Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Fourier transform microwave spectroscopy of some metal-containing compounds produced by laser ablation Walker, Kaley Anne 1998

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1998-272664.pdf [ 5.91MB ]
Metadata
JSON: 831-1.0061575.json
JSON-LD: 831-1.0061575-ld.json
RDF/XML (Pretty): 831-1.0061575-rdf.xml
RDF/JSON: 831-1.0061575-rdf.json
Turtle: 831-1.0061575-turtle.txt
N-Triples: 831-1.0061575-rdf-ntriples.txt
Original Record: 831-1.0061575-source.json
Full Text
831-1.0061575-fulltext.txt
Citation
831-1.0061575.ris

Full Text

F O U R I E R T R A N S F O R M M I C R O W A V E S P E C T R O S C O P Y O F S O M E M E T A L - C O N T A I N I N G C O M P O U N D S P R O D U C E D B Y L A S E R A B L A T I O N By Kaley Anne Walker B. Sc. (Chemistry) University of Waterloo A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E D E G R E E OF D O C T O R OF PHILOSOPHY IN T H E FACULTY OF GRADUATE STUDIES CHEMISTRY We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA 1998 © Kaley Anne Walker, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Chemistry The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1Z1 Date: A b s t r a c t A laser ablation source has been constructed for a pulsed jet cavity Fourier transform microwave (FTMW) spectrometer. This source is mounted in one of the microwave cavity mirrors and includes a mechanism for rotating and translating the target metal rod. Seven metal-containing species, namely MgS, MgBr, AlBr, MgNC, A1NC, Y F and Y B r , have been prepared using this apparatus and their pure rotational spectra have been measured by F T M W spectroscopy. The first laser ablation-FTMW measurement of a metal sulfide, MgS, has been made. The J = 1 — 0 transition near 16 GHz has been measured for 4 isotopomers in the ground vibrational state, as well as for the main isotopomer in the first excited vibrational state. 2 5 M g nuclear hyperfine structure has been observed and the nuclear quadrupole coupling constant has been determined. The pure rotational spectra of magnesium monobromide and aluminium monobro-mide have been measured between 9.3 and 20.1 GHz. For MgBr, this is the first report of such a spectrum. Rotational, fine structure and several Br hyperfine parameters have been obtained for this radical and an accurate equilibrium bond length has been deter-mined. From the nuclear quadrupole and magnetic hyperfine constants MgBr has been found to be highly ionic, with the unpaired electron residing almost entirely on Mg. For AlBr, accurate hyperfine parameters have been obtained, including the first values for the A l 8 1 B r isotopomer. These, too, are consistent with highly ionic bonding. The calculated ionic characters follow trends predicted from electronegativity values: MgBr ii exhibits more covalent character than Ca and heavier alkaline earth monobromide species and AlBr shows less covalent character than GaBr. Pure rotational spectra of aluminium isocyanide and magnesium isocyanide have been measured in the frequency range 11.9 - 23.9 GHz. The hyperfine structure in MgNC caused by the 1 4 N nucleus has been measured and the nuclear quadrupole coupling, Fermi contact and dipole-dipole interaction constants have been obtained. From the measured transitions of A1NC, nuclear quadrupole coupling constants and nuclear spin-rotation constants have been determined for both the 1 4 N and the 2 7 A1 nuclei along with an Al-N nuclear spin-spin constant. The degree of sp-hybridisation of the bonding orbitals of A1NC and MgNC have been estimated from the nuclear quadrupole coupling constants. Comparisons have been made to similar linear metal isocyanide and metal monohalide species. The first high resolution spectrum of yttrium monobromide has been measured be-tween 7.4 and 22.5 GHz. In addition, nuclear spin-rotation splitting has been observed in the spectrum of yttrium monofluoride. Equilibrium rotational parameters have been determined for Y B r and used to calculate an equilibrium bond distance. Hyperfine struc-ture due to the bromine nuclei has been observed and nuclear quadrupole and nuclear spin-rotation constants have been determined. From them, Y B r has been found to be highly ionic and very similar in behaviour to the alkali metal bromide species. The F T M W results for Y F have been combined with data from other pure rotational studies to determine the nuclear spin rotation constant. iii Contents Abstract ii List of Tables viii List of Figures xi Acknowledgement xiii Dedication xiv 1 Introduction 1 2 Theory 5 2.1 Molecular Rotation 5 2.1.1 Rigid Rotor Approximation 5 2.1.2 Selection Rules 6 2.1.3 Vibrating Rotor 7 2.1.4 Rotational Quantum Numbers 9 2.2 Fine Structure 10 2.2.1 Electron Spin-Rotation Coupling 10 2.3 Nuclear Hyperfine Structure 11 2.3.1 Nuclear Quadrupole Coupling 12 iv 2.3.2 Nuclear Spin-Rotation Coupling 15 2.3.3 Spin-Spin Coupling 16 2.4 Bond Length Determination 19 2.5 Interpretation of Hyperflne Parameters 21 2.5.1 Nuclear Quadrupole Coupling Constants 22 2.5.2 Electron Spin-Nuclear Spin Coupling Constants 25 3 Experimental Technique 27 3.1 Introduction 27 3.2 Theoretical Description of F T M W Experiment 27 3.3 Microwave Cavity 34 3.4 Microwave Source 36 3.5 Experiment Sequence 36 3.6 Data Acquisition 37 3.7 Gas Sample 40 3.8 Helmholtz Coils 41 4 Development of Laser Ablation Source 43 4.1 Introduction 43 4.2 Ablation Source Design 44 4.3 Experimental Details 49 4.4 Testing of Laser Ablation Source 49 5 F T M W Spectroscopy of MgS 54 5.1 Introduction 54 5.2 Experimental Details 55 5.3 Observed Spectra and Analyses ' 56 v 5.4 Discussion 59 5.4.1 Equilibrium Bond Distance 59 5.4.2 Nuclear Quadrupole Hyperfine Structure 61 5.5 Conclusion • • 62 6 Pure Rotational Spectra of MgBr and AlBr 70 6.1 Introduction 70 6.2 Experimental Details 73 6.3 Assignment of Spectra 73 6.3.1 MgBr 73 6.3.2 AlBr 74 6.4 Analyses 78 6.5 Discussion 82 6.5.1 Equilibrium Bond Distance of MgBr 82 6.5.2 Electron Spin-Nuclear Spin Hyperfine Parameters 84 6.5.3 Nuclear Quadrupole Coupling Constant 85 6.5.4 AlBr Nuclear Spin-Spin Constant 87 6.6 Conclusion 87 7 Microwave Spectroscopy of MgNC and A1NC 101 7.1 Introduction 101 7.2 Experimental Details 103 7.3 Observed Spectra 103 7.3.1 MgNC 103 7.3.2 A1NC 104 7.4 Analyses 106 vi 7.4.1 MgNC 106 7.4.2 A1NC 109 7.5 Discussion I l l 7.5.1 Nuclear Quadrupole. Coupling Constants . . . 112 7.5.2 Electron Spin-Nuclear Spin Hyperfine Parameters for MgNC . . . 115 7.5.3 Nuclear Spin-Spin Constant for A1NC 117 7.6 Conclusion 117 8 F T M W Spectroscopy of Yttrium Monohalides: Y F and YBr 128 8.1 Introduction 128 8.2 Experimental Details 130 8.3 Spectral Search and Assignment 131 8.3.1 Y F 131 8.3.2 YBr . . 131 8.4 Analyses 133 8.4.1 Y F 133 8.4.2 YBr 137 8.5 Discussion 138 8.5.1 Equilibrium Bond Distance of Y B r 138 8.5.2 Estimate of Vibration Frequency 140 8.5.3 Y B r Nuclear Quadrupole Coupling Constants 141 8.6 Conclusion 141 Bibliography 154 vii L i s t o f T a b l e s 4.1 F T M W Spectroscopy of Molecules Produced by Laser Ablation 53 5.1 Observed frequencies for 2 4 M g 3 2 S 63 5.2 Molecular constants calculated for 2 4 M g 3 2 S 64 5.3 Frequencies for the J = 1 — 0 transition of isotopomers of MgS and derived Bo values 65 5.4 Frequencies of measured hyperfine components of 2 5 M g 3 2 S 66 5.5 Molecular constants for 2 5 M g 3 2 S 67 5.6 Substitution structure results for 2 4 M g 3 2 S 68 5.7 Equilibrium bond length calculated for 2 4 M g 3 2 S 69 6.1 Measured frequencies of N = 1 — 0 and N — 2 — 1 transitions of 2 4 M g 7 9 B r in v = 0 and v — 1 vibrational states 89 6.2 Measured frequencies of N = 1 — 0 and N = 2 — 1 transitions of 2 4 M g 8 1 B r in v = 0 and v = 1 vibrational states 90 6.3 Measured frequencies of J = 1 — 0 and J = 2 — 1 transitions of A l 7 9 B r in v — 0 and v = 1 vibrational states 91 6.4 Measured frequencies of J = 1 — 0 and J = 2 — 1 transitions of A l 8 1 B r in v = 0 and v = 1 vibrational states 92 6.5 Molecular constants calculated for MgBr 93 v n i 6.6 Molecular constants calculated for AlBr 94 6.7 Calculated ratios of hyperfine parameters compared to nuclear and molec-ular properties of MgBr and AlBr 95 6.8 Equilibrium parameters calculated for MgBr 96 6.9 Comparison of equilibrium bond length estimates for AlBr 97 6.10 Summary of equilibrium bond length estimates for MgBr 98 6.11 Spin densities calculated from magnetic hyperfine constants for MgBr and CaBr 99 6.12 Comparison of AlBr, MgBr and related metal monobromide nuclear quadrupole coupling constants 100 7.1 Observed frequencies of 2 4 M g 1 4 N 1 2 C in its ground vibrational state. . . . 119 7.2 Observed ground vibrational state frequencies of A1NC 120 7.3 Molecular constants calculated for 2 4 M g 1 4 N 1 2 C 122 7.4 Molecular constants calculated for A1NC 123 7.5 Comparison of experimental and theoretical rotational constants for A1NC. 124 7.6 Comparison of nuclear quadrupole coupling constants of MgNC, A1NC and related cyanides and isocyanides 125 7.7 s-character of Al bonding orbital calculated from Al nuclear quadrupole coupling constants 126 7.8 Unpaired electron spin densities calculated at the 1 4 N nucleus from mag-netic hyperfine constants for MgNC and CaNC 127 8.1 Observed transitions of Y F in the v = 0 and v = 1 vibrational states. . . 143 8.2 Measured transition frequencies of Y 7 9 B r in v = 0 and v — 1 vibrational states 144 ix 8.3 Measured transition frequencies of Y 8 1 B r in v = 0 and v = 1 vibrational states 145 8.4 Molecular constants obtained by direct calculation for Y F 146 8.5 Ground vibrational state molecular constants determined for Y F 147 8.6 Molecular constants of YBr 148 8.7 Calculated ratios of hyperfine parameters compared to nuclear and molec-ular properties of Y B r 149 8.8 Equilibrium parameters calculated for Y B r 150 8.9 Summary of equilibrium bond length estimates for Y B r 151 8.10 Estimate of vibration frequency of YBr 152 8.11 Calculated ionic character of Y 7 9 B r and related alkali metal bromides. . . 153 x List of Figures 3.1 Schematic diagram of microwave cavity 35 3.2 Schematic pulse sequence diagram 38 3.3 Schematic circuit diagram 39 4.1 Top view of laser ablation nozzle cap and part of fixed aluminium mirror. 46 4.2 View of nozzle cap and motorized actuator 47 4.3 Side view of fixed mirror. 48 4.4 Diagram of laser coupling scheme 50 4.5 Comparison of spectra of YC1 produced by the two laser ablation systems. 52 5.1 The J = 1 - 0 rotational transition of 2 4 M g 3 2 S 58 5.2 The J = 1 - 0 transition of 2 5 M g 3 2 S 60 6.1 The N = 1 - 0, J = 3/2 - 1/2, F = 2 - 2 transition of 2 4 M g 8 1 B r 75 6.2 Comparison of spectra of 2 4 M g 7 9 B r with Helmholtz coils on and off. . . . 76 6.3 The N = 1 - 0 rotational transition of Mg 7 9 Br and M g 8 1 B r 77 6.4 Composite spectrum of the J = 1 — 0 rotational transition of A l 7 9 B r . . . 79 7.1 The N = 1 - 0, J = 3/2 - 1/2, F = 3/2 - 1/2 rotational transition of 2 4 M G 1 4 N 1 2 C ; 1 Q 5 7.2 Composite spectrum of the J = 1 — 0 rotational transition of A1NC. . . . 107 XI 7.3 Detail of the J = 1 - 0 transition of A1NC, showing the F x = 7/2 - 5/2 hyperfine transition 108 8.1 The J = 1 - 0 rotational transition of Y F 132 8.2 The A F = +1 hyperfine components of the J = 4 - 3 transition of Y 8 1 B r . 134 xii Acknowledgement I would like to thank my research supervisor Mike Gerry for his patience and encour-agement during the past five years. I would also like to thank my co-workers for their assistance. I thank Wolfgang Jager, Yunjie Xu and Kristine Hensel for teaching me how to use the spectrometer, Mark Barnes and Thomas Brupbacher for many, many discus-sions during the construction and testing of the laser ablation system, Holger Miiller for answering my Pickett questions, and Jiirgen PreuBer for attempting to improve my German pronunciation. I would like to thank Beth Gatehouse for being my friend and partner in crime (and leak detecting) for the last five years. Thank you also to Peggy Athanassenas, Dave Gillett, Chris Kingston, Greg Metha, and Jim Peers. I also wish thank my friends and family far and near for their support during this thesis work. Specifically, I would like to thank Kate Mclnturff, Meredith Browne and Mark Salter for taking me to the movies, keeping me in touch with the world outside of science and trying to convince me that "there is a law that says: you can only be in the lab for 12 hours per day". I would like to thank Almira Blazek for many fabulous theatre outings. Thank you also to Sean Walker and Taunya Boughtflower for going to see some very bad films and making sure that I remembered to eat. Finally, I would like to thank my parents for their support, understanding and encouragement throughout the years. xiii This thesis is dedicated to Dr. E . E . W. Walker (1888-1978) xiv C h a p t e r 1 I n t r o d u c t i o n Microwave spectroscopy is primarily the study of pure rotational transitions of gas phase molecules possessing permanent dipole moments. The development of sources and detec-tors for microwave radar during World War II made possible the beginning of microwave spectroscopy. As the field has grown over the past fifty years, many molecules have been characterised via their microwave spectra [1-3]. Radioastronomical observations have identified, via their microwave spectra, many species present in interstellar space and have contributed to the understanding of interstellar chemistry [4-7]. The development of pulsed jet cavity Fourier transform microwave (FTMW) spec-troscopy over the past two decades has improved the sensitivity and resolution possi-ble in microwave measurements [8-10]. The spectra of reactive or otherwise unstable molecules can be measured because the pulsed jet expansion stabilises transient species. Narrow line widths are obtained in these experiments and the resolution is, thus, very high. The very precise rotational constants obtained can provide accurate molecular geometries. Nuclear hyperfine structure, including very small hyperfine contributions caused by nuclear spin-rotation and spin-spin interactions, can easily be resolved by this technique. Hyperfine interactions provide detailed information about the electronic structures of molecules. One of the major contributions to these interactions is nuclear quadrupole 1 Chapter 1. Introduction 2 coupling. This has been used to investigate bonding in many molecules [2] by providing a method of probing the electric field gradients in the molecule. In the spectra of param-agnetic molecules, a second major contribution is magnetic hyperfine coupling between the spin of the unpaired electron(s) and the nuclear spin(s) in the molecule. From this coupling, the unpaired electron spin density in the molecule can be probed [11,12]. The information obtained can be used to draw conclusions about the bonding in the species under investigation. In this thesis, pure rotational spectra of several diatomic and linear triatomic metal-containing molecules are presented. From these spectra, geometries have been calculated and bond characteristics have been investigated through the hyperfine parameters. Gas phase samples of the species of interest were prepared using a newly built laser ablation source and their spectra were measured by F T M W spectroscopy. The laser ablation apparatus is mounted in one of the F T M W cavity mirrors and incorporates a mechanism for translating and rotating the target metal rod. The development of this system is described in Chapter 4. The laser ablation apparatus was tested by measuring the spectra of four isotopomers of magnesium sulfide, including species of low abundance. These experiments, described in Chapter 5, are the first F T M W measurement of the spectrum of a metal sulfide produced by reacting ablated metal with a source of sulfur. An equilibrium bond length has been obtained for MgS along with the 2 5 M g nuclear quadrupole coupling constant. Chapter 6 describes the pure rotational spectroscopy of magnesium monobromide and aluminium monobromide. For MgBr, this represents the first complete rotational analysis. Accurate rotational and centrifugal distortion constants have been determined as well as new fine and hyperfine parameters. In addition, an accurate equilibrium bond length has been obtained. For AlBr, the nuclear quadrupole structure in the spectrum Chapter 1. Introduction 3 of the 8 1 Br isotopomer has been observed for the first time. As well, improved nuclear quadrupole coupling constants have been obtained for A l 7 9 B r and nuclear spin-rotation and spin-spin constants have been determined for both isotopomers. The bonding in magnesium and aluminium monobromide has been found to follow the trends predicted from electronegativities; MgBr exhibits more covalent character than the corresponding Ca and heavier alkaline earth monobromides and AlBr exhibits less covalent character than GaBr. The F T M W spectra of aluminium isocyanide and magnesium isocyanide are dis-cussed in Chapter 7. This is the first measurement of the hyperfine interactions in these molecules. The F T M W results obtained for MgNC were combined with those of an earlier millimetre wave study to determine an improved set of rotational constants. Nu-clear quadrupole and magnetic hyperfine parameters have been determined for A1NC and MgNC. From the nuclear quadrupole coupling constants, the sp-hybridisation of the bonding orbitals of both molecules has been investigated. Similarities in the bond properties of aluminium and magnesium isocyanide have been found with those of other linear metal isocyanides and metal monohalides. Chapter 8 describes the pure rotational spectroscopy of two yttrium monohalide molecules, Y B r and Y F . For the former, this work is the first high resolution spec-troscopic study of any kind. Rotational and centrifugal distortion constants have been determined and an accurate equilibrium bond length has been calculated. The vibration frequency of Y B r has been estimated and has been found to agree well with results ob-tained by low resolution laser induced fluorescence spectroscopy. The ionic character of the Y-Br bond has been estimated from the Br nuclear quadrupole coupling constant; it has been found to be very similar to that of the alkali metal bromide species. Nu-clear spin-rotation splitting has been measured in the spectrum of yttrium monofluoride. Chapter 1. Introduction 4 The 1 9 F spin-rotation coupling constant has been determined by combining the F T M W results with the results from other pure rotational studies. To aid the reader, the tables of data and results are collected at the end of every chapter. The figures, however, are located in the body of the text near where they are first cited. Chapter 2 Theory This chapter outlines the theory pertinent to the spectral assignment and analysis of the microwave spectra of the diatomic and linear triatomic molecules described in this thesis. The Hamiltonian appropriate for these systems is H = Hrot + ^distort + -f/fine + ^hyperfine (2-1) where HTOt, ^distort? #fine a n d ^hyperfine are the rotational, centrifugal distortion, fine and hyperfine Hamiltonians. Each of these contributions is discussed separately. A through treatment of pure rotational spectroscopy is available from several standard textbooks [1,2,13]. The calculation of bond distances from rotational constants and the interpretation of hyperfine parameters are also discussed in this chapter. 2.1 Molecular Rotation 2.1.1 Rigid Rotor Approximation The gross features of the rotational spectrum of a molecule can be described by the rigid rotor model. The general rigid rotor Hamiltonian is given as: #rot = BxRl + ByR2y + BzR2z (2.2) 5 Chapter 2. Theory 6 where x, y, and z are the principal inertial axes of the molecule and Rg (g = x,y,z) are the components of the rotational angular momentum about each of the principal axes. The molecular rotational constants, BG are related to the moments of inertia, IG, by B' = sk- <2-3> For linear molecules the 2-axis is taken to be along the molecular bond axis. There is no rotational angular momentum about this axis and the moments of inertia about the other two axes are equal(/^ = 0 and IX = IY = I). Thus the rigid rotor Hamiltonian for a linear molecule can be expressed as Hrot = B{Rl + Rl) (2.4) = B R 2 (2.5) where BX = BY = B. The rotational energy levels obtained from this equation are, in frequency units, Erot = BR{R + l) (2.6) where R is the rotational quantum number. 2.1.2 Selection Rules Pure rotational transitions are induced by the interaction of electromagnetic radiation with the permanent electric dipole moment of a molecule, \x. The probability of a tran-sition from one state \RM) to another state \R'M') in unit time, PRM^R'M'I is PRM^R'M' = piyRMR'M') BRM-+R'M' (2.7) where P(VRMR'M') 1 S the density of radiation oscillating with frequency URMR'M' a n d BRM^R'M' is the Einstein coefficient of absorption for the \RM) —V \R'M') transition. Chapter 2. Theory 7 In microwave experiments, plane polarised radiation is used which is arbitrarily chosen to be polarised along the space-fixed Z-axis, hence P>RM-+R'M' = (^j\{RM\az\R'M')\2. (2.8) The matrix element of \iz has to be non-zero for a transition to occur. The molecule-fixed components of the molecular dipole moment, fix, \iy and fiz, are related to the space-fixed component nz by the direction cosines, §zgi In the diatomic and linear triatomic molecules considered here, the permanent electric dipole lies along the z axis, so fix — fiy — 0 and therefore (RM\yz\R'M') = iuz(RM\$zz\R'M'). (2.10) Non-zero direction cosine matrix elements are tabulated in Ref. 2 and from these the rotational selection rules for these linear species are found to be AR = ± 1 (2.11) AM = 0. (2.12) 2.1.3 Vibrating Rotor The rigid rotor approximation provides a general description of the molecular rotational energy levels. However molecules are not rigidly bound; the bonds are flexible. Two contributions to the rotational energies result from these molecular vibrations. As the molecule rotates, it distorts as a result of centrifugal distortion. In addition, the rotational constant decreases with vibrational excitation because of vibration-rotation interaction effects [14,15]. Chapter 2. Theory 8 The centrifugal distortion Hamiltonian for a linear molecule is ^distort = -D(R2)2 + H(R2)3 + ... (2.13) where D and H are the quartic and sextic centrifugal distortion constants, respectively, and R is the rotational angular momentum operator. Combining the rotational and centrifugal distortion Hamiltonians ^vib-rot = ^rot + ^distort (2-14) the vibration-rotation Hamiltonian results. The vibration-rotation energy expression is given as £vib-rot = BvR(R + l) - DVR2(R + 1)2 (2.15) where Bv and Dv are the rotational and quartic centrifugal distortion constants, re-spectively, for the vth vibrational state and R and v are the rotational and vibrational quantum numbers, respectively. The energy expression is truncated following the quar-tic centrifugal distortion constant because higher order distortion constants were not required to fit the data obtained in these studies. The vibrational dependence of the rotational and centrifugal distortion constants is due to vibration-rotation interaction. For a diatomic molecule, this is given by Bv = Be-ae(v + ^)+%(v + ^j2 + ... (2.16) Dv = De + pe(v + ^+... (2.17) In these equations, ae, 7 e and /3e are vibration-rotation interaction constants and Be and De are the equilibrium rotational and centrifugal distortion constants, respectively. These are the values of these parameters at the minimum of the potential energy surface. To calculate these constants, rotational transitions must be measured in at least two Chapter 2. Theory 9 vibrational states. Measurements were made in the ground and first excited vibrational states for four diatomic species discussed in this thesis and from these data Be and a e were determined. Equilibrium constants were not determined for the two linear triatomic species studied because transitions were measured in the ground vibrational state only. Vibration-rotation effects in the centrifugal distortion constant were found to be smaller than the uncertainty in the determined parameter. The rotational energy expression for a linear triatomic molecule is identical to Eq. (2.15). In this case, however, the vibrational dependence of the rotational and centrifugal distortion constants must include contributions from each of the vibrational modes of the molecule. Thus, the expressions are Bv = Be-^cti^vi + ^j (2.18) Dv = De + '£8i(vi + ^j (2.19) where i>t- is the vibrational quantum number of the ith vibrational mode, dj is the degen-eracy and ^ and /?,• are the vibration-rotation interaction constants for the «th vibrational mode. 2.1.4 Rotational Quantum Numbers So far in the discussion of rotational energy levels, the rotational angular momentum R has been used. This has been done to simplify the initial discussion. At this point, the coupling of electronic and rotational angular momenta will be brought into the picture. R is the rotational angular momentum of the molecule which can couple to the electron orbital angular momentum L to produce N . Then rotational angular momentum includ-ing L can couple with the electron spin angular momentum S to produce J, the total rotational angular momentum excluding nuclear spin angular momentum. This scheme Chapter 2. Theory 10 can be expressed as R + L = N (2.20) N + S = J . (2.21) All the molecules investigated in this work have S ground electronic states, for which there is no electron orbital angular momentum, so A = 0, and thus, N = R. Also most are diamagnetic species, with S — 0, so N = J and thus the rotational energy expression is £vib-rot = BVJ(J+ l)-DvJ2(J + l)2 (2.22) and the selection rules are A J = ± 1 . Two of the molecules studied are paramagnetic; these have 2 E + ground electronic states. Since S — | , N ^ J and the rotational energy expression for these species is E v i h . r o t = BVN(N + 1) - DVN2{N + l ) 2 . (2.23) The selection rules are AiV = ± 1 and A J = 0, ± 1 . 2.2 Fine Structure 2.2.1 Electron Spin-Rotation Coupling For molecules having 2 E + ground electronic states, an electron spin-rotation term must also be added to the vibration-rotation Hamiltonian. The unpaired electron spin interacts with the magnetic field generated by the rotation of the molecule giving rise to fine structure in the spectrum. The Hamiltonian for this interaction is -fi^ ne = 7 . N - S (2.24) Chapter 2. Theory 11 where 7„ is the electron spin-rotation constant for the vth vibrational state. This doubles each of the molecular rotational levels, so J = N ± | for N > 0. The resulting vibration-rotation energy expressions, including fine structure, are £ v i b - r o t ( j = N + )^ = BvN(N + l)-DvN2(N-rl)2 + jN (2.25) £ v i b - r o t (J = N - = BVN(N + 1)- DvN2(N + l)2-^-{N + l). (2.26) 2.3 Nuclear Hyperfine Structure Interactions involving nuclear spin angular momentum, I, are referred to as hyperfine interactions. The nuclear spin angular momentum can couple to the total rotational angular momentum, J , to form F, the total angular momentum, I + J = F. (2.27) For molecules with two nuclei having non-zero spin, two coupling schemes are possible. If the coupling energies of the two nuclei are equal or nearly so, then the "parallel" scheme is employed; the two nuclear spins couple to form a resultant nuclear spin angular momentum, I, which then couples to J , l ! + I 2 = I (2.28) I + J = F. (2.29) The "series" scheme is employed if the coupling energy of one nucleus is much greater than that of the other. The first nuclear spin, Ii , couples to J to form the intermediate F i ; then the second nuclear spin, I2, couples to F j , I i + J = F x I 2 + F! = F. (2.30) (2.31) Chapter 2. Theory 12 The "series" scheme best describes the hyperfine interactions observed for the metal-containing species with two magnetic nuclei studied in this thesis. Nuclear hyperfine interactions occur via electrostatic and magnetic means. The ob-served hyperfine structure can be classified into three types, i^hyperfiri H. quadrupole spin—rotation ~\~ iJsoin— spin spin (2.32) where //quadrupole describes the nuclear electric quadrupole interaction and Z/ S pin-rotation and / / S p i n - s p i n describe the magnetic nuclear spin-rotation and spin-spin interactions, respectively. 2.3.1 Nuclear Quadrupole Coupling Nuclear quadrupole hyperfine structure arises from the interaction of a nuclear electric quadrupole moment with the electric field gradient at that nucleus. The nucleus must have a spin, / > 1, to possess a nuclear quadrupole moment. The Hamiltonian for the nuclear quadrupole coupling of a single quadrupolar nucleus can be written as the product of two second rank tensors, H, quadrupole - i q = V E 1 (2.33) (2.34) t,]=x,y,z where Q and V E are the nuclear electric quadrupole moment and electric field gradient tensors, respectively, and Vij — — V F , j . For a diamagnetic molecule, the matrix elements of this Hamiltonian are given by [2] ( J'lF | i/quadrupole \JIF) '-l)J+I+F F I J' J 2 J J 0 - J 2 J I - l 1 2 1 -I 0 I eQqj.j (2.35) Chapter 2. Theory 13 where the 6j and 3j symbols can be evaluated using formulae given in Ref. 16. eQqjij are the nuclear quadrupole coupling constants in the space fixed axis system; these are transformed into the molecule fixed system by [2] eQqj'j = ( - 1 ) J [ ( 2 J + 1 ) (2J ' + 1)]? / x ' ^ ( J 2 J ' ^ V eQqo ^ 0 0 0 / (2.36) J 2 J'J 0 - J where eQq0 is the molecular nuclear quadrupole coupling constant. The matrix elements for the nuclear quadrupole interaction in a linear paramagnetic molecule in a 2 E state can be calculated from [12] f_1 )2J+I+F+S+2N' (N'SJ'IF\Hquadrupole\NSJIF) = ^ x[ (2J + 1) (2J ' + 1)(2N + 1)(2N' + l)]a x ( /+ 1)(2/+ l)(2/ + 3) 7(2 / - 1) / N' 2 N 0 0 0 I J' F ' N' J S X i > i J I 2 J J N 2 J qo- (2.37) The Hamiltonian for coupling due to two nuclei coupled in "series" is ^quadrupole = HQ(1) + HQ(2) (2.38) where HQ(1) and HQ(2) are the nuclear quadrupole Hamiltonians for nuclei Ii and I2, respectively. The matrix elements for the more strongly coupled spin, Ix, are identical to those of the singly coupled nucleus [2] (J'lMHQ^lJhF,) = (-1) J+h+Fi Fi h J' 2 J h x J 2 J J 0 -J h 2 h \ - h 0 h J eQqj,j(l). (2.39) Chapter 2. Theory 14 The matrix elements for the more weakly coupled spin, I2, are then evaluated in the coupled basis \JhFxI2F) [2] {J'hF[I2F\HQ{2)\JhFJ2F) = ^_iy'+Ii+I2+2Fi+F X < J' F{ h Fx J 2 > < [(2^ + 1X2^ + 1)]' F h F{ 2 Fx I2 t J 2 J>\*( h 2 I2 -I2 0 / 2 / eQqj,j(2) (2.40) V J 0 -JJ v In Eqs. (2.39) and (2.40), eQqj>j(i) can be determined using Eq. (2.36). For paramagnetic species, the matrix elements for the more strongly coupled nucleus are [12] (N'SJ'IMHQWNSJIM = {—t x[(2J + 1)(2J' + 1)(2N + 1){2N' + x (/1 + l)(2/ 1 + l)(2/ 1 +3) / 1 ( 2 / 1 - 1 ) / N' 2 N x < > < N' J S J N 2 0 0 0 > eQq0(l). (2.41) h J' Fx J h 2 Then the matrix elements of the more weakly coupled nucleus can be evaluated from [12] {N'SJ'hF[l2F\HQ{2)\NSJhFLI2F) = x[(2J + 1)(2J' + l)(2N + 1){2N' + h J' F{ 2 Fx J "(/2 + l)(2/ 2 + l)(2/ 2 + 3) x[(2F +1)(2F' + 1)H / 2(2/ 2 - 1) * ( N' 2 N N v 0 0 0 j Chapter 2. Theory 15 F ' N' J S < - < h 2 J N 2 eQq0(2). (2.42) The molecular nuclear quadrupole coupling constant, eQq, is related to the electric field gradient at the nucleus, q, and the nuclear quadrupole moment, Q. This field gradient can be considered to be due only to the electron configuration in the valence p-shell of the coupling atom. Thus the experimentally determined quadrupole coupling constant can be interpreted in terms of "unbalanced" p-electrons. The Townes-Dailey model relates the molecular nuclear quadrupole coupling constant to the quadrupole coupling constant of an electron in an np-orbital [17] eQq{mo\) = (nz - " x ^ eQqnl0(atom) (2.43) where nx, ny and nz are the numbers of electrons in the npx, npy and npz orbitals, respectively. Values of eQt7„io(atom) are listed in Ref. 2. By relating nx, ny and nz to the molecular orbital populations, this model can be used to estimate bonding characteristics such as ionic character and orbital hybridisation. 2.3.2 Nuclear Spin-Rotation Coupling The nuclear magnetic dipole moment of one of the atoms in a molecule can interact with the magnetic field generated by the rotating molecule to give rise to nuclear spin-rotation splitting. This interaction is analogous to electron spin-rotation splitting which was described in Sec. 2.2.1. The Hamiltonian for this interaction, in diamagnetic species, is - ^ s p i n - r o t a t i o n = Cjl • J (2.44) where C j , the nuclear spin-rotation constant in the Jth rotational state, equals CJ = jrj\^{C,AJ2x) + Cyy(J^ (2.45) Chapter 2. Theory 16 For a linear molecule with no resultant angular momentum about the molecular axis, Jz = 0 and symmetry makes Cxx = Cyy = Cj , so that c > = J(7TT)C'<J2) { 2 M ) = C,. (2.47) The nuclear spin-rotation constant, Ci, is equal to Ci = -gipNhxx (2.48) where gi is the nuclear g-factor for the magnetic nucleus, pj^ is the nuclear magneton and hxx is the component of the magnetic field perpendicular to the molecular bond axis. The nuclear spin-rotation energy expression is given by ^pin-rot. = y [ F ( F + l ) - J ( J + l ) - / ( / + l)]. (2.49) The nuclear spin-rotation Hamiltonian for a molecule with a 2 E + ground electronic state is Hspm—rotation — C/I • N (2.50) This expression is identical to that described above for diamagnetic molecules; however the operator for rotational angular momentum minus electron spin, N, must be used instead of J. The matrix elements of this Hamiltonian are given in Refs. 12,18. 2.3.3 Spin-Spin Coupling Electron Spin-Nuclear Spin Interaction The Hamiltonian for the magnetic interaction between a nuclear spin, I, and an electron spin, S, in a molecule with a 2 E + ground electronic state is ^spin-spin = M • S + C (lzSz - U • S) (2.51) Chapter 2. Theory 17 where Iz and Sz are the components of I and S along the internuclear axis, respectively, and bp and c are the Fermi contact and dipole-dipole interaction constants, respectively. Matrix elements of this Hamiltonian can be found in Refs. 12,19. The Fermi contact and dipole-dipole interaction constants were defined by Frosh and Foley [20], and have the form: bF = y<7e<M^Ar |*(0)| 2 (2.52) and c = - # e £ W j 9 M ; v ( ( 3 c o s 2 0 - l ) / r 3 ) (2.53) where ge and gw are the electronic and nuclear ^-factors and p,s and fj.^ are the Bohr and nuclear magnetons, respectively; |^(0)|2 is the probability of the unpaired spin at the magnetic nucleus; r is the distance between the magnetic nucleus and the unpaired electron, and 0 is the angle between the r-vector and the molecular axis. The non-zero nuclear spin of an atom in a molecule with a 2 E + ground electronic state can be used as a probe of the unpaired electron spin density in the atomic orbitals of that atom. For the paramagnetic molecules studied, the unpaired electron spin densities, p(s) and p{p) for an s-type and p-type orbital, respectively, were calculated from [21] l*(0)l2(mol) . . . . p { s ) = |*(0)|'(atom) ( 2 - 5 4 ) " _ ( (3cos 2 e - l ) / r3 ) ( m o l ) P [ P ) ~ <(3cos 'e-l)/r3)(atom) 1 ' where |$(0)|2(mol) and ((3cos 20 — l)/r 3)(mol) were calculated from the experimental bp and c values, respectively, and |\P(0)|2(atom) and ((3cos 20 — l)/r 3)(atom) were cal-culated for the appropriate s and p orbitals, respectively, using atomic parameters taken from Morton and Preston [22]. Chapter 2. Theory 18 Nuclear Spin-Nuclear Spin Interaction Nuclear spin-spin coupling arises from the interaction of the nuclear magnetic dipole moments of two nuclei in a molecule. The interaction of two nuclear magnetic moments can be described using the Hamiltonian: ^spin-spin =  c4^1 ' ^ 2 + 3c3 {^Ilzhz — ^II ' (2.56) where c\ and c 3 are the scalar and tensor contributions to the nuclear spin-spin inter-action. The form of this equation is identical to the Hamiltonian for the electron spin-nuclear spin interaction. The magnitude of the nuclear spin-spin interaction, however, is 4 to 5 orders of magnitude smaller than that observed for the electron spin-nuclear spin interaction. The scalar constant, C4, is very small, on the order of 10 Hz for most molecules. It could not be determined for the species studied and so will not be discussed further. There are two contributions to the tensor constant, C3 c 3 = c3(dir.) + c3(ind.). (2.57) The first arises from the direct dipole-dipole interaction and can be calculated from the geometry of the molecule. The second contribution is due to an electron-coupled inter-action. In this, the nuclear spin interacts magnetically with the electron spin of its own atom. This causes the electron spin to align antiparallel to the nuclear spin. The sec-ond nuclear spin interacts similarly with the electron spin of its own atom. Because the ground electronic state is a singlet state, the two electron spins have to be aligned antipar-allel and thus the two nuclear spins also must be aligned antiparallel. This mechanism couples the two nuclear spins via the electron spins. The direct contribution dominates the tensor spin-spin constant. For most molecules containing light atoms the indirect contribution can be neglected [23-25] and this has Chapter 2. Theory 19 been done for the molecules examined in this thesis. The tensor spin-spin constant 3c3 has been approximated to equal a 1 2 , the direct nuclear spin-spin constant. For a linear molecule, 0:12 is defined as [26]: = -^N9i92 ( 2 5 8 ) where fi^ is the Bohr magneton, r 1 2 is the internuclear distance, and gi and g2 are the nuclear ^-factors for nuclei 1 and 2, respectively. 2.4 Bond Length Determination The precise rotational constants obtained from microwave spectroscopy can be used to determine geometrical parameters. The internuclear bond length, r i 2 , of a diatomic molecule can be determined from the rotational constant, B, given in frequency units, B = T T ^ T (2-59) where the reduced mass, ju, is » = (2.60) and mi and m 2 are the atomic masses of the two atoms in the molecule. The effective bond length in the ground vibrational state, r 0 , can be determined by using Bo in Eq. (2.59). Its accuracy is limited by zero-point energy contributions. These vibrational contributions can be accounted for by calculating an equilibrium rotational constant, Be (from Eq. (2.16)) using rotational constants obtained in two or more vibrational states; then r e can be determined from Be. This is the bond length for the hypothetical vibrationless state at the minimum of the potential energy curve. The ground state rotational constants obtained for different isotopomers can also be used to obtain an r e distance. Costain showed that for a diatomic molecule [27] r e = 2rs-rQ (2.61) Chapter 2. Theory 20 where rs is the substitution bond length. Using Costain's method [27], the distance of an atom, i , from the centre of mass, z,, in a diatomic molecule is given as: J = ( I J A i J (2.62) where AI°B = IB'-I°B (2-63) is the difference in the ground vibrational state moment of inertia between the substituted molecule, IB', and the parent molecule, IB. The substitution reduced mass is = I T t a ( 2 ' 6 4 ) where M is the mass of the parent molecule and A m is the change in mass upon isotopic substitution. If isotopic substitutions are made at both atoms, rs can be calculated from z\ + z2. In these two methods only vibrational contributions have been taken into account. Electronic contributions can also be important when precise rotational constants from microwave spectroscopy are used to calculate re. In the Born-Oppenheimer approxima-tion, the nuclear and electronic motions are taken to be separable; the electrons in the molecule are assumed to adjust immediately to any movement of the nuclei because the electrons are much lighter than the nuclei and are assumed to move much more quickly. However, in real molecules, the electrons do not adapt instantaneously to the movement of the nuclei. Corrections need to be made to re to account for deviations from the Born-Oppenheimer approximation. The first and largest contribution arises from the reduced mass used to calculate re; the reduced mass expression (Eq. (2.60)) employs atomic masses for which the electrons associated with each atom were assumed to be concentrated at the nucleus. Chapter 2. Theory 21 A better description is that the electrons are arranged in a spherical distribution around each of the nuclei and that this distribution is distorted to some degree by bonding. For ionic species, such as the metal diatomic molecules studied, the charge displacement due to bonding can be quite significant. The second contribution arises from the interaction of the rotational and electronic motions. This causes the rotating nuclear frame to wobble and thus induces distortions along the internuclear axis. Corrections to account for both of these electronic effects are described in Refs. 28-30. As the precision of spectroscopic measurements has increased over the past several years, further improvements have been made to the treatment of the breakdown of the Born-Oppenheimer approximation by Bunker [31,32] and Watson [33,34]. In the r e calculations discussed in this thesis, (see Sec. 6.5.1 and Sec. 8.5.1), the uncertainty in the calculated r e value has been examined by estimating the effect of the non-spherical charge distribution. This has been done by calculating r e using ion masses instead of atomic masses. Also theoretical results from Watson [33] and Bunker [31] have been used to provide a second estimate for the uncertainty in the equilibrium bond distance. 2.5 Interpretation of Hyperfine Parameters Hyperfine parameters, such as nuclear quadrupole and electron spin-nuclear spin coupling constants, can be used to investigate the electronic structures of molecules. For the metal-containing species discussed in this thesis, the bonding can be described as mostly ionic with some covalent character. This bond character can be examined semi-quantitatively using a molecular orbital picture. This approach also can be used to investigate orbital hybridisation. Consider as a model system, the singly bonded molecule, A B , with valence molecular Chapter 2. Theory 22 orbitals fa = a^A + VT^^B (2-65) and = Vl - a2il>A - aipB- (2-66) where a2 and (1 — a2) are the fractional weights of the atomic orbitals tpA and tpB in the bonding molecular orbital ipa, respectively. Gordy and Cook [2] have related the ionic character, ic, of the A-B bond to the difference in the fractional weights of ipA and V's in the molecular orbital, ^V, ic = \a2 - (1 - a2)\ = \2a2-l\. (2.67) For a purely covalent bond, there are equal contributions to ipa from ipA and tpB\ therefore a 2 = 0.5 and ic = 0. Similarly for a purely ionic interaction, ic = 1 and a2 is either zero or one, depending on whether it is the positive or negative pole of the A-B bond, respectively. The ionic character of the A-B bond can be calculated by relating a2 to an experimentally determinable quantity. 2.5.1 Nuclear Quadrupole Coupling Constants Consider A B to be a metal halide molecule where A is the quadrupolar halogen nucleus. Using the Townes-Dailey model (Eq. (2.43)), the nuclear quadrupole coupling constant of A can be related to the p-orbital occupation of atom A. This expression is repeated here eQq(A) = ^nz-^±^yQqnW{k). (2.68) Chapter 2. Theory 23 The z axis is taken to be the molecular axis. The valence shell configuration of A is ns2np5; the npx and npy orbitals will be filled, so nx = ny = 2. The occupation of the npz orbital depends on the participation of ^u(= ^nPz) in the molecular orbital ipa. So nz equals 2a 2, the fraction of the ip„ bond pair of electrons associated with atom A. Substituting these values into Eq. (2.68) results in eQq(A) = (2a2 - ^ ) eQqnl0(A) = (2a2 - 2) eQqnW{A). (2.69) Since A is the negative pole of the AB bond, a 2 > 0.5 and a 2 = ! i ± l . (2.70) This result can be combined with Eq. (2.69) and then an expression for ic can be obtained eQqnw{k) where the term ?9q^K)Ks is negative and less than one. From this equation it can be seen that the observed nuclear quadrupole coupling constant decreases as the ionic character of the A-B bond increases; as ic —> 1 eQq(A) —> 0. So far in this discussion, the effects of nuclear screening and orbital hybridisation have been neglected. The screening of the halogen nucleus is increased as the ionic character of the A-B bond increases. This can be accounted for by a multiplicative factor [1]. Including the correction for nuclear screening, Eq. (2.71) becomes eQg(A)(l+ice) lc = 1 + 7\ 7T\ (2.72) where e values are tabulated in Ref. 1. Neglecting the effects of nuclear screening changes the calculated ionic character by only ~ 1.5%. This difference is not significant for the metal halide species studied. There should be no significant orbital hybridisation on Chapter 2. Theory 24 the halogen on the negative pole of the AB bond, because the dipole moment should suppress the hybridisation [2,35]. Orbital hybridisation, however, could not be ignored for all species studied. The most important contribution to orbital hybridisation was sp-hybridisation. Con-sidering sp orbital hybridisation on the quadrupolar nucleus A, the atomic orbital ^ will be *I>A = + \A ~ al^pz (2-73) and the counterhybridised orbital will be ipA' = yfl - a2srps - asrppz (2-74) where a 2 is the fractional weight of the s-orbital in the sjo-hybrid. This sp-hybridisation must be accounted for in the Townes-Dailey model. The number of electrons in the npz orbital will be nz = M{\-a2s) + Na] (2.75) where M and /V are the number of electrons in the hybridised and counterhybridised orbitals, respectively. Since ipA is P a r t of the molecular orbital M will equal 2a 2, the fraction of the ipa bond pair associated with the atomic orbital tpA- The value of iV depends on the occupation of tpA - So when sp-hybridisation is included Eq. (2.68) becomes eQq(A) = (2a 2(l - a2s) + Na] - !!^±^) eQqnl0(A) (2.76) where a2 can be related to the ionic character of the AB bond using Eq. (2.67). Eq. (2.76) relates two unknown parameters, the degree of sp-hybridisation, a 2 , and the ionic character (through a 2), to one measurable parameter, eQq(A). By finding an alternate method of determining ic, the orbital hybridisation on the A nucleus can be calculated. Chapter 2. Theory 25 The electronegativity, x, describes the ability of an atom to attract electrons to itself in a chemical bond. The difference in electronegativity values should then be related to the ionic character of the bond. This relation has been investigated for many halogen-containing diatomic molecules [2,35]. As a first approximation, this simple expression can be used to calculate ic ic = lxM~Xxl, (2.77) where \XM — xx\ < 2 [35]. By fitting to the experimental results, a more exact relation for ionic character was derived, 1 ic = 1.15 exp where A x = \XM — xx\ < 2 [2]. - ( 2 - A x ) 2 -0.15 (2.78) 2.5.2 Electron Spin-Nuclear Spin Coupling Constants The ionic character of a paramagnetic molecule can be investigated qualitatively via the electron spin-nuclear spin hyperfine constants bp and c. These parameters are related to the unpaired electron spin density in the atomic orbitals of the atom with non-zero nuclear spin. The method for calculating these spin densities is described in Sec. 2.3.3. Consider a 2 S + ground electronic state molecule AB where atom A has a non-zero nuclear spin. The valence molecular orbitals are the same as those given in Eqs. (2.65) and (2.66) Vv = aipA + Vl - a2ipB i^a. = Vl - atijiA - aipB where the ip„ bonding orbital has a bond pair of electrons and the unpaired electron is in the T/V* antibonding orbital. The valence atomic orbitals for A are sp-hybridised (Eqs. Chapter 2. Theory 26 (2.73) and (2.74)), ipA = as*Ps + \A - a2sippz ^A = \A ~  Q ^ S ~ A ^ P Z where a 2 is the fractional weight of the s-orbital in the sp-hybrid. The unpaired electron spin densities for s and p atomic orbitals on atom A, p(s) and p(p) respectively, are proportional to p(s) ex ( l - a 2 ) a 2 (2.79) p(p) cx ( l - a 2 ) ( l - a 2 ) (2.80) where (1 — a2) is the fractional weight of if)A in the antibonding orbital and a2 and (1 — a2) are the fractional weights of ips and tppz in the atomic orbital I\>A-> respectively. If both p(s) and p(p) are small, the (1 — a2) must be small (and a2 large). Therefore the ionic character of the A-B bond must be large, since from Eq. (2.71) ie = | 2 a 2 - l | . As ic —>• 1 then p(s) —> 0 and p(p) —> 0. So the smaller the unpaired electron spin densities in the atomic orbitals on atom A, the larger the ionic character of A B . Chapter 3 Experimental Technique 3.1 Introduction The experiments described in this thesis were performed using a cavity pulsed jet Fourier transform microwave (FTMW) spectrometer. This type of spectrometer was developed by Balle and Flygare as a method of measuring the spectra of weakly bound species [8,9]. The spectrometer consists of a microwave cavity into which a molecular sample is intro-duced as a supersonic expansion. A pulse of microwave radiation is coupled into the cavity where it interacts with the molecules travelling through the cavity inducing a macroscopic polarisation in the molecular sample. Once the microwave pulse decays, the coherent molecular emission is recorded in the time domain and then is Fourier trans-formed to obtain the spectrum. The introduction of the F T M W technique has caused a renaissance in microwave spectroscopy; currently there are at least fifteen research groups worldwide using these instruments. This chapter outlines the theory describing pulsed excitation experiments and the operation of the F T M W spectrometer. 3.2 Theoretical Description of F T M W Experiment In an F T M W experiment, a pulse of microwave energy interacts with the dipole moments of the molecules in the gas sample to create a macroscopic polarisation. The molecules 27 Chapter 3. Experimental Technique 28 emit radiation at the characteristic transition frequency after the microwave excitation pulse has ended. As the molecules relax to thermal equilibrium, the molecular emission signal decays. A theoretical description of an F T M W experiment can be made using the time dependent Schrodinger equation in density matrix formalism [36]. The derivation given here is based on the work of McGurk et al. [37] and Dreizler [10,38]. The molecules in the gas sample can be considered as an ensemble of two-level par-ticles, each with rotational wavefunction where (f>i and <p2 are eigenfunctions of the time independent molecular rotational Hamil-tonian, I*) ci|^i) + c2\<h) (3.1) Hrot<t>i — Ei4>i for i = 1,2. (3.2) The density operator for one of these particles is P = l*><* (3.3) = + c^^M + cK^i) (3.4) and the density matrix is c l c l c l C 2 (3.5) P = C 2 c l C 2 C 2 such that Pij CjC-. For an ensemble comprised of N two level molecules, the density matrix is (3.6) Chapter 3. Experimental Technique 29 The microwave excitation pulse can be considered as a time dependent perturbation of this ensemble of molecules. The Hamiltonian for this system is given by H = HIot + H, rot i "perturbation- (3.8) •^perturbation describes the time dependent interaction of the molecular dipole moment operator, ft, with the applied microwave field, //perturbation = 1fl€ COs{uit -f- <^>). (3.9) where 2e, u> and <j> are the amplitude, angular velocity and phase, respectively, of the field. In the {</>i, <f>2} basis, the matrices of the operators in Eq. (3.8) are: //rot = Ex 0 0 E2 (3.10) and //, perturbation — 0 —2/ii2£ cos(ut + (f)) —1\i\2£ cos(u>£ + </>) 0 The time dependence of the system is calculated from (3.11) •*dP (3.12) The resulting time dependent matrix elements are Pn = *(P21 — pi2)x cos(u;i + <f>) P22 = ~*(P21 — p\2)x cos(u;£ + (f>) Pl2 ~ i(P22 - pn)x cos(ut + (f>) + ipn^o p21 = ~i{p22 - pu)x cos(ut + </>) - ip2iUo (3.13) (3.14) (3.15) (3.16) Chapter 3. Experimental Technique 30 where x = 2p12e/h and u>0 = (E2 — Ei)/h, the angular frequency of the rotational tran-sition. The matrix elements, can then be transformed into a "rotating" coordinate system using Pn = Pn (3.17) P22 = P22 (3.18) Pn = / 5 1 2 e W ) (3.19) P21 = p2ie-l(ut+4,) (3.20) to obtain Pn = %-^{p2i-pi2) (3.21) P22 = -y (P2i-Pi2) (3.22) P12 = -J(P22-PU) + i(uo - u)pi2 (3.23) /52i = -y(P22 - Pn) - i(u>o - v)pi2- (3.24) Then the real quantities s, u, v, and u> are defined as s = /5n + P22 = 1 (3.25) u = P2i+P\2 (3.26) -iv = hi ~ Pn (3.27) w = Pn- P22 (3.28) where s is the trace of the density matrix, which is constant, w is related to the population difference between the two rotational levels, AN, and u and v are the real and imaginary parts, respectively, of the macroscopic polarisation, P. The derivatives of these quantities can be obtained by neglecting terms in 2LU (using the rotating wave approximation [10]) Chapter 3. Experimental Technique 31 and choosing the phase of the microwave pulse such that cf> = 0, s = 0 (3.29) u = -vAu (3.30) v = uAu — wx (3.31) w = xv (3.32) where Ato = LOQ — u is the difference between the transition frequency, UQ and the fre-quency of the applied microwave pulse, to. In an F T M W experiment, the population difference between the two rotational levels, A./V, before the microwave excitation is applied is N,-N2 = N { P l l - P 2 2 ) (3.33) = Nw0. (3.34) Also uo = v0 — 0, since the density matrix is diagonal before the microwave pulse is applied. At time t = 0, a pulse of microwave radiation of angular velocity u> is applied, where OJ is near resonant with the rotational transition frequency, u>o, so that Au; is small. If x, the amplitude of the microwave energy, is chosen to be x = ^ £ » A a > , (3.35) n then Eqs. (3.29) - (3.32) can be approximated as s = 0 (3.36) u = 0 (3.37) v = —xw (3.38) w = xv. (3.39) Chapter 3. Experimental Technique 32 The solution to these differential equations is v(t) = -w0sm(xt) (3.40) w(t) = w0cos(xt) (3.41) u{t) = 0 (3.42) because v0 = 0. So during the microwave excitation pulse v(t) and w(t) oscillate between wo and — wo at angular velocity x. At time t = tp, the microwave excitation is turned off and u p 0 (3.43) vp = -w0sm(xtp) (3-44) wp = w0 cos(xtp). (3.45) When the amplitude of the microwave excitation goes to zero, x becomes zero. Neglecting relaxation effects, Eqs. (3.29) - (3.32) become s = 0 (3.46) ii = -vAu (3.47) v = UAOJ (3.48) w = 0. (3.49) Solving these differential equations results in u{t) = -VpSm(Aut) (3.50) v(t) - VpCos(Aut) (3.51) w(t) = wp (3.52) for t > tp. Chapter 3. Experimental Technique 33 The macroscopic polarisation induced in the sample by the microwave pulse is ex-pressed as P(t) = N(fi) NTr(fip) = NTr 0 1*12 Pn P12 0 _ P21 P22 Npi2 (P21 + Pn) Npi2 (u(t) cos(u>t) — v(t) s i n ( u > i ) ) (3.53) (3.54) (3.55) (3.56) (3.57) Then substituting in for u(t) and v(t) results in N/J.12 {—vp sin(Acji) cos(ut) — vp cos(Aa;£) sin(u;t)) Np-nVp (sin [(Aw + w)]) Nfj,l2vp(sm(u)0t)) Np,i2{w0 sm(xtp))(s'm((jJot)). (3.58) (3.59) (3.60) (3.61) From this expression, it can be seen that the macroscopic polarisation will oscillate at u>o, the frequency of the rotational transition. P(t) depends on the initial population dif-ference, woN, the transition dipole moment, pi2, and the length of microwave excitation pulse, tp. The macroscopic polarisation can be optimised by maximising s'm(xtp); this occurs when the microwave pulse length, tp, satisfies xtp = 2pi2StPlh = mr/2 where n is an integer. This is called the "7r/2" condition. For a constant e, the smaller the transition dipole moment the longer the pulse length needed to obtain-the "7r/2" condition. Eq. (3.61) was derived without considering relaxation effects. In a real F T M W exper-iment, the macroscopic polarisation, P(t), decays to zero and the population difference, AJV = wN, returns to thermal equilibrium. Exponential terms describing both types of Chapter 3. Experimental Technique 34 relaxation can be added phenomenologically to the expressions derived above to account for these effects [10,37]. 3.3 Microwave Cavity A Fabry-Perot microwave cavity forms the heart of a F T M W spectrometer. The cavity consists of two spherical aluminium mirrors with radius of curvature of 38.4 cm and diameter 28 cm placed approximately 30 cm apart. One of the mirrors is movable so the cavity can be manually tuned into resonance at the microwave excitation frequency using a micrometer screw; the other mirror is held fixed. A schematic diagram of the microwave cavity is given in Fig. 3.1. In the original F T M W spectrometer design [9], the pulsed nozzle was mounted so that the molecular jet and the microwave cavity axis were perpendicular. However, it has since been observed that injecting the molecular sample parallel to the cavity axis increases the sensitivity of the spectrometer [39,40]. To operate in the "parallel" configuration, the pulsed nozzle is mounted slightly off centre (~2-3 cm) in the fixed mirror. Because the line widths obtained with this configuration are between ~7-10 kHz, each line appears as a doublet due to the Doppler effect. The microwave mirrors are mounted on translation rods inside a vacuum chamber, which is pumped by a 6 in. diffusion pump backed by a mechanical pump. The experimental repetition rate is limited to approximately 1 Hz by the efficiency of the pumping system. The microwave excitation pulse is coupled into the cavity via an antenna located at the centre of one of the microwave mirrors. The cavity has a bandwidth of 1 MHz when operating at 10 GHz, which restricts the maximum frequency step-size while searching to 1 MHz. The operating range of the spectrometer is 4-26 GHz. Chapter 3. Experimental Technique 35 Figure 3.1: Schematic diagram of microwave cavity showing location of mirrors, nozzle and antennae. Chapter 3. Experimental Technique 36 3.4 Microwave Source A Hewlett-Packard 8340A synthesiser was used as the microwave source for the experi-ments described in this thesis. During the experiments on MgS, MgBr and MgNC the synthesiser was referenced to an internal 10 MHz standard which has an aging rate of l x l O - 9 per day. The HP synthesiser is now referenced to a 10 MHz frequency obtained from a Loran C frequency standard which is accurate to 1 part in 10 - 1 2 . The remaining experiments, on A1NC, AlBr, Y F and YBr, were performed using this setup. The 10 MHz signal is also used to control the timing of the experiment and to do up- and down-frequency conversions. 3.5 Experiment Sequence To perform an experiment, the cavity must first be tuned into resonance at the excitation frequency, u^w- To do this the microwave synthesiser is swept over a range of frequencies centred about the microwave excitation frequency, VMW- An antenna in the movable mirror is used to couple the microwave energy into the cavity. The signal is detected using an antenna located at the centre of the fixed mirror and the cavity modes are monitored using an oscilloscope. The size of the cavity is changed using a micrometer screw to optimise the transmission of radiation at the microwave excitation frequency. The cavity must be re-tuned every time the excitation frequency is changed to ensure the maximum transmission of energy. The trigger signals for the experiment are generated using a home built pulse genera-tor. Schematic diagrams of the measurement pulse sequence and spectrometer electronics are shown in Figs. 3.2 and 3.3. One F T M W experiment cycle consists of two parts; first, the decay of the cavity without a molecular pulse is measured and then the decay of the cavity and the molecular signal is recorded. The cavity background signal is subtracted Chapter 3. Experimental Technique 37 from the cavity plus molecular decay to remove any residual cavity "ringing" effects. Since the measurement sequences for both parts of the experiment cycle are basically identical, only the second part (with the molecular pulse) will be described in detail. The microwave synthesiser produces a frequency, VMW •+ 20 MHz, which is divided and part is mixed with 20 MHz in the single sideband modulator to generate VMW-The microwave excitation pulse is produced by opening and closing a PIN diode switch (labelled MW-switch in Fig. 3.3). This is coupled into the microwave cavity through the circulator. Here the radiation interacts with a gas sample which has been injected into the cavity. After the microwave pulse is turned off, the molecules emit a coherent signal, — VMW + Au, which is slightly off resonant from the the excitation frequency, UMW, by Au. The molecular signal is coupled out of the cavity via the circulator. A second PIN diode switch (labelled protective MW-switch in Fig 3.3) is used to protect the detection circuit from being damaged by the microwave excitation pulse. The molecular signal is then amplified, down-converted to 20 MHz + Au, using the output of the microwave synthesiser, and then down-converted to 5 MHz + Au, using the 25 MHz signal. 3.6 Data Acquisition The decay signals from each part of the measurement cycle are collected using a transient recorder (plug-in A / D board with maximum sampling rate 25 MHz). Since the molecular signal is being measured at discrete intervals, care must be taken so that the complete spectrum can be recovered from the sampled values. This is accomplished by sampling the function at at least twice the highest frequency desired because two points are needed per wavelength to recover the entire spectrum. Failure to do this results in aliasing, in which higher frequency lines appear at lower incorrect frequencies in the resulting spectrum. In the F T M W experiments, the transient recorder measures frequencies centred about Chapter 3. Experimental Technique valve trigger valve response laser trigger M W pulse - \ V protective MW-switch measurement trigger cavity cavity + molecular signal Figure 3.2: Schematic pulse sequence diagram. Chapter 3. Experimental Technique 39 protective MW-switch \ MW-switch detector oscilloscope x 2 20 MHz A V M W 10 MHz MW-synthesiser vM W + 20 MHz single sideband modulator 10 MHz power divider MW-amplifier VMW + AV MW-mixer 20MHz-Av frequency standard x2.5 25 MHz personal computer RF-amplifier RF-mixer 5 MHz + Av transient recorder 5 MHz bandpass RF-amplifier Figure 3.3: Schematic circuit diagram. Chapter 3. Experimental Technique 40 5 MHz using a sampling interval of 50 ns and aliasing is prevented by using a 5 MHz bandpass filter prior to digitising the signal. 4 K data points are recorded. The molecular decay signal, obtained by subtracting the cavity-only signal from the cavity-plus-molecular signal, is stored in the computer and the results of successive ex-periments are co-added. The time domain signal is transformed into frequency domain by a discrete Fourier transform N-l F(u) = ^ / ( n A f j e - ' ' 2 ^ ' (3.62) n=0 where f(nAt) is the time domain signal consisting of n data points collected with At sampling interval. The molecular signal is displayed as a power spectrum which is ob-tained by summing the squares of the real and imaginary parts of the Fourier transform. Peak positions of strong unblended lines are determined by averaging the frequencies of the two Doppler components obtained from the power spectrum. For closely spaced or overlapped lines, distortions occur in the power spectrum [41] and to determine the line positions accurately a fit must be made to the time domain signal [42]. The digital resolution of the obtained spectrum is limited by the uncertainty principle. The frequency interval between data points in the spectrum is inversely proportional to the acquisition time, thus the resolution of the spectrum can be increased by increasing the measurement time. This can be simulated using a technique called "zero-filling" where zeros are added to the end of the spectrum after measurement to artificially enhance the digital resolution [43]. The accuracy of the lines measured in these experiments is estimated to be better than ± 1 kHz. 3.7 Gas Sample The molecular samples were injected into the microwave cavity through a General Valve Series 9 nozzle, which was operated with a backing pressure of 5-7 bar. The compounds Chapter 3. Experimental Technique 41 studied in this work were prepared by reacting the ablated target metal atoms with precursor molecules, which were present as no more than 0.5% in Ar carrier gas. The details of the laser ablation setup are discussed in Chapter 4. The metal-containing species are formed through collisions in the nozzle. In the supersonic expansion, the translational and rotational energies are converted into mass flow along the axis of ex-pansion; this results in very low rotational temperatures (~1 K). Narrow line widths (~7-10 kHz) are obtained because the near collision-less environment of the jet removes pressure broadening, which is the major contribution to line broadening in traditional microwave experiments. Vibrational cooling of the molecules is less efficient and more dependent on the com-position of the gas sample. This can be seen in the difference in vibrational temperatures estimated for MgS and MgBr. The strongest transition for each molecule (J = 1 — 0 for MgS and N = 1 - 0, J = 3/2 - 1/2, F = 3 - 2 for MgBr) was measured in both the v = 0 and v = 1 vibrational states, taking 1000 averaging cycles for each spectrum. The signal to noise ratios and intensities of these spectra were used to estimate the vibrational temperatures, Tvib- For MgBr, T v j D was estimated to be ~ 320 K, using a gas mixture of 0.1% Br 2 in 6.5 bar Ar. A higher vibrational temperature of ~ 550 K was obtained for the MgS experiments where a mixture of 0.2% OCS in 5.5 bar Ar was used. This range of Tvib values is typical for F T M W laser ablation experiments [44-46]. 3.8 Helmholtz Coils Special care had to be taken when measuring the spectra of MgNC and MgBr because these species are paramagnetic and the rotational spectra would show first order Zee-man splitting due to the earth's magnetic field. This effect could generally be removed using a set of three mutually perpendicular Helmholtz coils [47] to collapse the Zeeman Chapter 3. Experimental Technique 42 pattern down to the expected Doppler components. Fig. 6.1 shows an example transi-tion of MgBr measured with the Zeeman splitting removed using the Helmholtz coils. The transition frequency could then be determined in the usual way by averaging the frequencies of the Doppler components obtained from the power spectrum. However, residual Zeeman splitting was observed in some transitions; this is shown in Fig. 7.1, a transition of MgNC. To measure the centre frequencies of these transitions accurately, the positions of these closely spaced lines were determined by a fit to the time domain signals [42] and the frequencies of the components were averaged. For some transitions, use of the Helmholtz coils produced a very wide Doppler doublet with the Zeeman split-ting incompletely removed (see the upper spectrum of Fig. 6.2). For this line and some others, the most accurate determination of the transition frequency was made by mea-suring the components of the Zeeman pattern obtained without the Helmholtz coils (see lower spectrum of Fig. 6.2). In these cases, the line positions of the closely spaced Zee-man components were determined by fitting to the time domain signals [42] and then the component frequencies were averaged to obtain the line positions. Centre frequencies calculated for the spectra of several lines taken with the Helmholtz coils both on and off indicated that the uncertainty introduced by the averaging method is less than ± 2 kHz. Chapter 4 Development of Laser Ablation Source 4.1 Introduction Laser ablation coupled with supersonic expansion has been shown to be an effective method for producing gas phase metal-containing compounds [48-50]. The main advan-tage of this method is that the setup can be operated at room temperature; the energy needed to vaporize the metal sample is introduced as a pulse of laser radiation. Earlier methods of producing gas phase metal species used high temperature oven systems. The heating apparatus and insulation required to operate one of these systems would be quite difficult to mount into an F T M W spectrometer. In contrast, laser ablation sources have been successfully incorporated into several F T M W spectrometers. They have provided data on various compounds such as: carbides [51], oxides [44,52,53], halides [45,46,54-56], isocyanides [57], and hydroxides, [58,59]. More recently, larger molecules such as boro-hydrides [60], glycine [61] and urea [62] have been investigated in this manner. The most prevalent method of producing laser ablated samples for F T M W spec-troscopy is vaporization of a solid sample of the molecule of interest. A second method, ablation of the target metal followed by reaction with a gas phase precursor, has been used to a lesser extent. The limitation of the vapourisation method is that it is often dif-ficult to produce a rod of the desired compound. The ablate and react method provides 43 Chapter 4. Development of Laser Ablation Source 44 more flexibility in producing transient species. A complete list of the F T M W studies of species produced by each method prior to the present work is given in Table 4.1. Almost all the laser ablation-FTMW spectrometers used to measure these spectra operate in the "perpendicular" configuration, with the molecular beam travelling per-pendicular to the microwave cavity axis [44,45,62]. This configuration has the advantage that the nozzle is completely independent of other equipment, and variations in noz-zle design can be easily implemented. Yet with most spectrometers, and especially the one used for these experiments, this arrangement has reduced resolution and sensitivity compared with that obtained with the "parallel" configuration, in which the nozzle is mounted in one of the mirrors and the molecular beam travels parallel to the cavity axis [39,40]. The location of the nozzle in the perpendicular and parallel configurations is shown in Fig. 3.1. In the earlier laser ablation studies from this laboratory, the parallel configuration was used [46,54,56]. In this source, the metal rod was kept in a fixed position to simplify construction. However, other work has suggested that rotating the rod provides better signal strength and stability over a series of experiments [63]. Although it was somewhat awkward to design, a laser ablation system has been constructed which is mounted in the mirror and incorporates a rotating rod. 4.2 Ablat ion Source Design The nozzle cap design was based on the system of Barnes et al. [64]. The laser ablation source consists of a stainless steel nozzle cap which holds a metal rod 5 mm from the orifice of a General Valve Series 9 pulsed nozzle. A schematic diagram of the nozzle cap and its location in the mirror is shown in Figure 4.1. In order to operate in the parallel configuration, the laser ablation source had to be mounted in the fixed mirror. This was Chapter 4. Development of Laser Ablation Source 45 done by recessing the back of the fixed mirror to hold the nozzle cap and other equipment. The gas channel, in the nozzle cap, begins at 1.5 mm in diameter at the nozzle orifice and increases to 5 mm at the point of ablation. The total length is 2 cm and the outlet of the nozzle cap is 2.5 mm from the front surface of the fixed mirror. The last 5 mm of the gas channel is an inter-changeable brass nozzle cap extension. This was included in the design so that the expansion conditions could be varied. Two parameters were varied to obtain the final design for the nozzle cap, the exit conditions and the gas channel diameter. In the preliminary design, a cone shaped nozzle cap extension, with the inlet larger than the outlet, was used in an attempt to enhance cooling of the gas sample. This, however, proved only to reduce signal strength. A straight nozzle cap extension provided the strongest signals; the signal to noise ratio improved by an order of magnitude when using the straight extension instead of the cone shaped extension. The nozzle cap gas channel diameter, initially 1.5 mm, was changed incrementally. It was found that signal strength increased as the diameter of the channel was increased. The gas channel diameter is limited to 5 mm by the size of hole which can be drilled in the mirror without affecting spectrometer sensitivity. A 5 mm diameter rod of the target metal is supported in the nozzle cap and is translated and rotated by a motorised actuator (Oriel Motor Mike). A diagram of the rotating rod setup is shown in Fig. 4.2. As had been anticipated, it was found that rotating the rod did maintain signal strength over a series of experiments [63]. When the rod was not rotated, the signal strength was found to decrease by up to 50% over 2000 laser pulses. A side view of the fixed mirror with the nozzle cap and rotating rod assembly mounted is shown in Fig. 4.3. Chapter 4. Development of Laser Ablation Source 46 Figure 4.1: Top view of laser ablation nozzle cap and part of fixed aluminium mirror. The nozzle cap is mounted slightly off centre in the mirror. Shaded part at the end of the gas channel is the nozzle cap extension; see Sec. 4.2 for details. The motorized actuator (not shown in diagram) is located below the plane of the paper. Chapter 4. Development of Laser Ablation Source 47 Nd:YAG 532 nm Target Metal Rod Stainless steel nozzle cap Flexible coupling Motorized Actuator Figure 4.2: View of laser ablation nozzle cap and motorized actuator. The metal rod is coupled to the motorized actuator with a length of flexible rubber tubing. Figure 4.3: Side view of fixed mirror showing location of nozzle cap and motorized actuator. The dashed vertical line shows the recesses needed to mount the laser ablation setup in the back of the mirror. Chapter 4. Development of Laser Ablation Source 49 4.3 Experimental Details In the experiments described in this thesis, the rod was ablated using the frequency doubled output of a Q-switched Nd:YAG laser (Continuum Surelite 1-10). The second harmonic frequency was initially used because it is in the visible region and therefore it was easier to align the system. Strong signals were obtained for all the species studied, so no attempt was made to use other laser frequencies. The laser energy was directed into the vacuum chamber using a set of mirrors. The beam was focused to a spot less than 1 mm in diameter at the point of ablation using a lens located just outside the chamber. Fig. 4.4 shows a schematic diagram of the laser coupling system. The laser energy enters the nozzle cap through a channel which is at right angles to the gas expansion channel (for detail see Fig. 4.1). The laser power was not monitored during the experiment but was estimated to be ~ 5-10 mJ/pulse. The timing of the laser pulse with respect to the nozzle opening was crucial. The pulse sequence for the experiment is shown in Fig. 3.2. The optimum delay between the nozzle being fully open and the laser pulse was ~ 300-350 /is. 4.4 Testing of Laser Ablation Source The performance of the laser ablation setup was evaluated by measuring the spectra of several molecules investigated with the fixed rod laser ablation setup. Preliminary tests were done using AgCl and CuCl [54]; the spectra obtained with the rotating rod setup had signal to noise ratios which were about five times those obtained with the fixed rod system. The final molecule measured with the fixed rod system was yttrium monochloride [56]. The transitions observed in this work were reported as being "frustratingly weak". Fig. 4.5 compares the results obtained for the strongest hyperfine components of the J = 2 — 1 Chapter 4. Development of Laser Ablation Source 50 Figure 4.4: Diagram showing method of coupling laser energy into the spectrometer cavity. Chapter 4. Development of Laser Ablation Source 51 transition of Y 3 5 C1 using the fixed rod (upper spectrum) and the rotating rod (lower spectrum) systems. The magnitude of the Doppler splitting differs between the two spectra because different backing gases were used in the expansion. It can be seen that this rotating rod laser ablation setup marks an improvement in the F T M W spectroscopy of metal-containing species. The final test of the rotating rod laser ablation setup was the measurement of magne-sium sulfide. These experiments, which are described in Chapter 5, are the first F T M W measurement of a metal sulfide produced by reacting ablated metal with a source of sul-fur; there had been no previous F T M W measurements of MgS or other metal sulfides. Several species of low natural abundance were observed. This study demonstrates the utility and sensitivity of the rotating rod laser ablation setup. Chapter 4. Development of Laser Ablation Source 52 Figure 4.5: Comparison of spectra taken of the overlapped hyperfine components F = 5/2 - 3/2, 7/2 - 5/2 of the J = 2 - 1 transition of Y 3 5 C1. Both spectra were recorded with 320 averaging cycles. 4 K data points were recorded and the spectra are displayed as 8 K transformations. The upper and lower spectra were recorded using the fixed rod system and the rotating rod setups, respectively. The excitation frequencies used to obtain the upper and lower spectra were 14160.300 MHz and 14160.525 MHz, respectively. Chapter 4. Development of Laser Ablation Source Table 4.1: F T M W Spectroscopy of Molecules Produced by Laser Ablation. Vapourization of Sample: Carbides SiC 2 Suenram et al. 1989 [51] Oxides Y O , LaO, ZrO, HfO Suenram et al. 1990 [44] V O , NbO Suenram et al. 1991 [52] SrO, BaO Blom et al. 1992 [53] Halides CuCl, CuBr Low et al. 1993 [55] Hydroxides NaOH, K O H , RbOH, CsOH Kawashima et al. 1996 [58] InOH Lakin et al. 1997 [59] Larger K B H 4 , NaBH 4 Kawashima et al. 1995 [60] glycine Lovas et al. 1995 [61] urea Kretschmer et al. 1996 [62] Ablation and Reaction to form Sample: Halides AgCl, A1C1, CuCl Hensel et al. 1993 [54] MgCl Ohshima and Endo 1993 [45] YC1 Hensel and Gerry 1994 [56] InF, InCl, InBr Hensel and Gerry 1997 [46] Isocyanides CaNC Scurlock et al. 1994 [57] Chapter 5 F T M W Spectroscopy of MgS 5.1 Introduction Significant spectroscopic interest in many compounds containing refractory metals has arisen because of the observed depletion of these metals in interstellar clouds [65,66]. Most of the depleted elements are contained in dust grains, but gas phase molecules containing metals such as Mg should be detectable [67]. By searching for refractory metal compounds in space, a greater understanding of their chemistry in both the gas phase and on dust grains can be obtained [6,67]. Thus far the only magnesium bearing molecule observed has been MgNC, found via its millimetre wave spectrum in IRC +10216 [68,69]. Hence there is particular interest in other simple Mg containing compounds. One of these, MgS, has been the target of several astrophysical searches. Features in the far infrared spectra of several carbon-rich stars have been attributed to the vibration of MgS on dust grains [70]. This assignment was based on laboratory far infrared spec-troscopy of powdered MgS samples prepared in polyethylene [71]. Further laboratory work in the optical region [72] confirmed this assignment but suggested that FeS and mixed MgFe sulfides might also contribute to this feature. The first radio astronomical search for gaseous MgS was reported by Takano et al. as part of a laboratory millimetre wave study [73]. This search proved unsuccessful. This molecule was also part of a larger 54 Chapter 5. FTMW Spectroscopy of MgS 55 search for refractory compounds carried out by Turner [67]; again it was not found. Even with this interest from the astrophysical community, only three high resolution gas phase spectroscopic studies have been made of MgS. The initial vibrational analysis of the B 1 S + — X 1 S + optical transition of the main isotopomer, 2 4 M g 3 2 S , was done by Wilhelm [74] in 1932. This work was extended by Marcano and Barrow [75], who measured the rotationally resolved absorption spectrum of the same transition. They determined an equilibrium bond length and also measured the isotopic shifts of the other two Mg 3 2 S isotopomers, 2 5 M g 3 2 S and 2 6 M g 3 2 S . The most recent study was that of the millimetre wave spectrum of the main isotopomer by Takano et al. , mentioned above [73]. In all of these studies, a furnace system was used to produce MgS by reaction of magnesium and sulfur in the gas phase. This chapter presents the low frequency pure rotational spectrum of MgS. This work was undertaken as a test of the laser ablation source. Of the four isotopomers studied, 2 4 M g 3 4 S has been observed for the first time. Nuclear hyperfine structure due to the 2 5 M g nucleus has been resolved and its quadrupole coupling constant determined. This is the first measurement of a metal quadrupole coupling constant for an alkaline earth metal sulfide molecule. The equilibrium geometry has been obtained by two methods and the results have been compared with those of previous studies. 5.2 Experimental Details Magnesium sulfide was produced by reacting ablated magnesium metal (rod from A. D. MacKay, 99.9%) with OCS present as 0.2 — 0.5% in Ar carrier gas. Magnesium sulfide was produced in sufficient quantity to observe the 2 4 M g 3 2 S isotopomer J = 1 — 0 transition in 5 cycles. Since this result was satisfactory for testing purposes, no attempt was made to use any other sulfur-containing compound in the gas mixture. Chapter 5. FTMW Spectroscopy of MgS 56 5.3 O b s e r v e d S p e c t r a a n d A n a l y s e s The J = 1 — 0 pure rotational transition near 16 GHz was the only transition of MgS available in the frequency range of the spectrometer. It was measured for 4 isotopic species in natural abundance: those for all 3 isotopes of Mg with 3 2 S, specifically 2 4 M g 3 2 S , 2 5 M g 3 2 S , and 2 6 M g 3 2 S , and one isotopomer containing 3 4 S, namely 2 4 M g 3 4 S . The natural abundances of these species range from 74.7% for the main isotopomer, 2 4 M g 3 2 S , to 3.3% for 2 4 M g 3 4 S . The transition frequency for the main isotopomer was predicted using the millimetre wave constants [73]; the transition was found within 20 kHz of the calculated frequency. This microwave transition was fit together with the millimetre wave data, using Pickett's nonlinear least squares fitting program, S P F I T [76], to obtain the rotational constant, Bo, and centrifugal distortion constant, Do- A relative weighting of 900:1 was given to the microwave line with respect to the millimetre wave data, to take account of the estimated experimental accuracies. The transition frequencies are listed in Table 5.1. The constants derived from the fit are listed in Table 5.2 under the heading Combined Fit. Also listed are the rotational constants obtained from the millimetre wave study of Takano et al. [73]. As was expected, there is not a significant change in the B0 and D0 values with the addition of the microwave transition. The vibrational temperature was sufficiently high that the J = 1 — 0 transition could be measured for the main isotopomer in the v = 1 state. The frequency was predicted using the rotational constants from Marcano and Barrow [75]. The transition was found within 400 kHz of the prediction. The observed frequency is listed in Table 5.1. Bo and B\ were calculated from the v = 0 and v = 1 transition frequencies by assuming that D 0 and Di were equal to D0 from the combined fit described above. Use of Di constant scaled according to the values of Marcano and Barrow [75] introduced no significant Chapter 5. FTMW Spectroscopy of MgS 57 variation in Bx. The Be and cte constants were then calculated directly from B0 and B using Eq. (2.16), which is shown here for reference This expression was truncated following the ae term. The constants obtained are listed in Table 5.2 under the heading Direct Calculation. Fig. 5.1 shows the two measured J = 1 - 0 transitions for 2 4 M g 3 2 S . The main isotopomer B0 value was used to predict the transition frequencies for 2 6 M g 3 2 S and 2 4 M g 3 4 S by scaling Bo using the reduced masses. Again the transitions were found very close to the predicted frequencies (within 1 MHz). Since only one transition was available for each of the minor isotopomers, rotational constants were calculated by holding Do fixed at a value obtained by scaling the main isotopomer Do value inversely as the square of the reduced mass. The transition frequencies and derived constants are listed in Table 5.3. Searching for 2 5 M g 3 2 S was not quite so straightforward as it had been for the other isotopomers. Since the 2 5 M g nucleus has a spin, / , of | , the transition was split into three components, with consequently lower signal intensity. In addition, an initial estimate for the quadrupole coupling constant turned out to be much larger than the value eventually found, so the search region was larger than necessary. The B0 value was predicted by the same procedure used for the other minor isotopomers. All the nuclear hyperfine structure was observed within one cavity width. The transition was quite weak, and a very large number of averaging cycles was needed to see it. The spectrum shown in Fig. 5.2 was the result of 2 | hours of signal accumulation. The frequencies of the three hyperfine components are listed in Table 5.4. These were fit using the S P F I T program [76] to determine the B0 rotational constant and eQq( 2 5Mg), which are listed in Table 5.5. Again, the DQ constant was held fixed at the value scaled from that of Bv = B e - a e [ v + - + 7 e ( u + r ) + ••• Chapter 5. FTMW Spectroscopy of MgS 58 v = 0 i 1 15908.420 MHz 15908.820 MHz Figure 5.1: The J = 1 - 0 rotational transition of 2 4 M g 3 2 S was measured in both the v = 0 and v = 1 vibrational states. Each spectrum was measured with 1000 averaging cycles. The microwave excitation frequencies were 16013.820 MHz and 15908.620 MHz for the v = 0 and v = 1 transitions respectively. 4 K data points were measured for each spectrum with a 50 ns sampling interval and each power spectrum is displayed as an 4 K transformation. Chapter 5. FTMW Spectroscopy of MgS 59 2 4 M g 3 2 S by the inverse square of the reduced mass. 5.4 Discussion 5.4.1 Equi l ibrium Bond Distance Sufficient data were available that both isotopic substitution and the vibrational data could be used to determine the equilibrium bond length, re. Since isotopic data were available for both atoms, a complete substitution structure (rs) could be calculated for the main isotopomer, 2 4 M g 3 2 S . This method is described in detail in Sec. 2.4. The distance of an atom from the centre of mass, Z{, is given by Eq (2.62) The calculated values z,-, for zMg and zs, and the resulting rs value with estimated uncertainties, are given in Table 5.6. For a diatomic molecule, the re value can be evaluated from Eq. (2.61): using the r0 value determined from B0 for 2 4 M g 3 2 S . This re value is listed in Table 5.7 as re (Subst.). A second value for r e , calculated directly from Be, is also listed in Table 5.7 as r e (Vibr.). The uncertainty given reflects those of the rotational constants, the fundamental constants and the atomic masses. It takes no account of electronic effects: the value of r e in the Born-Oppenheimer approximation can be expected to differ by ~ 10 - 5 A, and possibly more [33]. The uncertainty in calculating re is discussed further in Sees. 2.4 and 6.5.1. For comparison, Table 5.7 also contains the re value determined by Marcano and = 2rs - r0 Chapter 5. FTMW Spectroscopy of MgS 60 F'-F"-5/2 - 5/2 7/2-5/2 r 3/2-5/2 , i 1 15647.800 MHz 15648.000 MHz Figure 5.2: The J = 1 — 0 transition of 2 5 M g 3 2 S showing hyperfine structure due to 2 5 M g nuclear quadrupole coupling. The excitation frequency was 15 647.80 MHz. The corresponding time domain signal consists of 4K points and was recorded with 10 000 averaging cycles. The power spectrum was obtained after an 8 K transformation. Line positions of the labelled transitions and the constants obtained are listed in Tables 5.4 and 5.5, respectively. Chapter 5. FTMW Spectroscopy of MgS 61 Barrow in their optical study [75]; they gave no estimate of the uncertainty. The two new values agree with that of the optical study. 5.4.2 Nuclear Quadrupole Hyperfine Structure The nuclear quadrupole coupling constant, eQq^Mg), is the first metal nuclear quadrupole coupling constant measured for an alkaline earth sulfide molecule. Therefore comparisons cannot be made to similar molecules. However, it can be used to gain insight into the electron charge distribution at the magnesium nucleus. In terms of simple bonding theo-ries, the MgS bond is ionic, with the molecule containing M g 2 + and S2~ ions. At infinite separation, both ions are spherically symmetric, making any nuclear quadrupole coupling constants zero. Since M g 2 + has the same electron configuration as Ne (ls 22s 22p 6), the non-zero 2 5 M g coupling constant could be considered as due to a small "hole" in the 2p configuration, resulting from a 3s «— 2p excitation induced by the proximity of the S 2 _ ion. The coupling constant can thus be interpreted in terms of unbalanced p-electrons using the Townes-Dailey model [17]. This was discussed in Sec. 2.3.1 and Eq. (2.43) is reprinted here substituting in the appropriate nuclear quadrupole coupling constants for 2 5 MgS: ^ ( 2 5 M g ) = (n, - e g g 2 1 0 ( 2 5 M g ) Although a value for eQq2io(25Mg) is unavailable, that of eQq310(25Mg) is known: —16 MHz [2]. It is expected that e(5<?2io(25Mg) will be a larger negative value since these constants are proportional to ( r - 3 ) , where r is the distance from the nucleus to an electron in the orbital in question. From the expression above it can be seen that the term relating the quadrupole coupling constants is very small and negative. This suggests that the electron density in the 2px and 2py orbitals is slightly greater than that in the 2pz orbital, making Chapter 5. FTMW Spectroscopy of MgS 62 the electron cloud around the Mg nucleus slightly oblate in shape. 5.5 Conclusion Measurement of the spectra of four isotopomers of MgS, including species of low abun-dance, has demonstrated the utility and sensitivity of the new laser ablation system. These experiments represent the first time MgS has been detected by F T M W spec-troscopy. An equilibrium bond length has been obtained for MgS, along with the 2 5 M g quadrupole coupling constant. Chapter 5. FTMW Spectroscopy of MgS 63 Table 5.1: Observed frequencies for 2 4 M g 3 2 S in MHz. Transition Observed Frequency" Obs.-Calc.6 v' J' v" J" (MHz) (kHz) 0 1 0 0 16 013.8215 -0.2 1 1 1 0 15 908.6190 0 14 0 13 224103.178 26 0 16 0 15 256086.116 -1 0 17 0 16 272072.920 -12 0 18 0 17 288056.376 3 0 19 0 18 304036.237 -1 0 22 0 21 351952.415 12 0 23 0 22 367915.973 -12 a J = 1 — 0 data from present work. Other data taken from millimeter wave study [73]. 6 Observed minus calculated frequencies from combined fit of all v = 0 transitions. See Sec. 5.3 for details. Chapter 5. FTMW Spectroscopy of MgS 64 Table 5.2: Molecular constants calculated for 2 4 M g 3 2 S in MHz. Parameter Combined Fit 0 ' 6 Direct Calculation0'"* Lit. 5 B0 Br Do Be a* 8006.92739(45) 0.00827291(66) 8006.9273(5) 7954.3260(5) [0.008273e] [0.0082736] 8033.2280(6)' 52.6013(7)/ 8006.9278(15) 0.0082744(19) a Fit combining present results and millimeter wave data [73]. 6 One standard deviation in parentheses, in units of least significant digit. 0 Bo and B\ calculated from measured J = 1 — 0 frequencies. d Estimated errors reflecting measurement uncertainty given in parentheses, in units of least significant digit. e Centrifugal distortion constants, D0 and Di, were held fixed at D0 value determined in combined fit; for detail see Sec. 5.3. f Be and ae calculated from Bo and Bx. 9 From millimeter wave study of Takano et al. [73]. Three standard deviations in parentheses, in units of least significant digit. Chapter 5. FTMW Spectroscopy of MgS 65 Table 5.3: Frequencies for the J = 1 — 0 transition of isotopomers of MgS and derived BQ values in MHz. Isotopomer Observed Frequency B 0 A D0 2 6 M g 3 2 S 15311.4750 7655.7526 [0.007563] 2 4 M g 3 4 S 15611.1768 7805.6041 [0.007863] a Calculated by holding centrifugal distortion constant fixed at value scaled from that calculated for 2 4 M g 3 2 S in combined fit. Chapter 5. FTMW Spectroscopy of MgS 66 Table 5.4: Frequencies of measured hyperfine components of 2 5 M g 3 2 S in MHz. Transition Observed Frequency" J' F' J" F" 1 3/2 0 5/2 15647.8878(21) 1 7/2 0 5/2 15647.9053(31) 1 5/2 0 5/2 15647.9300(09) a Observed minus calculated frequencies in parentheses, in units of the least significant digit. Chapter 5. FTMW Spectroscopy of MgS 67 Table 5.5: Molecular constants for 2 5 M g 3 2 S in MHz. Parameter Value" B0 7823.9703(6) Do [0.0079006] eQq 0.1366(92) v0 15647.9090c a One standard deviation in parentheses, in units of the least significant digit. 6 Centrifugal distortion constant held fixed in fit at value scaled from that calculated for 2 4 M g 3 2 S in combined fit. c Hypothetical unsplit frequency calculated from B0 and D0 values. Chapter 5. FTMW Spectroscopy of MgS 68 Table 5.6: Substitution structure results for 2 4 M g 3 2 S in A a . ZMg ZS ^ 2 4 M g 3 2 S 1.225213(19) 0.919118(23) 2.144331(30) a Estimated uncertainties in parentheses, in units of least significant digit, reflect the uncertainties in the rotational constants, the fundamental constants and the atomic masses only. Chapter 5. FTMW Spectroscopy of MgS 69 Table 5.7: Equilibrium bond length calculated for 2 4 M g 3 2 S in A A . Subst.6 Vibr. c Lit . d 2 4 M g 3 2 S 2.142573(60) 2.1425728(10) 2.1425 a Estimated uncertainties in parentheses, in units of least significant digit, reflect the uncertainties in the rotational constants, the fundamental constants and the atomic masses only. Calculated from substitution data using r 0 = 2.1460889(10)A. c Calculated from vibrational data. d From optical study by Marcano and Barrow [75]. Chapter 6 Pure Rotational Spectra of M g B r and A l B r 6.1 Introduction Aluminium and magnesium are among the most abundant metals in the Earth's crust and both are quite reactive. The monobromide compounds of these metals differ in that MgBr is paramagnetic ( 2 E + ground electronic state) and AlBr is diamagnetic. Their electronic structures can be investigated through their hyperfine constants. The ionic character of the metal-halogen bond can be calculated from the halogen nuclear quadrupole coupling constant. The unpaired electron spin density in the alkaline earth monohalides (such as MgBr) can be calculated from the electron spin-nuclear spin coupling constants. These hyperfine interactions in the pure rotational spectra of two metal monohalides, magne-sium monobromide and aluminium monobromide, will be used to examine bonding in the species. Hyperfine structures in the spectra of only two magnesium monohalides, MgF and MgCl, have been investigated in any detail. Electron spin resonance and millimetre wave spectroscopy have been used to observe the spectra of MgF [77-79], and Fourier trans-form microwave (FTMW) and millimetre wave spectroscopy have been applied to the investigation of MgCl [45,80]. These methods have provided precise hyperfine parame-ters which have been used to compare bonding trends within the molecules. Though MgF 70 Chapter 6. Pure Rotational Spectra of MgBr and AlBr 71 and MgCl are quite ionic, they appear to have greater covalent character than the other alkaline earth monofluorides and monochlorides [79]. The present study was undertaken to determine whether magnesium monobromide follows this trend. The spectroscopy of magnesium monobromide has been of interest since 1906, when Olmsted photographed the band spectra of several alkaline earth halides, including MgBr, in emission [81]. This work was extended, in 1928, by Walters and Barratt, who made an absorption study of the same region [82]. The first vibrational analysis was done of the A2U — X2E+ transition by Morgan in 1936 [83]. In this study, the band heads due to the two isotopes of bromine could not be completely resolved. Several other studies have examined the A — X transition [84,85] and transitions from higher excited electronic states to the ground state [86,87]. MgBr has been included in larger theoretical studies of spin-orbit splittings [88] and Franck-Condon factors [89]. Recently, both theoretical and experimental studies have been made of predissociation in the A2H state [90,91]. There has however been only one study of a rotationally resolved spectrum. In 1969, Patel and Patel did a partial rotational analysis of the A 2II — X2T,+ (0-0) band [92]. They, too, did not resolve any isotope effects. There has been no previous microwave spectroscopic study of MgBr. Aluminium monobromide provides an interesting comparison for magnesium mono-bromide, as both metals are in the same row of the periodic table. Microwave and millime-tre wave spectroscopy have been used to investigate the hyperfine structure of A1F [93-96] and A1C1 [54,93,97,98]. For AlBr, millimetre wave spectra have been recorded for both isotopomers in several vibrational states (v = 0 — v = 5) [97]. Nuclear quadrupole hy-perfine structure has been measured only for the J = 1 — 0 transition of A l 7 9 B r by Hoeft et al. [98]. The measurements described in this chapter were made to provide further information on the hyperfine structure. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 72 The electronic spectroscopy of aluminium monobromide has been examined in some detail. The initial investigations were made in the 1930's by Crawford and Ffolliott [99] and by Miescher [100,101]. From these studies two electronic transitions, A 1II — X 1 £ + and a 3II — X 1 E + , were identified. The vibrational analyses of the A *n — X 1 E + transition were made by both Howell [102] and Mahanti [103] in 1935. Jennergren made the first rotational analysis of this transition in 1948 [104,105]. In further studies, predissociation in the A lYl state was identified [106]. This was investigated in detail by grating spectroscopy [107-109], pulsed dye laser spectroscopy [110] and Fourier transform spectroscopy [111]. Langhoff et al. [112] calculated spectroscopic constants for the A 1U and X states of AlBr as part of their theoretical study of the aluminium monohalides. Vibrational analysis of the a 3U — X 1 E + electronic transition was made by Sharma [113] in 1951. Lakshminarayana and Haranath [114] carried out the first rotational analysis of this transition. Their work was extended by Griffith and Mathews [108] and by Bredohl et al. [115]. Bredohl et al. also identified a third electronic transition, the b 3H — X 1 £ + system, and did a vibrational analysis. More recently, Uehara et al. used a Fourier transform infrared spectrometer to measure the ro-vibrational spectrum of aluminium bromide in emission [116]. They combined their results with those of the millimetre wave study [97] to determine Dunham potential coefficients. This chapter describes the pure rotational spectra of MgBr and AlBr in their ground and first excited vibrational states. This is the first complete rotational analysis of mag-nesium monobromide. The rotational, fine and hyperfine parameters of both isotopomers of MgBr, in its 2 E + ground electronic state, have been determined. These have been used to evaluate the equilibrium bond distance and to draw conclusions about unpaired elec-tron density in the molecule. The first measurement of the hyperfine spectrum of A l 8 1 B r has been made. Nuclear quadrupole, spin-rotation and spin-spin coupling constants have Chapter 6. Pure Rotational Spectra of MgBr and AlBr 73 been determined for both isotopomers of aluminium monobromide. The hyperfine pa-rameters of MgBr and AlBr have also been used to investigate the ionic character of these species and to make comparisons with other metal monohalides. 6.2 Experimental Details MgBr and AlBr were produced by reaction of Br 2 , which was present as 0.05 — 0.2% in Ar carrier gas, with ablated Mg(rod from Goodfellow 99.9%) or ablated Al(rod from Alfa A E S A R 99.999%), respectively. The strongest transitions could be seen easily with fewer than 5 averaging cycles. As was found in the F T M W investigation of A1C1 [54], a very low concentration of the halogen precursor, Br 2 , had to be used to promote formation of the metal monohalide rather than di- and trihalides. When measuring the spectrum of the free radical MgBr, a set of three mutually perpendicular Helmholtz coils was used to collapse the Zeeman splitting due to the earth's magnetic field. Use of these coils is discussed in Section 3.8. 6.3 Assignment of Spectra 6.3.1 M g B r The search for the pure rotational transitions of MgBr presented a challenge since there were no precise rotational constants to provide search parameters. The one rotational constant available was from the partial analysis of the A — X band [92]; it was not well determined and was for an unspecified isotopomer. Also the spectrum of MgBr is complicated by the fact that the two main isotopomers have almost equal natural abundance (40.04% and 38.95% for 2 4 M g 7 9 B r and 2 4 M g 8 1 B r , respectively) and is further complicated by hyperfine structure, since each isotope of bromine has a nuclear spin of I — | . Since there have been no theoretical studies of the spectroscopic properties of Chapter 6. Pure Rotational Spectra of MgBr and AlBr 74 MgBr, estimates also had to be made for the fine structure and hyperfine parameters. This problem was approached by making a series of predictions by examining trends within the measured spectroscopic parameters of several magnesium and calcium mono-halides. Then the predicted N = 1 — 0 spectra were compared and a wide initial search range (~ 200 MHz) was established. Within this range, 10 transitions were found. The search was continued and 28 lines in total were measured for the N = I — 0 transi-tion. These lines belong to four overlapped groups, one for each of the two isotopomers, 2 4 M g 7 9 B r and 2 4 M g 8 1 B r , in each of the v = 0 and v = 1 vibrational states. The initial assignment was made using pattern recognition and then confirmed using the observed Zeeman patterns and the prediction of the TV = 2 — 1 transition. In the end, a rich hy-perfine spectrum comprised of 50 components was measured between 9.4 and 20.1 GHz. Only the two lowest N rotational transitions were available for study in the frequency range of the spectrometer. Example spectra are shown in Figs. 6.1 and 6.2. Figure 6.3 shows all observed v = 0 and v = 1 components of the N = 1 — 0 transition for Mg 7 9 Br and Mg 8 1 Br. The observed transitions for the 2 4 M g 7 9 B r and 2 4 M g 8 1 B r species are listed in Tables 6.1 and 6.2, respectively. Spectra for species containing the minor isotopes of magnesium, 2 5 M g and 2 6 M g , were not sought. 6.3.2 A l B r In contrast to MgBr, the initial search range for AlBr was quite narrow because the rotational and centrifugal distortion constants of both isotopomers were known from the millimetre wave study [97]. However as was found for MgBr, only the two lowest J rotational transitions of AlBr were available in the frequency range of the spectrome-ter. Nuclear quadrupole interactions due to both Br(7 = | for both isotopes, 7 9 B r and 8 1 B r ) and 2 7A1(7 = |) were included in the prediction using the 2 7 A1 and 7 9 B r nuclear Chapter 6. Pure Rotational Spectra of MgBr and AlBr 75 Figure 6.1: The N — 1-0, J — 3/2-1/2, F = 2 -2 transition of 2 4 M g 8 1 B r was measured using a set of mutually perpendicular Helmholtz coils to remove the effects of the earth's magnetic field. This spectrum was obtained with 50 averaging cycles. The microwave excitation frequency was 9960.710 MHz. 4 K data points were measured with a 50 ns sampling interval and the power spectrum is displayed as an 8 K transformation. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 76 I 19966.202 MHz 1 19967.202 MHz 79 kHz I 19966.202 MHz 1 19967.202 MHz Figure 6.2: Two spectra of the iV = 2 — 1, «/ = 5/2 - 3/2, F = 4 - 3 transition of 2 4 M g 7 9 B r . The upper spectrum was measured with 400 averaging cycles and using the Helmholtz coils to cancel the earth's magnetic field. The lower spectrum was obtained with 1000 averaging cycles. The Helmholtz coils were not used for this measurement and thus the first order Zeeman splitting due to the earth's magnetic field was observed. For both spectra, the excitation frequency was 19966.702 MHz, 4 K data points were recorded and the power spectra shown here were obtained with an 8 K transformation. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 77 I till 24TV IT 79 M g ' y B r v=0 2 4 M g 8 1 B r v=0 2 4 M g 7 9 B r v=l 2 4 M g 8 1 B r v=l 9439.67 M H z I 10180.14 M H z Figure 6.3: Stick spectrum showing all observed v — 0 and v = 1 hyperfine components of the N = 1 — 0 rotational transition for Mg 7 9 Br and Mg 8 1 Br. This composite was produced by using the measured transition frequencies along with the predicted transition intensities. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 78 quadrupole coupling constants reported for A l 7 9 B r by Hoeft et al. [98]. The J = 1 — 0 transition of A l 7 9 B r was measured first. Seventeen hyperfine com-ponents were observed and were assigned using the coupling scheme J + Isr = F i ; F i + IAI = F . An overview spectrum of the J = 1 — 0 transition, shown in Fig. 6.4, shows the relative magnitude of the Br and Al splittings: the Br quadrupole coupling splits the transition into three lines which are further split by the A l quadrupole cou-pling. A preliminary fit was made holding D0 fixed at the millimetre wave value to obtain improved 2 7 A l and 7 9 B r nuclear quadrupole coupling constants and to determine the Al and 7 9 B r nuclear spin-rotation constants. The improved value of eQq(79Bv) was scaled, by the ratio of nuclear quadrupole moments, to obtain a value for eQq(81Br) which was used to predict the J = 1 — 0 transition of A l 8 1 B r . Sixteen hyperfine components were measured for this isotopomer. A further 13 lines were measured for each isotopomer for the J = 2 — 1 transition. The measured ground vibrational state transitions of A l 7 9 B r and A l 8 1 B r are listed in Tables 6.3 and 6.4, respectively. A method similar to that used for the v — 0 transitions was used to predict and measure the hyperfine components of the J = 1 — 0 and J = 2 — 1 transitions in the v = 1 excited vibrational state for A l 7 9 B r and A l 8 1 B r . The lines of A l 7 9 B r and A l 8 1 B r measured in the v — 1 vibrational state are also listed in Tables 6.3 and 6.4, respectively. 6.4 Analyses The transitions for each vibrational state of each isotopomer of MgBr were fit separately using Pickett's exact fitting program, S P F I T [76]. This program employs a Hund's case (b/3j) coupling scheme; N -f S = J; J + Ier = F . The fit determined the rotational, centrifugal distortion and fine structure constants (B, D, and 7 , respectively) as well as several hyperfine parameters for the bromine nucleus (the Fermi-contact constant, bp, the Chapter 6. Pure Rotational Spectra of MgBr and AlBr 79 Fj = 5/2 - 3/2 F2 = 1/2 - 3/2 F, = 3/2 - 3/2 I 9495.0 MHz 9540.0 MHz Figure 6.4: Composite spectrum of the J = 1 — 0 rotational transition of A l 7 9 B r . The transition is split into three groups by the 7 9 B r nucleus and the further splitting within each group is due to the 2 7A1 nucleus. The results of twelve different microwave exper-iments were used to produce this composite. The individual power spectra were scaled to reproduce predicted intensities. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 80 dipole-dipole interaction constant, c, the nuclear quadrupole coupling constant, eQq(Br) and the nuclear spin-rotation constant, C/(Br)). All parameters determined are listed in Table 6.5. It is difficult to compare the rotational constants obtained in this study with that obtained by Patel and Patel [4932(15) MHz] since their study could not separate transitions due to the different isotopomers. For AlBr, the transitions for each isotopomer in each vibrational state were fit sep-arately using Pickett's exact fitting program S P F I T to determine the rotational and centrifugal distortion constants, B and D, along with the nuclear quadrupole coupling constants, eQq, and nuclear spin-rotation constants, Cj for both the aluminium and bromine nuclei and the nuclear spin-spin constant, ctAi-Br- The lines observed for the overlapped hyperfine components of the J = 1 — 0 transition were fit as blended lines using predicted intensities as weighting factors. The determined constants are listed in Table 6.6. The calculated rotational and centrifugal distortion constants agree quite well, within about one standard deviation, with those determined by Wyse and Gordy [97]. Also the nuclear quadrupole coupling constants, eQq(27A\) and eQq(79Br) determined for the A l 7 9 B r isotopomer are within one standard deviation of those determined by Hoeft et al. [98]. However, the nuclear quadrupole coupling constants determined in this study are two orders of magnitude more precise than those of Hoeft et al.. The ratios of the fine and hyperfine parameters found for 2 4 M g 7 9 B r and 2 4 M g 8 1 B r and of the hyperfine parameters determined for A l 7 9 B r and A l 8 1 B r should be equal to the ratios of certain nuclear and molecular properties. The 7 parameter ratio is equal to the inverse ratio of the reduced masses. The ratios of the hyperfine parameters are equal to the ratios of certain nuclear moments, specifically, the nuclear magnetic moments for bp, c and Ci, and the nuclear electric quadrupole moments for eQq. The ratio of the nuclear spin-rotation constants also depends on the inverse ratio of the reduced masses. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 81 These ratios have been calculated for the parameters derived for the two vibrational states of both MgBr and AlBr and are listed in Table 6.7 along with ratios of reduced masses and/or nuclear moments obtained from the literature. The ratios for eQq(Bv) and c agree quite well with the ratios from the literature, within the calculated uncertainties. The C/(Br) ratios also agree with ratios of the literature values, though the uncertainties are quite large. However for 7 and bp, this is not the case. This deviation observed for the 7 and bp ratios is due to vibrational effects, because, strictly speaking, the equilibrium values of the fine and hyperfine parameters should be used to calculate the ratios [117, 118]. To account for this, an expansion in terms of vibrational contributions, of the form was used to calculate the equilibrium values of each of the parameters. The vibrational dependencies of the four well determined parameters of MgBr, in MHz, can be sum-marised by the following expressions: (6.1) 7 , ( 8 1 Br) 179.6020(18) 178.5673(17) 2.5708(21) 2.5944(24) eg^( 8 1 Br) eQqv{79Bv) 109.3761(50) 91.3736(49) + + 1.8744(69) 1.5593(69) M 8 1 B r ) W 7 9 B r ) 186.3870(25) 172.9049(25) 1.2580(43) 1.1681(43) Chapter 6. Pure Rotational Spectra of MgBr and AlBr 82 C t ,( 8 1Br) = 222.6568(35) + 1.1215(50) \v + - J . The expressions for the vibrational dependence of the nuclear quadrupole coupling con-stants of AlBr, in MHz, are: eQqv(79Br) = 79.4193(19) - 1.4258(27) (v + eQqv(slBr). = 66.3427(20) - 1.1903(28) ( v + \ ) -The ratios calculated using the equilibrium values of the parameters are also listed in Table 6.7. These equilibrium parameter ratios agree more consistently with the ratios from the literature, to within 1.5 times the calculated uncertainties. The 7 and bp constants are sufficiently well determined that vibrational effects on the ratios are evident; this reflects the high precision available from the F T M W technique. 6.5 Discussion 6.5.1 Equi l ibrium Bond Distance of M g B r In the millimetre wave study of the similar molecule MgCl [119], the observed transitions were fit to Dunham coefficients from which a bond length could be determined. There are insufficient rotational and vibrational data for MgBr to employ this method. Instead, Eq. (2.16) was used: Bv = £ e - a e ( v + + 7e (t> + ^ ) where Be is the equilibrium rotational constant, Bv is the rotational constant of the uth vibrational state and cte and 7 e are higher order vibrational correction terms. This expression was used in three different calculations to estimate the equilibrium rotational constant and equilibrium bond distance. The details of this calculation of re have been Chapter 6. Pure Rotational Spectra of MgBr and AlBr 83 discussed in Sec. 2.4. For the first method, Eq. (2.16) was truncated after the ae term. Using the B0 and B± data, Be and ae were determined for both isotopomers and from these r e was determined using atomic masses and fundamental constants from Ref. 120. These results are listed in Table 6.8 under the heading Method I. In the second method, the higher order correction constant fe was substituted by 10 - 3 • ae in Eq. (2.16). This value is similar to those found for CaBr [121] and BaCl [18]. Two more values of Be and re were determined from the Bo and B\ data by employing this approximation. These are listed in Table 6.8 under Method II. The re obtained using Method II agrees fairly well with that calculated by Method I. The uncertainties given for each of these results, which are on the order of 10 - 6 A, reflect the uncertainties in the rotational and fundamental constants only. So far no account has been taken of electronic effects; these have been described in Sec. 2.4. An estimate of the order of magnitude of the effect of non-spherical charge distribution can be made by considering MgBr as the completely ionic molecule, M g + B r _ . The same estimate of 7 e was made as in Method II and Be was calculated for the two isotopomers of MgBr; however to calculate r e , ion masses were used instead of atomic masses. This provided a third estimate of r e which is listed under Method III in Table 6.8. The difference in re obtained for Methods II and III is on the order of 10~5 A; the uncertainty due to electronic effects is estimated to be of this order of magnitude. This is also expected to be a good measure of the deviation of re from that obtained in the Born-Oppenheimer approximation. This estimate can be verified using AlBr, since the equilibrium bond distance in the Born-Oppenheimer approximation is known from the study of Wyse and Gordy [97]. In their study, Be was calculated from the Dunham coefficient Y01 using a method after Bunker [31] which also accounted for the breakdown of the Born-Oppenheimer Chapter 6. Pure Rotational Spectra of MgBr and AlBr 84 approximation [30]. For this comparison, re was calculated for AlBr using the three methods described above. These values are listed in Table 6.9 along with the r e value in the Born-Oppenheimer approximation from the millimetre wave study. The differences between the re values estimated by Methods I, II, and III and the Born-Oppenheimer re are all of the order of magnitude of 10 _ 5 A, which is equal to the estimate of uncertainty in re made above for MgBr. Table 6.10 presents a summary of the re values calculated for MgBr by each method and also a best estimate of re, which is an average of the results of Methods II and III. These results can be compared to the two literature values, the r 0 value from the partial rotational analysis [92] and an re value from a recent ab initio study [90]. The results of this F T M W study have clearly provided the first accurate value for the equilibrium bond distance for magnesium monobromide. 6.5.2 Electron Spin-Nuclear Spin Hyperfine Parameters The magnetic hyperfine constants bp and c were used to characterise the bonding in MgBr via the unpaired electron spin densities in the bromine atomic orbitals. This method is discussed in detail in Sec. 2.3.3. The definitions of the Fermi contact and dipole-dipole interaction constants, Eq. (2.52) and Eq. (2.53), are shown here for reference 87T bF = Y9egN^BfiN^^ 12 c = ^ e S T v / W i v ^ c o s 2 © ~ 1)/ r ' 3) • Values of |*(0)|2 and ((3 cos2 0 - l ) /r 3 ) were calculated for M g 7 9 B r and C a 7 9 B r from bF and c using Eqs. (2.52) and (2.53) and constants from Ref. 120. These values are listed in Table 6.11. Also listed are corresponding values for the bromine atom, which were calculated by considering the unpaired electron to be in the bromine atom As orbital, for 1^ (0) | 2 , or the 4pz orbital, for ((3 cos2 0 — l ) /r 3 ) , and using atomic parameters calculated Chapter 6. Pure Rotational Spectra of MgBr and AlBr 85 by Morton and Preston [22]. A value of ( 3 c o s 2 © — 1) = | was used for the pz orbital and a relativistic correction, on the order of 16.7%, was included for |\I/(0)|2 [22]. The unpaired spin densities, p(s) and p(p) listed in Table 6.11, were calculated for the 4s and 4pz orbitals in MgBr and CaBr by taking ratios of the experimental molecular to calculated atomic values for I^O)]2 and ( ( 3 c o s 2 © — l ) / r 3 ) , respectively. From these, it can be seen that there is very little unpaired electron spin density on the bromine in these species. The unpaired electron can be considered to reside almost entirely on the metal, indicating that the radicals are almost completely ionic, M + B r ~ . The spin densities for MgBr, however, are approximately twice those of CaBr. This higher unpaired spin density on the halogen nucleus, as compared to the other alkaline earth monohalides, has been observed for both MgF [79] and MgCl [45]. It appears that the amount of covalent character in the metal-halide bond increases as the mass of the alkaline earth atom decreases [79] and these results for MgBr are consistent with this observation. 6.5.3 Nuclear Quadrupole Coupling Constant The ionic character of the metal bromide bond can be calculated from the nuclear quadrupole coupling constant, eQo(Br). This method has been described in Sec. 2.5. Eq. (2.71) is given here for reference .c = x ( eQq(Bv) ^  eQo 4i 0(Br)' where e(^94io(79Br) is -769.76 MHz [2]. Table 6.12 presents the ionic character calculated for MgBr, AlBr and several other metal monobromide species using this expression. For the alkaline earth and alkali metal monobromides, these results follow the expected periodic trends in electronegativity; MgBr and NaBr are less ionic than CaBr and KBr, respectively, and the greatest difference in ionic character observed is between MgBr and KBr. These results also support the observation from analysis of the electron spin-nuclear Chapter 6. Pure Rotational Spectra of MgBr and AlBr 86 spin hyperfine constants that the magnesium monohalides exhibit more covalent bond character than the corresponding calcium species. However, for the Al and Ga species, the calculated ionic character results do not appear follow the trend expected from the literature electronegativity values. This discrepancy can be investigated by calculating the electronegativity difference between the two atoms in the molecule from its ionic character. These relations are described in detail in Sec. 2.3.1. Eq. (2.78), given here for reference, 1 ic = 1.15 exp •§(2 - A x ) 2 0.15 was used to calculate the difference in electronegativities, Ax, for AlBr and GaBr [122] using the ionic characters obtained from the bromine nuclear quadrupole coupling con-stants. From these Ax values, the electronegativities of aluminium and gallium were determined using halogen electronegativity values taken from Ref. 2. This method was repeated using the corresponding monochloride species, A1C1 [54] and GaCl [123]. The average electronegativity values are listed in Table 6.12 as xjv/(calc). This difference between the literature aluminium electronegativity value, 1.5 [2], and that calculated from the nuclear quadrupole coupling constants, 1.3, was also noted by \Wyse and Gordy [97]. This difference was ascribed to the method used to obtain the electronegativity values. The literature value was obtained from solid phase data where aluminium would most likely be present in its trivalent state rather than its monovalent state and the electronegativity values are expected to be 0.2 to 0.3 higher for trivalent aluminium than for monovalent aluminium [97]. Wyse and Gordy estimated the elec-tronegativity of monovalent aluminium to be 1.3. This value agrees with that determined from the more accurate nuclear quadrupole coupling constants for AlBr and A1C1 [54] obtained by F T M W spectroscopy. The Al nuclear quadrupole coupling constants can be related to the degree of sp Chapter 6. Pure Rotational Spectra of MgBr and AlBr 87 hybridisation on the Al atom. This will be discussed in conjunction with the Al nuclear quadrupole coupling constants of aluminium isocyanide and other related aluminium halides in Sec. 7.5.1. 6 . 5 . 4 A l B r N u c l e a r S p i n - S p i n C o n s t a n t The nuclear spin-spin constant, a^i-Br, should be consistent with the calculated bond length. Using Eq. (2.58) from Sec. 2.3.3, otAi-Br can be expressed as — ^r^NdAWBr dAl-Br = 3" rAl-Br where PM is the nuclear magneton and gAi and ger are the nuclear ^-factors for the Al and Br nuclei. Internuclear bond distances of 2.31(13) A and 2.47(17) A were calculated from the nuclear spin-spin constants of A l 7 9 B r and A l 8 1 B r , respectively. The large uncertainties in the estimated bond distances are due to uncertainties in the respective constants. Despite the large uncertainties, the estimated internuclear distances agree with the re value of ~ 2.29A. 6 .6 C o n c l u s i o n The first complete rotational analysis of the spectrum of magnesium monobromide has been made. Accurate rotational and centrifugal distortion constants have been deter-mined as well as new fine and hyperfine parameters. The first accurate equilibrium bond length has been determined for MgBr. The 8 1 Br nuclear quadrupole structure of A l 8 1 B r has been observed for the first time. Improved nuclear quadrupole coupling constants have also been obtained for A l 7 9 B r and nuclear spin-rotation and nuclear spin-spin constants have been determined for both isotopomers. The analyses of the hyperfine structure has shown that the bonding in MgBr and AlBr follow the trends predicted from Chapter 6. Pure Rotational Spectra of MgBr and AlBr 88 electronegativities. Also MgBr has been found to follow the same trends in bonding as MgF and MgCl: all three species exhibit greater covalent character than the correspond-ing Ca and other alkaline earth monohalides. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 89 Table 6.1: Measured frequencies of TV = 1 — 0 and N = 2 — 1 transitions of 2 4 M g 7 9 B r in v = 0 and v = 1 vibrational states. Transition v = 0 Obs. - calc. v = 1 Obs. - calc. N' J' F' /V" J" F" (MHz) (kHz) (MHz) (kHz) 1 1/2 1 0 1/2 2 9524.7196 -0.2 1 3/2 1 0 1/2 2 9835.8658 -0.5 9780.8303 1.6 1 1/2 1 0 1/2 1 9868.9931 0.3 9814.4948 0.0 1 1/2 2 0 1/2 1 9873.9752 -1.1 9820.2456 -1.4 1 3/2 3 0 1/2 2 10007.5349 0.5 9950.8962 0.7 1 3/2 2 0 1/2 2 10018.5122 0.4 9963.9149 0.0 1 3/2 0 0 1/2 1 10040.5588 1.2 9983.8199 0.2 1 3/2 1 0 1/2 1 10180.1367 -2.6 2 3/2 3 1 1/2 2 19806.7336 1.3 19697.8937 1.1 2 5/2 2 1 3/2 2 19860.1058 -0.1 19748.6261 -0.5 2 3/2 2 1 1/2 1 (19854.946)a 2 5/2 3 1 3/2 2 19954.1031 0.2 19842.2139 -0.6 2 5/2 3 1 3/2 3 19965.0798 -0.5 2 5/2 4 1 3/2 3 19966.6855 -1.1 (19854.946)° 2 5/2 2 1 3/2 1 20042.7515 0.1 ° Blended lines not included in fit. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 90 Table 6.2: Measured frequencies of N = 1 - 0 and N = 2 - 1 transitions of 2 4 M g 8 1 B r in v = 0 and v = 1 vibrational states. Transition v = 0 Obs. - calc. v = 1 Obs. - calc. TV' J' F' N" J" F" (MHz) (kHz) (MHz) (kHz) 1 1/2 1 0 1/2 2 9439.6747 0.6 1 3/2 1 0 1/2 2 9774.2372 -1.8 9719.8268 -0.9 1 1/2 1 0 1/2 1 9810.8129 -0.1 9756.6116 -0.1 1 1/2 2 0 1/2 1 9821.2344 -1.4 9767.9234 0.2 1 3/2 3 0 1/2 2 9949.1867 1.5 9893.0409 0.0 1 3/2 2 0 1/2 2 9960.7121 -0.1 9906.6172 0.0 1 3/2 0 0 1/2 1 9990.1631 1.4 9934.0030 -0.0 1 3/2 1 0 1/2 1 10145.3776 -0.3 2 3/2 3 1 1/2 2 19695.5304 0.5 19587.6184 -0.1 2 5/2 2 1 3/2 2 19741.3556 0.5 19630.9493 0.2 2 3/2 2 1 1/2 1 19744.5411 1.5 2 5/2 3 1 3/2 2 19836.5686 -0.2 19725.6566 0.2 2 5/2 3 1 3/2 3 19848.0947 -1.0 2 5/2 4 1 3/2 3 19851.5795 -2.0 19740.8692 -0.3 2 5/2 2 1 3/2 1 19927.8289 0.6 Chapter 6. Pure Rotational Spectra of MgBr and AlBr Table 6.3: Measured frequencies of J = 1 — 0 and J v = 0 and v = 1 vibrational states. 2 - 1 transitions of A l 7 9 B r Transition v - 0 Obs. - calc. v = 1 Obs. - calc. J' F{ F' J" F[' F" / M H z /kHz / M H z / k H z 1/2 1/2 5/2 5/2 3/2 3/2 0 3/2 0 3/2 1/2 2 0 3/2 0 3/2 0 3/2 5/2 3 0 3/2 5/2 5/2 5/2 5/2 5/2 0 0 3/2 0 3/2 0 3/2 0 3/2 0 3/2 0 3/2 0 3/2 4 2 3 1 2 3 4 3 4 2 3 1 2 3 4 i } 1} 4 9498.8843 9498.8913 9499.3000 9513.1626 9513.1697 9514.6912 9515.8005 9515.8088 9516.9414 9517.4427 9519.4344 9532.6899 9534.4667 -0.4 0.5 0.8 -0.7 0.2 -1.2 -0.6 0.9 -0.4 -0.5 1.1 1.0 -0.1 9447.2081 9447.2129 9461.7707 9461.7765 9463.2601 9465.5128 9483.4006 0.6 -0.8 0.3 -0.2 0.6 -0.3 -0.0 1 3/2 4 0 3/2 3 9534.4734 0.4 9483.4068 -0.1 1 3/2 2 0 3/2 1 9536.1761 -0.8 1 3/2 2 0 3/2 3 9536.1870 0.8 1 3/2 3 0 3/2 9537.7080 -0.9 9486.6262 -0.0 2 3/2 4 1 3/2 6 ) 4 19023.5363 0.0 2 5/2 4 1 3/2 3 19033.9816 -0.1 18931.2710 0.2 2 7/2 4 1 5/2 3 19035.4116 0.5 18932.7194 0.0 2 7/2 3 1 5/2 2 19035.9549 -0.4 2 7/2 5 1 5/2 4 19037.1585 -0.1 18934.4273 -0.9 2 7/2 6 1 5/2 5 19037.7460 0.4 18935.0157 -0.2 2 5/2 5 1 3/2 4 19038.7946 0.6 18936.0618 0.8 2 1/2 3 1 1/2 2 19038.9670 -1.2 2 1/2 2 1 1/2 3 19039.1645 0.1 2 1/2 3 1 1/2 3 19039.3799 -0.3 2 3/2 2 1 1/2 2 19058.8521 -0.1 2 3/2 4 1 1/2 3 19059.1193 0.9 2 3/2 3 1 1/2 2 19059.2005 -0.4 Chapter 6. Pure Rotational Spectra of MgBr and AlBr Table 6.4: Measured frequencies of J = 1 — 0 and J = 2 — 1 transitions of A l 8 1 B r v = 0 and v = 1 vibrational states. Transition v = 0 Obs. - calc. v = 1 Obs. - calc. J' F{ F' J " F{> F" / M H z /kHz / M H z / k H z 1 1/2 3 0 3/2 9442.1516 -0.2 9391.0201 -0.3 1 1/2 3 0 3/2 J 3 1 ^ 9442.1572 0.3 9391.0257 0.1 1 1/2 2 0 3/2 X 1 2 I 3 1 9442.6367 -0.3 5/2 4 0 3/2 4 1 3 J 9453.9378 0.0 9403.0418 0.3 1 5/2 3 0 3/2 9455.6860 -0.4 9404.7448 0.1 1 5/2 2 0 3/2 * ) 1 _ \ 9456.6388 -0.7 1 5/2 2 0 3/2 9456.6464 1.2 1 5/2 5 0 3/2 J 4 9457.7853 -0.3 9406.8512 -0.1 1 5/2 1 0 3/2 9458.1142 -0.7 1 5/2 0 0 3/2 J 1 9460.2789 0.7 1 3/2 1 0 3/2 9470.4626 0.8 1 3/2 4 0 3/2 J 4 9472.1403 -0.1 9421.5076 0.3 1 3/2 4 0 3/2 3 9472.1459 0.3 9421.5121 -0.5 3/2 2 0 3/2 1 9473.8751 -1.1 1 3/2 2 0 3/2 3 9473.8851 1.1 1 3/2 3 0 3/2 9475.3213 -0.4 9424.6748 0.1 2 3/2 4 1 3/2 6 ) 4 18906.3863 -0.2 2 5/2 4 1 3/2 3 18914.7191 0.3 18812.9761 0.0 2 7/2 4 1 5/2 3 18915.9108 0.0 18814.1951 0.2 2 7/2 3 1 5/2 2 18916.5822 -0.1 2 7/2 5 1 5/2 4 18917.8648 0.0 18816.1040 -0.6 2 7/2 6 1 5/2 5 18918.4175 -0.1 18816.6581 -0.6 2 5/2 5 1 3/2 4 18919.4318 0.5 18817.6710 1.0 2 1/2 2 1 1/2 3 18919.6381 0.4 2 1/2 3 1 1/2 3 18919.8830 -0.0 2 3/2 2 1 1/2 2 18936.0620 -0.7 2 3/2 4 1 1/2 3 18936.3751 -0.0 Chapter 6. Pure Rotational Spectra of MgBr and AlBr 93 Table 6.5: Molecular constants calculated for MgBr in M H z a . Parameter 2 4 M g 7 9 B r 2 4 M g s l B r v = 0 v - 1 v = 0 v = 1 B 4972.20127(57) 4944.62754(69) 4943.62546(57) 4916.28928(68) D 0.003945(82) 0.00392(11) 0.003849(80) 0.00390(10) 7 178.3048(14) 175.7104(19) 177.2819(13) 174.7111(17) C/(Br) 0.00553(39) 0.00545(50) 0.00595(39) 0.00555(48) bF 172.3208(12) 171.1527(41) 185.7580(12) 184.5000(41) c 207.0793(26) 208.1257(46) 223.2175(24) 224.3390(44) eQq(Bv) 110.3133(36) 112.1877(59) 92.1532(35) 93.7125(60) a One standard deviation in parentheses, in units of least significant digit. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 94 Table 6.6: Molecular constants calculated for AlBr in M H z a . Parameter A l 7 £ Br A l 8 1 Br V = 0 v = 1 v = 0 v = 1 B 4759.72699(17) 4734.05280(24) 4729.82499(18) 4704.39229(26) D 0.003414(25) 0.003382(37) 0.003360(26) 0.003319(41) eQq(Al) -28.0059(34) -27.8019(51) -28.0061(35) -27.8068(53) eQq(Bv) 78.7064(14) 80.1322(23) 65.7476(15) 66.9379(24) C/(A1) 0.00412(12) 0.00450(27) 0.00406(12) 0.00408(27) C/(Br) 0.01356(13) 0.01348(22) 0.01451(13) 0.01463(24) OLAl-Br —0.00191(33) -0.001916 -0.00170(35) -0.001706 a One standard deviation in parentheses, in units of least significant digit. 6 Nuclear spin-spin constant held fixed at value obtained from v = 0 fit. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 95 Table 6.7: Calculated ratios of hyperfine parameters compared to nuclear and molecular properties of MgBr and AlBr. MgBr v=0 v=l E q . a Lit. 7 ( 7 9 J B r ) / 7 ( 8 1 £ r ) 1.00577(1) 1.00572(1) 1.00579(1) 1.0057885(1)" 6 F ( 7 9 Br) /6 F ( 8 1 Br) c( 7 9 Br)/c( 8 1 Br) 0.92766(1) 0.92770(2) 0.92766(3) 0.92773(3) 0.92767(2) 0.92769(2) 0.927700(2)c 0.927700(2)c eQo( 7 9 Br)/ e Qo( 8 1 Br) 1.19706(6) 1.19715(10) 1.19702(7) 1.19707(3)d C7,( 7 9Br)/C7( 8 1Br) 0.929(89) 0.982(124) - 0.933573(2)e AlBr v=0 v=l E q . a Lit. eQo( 7 9 Br) / e Q 0 ( 8 1 Br) 1.19710(6) 1.19711(6) 1.19711(5) 1.19707(3)d C7/( 7 9 Br)/C/( 8 1 Br) 0.934(12) 0.921(21) - 0.933573(2)' a For method of calculation, see text Sec. 6.4. 6 Inverse ratio of reduced masses of 2 4 M g 7 9 B r and 2 4 M g 8 1 B r , calculated using atomic masses in Ref. 120. c Ratio of nuclear moments of 7 9 B r and 8 1 B r , calculated using values in Ref. 120. d Ratio of electric quadrupole moments of 7 9 B r and 8 1 B r , taken from Ref. 2. e Ratio of nuclear magnetic moments of 7 9 B r and 8 1 Br multiplied by inverse ratio of reduced masses of Mg 7 9 Br and Mg 8 1 Br, calculated using values in Ref. 120. ' Ratio of nuclear magnetic moments of 7 9 B r and 8 1 Br multiplied by inverse ratio of reduced masses of A l 7 9 B r and A l 8 1 B r , calculated using values in Ref. 120. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 96 Table 6.8: Equilibrium parameters calculated for M g B r a ' \ Method I 2 4 M g 7 9 B r 2 4 M g 8 1 B r j5 e /MHz 4985.9881(7) 4957.2936(7) « e / M H z 27.57373(89) 27.33618(89) r e / A 2.347408(1) 2.347408(1) Method II 2 4 M g 7 9 B r 2 4 M g 8 1 B r £ e / M H z 4985.9675(7) 4957.2731(7) a e / M H z 27.51869(89) 27.28162(89) rjk 2.347413(1) 2.347413(1) Method III 2 4 M g 7 9 B r 2 4 M g 8 1 B r 5 e / M H z 4985.9675(7) 4957.2731(7) a e / M H z 27.51869(89) 27.28162(89) 2.347432(1) 2.347432(1) a For methods of calculation, see Sec. 6.5.1. 6 Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 97 Table 6.9: Comparison of equilibrium bond length estimates for AlBr". Method I6 Method II6 Method III6 Lit. Exp. r e / A 2.294870(1) 2.294878(1) 2.294893(1) 2.29480(3)c a For description of methods see Sec. 6.5.1. 6 Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. 0 re from Wyse and Gordy [97]. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 98 Table 6.10: Summary of equilibrium bond length estimates for MgBr 3 . Method I6 Method II6 Method III6 Ave. Lit. Exp. Lit. Theo. r e / A 2.347408(4) 2.347413(4) 2.347432(4) 2.34742(2)c 2.36d 2.40e a For description of methods see Sec. 6.5.1. 6 Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. 0 Average of Method II and III. Uncertainty estimated from range of values. d r0 from partial rotational analysis [92]. e re from Ref. 90. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 99 Table 6.11: Spin densities calculated from magnetic hyperfine constants for MgBr and CaBr. Parameter 2 4 M g 7 9 B r 4 0 C a 7 9 B r ° 7 9 B r atom6 6^/MHz c/MHz 172.321 207.079 121.202 77.620 : |$(0)| 2 /au- 3 ( ( 3 c o s 2 0 - l ) / r 3 ) / a u - 3 0.153345 1.02919 0.107855 0.385774 28.56 12.20 p(s)/% p(p)/% 0.5369 8.436 0.3776 3.162 -a Taken from Ref. 118. 6 Calculated from data in Ref. 22. Chapter 6. Pure Rotational Spectra of MgBr and AlBr 100 Table 6.12: Comparison of AlBr, MgBr and related metal monobromide nuclear quadrupole coupling constants. 2 3 N a 7 9 B r ° 3 9 K 7 9 B r 6 2 4 M g 7 9 B r 4 0 C a 7 9 B r c 2 7 A 1 7 9 B r 6 9 G a 7 9 B r r f eQo( 7 9 Br)/MHz 58.60801 10.2383 110.313 20.015 78.706 106.2 ij% 92.5 98.7 85.7 97.4 89.8 86.2 xMe 0.9 0.8 1.2 1.0 1.5 1.5 xjvf(calc)' 1.3 1.4 a Results taken from Ref. 124. 6 Results taken from Ref. 125. c Results taken from Ref. 118. d Results taken from Ref. 122. e Electronegativities taken from Ref. 2. ' Average of electronegativites calculated from ionic character of the respective MCI and MBr species. Uncertainty is estimated to be in the least significant digit. See Sec. 6.5.3 for method. Chapter 7 Microwave Spectroscopy of M g N C and A 1 N C 7.1 Introduction The spectra of refractory-element molecules in circumstellar clouds provide information which will further our understanding of the chemistry of these elements in space [6]. Laboratory spectra provide search parameters for new species and can be used to identify (and verify) lines in the spectra of interstellar sources. Theoretical studies have predicted that magnesium-bearing compounds should be present in circumstellar shells; however, searches for MgS, MgH and MgO have so far proved unsuccessful [73, 126, 127] and consequently other Mg-species have been suggested. A study of interstellar refractory-element chemistry by Turner suggested nitrogen containing species, such as MgN, could have a greater abundance than either sulfide or oxide species [67]. This prediction was supported by the discovery of MgNC, the first magnesium-bearing molecule found in space [68,69]. The detection of this and NaCN [128] in the circumstellar envelope of IRC + 10216 has raised the possibility that other metal cyanides and isocyanides might be present in interstellar sources. Specifically, A1NC/A1CN has been suggested [129]. This seems promising because Al and Mg have comparable cosmic abundances, and A1C1 [130] and A1F [130,131] have also been detected in IRC + 10216. The first astronomical observation of MgNC was made by Guelin et al. in 1986 [68]. 101 Chapter 7. Microwave Spectroscopy of MgNC and A1NC 102 They reported the measurement of three millimetre wave transitions of a then unknown paramagnetic molecule in IRC + 10216. In 1993, these lines were identified by Kawaguchi et al. [69] from the results of a laboratory based millimetre wave study. These results were extended by Anderson and Ziurys to include the other magnesium isotopomers, 2 5 M g N C and 2 6 M g N C [132], which were subsequently also identified in space [133]. The rotational spectrum in the v2 excited bending state has been measured and these results have been used to discuss the flexibility of the molecule [134]. The electronic spectroscopy has also been investigated [135,136]. The first theoretical study was done in 1985 by Bauschlicher et al. as part of a larger study of the alkaline earth isocyanides [137]. There have been four ab initio studies done to predict the spectroscopic constants and structural parameters of MgNC and several related isocyanides [138-141]. Theoretical studies have also been made of the thermochemistry of MgNC and of its protonated and hydrogenated derivatives [142,143]. Recently two low frequency transitions, iV = 3 — 2 and N = 4 — 3, have been measured as part of a larger survey of IRC + 10216 [144]; however, the N = 3 — 2 transition was overlapped by lines due to other molecules and the hyperfine splitting was not examined. There have been no measurements of low N transitions of MgNC where the hyperfine structure due to 1 4 N has been resolved. The current work was undertaken to measure this hyperfine structure. A1NC and A1CN were first detected by mass spectroscopy by Gingerich in 1967 [145]. Subsequently, three ab initio studies have been made of the structures of these molecules [129,140,146]. These studies predict that A1NC and A1CN should be linear, and that A1NC should be more stable than A1CN by about ~ 23 kJ/mol. Two experimental studies have been reported quite recently. Robinson et al. have measured the millimetre wave spectrum of A1NC in both the ground vibrational state and excited states of the bending mode, u2 [147]. Fukushima has reported investigation of the 1A' — X 1 E + electronic Chapter 7. Microwave Spectroscopy of MgNC and A1NC 103 transition of A1NC and A1CN by laser induced fluorescence [148]. This chapter reports the first measurements made of the hyperfine structure in magne-sium and aluminium isocyanide. The two lowest rotational transitions of both molecules in their ground vibrational states have been measured. Hyperfine structure due to the 1 4 N nucleus has been observed in the spectra of both molecules along with nuclear hy-perfine splitting due to the 2 7 A1 nucleus in A1NC. The derived constants have been used to investigate orbital hybridisation in these species. 7.2 Experimental Details MgNC and A1NC were prepared by reacting ablated Mg metal (rod from A. D. MacKay 99.9%) or ablated Al metal (rod from Goodfellow 99.999%) with cyanogen present as 0.2-0.5% in Ar backing gas. To measure the transition frequencies of the paramagnetic species MgNC, a set of three mutually perpendicular Helmholtz coils was used to collapse the Zeeman splitting due to the earth's magnetic field. This procedure was described in detail in Sec. 3.8. The signals for A1NC were so strong that the J = 1 — 0 transitions were easily observable in a few measurement cycles; 10 averaging cycles produced a power spectrum with 50:1 S/N. 7.3 Observed Spectra 7.3.1 M g N C The millimetre wave spectrum of the free radical MgNC had been measured previously [69] and hence the rotational, centrifugal distortion and fine structure constants were all well determined. These results narrowed the search range for the microwave study because only the hyperfine parameters had to be estimated for the initial prediction. The magnetic hyperfine coupling constants, bp and c, were estimated by scaling the Chapter 7. Microwave Spectroscopy of MgNC and AINC 104 results from MgF [78] by the ratio of the nuclear ^-factors, gj( 1 4 N)/g/( 1 9 F). The nuclear quadrupole coupling constant eQq0(14N) was assumed to be equal to that of CaNC [57]. Only the two lowest N rotational transitions, N = 1 — 0 and ./V = 2 — 1, were available in the frequency range of the spectrometer. An initial prediction was made for the N = 1 — 0 transition from the millimetre wave parameters and the estimated hyperfine parameters. The most intense component was found 400 kHz from the predicted frequency. After further searching, five components of the N — 1 — 0 transition were found. These lines were fit to BQ, 7 and the three hyperfine parameters, with Do held fixed at the value obtained from the millimetre wave study [69]. These improved parameters were used to predict the = 2 — 1 transitions. In total, 12 hyperfine components of the two transitions were measured; their frequencies are listed in Table 7.1. Transitions for the minor isotopomers of MgNC were not sought. An example spectrum is shown in Fig. 7.1. 7.3.2 A I N C When this study was undertaken no experimental results had been presented, so the transition frequencies were predicted using results from the theoretical study by Ma et al. [129]. Experience with the similar species MgNC provided some added insight into how the theoretical results could be employed. For MgNC, it was found that calculations made at the SDCI/TZ2P level of theory produced a rotational constant B that was about 27 MHz lower in frequency than that obtained from experiment [138]. In their theoretical study of AINC, Ma et al. found that B0 and Be differed by only about 5 MHz. Consequently the Be constant predicted for AINC using the same level of theory as for MgNC was chosen to calculate the initial search range. To estimate the magnitude of the hyperfine splitting, eQq(27A\) from A1F [96] and eQ<?(14N) from MgNC were included in Chapter 7. Microwave Spectroscopy of MgNC and A1NC 105 49 kHz I 1 11932.041 MHz 11932.441 MHz Figure 7.1: The N = 1 - 0, J = 3/2 - 1/2, F = 3/2 - 1/2 transition of 2 4 M g 1 4 N 1 2 C was measured using a set of mutually perpendicular Helmholtz coils to remove the effects of the earth's magnetic field. In addition to the 49 kHz Doppler splitting, a residual Zeeman splitting, on the order of 10 kHz, is present in this spectrum. This spectrum was obtained with 400 averaging cycles. The microwave excitation frequency was 11932.241 MHz. 4 K data points were measured with a 50 ns sampling interval and the power spectrum is displayed as an 4 K transformation. Chapter 7. Microwave Spectroscopy of MgNC and AINC 106 the prediction. The J = 1 — 0 transitions were found less than 40 MHz from the predicted values. Two rotational transitions, J = 1 — 0 and J = 2 — 1, were available in the frequency range of the spectrometer. Twenty seven lines were measured for the main isotopomer 2 7 A 1 1 4 N 1 2 C (98.53% natural abundance). Spectra of species containing other isotopes of N and C were not sought. Nuclear hyperfine structure due to both 2 7 A l (I = |) and 1 4 N (/ = 1) was observed. Since the splittings due to 2 7 A1 were larger than those due to 1 4 N , the lines were easily assigned in terms of the coupling scheme J + IAI = F 2 ; F X + IN = F . An overview spectrum of the J = 1 — 0 transition, shown in Fig. 7.2, shows the relative magnitudes of these splittings: the 2 7A1 quadrupole coupling produces three lines which are then split further by the 1 4 N quadrupole coupling. An expanded view of the i*\ = 7/2 — 5/2 section of the J — 1 — 0 transition is given in Fig. 7.3. All the measured lines and their assignments are listed in Table 7.2. 7.4 Analyses 7.4.1 M g N C The measured transition frequencies of MgNC were fit using Pickett's exact fitting pro-gram S P F I T [76], which employs a Hund's case (bpj) coupling scheme, N + S = J ; J + IN = F . This fit determined the rotational and centrifugal distortion constants, B0 and D0, the spin-rotation parameter, 7 , the nuclear quadrupole coupling constant, eQ<7o(14N), and the magnetic hyperfine parameters, the Fermi contact constant, bp, and the dipole-dipole coupling constant, c. The parameters are listed in Table 7.3 under the heading Microwave Fit, along with the millimetre wave parameters obtained by Kawaguchi et al. [69]. The rotational and centrifugal distortion constants obtained agree well with those of the millimetre wave study, within three standard deviations. However, Chapter 7. Microwave Spectroscopy of MgNC and AINC 107 F 1 = 5/2 - 5/2 n wvuv i 11960.500 M H z F , = 7/2 - 5/2 n u = 3/2 - 5/2 n 1 11976.500 M H z Figure 7.2: Composite spectrum of the J = 1 — 0 rotational transition of AINC. The results of three different microwave experiments were used to produce this composite. Each experiment consisted of 200 averaging cycles. 4 K data points were collected at 50 ns sampling interval and transformed. Chapter 7. Microwave Spectroscopy of MgNC and AINC 108 45 k H z F = 9/2 -7/2 F _ 7/2-5/2 * 7/2 - 7/2 V 5/2 - 5/2 I F= 5/2-7/2 5/2 - 3/2 l 11970.535 MHz I 11971.585 MHz Figure 7.3: Detail of the J - 1 - 0 transition of AINC, showing the Fx = 7/2 - 5/2 hyperfine transition. This spectrum was obtained with 75 averaging cycles. 4 K data points were measured and the power spectrum is displayed with an 8 K transformation. The microwave excitation frequency was 11970.835 MHz. Chapter 7. Microwave Spectroscopy of MgNC and AINC 109 the spin-rotation parameter 7 does not compare as well. This is most likely the result of spin-rotation distortion effects, which were potentially significant in the higher /V tran-sitions measured at the millimetre wave lengths, but not in the lowest N transitions measured in our study. To confirm this deduction, a global fit was made using both the microwave and mil-limetre wave data. The transitions used are listed in Table 7.1. The data were fit simultaneously, using all lines to determine the rotational and quartic and sextic cen-trifugal distortion constants, B0, D0, and H0, the spin-rotation constants, 7 and 70, and the hyperfine parameters. In this fit, the microwave data were given a relative weighting of 100:1 with respect to the millimetre wave results to account for the measurement un-certainties. The parameters determined are listed in Table 7.3 under the heading Global Fit. The rotational and centrifugal distortion parameters agree well with those obtained from the millimetre wave study [69], to within three standard deviations. Distortion effects do appear to be the source of the discrepancy between the spin-rotation constants determined in the microwave and millimetre wave studies. In the Global Fit, the spin-rotation distortion parameter, 7^, was determined to better than 1 part in 10, which was not possible from the millimetre wave data alone. By fitting these results together with the microwave data, this constant could be determined. 7.4.2 A I N C The measured frequencies of AINC were fit using Pickett's program S P F I T [76], to the rotational constant B0, the centrifugal distortion constant DQ, the nuclear quadrupole and nuclear spin rotation coupling constants, eQq and Ci, for both the Al and N nuclei, and the nuclear spin-spin constant, C<AI-N- The lines observed for the overlapped hyperfine components of the J = 1 — 0 transition were fit as blended lines using predicted intensities Chapter 7. Microwave Spectroscopy of MgNC and AINC 110 as weighting factors. The resulting constants are listed in Table 7.4. Table 7.4 also compares the present results with those of Robinson et al. [147]. The rotational and centrifugal distortion constants agree quite well, within one standard de-viation. Our high resolution F T M W study produced a more precise Bo- However the value of D0 derived from the millimetre wave study was more precise because rotational transitions up to J = 31 were measured, where distortion effects are larger. It is interest-ing that in the present work a value of Do precise to three figures could be obtained. This too reflects the high precision of F T M W spectroscopy. To parallel the approach taken for MgNC, a fit of the F T M W and millimetre wave results for AINC was made. The re-sulting constants are listed in Table 7.4 under the heading Global Fit. The measurement uncertainties were used to obtain a relative weighting of 400:1 for the microwave lines with respect to the millimetre wave data. The rotational and centrifugal distortion con-stants obtained from the global fit compare well with those obtained from the millimetre wave study [147]. The BQ rotational constant also compares fairly well with the theoretical values of Ma et al. [129] as shown in Table 7.5. It appears that the TZ2P + f CISD level of calculations provided the best estimate of the rotational constant, to within 17 MHz of the experimental result. The predicted Be labelled by Ma et al. as the most reliable, however, proved to be about 100 MHz lower in frequency. The assumed quadrupole coupling constants, derived from A1F and MgNC, were found to provide excellent estimates of those of AINC, thereby showing the similarities between these three molecules. Chapter 7. Microwave Spectroscopy of MgNC and AINC 111 7.5 Discussion The three possible equilibrium structures for metal cyanide compounds are the linear cyanide, the linear isocyanide, and the non-linear T-shaped configurations. The struc-tures observed have been described as resulting from a subtle balance between long-range (classical electrostatic and induction) and short-range (exchange and penetration) forces [149]. This picture was proposed by Essers et al. to explain the structures of the alkali metal cyanides(K, Na and Li). The almost completely ionic compounds K C N and NaCN are both T-shaped because the short-range interaction predominates, while the slightly less ionic LiNC has the linear isocyanide structure. This structure was described as a compromise between the T-shaped configuration, favoured by the short-range in-teraction, and the linear cyanide structure, favoured by the long-range interaction [149]. This linear isocyanide structure was also predicted to be favoured for aluminium mono-cyanide [129,147] and the alkaline earth monocyanides [57,137,150,151]. When considering the experimental results for AINC and MgNC, comparisons can be made with two types of compounds; namely the linear metal isocyanides and the metal monohalides. The linear isocyanide structure is preferred for lithium [152] and the alkaline earth [137] as well as aluminium [129] cyanides. It has been observed that the ionic character of the M-NC bond decreases as the calculated energy difference between the linear isocyanide and cyanide structures of these molecules increases [129]. Since AINC has the greatest calculated energy difference of the linear metal isocyanides, the AI-NC bond should be less ionic than that of MgNC and the other alkaline earth and alkali metal isocyanides. Also the properties of the magnesium and aluminium isocyanides should be comparable to those of the magnesium and aluminium monohalides, since the electronegativity of the CN group is similar to those of F and CI. Information obtained from the hyperfine constants can be used to determine whether AINC and MgNC follow Chapter 7. Microwave Spectroscopy of MgNC and AINC 112 these predicted bonding trends. 7.5.1 Nuclear Quadrupole Coupling Constants The bonding in the metal cyanides and isocyanides can be investigated through their nuclear quadrupole coupling constants. Table 7.6 lists the 1 4 N quadrupole coupling con-stants for several of these species. For NaCN and K C N , the eQqz constant is listed. This allows comparisons to be made to constants obtained for the linear isocyanides because the z-axis in the T-shaped K C N and NaCN compounds was found to be almost parallel to the C N bond [153,154]. Also listed in Table 7.6 is the nuclear quadrupole coupling constant determined for the nearly completely covalent molecule HNC [155]. The con-stants for NaCN and K C N are in close agreement with that calculated for the free C N ~ ion [154], showing that these are indeed almost completely ionic compounds. It can be seen, by comparison with K C N , NaCN and HNC, that the linear metal isocyanides are fairly ionic species. However, they do appear to have some covalent character. To in-vestigate further the bonding in these species, the degree of sp-hybridisation of the 1 4 N atom was calculated from the nuclear quadrupole coupling constants. The 1 4 N nuclear quadrupole coupling constants can be interpreted in terms of valence p-shell electrons using the Townes-Dailey model [17], which was described in detail in Sec. 2.3.1. Eq. (2.43) relates the measured molecular quadrupole coupling constant to the nuclear quadrupole coupling constant of an np-electron. This expression is repeated here for reference: where nx, ny and nz are the number of electrons in the npx, npy and npz orbitals, respectively. By estimating values for nx, ny and nz, this model can be used to probe orbital hybridisation [2,35,93]. The molecular orbital basis for this discussion can be Chapter 7. Microwave Spectroscopy of MgNC and AINC 113 found in Sec. 2.5. We will consider an spz-hybv\d orbital on N in a linear metal isocyanide molecule; d orbital contributions will be neglected. In this discussion of linear molecules, the z-axis will be taken to be the molecular axis. The number of p2-electrons in the two hybrid orbitals can be calculated from Eq. (2.75) nz = 2a 2(l - a2) + Na2s where the first term is from the sp-hybrid bonding orbital and the second from the counterhybridised orbital, which may or may not be involved in another bond. In this expression, a2 is the fractional weight of the sp hybrid in the M-N bond molecular orbital, al is the ^-character of the hybrid orbital and iV is the number of electrons in the counterhybridised orbital. The a2 value can be estimated from the ionic character of the molecule, ic, using Eq. (2.67). Methods of calculating ionic character are discussed in Sec. 2.5. For all species discussed here, ic has been calculated using the approximate expression Eq. (2.77): \ x M - x N C \ if = ~ 2 The electronegativity values, x, are taken from Ref. [2], except for xAr, for it the value derived from the nuclear quadrupole coupling constants of AlBr and A1C1 in Chapter 6 was used. (The calculated a2s values changed by only 5% when using the more exact expression, Eq. (2.78), for ic.) In a linear metal isocyanide compound, M-NC, the N is on the negative pole of the bond and therefore 2ct2 is equal to (1 + ic). Care must be taken in determining the p-electron distribution because N is part of the NC ligand. The sp-hybrid orbital forms the M-N bond and the counterhybridised orbital forms the N-C a bond. The bonding in the N=C group is assumed to be completely covalent, so each of the pure 2px and 2py orbitals Chapter 7. Microwave Spectroscopy of MgNC and AINC 114 and the sp counterhybridised orbital have one half of a bond pair (nx = ny = N = 1). Using Eq. (2.43) and (2.75) and substituting the above values, the following equation results 1 + 1-eQq(^) eC?92io( 1 4 N) = [(1 + 0 ( 1 - ^ ) +a2. = ic(l - a 2 ) e Q 9 2 1 0 ( 1 4 N ) . (7.1) A further correction must be added to account for the screening effect of the negative charge on the NC group, e % ( » N ) = y i - . f l ^ j g Q , (7.2) where e = 0.3 [1]. The value of a 2 was calculated for the bonding orbital of N for MgNC, AINC and several other linear isocyanides using Eq. (7.2); the results are listed in Table 7.6. Since s-character values for the various linear isocyanides are approximately equal (within ~ 10%), the bonding orbital in each of the isocyanide groups must be similar. The differences in the observed nuclear quadrupole coupling constants appear to arise solely from differences in the ionic character of the M-NC bond, which decreases from LiNC to AINC. As the M-NC bond becomes more ionic, more electron density is transferred from the metal atom to the N, thereby increasing the magnitude of the quadrupole coupling constant, as predicted by Eq. (7.1). The nuclear quadrupole coupling constants are listed in the table in order of decreasing ionic character of the M-NC bond, so the effects of charge transfer, from the metal atom to the cyanide ligand, on the field gradient at the nitrogen nucleus can be seen in the decreasing quadrupole coupling constants. In the case of AINC, there is a significant contribution to the coupling constants from orbital hybridisation on both Al and N nuclei. The sp-hybridisation of the Al bonding orbital can be investigated using a method similar to that described above for N. In this discussion several Al-X compounds will be considered. Chapter 7. Microwave Spectroscopy of MgNC and AINC 115 The valence shell configuration of Al is 3s23p1. The value of 2a 2 is (1 — i c), since Al is the positive pole of the Al-X bond [2]. N will be taken to be 2, because the counterhybridised orbital will have an unshared pair, and the 3px and 3py orbitals are unfilled, so nx = ny = 0. By combining Eqs. (2.43) and (2.75) and substituting, the following expression results: A further correction must be added to account for decreased nuclear screening of the positive A l nucleus, where e = 0.35 for Al [1]. Eq. (7.4) was used to estimate the s-character of the sp-hybridised bonding orbital of Al for AINC, A1F, A1C1 and AlBr and the results are listed in Table 7.7. These four species are quite ionic compounds (completely so in the case of A1F) and without contributions from sp-hybridisation the Al quadrupole coupling constants would be be negligible. The s-character calculated for AINC is intermediate between that of A1F and A1C1 and the values of both eQq(27A\) and a 2 decrease from F to NC to CI to Br. 7.5.2 Electron Spin-Nuclear Spin Hyperfine Parameters for M g N C The nature of the bonding in MgNC can be examined by calculating the unpaired elec-tron spin density in the nitrogen atomic orbitals from the electron spin-nuclear spin hyperfine coupling constants. In a completely ionic alkaline earth isocyanide compound, the unpaired electron should be centred solely on the metal ion, M + , i.e. with no un-paired electron density at nitrogen. The unpaired electron spin densities in the nitrogen eQq{27A\) = [ ( l - i c ) ( l - a 2 ) + 2a 2]eg 0 3io( 2 7Al). (7.3) e g 0 ( 2 7 A l ) = [ ( l - g ( l - a 2 ) + 2a2](l + i c e) e go 3 1 o( 2 7 Al) (7.4) Chapter 7. Microwave Spectroscopy of MgNC and AINC 116 atomic orbitals are related to the Fermi contact constant, bp, and to the dipole-dipole in-teraction constant, c. Definitions of these constants were given in Eqs. (2.52) and (2.53) and discussed in detail in Sec. 2.3.3. These equations are repeated here for reference bF = Y ^ t f e / W e l ^ O ) ! 2 3 c = 29N9etXNfiB^cos2 Q ~ l)/r3)i From bp and c, values of |$(0)|2 and ((3 cos2 0 — l ) / r - 3 ) were calculated for MgNC and CaNC. These are listed in Table 7.8. Also listed are corresponding values for the nitrogen atom which were calculated by taking the unpaired electron to be entirely on the nitrogen, in either the 25 orbital or the 2p2 orbital. Atomic parameters for the calculations were taken from Morton and Preston [22]. Unpaired electron spin densities, p(s) and p(p), were determined for MgNC and CaNC by taking the ratios of the respective experimental molecular to calculated atomic values. The values obtained are listed in Table 7.8. These are quite small for both species, indicating that there is very little unpaired electron spin density on the nitrogen nucleus and that these are highly ionic compounds. However, the N spin densities calculated for MgNC are more than twice those for CaNC. A similar trend has been observed for MgBr and the other alkaline earth monohalide compounds: as the mass of the alkaline earth atom decreases, the covalent character of the M-X bond increases [79]. It appears that this trend is also followed in the alkaline earth isocyanides. The electron spin-nuclear spin hyperfine parameters for the alkaline earth isocyanides can also be compared to those of the corresponding alkaline earth fluorides. The magnetic hyperfine parameters used in the initial prediction for MgNC were calculated by scaling those of MgF by the ratio of the nuclear ^-factors, #/(14N)/<7/(19F). This estimation method had been used for CaNC [57] and provided values which were of the right order of magnitude. However when this method was used for MgNC, the values predicted from MgF [&F = 16.5 MHz and c = 13.7 MHz] did not agree well with the experimentally Chapter 7. Microwave Spectroscopy of MgNC and AINC 117 determined values [bF = 29.167 MHz and c = 5.386 MHz]. This suggests that the electronic structures of CaF and CaNC are more similar than those of MgF and MgNC. 7 . 5 . 3 N u c l e a r S p i n - S p i n C o n s t a n t f o r A I N C From the nuclear spin-spin coupling constant, an estimate of the Al-N bond distance can be made. The nuclear spin-spin constants are described in detail in Sec. 2.3.3. ct^i-N was defined in Eq. (2.58) as —3p%gAi9N CtAl-N — 3 • rAl-N A value of rAi-N = 1.75(20) A was obtained from this expression. The large uncertainty comes from the relatively large uncertainty in ctAi-N- This result compares well, within the uncertainty, with the experimental value determined by Robinson et a/.(1.849 A) [147] and the theoretical values calculated by Ma et al. [129]. Also this Al-N bond distance is intermediate between the corresponding distances in A1F [re = 1.65436 A [94,95]] and A1C1 [re = 2.13011 A [97]], parallelling the bond properties obtained from the Al quadrupole coupling constants and again showing the similarities between these three Al-X species. 7 .6 C o n c l u s i o n Laser ablation has been shown to be an effective route to produce metal isocyanides for investigation by F T M W spectroscopy. This first measurement of the hyperfine structure of aluminium isocyanide and magnesium isocyanide has produced several new parameters. The nuclear quadrupole and nuclear spin-rotation constants for the N nuclei, in each molecule, have been determined along with those for the A l nuclei in AINC. The sp-hybridisation in the bonding orbitals of AINC and MgNC have been investigated through Chapter 7. Microwave Spectroscopy of MgNC and AINC 118 the nuclear quadrupole coupling constants. The orbital hybridisation calculated for N in the linear metal isocyanides is quite similar. The Mg-NC bond has been found to have greater covalent character than that found in CaNC; this trend mirrors that found in the alkaline earth monohalides. The AINC bond properties have been found to be intermediate between those of A1F and A1C1. Chapter 7. Microwave Spectroscopy of MgNC and AINC 119 Table 7.1: Observed frequencies of 2 4 M g 1 4 N 1 2 C in its ground vibrational state". Transition Obs. Freq. Au Microwave F i t 6 , c Av Global F i t 0 ' 0 N' J' F' N" J" F" (MHz) (kHz) (kHz) 1 1/2 1/2 0 1/2 3/2 11922.9251 -0.9 -0 .9 1 1/2 3/2 0 1/2 1/2 11928.6450 0.5 0.7 1 3/2 3/2 0 1/2 3/2 11932.2411 0.3 0.2 1 3/2 1/2 0 1/2 1/2 11935.7735 -1 .0 -0 .8 1 3/2 5/2 0 1/2 3/2 11941.2144 1.1 1.1 2 3/2 5/2 1 1/2 3/2 23861.2286 2.0 2.2 2 5/2 3/2 1 3/2 3/2 23863.0750 -0.1 0.1 2 3/2 3/2 1 3/2 1/2 23863.7795 -1.4 -1.1 2 5/2 5/2 1 3/2 5/2 23864.6542 0.3 0.6 2 5/2 3/2 1 1/2 1/2 23872.3887 -1.3 -1 .2 2 5/2 5/2 1 3/2 3/2 23873.6278 1.4 1.8 2 5/2 7/2 1 3/2 5/2 23875.0396 -0.9 -0 .4 21 41/2 20 39/2 250445.992 4 21 43/2 20 41/2 250461.245 - 7 22 43/2 21 41/2 262356.464 - 1 8 22 45/2 21 43/2 262371.679 - 6 0 23 47/2 22 45/2 274279.991 - 4 0 24 47/2 23 45/2 286170.795 6 24 49/2 23 47/2 286186.023 - 9 26 51/2 25 49/2 309975.563 8 26 53/2 25 51/2 309990.788 6 27 53/2 26 51/2 321874.135 10 27 55/2 26 53/2 321889.423 79 28 57/2 27 55/2 333785.266 28 29 57/2 28 55/2 345663.196 23 29 59/2 28 57/2 345678.383 9 30 59/2 29 57/2 357553.444 - 2 3 30 61/2 29 59/2 357568.654 - 6 31 61/2 30 59/2 369440.810 - 1 1 31 63/2 30 61/2 369455.973 - 3 1 a Results between 11.9-23.9 GHz are from present study. Other data taken from Ref. [69]. 6 Observed minus calculated frequencies listed as Au. c Results for microwave and global fits are listed in Table 7.3. Chapter 7. Microwave Spectroscopy of MgNC and AINC 120 Table 7.2: Observed ground vibrational state frequencies of A l N C a . Transition Obs. Freq. Av Microwave b , c Av Global" ' 0 J' F{ F' J" F[' F" (MHz) (kHz) (kHz) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5/2 5/2 5/2 7/2 7/2 7/2 3/2 3/2 9/2 9/2 7/2 9/2 7/2 7/2 1/2 5/2 5/2 5/2 2 3/2 2 3/2 11 12 13 14 15 1/2 7/2 7/2 5/2 9/2 7/2 5/2 3/2 9/2 11/2 7/2 7/2 9/2 5/2 3/2 5/2 7/2 3/2 3/2 1/2 5/2 0 5/2 0 5/2 5/2 5/2 0 5/2 7/2 7/2 0 5/2 7/2 9/2 0 5/2 7/2 5/2 0 5/2 3/2 3/2 0 5/2 3/2 1/2 0 5/2 3/2 5/2 0 5/2 3/2 7/2 7/2 7/2 3/2 3/2 7/2 7/2 5/2 7/2 5/2 5/2 3/2 5/2 5/2 5/2 5/2 5/2 11963.2831 -0.1 -0 .0 11963.4981 -0 .0 0.1 11963.9959 0.0 0.2 11970.8348 -0.1 0.0 11971.2387 -0 .5 -0 .3 11971.2646 0.1 0.2 11974.2358 0.1 0.1 11974.4227 0.7 0.7 11974.4597 -0.1 0.0 23930.8749 0.4 0.4 23932.3001 0.8 0.9 23932.3737 -0.5 -0 .5 23932.6368 -0 .0 0.0 23935.9314 -0 .3 -0 .3 23936.5199 -0 .7 -0 .7 23939.2513 0.1 0.1 23939.4034 -0.3 0.2 23939.4758 -0.1 0.1 23939.5286 0.7 0.8 23940.1152 -0 .0 0.0 23940.2807 0.1 0.2 23940.5822 0.1 0.0 23941.6089 0.1 0.2 23941.8364 0.2 0.3 23941.9025 -0 .4 -0 .4 23946.7609 -0.1 -0 .1 23946.8933 -0.1 -.0.1 131642.189 - 1 6 143605.379 - 1 7 155567.428 - 4 3 167528.343 3 179487.893 - 1 8 Chapter 7. Microwave Spectroscopy of MgNC and AINC 121 Observed ground vibrational state frequencies of A l N C a (cont.). Transition Obs. Freq. A i / Microwave*'0 Au Global" ' 0 J' F{ F' J" F[' F" / M H z (kHz) / k H z 18 17 215357.910 - 8 19 18 227311.359 - 2 5 20 19 239263.086 - 1 0 21 20 251212.965 - - 2 22 21 263160.905 - 0 23 22 275106.835 12 24 23 287050.637 7 25 24 298992.248 8 26 25 310931.575 11 27 26 322868.534 19 28 27 334803.018 12 29 28 346734.944 - 6 30 29 358664.263 1 31 30 370590.854 - 2 32 31 382514.633 - 1 5 a Results between 11.9-23.9 GHz are from present study. Other data taken from Ref. [147]. 6 Observed minus calculated frequencies listed as Au. c Results for microwave and global fits are listed in Table 7.4. Chapter 7. Microwave Spectroscopy of MgNC and AINC Table 7.3: Molecular constants calculated for 2 4 M g 1 4 N 1 2 C in M H z a . Parameter Microwave Fit 6 Global Fit c Lit . d B0 5966.90349(63) 5966.90349(19) 5966.8969(24) D0 0.004233(88) 0.00424336(43) 0.0042338(35) tfoxlO7 - 0.3521(30) 0.308(16) 7 15.3320(20) 15.3322(19) 15.219(13) 7DX10 4 - -0.518(45) bF 29.1645(79) 29.1637(77) c 5.3838(82) 5.3840(77) eQg0(l4N) -2.3232(55) -2.3231(53) a One standard deviation in parentheses, in units of least significant digit. b Fit of microwave data only; for details see Sec 7.4.1. c Fit of microwave and millimeter wave data; for details see Sec. 7.4.1. d From millimeter wave study [69]. Chapter 7. Microwave Spectroscopy of MgNC and AINC Table 7.4: Molecular constants calculated for AINC in M H z a . Parameter Microwave Fit 6 Global Fit c Lit. r f 5984.676685(59) 5984.6752(14) 0.00388947(34) 0.0038870(24) 0.2551(26) 0.243(13) -35.6268(16) -2.1508(19) 0.003841(84) 0.00155(25) -0.00126(42) ° One standard deviation in parentheses, in units of least significant digit. b Fit of microwave data only; for details see Sec 7.4.2. c Fit of microwave and millimeter wave data; for details see Sec. 7.4.2. d Results from millimeter wave study [147]. B0 5984.67681(23) Do 0.003898(30) # 0 xl0 7 eQq{27k\) -35.6268(16) eQq(14N) -2.1508(19) C/( 2 7A1) 0.003850(84) C/( 1 4 N) 0.00156(25) aAl_N -0.00127(43) Chapter 7. Microwave Spectroscopy of MgNC and AINC 124 Table 7.5: Comparison of experimental and theoretical rotational constants for AINC. 5 / M H z Bo exp. 5984.6768 Be TZ2P + f CISD 5968° Be TZ2P + f CCSD(T) 5882a a From Ref. [129]. Be was calculated since it was determined that Be and B0 differ by less than 5 MHz. Chapter 7. Microwave Spectroscopy of MgNC and AINC 125 Table 7.6: Comparison of nuclear quadrupole coupling constants of MgNC, AINC and related cyanides and isocyanides. Species Structure eQ ? 0( 1 4N)7MHz 2^  K C N T-shaped —4.116'c NaCN T-shaped -4.219 M LiNC linear NC -2.9416 0.59 0.93 CaNC linear NC -2.697' 0.62 0.90 MgNC linear NC -2.323 0.64 0.80 AINC linear NC -2.151 0.65 0.75 HNC linear NC +0.283 a Molecular properties listed in order of decreasing ionic character of M-NC bond. 6 Using eQqz which is along C-N axis ( ± 1 deg). c From Ref. 153. d From Ref. 154. e From Ref. 152. 1 From Ref. 57. 9 From Ref. 155. h 5-character of 1 4 N bonding orbital calculated from the 1 4 N nuclear quadrupole coupling constant. For details, see Sec. 7.5.1. 1 Ionic character of M-NC bond calculated from electronegativities using Eq. (2.77). Chapter 7. Microwave Spectroscopy of MgNC and AINC 126 Table 7.7: s-character of Al bonding orbital calculated from Al nuclear quadrupole cou-pling constants. Species eQo( 2 7 Al)/MHz al A1F -37.49a 0.37 AINC -35.627 0.29 A1C1 -30.4086 0.26c AlBr -28.006a 0.20c a From Ref. [96]. b From Ref. [54]. c Differs from value in Ref. [2], because of the method used to calculate ic. d Result from Chapter 6. Chapter 7. Microwave Spectroscopy of MgNC and AINC 127 Table 7.8: Unpaired electron spin densities calculated at the 1 4 N nucleus from magnetic hyperfine constants for MgNC and CaNC. Parameter MgNC C a N C a 1 4 N atom6 6 F / M H z c/MHz 29.167 5.389 12.4815 2.074 -|*(0)| 2/au" 3 ( ( 3 c o s 2 0 - l ) / r 3 ) / a u - 3 0.0902704 0.093143 0.0386299 0.035842 5.606 2.8792 p{s)l% P(P)I% 1.61 3.23 0.689 1.24 -a Taken from Ref. 57. b Calculated from data in Ref. 22; for details see Sec. 7.5.2. Chapter 8 F T M W Spectroscopy of Yttrium Monohalides: Y F and Y B r 8.1 Introduction Interest in the spectroscopy of transition metal containing diatomic molecules has been motivated by the desire to understand the role that d orbitals play in bonding [156]. The yttrium and scandium monohalides have been used as prototype systems by theoreticians because Y and Sc have the simplest open d shell configuration [(core)nc?1(n + l)s2] [157]. Transition metal halides are also of interest in high temperature chemistry [158]. The chemiluminescent reactions of Sc, Y, and La atoms with halogen molecules have been investigated as part of the search for new chemical laser systems [159-161]. Over the past several years, spectroscopic studies of the electronic transitions of the yttrium and scandium monohalides have furthered our understanding of the electronic structures of these molecules. This chapter describes the F T M W spectroscopy of two of these species, Y F and YBr. The most thoroughly studied yttrium monohalide is yttrium monofluoride, whose electronic spectroscopy has been investigated in some detail. Initial studies by Barrow and co-workers [162,163], and by Shenyavskaya and co-workers [164-167], provided ro-tational analyses of six singlet transitions [BlW - X 1 S + , C 1 S+ - X 1 ^ , D1!! - X J E + , ElU - F1YJ - XXY,+ , and GlW - XLZ+) and one triplet transition (d3$ - a3A). 128 Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 129 Further studies by Kaledin and Shenyavskaya [168, 169] have improved the rotational constants available for the X 1 ^ and C 1 E + states and have provided rotational anal-yses of five new transitions (&3II - X^+, e3II(ft = 1) - X 1 E + , 3 n - a 3A, 3II - b3Il, and 3 f l — In the most recent study by Kaledin et al. [170], improved molecular constants have been determined for several electronic states and ligand field theory cal-culations were used to propose electronic configurations for the excited electronic states of Y F . Theoretical spectroscopic constants have been calculated by Langhoff et al. [157]. The permanent electric dipole moments of the X 1 E + ground electronic state and the BlW excited electronic state were determined by molecular beam optical Stark spec-troscopy [171]. Pure rotational transitions of Y F , in the ground electronic state, have been measured by molecular beam double resonance techniques. In the first study an effusive oven source was used to produce Y F and its spectrum was measured via a mil-limetre wave optical pump/probe technique [172]. A laser ablation source coupled to a pump/probe microwave optical double resonance spectrometer was used in the second study [173]. Both studies produced rotational constants for the ground vibrational state. Even though low J rotational transitions were measured, hyperfine structure due to the 1 9 F nucleus was not reported in either study. The spectroscopies of yttrium monochloride and monoiodide have been investigated to a lesser extent. The first study of YC1 was made in 1966 by Janney [174]. More recently, rotationally resolved studies have been made of six singlet transitions [Bll\ — X x £ + , C 1S+-X 1S+, D 1 n - X 1 £ + , D^-A'A, J 1 I I - X 1 E + , A r ln-X 1E+) [175-179]. In ad-dition a triplet transition (d3$ — a3A) and an intercombination band (D1!! — a3A) have been investigated [180]. The permanent electric dipole moments in the C 1 E + excited electronic state and X 1 ^ ground electronic state have been determined by molecular beam Stark spectroscopy [181]. The pure rotational spectrum has been measured by Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 130 Fourier transform microwave spectroscopy and the hyperfine parameters of both iso-topomers of YC1 have been determined [56]. Two ro-vibrational studies have been made of the spectrum of yttrium monoiodide in the infrared region by Bernard et al. [182,183]. Yttrium monobromide is the least studied of the yttrium monohalides. Low resolution spectra of two electronic transitions of Y B r have been measured by laser induced fluo-rescence [175]. In this study, rotational features could not be resolved and the molecular constants were determined using an iterative computer simulation technique. Accurate rotational constants could not be determined by this method since a ground state equi-librium bond length had to be assumed for YBr to perform the calculations. This chapter reports the first high resolution spectroscopic study of yttrium mono-bromide and the first measurement of the 1 9 F nuclear spin-rotation splitting in the spec-trum of yttrium monofluoride. Transitions for both molecules have been measured in the ground and first excited vibrational states. Rotational constants, Bo and B\, have been determined for both isotopomers of Y B r and from these the equilibrium bond length has been calculated. Equilibrium vibrational parameters have also been estimated. Nuclear quadrupole and nuclear spin-rotation hyperfine structure have been observed and cou-pling constants have been determined for YBr. By combining the F T M W results with data from other microwave studies, the nuclear spin-rotation constant of Y F has been determined. 8.2 Experimental Details The gas phase yttrium monobromide and yttrium monofluoride samples were prepared by reacting ablated Y metal (rod from Goodfellow 99.9%) with either bromine or sulfur hexafluoride, present as 0.05-0.1% in Ar carrier gas. The strongest transitions were seen easily with a few averaging cycles. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 131 8.3 Spectral Search and Assignment 8.3.1 Y F Yttrium monofluoride has only one isotopomer, 8 9 Y 1 9 F , and both 8 9 Y and 1 9 F have a nuclear spin of | . Only the lowest rotational transition, J = 1 — 0 near 17.3 GHz, was available in the frequency range of the spectrometer. This transition was measured in both the ground and first excited vibrational states. The v = 0 transition frequency was predicted using the millimetre wave results of Shirley et al. [172]; this value was within 100 kHz of the observed frequency. Following this, the results of Kaledin et al. [169,170] were used to predict the v = 1 transition; it was found within 60 kHz. Nuclear spin-rotation splitting due to the 1 9 F nucleus was observed in the measured transitions; this is shown in Fig. 8.1. Splitting due to the 8 9 Y nucleus, however, was not seen. This is not surprising because the magnitude of the magnetic moment of 8 9 Y is almost 20 times smaller than that of 1 9 F and also nuclear spin-rotation splitting due to 8 9 Y had not been observed in the F T M W study of the similar species YC1 [56]. The frequencies of the measured hyperfine components and their assignments are listed in Table 8.1. 8.3.2 YBr No previous high resolution spectroscopic measurements had been made of yttrium mono-bromide, so accurate rotational constants were not available to facilitate the search. The laser-induced fluorescence results of Fischell et al. [175] could not be used to predict the initial search parameters since the ground state rotational constants were not sufficiently accurate. So, the initial search parameters were calculated using the theoretical results of Langhoff et al. [157]. The uncertainty in the bond length was estimated by comparing their calculated r e for YC1 with that obtained experimentally by Simard et al. [181]. Nu-clear quadrupole coupling constants for each of the bromine nuclei, 7 9 B r and 8 1 B r (both Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 132 F=l/2-1/2-66 kHz < — • -F = 3/2 -1/2 i 17366.971 MHz 1 17367.371 MHz Figure 8.1: The J = 1 — 0 rotational transition of Y F . The nuclear spin-rotation splitting observed is due to the 1 9 F nucleus. This spectrum was obtained with 100 averaging cycles. The microwave excitation frequency was 17367.171 MHz. 4 K data points were measured with a 50 ns sampling interval and the power spectrum is displayed as an 8 K transformation. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 133 isotopes have / = |) were estimated using results obtained for KBr [125]. Five rotational transitions, J — 2 — l t o J = 6 — 5, were available in the frequency range of the spectrometer. The initial search range was calculated for the J = 2 — 1 transition; a line was found within 10 MHz of the prediction. The assignment was made by observing transitions due to both isotopomers, Y 7 9 B r and Y 8 1 B r , which have almost equal natural abundance (50.69% and 49.31%, respectively) and was verified by prediction and measurement of higher J transitions. The measured transition frequencies for Y 7 9 B r and Y 8 1 B r in the ground vibrational state are listed in Tables 8.2 and 8.3, respectively. The hyperfine structure observed was due only to the bromine nucleus. As was found for Y F and YC1, splitting due to yttrium (/ = 1) spin-rotation interaction could not be resolved. The rotational transitions of YBr in the v = 1 vibrationally excited state were predicted by estimating the vibration-rotation constant cte. This was done by comparing the values of a e for A1F, A1C1 and AlBr [184] with those of Y F [170] and YC1 [181]. This method proved to be quite accurate as the J = 2 — 1 rotational transitions in the first excited vibrational state were found within 5 MHz of the predicted values. The observed transition frequencies for Y 7 9 B r and Y 8 1 B r in the v = 1 state are also listed in Tables 8.2 and 8.3, respectively. 8.4 Analyses 8.4.1 Y F The results obtained in this study were used alone and in combination with the results of other pure rotational studies to determine molecular constants of Y F . First, the nu-clear spin-rotation constants for each vibrational level were calculated directly from the measured transitions; these calculations are referred to below as the direct calculation. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 134 F= 11 / 2 -9 / 2 F =9/2 - 7 / 2 i 1 14833.161 MHz 14833.761 MHz Figure 8.2: The AF = +1 hyperfine components of the J = 4 — 3 transition of Y 8 1 B r . 50 averaging cycles were co-added to obtain this spectrum. The excitation frequency was 14833.461 MHz. 4 K data points were recorded and this power spectrum was obtained with an 8 K transformation. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 135 The nuclear spin-rotation contribution to the molecular energy is given by Eq. (2.49): ^spin-rot. = y [ F ( F + l ) - J ( J + l ) - / ( / + l ) ] . This expression was used to relate the energy difference between the measured hyperfine components in each vibrational level to the nuclear spin-rotation constant, C / and the hypothetical unsplit frequency, v. The results are listed in Table 8.4. The Cj values are equal within the calculated uncertainties and indicate that the vibrational dependence of the nuclear spin-rotation constants is less than the estimated error. A full fit could only be made by combining data from another study with the present results because only one rotational transition was measured in the F T M W study. The J = 2 — 1 and J = 3 — 2 transitions obtained in the pump/probe microwave-optical double resonance (PPMODR) study [173] were employed with the v = 0 F T M W results to calculate ground vibrational state parameters. The P P M O D R transitions were treated as overlapped hyperfine components and were fit as blended lines using the predicted intensities as weighting factors. The rotational constant, B0, the centrifugal distortion constant, D0, and the 1 9 F nuclear spin-rotation coupling constant, CT, were determined using Pickett's exact fitting program S P F I T . A relative weighting of 9:1 was given to the F T M W lines with respect to the other pure rotational data; this ratio was obtained from the estimated measurement uncertainties. The constants determined are listed in Table 8.5 under the heading Combined Fit. Values of Ci(v = 0) and B0 obtained from the direct calculation are listed under the heading Direct Calculation; the B0 quoted for the direct calculation was obtained from the hypothetical unsplit frequency by fixing D0 at the value from the P P M O D R study. Also listed are the B0 and D0 values from the P P M O D R study [173]. The rotational constant and the 1 9 F nuclear spin-rotation coupling constant from the combined fit compare quite well with those determined by direct calculation. However, the B0 and D0 results from the combined fit do not compare Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 136 as well with those obtained from the PPMODR study; neither constant is within three standard deviations. One source of this difference could be shifts in the spectrum due to partially resolved hyperfine splitting; the J = 1 - 0 transition listed in the P P M O D R study is within 3 kHz of the J = 1 — 0 F — 3/2 — 1/2 component measured in this study. To test this possibility, the P P M O D R results were fit alone. These were not treated as blended lines; the frequencies were assigned to the most intense hyperfine component of each transition. BQ and D0 were determined while Ci was held fixed at the value of Ci(v — 0) determined by direct calculation. The results are listed in Table 8.5 under the heading P P M O D R Refit. The calculated constants agree much better with those of the combined fit; BQ and DQ are within two standard deviations. It appears that the discrepancy between the B0 obtained using the F T M W results (either in the combined fit or direct calculation) and the published P P M O D R results are most likely due to partially resolved hyperfine effects. 1 Finally, a fit using the F T M W data and the millimetre wave optical pump/probe data [172] was attempted. Unfortunately, this did not prove fruitful because there was some difficulty in producing observed minus calculated values that were in the range of the estimated measurement uncertainties. A similar difficulty had been found in the P P M O D R study; a slight discrepancy was found between the constants obtained in the millimetre wave study [172] and those of the PPMODR study [173]. Poor calibration of the millimetre wave source was suggested as a possible source of this difference [173]. l\t was also noted that the molecular constants reported in the P P M O D R study do not reproduce the reported transition frequencies well. A refit of the reported lines produces Bo and Do constants which are within three standard deviations of those listed in the P P M O D R paper. However, this difference in constants is about one third of the difference between the combined fit and the reported P P M O D R constants so hyperfine effects in the P P M O D R results appear to be still significant. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 137 8.4.2 YBr The frequencies obtained for each isotopomer of Y B r in each vibrational state were fit separately using Pickett's non-linear least squares fitting program S P F I T [76]. In each fit, the rotational constant, B, and centrifugal distortion constant, D, were determined along with the hyperfine parameters for the bromine nuclei, the nuclear quadrupole cou-pling constant, eQq(Br), and the nuclear spin-rotation constant, C/(Br). The obtained parameters are listed in Table 8.6. There are no previous rotationally resolved stud-ies with which to compare these results; however, the isotopic ratios of the hyperfine parameters should provide a reasonable comparison. The ratios of the hyperfine parameters of the two isotopomers of yttrium monobro-mide, Y 7 9 B r and Y 8 1 B r , should be equal to the ratios of certain molecular and nuclear properties. This method is identical to that employed in Sec. 6.4 for MgBr and AlBr. The ratio of the eQq(Br) and C/(Br) constants are equal to the ratio of the electric quadrupole moments and the nuclear magnetic moments of the bromine nuclei, respec-tively. The ratio of the nuclear spin-rotation constants also depends on the inverse ratio of the reduced masses. The ratios of the hyperfine parameters have been calculated for both the v = 0 and v = 1 vibrational states and are listed in Table 8.7. Also listed are the ratios of the appropriate nuclear and molecular parameters calculated from data taken from Ref. 120. The nuclear spin-rotation constants were not very well determined; however, the ratios agree well with the literature value, within the large estimated un-certainty. The ratios of the nuclear quadrupole coupling constants do not agree quite as well. There appears to be a small deviation in the ratio obtained for the v = 0 constants. Strictly, the ratios of the nuclear and molecular properties are equal to the ratio of the equilibrium hyperfine parameters [117,118]. As was done for MgBr and AlBr, the vibra-tional dependence of the nuclear quadrupole coupling constants was calculated using an Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 138 expansion in terms of the vibrational contribution: eQqv = eQqe + eQqx [v + - (8.1) where eQqe is the equilibrium nuclear quadrupole coupling constant and eQqi is the vibration-rotation correction term. The vibrational dependence of the nuclear quadrupole coupling constants can be summarised by the following expressions, The ratio of the equilibrium nuclear quadrupole coupling constants is listed in Table 8.7. This value agrees more closely with the literature value than the result obtained of the v = 0 parameters. Evidently there is a small vibrational dependence of the nuclear quadrupole coupling constants. 8.5 Discussion 8.5.1 Equi l ibrium Bond Distance of Y B r The same procedure was used to estimate the equilibrium bond distance of yttrium monobromide as was used for magnesium monobromide in Sec. 6.5.1. The vibrational dependence of the rotational constant, B, can be expressed in terms of the equilibrium rotational constant, Be, and the vibration-rotation constants, cte and -ye using Eq. (2.16) which is repeated here for convenience, This expression was employed in three calculations to estimate the equilibrium rotational constant and the equilibrium bond distance of YBr. For the first calculation, Eq. (2.16) V Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 139 was truncated following the a e term. Be and ae were calculated directly from B0 and Bi and r e was calculated from Be using atomic masses and fundamental constants from Ref. 120. The values of Be, ae and r e obtained are listed in Table 8.8 under the heading Method I. The difference in r e values obtained for the two isotopomers is within the cal-culated uncertainty and is most likely due to the uncertainties of the masses, which are greater than those of the rotational constants. For the second calculation, an estimate was made for the higher order vibration-rotation contribution. The value of 7 e was esti-mated as 10~3 • ae by comparisons with KBr [185] and RbBr [186]. Be was determined by including the estimated 7 e value in the calculation and thus a second value of re was obtained. These results are listed in Table 8.8 under the heading Method II. The calcu-lated uncertainty in r e is derived only from the uncertainties in the rotational constants, fundamental constants and masses used in the calculation. The difference between the re value determined by this method and that calculated by Method I is of the order of 10" 6A. In these two calculations no attempt was made to take account of electronic effects. A description of these effects can be found in Sec. 2.4. To estimate the magnitude of the effects due to non-spherical charge distribution, yttrium monobromide was considered to be the completely ionic species Y + B r ~ . This provides a third estimate of the equilibrium bond distance of YBr. Be and cte were calculated just as they were in Method II and then r e was determined using a reduced mass calculated using ion masses instead of atomic masses. The resulting values are listed in Table 8.8 under the heading Method III. The equilibrium bond distances calculated by Method II and Method III differ by only 10~6A, which is on the order of the estimated uncertainty of r e . This small change was not unexpected, since the masses of Y and Br are much greater than the mass of Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 140 an electron. A reasonable upper limit for the deviation of re from that in the Born-Oppenheimer approximation is ~ IO"5 A, as was found for MgBr and AlBr in Sec. 6.5.1. Table 8.9 presents the equilibrium bond distances calculated by each method and an average of all three values. Also listed are the value calculated in the theoretical study by Langhoff et al. [157] and the assumed value from the laser-induced fluorescence study by Fischell et al. [175] for comparison. The result from the present study is the first accurate determination of the equilibrium bond distance of yttrium monobromide. 8.5.2 Estimate of Vibration Frequency The vibration frequency, uje, and the anharmonicity constant, tvexe, of Y B r can be esti-mated using the relations developed by Kratzer [187] and Pekeris [15], respectively, I4B3 u , = ^ (8.2) u>e*. = B<(fg + l ) 2 (8.3) where Be and De are the equilibrium rotational and centrifugal distortion constants and ae is the vibration-rotation constant. Though these expressions are exact only for a Morse potential function, they do provide a reasonable estimate of the desired constants. An estimate of the uncertainty in the calculated values was obtained by determining oje and uexe from Eqs. (8.2) and (8.3) for Y F and YC1 using the molecular constants in Refs. 169 and 176, respectively. The percentage differences between the experimentally determined oje and u>exe values and those calculated using the Kratzer and Pekeris relations are ~ 0.5% and ~ 6%, respectively. The u>e and u>exe parameters were calculated for both Y 7 9 B r and Y 8 1 B r and are listed in Table 8.10. In the calculations, De was approximated as D0, since the centrifugal distortion constants are not sufficiently well determined to calculate the vibrational dependence. Be values from Method I and Method II (see Sec. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 141 8.5.1) produced identical u>e and u>exe values, within the number of significant figures given. Vibration frequency and anharmonicity constant values determined in the laser-induced fluorescence study [175] and the theoretical study of LanghofF et al. [157] are also listed in Table 8.10. These values are for an unspecified isotopomer because features due to the individual species could not be resolved. The cue and u>exe results from Fischell et al. [175] compare reasonably well with those derived from the F T M W results. 8.5.3 Y B r Nuclear Quadrupole Coupling Constants The ionic character of the Y-Br bond can be estimated from the bromine nuclear quadrupole coupling constant, eQq(Br) using Eq. (2.71), which is repeated here for reference eQe4io(Br) The derivation of this expression is found in Sec. 2.5. The ionic character calculated for Y B r is listed in Table 8.11 along with the bromine nuclear quadrupole coupling constants and calculated ionic characters of several related alkali metal bromides. All four compounds are very ionic and it can be seen by comparing the values of ic that Y B r is very similar in ionicity to the alkali metal bromides. A similar result has also been found for YC1 [56]. 8.6 Conclusion The first high resolution study of the spectra of Y 7 9 B r and Y 8 1 B r , and the first measure-ment of the nuclear spin-rotation structure for yttrium monofluoride, have been made by F T M W spectroscopy. Accurate rotational constants have been determined for yt-trium monobromide and have been used to obtain an accurate equilibrium bond length. Nuclear quadrupole hyperfine parameters have been determined and used to compare Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 142 the ionic character of the Y-Br bond to that of the alkali metal bromides. Through a series of fits, the 1 9 F nuclear spin-rotation coupling constant of yttrium monofluoride has been determined. Discrepancies between the results of this study and those of other pure rotational studies have been investigated. The source of these discrepancies appears to be partially resolved hyperfine structure. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 143 Table 8.1: Observed transitions of Y F in the v = 0 and v = 1 vibrational states in MHz. v' J' F' v" J" F" Observed Frequency"'7" 0 1 3/2 0 0 1/2 17367.2044(-7) 0 1 1/2 0 0 1/2 17367.1450(-4) 1 1 3/2 1 0 1/2 17269.2718 1 1 1/2 1 0 1/2 17269.2128 0 1 0 0 17367.202 0 2 0 1 34734.210( 8) 0 3 0 2 52100.882(-2) ° Results for hyperfine transitions are from present study. Other data taken from P P M O D R study [173]. 6 Observed minus calculated frequencies from combined fit in parentheses, in units of least significant digit. Constants obtained in fit are listed in Table 8.5 under heading Combined Fit. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 144 Table 8.2: Measured transition frequencies of Y 7 9 B r in v = 0 and v = 1 vibrational states. Transition v = 0 Obs. - calc. v = 1 Obs. - calc. J' F' J" p" /MHz /kHz / M H z /kHz 2 3/2 1 3/2 7512.3489 0.9 7488.7459 0.4 2 5/2 1 3/2 7514.6779 -0.3 7491.3247 -1.2 2 7/2 1 5/2 7514.6873 0.3 7491.3357 0.9 2 1/2 1 1/2 7514.9342 0.2 2 5/2 1 5/2 7517.8909 -0.0 2 3/2 1 1/2 7518.1816 0.0 3 3/2 2 3/2 11269.7894 0.4 3 5/2 2 5/2 11270.7146 0.2 11235.5503 -0.1 3 7/2 2 5/2 11272.2519 -0.9 11237.2520 -0.7 3 9/2 2 7/2 11272.2621 0.7 11237.2619 0.4 3 3/2 2 1/2 11273.0349 -1.7 11238.1228 0.0 3 5/2 2 3/2 11273.0451 0.5 11238.1317 0.9 3 7/2 2 7/2 11275.4572 0.4 4 5/2 3 5/2 15026.8330 -0.5 4 7/2 3 7/2 15028.5591 -0.0 4 9/2 3 7/2 15029.7309 -0.2 14983.0760 -0.2 4 11/2 3 9/2 15029.7399 0.2 14983.0846 -0.4 4 5/2 3 3/2 15030.0878 -1.3 14983.4736 -0.8 4 7/2 3 5/2 15030.0983 0.8 14983.4836 0.6 4 9/2 3 9/2 15032.9269 0.5 5 11/2 4 9/2 18787.1446 -0.3 18728.8319 -0.7 5 13/2 4 11/2 18787.1537 0.2 18728.8420 0.6 5 7/2 4 5/2 18787.3489 -0.6 18729.0613 0.4 5 9/2 4 7/2 18787.3589 0.9 18729.0696 0.0 6 13/2 5 11/2 22544.4988 0.6 6 15/2 5 13/2 22544.5062 -0.6 Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 145 Table 8.3: Measured transition frequencies of Y 8 1 B r in v = 0 and v = 1 vibrational states. Transition v = 0 Obs. - calc. v = 1 Obs. - calc. J' F' J" F" /MHz /kHz / M H z /kHz 2 3/2 1 3/2 7414.5535 0.5 7391.4534 -0.2 2 5/2 1 3/2 7416.5039 -0.1 7393.6124 -0.4 2 7/2 1 5/2 7416.5134 0.1 7393.6220 -0.2 2 1/2 1 1/2 7416.7116 -0.9 2 5/2 1 5/2 7419.1812 -0.5 2 3/2 1 1/2 7419.4271 -0.3 3 3/2 2 3/2 11122.8849 0.5 3 5/2 2 5/2 11123.6571 0.1 11089.2082 0.5 3 7/2 2 5/2 11124.9487 -0.1 11090.6353 -0.3 3 9/2 2 7/2 11124.9581 0.1 11090.6452 0.3 3 3/2 2 1/2 11125.5978 -1.5 11091.3577 -0.5 3 5/2 2 3/2 11125.6091 1.1 11091.3679 1.0 3 7/2 2 7/2 11127.6178 0.6 4 5/2 3 5/2 14830.8801 -0.5 4 7/2 3 7/2 14832.3215 0.1 4 9/2 3 7/2 14833.3086 -0.6 14787.5673 -0.7 4 11/2 3 9/2 14833.3188 0.4 14787.5776 0.4 4 5/2 3 3/2 14833.6036 -0.5 14787.8963 -0.4 4 7/2 3 5/2 14833.6135 0.3 14787.9060 0.3 4 9/2 3 9/2 14835.9692 0.8 5 11/2 4 9/2 18541.6102 -0.2 18484.4390 0.2 5 13/2 4 11/2 18541.6201 0.5 18484.4477 -0.3 5 7/2 4 5/2 18541.7764 -0.9 18484.6248 -0.8 5 9/2 4 7/2 18541.7873 0.9 18484.6356 0.9 6 13/2 5 11/2 22249.8551 0.7 6 15/2 5 13/2 22249.8626 -1.0 Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr Table 8.4: Molecular constants obtained by direct calculation for Y F in MHz. Parameter Value" 17367.1846(13) 17269.2521(13) d(v = 0) 0.0396(9) Ci{v = 1) 0.0393(9) a Error estimated from measurement uncertainty in parentheses. b uv is the hypothetical unsplit J = 1 — 0 frequency of the vth vibrational state. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 147 Table 8.5: Ground vibrational state molecular constants determined for Y F in MHz. Parameter Direct Calc. 0' 6 Combined Fit c P P M O D R Rentc'd P P M O D R L i t . c e Bo 8683.60734(67) 8683.60658(41) 8683.6045(11) 8683.6156(11) Do [0.007521] 0.006996(39) 0.007086(72) 0.007521(74) Ci 0.0396(9) 0.03983(94) [0.0396] ° B0 determined from hypothetical unsplit frequency uQ using Do from P P M O D R study [173]. 6 Error estimated from measurement uncertainty in parentheses. c One standard deviation in parentheses, in units of the least significant digit. d Fit of three lines from P P M O D R study, assigning each line as the most intense hyperfine component in each rotational transition. Ci was held fixed at the value determined in the v = 0 direct calculation. e Taken from P P M O D R study of Fletcher et al. [173]. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 148 Table 8.6: Molecular constants calculated for Y B r in MHz°. Parameter Y<"9 Br y 8 1 Br v = 0 v = 1 V = 0 v = 1 B 1878.741007(71) 1872.910362(97) 1854.185861(71) 1848.469305(97) D 0.0004033(15) 0.0004004(25). 0.0003923(15) 0.0003923(25) eQqiBr) •12.9352(16) 14.3349(45) 10.8017(16) 11.9683(45) C/(Br) 0.00858(12) 0.00877(20) 0.00918(12) 0.00921(20) ° One standard deviation in parentheses, in units of least significant digit. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 149 Table 8.7: Calculated ratios of hyperfine parameters compared to nuclear and molecular properties of YBr. v=0 v=l Eq.° Lit. eQq(79Br)/eQq(81Br) 1.1975(2) 1.1977(6) 1.1974(4) 1.19707(3)6 C7( 7 9 Br) /C/( 8 1 Br) 0.935(18) 0.952(30) - 0.939995(2)c a For method of calculation, see text Sec. 8.4.2. b Ratio of electric quadrupole moments of 7 9 B r and 8 1 B r , taken from Ref. 2. c Ratio of nuclear magnetic moments of 7 9 B r and 8 1 Br multiplied by inverse ratio of reduced masses of Y 7 9 B r and Y 8 1 B r , calculated using values in Ref. 120. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 150 Table 8.8: Equilibrium parameters calculated for Y B r a ' 6 . Method I Y 7 9 B r Y 8 1 B r fie/MHz a e / M H z r e / A 1881.65633(9) 5.83065(12) 2.534613(1) 1857.04414(9) 5.71656(12) 2.534612(1) Method II Y 7 9 B r Y 8 1 B r 5 e / M H z a e / M H z rjk 1881.64906(9) 5.81901(12) 2.534618(1) 1857.03701(9) 5.70515(12) 2.534617(1) Method III Y 7 9 B r Y 8 1 B r B e / M H z a e / M H z r e / A 1881.64906(9) 5.81901(12) 2.534617(1) 1857.03701(9) 5.0515(12) 2.534616(1) a For methods of calculation, see Sec. 8.5.1. b Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 151 Table 8.9: Summary of equilibrium bond length estimates for YBr". Method I6 Method II6 Method III6 Ave. c Lit. Theo. Lit. LIF r e / A 2.534613(1) 2.534618(1) 2.534617(1) 2.53462 2.605° 2.800e a For description of methods see Sec. 8.5.1. 6 Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. c Average of values obtained by three methods. The deviation of r e from that obtained in the Born-Oppenheimer approximation is estimated to be on the order of 10 - 5 A. d re from Ref. 157. e Value of re used in laser fluorescence study [175]. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 152 Table 8.10: Estimate of vibration frequency of YBr. Y 7 9 B r a ' C ) Y 8 1 B r a , b Lit. Expt. c Lit Theo. a c^e/cm-1 271.1 269.5 268(2) 259 u)exe/cm~l 0.66 0.65 0.8(2) a For description of calculations see Sec. 8.5.2. 6 Uncertainties in u>e and uexe are estimated to be ~ 0.5% and ~ 6%, respectively. c Results taken from Ref. 175. Features due to each of the isotopomers of Y B r could not be resolved. d Taken from Ref. 157. Chapter 8. FTMW Spectroscopy of Yttrium Monohalides: YF and YBr 153 Table 8.11: Calculated ionic character of Y 7 9 B r and related alkali metal bromides. Y 7 9 B r 2 3 N a 7 9 B r a 3 9 K 7 9 B r b 8 5 R b 7 9 B r c e<2<?(79Br)/MHz 12.935 58.60801 10.2383 3.50 ij% 98.3 92.5 98.7 99.5 a Results taken from Ref. 124. b Results taken from Ref. 125. c Results taken from Ref. 188. Bibliography [1] C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (Dover Publications, New York, 1975). [2] W. Gordy and R. L. Cook, Microwave Molecular Spectra, No. XVIII in Techniques of Chemistry, 3rd ed. (John Wiley & Sons, New York, 1984), . [3] Landolt-Bornstein, edited by W. Hiittner (Springer-Verlag, Berlin, 1967, 1974, 1982, 1992), Vol. 11/4, 11/6, 11/14, 11/19. [4] G. Winnewisser, E . Herbst, and H. Ungerechts, in Spectroscopy of the Earth's Atmosphere and Interstellar Medium, edited by K. N. Rao and A. Weber (Academic Press, London, 1992), pp. 423-517. [5] A. Omont, J. Chem. Soc. Faraday Trans. 89, 2137 (1993). [6] B. E . Turner, Astrophys. Space Sci. 224, 297 (1995). [7] E . Herbst, Ann. Rev. Phys. Chem. 46, 27 (1995). [8] T. J . Balle, E . J. Campbell, M . R. Keenan, and W. H. Flygare, J. Chem. Phys. 7 1 , 2723 (1979). [9] T. J. Balle and W. H. Flygare, Rev. Scient. Instrum. 52, 33 (1981). [10] H. Dreizler, Mol. Phys. 59, 1 (1986). [11] J. R. Morton, Chem. Rev. 64, 453 (1964). [12] E . Hirota, High-Resolution Spectroscopy of Transient Molecules, Vol. 40 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1985), . [13] H. W. Kroto, Molecular Rotation Spectra, 2nd ed. (Dover Publications, New York, 1992). [14] P. M . Morse, Phys. Rev. 34, 57 (1929). 154 Bibliography 155 [15] C. L. Pekeris, Phys. Rev. 4 5 , 98 (1934). [16] R. N. Zare, Angular Momentum (John Wiley and Sons, New York, 1988). [17] C. H. Townes and B. P. Dailey, J. Chem. Phys. 1 7 , 782 (1949). [18] Ch. Ryzlewicz, H.-U. Schiitze-Pahlmann, J. Hoeft, and T. Torring, Chem. Phys. 7 1 , 3 8 9 (1982). [19] T. A. Dixon and R. C. Woods, J. Chem. Phys. 6 7 , 3956 (1977). [20] R. A. Frosch and H. M . Foley, Phys. Rev. 8 8 , 1337 (1952). [21] W. Weltner, Jr., Magnetic Atoms and Molecules (Van Nostrand, New York, 1983). [22] J . R. Morton and K. F. Preston, J. Magn. Reson. 3 0 , 577 (1978). [23] N. F. Ramsey, Molecular Beams (Oxford University, London, 1956). [24] T. R. Dyke and J. S. Muenter, in Molecular Structure and Properties, Vol. 2 of International Review of Science, Physical Chemistry, Series 2, edited by A. D. Buckingham (Butterworth and Co., London, 1975), pp. 27-92. [25] C. Schlier, Fortschr. Phys. 9 , 455 (1961). [26] C. Styger and M . C. L. Gerry, J. Mol. Spectrosc. 1 5 8 , 328 (1993). [27] C. C. Costain, J. Chem. Phys. 2 9 , 864 (1958). [28] J . H. Van Vleck, J. Chem. Phys. 4 , 327 (1936). [29] B. Rosenblum, A. H. Nethercot, Jr., and C. H. Townes, Phys. Rev. 1 0 9 , 400 (1958). [30] F. C. De Lucia, P. Helminger, and W. Gordy, Phys. Rev. A 3 , 1849 (1971). [31] P. R. Bunker, J. Mol. Spectrosc. 3 5 , 306 (1970). [32] P. R. Bunker, J. Mol. Spectrosc. 6 8 , 367 (1977). [33] J. K. G. Watson, J. Mol. Spectrosc. 4 5 , 99 (1973). [34] J. K. G. Watson, J. Mol. Spectrosc. 8 0 , 411 (1980). [35] W. Gordy, Faraday Discuss. Chem. Soc. 1 9 , 14 (1955). [36] U. Fano, Revs. Modern Phys. 2 9 , 74 (1957). [37] J. C. McGurk, T. G. Schmalz, and W. H. Flygare, Adv. Chem. Phys. 2 5 , 1 (1974). Bibliography 156 [38] H. Dreizler, Ber. Bunsenges. Phys. Chem. 99, 1451 (1995). [39] J.-U. Grabow and W. Stahl, Z. Naturforsch. Teil A 45, 1043 (1990). [40] Y. Xu, W. Jager, M . C. L. Gerry, and I. Merke, J. Mol. Spectrosc. 160, 258 (1993). [41] I. Merke and H. Dreizler, Z. Naturforsch. Teil A 43, 196 (1988). [42] J. Haekel and H. Mader, Z. Naturforsch. Teil A 43, 203 (1988). [43] A. E . Derome, Modern NMR Techniques for Chemistry Research (Pergamon, Ox-ford, 1987). [44] R. D. Suenram, F. J. Lovas, G. T. Fraser, and K. Matsumura, J. Chem. Phys. 92, 4724 (1990). [45] Y. Ohshima and Y. Endo, Chem. Phys. Lett. 213, 95 (1993). [46] K. D. Hensel and M . C. L. Gerry, J. Chem. Soc. Faraday Trans. 93, 1053 (1997). [47] A. H. Firester, Rev. Scient. Instrum. 37, 1264 (1966). [48] T. G. Dietz, M . A. Duncan, D. E. Powers, and R. E . Smalley, J . Chem. Phys. 74, 6511 (1981). [49] V. E . Bondybey and J. H. English, J. Chem. Phys. 74, 6978 (1981). [50] R. E . Smalley, Laser Chem. 2, 167 (1983). [51] R. D. Suenram, F. J. Lovas, and K. Matsumura, Astrophys. J. 342, L103 (1989). [52] R. D. Suenram, G. T. Fraser, F. J. Lovas, and C. W. Gillies, J. Mol. Spectrosc. 148, 114 (1991). [53] C. E . Blom, H. G. Hedderich, F. J. Lovas, R. D. Suenram, and A. G. Maki, J. Mol. Spectrosc. 152, 109 (1992). [54] K. D. Hensel, C. Styger, W. Jager, A. J. Merer, and M . C. L. Gerry, J. Chem. Phys. 99, 3320 (1993). [55] R. J . Low, T. D. Varberg, J. P. Connelly, A. R. Auty, B. J. Howard, and J. M . Brown, J. Mol. Spectrosc. 161, 499 (1993). [56] K. D. Hensel and M . C. L. Gerry, J. Mol. Spectrosc. 166, 304 (1994). [57] C. T. Scurlock, T. C. Steimle, R. D. Suenram, and F. J. Lovas, J. Chem. Phys. 100, 3497 (1994). Bibliography 157 [58] Y. Kawashima, R. D. Suenram, and E. Hirota, J. Mol. Spectrosc. 175, 99 (1996). [59] N. M . Lakin, T. D. Varberg, and J. M . Brown, J. Mol. Spectrosc. 183, 34 (1997). [60] Y. Kawashima, Y. Ohshima, Y. Endo, and E. Hirota, J. Mol. Spectrosc. 174, 279 (1995). [61] F. J . Lovas, Y. Kawashima, J.-U. Grabow, R. D. Suenram, G. T. Fraser, and E . Hirota, Astrophys. J. 455, L201 (1995). [62] U. Kretschmer, D. Consalvo, A. Knaack, W. Schade, W. Stahl, and H. Dreizler, Mol. Phys. 87, 1159 (1996). [63] D. E . Powers, S. G. Hansen, M . E. Geusic, A. C. Puiu, J. B. Hopkins, T. G. Dietz, M . A. Duncan, P. R. R. Langridge-Smith, and R. E . Smalley, J . Phys. Chem. 86, 2556 (1982). [64] M . Barnes, M . M . Fraser, P. G. Hajigeorgiou, A. J. Merer, and S. D. Rosner, J. Mol. Spectrosc. 170, 449. (1995). [65] D. C. Morton, J. F. Drake, E . B. Jenkins, J. B. Rogerson, L. Spitzer, and D. G. York, Astrophys. J. 181, L103 (1973). [66] D. C. Morton, Astrophys. J. 193, L35 (1974). [67] B. E . Turner, Astrophys. J. 376, 573 (1991). [68] M . Guelin, J. Cernicharo, C. Kahane, and J. Gomez-Gonzalez, Astron. Astrophys. 157, L17 (1986). [69] K. Kawaguchi, E . Kagi, T. Hirano, S. Takano, and S. Saito, Astrophys. J . 406, L39 (1993). [70] J . H. Goebel and S. H. Moseley, Astrophys. J. 290, L35 (1985). [71] J . A. Nuth, S. H. Moseley, R. F. Silverberg, J. H. Goebel, and W. J . Moore, Astrophys. J. 290, L41 (1985). [72] B. Begemann, J. Dorschner, T. Henning, H. Mutschke, and E . Thamm, Astrophys. J . 423, L71 (1994). [73] S. Takano, S. Yamamoto, and S. Saito, Chem. Phys. Lett. 159, 563 (1989). [74] H. A. Wilhelm, Iowa State College J. Sci. 6, 475 (1932). [75] M . Marcano and R. F. Barrow, J. Chem. Soc. Faraday Trans. 65, 2936 (1970). Bibliography 158 [76] H. M . Pickett, J. Mol. Spectrosc. 148, 371 (1991). [77] L. B. Knight, Jr., W. C. Easley, and W. Weltner, Jr., J. Chem. Phys. 54, 322 (1971). [78] M . A. Anderson, M . D. Allen, and L. M . Ziurys, Astrophys. J. 425, L53 (1994). [79] M . A. Anderson, M . D. Allen, and L. M . Ziurys, J. Chem. Phys. 100, 824 (1994). [80] M . A. Anderson and L. M . Ziurys, Chem. Phys. Lett. 224, 381 (1994). [81] C. M . Olmsted, Zeitschr. f. wiss. Phot. 4, 293 (1906). [82] O. H. Walters and S. Barratt, Proc. R. Soc. London A 118, 120 (1928). [83] F. Morgan, Phys. Rev. 50, 603 (1936). [84] R. E . Harrington, Ph.D. thesis, University of California, 1942. [85] S. N. Puri and H. Mohan, Curr. Sci. 43, 442 (1974). [86] B. R. K. Reddy and P. T. Rao, Curr. Sci. 39, 509 (1970). [87] V . M . Rao, M . L. P. Rao, and B. R. K. Reddy, J. Phys. B 15, 4161 (1982). [88] D. P. Nanda and B. S. Mohanty, Ind. J. Pure Appl. Phys. 18, 324 (1980). [89] N. E . Kuz'menko and L. V. Chumak, J. Quant. Spectrosc. Radiat. Transfer 35, 419 (1986). [90] R. G. Sadygov, J. Rostas, G. Taieb, and D. R. Yarkony, J . Chem. Phys. 106, 4091 (1997). [91] F. Fethi, Ph.D. thesis, Universite de Paris XI, 1995. [92] M . M . Patel and P. D. Patel, J. Phys. B 2, 515 (1969). [93] D. R. Lide, Jr., J. Chem. Phys. 42, 1013 (1965). [94] F. Wyse, W. Gordy, and E. F. Pearson, J. Chem. Phys. 52, 3887 (1970). [95] J . Hoeft, F. J. Lovas, E . Tiemann, and T. Torring, Z. Naturforsch. Teil A 25, 1029 (1970). [96] R. Honerjager and R. Tischer, Z. Naturforsch. Teil A 29, 342 (1974). [97] F . ' C . Wyse and W. Gordy, J. Chem. Phys. 56, 2130 (1972). Bibliography 159 [98] J. Hoeft, T. T6rring, and E . Tiemann, Z. Naturforsch. Teil A 28, 1066 (1973). [99] F. H. Crawford and C. F. Ffolliott, Phys. Rev. 44, 953 (1933). [100] E . Miescher, Helv. Phys. Acta 8, 279 (1935). [101] E . Miescher, Helv. Phys. Acta 9, 693 (1936). [102] H. G. Howell, Proc. R. Soc. London A 148, 696 (1935). [103] P. C. Mahanti, Ind. J. Phys. 9, 369 (1935). [104] C. G. Jennergren, Nature 161, 315 (1948). [105] C. G. Jennergren, Ark. Mat. Astr. Fys. 35A, 1 (1948). [106] R. S. Ram, K. N. Upadhya, D. K. Rai, and J. Singh, Opt. Pura Apl. 6, 38 (1973). [107] R. S. Ram, Spectrosc. Lett. 9, 435 (1976). [108] W. B. Griffith, Jr. and C. W. Mathews, J. Mol. Spectrosc. 104, 347 (1984). [109] H. Bredohl, I. Dubois, E . Mahieu, and F. Melen, J. Mol. Spectrosc. 145, 12 (1991). [110] U. Wolf and E. Tiemann, Chem. Phys. 119, 407 (1988). [Ill] P. E . Fleming and C. W. Mathews, J. Mol. Spectrosc. 175, 31 (1996). [112] S. R. Langhoff, C. W. Bauschlicher, Jr., and P. R. Taylor, J. Chem. Phys. 88, 5715 (1988). [113] D. Sharma, Astrophys. J. 113, 219 (1951). [114] A. Lakshminarayana and P. B. V. Haranath, Curr. Sci. 39, 228 (1970). [115] H. Bredohl, P. Danguy, I. Dubois, E . Mahieu, and A. Saouli, J . Mol. Spectrosc. 151, 178 (1992). [116] H. Uehara, K. Horiai, Y. Ozaki, and T. Konno, Chem. Phys. Lett. 214, 527 (1993). [117] W. J . Childs, D. R. Cok, and L. S. Goodman, J . Chem. Phys. 76, 3993 (1982). [118] W. J. Childs, D. R. Cok, G. L. Goodman, and L. S. Goodman, J. Chem. Phys. 75, 501 (1981). [119] M . Bogey, C. Demuynck, and J. L. Destombes, Chem. Phys. Lett. 155, 265 (1989). Bibliography 160 [120] I. Mills, T. Cvitas, K. Homann, N. Kallay, and K. Kuchitsu, Quantities, Units and Symbols in Physical Chemistry, 2nd ed. (Blackwell Science, Oxford, 1993). [121] K. Moller, H.-U. Schiitze-Pahlmann, J. Hoeft, and T. Torring, Chem. Phys. 68, 399 (1982). [122] S. Pfaffe, E . Tiemann, and J. Hoeft, Z. Naturforsch. Teil A 33, 1386 (1978). [123] E . Tiemann, M . Grasshoff, and J. Hoeft, Z. Naturforsch. Teil A 27, 753 (1972). [124] J . Cederberg, D. Nitz, A. Kolan, T. Rasmusson, K. Hoffman, and S. Tufte, J. Mol. Spectrosc. 122, 171 (1987). [125] F. H. de Leeuw, R. van Wachem, and A. Dymanus, J. Chem. Phys. 50, 1393 (1969). [126] L. W. Avery, M . B. Bell, C. T. Cunningham, P. A. Feldman, R. H. Hayward, J. M . MacLeod, H. E . Matthews, and J. D. Wade, Astrophys. J. 426, 737 (1994). [127] T. J. Millar, J. Ellder, A. Hjalmarson, and H. Olofsson, Astron. Astrophys. 182, 143 (1987). [128] B. E . Turner, T. C. Steimle, and L. Meerts, Astrophys. J. 426, L97 (1994). [129] B. Ma, Y. Yamaguchi, and H. F. Schaefer III, Mol. Phys. 86, 1331 (1995). [130] J. Cernicharo and M . Guelin, Astron. Astrophys. 183, L10 (1987). [131] L. M . Ziurys, A. J. Apponi, and T. G. Phillips, Astrophys. J. 433, 729 (1994). [132] M . A. Anderson and L. M . Ziurys, Chem. Phys. Lett. 231, 164 (1994). [133] M . Guelin, M . Forestini, P. Valiron, L. M . Ziurys, M . A. Anderson, J. Cernicharo, and C. Kahane, Astron. Astrophys. 297, 183 (1995). [134] E . Kagi, K. Kawaguchi, S. Takano, and T. Hirano, J. Chem. Phys. 104, 1263 (1996). [135] D. E . Powers, M . Pushkarsky, and T. A. Miller, 50th Ohio State University Inter-national Symposium on Molecular Spectroscopy (1995), paper RJ12. [136] R. Rubino, C. C. Carter, J. M . Williamson, D. E. Powers, and T. A. Miller, 51st Ohio State University International Symposium on Molecular Spectroscopy (1996), paper TF04. [137] C. W. Bauschlicher, Jr., S. R. Langhoff, and H. Partridge, Chem. Phys. Lett. 115, 124 (1985). Bibliography 161 [138] K. Ishii, T. Hirano, U. Nagashima, B. Weis, and K. Yamashita, Astrophys. J. 410, L43 (1993). [139] K. Ishii, T. Hirano, U. Nagashima, B. Weis, and K. Yamashita, J . Mol. Struct. ( T H E O C H E M ) 305, 117 (1994). [140] S. Petrie, J. Phys. Chem. 100, 11581 (1996). [141] T. Hirano, K. Takano, T. Kinoshita, K. Ishii, and K. Yamashita, 52nd Ohio State University International Symposium on Molecular Spectroscopy (1997), pa-per RB01. [142] C. Barrientos and A. Largo, J. Mol. Struct. (THEOCHEM) 336, 29 (1995). [143] S. Petrie, J. Chem. Soc. Faraday Trans. 92, 1135 (1996). [144] K. Kawaguchi, Y. Kasai, S. Ishikawa, and N. Kaifu, Publ. Astron. Soc. Japan 47, 853 (1995). [145] K. A. Gingerich, Naturwiss. 54, 646 (1967). [146] C. Thomson, Int. J. Quantum Chem. Symp. 10, 85 (1976). [147] J . S. Robinson, A. J. Apponi, and L. M . Ziurys, Chem. Phys. Lett. 278, 1 (1997). [148] M . Fukushima, 52nd Ohio State University International Symposium on Molecular Spectroscopy (1997), paper MH09. [149] R. Essers, J. Tennyson, and P. E. S. Wormer, Chem. Phys. Lett. 89, 223 (1982). [150] C. J . Whitham, B. Soep, J.-P. Visticot, and A. Keller, J . Chem. Phys. 93, 991 (1990). [151] M . Douay and P. F. Bernath, Chem. Phys. Lett. 174, 230 (1990). [152] J. J. van Vaals, W. L. Meerts, and A. Dymanus, Chem. Phys. 82, 385 (1983). [153] J. J. van Vaals, W. L. Meerts, and A. Dymanus, J. Mol. Spectrosc. 106, 280 (1984). [154] J . J . van Vaals, W. L. Meerts, and A. Dymanus, Chem. Phys. 86, 147 (1984). [155] M . A. Frerking, W. D. Langer, and R. W. Wilson, Astrophys. J . 232, L65 (1979). [156] S. R. Langhoffand C. W. Bauschlicher, Jr., Ann. Rev. Phys. Chem. 39, 181 (1988). Bibliography 162 [157] S. R. LanghofT, C. W. Bauschlicher, Jr., and H. Partridge, J. Chem. Phys. 89, 396 (1988), ; S. R. LanghofT, C. W. Bauschlicher, Jr. and H. Partridge, J . Chem. Phys. 89, 7649 (1988). [158] C. J . Cheetham and R. F. Barrow, Adv. High Temp. Chem. 1, 7 (1967). [159] J . L. Gole, in Electronic Transition Lasers II: Proceedings of the 3rd Summer Col-loquium on Electronic Transition Lasers, Snowmass, Colo. 1976, edited by L. E. Wilson, S. N. Suchard, and J. I. Steinfeld (M. I. T. Press, Cambridge, Mass., 1977), pp. 136-165. [160] J. A. Gole and C. L. Chalek, in Proceedings of the Symposium of High Tempera-ture Metal Halide Chemistry, edited by D. L. Hildenbrand and D. D. Cubicciotti (Electrochemical Society, Princeton, N.J., 1978), pp. 278-309. [161] H. C. Brayman, D. R. Fischell, and T. A. Cool, J. Chem. Phys. 73, 4247 (1980). [162] R. F. Barrow and W. J. M . Gissane, Proc. Phys. Soc. 84, 615 (1964). [163] R. F. Barrow, M . W. Bastin, D. L. G. Moore, and C. J. Pott, Nature 215, 1072 (1967). [164] E . A. Shenyavskaya, A. A. Mal'tsev, and L. V. Gurvich, Opt. Spectrosk. 21, 680 (1966). [165] E . A. Shenyavskaya, A. A. Mal'tsev, and L. V. Gurvich, Vestn. Mosk. Univ., Ser. 2, Khim, 22, 104 (1967). [166] E . A. Shenyavskaya and R. B. Ryabov, J. Mol. Spectrosc. 63, 23 (1976). [167] E . A. Shenyavskaya and L. V. Gurvich, J. Mol. Spectrosc. 68, 41 (1977). [168] L. A. Kaledin and E . A. Shenyavskaya, Mol. Phys. 70, 107 (1990). [169] L. A. Kaledin and E . A. Shenyavskaya, Mol. Phys. 72, 1203 (1991). [170] L. A. Kaledin, J. E . McCord, M . C. Heaven, and R. F. Barrow, J. Mol. Spectrosc. 169, 253 (1995). [171] J. Shirley, C. Scurlock, T. Steimle, B. Simard, M . Vasseur, and P. A. Hackett, J . Chem. Phys. 93, 8580 (1990). [172] J. E . Shirley, W. L. Barclay, Jr., L. M . Ziurys, and T. C. Steimle, Chem. Phys. Lett. 183, 363 (1991), ; J. E . Shirley, W. L. Barclay, Jr., L. M . Ziurys and T. C. Steimle, Chem. Phys. Lett. 191, 378 (1992). Bibliography 163 [173] D. A. Fletcher, K. Y. Jung, C. T. Scurlock, and T. C. Steimle, J. Chem. Phys. 98, 1837 (1993). [174] G. M . Janney, J. Opt. Soc. Am. 56, 1706 (1966). [175] D. R. Fischell, H. C. Brayman, and T. A. Cool, J. Chem. Phys. 73, 4260 (1980). [176] J . Xin, G. Edvinsson, and L. Klynning, J. Mol. Spectrosc. 148, 59 (1991). [177] J. Xin, G. Edvinsson, and L. Klynning, Physica Scripta. 47, 75 (1993). [178] J. Xin, G. Edvinsson, L. Klynning, and P. Royen, J. Mol. Spectrosc. 158, 14 (1993). [179] J . Xin and L. Klynning, J. Mol. Spectrosc. 175, 217 (1996). [180] J . Xin, L. Klynning, and P. Royen, J. Mol. Spectrosc. 176, 1 (1996). [181] B. Simard, A. M . James, and P. A. Hackett, J. Chem. Phys. 96, 2565 (1992). [182] A. Bernard, S. Roux, and J. Verges, J. Mol. Spectrosc. 80, 374 (1980). [183] A. Bernard and R. Gravina, Z. Naturforsch. Teil A 39, 27 (1984). [184] K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure IV. Con-stants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). [185] B. P. Fabricand, R. 0. Carlson, C. A. Lee, and I. I. Rabi, Phys. Rev. 91, 1403 (1953). [186] A. Honig, M . Mandel, M . L. Stitch, and C. H. Townes, Phys. Rev. 96, 629 (1954). [187] A. Kratzer, Z. Naturforsch. Teil A 3, 289 (1920). [188] E . Tiemann, B. Holzer, and J. Hoeft, Z. Naturforsch. Teil A 32, 123 (1977). 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0061575/manifest

Comment

Related Items