small amount of singlet character. Its most likely source is second-order spin-orbit mixing with an isoconfigurational, higher energy *n state, analogous to that described in Section 3.3(d)(iv) for a 3 E + \/ 1 E _ or 3 S _ \/ 1 E + pair of states. This mutual interaction pushes the 3TI1 and lH levels apart, producing an asymmetry in the spin-orbit structure of the 3n(a) state. The Q 1 = 1 - 2 splitting is about 127 cm - 1 , and if the location of the Q' = 0 level is taken from the e parity component, then the Q! = 0 - 1 splitting is only about 118 c m - 1 . Arguments fashioned after Lefebvre-Brion and Field (79) using the positions of the observed bands locate the *n perturbing state approximately 3500 c m - 1 above the 3 I I 1 level, near 19500 c m - 1 , which is unfortunately beyond the region of investigation and cannot be observed, even upon excitation from a 1 Z + , v = 0. This calculation represents the low energy limit of the lH perturber; setting the Q.' = 0 location any lower decreases the spin-orbit asymmetry which in turn increases the *n - 3TIi separation. While this second order spin-orbit interaction decreases the energy of the [16.2]3IIi, u = 0 level, its rotational energy level pattern is unaffected. In fact, this level is one of the few observed above 16000 c m - 1 for which a least squares fit of its rotational energies is feasible; these can be fitted to the standard Hund's case (c) expression for an Q = 1 level: X 3 Z + , u = 0 attenuated laser scatter I x s to TO -1000 displacement from laser \/ cm -2000 -3000 Figure 3.28 DF spectrum of the [16.2] n l 3 u = 0 level of ZrC. Weak fluorescence features to the low-lying singlet states, marked 3 1 by asterisks, indicate a small amount of singlet character in the excited state, probably due to isoconfigurational f l j ~ f l mixing. Os Chapter 3 Visible Spectrum of ZrC 137 F(J) = T + BJ(J+1) - D[J(J+1)]2 \u00b1 1 {qJ(J+l) + qD[J(J+l)]2}, [3.12] where the positive (negative) sign is taken for \/ (e) parity rotational levels. The results of these fits are shown in Table 3.10 for the three most abundant isotopomers. Table 3.10 ZrC, [16.2]3TIi, v = 0: Effective rotational and fine structure constants3 90ZrC 9 2 Z r C (calc.)b 92ZrC 9 4 Z r C (calc.)b 9 4 Z r C 2 = p\/p* 0.9974374 0.9949822 10-4TC 1.61784261(3) 1.61785261(6) 1.61786243(5) B 0.4260501(69) 0.424958 0.424958(20) 0.423912 0.423902(12) 10 6D 1.004(31) 0.999 0.99(13) 0.994 0.989(60) 103q --1.139(10) -1.136 -1.140(16) -1.133 -1.121(16) 107qD 4.70(56) 4.68 4.68d 4.65 4.5(10) r\/A 1.933229(16) 1.933229 1.933229(45) 1.9332294 1.933252(27) rms 0.0003106 0.0004726 0.0004035 #e 34 21 27 j f J max 20 13 17 Kratzer estimate of vibrational frequency, 9 0 Z r C : coe = 555 a A l l constants in c m - 1 units except as indicated, with 3 a errors in parentheses bValues isotopically scaled from 9 0 Z r C constants cMeasured with respect to fictitious F 2(N=0) level of X 3 S + , v = 0 d Fixed in the least squares fit eNumber of term values used in least squares fit fffighest value of quantum number J appearing in data set While the constants of Eq. [3.12] must strictly be regarded as effective fitting parameters, their isotopic scaling within experimental error lends validity to their interpretation as true mechanical constants. For example, the B Q value can be regarded as deriving from the r 0 bond length. In addition, from the 9 0 Z r C constants and the Kratzer relation, the vibrational frequency estimated for this electronic state is 555 c m - 1 , about 38% less than the 889 c m - 1 value for the ground state. Positions and Av( 9 0 Zr - 9 4 Zr ) isotope shifts of higher vibrational levels can be estimated for this electronic state and compared against the levels plotted in Fig. 3.25. This point is discussed in Section 3.3(e)(ii). Chapter 3 Visible Spectrum of ZrC 138 Inasmuch as the [16.2]3EL. - X 3 Z + (0,0) band can be described by the promotion of a single electron, the regular spin-orbit structure of the upper state rules out the promotion of a 5% electron to one of the a orbitals. Clearly, either the 11a or 12a electron is promoted, most likely to the antibonding 6% orbital. The stronger bonding character of the 11a orbital and the moderate increase in bond length favour a 12a \u2014\u00bb 6% promotion. The resulting (10a)2(57c)4(lla)1(67t)1 configuration yields both the [16.2]3fL state and the lU state responsible for its asymmetric spin-orbit splitting some 3500 c m - 1 above it. Additional perturbations appear in the rotational energy level structure of the Q! = Oe and Q' = 2 bands. Figs. 3.29(a) and 3.29(b) show the upper state reduced rotational energy plots for the 9 0 Z r C isotopomer. The Q! = Oe level exhibits an avoided crossing near J = 6, although this perturbation does not appear in the Q' = 0\/level. For the \u00a31' = 2 level, the nearly parabolic curvature of the plot in Fig. 3.29(b), with a minimum near J = 6, represents a severe global perturbation. This cannot be explained, for example, by the normal 3 n 2 spin-uncoupling effect that arises from the off-diagonal Hund's case (a) matrix elements of the B(J - L - S) 2 term of the Hamiltonian. These matrix elements merely change the effective rotational constant of the 3 n 2 level from the mechanical B value to an effective value B e f f given by the Mulliken relation: B e f f = B ( l + 2 B S \/ A A ) , [3.13] so that a plot of the energies versus J(J+1) should remain linear. This level is further disrupted near J = 11 by another perturbation which must derive from a degenerate (Q > 0) electronic state since it affects both e and\/ parity components in essentially identical fashion. Since these are the lowest energy bands observed in the spectrum for their respective Q.' values, the source of their perturbations must be high-u levels of lower-lying electronic states. The presence of these perturbations is not surprising in view of the great number of anomalies already identified in Sections 3.3(c) and 3.3(d). Moreover, the perturbed nature of even the Chapter 3 Visible Spectrum of ZrC 139 2.0 1.6 3 1.2 0.8 0.4 20 40 60 J(J+1) 80 100 120 2.4 ~ 2.0 'e o ? 1 6 3 l o H I H 1.2 0.8 H Figure 3.29 Reduced rotational energies of the (a) Q = 0e and (b) O = 2 spin-orbit components of the [16.2]3nr, u = 0 level of 9 0 Z r C . The Cl = 0e level has an avoided crossing near J = 7; the Q = 2 level is globally perturbed in both e and\/ parities. In the plotted quantity, T Q = 16061 (a) and 16305 c m - 1 (b); k = 0.427 c m - 1 in both plots. Chapter 3 Visible Spectrum of ZrC 140 [16.2]3n, u = 0 level, the lowest-lying upper state found in the electronic spectrum, suggests that perturbations will be the rule rather than the exception for the remainder of the higher-lying levels discussed below. 3.3(e)(ii) Higher-lying levels of ZrC in the visible region The upper states of all bands recorded at high-resolution have been classified according to their \u00a32' values and are plotted as an energy level diagram in Fig. 3.25. The numbers of upper state levels identified with \u00a32' = 0+e, 0\"f 1 and 2 are in the approximate ratio of 1:1:2:1. The simplest interpretation of these levels is that they represent the Hund's case (a) spin-orbit components of a collection of 3n levels, while the extra \u00a32 = 1 levels are isoconfigurational lH states. All of the observed \u00a3 2 = 1 levels are then mixtures of the 3ni and *n states. Constants from the least squares fit of the [16.2]3ni, v = 0 rotational energies of 9 0 Z r C predict coe = 555 c m - 1 for this state, much less than the 889 c m - 1 value for the ground state. On this basis, estimated energies and Av( 9 0 Zr - 9 4 Z r ) isotope shifts for higher levels of the [16.2]3n state up to v = 5 have been plotted in Fig. 3.30 (dashed lines) with the observed levels (solid lines) from Fig. 3.25. The predicted isotope shifts are independent of \u00a32 and for clarity are given only for the 3 n 2 levels. The spin-orbit structure of the calculated levels was assumed to be identical to that observed for rj = 0, and (HQX^COQ = 0.0047 was chosen to match the ground state. These calculations show only the most modest agreement to the observed levels. For example, the calculated \u00a32 = 2 levels are typically about 50 c m - 1 from the closest matching observed levels, and the observed isotope shifts are generally larger. These anomalies no doubt result from the presence of at least one other 3n level in this region. In fact, the six \u00a32 = 1 levels in the 17650 - 17950 c m - 1 region lie too close together for any pair of them to belong to the same electronic state, so at least this many electronic states must be producing the complicated energy level pattern in Figs. 3.25 and 3.30. Chapter 3 Visible Spectrum of ZrC E \/ c m - 1 19000 18500 18000 17500 17000 H 16500 A 16000 H [6.3] (5.7) (5.8) [5.1] (9.1) (3.6) [3.8] (3.6) (2.3) [2.5] [1.2] (-0.1) u = 0 (10.5) (5.4) (2.9) -(9.7), (2.7) (10.3) (1.2) (5A) (6.6) (16.4) (13-6) (-0.2) u = 0 (6.8) i3_9 l (15.9) (11.9) (6.9) (15) (2.2) o = 0 141 (7.5) (4.5) (18-3) (61) (10-3) (9.3) (3-2) u = 0 (-0.1) a = 2 (3n2) a -1 ( 3n : and lu) a = oe (3n0e) a = o\/(3n0\/) on QA Figure 3.30 Calculated u = 1 - 5 levels (dashed lines) and AE( ZrC - ZrC) isotope shifts (in 3 90 brackets for the Q = 2 components) of the [16.2] 11(a) state of ZrC, extrapolated from the observed u = 0 levels shown (see text for details of calculations). Strong perturbations in these levels result in poor agreement with observed levels (solid lines, taken from Fig. 3.25). Chapter 3 Visible Spectrum of ZrC 142 Not surprisingly, virtually every vibrational level in the 16000-19000 c m - 1 region has global rotational perturbations; the J(J+Independence of their rotational energies is often very non-linear. The cold bands in the 16640 - 16710 c m - 1 region, shown in the right inset of Fig. 3.4, are a good example of this; their reduced upper state rotational energies are plotted in Fig. 3.31 for the three most abundant isotopomers of ZrC. Of the four \u00a3 2 = 1 states in this region, the three highest are obviously interacting strongly. In 9 0 Z r C , the 16681 c m - 1 level has particularly bizarre \u00a32-type doubling. The normal ATy e = qJ(J+l) behaviour is replaced by a strongly non-linear splitting, as shown in Fig. 3.32; it is already rather large at J = 1 and 2, then decreases until it changes sign, immediately reverses sign once again and rapidly increases. It appears that, in addition to the interactions with the other two \u00a32=1 states, the \/ parity levels of this state are also interacting with the \u00a32 = 0\/ state that lies just 0.3 c m - 1 beneath it. The perturbed nature of the three \u00a3 2 = 1 states is also clear from the isotope dependence in the intensity distribution patterns in their cold absorption bands. In 9 0 Z r C , the three band origins are at 16681, 16694 and 16702 c m - 1 , and the first of these bands is by far the strongest of the three, with the other two each about five times weaker; this can be expressed as a 30:6:6 intensity ratio. This ratio changes both for 9 2 Z r C , for which these band origins lie at 16676, 16687 and 16693 cm- 1 , and for 9 4 Z r C , where they appear at 16670, 16681 and 16686 cm- 1 . Extending the previous intensity ratio scheme to these species leads to an 8:8:3 ratio for 9 2 Z r C and a 1:5:10 ratio for 9 4 Z r C . The sum of the intensities is fairly consistent with the natural abundance of the isotopomers, but their distribution changes in the three species. Evidently, the \u00a32 = 1 levels are composed of three strongly interacting zero-order basis states with very different transition moments; their composition is isotope-sensitive, and the intensities of the above bands are transformed accordingly. With increasing Zr mass, intensity is transferred from the lowest to the highest of the three levels. Other than the [16.2]3n(a), v = 0 levels already discussed, those shown in Fig. 3.31 are 16710 16700 16690 'g 16680 o + 16670 H OS 1 16660 16650 16640 16630 16702 (0 = le) 16694 (0 = 1\/0 16681 (0 = 1\/) 16681 (0= le) 16680 (O = Of) 16655 (O = Oe) 16643 (O = If) 16643 (0= le) 90 ZrC 0 = 1\/ 0 = le 0=1\/ O = 0e 0=1\/ 0= le 92 ZrC 0= le 0 = 1\/ ' 0 = 1 \/ 0= le 0 = 1 \/ 0 = le O = 0e 0 = 1 \/ 0 = le 94 ZrC 0 100 200 300 J(J+1) 400 500 0 100 200 J(J+1) 300 0 100 200 JYJ+1) 300 Figure 3.31 Reduced rotational energies of the 16681 cm 1 group of levels of 9 0 Z r C , 9 2 Z r C and 9 4 Z r C . Corresponding O levels have the same energy order in all isotopomers. Strong interactions occur among the three highest-lying O = 1 levels. Chapter 3 Visible Spectrum of ZrC 144 T , - T \/ c m - 1 200 J(J+1) 90 \u20141 Figure 3.32 Anomalous Q-type splitting of the Q = 1 level of ZrC at 16681 cm . Two turning points are produced by interactions with the other nearby levels plotted in Fig. 3.31. Chapter 3 Visible Spectrum of ZrC 145 among the lowest-lying levels of the observed upper states, and underscore the complexity of the ZrC energy level pattern. In fact, the large A E ( 9 0 Z r C - 9 4 Z r C ) isotope shifts of some of the levels in Fig. 3.31, at least 10 c m - 1 in magnitude, suggest that these are high-u levels from lower-lying states than those presently observed. It seems likely that low-o' bands from these states should appear below those shown in Fig. 3.25; however, WSF survey scans down to 15000 c m - 1 revealed none of these. Perturbations appear in nearly all of the upper states shown in Fig. 3.25. One example of a perturbed Q, level, for each of Q. = Oe, Of, 1 and 2, is shown in Fig. 3.33 in the form of a reduced rotational energy plot. While numerous perturbations appear, it is interesting that very few doubled rotational levels could be assigned. A rare instance of this is the Q = 2 level at 17342 c m - 1 , shown in Fig. 3.33(d), whose J = 7\/ and Se levels are both split into two components; in each case, the splitting is about 0.5 c m - 1 . More generally, in most of the bands the line intensities become very weak at the onset of a perturbation, beyond which the rotational structure cannot be followed. The perturbations are so pervasive that there is little point in attempting least squares fits of the rotational levels of any of the excited states. For most of these states, there is no simple model to which the data can be fitted. Even where such a model exists, it is essentially phenomenological, does not always describe the full range of observed rotational levels and offers little physical insight, especially since the results, with their limited success, would only apply to a scattered few out of the many levels studied. This section concludes with an example of an attempted deperturbation of the Q. = Oe and 1 levels near 17833 c m - 1 . To fit the data, a 3 x 3 Hamiltonian matrix was devised, with standard Hund's case (c) level expressions for the diagonal elements: F F L (J , \/ \/ e ) = BQJ(J+1) - D Q J 2 ( J + 1 ) 2 \u00b1 i 5 A I [ Q I J ( J + l ) + q D 1 J 2 ( J + l ) 2 ] , [3.14a] while only one off-diagonal element was used to model the heterogeneous interaction between Chapter 3 Visible Spectrum of ZrC 10.0 146 1.0 0.8 0.6 0.4 4 0.2 (b)Q = 0\/ 40 80 120 160 J(J+1) \u2014i 1 1 1 1 1 0 50 100 150 200 250 300 J(J+1) 1.1 1.0 T3 l 0 > 0.9 4 0.8 0.8 0.4 0.0 n r 0 50 100 150 200 250 300 J(J+1) T 1 1 r 0 200 400 600 800 1000 J(J+1) Figure 3.33 Reduced rotational energies of selected ZrC levels. Each is strongly perturbed. The quantity E + kJ(J+l) has been subtracted from the energies to expand the vertical scale, where E and k are (in cm\"1): (a) 17700 and 0.430, (b) 16488 and 0.434, (c) 17689 and 0.412 and (d) 17342 and 0.431. Open and filled circles respectively mark e and\/parity levels. Chapter 3 Visible Spectrum of ZrC 147 the Q. = Oe level and the e parity component of the Q. \u2014 1 level: Ho e\/i e(J) = HoiVJ(J + l ) . [3.14b] With this matrix, only 30 of the 48 observed rotational energies from the two states could be fitted with an rms error commensurate with their uncertainties. The constants determined from the fit are given in Table 3.11. Fig. 3.34 is a plot of the observed energy levels; the calculated patterns are plotted as solid curves. It is clear that Eq. [3.14] does not accurately describe the data at high J. In the Q. = le component, for example, there is an avoided crossing for which the matrix cannot give account. Even if Eq. [3.14] were valid in this case, the results of the fit show a model deficiency in the physically unreasonable negative D 0 and D i constants. Table 3.11 Constants3 from the attempted deperturbation of the nearly degenerate Q = Oe and 1 levels of 9 0 Z r C near 17833 cm\" 1 To 17833.0247(17) B 0 0.38911(20) 10 6 D 0 -24.0(14) T i 17832.9780(11) B i 0.42625(12) 10 6D, -2.13(83) qi -0.000181(21) 1 0 5 q D l 1.47(16) Hoi 0.59043(20) rms 0.0004722 #b 30 J b 11 J max a A l l constants in c m - 1 units except as indicated, with 3 a errors in parentheses bThese have the same meaning as in Table 3.5. Figs. 3.33 and 3.34 are typical of the complicated rotational level patterns encountered in the upper states of the observed ZrC bands; it is unfortunate that so few of them can be analysed as successfully as the low-lying levels. Fligh-level ab initio calculations may be helpful in interpreting the observed level structure, but the density of the observed electronic Chapter 3 Visible Spectrum of ZrC 148 -1 1 1 1 1 1 1 1 : 1\u20141 0 50 100 150 200 250 300 350 J(J+1) 90 Figure 3.34 Attempted deperturbation of the nearly degenerate fl = Oe and 1 levels of ZrC near 17833 c m - 1 . The curves are the calculated eigenvalues of the matrix in Eq. [3.14], using constants in Table 3.11; the constants were generated from a fit of the data plotted as filled circles. Open circles are observed data that cannot be fitted to an accuracy commensurate with their measurement uncertainty; the deperturbation is successful only at low J. Chapter 3 Visible Spectrum of ZrC states offer little hope that such calculations will be reliable. 149 3.4 Conclusions This chapter has described the experimental details of the jet-cooled spectroscopic studies of three molecules presented in this thesis. In the first of these studies, the electronic spectrum of zirconium monocarbide, ZrC, was recorded at high resolution in the 16000-19000 c m - 1 region. A total of 56 bands, most with perturbed upper states, have been examined in the first spectroscopic investigation of this molecule, and a large number of electronic states have been identified. ZrC has a rare X 3 Z + ground state, unlike the isoelectronic species Y N whose ground state is Xi'Z+; its analogue in 9 0 Z r C lies at T 0 = 187.83 c m - 1 and is readily populated even under jet-cooled conditions. Rotational analyses of the X 3 Z + ( r 0 = 1.8065 A, a>e = 889 cm\" 1 for 9 0 Z r 1 2 C ) and a 1 ^ (r 0 = 1.7394 A, A G 1 \/ 2 = 890 cm- 1) states reveal a much shorter bond length for the latter. Two additional 1 E + states lying below 2500 c m - 1 have been identified in dispersed fluorescence spectra; anomalous vibrational intervals and 1 2 C \/ 1 3 C isotope shifts observed in dispersed fluorescence in the three low-lying states show that they all have the same symmetry. This evidence, plus the consistency of the small effective spin-spin constant = 0.5140 c m - 1 of the ground state with a aa' electron configuration, indicates that the four lowest electronic states, X 3 E + , a 1!^, blI.+ and c 1 ^ represent all possible arrangements of two electrons in the nearly degenerate 11a and 12a orbitals (both formed from Zr 55a + C 2pa). In particular, the tightly bound alIf state originates from the closed shell 11a 2 configuration. Hyperfine structure in the ground state of 9 1 Z r C (11.22% natural abundance, I = 5\/2) has been studied; internal hyperfine perturbations (IHPs) have been analysed in a 3 Z + electronic state for the first time. The data show that a second order IHP occurs where the Fj and F 3 spin components cross near N = 2, and suggest that a first order IHP should appear near N = 23, Chapter 3 Visible Spectrum of ZrC 150 where the F 3 and F 2 spin components cross. Both fflPs arise via coupling of the fine structure components by the large Fermi contact interaction (bp = -0.0317 cm - 1 ) and further confirm the Zr(5sa) character of the ground state electron configuration. The confused level structure above 16000 c m - 1 , consisting of at least four close-lying, strongly perturbed II states (two singlets and two triplets, including the [16.2]3TL, state), is also consistent with this molecular orbital scheme and can be explained by the promotion of either a electron to a n orbital. Large A E ( 9 0 Z r - 9 4 Zr ) isotope shifts and rotational perturbations near the bottom of this level structure suggest further electronic structure below 16000 cm - 1 . Investigations of this region are warranted to improve understanding of the current data. High level ab initio calculations may also provide further insight. Chapter 4 151 Laser Spectroscopy of Zirconium Methylidyne (ZrCH, ZrCD and Zr 1 3 CH) 4.1 Background The significance of free radicals, in particular those containing transition metals (TMs), has motivated a large body of research on their microwave, infrared and electronic spectra in the last 75 or so years. Diatomic species, the simplest TM-bearing molecules and easiest to prepare with traditional high temperature sources, have received the overwhelming majority of this attention (1, 2). However, the dwindling number of such systems that remain unstudied and the wider applicability of laser ablation and jet-cooling techniques have begun shifting the focus to polyatomic (especially triatomic) systems. Analyses of their spectra are doubtless far more challenging than for similar diatomic molecules; added complexity arises from the much higher density of vibrational and rotational states and, for linear species, the Renner-Teller effect. For TM-containing triatomic molecules, the amount of rotationally analysed electronic data is still sufficiently small that it can be reviewed completely. The first rotational analysis of a TM-containing triatomic molecule appeared in 1983, when Trkula and Harris (3) reported 1 A \" - X^A! electronic spectra from the bent species CuOH(D). The molecules were prepared by reaction with peroxide ( H 2 0 2 or D 2 0 2 ) of copper atoms from a hollow cathode sputtering source; r 0 structures were derived for each electronic state. Virtually all subsequent research on such species has employed jet-cooled techniques, beginning with work on the visible spectra of the Y N H , Y N D and Y 1 5 N H isotopomers of linear yttrium imide, first reported in 1990 by Simard et al. (4). Two later papers from the same lab described the rotational, fine and hyperfine structures of the (0,0) bands of its B 2 E + - X 2 Z + (5), A 2 n - X 2 Z + and A\" 2n - X 2 S + systems (6). Numerous rotational perturbations were identified in these bands. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 152 In a series of publications, Steimle and co-workers (7-9) provided a detailed account of the near infrared A 2 A j - X 2 A j system of Y C 2 , including the ground state vibrational structure, as well as the geometry, fine and hyperfine structures and dipole moments of both states; they also reported corresponding results for the A 2 n - X 2 S + system of ScNH (10). While the latter species is linear, the strongly bent C 2 v geometry of Y C 2 is more properly regarded as T-shaped, with the metal ionically bonded to the side of the relatively stable C 2 moiety. High-resolution electronic data have also appeared recently for the coinage metal dichloride family. The Brown group at Oxford has produced the first rotational analyses (11, 12) of the well-known 460 nm and 360 nm systems of N i C l 2 (13-19), providing the first conclusive evidence of its X 3 Z g ~~ ground state symmetry. A similar body of low- to medium-resolution studies on C u C l 2 dating from the early 1960s (13, 14, 20-22) long presaged extensive subsequent rotational analyses and identification of its inverted X 2 n g ground state (23-30). Very recently, the Brown group has also reported a preliminary rotational analysis (31) of the 310 nm band system of C o C l 2 (14) indicating that this molecule has an X 4 A g ground state. The isomeric possibilities from bonding the C N ligand to TMs, i.e., M C N and M N C , the linear cyanide and isocyanide, and the T-shaped structure, raise the question of the most energetically favourable conformer; recent electronic data provides answers for two cases. Lie and Dagdigian (32) observe an isocyanide geometry for iron based on the F e N 1 2 C \u2014> F e N 1 3 C rotational isotope effect; its X 6 A ground state is analogous to those of several iron monohalides. The most favourable conformer for nickel was recently established here in the Merer lab as the cyanide via 1 4 N \u2014* 1 5 N isotopic substitution (33). These are the first high-resolution optical studies of a TM-containing isocyanide and cyanide respectively. Further work in the Merer lab has generated data for many triatomic TM-containing species. The electronic spectrum of lanthanum imide, LaNH(D), the third and final Group 3 Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 153 imide studied under high resolution, appears mostly in the red and near infrared and is discussed in Chapter 5 of this thesis; the results of this analysis were used by Steimle et al. to measure dipole moments of its X 2 \u00a3 + and B 2 \u00a3 + states (34). A search for the still unobserved yttrium methylidyne (YCH) species led to the serendipitous discovery of Y O H (35), making it the first spectroscopic study of a linear T M hydroxide. Vibronic coupling effects are strongly pronounced for both Y O H and LaNH. The T M methylidyne species M C H have been of interest to the Merer group for about a decade now, and while attempts to observe methylidynes of yttrium, molybdenum and rhenium have thus far been unfruitful, studies with other TMs have met with resounding success. As of this writing, LIF spectra have been observed for the methylidynes and deuterated counterparts of vanadium (36), tungsten (37), titanium (38), chromium (39), niobium (40), tantalum (40) and zirconium. These species are linear in all observed electronic states, and in most cases have ground state symmetries identical to those of the corresponding isoelectronic T M mononitrides; the last of these forms the subject of this Chapter. Relevant to the present results is work on isoelectronic ZrN. The first analysis of this molecule by Bates and Dunn (41) identified two electronic systems, the A 2 n - X 2 2 + yellow system (origin near 17400 cm - 1 ) and the B 2 S + - X 2 S + violet system (origin near 24700 cm - 1 ) . This work and extensive subsequent studies of both systems (42-50) reveal numerous excited state rotational perturbations, as is the case for the isoelectronic species Y N H (5-6). Similarities in the electronic structures of ZrCH, ZrN and Y N H are expected; in fact, these three species are part of a larger family of isovalent TM-bearing species, most of whose B 2 E + , A 2 n and X 2 E + states have been studied in detail. Some of these have already been reviewed above; others are identified in the later discussion. This Chapter presents studies of the ZrCH, ZrCD and Z r 1 3 C H isotopomers of zirconium methylidyne. The next Section discusses the experimental apparatus and techniques used in the Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 154 current work; these are very similar to those described in detail in Chapter 3, so only major differences are explained. Section 4.3 describes the appearance of the recorded spectra, the vibrational and rotational structure of the ground state, and the excited state vibronic and rotational structure. A discussion and conclusions are given in Section 4.4. 4.2 Experiment All the apparatus used in the ZrC study of Chapter 3 was also used here for the methylidyne experiments; the only additional component, a pulsed dye amplifier (PDA), is described later in this section. Since essentially the same laser ablation and LIF techniques of that study were also used, only major differences need be described. In fact, in the earliest (low-resolution) WSF experiments, ZrC and ZrCH often appeared in the same scan, so the complete lack of prior spectroscopic data on either of these species posed two challenges. The first was establishing the spectral carrier for each of the various new WSF bands. The second was to minimise such ambiguities by identifying what experimental conditions, if any, favoured the yield of one molecule over the other in the plasma chemistry. Extensive trial and error with various experimental parameters revealed two discriminating factors. One was the methane concentration of the CH 4 \/He gas mixture. While the ZrC yield was steady and high over a wide range of C H 4 concentration (1-8%), maximum ZrCH production required the full 8% concentration. Occasional contamination of ZrCH signals by ZrC occurred as a result. Fortunately, the visible spectra of these molecules do not completely overlap; while the ZrC spectrum appears in the 16000-19000 c m - 1 region, ZrCH bands were found in the 15100-17600 c m - 1 region, above which no searches were conducted for this species. Otherwise, dispersed fluorescence (DF) data and deuteration (replacement of C H 4 by C D 4 ) were sufficient at low resolution to distinguish between ZrC and ZrCH bands. None of the high-resolution methylidyne data were blended by ZrC features. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 155 The other factor was the length of the reaction channel in the Smalley source. The best ZrC signal appeared with a 7 mm long channel, as shown in Fig. 3.2, while shorter channels gave progressively better methylidyne signals. In fact, the best Z rCH results came with essentially no reaction channel; it was machined from the top of the source to expose about 50% of the rod diameter to easy view from point D in Fig. 3.2. It should be noted, however, that some ZrC signal remained even under these conditions, while the 7 mm channel almost completely quenched the ZrCH signal. Z rCH was first identified from WSF scans monitoring resonance fluorescence. DF scans of new ZrCH features located its five lowest ground state vibrational levels, i.e., (001), (002), (010), (020) and (011). The (t)it) 2 u3) numbering here identifies quanta of the V i ( a + , C -H stretch), v2(7t, bend) and v 3 (o + , Zr -C stretch) vibrations. Low-resolution WSF scans monitoring fluorescence to each of these levels were systematically recorded. This was repeated for ZrCD using deuterated methane in the gas mixture. The five sets of WSF scans so recorded for each isotopomer cover the 14700-17600 c m - 1 region. Those recorded for ZrCH while monitoring LIF to (001) required the slightly slower laser scan rate given by Eq. [3.1]; this helped remove spurious signals caused by the coincidental near degeneracy of this interval with the AG1\/2 quanta of both the X 3 E + and a 1 ^ states of diatomic ZrC (862 versus about 885 cm - 1 ) , and with vibrational intervals of the metastable a 3 A state of ZrO. As discussed in Chapter 3, this allowed a narrower monochromator slitwidth (1 mm versus 3 mm for the other WSF scans) to preserve molecular selectivity. DF spectra were recorded for all observed WSF features. Corresponding Z r 1 3 C H data were also recorded for some key bands, albeit with somewhat poorer quality as the limited availability of 1 3 C H 4 required some sacrifice of S\/N optimisation. The strong WSF bands of ZrCH and ZrCD at the red end of the spectrum were also recorded at high resolution. They are generally weaker than those of ZrC; the cw ring laser Chapter 4 Visible Spectra of ZrCH, ZrCD andZr13CH 156 alone was insufficient to record some of them. A P D A (Lambda Physik FL2003) was therefore added to the experiment; its laser output gave a reasonable compromise between the low-flux, narrow-linewidth cw laser output and the high-flux, broad-linewidth output of the pulsed laser described in Section 3.2(c)(i). This apparatus is now described. The working principle of the P D A is almost identical to that of the pulsed dye laser, with only minor differences. Whereas the pulsed dye laser emission is self-stimulated with a reflexion grating tuned to a wavelength within the spontaneous broadband emission of the dye, the P D A amplifies external laser light, in this case the cw ring laser. Three dye cuvettes (two pre-amplifiers and one main amplifier) lie along the propagation axis of the cw beam; these are each pumped by a 308 nm pulsed (15 Hz) XeCl excimer laser (Lambda Physik, Compex 102) fed into each cuvette at right angles to the cw beam. A cylindrical lens focusses the excimer beam into a plane to match the dye volume through which the two lasers propagate. The cw beam stimulates pulsed laser emission from the first cuvette, which the other two cuvettes amplify. The resulting high-flux, low-linewidth pulsed output (Av ~ 200 MHz, slightly greater than the residual Doppler linewidth of spectral lines recorded with the cw laser alone) has the same wavelength as the cw input. Depending on the type and quality of dye used in the PDA, the intensity ratio of laser emission to A S E can be up to 100. As with the low-resolution pulsed dye laser, the digital delay generator (described in Section 3.2(d)) controls the XeCl pulse timing relative to other events in the pulsing sequence. The broadened output requires that the cw laser be scanned at about half the normal rate for maximum spectral resolution. 4.3 The Visible Spectrum of Zirconium Methylidyne 4.3(a) Description of the Spectrum More than 50 vibrational bands have been observed by low-resolution WSF and DF for Chapter 4 Visible Spectra of ZrCH, ZrCD andZr13CH 157 each of Z rCH and ZrCD in the 15100-17600 c m - 1 region; stick spectra for both species, given in Fig. 4.1, show the locations and intensities of the heads of the cold bands, i.e., those that arise from the zero-point vibrational level. The intensities approximate the signal-to-noise (S\/N) ratio of the strongest feature in the DF spectrum from the upper state of each band. Numerous other bands arising from excited vibrational levels, i.e., hot bands, also appear; these are assigned via identification of corresponding cold bands in Fig. 4.1 and on the basis of their DF spectra as described in Section 4.3(b)(i). At this resolution, the zirconium isotope structure ( 9 0 Zr, 51.45%; 9 1 Z r , 11.22%; 9 2 Z r , 17.15%; 9 4 Z r , 17.38% and 9 6 Z r , 2.80%) is not resolved and the bands are all very similar in appearance, with rather weak P-type structure accompanied by two R-type heads. One R-head is generally much stronger than and lies slightly to the red of the other, although their relative intensities vary somewhat among the bands. Eleven of the strongest bands of each of ZrCH and ZrCD, from Fig. 4.1, lying mostly at the red end of the spectrum, were recorded at high (rotational) resolution; rotational assignments and line measurements are given for these in Appendices IV and V. For each of these bands, the first lines of each of its branches for the 9 0 ZrCH(D), 9 2 ZrCH(D) and 9 4 ZrCH(D) isotopomers can be assigned, from which the X 2 E+ ground state electronic symmetry can be unambiguously identified, as in ZrN and Y N H . In addition, the projection quantum number was determined for the upper state of each of these bands. Here, I is the bending vibrational angular momentum quantum number; for a given bending vibrational quantum number u 2 : The minimum value -|(1 - ( - 1 ) \u00b0 2 ) is 0 or 1 as u 2 is even or odd, and the energy dependence of the \u20ac components is given by g 2 2 \u00a3 2 , where the anharmonicity constant g 2 2 is generally much less than the bending frequency a>2. The cold bands have P\" = 1\/2, so the selection rule p = A + e + s , [4.1] |\u00a3| = n 2 , u 2 - 2 , u 2 - 4 , I ( i - ( - l ) 0 * ) . [4.2] s TO TO TO N 8 (a) (b) 17000 16500 16000 15500 laser wavenumber \/ cm Figure 4.1 Stick spectrum of (a) 9 0 Z r C H and (b) 9 0 Z r C D WSF bands. The plot indicates the location of the band head and its intensity 2 + as measured from its wavelength of maximal fluorescence. Only cold bands (i.e., those arising from X I , u = 0) are shown. oi 00 Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 159 AP = 0, \u00b11 [4.3] limits the allowed P' values to 1\/2 or 3\/2. Faint hints of 9 6 ZrCH(D) and of the anticipated hyperfine structure of 9 1 ZrCH(D) (I = 5\/2) occasionally appear in the rotational structure, but no analyses of these data were attempted. In fact, only for the most abundant 9 0 ZrCH(D) species do the branches extend high enough in N for satisfactory least squares fitting; nevertheless, isotope shifts of rotational lines of 9 2ZrCF\u00a3(D) and 9 4 ZrCH(D) proved valuable in assigning the upper state spin-orbit and vibrational structure in the observed bands. Nearly every band of ZrCH and ZrCD recorded at high resolution suffers to some extent from local rotational perturbations. In most cases the interacting states are dark and have very different rotational constants, as usually only one or two upper J levels are doubled by a perturbation; occasionally multiple local perturbations occur at various J values in a particular vibrational level, rendering least squares fitting of the data impossible. Some upper state progressions in the V2(bend) and V3(Zr-C stretch) vibrations were assigned from the WSF data, while the DF spectra provided corresponding ground state data. Only a slight amount of activity in the V j ( C - H stretch) vibration appeared in a few of the DF spectra, indicating that the observed electronic transitions are dominated by promotions of metal-based electrons. The rest of this Section discusses the vibrational and rotational structure of the ground electronic state, excited levels in the 15100-15800 c m - 1 range and higher lying excited levels. 4.3(b) The X 2 E + State 4.3(b)(i) Vibrational analysis Extensive DF data of ZrCH and ZrCD have mapped many ground state vibrational levels for these species; no evidence of other low-lying electronic states was found. Some typical DF spectra appear in Figs. 4.2-4.7; these are now discussed individually. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 160 Fig. 4.2 shows the patterns from the 15179 c m - 1 level of ZrCH in trace (a) and from its 15189 c m - 1 ZrCD counterpart in trace (b); these are the lowest-lying upper state levels found for their respective isotopomers. Based on the blue shift upon deuteration, the P' values obtained from high-resolution data and analogy with the A - X system origin of ZrN at 17400 c m - 1 , the cold absorption bands to these levels are assigned as A 2 ni\/ 2 - X 2 E + (0,0); these are discussed in more detail in Section 4.3(c). The principal features of trace (a) form a progression in the V3 vibration, whose frequency is about 862 c m - 1 . This assignment is based on deuteration shifts (vide infra), analogy with similar results on previously studied methylidynes (36-40) and comparison with the known ground state value of co e = 889 c m - 1 of ZrC from Chapter 3. Its intensity distribution also supports the vibrational assignment of the laser band; the absence of a local minimum can be attributed to a nodeless upper state vibrational wavefunction, which is the case for the zero-point vibrational level only. Since the only emission from the A 2ni\/ 2(00\u00b00) level allowed by the vibrational selection rules is to totally symmetric (even u 2 with I = 0) levels, the weak appearance in this trace of the v 2 bending fundamental at 596 c m - 1 suggests some degree of vibronic coupling in the A 2 n state, i.e., the Renner-Teller effect. The At = 1 selection rule of this feature and the anticipated presence of a nearby B 2 S + state favour this interpretation. More evidence of vibronic coupling in this state appears later in the Chapter. The corresponding ZrCD spectrum in trace (b) differs slightly. The features identified for ZrCH are all present with a similar intensity distribution, but an additional progression in v 3 built on the overtone of v 2 also appears. A Fermi resonance that mixes levels within each (0u 2*U3) polyad, for which u 2 + 2U3 and I are constant, induces these features. A similar Fermi resonance enhancement upon deuteration was also observed for the ground states of T iCH and TiCD (38). In both cases, the mixing is stronger in M C D than in M C H because the v 3 and v 2 vibrational frequencies are more nearly in a 2:1 ratio, although even in the deuterated species, 13, Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr CH 161 (001) laser scatter (a) (010) (002) (003) 1 \u2014 1 \u2014 1 \u2014 < ~ (001) laser scatter (010) ( b ) (002) (020) (021) ( 0 0 3 ) ( o 2 2 ) 1 r --2000 -500 -1000 -1500 -2500 displacement from laser \/ cm -1 Figure 4.2 DF spectra of the A 2 n 1 \/ 2 , u = 0 levels of (a) ZrCH at 15179 cm 1 and (b) ZrCD at 15189 c m - 1 . A Fermi resonance in the ground state of ZrCD enhances the (02u3) progression. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr]3CH 162 the relative intensities of the principal (00\u00b0 1) and induced (02\u00b00) features, shown in Fig. 4.2(b) for ZrCD in particular, show sufficiently weak mixing that u 2 and 03 may still be regarded as approximately good quantum numbers. As expected, the principal progression that carries the oscillator strength and the induced progression have essentially the same intensity profile. The assignments of the v 2 and V3 vibrations are supported by their isotope shifts; v 2 should have the larger shift as it is essentially a hydrogen wagging motion. The richest DF spectrum of ZrCH is from the 15988 c m - 1 level, as shown in Fig. 4.3(a). Fluorescence to no less than 10 ground state vibrational levels occurs; features marked by asterisks are from the frequently encountered ZrO impurity. Once again, both totally symmetric and non-totally symmetric fluorescence features betray the presence of excited state vibronic coupling. The (020) peak is somewhat broader than the others due to unresolved splitting of the \u20ac = 0 and 2 levels. In some of the other DF spectra, this feature is sharp and unblended with measurements that cluster around two averages of 1164 and 1189 cm - 1 , suggesting an I splitting of about 25 cm - 1 . An example of a DF spectrum for which \u00a3 structure is resolved is presented shortly. The limited available supply of 1 3 C H 4 was sufficient to locate the corresponding band head of Z r 1 3 C H near 15980 c m - 1 (among others) and record its DF spectrum; the latter is the only DF spectrum recorded for this isotopomer and appears in Fig. 4.3(b). Some broad laser artefacts and weak unassigned features appear in this spectrum, but most of the vibrational levels from Fig. 4.3(a) can be identified. Since the bending vibration involves little carbon motion, its frequency is not very sensitive to isotopic substitution on this atom, while 0D3 drops by 4%. In Fig. 4.4, the DF spectrum of the 16461 c m - 1 level of Z rCH shows resolved I components of the features with u 2 = 2; however, without high-resolution absorption spectra from these levels, unambiguous \u20ac\" assignments, which establish the sign of g 2 2 , cannot be 13, Chapter 4 Visible Spectra of ZrCH, ZrCD andZrJCH 163 (022) * (013) -500 -1000 -1500 -2000 -1 -2500 -3000 displacement from laser \/ cm Figure 4.3 DF spectra of the (a) 15988 cm 1 level of Z rCH and (b) the corresponding 15980 \u20141 13 cm level of Zr CH. Asterisks in trace (a) mark ZrO features. Nine of the ten levels in ZrCH 13 can be identified in Zr CH. T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 0 -500 -1000 -1500 -2000 -2500 -3000 displacement from laser \/ cm - 1 Figure 4.4 DF spectrum of the 16461 c m - 1 level of ZrCH. The \/-type splittings of the (02\u00b0 ' 2 l ) and (02\u00b0' 22) peaks are resolved in this spectrum. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 165 made. The (02\u00b0 1) and (0221) features are discernible; one appears as a weaker shoulder slightly to the red of the other with about a 26 c m - 1 separation. The nature of the DF scans allows better resolution of the (02^2) features. They typically cover a monochromator wavelength range of AXM = 200 nm and the AX = 1.1 nm bandpass is constant in wavelength, so the wavenumber resolution Av = A A A , M 2 improves with X M . Thus the 4 g 2 2 = 28 c m - 1 splitting is best resolved in the highest members of the (02*1)3) progression. DF spectra of ZrCD offer a clue in establishing the sign of g 2 2 . Since the Fermi resonance mechanism is diagonal in \u00a3 and the (00\u00b0 1) level appears below (02\u00b00) in this isotopomer, the separation of the \u00a3 components of the bending overtone level increases upon deuteration if g 2 2 is negative, or decreases if g 2 2 is positive. No \u00a3 splittings were observed in any DF spectra of ZrCD, which suggests that the Fermi resonance suppresses them and that g 2 2 = +7.0 cm- 1 . Several hot absorption bands from the (01*0) and (00\u00b01) levels appeared in the WSF spectra; these were generally rather weak, consistent with the cold molecular beam, and could usually be identified from DF spectra of their upper states on the basis of a (00\u00b00) feature appearing respectively 596 or 862 c m - 1 to the blue of a laser band. An example is shown in Fig. 4.5. Trace (a) shows DF from the upper state of the 15109 c m - 1 Z rCH band. Its lowest wavelength feature appears 596 c m - 1 to the blue of the laser band, which represents an upper state appearing at 15705 c m - 1 . Such a level does indeed exist; its DF spectrum is shown as trace (b). The two traces are essentially identical, except that trace (a) has a better S\/N ratio. Evidently, the Franck-Condon factor for absorption to this level is so much larger for (010) than for (000) that it overcomes the low population of the excited vibrational level. Weak features in some DF spectra suggest v^ activity. The clearest evidence is from the 16680 c m - 1 level of ZrCH; its DF spectrum is shown in Fig. 4.6. Unfortunately, this region of the absorption spectrum also has many closely-spaced ZrC bands (see the right inset of Fig. J3, Chapter 4 Visible Spectra of ZrCH, ZrCD andZrJCH (010) 166 laser scatter (000) (Oil) (020) (a) (012) - i 1 1 1 1 r (000) laser scatter (010) (b) (Oil) (020) (012) T | i i i i | i i i i | l i i i | i i i i | i 1 i i 1 1 0 500 1000 1500 2000 2500 displacement from (000) \/ c m - 1 Figure 4.5 DF spectra of the 15705 c m - 1 level of ZrCH, after population by absorption from (a) the (010) level and (b) the (000) of the ground state. Apart from laser scatter effects and a global difference in signal quality, the two traces are identical. attenuated laser scatter (002) (031) (110) (100) (022) (013) - i \u2014 i 1 \u2014 i \u2014 3000 TO TO TO 8 i a. - i i i | 500 \u2014 i 1 \u2014 i 1 \u2014 i 1 1 \u2014 i \u2014 i \u2014 i \u2014 i \u2014 1000 1500 2000 displacement from laser \/ cm\" 2500 3500 Figure 4.6 DF spectrum from the 16680 cm 1 level of ZrCH. The (100) and (110) features are present in this spectrum. Asterisks mark ZrC features or ZrCH features thereby blended. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 168 3.4), so X 3 E + , al2Z+ and blIf features of ZrC contaminate the spectrum; these are marked by asterisks in the figure and can be assigned using Table 3.2. The X 3 S + features blend with the (00u3) features of ZrCH; measurements of the resulting peaks fall between the known ZrC and ZrCH energies taken from unblended DF data. Nevertheless, two features in Fig. 4.6 that cannot be attributed to either ZrC or the (OU2U3) ground state vibrational manifold of ZrCH appear at 2832 and 3421 c m - 1 . The first measurement is similar to the coe(X2nr) = 2859 c m - 1 frequency of diatomic C H (1), while the 589 c m - 1 interval between them is close to the (010) energy of 596 c m - 1 . The simplest assignments for these levels therefore are (100) and (110) of the ground state. Unfortunately, the ZrCD data show no evidence of these levels, which are anticipated to lie near 2100 and 2561 c m - 1 by comparison with CD (1), so the possibility that these two levels represent another electronic state cannot be totally dismissed, although it seems unlikely. One vexing characteristic of some of the DF spectra of Z rCH (and ZrC) is that they show two independent, overlapped DF patterns from different simultaneously pumped laser bands; these were challenging to disentangle in early experiments before the low-lying vibrational structures of ZrC and ZrCH were fully understood. Fig. 4.6 just discussed is an example for which the two laser bands have different carriers. Fig. 4.7 is an example for which the two laser bands originate from ZrCH. In trace (a), two laser bands at 16198 c m - 1 , one cold and another hot from (001), are simultaneously pumped; the features they induce are labelled C and H respectively. The upper state of the hot laser band lies at 17059 c m - 1 ; the DF spectrum obtained by pumping from (000) to this level appears in trace (b). The 16168 c m - 1 ZrCD analogue of the 16198 c m - 1 cold ZrCH band is not overlapped by a hot band; the DF spectrum from its upper level appears in trace (c). The assignments in trace (a) require comparison of all three traces. For example, C(001) in trace (a) does not appear in trace (b), so the cold laser band must induce it; its Chapter 4 Visible Spectra of ZrCH, ZrCD andZr3CH 169 H(000) H(001) +C(000) laser scatter C(OOl) H(Ol l ) H(020) + C ( \u00b0 1 0 ) (a) ZrCH, 16198 cm\" C(002) H(021) H (012) A C(021) Z r l laser scatter (001) (b)ZrCH, 17059 cm 1 ZrO (\u00b0 2 0 > (Oil) (021) (c)ZrCD, 16168 cm -l (002) (021) 1 1 1 1 1 I 1 1 1 1 I 1 1 L _ - I 1 1 1 1 1 1 -500 -500 -1000 \u20221500 -2000 relative wavenumber \/ cm - l Figure 4.7 DF spectra from various levels of ZrCH and ZrCD. In trace (a), two laser bands at 16198 c m - 1 , one hot from (001) and another cold, are simultaneously pumped and give separate overlapped emission patterns. To assign the peaks in this spectrum, comparisons are made with the DF spectra in traces (b) and (c). See text for details. In trace (a), the letter C or H added to the assignment of each peak indicates whether the hot or cold laser band induces it. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 170 position yields the (001) assignment. The appearance of (001) in the ZrCD spectrum gives added confirmation, although, as Fig. 4.2 shows, the Fermi resonance in ZrCD can obfuscate such comparisons. DF spectra from two simultaneously pumped laser bands, such as those in Figs. 4.6 and 4.7, were often encountered in work on the Zr-bearing molecules. Table 4.1 Measurements (in cm - 1 ) of assigned excited vibrational levels in the X 2 Z + ground states of ZrCH, ZrCD and Z r 1 3 C H Level Z r C H a ZrCD Z r 1 3 C H 010 596 461 590 001 862 821 833 020 1164, 1189 918 1183 011 1452 1270 1421 030 1784 1372 002 1718 1635 1661 021 2013, 2039 1713 2009 040 1823 012 2302 2070 2249 031 2633 2158 050 2274 003 2565 2439 2486 100 2832 022 2859, 2887 2500 041 3227 2598 060 2723 013 3148 2862 3056 110 3421 032 2933 051 3038 070 3170 004 3408 3228 023 3276 042 3362 a Two entries given for a particular vibrational level represent its i = 0 and 2 angular momentum components; data for ZrCD do not resolve this structure and suggest a regular energy ordering (see text for discussion). Measurements of the available DF spectra have assigned large numbers of excited vibrational levels; these are listed in Table 4.1 and plotted in Fig. 4.8. The values listed are weighted averages determined in identical fashion to those for ZrC listed in Table 3.2; uncertainties in the methylidyne data are typically 5-10 c m - 1 . For ZrCH, fourteen (OU2U3) E\/crrf1 Z r C H Z r C D Z r 1 3 C H S _004_ _ H p _ Q 4 2 | 3000 2000 1000 0 1 3 070 \u2014 0 0 4 Oil 051 013 s M = I O O _ P i 3 _ I 060 ^ ^ - 003 041 \u2014 ^ 2 _ ^ 0 3 _ - 9 \u00ab _ \u00a3 _012_ 050 _012_ ^ J=c: 021 N 031 021 _012 030 040 b 002 021 002 002 020 020 ft. 030 -P-U-0 0 1 001 001 010 010 010 000 000 000 13 Figure 4.8 Ground state vibrational levels of ZrCH, ZrCD and Zr CH. The vibrational quantum numbers o ^ U g pertain respectively to the C - H stretch, the bend and the Zr -C stretch vibrational modes. - j Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr]3CH 172 ground state levels, not counting I degeneracies, plus two with x>\\ = 1 have been identified; for ZrCD, 22 of its (0u 2u 3) levels are observed. Mixing of the u 2 + 2o 3 = 4, 5, 6 and 7 Fermi polyads of ZrCD allows observation of (0o20) levels with these u 2 values that were undetected for ZrCH. Data from Fig. 4.3(b) for Z r 1 3 C H are also given. 4.3(b)(ii) Rotational analysis Previous work on isoelectronic Y N H and ZrN (4-6, 41-50) gave X 2 \u00a3 + symmetries for both species, which suggested the same result for ZrCH. High-resolution WSF data taken for some of the ZrCH and ZrCD bands shown in Fig 4.1 quickly confirmed this hypothesis. As an example, Fig. 4.9 shows a portion of the 15179 c m - 1 band, the lowest wavenumber cold band appearing in the spectrum; its upper state DF spectrum was given in Fig. 4.2(a). Six branches can be identified from the rotational structure; first lines with J' = 1\/2 appear for most of these. Structure from the 9 0 Zr - , 9 2 Z r - and 94Zr-bearing species is resolved; each line appears at higher wavenumber with increasing Zr mass. All of these facts, and analogy with the 17400 c m - 1 A -X system of ZrN, assign this band as A 2 ni\/ 2 - X 2 S + (0,0) . Various authors have proposed different notations to label the branches of such a transition. The Mulliken scheme (51) is used in Fig. 4.9, whereby the labels 3\/2R, 1\/2R, 1\/2P and 3\/2P denote, respectively, the four allowed values of J' - N \" = +3\/2, +1\/2, -1\/2 and -3\/2. Subscripts 1 or 2 denote the lower state spin component (vide infra) of each branch. The AJ = 0, \u00b11 selection rule allows both of them for the | J ' - N \" | = 1\/2 branches, which are therefore doubled, but only one for those with | J' - N \" | = 3\/2. This labelling scheme also applies for 2 S + or 2n 3\/ 2 upper states, but first lines of the branches vary in the three cases. All possible lower state combination differences were evaluated from the unblended lines of all (cold) bands of Z r C H recorded at high resolution, with duplicates averaged. Data fitting requires the usual 2 S + Hamiltonian: 9f = BN2 - D N 4 + yN-S, [4.4] F 2 \" F j \" 1\/2P(N) 15178.5 15178.0 wavenumber \/ cm --1 15177.5 15177.0 Figure 4.9 Low-N lines in the 1\/2P branch of the 15179 cm band of ZrCH. The presence of the 1\/2P(1) features shows that P' = 1\/2 for this band. The doubling of the lines is due to the ground state spin-rotation splitting; F1(N=J+l\/2) components lie to 90 92 94 the right of the F 2(J=N-l\/2) features in this spectrum, as indicated at N = 5. The Zr \/ Zr \/ Zr isotope structure is indicated for the N = 4 lines. 9 s ST* TO TO 8 oo Chapter 4 Visible Spectra of ZrCH, ZrCD andZr13CH 174 which is diagonal for a Hund's case (b) basis with energies F,(N) = BN(N+1) - DN 2 (N+1) 2 + ^ yN and F 2 (N) = BN(N+1) - DN 2 (N+1) 2 - \\ y(N+l), [4.5b] [4.5a] where J = N+l\/2 and N - l \/ 2 for the Fj and F 2 spin components respectively. Compared to ZrC, two factors limited the amount of available combination difference data for ZrCH. The rotational temperature of the methylidyne in the free jet expansion appears to be much lower (25 versus 70 K, as estimated from intensities of rotational lines); even the much lower B value, which affords higher N values at the same rotational energy, cannot compensate for it. This is difficult to understand since the experimental conditions for ZrC and ZrCH were essentially the same except for the higher C H 4 concentration in the plasma (8% versus 1%). The much smaller Zr isotope shifts in ZrCH also limit the data. Most of the bands of both ZrC and ZrCH have Zr shifts opposite in sense to those in Fig. 4.9. Those of ZrC are generally large; in most cases, the R-type (i.e., Rj and R 2 ) band heads of 9 4 Z r C and 9 2 Z r C usually lie below the first R-type lines of 9 2 Z r C and 9 0 Z r C respectively, and produce widely separated R-type structures with mostly unblended lines for all three isotopomers. In ZrCH bands, however, 1\/2R heads of 9 4 Z r C H and 9 2 Z r C H generally both appear between the first line and head of the corresponding 1\/2R branch of 9 0 Z r C H ; for the minor isotopomers, combination differences between 1\/2R^ and 1\/2R2 lines are often lost in the congestion. Moreover, combination differences between l\/2Rj (or 1\/2R2) and 3\/2P2 are scarce because of the weakness of the latter branch. Nevertheless, sufficient ground state combination differences were obtained for least squares fits for each of the six most abundant isotopomers: 9 0 Z r C H , 9 2 Z r C H , 9 4 Z r C H , 9 0 Z r C D , 9 2 Z r C D and 9 4 Z r C D . Ground state constants obtained from these fits appear in Table 4.2. The spin-rotation constants agree well with the expected scaling: 175 [4.6a] Chapter 4 Visible Spectra of ZrCH, ZrCD andZr13CH y B Only for 9 0 Z r C H was a well-determined centrifugal distortion constant D obtained; for the remaining isotopomers, it was fixed according to the following scaling law: D r \\ 2 [4.6b] Table 4.2 Molecular constants3 and structure of the X 2 E + , u = 0 levels of various isotopomers of zirconium methylidyne species B 10 7D y rms #b N c 90ZrCH 0.394195(10) 2.57(45) -0.018857(23) 0.000261 47 17 9 2 Z r C H 0.393143(11) 2.55 d -0.018788(47) 0.000361 34 12 9 4 Z r C H 0.392125(16) 2.54d -0.018728(70) 0.000472 31 11 9 0ZrCD 0.337843(7) 1.88d -0.016268(28) 0.000288 46 15 9 2 Z r C D 0.336896(14) 1.87d -0.016259(58) 0.000442 34 12 9 4 Z r C D 0.336002(17) 1.86d -0.016190(62) 0.000397 27 9 Structure 9(>ZrCH 9 2 Z r C H 9 4 Z r C H weighted mean r 0 (Zr-C) \/ A 1.830642(84) 1.83063(12) 1.83073(16) 1.830652(62) r 0 (C-H) \/ A 1.08682(48) 1.08681(72) 1.08611(95) 1.08671(37) a A l l constants in c m - 1 units except as indicated, with 3a errors in parentheses bNumber of combination differences used in least squares fit cHighest value of quantum number N appearing in data set d Fixed at this value in the least squares fit For each pair of isotopomers of equal Zr mass, an r 0 structure was determined from their rotational constants; these results were averaged. The C - H bond length agrees well with the diatomic r e (C-H) = 1.12 A value (1) and is essentially the same as that determined for other M C H ground states (36-40), while r 0 (Zr-C) is greater than in either the X 3 Z + state (1.8066 A) Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 176 or a!Z + state (1.7394 A) of ZrC. Further insight comes from applying arguments of Barnes et al. (38), who noted the increase in ground state metal-ligand bond lengths of the isoelectronic TiN, ScO and TiCH series (r 0 = 1.583 (52), 1.668 (53) and 1.728 A (38) respectively). They attribute the relatively short bond length of T iN to a good energy match between the metal 3^ 7i and ligand 2pm atomic orbitals (AOs) and the resultant strongly bonding 37t molecular orbital. The drop in ionisation potential (IP) in the N , O, C series worsens this match, reducing the 3TC bonding character and increasing the bond length accordingly. The isoelectronic series formed by replacing the first row TMs with their isovalent second row counterparts, viz., ZrN, Y O and ZrCH, behaves identically: their increasing r 0 bond lengths of 1.697 (49), 1.790 (54) and 1.831 A are due to the decreased bonding character of the 47i molecular orbital (metal 4dn AO + ligand 2pn AO) caused by the decrease in ligand IP. The rather large spin-rotation constant y is also interesting. This parameter has been determined for many isovalent molecules, as listed in Table 4.3. As discussed in Chapter 2 (see Eq. [2.104]) and noted by Simard et al. (64), it has two contributions, one of first order and another of second order. The first-order contribution, referred to as y S R in Eq. [2.104], is an interaction between the rotational and electron spin magnetic moments. Only for molecules containing atoms with very small spin-orbit couplings does this contribution dominate. Otherwise, particularly for TM-containing molecules, the second-order contribution dominates. This second-order contribution, referred to as y s o in Eq. [2.104], results from a cross term between the Coriolis interaction operator #C 0 r = - B ( N + L \" + N - L + ) [4.7] and the spin-orbit Hamiltonian given by Eq. [2.93]: e e Both !HQ0T and # \u00a7 0 connect 2 E + and 2n.\\\/2 states, and the value of y s o is given by (64) Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 177 y = 2 y < 2 ^ - l \/ 2 I B L - \\r\\ 2 n 1 \/ 2 >(ri 2 n 1 \/ 2 |Z e a e l+s -1 2 \u00a3 1 \/ 2 ) [ 4 9 ] T, E ( T ! 2 n ) - E ( 2 S ) The summation is taken over all 2 T I i \/ 2 states in the molecule. The 2 \u00a3 + state of interest is the ground state, so the denominator is always positive, but the a e term in Eq. [4.9] dictates a positive or negative contribution from each 2TI state according as it is regular or inverted. Table 4.3 Comparison of spin-rotation constants* for X 2 S + states of various isovalent species Molecule y 0 \/ c m - 1 Reference ScO 0.000107324(40) 55 ScS 0.0032(3) 56 ScNH 0.00266(90) 10 TiN -0.00174144(13) 57 TiCH -0.00587(6) 38 Y O -0.000307726(10) 58 YS 0.001408915(20) 59 Y N H -0.001838(24) 6 Z r O + -0.0003(3) 60 ZrN -0.00258(3) 49 ZrCH -0.018857(23) present work LaO 0.002201740(40) 61 LaS -0.000775(18) 62 LaNH -0.002461(76) present work b H f N c -0.05457(57) 63 c a A l l values are quoted in c m - 1 units for the most abundant isotopomer, with 3o errors in parentheses bSee Chapter 5 of this thesis T h e authors express some uncertainty over the assignment of the observed 2 E + state as the ground state If only one 2 n state contributes significantly, and the electron configurations of the 2 n and 2 2 states differ only by one electron of pn and pa character respectively, then the two states may be regarded as mutual, unique perturbers of each other and are said to satisfy the postulate of \"pure precession\" (65, 66). Under these conditions, if the 2 n and 2 E + states have identical potential curves, then y(22Z+) = p( 2H), and Eq. [4.9] reduces to Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 178 4 A R Y(2s+) = p ( 2 n) = 4 A B . [4.io] E ( 2 n ) - E ( 2 S ) This is not the case for the ground state, although it does apply to good approximation to the A2Ur and B 2 E + states of many of the molecules listed in Table 4.3; this point is addressed later. In the application of Eq. [4.9] to the X 2 S + states of the molecules in Table 4.3, two 2TI states are particularly relevant. One, the A 2 I L , state, results from promoting the lone valence electron, of predominantly nso metal character, where n = 3, 4 or 5 depending on the metal, into a predominantly (n-l)fi&i antibonding orbital. This state is generally well characterised for many of these molecules; where identified, the transition to it lies in the visible region, e.g., its Q. = 1\/2 component lies near 15179 c m - 1 for ZrCH. Usually, the spin-orbit constant of this state is fairly insensitive to the ligand, depending mostly on the metal dn electron, although this is difficult to verify for Z rCH (vide infra). The other state results from promoting an electron from the filled ligand 2p% (or 3pn) bonding orbital to the aforementioned nso orbital. The resulting (pn)3 (so)2 configuration generates an inverted state usually referred to as A\" 2 n , . These states are generally believed to lie below their A 2 n r counterparts and are comparatively poorly understood; among the molecules in Table 4.3, it has only been observed tentatively for Y N H as a Q. = 1\/2 level lying about 460 c m - 1 below the A 2 n r state (6). Contributions to y ( X 2 E + ) from these two states carry opposite sign, and often nearly cancel each other, as seen by its small magnitude for many of the species listed in Table 4.3. There are, however, three notable exceptions. The largest |y| occurs for HfN, but since Ram and Bernath express some doubt that the state in question is actually the ground state (63), it is ignored in the present discussion. Of the remaining molecules, T iCH and ZrCH stand out with much larger |y| values than the others; that the two methylidynes should do so is considered no coincidence. As discussed Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 179 in Chapter 3, the relatively low IP of carbon causes profound differences in the electronic structures of T M monocarbides and their isoelectronic mononitrides. The same effect appears to be present here; the low IP creates a better energy match between the metal d% and ligand pn orbitals, which in turn greatly stabilises the % bonding MO. This results in a rather lower-lying A\" 2 I I ; state and a large contribution to the ground state spin-rotation constant, to the extent that it is overwhelmingly larger and more negative than in other similar molecules. The y value for ZrCH is much more negative than in TiCH; evidently the A\" 2 n z state must lie much lower in ZrCH than in TiCH. 4.3(c) Levels of the A 2 H State in the 15100-15800 cm\"1 Region 4.3(c)(1) Assignment of the A 2 n i \/ 2 and A 2 n 3 \/ 2 , v = 0 levels Fig. 4.10 is a detail of Fig. 4.1 showing the set of cold WSF bands observed for both ZrCH and ZrCD in the 15100-15800 cm\" 1 region. Low-resolution WSF data for Z r 1 3 C H were also recorded in this region to obtain A E ( 1 2 C - 1 3 C ) isotope shifts of most of the ZrCH bands. High-resolution spectra for all but the ZrCD band at 15597 c m - 1 have determined their P' values and A E ( 9 0 Z r - 9 4 Z r ) isotope shifts; these data are given in the figure. The isotope shifts and P' values help assign the spin-orbit and vibrational structure of these bands. The lowest wavenumber bands of ZrCH and ZrCD at 15179 and 15189 c m - 1 have already been assigned in Section 2.3(b)(i) as A 2 H ] \/ 2 - X 2 Z + (0,0) for each molecule. These assignments are supported by not only the first lines of the bands but also the observed upper state A-doubling. For a 2 n 1 \/ 2 level, the energy splitting ATj-e = T y - Te between e and \/ parity components of a J level goes approximately as p(J+l\/2); for 2 n 3 \/ 2 levels, ATfe is much smaller and goes approximately as J 3 (67). The ATfe plot in Fig. 4.11 for the 15179 c n r 1 9 0 Z r C H level leaves little doubt that P = 1\/2; p = -0.207 c m - 1 can be estimated as the slope of the plot (although weak perturbations, not obvious at this scale, disrupt the level pattern somewhat). The related P' = 3\/2 spin-orbit component could not be conclusively identified, Chapter 4 Visible Spectra of ZrCH, ZrCD andZr1JCH 180 (a) A E ( 1 2 C - 1 3 C ) A E ( 9 0 Z r - 9 4 Z r ) 3\/2 1\/2 1\/2 0 9 -0.24-0.13 0.82 o r - I m o 00 in 3\/2 -0.25 1\/2 -4 -0.31 00 m o r-( b ) 90^, 94,, N AE( Zr - Zr) 1\/2 0.82 1\/2 -0.20 3\/2 -0.27 1\/2 -0.33 m m m o ON in 15800 15600 15400 wavenumber \/ cm -1 15200 Figure 4.10 Stick spectrum of cold WSF bands of (a) 9 0 Z r C H and (b) 9 0 Z r C D in the 15100 - 15800 c m - 1 region. High-resolution data for all but one of these bands, whose P value is 12 13 90 94 therefore unknown, have been recorded. The AE( C - C) and AE( Zr - Zr) isotope shifts (in cm - 1 ) have been determined from pulsed and cw laser spectra respectively. -0.5 H -1.0 H I r ^ \u20221.5 -2.0 -1 Figure 4.11 A-doubling in the 15179 cm level of 90 ZrCH. P' = 1\/2 follows from the linearity of the plot. The A-doubling constant p = -0.207 cm -1 0.9 0.8 0.7 \u00a7 0.6 \u2022o <L> I 0.5 <L> 0.4 H 0.3 0.2 (J + 1\/2)2 Figure 4.12 Reduced rotational energies of the 15179 and 15428 c m - 1 levels of 9 0 Z r C H , plotted as filled and open circles respectively. The same J-dependent quantity has been substracted in both cases (see text for details); the lower-lying level clearly has the larger B value. TO* 5 \u00ab\u2022\u00ab\u00ab.. o TO TO TO 8 Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 182 however. Its isotope shifts should equal those of the P' = 1\/2 component since spin-orbit constants are mass-independent, and even though the P' = 3\/2 band at 15428 c m - 1 closely satisfies this condition, other factors cast doubt on its assignment as A 2 n 3 \/ 2 - X 2 E + (0,0). One of these is the unreasonably small A = 249 c m - 1 spin-orbit constant that results. For the molecules in Table 4.3, the A 2 I I state derives predominantly from a one-electron metal dn valence electron configuration. This electron essentially determines the value of A, which is rather ligand-insensitive; Table 4.4 gives this value for most of the molecules in Table 4.3 (for purposes of later discussion, those of p(A 2II) and y(B 2 S + ) are also given, where available). The A value derived here is much less than those for either ZrN or Z r O + and argues against the proposed assignment. Table 4.4 Some fine structure constants of several molecules isovalent to Z rCH (in cm *) Molecule A(A 2n r) p(A 2H r) y(B2E+) Reference(s) ScO 115 -0.066 -0.067 53, 68 ScS 112 -0.058 56, 69 a ScNH 102 -0.184 10 Y O 429 -0.150 -0.144 54 YS 457 -0.169 -0.152 70, 71, 72 Y N H 444 -0.283 -0.215 6 Z r O + 595 -0.068 60 ZrN 574b -0.104 -0.098 43, 48, 49 LaO 863 -0.241 -0.253 61, 73 LaS 868 -0.107 -0.096 62, 74 LaNH 1010 -0.230 present work c aValue of A estimated by author from bandhead wavelengths quoted in this work b Value of A determined for 9 1 Z r N cSee Chapter 5 of this thesis The effective rotational constant B e f f rj of the 15428 c m - 1 level further argues against an A 2 n 3 \/ 2 , o = 0 assignment. According to the Mulliken formula (51), each Hund's case (a) spin-orbit component of a doublet state has Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 183 where B is the true mechanical constant. Since A 2 n is regular, B e g; 3 \/2 > B e f f y 2 1 S expected. Rotational perturbations in the two levels preclude accurate determination of these constants, but a plot of their reduced rotational energies, taken as T Q = 1 \/ 2 ( J ) - 15179 - 0.35(J+l\/2) 2 and T Q = 3 \/ 2 ( J ) - 248.3 - 15179 - 0.35(J+l\/2) 2 in Fig. 4.12, shows that B e f f 3 \/ 2 < B e f f 1 \/ 2 ; i.e., the two levels cannot be interpreted as spin-orbit components of the same state. Here, TQ ( J ) is the mean of the e- and \/-parity energies. Another difficulty associated with the proposed assignment of the 15428 c m - 1 level arises from its DF spectrum, shown in Fig. 4.13(a). The peak intensities, essentially Franck-Condon factors, should carry only vibrational dependence; i.e., the DF spectra of Fig. 4.13(a) and Fig. 4.2(a) should be identical, which is clearly not the case. The (002) feature is much more pronounced for the 15428 c m - 1 level, producing a local maximum in the u 3 progression. On the other hand, the pattern in Fig. 4.13(b) from the ZrCD analogue level at 15441 cm - 1 , does appear to satisfy the intensity requirements: if allowance is made for the ground state Fermi resonance as in Fig. 4.2(b), the spectrum is essentially a VJ3\" progression with no local minimum. The difference in the two traces of Fig. 4.13 is difficult to rationalise. From its isotope shifts and rotational structure, it seems apparent that the upper state of the 15428 c m - 1 Z rCH band is the zero-point level of a P' =3\/2 state; what remain unclear are its other good case (a) quantum numbers (if it has any). Its position makes it the most reasonable candidate for the zero-point level of A 2 n 3 \/ 2 , but other evidence suggests this is not the case. Two other possible assignments of this level, based on the electronic structure of other isovalent molecules, are now considered. Most of the molecules in Table 4.3 have fairly strong A 2 n r - X 2 2 + and B 2 S + - X 2 E + systems in the visible region that are well characterised. Less understood for the most part are Chapter 4 Visible Spectra of ZrCH, ZrCD andZr3CH 184 laser scatter -i 1 r 0 -500 -1000 -1500 -2000 displacement from laser \/ c m - 1 Figure 4.13 DF spectra of the (a) 15428 c m - 1 level of Z rCH and the (b) 15441 c m - 1 level of ZrCD. The intensity profile of the u 3 progression shows a local maximum at u 3 = 2 for ZrCH but steadily decreases for ZrCD. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr]3CH 185 two other doublet states lying somewhat below A2Ylr One of these, A\" 2 I L , was previously discussed in reference both to the observation in Y N H of its P = 1\/2 component about 460 c m - 1 below A 2 n i \/ 2 (6), and to its negative contribution in ZrCH to the ground state spin-rotation constant. Y N H is the only molecule in Table 4.3 for which this state has been identified. The 15428 c m - 1 level of ZrCH, however, does not represent its A \" 2 n 3 \/ 2 , v = 0 state, because as argued above, the large negative value of y ( X 2 E + ) indicates a low-lying A\"2ny state. This contrasts with Y N H , for which the much smaller y ( X 2 2 + ) = -0.00184 c m - 1 can be attributed to the proximity of A\" 2 n , and A 2 n r , which nearly cancels their contributions to y in Eq. [4.9]. The A'2Ar state can also be considered as the source of the 15428 c m - 1 level; it corresponds to shifting the lone valence electron from the Zr (5srj) + C(2pn) orbital (whose occupation yields the ground state) to the Zr(4dS) orbital. This state has been previously observed in 2 n - 2Ar systems of isovalent LaO (73, 75, 76) and LaS (74) recorded with conventional high temperature sources. Others species, such as ScO (77, 78) and Y O (77, 79), reveal nominally forbidden A' 2Ar - X 2 S + systems through A' 2Ar ~ 2Tir mixing. This mixing occurs either through the spin-orbit Hamiltonian of Eq. [4.8], which couples states with A A = - A S = \u00b11 and AO. = 0 (e.g., 2 n 3 \/ 2 and 2 A 3 \/ 2 ) , or through the Coriolis operator of Eq. [4.7], which couples states with AL = 0 and AQ = A A = \u00b11, (e.g., 2Yly2 and 2 A 3 \/ 2 , or 2 n 3 \/ 2 and 2 A 5 \/ 2 ) . The spin-orbit mixing is independent of rotation and accounts for the A ' 2 A 3 \/ 2 - X 2 S + subbands of both ScO and Y O (77-79). The Coriolis coupling, on the other hand, increases with rotation, consistent both with the presence of A' 2 A 5 \/ 2 - X 2 S + features in the high temperature spectra of ScO (77, 78) and Y O (77), and with their absence from the jet-cooled Y O spectra of Simard et al. (79). The above discussion suggests that the 15428 c m - 1 level represents an A ' 2 A 3 \/ 2 , u = 0 level whose oscillator strength derives from spin-orbit mixing with the A 2 n 3 \/ 2 state, or possibly the reverse, that it is nominally A 2 n 3 \/ 2 , u = 0 with partial spin-orbit quenching by the Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 186 A' 2 A 3 \/2 level. It bears mentioning that the A 2 n 3 \/ 2 , u = 0 level of ZrN is severely perturbed (41, 43, 49) by another nearby Q = 3\/2 level, but several attempted deperturbations by Peers (43) suggest that the perturber is not simply a single state of 2 A 3 \/ 2 symmetry. To summarise, consideration of the available spectroscopic evidence yields no definitive assignment for the 15428 c m - 1 level of ZrCH. While its isotope shifts, P = 3\/2 value and energy make it the best available candidate for the A 2 n 3 \/ 2 , o = 0 level, other factors, including the unexpectedly small value of the A 2 n state spin-orbit constant, its anomalous effective rotational constant, and the marked dissimilarity of its DF spectrum from that of the A 2 n 1 \/ 2 , o = 0 level argue against such an assignment. The large magnitude of y ( X 2 S + ) rules out an A\" 2 n 3 \/ 2 assignment. The most probable assignment appears to be a mixture of A 2 n 3 \/ 2 and A ' 2 A 3 \/ 2 character. Similar spin-orbit anomalies occur for TiCH; although P = 1\/2 and 3\/2 levels appear where its A 2 n state might be expected, there are no spin-orbit intervals of about 157 c m - 1 as for TiN (52, 80, 81). 4.3(c)(ii) Remaining levels up to 15800 cm - 1 : Vibrational structure of the A 2 n r state The v2(bend) fundamental The difficulty in assigning even the origin levels of the A 2 n r state suggests little hope of successfully identifying its vibrational structure. Nevertheless, definite conclusions can be drawn; these are given after a discussion of the vibrational structure expected for a 2 n r electronic state in a linear triatomic molecule. ' Jungen and Merer (82) have already discussed this in detail; only a review need be given here. The v 3 (Zr-C stretch) is totally symmetric and carries no vibrational angular momentum, so there is nothing unusual about, for example, the (001) level or any other member of the (00u3) progression; their structures are essentially the same as that of the (000) level. The same is true for v i , although this is irrelevant here since its expected vibrational frequency of about Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 187 2800 c m - 1 is greater than the range over which the spectrum has been studied. However, the v2(bend) vibration carries vibrational angular momentum, so its level structure is different. The structure of the bending vibrational manifold up to u 2 = 3 is shown in Fig. 4.14; for each VJ2, two sets of vibrational levels appear, corresponding to the two values of S = \u00b11\/2. As explained by Jungen and Merer (82), the Renner-Teller effect, described in Section 2.2(b), lifts the degeneracy within each 2 component of the various angular momentum states. The splittings depend on the strength of the vibronic coupling, which can be quantified by the dimensionless Renner parameter e; the plot in Fig. 4.14 assumes A \u00bb eco2. The energies of the various levels in terms of their n 2 , K = |\u00b1 A \u00b1 \u00a3 | and 2 quantum numbers, written to terms up to order e2, are (82) E(u 2 , K , 2) = Q 2 ( n 2 + 1 ) \u00b1 r - {e 2(0 2 (u 2 +l)(l \u00b1 AK2\/r), [4.12a] where the quantity r is given by r 2 \\^K2 + s 2 c o ^ [ ( u 2 + l ) 2 - K 2 ] . [4.12b] The first term in Eq. [4.12a] is the harmonic vibrational energy; the others represent the combined effect of the spin-orbit and Renner-Teller couplings. For each vibrational level, a pair of levels with K = u 2 +l exists, one in each spin-orbit component; these have nearly the full spin-orbit separation A of the electronic state; if Eq. [4.12] is taken to order s4, the effective spin-orbit coupling constant is (83) A e f f = A [ l - J 8 2 K ( K + l ) ] . [4.13] Other lower, non-negative values of K also appear: K = ( u 2 + l ) -2 , (u 2 +l) -4 , . . . . [4.14] Each K 4- ^ 2 + l or 0 appears four times, one pair within each spin-orbit component; for each pair, the two values of P = K \u00b1 1\/2 are present and form the equivalent of a Hund's case (a) coupled state with.effective spin-orbit coupling A eff =+^ 2 t t 2 AK(u 2 +l) \/A-, [4.15] Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 188 2 2\u00a3i\/2(c) 3 3\/2 Z=r________________________________________________Z_________Z=Z_^ ZZ^  2A y(a) A 9 \/2 3\/2 1\/2 1 1\/2 A 7 \/ 2 1\/2 = 2A r(a) -2 1 \/ 2(c) 2n ((a) 2 \u00b0 7 \/ 2 S \/ 2 2n,(a) 2I 1 \/ 2(c) 1 3\/2 2 A A 5 \/ 2 2 A A 3 \/ 2 2 S 1 \/ 2 ( c ) 0 3\/2 0 1\/2 3\/2 1 \/2 Figure 4.14 Vibronic energy levels of a linear triatomic molecule in a IL. electronic state for u 2 = 0, 1,2 and 3. The (a) and (c) labels refer to the Hund's coupling case that best describes the level. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 189 where r is given by Eq. [4.12b]; this effective coupling constant is much less than the true A. The \u00b1 sign indicates that the effective spin-orbit coupling is inverted in the upper spin-orbit component and regular in the lower spin-orbit component if A > 0, and vice versa if A < 0. If o 2 is odd and A is large, a 2 \u00a3 level of undefined Kronig symmetry also appears in each spin-orbit component. Fig. 4.14 can be compared to the observed spectrum depicted in Fig. 4.10 to identify the bending fundamental in the A 2 TI state. From their P = 1\/2 and 3\/2 values, the upper states of the bands at 15680 and 15705 c m - 1 can be assigned respectively as the 2 E and 2 A 3 \/ 2 components of A 2 ni \/ 2 (010). Their 25 c m - 1 separation indicates a non-negligible Renner-Teller coupling in this state; this is discussed later. Beyond their P values, other evidence outlined below supports the assignments of these levels. First, the two bands have similar A E ( 9 0 Z r - 9 4 Zr ) isotope shifts, which indicates that they share the same upper state (U1U2O3) values. Also, from Table 4.1, the ground state bending frequency drops by about 23% upon deuteration. Taking the excited state bending frequency as the interval between the 15680 and 15179 c m - 1 bands yields a>2 = 501 c m - 1 , which should drop to 388 c m - 1 in ZrCD assuming the same percentage change as in the ground state. Adding this to the observed A 2 n i \/ 2 - X 2 E + (0,0) ZrCD band position gives 15577 cm - 1 , in excellent agreement with the observed P' = 1\/2 band of ZrCD at 15576 c m - 1 . The same argument applies to the low resolution Z r 1 3 C H data. The ground state bending frequency is about 1% less than that of Z r 1 2 C H ; the same decrease in the excited state yields (02' = 496 c m - 1 , which, added to the observed 15191 c m - 1 Z r 1 3 C H origin band position, gives 15687 c m - 1 ; this agrees well with an observed band at 15680 c m - 1 , although its P' was of course not determined. The A E ( 9 0 Z r - 9 4 Z r ) isotope shifts of the ZrCH and ZrCD P' = 1\/2 bands are also very similar. In further agreement are the DF spectra of these bands, shown in Fig. 4.15; each of them is essentially a 0 3 \" progression of diminishing intensity built on the 13, Chapter 4 Visible Spectra of ZrCH, ZrCD andZrJCH 190 laser scatter (010) 1 r -2000 -2500 displacement from laser \/ cm - l Figure 4.15 DF spectra from the (a) 15680 cm 1 level of Z rCH and the (b) 15576 cm 1 level of ZrCD. Each spectrum consists mainly of a progression in u 3 built on the (010) level; the two levels can be assigned as the A n 1 \/ 2 (010, P' =1\/2) levels of their respective isotopomers. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 191 X 2\u00a3 +(010) level; the extra features in the ZrCD scan are due to the ground state Fermi resonance. The 15597 c m - 1 band of ZrCD is too weak to record at high resolution to confirm its P' value and match with the 15705 c m - 1 Z rCH band, but other circumstantial evidence supports a P' = 3\/2 assignment. The intensities of the 15597 and 15576 c m - 1 bands of ZrCD are in about a 1:2 ratio; this is also the case for the corresponding 15705 and 15680 c m - 1 Z rCH bands. In addition, the DF spectra from the upper states of the 15597 and 15705 c m - 1 bands share the same features; they are essentially the same as those in Fig. 4.15. The rotational constants of the 15680 and 15705 c m - 1 levels show the proper behaviour as well. The bending vibration acts to lessen the average inertial moment of the molecule, which should increase the rotational constant of the u 2 = 1 level, thereby increasing the N \" value at which the 1\/2R head of its cold band appears. This is indeed the case, as these two bands have heads at N \" = 8 and 5 respectively, higher than the N \" = 3 value of the origin band. The same behaviour is observed for ZrCD; the 1\/2R branch of the P1 = 1\/2 component of the 2 0 band forms a head at least as high as N \" = 6; the branch intensity has completely vanished by this point. The origin band at 15189 cm - 1 , on the other hand, has a band head at N \" = 3. To summarise, the available data show that the 15680 (15576) and 15705 (15597) c n r 1 levels of Z rCH (ZrCD) respectively represent the 2 \u00a3 and 2 A 3 \/ 2 components of the A 2 n 1 \/ 2 (010) vibrational level. The splitting of these components, about 20 c m - 1 , indicates that the A 2 n state is vibronically coupled to another electronic state. Two possibilities for this state based on the A A = \u00b11 selection rules are the A ' 2 A r and B 2 E + states. As suggested above, the P = 3\/2 level at 15428 c m - 1 may have some A ' 2 A r , v = 0 character and therefore play a role in this perturbation. The v 3 ( Z r - C stretch) fundamental The discussion so far has covered all cold bands of Z rCH and ZrCD in the 15100-Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 192 15800 c m - 1 region save one of each isotopomer, whose upper levels lie at 15621 and 15623 c m - 1 respectively, or 442 and 434 c m - 1 above their A 2 n 1 \/ 2 , v = 0 levels. Given that the ground state v 3 fundamentals appear at 862 and 821 c m - 1 respectively, it seems improbable that these are the v 3 fundamentals of A 2 n 1 \/ 2 , but there is evidence to support this surprisingly large (nearly 50%) drop in a)3. First, high-resolution WSF data show that they each have the required P = 1\/2 value. Next, their DF spectra, shown in Fig. 4.16, can be considered. In trace (a), for ZrCH, the u 2 \" progression has rapidly diminishing intensity with o 2\"; reasoning similar to that applied to the DF spectrum of A 2 n i \/ 2 , v = 0 in Fig. 4.2 indicates that u 2 ' = 0. Also, the u 3 \" progression, with a local intensity minimum at U3\" = 1, reveals a node in the excited state vibrational wavefunction, consistent with u 3 ' ^ 0; the level position makes u 3 ' = 1 the most reasonable assignment. The same arguments can be applied to trace (b) for ZrCD, once the ground state Fermi resonance has been taken into account. The clearest evidence comes from isotope shift data, since co3 is proportional to the square root of the Wilson G 3 3 matrix element (in the approximation that the G matrix is diagonal): G 3 3 = l \/m^ + l \/ m Z r . [4.16] Table 4.5 Calculated and observed isotope shifts of co3 for various states of ZrCH(D) X 2 Z + A 2 n co 3 ( 9 0 Zr 1 2 CH) \/ cm\" 1 862 442 a calculated observed calculated observed Aco 3 ( 1 2 C - 1 3 C ) \/ cm\" 1 30 29 15 13 A ( \u00bb 3 ( 9 0 Z r - 9 4 Z r ) \/ c m - 1 2.16 1.11,1.09\u00b0 1.13,1.15\u00b0 G 3 3 1 \/ 2 \/ (mol\/g) 1 \/ 2 : 9 0 Z r 1 2 C H and 9 0 Z r 1 2 C D , 0.30732; 9 0 Z r 1 3 C H , 0.29671; 9 4 Z r 1 2 C H and 9 4 Z r 1 2 C D , 0.30655 a434 cm\" 1 for 9 0 Z r 1 2 C D \u2022Values for Z r 1 2 C D Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr CH 193 laser scatter \" T 1 1 ( 1 r - -1 i i i | i i i i | I r -0 -500 \u20221000 \u20221500 -2000 -2500 displacement from laser \/ cm -1 Figure 4.16 DF spectra from the (a) 15621 cm 1 level of ZrCH and the (b) 15623 cm 1 level of ZrCD. These are the A TLL\/2 (001, P = 1\/2) levels of their respective isotopomers, as indicated by the intensity distributions in the u 2 \" a n d u 3 \" progressions above. See text for details. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr]3CH 194 This proportionality holds to good approximation for the ground state; from Table 4.1, a 3 (Zr 1 3 CH) \/\u00a9 3 (Zr 1 2 CH) = 0.966, while mass data give G 3 3 1 \/ 2 ( Z r 1 3 C H ) \/ G 3 3 1 \/ 2 ( Z r 1 2 C H ) = 0.965. Table 4.5 compares the predicted and observed isotope shifts of \u00a9 3 for the X2S+ and A 2 TI state of Z r C H and ZrCD; their agreement supports the A 2 n 1 \/ 2 (001) - X2S+(000) assignment of the 15621 (15623) cm\" 1 band of ZrCH (ZrCD), and the 15100-15800 cm- 1 region is now completely assigned. 4.3(d) Levels above 15800 cm\" 1 4.3(d)(i) The 15800-16250 cm\" 1 region Fig. 4.17 shows a stick spectrum of the cold bands in the 15800-16250 c m - 1 region for ZrCH and ZrCD. Several weak bands appear in this region for which high-resolution data, and therefore their P' values, could not be obtained, especially for ZrCH. In fact, DF spectra of their upper levels are usually the only evidence of their carrier. These bands will not be further discussed. The vibrational frequencies oo 2 = 501 (387) c m - 1 and co3 = 442 (434) c m - 1 of the A 2ny 2 state of ZrCH (ZrCD), determined from the previous discussion, help assign higher vibrational structure of this state, with the help of Fig. 4.14. The pair of 2Q3Q bands of ZrCH should appear about 442 c m - 1 above the 2 0 band with a similar appearance. The 16112 and 16158 c m - 1 pair of bands is overwhelmingly the most suitable choice. Their relative intensities and P' values are correct, and they share essentially identical DF patterns with strong emission to the X2S+(010) level and little else. Their A E ( 1 2 C - 1 3 C ) isotope shifts of about 13 cm\" 1 each are nearly identical and match the expected value based on corresponding data for the (0,0), 2Q and 3Q bands of the A 2ny 2 - X22+ system. The corresponding assignment is further substantiated by the 16007 and 16057 c m - 1 bands of ZrCD, which also satisfy all the above consistency checks where the data are available. The separation of the 2 S + and 2 A 3 \/ 2 components is slightly different in the various o 2 ' = 1 bands. In ZrCH, they are separated by 25 Chapter 4 Visible Spectra of ZrCH, ZrCD andZrJCH 195 (a) Z r C H P' 3\/2 1\/2 3\/2 A E ( 1 2 C - 1 3 C ) 14 13 8 A E ( 9 0 Z r - 9 4 Z r ) 0.82 0.77 00 m 00 00 O N m m oo oo m 00 s o m oo in (b) Z r C D p1 A E ( 9 0 Z r - 9 4 Z r ) 1\/2 00 lO 16200 O 3\/2 3\/2 1\/2 0.80 0.60 0.82 in o CN <N O o o O N m 3\/2 0.26 O N m 16000 wavenumber \/ cm - l m O N 00 in 3\/2 -0.12 B o in oo m 15800 Figure 4.17 ZrCH(D) bands in the 15800 - 16250 cm Region. FJigh-resolution data have 19 11 Qfl 94 generated P' values for most of these bands. The A E ( 1 Z C - C) and AE(\u2122Zr - \u2122Zr) isotope shifts (in cm - 1 ) have been determined from pulsed and cw laser spectra respectively. Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 196 and 46 c m - 1 in the 2 0 and 2 0 3 0 bands, while the corresponding separations in ZrCD are 21 and 50 c m - 1 . The vibronic coupling evidently carries a slight rj 3 ' dependence. The only other strong band of ZrCH below the 203o pair lies at 15988 cm - 1 ; its very rich DF spectrum appears in Fig. 4.3(a). The P' = 3\/2 value of this band rules out the assignment A 2 n 3 \/ 2 (010 , 2 E + ) - X 2\u00a3+(000), and there is no possible remaining A 2 n 1 \/ 2 - X 2 E + assignment. Its upper level might be postulated as dark, appearing only through mixing with the A 2 n state, but its strength indicates that it carries its own oscillator strength. Its Zr isotope shift of 0.82 c m - 1 suggests u 3 ' = 1, possibly built on the poorly understood 15428 c m - 1 level, which also has P' = 3\/2; however, there is no obvious match for it in the ZrCD spectrum. A number of other bands for both ZrCH and ZrCD have been investigated in this region at high resolution, but their P' values and band positions in Fig. 4.17 suggest no obvious assignments. 4.3(d)(ii) Evidence for the B 2 E + state: The 16548 cm\" 1 band The confused level structure of ZrCH beginning at about 16400 c m - 1 in Fig. 4.1 is mostly too dense to discern any trends from it, but the 16548 c m - 1 band has unusual branch intensity patterns with implications for the electronic structure. The origin region of this band is shown in Fig. 4.18. Its first lines show clearly that P' = 1\/2, and that only four branches are present, unlike all the other bands of ZrCH and ZrCD recorded at high resolution, which have six. At first glance this looks like a 2 Z + - 2 S + transition with Ri, R 2 , Pj and P 2 branches, but the ground state combination differences derived on this basis, A 2Fl(N) = R i t N - l ) - Pi(N+l) = (4B - 6D) (N+l\/2) 2 - 8D (N+l\/2) 3 - y [4.17a] and A 2 F 2 (N) = R 2 (N-1) - P2(N+1) = (4B - 6D) (N+l\/2) 2 - 8D (N+l\/2) 3 + y, [4.17b] do not agree with the rotational constants in Table 4.2. In fact, it happened that this was the first band recorded at high resolution and the A2F1(]Sr) and A 2 F 2 (N) combination differences obtained on this basis were equal, so the spin-rotation constant was assumed to be too small to distinguish in Eq. [4.17]. Given its small magnitude in other molecules (see Table 4.3), this 1\/2R,(N) 1 0 1\/2P2(N) 1 2 2 3 4 5 6 7 8 9 10 11 12 13 i 16548 16547 16546 16545 16544 laser wavenumber \/ c m - 1 Figure 4.18 A portion of the high-resolution spectrum of the 16548 c m - 1 band of ZrCH. The 1\/2R2 and 1\/2P1 branches are missing because of an intensity cancellation effect (see text for details). At low N , the same effect causes I\/IR-^ lines to be much weaker than 90 1\/2P2 lines, but their intensities gradually become more alike as N increases. Only ZrCH lines have been marked. 9 s S3. TO TO 8 I sO Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13 CH 198 conjecture did not seem unreasonable. The correct assignment of the four branches, consistent with the ground state combination differences from the six-branch bands at lower frequency, is 3\/2R 1 ; l \/2Ri , 1\/2P2 and 3\/2P2. The combination differences originally calculated for this band are actually A 2 F 2 1 (N) : =F 2 (N+1) -F 1 (N-1 ) = [ 4 ( B - y\/4) - 6D](N+l\/2) - 8D (N+l\/2) 3, [4.18] so the initial confusion is now understood: the combination differences of Eqs. [4.17] and [4.18] are equal if y is neglected, while the B value obtained from Eq. [4.17] is too small by y\/4. Of course, the absence of the 1\/2R2 and l\/2Pi branches should be explained; it stems from a peculiarity of \u00a31 = 1\/2 - 1\/2 transitions described by Kopp and Hougen (84) and by Lefebvre-Brion and Field (85). The electronic eigenfunctions of \u00a31 = 1\/2 states are Wang sums and differences of signed basis functions: | Q = l \/ 2 \u00b1 > = 2 - 1 \/ 2 { | Q = +l\/2> \u00b1 | Q = -l\/2>}. [4.19] Since the \u00a3i' - \u00a31\" = 0, \u00b11 selection rule applies strictly to the signed basis quantum number, an \u00a31 = 1\/2 - 1\/2 transition can have both parallel and perpendicular transition moments (py and p_l_). The total transition moment is the sum of these, so the intensity of the transition is i i . . . proportional to |p| = |p|| + p_J . If py and pj^ happen to carry opposite sign, intensity cancellation effects are possible; these occur in the 16548 c m - 1 band of ZrCH. The rotational linestrengths for 1\/2 - 1\/2 transitions listed by the above authors use different normalisation conditions; those in Table 4.6 use the Lefebvre-Brion and Field convention (85), for which PH = <n, Q = 1\/2 I p z I r|', \u00a31 = 1\/2) [4.20a] and p 1 = 2\" 1 \/ 2 <ri ,0 = - l \/ 2 | p x - \/ p y | T I ' , Q = 1\/2>, [4.20b] where the p, (\/ = x, y, z) are the space-fixed components of the dipole moment operator. From this table, the missing l\/2Pi and 1\/2R2 branches in Fig. 4.18 indicate that p_l_ = V2 U j | , and the 1\/2RT and 1\/2P2 branches therefore have an intensity ratio of Chapter 4 Visible Spectra of ZrCH, ZrCD andZr13CH I 1 \/ 2 R 1 i \/\u2122. f J V* A 1 \/ 2 P 7 Vl+ly 199 [4.21] which means that l\/2Rj is much weaker than 1\/2P2 at low J, but gradually increases in linestrength with J until they are nearly alike. This is indeed the case in Fig. 4.18. Similarly, [4.22] I 3 \/ 2 P 2 _ I 3 \/ 2 R 1 (J-1\/2)(J+1) J(J+3\/2) so that the 3\/2P2 branch is weak at low J compared to 3\/2Rj but catches up as in this previous pair of branches. This again is the observed intensity pattern for the 16548 c m - 1 band of ZrCH. Table 4.6 Rotational linestrengths for Q! - Q\" = 1\/2 - 1\/2 transitions Branch | < T 1 , , Q , = 1 \/ 2 , J > | T 1 , Q = 1 \/2,J>|2 3\/2P2(J = N - 1\/2) (J+l\/2)(J- l \/2)[ . nr]2 1\/2P2(J = N - 1\/2) l ^ P ^ J = N + l \/ 2 ) ( j + i \/ 23) ( ; - 1 \/ 2 > h r ^ ^ ] 2 l ^ R ^ J 1\/2R2(J = N + 1\/2) = N - l \/ 2 ) 3\/2R,(J = N + 1\/2) Since the upper state of the 16548 c m - 1 band is more nearly 2 n 1 \/ 2 rather than 2 \u00a3 + , the source of its p|| moment must be determined. The simplest answer is the B 2 E + state, which implies that this state lies much lower in ZrCH than in ZrN, for which it has T 0 = 24670 crcr 1 (41, 50) (for comparison, T 0 (A 2 n 1 \/ 2 ) = 17117 c n r 1 for ZrN (43) and 15179 c n r 1 for ZrCH). Chapter 4 Visible Spectra ofZrCYj, ZrCD and Zr13C\u00a5i 200 In this regard, Z rCH is similar to Y N H , whose A 2 n 1 \/ 2 and B 2 E + states lie respectively at 15204 and 16993 c n r 1 (6). Further investigation of ZrCH is warranted above 16500 c m - 1 to locate the B 2 E + state. The value of y(B 2 S + ) , compared to p(A2n), may indicate the extent of its interaction with A 2 H Table 4.4 gives the values for these parameters for several isovalent molecules; it can be seen that in most cases they are very similar, consistent with a \"pure precession\" unique perturber interpretation. For one noteable exception, polyatomic Y N H , the agreement is rather poor, but easily understood; the presence of two 2 ni \/ 2 states (from A and A\") less than 2300 c m - 1 below B 2 S + renders Eq. [4.10] inapplicable. It would be interesting to determine if ZrCH exhibits similar behaviour, because no other 2 n i \/ 2 states have been identified. Moreover, the B 2 S + state is potentially responsible for the large Renner-Teller effect in the u 2 ' = 1 features of the A 2 n i \/ 2 - X 2 S + system; data from this state would help confirm its role in this regard. For the same reason, the A ' 2 A r state is also of interest; further investigations to the red are also warranted. 4.4 Conclusions This chapter reports the first spectroscopic investigation of the zirconium methylidyne molecule. Its electronic spectrum contains more than fifty bands in the 15100-17600 c m - 1 region. High-resolution data from the strongest of these show that the molecule is linear in its ground state, as are all the other transition metal-bearing methylidynes (36-40); like isoelectronic ZrN and Y N H , its ground state has 2 S + symmetry. Simple arguments invoking the ligand ionisation potential qualitatively account for the r 0 (Zr-C) and large yo of the ground state. Ground state frequencies were determined for two of the three vibrational modes, v 3 (Zr-C stretch) and v2(bend), of the ZrCH, ZrCD and Z r 1 3 C H isotopomers, with a tentative Chapter 4 Visible Spectra of ZrCH, ZrCD and Zr13CH 201 determination of the V i ( C - H stretch) frequency. Large numbers of excited vibrational levels of the ground state have been identified from dispersed fluorescence spectra: 17 for ZrCH, 22 for ZrCD and 9 for Z r 1 3 C H . In ZrCH, the splitting of the I = 0 and 2 vibrational angular components of the (02*1)3) ground state levels with u 3 = 0, 1 and 2 was determined, giving g 2 2 = 7.0 c m - 1 . A Fermi resonance in ZrCD quenches this splitting and establishes that g 2 2 is positive. Mixing within the various u 2+2u 3 Fermi polyads in ZrCD allows observation of many high-u2 levels in dispersed fluorescence that are not seen for ZrCH. The electronic spectrum is fairly sparse up to about 16000 c m - 1 ; it can be assigned mostly as vibrational structure of a 2U.y2 - X 2 E + electronic system analogous to the A - X system of ZrN, although the correspondence is not complete. The observed spin-orbit structure (A = 574 cm - 1 ) of the ZrN system is not apparent in the ZrCH spectrum; no Q.' = 3\/2 features occur where expected. Such bands must lie elsewhere; these may be due to mixing of the dark A ' 2 A 3 \/ 2 state with A 2 n 3 \/ 2 through the spin-orbit Hamiltonian. The 25 c m - 1 separation of the 2 A 3 \/ 2 and 2 \u00a3 + components of the 2J, band indicate that the A 2 n state experiences a significant degree of vibronic coupling. The co3 = 442 c m - 1 vibrational frequency of the A 2 nj\/ 2 state is barely half that of the ground state; nevertheless, the observed C and Zr isotope shifts of the 3J, band support this unusual result. Above 16000 c m - 1 , the band density rapidly increases, with many bands appearing. An Q' - Q.\" = 1\/2 - 1\/2 cold band at 16548 cm\" 1, with missing 1\/2R2 and l\/2Pl branches, betrays a parallel transition moment believed to originate from the B 2 E + state, which, like A 2 n r , appears to lie much lower in ZrCH than in ZrN. This state may be responsible for the Renner-Teller effect seen in the 2Q and 2Q3Q bands of the A 2 n 1 \/ 2 - X 2 E + system; further data are needed to investigate this possibility. Chapter 5 202 Laser Spectroscopy of Lanthanum Imide (LaNH and LaND) 5.1 Background 5.1(a) Introduction While spectra from the Group 3 monoxides, i.e., ScO, Y O and LaO, have been known from high temperature sources for over seventy years (1), studies of the corresponding isoelectronic Group 3 imides (ScNH, Y N H and LaNH) only began in 1990 (2), when the availability of laser-ablation and jet-cooling techniques made them easy to prepare (3-6). This chapter presents the first spectroscopic investigation of LaNH; it has been the basis of Stark effect experiments to measure the electric dipole moments of two of its electronic states (6). The very similar electronic structures of the six aforementioned molecules are described in Section 5.1(b). Section 5.2 discusses the experimental details; these differ little from those for ZrC and ZrCH, studied in previous chapters, so the description is brief. An overview of the spectrum is given in Section 5.3, while Sections 5.4 and 5.5 discuss respectively the ground and the two observed excited electronic states; in particular the latter section also presents evidence for vibronic coupling between these two excited states. Conclusions are presented in Section 5.6. 5.1(b) Electronic Structures of ScO, ScNH, YO, YNH, LaO, LaS and LaNH Each of the Group 3 metals has only one abundant isotope and this has a non-zero spin (Igc = 7\/2, I Y = 1\/2 and I L 3 = 7\/2). Their monoxides and imides are an isovalent family of molecules whose visible and near-infrared spectra are dominated by two strong electronic systems, A 2 n r - X 2 E + and B 2 S + - X 2 S + . Key spectroscopic constants of the three states comprising these systems are given in Table 5.1; only data for the B 2 S + state of ScNH remain unavailable. This isovalent set of molecules can be extended to include the Group 3 Chapter 5 Visible Spectra of LaNH and LaND monosulphides, although only for LaS have all three of these states been characterised, data for this species are also included. 203 Recent Table 5.1 Characteristic molecular constants (in cm - 1 ) of some isovalent Group 3 molecules X 2 S + (bp S ) A 2 H(a p ) B2\u00a3+(b p j) ~ b 0 103Yo To Ao Po To TO ScO 0.064a 0.11 a 16498\u00b0 115\u00b0 -0.066\u00b0 20571 c -0.067 c Y O -0.026 d -0.3 l d 16509e 429 e -0.150 e 20742e -0.144 e LaO 0.121 f 2.21 f 130678 863 h -0.24 l h 17837i -0.253 f LaS 0.117) -0.78J 10472k 868 k -0.107 k 13767J -0.096) ScNH 1 0.057 -2.66 15023 102 -0.184 Y N H m -0.022 -1.84 15204 444 -0.283 16693 -0.215 L a N H n 0.111 -2.46 12640\u00b0 1010\u00b0 15200 -0.230P \"Reference 7 dReference 10 ^Reference 13 JReference 16 \"\"Reference 5 tentative, estimated from bReference8 Reference 11 Reference 14 Reference 17 \"Present work pulsed laser data Reference 9 Reference 12 'Reference 15 'Reference 3 Ptaken from D 3 = 1 level Where the data are available for confirmation, the electronic structures of these states are well described in first approximation by a single valence electron of predominantly metal parentage, which occupies the nsa, (n-\\)dn or (n-l)da orbitals (n = 4, 5 or 6 for Sc, Y , or La) for X 2 \u00a3 + , A 2 T I r and B 2 E + respectively. As discussed in Section 4.3(b)(ii), the electron spin-rotation interaction in the X 2 Z + states of these species is very small; in fact, the Fermi contact interaction between the spins of the unpaired nsa electron and the metal nucleus is much larger, so the ground states all follow Hund's case (bp\u00a7) coupling. The A 2 n r - X 2 Z + systems correspond to the nsa \u2014\u2022 (n-l)dn promotion, and the upper state inherits the large spin-orbit coupling of the (n-l)dn electron, so that its coupling conforms closely to Hund's case (ap). Finally, since the configuration for B 2 Z + has no unpaired s electrons, its Fermi contact interaction is very small; the electron spin-rotation interaction (which is in fact a second order spin-orbit effect as discussed in Chapter 4, due primarily to interaction with the nearby A 2 n i \/ 2 Chapter 5 Visible Spectra of LaNH and LaND 204 state) is much larger and Hund's case (bpj) coupling applies. An interesting result for the diatomic species in Table 5.1, is that the A-type doubling parameter p of A 2 n and the spin-rotation constant y of B 2 Z + are very similar, which indicates that the two states closely satisfy the unique perturber approximation. The trend for the imides is less certain; for Y N H , the only imide for which both constants are known, the approximation is clearly not valid, but for good reason. As pointed out in Chapter 4, Y N H has two 2 n electronic states, A 2 n r and A\" 2n ;, within 2300 c m - 1 of B 2 E + , both of which contribute to its y value. 5.2 Experiment The experimental details of the LaNH(D) studies are essentially identical to those discussed previously for ZrC and ZrCH; only a brief description follows. Lanthanum imide molecules were produced by reaction of gas phase lanthanum atoms with ammonia. The metal atoms were ablated from a solid rod of La (30 mm x 5 mm, Cambridge Corp.) by a frequency-tripled N d : Y A G laser; a mixture of 8% NH3 or N D 3 seeded in a stream of helium gas was passed over the resulting plasma. LJJF signals from Smalley sources with various lengths of reaction channel were examined; as was the case for ZrCH, the best performance came without any channel. The pulsed laser system was used to record low-resolution WSF and DF spectra of bands in the region 570 - 870 nm (approximately 17500 - 11500 cm - 1 ) . WSF data were collected for each isotopomer while monitoring LIT to the (010) ground state vibrational level in the 570 - 870 nm range, and to the (001) ground state vibrational level in the 570 - 845 nm range; in each case the maximum wavelength corresponds approximately to a monochromator setting of about 900 nm, beyond which the PMT loses sensitivity. DF spectra from all sufficiently strong WSF bands were also recorded. A few bands above 15000 c m - 1 were recorded at high-resolution, using the cw ring laser either alone or in combination with the Chapters Visible Spectra of LaNH and LaND 205 PDA. As shown in the next section, rotational lines in most of the bands had rather compact hyperfine structure compared to their spacings; these bands were usually recorded in two stages. In the first stage, the entire band was recorded as 0.75 c m - 1 adjoining scans taking about five minutes each, or ten if the P D A was used; these permitted rotational assignments to be made. In the second stage, selected rotational lines were scanned individually to resolve as much of their hyperfine structure as possible. These scans typically covered about 0.15 c m - 1 over a five minute duration, with a commensurate increase in signal averaging. To ensure no offset error, all scans were calibrated separately with optogalvanic uranium lines scanned under the same conditions as the sample spectra. The presence and nature of hyperfine structure in the bands of LaNH means that the recording and analysis of even one of them is, in comparison to the Zr-bearing species discussed in the previous two chapters, much more laborious. For discussion purposes in this Chapter, the slow (second stage) scans will be referred to as hf-resolution scans, while the faster (first stage) scans will be called high-resolution. 5.3 Description of the W S F Spectrum The WSF spectra of LaNH and LaND were investigated in the 580-825 nm region. Approximately 50 bands of L a N H were identified; only 25 were found in the generally weaker spectrum of LaND. As is described in more detail later in the Chapter, the spectrum can be conveniently separated into two regions above and below 15000 c m - 1 . Even though no high-resolution data were recorded in the lower region, A 2 n - X 2 E + system bands have been identified; these are discussed in Section 5.4. Above 15000 c m - 1 , a number of bands comprising the B 2 E + - X 2 E + system have been studied at high- and hf-resolution. The rotational and hyperfine assignments and wavenumber Chapter 5 Visible Spectra of LaNH and LaND 206 measurements of the lines of these bands are given in Appendix VI. As an example, Fig. 5.1 shows two details from the 3Q band of this system recorded at high resolution; the four branches in this band are designated by the Mulliken scheme described in Chapter 4, rather than the more common Ri, R 2 P i and P 2 nomenclature, for two reasons. The adopted scheme is applicable to excitation bands to both 2 n 1 \/ 2 and 2 E + levels and facilitates comparisons between them; also, the upper electronic state in this band is not purely 2 \u00a3 + but, as later discussed, contains some 2 I I 1 \/ 2 character. The first lines in each of the four branches, shown in the top trace, clearly indicate aP = 1\/2 - 1\/2 transition. The spacing of 1\/2R(0) and 3\/2R(0) results from the large y(N'+l\/2) spin-rotation splitting (as given by Eq. [4.5]) of the N ' = 1 level shared by these features. Since y(B 2 E + ) , given in Table 5.1, has a large negative value, 3\/2R(0) appears much lower in wavenumber and closer to the band origin than 1\/2R(0). The upper state hyperfine structure (hfs) is completely resolved in the top trace and each peak can be labelled by its F' value, although the N ^ 0 peaks have only partially resolved lower state hfs. In both traces, each branch has two components split by an amount (0.44 cm - 1 ) essentially independent of N ; this splitting, observed in all of the bands recorded at high-resolution, is due to the large Fermi contact interaction in the ground state. The pseudospin quantum numbers G = 3 and 4 labelling each component result from the addition of the S = 1\/2 electron spin angular momentum and the \\ & = 7\/2 nuclear spin. The ground state electron spin-rotation interaction further splits each G level into 2-min(N,G)+l components labelled by the total angular momentum quantum number F, which has integer values ranging from |N-G | up to N+G. At high N , the appearance of the two G components of each branch in the spectrum is different; the 1\/2PG=3 and 3\/2PG = 4 branches appear as single sharp lines, as do the 3\/2R4 and 1\/2R3 branches (not shown). The other G component in the four branches appears as a large number of partially resolved components. This appearance is explained in the next Chapter 5 Visible Spectra of LaNH and LaND 207 G = 4 4 3 2 5 4 3 F 3\/2P(2) F 3 4 Figure 5.1 Portions of the B 2 Z + (001) - X 2 Z + (000) band of LaNH. The top trace shows the first lines of all the branches, from which it is clear that P' = 1\/2. Unlabelled 3\/2R(l) features with G = 4 partially overlap the 3\/2R(0), G = 3 features. The bottom trace shows high-N lines of the 1\/2P and 3\/2P branches. Fig. 5.2 shows a higher dispersion spectrum of the feature marked by the asterisk. Chapter 5 Visible Spectra of LaNH and LaND 208 section. The incomplete resolution of this latter splitting necessitated the slower hf-resolution scans described earlier, an example of which appears in Fig. 5.2. This scan shows the 1\/2P4(13) line from Fig. 5.1, which contains hyperfine features p(10) through p(17) and q(9) through q(16); the anticipated r(9) through r(15) features are too weak to appear. Even with a much slower scan rate, the resolution is still not complete, as is the case with nearly all of the scans recorded in this fashion, but it is sufficient to assign the high-F p- and q-type hyperfine features. The intensities of the p-type features generally increase with F, while an intensity maximum appears in the q-type features. Although hyperfine features of different AF were usually not difficult to distinguish within a given rotational line, their exact AF were not immediately obvious. In fact, it was not even initially clear whether the upper state had 2 E + or 2TT 1\/ 2 symmetry. Only its P' = 1\/2 value was readily established by inspection. To determine the correct upper state symmetry and assign the hfs of each rotational line, detailed calculations of the hyperfine intensities, determined from matrix elements of the electric dipole transition moment, were necessary. These calculations, discussed later in the Chapter, showed that while the upper state is nominally 2 \u00a3 + (so that the P = 1\/2 - 1\/2 transition is nominally parallel), it also has a non-negligible amount of 2IIi\/2 character, which contributes a perpendicular transition moment. This phenomenon was previously discussed in Chapter 4 to account for unusual intensity patterns in the 16548 c m - 1 band of ZrCH. Here, the perpendicular transition moment is believed to originate from the A 2 n state, and is regarded as evidence for vibronic coupling between the A 2 n and B 2 S + states. Other evidence for this coupling is discussed throughout the Chapter. Chapter 5 Visible Spectra of LaNH and LaND 209 Figure 5.2 Hyperfine structure of the 1\/2P4(13) line of the B 2 S + (001) - X 2 E + (000) band of LaNH. As discussed in Section 5.5(b)(ii), the unusual intensity pattern in the q(F) branch, with the appearance of a local maximum, results from the presence of a perpendicular transition moment. A simulation of this line appears in Fig. 5.13. Chapter 5 Visible Spectra of LaNH and LaND 210 5.4 The X 2 L + State of LaNH and LaND 5.4(a) Vibrational analysis DF spectra were collected for the upper states of all sufficiently strong WSF bands of both isotopomers. Examples are shown in Fig. 5.3 for the u = 0 levels of the B 2 \u00a3 + states of LaNH (trace a) and LaND (trace b), their origin bands appear at 15198 and 15157 c m - 1 respectively. The isotope shift is anomalous; deuteration normally shifts system origin bands to the blue (the A 2 n i \/ 2 - X 2 S + (0,0) band of ZrCH discussed in Chapter 4 is a typical example) because the various vibrational frequencies usually decrease on electronic excitation. In the B 2 S + state, the v 2(7i) bending vibrational frequency is actually about 33% higher than in the X 2 Z + state, for both isotopomers. This is an artefact of its vibronic coupling with the A 2 n state and is explored in further detail in Section 5.5. The arguments leading to the assignment of the various peaks in Fig. 5.3 to ground state vibrational levels are similar to those applied to the DF spectra of ZrCH(D) in Chapter 4 and need not be repeated here. Many ground state vibrational levels of LaNH can be identified in Fig. 5.3(a); the most prominent is the fundamental of the V3(o +) L a - N stretching vibration, whose frequency is about 752 c m - 1 . The v 2(7t) fundamental also appears in this spectrum at 464 c m - 1 . As with ZrCH, the presence of both totally and non-totally symmetric vibrational features offers further evidence of vibronic perturbations in the upper state. Trace (b) is the corresponding LaND spectrum, which is much weaker and shows fewer vibrational levels. As in Z rCH and ZrCD, the v 3 (o + ) and v 2(7t) vibrational frequencies are more nearly in a 2:1 ratio in the deuterated isotopomer, so its ground state has a Fermi resonance that does not affect the principal species. Thus, while in trace (a), the peak for (02\u00b00) is much weaker than that for (001), their intensities are about equal in trace (b). This also explains the small isotope shift of the (001) level. The v 2(7i) fundamental of LaND appears at 353 c m - 1 , so the overtone energy, at 680 c m - 1 , is much lower than its expected value (neglecting Chapter 5 Visible Spectra of LaNH and LaND 211 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 0 -500 -1000 -1500 -2000 displacement from laser \/ c m - 1 Figure 5.3 DF spectra of the B 2 \u00a3 + , o = 0 levels of (a) LaNH at 15198 c m - 1 and (b) LaND at 15157 era\"1. A Fermi resonance in the ground state of LaND enhances the (020) feature and almost completely negates the isotope shift of the (001) level (see text for explanation). Chapter 5 Visible Spectra of LaNH and LaND 212 anharmonicity effects) of 706 c m - 1 . This shift is matched by an increase in the (001) level energy that cancels a large fraction of its negative isotope shift, and so (001) appears only 5 c m - 1 lower in LaND than in LaNH. Table 5.2 Measurements (in cm - 1 ) of assigned excited vibrational levelsa in the X 2 S + ground states of LaNH and LaND Level LaNH LaND 010 464 353 001 752 747 020 896, 926 680, 706 011 1208 1104 030 1330, 1393 1009, 1061 002 1500 1492 021 1633, 1661 1418, 1457 040 1731 1316, 1345 012 1953 1849 031 2056 1748 050 2167 1630 003 2244 2229 022 2366, 2390 2165, 2211 041 2056 060 2540 1941 013 2686 2591 032 2769 2496 051 2638 2374 004 2987 2970 023 3118 2692 008 3331 014 3420 042 2798 061 2683 Two entries given for a particular vibrational level represent its I = 0 and 2 angular momentum components i f v 2 is even or I = 1 and 3 i f it is odd This can be checked by applying Wilson's F G matrix treatment to the observed (010) and (001) level positions of LaNH; the calculated values for LaND, assuming the same force constants, are 350 and 728 c m - 1 . The (010) level is unaffected by the Fermi resonance and the calculation agrees well with experiment. If the calculated energy of the (02\u00b00) level is taken as Chapter 5 Visible Spectra of LaNH and LaND 213 twice that of (010) and compared with the observed value, then the Fermi resonance shifts this level down by 20 c m - 1 . This correction, applied to the calculated energy for (001), gives 748 cm - 1 , which is once again close to the observed value. Table 5.2 lists the vibrational levels identified for L a N H and LaND from their DF spectra and their energies; they are also plotted in Fig. 5.4. DF spectra from the upper states of hot vibronic bands of the form 2A(a) - X 2 \u00a3 + (010 , 2TI) and 2<X>(a) - X 2 \u00a3 + ( 0 2 2 0 , 2 A ) have allowed the identification of both the I = 1 and 3 components of the (030) pure bending vibrational level. Their 63 c m - 1 separation is about twice that of the 1 = 0 and 2 components of (020), as expected from their \u00a3 2 energy dependence. These hot bands are discussed later in the Chapter. 5.4(b) Rotational, fine and hyperfine structure of the v = 0 level From the outset of this study, similarities were expected in the electronic structure of LaNH and the isovalent molecules of Table 5.1. In particular, the ground state symmetry was expected to be 2 S + , conforming to Hund's case (bps) coupling. This was immediately confirmed from high-resolution data such as that shown in Fig. 5.1. The required Hamiltonian for this electronic state and its matrix elements are written in terms of Wigner 3-, 6- and 9-j symbols in Section 2.6(b)(ii). The exact algebraic forms of the matrix elements are given in Table 5.3. The rotational energy is simply the familiar quantity BN(N+1) - D[N(N+1)]2; the hyperfine energy level pattern for each rotational level is most easily understood from the dominant diagonal matrix elements, which depend on the Fermi contact and electron spin-rotation parameters b and y. These are <N,G = 3,F|bI-S + y N - S | N , G = 3,F> = -9b \/4 -y [F(F+1)-N(N+1)-12]\/16 [5.1a] and <N,G = 4,F|bI-S + y N - S | N , G = 4,F> = 7b\/4 + y [F(F+1)-N(N+1) -20]\/16. [5.1b] If the state conforms closely to Hund's case (bps) coupling, for which | b\/y | \u00bb 1, then each rotational level of sufficiently large N has sixteen hyperfine components: seven closely spaced LaNH C O O 3 H 080 060 050 040 030 020 051 031 021 Oil 001 032 022 012 002 023 013 003 014 004 LaND 030 020 041 031 021 Oil 001 042 032 022 012 002 023 013 003 u, s a. o TO TO TO I 1 b 010 010 0 000 Figure 5.4 Ground state (X 2 ) vibrational levels of LaNH and LaND. The small isotope shift of the (001) level results from a Fermi resonance in LaND. 000 to Chapter 5 Visible Spectra of LaNH and LaND 215 G = 3 components with F ranging from N-3 to N+3, and nine closely spaced G = 4 components with F ranging from N - 4 to N+4. The 4b separation of the two sets of G components is much greater than the total hyperfine width within either G component. This is shown schematically in Fig. 5.5. Table 5.3 Hamiltonian matrix elements for a 2 E + (bp\u00a7, I =7\/2) electronic statea N' , G', G <N'G'F|7\/-|NGF> N , 3 , 3 F r o t ( N ) -yR(F) _ 9 16 4 (b+{c) + N , 4 , 4 F ro t(N)+^P+^(b+lc) c -c + 5eQq 0 14 j \\ 3eQq 0 14 R(F)x R(F)x 3(R(F) + 1)-48N(N + 1) 48(2N-l ) (2N + 3) 3(R(F) + 1)-80N(N + 1) 48(2N-l ) (2N + 3) N . 4 , 3 -N-2 , 3, 3 N-2 , 4, 4 N-2 , 3, 4 N-2 , 4, 3 e Q q 0 ) R ( F ) - 3 14 ( 2 N - l ) ( 2 N + 3) r 5eQq 0 ^ -c + v 14 j A\/(F + N + 5)(F + N - 3 ) ( N - F + 4 ) ( F - N + 4) Yi(FNG) Y 2 ( F N G ) f c + 3eQq 0 14 32(2N - l)V(2N + l)(2N-3) Yi (FNG) Y 2 (FNG) 32(2N - l)V(2N + l)(2N-3) eQqo^l A\/(F + N - 4 ) ( F - N + 5) A(F + N + 5) A ( N - F + 4) 14 J 32(2N - 1)V(2N + 1)(2N - 3) f e Q q 0 ^ V( F + N + 4 X N - F + 3) A( F + N - 3 ) A ( F - N + 6) 14 J 32(2N - l) A\/(2N + l ) (2N-3) a In these matrix elements, the following functions are used: F r o t (N) = B N ( N + 1 ) - Dls^CN+l) 2, R(F) = F ( F + 1 ) - N ( N + 1 ) - G ( G + 1 ) YjCFNG) = [(F+N+G)(F+N+G+1)(N-F+G-1)(N-F+G)] 1 \/ 2 Y 2 ( F N G ) = [(F+N-G-l)(F+N-G)(F-N+G+l)(F-N+G-i-2)] 1 \/ 2 A(x) = x(x-l)(x-2) The signs of b and y determine the relative locations of the various hyperfine components. The G ordering is regular (inverted) for positive (negative) b. The F hypermultiplets within the G components are always oppositely ordered (one regular and one Chapter 5 Visible Spectra of LaNH and LaND 216 F Figure 5.5 Hyperfine energy level pattern, drawn to scale, for N = 18 of the ground state of LaNH. The positive sign of b results in regular G ordering, but the F ordering within each G is different and determined by the sign of y; it is regular for G = 3 and inverted for G = 4. This helps explain the G dependence of the hyperfine profiles in Fig. 5.1. See text for details. Chapter 5 Visible Spectra of LaNH and LaND 217 inverted) since they have essentially the same y dependence, except for a sign difference. As shown in Table 5.1, y is negative for LaNH, while b is positive. Thus, for each N , the G = 3 and 4 hypermultiplets are respectively regular and inverted, as shown in Fig. 5.5. This helps explain the strong G dependence in the hyperfine profiles of Fig. 5.1; the argument follows. If J' has a regular F' hypermultiplet of width similar to those in the ground state, then for the regular G = 3 component of a transition, the - F m a x and F ^ ' - F ^ hyperfine features are nearly overlapped. This is the case for the 1\/2P branch in the bottom trace of Fig. 5.1. For the inverted G = 4 component, however, the F m a x ' - F m a x and F^^ - F ^ features of the same 1\/2P line are relatively distant from those for F ^ ; its total hyperfine width is about twice the hyperfine width of the J' (or N , G = 4) rotational level involved. Thus, each 1\/2P3 line is very narrow and strong because it has many blended hyperfine components, while the 1\/2P4 branch has widely separated hyperfine components. The 3\/2R branch behaves identically. The situation is reversed for the 3\/2P3 and 3\/2P4 branches in Fig. 5.1, which means that the F' hypermultiplets of the relevant J' levels are inverted. This is a natural consequence of the Hund's case (bpj) coupling in the B 2 Z + excited state; the J' levels that form the 1\/2P and 3\/2R branches are the Fj electron spin components (with e parity and J1 = N + 1\/2), while the F 2 spin components (with \/ parity and J' = N - 1\/2) form the 3\/2P and 1\/2R branches. These G-dependent hyperfine patterns are not unusual for transitions involving a state in Hund's case (bps) coupling; similar behaviour has been observed in the B 2 S + (bps)-X 2 \u00a3 + (bpj) (0,0) band of 1 1 5 InO( I = 9\/2)(18). Least squares fitting of the v = 0 data The method of combination differences was used to determine molecular constants for the o = 0 levels in the ground state of LaNH. All possible combination differences from unblended single hyperfine lines measured from hf-resolution spectra of B 2 E + - X 2 E + system Chapter 5 Visible Spectra of LaNH and LaND 218 bands were used in these fits. These came mostly from three bands, all with 2 E + - 2 E + vibronic symmetry: the strongly perturbed (0,0) band at 15198 c m - 1 , the 3 0 band at 15889 cm - 1 , and the 2 Q band near 16412 c m - 1 . For most rotational lines, the low-F end is blended as in Fig. 5.2, so only the high-F side gives useful data. Several types of ground state combination differences, described presently, were extracted from these bands. Pure hyperfine splittings were taken from within a single G component of individual rotational lines; the spin-rotation constant y is sensitive to these data. These include, for example, the combination difference of the p(17) and q(16) features in Fig. 5.2, which represents the splitting of the F = 16 and 17 hyperfine components of the N = 13, G = 4 level. These combination differences were followed up to N = 19 and 20 for G = 4 and 3 respectively, where the maximum observed splittings are nearly 0.0100 c m - 1 . The familiar A 2 F(N) rotational combination differences were also taken from all three bands between 1\/2R3(N-1) and 3\/2P3(N+l) lines, and between 3\/2R 4 (N-l) and 1\/2P4(N+1) lines, but only between unblended hyperfine features with the same upper state hyperfine level. No attempt was made to utilise the sharp, but hf-blended, features from the other G components of these four branches from any of the bands. An unfortunate happenstance further limited these data: for the observed bands, the spacing of adjacent 3\/2RQ lines changes very slowly and is about equal to the Fermi contact splitting between 3\/2R3(N) and 3\/2R 4(N) lines. This blends some otherwise well-resolved hyperfine features of the 3\/2R 4(N+l) lines with sharp 3\/2R3(N) lines. Fig. 5.1 shows an example; the 3\/2R 4(l) and 3\/2R3(0) features partially overlap. Nevertheless, A 2 F(N) differences were generated between at least one pair of hf components up to N = 18 for G = 4 and up to N = 21 for G = 3, for nearly every N . Combination differences between different G components of the same rotational level, to which the Fermi contact parameter b is most sensitive, were generally not available for LaNH, as is clear from Fig. 5.1, except at very low N , where only a small number of F levels Chapter 5 Visible Spectra of LaNH and LaND 219 exist within each G component. These low-N A G = 1 combination differences were available from all three bands, and from some others that are discussed in the next section. Unlike the ground state combination difference analyses of ZrC and ZrCH in the preceding Chapters, data were taken from relatively few bands, so no attempt was made to average over duplicate combination differences; each one was effectively weighted by the inclusion and distribution of all available measurements. Data fitting for LaND proceeded differently, because only for the origin band were extensive hf-resolution data obtained. Since this band was unperturbed over a sufficiently wide range of N , the line frequencies were fitted directly; for this purpose, an additional Hamiltonian matrix for the 2 Z + excited state was used. Matrix elements were taken using Hund's case (bpj) basis functions; these are given by Dickinson et al. (19). Fortunately for LaND, the upper and lower state hyperfine widths were sufficiently different that individual hyperfine features from both G components of a rotational line could be measured up to N = 8. The ground state molecular constants of LaNH and LaND determined from the least squares fits are listed in Table 5.4. They are all well determined except for the quadrupolar parameters, but these were retained because their inclusion improves the fit slightly. A comparison of the remaining constants shows that while the rotational constants B and D of LaNH are better determined, the more precise fine and magnetic hyperfine parameters are those of LaND. This is due to the nature of the data: those for LaNH extend to higher N levels, while those for LaND carry more information on the structure within each rotational level. Fig. 5.6 shows how the hyperfine structure of the X 2 E + , v = 0 level of LaNH varies with N . The quantity plotted is the calculated energy from the fit, less the purely rotational energy B 0N(N+1) - D 0[N(N+1)] 2; it should be noted that the break in the energy axis, which represents the large Fermi contact splitting of the G components, is much larger than the range plotted on either side of it. The departure from the Lande-type splittings of Eq. [5.1] can be \u2022 G = 3 -0.24 - N + 3 \u2022 -0.25 -^ \u2014 \" N _ 1 -0.26 - N - 2 N - 3 T 1 1 1 1 1 1 1 1 1 r N = 0 2 4 6 8 10 12 Figure 5.6 Hyperfine structure (hfs) of the o = 0 level of the X \u00a3 state of LaNH. At low N , hyperfine reversals occur; these result from the effect of the dipolar parameter c. The F values for the curves are given at the far right. The energy axis and the vertical scale in the two plots are the same. Chapter 5 Visible Spectra of LaNH and LaND 221 noted below N = 6, where there is a folding back of the energy level pattern at the low-F end of each G component. Table 5.4 Molecular constants3 and structure of the X 2 E + , v = 0 levels of LaNH and LaND Constant LaNH LaND B 0.3056116(63) 0.268894(12) 10 7D 1.88(12) 2.00(58) y -0.002461(76) -0.002192(38) b 0.11068(13) 0.110292(99) c 0.00352(35) 0.00405(27) eQqo -0.0036(12) -0.0045(17) rms 0.000620 0.000371 408 267 N c 22 12 Structure: r 0 (La-N) \/ A = 1.93273(10), r 0 (N-H) \/ A = 1.00717(81) Laurie-corrected structure: r 0 (La-N) \/ A = 1.932072(11), r 0 (N-H) \/ A= 1.01357(31) a A l l constants in c m - 1 units except as indicated, with 3 a errors in parentheses bNumber of combination differences (LaNH) or lines (LaND) used in least squares fit \u00b0Highest value of quantum number N appearing in data set Similar behaviour has been reported for the ground state of isovalent LaS by He et al, where these reversals persist up to N = 20 (16); this contrasts with the X 2 2 + (bp\u00a7) state of CoC ( I C o = 7\/2) (20), which has no such hyperfine reversals. The Fermi contact parameters are similar in all three molecules, while the y value is smallest in magnitude for LaS, three times larger for LaNH and almost 17 times larger again for CoC; He et al. claim that the hyperfine reversals in LaS are \"due primarily to the fact that y is small and negative,\" (16) but this author believes that the magnetic dipolar parameter c is most responsible for this behaviour. A recalculation of the hyperfine patterns of LaS with all constants set to those quoted by He et al. (16), but with c = 0, almost completely removes all of the hyperfine reversals, and the amount of reversal in those that remain is very slight. Subsequent trials with c = 0, for which y is set Chapter 5 Visible Spectra of LaNH and LaND 222 one and two orders of magnitude smaller, do little to restore the reversals; they mostly collapse the F levels of each G component into near degeneracy. Similar calculations for LaNH produce the same results. The large Fermi contact parameter bp = b + c\/3 = 0.11186(17) c m - 1 is consistent with a (65a) 1 electron configuration. With p L a = 2.783 p N (21), and <v|\/2(0)>6s = 5.492 a.u.\"3 from Morton and Preston (22), Eq. [2.116] gives the calculated atomic value b F = 0.11656 cm - 1 , only slightly greater than that found for LaNH. The nature of the spin-rotation constants of several isovalent molecules was discussed in detail in the previous Chapter; they indicate the relative locations of the A2Yir and A\" 2 n, states. Inspection of Table 4.3 shows that, in contrast to ZrCH, LaNH has a typically small y value, so that the two states are probably similar in energy for LaNH, although this is not obvious from the survey spectrum. The bond lengths have been derived from the B values using two methods: the conventional r 0 structure and the Laurie-corrected r 0 structure. The latter approach was explained in Section 2.6(b)(i); the r 0 bond lengths were determined by fixing r 0 (N-H) - r 0 ( N -D) = 0.00288 A for LaNH, as in N H (23), resulting in lower uncertainties. In either case, the r 0 (N-H) bond length is somewhat shorter here than in the diatomic species, where it is 1.04643 A. The conventional r 0 bond length is very close to the 1.0039(14) A value found for Y N H (5). A comparison for the metal-ligand bond length is less straightforward because LaN has yet to be studied spectroscopically, but its ligand dependence in the Group 3 metal monoxides, monosulphides and imides can be considered. These bond lengths are listed in Table 5.5 for all nine species; in the case of ScNH, the rotational constant for ScND was not measured, so the bond length was found by fixing r 0 (N-H) to 1.0067 A, the average of the corresponding values for Y N H and LaNH. In substituting S for O in the YO, ScO, LaO series, the metal-ligand bond length increases respectively by 27%, 28% and 29%. For N H substitution on O these Chapter 5 Visible Spectra of LaNH and LaND 223 percentages are 4.9%, 5.1% and 5.7%. The percentage increase for substitution with a given ligand is nearly constant, but with a slight increase through the metal series. Table 5.5 Bond lengths (in A) of the Group 3 monoxides, monosulphides and imides Metal M O Ref. MS Ref. M N H Ref. Sc 1.668 9 2.139 24 1.753 3 Y 1.790 10 2.272 25 1.878 5 La 1.828 15 2.355 26 1.933 this work 5.4(c) The v2 = 1 Level of the Ground State of L a N H Aside from the cold bands discussed above, some hot bands were recorded at high-resolution; one of these is the B 2 S + (02 2 0, 2A(a)) - X ^ O ^ O , 2n(b)) band at 15977 cnr 1 , where the notation indicates electronic and vibronic symmetries of the upper and lower states. Portions of this band are shown in Fig. 5.7. Even though the B 2 E + state has no electron spin-orbit coupling, the upper vibronic level of this band conforms to Hund's case (a) coupling. This is because its mixing with the A 2 n r state transfers to it some spin-orbit coupling that appears in the degenerate bending vibrational levels. This \"spin-vibration\" structure is discussed in more detail in Section 5.5. The top trace in Fig. 5.7 shows the first lines of the 1\/2R and 1\/2P branches from the 2 A 3 \/ 2 spin-vibration component; since P' = 3\/2 and the lower state has n vibronic symmetry, the first 1\/2R and 1\/2P lines have N = 1 and 2 respectively. It is clear from this figure that the hyperfine structure of the (010) level is rather different from that of the zero-point level already described. The Fermi contact interaction still produces a constant splitting of the G = 3 and 4 components that is about the same as for v = 0, but the similarity stops there. The spin-rotation interaction appears to be quenched, as both G components remain fairly sharp as high as they can be followed; hyperfine patterns of the type Chapter 5 Visible Spectra of LaNH and LaND 224 1\/2P(N), G = 4 8 9 10 11 12 13 14 Figure 5.7 The B 2 E + (02 2 0 , 2 A 3 \/ 2 ) - X2Z+(0ll0, 2lT(b)) hot band of LaNH. The missing 1\/2R(0) and 1\/2P(1) lines are characteristic of transitions of this type. At higher N (bottom trace) the \/-doubling of the lower state rotational levels is apparent. Chapter 5 Visible Spectra of LaNH and LaND 225 shown in Fig. 5.2 no longer appear. They are replaced by a splitting of each G component that increases quadratically with rotation. This is referred to as f-type doubling; it is analogous to A-type doubling in electronic states. The 2TI vibronic symmetry of this level arises because it has one unit of bending vibrational angular momentum (|f| = 1). As explained in Section 2.7, A-type doubling occurs in a IT electronic state because its A = \u00b11 components interact through a distant E electronic state. Similarly, the fundamental of the n bending vibration has \u00a3 = \u00b11 components which interact via Coriolis coupling with the two o + vibrations. This lifts the degeneracy of these components; the energy splitting can be expressed as q^N(N+l), where the f-type doubling parameter q^ is given by Nielsen's formula (27) rotation interaction does not allow resolution of the individual F components, the energies of these rotational levels were modelled using four equations: where N > 1 and the + and - signs refer to the upper and lower f-type doubling components. These energy expressions and the appropriate upper state Hamilton matrix discussed in Section 5.5 were used to fit the rotational lines of this band. Since the upper state has 2 A vibronic determined directly except by fixing the T parameter to the 464 c m - 1 value measured from DF spectra. The lower state constants T, B, D, b and q^ determined from this fit are shown in Table 5.6. The B, D and b constants can be compared to the corresponding values for the u = 0 level given in Table 5.4. The uncertainties of the u 2 = 1 constants are somewhat larger because of FG=3(N) = T + BN(N+1) \u00b1 i q \u00a3N(N+l) - DN 2 (N+1) 2 - 9b\/4 and F G = 4 ( N ) = T + BN(N+1) \u00b1\u00b1 q \u20acN(N+l) - DN 2 (N+1) 2 + 7b\/4, [5.3b] [5.3a] symmetry, it does not connect to the X 2 Z + , v = 0 level and its absolute energy T' cannot be Chapter 5 Visible Spectra of LaNH and LaND 226 the smaller quantity of data and the model deficiencies associated with Eq. [5.3]. In particular, D is poorly determined for the bending fundamental and retained only for fit quality. The Fermi contact parameters of the two levels are consistent with each other as expected, while the B value of (010) is greater than that of (000). This is also expected from the nature of the bending motion, during which the molecule spends a larger fraction of its period at the turning points, when it is maximally bent, than at the linear (equilibrium) configuration. Thus, the time-averaged moment of inertia for its end-over-end rotation is less than that measured for the zero-point vibrational level; the resulting increase in B is about 0.21%. Table 5.6 Molecular constants3 (in cm - 1 ) of the X 2 Z + , VJ 2 = 1 level of L a N H T 464.0 (fixedb) B 0.306263(98) 10 7D 2.8(35) 10 4 q \u00a3 4.788(95) b 0.11095(69) a 3o errors are quoted b Fixed from D F measurements The value of q^ can be checked using the Kratzer relation, Eq. [2.77b], since the dimensionless Coriolis coupling coefficients C21 a n d C23 a r e m e same as those in Eq. [5.2]. If the vibrational frequencies are taken as \u00a9j = 3250, co2 = 464 and a>3 = 752 c m - 1 , and the normalisation condition ^21 + C23 = 1 l s used, then the B and D values from Table 5.4 give C,2i = 0.0728 and C 2 3 = 0.9272. Eq. [5.2] then predicts q \u00a3 = 4.5 x 10 - 4 cm- 1 , which compares favourably to the value in Table 5.6. 5.5 The Excited Electronic States: A 2 H r and B 2 \u00a3 + 5.5(a) The A 2 H r State As mentioned in Section 5.3, the survey spectra of LaNH and LaND divide into two regions below and above 15000 c m - 1 . Stick spectra of the LaNH and LaND bands found in the Chapters Visible Spectra of LaNH and LaND 227 former region are shown in Fig. 5.8. The observed band density for LaNFf is higher simply because it has a stronger spectrum. It appears to be too high for a single electronic system; a second system, perhaps originating from the A \" 2 I L or A \" 2 A electronic states probably runs through this region. Unfortunately, no high-resolution data have been recorded for any of these bands to confirm their P' values, so many of the A 2 FL. - X 2 \u00a3 + band system assignments are based on circumstantial evidence such as DF spectra and comparisons with the isovalent LaO and LaS species, which necessarily creates a degree of speculation. The D! = 1\/2 and 3\/2 subbands of the A 2 F L - X 2 S + (0,0) band of LaO appear at 12636 and 13498 c m - 1 respectively. For the other Group 3 imides, Table 5.1 shows that these bands shift somewhat to the red compared to the oxides and have similar upper state spin-orbit couplings, so that the same behaviour was expected for LaNH. This makes the lowest observed band at 12137 c m - 1 the most reasonable to assign as the A 2 n i \/ 2 - X 2 E + (0,0) subband of LaNH. The corresponding band of LaND appears at 12143 c m - 1 ; the blue shift supports its assignment as an origin band. The most reasonable of the observed bands to assign as the A 2 n 3 \/ 2 - X 2 S + origin subband of LaNH is located at 13149 c m - 1 , which gives a spin-orbit interval of about 1010 c m - 1 . The most reasonable LaND counterpart is at 13155 cm - 1 , although the dissimilarity of the DF spectra taken from the two bands seems not to support this assignment; for LaNH, the proposed A 2 n 3 \/ 2 , u = 0 level emits mostly to the (0220) level, while the most intense emission of the corresponding LaND level is to the (0111) level. From the ground state vibrational frequencies, locations of the excited A 2 n 1 \/ 2 vibrational levels of LaNH can be estimated. The band at 12830 c m - 1 is most likely the 3 0 band, which gives co3 = 693 c m - 1 , about 8% lower than the ground state value. The corresponding LaND band appears to lie at 12764 c m - 1 ; this assignment gives a vibrational frequency of about 682 c m - 1 . The small change in this frequency suggests that Fermi resonance, already identified in the LaND ground state, is also operating in the A state. L a N H -1 1 r i ' 1 \u2014 \u2014 ^ (0,0) (0,0) TO TO I b L a N D 14500 14000 13500 13000 12500 wavenumber \/ c m - 1 Figure 5.8 Excitation spectra of LaNH and LaND observed below 15000 cm - 1 . Some bands have been tentatively assigned to the A FX, - X I system in both isotopomers; dotted lines join the corresponding bands. The assignments, if correct, suggest the presence of a Fermi resonance in the A FL state of LaND. The (0,0) assignments are based on the derived 1010 cm upper state to spin-orbit constant for LaNH and the isotope shifts of these bands. oo Chapter 5 Visible Spectra of LaNH and LaND 229 A cluster of features appears in the 12500 - 12550 c m - 1 region, which must surely contain the 2 0 band. From the discussion of the A - X system of Z rCH in Chapter 4, the upper state of this band should have two Renner-Teller components with 2 E and 2 A 3 \/ 2 symmetry, which at least partially account for the complexity of the structure in this region. This leads to an excited state bending frequency of about 380 c m - 1 , about 17% less than the ground state value. For LaND, a similar cluster of bands lies some 75 c m - 1 to the red; its 2 0 band must be among these. 5.5(b) The B 2 \u00a3 + S t a t e Fig. 5.9 shows the vibrational structure observed in WSF survey spectra of LaNH and LaND above 15000 c m - 1 ; the principal bands belong to the B 2 S + - X 2 E + system. Several of these have also been studied at high-resolution; some have already been discussed in Section 5.4 in relation to the analysis of the ground state. The lowest energy bands of LaNH and LaND, at 15198 and 15157 c m - 1 respectively, are the B 2 E+ - X 2 S+ (0,0) bands. The 31, bands appear at 15889 and 15823 c m - 1 , so that the respective \u00a93 vibrational frequencies are 691 and 663 c m - 1 ; the large deuteration shift indicates that, unlike the X and A states, there is no Fermi resonance in this state. High and hf-resolution data have been obtained for all of these bands except the 15823 c m - 1 band of LaND. The 15198 c m - 1 level of LaNH is too extensively perturbed for least squares fitting. This has only been done for the 15157 c m - 1 band of LaND and the 15889 c m - 1 band of LaNH; the constants for these bands appear in Table 5.7. In both cases it is clear that the spin-rotation constant is much larger in magnitude than the Fermi contact parameter, so that the B 2 Z + state conforms most closely to Hund's case (bpj) coupling. However, the y values are inconsistent; these should scale in the same manner as B, but this is clearly not the case. The reasons for this are obscured by the fact that different vibrational levels of the two isotopomers are being compared, but it seems unlikely that the vibrational dependence of y is strong enough to explain such a large discrepancy; it must stem L a N H z c r o \\ \\ \\ \\ L a N D \\ \\ \\ \\ \\ \\ \\ 17000 2 1 3 1 Z(T0 W \\ (0,0) 16500 16000 15500 wavenumber \/ cm -1 ~2 + ~2 + Some bands have been assigned to the B Z - X Z Figure 5.9 Excitation spectra of LaNH and LaND observed above 15000 cm system in both isotopomers; dotted lines join the corresponding bands. The large bending frequency in the B zZTstate results from ~2 + vibronic coupling between the B Z and sequence of bands is shown in Fig. 5.10. ^ 2 vibronic coupling between the B Z and A II states, as discussed in Section 5.5(b)(i). A low-resolution spectrum of the A o 2 = +1 TO* O TO TO i b o Chapter 5 Visible Spectra of LaNH and LaND 231 from the second order contribution to this constant, which depends on the relative locations of the 2 II i \/2 states with which the B 2 E + state is interacting. There is precedent for such anomalous scaling of y; for Y N H , the corresponding state has B 0 ( Y N D ) \/ B 0 ( Y N H ) = 0.863 and Y 0 (YND)\/y 0 (YNH) = 0.55. Table 5.7 Molecular constants2* of the B 2 S + states of LaNH and LaND Constant LaNH LaND T 15884.5157(3) 15157.1629(2) B 0.294262(32) 0.258452(13) 10 7D 22.8(21) 0.34(67) y -0.23080(30) -0.309420(26) b 0.01043(13) 0.012249(85) c 0.00152(63) 0.00299(51) eQqo -0.0054(26) -0.0080(16) rms 0.000717 0.000371 #c 153 267 N d 1 N max 10 12 a A l l constants in c m - 1 units except as indicated, with 3 a errors in parentheses b L a N H constants are for the (001) level; those of LaND are for the (000) level cNumber of lines used in least squares fit dHighest value of quantum number N appearing in data set It is also worth noting that the hyperfine parameters are somewhat difficult to interpret because the B state, though nominally 2 S + , also contains some 2TL\\\/2 character. This means, for example, that the Fermi contact parameter in Table 5.7 is contaminated by the d hyperfine parameter of the 2TL\\\/2 state. 5.5(b)(i) Pure bending vibrational structure of the B 2 L + state Fig. 5.10 shows the A o 2 = +1 sequence of bands. The tendency toward Hund's case (a) coupling in the B 2 E + (02 2 0) vibrational level has already been noted above; this behaviour is also evident in the o 2 = 1 and 3 pure bending vibrational levels, although in the latter case the 16100 16000 15900 15800 wavenumber \/ c m - 1 Figure 5.10 The A u 2 = +1 sequence of the B \u00a3 - X I system of LaNH. A high-resolution spectrum of the P' = 1\/2 component of the u 2 = 1 - 0 band near 15820 c m - 1 appears in Fig. 5.14. Chapter 5 Visible Spectra of LaNH and LaND 233 effect on the I = 1 component is not obvious. The bands in Fig. 5.10 for which P' assignments are given, except the 2 0 7 \/ 2 - 2 A subband, have been recorded at high resolution; their first lines are consistent with these P' values. The observed I' levels have \u00a3 = u 2 and an effective spin-orbit coupling of Al, where A is approximately -14 c m - 1 . The case (a) behaviour here is not fully understood. The B 2 S + state has no spin-orbit coupling of its own, so this coupling must be transferred from a 2 n electronic state, and can only appear in the B 2 S + state if there is nonzero bending vibrational angular momentum present. In this thesis it will be called \"spin-vibration\" coupling. However, the sign of the coupling constant is not understood. In all of the bands, the spin-vibration coupling is inverted, so that the spin-orbit coupling of the 2 n source state should be as well; yet the A2Ur state is regular. It could be the case that the A \" 2 ^ inverted state is the dominant contributor of spin-orbit coupling to B 2 Z + ; high-resolution data are required to ascertain the properties of the bands plotted in Fig. 5.8. Merer and Allegretti (28) have examined, for a linear triatomic molecule, the effect of spin-vibration coupling on a 2 S electronic state. They formulated, and derived matrix elements for, a Hamiltonian for the u 2 = 1 and 2 levels of such a state. The determinable parameters of these matrices are T + g 2 2 \u00a3 2 , B, D, y, the effective spin-vibration coupling constant A and the I-doubling constants q and p+2q; the last constant is only relevant if o 2 = 1, i.e., if a 2Tly2 spin-vibration component is present. With these matrices, the upper state rotational structure of the 1 2 2Q and 2j sequence bands of LaNH were fitted; the resulting constants are in Table 5.8; in each case, the spin-vibration coupling constant is about -14 c m - 1 . The rms errors are about an order of magnitude larger than normal because lines in these bands are broadened by unresolved hyperfine structure. In addition to the Hund's case (a) structure of the pure bending levels, the bending frequency itself is interesting because it shows evidence for vibronic coupling in the B 2 S + state. Chapter 5 Visible Spectra of LaNH and LaND 234 From the separation of the (0,0) and 2 0 bands, a>2 is about 615 c m - 1 , or about 33% larger than in the ground state; LaND shows approximately the same percentage increase. As shown in Section 2.2(b)(i) and Fig 2.1, this results from vibronic coupling with a lower-lying n electronic state; A 2 FL, and A \" 2 ! ! , are obvious candidates for this state. This effect was previously observed for Y O H (29); in this case, vibronic coupling of the B^n and C 1 ^ states, less than 2000 c m - 1 apart, raises the bending frequency of the latter to 460 c m - 1 , or about 50% higher than in the X 1 E + state. Table 5.8 Molecular constants3 of the v2 = 1 and 2 levels of the B 2 E + state of LaNH Constant o 2 = l ( f = l ) u 2 = 2 (\u00a3 = 2) T + g 2 2 \u00a3 2 15812.8134(30) 16441.5955(18)b B 0.295605(49) 0.29554(10) 10 7D 2.2(fixed) 5.1(37) A -13.7381(64) -14.2289(16) y -0.0533(28) -0.16976(92) p+2q -0.0511(11) q -0.00030(21) rms 0.00396 0.00180 43 75 J d J max 33\/2 33\/2 a A U constants in c m - 1 units except as indicated, with 3 a errors in parentheses bDetermined by adding 464.0 c n r 1 (found from DF data) to the B 2E+(02 20, 2 A,) - X ^ O ^ O , 2IT) band origin cNumber of data used in least squares fit dHighest value of quantum number J appearing in data set 5.5(b)(ii) Anomalous intensity patterns in B 2 E + - X 2 \u00a3 + system bands The first lines in the various branches of the 3 0 band of the B 2 Z + - X 2 2 + system of LaNH are shown in Fig. 5.1; these immediately established this band as a P = 1\/2 - 1\/2 transition. While the 2 E + (bp\u00a7) lower state symmetry was recognised from the hyperfine structure, it was not clear whether the upper state symmetry was 2 \u00a3 i \/ 2 or 2TL\\\/2, it was not clear whether the band was parallel or perpendicular. As discussed in Section 4.3(c)(i), both Chapter 5 Visible Spectra of LaNH and LaND 235 moments may be present in such a transition, but the linestrengths in Table 4.6 are inapplicable because hyperfine structure in the band complicates the branch intensities. Therefore, to determine the upper state symmetry of the band, it was necessary to undertake intensity calculations using the formalism of Section 2.8; these calculations are also described by Barnes et al. (20) for the case of CoC, which also has a 2 \u00a3 + (bps , I =7\/2) ground state. The calculated intensity profile for the 1\/2P4(13) line of Fig. 5.2 is shown in Fig. 5.11. Calculations for completely parallel and completely perpendicular transition moments appear in parts (a) and (b) of the Figure, but a comparison with Fig. 5.2 shows that neither prescription is correct. The transition moment is clearly a weighted sum of the perpendicular and parallel moments. Intensity profiles for various weightings were also calculated, with the percentage of parallel transition moment varying from 100 to 0 in steps of 5%. Since the line intensities are proportional to the square of the sum of the two transition moments, the relative phase of the transition moments (zero or rc) was also considered. The best match to the observed hyperfine profile was found to be 80% parallel and 20% perpendicular, with a relative phase of 7i. The critical role of the phase is seen in traces (c) and (d) of Fig. 5.11. For a relative phase of zero, the spectrum is scarcely changed from trace (a); only when the TC phase is included is the local maximum in the q(F) features reproduced. Further examples of intensity calculations are given in Fig. 5.12 for the 1\/2P(1) lines of both the 3 0 band and the P' = 1\/2 spin-vibration component of the 2 0 band; the observed traces are shown at identical scale. The F' assignments of these lines were perhaps the most difficult to ascertain because in both bands, these are the only lines going to the J' = \\l2e level while, with only two F' levels, Lande-type intervals cannot be identified. In neither case is the F\" structure of the lines completely resolved; this leads to a phase ambiguity, but the presence of the perpendicular moment is nevertheless clear. In the case of the 3 0 band, the F' - G = 4 - 3 and 3 - 4 features appear only with the Chapter 5 Visible Spectra of LaNH and LaND 236 (a) Figure 5.11 Results of hyperfine intensity profile calculations for the 1\/2P4(13) line in Fig. 5.2. Various transition moment compositions have been considered: (a) purely parallel, (b) purely perpendicular, (c) 80% parallel, 20% perpendicular, with zero phase and (d) as in (c) but with a phase of n. A comparison with Fig. 5.2 shows that trace (d) gives the best match. Chapter 5 Visible Spectra of LaNH and LaND 237 (a) % p.. I % p 1 100\/0 3 j b a n d ( V - V ) ( b ) (c) (d) 80\/20 50\/50 20\/80 \/ \\ (Reversed hfs \/ \\ \/ \\ . \/ \\ \/ \\ in upper state) \/ \\ \/ \\ \/ \\ 3-3 4-3 3-4 4-4 (e) 0\/100 F' -G\": 4-3 3-3 4-4 3-4 2 Q band ( 2 n l \/ 2 _ 2 ^ + ) Figure 5.12 Hyperfine intensities calculated for 1\/2P(1) F - G\" features in P = 1\/2 - 1\/2 transitions of the B - X system of LaNH. Five stick spectra above left show the patterns as the transition moment evolves from completely parallel (a) to completely perpendicular (e). The patterns at right observed for the indicated bands match the calculated profiles immediately to the left. Compared to (001), the hfs of (010) is smaller and reversed. Chapter 5 Visible Spectra of LaNH and LaND 23 8 presence of the perpendicular moment; these are completely absent for a purely parallel transition. The upper state of the 2Q band should be orthogonal to that of the 3Q band, meaning that the moment mixture in this case must be 80% perpendicular and 20% parallel; the calculations in this case agree fairly well with the observed profiles and indicate that the upper state hfs of this feature is reversed from that of the corresponding 3 0 feature. The proper phase relationship between the two transition moments for the l\\ band can in principal be established from satellite hfs of high-N 1\/2P lines, as it was for the 3 0 band, but these features are not resolved here. Fortunately, the rotational intensity profiles of the various branches are also sensitive to this phase; these are plotted in Fig. 5.13. These were determined by summing the hyperfine component intensities over F' and F for each line and then weighting the result with the Boltzmann factor for the observed rotational temperature of 50 K; the effect of the phase is clear. The top portion of the figure shows the profiles for zero phase; the 1\/2P branch is strongest and the 3\/2R branch is vanishingly weak, while the other two branches have intermediate intensity. In the bottom half, the case for it is considered, for which the 1\/2R branch is the most intense and the 3\/2P branch is vanishingly weak. The observed spectrum in Fig. 5.14 shows that the zero phase relationship is the correct one; the 3\/2R branch is so weak that the tie lines labelling it in the figure could only be drawn on the basis of combination difference calculations with the strong 1\/2P branch, rather than direct observation. The source of the 20% perpendicular transition moment is presumably vibronic mixing with the A 2 TIi\/2 state. It should be emphasised, however, that the intensity ratio does not mean that the electronic state has 80% B 2 E + and 20% A 2 I I i \/2 character. The determined percentages result from a convolution of the mixing ratio with the inherent transition moments of the (zero-order) B 2 I + - X 2 Z + and A 2 TIi\/2 - X 2 E + transitions, so that, for example, B 2 E + might contain as much as 50% A 2 ITi\/2 character, which is masked by a low inherent A 2 ! ! ^ - X 2 E + transition strength. This is unfortunate because knowledge of the percentage characters would facilitate Chapter 5 Visible Spectra of LaNH and LaND 239 Figure 5.13 Effect of relative phase on calculated rotational profiles for a P = 1\/2 - 1\/2 transition. The transition moment mixture is 80% perpendicular and 20% parallel in both cases, but with zero relative phase in (a) and Tt relative phase in (b). s 2 1 0 2 3 4 5 6 3\/2R(N) 3\/2P(N) Figure 5.14 High-resolution spectrum of the B 2 E + (010, 2 n 1 \/ 2 ) - X 2 I + (000 , 2 S + ) band of LaNH. The strength of the 1\/2P branch and the weakness of the 3\/2R branch shows, by comparison with Fig. 5.13, that the transition moment mixture (80% perpendicular and 20% parallel) occurs with a relative phase of 0. For each N , the shorter (longer) tie line marks the G = 3 (4) component. \u00a3 Chapters Visible Spectra of LaNH and LaND 241 the interpretation of the LaNH hyperfine parameters in Table 5.7. Ab initio calculations would be helpful here to sort out this matter. Hf-resolution data from the A 2 n i \/ 2 state are needed to confirm its role in altering the hfs intensity profiles in various P' = 1\/2 bands of the B - X system. If it truly is the lone source of these intensity anomalies, then not only should anomalies appear in A 2TIi\/2 - X 2 \u00a3 + system bands, they should follow a mixture that is orthogonal to what was observed for the B 2 Z + -X 2 E + bands. 5.6 Conclusions The first spectroscopic study of lanthanum imide has been presented; the ground state of this molecule is now well understood. Like many other isovalent species, the ground state has 2S+(bpg) symmetry, with an unpaired La(6sa) electron comprising its leading configuration. The derived bond lengths for this state are consistent with those of other Group 3 monoxides, monosulphides and imides. Frequencies for the bending and L a - N stretching vibrations have been determined; a Fermi resonance is evident in the deuterated isotopomer. High-resolution spectra of the A 2 n - X 2 Z + system have not yet been recorded, though many arguments have been given highlighting the need for these. 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Allegretti, Can. J. Phys. 49, 2859 (1971). 29. A. G. Adam, K. Athanassenas, D. A. Gillett, C. T. Kingston, A. J. Merer, J. R. D. Peers and S. J. Rixon, J. Mol . Spectrosc. 196, 45-69 (1999). 257 Appendix I: Rotational assignments and line measurements (in cm - 1) of triplet bands of ZrC This appendix tabulates the rotational assignments and line measurements of the excitation bands of ZrC from the X 3 E + state. The bands are identified by the band origin wavenumber v 0 (in c m - 1 to the nearest integer) of the 9 0 Z r C isotopomer and listed by increasing v 0 , and in increasing Zr mass number order within (90 and, if available, 92 and 94). The branch labels S, R, Q, P and O denote J' - N \" = +2, +1, 0, -1 and -2 respectively; subscripts \/' = 1, 2 and 3 on these branch labels denote the ground state spin component F, (Fh F 2 and F 3 denote J = N+l , N and N - l ) . This Q'-independent scheme is used since the upper states all have essentially Hund's case (c) coupling. All of the bands are \"cold\" (i.e., u\" = 0) except for a few \"hot\" bands with v\" = 1 and with upper states that appear among the cold bands. These hot and cold pairs of bands are cross-referenced with identifying footnotes. Similar cross-references are given to bands whose upper states appear among the singlet bands listed in Appendix II. A bold entry denotes a measurement of a blended line; an underlined entry denotes an uncertain measurement (due to asymmetry or line weakness). None of these lines were used in any least squares fits. A long dash indicates a nonexistent line. The measurement uncertainty is generally about 0.0005 c m - 1 . Table AI.l(a). Rotational assignments and line measurements of the 16028\/61 c m - 1 band of 9 0 Z r C (3TIo - X 3 E + ) . N SjfN) Ri(N) RjCN) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16030.9668 16062.3105 \u2014 -\u2014 \u2014 \u2014 \u2014 \u2014 0 1 16032.5928 16063.1794 16062.6701 16028.3525 16027.8443 \u2014 16059.9891 \u2014 1 2 16034.0718 16063.9410 16063.3944 16028.1348 16028.1417 16027.5881 16059.4848 16058.9318 2 3 16035.4168 16064.6005 16064.0229 16027.7826 16027.7010 16027.2053 16058.2883 16057.7920 16023.4608 3 4 16036.6314 16065.1468 16064.5413 16027.3001 16027.1529 16026.6946 16057.0226 16056.5640 16021.2163 4 5 16037.7173 16065.5445 16064.9134 16026.6892 16026.4853 16026.0576 16055.6688 16055.2411 16018.8511 5 6 16038.6749 16065.6432 16064.9861 16025.9512 16025.6934 16025.2933 16054.2087 16053.8088 16016.3625 6 7 16039.5045 16025.0844 16024.7755 16024.4020 16052.6024 16052.2298 16013.7476 7 8 16040.2046 16024.0901 16023.7311 16023.3838 16011.0074 8 9 16040.7757 16022.9681 16022.5598 16022.2371 16049.7696 16049.4507 16008.1399 9 10 16041.2168 16021.7174 16021.2616 16020.9627 16047.7539 16047.4549 16005.1464 10 11 16041.5265 16020.3382 16019.8341 16019.5601 16045.6879 16045.4119 16002.0258 11 12 16041.7048 16018.8289 16018.2774 16018.0268 15998.7778 12 13 16041.7472 16017.1899 16016.5902 16016.3625 15995.4020 13 14 16041.6647 16015.4180 16014.7724 16014.5689 15991.8971 14 15 16041.4232 16013.5116 16012.8190 16012.6394 15 16 16011.4810 16010.7409 16010.5851 16 17 16009.2920 16008.5047 16008.3727 17 18 16006.9517 16006.1198 16006.0092 18 19 16004.4244 16003.5455 16003.4584 19 Table A l . 1(b). Rotational assignments and line measurements of the 16028\/61 c m - 1 band of 9 2 Z r C (3UQ - X 3 S + ) . N SjCN) Ri(N) Rj(N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16031.0089 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16032.6301 not observed not observed 16028.4039 16027.8955 \u2014 1 2 16034.1022 16028.1853 16027.6390 not observed not observed 2 3 16035.4407 16027.8320 16027.2548 16023.5242 3 4 16036.6480 16027.3488 16027.2053 16026.7434 16021.2856 4 5 16037.7257 16026.7365 16026.5318 16026.1052 16018.9238 5 6 16038.6749 16025.9944 16025.7380 16025.3380 16016.4380 6 TO 3 8-o & o 3 | Co TO \u00a7 a. TO 3 TO I TO s TO TO-I to oo N SjfN) Rl(N) Ra(N) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 7 16039.4893 not observed not observed 16025.1236 16024.8154 16024.4424 not observed not observed 16013.8271 7 8 16040.1743 16024.1240 16023.7667 16023.4193 16011.0895 8 9 16040.7244 16022.9953 16022.5881 16022.2645 16008.2216 9 10 16041.1380 16021.7286 16021.2743 16020.9804 16005.2296 10 11 16041.4232 16020.3382 16019.8341 16019.5601 11 12 16018.2590 16018.0081 12 13 16017.1426 16016.3173 13 14 16014.4928 14 Table Al. 1(c). Rotational assignments and line measurements of the 16028\/61 c m - 1 band of 9 4 Z r C (3no - X 3 E + ) . N S!(N) Rl(N) Rj(N) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2 (N) 0 3(N) N 0 16030.8237 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16032.4140 not observed not observed 16028.2368 16027.7266 \u2014 \u2014 1 2 16033.8449 16028.0040 16028.0100 16027.4575 not observed not observed 2 3 16035.1228 16027.6276 16027.5458 16027.0507 3 4 16036.2394 16027.1081 16026.9614 16026.5024 4 5 16037.1705 16026.4392 16026.2361 16025.8083 5 6 16038.2947 16025.6111 16025.3559 16024.9548 16016.2234 6 7 16039.5538 16024.6005 7 Table AI.2(a). Rotational assignments and line measurements of the 16178 c m - 1 band of 9 0 Z r C (3TIi - X 3 E + ) . N SjfN) Ri(N) R 2 (N) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2 (N) 0 3(N) N 0 16181.0650 16179.3649 \u2014. \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16182.7001 16180.1535 not observed 16178.4452 16178.9411 not observed \u2014 \u2014 \u2014 1 2 16184.1893 16180.7993 16178.2328 16178.2399 16176.5409 not observed \u2014 2 3 16185.5478 16181.3156 16177.8893 16177.8080 16175.2614 16173.5526 3 4 16186.7782 16181.7062 16177.4177 16177.2711 16173.8810 16171.3143 4 5 16187.8810 16181.9724 16176.8209 16176.6160 16172.3839 16168.9580 5 6 16188.8592 16182.1152 16176.0971 16175.8391 16170.7678 16166.4799 6 7 16189.7111 16182.1340 16175.2476 16174.9388 16169.0304 16163.8790 7 8 16190.4363 16182.0288 16174.2734 16173.9145 16167.1712 16161.1536 8 TO I O \u00a7 3 TO \u00a7 a. a TO TO s s TO TO I N Si(N) RjCN) RjfN) Qi(N) Q 3 (N) Q 2(N) P 3 (N) P 2(N) 0 3 (N) N 9 16191.0372 16181.7999 not observed 16173.1740 16172.7661 not observed 16165.1902 not observed 16158.3039 9 10 16191.5129 16181.4485 .16171.9494 16171.4934 16163.0858 16155.3315 10 11 16191.8620 16180.9733 16170.5999 16170.0954 16160.8587 16152.2320 11 12 16192.0855 16180.3712 16169.1243 16168.5732 16158.5095 16149.0104 12 13 16192.1835 16179.6485 16167.5238 16166.9263 16156.0360 16145.6636 13 14 16192.1522 16178.8009 16165.7985 16165.1533 16153.4389 16142.1922 14 15 16192.0022 16177.8273 16163.9482 16163.2550 16150.7196 16138.5957 15 16 16191.7219 16176.7204 16161.9717 16161.2321 16 17 16191.3158 16175.4754 16159.8705 16159.0833 16144.9088 17 18 16190.7849 16157.6430 16156.8094 18 19 16190.1958 16154.4104 19 20 16189.5426 16151.8845 20 Table AI.2(b). Rotational assignments and line measurements of the 16178 c m - 1 band of 9 2 Z r C ( 3 n 1 - X 3 Z + ) . N SifN) RjCN) R 2 (N) Qj(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3 (N) N 0 16181.1577 16179.4635 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16182.7894 16180.2502 not observed 16178.5450 not observed \u2014 \u2014 \u2014 1 2 16184.2748 16180.8935 16178.3340 16178.3409 16176.6462 not observed \u2014 2 3 16185.6311 16181.4087 16177.9100 16175.3698 16173.6651 - 3 4 16186.8574 16181.7999 16177.5223 16177.3740 16173.9927 16171.4325 4 5 16187.9574 16182.0641 16176.9251 16176.7204 16172.4999 5 6 16188.9331 16182.2072 16176.2028 16175.9464 16170.8875 16166.6107 6 7 16189.7819 16182.2244 16175.3563 16175.0481 16169.1547 16164.0159 7 8 16190.5058 16182.1152 16174.3852 16167.2997 8 9 16191.1060 16181.8893 16173.2873 16172.8811 16165.3243 9 10 16191.5777 16181.5402 16172.0658 16171.6109 16163.2262 16155.4893 10 11 16191.9280 16181.0650 16170.7196 16170.2172 16161.0041 16152.4003 11 12 16192.1522 16169.2486 16168.6989 16158.6604 12 13 16167.6519 16167.0543 16156.1939 13 14 16192.2162 16153.6003 14 15 16192.0654 16177.9344 15 S3 TO & O & 3-. O 3 *\u2014. | TO 3 I 3r 3 TO 3 TO TO TO 3 TO* \u00a7 to ON o Table AI.2(c). Rotational assignments and line measurements of the 16178 c m - 1 band of 9 4 Z r C (3TTn - X 3 Z + ) . N SjfN) R,(N) RjCN) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3 (N) N 0 16179.5598 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16182.8781 16180.3447 not observed not observed \u2014 \u2014 1 2 16180.9859 16178.4328 16178.4405 16176.7311 no: observed \u2014 2 3 16185.7105 16181.5000 16178.0906 16178.0094 16175.4754 3 4 16186.9342 16181.8893 16177.6221 16177.4757 16174.1019 16171.5476 4 5 16188.0338 16182.1532 16177.0273 16176.8209 16172.6135 16169.2042 5 6 16189.0046 16182.2947 16176.3076 16176.0511 16171.0043 16166.7386 6 7 16189.8527 16182.3130 16175.4630 16175.1546 16169.2759 16164.1498 7 8 16190.5752 16182.2072 16174.4929 16174.1355 16167.4256 8 9 16191.1726 16181.9800 16173.3985 16172.9921 16165.4542 16158.6026 9 10 16191.6459 16181.6302 16172.1805 16171.7264 16163.3597 10 11 16191.9928 16181.1583 16170.8368 16170.3360 16161.1441 11 12 16180.5581 16169.3680 16168.8198 16158.8061 12 13 16167.7760 16167.1816 16156.3449 13 14 16165.4163 14 15 16192.1304 16164.2214 15 16 16161.5152 Table AI.3(a). Rotational assignments and line measurements of the 16306 c m - 1 band of 9 0 Z r C ( 3 n 2 - X 3 E + ) . N SjCN) Ri(N) RafN) Q,(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3 (N) N 0 16308.3515 \u2014 \u2014 \u2014 \u2022\u2014 \u2014 \u2014 \u2014 \u2014 0 1 16309.9206 16307.4303 16306.9226 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 16311.3333 16308.0083 16307.4610 16305.5162 16305.5253 16304.9708 \u2014 \u2014 \u2014 2 3 16312.6070 16308.4350 16307.8608 16305.1096 16305.0276 16304.5320 16302.5399 16302.0427 \u2014 3 4 16313.7549 16308.7323 16308.1270 16304.5632 16304.4133 16303.9555 16301.0876 16300.6285 16298.5998 4 5 16314.7805 16308.9022 16308.2714 16303.8818 16303.6768 16303.2496 16299.5045 16299.0783 16296.1777 5 6 16315.6909 16308.9529 16308.2943 16303.0732 16302.8161 16302.4166 16297.7937 16297.3931 16293.6258 6 7 16316.4856 16308.8869 16308.2046 16302.1473 16301.8383 16301.4657 16295.9603 16295.5873 16290.9368 7 8 16317.1643 16308.7060 16307.9996 16301.1054 16300.7475 16300.3985 16294.0079 16293.6605 16288.1299 8 9 16317.6832 16308.4063 16307.6772 16299.9493 16299.5417 16299.2182 16291.9426 16291.6176 16285.2039 9 TO Br X o & a-, o g 1 3 TO a I a, a? a r& TO i 3 TO a TOT \u00a7 to ON N SjfN) R,(N) RjCN) Ql(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 10 16318.2307 16307.9515 16307.1965 16298.6765 16298.2201 16297.9214 16289.7627 16289.4632 10 11 16318.5616 16307.5247 16306.7476 16297.2467 16296.7433 16296.4668 16287.4657 16287.1920 11 12 16318.7838 16306.8806 16306.0790 16295.8449 16295.2930 16295.0418 16285.0129 16284.7633 12 13 16318.8905 16306.1286 16305.3034 16294.2223 16293.6258 16293.3975 16282.5877 16282.3617 13 14 16318.8795 16305.2612 16304.4133 16292.4942 16291.8518 16291.6474 14 15 16318.7506 16304.2764 16303.4039 16290.6567 16289.9616 16289.7823 15 16 16318.4990 16 17 16318.1260 17 Table AI.3(b). Rotational assignments and line measurements of the 16306 c m - 1 band of 9 2 Z r C ( 3 ^ - X 3 Z + ) . N SjfN) Rl(N) R2CN) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16307.5414 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16309.1688 16307.2590 16306.7145 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 16310.6559 16304.7095 16304.7194 16304.1683 \u2014 \u2014 \u2014 2 3 16312.0127 16307.7630 16307.1906 16304.3699 16304.2895 16303.7944 \u2014 3 4 16313.2449 16308.1492 16307.5414 16303.9038 16303.7554 16303.2950 16300.4256 16297.8132 4 5 16314.3478 16308.4063 16307.7708 16303.3094 16303.1049 16302.6771 5 6 16315.3301 16308.5343 16307.8783 16302.5919 16302.3333 16301.9315 16297.2377 16296.8364 16292.9910 6 7 16316.1921 16308.5472 16307.8606 16301.7436 16301.4374 16301.0646 16295.1191 7 8 16316.9291 16308.4281 16307.7245 16300.4256 16300.0781 16293.6258 16293.2834 16287.6852 8 9 16317.5389 16308.1923 16307.4610 16299.6960 16299.2908 16298.9668 16284.8478 9 10 16318.0333 16307.8358 16298.0342 16297.7343 16289.2360 10 11 16307.3677 16306.5912 11 12 16295.7019 12 13 16305.9871 13 Table AI.3(c). Rotational assignments and line measurements of the 16306 c m - 1 banda of 9 4 Z r C ( 3 ^ 2 - X3 Z + ) . N S!(N) Ri(N) R 2 (N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16307.4116 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16309.0411 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 16310.5307 16304.5911 16304.5991 16304.0449 \u2014 \u2014 \u2014 2 TO s-: \u00bb. o a a I . to TO 3 I 3? 3 TO TO i 3 TO 3 TO-ON to N S!(N) Rl(N) R 2 (N) Qi(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3 ( N ) N 3 16311.8897 16304.2524 16304.1683 not observed \u2014 3 4 16313.1227 16307.9804 16307.3764 16303.7944 16303.6484 16303.1876 4 5 16314.2302 16307.6623 16302.5746 16295.3655 5 6 16315.2139 16302.2348 16292.9072 6 7 16316.0746 16307.6275 16301.3502 16300.9777 16295.4168 16290.3295 7 8 16316.8096 16308.0335 16307.3270 16300.7012 16300.3447 16299.9951 8 9 16299.6191 16298.8920 9 10 16307.7384 16306.9847 16298.4153 16297.9611 16297.6629 10 11 1 0 16318.2606 16307.2590 16306.4776 11 1 9 13 16293.4500 1Z 13 a This band is rather weak with poorly formed lines. Table AI.4(a). Rotational assignments and line measurements of the 16488\/502 c m - 1 band of 9 0 Z r C (3TIo - X 3 E + ) . N S!<N) Ri(N) R2(N) Ql(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3 ( N ) N 0 16491.0209 16503.1988 \u2014 16488.4224 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16492.7029 16504.0341 16503.5251 16488.3716 16487.8621 \u2014 16500.8930 \u2014 1 2 16494.2568 16504.7504 16504.2050 16488.1897 16488.1958 16487.6434 16500.3732 16499.8193 16485.5991 2 3 16495.6991 16505.3639 16504.7866 16487.8932 16487.8114 16487.3158 16499.1415 16498.6462 16483.4792 3 4 16497.0352 16505.8761 16505.2701 16487.4857 16487.3392 16486.8807 16497.8334 16497.3751 16481.2712 4 5 16498.2674 16506.2885 16505.6565 16486.9726 16486.7681 16486.3404 16496.4327 16496.0050 16478.9615 5 6 16499.3994 16506.6039 16505.9470 16486.3547 16486.0967 16485.6973 16494.9375 16494.5377 16476.5476 6 7 16500.4347 16506.8220 16506.1398 16485.6342 16485.3250 16484.9522 16493.3463 16492.9734 16474.0303 7 8 16501.3741 16506.9445 16506.2397 16484.8143 16484.4553 16484.1085 16491.6601 16491.3120 16471.4107 8 9 16502.2208 16506.9729 16506.2397 16483.8986 16483.4906 16483.1683 16489.8782 16489.5550 16468.6901 9 10 16502.9773 16506.9068 16506.1505 16482.8872 16482.4312 16482.1332 16488.0015 16487.7037 16465.8718 10 11 16503.6448 16506.7467 16505.9683 16481.7838 16481.2791 16481.0055 16486.0311 16485.7566 16462.9568 11 12 16504.2227 16506.4939 16505.6924 16480.5895 16480.0380 16479.7883 16483.9670 16483.7170 16459.9484 12 13 16504.7143 16506.1505 16505.3243 16479.3065 16478.7079 16478.4813 16481.8106 16481.5838 16456.8474 13 14 16505.1165 16505.7120 16504.8626 16477.9370 16477.2908 16477.0877 16479.5617 16479.3590 14 15 16505.1810 16504.3093 16476.4789 16475.7863 16475.6064 16477.2209 16477.0414 16450.3788 15 16 16504.5533 16503.6580 16474.9330 16474.1930 16474.0359 16474.7890 16474.6324 16 TO & O & o g I Co I TO a I a TO TO 1 TO a TO O i to O N N 17 18 19 Si(N) Ri(N) R 2 (N) Ql(N) Q 3 (N) Q 2(N) 16503.8200 16502.9011 P 3(N) 16472.2632 16469.6412 16466.9146 P 2(N) 16472.1304 16469.5328 16466.8285 0 3(N) N TT 18 19 Table AI.4(b). Rotational assignments and line measurements of the 16488\/502 c m - 1 band of 9 2 Z r C ( 3rio - X 3 S + ) . N Si(N) RjCN) R2(N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16489 2237 16501.9374 \u2014 16486.6095 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16490 9220 16502.7771 16502.2683 16486.5659 . 16486.0564 \u2014 16499.6350 \u2014 1 2 16492 4992 16503.5008 16502.9532 16486.3993 16486.4053 16485.8517 16499.1202 16498.5656 16483.7923 2 3 16493 9706 16504.1219 16503.5442 16486.1241 16486.0418 16485.5460 16497.8978 16497.4010 16481.6870 3 4 16495 3408 16504.6456 16504.0410 16485.7457 16485.5991 16485.1408 16496.5997 16496.1413 16479.4975 4 5 16496 6120 16505.0727 16504.4410 16485.2652 16485.0622 16484.6346 16495.2136 16494.7856 16477.2154 5 6 16497 7867 16505.4047 16504.7504 16484.6876 16484.4304 16484.0306 16493.7349 16493.3350 16474.8355 6 7 16498 8667 16505.6412 16504.9601 16484.0106 16483.7028 16483.3295 16492.1631 16491.7894 16472.3568 7 8 16499 8522 16505.7849 16505.0788 16483.2391 16482.8820 16482.5330 16490.4980 16490.1511 16469.7821 8 9 16500 7469 16482.3727 16481.9654 16481.6427 16488.7410 16488.4176 16467.1099 9 10 16501 5490 16481.4133 16480.9576 16480.6588 16486.8893 16486.5918 16464.3439 10 11 16502 2597 16480.3611 16479.8584 16479.5842 16461.4841 11 12 16479.2186 16478.6686 16478.4174 16458.5320 12 13 16477.9838 16477.3865 16477.1600 16455.4889 13 Table AI.4(c). Rotational assignments and line measurements of the 16488\/502 c m - 1 band of 9 4 Z r C (3TTo - X 3 Z + ) . N S,(N) Rl(N) R2(N) Ql(N) Q 3 (N) Q 2 (N) P 3 (N) P 2(N) 0 3 (N) N 0 16487.8163 16500.8798 \u2014 16485.1957 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16489.5252 16501.7212 16501.2124 16485.1573 16484.6483 \u2014 16498.5828 \u2014 1 2 16491.1157 16502.4490 16501.9028 16484.9997 16485.0058 16484.4553 16498.0697 16497.5165 2 3 16492.6043 16503.0760 16502.4986 16484.7389 16484.6571 16484.1618 16496.8537 16496.3579 16480.2902 3 4 16493.9946 16503.6066 16503.0015 16484.3785 16484.2323 16483.7737 16495.5646 16495.1064 16478.1158 4 5 16495.2888 16504.0410 16503.4116 16483.9217 16483.7170 16483.2902 16494.1891 16493.7617 16475.8519 5 6 16496.4885 16504.3856 16503.7295 16483.3679 16483.1109 16482.7112 16492.7231 16492.3232 16473.4953 6 7 16497.5945 16504.6355 16503.9535 16482.7184 16482.4119 16482.0380 16491.1655 16490.7923 16471.0436 7 TO I o o' 1 TO 1 a? a TO TO 8 \u00ab TO TO TO\" \u00a7 8-to as N Si(N) Rl(N) Ql(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 8 16498.6057 16504.7913 16504.0854 16481.9768 16481.6196 16481.2712 16489.5170 16489.1675 16468.4989 8 9 16499.5189 16504.8544 16504.1229 16481.1411 16480.7360 16480.4114 16487.7756 16487.4516 16465.8601 9 10 16500.3140 16504.8236 16504.0700 16480.2113 16479.7569 16479.4583 16485.9429 16485.6422 16463.1292 10 11 16504.6965 16503.9199 16479.1839 16478.6823 16478.4069 16484.0172 16483.7424 16460.3043 11 12 16504.4663 16503.6654 16478.0383 16477.4895 16477.2378 16481.9995 16481.7484 16457.3863 12 13 16504.0748 16503.2518 16479.8854 16479.6583 13 14 16503.2932 16502.4490 16477.6689 16477.4645 14 15 16475.2925 16475.1112 15 16 16472.5243 16472.3670 16 Table AT 5. Rotational assignments and line measurements of the hot 16626 c m - 1 band3 of 9 0 Z r C (3rio - X 3 E + , u = 1). N SjfN) Rl(N) RjCN) Qi(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 not observed 16626.9599 \u2014 not observed \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16627.7381 16627.2260 not observed not observed \u2014 16624.6904 \u2014 1 2 16628.3696 16627.8192 16624.1478 16623.5953 not observed 2 3 16628.8661 16628.2838 16622.8682 16622.3739 3 4 16629.2291 16628.6187 16621.4826 16621.0271 4 5 16629.4582 16628.8199 16619.9746 5 6 16629.5479 16628.8849 6 7 16629.4966 16628.8077 7 8 16629.2989 16628.5852 8 9 16628.9495 16628.2098 9 10 16628.4408 16627.6770 10 11 16627.7663 16626.9771 11 12 16626.9178 16626.1025 12 \"a TO a S-O a-, o g TO a \u00a7 a. a? a TO TO I S TO a S3\" TO I a This band has the same upper state as the 17494\/506 c n r 1 band of 9 0 Z r C ( 3 n 0 - X 3 S + ) listed in Table A L 19(a). to ON Table AI.6(a). Rotational assignments and line measurements of the 16643 c m - 1 band of 9 0 Z r C (3n1 - X 3 E + ) . N SjfN) RjCN) R 2 (N) Qi(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16645.2828 16643.2596 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16647.0347 16643.7649 not observed 16642.5541 16643.0497 not observed \u2014 \u2014 1 2 16648.5712 16644.0137 16642.4514 16642.4582 16640.4362 not observed \u2014 2 3 16649.8239 16644.0486 16642.2241 16642.1421 16638.8726 16637.6620 3 16650.4779 4 16651.8015 16643.8964 16641.8007 16641.6530 16637.0953 16635.5328 4 5 16652.9969 16643.5722 16641.0973 16640.8931 16635.1170 16633.2923 5 16641.7512 16641.5467 6 16654.0389 16643.0820 16641.1202 16640.8630 16632.9579 16630.8618 6 7 16654.9198 16642.4257 16640.3637 16640.0543 16630.6297 16628.1547 7 16628.8086 8 16655.6364 16639.4535 16639.0948 16628.1402 16626.1764 8 9 16656.1893 16638.3814 16637.9737 16625.4825 16623.4192 9 10 16637.1471 16636.6914 16620.5105 10 11 16635.7530 16635.2482 11 Table AI.6(b). Rotational assignments and line measurements of the 16643 c m - 1 band of 9 2 Z r C ( 3 f l 1 - X3 E + ) . N Si(N) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 16644.4078 16642.5541 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16645.9621 16642.8978 not observed 16641.8497 16642.3466 not observed \u2014 \u2014 \u2014 1 2 16647.3571 16642.9405 16641.5841 16641.5902 16639.7405 not observed \u2014 2 3 16648.6108 16642.7582 16641.1642 16641.0825 16638.0183 16636.9731 3 4 16649.7330 16642.4174 16640.6033 16640.4572 16636.0392 16634.6830 4 5 16650.7228 16641.9765 16639.9069 16639.7033 16633.8496 16632.2556 5 6 16651.5826 16639.0793 16638.8221 16631.5076 16629.6928 6 7 16652.3094 16638.1222 16637.8138 16629.0674 16626.9978 7 8 16652.9002 16637.0340 16636.6766 16624.1733 8 9 16635.8150 16635.4090 16621.2210 9 10 16634.4595 16634.0050 10 ts TO I X >} o a. o a a TO I a? a TO TO 8 s >! TO 3 TO a \u00a7 to ON Table AT6(c). Rotational assignments and line measurements of the 16643 cm- 1 bandof 9 4 ZrC ( 3 n x - X 3 S + ) . N SiCN) R t (N) RafN) Ql(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 16643.4608 16641.8497 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16644.7132 16641.9936 not observed 16641.1385 16641.6342 not observed \u2014 \u2014 \u2014 1 2 16645.7635 16641.8007 16640.6434 16640.6504 16639.0369 not observed \u2014 2 3 16646.6523 16641.3564 16639.9255 16639.8449 16637.1252 16636.2714 3 4 16647.4036 16640.7124 16639.0261 16638.8787 16634.9185 16633.7592 4 5 16648.0348 16639.9255 16637.9695 16637.7666 16632.4697 16631.0404 5 6 16648.5566 16636.7764 16636.5195 16629.8277 16628.1402 6 7 16648.9798 16635.4627 16635.1570 16627.0454 16625.0917 7 8 16634.0451 16633.6880 16621.9073 8 9 16632.5252 16632.1194 9 Table AI.7(a). Rotational assignments and line measurements of the 16655\/80 c m - 1 band of 9 0 Z r C (3TIo - X 3 E + ) . N S!(N) R,(N) RjCN) Qi(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 16681.9244 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16683.1371 not observed 16679.6363 16680.1322 not observed \u2014 not observed \u2014 1 2 16684.1036 16657.8775 16679.0924 16679.0998 2 3 16684.8327 16658.7778 16678.3264 16678.2450 16674.7442 3 4 16685.3272 16659.5983 16677.3329 16677.1853 16650.9602 16672.1743 4 5 16685.5869 16660.3191 16676.1065 16675.9016 16649.8469 16669.3961 5 6 16685.5869 16660.9272 16674.6459 16674.3884 16648.6587 16666.3942 6 7 16661.4101 16672.9520 16672.6434 16647.3768 16663.1638 7 8 16661.7619 16671.0008 16670.6333 16645.9827 16659.7021 8 9 16661.9753 16644.4665 16656.0091 9 10 16662.0458 16642.8182 10 11 16661.9703 16641.0332 11 12 16661.7434 16639.1062 12 13 16661.3623 16637.0340 13 14 16660.8215 16634.8106 14 15 16660.1161 16632.4333 15 16 16659.2351 16629.8972 16 ts TO I >-~l O & o \u00ab\"\u00bb\u00ab 1 \u00a7 TO I a? TO 3 TO s >! TO 3 TO a TO* I to ON Table AI.7(b). Rotational assignments and line measurements of the 1 6 6 5 5 \/ 8 0 c m - 1 band of 9 2 Z r C (31TQ - X 3 E + ) . N SifN) Ri(N) RafN) QjCN) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 3 not observed 16658.0504 not observed not observed not observed not observed not observed not observed 3 4 16658.8236 4 5 16659.5021 16649.1444 5 6 16660.0697 16647.9121 6 7 16660.5149 16646.5923 7 8 16660.8284 16645.1643 8 9 16661.0023 16643.6140 9 10 16661.0265 16641.9335 10 11 16660.8963 16640.0543 11 12 16660.5983 16638.1460 12 13 16660.1200 16636.0223 13 14 16633.7356 14 15 16631.2657 15 Table AI.7(c). Rotational assignments and line measurements of the 1 6 6 5 5 \/ 8 0 c m - 1 band of 9 4 Z r C (3TIo - X 3 S + ) . N SjfN) Rl(N) RjfN) Q!(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 3 not observed 16657.3593 not observed not observed not observed not observed not observed not observed 3 4 16658.0795 4 5 16658.6944 16648.4714 5 6 16659.1879 16647.1954 6 7 16659.5449 16645.8168 7 8 16659.7483 16644.3189 8 9 16659.7773 16642.6855 9 10 16659.6053 16640.8992 10 11 16638.9410 11 12 16636.7802 12 ts TO I \u00a9 a. \u00a9 r\u00ab I a re 3 re 8 s 3 re re~ I K> ON OO Table AI.8. Rotational assignments and line measurements of the hot 16655\/58 c m - 1 band3 of 9 0 Z r C ( 3 n 0 - X 3 Z + , v = 1). N Sj(N) Rl(N) QlCN) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 1 16659.0751 16658.5641 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 \u2014 1 2 16659.5678 16659.0165 16653.7368 16655.5792 16655.0267 \u2014 2 3 16659.8829 16659.3005 16653.1007 16653.7113 3 4 16661.2183 16660.0273 16659.4170 16652.6807 16652.2249 4 5 16661.7161 16660.0042 16659.3657 16651.6213 16651.1988 16650.5680 5 6 16662.0092 16659.8174 16659.1534 16650.5973 16649.9343 16649.1374 16648.7428 6 7 16662.0974 16659.4679 16658.7813 16648.4644 16646.7524 7 8 16658.9699 16658.2545 16644.9406 16644.5989 16635.7210 8 9 16658.3200 16657.5783 16645.2300 16644.9143 16642.6029 16642.2871 9 10 16657.5253 16656.7611 16643.6070 16643.1323 16642.8422 16640.1122 10 11 16656.5974 16655.8079 16637.2054 11 12 16655.5423 16654.7291 16638.3699 16634.6913 12 13 16654.3698 16653.5333 16635.4980 16631.5569 13 14 16653.0922 16652.2284 14 15 16650.8301 15 16 16649.3469 16 \"This band has the same upper state as the 17535\/38 c n r 1 band of 9 0 Z r C ^ITQ - X 3 I + ) listed in Table AI.20(a). Table AI.9(a). Rotational assignments and line measurements of the 16681 c m - 1 band of 9 0 Z r C ( 3 n 1 X 3 Z + ) . N Rl(N) R2(N) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 16682.8973 16680.8665 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16684.6169 16681.7176 16681.2071 16680.1719 16680.6676 16679.6619 \u2014 \u2014 \u2014 1 2 16686.1792 16682.4521 16681.9053 16680.0657 16680.0721 16679.5190 16678.0411 16677.4880 \u2014 2 3 16687.6051 16683.0781 16682.5006 16679.8054 16679.7242 16679.2284 16676.8256 16676.3294 16675.2805 3 4 16688.9006 16683.5902 16682.9826 16679.4071 16679.2605 16678.8026 16675.5339 16675.0758 16673.1468 4 5 16690.0671 16683.9793 16683.3479 16678.8777 16678.6734 16678.2450 16674.1466 16673.7191 16670.8751 5 6 16691.1022 16684.2308 16678.2195 16677.9619 16677.5629 16672.6519 16672.2523 16668.4696 6 7 16692.0036 16684.3256 16677.4334 16677.1243 16676.7504 16671.0372 16670.6649 16665.9356 7 8 16692.7641 16684.2375 16676.5172 16676.1585 16675.8102 16669.2869 16668.9388 16663.2757 8 ts TO 8-x O & 3 . o 3 1 \u00a7 3 TO 3 \u00a7 a, 3? 3 TO TO I TO 3 TO\" I to as so N SiCN) Ri(N) RjCN) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 9 16693.3742 16683.9319 16675.4672 16675.0602 16674.7368 16667.3820 16667.0585 16660.4891 9 10 16693.8187 16683.3568 16674.2772 16673.8217 16673.5216 16665.2950 16664.9961 16657.5733 10 11 16694.0756 16682.4521 16672.9369 16672.4324 16672.1579 16662.9899 16662.7158 16654.5260 11 12 16694.1184 16681.1403 16671.4309 16670.8788 16670.6282 16660.4178 16660.1670 16651.3387 12 13 16693.9121 16669.7383 16669.1389 16668.9123 16657.5134 16657.2855 16648.0002 13 14 16693.4185 16667.8312 16667.1856 16654.2087 16654.0045 16644.4978 14 15 16692.6115 16665.6758 16664.9827 16640.8090 15 16 16691.4720 16663.2353 16662.4956 16636.9064 16 17 16660.4797 16659.6931 17 18 16657.3927 16656.5591 18 Table AI.9(b). Rotational assignments and line measurements of the 16681 c m - 1 band of 9 2 Z r C ( 3II 1 -X 3Z+). N Si(N) Rl(N) P^CN) Q,(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 16679.0784 16677.3875 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16680.6853 16678.1442 not observed not observed \u2014 \u2014 \u2014 1 2 16682.1300 16678.7331 16676.2543 16676.2616 16674.5694 not observed \u2014 2 3 16683.4198 16679.1552 16675.8877 16675.8065 16673.2649 3 4 16684.5489 16679.4006 16675.3769 16675.2299 16671.8322 16669.3533 4 5 16685.5102 16679.4486 16674.7152 16674.5117 16670.2473 16666.9796 5 6 16686.2943 16679.2813 16673.8960 16673.6385 16668.4895 16664.4656 6 7 16686.8907 16672.9094 16672.6017 16666.5403 16661.8056 7 8 16687.2863 16671.7466 16671.3885 16664.3763 16658.9913 8 9 16687.4727 16670.3966 16669.9897 16656.0091 9 10 16687.4350 16668.8469 16668.3922 16652.8522 10 11 16667.0866 16666.5831 16649.5089 11 12 16665.1048 16664.5537 16645.9621 12 Table AI.9(c). Rotational assignments and line measurements of the 16681 cm- 1 bandof 9 4 ZrC ( 3 n x - X3E+). N SjCN) Ri(N) RjCN) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 16672.2280 16670.5944 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16673.7308 16671.2490 not observed 16669.7034 not observed \u2014 \u2014 \u2014 1 ts TO I o & a. o 8 1 TO \u00a7 a. ft? as TO 3 TO -s TO 3 TO a ^ ^ ' TO 8-to o N SjfN) Ri(N) R2(N) Ql(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 2 16675.0422 16671.6895 not observed 16669.4130 16669.4200 not observed 16667.7834 not observed \u2014 2 3 16676.1713 16671.9267 16668.9449 16668.8651 16666.3818 3 4 16677.1185 16671.9583 16668.3050 16668.1576 16664.8049 16662.5282 4 5 16677.8804 16667.4881 16667.2842 16663.0392 16660.0580 5 6 16678.4500 16666.4907 16666.2347 16661.0739 16657.4219 6 7 16665.3087 16664.9980 7 8 16663.9370 16663.5807 8 Table A l . 10(a). Rotational assignments and line measurements of the 16694 c m - 1 band of 9 0 Z r C ( 3 n 1 - X 3 E + ) . N Si(N) Ri(N) RjfN) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16696.7680 16695.1300 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16698.2241 16695.6819 not observed 16694.2673 16694.7628 not observed \u2014 \u2014 \u2014 1 2 16699.4738 16695.9745 16693.9361 16693.9435 16692.3042 not observed \u2014 2 3 16700.5300 16696.0204 16693.4151 16693.3319 16690.7896 16689.3746 3 4 16701.3961 16695.8231 16692.7023 16692.5548 16689.0558 16687.0172 4 5 16702.0717 16695.3845 16691.8035 16691.5990 16687.0886 16684.4800 5 6 16702.5582 16694.7067 16690.7152 16690.4574 16684.8850 16681.7629 6 7 16702.8556 16693.7944 16689.4388 16689.1295 16682.4425 16678.8610 7 8 16702.9658 16692.6801 16687.9728 16687.6137 16679.7630 16675.7715 8 9 16702.8920 16691.2661 16686.3191 16685.9110 16676.8502 16672.4934 9 10 16702.6380 16689.6877 16684.4798 16684.0223 16673.7359 16669.0298 10 11 16702.1931 16687.9137 16682.4521 16681.9493 16670.3263 16665.3782 11 12 16701.5867 16685.9650 16680.2500 16679.6984 16666.7486 16661.5393 12 13 16700.7945 16683.8493 16677.8559 16677.2570 16662.9772 16657.5166 13 14 16699.8002 16681.5473 16675.3001 16674.6541 16659.0321 16653.3179 14 15 16698.5682 16679.0718 16672.5585 16671.8654 16654.9200 16648.9276 15 16 16697.0553 16669.6159 16668.8754 16650.6242 16 17 16666.4356 16665.6491 17 18 16662.9772 16662.1432 18 ts TO | X' O & 3-. O | TO 3 I 3? 3 TO 3 TO 8 s TO 3 TO 3 TO-I Co Table A l . 10(b). Rotational assignments and line measurements of the 16694 c m - 1 band of 9 2 Z r C ( 3 n 1 - X 3 \u00a3 + ) . N S L(N) Rl(N) RjfN) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16688.8793 16687.2863 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16690.3848 16687.8626 not observed not observed \u2014 \u2014 1 2 16691.7046 16688.2740 16686.0544 16686.0623 not observed \u2014 2 3 16692.8509 16688.4812 16685.5869 16685.5054 16682.9826 3 4 16693.8308 16688.4861 16684.9511 16684.8038 16681.3734 4 5 16694.6421 16688.2875 16684.1470 16683.9421 16679.5720 16676.6779 5 6 16695.2841 16687.8744 16683.1773 16682.9200 16677.5748 16674.0371 6 7 16695.7514 16687.2297 16682.0415 16681.7324 16675.3769 16671.2379 7 8 16696.0346 16686.3344 16680.7374 16680.3785 16672.9681 16668.2726 8 9 16696.1172 16685.2008 16679.2605 16678.8505 16670.3287 16665.1400 9 10 16695.9791 16677.5946 16677.1402 16667.4393 16661.8413 10 11 16695.6085 16675.7312 16675.2299 16658.3688 11 12 16673.6491 16673.0994 16654.7117 12 13 16671.3337 16670.7360 16650.8596 13 Table Al . 10(c). Rotational assignments and line measurements of the 16694 c m - 1 band of 9 4 Z r C ( 3 f l 1 - X 3 2 + ) . N Sj(N) Ri(N) Ql(N) Q 3 (N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 16683.2221 16681.5952 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16684.6994 16682.2165 not observed 16680.7116 16681.2053 not observed \u2014 \u2014 1 2 16685.9749 16682.6031 16680.4042 16680.4101 16678.7844 not observed \u2014 2 3 16687.0577 16682.7591 16679.9128 16679.8314 16677.3491 16675.8442 3 4 16687.9421 16682.6734 16679.2373 16679.0924 16675.7204 16673.5192 4 5 16688.6234 16682.3372 16678.3732 16678.1704 16673.8723 16671.0267 5 6 16689.0953 16681.7397 16677.3145 16677.0578 16671.7904 16668.3535 6 7 16689.3503 16680.8783 16676.0532 16675.7455 16669.4601 16665.4965 7 8 16689.3858 16674.5827 16674.2258 16666.8715 16662.4453 8 9 16672.8969 16672.4934 16664.0200 16659.1931 9 10 16670.9915 16670.5382 16655.7349 10 11 16652.0605 11 TO o \u00a9' Si | Co I TO a \u00a7 a, a? a TO TO 1 3 TO a S 3 -to to Table Al. 11(a). Rotational assignments and line measurements of the 16702 c m - 1 band of 9 0 Z r C - X 3 E + ) . N Si(N) R,(N) R ^ N ) Ql(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16704.8617 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16706.2498 16703.6287 not observed not observed \u2014 \u2014 \u2014 1 2 16707.4094 16703.7471 16702.0313 16702.0380 not observed \u2014 2 3 16708.3559 16703.6035 16701.4385 16701.3561 3 4 16709.0920 16703.2225 16700.6378 16700.4912 16696.8279 4 5 16709.6190 16702.6224 16699.6285 16699.4230 16694.6704 5 6 16709.9437 16701.8195 16698.4109 16698.1532 16692.2845 6 7 16710.0634 16700.8319 16696.9866 16696.6781 16689.6798 7 8 16709.9850 16699.6810 16695.3585 16694.9991 16686.8748 8 9 16709.7125 16698.3943 16693.5268 16693.1190 16683.8876 16680.0428 9 10 16709.2571 16697.0084 16691.4966 16691.0419 16680.7374 16676.4136 10 11 16708.6360 16695.5702 16689.2746 16688.7712 16677.4524 16672.5856 11 12 16707.8740 16694.1328 16686.8693 16686.3191 16674.0689 16668.5574 12 13 16707.0141 16692.7492 16684.2980 16683.6991 16670.6343 16664.3388 13 14 16706.1158 16691.4509 16681.5872 16680.9414 16667.2006 16659.9375 14 15 16705.2531 16690.2350 16678.7782 16678.0855 16663.8206 16655.3698 15 16 16704.4914 16689.0690 16675.9316 16675.1918 16660.5261 16650.6635 16 17 16703.8433 16687.9006 16673.1224 16672.3350 16657.3167 17 18 16703.2767 16686.6618 16670.4115 16669.5788 16654.1570 18 19 16702.7329 16685.2008 16667.8180 16666.9378 16650.9954 19 20 16702.1617 16665.3028 16664.3763 16647.7647 20 21 16662.8138 16661.8413 16644.3090 21 22 16660.2981 16659.2782 22 Table Al. 11(b). Rotational assignments and line measurements of the 16702 c m - 1 band of 9 2 Z r C ( 3 n 1 - X 3 Z + ) . N SjCN) R,(N) R 2 (N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16695.9297 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16697.3504 not observed not observed \u2014 \u2014 \u2014 1 2 16698.5588 16693.1058 16693.1120 not observed \u2014 2 3 16699.5705 16692.5548 16692.4717 3 ts 3^ TO | O & a-, o 1 1 \u00a7 3 TO a I a* a' TO 3 TO a TO I N S,(N) Ri(N) ^ ( N ) Qi(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 4 16700.3953 16695.0145 not observed 16691.8035 16691.6574 not observed not observed 4 5 16701.0405 16694.6704 16690.8661 16690.6619 16683.6440 5 6 16701.5148 16694.1762 16689.7419 16689.4836 16684.1036 16680.8945 6 7 16701.8350 16693.5751 16688.4391 16688.1316 16681.7609 16677.9600 7 8 16702.0189 16692.9131 16686.9670 16686.6094 16679.2696 16674.8371 8 9 16702.0915 16692.2305 16685.3401 16684.9339 16676.6753 16671.5386 9 10 16702.0313 16691.5529 16683.5788 16683.1233 16674.0181 16668.0725 10 11 16690.8848 16681.7067 16681.2038 16671.3424 16664.4524 11 12 16690.2153 16668.6726 16660.6982 12 13 16689.5207 16666.0128 13 14 16688.7712 16663.3509 14 15 16687.9065 16660.6654 15 16 16657.9265 16 17 16655.0738 17 Table A l l 1(c). Rotational assignments and line measurements of the 16702 c m - 1 band of 9 4 Z r C ( 3 f l 1 - X 3 Z + ) . N S!(N) Rl(N) R2(N) Q,(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16688.6863 16687.0463 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16690.2291 16687.7563 not observed 16686.1392 not observed \u2014 \u2014 \u2014 1 2 16691.6082 16688.3013 16685.8691 16685.8768 16684.2375 \u2014 2 3 16692.8456 16688.7080 16685.4428 16685.3609 16682.8887 16681.2709 3 4 16693.9551 16688.9991 16684.8710 16684.7241 16681.4165 16678.9847 4 5 16694.9453 16689.1906 16684.1623 16683.9592 16679.8215 16676.5554 5 6 16695.8278 16689.2978 16683.3272 16683.0710 16678.1153 16677.7146 16673.9870 6 7 16696.6120 16689.3290 16682.3755 16682.0684 16676.3138 16675.9388 16671.2849 7 8 16697.3024 16689.2874 16681.3164 16680.9593 16674.4284 16674.0794 16668.4583 8 9 16697.9044 16689.1729 16680.1581 16679.7531 16672.4694 16672.1458 16665.5165 9 10 16698.4198 16688.9817 16678.9076 16678.4537 16670.4393 16670.1389 16662.4683 10 11 16698.8481 16688.7039 16677.5679 16677.0677 16668.3362 16668.0607 16659.3210 11 12 16699.1840 16688.3556 16676.1440 16675.5955 16666.1569 16656.0832 12 13 16699.4166 16687.9421 16674.6323 16674.0371 16663.8912 16652.7573 13 14 16699.5157 16673.0289 16672.3861 16661.5575 16649.3468 14 TO a B* \u00a9 a. o a a i 3 TO a I a? a TO 3 TO s X TO 3 TO a N -1^ N SifN) Ri(N) RjCN) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 15 16699.3931 not observed 16671.3216 16670.6333 not observed 16659.1604 16645.8489 15 16 16669.4822 16668.7460 16642.2604 16 17 16667.4212 16666.6385 17 Table A l . 12(a). Rotational assignments and line measurements of the 16910 c m - 1 band of 9 0 Z r C ( 3 n 2 - X 3 Z + ) . N S,(N) Ri(N) R 2 (N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16912.8316 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16914.4935 16911.9141 16911.4061 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 16916.0196 16912.5794 16912.0330 16909.9996 16910.0073 16909.4535 \u2014 \u2014 \u2014 2 3 16917.4260 16913.1232 16912.5459 16909.6825 16909.6008 16909.1045 16907.0218 16906.5268 \u2014 3 4 16918.7201 16913.5520 16912.9462 16909.2483 16909.1022 16908.6430 16905.6606 16905.2020 16903.0817 4 5 16919.9007 16913.8678 16913.2354 16908.6996 16908.4946 16908.0675 16904.1923 16903.7643 16900.7509 5 6 16920.9732 16914.0724 16913.4154 16908.0396 16907.7817 16907.3819 16902.6134 16902.2137 16898.3100 6 7 16921.9376 16914.1680 16913.4861 16907.2677 16906.9593 16906.5855 16900.9248 16900.5518 16895.7566 7 8 16922.7953 16914.1563 16913.4479 16906.3877 16906.0291 16905.6812 16899.1281 16898.7806 16893.0965 8 9 16923.5482 16914.0391 16913.3086 16905.3999 16904.9929 16904.6702 16897.2235 16896.9004 9 10 16924.1973 16913.8171 16913.0625 16904.3078 16903.8523 16903.5535 16895.2129 16894.9150 10 11 16924.7419 16913.4898 16912.7120 16903.1107 16902.6066 16902.3322 16893.0965 16892.8241 11 12 16925.1835 16913.0625 16912.2583 16901.8091 16901.2580 16901.0076 12 13 16925.5201 16912.5266 16911.7012 16900.4049 16899.8059 16899.5789 13 14 16925.7525 16911.8886 16911.0399 16898.8964 16898.2497 16898.0472 14 15 16925.8804 16911.1476 16910.2747 16897.2838 16896.5910 16896.4116 15 16 16925.9014 16910.3002 16909.4041 16895.5687 16894.8291 16894.6729 16 17 16925.8171 16893.7495 16892.9614 16892.8275 17 Table A l . 12(b). Rotational assignments and line measurements of the 16910 c m - 1 band of 9 2 Z r C ( 3 n 2 - X3 Z + ) . N SiCN) R,(N) R2(N) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 16911.5268 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16913.1973 16910.6111 16910.1016 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 16914.7373 16911.2879 16910.7418 16908.6996 16908.7086 16908.1553 \u2014 \u2014 \u2014 2 3 16916.1617 16911.8482 16911.2709 16908.3989 16908.3175 16907.8220 16905.7312 16905.2352 \u2014 3 3^ TO a Br o & a. o a | TO a 1 a? a TO TO S >! TO TO a TO t o - J 1^ 1 N SjfN) Ri(N) RjfN) Qi(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 4 16917.4744 16912.2971 16911.6911 16907.9828 16907.8363 16907.3785 16904.3874 16903.9289 16901.8006 4 5 16918.6779 16912.6344 16912.0028 16907.4567 16907.2526 16906.8241 16902.9397 16902.5119 16899.4904 5 7 16920.7625 16912.9867 16912.3047 16906.0766 16905.7684 16905.3958 16899.7254 16899.3520 16894.5476 7 8 16921.6476 16913.0030 16912.2971 16905.2261 16904.8682 16904.5207 16897.9580 16897.6102 8 9 16922.4263 16912.9146 16912.1839 16904.2692 16903.8635 16903.5383 16896.0859 16895.7617 9 10 16923.1019 16912.7197 16911.9512 16903.2077 16902.7527 16902.4533 16894.1088 16893.8092 10 11 16923.6740 16912.4226 16911.6444 16902.04 16901.5389 16901.2643 11 12 16924.1369 16912.0197 16911.2185 16900.7703 16900.2201 16899.9691 12 13 16924.4941 16911.5144 16899.3959 16898.7990 16898.5708 13 14 16924.7353 16897.9169 16897.2730 16897.0692 14 15 16924.9033 16896.3345 16895.6446 16895.4615 15 Table A l . 12(c). Rotational assignments and line measurements of the 16910 c m - 1 band of 9 4 Z r C ( 3 n 2 - X 3 E + ) . N Si(N) R,(N) RzfN) Ql(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 16910.5583 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16912.2338 16909.6456 16909.1363 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 16913.7796 16910.3285 16909.7821 16907.7417 16907.7486 16907.1948 \u2014 \u2014 \u2014 2 3 16915.2122 16910.8969 16910.3205 16907.4465 16907.3662 16906.8696 16904.7782 16904.2813 \u2014 3 4 16916.5351 16911.3562 16910.7514 16907.0420 16906.8943 16906.4371 16903.4445 16902.9859 16900.8588 4 5 16917.7501 16911.7069 16911.0761 16906.5268 16906.3251 16905.8972 16902.0111 16901.5826 16898.5608 5 6 16918.8591 16911.9512 16911.2942 16905.9095 16905.6515 16905.2512 16900.4734 16900.0728 16896.1595 6 7 16919.8623 16912.0890 16911.4061 16905.1800 16904.8723 16904.4991 16898.8295 16898.4564 16893.6513 7 8 16920.7625 16912.1203 16911.4147 16904.3472 16903.9906 16903.6414 16897.0822 16896.7332 8 9 16921.5527 16912.0478 16911.3183 16903.4092 16903.0025 16902.6794 16895.2293 16894.9052 9 10 16922.2411 16911.8700 16911.1168 16902.3655 16901.9117 16901.6119 16893.2729 16892.9724 10 11 16922.8236 16911.5881 16910.8109 16901.2172 16900.7162 16900.4400 11 12 16923.3032 16911.2019 16910.4017 16899.9656 16899.4168 16899.1645 12 13 16923.6740 16898.6096 16898.0138 16897.7850 13 14 16923.9410 16897.1494 16896.5044 16896.3003 14 15 16924.0999 16895.5837 16894.8913 16894.7113 15 16 16893.9081 16893.1737 16893.0159 16 32 re I \u00a9 \u00a9 1 to $ 3 re 3 \u00a7 a. re re I 3 re s o I ON N SX(N) Rj(N) P^CN) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 16913.3728 not observed \u2014 16910.8989 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16914.9325 not observed 16910.8038 16911.3026 16910.2944 \u2014 not observed \u2014 1 2 16916.3195 16910.5410 16910.5478 16909.9941 not observed 16908.0675 2 3 16917.5472 16910.1215 16910.0397 16909.5444 16905.9117 3 4 16918.6168 16909.5467 16909.4007 16908.9426 16903.6222 4 5 16919.5267 16908.8196 16908.6159 16908.1877 16901.1908 5 6 16920.2782 16907.9346 16907.6763 16907.2773 16898.6096 6 7 16920.8659 16906.8943 16906.5855 16906.2111 16895.8774 7 8 16921.2882 16905.6929 16905.3341 16904.9869 16892.9906 8 9 16921.5409 16904.3296 16903.9217 16903.5987 9 10 16921.6210 16902.7998 16902.3437 16902.0461 10 11 16901.1026 16900.5994 16900.3251 11 12 16899.2327 16898.6820 16898.4312 12 13 16897.1863 16896.5910 16896.3616 13 Table Al. 13(b). Rotational assignments and line measurements of the 16911 c m - 1 band of 9 2 Z r C (3rLy- X 3 S + ) . N S!(N) R t (N) P^CN) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2 (N) 0 3(N) N 1 16910.5916 not observed not observed 16906.4240 16906.9191 16905.9117 \u2014 not observed \u2014 1 2 16911.9319 16906.2433 16906.2497 16905.6929 not observed 2 3 16913.1062 16905.7935 16905.7125 16905.2157 3 4 16914.1084 16905.1800 16905.0330 16904.5744 16899.3432 4 5 16914.9435 16904.4005 16904.1923 16903.7681 16896.8844 5 6 16915.6071 16903.4563 16903.1982 16902.7998 6 7 16916.0984 16902.3437 16902.03 16901.6605 7 8 16901.0598 16900.7024 16900.3535 8 9 16899.6017 16899.1974 16898.8741 9 ts ^3 TO I X o Co ! TO a \u00a7 a. 3 : a TO TO 1 3 TO a TO - J - J N SifN) Ri(N) R2(N) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 1 not observed not observed 16901.0385 \u2014 not observed \u2014 1 2 16906.9432 16901.3405 16901.3467 16900.7936 not observed 2 3 16908.0675 16900.8588 16900.7794 16900.2821 3 4 16909.0014 16900.2061 16900.0598 16899.6017 16894.4567 4 5 16899.3775 16898.7469 5 6 16898.3732 16898.1166 16897.7170 6 Table A l . 14(a). Rotational assignments and line measurements of the 16935\/41 c m - 1 band of 9 0 Z r C ( 3 no - X 3 I + ) . N SjfN) Rj(N) RjCN) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 16943.9137 16935.9593 \u2014 16941.5359 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16945.3746 16936.7232 16936.2141 16941.4104 16940.9017 \u2014 16933.6910 \u2014 1 2 16946.6341 16937.3316 16936.7847 16941.0819 16941.0889 16940.5348 16933.1352 16932.5811 16938.7111 2 3 16947.7054 16937.7980 16937.2210 16940.5644 16940.4833 16939.9869 16931.8306 16931.3351 16936.5178 3 4 16948.5964 16938.1261 16937.5208 16939.8625 16939.7156 16939.2567 16930.4126 16929.9548 16934.1643 4 5 16949.3078 16938.3177 16937.6855 16938.9785 16938.7744 16938.3471 16928.8660 16928.4393 16931.6325 5 6 16949.8430 16938.3729 16937.7170 16937.9157 16937.6574 16937.2581 16927.1877 16926.7875 16928.9238 6 7 16950.2054 16938.2918 16937.6098 16936.6745 16936.3653 16935.9920 16925.3758 16925.0018 16926.0363 7 8 16950.3960 16938.0728 16937.3672 16935.2578 16934.8995 16934.5519 16923.4287 16923.0811 16922.9714 8 9 16950.4183 16937.7170 16936.9874 16933.6692 16933.2615 16932.9385 16921.3472 16921.0239 16919.7302 9 10 16950.2758 16937.2210 16936.4687 16931.9091 16931.4536 16931.1546 16919.1301 16918.8311 16916.3150 10 11 16949.9685 16936.5878 16935.8091 16929.9817 16929.4768 16929.2029 16916.7763 16916.5018 16912.7272 11 12 16949.5004 16935.8091 16935.0071 16927.8876 16927.3359 16927.0857 16914.2834 16914.0357 16908.9699 12 13 16948.8722 16934.8824 16934.0567 16925.6317 16925.0326 16924.8062 16911.6516 16911.4240 16905.0461 13 14 16948.0830 16933.8010 16932.9525 16923.2134 16922.5678 16922.3651 16908.8771 16908.6734 16900.9543 14 15 16947.1339 16932.5574 16931.6855 16920.6362 16919.9448 16919.7628 16905.9537 16905.7726 15 16 16931.1379 16930.2431 16917.8981 16917.1589 16917.0028 16902.8756 16902.7227 16 17 16929.5201 16928.6015 16915.0007 16914.2143 16914.0819 16899.6385 16899.5072 17 18 16927.7288 16926.7875 16896.2245 16896.1186 18 33 TO I O & 1 Co ! TO a \u00a7 a. a TO T  s 3 TO rs TO-I t o - J 00 Table A l . 14(b). Rotational assignments and line measurements of the 16935\/41 c m - 1 band of 9 2 Z r C (3fIo - X 3 \u00a3 + ) . N SjCN) Ri(N) Rj(N) Ql(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3 (N) N 0 16938.3384 16932.2336 \u2014 16935.9453 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16939.8158 16933.0044 16932.4951 16935.8270 16935.3186 \u2014 16929.9670 \u2014 1 2 16941.0995 16933.6236 16933.0772 16935.5132 16935.5196 16934.9670 16929.4160 16928.8660 16933.1270 2 3 16942.2024 16934.1059 16933.5282 16935.0181 16934.9363 16934.4406 16928.1244 16927.6289 16930.9480 3 4 16943.1302 16934.4530 16933.8477 16934.3455 16934.1987 16933.7401 16926.7226 16926.2637 16928.6128 4 5 16943.8844 16934.6670 16934.0351 16933.4977 16933.2939 16932.8668 16925.1971 16924.7688 16926.1103 5 6 16944.4666 16934.7465 16934.0896 16932.4769 16932.2193 16931.8197 16923.5428 16923.1422 16923.4333 6 7 16944.8793 16934.6909 16934.0094 16931.2835 16930.9749 16930.6023 16921.7580 16921.3837 16920.5885 7 8 16945.1204 16934.4983 16933.7926 16929.9195 16929.5622 16929.2133 16919.8412 16919.4925 16917.5710 8 9 16945.1908 16934.1643 16933.4358 16928.3850 16927.9785 16927.6555 16917.7905 16917.4667 16914.3818 9 10 16945.0863 16933.6877 16932.9338 16926.6809 16926.2246 16925.9265 16915.6023 16915.3048 16911.0247 10 11 16944.8043 16933.0556 16932.2783 16924.8062 16924.3025 16924.0273 16913.2766 16913.0030 16907.4971 11 12 16944.3388 16922.7560 16922.2056 16921.9550 16910.8109 16910.5530 12 13 16920.5291 16919.9325 16919.7053 16908.1850 16907.9531 13 14 16918.1189 16917.4744 16917.2714 14 Table A l . 14(c). Rotational assignments and line measurements of the 16935\/41 c m - 1 band of 9 4 Z r C (3TIQ - X 3 E + ) . N SjfN) Rl(N) Ra(N) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2 (N) 0 3(N) N 0 16933.6070 16929.0892 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16935.0291 16929.8579 16929.3484 16931.1379 16930.6280 \u2014 16926.8245 \u2014 1 2 16936.2392 16930.4759 16929.9298 16930.7897 16930.7964 16930.2431 16926.2776 16925.7243 2 3 16937.2524 16930.9544 16930.3779 16930.2431 16930.1613 16929.6655 16924.9910 16924.4941 16926.2703 3 4 16938.0728 16931.2963 16930.6910 16929.5018 16929.3562 16928.8967 16923.5915 16923.1329 16923.91 4 5 16938.6960 16931.4965 16930.8652 16928.5678 16928.3633 16927.9359 16922.0689 16921.6406 16921.3555 5 6 16939.1292 16931.5483 16930.8910 16927.4425 16927.1877 16926.7875 16920.4126 16920.0124 16918.6168 6 7 16939.3695 16931.4340 16930.7523 16926.1247 16925.8171 16925.4441 16918.6168 16918.2455 16915.6911 7 8 16939.4165 16931.1196 16930.4126 16924.6162 16924.2598 16923.9103 16916.6798 16916.3300 8 9 16939.2567 16930.5456 16929.8156 16922.9157 16922.1864 16914.5743 16914.2504 16909.2660 9 10 16938.8952 16912.2706 16911.9707 10 11 16909.7081 16909.4332 11 TO o & a. o a \u00a35 | Co ! re as \u00a7 a. s~ a' re re re s re a x1 TO\" I to Table A l . 15(a). Rotational assignments and line measurements of the 17089 c m - 1 band of 9 0 Z r C ( 3TI 1 - X 3 \u00a3 + ) . N SX(N) Rj(N) R2(N) Qi(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 17091.4993 17089.7974 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17093.1370 17090.5848 not observed 17088.8780 17089.3739 \u2014 \u2014 \u2014 1 2 17094.6298 17091.2286 17088.6677 17088.6742 17086.9725 \u2014 2 3 17095.9905 17091.7426 17088.3265 17088.2453 17085.6931 17085.1968 17083.9866 3 4 17097.2231 17092.1302 17087.8584 17087.7111 17084.3097 17083.8526 17081.7492 4 5 17098.3264 17092.3905 17087.2631 17087.0593 17086.6316 17082.8119 17082.3845 17079.3949 5 6 17099.3015 17092.5247 17086.5420 17086.2841 17085.8847 17081.1918 17080.7922 17076.9199 6 7 17100.1451 17092.5282 17085.6931 17085.3840 17085.0119 17079.4485 17079.0754 17074.3213 7 8 17100.8568 17092.4044 17084.7165 17084.3574 17084.0098 17077.5797 17077.2321 17071.5980 8 9 17101.4327 17092.1478 17083.6089 17083.2017 17082.8774 17075.5849 17075.2623 17068.7497 9 10 17101.8691 17091.7562 17082.3705 17081.9128 17081.6151 17073.4613 17073.1629 17065.7725 10 11 17102.1610 17091.2286 17080.9949 17080.4910 17080.2109 17071.2063 17070.9311 11 12 17102.3048 17090.5525 17079.4810 17078.9296 17078.6786 17068.8171 17068.5676 12 13 17102.2898 17089.7301 17077.8242 17077.2254 17066.3144 13 14 17102.1083 17088.7501 17076.0178 17075.3711 14 15 17101.7502 17087.6034 17074.0548 17073.3616 15 16 17071.9238 17071.1839 16 17 17069.6179 17068.8317 17 Table A l . 15(b). Rotational assignments and line measurements of the 17089 c m - 1 band of 9 2 Z r C (3Ui - X 3 E + ) . N SjCN) Rl(N) R2CN) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17090.0774 17088.3765 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17091.7165 17089.1655 not observed 17087.4597 17087.9568 not observed \u2014 \u2014 \u2014 1 2 17093.2115 17089.8127 17087.2528 17087.2631 17085.5582 \u2014 2 3 17094.5758 17090.3320 17086.9181 17086.8412 17084.2862 17083.7902 17082.5802 3 4 17095.8131 17090.7251 17086.4575 17086.3103 17082.9123 17082.4552 17080.3526 4 5 17096.9227 17090.9931 17085.8713 17085.6670 17081.4236 17078.0101 5 6 17097.9051 17091.1357 17085.1595 17084.9026 17079.8144 17079.4138 17075.5472 6 7 17098.7569 17091.1507 17084.3219 17084.0135 17078.0834 17072.9633 7 8 17099.4776 17091.0356 17083.3572 17082.9994 17076.2301 17070.2539 8 ts TO O 3-. o g I f TO 3 I 3? 3 TO TO 1 TO 3 TO 3 TO~ I 8-to 00 o N SX(N) Rl(N) RjfN) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 9 17100.0647 17090.7923 not observed. 17082.2631 17081.8568 not observed 17074.2498 17067.4210 9 10 17100.5141 17090.4145 17081.0383 17080.5830 17072.1419 17064.4629 10 11 17100.8229 17089.8998 17079.6795 17079.1770 17069.9038 11 12 17100.9826 17089.2435 17078.1846 17067.5342 12 13 17100.9900 17088.4409 17076.5467 17075.9500 17065.0267 13 14 17074.7633 17074.1201 14 15 17072.8258 15 Table A l . 15(c). Rotational assignments and line measurements of the 17089 c m - 1 band of 9 4 Z r C (3Tli - X 3 E + ) . N SjfN) Ri(N) R2(N) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17088.7284 17087.0299 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17090.3646 17087.8184 not observed 17086.1155 17086.6115 \u2014 \u2014 \u2014 1 2 17091.8590 17088.4661 17085.9113 17085.9184 not observed 17084.2191 not observed \u2014 2 3 17093.2241 17088.9878 17085.5784 17085.4975 17082.9507 17081.2479 3 4 17094.4625 17089.3835 17085.1225 17084.9757 17081.5833 17079.0274 4 5 17095.5748 17089.6554 17084.5406 17084.3369 17080.1010 17076.6925 5 6 17096.5599 17089.7974 17083.8358 17083.5796 17078.4999 17074.2386 6 7 17097.4170 17089.8225 17083.0052 17082.6979 17076.7784 17071.6641 7 8 17098.1450 17089.7169 17082.0482 17081.6911 17074.9335 17068.9666 8 9 17098.7390 17089.4814 17080.9642 17080.5581 17072.9633 17066.1453 9 10 17099.1990 17089.1132 17079.7495 17079.2952 17070.8684 10 11 17099.5204 17088.6110 17078.4044 17077.9028 17068.6448 11 12 17099.6958 17087.9709 17076.9199 17076.3741 12 13 17099.7210 17087.1847 17075.3035 17074.7078 13 14 17099.5867 17073.5422 17072.8987 14 Table A l . 16(a). Rotational assignments and line measurements of the 17112 c m - 1 band of 9 0 Z r C (3H.i - X 3 Z + ) . N S,(N) Ri(N) R 2 (N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 17114.6045 17113.0428 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17116.0290 17113.6887 not observed 17112.1250 17112.6218 not observed \u2014 \u2014 \u2014 1 2 17117.2406 17114.1191 17111.7715 17111.7792 17110.2186 not observed \u2014 2 TO I o & \u00a7\u2022 S5 <\u2014\u00ab $ 3 re \u00a7 a. a? 3 re 3 re I 3 re 3 x1 TO~ OO N Sj(N) Ri(N) RjCN) Qi(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 3 17118.2587 17114.3511 not observed 17111.2191 17111.1372 not observed 17108.7960 not observed 17107.2334 3 4 17119.0019 17114.3950 17110.4688 17110.3228 17107.2006 17104.8544 4 17119.1398 5 17119.6507 17114.1584 17109.5310 17109.3271 17105.4201 17102.2893 '5 17114.2939 6 17120.0820 17113.8423 17108.3215 17108.0637 17103.4569 17099.5307 6 17108.4597 17108.2018 7 17120.3201 17113.3058 17107.0172 17106.7079 17101.2176 17096.5885 7 17101.3526 8 17120.3698 17112.5767 17105.4967 17105.1389 17098.8984 8 9 17120.2333 17111.6598 17103.7843 17103.3764 17096.3607 9 10 17119.9154 17110.5587 17101.8824 17101.4260 17093.6328 10 11 17119.4188 17109.2789 17090.7191 11 12 17118.7516 17107.8231 17087.6182 12 13 17117.9176 17106.1980 13 14 17116.9267 17104.4092 14 15 17115.7893 15 16 17114.6045 17113.0428 16 Table AI.l6(b). Rotational assignments and line measurements of the 17112 c m - 1 band of 9 2 Z r C (3Tli - X 3 Z + ) . N Si(N) Ri(N) RjfN) Ql(N) Q 3 (N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 3 17116.8032 not observed not observed not observed not observed not observed not observed 3 4 17117.5947 17108.7739 17108.6267 4 5 17118.1882 17108.0982 17107.8954 5 6 17118.5843 17106.9412 17106.6856 6 7 17118.7897 17105.5872 17105.2777 7 8 17118.7941 17104.0363 17103.6784 8 TO I \u00a9 a-, o a 1 TO a a. 3? a TO 3 TO 1 >! TO 3 TO a TO\" I to 00 Table A l . 17(a). Rotational assignments and line measurements of the 17342 c m - 1 band of 9 0 Z r C (3n2 - X 3 \u00a3 + ) . N Si(N) Rj(N) R2(N) Q,(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3 ( N ) N 0 17344.9343 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17346.5882 17344.0164 17343.5075 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 17348.1015 17344.6747 17344.1281 17342.1026 17342.1097 17341.5555 \u2014 \u2014 \u2014 2 3 17349.4813 17345.2056 17344.6289 17341.7783 17341.6967 17341.2004 17339.1241 17338.6285 \u2014 3 4 17350.7120 17345.6129 17345.0078 17341.3295 17341.1825 17340.7242 17337.7562 17337.2984 17335.1832 4 5 17351.6449 17345.8902 17345.2591 17340.7545 17340.5499 17340.1224 17336.2747 17335.8461 17332.8462 5 17352.1712 6 17353.0851 17346.0177 17345.3606 17340.0310 17339.7734 17339.3741 17334.6746 17334.2747 17330.3914 6 7 17353.9819 17345.8702 17345.1881 17339.0113 17338.7029 17338.3293 17332.9486 17332.5753 17327.8121 7 17346.4520 17345.7693 17339.5379 17339.2290 17338.8551 8 17354.7853 17346.2550 17345.5481 17338.5000 17338.1399 17337.7935 17331.0735 17330.7260 17325.0877 8 9 17355.4826 17346.0523 17345.3215 17337.4460 17337.0378 17336.7152 17328.9256 17328.6034 17322.0671 9 17329.5095 17329.1848 17322.5938 10 17356.0722 17345.7628 17345.0078 17336.2977 17335.8420 17335.5433 17327.3112 17327.0133 17319.5563 10 11 17356.5551 17345.3728 17344.5946 17335.0449 17334.5411 17334.2660 17325.1110 17324.8360 17316.5041 11 12 17356.9316 17344.8784 17344.0762 17333.6847 17333.1332 17332.8826 17322.8238 17322.5731 17313.3590 12 13 17357.2023 17344.2796 17343.4531 17332.2174 17331.6184 17331.3921 17320.4364 17320.2100 17310.1090 13 14 17357.3688 17343.5760 17342.7275 17330.6463 17329.9988 17329.7962 17317.9455 17317.7432 17306.7516 14 15 17357.4314 17342.7694 17341.8972 17328.9669 17328.2741 17328.0948 17315.3512 17315.1715 17303.2891 15 16 17357.3892 17341.8591 17340.9635 17327.1848 17326.4445 17326.2887 17312.6526 17312.4961 17299.7213 16 17 17357.2451 17340.8464 17339.9272 17325.2990 17324.5129 17324.3799 17309.8503 17309.7187 17296.0490 17 18 17356.9971 17339.7321 17338.7885 17323.3087 17322.4775 17322.3676 17306.9467 17306.8372 18 19 17356.6450 17338.5128 17337.5459 17321.2189 17320.3401 17320.2530 17303.9415 17303.8551 19 20 17356.1888 17337.1914 17336.2022 17319.0244 17318.0976 17318.0354 17300.8323 17300.7699 20 21 17316.7269 17315.7542 17315.7145 17297.6222 17297.5830 21 22 17314.3242 17313.3051 17313.2897 17294.3091 17294.2926 22 23 17310.7524 17310.7601 23 24 17309.2061 17308.0935 17308.1239 24 25 17306.4826 17305.3248 17305.3776 25 26 17303.6479 17302.4418 17302.5202 26 27 17300.6970 17299.4450 17299.5448 27 ts TO | X' \u00a9 a-, o g to TO a \u00a7 a, a? a TO TO 1 3 TO a TO I 00 N SjCN) Rl(N) RjfN) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 28 17297.6222 17296.3232 17296.4456 28 29 17294.5738 29 Table Al. 17(b). Rotational assignments and line measurements of the 17342 c m - 1 band of 9 2 Z r C ( 3 n 2 - X 3 E + ) . N Si(N) Ri(N) R 2 (N) Qi(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 17342.8658 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17344.5310 17341.9505 17341.4417 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 17346.0629 17342.6221 17342.0756 17340.0406 17340.0479 17339.4945 \u2014 \u2014 \u2014 2 3 17347.4745 17343.1745 17342.5967 17339.7321 17339.6517 17339.1563 17337.0705 17336.5737 \u2014 3 4 17348.7705 17343.6102 17343.0046 17339.3090 17339.1618 17338.7029 17335.7216 17335.2631 17333.1402 4 5 17349.9525 17343.9316 17343.3002 17338.7694 17338.5662 17338.1399 17334.2660 17333.8380 17330.8252 5 6 17351.0222 17344.1394 17343.4827 17338.1175 17337.8597 17337.4601 17332.7000 17332.2993 17328.3982 6 7 17351.9804 17344.2365 17343.5549 17337.3516 17337.0423 17336.6696 17331.0225 17330.6484 17325.8604 7 8 17352.8271 17344.2215 17343.5161 17336.4743 17336.1165 17335.7684 17329.2343 17328.8864 17323.2102 8 9 17353.5643 17344.0966 17343.3654 17335.4860 17335.0794 17334.7558 17327.3362 17327.0133 17320.4508 9 10 17354.1932 17343.8614 17343.1074 17334.3866 17333.9322 17333.6336 17325.3267 17325.0280 17317.5798 10 11 17354.7118 17343.5161 17342.7397 17333.1791 17332.6766 17332.4013 17323.2102 17322.9333 17314.5979 11 12 17355.1232 17343.0655 17342.2644 17331.8619 17331.3123 17331.0625 17320.9809 17320.7296 17311.5066 12 13 17355.4268 17342.5065 17341.6816 17330.4366 17329.8383 17329.6122 17318.6444 17318.4176 17308.3065 13 14 17355.6245 17341.8393 17340.9907 17328.9039 17328.2598 17328.0558 17316.2019 17315.9983 17304.9981 14 15 17355.7151 17341.0664 17340.1947 17327.2644 17326.5726 17326.3927 17313.6513 17313.4715 17301.5823 15 16 17355.6984 17340.1869 17339.2938 17325.5176 17324.7795 17324.6230 17310.9946 17310.8389 17298.0578 16 17 17355.5775 17339.2036 17338.2845 17323.6647 17322.8799 17322.7473 17308.2325 17308.0990 17294.4293 17 18 17355.3472 17338.1114 17337.1711 17321.7063 17320.8759 17320.7648 17305.3643 17305.2549 18 19 17336.9158 17335.9495 17319.6418 17318.7647 17318.6769 17302.3911 17302.3050 19 20 17317.4710 17316.5477 17316.4827 17299.3118 17299.2483 20 21 17315.1930 17314.2228 17314.1826 17296.1280 17296.0873 21 tS re | O o I S TO \u00a7 a, ST? s TO TO I TO 3 E * TOT 8-to 00 -1^  Table Al. 17(c). Rotational assignments and line measurements of the 17342 c m - 1 band of 9 4 Z r C ( 3 n 2 - X 3 E + ) . N SjfN) Rl(N) R^CN) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17341.2793 \u2014 \u2014 \u2014\u2022 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17342.9429 17340.3659 17339.8569 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 17344.4740 17341.0385 17340.4922 17338.4617 17338.4680 17337.9152 \u2014 \u2014 \u2014 2 3 17345.8902 17341.5923 17341.0156 17338.1562 17338.0747 17337.5793 17335.4966 17335.0025 \u2014 3 4 17347.1861 17342.0321 17341.4275 17337.7364 17337.5904 17337.1317 17334.1547 17333.6959 17331.5778 4 5 17348.3729 17342.3594 17341.7278 17337.2040 17337.0005 17336.5737 17332.7051 17332.2776 17329.2699 5 6 17349.4476 17342.5740 17341.9179 17336.5592 17336.3016 17335.9029 17331.1479 17330.7483 17326.8528 6 7 17350.4117 17342.6777 17341.9967 17335.8030 17335.4966 17335.1216 17329.4814 17329.1073 17324.3270 7 8 17351.2656 17342.6719 17341.9666 17334.9356 17334.5784 17334.2301 17327.7050 17327.3567 17321.6905 8 9 17352.0095 17342.5555 17341.8263 17333.9583 17333.5524 17333.2293 17325.8195 17325.4951 17318.9438 9 10 17352.6448 17342.3311 17341.5775 17332.8706 17332.4170 17332.1179 17323.8238 17323.5242 17316.0875 10 11 17353.1706 17341.9967 17341.2197 17331.6745 17331.1733 17330.8977 17321.7196 17321.4429 17313.1210 11 12 17353.5889 17341.5555 17340.7545 17330.3687 17329.8203 17329.5684 17319.5066 17319.2550 17310.0466 12 13 17353.8987 17341.0039 17340.1799 17328.9559 17328.3593 17328.1323 17317.1852 17316.9576 17306.8631 13 14 17354.1006 17340.3460 17339.4945 17327.4339 17326.7916 17326.5864 17314.7558 17314.5519 17303.5707 14 15 17354.1932 17339.5796 17338.7111 17325.8048 17325.1110 17324.9337 17312.2198 17312.0396 17300.1714 15 16 17354.1807 17338.7111 17337.8136 17324.0677 17323.3324 17323.1730 17309.5770 17309.4191 17296.6646 16 17 17354.0596 17337.7268 17336.8111 17322.2244 17321.4429 17321.3065 17306.8267 17306.6929 17 18 17353.8287 17336.6422 17335.6999 17320.2719 17319.4438 17319.3321 17303.9703 17303.8590 18 19 17335.4435 17334.4810 17318.2138 17317.3389 17317.2504 17301.0067 17300.9181 19 20 17316.0459 17315.1247 17315.0606 17297.9358 17297.8704 20 21 17313.7714 17312.8032 17312.7591 17294.7569 17294.7145 21 Table A I . l 8. Rotational assignments and line measurements of the hot 17458 c m - 1 band3 of 9 0 Z r C (31T l - X 3 E + , o = 1). N S!(N) Rl(N) R 2 (N) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17460.4398 17458.7896 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17462.0025 17459.5309 not observed not observed \u2014 \u2014 \u2014 1 2 17463.3972 17460.1020 not observed not observed \u2014 2 3 17464.6356 17460.5211 17457.2197 17457.1285 not observed 3 4 17465.7185 17460.7891 17456.6642 17456.5100 4 ts TO \u00a9 a. o I 1 TO I a? a TO 3 TO I 3 TO a TO \u00a7 to 00 N SjfN) Rl(N) R 2 (N) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 5 17466.6445 17460.9011 not observed 17455.9577 17455.7438 not observed not observed not observed not observed 5 6 17467.4122 17460.8592 17455.0978 17454.8297 6 7 17468.0145 17460.6581 17454.0832 17453.7623 7 8 17468.4469 17460.2929 17452.9099 17452.5356 8 9 17468.6826 17459.7579 17451.5704 17451.1482 9 10 17459.0223 10 a This band has the same upper state as the 18338 cm 1 band of 9 0 Z r C ^ - X 3E+) listed in Table AI.34(a). Table A l . 19(a). Rotational assignments and line measurements of the 17494\/506 c m - 1 band3 of 9 0 Z r C ^ T T Q - X 3 Z + ) . N SifN) Rl(N) R2(N) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2 (N) 0 3(N) N 0 17497.1409 17507.3603 \u2014 17494.5412 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17498.8187 17508.1333 17507.6237 17494.4905 17493.9810 \u2014 17505.0879 \u2014 1 2 17500.3572 17508.7531 17508.2065 17494.3086 17494.3147 17493.7618 17504.5353 17503.9825 17491.7171 2 3 17501.7486 17509.2331 17508.6556 17494.0073 17493.9263 17493.4308 17503.2403 17502.7455 17489.5978 3 4 17503.2794 17509.5741 17508.9687 17493.5867 17493.4390 17492.9806 17501.8349 17501.3764 17487.3902 4 17502.8647 5 17504.4039 17509.7750 17509.1432 17493.0225 17492.8176 17492.3899 17500.3017 17499.8739 17485.0765 5 6 17505.4602 17509.8326 17509.1750 17492.5981 17492.3404 17491.9411 17498.6357 17498.2362 17482.6476 6 17492.1851 17491.9273 17491.5277 7 17506.4024 17509.7431 17509.0608 17491.7709 17491.4622 17491.0887 17496.8327 17496.4601 17480.0798 7 8 17507.2157 17509.5013 17508.7947 17490.8747 17490.5165 17490.1691 17494.8888 17494.5412 17477.6538 8 17477.2411 9 17507.8926 17509.1025 17508.3724 17489.8659 17489.4586 17489.1352 17492.7989 17492.4763 17474.8268 9 10 17508.4210 17508.5393 17507.7852 17488.7287 17488.2729 17487.9742 17490.5581 17490.2597 17471.9320 10 11 17508.7895 17507.8052 17507.0266 17487.4547 17486.9528 17486.6783 17488.1610 17487.8868 17468.9242 11 12 17508.9815 17506.8898 17506.0880 17486.0333 17485.4825 17485.2318 17485.5999 17485.3502 17465.7897 12 13 17508.9815 17505.7856 17504.9603 17484.4520 17483.8531 17483.6271 17482.8699 17482.6425 17462.5196 13 14 17508.7617 17504.4834 17503.6341 17482.6962 17482.0498 17481.8467 17479.9572 17479.7541 17459.1014 14 15 17508.2972 17502.9706 17502.0983 17480.7451 17480.0526 17479.8730 17476.8576 17476.6786 17455.5244 15 16 17507.5581 17501.2396 17500.3443 17478.5775 17477.8384 17477.6822 17473.5595 17473.4036 17451.7719 16 17 17506.5116 17499.2754 17498.3586 17476.1652 17475.3794 17475.2470 17470.0527 17469.9192 17 32 re a 8-o & a. o a a l f 3 re a S? I a* a' re re I 3 re a S 3 -\"a re-to 00 ON N Si(N) Ri(N) Ra(N) Qm Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 18 17505.1298 17497.0729 17496.1334 17473.4790 17472.6459 17472.5364 17466.3262 17466.2168 18 19 17470.4859 17469.6072 17469.5199 17462.3708 17462.2853 19 20 17467.1583 17466.2331 17466.1695 17458.1117 20 T h i s band has the same upper state as the hot 16626 cm\" 1 band of 9 0ZrC ^UQ-X3!,*, v= 1) listed in Table AI.5. Table A l . 19(b). Rotational assignments and line measurements of the 17494\/506 c m - 1 b a n d o f 9 2 Z r C ( 3 n o - X 3 Z + ) . N R,(N) R2(N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 17494.2534 17502.1242 \u2014 17491.6699 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17495.9151 17502.8609 17502.3521 17491.6171 17491.1079 \u2014 17499.8739 \u2014 1 2 17497.4353 17503.4312 17502.8846 17491.4295 17491.4364 17490.8809 17499.3059 17498.7531 17488.8537 2 3 17498.8261 17503.8434 17503.2662 17491.1170 17491.0351 17490.5385 17497.9819 17497.4859 17486.7391 3 4 17500.0879 17504.0999 17503.4948 17490.6810 17490.5347 17490.0763 17496.5306 17496.0720 17484.5286 4 5 17501.2169 17504.1987 17503.5669 17490.1211 17489.9173 17489.4902 17494.9346 17494.5069 17482.2079 5 6 17502.2079 17504.1355 17503.4779 17489.4341 17489.1773 17488.7778 17493.1896 17492.7896 17479.7702 6 7 17503.0564 17503.9061 17503.2238 17488.6163 17488.3079 17487.9348 17491.2895 17490.9159 17477.2122 7 8 17503.7503 17503.5039 17502.7986 17487.6617 17487.3036 17486.9528 17489.2290 17488.8810 17474.5311 8 9 17504.2776 17502.9263 17502.1959 17486.5622 17486.1561 17485.8326 17487.0045 17486.6783 17471.7155 9 10 17504.6243 17502.1640 17501.4093 17485.3093 17484.8551 17484.5560 17484.6104 17484.3104 17468.7670 10 11 17504.7773 17501.2110 17500.4332 17483.8917 17483.3893 17483.1142 17482.0392 17481.7647 17465.6746 11 12 17504.7187 17500.0587 17499.2573 17482.2944 17481.7461 17481.4938 17479.2833 17479.0320 17462.4290 12 13 17504.4466 17498.7015 17497.8774 17480.5021 17479.9042 17479.6777 17476.3386 17476.1105 17459.0186 13 14 17497.1310 17496.2830 17478.4990 17477.8555 17477.6538 17473.1942 17472.9904 17455.4307 14 15 17495.3200 17494.4492 17476.2835 17475.5913 17475.4120 17469.8465 17469.6659 17451.6479 15 16 17493.2747 17492.3899 17473.1051 17472.9481 17466.2855 17466.1287 16 17 17471.1833 17470.3990 17470.2687 17 Table A l . 19(c). Rotational assignments and line measurements of the 17494\/506 c m - 1 bandof 9 4 ZrC ( 3 n 0 - X 3 E + ) . N Sx(N) Ri(N) R2(N) Ql(N) Q 3 (N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 17490.9519 17495.4688 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17492.5643 17496.1683 17495.6586 17488.3547 17487.8455 \u2014 17493.2219 \u2014 1 2 17494.0210 17496.6812 17496.1334 17488.1344 17488.1417 17487.5886 17492.6572 17492.1045 2 TO S-\u00ab' >3 O & Sr. o I f 3 TO a 1 a? a TO TO S >! TO TO a TO I OO N SjfN) Rl(N) R2CN) Ql(N) Q 3(N) Q2CN) P 3(N) P 2(N) 0 3 ( N ) N 3 17495.3321 17497.0196 17496.4424 17487.7782 17487.6974 17487.2010 17491.3003 17490.8046 17483.4871 3 4 17496.4945 17497.1837 17496.5783 17487.2836 17487.1372 17486.6783 17489.7983 17489.3388 17481.2509 4 5 17497.5013 17497.1727 17496.5415 17486.6489 17486.4457 17486.0176 17488.1344 17487.7042 17478.8906 5 6 17498.3429 17496.9838 17496.3263 17485.8675 17485.6111 17485.2121 17486.2994 17485.8995 17476.4008 6 7 17499.0073 17496.6130 17495.9319 17484.9316 17484.6241 17484.2506 17484.2962 17483.9216 17473.7711 7 8 17499.4803 17496.0560 17495.3498 17483.8314 17483.4740 17483.1253 17482.1149 17481.7647 17470.9984 8 9 17499.7435 17495.3085 17494.5791 17482.5540 17482.1480 17481.8248 17479.7541 17479.4301 17468.0722 9 10 17499.7800 17493.6134 17481.0857 17480.6314 17480.3316 17477.2100 17476.9076 17464.9829 10 11 17499.5716 17479.4088 17478.9070 17478.6316 17474.4715 17474.1968 17461.7171 11 12 17477.5048 17476.9558 17476.7045 17471.5390 17471.2891 17458.2606 12 13 17475.3562 17474.7610 17474.5311 17454.5971 13 Table AI.20(a). Rotational assignments and line measurements of the 1 7 5 3 5 \/ 3 8 c m - 1 band3 of 9 0 Z r C (3ITQ - X 3 E + ) . N Si(N) Ri(N) R 2 (N) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2 (N) 0 3 ( N ) N 0 17537.5014 17538.7925 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17538.8594 17539.4705 17538.9615 17535.0662 17534.5576 \u2014 17536.5685 \u2014 1 2 17539.9800 17539.9510 17539.4044 17534.6693 17534.6772 17534.1237 17535.9677 17535.4144 2 3 17540.8795 17540.2496 17539.6715 17534.0487 17533.9666 17533.4708 17534.5783 17534.0818 17530.1743 3 4 17541.5631 17540.3715 17539.7662 17533.2093 17533.0637 17532.6038 17533.0330 17532.5741 17527.7504 4 5 17542.0324 17540.3205 17539.6890 17532.1528 17531.9482 17531.5214 17531.3182 17530.8909 17525.1182 5 6 17542.2913 17540.1009 17539.4439 17530.8824 17530.6243 17530.2251 17529.4331 17529.0341 17522.2708 6 7 17542.3441 17539.7163 17539.0343 17529.3987 17529.0901 17528.7174 17527.3780 17527.0055 17519.2102 7 8 17542.1927 17539.1714 17538.4647 17527.7062 17527.3474 17527.0006 17525.1579 17524.8093 17515.9379 8 9 17541.8433 17538.4708 17537.7410 17525.8075 17525.3989 17525.0760 17522.7717 17522.4492 17512.4547 9 10 17541.3020 17537.6239 17536.8697 17523.7074 17523.2486 17522.9500 17520.2284 17519.9296 17508.7617 10 11 17540.5770 17536.6359 17535.8575 17521.4053 17520.9030 17520.6271 17517.5294 17517.2559 17504.8667 11 12 17539.6759 17535.5153 17534.7139 17518.9143 17518.3630 17518.1131 17514.6855 17514.4345 17500.7664 12 13 17538.6176 17534.2730 17533.4480 17516.2391 17515.6409 17515.4146 17511.6998 17511.4735 17496.4688 13 14 17537.4113 17532.9188 17532.0692 17513.3917 17512.7453 17512.5418 17508.5846 17508.3801 17491.9855 14 15 17536.0808 17531.4624 17530.5908 17510.3820 17509.6892 17509.5091 17505.3453 17505.1656 15 16 17534.6491 17529.9174 17529.0215 17507.2295 17506.4861 17506.3314 17501.9953 17501.8380 16 ts TO a & X >) & a. o a a \u00ab\u00bb\u2022\u00ab I \u00a7 TO a I a, a~ a' TO 3 TO I 3 TO a TO-I to OO 00 N S,(N) R X (N) R 2 (N) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3 (N) N 17 17533.1445 17528.2923 17527.3724 17503.9492 17503.1622 17503.0300 17498.5445 17498.4125 17 TO a 18 17531.6021 17526.5976 17525.6550 17500.5698 17499.7365 17499.6268 17495.0047 17494.8946 18 a. 19 17524.8401 17523.8738 17497.1202 17496.2402 17496.1535 17491.3853 17491.3003 19 20 17523.0264 17522.0369 17487.6974 17487.6348 20 21 17521.1578 17520.1455 17483.9507 17483.9090 21 & 22 17519.2358 17518.2009 17480.1424 17480.1270 22 a. \u00a7 23 17517.2559 17516.2001 17476.2835 17476.2896 23 \u00a35 24 17472.3741 17472.4015 24 ass T h i s band has the same upper state as the hot 16655\/58 cm\" 1 band of 9 0 Z r C C3!^ - X 3 \u00a3 + , v = 1) listed in Table AI.8. 1 Table AI.20(b). Rotational assignments and line measurements of the 17535\/38 c m - 1 band of 9 2 Z r C (3Ilo - X 3 E + ) . znts at N Si(N) Rl(N) RjfN) Qi(N) Q3CN) Q 2 (N) P 3(N) P 2(N) 0 3 (N) N ~ i a. 3\" 0 17529.8583 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 a' TO 1 17530.5707 17530.0612 \u2014 17527.6172 \u2014 1 3 TO 2 17531.1045 17530.5579 17525.1259 17525.1342 17524.5795 17527.0427 17526.4870 2 a 3 17531.3902 17531.4769 17530.8989 17524.5229 17523.9461 17525.6912 17525.1951 3 4 17532.1082 17531.6929 17531.0889 17523.7074 17523.5628 17523.1031 17524.2047 17523.7459 17518.2251 4 3 TO 5 17532.6248 17531.7569 17531.1254 17522.6851 17522.4814 17522.0534 17522.5679 17522.1403 17515.6154 5 a S 3 \" 6 17532.9422 17531.6741 17531.0172 17521.4558 17521.1980 17520.7982 17520.7819 17520.3827 6 7 17533.0637 17531.4497 17530.7681 17520.0238 17519.7144 17519.3430 17518.8484 17518.4737 17509.7750 7 8 17533.0042 17531.0889 17530.3835 17518.3938 17517.6897 17516.7690 17516.4202 17506.5507 8 TO* 9 17532.7645 17530.5984 17529.8682 17516.5725 17516.1650 17515.8423 17514.5495 17514.2260 17503.1240 9 10 17532.3564 17529.9857 17529.2311 17514.5637 17514.1090 17513.8099 17512.1943 17511.8955 17499.4989 10 1 11 17531.7938 17529.2558 17528.4780 17512.3793 17511.8741 17511.6009 17509.7108 17509.4356 17495.6844 11 12 17528.4170 17527.6172 17510.0261 17509.4759 17509.2258 17507.1052 17506.8545 12 13 17527.4770 17526.6533 17507.5199 17506.9139 17506.6947 17504.3835 17504.1548 17487.5074 13 14 17526.4436 17525.5950 17504.2307 17504.0276 17501.5551 17501.3504 17483.1612 14 15 17498.6229 17498.4435 15 16 17495.5994 17495.4424 16 OO Table AI.20(c). Rotational assignments and line measurements of the 17535\/38 c m - 1 band of 9 4 Z r C (3TIo - X 3 S + ) . N Si(N) Rl(N) R 2 (N) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3 (N) N 0 17519.1937 17522.9026 \u2014 \u2014 \u2014 \u2014 0 1 17520.5884 17523.6564 17523 1472 17516.2303 \u2014 17520.6473 \u2014 1 2 17521.7645 17524.2539 17523 7074 17516.3728 17516 3804 17515.8247 17520.0921 17519.5401 2 3 17522.7411 17524.7109 17524 1334 17515.8007 17515 7193 17515.2238 17518.7888 17518.2930 3 4 17523.5247 17525.0321 17524 4278 17515.0282 17514 8813 17514.4231 17517.3699 17516.9111 4 5 17524.1207 17525.2242 17524 5928 17514.0576 17513 8553 17513.4264 17515.8247 17515.3956 17506.9139 5 6 17524.5378 17525.2884 17524 6326 17512.8971 17512 6403 17512.2415 17514.1483 17513.7486 6 7 17524.7840 17525.2319 17524 5508 17511.5508 17511 2439 17510.8700 17512.3468 17511.9720 17501.1811 7 8 17524.8696 17525.0571 17524 3520 17510.0261 17509 6689 17509.3198 17510.4200 17510.0714 17498.0291 8 9 17524.8093 17524.7682 17524 0383 17508.3300 17507 9246 17507.6008 17508.3724 17508.0496 17494.6915 9 10 17524.6136 17524.3694 17523 6158 17506.4768 17506 0211 17505.7214 17506.2091 17505.9089 10 11 17524.3036 17523.8655 17523 0887 17504.4733 17503 9713 17503.6953 17503.9319 17503.6559 17487.4927 11 12 17523.8971 17523.2594 17522 4591 17502.3374 17501 7887 17501.5379 17501.5454 17501.2930 12 13 17523.4145 17522.5546 17521 7301 17500.0879 17499 4916 17499.2638 17499.0538 17498.8261 13 14 17521.7528 17520 9054 17497.7424 17496.8942 17496.4601 17496.2571 17475.5398 14 15 17520.8580 17519 9872 17495.3200 17494 6303 17494.4492 17493.7694 17493.5867 15 16 17518 9765 17490.8256 16 17 17518.7888 17517 8723 17 18 17517.6191 17516 6783 18 Table AJ.21(a). Rotational assignments and line measurements of the 17673 c m - 1 band3 of 9 0 Z r C (^H - X 3 \u00a3 + ) . N SjfN) Ri(N) R2(N) Q,(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3 (N) N 0 17676.0238 17674.3217 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17677.6575 17675.1097 17674.5993 17673.4027 17673.8994 \u2014 \u2014 \u2014 1 2 17679.1437 17675.7493 17673.1920 17673.1984 17671.4973 \u2014 2 3 17680.4937 17676.2576 17672.8474 17672.7665 17672.2695 17670.2174 17669.7204 17668.5111 3 4 17681.7065 17676.6326 17672.3727 17672.2258 17671.7664 17668.8314 17668.3729 17666.2745 4 5 17682.7806 17676.8745 17671.7664 17671.5619 17671.1321 17667.3265 17666.8987 17663.9161 5 6 17683.7137 17676.9800 17671.0259 17670.7677 17670.3677 17665.6948 17665.2947 17661.4344 6 7 17684.4984 17676.9447 17670.1475 17669.8373 17669.4654 17663.9330 17663.5590 17658.8244 7 ts TO | X ' O a-, o g 1 3 TO a \u00a7 a. a? a TO TO i 3 TO a 8-to o N SjfN) Rl(N) RjfN) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 8 17685.1320 17676.7641 17669.1281 17668.7699 17668.4225 17662.0370 17661.6883 17656.0820 8 9 17685.6098 17676.4327 17667.9632 17667.5553 17667.2324 17660.0009 17659.6780 17653.2040 9 10 17675.9444 17666.6460 17666.1896 17657.8212 17657.5233 10 11 17675.2929 17665.1721 17664.6679 17664.3915 17655.4912 17655.2164 11 12 17674.4694 17663.5337 17662.9821 17662.7317 17653.0054 12 13 17673.4686 17661.7247 17661.1269 13 14 17659.7383 17659.0950 14 15 17657.5678 17656.8758 15 a This band has the same upper state as the 17485 cm\" 1 band of 9 0 Z r C (Q' = 1 - a1!*) listed in Table AI I . l . Table AI.21(b). Rotational assignments and line measurements of the 17673 c m - 1 banda of 9 2 Z r C ( i f l - X 3 \u00a3 + ) . N SjCN) Ri(N) RzCN) Ql(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 17671.0675 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17674.3607 17671.8372 not observed not observed \u2014 \u2014 \u2014 1 2 17675.8150 17672.4563 17669.9251 not observed \u2014 2 3 17677.1272 17672.9348 17669.5618 17669.4802 17666.9589 3 4 17678.2948 17673.2766 17669.0596 17668.9141 17663.0256 4 5 17673.4756 17668.4225 17668.2182 17664.0265 17660.6537 5 6 17680.1919 17673.5302 17667.6453 17667.3848 17662.3666 6 7 17673.4381 17666.7176 17666.4093 17660.5661 7 8 17673.1920 17665.6431 17665.2868 17658.6247 8 9 17672.7879 17664.4175 17664.0134 17656.5376 9 10 17663.0321 17662.5781 17654.2984 10 11 17661.4836 17660.9828 11 12 17659.7636 12 a This band has the same upper state as the 17485 cm\" 1 band of 9 2 Z r C (fi' = 1 - a 1 S + ) listed in Table AIL 1. 32 re I o & a. o \u00a3i I 3 re a I a~ a' re re I 3 re 3 re \u00ab\u2022* o I Co Table AI.21(c). Rotational assignments and line measurements of the 17673 c m - 1 banda of 9 4 Z r C (lYl - X 3 2 + ) . N SjCN) RjCN) RafN) Qi(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17667.7053 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17670.9577 not observed not observed \u2014 \u2014 \u2014 1 2 17672.3786 17669.0596 not observed \u2014 2 3 17673.6509 17669.5063 17666.1699 17666.0903 17664.8966 not observed 3 4 17674.7740 17669.8092 17665.6431 17665.4964 4 5 17675.7493 17669.9652 17664.9678 17664.7653 17660.6189 5 6 17669.9652 17664.1469 17663.8914 6 7 17669.8157 17663.1742 17662.8683 7 8 17669.5049 17662.0451 17661.6883 8 9 17660.7567 17660.3514 9 \"This band has the same upper state as the 17485 c n r 1 band of 9 4 Z r C (Q! = 1 - a1!*) listed in Table AI I . l . Table Al.22(a). Rotational assignments and line measurements of the 17689 c m - 1 banda of 9 0 Z r C (LIJ - X 3 \u00a3 + ) . N R,(N) R 2 (N) Qi(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17692.3727 17690.7615 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17693.9040 17691.4890 17689.8296 17690.3247 17689.3205 \u2014 \u2014 \u2014 1 2 17695.2666 17692.0438 17689.5407 17689.5482 17688.9948 17687.9357 \u2014 2 3 17696.4783 17692.4411 17689.0927 17689.0127 17688.5160 17686.5966 17684.9380 3 4 17697.5416 17692.6823 17688.4954 17688.3485 17687.8906 17685.1253 17682.6230 4 5 17698.4637 17692.7744 17687.7502 17687.5459 17687.1194 17683.5095 17680.1619 5 6 17699.2370 17692.7159 17686.8613 17686.6025 17686.2048 17681.7446 17677.5572 6 7 17699.8738 17692.5102 17691.8299 17685.8281 17685.5185 17685.1452 17679.8324 17679.4594 17674.8084 7 8 17700.3684 17692.1587 17691.4502 17684.6536 17684.2940 17683.9470 17677.7725 17677.4267 17671.9173 8 9 17700.7240 17691.6590 17690.9279 17683.3372 17682.9297 17682.6070 17675.5658 17675.2416 17668.8842 9 10 17700.9380 17691.0169 17681.8811 17681.4262 17681.1274 17673.2139 17672.9150 17665.7099 10 11 17701.0101 17690.2297 17689.4507 17680.2867 17679.7832 17679.5081 17670.7176 17670.4428 17662.3956 11 12 17700.9380 17689.2983 17688.4954 17678.5509 17678.0003 17677.7492 17668.0779 17667.8272 17658.9432 12 13 17700.7108 17688.2194 17676.6680 17676.0753 17675.8478 17665.2947 17665.0671 17655.3507 13 14 17700.3312 17686.9877 17674.6516 17674.0055 17673.8029 17662.3666 17662.1637 14 ts ts TO a 8-x' \u00a9 a. o a I 3 TO a 1 a TO 3 TO 8 \u00ab TO 3 TO a 55* \u00a7 to to N S,(N) R , ( N ) R 2 ( N ) Q , ( N ) Q 3 ( N ) Q 2 ( N ) P 3 ( N ) P 2 ( N ) 0 3 ( N ) N 1 5 1 7 6 8 5 . 5 9 5 7 1 7 6 7 2 . 4 7 9 0 1 7 6 7 1 . 7 8 5 7 1 7 6 7 1 . 6 0 6 4 1 7 6 5 9 . 2 9 1 2 17659.1123 1 5 1 6 1 7 6 8 4 . 0 3 8 3 17670.1475 1 7 6 6 9 . 4 0 6 8 1 7 6 6 9 . 2 5 1 4 1 7 6 5 6 . 0 6 4 2 1 7 6 5 5 . 9 0 7 7 1 6 1 7 17667.6453 1 7 6 6 6 . 8 5 7 9 1 7 6 6 6 . 7 2 5 8 1 7 6 5 2 . 6 7 8 4 1 7 1 8 1 7 6 6 4 . 9 5 7 0 1 7 6 6 4 . 1 2 3 6 1 7 6 6 4 . 0 1 3 4 1 8 1 9 1 7 6 6 2 . 0 6 5 4 1 7 6 6 1 . 1 8 5 5 1 7 6 6 1 . 0 9 9 9 1 9 2 0 17659.1123 1 7 6 5 8 . 1 2 6 6 2 0 a T h i s b a n d h a s t h e s a m e u p p e r s t a t e a s t h e 1 7 5 0 1 c m \" 1 b a n d o f 9 0 Z r C ( Q ' = 1 - alI,+) l i s t e d i n T a b l e A I I . 2 . TO a & o & a-, o a **** | Table AI.22(b). Rotational assignments and line measurements of the 17689 c m - 1 banda of 9 2 Z r C (Ifl - X 3 \u00a3 + ) . N S ! < N ) R l ( N ) R j C N ) Q l ( N ) Q 3 ( N ) Q 2 ( N ) P 3 ( N ) P 2 ( N ) 0 3 ( N ) N 0 1 7 6 8 7 . 5 4 1 1 1 7 6 8 5 . 8 9 7 3 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17689.0927 1 7 6 8 6 . 6 2 3 9 n o t o b s e r v e d 1 7 6 8 4 . 9 8 2 9 1 7 6 8 5 . 4 7 8 6 \u2014 \u2014 \u2014 1 2 1 7 6 9 0 . 4 6 8 4 1 7 6 8 7 . 1 7 7 3 1 7 6 8 4 . 7 1 6 5 1 7 6 8 4 . 7 2 3 8 1 7 6 8 4 . 1 7 1 2 1 7 6 8 3 . 0 8 0 6 n o t o b s e r v e d \u2014 2 3 1 7 6 9 1 . 6 8 7 8 1 7 6 8 7 . 5 7 2 2 17684.2940 1 7 6 8 4 . 2 1 0 0 17683.7138 17681.7446 3 4 1 7 6 9 2 . 7 5 6 8 17687.8123 1 7 6 8 3 . 7 1 3 7 1 7 6 8 3 . 5 6 7 4 1 7 6 8 0 . 2 7 7 5 1 7 6 7 7 . 8 1 4 7 4 5 1 7 6 9 3 . 6 7 3 3 1 7 6 8 7 . 9 0 1 3 1 7 6 8 2 . 9 8 4 4 1 7 6 8 2 . 7 8 0 6 1 7 6 7 8 . 6 6 4 2 1 7 6 7 5 . 3 8 3 5 5 6 1 7 6 9 4 . 4 4 0 9 1 7 6 8 7 . 8 3 9 9 1 7 6 8 2 . 1 0 3 2 1 7 6 8 1 . 8 4 6 0 1 7 6 7 6 . 9 0 4 3 1 7 6 7 2 . 8 0 4 3 6 7 1 7 6 9 5 . 0 5 8 6 1 7 6 8 7 . 6 2 6 3 1 7 6 8 1 . 0 7 2 4 1 7 6 8 0 . 7 6 5 0 1 7 6 8 0 . 3 9 0 8 1 7 6 7 4 . 9 9 4 0 1 7 6 7 0 . 0 7 4 7 7 8 1 7 6 9 5 . 5 2 7 4 1 7 6 8 7 . 2 6 0 3 1 7 6 7 9 . 8 9 1 8 1 7 6 7 9 . 5 3 5 8 1 7 6 7 2 . 9 3 4 8 1 7 6 6 7 . 1 9 8 6 8 9 1 7 6 9 5 . 8 4 0 0 1 7 6 8 6 . 7 4 4 0 1 7 6 7 8 . 5 6 4 7 1 7 6 7 8 . 1 5 8 0 1 7 6 7 0 . 7 2 5 4 1 7 6 6 4 . 1 7 2 2 9 1 0 1 7 6 8 6 . 0 7 8 4 1 7 6 7 7 . 0 8 6 0 17676.6326 1 7 6 6 8 . 3 6 6 9 1 7 6 6 0 . 9 9 8 9 1 0 1 1 17685.2485 1 7 6 7 5 . 4 5 5 7 1 7 6 7 4 . 9 5 3 6 1 7 6 6 5 . 8 5 7 8 1 7 6 5 7 . 6 7 7 3 1 1 1 2 1 7 6 9 5 . 8 5 2 7 1 7 6 8 4 . 2 6 7 8 1 7 6 6 3 . 1 9 6 8 1 7 6 5 4 . 2 0 6 0 1 2 1 3 17683.1227 1 7 6 6 0 . 3 8 1 5 1 3 1 4 1 7 6 5 7 . 4 0 5 9 1 4 1 5 1 7 6 5 4 . 2 6 7 1 1 5 3 TO a 55* I a TO TO \u00ab TO 2 TO a x* TO\"\" X ^ a T h i s b a n d h a s t h e s a m e u p p e r s t a t e a s t h e 1 7 5 0 1 c n r 1 b a n d o f 9 2 Z r C ( O ' = 1 - a 1 ! * ) l i s t e d i n T a b l e A I I . 2 to sD Table Al.22(c). Rotational assignments and line measurements of the 17689 c m - 1 banda of 9 4 Z r C ( i f l - X 3 \u00a3 + ) . N SifN) Rj(N) RjfN) Ql(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3 (N) N 0 17682.6583 17681.0207 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17684.1938 17681.7410 not observed 17680.1081 not observed \u2014 \u2014 \u2014 1 2 17685.5594 17682.2859 17679.8455 17678.2101 not observed \u2014 2 3 17686.7635 17682.6706 17679.4085 17679.3269 17676.8745 3 4 17687.8123 17682.8983 17678.8210 17678.6756 17675.4024 17672.9547 4 5 17688.7011 17682.9692 17678.0810 17677.8773 17673.7845 17670.5216 5 6 17689.4348 17682.8838 17677.1836 17676.9278 17672.0157 17667.9385 6 7 17690.0099 17682.6426 17676.1313 17675.8244 17670.0925 17665.2031 7 8 17690.4233 17682.2406 17674.9222 17674.5659 17668.0159 17662.3155 8 9 17690.6707 17681.6777 17673.5568 17673.1512 17665.7825 17659.2729 9 10 17690.7515 17680.9507 17672.0296 17671.5751 17663.3923 17656.0744 10 11 17690.6524 17680.0546 17670.3372 17669.8373 17660.8415 11 12 17690.3731 17678.9838 17668.4755 17667.9269 17658.1266 12 13 17677.7290 17666.4389 17665.8418 17655.2436 13 14 17676.2863 17664.2180 17663.5742 17652.1853 14 15 17674.6395 15 a This band has the same upper state as the 17501 cm\" 1 band of 9 4 Z r C (Q'=l- listed in Table AII.2. Table AT23 (a). Rotational assignments and line measurements of the 17690\/700 c m - 1 banda of 9 0 Z r C (3rio - X 3 E + ) . N SX(N) R X (N) R 2 (N) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3 (N) N 0 17692.8189 17701.0273 \u2014 17690.2544 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17694.4534 17701.7769 17701.2679 17690.1944 17689.6850 \u2014 17698.7655 \u2014 1 2 17695.9313 17702.3641 17701.8176 17689.9872 17689.4404 17698.2025 17697.6482 17687.4307 2 3 17697.2665 17702.8036 17702.2263 17689.6423 17689.5613 17689.0656 17696.8843 17696.3896 17685.3023 3 4 17698.4637 17703.0985 17702.4937 17689.1595 17689.0127 17688.5541 17695.4461 17694.9877 17683.0712 4 5 17699.5240 17703.2508 17702.6183 17688.5396 17688.3350 17687.9080 17693.8725 17693.4453 17680.7113 5 6 17700.4489 17703.2606 17702.6032 17687.7829 17687.5258 17687.1263 17692.1587 17691.7605 17678.2206 6 7 17701.2405 17703.1290 17702.4468 17686.8908 17686.5822 17686.2076 17690.3081 17689.9360 17675.5983 7 8 17701.8992 17702.8563 17702.1504 17685.8639 17685.5049 17685.1581 17688.3164 17687.9690 17672.8393 8 9 17702.4283 17702.4468 17701.7126 17684.7043 17684.2940 17683.9738 17686.1855 17685.8639 17669.9475 9 ts TO I a. \u00a9 I I 1 TO \u00a7 a? a TO TO I 3 TO a TO \u00ab>\u2022*. I N $m Ri(N) Ra(N) Ql(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 10 17702.8270 17701.8884 17701.1341 17683.4132 17682.9570 17682.6583 17683.9140 17683.6153 17666.9210 10 11 17703.0985 17701.1938 17700.4157 17681.9913 17681.4877 17681.2124 17681.5007 17681.2272 17663.7636 11 12 17703.2416 17700.3594 17699.5553 17680.4396 17679.8918 17679.6384 17678.9488 17678.6988 17660.4733 12 13 17703.2606 17678.7603 17678.1596 17677.9348 17676.2576 17676.0306 17657.0551 13 14 17703.1499 17676.9545 17676.3084 17676.1058 17673.2218 14 15 17675.0230 17674.3292 17674.1503 15 16 17702.5609 17672.9656 17672.2258 17672.0702 16 17 17702.0832 17670.7872 17670.0012 17669.8677 17 18 17668.4818 17667.6475 17667.5396 18 19 17666.0551 17665.1721 17665.0890 19 20 17663.5337 17662.5432 20 21 17660.8352 17659.8220 21 22 17658.0421 17657.0061 22 23 17655.1278 17654.0666 23 aThis band has the same upper state as the 17502 cm\" 1 band of 9 0 ZrC (Q' = 0~ - a 12 +) listed in Table AII.3. Table Al.23(b). Rotational assignments and line measurements of the 17690\/700 c m - 1 b a n d o f 9 2 Z r C ( 3 r i 0 - X 3 \u00a3 + ) . N SjfN) Rl(N) R 2 (N) Qi(N) Q 3 (N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 17698.9358 \u2014 17688.7011 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17692.8324 17699.6835 17699.1732 17688.6246 17688.1156 \u2014 \u2014 1 2 17694.2891 17700.2697 17699.7228 17688.3989 17688.4049 17687.8517 17696.1158 17695.5632 17685.8838 2 3 17695.6088 17700.7108 17700.1324 17688.0334 17687.9520 17687.4568 17694.8036 17694.3079 17683.7458 3 4 17696.7943 17701.0062 17700.4015 17687.5345 17687.3879 17686.9303 17693.3695 17692.9111 4 5 17697.8492 17701.1596 17700.5279 17686.9048 17686.7000 17686.2724 17691.8022 17691.3722 17679.1262 5 6 17698.7717 17701.1722 17700.5147 17686.1431 17685.8838 17685.4849 17690.0949 17689.6953 17676.6248 6 7 17699.5656 17701.0424 17700.3594 17685.2485 17684.9380 17684.5674 17688.2504 17687.8766 17673.9953 7 8 17700.2299 17700.7712 17700.0664 17684.2252 17683.8669 17683.5194 17686.2724 17685.9194 8 9 17700.3594 17699.6298 17683.0712 17682.6650 17682.3427 17684.1425 17683.8183 9 10 17681.7936 17681.3377 17681.0376 17681.5794 10 11 17680.3821 17679.8781 17679.6055 17679.1971 11 12 17678.8462 17678.2948 17678.0440 12 13 17677.1836 17676.5854 17676.3582 13 ts re I \u00a9 O I 1 TO a, a? a TO TO 1 >! TO 5 TO a TO\"* o \u00a7 N S,(N) Rl(N) RjfN) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 14 17675.3935 17674.5451 14 15 17673.4756 17672.6082 15 16 17671.4384 17670.5452 16 Table Al.23(c). Rotational assignments and line measurements of the 17690\/700 c m - 1 bandof 9 4 ZrC ( 3 IIo -X 3 S + ) . N Rl(N) RjfN) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 17697.1330 \u2014 17687.3077 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17691.4280 17697.8800 17697.3715 17687.2330 17686.7250 \u2014 \u2014 1 2 17692.8828 17698.4637 17697.9190 17687.0072 17687.0132 17686.4610 17693.7694 2 3 17694.1971 17698.9031 17698.3256 17686.6429 17686.5618 17686.0662 17693.0129 17692.5165 17682.3668 3 4 17695.3791 17699.1978 17698.5932 17686.1431 17685.9984 17685.5401 17691.5820 17691.1232 17680.1234 4 5 17696.4286 17699.3495 17698.7188 17685.5143 17685.3104 17684.8826 17690.0175 17689.5881 17677.7574 5 6 17697.3498 17699.3594 17698.7026 17684.7520 17684.4984 17684.0951 17688.3164 17687.9140 17675.2616 6 7 17698.1409 17699.2299 17698.5459 17683.8593 17683.5527 17683.1786 17686.4727 17686.0994 17672.6366 7 8 17698.9569 17698.2515 17682.8374 17682.4806 17682.1319 17684.4896 17684.1425 17669.8833 8 9 17698.5459 17697.8151 17681.6869 17681.2815 17680.9573 17682.3696 17682.0467 9 10 17697.2374 17680.2867 17679.8324 17679.5358 17679.8080 10 11 17677.7077 17677.4324 11 12 17674.9148 12 Table AI.24(a). Rotational assignments and line measurements of the 17815 c m - 1 band of 9 0 Z r C ( 3 n 1 - X 3 Z + ) . N SjfN) Ri(N) RjfN) Qi(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17817.4735 17815.7955 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17819.0510 17816.5128 not observed 17814.8913 17815.3872 not observed \u2014 \u2014 \u2014 1 2 17820.4645 17817.0520 17814.6422 17814.6474 17812.9693 not observed \u2014 2 3 17821.7241 17817.4245 17814.2406 17814.1598 17811.6214 17809.9965 3 4 17822.8332 17817.6333 17813.6937 17813.5465 17810.1335 17807.7233 4 5 17823.7873 17817.6768 17812.9977 17812.7922 17808.4927 17805.3090 5 6 17824.5801 17817.5519 17812.1531 17811.8950 17806.6946 17802.7547 6 7 17825.1887 17817.2545 17811.1545 17810.8451 17804.7347 17800.0547 7 8 17825.5595 17816.7743 17809.9965 17809.6356 17802.6080 8 ts ts TO 8. as \u00a35 Co 3 TO a S 3 -\u00a7 a, a* a' TO TO I 3 TO a ts TO I to ON N Si(N) R,(N) RjfN) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 9 17825.5798 17816.1004 not observed 17808.6523 17808.2439 not observed 17800.3100 not observed 9 10 17807.0731 17806.6161 10 11 17805.1418 17804.6387 11 Table AI.24(b). Rotational assignments and line measurements of the 17815 c m - 1 band of 9 2 Z r C (3ITi - X 3 E + ) . N S,(N) Rl(N) RjCN) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17814.3218 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17817.5904 17815.0637 not observed not observed \u2014 \u2014 \u2014 1 2 17819.0185 17815.6371 17813.1666 17813.1756 not observed \u2014 2 3 17820.2963 17816.0593 17812.7922 17812.7110 17810.1843 3 4 17821.4271 17816.3281 17812.1172 17808.7380 17806.2639 4 5 17816.4467 17811.5918 17811.3872 17807.1504 17803.8848 5 6 17816.4144 17810.7737 17810.5172 17805.4202 17801.3550 6 7 17816.2329 17803.5384 7 8 17815.9045 17801.5075 8 9 17815.4297 17799.3329 9 10 17814.8025 10 Table AI.24(c). Rotational assignments and line measurements of the 17815 c m - 1 band of 9 4 Z r C ( 3 n 2 -X 3Z+). N Si(N) Rl(N) R2CN) Ql(N) Q 3 (N) Q 2 (N) P 3 (N) P 2 (N) 0 3(N) N 0 17814.5432 17812.8807 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17816.1167 17813.6045 not observed not observed \u2014 \u2014 \u2014 1 2 17817.5289 17814.1598 17811.7277 17811.7345 not observed \u2014 2 3 17818.7877 17814.5636 17811.3312 17811.2497 17808.7380 3 4 17819.9017 17814.8118 17810.7906 17810.6454 17807.2793 17804.8424 4 5 17820.8679 17814.9127 17810.1047 17809.9023 17805.6779 17802.4432 5 6 17821.6876 17814.8611 17809.2739 17809.0173 17803.9296 6 7 17822.3608 17814.6618 17808.2974 17807.9917 17802.0359 7 8 17822.8847 17814.3179 17807.1773 17806.8185 17799.9953 8 9 17823.2470 17813.8264 17805.9067 17805.5012 9 10 17804.4907 17804.0378 10 ts re I X' o o' a \u00a35 I TO 55-\u00a7 a-a' TO TO I 3 TO a TO* to N O Table AI.25(a). Rotational assignments and line measurements of the 17832 c m - 1 band of 9 0 Z r C ( 3 f l 1 - X 3 \u00a3 + ) . N SjCN) Ri(N) R 2 (N) Qi(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 17835.6161 17834.7390 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17837.2510 17836.0682 not observed 17832.9972 17833.4931 not observed \u2014 \u2014 \u2014 1 2 17838.7427 17837.2099 17832.7845 17832.7913 17831.9142 not observed \u2014 2 3 17840.1054 17838.1888 17832.4410 17832.3593 17831.1760 17828.1048 3 4 17841.3426 17839.0144 17831.9709 17831.8238 17830.2910 17825.8661 4 5 17842.4585 17839.6890 17831.3778 17831.1737 17829.2569 17823.5092 5 6 17843.4548 17840.2177 17830.6621 17830.4036 17828.0757 17821.0323 6 7 17844.3274 17840.6018 17829.8256 17829.5163 17826.7468 17818.4351 7 8 17845.1139 17840.8451 17828.8693 17828.5101 17825.2735 17815.7174 8 9 17845.7591 17840.9467 17827.7901 17827.3826 17823.6573 17812.8807 9 10 17846.2964 17840.9100 17826.6268 17826.1706 17821.9015 17809.9254 10 11 17846.7233 17840.7323 17825.3203 17824.8167 17820.0045 17806.8492 11 12 17847.0447 17840.4150 17823.9087 17823.3564 17817.9704 17803.6868 12 13 17847.2445 17839.9513 17822.3851 17821.7863 17815.7955 17800.3846 13 14 17847.3324 17839.3291 17820.7574 17820.1118 17813.4825 14 15 17847.2964 17838.4747 17819.0091 17818.3154 17811.0238 15 16 17847.1228 17838.1438 17817.1482 17816.4083 17808.4052 16 17 17815.1660 17814.3783 17805.5559 17 18 17813.0427 17812.2086 17803.2314 18 19 17800.0027 19 Table AI.25(b). Rotational assignments and line measurements of the 17832 c m - 1 band of 9 2 Z r C (3TI1 - X 3 \u00a3 + ) . N SjfN) Ri(N) RjfN) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17832.7980 17832.2389 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17834.4323 17833.5610 not observed 17830.1841 17830.6807 not observed \u2014 \u2014 \u2014 1 2 17835.9212 17834.7070 17829.9733 17829.9801 not observed \u2014 2 3 17837.2849 17835.6898 17829.6329 17829.5515 17825.3047 3 4 17838.5228 17836.5226 17829.1672 17829.0202 17827.8043 17823.0726 4 5 17839.6411 17837.1991 17828.5800 17828.3758 17826.7815 17820.7251 5 6 17840.6388 17837.7295 17827.8698 17827.6129 17825.6130 17818.2560 6 re a S-x' O & Et. O f TO a \u00a7 a. s? a TO TO i s TO a E? TO* I oo N Si(N) Ri(N) RzCN) Ql(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 7 17841.5201 17838.1121 not observed 17827.0400 17826.7316 not observed 17824.2905 not observed 17815.6708 7 8 17842.2828 17838.3483 17826.0892 17825.7326 17822.8237 17812.9633 8 9 17842.9231 17838.4392 17825.0255 17824.6179 17821.2096 17810.1367 9 10 17843.4922 17838.3860 17823.8416 17823.3869 17819.4531 17807.1960 10 11 17843.8937 17838.1888 17822.5379 17822.0347 17817.5519 17804.1391 11 12 17844.1924 17837.8405 17821.1607 17820.6117 17815.5056 17800.9612 12 13 17844.3713 17837.3412 13 14 17844.4283 14 15 17844.3017 15 16 17844.0779 16 Table Al.25(c). Rotational assignments and line measurements of the 17832 c m - 1 band of 9 4 Z r C ( 3 n 1 - X 3 E + ) . N SjfN) Rl(N) R2CN) Ql(N) Q 3 (N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 17830.2157 17830.0381 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17831.8420 17831.3167 not observed 17827.6129 17828.1048 not observed \u2014 \u2014 \u2014 1 2 17833.3269 17832.4410 17827.3987 17827.4062 not observed \u2014 2 3 17834.6802 17833.4028 17827.0553 17826.9757 17826.4494 3 4 17835.9083 17834.2161 17826.5895 17826.4439 17825.5595 17820.5147 4 5 17837.0151 17834.8751 17825.9967 17825.7941 17824.5159 17818.1688 5 6 17837.9982 17835.3844 17825.2820 17825.0255 17823.3330 17815.7055 6 7 17838.8615 17835.7415 17824.4438 17824.1368 17822.0003 17813.1199 7 8 17839.6035 17835.9486 17823.4869 17823.1296 17820.5147 17810.4124 8 9 17840.2235 17836.0027 17822.4091 17822.0003 17818.8807 17807.5854 9 10 17840.7211 17835.9039 17821.2096 17820.7574 17817.0977 17804.6387 10 11 17841.0800 17835.6502 17819.8878 17819.3867 17815.1660 17801.5711 11 12 17841.3426 17835.2346 17818.4446 17817.8958 17813.0793 17798.3839 12 13 17841.4836 17834.6545 13 14 17841.4448 17833.9024 14 ts TO a & o & \u00bb. o a a l 3 TO a I 3 \" a' TO  a 3 3 TO a TO\" Table AI.26. Rotational assignments and line measurements of the 17833 c m - 1 band of 9 0 Z r C (3IToe - X 3 \u00a3 + ) . N SiCN) Rl(N) R 2 (N) Ql(N) Q 3 (N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 not observed 17833.0688 \u2014 not observed \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17833.1695 not observed not observed \u2014 not observed \u2014 1 2 17833.0990 17832.5525 17830.2433 not observed 2 3 17832.8616 17832.2848 17828.2766 3 4 17832.4583 17831.8500 17826.1800 4 5 17831.8905 17831.2586 17823.9303 5 6 17831.1594 17821.5195 6 7 17830.2654 17818.9492 7 8 17829.2098 17816.2153 8 9 17827.9956 17813.3209 9 10 17810.2659 10 11 17807.0542 11 12 17803.6868 12 13 17800.1627 13 Table AI.27(a). Rotational assignments and line measurements of the 17908 c m - 1 banda of 9 0 Z r C ( 3 n 2 - X3E+). N Si(N) Rl(N) R 2 (N) Q!(N) Q 3 (N) Q 2 (N) P 3(N) P 2 (N) 0 3(N) N 0 17910.2770 \u2014 \u2014 \u2014 \u2014 \u2014- \u2014 \u2014 \u2014 0 1 17911.8328 17909.3599 17908.8506 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 17913.2150 17909.9203 17909.3741 17907.4440 17907.4517 17906.8985 \u2014 \u2014 \u2014\u2022 2 3 17914.4386 17910.3247 17909.7477 17907.0217 17906.9404 17906.4447 17904.4677 17903.9719 \u2014 3 4 17915.5063 17910.5754 17909.9697 17906.4447 17906.2962 17905.8387 17903.0026 17902.5440 17900.5261 4 5 17916.4215 17910.6753 17910.0438 17905.7112 17905.5075 17905.0800 17901.3922 17900.9655 17898.0901 5 6 17917.1864 17910.6266 17909.9697 17904.8257 17904.5675 17904.1686 17899.6367 17899.2372 17895.5050 6 7 17917.8029 17910.4315 17909.7477 17903.7882 17903.4793 17903.1067 17897.7331 17897.3598 17892.7698 7 8 17918.2741 17910.0923 17909.3855 17902.6013 17902.2419 17901.8946 17895.6827 17895.3356 17889.8819 8 9 17918.6021 17909.6095 17908.8790 17901.2669 17900.8588 17900.5358 17893.4877 17893.1657 17886.8443 9 10 17918.7884 17908.9857 17908.2308 17899.7870 17899.3309 17899.0328 17891.1487 17890.8508 17883.6577 10 11 17918.8345 17908.2228 17907.4440 17898.1644 17897.6603 17897.3858 17888.6686 17888.3939 11 12 17918.7402 17907.3163 17906.5150 17896.4007 17895.8489 17895.5988 17886.0461 17885.7952 12 ts TO I o | Co TO 3 St \u00a7 a. 3? 3 TO TO I \u00a7 TO 3 St ts TO | o o N SifN) Rl(N) R2(N) Q,(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 13 17918.5043 17906.2712 17905.4464 17894.4970 17893.9014 17893.6717 17883.2849 17883.0587 13 14 17918.1220 17905.0843 17904.2369 17892.4529 17891.8079 17891.6047 14 15 17917.5848 17903.7519 17902.8784 17890.2691 17889.5766 17889.3962 15 16 17916.8673 17902.2653 17901.3687 17887.9387 17887.2010 17887.0429 16 17 17915.9788 17900.6093 17899.6930 17885.4524 17884.5345 17 18 17882.7870 17881.9558 17881.8450 18 a This band has the same upper state as the 17720 cm\" 1 band of 9 0 Z r C (Q' = 2 - a 1!^) listed in Table AII.4. Table Al.27(b). Rotational assignments and line measurements of the 17908 c m - 1 band3 of 92ZrC ( 3 n 2 - X 3Z+). N SjCN) Rl(N) R2(N) Qi(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 17908.1440 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17909.6379 17907.2293 17906.7207 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 17910.9552 17907.7329 17907.1862 17905.3192 17905.3261 17904.7732 \u2014 \u2014 \u2014 2 3 17912.1141 17908.0751 17907.4977 17904.8400 17904.7583 17904.2631 17902.3492 17901.8531 \u2014 3 4 17913.1251 17908.2670 17907^6616 17904.2011 17904.0539 17903.5956 17900.8321 17900.3754 4 5 17913.9920 17908.3158 17907.6840 17903.4094 17903.2050 17902.7778 17899.1656 17898.7386 5 6 17914.7186 17908.2228 17907.5669 17902.4717 17902.2165 17901.8155 17897.3598 17896.9575 17893.2900 6 7 17915.3059 17907.9940 17907.3129 17901.3922 17901.0825 17900.7095 17895.4072 17895.0332 7 8 17915.7549 17907.6281 17906.9217 17900.1714 17899.4638 17893.3178 17892.9700 8 9 17916.0663 17907.1267 17906.3956 17898.8126 17898.0817 17891.0932 17890.7702 9 10 17916.2334 17906.4891 17905.7324 17897.3157 17896.8620 17896.5609 17888.7319 17888.4349 10 11 17905.7112 17904.9331 17895.6827 17894.9026 17886.2369 17885.9632 11 12 17904.7928 17903.9908 17893.9014 17893.1026 17883.3559 12 13 17903.7379 17902.9128 17891.9526 17891.1284 13 14 17902.5251 17901.6766 14 a This band has the same upper state as the 17720 cm\" 1 band of 9 2 Z r C (Q' = 2 - a1!\"1\") listed in Table AII.4. Table Al.27(c). Rotational assignments and line measurements of the 17908 c m - 1 band3 of 9 4 Z r C ( 3 n 2 - X 3E+). N S!(N) R,(N) Ra(N) Qi(N) Q 3(N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 17906.6309 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17908.0166 17905.7186 17905.2098 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 ts I O o 1 TO \u00a7 a, a re re a 3 s re a ts re O I o N SiCN) Rl(N) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 2 17909.2323 17906.1167 17905.5698 17903.8132 17903.8210 17903.2671 \u2022\u2014 \u2014 \u2014 2 3 17910.3020 17906.3599 17905.7830 17903.2305 17903.1520 17902.6534 17900.8518 17900.3555 \u2014 3 4 17911.2328 17906.4630 17905.8578 17902.4949 17902.3492 17901.8912 17899.2366 17898.7732 not observed 4 5 17912.0310 17906.4326 17905.8008 17901.6186 17901.4141 17900.9870 17897.0450 5 6 17912.6973 17906.2712 17905.6142 17900.6062 17899.9495 17895.1794 6 7 17913.2324 17905.9776 17905.2962 17899.4614 17898.7796 17893.5550 17893.1805 7 8 17913.6349 17905.5529 17904.8465 17898.1851 17897.8240 17897.4797 17891.4032 17891.0531 8 9 17913.9029 17904.9930 17904.2631 17896.7783 17896.3730 17896.0495 17889.1208 17888.7944 9 10 17914.0332 17904.2922 17903.5394 17895.2402 17894.7883 17894.4875 17886.4048 10 11 17914.0220 17903.4456 17902.6680 17893.5673 17892.7897 17883.8803 11 12 17913.8604 17902.4392 17901.6382 17891.7575 17890.9578 17881.2173 12 13 17901.2770 17900.4562 17889.8065 17888.9830 13 14 17887.7063 17886.8587 14 a This band has the same upper state as the 17720 cm\" 1 band of 9 4 Z r C (fl' = 2 - a ' i : + ) listed in Table AII.4. Table AI.28(a). Rotational assignments and line measurements of the 17912 c m - 1 banda of 9 0 Z r C (lTI - X 3 \u00a3 + ) . N SjfN) Rj(N) R 2 (N) Qi(N) Q 3 (N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 17913.5950 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17915.2702 17912.7010 17912.1928 \u2014 \u2014 \u2014 1 2 17916.8177 17913.4085 17912.8613 17910.7621 17910.7693 \u2014 2 3 17918.2478 17914.0033 17913.4259 17910.4618 17910.3795 3 4 17919.5646 17914.4924 17913.8856 17910.0438 17909.8991 17909.4426 17903.8428 4 5 17920.7666 17914.8709 17914.2393 17909.5211 17909.3162 17908.8879 17905.0731 17904.6450 17901.5296 5 6 17921.8531 17915.1402 17914.4832 17908.6258 17903.5523 17903.1520 17899.1090 6 7 17922.8205 17915.2960 17914.6143 17908.1341 17907.8247 17907.4517 17901.9282 17901.5556 17896.5793 7 8 17923.6628 17915.3346 17914.6283 17907.2681 17906.9092 17906.5621 17900.1966 17899.8494 17893.9391 8 9 17924.3693 17915.2480 17914.5171 17906.2835 17905.8769 17905.5529 17898.3524 17898.0320 17891.1891 9 10 17924.9201 17915.0218 17914.2671 17905.1757 17904.7207 17904.4232 17896.3921 17888.3252 10 11 17925.2559 17914.6328 17913.8538 17903.9335 17903.4291 17903.1520 17894.3067 17894.0316 17885.3434 11 12 17925.3133 17901.9797 17901.7314 17892.0832 17891.8337 17882.2356 12 S3 \"a TO I o & o' 3 \u00a35 1 \u00a7 TO 3 St \u00a7 ft. 3? 3 TO 3 TO I 3 TO 3 St I o to N Ri(N) R2(N) Qi(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 13 17900.3209 17900.0936 17889.6959 17889.4687 13 14 17887.0825 14 a This band has the same upper state as the 17724 cm 1 bandaf 9 0 ZrC ( f i ' = 1 - a1!4-) listed in Table AII.5. Table AI.28(b). Rotational assignments and line measurements of the 17912 c m - 1 band of 9 2 Z r C (lTl - X 3 \u00a3 + ) . N S,(N) Ri(N) R2CN) Qi(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 17910.6970 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 17912.3955 17909.8085 \u2014 \u2014 \u2014 1 2 17913.9407 17910.5354 17907.8746 17907.8814 \u2014 2 3 17915.3195 17911.1275 17910.5487 17907.5967 17907.5165 3 4 17916.4856 17911.5525 17910.9462 17907.1862 17907.0381 17906.5819 17900.9733 4 5 17911.7595 17911.1275 17906.6145 17906.4123 17902.2165 5 6 17905.5755 17905.1797 17900.6424 17900.2427 17896.2771 6 7 17899.0328 17893.7067 7 8 17890.9283 8 a This band has the same upper state as the 17724 cm- 1 band of 9 2 Z r C (Q' = 1 - a1!\"1\") listed in Table AII.5. Table AI.28(c). Rotational assignments and line measurements of the 17912 c m - 1 band of 9 4 Z r C f^II - X 3 Z + ) . N S!(N) Rl(N) R2CN) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 1 17910.3628 \u2014 \u2014 \u2014 1 2 17912.0539 17908.4890 17907.9431 not observed \u2014 2 3 17913.6188 17909.2196 17905.5755 17905.4950 3 4 17915.0537 17909.8245 17909.2196 17905.3192 17905.1694 17904.7120 4 5 17916.3588 17910.3020 17909.6703 17904.9331 17904.7314 17904.3019 5 6 17917.5285 17909.9830 17904.4232 17904.1686 17903.7696 17894.4327 6 7 17918.5629 17910.1456 17903.7882 17903.4793 17903.1067 17897.4258 17892.0572 7 8 17919.4602 17910.1329 17902.6589 17902.3117 17889.5564 8 9 17902.1091 17901.7049 17886.9298 9 10 17900.3106 10 11 17899.0899 11 a This band has the same upper state as the 17724 cm\" 1 band of 9 4 Z r C (Q' = 1 - a 1 S + ) listed in Table AII.5. ts re I o & 1 re as \u00a7 a-a - 4 a' re re a 3 re a re~ I to o Table AI.29. Rotational assignments and line measurements of the 18093 c m - 1 band of 9 0 Z r C (3n2 - X 3 Z + ) . N Ri(N) RafN) Ql(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 18095.4259 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18097.0982 18094.5081 18093.9987 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18098.6313 18095.1848 18094.6376 18092.5945 18092.6012 18092.0477 \u2014 \u2014 \u2014 2 3 18100.0322 18095.7322 18095.1552 18092.2882 18092.2066 18091.7103 18089.6169 18089.1212 \u2014 3 4 18101.3109 18096.1567 18095.5511 18091.8574 18091.7103 18091.2523 18088.2656 18087.8084 not observed 4 5 18102.4682 18096.4579 18095.8276 18091.3044 18091.1004 18090.6726 18086.8013 18086.3733 5 6 18103.5047 18096.6391 18095.9835 18090.6296 18090.3729 18089.9731 18085.2195 18084.8184 6 7 18104.4187 18096.6996 18096.0178 18089.8355 18089.5264 18089.1538 18083.5174 18083.1435 7 8 18105.2120 18096.6391 18095.9313 18088.9197 18088.5601 18088.2124 18081.6959 18081.3488 8 9 18105.8816 18096.4579 18095.7255 18087.8825 18087.4749 18087.1520 9 10 18106.4290 18096.1512 18095.3964 18086.7237 18086.2684 18085.9696 10 11 18106.8498 18095.7255 18094.9496 18085.4449 18084.9421 18084.6664 11 12 18107.1433 18095.1685 18094.3662 18084.0403 18083.4892 18083.2380 12 13 18107.2924 18094.4874 18093.6614 18082.5117 18081.9142 18081.6871 13 14 18107.3021 18093.6725 18092.8241 14 15 18092.7146 18091.8417 15 Table AI.30. Rotational assignments and line measurements of the hot 18101 c m - 1 banda of 9 0 Z r C (3n2 - X 3 E + , v = 1). N SjCN) Rl(N) R2CN) Q,(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 18103.2431 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18104.7722 18102.3325 18101.8212 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18106.1233 18102.8727 18102.3196 18100.4345 18100.4424 18099.8800 \u2014 \u2014 \u2014 2 3 18107.3065 18103.2431 18102.6609 18099.9905 18099.9014 18099.4081 18097.4626 18096.9686 \u2014 3 4 18108.3307 18103.4568 18102.8466 18099.3891 18099.2350 18098.7795 18095.9835 18095.5270 4 5 18109.1947 18103.5104 18102.8727 18098.6291 18098.4157 18097.9919 18094.3524 18093.9284 5 6 18109.8874 18103.4062 18102.7432 18097.7106 18097.4428 18097.0470 18092.5671 18092.1720 18088.5010 6 7 18110.3989 18103.1439 18102.4542 18096.6299 18096.3095 18095.9408 18090.6296 18090.2593 18085.7462 7 8 18110.5250 18102.7184 18102.0046 18095.3846 18095.0120 18094.6704 18088.5296 18088.1881 8 ts ts TO I O & a-. \u00a7 I I' 3 TO a \u00a7 a. a? a TO TO 3 TO a S 3 -TO\" I o N Sj(N) Rl(N) RjCN) Ql(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 9 18111.2650 18102.1337 18101.3929 18093.9553 18093.5311 18093.2157 18086.2764 18085.9607 9 10 18111.2650 18101.3783 18100.6147 \u2022 18092.1400 18091.6679 18091.3760 18083.8617 18083.5713 10 T h i s band has the same upper state as the 18981 cnr 1 band of 9 0 Z r C (3n2 - X 3E+) listed in Table AI.38(a). Table AI.31(a). Rotational assignments and line measurements of the 18107 c m - 1 band of 9 0 Z r C ( 3 n 2 - X 3 Z + ) . N S,(N) Ri(N) R2(N) Qi(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 18109.7202 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18111.3770 18108.8029 18108.2937 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18112.8954 18109.4633 18108.9172 18106.8881 18106.8961 18106.3416 \u2014 \u2014 \u2014 2 3 18114.2871 18109.9989 18109.4209 18106.5673 18106.4850 18105.9895 18103.9109 18103.4148 \u2014 3 4 18115.5556 18110.4122 18109.8066 18106.1233 18105.9772 18105.5184 18102.5443 18102.0863 18099.9718 4 5 18116.7009 18110.7034 18110.0724 18105.5598 18105.3560 18104.9283 18101.0670 18100.6401 18097.6344 5 6 18117.7135 18110.8718 18110.2148 18104.8748 18104.6177 18104.2177 18099.4739 18099.0740 18095.1848 6 7 18118.6783 18110.9093 18110.2265 18104.0675 18103.7584 18103.3852 18097.7612 18097.3880 18092.6179 7 8 18119.4240 18110.8981 18110.1916 18103.1278 18102.7697 18102.4212 18095.9285 18095.5809 18089.9309 8 9 18120.0687 18110.6680 18109.9372 18102.1428 18101.7342 18101.4113 18093.9649 18093.6421 18087.1233 9 10 18120.5865 18110.3369 18109.5822 18100.9364 18100.4812 18100.1829 18091.9549 18091.6561 18084.1853 10 11 18120.9747 18109.8814 18109.1021 18099.6313 18099.1276 18098.8530 18089.7270 18089.4521 18081.2003 11 12 18121.2274 18109.2921 18108.4903 18098.1990 18097.6484 18097.3980 18087.3984 18087.1520 12 13 18121.3437 18108.5707 18107.7465 18096.6391 18096.0376 18095.8114 18084.9421 18084.7166 13 14 18121.3210 18107.7137 18106.8643 18094.9434 18094.2950 18094.0925 18082.3600 18082.1579 14 15 18121.1538 18106.7150 18105.8426 18093.1104 18092.4158 18092.2367 15 16 18120.8398 18105.5718 18104.6764 18091.1369 18090.3977 18090.2412 16 17 18120.3742 18104.2650 18103.3458 18089.0223 18088.2355 18088.1021 17 18 18102.8557 18101.9141 18086.7513 18085.9278 18085.8182 18 Table AI.31(b). Rotational assignments and line measurements of the 18 107 cm- 1 band of 9 2 Z r C ( 3 H. 2 - X 3 Z + ) . N SjfN) Ri(N) R2(N) Ql(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 18104.6461 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18106.2913 18103.7315 18103.2220 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18107.7950 18104.3815 18103.8349 18101.8212 18101.8285 18101.2751 \u2014 \u2014 \u2014 2 ts TO I \u00a9 a. \u00a9 g Co 3 TO St \u00a7 a, 3? 3 TO TO \u00a3 3 TO 3 Et TO\" o N S j ( N ) R i ( N ) R 2 ( N ) Q l ( N ) Q 3 ( N ) Q 2 ( N ) P 3 ( N ) P 2 ( N ) 0 3 ( N ) N 3 1 8 1 0 9 . 1 6 9 9 1 8 1 0 4 . 9 0 6 2 1 8 1 0 4 . 3 2 8 2 18101.4934 1 8 1 0 1 . 4 1 1 3 1 8 1 0 0 . 9 1 5 8 18098.8530 1 8 0 9 8 . 3 5 5 4 \u2014 3 4 1 8 1 1 0 . 4 1 8 3 1 8 1 0 5 . 3 0 5 7 1 8 1 0 4 . 6 9 9 5 1 8 1 0 1 . 0 4 0 7 1 8 1 0 0 . 8 9 4 0 1 8 1 0 0 . 4 3 4 5 18097.4810 1 8 0 9 7 . 0 2 2 2 4 5 1 8 1 1 1 . 5 4 2 0 1 8 1 0 5 . 5 7 9 3 1 8 1 0 4 . 9 4 7 3 1 8 1 0 0 . 4 6 5 4 1 8 1 0 0 . 2 6 1 2 1 8 0 9 9 . 8 3 3 2 1 8 0 9 5 . 9 9 6 7 1 8 0 9 5 . 5 6 9 7 1 8 0 9 2 . 5 8 4 5 5 6 1 8 1 1 2 . 5 3 9 2 1 8 1 0 5 . 7 2 8 6 18105.0709 1 8 0 9 9 . 7 6 5 4 1 8 0 9 9 . 5 0 9 1 1 8 0 9 9 . 1 0 8 9 1 8 0 9 4 . 3 9 4 7 1 8 0 9 3 . 9 9 5 0 1 8 0 9 0 . 1 2 9 9 6 7 1 8 1 1 3 . 4 0 7 0 1 8 1 0 5 . 7 5 2 3 18105.0709 1 8 0 9 8 . 9 4 0 6 18098.6291 1 8 0 9 8 . 2 6 0 0 1 8 0 9 2 . 6 7 0 5 1 8 0 9 2 . 2 9 6 9 7 8 1 8 1 1 4 . 1 4 4 1 1 8 1 0 5 . 6 4 6 9 1 8 1 0 4 . 9 3 8 9 18097.9919 18097.6344 1 8 0 9 7 . 2 8 5 9 1 8 0 9 0 . 8 2 2 5 1 8 0 9 0 . 4 7 5 2 1 8 0 8 4 . 8 6 1 4 8 9 1 8 1 1 4 . 7 4 8 3 1 8 1 0 5 . 4 1 0 3 1 8 1 0 4 . 6 7 9 5 1 8 0 9 6 . 9 1 2 4 1 8 0 9 6 . 5 0 5 7 1 8 0 9 6 . 1 8 2 8 1 8 0 8 8 . 8 5 1 6 1 8 0 8 8 . 5 2 9 6 1 8 0 8 2 . 0 4 1 2 9 1 0 1 8 1 1 5 . 2 1 5 9 1 8 1 0 5 . 0 4 1 1 1 8 1 0 4 . 2 8 6 3 1 8 0 9 5 . 7 0 4 6 1 8 0 9 5 . 2 4 9 4 1 8 0 9 4 . 9 4 9 6 18086.7513 1 8 0 8 6 . 4 5 1 3 1 0 1 1 1 8 1 1 5 . 5 4 4 9 1 8 1 0 4 . 5 3 6 5 18103.7584 1 8 0 9 4 . 3 6 1 6 18093.8594 1 8 0 9 3 . 5 8 4 1 1 1 1 2 1 8 1 1 5 . 7 3 1 5 1 8 1 0 3 . 8 9 3 0 1 8 1 0 3 . 0 9 0 2 1 8 0 9 2 . 8 8 5 5 18092.3356 1 8 0 9 2 . 0 8 3 9 1 2 1 3 1 8 1 1 5 . 7 7 2 1 1 8 0 9 1 . 2 6 9 9 18090.6726 1 8 0 9 0 . 4 4 4 6 1 3 1 4 1 8 1 1 5 . 6 6 1 2 1 8 0 8 9 . 5 1 1 4 1 8 0 8 8 . 8 6 6 4 1 8 0 8 8 . 6 6 5 8 1 4 Table AI.31(c). Rotational assignments and line measurements of the 18107 c m - 1 band of 9 4 Z r C ( 3 n 2 - X 3 Z + ) . N S , ( N ) R j f N ) R 2 ( N ) Q l ( N ) Q 3 ( N ) Q 2 ( N ) P 3 ( N ) P 2 ( N ) 0 3 ( N ) N 0 18100.6401 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 1 8 1 0 2 . 2 6 6 4 1 8 0 9 9 . 7 2 5 4 1 8 0 9 9 . 2 1 5 8 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 1 8 1 0 3 . 7 5 0 8 1 8 1 0 0 . 3 6 2 1 1 8 0 9 9 . 8 1 6 0 1 8 0 9 7 . 8 1 9 5 1 8 0 9 7 . 8 2 7 2 1 8 0 9 7 . 2 7 4 3 \u2014 \u2014 \u2014 2 3 1 8 1 0 5 . 1 0 1 1 1 8 1 0 0 . 8 6 7 4 1 8 1 0 0 . 2 9 1 4 18097.4810 18097.3980 1 8 0 9 6 . 9 0 4 0 1 8 0 9 4 . 8 5 7 5 18094.3616 \u2014 3 4 1 8 1 0 6 . 3 2 1 7 1 8 1 0 1 . 2 4 5 2 18100.6401 1 8 0 9 7 . 0 1 3 4 1 8 0 9 6 . 8 6 6 3 1 8 0 9 6 . 4 0 8 3 1 8 0 9 3 . 4 7 9 8 1 8 0 9 3 . 0 1 9 3 1 8 0 9 0 . 9 3 7 4 4 5 1 8 1 0 7 . 4 1 2 1 18101.4934 1 8 1 0 0 . 8 6 2 2 1 8 0 9 6 . 4 1 8 5 1 8 0 9 6 . 2 1 5 0 1 8 0 9 5 . 7 8 6 5 1 8 0 9 1 . 9 8 1 4 1 8 0 9 1 . 5 5 3 3 1 8 0 8 8 . 5 9 5 1 5 6 1 8 1 0 8 . 3 7 0 8 1 8 1 0 1 . 6 1 2 6 1 8 1 0 0 . 9 5 5 8 1 8 0 9 5 . 6 9 5 2 1 8 0 9 5 . 4 3 8 2 1 8 0 9 5 . 0 3 8 0 1 8 0 9 0 . 3 6 1 7 1 8 0 8 9 . 9 6 2 5 1 8 0 8 6 . 1 2 9 0 6 7 1 8 1 0 9 . 1 9 4 7 1 8 1 0 1 . 6 0 1 2 1 8 1 0 0 . 9 1 9 7 1 8 0 9 4 . 8 4 1 7 1 8 0 9 4 . 5 3 4 6 1 8 0 9 4 . 1 6 0 6 1 8 0 8 8 . 6 1 5 8 1 8 0 8 8 . 2 4 1 4 1 8 0 8 3 . 5 3 8 8 7 8 1 8 1 0 9 . 8 8 1 4 1 8 1 0 1 . 4 5 4 5 1 8 1 0 0 . 7 4 9 3 18093.8594 1 8 0 9 3 . 5 0 1 6 1 8 0 9 3 . 1 5 3 1 1 8 0 8 6 . 7 4 3 9 1 8 0 8 6 . 3 9 4 4 8 9 1 8 1 1 0 . 4 3 3 1 1 8 1 0 1 . 1 7 2 1 1 8 1 0 0 . 4 4 2 4 1 8 0 9 2 . 7 4 1 7 18092.3356 1 8 0 9 2 . 0 1 2 7 1 8 0 8 4 . 7 4 1 6 18084.4187 9 1 0 1 8 1 1 0 . 8 4 1 0 18100.7493 1 8 0 9 9 . 9 9 8 0 1 8 0 9 1 . 4 9 0 0 1 8 0 9 1 . 0 3 5 3 1 8 0 9 0 . 7 3 6 1 1 8 0 8 2 . 6 0 5 8 1 8 0 8 2 . 3 0 6 2 1 0 1 1 1 8 1 1 1 . 1 0 3 0 18100.1875 1 8 0 9 9 . 4 1 1 3 1 8 0 8 9 . 5 9 6 4 1 8 0 8 9 . 3 2 0 7 1 1 1 2 1 8 1 1 1 . 2 1 5 8 1 8 0 9 9 . 4 8 0 7 1 8 0 9 8 . 6 8 0 6 18088.5620 1 8 0 8 8 . 0 1 7 1 1 8 0 8 7 . 7 6 5 0 1 2 1 3 1 8 1 1 1 . 1 7 5 0 18098.6270 1 8 0 9 7 . 8 0 0 9 1 8 0 8 6 . 8 8 7 3 1 8 0 8 6 . 2 9 1 7 1 8 0 8 6 . 0 6 4 3 1 3 1 4 1 8 1 1 0 . 9 7 6 7 1 8 0 9 7 . 6 1 3 6 1 8 0 9 6 . 7 6 5 5 1 8 0 8 5 . 0 6 2 2 18084.4187 1 8 0 8 4 . 2 1 3 3 1 4 1 5 1 8 0 8 2 . 2 1 0 4 1 5 32 re a \u00a9 o 5fl TO a s? I Err a TO 3 TO I TO a I o as Table AT32(a). Rotational assignments and line measurements of the 1 8 1 5 9 \/ 8 2 crrr 1 band of 9 0 Z r C ^ I T Q - X 3 S + ) . N Sj(N) Rl(N) R2(N) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 18161.8847 18182 4769 18159 3649 \u2014 \u2014 \u2014 \u2014 0 1 18163.4861 18183 2768 18182 7671 18159 2867 18158.7777 18180.1922 \u2014 1 2 18164.9209 18183 9382 18183 3915 18159 0537 18159.0607 18158.5073 18179 6530 18179.0993 2 3 18166.1993 18184 4753 18183 8977 18158 6755 18158.5931 18158.0979 18178 3844 18177.8892 18154.3940 3 4 18167.3139 18184 8914 18184 2857 18158 1492 18158.0027 18157.5440 18177 0197 18176.5611 18152.1359 4 5 18168.2526 18185 1877 18184 5560 18157 4720 18157.2677 18156.8405 18175 5437 18175.1163 18149.7435 5 6 18168.9978 18185 3641 18184 7071 18156 6331 18156.3753 18155.9762 18173 9530 18173.5532 18147.2110 6 7 18169.5273 18185 4205 18184 7388 18155 6192 18155.3098 18154.9368 18172 2452 18171.8726 18144.5295 7 8 18169.8158 18185 3564 18184 6499 18154 4121 18154.0543 18153.7059 18170 4212 18170.0730 18141.6889 8 9 18169.8349 18185 1683 18184 4379 18152 9909 18152.5828 18152.2608 18168 4762 18168.1537 9 10 18169.5587 18184 8556 18184 1008 18151 3277 18150.8723 18150.5734 18166 4132 18166.1139 10 11 18168.9777 18184 4130 18183 6352 18149 3973 18148.8933 18148.6200 18164 2263 18163.9516 11 12 18183 8371 18183 0349 18146.6192 18146.3689 18161 9167 18161.6645 12 13 18183 1180 18182 2931 18143.8155 18159 4768 18159.2511 13 14 18182 2423 18181 3945 18156 9049 18156.7012 14 15 18181 1923 18180 3197 18154 1899 18154.0095 15 16 18179 9338 18179 0383 18151 3190 18151.1635 16 17 18148 2734 18148.1425 17 18 18144.9119 18 Table AI.32(b). Rotational assignments and line measurements of the 18159\/82 c m - 1 band of 9 2 Z r C ^ILj - X 3 E + ) . N S,(N) Ri(N) Rz(N) Ql(N) Q 3(N) Q 2 (N) P 3 (N) P 2(N) 0 3(N) N 0 18158.4156 18178.9904 \u2014 18155.9210 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18160.0299 18179.7877 18179.2773 18155.8142 18155.3098 \u2014 18176.7086 \u2014 1 2 18161.4881 18180.4463 18179.9002 18155.5936 18155.6020 18155.0457 18176.1716 18175.6179 \u2014 2 3 18162.7919 18180.9839 18180.4059 18155.2313 18155.1498 18154.6545 18174.9077 18174.4119 18150.9354 3 4 18163.9436 18181.3987 18180.7942 18154.7310 18154.5839 18154.1263 18173.5466 18173.0882 18148.6927 4 5 18164.9339 18181.6934 18181.0616 18154.0866 18153.8825 18153.4549 18172.0751 18171.6470 18146.3223 5 6 18165.7456 18181.8667 18181.2103 18153.2911 18153.0335 18152.6338 18170.4889 18170.0890 18143.8207 6 7 18166.3601 18181.9164 18181.2346 18152.3327 18152.0251 18151.6520 18168.7842 18168.4118 7 ts ts re 3 & O o' | $ 3 re 3 5f I 3? 3 re r  \u00ab re 3 re 3 x*-rer I x^  u> o \u2014] N S!(N) Rl(N) RjfN) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 8 18166.7507 18181.8412 18181.1346 18151.1975 18150.8414 18150.4916 18166.9614 18166.6137 8 9 18166.8924 18181.6340 18180.9045 18149.8659 18149.4592 18149.1366 18165.0154 18164.6927 9 10 18181.2886 18180.5353 18148.3107 18147.8559 18147.5570 18162.9448 18162.6451 10 11 18180.7942 18180.0184 18146.5071 18146.0033 18145.7288 18160.7459 18160.4716 11 12 18180.1334 18179.3333 18158.4156 18158.1567 12 13 18155.9210 18155.6948 13 14 18153.2665 18153.0660 14 Table AI.32(c). Rotational assignments and line measurements of the 18159\/82 c m - 1 band of 9 4 Z r C (3IIo - X 3 E + ) . N S,(N) Rl(N) R2CN) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 18175.6542 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18158.9504 18176.4471 18175.9375 18154.7930 18154.2830 \u2014 18173.3795 \u2014 1 2 18160.3750 18177.1001 18176.5537 18154.5493 18154.5557 18154.0031 18172.8443 18172.2912 2 3 18161.6645 18177.6279 18177.0501 18154.1631 18154.0814 18153.5854 18171.5791 18171.0839 18149.9248 3 4 18162.8163 18178.0291 18177.4244 18153.6374 18153.4919 18153.0335 18170.2167 18169.7579 18147.6662 4 5 18163.8340 18178.3056 18177.6725 18152.9795 18152.7763 18152.3488 18168.7404 18168.3124 18145.2754 5 6 18164.7124 18178.4483 18177.7919 18152.1891 18151.9327 18151.5330 18167.1453 18166.7447 18142.7565 6 7 18165.4395 18178.4531 18177.7726 18151.2641 18150.9573 18150.5832 18165.4263 18165.0531 18140.1038 7 8 18166.0017 18178.3056 18177.6012 18150.1995 18149.8437 18149.4947 18163.5790 18163.2308 8 9 18166.3757 18177.9822 18177.2534 18148.9873 18148.5798 18148.2562 18161.5955 18161.2712 9 10 18166.5337 18177.4425 18176.6886 18146.8541 18159.4579 18159.1581 10 11 18176.6424 18175.8653 18145.5389 18145.2642 18157.1478 18156.8693 11 12 18175.5637 18174.7630 18143.4588 18154.6164 18154.3654 12 Table AI.33. Rotational assignments and line measurements of the 18169 c m - 1 band of 9 0 Z r C (3UQJJIJ^ - X 3 Z + ) . N S!(N) Ri(N) R 2 (N) Qi(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 1 18173.1639 not observed not observed 18168.8382 \u2014 not observed \u2014 1 2 18174.3121 18168.4118 not observed 2 3 18175.2495 18168.3531 18167.7761 18164.4542 3 4 18175.9934 18167.5399 18167.3933 18166.9342 18162.0414 4 5 18176.5497 18166.5233 18166.3178 18165.8910 18159.4231 5 ts TO I o & a-, o a f s TO a I a* a ' TO \u00ab 3 TO a ts TO O I o 00 N Si(N) Ri(N) R 2 (N) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3 (N) N 6 18176.9366 not observed not observed 18165.3115 18165.0531 18164.6548 not observed not observed 18156.6030 6 7 18177.1750 18163.9161 18163.6071 18163.2337 18153.5854 7 8 18177.2793 18162.3515 18161.9926 18161.6451 18150.3679 8 9 18177.2793 18160.6365 18160.2298 18159.9074 9 10 18177.1750 18158.7927 18158.3363 18158.0380 10 11 18176.9708 18156.8405 18156.3357 18156.0602 11 12 18154.7877 18154.2364 18153.9844 12 13 18152.6338 18152.0351 18151.8081 13 14 18150.3588 18149.7118 18149.5097 14 re a S-O & a-, o a a | Co TO a Table Al.34(a). Rotational assignments and line measurements of the 18338 c m - 1 banda of 9 0 Z r C ( 3TI 1 - X 3 \u00a3 + ) . N SjCN) Rl(N) R2(N) Ql(N) Q 3 (N) Q 2(N) P 3 (N) P 2(N) 0 3 (N) N 0 18340.8404 18339.1903 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18342.3969 18339.9222 not observed 18338.2718 18338.7681 not observed \u2014 \u2014 \u2014 1 2 18343.7808 18340.4858 18338.0087 18338.0153 18336.3658 not observed \u2014 2 3 18345.0019 18340.8880 18337.5866 18337.5048 18335.0318 18333.3801 3 4 18346.0629 18341.1324 18337.0089 18336.8619 18333.5669 18331.0903 4 5 18346.9622 18341.2176 18336.2750 18336.0704 18331.9568 18328.6557 5 6 18347.6959 18341.1427 18335.3817 18335.1234 18330.1938 18326.0708 6 7 18348.2613 18340.9037 18334.3285 18334.0197 18328.2755 18323.3320 7 8 18348.6488 18340.4957 18333.1109 18332.7521 18326.2000 18320.4379 8 9 18348.8378 18339.9095 18331.7242 18331.3162 18323.9595 18317.3837 9 10 18349.0215 18339.1223 18330.1613 18329.7063 18321.5517 10 11 18348.8378 18338.3331 18328.3982 18327.8943 18318.9694 11 12 18348.4990 18337.1848 18326.6332 18326.0821 12 13 18347.9747 18335.8775 18324.5007 18323.9020 13 14 18347.2544 18334.3861 18322.2140 18321.5675 14 15 18346.3339 18332.7023 18319.7394 18319.0467 15 16 18345.2079 18330.8232 18317.0707 16 a TO TO TO TO a o NO N Si(N) RjCN) RjCN) Ql(N) Q3(N) Q2(N) P3(N) P2(N) 03(N) N 17 18328.7440 not observed not observed not observed 17 18 18326.4690 18 T h i s band has the same upper state as the hot 17458 cm\" 1 band of 9 0 Z r C ( 3 n 0 - X 3 S + , v= 1) listed in Table Al. 18. Table AI.34(b). Rotational assignments and line measurements of the 18338 c m - 1 band of 9 2 Z r C ( 3 n 1 - X3E+). N SjCN) RjCN) R2(N) Ql(N) Q3(N) Q2(N) P3(N) P2(N) 03(N) N 0 18335.5430 18333.9059 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18337.0813 18334.6279 not observed 18332.9896 18333.4869 not observed \u2014 \u2014 \u2014 1 2 18338.4429 18335.1735 18332.7177 18332.7255 18331.0879 not observed \u2014 2 3 18339.6254 18335.5552 18332.2837 18332.2031 18329.7476 3 4 18340.5792 18335.7628 18331.6892 18331.5409 18328.2755 18325.8162 4 5 18341.3435 18335.7418 18330.9201 18330.7173 18326.6473 18323.3748 5 6 18342.0411 18329.9264 18329.6693 18324.8520 18320.7775 6 7 18342.5931 18335.2584 18328.7440 18328.4356 18322.8331 18318.0110 7 8 18342.9615 18327.4924 18327.1351 8 9 18343.1469 18326.0990 18325.6933 18318.3582 9 10 18342.9615 18324.5217 18324.0690 10 11 18342.5854 18322.7621 18322.2545 11 12 18342.0192 18320.6282 12 Table Al.34(c). Rotational assignments and line measurements of the 18338 c m - 1 band of 9 4 Z r C ^ITj - X 3 Z + ) . N SjCN) RjCN) R2(N) Qi(N) Q3(N) Q2(N) P3(N) P2(N) 03(N) N 0 18330.3012 18328.6830 \u2014 \u2014 \u2022\u2014 \u2014 \u2014 \u2014 \u2014 0 1 18331.8165 18329.3890 not observed 18327.7692 18328.2662 not observed \u2014 \u2014 \u2014 1 2 18333.1461 18329.9143 18327.4844 18327.4924 18325.8730 not observed \u2014 2 3 18334.3054 18330.2677 18327.0294 18326.9480 18324.5217 18322.9014 3 4 18335.2959 18330.4536 18326.4092 18326.2626 18323.0295 4 5 18336.1170 18330.4734 18325.6223 18325.4192 18321.3802 18318.1426 5 6 18336.7663 18330.3237 18324.6675 18324.4112 18319.5707 6 ts ts TO I SB O & 3 . 1 3 TO a \u00a7 a. a? a TO 3 TO S 3 TO a I o N S i ( N ) R i ( N ) R2CN) Q l ( N ) Q 3 ( N ) Q 2 ( N ) P 3 ( N ) P 2 ( N ) 0 3 ( N ) N 7 1 8 3 3 7 . 2 4 3 8 1 8 3 3 0 . 0 0 4 3 1 8 3 2 3 . 5 4 7 0 1 8 3 2 3 . 2 3 9 2 1 8 3 1 7 . 5 9 5 8 1 8 3 1 2 . 7 4 5 4 7 8 1 8 3 3 7 . 5 4 6 7 1 8 3 2 9 . 5 1 3 1 1 8 3 2 2 . 2 5 4 5 1 8 3 2 1 . 8 9 7 2 8 9 1 8 3 3 7 . 6 7 0 7 1 8 3 2 8 . 8 4 5 6 1 8 3 2 0 . 7 9 1 3 1 8 3 2 0 . 3 8 4 1 9 1 0 1 8 3 3 7 . 6 1 7 1 1 8 3 2 8 . 0 0 1 8 1 0 1 1 1 8 3 3 7 . 3 8 2 1 1 8 3 2 6 . 9 7 8 7 1 1 1 2 1 8 3 3 6 . 9 6 5 7 1 8 3 2 5 . 7 7 2 8 1 2 1 3 1 8 3 2 4 . 3 8 7 7 1 3 1 4 1 8 3 2 2 . 8 2 0 5 1 4 Table AI.35(a). Rotational assignments and line measurements of the 18467 \/79 c m - 1 band of 9 0 Z r C (3fIo - X 3 2 + ) . N S ! ( N ) R l ( N ) R j C N ) Q l ( N ) Q 3 ( N ) Q 2 ( N ) P 3 ( N ) P 2 ( N ) 0 3 ( N ) N 0 1 8 4 8 2 . 0 2 6 9 1 8 4 6 7 . 8 9 1 9 \u2014 1 8 4 7 9 . 5 5 9 0 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 1 8 4 8 3 . 5 7 7 2 1 8 4 6 8 . 5 7 4 2 1 8 4 6 8 . 0 6 4 5 1 8 4 7 9 . 4 6 3 7 1 8 4 7 8 . 9 5 4 6 \u2014 1 8 4 6 5 . 6 6 5 1 \u2014 1 2 1 8 4 8 4 . 9 5 2 7 1 8 4 6 9 . 0 5 7 2 1 8 4 6 8 . 5 0 9 8 1 8 4 7 9 . 1 9 5 3 1 8 4 7 9 . 2 0 1 7 1 8 4 7 8 . 6 4 8 6 1 8 4 6 5 . 0 6 7 9 1 8 4 6 4 . 5 1 3 6 1 8 4 7 6 . 7 3 5 2 2 3 1 8 4 8 6 . 1 6 9 6 1 8 4 6 9 . 3 7 4 4 1 8 4 6 8 . 7 9 6 8 1 8 4 7 8 . 7 6 6 3 1 8 4 7 8 . 6 8 4 8 1 8 4 7 8 . 1 8 8 5 1 8 4 6 3 . 6 8 1 6 1 8 4 6 3 . 1 8 6 7 1 8 4 7 4 . 5 7 2 0 3 4 1 8 4 8 7 . 2 3 0 1 1 8 4 6 9 . 4 9 5 4 1 8 4 6 8 . 8 8 9 9 18478.1814 1 8 4 7 8 . 0 3 4 5 1 8 4 7 7 . 5 7 5 8 1 8 4 6 2 . 1 3 8 4 1 8 4 6 1 . 6 7 9 6 1 8 4 7 2 . 2 7 7 3 4 5 1 8 4 8 8 . 1 3 5 6 1 8 4 6 9 . 4 4 2 1 1 8 4 6 8 . 8 0 9 9 1 8 4 7 7 . 4 4 2 3 1 8 4 7 7 . 2 3 8 0 1 8 4 7 6 . 8 1 1 1 1 8 4 6 0 . 4 4 3 0 1 8 4 6 0 . 0 1 5 5 1 8 4 6 9 . 8 3 5 3 5 6 1 8 4 8 8 . 8 8 5 3 1 8 4 6 9 . 2 1 1 7 1 8 4 6 8 . 5 5 4 4 1 8 4 7 6 . 5 4 9 4 1 8 4 7 6 . 2 9 1 3 1 8 4 7 5 . 8 9 1 9 18458.5578 1 8 4 5 8 . 1 5 7 8 1 8 4 6 7 . 2 4 4 3 6 7 1 8 4 8 9 . 4 8 1 5 1 8 4 6 8 . 8 0 4 1 1 8 4 6 8 . 1 2 2 4 1 8 4 7 5 . 5 0 1 8 1 8 4 7 5 . 1 9 2 8 1 8 4 7 4 . 8 1 9 5 1 8 4 5 6 . 5 0 0 0 1 8 4 5 6 . 1 2 7 0 1 8 4 6 4 . 5 0 0 6 7 8 1 8 4 8 9 . 9 2 1 4 1 8 4 6 8 . 2 1 9 0 1 8 4 6 7 . 5 1 2 2 1 8 4 7 4 . 2 9 9 9 1 8 4 7 3 . 9 4 1 9 18473.5940 1 8 4 5 4 . 2 6 8 4 1 8 4 5 3 . 9 2 1 4 1 8 4 6 1 . 6 0 5 3 8 9 1 8 4 9 0 . 2 0 7 7 1 8 4 6 7 . 4 5 5 9 1 8 4 6 6 . 7 2 4 4 1 8 4 7 2 . 9 4 5 9 1 8 4 7 2 . 5 3 7 5 1 8 4 7 2 . 2 1 4 5 18458.5578 9 1 0 1 8 4 9 0 . 3 3 1 2 1 8 4 6 6 . 5 1 2 3 1 8 4 6 5 . 7 5 8 4 1 8 4 7 1 . 4 3 4 3 1 8 4 7 0 . 9 7 8 3 1 8 4 7 0 . 6 7 9 9 1 8 4 5 5 . 3 5 7 8 1 0 1 1 1 8 4 9 0 . 2 8 7 1 1 8 4 6 5 . 3 8 9 8 1 8 4 6 4 . 6 1 1 8 1 8 4 6 9 . 7 7 0 2 1 8 4 6 9 . 2 6 6 5 1 8 4 6 8 . 9 9 1 9 1 1 1 2 1 8 4 9 0 . 0 2 6 3 1 8 4 6 4 . 0 8 6 1 1 8 4 6 3 . 2 8 3 8 1 8 4 6 7 . 9 4 4 2 1 8 4 6 7 . 3 9 2 8 18467.1420 1 2 1 3 1 8 4 6 5 . 9 4 9 8 1 8 4 6 5 . 3 5 1 0 1 8 4 6 5 . 1 2 3 9 1 3 1 4 1 8 4 6 3 . 7 4 0 6 1 8 4 6 3 . 0 9 4 2 1 8 4 6 2 . 8 9 1 3 1 4 Table AI.35(b). Rotational assignments and line measurements of the 1 8 4 6 7 \/ 7 9 c m - 1 band of 9 2 Z r C ( 3 T I Q - X 3 S + ) . N S i ( N ) R i ( N ) R j f N ) Q i ( N ) Q 3 ( N ) Q 2 ( N ) P 3 ( N ) P 2 ( N ) 0 3 ( N ) N 0 1 8 4 7 8 . 1 6 4 7 \u2014 1 8 4 7 5 . 7 0 4 9 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 1 8 4 7 9 . 7 1 2 1 1 8 4 7 5 . 6 0 9 1 1 8 4 7 5 . 0 9 9 1 \u2014 n o t o b s e r v e d \u2014 1 ts ts re a SJ X >a o 15 a. o a El I \u00a7 re I Er-rs re s re I re a S3-fe-re I N S-.CN) Rl(N) R 2 (N) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 2 18481.0864 Lines for these branches are 18475.3416 18475.3474 18474.7931 not observed not observed 2 3 4 5 18482.2990 18483.3578 18484.2602 tentatively identified. See Table AI.35(c) for further explanation. 18474.9137 18474.3314 18473.5940 18474.8380 18474.1840 18473.3904 18474.3362 18473.7250 18472.9628 18470.7288 18468.4395 18466.0047 3 4 5 6 18485.0083 18472.7041 18472.4470 18472.0470 18463.4213 6 7 18485.6027 18471.6604 18471.3510 18470.9783 18460.6856 7 8 18486.0408 18470.4600 18470.1033 18469.7548 18457.7982 8 9 18468.7009 18468.3776 18454.7593 9 10 18467.6013 18467.1420 18466.8479 10 11 18465.9380 18465.4364 18465.1614 11 Table AI.35(c). Rotational assignments and line measurements of the 18467\/79 c m - 1 band3 of 9 4 Z r C (3TIo - X 3 E + ) . N SjfN) Ri(N) R 2 (N) Qi(N) Q 3 (N) Q 2(N) P 3(N) P 2 (N) 0 3(N) N 0 \u2014 18472.0282 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18476.0237 18471.9344 18471.4245 \u2014 not observed \u2014 1 2 18477.3902 18461.5518 18461.0033 18471.6647 18471.1196 not observed 2 3 18478.5970 18461.8355 18461.2566 18471.2368 18471.1548 18470.6607 3 4 18479.6466 18461.9370 18461.3318 18470.6533 18470.5067 18470.0484 4 5 18480.5397 18461.8582 18461.2261 18469.9132 18469.7105 18469.2815 18462.3513 5 6 18481.2776 18461.6053 18460.9326 18469.0188 18468.7635 18468.3614 18459.7699 6 7 18481.8581 18461.1549 18460.4735 18467.9708 18467.6624 18467.2891 18457.0369 7 8 9 10 18482.2827 18482.5492 18482.6575 These Rj(N) and RjfN) lines cannot be distinguished as 18466.7657 18465.4060 18463.8896 18466.4083 18463.4357 18466.0602 18464.6767 18463.1359 8 9 10 11 12 18482.6023 or ^ ru . See footnote. 18462.2155 18460.3834 18461.7138 18461.4383 18459.5812 11 12 ta-re a & >3 O a-, o &0 re a S 3 -I a-a? a re re I s re a s? -s-re-I aNote: The Rj(N) and R ^ N ) lines may actually belong to 9 2 Z r C because their combination differences with each other are not very sensitive to Zr isotope; their combination differences with P 3 (N) and P 2 (N) lines are isotope-sensitive, but none of these could be located, leaving an indeterminacy in the carrier of the Rj(N) and R^fN) lines. For this reason, these were not used in any least squares fits, in spite of their (mostly) accurate measurements. i\u2014* to Table Al.36(a). Rotational assignments and line measurements of the 18569 c m - 1 band of 9 0 Z r C ( 3 n 2 - X 3 E + ) . N Si(N) Rl(N) R 2 (N) Q,(N) Q 3(N) Q 2(N) P 3 (N) P 2(N) 0 3(N) N 0 18571.1560 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18572.7657 18570.2397 18569.7302 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18574.2082 18570.8512 18570.3042 18568.3255 18568.3321 18567.7788 \u2014 \u2014 \u2014 2 3 18575.4970 18571.3123 18570.7356 18567.9531 18567.8738 18567.3778 18565.3474 18564.8514 \u2014 3 4 18576.6338 18571.6250 18571.0201 18567.4369 18567.2901 18566.8322 18563.9315 18563.4739 18561.4076 4 5 18577.6099 18571.7884 18571.1560 18566.7706 18566.5664 18566.1386 18562.3813 18561.9534 18559.0233 5 6 18578.4643 18571.7895 18571.1331 18565.9531 18565.6951 18565.2960 18560.6869 18560.2877 18556.4989 6 7 18579.1500 18571.6742 18570.9916 18564.9761 18564.6675 18564.2936 18558.8458 18558.4720 18553.8285 7 8 18579.6897 18571.3888 18570.6830 18563.8789 18563.5210 18563.1733 18556.8470 18556.4989 18551.0097 8 9 18580.0816 18570.9590 18570.2282 18562.6142 18562.2062 18561.8834 18554.7298 18554.4066 18548.0323 9 10 18580.3268 18570.3827 18569.6280 18561.2016 18560.7461 18560.4471 18552.4467 18552.1482 18544.9378 10 11 18580.4222 18569.6605 18568.8814 18559.6441 18559.1397 18558.8657 18550.0182 18549.7422 11 12 18580.3629 18568.7913 18567.9898 18557.9387 18557.3881 18557.1376 18547.4426 18547.1926 12 13 18580.1365 18567.7723 18566.9466 18556.0862 18555.4858 18555.2579 18544.7250 18544.4985 13 14 18579.7085 18566.5929 18565.7444 18554.0754 18553.4304 18553.2280 14 15 18551.9007 18551.2086 18551.0283 15 Table AI.36(b). Rotational assignments and line measurements of the 18569 c m - 1 band of 9 2 Z r C ( 3 n 2 - X 3 E + ) . N SifN) Rl(N) R2CN) Ql(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 0 18568.0979 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18569.6669 18567.1823 18566.6731 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18571.0696 18567.7572 18567.2114 18564.7268 \u2014 \u2014 \u2014 2 3 18572.3188 18568.1823 18567.6037 18564.8687 18564.7866 18564.2936 18562.3037 \u2014 3 4 18573.4193 18568.4551 18567.8505 18564.3153 18564.1679 18563.7103 18560.8579 18560.3983 18558.3733 4 5 18574.3711 18568.5822 18567.9531 18563.6145 18563.4113 18562.9833 18559.2741 18558.8458 5 6 18575.1746 18568.5613 18567.9044 18562.7671 18562.5099 18562.1104 18557.5459 18557.1453 6 7 18575.8284 18568.3927 18567.7107 18561.7711 18561.4624 18561.0885 18555.6738 18550.7062 7 8 18576.3317 18568.0745 18567.3682 18560.6282 18560.2710 18559.9202 18553.6550 18547.8598 8 9 18576.6804 18567.6037 18566.8738 18559:3342 18558.9279 18558.6039 18551.4909 18551.1689 18544.8701 9 10 18576.8675 18566.9724 18566.2182 18557.4369 18557.1453 18549.1791 18548.8799 10 ts ts TO I >) o & 3 . o a a I S? TO a a, a? a TO TO I 3 TO a ts TO I N S,(N) RjfN) RafN) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3 (N) N 11 18576.8811 18566.1696 18565.3905 18555.7939 18555.5165 18546.7148 18546.4397 11 12 18576.6921 18543.8407 12 Table AI.36(c). Rotational assignments and line measurements of the 18569 c m - 1 band o f 9 4 Z r C ( 3 n : I ~ X 3 2 + ) . N SjfN) Ri(N) R 2 (N) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2(N) 0 3 (N) N 0 18565.2960 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18566.8519 18564.3864 18563.8789 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18568.2356 18564.9480 18564.4010 18562.4883 18561.9349 \u2014 \u2014 \u2014 2 3 18569.4629 18565.3522 18564.7752 18561.9842 18561.4886 18559.5184 \u2014 3 4 18570.5400 18565.6062 18565.0004 18561.4982 18561.3516 18560.8930 18558.0643 4 5 18571.4669 18565.7063 18565.0760 18560.7814 18560.5780 18560.1483 18556.4660 18556.0382 5 6 18572.2436 18565.6553 18565.0004 18559.6561 18559.2575 18554.7208 18554.3221 18550.6136 6 7 18572.8685 18565.4401 18564.7594 18558.8972 18558.5893 18558.2158 18552.8302 18552.4568 18547.9033 7 8 18573.3417 18565.0321 18564.3272 18557.7307 18557.3734 18557.0254 18550.7858 18550.4373 8 9 18573.6563 18556.0100 18555.6858 18548.2579 9 10 18573.8048 18554.4942 18554.1932 18546.1854 18545.8843 10 11 18573.7734 18552.8193 18552.5444 11 Table AI.37. Rotational assignments and line measurements of the 18616 c m - 1 band of 9 0 Z r C ( 3IIi - X 3 S + ) . N S,(N) RjfN) RjfN) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2 (N) 0 3 (N) N 0 18617.9513 18616.3906 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18619.3781 18617.0396 not observed 18615.4725 18615.9671 not observed \u2014 \u2014 \u2014 1 2 18617.4742 18615.1186 18615.1261 18613.5658 not observed \u2014 2 3 18617.7103 18614.5670 18614.4860 18612.1467 3 4 18617.7484 18613.8168 18613.6700 18610.5553 18608.2011 4 5 18617.5923 18612.8713 18612.6662 18608.7786 18605.6353 5 6 18617.2398 18611.7276 18611.4709 18606.8097 6 7 18616.6912 18610.3898 18610.0809 7 8 18615.9460 18608.8548 18608.4966 8 9 18615.0036 18607.1246 18606.7168 9 10 18613.8629 10 ts ta TO I o a. o a a I f 3 TO a 1 a* a' TO  a S 3 TO a TO-I N S!(N) Rl(N) R2(N) Qi(N) Q 3(N) Q 2 (N) P 3(N) P 2(N) 0 3(N) N 11 18612.5216 not observed not observed not observed 11 12 18610.9795 12 Table AI.38(a). Rotational assignments and line measurements of the 18981 c m - 1 band3 of 9 0 Z r C ( 3 n 2 -X 3E+). N SjfN) RjfN) RjCN) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2 (N) 0 3(N) N 0 18983.6455 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18985.1673 18982.7274 18982.2177 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18986.5055 18983.2542 18982.7067 18980.8134 18980.8211 18980.2668 \u2014 \u2014 \u2014 2 3 18987.6744 18983.6108 18983.0334 18980.3563 18980.2752 18979.7784 18977.8351 18977.3381 \u2014 3 4 18988.6759 18983.8006 18983.1959 18979.7345 18979.5879 18979.1290 18976.3345 18975.8763 4 5 18989.5091 18983.8281 18983.1959 18978.9478 18978.7433 18978.3151 18974.6792 18974.2508 18971.4251 5 6 18990.1716 18983.6913 18983.0334 18977.9946 18977.7372 18977.3381 18972.8630 18972.4631 18968.7959 6 7 18990.6452 18983.3891 18982.7067 18976.8765 18976.5678 18976.1942 18970.8861 18970.5131 18966.0056 7 8 18990.7272 18982.9214 18982.2177 18975.5876 18975.2282 18974.8809 18968.7465 18968.3989 18963.0509 8 9 18991.4186 18982.2861 18981.5554 18974.1084 18973.7010 18973.3776 18966.4446 18966.1216 9 10 18991.3638 18981.4780 18980.7234 18972.2377 18971.7839 18971.4847 18963.9780 18963.6794 10 11 18991.1919 18980.4889 18979.7110 18970.9801 18970.4757 18970.2022 11 12 18990.8586 18978.4983 18968.4223 18968.1731 12 13 18966.2555 18966.0279 13 14 18963.9298 18963.7257 14 T h i s band has the same upper state as the hot 18101 cm\" 1 band of 9 0 Z r C ( 3 f l 2 - X 3 E+ -0 = 1) listed in Table AI.30. Table AI.38(b). Rotational assignments and line measurements of the 18981 c m - 1 band of 9 2 Z r C ( 3 n 2 - X 3 E + ) . N SX(N) Rl(N) RafN) Ql(N) Q 3 (N) Q 2 (N) P 3(N) P 2 (N) 0 3(N) N 0 18980.7776 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18982.2996 18979.8629 18979.3530 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18983.6381 18980.3901 18979.8433 18977.9519 18977.9608 18977.4077 \u2014 \u2014 \u2014 2 3 18984.8086 18980.7491 18980.1716 18977.5046 18977.4188 18976.9237 18974.9819 18974.4868 \u2014 3 4 18985.8142 18980.9456 18980.3396 18976.8840 18976.7370 18976.2784 18973.4883 18973.0294 not observed 4 5 18986.6561 18980.9777 18980.3457 18976.1037 18975.8990 18975.4733 18971.8418 18971.4137 5 6 18987.3293 18980.8480 18980:1916 18975.1607 18974.9034 18974.5035 18970.0346 18969.6359 6 ts re 8. to o & a. o a a | TO a 5? \u00a7 a-a' TO TO TO 3 TO a ts TO \u00bb*. | N Si(N) Ri(N) RzCN) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 7 18987.8325 18980.5559 18979.8740 18973.7484 18973.3740 18968.0689 18967.6948 not observed 7 8 18980.1019 18979.3938 18972.0778 18965.9438 18965.5948 8 9 18979.4813 18978.7504 18970.9319 18970.6081 18963.6553 9 10 18978.6915 18977.9383 18968.9407 10 11 18976.9541 11 Table AI.38(c). Rotational assignments and line measurements of the 18981 c m - 1 band of 9 4 Z r C ( 3 n 2 - X 3 Z + ) . N Sx(N) Ri(N) RjCN) Ql(N) Q 3 (N) Q 2(N) P 3(N) P 2(N) 0 3(N) N 0 18977.9449 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 18979.4629 18977.0339 18976.5230 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 18980.7970 18977.5585 18977.0109 18975.1284 18975.1353 18974.5812 \u2014 \u2014 \u2014 2 3 18981.9636 18977.9177 18977.3381 18974.6792 18974.5951 18974.0986 18972.1644 18971.6693 \u2014 3 4 18982.9651 18978.1095 18977.5046 18973.9131 18973.4544 18970.2157 not observed 4 5 18983.7950 18978.1393 18977.5071 18973.2815 18973.0775 18972.6492 18969.0285 18968.6011 5 6 18984.4681 18978.0056 18977.3490 18972.3365 18972.0837 18971.6801 18967.2257 18966.8275 6 7 18984.9648 18977.7067 18977.0252 18970.9206 18970.5490 18965.2621 18964.8875 7 8 18985.2795 18977.2387 18976.5348 18969.6030 18969.2513 18963.1368 18962.7897 8 9 18975.8950 18967.7814 9 10 18966.1301 10 ts ts to o & a. o g 1 1 TO a \u00a7 a, 3r a TO TO TO s TO a st t a TO I I\u2014\u00bb 317 Appendix II: Rotational assignments and line measurements (in cm - 1) of singlet bands of ZrC This appendix tabulates the rotational assignments and line measurements of the ZrC bands with lower state al2Z+, v\" = 0. The bands are identified by band origin wavenumber v 0 (in c m - 1 to the nearest integer) of the 9 0 Z r C isotopomer and listed by increasing v 0 . The R, Q and P branch labels have their usual AJ = +1, 0 and -1 meaning. Most of the bands have upper states that appear among the cold bands of Appendix I; these are cross-referenced with identifying footnotes. As in Appendix I, a bold entry denotes a measurement of a blended line and an underlined entry denotes an uncertain measurement (due to asymmetry or line weakness). None of these lines were used in any least squares fits. A long dash indicates a nonexistent line. The measurement uncertainty is generally about 0.0005 c m - 1 . Table A I I I . Rotational assignments and line measurements of the 17485 c m - 1 banda of ZrC (Q' = 1 - a1^\"1\"). 90ZrC 92ZrC 94ZrC J R(J) Q(J) P(J) R(J) Q(J) P(J) R(J) Q(J) P(J) J 0 17486.4061 17483.1844 \u2014 \u2014 17479.8513 \u2014 0 1 17487.0577 17485 3522 17483.8219 17483.1844 . \u2014 17480.4789 17478 8101 \u2014 1 2 17487.5079 17484 9499 17483 2480 17484.2515 17483.8219 17480.0364 17480.8849 17478 3818 17478.8101 2 3 17487.7544 17484 3442 17481 7949 17484.4705 17484.2515 17478.5735 17481.0736 17477 7375 17478.3818 3 4 17487.7950 17483 5344 17480 1401 17484.4745 17484.4705 17476.9024 17481.0423 17476 8757 17477.7375 4 5 17487.6268 17482 5177 17478 2819 17484.2663 17484.4745 17475.0216 17480.7887 17475 7947 17476.8757 5 6 17487.2457 17481 2912 17476 2178 17483.8362 17484.2663 17472.9284 17480.3091 17474 4887 17475.7947 6 7 17486.6481 17479 8513 17473 9448 17483.1844 17483.8362 17470.6195 17479.5982 17472 9567 17474.4887 7 8 17485.8289 17478 1931 17471 4603 17482.3006 17483.1844 17468.0919 17478.6518 17471 1922 17472.9567 8 9 17484.7827 17476 3127 17468 7581 17481.1855 17482.3006 17465.3393 17477.4638 17469 1918 17471.1922 9 10 17483.5032 17474 2049 17465 8357 17479.8513 17481.1855 17462.3579 17476.0283 17466 9512 17469.1918 10 11 17481.9825 17471 8629 17462 6856 17478.2819 17479.8513 17459.1441 17474.3215 17464 5208 11 12 17480.2166 17469 2805 17459 3027 17478.2819 17472.4333 12 13 17478.1676 17466 4510 17483.1844 13 14 17475.9111 17463 3667 17483.8219 14 15 17460 0250 15 aThis band has the same upper state as the 17673 cn r 1 band of ZrC (Q' = 1 - X 3 Z + ) listed in Table AI.21. Table Al l .2 . Rotational assignments and line measurements of the 17501 c m - 1 banda of ZrC (Q1 = 1 - al2Z+). 90ZrC 92ZrC 94ZrC J R(J) Q(J) P(J) R(J) Q(J) P(J) R(J) Q(J) P(J) J 0 17502.8446 \u2014 \u2014 17498.0189 \u2014 \u2014 17493.1714 \u2014 \u2014 0 1 17503.4380 17501.7791 \u2014 17498.6092 17496.9687 \u2014 17493.7579 17492.1250 \u2014 1 2 17503.8023 17501.2993 17499.6872 17498.9724 17496.5119 17494.8675 17494.1137 17491.6645 17490.0306 2 3 17503.9373 17500.5911 17498.1756 17499.1073 17495.8267 17493.3606 17494.2379 17490.9757 17488.5215 3 4 17503.8448 17499.6577 17496.4348 17499.0142 17494.9142 17491.6240 17494.1322 17490.0559 17486.7830 4 5 17503.5262 17498.5027 17494.4651 17498.6939 17493.7754 17489.6592 17493.7952 17488.9066 17484.8126 5 6 17502.9814 17497.1268 17492.2686 17498.1455 17492.4097 17487.4665 17493.2255 17487.5257 17482.6128 6 ts TO | to \u00a9 3 . o 8 I TO a I a? a TO TO TO s TO a St I 00 J R(J) 90ZrC Q(J) P(J) R(J) 92ZrC Q(J) P(J) R(J) 94ZrC Q(J) P(J) J 7 17502.2137 17495.5314 17489.8453 17497.3712 17490.8182 17485.0463 17492.4248 17485.9140 17480.1815 7 8 17501.2220 17493.7176 17487.1961 17496.3718 17489.0013 17482.4008 17491.3877 17484.0715 17477.5183 8 9 17500.0090 17491.6874 17484.3237 17495.1406 17486.9607 17479.5276 17490.1136 17481.9927 17474.6238 9 10 17498.5753 17489.4407 17481.2287 17493.6833 17484.6929 17476.4274 17488.5988 17479.6789 17471.4933 10 11 17496.9203 17486.9776 17477.9128 17491.9942 17482.1974 17473.0995 17477.1218 17468.1273 11 12 17495.0446 17484.3237 17474.3760 17699.7024 12 13 17492.9459 17470.6195 13 14 17490.6165 17466.6399 14 15 17488.0522 15 16 17485.2408 16 aThis band has the same upper state as the 17689 cn r 1 band of ZrC (Q! = 1 - X 3 S + ) listed in Table AI.22. Table Al l .3 . Rotational assignments and line measurements of the 17502 and 17584 c m - 1 bands of 9 0 Z r C . 17502 cm\" 1 band a, Q'=0' - a 1 ! * 17584 cm\" 1 band, \u00a32'=1 - a ! I + J Q(J) R(J) Q(J) P(J) J 0 \u2014 17584.7901 \u2014 \u2014 0 1 17502.1435 17585.2791 17583.7484 \u2014 1 2 17501.7469 17585.4828 17583.2073 17581.6316 2 3 17501.1405 17585.3995 17582.3944 17580.0165 3 4 17500.3221 17585.0231 17581.3053 17578.1152 4 5 \u2022 17499.2916 17584.3516 17579.9368 17575.9271 5 6 17498.0483 17583.3771 17578.5846 17573.4466 6 7 17496.5946 17582.0962 17576.3445 7 8 17494.9296 17580.5047 17574.1106 8 9 17493.0538 17578.5988 9 10 17576.3753 10 11 17573.8329 11 ts t a re 3 & X >3 O & a. o 3 a. | Co 3 re 3 S? 1 a* 3 TO  s X TO 3 TO 3 Co t I X ^ aThis band has the same upper state as the 17690 cm\" 1 band of 9 0 Z r C (Q' = 0~ - X 3 E + ) listed in Table AI.23(a). NO Table AII.4. Rotational assignments and line measurements of the 17720 cm- 1 banda of ZrC (Q' = 2 - a 1 ^ ) . 90ZrC 92ZrC 94ZrC J R(J) Q(J) P(J) R(J) Q(J) P(J) R(J) Q(J) P(J) J 1 17721.3058 \u2014 \u2014 17719.2142 \u2014 \u2014 17717.7395 \u2014 \u2014 1 2 17721.6780 17719.2027 \u2014 17719.5276 17717.1129 \u2014 17717.9417 17715.6388 \u2014 2 3 17721.8213 17718.5179 17716.0454 17719.6073 17716.3738 17717.9417 17714.7974 17712.5001 3 4 17721.7358 17717.6041 17714.3093 17719.4661 17715.4001 17712.1778 17717.6960 17713.7288 17710.6112 4 5 17721.4256 17716.4631 17712.3476 17719.1054 17714.1998 17710.1593 17717.2573 17712.4432 17708.5017 5 6 17720.8916 17715.0908 17710.1593 17718.5294 17712.7772 17707.9206 17716.6119 17710.9467 17706.1771 6 7 17720.1346 17713.4915 17707.7441 17711.1345 17705.4589 17715.7592 17709.2432 17703.6436 7 8 17719.1554 17711.6646 17705.1054 17709.2784 17702.7827 17707.3314 17700.9055 8 9 17717.9582 17709.6181 17702.2445 17707.2063 17705.2138 9 10 17716.5429 17707.3443 17699.1626 17704.9215 17702.8870 10 11 17714.9121 17704.8554 17702.4213 17700.3511 11 12 17713.0633 17702.1468 17699.7024 12 13 17710.9967 17699.2219 13 14 17708.7114 14 15 17706.2081 15 16 17703.4697 16 17 17700.4889 17 aThis band has the same upper state as the 17908 c n r 1 band of ZrC (Q' = 2- X 3 S + ) listed in Table AI.27. Table AIL 5. Rotational assignments and line measurements of the 17724 c m - 1 band3 of ZrC (Q' = 1 - a 1 Z + ) . 90ZrC 92ZrC 94ZrC J R(J) Q(J) P(J) R(J) Q(J) P(J) R(J) Q(J) P(J) J 0 17723.9567 \u2014 \u2014 17721.0746 \u2014 \u2014 17718.8352 \u2014 \u2014 0 1 17724.6513 17722.8955 \u2014 17721.7930 17720.0159 \u2014 17719.6583 17717.7827 \u2014 1 2 17725.1659 17722.5193 17720.7984 17722.3290 17719.6680 17717.9258 17720.3160 17717.5467 17715.6933 2 3 17725.5003 17721.9571 17719.3884 17722.6592 17719.1314 17716.5429 17720.7855 17717.1429 17714.4231 3 4 17725.6533 17721.2091 17717.7990 17722.7513 17718.3866 17714.9810 17721.0586 17716.5487 17712.9851 4 5 17725.6220 17720.2726 17716.0279 17722.5518 17717.4047 17713.2126 17721.1282 17715.7592 17711.3618 5 ts ta TO a & to o & a. o a i 3 TO a EJ-I 3? a TO TO TO 3 TO a S3-Co *\u2014I. t St-1 I to o J R(J) 90ZrC Q(J) P(J) R(J) 92ZrC Q(J) P(J) R(J) 94ZrC Q(J) P(J) J 6 17725.4062 17719.1488 17714.0763 17716.1399 17711.2048 17720.9814 17714.7669 17709.5386 6 7 17725.0007 17717.8363 17711.9412 17709.0850 17720.6089 17713.5689 17707.5127 7 8 17724.4005 17716.3329 17709.6181 17712.1634 17705.2734 8 9 17723.5973 17714.6333 17707.1094 17710.5446 17702.8098 9 10 17722.5809 17712.7348 17704.4052 17708.7114 10 11 17710.6229 17701.5010 17706.6518 11 12 17708.2798 17698.3804 12 aThis band has the same upper state as the 17912 cm\" 1 band of ZrC (Q.' = 1 - X 3 E + ) listed in Table AI.28. Table AII.6. Rotational assignments and line measurements of the 17975 c m - 1 band of ZrC (Q' = 1 - a 1 ^ ) . 90ZrC 92ZrC 94ZrC J R(J) Q(J) P(J) R(J) Q(J) P(J) R(J) Q(J) P(J) J 0 17975.5752 \u2014 \u2014 17973.9533 \u2014 \u2014 \u2014 \u2014 0 1 17976.2074 17974.5429 \u2014 17974.5811 17972.8952 \u2014 17971.0511 \u2014 1 2 17976.6303 17974.1081 17974.9970 17972.4509 17973.1243 17970.6323 2 3 17976.8424 17973.4845 17970.9449 17975.2033 17971.7786 17969.3316 17973.3162 17970.0012 3 4 17976.8424 17972.6538 17969.2638 17975.1982 17970.8620 17967.6492 17969.1628 17965.7936 4 5 17976.6333 17971.6171 17967.3692 17974.9802 17969.6769 17965.7543 17968.1112 17963.8915 5 6 17976.2154 17970.3760 17965.2664 17974.5500 17968.1884 17963.6514 17966.8543 6 7 17975.5842 17968.9305 17962.9534 17973.9101 17961.3332 17965.3867 7 8 17974.7445 17967.2819 17960.4308 17963.7160 8 9 17973.6919 17965.4306 9 10 17972.4280 17963.3718 10 11 17970.9516 17961.1008 11 \u2022=> ts re I o o rs \u00a7 3 re a I a' re re re re a C-5 322 Appendix III: Hyperfine assignments and line measurements (in cm - 1) from triplet bands of 9 1 Z r C This appendix tabulates the hyperfine and rotational assignments and line measurements from triplet bands of 9 1 Z r C . These come from the following bands, whose 90\/92\/94zrc i m e s a r e tabulated in Appendix I: those with origins at 16488\/502 (3UQ - X 3 Z + ) , 17089 (3UY - X 3 E + ) and 17342 c m - 1 ( 3 n 2 - X 3 Z + ) . The S, Q and P branch labels have the same meaning as in Appendix I. Some internally induced hyperfine features were observed in the two highest wavenumber bands; these are noted. As in the previous Appendices, a bold entry denotes a measurement of a blended line. None of these lines were used in any least squares fits. The measurement uncertainty is generally about 0.0005 c m - 1 . Table AIII.l . Hyperfine and rotational assignments and line measurements of the 16488\/502 c m - 1 band of 9 1 Z r C (Q! = 0 - X 3 \u00a3 + ) . ^ F - - F \" S^O) F' - F \" Si(7) F - F \" Qi(0) F' - F \" QjCl) F' - F \" Ql(2) F - F \" QiC3) 5\/2 -7 \/2 1 6 490.1380 23\/2 -21\/2 1 6 4 99.6833 5\/2 -7 \/2 1 6 487.5310 7\/2 -7 \/2 1 6 487.4231 9\/2 -9 \/2 1 6 487.2613 13\/2 - 13\/2 1 6 487.0278 5\/2 -5 \/2 90.0322 21\/2 -19\/2 99.6468 5\/2 -5 \/2 87.4231 5\/2 - 5\/2 87.3670 7\/2 - 7 \/ 2 87.2071 9\/2 - 9 \/ 2 86.9411 5\/2 -3 \/2 89.9564 19\/2 -17\/2 99.6117 1\/2 -1 \/2 87.3003 5\/2 - 5 \/ 2 87.1769 7\/2 - 7 \/ 2 86.9077 3\/2 - 3 \/ 2 87.1499 5\/2 - 5 \/ 2 86.8713 1\/2 - 1 \/ 2 87.1356 3\/2 - 3 \/ 2 86.8534 F - - F\" Ql(4) F' - F \" Q 2(l) F - F \" Q2(2) F' - F \" Q2(3) F - F \" Q 3(2) F - F \" Q 3(3) 15\/2 - 15\/2 1 6 486.6367 7\/2 - 7 \/ 2 1 6 486.9327 9\/2 -9 \/2 1 6 486.7090 11\/2 - 11\/2 1 6 486.3876 7\/2 - 7 \/ 2 1 6 487.2235 9\/2 - 9 \/ 2 1 6 486.8270 13\/2 -13\/2 86.5929 5\/2 - 5 \/ 2 86.8713 7\/2 -7 \/2 86.6740 5\/2 -5 \/2 87.2613 7\/2 -7 \/2 86.8713 11\/2 -11\/2 86.5566 3\/2 - 3 \/ 2 86.8385 5\/2 -5 \/2 86.6576 3\/2 - 3 \/ 2 87.2946 5\/2 - 5 \/ 2 86.9071 9\/2 -9 \/2 86.5219 3\/2 -3 \/2 86.6512 1\/2 -1 \/2 86.9411 7\/2 -7 \/2 86.4923 1\/2 -1 \/2 86.6512 5\/2 -5 \/2 86.4714 F - - F\" Q 3(4) F - F \" P 2(4) F - F \" P 2(6) F' - F\" P 2(9) F' - F \" P 3(4) F - F \" P 3(5) 7\/2 -7 \/2 1 6 486.4374 11\/2 - 13\/2 1 6 496.7401 15\/2 -17\/2 1 6 4 93.9159 21\/2 - 23\/2 1 6 488.7890 9\/2 - 11\/2 1 6 497.1391 11\/2 - 13\/2 1 6 495.7417 5\/2 -5 \/2 86.4623 9\/2 -11\/2 96.7186 13\/2 -15\/2 93.8966 19\/2 -21\/2 88.7717 7\/2 -9 \/2 97.1823 9\/2 -11\/2 95.7835 1\/2 -1 \/2 86.4923 7\/2 - 9 \/ 2 96.7067 5\/2 -7 \/2 97.2145 7\/2 - 9 \/ 2 95.8158 5\/2 - 7 \/ 2 96.7067 5\/2 - 7 \/ 2 95.8413 3\/2 - 5 \/ 2 96.7067 3\/2 -5 \/2 95.8603 1\/2 - 3 \/ 2 96.7067 1\/2 -3 \/2 95.8729 Table AIII.2. Hyperfine and rotational assignments and line measurements3 of the 17089 c m - 1 band3 of 9 1 Z r C (Q' = 1 - X 3 Z + ) . 5\/2-7\/2 1 7 090.8611 9\/2-9\/2 1 7 092.4354 15\/2- 13\/2 1 7 096.5529 5\/2-5\/2 90.7556 9\/2-7\/2 92.4999 13\/2- 11\/2 96.5153 re I S3 I ta re <3> a re 1 \u00a7 3 re a S? I a' re 3 re re 3 re a t a re 8 F - F \" Sx(0) F - F \" Sj(l) F - F \" Sx(4) |ST 5\/2-3\/2 89.6805 11\/2-9\/2 96.4810 ^ 9\/2 - 7\/2 96.4522 fS 7\/2-5\/2 96.4197 7\/2 - 5\/2 96.4275a aExtra line induced by internal hyperfine perturbation. <\u00b0, Appendix III Hyperfine assignments and line measurements of triplet bands of 9 1 ZrC 324 ON so oo as oo m O v> so ^ \u00a9 \u00a9 r i -r f so i\u2014< 0 0 so as as so so i - rt-\u00ab - t i \/ i rt ifl H M V) <s m i> \u00ab s \u00a9 \u00a9 \u00a9 o r- r-PH I PH CS <N ^ ^ C N C ^ C S C ^ C S C S C ^ C S C N r \u2014 i i - H O N O N t ^ m c O ' \u2014 < r~ 1^ V\"> I I I I I I I I I I I m ^ H n H O N O N t ^ i n c o O N I ^ i n PH I PH VI m oo ts r r \u2022-< CS >n \u00a9 r~ as rl-7-1 OS OS OS 0 0 0 0 0 0 r~ \u00a9 o \u00a9' \u00a9' \u00a9 \u00a9 \u00ab ! v i in v i CS CS CS ^ ^ _H Q C! CI ^H ^H i\u2014i o\\ as i n I I I I I I (S (S \u00ab (S N M \u00ab\/\"> r*i ' \u2014 a s in in oo as c*-> m H ; H ; H ; H ; fN i\u2014i ON m ON m n- ^H n- oo ON rt- m m in v i in m T l - T t T t Tfr PH I PH N (S (S <S (S (N M as as t t !n i n I I I I I I I CN CS CS CS CS CS CS I-H ON ON t i n t i n 0 0 ts 0 0 c i r i -0 0 - \u2014 i O ( ^ t s m r h N O f S o o o o c s r t - o o o N i n s o r ^ ' n r - o c o s o \u2014 ao oo r- i> r- so r- r~ C) p i n p i c i co m' to PH I PH t S t S f S t S f S f S J S f S t ^ t ^ m i n m c o c s c s I I I I I I I I f S C S t S C S C S C S C S C S ( ^ m t ^ i n r o i n t o ^ H r \u00a3 t \/T PH I PH so so \u00a9 ON ON i n ON ts oo so as \u00a9 r f i\u2014i r- r l - - H ON ON r~ r-; so so so; vit in ON ON ON ON ON OS OS T j - T j -CS CS CS J i n - C! C! 5 CJ _H - H _ i os ON in in I I I I I I I ts ts ts ts ts ts cs r- in m i\u2014i ON r~ r-PH I PH \u00a9 OS <=\u2022 \"if OS Os r|- r t ^H \\D in \u2022\u20141 0 0 0 0 0 0 0 0 0 0 r f r t T t Tl- TI-CS JS JS tS m co \u2022\u2014i i\u2014i C! 1-H 1-H 1-H 1-H OS I I I I I cs ts ts j s ts \u2022n m to i-H ,\u2014i GO d o '3 i-e \u2022g tl) OH <U d u OH \"c3 U O 'I (U d 325 Appendix IV: Rotational assignments and line measurements (in cm - 1) of bands of ZrCH This appendix tabulates the rotational assignments and line measurements of the P' (case c) - X 2 Z + bands of ZrCH. The bands are identified by the band origin wavenumber v 0 (in c m - 1 rounded to the nearest integer) of the 9 0 Z r C H isotopomer and listed by increasing VQ, and in increasing Zr mass number order within (90 and, if available, 92 and 94). The branch labels 3\/2R, 1\/2R, 1\/2P and 3\/2P denote J' - N \" = +3\/2, +1\/2, -1\/2 and -3\/2 respectively; subscripts \/ = 1 and 2 on these branch labels denote the ground state spin component F ; (Fj and F 2 denote J = N+l\/2 and N - l \/ 2 respectively). This fil'-independent scheme is used since the upper states all have essentially Hund's case (c) coupling. All of the bands are \"cold\" (i.e., v\" = 0). A bold entry denotes a measurement of a blended line; an underlined entry denotes an uncertain measurement (due to asymmetry or line weakness). None of these lines were used in any least squares fits; the data for 9 2 Z r C H and 9 4 Z r C H were too sparse for meaningful least squares analyses but are included here for completion. A long dash indicates a nonexistent line. The measurement uncertainty is generally about 0.0005 c m - 1 . Appendix IV Rotational Assignments and Line Measurements of ZrCH 3 26 Table AIV. 1(a) Rotational assignments and line measurements of the 15179 c n r 1 band of 9 0 Z r C H (P' = 1\/2). N mRjfN) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 15180.7984 15179.4076 \u2014 \u2014 \u2014 \u2014 0 1 15181.9217 15179.6028 15179.5759 15178.8364 15178.8086 \u2014 1 2 15182.9750 15179.7296 15179.6823 15178.4523 15178.4052 15177.0139 2 3 15183.9588 15179.7854 15179.7200 15177.9970 15177.9321 15175.6137 3 4 15184.8727 15179.7753 15179.6931 15177.4747 15177.3900 15174.1448 4 5 15185.7179 15179.6931 15179.5906 15176.8824 15176.7783 15172.6058 5 6 15186.4905 15179.5445 15179.4216 15176.2193 15176.0974 15171.0008 6 7 15187.1950 15179.3307 15179.1895 15175.4878 15175.3457 15169.3240 7 8 15187.8300 15179.0364 15178.8756 15174.6847 15174.5243 8 9 15188.3941 15178.6694 15178.4889 15173.8129 15173.6324 9 10 15188.8877 15178.2622 15178.0638 15172.8710 15172.6741 10 11 15189.3106 15171.8588 15171.6413 11 12 15170.7767 15170.5407 12 13 15169.6238 15169.3698 13 Table AIV. 1(b) Rotational assignments and line measurements of the 15179 c m - 1 band of 9 2 Z r C H (P1 = 1\/2) N 3\/2R x(N) 1\/2R!(N) 1\/2R2(N) 1\/2PX(N) 1\/2P2(N) 3\/2P2(N) N 0 15180.9542 15179.5655 \u2014 \u2014 \u2014 \u2014 0 1 15182.0742 15179.7581 15179.7296 15178.9960 15178.9666 \u2014 1 2 15183.1214 15179.8878 15179.8391 15178.6148 15178.5673 15177.1784 2 3 15184.1045 15179.9430 15179.8781 15178.1614 15178.0962 15175.7805 3 4 15185.0164 15179.9311 15179.8494 15177.6375 15177.5528 15174.3178 4 5 15185.8579 15179.8549 15179.7477 15177.0469 15176.9438 15172.7836 5 6 15186.6300 15179.7004 15179.5759 15176.3874 15176.2648 6 7 15187.3351 15179.4828 15179.3440 15175.6579 15175.5139 7 8 15187.9665 15174.6939 8 Table AIV. 1(c) Rotational assignments and line measurements of the 15179 cm 1 band of 9 4 Z r C H (P' = 1\/2) N 3\/2R!(N) 1\/2R2(N) . 1\/2P!(N) 1\/2P2(N) 3\/2P2(N) N 0 15181.1069 15179.7200 \u2014\u2022 \u2014 \u2014 \u2014 0 1 15182.2206 15179.9187 15179.8878 15179.1543 15179.1245 \u2014 1 2 15183.2689 15180.0292 15179.9827 15178.7708 15178.7236 15177.3430 2 3 15184.2474 15180.0948 15180.0295 15178.3182 15178.2532 15175.9511 3 4 15185.1576 15180.0841 15180.0017 15177.7985 15177.7127 15174.4754 4 5 15185.9983 15180.0017 15179.9072 15177.2085 15177.1050 5 6 15186.7668 15179.8549 15179.7200 15176.5496 15176.4281 6 7 15179.6339 15179.4828 15175.8233 15175.6780 7 8 15188.1013 15179.3440 15179.1895 15175.0246 15174.8645 8 Appendix IV Rotational Assignments and Line Measurements of ZrCH 327 Table AIV.2(a) Rotational assignments and line measurements of the 15428 c m - 1 band of 9 0 Z r C H (P' = 3\/2). N 3\/2R!(N) l\/2Rj(N) l \/ lRj fN) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 15429.2626 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15430.2341 15428.4839 15428.4557 \u2014 \u2014 \u2014 1 2 15431.1261 15428.6680 15428.6188 15426.9159 15426.8683 \u2014 2 3 15431.9245 15428.7659 15428.7015 15426.3106 15426.2451 15424.4936 3 4 15432.6328 15428.7779 15428.6930 15425.6262 15425.5419 15423.0830 4 5 15433.2604 15428.6930 15428.5866 15424.8457 15424.7441 15421.5872 5 6 15433.8039 15428.5401 15428.4171 15423.9789 15423.8586 6 7 15434.2480 15423.0336 15422.8902 7 8 15434.6131 15421.9965 15421.8367 8 9 15420.8669 15420.6880 9 Table AIV.2(b) Rotational assignments and line measurements of the 15428 c m - 1 band of 9 2 Z r C H (P' = 3\/2). N 3\/2Rj(N) l ^ C N ) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 15429.3916 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15430.3682 15428.6188 15428.5995 \u2014 \u2014 \u2014 1 2 15431.2458 15428.8060 15428.7595 15427.0048 \u2014 2 3 15432.0447 15428.8967 15428.8327 15426.4557 15426.3902 3 4 15432.7552 15428.9093 15428.8233 15425.6777 15423.2403 4 5 15433.3717 15428.8607 15428.7471 15424.9850 15424.8838 5 6 15433.9147 15428.6680 15428.5465 15424.1074 15424.0024 6 7 15434.3664 15423.1753 15423.0336 7 8 15434.7254 15422.1415 15421.9824 8 9 15421.0287 15420.8469 9 Table AIV.2(c) Rotational assignments and line measurements of the 15428 c m - 1 band of 9 4 Z r C H (P' = 3\/2). N 3\/2Rj(N) 1\/2RX(N) 1\/2R2(N) mPjfN) 1\/2P2(N) 3\/2P2(N) N 0 15429.5144 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15430.4841 15428.7377 15428.7121 \u2014 \u2014 \u2014 1 2 15431.3669 15428.9257 15428.8773 15427.1819 15427.1338 \u2014 2 3 15432.1619 15429.0230 15428.9581 15426.5806 15426.5164 3 4 15432.8694 15429.0353 15428.9496 15425.8968 15425.8109 15423.3683 4 5 15433.4928 15428.9581 15428.8571 15425.0144 15421.8781 5 6 15434.0272 15428.7950 15428.6680 15424.2555 15424.1353 6 7 15434.4712 15423.3148 15423.1753 7 8 15422.2826 15422.1242 8 9 15421.1656 15420.9843 9 Appendix IV Rotational Assignments and Line Measurements of ZrCH 328 Table AIV.3(a) Rotational assignments and line measurements of the 15621 c m - 1 band of 9 0 Z r C H (P1 = 1\/2). N 3\/2Rj(N) 1\/2R2(N) 1\/2P,(N) 1\/2P2(N) 3\/2P2(N) N 15622.3739 15622.4508 15623.4527 15623.5763 15624.6597 15625.0578 15625.6735 15626.0036 15626.6427 15626.9364 15627.5098 15627.7988 15628.3652 15628.5677 15628.7548 15629.1426 15629.2558 15629.6011 15629.9540 15620.8963 15621.0650 15621.1719 15621.2114 15621.1930 15621.1182 15620.9855 15620.6607 15620.4175 15621.0377 15621.1231 15621.1450 15621.1082 15621.0136 15620.8625 15620.5181 15620.2569 9 15630.6119 15620.0757 15619.8973 10 15631.1715 15631.2478 11 12 15619.6315 15619.4369 15620.3916 15620.0274 15620.1038 15619.5284 15619.6546 15619.1612 15619.5585 15618.5970 15618.9280 15617.9896 15618.2840 15617.2809 15617.5684 15616.5608 15616.7622 15616.9495 15615.7598 15615.8734 15616.2201 15614.9956 15614.0786 15614.1580 15613.0616 15613.1364 15620.3634 15619.9807 15620.0572 15619.4616 15619.5876 15619.0763 15619.4722 15618.4930 15618.8249 15617.8661 15618.1614 15617.1401 15617.4278 15616.3997 15616.6022 15616.7882 15615.5849 15615.6943 15616.0428 15614.7968 15613.8619 15613.9424 15612.8242 15612.9002 \u2014 1 15618.5038 2 15617.0766 3 15615.5849 4 15614.0311 5 15612.4173 6 15610.7460 7 15609.0187 8 15607.0986 9 15605.2553 10 11 12 Table AIV.3(b) Rotational assignments and line measurements of the 15621 c m - 1 band of 9 2 Z r C H (P' = 1\/2). N 3\/2RJCN) l\/2Rj(N) 1\/2R2(N) l \/ H ^ f N ) 1\/2P2(N) 3\/2P2(N) N 0 1 2 3 4 5 6 7 8 9 15622.0419 15623.2184 15624.4319 15625.4382 15626.5311 15620.4630 15620.6785 15620.7877 15620.8508 15620.8308 15620.8094 15620.6607 15620.4098 15620.6511 15620.7418 15620.7877 15620.7485 15620.7059 15620.5413 15620.2693 15619.7015 15619.3060 15618.9464 15618.3784 15617.9012 15619.6546 15619.2409 15618.2754 15617.7757 15618.0769 15616.9649 15615.2190 15613.6890 15610.4662 15606.8834 0 1 2 3 4 5 6 7 Appendix IV Rotational Assignments and Line Measurements of ZrCH 329 Table AIV.3(c) Rotational assignments and line measurements of the 15621 c m - 1 band of 9 4 Z r C H (P1 = 1\/2). N 3\/2R!(N) l^RjON) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P 2(N) N 0 15621.6322 \u2014 \u2014 \u2014 \u2014 0 1 15622.7606 15620.0896 15620.0624 15619.6546 15619.6315 \u2014 1 2 15623.8231 15620.2569 15620.2090 15619.2987 15619.2527 15617.4152 2 3 15624.8135 15620.3374 15620.2693 15618.8580 15618.7924 15616.1238 3 4 15625.8461 15620.3423 15620.2569 15618.3530 15618.2683 15614.6996 4 5 15620.2851 15620.1799 15617.7757 15617.6707 15613.1929 5 6 15620.1649 15620.0420 15617.2415 15617.1163 15611.6130 6 7 15619.9941 15620.8534 15609.9664 7 8 15608.2613 8 9 15606.5042 9 Table AIV.4(a) Rotational assignments and line measurements of the 15680 c m - 1 band of 9 0 Z r C H (P' = 1\/2) N 3\/2Rj(N) l\/2Rj(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 15680.6331 15680.1292 \u2014 \u2014 \u2014 \u2014 0 1 15681.4695 15680.6104 15680.5821 15678.9632 15678.9350 \u2014 1 2 15682.2368 15681.1082 15681.0610 15678.2867 15678.2396 15677.7356 2 3 15682.9448 15681.4749 15681.4094 15677.5464 15677.4806 15676.6210 3 4 15683.5896 15681.7852 15681.7004 15676.7377 15676.6519 15675.5237 4 5 15684.1704 15682.0326 15681.9279 15675.8663 15675.7642 15674.2949 5 6 15684.6928 15682.2151 15682.0920 15674.9365 15674.8134 15673.0094 6 7 15685.1305 15682.3324 15682.1914 15673.9404 15673.7992 15671.6613 7 8 15685.5013 15682.3762 15682.2151 15672.8861 15672.7260 15670.2489 8 9 15685.8237 15682.3324 15682.1543 15671.5692 15668.7709 9 10 15686.0907 15682.2896 15682.0920 15670.3451 15667.2203 10 11 15686.2535 15669.0725 15665.5800 11 12 15686.3880 15667.7448 15663.9429 12 13 15686.4525 15666.3119 13 Table AIV.4(b) Rotational assignments and line measurements of the 15680 c m - 1 band of 9 2 Z r C H (P' = 1\/2) N 3\/2R x(N) l\/2Rj(N) 1\/2R2(N) 1\/2PX(N) 1\/2P2(N) 3\/2P2(N) N 0 15680.7170 15680.2297 \u2014 \u2014 \u2014 \u2014 0 1 15681.5488 15680.7326 15679.0473 15679.0179 \u2014 1 2 15682.2955 15681.1727 15678.3740 15678.3280 15677.8421 2 3 15683.0250 15681.5488 15677.6383 15677.5708 15676.7533 3 4 15683.6782 15681.8634 15681.7779 15676.8180 15676.7287 15675.6031 4 5 15684.2634 15682.1103 15675.9677 15675.8663 15674.3875 5 6 15684.7427 15682.3115 15675.0480 15674.9245 15673.1114 6 7 15685.2028 15682.4151 15674.0605 15673.9199 15671.7677 7 8 15682.4703 15672.9711 15672.8070 15670.3756 8 Appendix TV Rotational Assignments and Line Measurements of ZrCH 330 N l ^R j fN) 1\/2R2(N) 1\/ZPifN) 1\/2P2(N) 3\/2P2(N) N 9 15682.4610 15671.6769 15668.8890 9 10 15667.3534 10 11 15665.7539 11 12 15664.0888 12 Table AIV.4(c) Rotational assignments and line measurements of the 15680 c m - 1 band of 9 4 Z r C H (P' = 1\/2) N 3\/2R1(H) 1\/21^ (N) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 15680.7726 15680.2562 \u2014 \u2014 \u2014 \u2014 0 1 15681.6070 15680.7374 15679.0793 \u2014 1 2 15682.3763 15681.1453 15678.4385 15678.3919 15677.8742 2 3 15683.0908 15681.7922 15681.7179 15677.7045 15677.6383 15676.7698 3 4 15683.7143 15682.0483 15681.9566 15676.9029 15676.8180 15675.5899 4 5 15684.3046 15682.2590 15676.0518 15675.9485 15674.6498 5 6 15684.8485 15682.4223 15675.1044 15674.9842 15673.3180 6 7 15685.2357 15682.5325 15674.1270 15673.9875 15671.9420 7 8 15682.5863 15673.1075 15672.9443 15670.5194 8 9 15682.5458 15671.7481 15669.0442 9 10 15667.5083 10 11 15665.8819 11 Table AIV.5(a). Rotational assignments and line measurements of the 15705 cm- 1 band o f 9 0 Z r C H ( P , = 3\/2) N mRjCsl) 1\/2R2(N) 1\/2P2(N) 3\/2P2(N) N 0 15706.5598 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15707.5929 15705.7805 15705.7523 \u2014 \u2014 \u2014 1 2 15708.5681 15706.0250 15705.9782 15704.2132 15704.1665 \u2014 2 3 15709.5039 15706.2115 15706.1464 15703.6700 15703.6041 15701.7905 3 4 15710.0393 15706.3577 15706.2732 15703.0681 15702.9830 15700.4411 4 15710.2193 15710.4401 5 15710.8773 15706.4979 15706.3936 15702.4269 15702.3231 15699.0317 5 6 15711.6334 15706.3936 15706.2732 15701.3866 15701.2635 15697.5824 6 15701.5671 15701.4436 15701.7874 15701.6644 7 15712.0765 15706.2732 15706.1300 15700.6475 15700.5063 15696.1265 7 15712.3774 8 15712.6925 15705.9707 15705.8095 15699.8275 15699.6672 15694.4294 8 9 15713.2157 15705.5522 15705.3726 15698.6938 15698.5154 15692.7162 9 15698.8153 10 15713.6823 15705.3381 15705.1399 15697.7344 15697.5352 15690.8137 10 11 15713.9467 15705.0224 15704.8060 15696.6806 15696.4633 11 12 15695.3355 12 13 15694.0053 13 Appendix IV Rotational Assignments and Line Measurements of ZrCH 331 Table AIV.5(b). Rotational assignments and line measurements of the 15705 c m - 1 band of 9 2 Z r C H (P' = 3\/2). N 3\/2RJCN) mRjCN) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 15706.7155 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15707.6969 15705.8848 15705.8598 \u2014 \u2014 \u2014 1 2 15708.6564 15706.1340 15706.0876 15704.3746 15704.3296 \u2014 2 3 15709.5285 15706.3084 15706.2420 15703.7838 15703.7185 15701.9033 3 4 15710.3348 15706.3936 15706.3084 15703.1705 15703.0857 15700.5647 4 5 15711.0710 15706.4100 15706.3084 15702.4703 15702.3671 15699.1460 5 6 15711.7344 15706.5598 15706.4307 15701.7043 15701.5819 15697.6409 6 7 15712.3365 15700.8684 15700.7272 15696.0720 7 8 15712.8743 15699.9593 15699.7996 8 9 15713.3785 15698.9910 15698.8113 9 10 15697.7587 Table AIV.5(c). Rotational assignments and line measurements of the 15705 c m - 1 band of 9 4 Z r C H (P' = 3\/2) N 3\/2Rx(N) 1\/2RX(N) mRjCN) 1\/2PX(N) 1\/2P2(N) 3\/2P2(N) N 0 15706.7974 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15707.8145 \u2014 \u2014 \u2014 1 2 15708.7639 15706.2549 15704.4630 15704.4165 \u2014 2 3 15709.6451 15706.4169 15706.3520 15703.9116 15703.8461 15702.0520 3 4 15710.4748 15703.2933 15703.2086 15700.6994 4 5 15711.2172 15706.5518 15706.4478 15702.6053 15702.5018 15699.2767 5 15711.3603 6 15711.8376 15701.8667 15701.7478 6 7 15712.4522 15701.0406 15700.9013 15696.2346 7 15701.0406 8 15712.9833 15700.0929 15699.9337 8 9 15699.1408 15698.9610 9 Table AIV.6(a) Rotational assignments and line measurements of the 15988 c m - 1 band of 9 0 Z r C H (P' = 3\/2) N 3\/2Rj(N) l\/2Rj(N) 1\/2R2(N) l^PjfN) 1\/2P2(N) 3\/2P2(N) N 0 15989.2775 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15990.3367 15988.4760 15988.4480 \u2014 \u2014 \u2014 1 2 15991.2088 15988.7194 15988.6723 15986.7030 15986.6558 \u2014 2 15986.9311 15986.8839 3 15992.1058 15988.8929 15988.8261 15986.4136 15986.3479 15984.4865 3 4 15992.9361 15989.0235 15988.9383 15985.7085 15985.6240 15983.1347 4 5 15993.7013 15989.0176 15988.9133 15985.0294 15984.9252 15981.7124 5 6 15994.4159 15988.7430 15988.6204 15984.2825 15984.1598 15980.2490 6 15989.0572 15988.9383 7 15995.0918 15988.7875 15988.6471 15983.4709 15983.3299 15978.6466 7 Appendix IV Rotational Assignments and Line Measurements of ZrCH 332 N l \/ ^ f N ) 1\/2R2(N) 1\/H^fN) 1\/2P2(N) 3\/2P2(N) N 8 15995.3535 15988.5145 15988.3548 15982.6106 15982.4496 15976.7766 8 15995.7299 15977.0905 9 15995.8974 15981.7124 15981.5305 15975.2267 9 15996.3773 10 15997.0299 15980.3952 15980.1974 10 15980.7703 15980.5734 11 15997.6366 15979.3633 15979.1434 11 15979.8399 15979.6202 12 15998.1978 15978.9150 15978.6800 12 13 15998.7118 13 14 15999.1806 14 Table AIV.6(b). Rotational assignments and line measurements of the 15988 c m - 1 band of 9 2 Z r C H (P = 3\/2) N 3\/2R x(N) 1\/2RX(N) 1\/2R2(N) 1\/2PX(N) 1\/2P2(N) 3\/2P2(N) N 0 15988.8261 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15989.8461 15988.0449 15988.0175 \u2014 \u2014 \u2014 1 2 15990.8190 15988.2781 15988.2303 15986.4833 15986.4363 \u2014 2 3 15991.7079 15988.4480 15988.3803 15985.9333 15985.8678 15984.0674 3 4 15992.5308 15988.5557 15988.4760 15985.3338 15985.2496 15982.7082 4 5 15993.2800 15988.5742 15988.4760 15984.6503 15984.5464 15981.2875 5 6 15993.9724 15988.5212 15988.3985 15983.9011 15983.7786 15979.8034 6 7 15994.5885 15983.0785 15982.9365 7 8 15994.7479 15982.1976 15982.0381 15976.5871 8 9 15981.2412 15981.0629 9 10 15979.8257 15979.6276 10 Table AIV.6(c). Rotational assignments and line measurements of the 15988 c m - 1 band of 9 4 Z r C H (P' = 3\/2) N 3\/2R x(N) mRjfN) 1\/2R2(N) 1\/H^fN) 1\/2P2(N) 3\/2P2(N) N 0 15988.4353 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15989.4474 15987.6593 15987.6312 \u2014 \u2014 \u2014 1 2 15990.3938 15987.8887 15987.8411 15986.0988 15986.0526 \u2014 2 3 15991.2735 15988.0449 15987.9779 15985.5447 15985.4787 15983.6911 3 4 15992.0913 15988.1297 15988.0449 15984.9252 15984.8381 15982.3332 4 5 15992.8548 15988.1454 15988.0449 15984.2343 15984.1311 15980.9072 5 6 15993.5516 15988.0940 15987.9716 15983.4829 15983.3611 15979.4005 6 7 15982.6775 15982.5368 15977.8289 7 8 15976.1898 8 Appendix IV Rotational Assignments and Line Measurements of ZrCH 333 Table AIV.7(a) Rotational assignments and line measurements of the 16112 c m - 1 band of 9 0 Z r C H (P1 = 1\/2). N 1\/2R2(N) l ^ P j f N ) 1\/2P2(N) 3\/2P 2(N) N 0 16112.9962 16112.3274 \u2014 \u2014 \u2014 \u2014 0 1 16113.8608 16112.7760 16112.7477 16111.2664 16111.2375 \u2014 1 2 16114.6857 16113.1561 16113.1092 16110.6508 16110.6030 16109.9364 2 3 16115.3868 16113.4829 16113.4180 16109.9364 16108.7856 3 4 16116.0776 16113.7195 16113.6350 16109.1860 16107.5708 4 5 16116.7084 16113.8924 16113.7958 16108.3104 16106.3035 5 6 16117.2704 16114.0150 16113.8924 16107.4242 16104.9428 6 7 16117.7587 16114.0632 16113.9214 16106.4788 16103.5266 7 8 16118.1743 16114.0378 16113.8783 16105.4643 16102.0496 8 9 16118.5314 16113.7736 16104.3757 16100.5030 9 10 16118.8180 16113.6083 16103.2164 10 11 16119.0374 16113.3896 16101.9957 11 12 16119.1903 16100.7066 12 13 16119.2796 16099.3494 13 14 16119.3010 14 Table AIV.7(b). Rotational assignments and line measurements of the 16112 c m - 1 band of 9 2 Z r C H (P' = 1\/2). N 3\/2R x(N) 1\/2RX(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P 2(N) N 0 16112.5531 16111.8856 \u2014 \u2014 \u2014 \u2014 0 1 16113.4370 16112.3952 16112.3689 16110.8380 16110.8097 \u2014 1 2 16114.2508 16112.7603 16112.7145 16110.2135 16109.4976 2 3 16114.9989 16113.0883 16113.0226 16109.5234 16108.4141 3 4 16115.6835 16113.3030 16113.2203 16108.7649 16107.1915 4 5 16116.2985 16113.4829 16113.3802 16107.9418 16105.9268 5 6 16116.8492 16107.0545 16104.5516 6 7 16117.3191 16106.0974 16103.1513 7 8 16117.7429 16105.0718 8 9 16118.0919 9 10 16118.4152 10 11 16118.6011 11 12 16118.7564 12 Table AIV.7(c). Rotational assignments and line measurements of the 16112 cm 1 band of 9 4 Z r C H (P' = 1\/2) N mRjCN) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 16112.1605 16111.5031 \u2014 \u2014 \u2014 \u2014 0 1 16113.0428 16111.9469 16111.9173 16110.4485 16110.4190 \u2014 1 2 16113.8608 16112.3220 16112.2754 16109.8264 16109.1222 2 3 16114.6225 16112.5682 16109.1407 16107.9783 3 4 16115.2405 16112.9321 16112.8511 16108.3905 16106.7665 4 Appendix IV Rotational Assignments and Line Measurements of ZrCH 334 N 3\/2RJCN) 1\/2RX(N) l^RjfN) mPjfN) 1\/2P2(N) 3\/2P2(N) N 5 16115.8656 16107.5830 16105.4913 5 6 16116.4277 16106.6316 16104.2045 6 7 16116.8936 16105.6881 7 8 16117.3191 8 Table AIV. 8(a) Rotational assignments and line measurements of the 16529 c m - 1 band of 9 0 Z r C H (P = 3\/2). N 3\/2Rx(N) mRjtN) 1\/2R2(N) 1\/2P,(N) 1\/2P2(N) 3\/2P2(N) N 0 16530.3959 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16531.3688 16529.6152 16529.5866 \u2014 \u2014 \u2014 1 2 16532.2611 16529.8009 16529.7543 16528.0496 16528.0026 \u2014 2 3 16533.0799 16529.8949 16529.8286 16527.4452 16527.3802 16525.6258 3 4 16533.7931 16529.9021 16529.8171 16526.7620 16526.6772 16524.2170 4 5 16534.4367 16529.8219 16529.7181 16526.0037 16525.8997 16522.7140 5 5 16534.4578 5 6 16535.0171 16529.6536 16529.5305 16525.1397 16525.0177 16521.1256 6 7 16535.5236 16529.4061 16529.2633 16524.2072 16524.0653 16519.4512 7 7 16524.2295 16524.0863 7 8 16535.7647 16529.0599 16528.8985 16523.2111 16523.0509 16517.6874 8 9 16536.0934 16522.1404 16521.9614 16515.8431 9 10 16536.3453 16520.8065 16520.6078 16513.9026 10 11 16519.5607 16519.3422 11 12 16518.2328 16517.9994 12 Table AIV. 8(b) Rotational assignments and line measurements of the 16529 c m - 1 band of 9 2 Z r C H (P = 3\/2). N 3\/2Rj(N) 1\/2R!(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 16529.4101 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16530.3871 16528.6322 16528.6042 \u2014 \u2014 \u2014 1 2 16531.2750 16528.8181 16528.7707 16527.0710 16527.0240 \u2014 2 3 16532.0769 16528.9152 16528.8471 16526.4746 16526.4087 16524.6539 3 4 16532.8045 16528.9152 16528.8314 16525.7900 16525.7048 16523.2478 4 5 16533.4446 16528.8386 16528.7353 16525.0177 16524.9164 16521.7520 5 6 16534.0053 16528.6708 16528.5491 16524.1738 16524.0517 16520.1629 6 7 16534.4708 16528.4091 16528.2684 16523.2420 16523.1010 16518.4958 7 8 16534.8412 16528.0378 16527.8779 16522.2291 16522.0706 16516.7384 8 9 16535.1432 16521.1256 16520.9457 16514.8838 9 10 16519.9209 16519.7259 10 Appendix IV Rotational Assignments and Line Measurements of ZrCH 335 Table AIV.8(c) Rotational assignments and line measurements of the 16529 c m - 1 band of 9 4 Z r C H (P' = 3\/2). N 3\/2Rj(N) 1\/2RJCN) 1\/2R2(N) 1119^ 1\/2P2(N) 3\/2P 2(N) N 0 16528.4897 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16529.4678 16527.7129 16527.6838 \u2014 \u2014 \u2014 1 2 16530.3587 16527.9032 16527.8561 16526.1553 16526.1083 \u2014 2 3 16531.1745 16528.0026 16527.9352 16525.5653 16525.4997 16523.7443 3 4 16531.8726 16528.0097 16527.9265 16524.8875 16524.8036 16522.3459 4 5 16532.5163 16527.9352 16527.8317 16524.1348 16524.0316 16520.8627 5 6 16533.0886 16527.7704 16527.6476 16523.2643 16523.1434 16519.2817 6 7 16533.5550 16522.3396 16522.2000 16517.6188 7 8 16533.9880 16521.3450 16521.1866 16515.8642 8 9 16534.2157 16520.2430 16520.0650 9 Table AIV.9(a) Rotational assignments and line measurements of the 16548 c m - 1 band of 9 0 Z r C H (P' = 1\/2) N 3\/2Rj(N) mRiCN) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 16549.9488 16548.3116 \u2014 \u2014 \u2014 \u2014 0 16550.1763 1 16551.2789 16548.4047 16547.8906 \u2014 1 2 16552.3905 16548.4252 16547.5549 16545.9172 2 16547.7821 3 16553.4560 16548.3747 16547.2897 16544.4153 3 4 16554.4354 16548.2086 These branches do not appear 16546.8072 16542.8412 4 16548.2806 because of transition moment 5 16555.3683 16548.0447 interference effects discussed in 16546.2757 16541.1933 5 6 16556.2428 16547.7755 Section 4.3(d)(ii). 16545.6589 16539.4316 6 16539.5049 7 16557.0153 16547.4433 16544.9975 16537.6738 7 16557.0889 8 16557.6998 16547.0053 16544.2776 16535.8081 8 16557.7356 9 16558.3751 16546.5312 16543.4543 16533.8813 9 16558.4108 16543.5280 10 16559.0065 16545.9622 16542.5412 16531.8477 10 16542.5790 11 16559.7315 16545.3292 16541.6229 16529.7780 11 16559.9716 16541.6592 12 16544.6305 16540.6610 16527.6153 12 13 16543.8415 16539.7895 16525.3953 13 16540.0308 14 16543.0104 16523.0955 14 15 16542.0844 16520.7144 15 16 16518.2855 16 17 16515.7659 17 18 16513.1724 18 Appendix IV Rotational Assignments and Line Measurements of ZrCH 336 Table AIV.9(b) Rotational assignments and line measurements of the 16548 c m - 1 band of 9 2 Z r C H (P' = 1\/2). N 3\/2R x(N) l\/2Rj(N) 1\/2R2(N) l \/ ^ f N ) 1\/2P2(N) 3\/2P 2(N) N 0 16549.5883 16547.9061 \u2014 \u2014 \u2014 \u2014 0 1 16550.7888 16548.0059 \u2014 1 2 3 4 16551.9132 16552.9551 16553.9093 16548.0255 16547.9819 16547.8462 These branches do not appear because of transition moment interference effects discussed in 16547.2025 16546.8080 16546.3438 16544.0251 16542.4558 2 3 4 5 16555.0654 16547.6549 Section 4.3(d)(ii). 16545.7934 16540.8213 5 6 16555.8878 16547.3451 16545.1559 16539.0920 6 7 16556.6626 16544.7230 16537.3109 7 8 16557.3695 16543.9540 16535.4103 8 9 16558.0130 16543.1363 9 10 16558.5947 16542.2539 10 12 16540.2968 12 Table AIV.9(c) Rotational assignments and line measurements of the 16548 c m - 1 band of 9 4 Z r C H (P1 = 1\/2). N 3\/2RJCN) l\/2Rj(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 16549.2346 16547.4837 \u2014 \u2014 \u2014 \u2014 0 1 16550.5426 16547.5873 \u2014 1 2 16551.6546 16547.6549 2 3 16552.6950 16547.6721 These branches do not appear because of transition moment 16546.5749 16543.6184 3 4 16553.6914 16547.3988 interference effects discussed in 16546.1006 16542.0980 4 5 16554.6090 16547.2255 Section 4.3(d)(ii). 16545.5539 16540.5276 5 6 16555.4587 16544.9611 16538.6712 6 7 16556.2420 16546.6349 16544.2908 16536.9060 7 8 16556.9389 16543.5565 8 9 16557.5644 16542.7450 16533.1471 9 10 16541.8642 10 12 16540.2968 12 Table AIV. 10(a) Rotational assignments and line measurements of the 16661 c m - 1 band of 9 0 Z r C H (P' = 3\/2) N 3\/2Rj(N) l\/2Rj(N) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P2(N) N 0 16661.8749 \u2014 \u2014 \u2014 \u2014 \u2014 0 16662.0572 1 16662.9060 16661.1731 16661.1436 \u2014 \u2014 \u2014 1 2 16663.7756 16661.3160 16661.2692 16659.5283 16659.4818 \u2014 2 16659.7108 16659.6640 3 16664.4488 16661.3993 16661.3332 16658.9824 16658.9165 16657.1829 3 16664.5705 4 16665.1901 16661.3805 16661.2959 16658.2751 16658.1901 16655.7314 4 Appendix TV Rotational Assignments and Line Measurements of ZrCH 337 N 3\/2Rl(N) 1\/2R2(N) 1\/2PX(N) 1\/2P2(N) 3\/2P2(N) N 16665.3099 16665.7079 16661.2877 6 16666.1633 7 16666.6299 8 16666.9347 9 16666.8363 16667.1535 10 11 16661.0309 16661.1847 16660.9080 16657.3725 16657.4941 16656.5358 16656.6570 16655.4779 16654.3575 16653.2498 16651.9767 16650.2952 16650.6171 16657.2683 16657.3898 16656.4133 16656.5358 16655.3371 16654.1967 16653.0682 16651.7784 16650.0799 16650.4015 16654.2196 5 16652.6050 6 16650.9187 7 16649.0628 8 9 10 11 Table AIV. 10(b) Rotational assignments and line measurements of the 16661 c m - 1 band of 9 2 Z r C H (P' = 3\/2). N 3\/2Rj(N) l\/2Rj(N) 1\/2R2(N) l ^ P j f N ) 1\/2P2(N) 3\/2P2(N) N 0 16661.6514 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16662.5859 16660.8776 16660.8501 \u2014 \u2014 \u2014 1 2 16663.4571 16661.0477 16661.0016 16659.3117 16659.2645 \u2014 2 3 16664.2530 16661.2449 16661.1800 16658.6723 16658.6064 16656.8982 3 4 16664.8210 16657.9720 16657.8870 16655.4779 4 5 16665.1451 16657.1968 16657.0930 16654.0851 5 5 16665.3638 5 6 16656.1903 16656.0693 6 7 16666.2328 16654.9474 16654.8044 7 7 16655.1613 16655.0215 7 8 16648.6989 8 9 16652.8859 16652.7074 9 Table AIV. 10(c) Rotational assignments and line measurements of the 16661 c m - 1 band of 9 4 Z r C H (P1 = 3\/2). N l ^ R i f N ) 1\/2R2(N) l ^ C N ) 1\/2P2(N) 3\/2P 2(N) N 0 16661.1298 \u2014 \u2014 \u2014 \u2014 \u2014 0 16661.2782 1 16662.2359 16660.5019 16660.4750 \u2014 \u2014 \u2014 1 2 16663.0781 16660.6735 16660.6251 16658.7974 16658.7571 \u2014 2 16658.9443 16658.8971 3 16663.8409 16660.7649 16660.7030 16658.3333 16658.2680 16656.5358 3 4 16664.4811 16660.7130 16660.6251 16657.6078 16657.5222 16655.1184 4 16664.5648 5 16665.0563 16660.6251 16660.5146 16656.8016 16656.6988 16653.6251 5 6 16665.5277 16660.3741 16660.2526 16655.8732 16655.7519 16651.9767 6 16655.9593 16655.8451 7 16660.1139 16659.9723 16654.8790 16654.7394 16650.3009 7 8 16653.7851 16653.6243 16648.4724 8 338 Appendix V: Rotational assignments and line measurements (in cm - 1) of bands of ZrCD This appendix tabulates the rotational assignments and line measurements of the P' (case c) - X 2 S + bands of ZrCD. The bands are identified by the band origin wavenumber VQ (in c m - 1 rounded to the nearest integer) of the 9 0 Z r C D isotopomer and listed by increasing v 0 , and in increasing Zr mass number order within (90 and, if available, 92 and 94). The branch labels 3\/2R, 1\/2R, 1\/2P and 3\/2P denote J' - N \" = +3\/2, +1\/2, -1\/2 and -3\/2 respectively; subscripts \/' = 1 and 2 on these branch labels denote the ground state spin component F7 (Fi and F 2 denote J = N+l\/2 and N - l \/ 2 respectively). This ^'-independent scheme is used since the upper states all have essentially Hund's case (c) coupling. All of the bands are \"cold\" (i.e., x>\" = 0). A bold entry denotes a measurement of a blended line; an underlined entry denotes an uncertain measurement (due to asymmetry or line weakness). None of these lines were used in any least squares fits. A long dash indicates a nonexistent line. The measurement uncertainty is generally about 0.0005 c m - 1 . Appendix V Rotational Assignments and Line Measurements of ZrCD 339 Table A V . 1(a) Rotational assignments and line measurements of the 15189 c m - 1 band of 9 0 Z r C D (P' = 1\/2). N 3\/2R!(N) l \/ lRj fN) 1\/2R2(N) l ^ r N ) 1\/2P2(N) 3\/2P 2(N) N 0 15190.1480 15188.9368 \u2014 \u2014 \u2014 \u2014 0 1 15191.1102 15189.1174 15189.0920 15188.4679 15188.4434 \u2014 1 15191.1680 2 15191.9882 15189.2408 15189.1993 15188.1369 15188.0972 15186.8863 2 15192.0461 3 15192.8162 15189.3325 15189.2758 15187.7477 15187.6908 15185.6962 3 15192.8952 15187.8045 15187.7477 4 15193.6909 15187.2746 15187.2013 15184.4531 4 15187.3324 15187.2595 5 15194.3566 15186.7504 15186.6625 5 15194.4500 15186.8304 15186.7416 6 15195.1156 15186.2756 15186.1687 6 7 15195.7571 15185.5882 15185.4670 7 15185.6821 15185.5604 8 15184.9970 15184.8591 8 9 15184.2878 15184.1319 9 Table A V . 1(b) Rotational assignments and line measurements of the 15189 c m - 1 band of 9 2 Z r C D (P' = 1\/2) N 3\/2Rj(N) l ^ R i f N ) mRjfN) l ^ P j f N ) 1\/2P2(N) 3\/2P2(N) N 0 15190.2856 15189.0920 \u2014 \u2014 \u2014 \u2014 0 1 15191.2530 15189.2662 15189.2408 15188.6055 15188.5814 \u2014 1 2 15192.1642 15189.3834 15189.3473 15188.2807 15188.2406 15187.0479 2 3 15193.0241 15189.4864 15189.4274 15187.9000- 15187.8443 15185.8562 3 4 15193.8057 15187.4646 15187.3922 15184.6104 4 5 15194.5536 15186.9763 15186.8863 5 6 15195.2920 15186.4096 15186.3046 6 7 15195.9357 15185.8100 15185.6877 7 Table A V . 1(c) Rotational assignments and line measurements of the 15189 c m - 1 band of 9 4 Z r C D (P' = 1\/2) N 3\/2R 1(N) l\/2Rj(N) 1\/2R2(N) l ^ P j f N ) 1\/2P2(N) 3\/2P 2(N) N 0 15190.4739 15189.2758 \u2014 \u2014 \u2014 \u2014 0 1 15191.4417 15189.4512 15189.4274 15188.7928 15188.7678 \u2014 1 2 15192.3542 15189.5509 15189.5141 15188.4728 15188.4342 15187.2367 2 3 15193.2099 15189.6217 15189.5650 15188.0972 15188.0420 15186.0506 3 4 15194.0108 15187.6656 15187.5937 15184.7927 4 5 15194.7539 15187.1790 15187.0902 5 6 15195.4457 15186.6354 15186.5297 6 7 15196.0826 15186.0339 15185.9134 7 Appendix V Rotational Assignments and Line Measurements of ZrCD 340 Table AV.2(a) Rotational assignments and line measurements of the 15441 c m - 1 band of 9 0 Z r C D (P' = 3\/2). N 3\/2R x(N) 1\/2R!(N) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 15442.0360 15442.0947 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15442.9108 15441.3688 15441.4262 15441.3432 15441.4015 \u2014 \u2014 \u2014 1 2 15443.6884 15441.5668 15441.5261 15440.0264 15440.0837 15439.9849 15440.0429 \u2014 2 3 15444.3930 15441.6702 15441.6132 15439.5485 15439.4915 15437.9485 15438.0068 3 4 15445.0248 15441.6984 15441.6252 15438.9754 15438.9026 15436.7810 4 5 15445.5867 15441.6552 15441.5668 15438.3279 15438.2382 15435.5157 5 6 15446.0699 15441.5400 15441.4340 15437.6092 15437.5030 15434.1757 6 7 15446.4881 15441.3483 15441.2286 15436.8202 15436.6975 15432.7653 7 8 15446.8361 15441.0904 15440.9529 15435.9518 15435.8130 8 9 15447.1070 15440.7643 15440.6089 15435.0209 15434.8642 9 10 15447.3136 15434.0054 15433.8438 10 11 15432.9357 15432.7653 11 Table AV.2(b) Rotational assignments and line measurements of the 15441 c m - 1 band of 9 2 Z r C D (P' = 3\/2). N 3\/2R!(N) l\/2Rj(N) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 15442.2122 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15443.0540 15441.5464 15441.5261 \u2014 \u2014 \u2014 1 2 15443.8248 15441.7144 15441.6702 15440.2067 15440.1665 \u2014 2 3 15444.5247 15441.8099 15441.7550 15439.7010 15439.6443 15438.1365 3 4 15445.1547 15441.8382 15441.7654 15439.1242 15439.0500 15436.9399 4 5 15445.7132 15441.7946 15441.7045 15438.4771 15438.3873 15435.6745 5 6 15446.1998 15441.6808 15437.7595 15437.6537 15434.3366 6 7 15446.6131 15441.4915 15441.3688 15436.9704 15436.8488 7 8 15446.9598 15441.2286 15441.0904 15435.9701 8 9 15435.1758 15435.0209 9 Table AV.2(c) Rotational assignments and line measurements of the 15441 cm- 1 band o f 9 4 Z r C D ( P ' = 3\/2) N 3\/2R!CN) l ^ f N ) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 15442.3458 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15443.1839 15441.6808 15441.6552 \u2014 \u2014 \u2014 1 2 15443.9538 15441.8480 15441.8091 15440.3459 15440.3059 \u2014 2 3 15444.6513 15441.9459 15441.8891 15439.8411 15439.7838 3 4 15445.2794 15441.9717 15441.8994 15439.2667 15439.1930 15437.0880 4 5 15445.8357 15441.9281 15441.8382 15438.6194 15438.5314 15435.8248 5 6 15446.3214 15437.9040 15437.7990 15434.4900 6 7 15446.7360 15437.1165 15436.9940 15433.0890 7 Appendix V Rotational Assignments and Line Measurements of ZrCD 341 N 3\/2Rj(N) l ^ R i C N ) 1\/2R2(N) 1\/2PX(N) 1\/2P2(N) 3\/2P2(N) N 8 15447.0809 15436.2557 15436.1192 8 9 15447.3529 15435.3284 15435.1758 9 10 15447.5537 10 Table AV.3(a) Rotational assignments and line measurements of the 15576 c m - 1 band of 9 0 Z r C D (P' = 1\/2) N 3\/2R x(N) 1\/2RX(N) 1\/2R2(N) l ^ f N ) 1\/2P2(N) 3\/2P 2(N) N 0 15576.7548 15576.0284 \u2014 \u2014 \u2014 \u2014 0 1 15577.5318 15576.3762 15576.3522 15575.2008 15575.1768 \u2014 1 2 15578.3014 15576.6728 15576.6326 15574.7145 15574.6740 15573.9768 2 3 15578.9600 15576.9166 15576.8606 15574.1700 15574.1118 15572.9573 3 15579.0731 4 15577.1194 15577.0461 15573.5880 15573.5148 15571.8861 4 5 15577.3044 15577.2217 15572.8942 15572.8056 15570.7611 5 15573.0078 15572.9193 6 15577.4835 15577.3770 15572.2567 15572.1526 6 Table AV.3(b) Rotational assignments and line measurements of the 15576 c m - 1 band of 9 2 Z r C D (P1 = 1\/2) N 3\/2Rj(N) l\/2Rj(N) 1\/2R2(N) 1\/2PJCN) 1\/2P2(N) 3\/2P2(N) N 0 15576.7423 15576.0003 \u2014 \u2014 \u2014 \u2014 0 1 15577.5796 15576.3298 15576.3056 15575.2055 15575.1830 \u2014 1 2 15578.2909 15576.6096 15576.5683 15574.7406 15574.7002 15573.9544 2 15578.3499 3 15579.0160 15576.8318 15576.7748 15574.2292 15574.1700 15572.9692 3 4 15577.0088 15576.9333 15573.5880 15573.5148 4 15573.6511 15573.5711 5 15577.1801 15577.0889 15572.9692 15572.8788 5 6 15577.3592 15577.2552 15572.2830 15572.1780 6 7 15571.5391 15571.4171 7 Table AV.3(c) Rotational assignments and line measurements of the 15576 c m - 1 band of 9 4 Z r C D (P' = 1\/2) N 3\/2RJCN) l\/2Rj(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P 2(N) N 0 15576.8506 15576.1211 \u2014 \u2014 \u2022 \u2014 \u2014 0 1 15577.6892 15576.4710 15576.4476 15575.3074 15575.2809 \u2014 1 2 15578.4551 15576.7668 15576.7261 15574.8591 15574.8176 15574.0751 2 3 15579.1682 15577.0088 15576.9497 15574.3446 15574.2890 15573.0826 3 4 15579.7748 15577.2056 15577.1325 15573.7679 15573.6955 4 5 15577.3930 15577.3100 15573.1378 15573.0493 5 6 15577.5699 15577.4666 15572.4246 15572.3158 6 Appendix V Rotational Assignments and Line Measurements of ZrCD 342 Table AV.4(a) Rotational assignments and line measurements of the 15623 c m - 1 banda of 9 0 Z r C D (P' = 1\/2). N 3^(1*1) mRjfN) 1\/2R2(N) l ^ P j f N ) 1\/2P2(N) 3\/2P2(N) N 0 15624.8165 \u2014 \u2014 \u2014 \u2014 0 1 15625.7706 15623.9459 15623.9207 15623.1570 15623.1326 \u2014 1 2 15626.6779 15624.1182 15624.0783 15622.8058 15622.7650 2 3 15627.5359 15624.2455 15624.1890 15622.4085 15622.3518 15620.5264 3 4 15628.3441 15624.3492 15624.2763 15621.9629 15621.8917 15619.3319 4 5 15629.1014 15624.3080 15624.2171 15621.4704 15621.3809 15618.0911 5 6 15629.8152 15620.9277 15620.8215 15616.8297 6 7 15630.4650 15620.3344 15620.2125 15615.4182 7 8 15631.0718 15619.6962 15619.5588 8 9 15631.6198 15631.6464 15618.9954 15618.8410 9 10 15632.0334 15618.2508 15618.0812 10 11 15632.5344 15617.4479 15617.4754 15617.2610 15617.2889 11 12 15616.6129 15616.4082 12 a Many other 1\/2R lines appear but these cannot all be assigned. See also the footnote of Table AV.4(c). Table AV.4(b) Rotational assignments and line measurements of the 15623 c m - 1 banda of 9 2 Z r C D (P' = 1\/2). N 3\/2RJCN) 1\/2R,.(N) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 15624.3576 \u2014 \u2014 \u2014 \u2014 0 1 15625.3146 15622.6916 15622.6683 \u2014 1 2 15626.2208 15622.3518 15622.3113 2 3 15627.0770 15623.7783 15623.7206 15621.9629 15621.9050 3 4 15627.8838 15623.9135 15623.8412 15621.5208 15621.4475 4 5 15628.6407 15621.0296 15620.9407 15617.6386 5 6 15629.3233 15629.3615 15620.4889 15620.3832 15616.4082 6 7 15630.0258 15619.8988 15619.7769 7 8 15630.5930 15619.2338 15619.2718 15619.0945 15619.1331 8 9 15631.1497 15618.5898 15618.4343 9 10 15631.6566 15617.8077 15617.6386 10 11 15631.1334 15617.0187 15616.8297 11 12 15616.1783 15615.9765 12 a Many other 1\/2R lines appear but these cannot all be assigned. See also the footnote of Table AV.4(c). Table AV.4(c) Rotational assignments and line measurements of the 15623 c m - 1 banda of 9 4 Z r C D (P' = 1\/2). N 3\/2RJCN) 1\/2R,_(N) l^Rj fN) l ^ P j f N ) 1\/2P2(N) 3\/2P2(N) N 0 15624.0004 \u2014 \u2014 \u2014 \u2014 0 1 15624.9493 15622.3518 15622.3310 \u2014 1 Appendix V Rotational Assignments and Line Measurements of ZrCD 343 N 3\/2R.JCN) l^RjfN) 1\/2R2(N) UlPfN) 1\/2P2(N) 3\/2P2(N) N 2 15625.8542 15622.0013 15621.9629 2 3 15626.5843 15626.7475 15621.6047 15621.5488 3 4 15627.4752 15621.1661 15621.0935 4 5 15628.2341 15620.5531 15620.7152 15620.4638 15620.6267 5 6 15628.9414 15628.9461 15620.0993 15619.9938 6 7 8 15629.6034 15630.2104 15619.5167 15618.8534 15618.8576 15619.3940 15618.7399 15618.7463 7 8 9 15618.1970 15618.0449 9 10 15617.4602 15617.2889 10 aMany 1\/2R lines appear for 9 0 ZrCD, 9 2 ZrCD and 9 4 ZrCD but not all of these can be assigned by combination differences with the 3\/2P2(N) branch because the latter is exceptionally weak. About 50 lines in the 15621-15625 cm - 1 region remain unassigned; these are all almost certainly 1\/2R(N) lines from the three isotopomers; some are perhaps induced by upper state perturbations that obfuscate the assignments. Table AV.5(a) Rotational assignments and line measurements of the 15851 c m - 1 band of 9 0 Z r C D (P' = 3\/2). N 3\/2Rj(N) l\/2Rj(N) 1\/2R2(N) mPifN) 1\/2P2(N) 3\/2P2(N) N 0 15851.7484 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15852.5457 15851.0807 15851.0556 \u2014 \u2014 \u2014 1 2 15853.2371 15851.1977 15851.1565 15849.7384 15849.6968 \u2014 2 3 15853.8397 15851.2104 15851.1535 15849.1837 15849.1269 15947.6601 3 4 15854.3733 15851.1977 15851.1288 15848.5228 15848.4501 15846.4103 4 5 15854.7835 15850.9603 15850.8715 15847.7743 15847.6855 15845.0533 5 6 15855.1241 15850.6865 15850.5804 15846.9553 15846.8492 6 7 15855.3029 15850.3227 15850.1999 15846.0171 15845.8921 7 8 15849.8075 15849.6676 8 9 15849.2668 15849.1130 9 10 15848.6340 15848.4620 10 Table AV.5(b) Rotational assignments and line measurements of the 15851 cm- 1 band of 9 2 Z r C D (P' = 3\/2) N S ^ C N ) 1\/2R!(N) 1\/2R2(N) 1\/2P1(N) 1\/2P2(N) 3\/2P2(N) N 0 15851.8221 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15852.5928 15851.1730 15851.1530 \u2014 \u2014 \u2014 1 2 15853.3097 15851.2914 15851.2510 15849.8149 15849.7766 \u2014 2 3 15853.9231 15851.3085 15851.2510 15849.2400 15849.1837 3 4 15854.4573 15851.2394 15851.1665 15848.6086 15848.5368 4 5 15854.8464 15850.9238 15850.8327 15847.8737 15847.7855 5 6 15850.7717 15850.6672 15847.0787 15846.9768 6 7 15850.4226 15850.3011 7 Appendix V Rotational Assignments and Line Measurements of ZrCD 344 Table AV.5(c). Rotational assignments and line measurements of the 15851 c m - 1 band of 9 4 Z r C D (P' = 3\/2). N 1\/2RJCN) 1\/2R2(N) 1\/^fN) 1\/2P2(N) 3\/2P2(N) N 0 15851.8386 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15852.6296 15851.2240 15851.1977 \u2014 \u2014 \u2014 1 2 15853.3268 15851.3203 15851.2794 15849.8406 15849.7983 \u2014 2 3 15853.9357 15849.2865 15849.2293 3 4 15854.4573 15848.6383 15848.5655 4 5 15854.8397 15850.9850 15850.8943 15847.9045 15847.8150 5 6 15850.7978 15850.6948 15847.0787 15846.9637 6 Table AV.6(a) Rotational assignments and line measurements of the 15941 c m - 1 band o f 9 0 Z r C D (P' = 3\/2) N 3\/2Rj(N) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P2(N) N 0 15942.0082 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15942.8544 15941.3576 15941.3333 \u2014 \u2014 \u2014 1 15942.9030 2 15943.5457 15941.5173 15941.4758 15939.9968 15939.9569 \u2014 2 15943.7062 15941.5470 3 15944.4206 15941.7128 15941.6567 15939.4931 15939.4360 15937.9391 3 . 15939.5406 15939.4839 4 15945.1583 15941.7342 15941.6599 15938.8328 15938.7594 15936.7299 4 15938.9925 15938.9190 15936.8015 5 15945.8176 15941.7855 15941.6952 15938.3574 15938.2662 15935.5585 5 15938.4480 15938.3574 6 15946.4165 15941.7653 15941.6599 15937.7423 15937.6368 15934.2122 6 7 15946.9603 15937.0497 15936.9283 7 8 15947.4399 15936.2975 15936.1592 8 9 15947.8530 15935.4908 15935.3358 9 10 15948.1647 15934.6192 15934.4491 10 Table AV.6(b). Rotational assignments and line measurements of the 15941 cm- 1 band o f 9 2 Z r C D ( P ' = 3\/2) N 3\/2R!(N) l\/2Rj(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 15941.9305 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15942.8121 15941.2658 15941.2407 \u2014 \u2014 \u2014 1 2 15943.6570 15941.4729 15941.4323 15939.9251 15939.8847 \u2014 2 3 15944.3612 15941.6372 15941.5811 15939.4585 15939.4027 15937.8563 3 15944.4482 4 15945.1588 15938.9570 15938.8833 15936.6991 4 15944.9142 5 15945.5937 15938.3121 15938.2252 15935.5004 5 16945.7835 15938.4011 15938.3121 6 15946.2822 15937.5173 15937.4124 6 Appendix V Rotational Assignments and Line Measurements of ZrCD 345 N 3\/2R!(N) l ^ C N ) 1\/2R2(N) 1\/2PJCN) 1\/2P2(N) 3\/2P2(N) N 15937.7638 15937.6559 7 15946.8092 15936.8506 15936.7299 7 15936.9190 8 15947.3382 15936.1922 15936.0534 8 9 15935.3725 9 Table AV.6(c). Rotational assignments and line measurements of the 15941 cm 1 band of 9 4 Z r C D (P' - 3\/2) N 3\/2RJCN) 1\/2RX(N) 1\/2R2(N) l\/2PjCN) 1\/2P2(N) 3\/2P2(N) N 0 15941.7539 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 15942.5921 15941.0900 15941.0662 \u2014 \u2022 \u2014 \u2014 1 15942.6444 2 15943.4000 15941.3091 15941.2658 15939.7544 15939.7138 \u2014 2 15943.4627 3 15944.2039 15941.4503 15941.3940 15939.2466 15939.1925 15937.6898 3 15939.3011 15939.2441 4 15944.9142 15938.7124 15938.6407 15936.5482 4 15938.7751 15938.7026 5 15945.5820 15938.1719 15938.0840 15935.3320 5 6 15946.1218 15937.5393 15937.4345 6 7 15946.6959 15936.8632 15936.7414 7 8 15947.1657 15936.0594 15935.9205 8 Table AV.7(a) Rotational assignments and line measurements of the 16007 c m - 1 band of 9 0 Z r C D (P' = 1\/2) N 3\/2Rj(N) 1\/2RX(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 0 16008.2749 16007.8691 \u2014 \u2014 \u2014 \u2014 0 16008.3527 1 16008.9912 16008.3006 16008.2749 16006.8725 16006.8482 \u2014 1 16009.0407 2 16009.6849 16008.6481 16006.2631 16006.2234 16005.8178 2 16006.3420 16006.3022 3 16010.3075 16008.9683 16005.6288 16005.5722 16004.8808 3 16005.6789 16005.6216 4 16010.8770 16009.2189 16004.9714 16004.8978 16003.9017 4 5 16011.3928 16009.4330 16004.2434 16004.1536 16002.8706 5 6 16011.8624 16009.5851 16003.4583 16003.3533 16001.7700 6 7 16012.2567 16009.6630 16002.6239 16002.5024 16000.6322 7 8 16012.6290 16001.7438 15999.4360 8 9 16000.7868 15998.1629 9 10 15996.8840 10 Appendix V Rotational Assignments and Line Measurements of ZrCD 346 Table AV.7(b). Rotational assignments and line measurements of the 16007 c m - 1 band of 9 2 Z r C D (P' = 1\/2). N 3\/2R!(N) l ^ f N ) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 16007.8544 16007.5067 \u2014 \u2014 \u2014 \u2014 0 1 16008.6007 16007.9681 16006.4969 16006.4733 \u2014 1 2 16009.2882 16008.3680 16005.8490 16005.8080 16005.4593 2 3 16009.9271 16008.6926 16005.2471 16005.1900 16004.5825 3 4 16010.5441 16009.9391 16004.5874 16004.5146 16003.6349 4 5 16011.0126 16009.1591 16003.8793 16003.7900 16002.6120 5 6 16009.3073 16003.1493 16003.0424 6 Table AV.7(c). Rotational assignments and line measurements of the 16007 c m - 1 band of 9 4 Z r C D (P' = 1\/2) N 3\/2R!(N) 1\/2R,_(N) l ^ R j f N ) 1\/2P!(N) 1\/2P2(N) 3\/2P 2(N) N 0 16007.4831 16007.0209 \u2014 \u2014 \u2014 \u2014 0 1 16008.1827 16007.6488 16006.0478 16006.0244 \u2014 1 2 16008.8669 16007.9713 16005.4825 16005.4412 16004.9816 2 3 16009.4878 16008.2563 16004.8382 16004.7828 16004.2730 3 4 16010.0557 16009.5021 16004.1799 16004.1081 16003.2516 4 5 16011.5774 16003.4564 16003.3670 16002.2002 5 6 16002.6812 16002.5736 6 Table A V . 8(a) Rotational assignments and line measurements of the 16022 c m - 1 band of 9 0 Z r C D (P' = 3\/2). N 3\/2R x(N) l ^ R j f N ) l ^ R j f N ) l\/2PjfN) 1\/2P2(N) 3\/2P2(N) N 0 16023.5698 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16024.4650 16022.9020 16022.8777 \u2014 \u2014 \u2014 1 2 16025.3101 16023.1219 16023.0803 16021.5586 16021.5187 \u2014 2 3 16026.1056 16023.2910 16023.2341 16021.1026 16021.0461 16019.4828 3 4 16026.7692 16023.4108 16023.3375 16020.5966 16020.5243 16018.3352 4 16026.8614 5 16027.5271 16023.4405 16023.3508 16020.0402 16019.9514 16017.1370 5 6 16028.1703 16023.4833 16023.3778 16019.3538 16019.2474 16015.8890 6 16019.4450 16019.3390 7 16028.7579 16018.7600 16018.6377 16014.5511 7 16014.6206 8 16029.2979 16018.0513 16017.9131 16013.2269 8 9 16029.7798 16017.2889 16017.1370 9 10 16030.2241 16016.4780 16016.3058 10 11 16030.5933 11 Appendix V Rotational Assignments and Line Measurements of ZrCD 347 Table A V . 8(b) Rotational assignments and line measurements of the 16022 c m - 1 band of 9 2 Z r C D (P' = 3\/2). N 3\/2RJL(N) 1\/2R!(N) 1\/2R2(N) l ^ f N ) 1\/2P2(N) 3\/2P 2(N) N 0 16023.2801 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16024.2019 16022.6266 16022.6013 \u2014 \u2014 \u2014 1 16024.1530 2 16024.9833 16022.8448 16022.8048 16021.2743 16021.2339 \u2014 2 16025.0531 3 16025.8015 16023.0160 16022.9591 16020.8469 16020.7909 16019.2156 3 16020.7994 16020.7420 4 16026.4863 16020.2888 16020.2162 16018.0722 4 16020.3516 16020.2787 5 16027.2008 16019.7537 16019.6645 5 6 16027.8479 16019.0900 16018.9856 6 7 16028.4377 7 8 16028.9811 8 Table AV.8(c) Rotational assignments and line measurements of the 16022 c m - 1 band of 9 4 Z r C D (P' = 3\/2) N 3\/2Rj(N) 1\/2RJCN) 1\/2R2(N) l^PjCN) 1\/2P2(N) 3\/2P2(N) N 0 16022.9664 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16023.8571 16022.3031 16022.2787 \u2014 \u2014 \u2014 1 2 16024.7025 16022.5224 16022.4818 16020.9664 16020.9269 \u2014 2 3 16025.4859 16022.6844 16022.6266 16020.5137 16020.4564 16018.9022 3 4 16026.2270 16022.8510 16022.7781 16019.9433 16017.7622 4 5 16026.9126 16019.4544 16019.3651 16016.5637 5 6 16027.5469 16018.8516 16018.7468 16015.3253 6 7 16028.1458 7 8 16028.7020 8 Table AV.9(a) Rotational assignments and line measurements of the 16057 c m - 1 band of 9 0 Z r C D (P' = 3\/2) N 3\/2Rj(N) l^RjfN) 1\/2R2(N) 1\/2P!(N) 1\/2P2(N) 3\/2P2(N) N 0 16058.3939 \u2014 \u2014 \u2014 \u2014 \u2014 0 16058.3354 1 16059.2452 16057.7259 16057.7010 \u2014 \u2014 \u2014 1 16059.2874 2 16060.0771 16057.9027 16057.8614 16056.3828 16056.3416 \u2014 2 16060.0902 16057.9437 16057.9027 16056.3245 16056.2840 3 16060.8356 16058.0519 16057.9948 16055.8830 16055.8259 16054.3068 3 16055.9273 16055.8683 4 16061.5410 16058.1424 16058.0693 16055.3629 16055.2905 16053.1151 4 16055.3767 16055.3031 16053.1583 5 16062.1867 16058.1718 16058.0820 16054.7702 16054.6812 16051.8968 5 Appendix V Rotational Assignments and Line Measurements of ZrCD 348 N 3\/2Rj(N) 1\/2RX(N) 1\/2R2(N) l\/2Pj(N) 1\/2P2(N) 3\/2P2(N) N 6 16062.7802 16058.1424 16058.0364 16054.1241 16054.0192 16050.6206 6 7 16063.2994 16058.0693 16057.9437 16053.4190 16053.2974 7 8 16063.7700 16057.9027 16057.7669 16052.6613 16052.5231 8 9 16064.1724 16051.8329 16051.6768 9 10 16064.5325 16050.9501 16050.7779 10 11 16064.8902 11 12 16065.0733 12 13 16065.2560 13 Table A V . 9(b) Rotational assignments and line measurements of the 16057 c m - 1 band of 9 2 Z r C D (P1 = 3\/2). N 3\/2Rj(N) 1\/2RX(N) 1\/2R2(N) l^PjfN) 1\/2P2(N) 3\/2P 2(N) N 0 16057.9743 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16058.8507 16057.3078 16057.2837 \u2014 \u2014 \u2014 1 2 16059.6688 16057.5117 16057.4712 16055.9686 16055.9273 \u2014 2 3 16060.4293 16057.6570 16057.6006 16055.4977 16055.4408 16053.9010 3 4 16061.1302 16057.7578 16057.6874 16054.9682 16054.8955 16052.7389 4 5 16061.7870 16057.7762 16057.6874 16054.3819 16054.2924 16051.5213 5 6 16062.3191 16062.4688 16057.7439 16057.6440 16053.7343 16053.6297 6 7 16062.9083 16053.0450 16052.9240 7 8 16063.3565 8 Table AV.9(c) Rotational assignments and line measurements of the 16057 c m - 1 band of 9 4 Z r C D (P' = 3\/2). N 3\/2R!(N) 1\/2RX(N) 1\/2R2(N) l^PjfN) 1\/2P2(N) 3\/2P2(N) N 0 16057.5806 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 16058.4486 16056.9163 16056.8915 \u2014 \u2014 \u2014 1 2 16059.2550 16059.2654 16059.2744 16057.1139 16057.0726 16055.5802 16055.5402 2 3 16060.0227 16055.1052 16055.0482 16053.5156 3 4 16060.7374 16054.5672 16054.5771 16054.5858 16054.4945 16054.5054 16054.5136 16052.3523 4 5 16061.3525 16053.9916 16053.9010 5 6 16061.9405 16053.3612 16053.2569 6 7 16062.4577 16052.6340 16052.5107 7 8 16062.8720 8 Appendix V Rotational Assignments and Line Measurements of ZrCD 349 Table A V . 10(a) Rotational assignments and line measurements of the 16437 c m - 1 band of 9 0 Z r C D (P' = 1\/2). N 3\/2RJCN) 1\/2RX(N) 1\/2R2(N) 1\/2P2(N) 3\/2P2(N) N 0 16438.3495 16436.8405 \u2014 \u2014 \u2014 0 1 16439.3557 16437.1056 16437.0935 \u2014 1 2 16440.3087 16437.1849 16437.1439 16436 3386 16436.2982 2 3 16441.2026 16437.1920 16437.1344 16435 9941 16435.9363 16433.6976 3 4 16442.0367 16437.1056 16437.0327 16435 5941 16435.5223 16432.3986 4 5 16442.8101 16437.0121 16436.9228 16435 1389 16435.0485 16431.0381 5 6 16443.5232 16436.7546 16436.6489 16434 6200 16434.5150 16429.5842 6 7 16444.2163 16436.5489 16436.4259 16434 0433 16433.9200 16428.1222 7 8 16444.7724 16436.2564 16436.1187 16433 4041 16433.2679 16426.4978 8 9 16445.3263 16435.9244 16435.8727 16435.7723 16435.7192 16432 7473 16432.5933 16424.9242 9 10 16445.8152 16435.4597 16435.5438 16435.2878 16435.3765 16431 9521 16431.7823 16423.2668 10 11 16446.2606 16434.9951 16434.8071 16431 1555 16430.9697 16421.5670 16421.5141 11 12 16446.5700 16434.4768 16434.2510 16430 2930 16430.0908 16419.7342 16419.7958 12 13 16446.8696 16429 3882 16429.1689 13 14 16447.1083 16428 3471 16428.1106 14 15 16447.3155 16427 2972 16427.0444 15 Table A V . 10(b) Rotational assignments and line measurements of the 16437 c m - 1 band of 9 2 Z r C D (P' = 1\/2). N l ^ f N ) 1\/2R2(N) 1\/2P2(N) 3\/2P2(N) N 0 16437.7778 \u2014 \u2014 \u2014 -\u2014 0 1 16438.7864 \u2014 1 2 16439.7365 16435.7723 16435.7323 2 3 16440.6373 16436.6328 16436.5782 16435.4335 16435.3765 3 4 16441.4568 16436.5658 16436.4941 16434.9951 16434.9461 16431.8241 4 5 16442.2474 16436.4458 16436.3564 16430.4874 5 6 16442.9481 16429.0660 6 7 16443.6681 16436.0328 16435.9066 16427.5823 7 8 16444.2062 16426.0263 8 9 16444.6960 16435.4335 16435.2878 16424.4396 9 10 16445.2282 16422.7719 10 11 16445.6708 16421.0838 11 12 16445.9866 16419.2388 12 13 16446.2841 13 14 16446.5193 14 Appendix V Rotational Assignments and Line Measurements of ZrCD 350 Table A V . 10(c) Rotational assignments and line measurements of the 16437 c m - 1 band of 9 4 Z r C D (P = 1\/2). N 3\/2Rj(N) l\/ZRifN) lftRjfN) 1\/2P2(N) 3\/2P 2(N) N 0 16437.2834 \u2014 \u2014 \u2014 \u2014 0 1 16438.2915 \u2014 1 2 16439.2337 16435.2384 2 3 16440.1219 16434.9461 16434.8909 3 4 16440.9529 16434.4768 16434.4128 4 5 16441.7220 5 6 16442.4454 16433.5784 16433.4738 6 7 16443.0950 16433.0027 16432.8826 16427.0931 7 8 16443.6164 16432.2462 16425.5442 8 9 16144.1640 16423.9603 9 10 16444.6806 16422.3143 10 11 16445.0353 16420.5870 11 12 16445.4530 16418.7712 12 13 16445.2211 13 14 16445.9706 14 351 Appendix VI: Hyperfine and rotational assignments and line measurements (in cm 1 ) of B 2 \u00a3 + - X 2 L + system bands of LaNH and LaND This appendix tabulates the hyperfine and rotational assignments and line measurements of bands from the B 2 \u00a3 + - X 2 \u00a3 + system of LaNH studied in this thesis. The bands are identified by vibrational assignment and band origin wavenumber VQ (in c m - 1 rounded to the nearest integer). LaNH bands for which hyperfine structure is resolved in most of the observed rotational lines have been listed first, in increasing order of Vo, followed by the remaining LaNH bands (for which hfs has been resolved in only a few of the lowest-N lines) also in increasing order of v 0 . Measurements of assigned hyperfine features from these bands follow in additional tables. One band of LaND, for which hfs is resolved in most of the observed rotational structure, is further listed. To save space, initial digits of the line measurements that are the same for all the lines of a given band have been suppressed in most of the tables; these are specified as necessary in footnotes. The branch labels 3\/2R, 1\/2R, 1\/2P and 3\/2P denote J' -N \" = +3\/2, +1\/2, -1\/2 and -3\/2 respectively; subscripts 3 and 4 on these branch labels denote the value of the G\" quantum number. This scheme is applicable for all of the listed bands. As in previous appendices, a bold entry denotes a measurement of a blended line. While the measurement uncertainty is generally about 0.0005 c m - 1 , the bands for which only limited hyperfine assignments are possible occasionally have very large linewidths (up to 0.03 cm - 1 ) due to unresolved hyperfine broadening; hence, the measurements of these lines are much more uncertain and therefore quoted only to the nearest 0.01 or 0.001 c m - 1 . Appendix VI Assignments and line measurements of LaNH and LaND 352 Table AVI . 1. Hyperfine assignments and line measurements3 (in cm - 1 ) of the B 2 Z + (000, 2 E + ) - X2E+(000, 2 \u00a3+) band of LaNH near 15198 cm- 1 . Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 3\/2R 3(N) r 95.2147 q 95.2050 p 95.1964 3\/2R 4(N) r 94.7773 q 94.7671 p 94.7573 1\/2R3(N) r 95.0856 q 95.0730 1\/2R4(N) q 94.6384 p 94.6258 3\/2R 4(N) r 95.3519 95.3386 q 95.3429 1\/2P3(N) r 94.0040 q 94.0003 94.9724 p 94.9700 1\/2P4(N) r 93.5545 q 93.5530 93.5230 p 93.5562 93.5210 3\/2R 4(N) r 95.8877 95.8797 1\/2P3(N) r 93.3909 93.3814 q 93.3877 p 93.3780 1\/2P4(N) r 92.9422 q 92.9317 p 92.9472 92.9228 92.9140 3\/2P3(N) r q 93.2530 93.2406 p 93.2490 93.2406 3\/2P4(N) r 92.8030 q 92.8030 92.7900 p 92.8030 92.7900 1\/2R3(N) r 96.3788 1\/2R4(N) q 95.9621 p 95.9573 1\/2P3(N) r 92.7407 q 92.7366 1\/2P4(N) q 92.2940 93.2406 Appendix VI Assignments and line measurements of LaNH and LaND 353 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 P 92.2985 4 1\/2P3(N) q 92.0488 1\/2P4(N) q 91.6076 p 91.6113 5 1\/2P4(N) q 90.8843 p 90.8996 90.8884 90.8761 6 3\/2R 4(N) r 97.6805 97.6688 97.6589 1\/2P3CN) q 95.1594 95.1652 1\/2P4(N) q 90.1252 90.1144 p 90.1298 90.1174 7 3\/2R 4(N) r 98.0498 98.0373 98.0272 1\/2P4(N) q 89.3334 89.3216 p 89.3388 89.3254 89.3148 8 3\/2R 4(N) r 98.3897 98.3773 98.3659 q 98.3815 98.3705 1\/2P4(N) q 88.5091 p 88.5151 88.5022 88.4920 9 3\/2R 4(N) r 98.7013 98.6882 98.6770 98.6689 1\/2P4(N) q 87.6559 87.6446 p 87.6623 87.6486 87.6389 10 3\/2R 4(N) r 98.9865 98.9730 98.9619 98.9518 98.9447 1\/2P4(N) q 86.7728 86.7599 p 86.7797 86.7659 11 3\/2R 4(N) r 99.2960 99.2816 99.2703 12 3\/2R 4(N) r 99.4795 99.4655 a A n offset of 15100 c m - 1 should be added to all measurements. Table AVI.2. Hyperfine assignments and line measurements3 (in cm - 1 ) of the B 2 E + (001, 2~L+) - X22:+(000) band of LaNH near 15889 a i r 1 . N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N-1 F = N - 2 F = N-3 F = N-4 0 3\/2R 3(N) r 85.2413 q 85.2282 p 85.2204 3\/2R 4(N) r 84.8142 q 84.7945 p 84.7811 1\/2R3(N) r 85.5861 q 85.5972 1\/2R4(N) q 85.1383 Appendix VI Assignments and line measurements of LaNH and LaND 354 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 p 85.1501 1 3\/2R 4(N) r q 85.2681 85.2500 85.2413 p 85.2538 85.2413 1\/2R3(N) r 86.2596 q 86.2835 p 86.2835 1\/2R4(N) r 85.8115 1\/2P3(N) r 84.1789 q 84.1757 84.1350 p 84.1327 1\/2P4(N) r 83.6849 q 83.7284 83.6849 p 83.7315 83.6849 2 1\/2P3(N) r 83.3932 83.3844 q 83.3932 83.3844 1\/2P4(N) r 82.9762 83.9557 83.9426 q 82.9340 p 82.9804 83.9557 83.9426 82.9340 3\/2P 3(N) r 83.7644 Q 84.7525 83.7644 p 83.7490 83.7644 3\/2P4(N) r 83.3033 83.3139 q 83.3033 83.3139 p 83.3033 83.3139 3 3\/2R 4(N) r 86.0977 86.0885 86.0804 86.0739 q 86.0885 86.0804 86.0739 1\/2R3(N) r 87.5448 87.5638 87.5700 87.5753 p 87.5753 1\/2P3(N) q 82.6238 p 82.6238 1\/2P4(N) r 82.1794 82.1716 p 82.1794 82.1716 3\/2P 3(N) r 83.2280 q 83.2015 83.2124 83.2215 83.2280 p 83.1982 83.2124 83.2215 83.2280 3\/2P 4(N) r 82.7695 82.7759 q 82.7545 82.7616 82.7695 82.7759 p 82.7545 82.7616 82.7695 82.7759 Appendix VI Assignments and line measurements of LaNH and LaND 355 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 4 3\/2R 4(N) r 86.5100 86.4875 86.4802 86.4736 86.4675 q 86.4802 86.4736 86.4675 1\/2R3(N) r 88.1548 88.1658 88.1732 88.1801 88.1862 1\/2P4(N) r 81.3849 81.3789 q 81.4175 p 81.4215 81.3927 81.3849 81.3789 3\/2P3(N) q 82.6594 82.6644 P 82.6594 82.6644 5 3\/2R 4(N) r 86.9009 86.8879 86.8715 86.8660 1\/2P4(N) r 80.5720 q 80.6094 80.5954 p 80.6134 80.5983 80.5858 80.5781 80.5720 3\/2P3(N) q 82.0637 82.0706 p 82.0423 82.0637 82.0706 6 3\/2R 4(N) r 87.3073 87.2963 87.2875 1\/2R3(N) r 89.3058 89.3153 89.3241 89.3311 q 89.3311 1\/2P4(N) q 79.7847 79.7702 p 79.7895 79.7747 3\/2P 3(N) q 81.4341 81.4443 p 81.4300 81.4416 81.4589 81.4644 7 3\/2R 4(N) r 86.9691 86.9578 86.6804 87.6706 1\/2R3(N) r 89.8443 89.8559 89.8701 89.8775 89.8830 89.8879 q 89.8701 89.8775 89.8830 89.8879 1\/2P4(N) q 78.9533 78.9187 78.9124 p 78.9582 78.9452 78.9250 78.9187 78.9124 3\/2P 3(N) p 80.7957 80.8066 80.8161 80.8237 80.8298 80.8342 80.8379 8 3\/2R 4(N) r 87.4740 87.4610 87.4501 87.4418 87.4344 q 87.4548 1\/2R3(N) r 90.3595 90.3704 90.3796 90.3869 90.3940 q 90.4002 1\/2P4(N) q 78.1365 p 78.1423 78.1294 3\/2P 3(N) p 80.1356 80.1575 80.1656 80.1727 80.1774 80.1810 9 3\/2R 4(N) r 87.8397 87.8250 87.8043 87.7956 87.7890 87.7841 87.7802 1\/2R3(N) r 90.8499 90.8608 90.8700 90.8791 q 90.8548 1\/2P4(N) q 76.5763 Appendix VI Assignments and line measurements of LaNH and LaND 356 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 p 76.5818 76.5693 76.5606 76.5511 3\/2P3(N) q 79.4572 79.4679 p 79.4525 79.4641 79.4745 79.4825 79.4909 79.4956 79.4999 10 3\/2R 4(N) r 88.1317 88.1177 88.0965 88.0872 88.0800 88.0737 88.0689 q 88.1231 1\/2P4(N) q 75.8584 75.8462 75.8362 p 75.8648 75.8514 75.8404 75.8294 3\/2P3(N) q 78.7511 p 78.7461 78.7582 78.7683 78.7770 78.7844 78.7901 78.7953 11 3\/2R 4(N) r 88.3831 88.3687 88.3568 88.3458 q 88.3756 88.3618 1\/2R3(N) r 91.7506 91.7624 91.7718 q 91.7948 91.8007 1\/2P4(N) q 75.0009 74.9888 74.9658 74.9532 74.9468 74.9415 p 75.0075 74.9933 74.9809 74.9696 3\/2P 3(N) q 78.0195 78.0306 p 78.0135 78.0260 78.0364 78.0458 78.0533 78.0588 78.0652 12 3\/2R 4(N) r 88.6046 88.5903 88.5780 88.5674 q 88.5972 1\/2R3(N) r 92.1522 92.1633 92.1729 92.1812 q 92.1565 92.1683 92.1773 1\/2P4(N) q 74.0723 74.0576 74.0363 p 74.0638 74.0404 3\/2P3(N) p 77.2567 77.3041 77.3100 13 3\/2R 4(N) r 88.8012 88.7735 1\/2R3(N) r 92.4770 92.4869 92.4955 92.7916 92.7997 92.8072 1\/2P4(N) q 73.1007 73.0870 73.0756 73.0651 P 73.1084 73.0933 73.0803 73.0694 3\/2P 3(N) q 76.4888 76.4981 P 76.4713 76.4836 76.4945 76.5057 76.5133 14 3\/2R 4(N) r 88.9762 88.9615 88.9489 88.9384 88.9288 88.9195 q 88.9689 88.9543 1\/2R3(N) r 93.0263 93.0377 93.0474 1\/2P4(N) q 72.0999 72.0861 72.074 72.0633 P 72.1079 72.0926 72.0797 72.0680 3\/2P 3(N) q 75.6572 P 75.6508 75.6632 75.6746 75.6842 75.6925 15 3\/2R 4(N) r 89.1358 89.1210 89.1083 89.0971 89.0867 89.0783 76.5204 76.5261 75.6992 75.7051 89.0706 89.0647 Appendix VI Assignments and line measurements of LaNH and LaND 357 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+l F = N F = N - l F = N - 2 F = N-3 F = N-4 q 89.1293 1\/2R3(N) r 93.3363 93.3484 93.3595 93.3697 q 93.3651 1\/2P4(N) q \u2022 71.0754 71.5606 71.0485 71.0369 p 71.0838 71.0678 71.0542 71.0421 3\/2P3(N) q 74.7783 p 74.7535 74.7644 74.7738 74.7819 74.7889 74.7953 74.8008 75.0693 75.0778 75.0847 16 3\/2R 4(N) r 89.2570 89.2417 89.2288 q 89.2500 89.2357 1\/2R3(N) r 93.6415 93.6537 93.6648 1\/2P4(N) q 70.0292 70.0145 69.9915 p 70.0373 70.0220 70.0079 69.9968 69.9857 3\/2P 3(N) q 74.1008 p 74.0943 74.1047 74.1141 74.1288 74.1348 17 3\/2R 4(N) r 89.3678 89.3528 1\/2R3(N) r 93.9213 1\/2P4(N) q 68.9657 68.9507 68.9392 p 68.9745 68.9583 68.9449 68.9328 68.9229 3\/2P3(N) q 73.2102 p 73.1720 73.1843 73.1965 73.2057 73.2150 73.2231 73.2294 18 1\/2R3(N) r 94.1693 94.1821 94.1932 94.2018 1\/2P4(N) q 67.8378 p 67.8743 67.8323 67.8217 3\/2P 3(N) q 72.2628 p 72.2551 72.2673 72.2791 72.2895 72.2993 72.3072 72.3147 19 1\/2R3(N) r 94.3803 94.7308 94.7410 94.7506 94.7588 1\/2P4(N) q 66.7699 66.7422 66.7308 p 66.7790 66.7633 66.7494 66.7370 66.7254 3\/2P 3(N) p 71.3130 71.3261 20 1\/2R3(N) r 94.9015 94.9141 1\/2P4(N) p 65.6751 65.6587 65.6446 65.6312 65.6203 3\/2P3(N) q 70.3621 70.3898 p 70.3417 70.3540 70.3648 70.3755 70.3845 70.3922 70.3988 21 3\/2P3(N) p 69.6820 69.6931 69.7022 69.7119 69.7184 69.7259 69.7316 22 1\/2R3(N) r 95.2272 95.2417 1\/2P4(N) p 63.1961 63.1806 63.1678 3\/2P3(N) p 68.6325 68.6455 68.6566 68.6663 68.6755 68.6830 68.6897 Appendix VI Assignments and line measurements of LaNH and LaND 358 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 23 3\/2P3(N) p 67.5805 67.5938 67.6054 67.6166 67.6268 67.6362 67.6447 24 3\/2P 3(N) p 66.5189 66.5458 66.5576 66.5767 66.5866 25 3\/2P3(N) p 65.4406 65.4559 65.4702 65.4818 65.4930 65.5036 26 3\/2P3(N) p 64.3443 64.3596 64.3745 64.4092 27 3\/2P 3(N) p 63.2273 63.2435 63.2848 a A n offset of 15800 c m - 1 should be added to all measurements. Table AVI.3. Hyperfine assignments and line measurements3 (in cm - 1 ) of the B 2 2 + (02\u00b00 , 2 Z + ) - X 2 \u00a3 + (000) band of LaNH near 16412 cnr 1 . N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N-1 F = N - 2 F = N-3 F = N-4 0 3\/2R 3(N) r 09.1374 q 09.1226 p 09.1123 3\/2R 4(N) r 08.7135 q 08.6900 p 08.6744 1\/2R3(N) r 09.4971 q 09.5084 1\/2R4(N) q 09.0494 p 09.0603 1 3\/2R 3(N) r 09.5929 3\/2R 4(N) r 09.1661 09.1454 q 09.1494 1\/2P3(N) r 08.0819 q 08.0775 08.0306 p 08.0274 1\/2P4(N) r q 07.5803 p 07.6328 07.5803 2 3\/2R 4(N) r 09.5974 09.5791 09.5588 09.5532 q 09.5588 09.5532 09.5486 p 09.5532 09.5486 1\/2P3(N) r 07.3276 07.2900 07.2798 q 07.3244 07.3051 1\/2P4(N) q 07.5803 p 07.5803 3\/2P3(N) r 07.6761 q 07.6647 07.6761 p 07.6612 07.6761 Appendix VI Assignments and line measurements of LaNH and LaND 359 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N - 4 3\/2P 4(N) r 07.2147 07.2256 q 07.2147 07.2256 p 07.2147 07.2256 3 1\/2R4(N) q 11.0492 11.0553 11.0616 P 11.0616 4 1\/2R4(N) q 11.6783 11.6830 6 3\/2R 4(N) r 11.1220 11.1071 11.0962 q 11.1120 11.0987 1\/2R4(N) q 12.2884 12.2928 12.2965 8 3\/2R 4(N) r 11.7680 11.7542 11.7416 11.7243 q 11.7580 11.7466 1\/2P4(N) q 01.9519 01.9377 P 01.9571 01.9415 10 3\/2R 4(N) r 12.3423 12.3275 q 12.3329 1\/2P4(N) q 00.1393 00.1270 P 00.1596 00.1441 00.1318 00.1102 a A n offset of 16400 c m - 1 should be added to all measurements. Table AVI.4 Rotational assignments and line measurements3 (in cm - 1 ) of the B 2 Z + (01 1 0, 2 n 3 \/ 2 ) - X2S+(000, 2S+) band of LaNH near 15803 cm- 1 . N 3\/2R 3(N) 3\/2R 4(N) 1\/2R3(N) 1\/2R4(N) 1\/2P3(N) 1\/2P4(N) 3\/2P 3(N) 3\/2P4(N) N 0 b b \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 0 1 807.62 807.18 b b \u2014 \u2014 \u2014 \u2014 1 2 808.419 807.98 806.40 805.96 b b \u2014 \u2014 2 3 809.17 808.73 806.58 806.14 804.57 804.13 b b 3 4 809.908 809.46 806.735 806.29 804.143 803.69 802.129 801.67 4 5 810.604 810.16 806.851 806.40 803.677 803.23 801.086 800.64 5 6 811.267 810.83 806.937 806.48 803.185 802.74 800.018 799.57 6 7 811.901 811.46 806.989 806.54 802.660 802.21 798.907 798.45 7 8 812.506 812.07 807.012 806.56 802.101 801.64 797.771 797.32 8 9 813.085 812.64 807.008 806.54 801.512 801.06 796.601 796.14 9 10 813.645 813.20 806.973 806.51 800.895 800.45 795.401 794.95 10 11 814.179 813.74 806.919 806.46 800.252 799.80 11 12 814.72 814.27 799.57 799.14 12 13 815.255 814.80 798.90 798.45 13 14 815.35 798.21 797.76 14 15 815.83 797.52 797.08 15 a A n offset of 15000 c m - 1 should be added to all measurements. bHyperfine structure has been assigned and measured for this line; see Table A V I . 8. Appendix VI Assignments and line measurements of LaNH and LaND 360 Table AVI . 5 Rotational assignments and line measurements3 (in cm l ) of the iV-l^iOX1^, 2 n 1 \/ 2 ) - X 2 Z + (000, 2Z+) band of LaNH near 15821 cm- 1 . N 3\/2R 3(N) 3\/2R 4(N) 1\/2R3(N) 1\/2R4(N) 1\/2P3(N) 1\/2P4(N) 3\/2P 3(N) 3\/2P4(N) N 0 b b b \u2014 \u2014 \u2014 \u2014 0 1 not observed0 820.501 820.054 b b \u2014 \u2014 1 2 820.767 820.319 b b b b 2 3 821.029 820.58 819.09 818.640 817.445 816.996 3 4 821.284 820.84 818.78 818.337 816.489 816.039 4 5 821.534 821.08 818.48 818.033 815.527 815.09 5 6 821.772 821.32 818.17 817.720 814.557 814.12 6 7 822.014 821.56 817.85 817.400 813.591 813.137 7 8 822.24 821.78 817.52 817.072 812.603 812.152 8 9 822.45 822.00 817.19 816.736 811.613 811.17 9 10 822.66 822.21 816.85 816.396 10 11 822.87 822.41 816.49 816.039 11 12 823.05 822.61 816.12 815.675 12 13 '823.22 822.78 815.75 815.297 13 14 823.38 822.94 815.37 . 814.915 14 15 823.10 814.97 814.514 15 16 814.56 814.107 16 17 813.68 17 18 813.26 18 19 812.80 19 20 812.32 20 a A n offset of 15000 c m - 1 should be added to all measurements. bHyperfine structure has been assigned and measured for this line; see Table A V I . 9. T h i s branch is very weak and cannot be observed without prohibitively high signal averaging. Table AVI . 6 Rotational assignments and line measurements1* (in cm - 1 ) of the B 2 Z + (02 2 0, 2 A 5 \/ 2 ) - X22Z+(0ll0, 2n(b)) band of LaNH near 15961 cm\" 1. N 3\/2R 3(N) 3\/2R 4(N) 1\/2R3(N) 1\/2R4(N) 1\/2P3(N) 1\/2P4(N) 3\/2P 3(N) 3\/2P4(N) N 1 63.65 \u2014 \u2014 \u2014 \u2014 \u2014 \u2014 1 2 64.46 64.016 62.42 61.98 \u2014 \u2014 \u2014 \u2014 2 3 65.235 64.797 62.62 62.18 60.59 60.15 \u2014 \u2014 3 4 65.988 65.531 62.79 62.339 60.172 59.721 58.14 57.688 4 65.547 62.355 59.734 5 66.694 66.25 62.920 62.48 59.721 59.263 5 66.709 62.939 59.734 59.280 6 67.377 66.94 63.02 62.58 59.236 58.80 55.06 6 67.398 63.04 59.263 7 68.028 63.09 58.728 58.30 54.98 54.53 7 68.057 63.11 58.755 8 68.648 63.12 58.185 57.725 54.829 53.35 8 68.681 63.162 58.220 57.759 54.861 9 69.237 63.13 57.610 57.15 9 Appendix VI Assignments and line measurements of LaNH and LaND 361 N 3\/2R 3(N) 3\/2R 4(N) 1\/2R3(N) 1\/2R4(N) 1\/2P3(N) 1\/2P4(N) 3\/2P 3(N) 3\/2P4(N) N 69.280 63.177 57.654 57.19 10 69.795 63.11 57.004 10 69.848 63.162 57.059 11 70.322 63.06 56.368 11 70.387 63.11 56.433 12 70.820 62.969 55.698 12 63.04 55.774 13 71.283 62.853 54.999 13 71.372 62.939 55.087 14 54.272 14 54.374 15 53.516 15 53.628 54.17 a A n offset of 15900 c m - 1 should be added to all measurements. bWhere two measurements are given, these represent the two \u20ac\"-type doubling components of the line; i f these are blended, a single measurement is given in bold, i f available. Table AVI . 7 Rotational assignments and line measurements313 (in cm - 1 ) of the B 2 E + (02 2 0, 2 A 3 \/ 2 ) - X 2 S + ( 0 l ! 0 , 2n(b)) band of LaNH near 15993 cm- 1 . N 3\/2R 3(N) 3\/2R 4(N) 1\/2R3(N) 1\/2R4(N) 1\/2P3(N) 1\/2P4(N) 3\/2P 3(N) 3\/2P4(N) N 1 93.32 91.84 91.40 \u2014 \u2014 \u2014 \u2014 1 2 93.77 92.12 91.67 90.61 90.18 \u2014 \u2014 2 3 95.09 94.63 92.38 91.94 90.28 89.83 88.78 88.34 3 4 92.621 92.637 92.184 92.200 89.93 89.475 89.491 87.819 87.836 87.375 87.389 4 5 92.865 92.88 92.43 89.12 86.87 86.42 5 6 93.097 93.12 92.650 92.668 89.20 88.745 88.764 85.886 85.91 85.45 6 7 93.32 93.349 92.865 92.88 88.83 88.360 88.385 84.91 84.454 84.482 7 8 93.066 93.097 88.43 87.958 87.994 83.455 83.488 8 9 93.252 93.299 87.994 88.04 87.551 87.590 82.442 82.486 9 10 93.426 93.478 87.123 87.176 81.42 81.470 10 11 93.586 93.649 87.15 87.20 86.684 86.745 11 12 93.734 93.808 86.234 86.307 12 13 93.87 93.951 85.765 85.850 13 14 85.282 85.387 14 Appendix VI Assignments and line measurements of LaNH and LaND 362 N 3\/2R 3(N) 3\/2R 4(N) 1\/2R3(N) 1\/2R4(N) 1\/2P3(N) 1\/2P4(N) 3\/2P 3(N) 3\/2P4(N) N 15 84.792 15 84.91 16 84.282 16 84.42 17 83.759 17 83.905 18 83.223 18 83.385 a A n offset of 15900 c m - 1 should be added to all measurements. bWhere two measurements are given, these represent the two t\"-type doubling components of the line; i f these are blended, a single measurement is given in bold, i f available. Table AVI.8. Hyperfine assignments and line measurements (in cm - 1 ) of the B ^ ^ O ^ O , 2 n 3 \/ 2 ) - X2S+(000) band of LaNH near 15803 cm\" 1. N branch F ' -F\" measurement N branch F ' -F\" measurement N branch F ' -F\" measurement 0 3\/2R 3 2-3 15806.7843 2 1\/2P3 5-5 15804.9751 3 3\/2P 3 5-6 15803.1395 3-3 15806.7911 4-5 15804.9639 5-5 15803.1438 4-3 15806.8001 3-4 15804.9588 5-4 15803.1438 3-3 15804.9588 4-5 15803.1337 0 3\/2R 4 3-4 15806.3440 3-2 15804.9588 4-4 15803.1354 4-4 15806.3528 2-3 15804.9516 4-3 15803.1354 5-4 15806.3631 2-2 15804.9516 3-4 15803.1264 2-1 15804.9516 3-3 15803.1264 1 1\/2R3 5-4 15806.1978 3-2 15803.1264 4-4 15806.1878 2 1\/2P4 5-6 15804.5326 2-3 15803.1189 4-3 15806.1909 5-5 15804.5283 2-2 15803.1189 3-4 15806.1791 5^1 15804.5283 2-1 15803.1189 2-3 15806.1751 4-5 15804.5174 4-4 15804.5174 3 3\/2P 4 5-6 15802.6956 1 1\/2R4 5-5 15805.7539 4-3 15804.5174 4-5 15802.6837 5-4 15805.7498 2 1\/2P4 3-4 15804.5092 4-4 15802.6837 4-5 15805.7430 3-3 15804.5092 4-3 15802.6837 4-3 15805.7430 3-2 15804.5092 3^t 15802.6743 3-4 15805.7327 2-3 15804.5018 3-3 15802.6743 3-3 15805.7327 2-2 15804.5018 3-2 15802.6743 2-3 15805.7257 Appendix VI Assignments and line measurements of LaNH and LaND 363 Table AVT.9. Hyperfine assignments and line measurements (in cm - 1 ) of the B 2 E + (01 1 0, 2 n 1 \/ 2 ) - X2S+(000) band of LaNH near 15821 cm- 1 . N branch F ' -F\" measurement N branch F ' -F\" measurement N branch F ' -F\" measurement 0 3\/2R 3 4-3 15821.2144 2 1\/2P3 5-5 15819.3721 2 1\/2P4 3-2 15818.9379 3-3 15821.2208 5-4 15819.3760 2-3 15818.9429 2-3 15821.2252 4-4 4-3 15819.3829 15819.3829 2-2 15818.9429 0 1\/2R3 4-3 15820.2286 3-4 15819.3888 2 3\/2P 3 4-5 15818.3926 3-3 15820.2324 3-3 3-2 15819.3888 15819.3888 4-4 4-3 15818.3969 15818.3969 0 1\/2R4 4-4 15819.7816 2-3 15819.3927 3-4 15818.4006 3-4 15819.7852 2-2 2-1 15819.3927 15819.3927 3-3 3-2 15818.4006 15818.4006 1 1\/2P3 4-4 15819.6604 4-3 15819.6635 2 1\/2P4 5-6 15818.9321 2 3\/2P 4 4-5 15817.9460 3-3 15819.6814 5-5 15818.9261 4-4 15817.9460 3-2 15819.6814 5-4 4-5 15818.9261 15818.9321 4-3 3-4 15817.9460 15817.9504 1 1\/2P4 4-4 15819.2135 4-4 15818.9321 3-3 15817.9504 4-5 15819.2167 4-3 15818.9321 3-2 15817.9504 3-3 15819.2322 3-4 15818.9379 3-2 15819.2322 3-3 15818.9379 Table AVI . 10. Hyperfine assignments and line measurements3 (in era - 1) of the B 2 S + (000, 2 S + ) - X 2 \u00a3 + (000 , 2 E + ) band of LaND near 15157 cm- 1 . N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 3\/2R 3(N) r 57.7775 q 57.7612 p 57.7509 3\/2R 4(N) r 57.3551 q 57.3310 p 57.3146 1\/2R3(N) r 58.2367 q 58.2493 1\/2R4(N) q 57.7906 p 57.8026 3\/2R 3(N) r 58.1264 q 58.1129 3\/2R 4(N) r 57.7001 57.6795 q 57.6836 Appendix VI Assignments and line measurements of LaNH and LaND 364 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 p 57.6526 1\/2R3(N) r 58.8790 58.8928 58.8987 q 58.8896 p 58.9096 1\/2R4(N) p 58.4539 58.4607 1\/2P3(N) r 56.9026 q 56.8993 56.8495 p 56.8466 1\/2P4(N) r 56.4542 q 56.4515 56.3999 p 56.4557 56.3999 2 3\/2R 4(N) r 58.0323 58.0160 58.0057 q 58.0189 58.0094 1\/2R3(N) r 59.5177 59.5262 59.5330 p 59.5213 59.5389 1\/2R4(N) p 59.0830 59.0888 1\/2P3(N) r 56.1610 56.1491 56.1384 q 56.1610 56.1491 56.1384 1\/2P4(N) r 55.7159 55.7000 q 55.6897 p 55.7159 55.7000 55.6897 3\/2P3(N) r q 56.6234 56.6370 p 56.6210 56.6370 3\/2P4(N) r 56.1755 q 56.1755 p 56.1755 3 3\/2R 3(N) r 58.7344 58.7280 58.7209 58.7159 58.7112 q 58.7239 58.7112 3\/2R 4(N) r 58.3082 58.2917 58.2795 58.2718 q 58.2953 58.2819 58.2650 58.2605 58.2570 1\/2R3(N) r 60.1114 60.1232 60.1315 60.1392 60.1453 60.1499 q 60.1201 p 60.1522 1\/2P4(N) r 54.9685 q 55.0099 54.9919 54.9577 p 55.0139 54.9919 54.9781 54.9615 54.9577 3\/2P3(N) p 56.2034 56.2132 3\/2P4(N) r 55.7697 Appendix VI Assignments and line measurements of LaNH and LaND 365 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 q 55.7697 p 55.7697 4 3\/2R 4(N) r 58.5948 58.5787 58.5669 q 58.5825 58.5694 1\/2R3(N) r 60.6983 60.7096 1\/2R4(N) r 60.2841 q 60.2615 60.2795 60.2841 p 60.2795 60.2841 1\/2P3(N) q 54.7069 54.6836 54.6792 54.6749 1\/2P4(N) p 54.2709 3\/2P 3(N) q 55.7752 p 55.7752 3\/2P4(N) r 55.3112 55.3178 55.3235 55.3272 q 55.3112 55.3178 55.3235 55.3272 p 55.3112 55.3178 55.3235 55.3272 5 3\/2R 4(N) r 58.8555 58.8403 58.8279 58.8194 q 58.8440 58.8306 58.8194 1\/2R3(N) r 61.2632 61.2794 61.2844 61.2911 61.2979 61.3034 q 61.2704 61.2814 61.2911 61.2979 61.3034 p 61.2911 61.2966 61.3034 1\/2R4(N) r 60.8251 60.8499 60.8538 60.8568 q 60.8290 60.8394 60.8454 60.8499 60.8538 60.8568 p 60.8499 60.8538 1\/2P3(N) q 53.9048 1\/2P4(N) q 53.4657 53.4504 p 53.4702 53.4531 3\/2P 3(N) q 55.2740 p 55.2695 3\/2P4(N) q 54.8474 54.8529 p 54.8356 54.8417 54.8474 54.8529 6 3\/2R 4(N) r 59.0946 59.0796 59.0679 59.0506 59.0436 59.0392 59.0349 q 59.0848 1\/2R3(N) r 61.8082 61.8209 61.8294 61.8371 61.8442 61.8497 61.8539 q 61.8150 61.8263 61.8371 61.8442 61.8497 61.8539 61.8577 p 61.8539 61.8577 1\/2R4(N) r 61.3711 q 61.3752 61.3902 61.3947 P 1\/2P3(N) q 53.1138 Appendix VI Assignments and line measurements of LaNH and LaND 366 Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 1\/2P4(N) q 52.6767 P 52.6816 3\/2P 3(N) q 54.7839 P 54.7806 54.7927 54.8037 54.8111 54.8174 54.8224 3\/2P 4(N) p 54.3439 54.3528 54.3574 3\/2R 3(N) r 59.7323 59.7124 59.7090 3\/2R 4(N) r 59.3125 59.2977 59.2851 59.2749 q 59.3019 59.2895 1\/2P3(N) q 52.2975 1\/2P4(N) q 51.8624 51.8475 P 51.8671 51.8517 3\/2P3(N) q 54.3020 54.3081 P 54.2830 54.2935 54.3020 54.3081 3\/2P4(N) q 53.8528 53.8568 P 53.8357 53.8388 53.8434 53.8479 53.8528 53.8568 53.8605 3\/2R 3(N) r 59.9214 59.9171 59.9054 3\/2R 4(N) r 59.4636 59.4573 59.4508 59.4462 q 59.4865 1\/2R3(N) r 62.8367 q 62.8432 1\/2P3(N) q 51.4590 1\/2P4(N) q 51.0111 P 51.0308 51.0153 3\/2P3(N) q 53.7453 P 53.7404 53.7529 53.7632 53.7717 53.7792 53.7846 53.7890 3\/2P4(N) p 53.3267 53.3306 3\/2R 4(N) r 59.6309 56.6200 1\/2R3(N) r 63.3197 63.3312 63.3509 q 63.3481 1\/2R4(N) r q 62.8925 62.9141 1\/2P3(N) q 50.5997 50.5906 1\/2P4(N) q 50.1676 50.1179 P 50.1729 50.1586 50.1179 50.1071 3\/2P3(N) q 53.1950 53.2063 P 53.1895 53.2016 53.2120 53.2214 53.2291 53.2354 53.2402 3\/2P 4(N) p 52.7715 52.7756 52.7795 3\/2R 4(N) r 59.8403 59.8250 59.8127 59.8017 q 59.8309 59.8049 50.9669 62.9141 50.1071 Appendix VI Assignments and line measurements of LaNH and LaND 367 N Branch, AF F = N+4 F = N+3 F = N+2 F = N+1 F = N F = N - 1 F = N - 2 F = N-3 F = N-4 1\/2R3(N) r q 63.7817 63.7882 63.7940 1\/2P4(N) q 49.2891 49.2629 49.2518 49.2266 p 49.2951 49.2795 49.2661 49.2557 3\/2P3(N) q p 52.6183 52.6237 52.6706 3\/2P 4(N) p 52.2079 52.2114 3\/2R 3(N) r 60.3759 60.3735 60.3703 3\/2R 4(N) r 59.9740 59.9591 59.9464 59.9351 1\/2P4(N) q 48.3892 48.3750 48.3525 P 48.3957 48.3803 48.3672 48.3557 3\/2P3(N) q 52.0327 p 52.0265 52.0385 52.0488 52.0597 52.0671 3\/2P 4(N) p 51.6081 51.6154 51.6202 3\/2R 4(N) r 60.0727 1\/2P4(N) q 47.4685 47.4554 47.4424 47.4314 47.4229 p 47.4748 47.4600 47.4465 47.4351 47.4259 3\/2P3(N) p 51.4138 51.4260 51.4370 51.4558 3\/2P4(N) p 51.0066 a A n offset of 15100 c m - 1 should be added to all measurements. 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