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

FOURIER TRANSFORM MICROWAVE SPECTROSCOPY METAL-CONTAINING COMPOUNDS  PRODUCED  B Y LASER  ABLATION By Kaley Anne Walker B. Sc. (Chemistry) University of Waterloo  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E O F D O C T O R O F PHILOSOPHY  IN T H E FACULTY O F G R A D U A T E STUDIES CHEMISTRY  We accept this thesis as conforming to the required standard  T H E UNIVERSITY  O F BRITISH COLUMBIA  1998 © Kaley Anne Walker, 1998  OF SOME  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 V 6 T 1Z1  Date:  Abstract  A laser ablation source has been constructed for a pulsed jet cavity Fourier transform microwave ( F T M W ) 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, M g N C , 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 monobromide 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 determined. 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 B r isotopomer. These, too, are consistent with highly ionic bonding. The 8 1  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 M g N C 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 nuclear spin-spin constant.  1 4  N and the A 1 nuclei along with an A l - N 27  The degree of sp-hybridisation of the bonding orbitals of  A1NC and M g N C 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 between 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 structure 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  2.2  2.3  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  Fine Structure  10  2.2.1  10  Electron Spin-Rotation Coupling  Nuclear Hyperfine Structure  11  2.3.1  12  Nuclear Quadrupole Coupling  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  '  v  56  5.4  5.5  Discussion  59  5.4.1  Equilibrium Bond Distance  59  5.4.2  Nuclear Quadrupole Hyperfine Structure  61  Conclusion  • •  6 Pure Rotational Spectra of MgBr and AlBr  62  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  7.5  7.6  7.4.1  MgNC  106  7.4.2  A1NC  109  Discussion  Ill  7.5.1  Nuclear Quadrupole. Coupling Constants  . . .  7.5.2  Electron Spin-Nuclear Spin Hyperfine Parameters for M g N C . . .  115  7.5.3  Nuclear Spin-Spin Constant for A1NC  117  Conclusion  112  117  8 F T M W Spectroscopy of Yttrium Monohalides: Y F and Y B r  128  8.1  Introduction  128  8.2  Experimental Details  130  8.3  Spectral Search and Assignment  131  8.3.1  YF  131  8.3.2  YBr  8.4  8.5  8.6  . .  131  Analyses  133  8.4.1  YF  133  8.4.2  YBr  137  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  Conclusion  141  Bibliography  154  vii  List of Tables  4.1  F T M W Spectroscopy of Molecules Produced by Laser Ablation  53  5.1  Observed frequencies for M g S  63  5.2  Molecular constants calculated for M g S  5.3  Frequencies for the J = 1 — 0 transition of isotopomers of MgS and derived  2 4  3 2  2 4  64  3 2  Bo values  65  5.4  Frequencies of measured hyperfine components of M g S  66  5.5  Molecular constants for M g S  67  5.6  Substitution structure results for M g S  5.7  Equilibrium bond length calculated for M g S  6.1  Measured frequencies of N = 1 — 0 and N — 2 — 1 transitions of  2 5  2 5  3 2  3 2  2 4  68  3 2  2 4  69  3 2  2 4  Mg Br 7 9  in v = 0 and v — 1 vibrational states 6.2  Measured frequencies of N = 1 — 0 and N = 2 — 1 transitions of  89 2 4  Mg Br 8 1  in v = 0 and v = 1 vibrational states 6.3  90  Measured frequencies of J = 1 — 0 and J = 2 — 1 transitions of A l B r in 7 9  v — 0 and v = 1 vibrational states 6.4  6.5  91  Measured frequencies of J = 1 — 0 and J = 2 — 1 transitions of A l B r in 8 1  v = 0 and v = 1 vibrational states  92  Molecular constants calculated for MgBr  93  vni  6.6  Molecular constants calculated for AlBr  94  6.7  Calculated ratios of hyperfine parameters compared to nuclear and molecular 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 M g N C in its ground vibrational state.  7.2  Observed ground vibrational state frequencies of A1NC  120  7.3  Molecular constants calculated for  122  7.4  Molecular constants calculated for A1NC  7.5  Comparison of experimental and theoretical rotational constants for A1NC. 124  7.6  Comparison of nuclear quadrupole coupling constants of M g N C , A1NC  2 4  1 4  1 2  2 4  . . .  Mg N C 1 4  1 2  123  and related cyanides and isocyanides 7.7  125  s-character of A l bonding orbital calculated from A l nuclear quadrupole coupling constants  7.8  119  126  Unpaired electron spin densities calculated at the  1 4  N nucleus from mag-  netic hyperfine constants for M g N C and CaNC  127  8.1  Observed transitions of Y F in the v = 0 and v = 1 vibrational states.  . .  8.2  Measured transition frequencies of Y B r in v = 0 and v — 1 vibrational  143  7 9  states  144  ix  8.3  Measured transition frequencies of Y B r in v = 0 and v = 1 vibrational 8 1  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 Y B r  148  8.7  Calculated ratios of hyperfine parameters compared to nuclear and molecular 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 Y B r  152  8.11 Calculated ionic character of Y B r and related alkali metal bromides. . .  153  7 9  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 M g S  58  5.2  The J = 1 - 0 transition of M g S  60  6.1  The N = 1 - 0, J = 3/2 - 1/2, F = 2 - 2 transition of M g B r  6.2  Comparison of spectra of M g B r with Helmholtz coils on and off.  6.3  The N = 1 - 0 rotational transition of M g B r and M g B r  6.4  Composite spectrum of the J = 1 — 0 rotational transition of A l B r .  7.1  The N = 1 - 0, J = 3/2 - 1/2, F = 3/2 - 1/2 rotational transition of  2 4  2 5  3 2  2 4  2 4  75  8 1  7 9  79  M G  14 12 N  C  . . .  77 . .  ;  Composite spectrum of the J = 1 — 0 rotational transition of A1NC. . . .  XI  76  81  7 9  24  7.2  3 2  79  1  Q  5  107  7.3  Detail of the J = 1 - 0 transition of A1NC, showing the F = 7/2 -  5/2  x  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 B r . 8 1  xii  134  Acknowledgement  I would like to thank my research supervisor Mike Gerry for his patience and encouragement during the past five years. I would also like to thank my co-workers for their assistance. I thank Wolfgang Jager, Yunjie X u and Kristine Hensel for teaching me how to use the spectrometer, Mark Barnes and Thomas Brupbacher for many, many discussions 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  Chapter 1  Introduction  Microwave spectroscopy is primarily the study of pure rotational transitions of gas phase molecules possessing permanent dipole moments. The development of sources and detectors 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 ( F T M W ) spectroscopy over the past two decades has improved the sensitivity and resolution possible 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  2  Chapter 1. Introduction  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 paramagnetic 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 metalcontaining 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. A n 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  3  Chapter 1. Introduction  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 B r and nuclear spin-rotation 7 9  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 discussed 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. Nuclear quadrupole and magnetic hyperfine parameters have been determined for A1NC and M g N C . 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 spectroscopic 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 obtained by low resolution laser induced fluorescence spectroscopy. The ionic character of the Y - B r 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. Nuclear spin-rotation splitting has been measured in the spectrum of yttrium monofluoride.  Chapter 1. Introduction  The  1 9  4  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 where H , TOt  ^distort? #fi  = a n  ne  H  rot  + ^distort + -f/fine + ^hyperfine  (2-1)  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 2.1.1  Molecular Rotation 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 + ByR 2y + BzR 2z 5  (2.2)  Chapter 2.  6  Theory  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, B  G  are related to the moments of inertia, I , by G  ' = sk-  <->  B  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 I = I = I). Thus the rigid rotor Hamiltonian for X  Y  a linear molecule can be expressed as  Hrot = B{Rl + Rl) =  where B  X  = B  Y  B R  (2.4) (2.5)  2  = B. The rotational energy levels obtained from this equation are, in  frequency units, E  =  rot  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 transition from one state  \RM)  to another state  PRM^R'M'  where BRM^R'M'  P(VRMR'M')  1  S  =  \R'M')  in unit time,  PRM^R'M'I  is  piyRMR'M') BRM-+R'M'  (2.7)  the density of radiation oscillating with frequency  is the Einstein coefficient of absorption for the  \RM)  —V  URMR'M'  \R'M')  a n  d  transition.  7  Chapter 2. Theory  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\a \R'M')\ . 2  (2.8)  z  The matrix element of \iz has to be non-zero for a transition to occur. The molecule-fixed components of the molecular dipole moment, fi , \i and fi , are related to the space-fixed x  component nz by the direction cosines,  y  z  §zgi  In the diatomic and linear triatomic molecules considered here, the permanent electric dipole lies along the z axis, so fi — fi — 0 and therefore x  y  (RM\y \R'M')  =  z  iu (RM\$zz\R'M'). z  (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  2.1.3  AR  =  ±1  (2.11)  AM  =  0.  (2.12)  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.  8  Theory  The centrifugal distortion Hamiltonian for a linear molecule is ^distort  =  -D(R ) 2  2  + H(R ) 2  + ...  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 where B  v  and D  v  =  B R(R + l) - D R (R  + 1)  2  v  2  V  (2.15)  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 quartic 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 B  v  =  B -a (v  D  v  =  D + p (v  In these equations, a , 7 e  e  e  + ^)+%(v  e  e  e  + ^+...  + ^j  2  + ...  (2.16) (2.17)  and /3 are vibration-rotation interaction constants and B e  e  and D are the equilibrium rotational and centrifugal distortion constants, respectively. e  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 B  e  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  B  v  =  Be-^cti^vi  + ^j  (2.18)  D  v  =  D + '£8 (v  + ^j  (2.19)  e  i  i  where i>- is the vibrational quantum number of the ith vibrational mode, dj is the degent  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 including 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  =  B J(J+  l)-D J (J  + l)  2  V  (2.22)  2  v  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  =  B N(N  + 1) - D N {N 2  V  V  + l) . 2  (2.23)  The selection rules are A i V = ± 1 and A J = 0, ± 1 .  2.2 2.2.1  F i n e Structure E l e c t r o n Spin-Rotation C o u p l i n g  For molecules having E ground electronic states, an electron spin-rotation term must 2  +  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.  11  Theory  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 vibrationrotation energy expressions, including fine structure, are  2.3  £vib-rot  (j = N +  £vib-rot  (J = N -  ^) = =  B N(N  + l)-D N (N-rl)  B N(N  + 1)-  2  v  + jN  2  v  V  D N (N 2  v  + l) -^-{N 2  (2.25) + l).  (2.26)  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+ J  = I  (2.28)  =  (2.29)  F.  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 ,  Ii+J  = F  x  (2.30)  I + F ! = F.  (2.31)  2  12  Chapter 2. Theory  The "series" scheme best describes the hyperfine interactions observed for the metalcontaining species with two magnetic nuclei studied in this thesis. Nuclear hyperfine interactions occur via electrostatic and magnetic means. The observed hyperfine structure can be classified into three types,  H.quadrupole  i^hyperfiri  where and  //quadrupole  // pin-spin S  (2.32)  spin—rotation ~\~ iJsoin— spin—spin  describes the nuclear electric quadrupole interaction and  Z/ pin-rotation S  describe the magnetic nuclear spin-rotation and spin-spin interactions,  respectively.  2.3.1  N u c l e a r 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  (2.33)  = V E  1  (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] '-l)J+I+F ( J'lF  | i/quadrupole  F  I  J'  2  J  I  \JIF)  - l  J  2  J  J  0  -J  1  1 2 -I  0  I  eQqj.j  (2.35)  Chapter 2.  13  Theory  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 ) [ ( 2 J + 1)(2J' + /  J  2  J'' ^ ( J  2  J' ^  V  J  0  - J  0  0  x where  eQq  0  1)]?  J  ^ 0  eQqo  (2.36)  /  is the molecular nuclear quadrupole coupling constant.  The matrix elements for the nuclear quadrupole interaction in a linear paramagnetic molecule in a E state can be calculated from [12] 2  f_1  (N'SJ'IF\H  \NSJIF)  =  quadrupole  )2J+I+F+S+2N'  ^  x [ ( 2 J + 1 ) ( 2 J ' + 1)(2N  x  + 1)(2N'  / N'  ( / + 1)(2/+ l)(2/ + 3) 7(2/ -  I  J'  F  J  I  2  1)  0  ' N'  > i  X i  J  S  N  2  l)]a 2  N  0  0  qo-  J  J  +  (2.37)  J  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 I , 2  respectively. The matrix elements for the more strongly coupled spin, I , are identical to x  those of the singly coupled nucleus [2]  (J'lMHQ^lJhF,)  =  (-1)  J+h+Fi  J  2  J  x J  0  -J  Fi  h  J'  2  J  h h  \ -h  2 0  h h J  eQqj,j(l).  (2.39)  14  Chapter 2. Theory  The matrix elements for the more weakly coupled spin, I , are then evaluated in the 2  coupled basis \JhFxI F) 2  [2]  {J'hF[I F\H {2)\JhFJ F) 2  Q  =  2  ^_iy'+Ii+I +2Fi+F 2  J'  [(2^ + 1 X 2 ^ + 1)]'  F{  h  X <  F  h  2  F  F{  > <  F  J  x  t J  V  2  2  J  J>\*(  0  v  2  2 I  h  -JJ  I  x  2  -I  eQqj,j(2)  (2.40)  0/2/  2  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]  = —t  (N'SJ'IMHQWNSJIM  {  x[(2J + 1)(2J' + 1)(2N + 1){2N' + x  (/ + l)(2/ + l ) ( 2 / + 3 ) 1  1  1  2  N  0  0  0  / (2/ -1) 1  x<  / N'  h  1  J' Fx >  J  h  N'  J  S  J  N  2  <  > eQq (l).  (2.41)  0  2  Then the matrix elements of the more weakly coupled nucleus can be evaluated from [12] {N'SJ'hF[l2F\H {2)\NSJhF I F) Q  L  =  2  x[(2J + 1)(2J' + l)(2N + 1){2N' + x[(2F +1)(2F' +  1)H  h  J'  F{  2  Fx  J  "(/ + l)(2/ + l)(2/ + 3) * ( N' 2 2  2  2  / ( 2 / - 1) 2  2  v  0  0  N 0  N  j  Chapter 2.  15  Theory  F  ' N'  J  S  J  N  2  eQq (2).  - <  <  h  2  (2.42)  0  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\) = where n , n x  y  and n  z  (n  - " ^  eQq (atom)  x  z  (2.43)  nl0  are the numbers of electrons in the np , np x  and np  y  z  orbitals,  respectively. Values of eQt7„io(atom) are listed in Ref. 2. By relating n , n and n to the x  y  z  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 spinrotation 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 -^spin-rotation  =  Cjl • J  (2.44)  where C j , the nuclear spin-rotation constant in the Jth rotational state, equals CJ  =  jrj\^{C,AJ ) 2  x  + C (J^ yy  (2.45)  Chapter 2.  Theory  16  For a linear molecule with no resultant angular momentum about the molecular axis, J = 0 and symmetry makes C z  = C  xx  yy  c  = C j , so that  > = J(7TT) '< C  =  J2)  { 2 M )  C,.  (2.47)  The nuclear spin-rotation constant, Ci, is equal to Ci  =  (2.48)  -gipNh  xx  where gi is the nuclear g-factor for the magnetic nucleus, pj^ is the nuclear magneton and h  xx  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)].  The nuclear spin-rotation Hamiltonian for a molecule with a E 2  +  (2.49) 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 E 2  +  ^spin-spin  ground electronic state is =  M • S + C (l S z  z  - U • S)  (2.51)  Chapter 2.  17  Theory  where I and S are the components of I and S along the internuclear axis, respectively, z  z  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:  b  =  F  y<7e<M^Ar|*(0)|  (2.52)  2  and c  =  -# £Wj9M;v((3cos 0 - l ) / r ) 2  (2.53)  3  e  where g and gw are the electronic and nuclear ^-factors and p,s and fj.^ are the Bohr e  and nuclear magnetons, respectively; |^(0)| is the probability of the unpaired spin at 2  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 E 2  +  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)l (mol)  .  2  =  p { s )  " P [ P )  |*(0)|'(atom)  ( 2  _  ((3cos e-l)/r3) ol)  ~  <(3cos'e-l)/r3)(atom)  ... -  5 4 )  2  ( m  1  '  where |$(0)| (mol) and ((3cos 0 — l)/r )(mol) were calculated from the experimental 2  2  3  bp and c values, respectively, and |\P(0)| (atom) and ((3cos 0 — l)/r )(atom) were cal2  2  3  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  =  4^1 ' ^2 + 3c  c  3  {^Ilzhz  —  ^II '  (2.56)  where c\ and c are the scalar and tensor contributions to the nuclear spin-spin inter3  action. The form of this equation is identical to the Hamiltonian for the electron spinnuclear 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  =  c (dir.) + c (ind.). 3  3  (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 interaction. 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 second 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 antiparallel 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.  19  Theory  been done for the molecules examined in this thesis. The tensor spin-spin constant 3c  3  has been approximated to equal a , the direct nuclear spin-spin constant. For a linear 1 2  molecule, 0 1 :2 is defined as [26]: =  where fi^ is the Bohr magneton, r  -^N9i92  (  2  5  8  )  is the internuclear distance, and gi and g are the  1 2  2  nuclear ^-factors for nuclei 1 and 2, respectively.  2.4  B o n d L e n g t h Determination  The precise rotational constants obtained from microwave spectroscopy can be used to determine geometrical parameters.  The internuclear bond length, r i , of a diatomic 2  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 are the atomic masses of the two atoms in the molecule. The effective 2  bond length in the ground vibrational state, r , can be determined by using Bo in Eq. 0  (2.59).  Its accuracy is limited by zero-point energy contributions.  These vibrational  contributions can be accounted for by calculating an equilibrium rotational constant, B  e  (from Eq. (2.16)) using rotational constants obtained in two or more vibrational  states; then r can be determined from B . This is the bond length for the hypothetical e  e  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 distance. Costain showed that for a diatomic molecule [27] e  r  e  =  2r -r s  Q  (2.61)  20  Chapter 2. Theory  where r is the substitution bond length. Using Costain's method [27], the distance of s  an atom, i , from the centre of mass, z,, in a diatomic molecule is given as:  J = (IJAiJ  (2.62)  AI°  (2-63)  where  B  =  IB'-I°B  is the difference in the ground vibrational state moment of inertia between the substituted molecule, I ', B  and the parent molecule, I . B  The substitution reduced mass is  = ITta  (2  '  64)  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, r can be calculated from s  z\ + z . 2  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 r . In the Born-Oppenheimer approximae  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 r to account for deviations from the Born-Oppenheimer e  approximation. The first and largest contribution arises from the reduced mass used to calculate r ; the reduced mass expression (Eq. (2.60)) employs atomic masses for which e  the electrons associated with each atom were assumed to be concentrated at the nucleus.  Chapter 2.  21  Theory  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 calculations discussed in this thesis, (see e  Sec. 6.5.1 and Sec. 8.5.1), the uncertainty in the calculated r value has been examined e  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 metalcontaining 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.  22  Theory  orbitals fa  =  a^  + VT^^B  =  Vl - a il> - aip -  A  (2-65)  and (2-66)  2  A  B  where a and (1 — a ) are the fractional weights of the atomic orbitals tpA and tp in the 2  2  B  bonding molecular orbital ip , respectively. Gordy and Cook [2] have related the ionic a  character, i , of the A-B bond to the difference in the fractional weights of ip and V's in c  A  the molecular orbital, ^V, i  c  =  \a - (1 -  =  \2a -l\.  2  a )\ 2  (2.67)  2  For a purely covalent bond, there are equal contributions to ip from ipA and tpB\ therefore a  a  2  = 0.5 and i  c  = 0. Similarly for a purely ionic interaction, i  = 1 and a is either 2  c  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 a to an 2  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)  =  ^n -^±^yQq {k). z  nW  (2.68)  23  Chapter 2. Theory  The z axis is taken to be the molecular axis. The valence shell configuration of A is ns np ; the np and np orbitals will be filled, so n 2  = n = 2. The occupation of the  5  x  y  x  y  np orbital depends on the participation of ^u(= ^n ) in the molecular orbital ip . So z  n  Pz  a  equals 2a , the fraction of the ip„ bond pair of electrons associated with atom A. 2  z  Substituting these values into Eq. (2.68) results in eQq(A)  =  (2a - ^ )  eQq (A)  =  (2a - 2) eQq {A).  2  nl0  (2.69)  2  nW  Since A is the negative pole of the A B bond, a > 0.5 and 2  a  =  2  !i±l.  (2.70)  This result can be combined with Eq. (2.69) and then an expression for i can be obtained c  eQq w{k) n  where the term  ?9 q^ 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 i —> 1 eQq(A) —> 0. c  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  c  l  =  1  +  eQg(A)(l+i e) 7\ 7T\ c  (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.  24  Theory  the halogen on the negative pole of the A B 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. Considering sp orbital hybridisation on the quadrupolar nucleus A , the atomic orbital  ^  will be  = + \A ~  *I>A  (2-73)  al^pz  and the counterhybridised orbital will be ip '  =  A  yfl - a rp - a rp  (2-74)  2  s  s  s  pz  where a is the fractional weight of the s-orbital in the sjo-hybrid. This sp-hybridisation 2  must be accounted for in the Townes-Dailey model. The number of electrons in the np  z  orbital will be n  =  z  M{\-a ) 2  s  + Na]  (2.75)  where M and /V are the number of electrons in the hybridised and counterhybridised orbitals, respectively.  Since ipA is P t of the molecular orbital  M will equal 2a ,  ar  2  the fraction of the ip bond pair associated with the atomic orbital tpA- The value of a  iV depends on the occupation of tpA - So when sp-hybridisation is included Eq. (2.68) becomes eQq(A) where a  2  =  (2a (l - a ) + Na] - !!^±^) 2  2  s  eQq (A)  (2.76)  nl0  can be related to the ionic character of the A B bond using E q . (2.67). Eq.  (2.76) relates two unknown parameters, the degree of sp-hybridisation, a , and the ionic 2  character (through a ), to one measurable parameter, eQq(A). 2  By finding an alternate  method of determining i , the orbital hybridisation on the A nucleus can be calculated. c  Chapter 2.  25  Theory  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 halogencontaining diatomic molecules [2,35]. As a first approximation, this simple expression can be used to calculate i  c  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, i  c  =  1.15 exp  1 -(2-Ax)  -0.15  2  (2.78)  where A x = \XM — xx\ < 2 [2].  2.5.2  E l e c t r o n 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 S 2  +  ground electronic state molecule A B 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 -  a ip  i^ .  =  Vl - atijiA -  aip  a  2  B  B  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.  26  Theory  (2.73) and (2.74)),  ipA  =  s*Ps  ^A  =  + \A  a  \A ~~  - a ippz 2  s  Q  ^  S  ~  A  ^P  Z  where a is the fractional weight of the s-orbital in the sp-hybrid. The unpaired electron 2  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 )a  p(p)  cx ( l - a ) ( l - a )  2  (2.79)  2  2  (2.80)  2  where (1 — a ) is the fractional weight of if)A in the antibonding orbital 2  (1 — a ) are the fractional weights of ip and tp 2  pz  s  and a and 2  in the atomic orbital I\>A-> respectively.  If both p(s) and p(p) are small, the (1 — a ) must be small (and a large). Therefore the 2  2  ionic character of the A - B bond must be large, since from Eq. (2.71) i  e  As i  c  =  —>• 1 then p(s) —> 0 and p(p) —> 0.  |2a -l|. 2  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 ( F T M W ) 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 introduced 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 transformed 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  28  Chapter 3. Experimental Technique  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  I*)  ci|^i) +  c \<h)  (3.1)  2  where (f>i and <p are eigenfunctions of the time independent molecular rotational Hamil2  tonian, for  H t<t>i — Ei4>i ro  The  (3.2)  density operator for one of these particles is  P  =  (3.3)  l*><*  = and  i = 1,2.  + c^^M + cK^i)  (3.4)  the density matrix is  P  c  l l c  c  C  2 l  C  l 2 C  = c  (3.5)  2 2 C  such that Pij  For  CjC-.  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  (3.8)  = H rot + H, i "perturbationIot  •^perturbation describes the time dependent interaction of the molecular dipole moment operator, ft, with the applied microwave field,  //perturbation  =  (3.9)  1fl€ COs{uit -f- <^>).  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  =  E  x  0  0  (3.10)  E  2  and  //,perturbation —  0  —2/ii2£ cos(ut + (f))  —1\i\2£ cos(u>£ + </>)  0  (3.11)  The time dependence of the system is calculated from •* P d  (3.12)  The resulting time dependent matrix elements are  Pn  =  *(P21 — pi2)x cos(u;i + <f>)  (3.13)  P22  =  ~*(P21 — p\2)x cos(u;£ + (f>)  (3.14)  Pl2  ~  p21  =  i(P22 - pn)x cos(ut + (f>) + ipn^o ~i{p22 - pu)x cos(ut  + </>) -  ip2iUo  (3.15) (3.16)  30  Chapter 3. Experimental Technique  where x = 2p e/h 12  and u> = (E — Ei)/h, the angular frequency of the rotational tran0  2  sition. The matrix elements,  can then be transformed into a "rotating" coordinate  system using  Pn  =  Pn  (3.17)  P22 = P22 Pn  =  P21 =  /5  (3.18) eW)  1 2  (3.19)  p ie-  (3.20)  l(ut+4,)  2  to obtain  Pn  -^{p2i-pi2)  %  =  P22 = - y ( P 2 i - P i 2 ) P12 = /5 i 2  =  -J(P22-PU)  (3.21) (3.22)  + i(uo - u)pi  2  -y(P22 - Pn) - i(u>o - v)pi2-  (3.23) (3.24)  Then the real quantities s, u, v, and u> are defined as  s  =  /5n + P22 = 1  u = P2i+P\2 -iv w  (3.25)  (3.26)  =  hi ~ Pn  (3.27)  =  Pn-  (3.28)  P22  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])  31  Chapter 3. Experimental Technique  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 frequency 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,-N  2  Also uo = v  0  =  N{  =  Nw .  P l l  -  P 2 2  0  )  (3.33) (3.34)  — 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 > , n  =  (3.35)  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)  32  Chapter 3. Experimental Technique  The solution to these differential equations is v(t)  =  -w sm(xt)  (3.40)  w(t)  =  w cos(xt)  (3.41)  u{t)  =  0  (3.42)  0  0  because v = 0. So during the microwave excitation pulse v(t) and w(t) oscillate between 0  wo and — wo at angular velocity x. At time t = t , the microwave excitation is turned off and p  0  up  v  p  w  p  (3.43)  =  -w sm(xtp)  (3-44)  =  w cos(xt ).  (3.45)  0  0  p  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  for t > t . p  u{t)  =  -VpSm(Aut)  (3.50)  v(t)  -  VpCos(Aut)  (3.51)  w(t)  =  w  (3.52)  p  Chapter 3. Experimental  33  Technique  The macroscopic polarisation induced in the sample by the microwave pulse is expressed as P(t)  =  =  N(fi)  (3.53)  NTr(fip)  (3.54)  NTr  1*12  0  P12  Pn  (3.55)  _ P21P22  0  Npi2 (P21 + Pn)  (3.56)  Npi2 (u(t) cos(u>t) — v(t) s i n ( u > i ) )  (3.57)  Then substituting in for u(t) and v(t) results in N/J.12 {—v sin(Acji) cos(ut) — v cos(Aa;£) sin(u;t))  (3.58)  Np-nVp (sin [(Aw + w)])  (3.59)  Nfj, v (sm(u) t))  (3.60)  p  l2  p  0  Np,i {w 2  p  0  (3.61)  sm(xt ))(s'm((jJot)). p  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 difference, woN, the transition dipole moment, pi , and the length of microwave excitation 2  pulse, t . p  The macroscopic polarisation can be optimised by maximising s'm(xt ); p  occurs when the microwave pulse length, t , satisfies xt p  p  = 2pi2St lh P  this  = 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 experiment, 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  3.4  36  Microwave Source  A Hewlett-Packard 8340A synthesiser was used as the microwave source for the experiments described in this thesis. During the experiments on MgS, MgBr and M g N C the synthesiser was referenced to an internal 10 MHz standard which has an aging rate of lxlO  - 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 1 0  -12  . The remaining  experiments, on A1NC, AlBr, Y F and Y B r , were performed using this setup. The 10 MHz signal is also used to control the timing of the experiment and to do up- and downfrequency conversions.  3.5  E x p e r i m e n t 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-  A n 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 generator. 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 VMWThe 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.  39  Experimental Technique  protective MW-switch  MW-amplifier \ detector  oscilloscope  A  10 MHz MWsynthesiser  v  MW  V  MW  single sideband modulator  20 MHz  x2  MW-switch  + 20 MHz  MWmixer  power divider  10 MHz  VMW + A V  20MHz-Av  frequency standard  RFamplifier x2.5  25 MHz  RFmixer 5 MHz + Av  personal computer  transient recorder  5 MHz bandpass  RFamplifier  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 experiments are co-added. The time domain signal is transformed into frequency domain by a discrete Fourier transform N-l  F(u)  =  ^/(nAfje-'' ^' 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 obtained 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  G a s 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  41  Chapter 3. Experimental Technique  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. species are formed through collisions in the nozzle.  The metal-containing  In the supersonic expansion, the  translational and rotational energies are converted into mass flow along the axis of expansion; 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 composition 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, T ib- For MgBr, T j was estimated to be ~ 320 K , using a gas mixture of v  v  D  0.1% B r in 6.5 bar Ar. A higher vibrational temperature of ~ 550 K was obtained for 2  the MgS experiments where a mixture of 0.2% OCS in 5.5 bar Ar was used. This range of T ib values is typical for F T M W laser ablation experiments [44-46]. v  3.8  H e l m h o l t z Coils  Special care had to be taken when measuring the spectra of M g N C and MgBr because these species are paramagnetic and the rotational spectra would show first order Zeeman 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 transition 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 M g N C . 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 splitting 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 measuring 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 Zeeman 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 A b l a t i o n 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 advantage 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 borohydrides [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 spectroscopy 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 difficult 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 perpendicular 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 nozzle 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  A b l a t i o n 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.  47  Chapter 4. Development of Laser Ablation Source  Target Metal Rod  Nd:YAG 532 nm  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  4.3  49  E x p e r i m e n t a l 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 A b l a t i o n 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 C 1 using the fixed rod (upper spectrum) and the rotating rod (lower 35  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 magnesium 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 sulfur; 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 C 1 . 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. 35  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  Oxides  Suenram et al. 1989  [51]  Y O , LaO, ZrO, HfO V O , NbO SrO, BaO  Suenram et al. 1990 Suenram et al. 1991 Blom et al. 1992  [44] [52] [53]  Halides  CuCl, CuBr  Low et al. 1993  [55]  Hydroxides  NaOH, K O H , RbOH, CsOH InOH  Kawashima et al. 1996 Lakin et al. 1997  [58] [59]  Larger  K B H , NaBH glycine urea  Kawashima et al. 1995 Lovas et al. 1995 Kretschmer et al. 1996  [60] [61] [62]  AgCl, A1C1, CuCl MgCl YC1 InF, InCl, InBr  Hensel et al. 1993 Ohshima and Endo 1993 Hensel and Gerry 1994 Hensel and Gerry 1997  [54] [45] [56] [46]  CaNC  Scurlock et al. 1994  [57]  2  4  4  Ablation and Reaction to form Sample: Halides  Isocyanides  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 spectroscopy 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 S 1  +  —X  1  S  +  optical transition of the main isotopomer,  by Wilhelm [74] in 1932.  2 4  M g S , was done 3 2  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 M g S isotopomers, 32  2 5  M g S and 3 2  26  M g S . The most recent study was that 32  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 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  3 4  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  E x p e r i m e n t a l 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 S isotopomer J = 1 — 0 transition 3 2  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  5.3  Spectroscopy of MgS  56  Observed Spectra and Analyses  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 S , specifically 3 2  2 5  2 4  Mg S, 3 2  M g S , and M g S , and one isotopomer containing S , namely M g S . The natural 3 2  2 6  3 2  3 4  2 4  abundances of these species range from 74.7% for the main isotopomer, for  2 4  3 4  2 4  M g S , to 3.3% 3 2  Mg S. 3 4  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 B  0  and D  0  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 D from the combined fit described above. Use of Di constant 0  scaled according to the values of Marcano and Barrow [75] introduced no significant  Chapter 5. FTMW  Spectroscopy of MgS  57  variation in B . The B and ct constants were then calculated directly from B x  e  e  0  and B  using Eq. (2.16), which is shown here for reference B  =  v  +7e (u+r)  B -a [v +e  e  + •••  This expression was truncated following the a term. The constants obtained are listed e  in Table 5.2 under the heading Direct Calculation. Fig. 5.1 shows the two measured J = 1 - 0 transitions for  2 4  Mg S.  The main isotopomer B  3 2  0  2 6  value was used to predict the transition frequencies for  M g S and M g S by scaling Bo using the reduced masses. Again the transitions were 3 2  2 4  3 4  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 M g S was not quite so straightforward as it had been for the other 2 5  3 2  isotopomers. Since the M g nucleus has a spin, / , of | , the transition was split into three 2 5  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 B  0  the same procedure used for the other minor isotopomers.  value was predicted by  A l l 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. program [76] to determine the B  rotational constant and eQq( Mg), which are listed 25  0  in Table 5.5.  These were fit using the S P F I T  Again, the DQ constant was held fixed at the value scaled from that of  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 M g 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 M H z 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. 2 4  3 2  Chapter 5. FTMW  2 4  Spectroscopy of MgS  59  M g S by the inverse square of the reduced mass. 3 2  5.4  Discussion  5.4.1  E q u i l i b r i u m B o n d Distance  Sufficient data were available that both isotopic substitution and the vibrational data could be used to determine the equilibrium bond length, r .  Since isotopic data were  e  available for both atoms, a complete substitution structure (r ) could be calculated for s  the main isotopomer,  2 4  M g S . This method is described in detail in Sec. 3 2  2.4.  The  distance of an atom from the centre of mass, Z{, is given by Eq (2.62)  The calculated values z,-, for z  Mg  and z , s  uncertainties, are given in Table 5.6.  and the resulting r  s  value with estimated  For a diatomic molecule, the r  e  value can be  evaluated from Eq. (2.61): =  2r -  r  s  0  using the r value determined from B for M g S . This r value is listed in Table 5.7 as 24  0  r  e  32  0  e  (Subst.). A second value for r , calculated directly from B , is also listed in Table 5.7 as r e  e  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 in the Born-Oppenheimer approximation can be expected to differ by ~ 1 0 e  -5  A , and  possibly more [33]. The uncertainty in calculating r is discussed further in Sees. 2.4 and e  6.5.1. For comparison, Table 5.7 also contains the r  e  value determined by Marcano and  Chapter 5. FTMW Spectroscopy of MgS  60  F'-F"5/2 - 5/2 7/2-5/2 3/2-5/2  r ,  1  i 15647.800 MHz  15648.000 MHz  Figure 5.2: The J = 1 — 0 transition of M g S showing hyperfine structure due to M g nuclear quadrupole coupling. The excitation frequency was 15 647.80 MHz. The corresponding time domain signal consists of 4 K 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. 2 5  2 5  3 2  Chapter 5.  FTMW  61  Spectroscopy of MgS  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 theories, the MgS bond is ionic, with the molecule containing M g  2 +  and S ~ ions. At infinite 2  separation, both ions are spherically symmetric, making any nuclear quadrupole coupling constants zero. Since M g non-zero  2 5  2 +  has the same electron configuration as Ne (ls 2s 2p ), the 2  2  6  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 E q . (2.43) is reprinted here substituting in the appropriate nuclear quadrupole coupling constants for 25  MgS: ^(  2 5  Mg)  =  Although a value for eQq io( Mg)  (n, -  e  g  ( Mg) 2 5  g 2 1 0  is unavailable, that of eQq ( Mg)  25  25  2  310  is known: —16 MHz  [2]. It is expected that e(5<?2io( Mg) will be a larger negative value since these constants 25  are proportional to ( r ) , where r is the distance from the nucleus to an electron in the - 3  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 2p and 2p orbitals is slightly greater than that in the 2p orbital, making x  y  z  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 abundance, 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 spectroscopy. A n equilibrium bond length has been obtained for MgS, along with the quadrupole coupling constant.  2 5  Mg  Chapter 5. FTMW  63  Spectroscopy of MgS  Table 5.1: Observed frequencies for M g S in MHz. 2 4  Transition v' J' v" J" 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0  14 16 17 18 19 22 23  0 0 0 0 0 0 0  13 15 16 17 18 21 22  Observed Frequency" (MHz) 16 013.8215 15 908.6190 224103.178 256086.116 272072.920 288056.376 304036.237 351952.415 367915.973  3 2  Obs.-Calc. (kHz) -0.2  6  26 -1 -12 3 -1 12 -12  J = 1 — 0 data from present work. Other data taken from millimeter wave study [73]. Observed minus calculated frequencies from combined fit of all v = 0 transitions. See Sec. 5.3 for details. a  6  Chapter 5. FTMW  64  Spectroscopy of MgS  Table 5.2: Molecular constants calculated for M g S in MHz. 2 4  Parameter B Br Do 0  Combined Fit ' 8006.92739(45) 0  3 2  Direct Calculation '"* Lit. 8006.9273(5) 8006.9278(15) 7954.3260(5) [0.008273 ] 0.0082744(19) [0.008273 ]  6  0  0.00827291(66)  5  e  6  8033.2280(6)' 52.6013(7)  B a* e  /  Fit combining present results and millimeter wave data [73]. One standard deviation in parentheses, in units of least significant digit. Bo and B\ calculated from measured J = 1 — 0 frequencies. Estimated errors reflecting measurement uncertainty given in parentheses, in units of least significant digit. Centrifugal distortion constants, D and Di, were held fixed at D value determined in combined fit; for detail see Sec. 5.3. f B and a calculated from Bo and B . From millimeter wave study of Takano et al. [73]. Three standard deviations in parentheses, in units of least significant digit. a  6  0  d  e  0  e  9  e  0  x  Chapter 5. FTMW  65  Spectroscopy of MgS  Table 5.3: Frequencies for the J = 1 — 0 transition of isotopomers of MgS and derived BQ values in MHz. Isotopomer Mg S Mg S 2 6  3 2  2 4  3 4  Observed Frequency 15311.4750 15611.1768  B  A 0  7655.7526 7805.6041  D  0  [0.007563] [0.007863]  Calculated by holding centrifugal distortion constant fixed at value scaled from that calculated for M g S in combined fit. a  2 4  3 2  Chapter 5. FTMW  66  Spectroscopy of MgS  Table 5.4: Frequencies of measured hyperfine components of M g S in MHz. 2 5  J' 1 1 1  Transition F' J" 3/2 0 7/2 0 5/2 0  3 2  Observed Frequency" F" 5/2 5/2 5/2  15647.8878(21) 15647.9053(31) 15647.9300(09)  Observed minus calculated frequencies in parentheses, in units of the least significant digit. a  Chapter 5. FTMW  Spectroscopy of MgS  67  Table 5.5: Molecular constants for M g S in MHz. 2 5  Parameter B Do eQq 0  v  6  2 4  c  Value" 7823.9703(6) [0.007900 ] 0.1366(92) 15647.9090 6  c  0  a  3 2  One standard deviation in parentheses, in units of the least significant digit. Centrifugal distortion constant held fixed in fit at value scaled from that calculated for M g S in combined fit. Hypothetical unsplit frequency calculated from B and D values. 3 2  0  0  Chapter 5. FTMW  68  Spectroscopy of MgS  Table 5.6: Substitution structure results for M g S in A . 2 4  ZMg 2 4  Mg S 3 2  1.225213(19)  ZS  0.919118(23)  3 2  a  ^  2.144331(30)  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. a  Chapter 5. FTMW  69  Spectroscopy of MgS  Table 5.7: Equilibrium bond length calculated for M g S in A . 2 4  Subst. 2.142573(60)  Vibr. 2.1425728(10)  6  2 4  Mg S 3 2  c  3 2  A  Lit. 2.1425  d  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 = 2.1460889(10)A. Calculated from vibrational data. From optical study by Marcano and Barrow [75]. a  0  c  d  Chapter 6  P u r e 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 ( E ground electronic state) and AlBr is diamagnetic. Their electronic 2  +  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, magnesium monobromide and aluminium monobromide, will be used to examine bonding in the species. Hyperfine structures in the spectra of only two magnesium monohalides, M g F 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 transform microwave ( F T M W ) and millimetre wave spectroscopy have been applied to the investigation of MgCl [45,80]. These methods have provided precise hyperfine parameters which have been used to compare bonding trends within the molecules. Though M g F  70  Chapter 6. Pure Rotational  Spectra of MgBr and  71  AlBr  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 A U — X E 2  2  +  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 A H state [90,91]. There 2  has however been only one study of a rotationally resolved spectrum. In 1969, Patel and Patel did a partial rotational analysis of the A II — X T, 2  2  +  (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 monobromide, as both metals are in the same row of the periodic table. Microwave and millimetre 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 hyperfine structure has been measured only for the J = 1 — 0 transition of A l B r by Hoeft 7 9  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 II — 1  X X  1  1  £  +  and a II — X 3  1  E , were identified. +  The vibrational analyses of the A *n —  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 Yl state was identified [106]. This was investigated in detail by l  grating spectroscopy [107-109], pulsed dye laser spectroscopy [110] and Fourier transform spectroscopy [111]. Langhoff et al. [112] calculated spectroscopic constants for the A U 1  and X  states of AlBr as part of their theoretical study of the aluminium monohalides.  Vibrational analysis of the a U — X 3  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 H — X 3  system, and did a vibrational analysis.  1  £  +  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 magnesium monobromide. The rotational, fine and hyperfine parameters of both isotopomers of MgBr, in its E 2  +  ground electronic state, have been determined. These have been used  to evaluate the equilibrium bond distance and to draw conclusions about unpaired electron density in the molecule. The first measurement of the hyperfine spectrum of A l B r 8 1  has been made. Nuclear quadrupole, spin-rotation and spin-spin coupling constants have  73  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  been determined for both isotopomers of aluminium monobromide. The hyperfine parameters 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  E x p e r i m e n t a l Details  MgBr and AlBr were produced by reaction of B r , which was present as 0.05 — 0.2% in 2  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, B r , had to be used to promote formation of 2  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 6.3.1  Assignment of Spectra MgBr  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 M g B r and M g B r , respectively) and is further 2 4  7 9  2 4  8 1  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  74  AlBr  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 monohalides. 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 transition. These lines belong to four overlapped groups, one for each of the two isotopomers, 2 4  M g B r and M g B r , in each of the v = 0 and v = 1 vibrational states. The initial 7 9  2 4  8 1  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 hyperfine 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 M g B r 79  and M g B r . The observed transitions for the M g B r and M g B r species are listed 81  2 4  7 9  2 4  8 1  in Tables 6.1 and 6.2, respectively. Spectra for species containing the minor isotopes of magnesium,  6.3.2  2 5  M g and M g , were not sought. 2 6  AlBr  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 spectrometer. Nuclear quadrupole interactions due to both Br(7 = | for both isotopes, 81  B r ) and A1(7 = |) were included in the prediction using the 27  27  A 1 and  7 9  7 9  B r and  B r nuclear  75  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  Figure 6.1: The N — 1-0, J — 3 / 2 - 1 / 2 , F = 2 - 2 transition of M g 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. 2 4  8 1  76  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  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 M g 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. 2 4  7 9  77  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  I till 24TV IT  79  M g ' B r v=0 y  2 4  M g B r v=0  2 4  M g B r v=l  2 4  M g B r v=l  8 1  7 9  8 1  I 9439.67 M H z  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 M g B r and M g B r . This composite was produced by using the measured transition frequencies along with the predicted transition intensities. 79  81  78  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  quadrupole coupling constants reported for A l B r by Hoeft et al. [98]. 79  The J = 1 — 0 transition of A l B r was measured first. Seventeen hyperfine com79  ponents were observed and were assigned using the coupling scheme J + Isr = F i ; F i + IAI = F . A n overview spectrum of the J = 1 — 0 transition, shown in Fig. 6.4, shows the relative magnitude of the Br and A l splittings: the Br quadrupole coupling splits the transition into three lines which are further split by the A l quadrupole coupling. A preliminary fit was made holding D fixed at the millimetre wave value to obtain 0  improved and  7 9  2 7  A l and B r nuclear quadrupole coupling constants and to determine the A l 7 9  B r nuclear spin-rotation constants. The improved value of eQq( Bv) was scaled, 79  by the ratio of nuclear quadrupole moments, to obtain a value for eQq( Br) which was 81  used to predict the J = 1 — 0 transition of A l B r . Sixteen hyperfine components were 81  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 B r 7 9  and A l B r are listed in Tables 6.3 and 6.4, respectively. A method similar to that used 8 1  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 B r 7 9  and A l B r . The lines of A l B r and A l B r measured in the v — 1 vibrational state are 81  79  81  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  F, = 3/2 - 3/2 F = 1/2 - 3/2 2  I 9495.0 MHz  9540.0 MHz  Figure 6.4: Composite spectrum of the J = 1 — 0 rotational transition of A l B r . The transition is split into three groups by the B r nucleus and the further splitting within each group is due to the A1 nucleus. The results of twelve different microwave experiments were used to produce this composite. The individual power spectra were scaled to reproduce predicted intensities. 79  7 9  27  Chapter 6. Pure Rotational  Spectra of MgBr and  80  AlBr  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 separately 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( A\) 27  and eQq( Br) 79  determined for  the A l B r isotopomer are within one standard deviation of those determined by Hoeft 7 9  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 B r and 7 9  2 4  Mg Br 8 1  and of the hyperfine parameters determined for A l B r and A l B r should be equal to 79  8 1  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 (6.1) was used to calculate the equilibrium values of each of the parameters. The vibrational dependencies of the four well determined parameters of MgBr, in M H z , can be summarised by the following expressions: 179.6020(18)  2.5944(24)  178.5673(17)  2.5708(21)  109.3761(50)  +1.8744(69)  91.3736(49)  + 1.5593(69)  Br)  172.9049(25)  1.1681(43)  M Br)  186.3870(25)  1.2580(43)  7,( Br) 81  eQq { Bv) 79  v  eg^( Br) 81  W  7 9  8 1  82  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  ,( Br) 81  Ct  =  222.6568(35) + 1.1215(50) \v + - J .  The expressions for the vibrational dependence of the nuclear quadrupole coupling constants of AlBr, in MHz, are: eQq ( Br)  =  79.4193(19) - 1.4258(27) (v +  eQq ( Br).  =  66.3427(20) - 1.1903(28) (  79  v  sl  v  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 6.5.1  Discussion E q u i l i b r i u m B o n d 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:  B  v  where B  e  =  £  e  - a  e  (v +  + 7e (t> + ^ )  is the equilibrium rotational constant, B  v  is the rotational constant of the  uth vibrational state and ct and 7 are higher order vibrational correction terms. This e  e  expression was used in three different calculations to estimate the equilibrium rotational constant and equilibrium bond distance. The details of this calculation of r have been e  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 a term. e  Using the B  0  and B± data, B and a e  e  were determined for both isotopomers and from  these r was determined using atomic masses and fundamental constants from Ref. 120. e  These results are listed in Table 6.8 under the heading Method I. In the second method, the higher order correction constant f  e  was substituted by 1 0  -3  •a  e  in E q . (2.16). This  value is similar to those found for CaBr [121] and BaCl [18]. Two more values of B and e  r were determined from the Bo and B\ data by employing this approximation. These are e  listed in Table 6.8 under Method II. The r obtained using Method II agrees fairly well e  with that calculated by Method I. The uncertainties given for each of these results, which are on the order of 1 0  -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. A n 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 was made as in Method II and B was calculated for the two e  e  isotopomers of MgBr; however to calculate r , ion masses were used instead of atomic e  masses. This provided a third estimate of r which is listed under Method III in Table e  6.8. The difference in r obtained for Methods II and III is on the order of 10~ A; the 5  e  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 r from that obtained in the e  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, B was calculated from the Dunham coefficient Y e  01  using a method  after Bunker [31] which also accounted for the breakdown of the Born-Oppenheimer  Chapter 6. Pure Rotational  approximation [30].  Spectra of MgBr and  84  AlBr  For this comparison, r was calculated for AlBr using the three e  methods described above. These values are listed in Table 6.9 along with the r value in e  the Born-Oppenheimer approximation from the millimetre wave study. The differences between the r values estimated by Methods I, II, and III and the Born-Oppenheimer r e  e  are all of the order of magnitude of 1 0 A , which is equal to the estimate of uncertainty _5  in r made above for MgBr. e  Table 6.10 presents a summary of the r values calculated for MgBr by each method e  and also a best estimate of r , which is an average of the results of Methods II and III. e  These results can be compared to the two literature values, the r value from the partial 0  rotational analysis [92] and an r value from a recent ab initio study [90]. The results e  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  c  =  Y  ^  9egN  ^^  1  BfiN  2  = ^ e S T v / W i v ^ c o s © ~ )/ ' ) • 2  1  r  3  Values of |*(0)| and ((3 cos 0 - l ) / r ) were calculated for M g B r and C a B r from b 2  2  3  79  79  F  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) | , or the 4p orbital, for ((3 cos 0 — l ) / r ) , and using atomic parameters calculated 2  2  z  3  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  85  by Morton and Preston [22]. A value of ( 3 c o s © — 1) = | was used for the p orbital 2  z  and a relativistic correction, on the order of 16.7%, was included for |\I/(0)| [22]. The 2  unpaired spin densities, p(s) and p(p) listed in Table 6.11, were calculated for the 4s and 4p  z  orbitals in MgBr and CaBr by taking ratios of the experimental molecular to  calculated atomic values for  I^O)] and ( ( 3 c o s © — l ) / r ) , respectively. From these, it 2  2  3  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  N u c l e a r Quadrupole C o u p l i n g 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 i (Br)' 4  0  where e(^94io( Br) is -769.76 MHz [2]. Table 6.12 presents the ionic character calculated 79  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 K B r , respectively, and the greatest difference in ionic character observed is between MgBr and K B r . 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 A l 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, i  c  =  1.15 exp  1 •§(2 - A x )  2  0.15  was used to calculate the difference in electronegativities, A x , for AlBr and GaBr [122] using the ionic characters obtained from the bromine nuclear quadrupole coupling constants. From these A x 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 electronegativity of monovalent aluminium to be 1.3. This value agrees with that determined from the more accurate nuclear quadrupole coupling constants for A l B r and A1C1 [54] obtained by F T M W spectroscopy. The A l 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 A l atom. This will be discussed in conjunction with the A l nuclear quadrupole coupling constants of aluminium isocyanide and other related aluminium halides in Sec. 7.5.1.  6.5.4  A l B r Nuclear Spin-Spin Constant  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, ot i-Br can be expressed as A  —  =  dAl-Br  ^r^NdAWBr 3" Al-Br r  where PM is the nuclear magneton and g i and ge are the nuclear ^-factors for the A l and A  r  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 B r and A l B r , respectively. The large uncertainties 79  81  in the estimated bond distances are due to uncertainties in the respective constants. Despite the large uncertainties, the estimated internuclear distances agree with the r  e  value of ~ 2.29A.  6.6  Conclusion  The first complete rotational analysis of the spectrum of magnesium monobromide has been made. Accurate rotational and centrifugal distortion constants have been determined as well as new fine and hyperfine parameters. bond length has been determined for MgBr.  The  8 1  The first accurate equilibrium  Br nuclear quadrupole structure  of A l B r has been observed for the first time. Improved nuclear quadrupole coupling 8 1  constants have also been obtained for A l B r and nuclear spin-rotation and nuclear spin79  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 corresponding 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 M g B r in v = 0 and v = 1 vibrational states. 2 4  N' 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2  J' 1/2 3/2 1/2 1/2 3/2 3/2 3/2 3/2 3/2 5/2 3/2 5/2 5/2 5/2 5/2  Transition F' /V" 1 0 1 0 1 0 2 0 3 0 2 0 0 0 1 0 1 3 1 2 2 1 1 3 1 3 4 1 2 1  0 (MHz) v =  J" 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 3/2 1/2 3/2 3/2 3/2 3/2  F" 2 2 1 1 2 2 1 1 2 2 1 2 3 3 1  9524.7196 9835.8658 9868.9931 9873.9752 10007.5349 10018.5122 10040.5588 10180.1367 19806.7336 19860.1058 (19854.946) 19954.1031 19965.0798 19966.6855 20042.7515  ° Blended lines not included in fit.  Obs. - calc. (kHz) -0.2 -0.5 0.3 -1.1 0.5 0.4 1.2 -2.6 1.3 -0.1  = 1 (MHz) v  7 9  Obs. - calc. (kHz)  9780.8303 9814.4948 9820.2456 9950.8962 9963.9149 9983.8199  1.6 0.0 -1.4 0.7 0.0 0.2  19697.8937 19748.6261  1.1 -0.5  19842.2139  -0.6  a  0.2 -0.5 -1.1 0.1  (19854.946)°  90  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  Table 6.2: Measured frequencies of N = 1 - 0 and N = 2 - 1 transitions of M g B r in v = 0 and v = 1 vibrational states. 2 4  Transition TV' 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2  J'  F'  N"  J"  1/2 3/2 1/2 1/2 3/2 3/2 3/2 3/2 3/2 5/2 3/2 5/2 5/2 5/2 5/2  1 1 1 2 3 2 0 1 3 2 2 3 3 4 2  0 0 0 0 0 0 0 0 1 1 1 1 1 1 1  1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 3/2 1/2 3/2 3/2 3/2 3/2  v = 0 F" (MHz) 2 9439.6747 2 9774.2372 1 9810.8129 1 9821.2344 2 9949.1867 2 9960.7121 1 9990.1631 1 10145.3776 2 19695.5304 2 19741.3556 1 19744.5411 2 19836.5686 3 19848.0947 3 19851.5795 1 19927.8289  Obs. - calc. (kHz) 0.6 -1.8 -0.1 -1.4 1.5 -0.1 1.4 -0.3 0.5 0.5 1.5 -0.2 -1.0 -2.0 0.6  v = 1 (MHz)  8 1  Obs. - calc. (kHz)  9719.8268 9756.6116 9767.9234 9893.0409 9906.6172 9934.0030  -0.9 -0.1 0.2 0.0 0.0 -0.0  19587.6184 19630.9493  -0.1 0.2  19725.6566  0.2  19740.8692  -0.3  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  Table 6.3: Measured frequencies of J = 1 — 0 and J  2 - 1 transitions of A l B r 7 9  v = 0 and v = 1 vibrational states. Obs. - calc. /kHz  v= 1 /MHz  Obs. - calc. /kHz  9498.8843  -0.4  9447.2081  0.6  9498.8913  0.5  9447.2129  -0.8  9499.3000  0.8  9513.1626 9513.1697  -0.7 0.2  9461.7707 9461.7765  0.3 -0.2  9514.6912  -1.2  9463.2601  0.6  9515.8005  -0.6  9515.8088  0.9  9516.9414  -0.4  9465.5128  -0.3  i}  9517.4427  -0.5  9519.4344  1.1  1}  9532.6899  1.0  9534.4667 9534.4734 9536.1761  -0.1 0.4 -0.8  9483.4006 9483.4068  -0.0 -0.1  9536.1870  0.8  9537.7080  -0.9  9486.6262  -0.0  19023.5363 19033.9816 19035.4116 19035.9549 19037.1585 19037.7460 19038.7946 19038.9670 19039.1645 19039.3799 19058.8521 19059.1193 19059.2005  0.0 -0.1 0.5 -0.4 -0.1 0.4 0.6 -1.2 0.1 -0.3 -0.1 0.9 -0.4  18931.2710 18932.7194  0.2 0.0  18934.4273 18935.0157 18936.0618  -0.9 -0.2 0.8  Transition  J' F{ F' J" F[' F" 1/2  0  3/2  1/2  0  3/2  0  3/2  0 0  3/2 3/2  0  3/2  5/2  0  3/2  5/2  0  3/2  5/2  0  3/2  5/2  0  3/2  0  3/2  3/2  0  3/2  1  3/2 3/2 3/2  4 2  0 0 0  3/2 3/2 3/2  1  3/2  2  0  3/2  1  3/2  3  0  3/2  1/2  2  5/2 5/2 5/2  5/2  1  2 2 2 2 2 2 2 2 2 2 2 2 2  3/2 5/2 7/2 7/2 7/2 7/2 5/2 1/2 1/2 1/2 3/2 3/2 3/2  3  0  4 4 4 3 5 6 5 3 2 3 2 4 3  1 1 1 1 1 1 1 1 1 1 1 1 1  4 2 3 1 2 3 4 3 4 2 3 1 2 3 4  4 3 1 3  6  3/2 3/2 5/2 5/2 5/2 5/2 3/2 1/2 1/2 1/2 1/2 1/2 1/2  4 3 3 2 4 5 4 2 3 3 2 3 2  )  v-0 /MHz  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 B r 8 1  v = 0 and v = 1 vibrational states.  J' F{ 1  1/2  Transition F' J " F{> 3  0  3/2  1/2  3  0  3/2  1/2  2  0  3/2  5/2  4  0  3/2  1  5/2  3  0  3/2  1  5/2  2  0  3/2  1  5/2  2  0  3/2  1  1  1  5/2  5  0  3/2  1  5/2  1  0  3/2  1  5/2  0  0  3/2  1  3/2  1  0  3/2  1 1  3/2 3/2 3/2  4 4 2  0 0 0  3/2 3/2 3/2  1  3/2  2  0  3/2  1  3/2  3  0  3/2  2 2 2 2 2 2 2 2 2 2 2  3/2 5/2 7/2 7/2 7/2 7/2 5/2 1/2 1/2 3/2 3/2  4 4 4 3 5 6 5 2 3 2 4  1 1 1 1 1 1 1 1 1 1 1  F" J  3 1X ^ 1  I1 1  2 3 4 3 J  * ) 1 _  4  1  4 3 1  J  J  J  3  6  3/2 3/2 5/2 5/2 5/2 5/2 3/2 1/2 1/2 1/2 1/2  \  4 3 3 2 4 5 4 3 3 2 3  )  v= 0  Obs. - calc. /kHz  v= 1 /MHz  Obs. - calc. /kHz  9442.1516  -0.2  9391.0201  -0.3  9442.1572  0.3  9391.0257  0.1  9442.6367  -0.3  9453.9378  0.0  9403.0418  0.3  9455.6860  -0.4  9404.7448  0.1  9456.6388  -0.7  9456.6464  1.2  9457.7853  -0.3  9406.8512  -0.1  9458.1142  -0.7  9460.2789  0.7  9470.4626  0.8  9472.1403 9472.1459 9473.8751  -0.1 0.3 -1.1  9421.5076 9421.5121  0.3 -0.5  9473.8851  1.1  9475.3213  -0.4  9424.6748  0.1  18906.3863 18914.7191 18915.9108 18916.5822 18917.8648 18918.4175 18919.4318 18919.6381 18919.8830 18936.0620 18936.3751  -0.2 0.3 0.0 -0.1 0.0 -0.1 0.5 0.4 -0.0 -0.7 -0.0  18812.9761 18814.1951  0.0 0.2  18816.1040 18816.6581 18817.6710  -0.6 -0.6 1.0  /MHz  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  93  Table 6.5: Molecular constants calculated for MgBr in M H z . a  Parameter B D 7 C/(Br) b c eQq(Bv) F  a  2 4  Mg 79  v =0 4972.20127(57) 0.003945(82) 178.3048(14) 0.00553(39) 172.3208(12) 207.0793(26) 110.3133(36)  B r  v - 1 4944.62754(69) 0.00392(11) 175.7104(19) 0.00545(50) 171.1527(41) 208.1257(46) 112.1877(59)  2 4  v = 0 4943.62546(57) 0.003849(80) 177.2819(13) 0.00595(39) 185.7580(12) 223.2175(24) 92.1532(35)  M  g  s l  Br  v =1 4916.28928(68) 0.00390(10) 174.7111(17) 0.00555(48) 184.5000(41) 224.3390(44) 93.7125(60)  One standard deviation in parentheses, in units of least significant digit.  94  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  Table 6.6: Molecular constants calculated for AlBr in M H z . a  Parameter B D eQq(Al) eQq(Bv) C/(A1) C/(Br) OLAl-Br a  6  Al V =0 4759.72699(17) 0.003414(25) -28.0059(34) 78.7064(14) 0.00412(12) 0.01356(13)  —0.00191(33)  7 £  Br  A l Br 8 1  v =1 4734.05280(24) 0.003382(37) -27.8019(51) 80.1322(23) 0.00450(27) 0.01348(22)  -0.00191  6  v = 0 4729.82499(18) 0.003360(26) -28.0061(35) 65.7476(15) 0.00406(12) 0.01451(13) -0.00170(35)  v = 1 4704.39229(26) 0.003319(41) -27.8068(53) 66.9379(24) 0.00408(27) 0.01463(24)  -0.00170  One standard deviation in parentheses, in units of least significant digit. Nuclear spin-spin constant held fixed at value obtained from v = 0 fit.  6  95  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  Table 6.7: Calculated ratios of hyperfine parameters compared to nuclear and molecular properties of MgBr and AlBr.  v=0 1.00577(1)  v=l 1.00572(1)  Eq. 1.00579(1)  Lit. 1.0057885(1)"  6 ( Br)/6 ( Br) c( Br)/c( Br)  0.92766(1) 0.92770(2)  0.92766(3) 0.92773(3)  0.92767(2) 0.92769(2)  0.927700(2) 0.927700(2)  eQo( Br)/ Qo( Br)  1.19706(6)  1.19715(10)  1.19702(7)  1.19707(3)  C7,( Br)/C7( Br)  0.929(89)  0.982(124)  AlBr eQo( Br)/ Q ( Br)  v=0 1.19710(6)  v=l 1.19711(6)  C7/( Br)/C/( Br)  0.934(12)  0.921(21)  MgBr ( Br)/ ( 7 9  7  J  8 1  7  79  £r)  81  F  F  79  81  79  81  e  79  81  79  81  e  79  0  81  a  d  e  a  1.19711(5) -  c  0.933573(2)  -  Eq.  c  Lit. 1.19707(3)  d  0.933573(2)'  For method of calculation, see text Sec. 6.4. Inverse ratio of reduced masses of M g B r and M g B r , calculated using atomic masses in Ref. 120. Ratio of nuclear moments of B r and B r , calculated using values in Ref. 120. Ratio of electric quadrupole moments of B r and B r , taken from Ref. 2. Ratio of nuclear magnetic moments of B r and Br multiplied by inverse ratio of reduced masses of M g B r and M g B r , calculated using values in Ref. 120. ' Ratio of nuclear magnetic moments of B r and Br multiplied by inverse ratio of reduced masses of A l B r and A l B r , calculated using values in Ref. 120. a  6  2 4  c  7 9  7 9  8 1  d  7 9  e  7 9  79  8 1  8 1  81  7 9  7 9  2 4  81  8 1  8 1  96  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  Table 6.8: Equilibrium parameters calculated for M g B r ' \ a  Method I j5 /MHz « /MHz e  e  r /A e  Method II £ /MHz a /MHz rjk e  e  Method III 5 /MHz a /MHz e  e  24  81  Mg Br 4985.9881(7) 27.57373(89) 2.347408(1)  4957.2936(7) 27.33618(89) 2.347408(1)  Mg Br 4985.9675(7) 27.51869(89) 2.347413(1)  Mg Br 4957.2731(7) 27.28162(89) 2.347413(1)  Mg Br 4985.9675(7) 27.51869(89) 2.347432(1)  Mg Br 4957.2731(7) 27.28162(89) 2.347432(1)  2 4  2 4  2 4  7 9  7 9  7 9  2 4  2 4  M  g  B  r  8 1  8 1  For methods of calculation, see Sec. 6.5.1. Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. a  6  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  97  Table 6.9: Comparison of equilibrium bond length estimates for AlBr". Method I r /A e  6  Method II  6  2.294870(1) 2.294878(1)  Method III  6  Lit. Exp.  2.294893(1) 2.29480(3)  c  For description of methods see Sec. 6.5.1. Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. r from Wyse and Gordy [97]. a  6  0  e  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  98  Table 6.10: Summary of equilibrium bond length estimates for M g B r . 3  Method I  r /A e  Method II Method III Ave. 2.347408(4) 2.347413(4) 2.347432(4) 2.34742(2) 6  6  6  c  Lit. Exp. 2.36  d  Lit. Theo. 2.40  e  For description of methods see Sec. 6.5.1. Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. Average of Method II and III. Uncertainty estimated from range of values. r from partial rotational analysis [92]. r from Ref. 90. a  6  0  d  0  e  e  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 6^/MHz c/MHz  Mg Br 172.321 207.079 2 4  |$(0)| /au((3cos 0-l)/r )/au2  3  2  3  p(s)/%  p(p)/% a  6  Taken from Ref. 118. Calculated from data in Ref. 22.  3  7 9  Ca Br° 121.202 77.620 4 0  7 9  0.153345 1.02919  0.107855 0.385774  0.5369 8.436  0.3776 3.162  7 9  B r atom  :  28.56 12.20  -  6  Chapter 6. Pure Rotational Spectra of MgBr and AlBr  Table 6.12: Comparison of AlBr, quadrupole coupling constants.  2 3  eQo( Br)/MHz 79  ij% x xjvf(calc)' e  M  a  6  c  d  e  Na Br° 7 9  58.60801 92.5 0.9  MgBr and related metal monobromide nuclear  K Br 10.2383 98.7 0.8  3 9  100  7 9  6  2 4  Mg Br 7 9  110.313 85.7 1.2  4 0  Ca Br 7 9  20.015 97.4 1.0  c  27  A 1  79  B r  78.706 89.8 1.5 1.3  6 9  Ga Br 106.2 86.2 1.5 1.4 7 9  r f  Results taken from Ref. 124. Results taken from Ref. 125. Results taken from Ref. 118. Results taken from Ref. 122. Electronegativities taken from Ref. 2.  ' Average of electronegativites calculated from ionic character of the respective MCI and M B r 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 refractoryelement 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 M g N C , 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 A l 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 M g N C 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 M g N C [132], which were subsequently also identified in space [133]. The 2 6  rotational spectrum in the v excited bending state has been measured and these results 2  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 M g N C and several related isocyanides [138-141]. Theoretical studies have also been made of the thermochemistry of M g N C 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 M g N C 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, u  [147]. Fukushima has reported investigation of the A' — X 1  2  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 magnesium 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 A 1 nucleus in A1NC. The derived constants have been used 27  to investigate orbital hybridisation in these species.  7.2  E x p e r i m e n t a l Details  M g N C and A1NC were prepared by reacting ablated Mg metal (rod from A . D. MacKay 99.9%) or ablated A l 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 M g N C , 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 7.3.1  Observed Spectra MgNC  The millimetre wave spectrum of the free radical M g N C 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  104  Chapter 7. Microwave Spectroscopy of MgNC and AINC  results from MgF [78] by the ratio of the nuclear ^-factors, g j ( N ) / g / ( F ) . The nuclear 14  19  quadrupole coupling constant eQq ( N) was assumed to be equal to that of CaNC [57]. 14  0  Only the two lowest N rotational transitions, N = 1 — 0 and ./V = 2 — 1, were available in the frequency range of the spectrometer.  A n 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 B , 7 and the three hyperfine parameters, with Do held fixed Q  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 M g N C were not sought. A n example spectrum is shown in Fig. 7.1.  7.3.2  AINC  When this study was undertaken no experimental results had been presented, so the transition frequencies were predicted using results from the theoretical study by M a et al. [129]. Experience with the similar species M g N C provided some added insight into how the theoretical results could be employed. For M g N C , 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, M a et al. found that B and B differed by only about 5 MHz. 0  e  Consequently the B constant predicted for AINC using the same level of theory as for e  M g N C was chosen to calculate the initial search range. To estimate the magnitude of the hyperfine splitting, eQq( A\) from A1F [96] and eQ<?( N) from M g N C were included in 27  14  105  Chapter 7. Microwave Spectroscopy of MgNC and A1NC  49 kHz  I 11932.041 MHz  1 11932.441 MHz  Figure 7.1: The N = 1 - 0, J = 3/2 - 1/2, F = 3/2 - 1/2 transition of M g N 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. 2 4  1 4  1 2  106  Chapter 7. Microwave Spectroscopy of MgNC and AINC  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 N C (98.53% natural abundance). Spectra of species containing other isotopes of 1 4  1 2  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 A 1 were larger than those due to N , 27  1 4  the lines were easily assigned in terms of the coupling scheme J + IAI = F ; F + IN = F . 2  X  An overview spectrum of the J = 1 — 0 transition, shown in Fig. 7.2, shows the relative magnitudes of these splittings: the A1 quadrupole coupling produces three lines which 27  are then split further by the  1 4  N quadrupole coupling. A n expanded view of the i*\ =  7/2 — 5/2 section of the J — 1 — 0 transition is given in Fig. 7.3. A l l the measured lines and their assignments are listed in Table 7.2.  7.4  Analyses  7.4.1  MgNC  The measured transition frequencies of M g N C were fit using Pickett's exact fitting program 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, B  0  e  and D , the spin-rotation parameter, 7 , the nuclear quadrupole coupling constant, 0  Q<7o( N), and the magnetic hyperfine parameters, the Fermi contact constant, bp, and 14  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  F, =  F  1  107  7/2 - 5/2  n  = 5/2 - 5/2  n  = 3/2 - 5/2  n  i  wvuv  11960.500 M H z  u  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.  108  Chapter 7. Microwave Spectroscopy of MgNC and AINC  45 k H z  F =  9/2 -7/2  _ 7/2-5/2 * 7/2 - 7/2 F  5/2 - 5/2 I F = 5/2-7/2 5/2 - 3/2 V l 11970.535 MHz  I 11971.585 MHz  Figure 7.3: Detail of the J - 1 - 0 transition of AINC, showing the F = 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. x  109  Chapter 7. Microwave Spectroscopy of MgNC and AINC  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 transitions 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 millimetre 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 centrifugal distortion constants, B , D , and H , the spin-rotation constants, 7 and 70, and 0  0  0  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 uncertainties. 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 spinrotation 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  AINC  The measured frequencies of AINC were fit using Pickett's program S P F I T [76], to the rotational constant B , the centrifugal distortion constant D , the nuclear quadrupole and 0  Q  nuclear spin rotation coupling constants, eQq and Ci, for both the A l 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 deviation. Our high resolution F T M W study produced a more precise Bo- However the value of D derived from the millimetre wave study was more precise because rotational 0  transitions up to J = 31 were measured, where distortion effects are larger. It is interesting 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 M g N C , a fit of the F T M W and millimetre wave results for AINC was made. The resulting 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 constants 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 B labelled by M a et al. as the most reliable, however, e  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  7.5  111  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 structures observed have been described as resulting from a subtle balance between longrange (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 interaction, and the linear cyanide structure, favoured by the long-range interaction [149]. This linear isocyanide structure was also predicted to be favoured for aluminium monocyanide [129,147] and the alkaline earth monocyanides [57,137,150,151]. When considering the experimental results for AINC and M g N C , 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 - N C 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 AIN C bond should be less ionic than that of M g N C 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 C N group is similar to those of F and CI. Information obtained from the hyperfine constants can be used to determine whether AINC and M g N C follow  112  Chapter 7. Microwave Spectroscopy of MgNC and AINC  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 eQq constant is listed. This z  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 H N C [155]. The constants 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 H N C , that the linear metal isocyanides are fairly ionic species. However, they do appear to have some covalent character. To investigate 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 n , x  n  respectively.  y  and n  z  are the number of electrons in the np , x  np  y  and np  z  orbitals,  By estimating values for n , n and n , this model can be used to probe x  y  z  orbital hybridisation [2,35,93]. The molecular orbital basis for this discussion can be  113  Chapter 7. Microwave Spectroscopy of MgNC and AINC  found in Sec. 2.5. We will consider an sp -hybv\d orbital on N in a linear metal isocyanide molecule; d z  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 p -electrons in the two hybrid 2  orbitals can be calculated from Eq. (2.75)  n  z  =  2a (l - a ) 2  2  + Na  2 s  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, a is the fractional weight of the sp hybrid in the M - N bond molecular orbital, 2  al is the ^-character of the hybrid orbital and iV is the number of electrons in the counterhybridised orbital. The a value can be estimated from the ionic character of the 2  molecule, i , using Eq. (2.67). Methods of calculating ionic character are discussed in c  Sec. 2.5. For all species discussed here, i has been calculated using the approximate c  expression Eq. (2.77):  if  \x -x M  =  ~  N C  \  2  The electronegativity values, x, are taken from Ref. [2], except for x r, for it the value A  derived from the nuclear quadrupole coupling constants of AlBr and A1C1 in Chapter 6 was used. (The calculated a values changed by only 5% when using the more exact 2  s  expression, E q . (2.78), for i .) c  In a linear metal isocyanide compound, M - N C , the N is on the negative pole of the bond and therefore 2ct is equal to (1 + i ). 2  c  Care must be taken in determining the p-  electron distribution because N is part of the N C 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 2p and 2p orbitals x  y  114  Chapter 7. Microwave Spectroscopy of MgNC and AINC  and the sp counterhybridised orbital have one half of a bond pair (n  x  = n  y  = N = 1).  Using E q . (2.43) and (2.75) and substituting the above values, the following equation results eQq(^)  1 + 1-  =  [(1 + 0 ( 1 - ^ ) +a .  =  i (l - a ) Q  2  2  c  e  eC?92io( N) 14  ( N). 1 4  9 2 1 0  (7.1)  A further correction must be added to account for the screening effect of the negative charge on the N C group, e%(»N)  =  y i - . f l ^ j g Q ,  (7.2)  where e = 0.3 [1]. The value of a was calculated for the bonding orbital of N for M g N C , 2  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 - N C bond, which decreases from L i N C to AINC. As the M - N C 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 - N C 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 A l and N nuclei. The sp-hybridisation of the A l bonding orbital can be investigated using a method similar to that described above for N. In this discussion several A l - X compounds will be considered.  115  Chapter 7. Microwave Spectroscopy of MgNC and AINC  The valence shell configuration of A l is 3s 3p . 2  1  A l is the positive pole of the A l - X bond [2].  The value of 2a is (1 — i ), since 2  c  N will be taken to be 2, because the  counterhybridised orbital will have an unshared pair, and the 3p and 3p orbitals are x  unfilled, so n  = n  x  y  y  = 0. By combining Eqs. (2.43) and (2.75) and substituting, the  following expression results: eQq{ A\) 27  =  (7.3)  [ ( l - i ) ( l - a ) + 2a ]eg io( Al). 2  2  27  c  03  A further correction must be added to account for decreased nuclear screening of the positive A l nucleus, g ( Al) 2 7  e  0  =  [ ( l - g ( l - a ) + 2a ](l + i e ) g o o ( A l ) 2  2  27  c  e  31  (7.4)  where e = 0.35 for A l [1]. Eq. (7.4) was used to estimate the s-character of the sphybridised bonding orbital of A l 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 A l 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( A\) and a decrease from F 27  2  to N C to CI to Br.  7.5.2  E l e c t r o n Spin-Nuclear Spin Hyperfine Parameters for M g N C  The nature of the bonding in M g N C can be examined by calculating the unpaired electron 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  116  Chapter 7. Microwave Spectroscopy of MgNC and AINC  atomic orbitals are related to the Fermi contact constant, bp, and to the dipole-dipole interaction 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 = c  Y^tfe/Wel^O)! 3 2  =  ^  9N9etXNfiB  cos2  2  Q  ~  )/ )i  l  r3  From bp and c, values of |$(0)| and ((3 cos 0 — l ) / r ) were calculated for M g N C and 2  2  - 3  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 2p orbital. Atomic parameters for the calculations were 2  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 M g N C were calculated by scaling those of MgF by the ratio of the nuclear ^-factors, #/( N)/<7/( F). This estimation 14  19  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 M g N C , the values predicted  from MgF [&F = 16.5 MHz and c = 13.7 MHz] did not agree well with the experimentally  117  Chapter 7. Microwave Spectroscopy of MgNC and AINC  determined values [b  F  = 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 M g N C .  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 for  AINC  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  CtAl-N  —  —3p%gAi9N 3 • Al-N  r  A value of r i-N A  = 1.75(20) A was obtained from this expression. The large uncertainty  comes from the relatively large uncertainty in ct i-N- This result compares well, within A  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 A l - N bond distance is intermediate between the corresponding distances in A1F [r = 1.65436 A [94,95]] e  and A1C1 [r = 2.13011 A [97]], parallelling the bond properties obtained from the A l e  quadrupole coupling constants and again showing the similarities between these three A l - X species.  7.6  Conclusion  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 sphybridisation 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.  119  Chapter 7. Microwave Spectroscopy of MgNC and AINC  Table 7.1: Observed frequencies of  N'  J'  1 1 1 1 1 2 2 2 2 2 2 2  1/2 1/2 3/2 3/2 3/2 3/2 5/2 3/2 5/2 5/2 5/2 5/2  21 21 22 22 23 24 24 26 26 27 27 28 29 29 30 30 31 31  41/2 43/2 43/2 45/2 47/2 47/2 49/2 51/2 53/2 53/2 55/2 57/2 57/2 59/2 59/2 61/2 61/2 63/2  Transition  F'  N"  1/2 3/2 3/2 1/2 5/2 5/2 3/2 3/2 5/2 3/2 5/2 7/2  0 0 0 0 0 1 1 1 1 1 1 1  20 20 21 21 22 23 23 25 25 26 26 27 28 28 29 29 30 30  J" F" 1/2 1/2 1/2 1/2 1/2 1/2 3/2 3/2 3/2 1/2 3/2 3/2 39/2 41/2 41/2 43/2 45/2 45/2 47/2 49/2 51/2 51/2 53/2 55/2 55/2 57/2 57/2 59/2 59/2 61/2  3/2 1/2 3/2 1/2 3/2 3/2 3/2 1/2 5/2 1/2 3/2 5/2  2 4  Mg  1 4  N  Obs. Freq. (MHz) 11922.9251 11928.6450 11932.2411 11935.7735 11941.2144 23861.2286 23863.0750 23863.7795 23864.6542 23872.3887 23873.6278 23875.0396  1 2  C in its ground vibrational state". Au Microwave F i t (kHz) -0.9 0.5 0.3 -1.0 1.1 2.0 -0.1 -1.4 0.3 -1.3 1.4 -0.9  250445.992 250461.245 262356.464 262371.679 274279.991 286170.795 286186.023 309975.563 309990.788 321874.135 321889.423 333785.266 345663.196 345678.383 357553.444 357568.654 369440.810 369455.973  Results between 11.9-23.9 GHz are from present study. Ref. [69]. Observed minus calculated frequencies listed as Au. Results for microwave and global fits are listed in Table 7.3.  a  6  c  6 , c  Av Global F i t ' (kHz) -0.9 0.7 0.2 -0.8 1.1 2.2 0.1 -1.1 0.6 -1.2 1.8 -0.4 0  0  4 -7 -18 -60 -40 6 -9 8 6 10 79 28 23 9 -23 -6 -11 -31 Other data taken from  Chapter 7. Microwave Spectroscopy of MgNC and AINC  120  Table 7.2: Observed ground vibrational state frequencies of A l N C . a  Transition  J' F{  F'  J"  F[' F"  Obs. Freq. (MHz)  Av Microwave (kHz)  b,c  Av Global"' (kHz)  5/2  1/2  0  5/2  11963.2831  -0.1  -0.0  5/2  7/2  0  5/2  11963.4981  -0.0  0.1  5/2  5/2  0  5/2  11963.9959  0.0  0.2  7/2  7/2  0  5/2  11970.8348  -0.1  0.0  7/2  9/2  0  5/2  11971.2387  -0.5  -0.3  7/2  5/2  0  5/2  11971.2646  0.1  0.2  3/2  3/2  0  5/2  11974.2358  0.1  0.1  3/2  1/2  0  5/2  11974.4227  0.7  0.7  3/2  5/2  0  5/2  11974.4597  -0.1  0.0  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 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  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  23930.8749 23932.3001 23932.3737 23932.6368 23935.9314 23936.5199 23939.2513 23939.4034 23939.4758 23939.5286 23940.1152 23940.2807 23940.5822 23941.6089 23941.8364 23941.9025  0.4 0.8 -0.5 -0.0 -0.3 -0.7 0.1 -0.3 -0.1 0.7 -0.0 0.1 0.1 0.1 0.2 -0.4  0.4 0.9 -0.5 0.0 -0.3 -0.7 0.1 0.2 0.1 0.8 0.0 0.2 0.0 0.2 0.3 -0.4  2  3/2  5/2  23946.7609  -0.1  -0.1  2  3/2  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  5/2  23946.8933  -0.1  -.0.1  11 12 13 14 15  131642.189 143605.379 155567.428 167528.343 179487.893  -16 -17 -43 3 -18  0  Chapter 7. Microwave Spectroscopy of MgNC and AINC  121  Observed ground vibrational state frequencies of A l N C Transition  J' F{ 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  F'  J" 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  F['  F"  Obs. Freq. /MHz 215357.910 227311.359 239263.086 251212.965 263160.905 275106.835 287050.637 298992.248 310931.575 322868.534 334803.018 346734.944 358664.263 370590.854 382514.633  a  (cont.).  A i / Microwave*' (kHz)  -  0  Au Global"' /kHz -8 -25 -10 -2 -0 12 7 8 11 19 12 -6 1 -2 -15  Results between 11.9-23.9 GHz are from present study. Other data taken from Ref. [147]. Observed minus calculated frequencies listed as Au. Results for microwave and global fits are listed in Table 7.4. a  6 c  0  Chapter 7. Microwave Spectroscopy of MgNC and AINC  Table 7.3: Molecular constants calculated for M g N C in M H z . 2 4  Parameter B D tfoxlO 7 7DX10 b c eQg ( N) 0  0  7  4  F  l4  0  a  b  c  d  Microwave Fit 5966.90349(63) 0.004233(88) 15.3320(20) 29.1645(79) 5.3838(82) -2.3232(55) 6  Global Fit 5966.90349(19) 0.00424336(43) 0.3521(30) 15.3322(19) -0.518(45) 29.1637(77) 5.3840(77) -2.3231(53) c  1 4  1 2  a  Lit. 5966.8969(24) 0.0042338(35) 0.308(16) 15.219(13) d  One standard deviation in parentheses, in units of least significant digit. Fit of microwave data only; for details see Sec 7.4.1. Fit of microwave and millimeter wave data; for details see Sec. 7.4.1. 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  B0 Do # xl0 eQq{ k\) eQq( N) C/( A1) C/( N) a _  Microwave Fit  6  5984.67681(23) 0.003898(30)  7  0  27  14  27  14  Al  N  -35.6268(16) -2.1508(19) 0.003850(84) 0.00156(25) -0.00127(43)  Global Fit 5984.676685(59) 0.00388947(34) 0.2551(26) -35.6268(16) -2.1508(19) 0.003841(84) 0.00155(25) -0.00126(42) c  Lit. 5984.6752(14) 0.0038870(24) 0.243(13) rf  ° One standard deviation in parentheses, in units of least significant digit. Fit of microwave data only; for details see Sec 7.4.2. Fit of microwave and millimeter wave data; for details see Sec. 7.4.2. Results from millimeter wave study [147]. b  c  d  124  Chapter 7. Microwave Spectroscopy of MgNC and AINC  Table 7.5: Comparison of experimental and theoretical rotational constants for AINC.  Bo exp. B TZ2P + f CISD B TZ2P + f CCSD(T) e  e  a  5/MHz 5984.6768 5968° 5882 a  From Ref. [129]. B was calculated since it was determined that B and B e  less than 5 MHz.  e  0  differ by  Chapter 7. Microwave Spectroscopy of MgNC and AINC  125  Table 7.6: Comparison of nuclear quadrupole coupling constants of M g N C , AINC and related cyanides and isocyanides. Species KCN NaCN LiNC CaNC MgNC AINC HNC  Structure T-shaped T-shaped linear NC linear N C linear N C linear N C linear NC  eQ ( N)7MHz 14  ?0  —4.11 ' -4.219 -2.941 -2.697' -2.323 -2.151 +0.28  2^  6 c  M  0.59 0.62 0.64 0.65  6  0.93 0.90 0.80 0.75  3  Molecular properties listed in order of decreasing ionic character of M - N C bond. Using eQq which is along C-N axis ( ± 1 deg). From Ref. 153. From Ref. 154. From Ref. 152. From Ref. 57. From Ref. 155. 5-character of N bonding orbital calculated from the N nuclear quadrupole coupling constant. For details, see Sec. 7.5.1. Ionic character of M - N C bond calculated from electronegativities using Eq. (2.77). a  6  z  c  d  e  1  9  h  1  1 4  1 4  Chapter 7. Microwave Spectroscopy of MgNC and AINC  126  Table 7.7: s-character of A l bonding orbital calculated from A l nuclear quadrupole coupling constants. Species A1F AINC A1C1 AlBr a  b  c  eQo( Al)/MHz -37.49 -35.627 -30.408 -28.006 27  a  6  a  al  0.37 0.29 0.26 0.20  c  c  From Ref. [96]. From Ref. [54]. Differs from value in Ref. [2], because of the method used to calculate i . Result from Chapter 6. c  d  Chapter 7. Microwave Spectroscopy of MgNC and AINC  127  Table 7.8: Unpaired electron spin densities calculated at the hyperfine constants for M g N C and CaNC. Parameter  MgNC  6 /MHz c/MHz  29.167 5.389  F  |*(0)| /au" ((3cos 0-l)/r )/au-  CaNC  1 4  N nucleus from magnetic  a  12.4815 2.074  0.0902704 0.093143  0.0386299 0.035842  p{s)l%  1.61  P(P)I%  3.23  0.689 1.24  2  3  2  3  3  a  Taken from Ref. 57.  b  Calculated from data in Ref. 22; for details see Sec. 7.5.2.  1 4  N atom -  5.606 2.8792 -  6  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? (n + l)s ] [157]. 1  2  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 Y B r . 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 rotational analyses of six singlet transitions [B W - X S + , C S + - X ^ , l  EU l  -  F YJ - X Y, 1  X  +  , and G W - X Z+) l  L  128  1  1  1  D !! - X E + , 1  J  and one triplet transition (d $ 3  -  a A). 3  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 E 1  yses of five new transitions (& II - X^+, 3  and f l —  states and have provided rotational anal-  +  e II(ft = 1) - X E + , n - a A, II - b Il, 3  1  3  3  3  3  In the most recent study by Kaledin et al. [170], improved molecular  3  constants have been determined for several electronic states and ligand field theory calculations 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 E 1  BW l  +  ground electronic state and the  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 millimetre 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 [B l\ l  C S+-X S+, D n - X £ + , 1  1  1  1  D^-A'A,  J II-X E , 1  1  +  A n-X E+) rl  1  — X £ , x  +  [175-179]. In ad-  dition a triplet transition (d $ — a A) and an intercombination band (D !! — a A) have 3  3  1  3  been investigated [180]. The permanent electric dipole moments in the C E 1  electronic state and X ^ 1  +  excited  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 isotopomers 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 fluorescence [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 equilibrium bond length had to be assumed for Y B r to perform the calculations. This chapter reports the first high resolution spectroscopic study of yttrium monobromide 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 coupling constants have been determined for Y B r . 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  E x p e r i m e n t a l 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  8.3 8.3.1  Spectroscopy of Yttrium Monohalides:  YF and YBr  131  Spectral Search and Assignment YF  Yttrium monofluoride has only one isotopomer,  8 9  Y F , and both 1 9  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 spinrotation 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 smaller than that of  1 9  8 9  Y is almost 20 times  F and also nuclear spin-rotation splitting due to  observed in the F T M W study of the similar species YC1 [56].  8 9  Y had not been  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 monobromide, 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 for YC1 with that obtained experimentally by Simard et al. [181]. Nue  clear quadrupole coupling constants for each of the bromine nuclei, B r and 7 9  8 1  B r (both  Chapter 8. FTMW  Spectroscopy of Yttrium  Monohalides:  132  YF and YBr  -F  = 3/2 -1/2  F=l/2-1/2-  <  66 kHz —•  i  1  17367.371 MHz  17366.971 MHz  Figure 8.1: The J = 1 — 0 rotational transition of Y F . The nuclear spin-rotation splitting observed is due to the 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. 1 9  Chapter 8. FTMW  Spectroscopy of Yttrium Monohalides: YF and YBr  133  isotopes have / = |) were estimated using results obtained for K B r [125]. Five rotational transitions, J — 2 — l t o J = 6 — 5, were available in the frequency The initial search range was calculated for the J = 2 — 1  range of the spectrometer.  transition; a line was found within 10 MHz of the prediction. The assignment was made by observing transitions due to both isotopomers, Y B r and Y B r , which have almost 7 9  8 1  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 B r 7 9  and Y B r in the ground vibrational state are listed in Tables 8.2 and 8.3, respectively. 8 1  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 Y B r in the v = 1 vibrationally excited state were predicted by estimating the vibration-rotation constant ct . This was done by comparing e  the values of a for A1F, A1C1 and AlBr [184] with those of Y F [170] and YC1 [181]. This e  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 B r and Y B r in the v = 1 state are also listed in Tables 8.2 7 9  8 1  and 8.3, respectively.  8.4 8.4.1  Analyses YF  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 nuclear 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  134  Spectroscopy of Yttrium Monohalides: YF and YBr  F= 1 1 / 2 - 9 / 2 F =9/2 - 7 / 2  i 14833.161 MHz  1  14833.761 MHz  Figure 8.2: The AF = +1 hyperfine components of the J = 4 — 3 transition of Y 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. 8 1  Chapter 8. FTMW  135  Spectroscopy of Yttrium Monohalides: YF and YBr  The nuclear spin-rotation contribution to the molecular energy is given by E q . (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, B , the centrifugal distortion 0  constant, D , and the 0  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 B obtained from 0  the direct calculation are listed under the heading Direct Calculation; the B  0  quoted  for the direct calculation was obtained from the hypothetical unsplit frequency by fixing D  0  at the value from the P P M O D R study. Also listed are the B  0  the P P M O D R study [173]. The rotational constant and the  1 9  and D  0  values from  F nuclear spin-rotation  coupling constant from the combined fit compare quite well with those determined by direct calculation. However, the B and D results from the combined fit do not compare 0  0  Chapter 8. FTMW  Spectroscopy of Yttrium Monohalides: YF and YBr  136  as well with those obtained from the P P M O D R 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 D were determined while Ci was held fixed at the value of Ci(v — 0) determined 0  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 B  obtained using the F T M W results (either in the combined fit or direct calculation)  0  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 P P M O D R study [173]. Poor calibration of the millimetre wave source was suggested as a possible source of this difference [173]. \t was also noted that the molecular constants reported in the P P M O D R study do not reproduce the  l  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  8.4.2  Spectroscopy of Yttrium Monohalides: YF and YBr  137  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 coupling 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 monobromide, Y B r and Y B r , should be equal to the ratios of certain molecular and nuclear 7 9  8 1  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, respectively. 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 uncertainty. 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 vibrational 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: eQq  v  =  eQq + eQq [v + e  (8.1)  x  where eQq is the equilibrium nuclear quadrupole coupling constant and eQqi is the e  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 8.5.1  Discussion E q u i l i b r i u m B o n d 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, B , and the vibration-rotation constants, ct and -y using Eq. (2.16) e  e  e  which is repeated here for convenience,  V  This expression was employed in three calculations to estimate the equilibrium rotational constant and the equilibrium bond distance of Y B r . For the first calculation, Eq. (2.16)  Chapter 8. FTMW  Spectroscopy of Yttrium Monohalides: YF and YBr  was truncated following the a  e  term. B and a e  e  139  were calculated directly from B and 0  Bi and r was calculated from B using atomic masses and fundamental constants from e  e  Ref. 120. The values of B , a and r obtained are listed in Table 8.8 under the heading e  e  e  Method I. The difference in r values obtained for the two isotopomers is within the cale  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 was estie  mated as 10~ • a 3  e  by comparisons with K B r [185] and RbBr [186]. B was determined e  by including the estimated 7 value in the calculation and thus a second value of r was e  e  obtained. These results are listed in Table 8.8 under the heading Method II. The calculated uncertainty in r is derived only from the uncertainties in the rotational constants, e  fundamental constants and masses used in the calculation. The difference between the r  e  value determined by this method and that calculated by Method I is of the order of  10" A. 6  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 Y B r . B and ct were calculated just as they were in Method II and e  e  then r was determined using a reduced mass calculated using ion masses instead of e  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~ A, which is on the order of the estimated uncertainty of r . This small change 6  e  was not unexpected, since the masses of Y and Br are much greater than the mass of  Chapter 8. FTMW  an electron.  Spectroscopy of Yttrium Monohalides: YF and YBr  140  A reasonable upper limit for the deviation of r from that in the Borne  Oppenheimer approximation is ~ IO" A, as was found for MgBr and AlBr in Sec. 6.5.1. 5  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 V i b r a t i o n Frequency  The vibration frequency, uj , and the anharmonicity constant, tv x , of Y B r can be estie  e  e  mated using the relations developed by Kratzer [187] and Pekeris [15], respectively, I4B  3  u,  u>e*.  =  ^  (8.2)  =  B<(fg + l )  (8.3)  2  where B and D are the equilibrium rotational and centrifugal distortion constants and e  e  a is the vibration-rotation constant. Though these expressions are exact only for a Morse e  potential function, they do provide a reasonable estimate of the desired constants. A n estimate of the uncertainty in the calculated values was obtained by determining oj and e  ux e  from Eqs. (8.2) and (8.3) for Y F and YC1 using the molecular constants in Refs. 169  e  and 176, respectively. The percentage differences between the experimentally determined oj and u> x values and those calculated using the Kratzer and Pekeris relations are e  e  e  ~ 0.5% and ~ 6%, respectively. The u> and u> x parameters were calculated for both e  e  e  Y B r and Y B r and are listed in Table 8.10. In the calculations, D was approximated 7 9  8 1  e  as D , since the centrifugal distortion constants are not sufficiently well determined to 0  calculate the vibrational dependence. B values from Method I and Method II (see Sec. e  Chapter 8. FTMW  141  Spectroscopy of Yttrium Monohalides: YF and YBr  8.5.1) produced identical u> and u> x values, within the number of significant figures e  e  e  given. Vibration frequency and anharmonicity constant values determined in the laserinduced 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 cu and u> x results from Fischell et e  e  e  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  eQe 4 io(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 i that Y B r c  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 B r and Y B r , and the first measure7 9  8 1  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' 0 0 1 1  J' 1 1 1 1  0 0 0  1 2 3  F' 3/2 1/2 3/2 1/2  v" 0 0 1 1  J" 0 0 0 0  0 0 0  0 1 2  F" 1/2 1/2 1/2 1/2  Observed Frequency"' " 17367.2044(-7) 17367.1450(-4) 17269.2718 17269.2128 7  17367.202 34734.210( 8) 52100.882(-2)  ° Results for hyperfine transitions are from present study. P P M O D R study [173].  Other data taken from  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. 6  Chapter 8. FTMW  Spectroscopy of Yttrium Monohalides: YF and YBr  144  Table 8.2: Measured transition frequencies of Y B r in v = 0 and v = 1 vibrational states. 7 9  J' 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 6 6  Transition F' J" 1 3/2 1 5/2 1 7/2 1 1/2 1 5/2 3/2 1 3/2 2 5/2 2 7/2 2 9/2 2 3/2 2 5/2 2 7/2 2 5/2 3 7/2 3 9/2 3 11/2 3 5/2 3 7/2 3 9/2 3 11/2 4 13/2 4 7/2 4 9/2 4 13/2 5 15/2 5  p" 3/2 3/2 5/2 1/2 5/2 1/2 3/2 5/2 5/2 7/2 1/2 3/2 7/2 5/2 7/2 7/2 9/2 3/2 5/2 9/2 9/2 11/2 5/2 7/2 11/2 13/2  v =0 /MHz 7512.3489 7514.6779 7514.6873 7514.9342 7517.8909 7518.1816 11269.7894 11270.7146 11272.2519 11272.2621 11273.0349 11273.0451 11275.4572 15026.8330 15028.5591 15029.7309 15029.7399 15030.0878 15030.0983 15032.9269 18787.1446 18787.1537 18787.3489 18787.3589 22544.4988 22544.5062  Obs. - calc. /kHz 0.9 -0.3 0.3 0.2 -0.0 0.0 0.4 0.2 -0.9 0.7 -1.7 0.5 0.4 -0.5 -0.0 -0.2 0.2 -1.3 0.8 0.5 -0.3 0.2 -0.6 0.9 0.6 -0.6  v = 1 /MHz 7488.7459 7491.3247 7491.3357  Obs. - calc. /kHz 0.4 -1.2 0.9  11235.5503 11237.2520 11237.2619 11238.1228 11238.1317  -0.1 -0.7 0.4 0.0 0.9  14983.0760 14983.0846 14983.4736 14983.4836  -0.2 -0.4 -0.8 0.6  18728.8319 18728.8420 18729.0613 18729.0696  -0.7 0.6 0.4 0.0  Chapter 8. FTMW  Spectroscopy of Yttrium  Monohalides:  145  YF and YBr  Table 8.3: Measured transition frequencies of Y B r in v = 0 and v = 1 vibrational states. 8 1  J' 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 6 6  Transition J" F' 1 3/2 1 5/2 1 7/2 1 1/2 5/2 1 3/2 1 3/2 2 5/2 2 7/2 2 9/2 2 3/2 2 5/2 2 7/2 2 5/2 3 7/2 3 9/2 3 11/2 3 5/2 3 7/2 3 9/2 3 11/2 4 13/2 4 4 7/2 9/2 4 13/2 5 15/2 5  F" 3/2 3/2 5/2 1/2 5/2 1/2 3/2 5/2 5/2 7/2 1/2 3/2 7/2 5/2 7/2 7/2 9/2 3/2 5/2 9/2 9/2 11/2 5/2 7/2 11/2 13/2  v =0 /MHz 7414.5535 7416.5039 7416.5134 7416.7116 7419.1812 7419.4271 11122.8849 11123.6571 11124.9487 11124.9581 11125.5978 11125.6091 11127.6178 14830.8801 14832.3215 14833.3086 14833.3188 14833.6036 14833.6135 14835.9692 18541.6102 18541.6201 18541.7764 18541.7873 22249.8551 22249.8626  Obs. - calc. /kHz 0.5 -0.1 0.1 -0.9 -0.5 -0.3 0.5 0.1 -0.1 0.1 -1.5 1.1 0.6 -0.5 0.1 -0.6 0.4 -0.5 0.3 0.8 -0.2 0.5 -0.9 0.9 0.7 -1.0  v =1 /MHz 7391.4534 7393.6124 7393.6220  Obs. - calc. /kHz -0.2 -0.4 -0.2  11089.2082 11090.6353 11090.6452 11091.3577 11091.3679  0.5 -0.3 0.3 -0.5 1.0  14787.5673 14787.5776 14787.8963 14787.9060  -0.7 0.4 -0.4 0.3  18484.4390 18484.4477 18484.6248 18484.6356  0.2 -0.3 -0.8 0.9  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  d(v = 0) Ci{v = 1) a  b  Value" 17367.1846(13) 17269.2521(13) 0.0396(9) 0.0393(9)  Error estimated from measurement uncertainty in parentheses. u is the hypothetical unsplit J = 1 — 0 frequency of the vth vibrational state. v  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 Bo Do Ci  Combined Fit Direct Calc. ' 8683.60734(67) 8683.60658(41) [0.007521] 0.006996(39) 0.03983(94) 0.0396(9) 0  6  c  P P M O D R Rent ' 8683.6045(11) 0.007086(72) [0.0396] c  d  PPMODR Lit. 8683.6156(11) 0.007521(74)  c e  ° B determined from hypothetical unsplit frequency u using Do from P P M O D R study [173]. Error estimated from measurement uncertainty in parentheses. One standard deviation in parentheses, in units of the least significant digit. 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. Taken from P P M O D R study of Fletcher et al. [173]. 0  6  c  d  e  Q  Chapter 8. FTMW  148  Spectroscopy of Yttrium Monohalides: YF and YBr  Table 8.6: Molecular constants calculated for Y B r in MHz°.  Y<"9  Parameter v = 0  B D eQqiBr) C/(Br)  1878.741007(71) 0.0004033(15) •12.9352(16) 0.00858(12)  y81  Br v =1  Br v = 1  V = 0  1872.910362(97) 1854.185861(71) 0.0003923(15) 0.0004004(25). 10.8017(16) 14.3349(45) 0.00918(12) 0.00877(20)  1848.469305(97) 0.0003923(25) 11.9683(45) 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 Y B r .  eQq( Br)/eQq( Br)  v=0 1.1975(2)  v=l 1.1977(6)  C7( Br)/C/( Br)  0.935(18)  0.952(30)  79  79  81  81  Eq.° 1.1974(4) -  Lit. 1.19707(3)  6  0.939995(2)  c  For method of calculation, see text Sec. 8.4.2. Ratio of electric quadrupole moments of B r and B r , taken from Ref. 2. Ratio of nuclear magnetic moments of B r and Br multiplied by inverse ratio of reduced masses of Y B r and Y B r , calculated using values in Ref. 120. a  b  7 9  c  7 9  7 9  8 1  8 1  8 1  Chapter 8. FTMW  Spectroscopy of Yttrium Monohalides: YF and YBr  150  Table 8.8: Equilibrium parameters calculated for Y B r ' . a  Method I fi /MHz a /MHz e  e  r /A e  Method II 5 /MHz a /MHz rjk e  e  Method III B /MHz a /MHz e  e  r /A e  Y Br  Y Br 1881.65633(9) 5.83065(12) 2.534613(1)  1857.04414(9) 5.71656(12) 2.534612(1)  Y Br  Y Br  1881.64906(9) 5.81901(12) 2.534618(1)  1857.03701(9) 5.70515(12) 2.534617(1)  Y Br  Y Br  7 9  7 9  7 9  1881.64906(9) 5.81901(12) 2.534617(1)  6  8 1  8 1  8 1  1857.03701(9) 5.0515(12) 2.534616(1)  For methods of calculation, see Sec. 8.5.1. Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. a  b  Chapter 8. FTMW  151  Spectroscopy of Yttrium Monohalides: YF and YBr  Table 8.9: Summary of equilibrium bond length estimates for YBr". Method I r /A e  6  Method II  6  2.534613(1) 2.534618(1)  Method III  6  Ave.  c  Lit. Theo.  2.534617(1) 2.53462  2.605°  Lit. LIF 2.800  e  For description of methods see Sec. 8.5.1. Estimated uncertainties in parentheses, in units of least significant digit, derived from rotational constants, fundamental constants and reduced masses. Average of values obtained by three methods. The deviation of r from that obtained in the Born-Oppenheimer approximation is estimated to be on the order of 1 0 A. r from Ref. 157. a  6  c  e  -5  d  e  e  Value of r used in laser fluorescence study [175]. e  Chapter 8. FTMW  152  Spectroscopy of Yttrium Monohalides: YF and YBr  Table 8.10: Estimate of vibration frequency of Y B r . Y Br 'C) 7 9  c^e/cmu) x /cm~ 1  l  e  e  a  271.1 0.66  Y Br 8 1  269.5 0.65  a , b  Lit. Expt. 268(2) 0.8(2)  c  Lit Theo.  a  259  For description of calculations see Sec. 8.5.2. Uncertainties in u> and u x are estimated to be ~ 0.5% and ~ 6%, respectively. Results taken from Ref. 175. Features due to each of the isotopomers of Y B r could not be resolved. Taken from Ref. 157. a  6  e  c  d  e  e  Chapter 8. FTMW  Spectroscopy of Yttrium Monohalides: YF and YBr  153  Table 8.11: Calculated ionic character of Y B r and related alkali metal bromides. 7 9  Y Br 12.935 98.3 7 9  e<2<?( Br)/MHz 79  ij% a  b  c  Results taken from Ref. 124. Results taken from Ref. 125. Results taken from Ref. 188.  Na Br 58.60801 92.5 2 3  7 9  a  K Br 10.2383 98.7 3 9  7 9  b  Rb Br 3.50 99.5 8 5  7 9  c  Bibliography  [1] C . H . Townes and A . L. Schawlow, Microwave New York, 1975).  Spectroscopy (Dover Publications,  [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  155  Bibliography  [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] C h . 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 . X u , 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, Oxford, 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 International 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), paper RB01. [142] C . Barrientos and A. Largo, J . Mol. Struct. ( T H E O C H E M ) 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 Colloquium 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 Temperature 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. Constants 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