"Science, Faculty of"@en . "Chemistry, Department of"@en . "DSpace"@en . "UBCV"@en . "Lin, Wei"@en . "2009-06-16T23:49:44Z"@en . "1999"@en . "Master of Science - MSc"@en . "University of British Columbia"@en . "The microwave spectra of three scandium monohalides, ScF, ScCl and ScBr, have been\r\nmeasured and analysed for the first time, using Fourier Transform Microwave (FTMW)\r\nspectroscopy. The samples were studied while entrained in pulsed jets of argon. They were\r\nprepared by the reaction of a precursor gas (SF\u00E2\u0082\u0086, Cl\u00E2\u0082\u0082 , Br\u00E2\u0082\u0082 ) in the argon with scandium plasma\r\nproduced by laser ablation from a scandium rod.\r\nScandium Monofluoride, ScF The J= 1-0 transition of ScF in the ground state was\r\nmeasured. The nuclear quadrupole coupling constant of Sc, the spin-rotation coupling\r\nconstants of both Sc and F, and the nuclear spin-nuclear spin constant were determined for\r\nthe first time. The hyperfine parameters have been interpreted to explain the bonding of ScF.\r\nScandium Monochloride, ScCl The J= 1-0 and J= 2-1 transitions of two isotopomers\r\nof ScCl have been measured in the ground vibrational state, along with the same transitions\r\nfor Sc\u00C2\u00B3\u00E2\u0081\u00B5Cl in the first excited vibrational state. Rotational constants, centrifugal distortion\r\nconstants, nuclear quadrupole coupling constants and nuclear spin-rotation coupling\r\nconstants for both nuclei, and nuclear spin-spin coupling constants have been determined. A\r\nnew equilibrium bond length r[sub e] has been evaluated, along with the infrared vibration\r\nfrequency. The dissociation energy, D[sub e], has also been estimated.\r\nScandium Monobromide, ScBr The J= 1-0, 2-1 and 3-2 transitions of \u00E2\u0081\u00B4\u00E2\u0081\u00B5Sc\u00E2\u0081\u00B7\u00E2\u0081\u00B9Br and\r\n\u00E2\u0081\u00B4\u00E2\u0081\u00B5Sc\u00E2\u0081\u00B8\u00C2\u00B9Br have been measured in the ground vibrational states, along with the latter two\r\ntransitions in the first excited vibrational states. This is the first high resolution spectroscopy\r\n\r\nof any kind carried out for this molecule. Precise rotational constants and centrifugal\r\ndistortion constants have been measured along with Sc and Br nuclear quadrupole coupling\r\nconstants, spin-rotation constants and a Sc-Br spin-spin constant. An equilibrium bond\r\nlength r[sub e] has been evaluated, along with the infrared vibration frequency. The dissociation\r\nenergy, D[sub e], has also been estimated.\r\nA plausible rationale for the nuclear quadrupole coupling constants has been produced\r\nusing the Townes-Dailey theory. The molecules are highly ionic, with ionic characters\r\ngreater than 94% . Reasonable absolute \u00E2\u0081\u00B4\u00E2\u0081\u00B5Sc quadrupole coupling constants and variations\r\nbetween molecules have been calculated using estimated constant values for eQq[sub n10] along\r\nwith orbital populations based on ab initio values for ScO. These results have been found to\r\nbe inconsistent with those based on populations from direct Hartree-Fock calculations for\r\nScO, ScF and ScCl. However, since the calculation itself produced reasonable coupling\r\nconstants, use of the Townes-Dailey theory for the Sc halides is questioned.\r\nMagnetic shieldings for all nuclei have been calculated from the spin-rotation constants.\r\nThe nuclear spin-nuclear spin coupling constants are consistent with a direct magnetic\r\ndipole-dipole interaction between nuclei."@en . "https://circle.library.ubc.ca/rest/handle/2429/9345?expand=metadata"@en . "2997756 bytes"@en . "application/pdf"@en . "FOURIER T R A N S F O R M M I C R O W A V E S P E C T R O S C O P Y O F SCANDIUM MONOHALDDES B y Wei L i n B.Sc (Chemistry) Xiamen University A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U E S T M E N T S F O R T H E D E G R E E O F M A S T E R OF S C I E N C E I N T H E F A C U L T Y OF G R A D U A T E S T U D I E S C H E M I S T R Y We accept this thesis as confirming to the required standard T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A 1999 \u00C2\u00A9 W e i L i n , 1999 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. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract The microwave spectra o f three scandium monohalides, ScF, ScC l and ScBr , have been measured and analysed for the first t ime, using Fourier Transform M ic rowave ( F T M W ) spectroscopy. The samples were studied while entrained in pulsed jets of argon. They were prepared by the reaction o f a precursor gas (SF 6 , C l 2 , Br 2 ) in the argon with scandium plasma produced by laser ablation from a scandium rod. Scandium Monofluoride, ScF The J= 1-0 transition o f ScF in the ground state was measured. The nuclear quadrupole coupl ing constant o f Sc, the spin-rotation coupl ing constants of both Sc and F, and the nuclear spin-nuclear spin constant were determined for the first time. The hyperfine parameters have been interpreted to explain the bonding o f ScF. Scandium Monochloride, ScCl The J= 1-0 and J= 2-1 transitions of two isotopomers o f S c C l have been measured in the ground vibrational state, along with the same transitions for S c 3 5 C l in the first excited vibrational state. Rotational constants, centrifugal distortion constants, nuclear quadrupole coupl ing constants and nuclear spin-rotat ion coup l ing constants for both nuclei, and nuclear spin-spin coupling constants have been determined. A new equ i l ib r ium bond length re has been evaluated, along wi th the infrared v ibra t ion frequency. The dissociation energy, Z)e, has also been estimated. Scandium Monobromide, ScBr The J= 1-0, 2-1 and 3-2 transitions o f 4 5 S c 7 9 B r and 4 5 S c 8 1 B r have been measured in the ground vibrational states, along wi th the latter two transitions in the first excited vibrational states. This is the first high resolution spectroscopy ii of any k ind carried out for this molecule. Precise rotational constants and centrifugal distortion constants have been measured along with Sc and B r nuclear quadrupole coupling constants, spin-rotation constants and a Sc-Br spin-spin constant. A n equi l ibr ium bond length re has been evaluated, along with the infrared vibration frequency. The dissociation energy, De, has also been estimated. A plausible rationale for the nuclear quadrupole coupling constants has been produced using the Townes-Dai ley theory. The molecules are highly ionic, wi th ionic characters greater than 9 4 % . Reasonable absolute 4 5 S c quadrupole coupling constants and variations between molecules have been calculated using estimated constant values for eQqDl0 along with orbital populations based on ab initio values for ScO. These results have been found to be inconsistent with those based on populations from direct Hartree-Fock calculations for ScO, ScF and S c C l . However, since the calculation itself produced reasonable coupling constants, use o f the Townes-Dailey theory for the Sc halides is questioned. Magnetic shieldings for all nuclei have been calculated from the spin-rotation constants. The nuclear spin-nuclear spin coupling constants are consistent wi th a direct magnetic dipole-dipole interaction between nuclei. in Table of Contents Abstract j \ List of Tables yj List of Figures y- j \u00E2\u0080\u00A2 Acknowledgement 1 Introduction 1 2 Theory 7 2.1 Rotational Spectroscopy 7 2.1.1 Born-Openheimor Approximation 7 2.1.2 Rigid Rotor and Centrifugal Distortion Approximation 9 2.1.3 The Equilibrium State 10 2.2 Nuclear Hyperfine Structure 12 2.2.1 The Coupling Schemes 12 2.2.2 Nuclear Quadrupole Coupling 14 2.2.3 Nuclear Spin-Rotation Coupling 16 2.2.4 Nuclear Spin-Nuclear Spin Coupling 19 3 Experimental Methods 21 3.1 Introduction 21 3.2 Theory 22 3.3 Instrumentation 23 4 Microwave Spectra and Geometries of Scandium Monohalides 28 iv 4.1 Pure Rotational Spectrum of Scandium Monofluoride 29 4.1.1 Introduction 29 4.1.2 Experimental Details 30 4.1.3 Observed Spectrum and Analysis 30 4.2 The Pure Rotational Spectrum of Scandium Monochloride 32 4.2.1 Introduction 32 4.2.2 Experimental Details 33 4.2.3 Observed Spectra and Analysis 33 4.2.4 The Equilibrium State and Vibration Frequency of Sc 3 S Cl 35 4.3 The Pure Rotational Spectrum of Scandium Monobromide 38 4.3.1 Introduction 38 4.3.2 Experimental Details 38 4.3.3 Observed Spectra and Analysis 38 5 Discussion and Conclusion 65 5.1 Nuclear Quadrupole Coupling Constants 65 5.2 Nuclear Spin-Rotation Coupling Constants and Nuclear Spin-Nuclear Spin Constants 70 5.3 Conclusions 71 V List of Tables 4.1 Measured hypeffine components of ScF 45 4.2 Molecular constants calculated for ScF in M H z 46 4.3 Measured hyperfine components of ScCl 47 4.4 Molecular constants calculated for ScCl in M H z 49 4.5 Comparison o f hyperfine constants for ScCl 50 4.6 Measured hyperfine components of the first excited vibrational state o f S c 3 5 C l 51 4.7 Molecular constants calculated for the first excited state o f S c 3 5 C l in M H z 52 4.8 Equilibrium parameters and vibration frequency calculated for S c 3 5 C l 53 4.9 Measured hyperfine components of Sc 7 9 Br 54 4.10 Measured hyperfine components of Sc 8 1 Br 56 4.11 Molecular constants calculated for ScBr in M H z 58 4.12 Comparison o f hyperfine constants for ScBr 59 4.13 Equilibrium parameters and vibration frequency calculated for ScBr 60 4.14 Comparison o f bond lengths in ground state and equilibrium state 61 5.1 Comparison o f / c for S c 3 5 C l and some other species 75 5.2 Comparison o f / c for Sc 7 9 Br and some other species 76 5.3 Comparison o f 4 5 Sc quadrupole coupling constants (MHz) in various Sc compounds... .77 5.4 Orbital populations for Sc in ScO 78 5.5 Comparison o f the calculated and experimental eQq0(Sc) m MHz 79 5.6 Nuclear and electronic contributions to the experimental spin-rotation constants and Vi corresponding paramagnetic shieldings in S c X 80 5:7 The magnetic shieldings of the nuclei in S c X 81 5.8 Comparison o f ScF, S c 3 5 C l and Sc 7 9 Br 82 5.9 Comparison o f hyperfine parameters of Y X and S c X 83 Vii Lis t of Figures 3.1 Schematic diagram o f microwave cavity 27 4.1 Composite spectra of the J= 1-0 rotational transitions of ScF and S c 3 5 C l 42 4.2 The Fx= 9/2-7/2, J= 1-0 transitions of S c 3 5 C l 43 4.3 Composite spectra of the J= 2-1 rotational transitions of Sc 8 1 Br 44 5.1 Schematic diagram o f the valence molecular orbital energy levels for ScCl 74 < Vii) Acknowledgement F i r s t I w o u l d l ike to express my gratefulness to my supervisor , M i k e Ge r ry , who continuously encourages me and gives me valuable guidance. I feel that I am very fortunate to work with such an experienced and nice supervisor. It has been a happy time working in an environment in which I always feel that I can learn something. So I would l ike to thank all o f my colleagues for their assistance: D r . Sara Beaton, for teaching me how to use the spectrometer; Dr . Corey Evans, for his theoretical calculations and many comments; Dr. Kaley Walker, for her great help; I would also like to thank M r . Daryl Rubinoff, Mr . Kenneth Suh, Ms . Lana Norman. I would l ike to thank my family. Without all their support and understanding, I would not possibly get anything done. iX Chapter 1 Introduction 1 Chapter 1 Introduction Microwave spectroscopy covers loosely spectroscopy carried out in the frequency range 1-1000 G H z . The bulk o f microwave studies in the literature is restricted to the region 4-40 G H z because this is where sources and cel ls are easiest and cheapest to b u i l d and transmission lines easiest to obtain. The spectra observed are almost always pure rotational spectra of gaseous molecules. The basic information obtained is rotational constants, used to evaluate molecular geometries. However, microwave spectroscopy is a high resolution technique with line widths (full width at half maximum) typically less than 10 k H z at 10 G H z , and line frequencies can be very accurately measured. Consequently many small effects not observable using other spectroscopic techniques can be studied. One o f these is centrifugal distortion, which is related to molecular flexibility and ultimately to the vibrational spectrum. Often there is an interaction between the nuclear spins and the rotation o f the molecule, which causes the rotational lines to be split into several components, to produce the so-called hyperfine patterns. O f several mechanisms producing hyperfine patterns, the most common one observed is nuclear quadrupole coupling, caused when a quadrupolar nucleus (I>l/2) is in a non-zero electric field gradient. Since this gradient arises mostly from the electrons, it gives detailed information about the electronic structure of the molecule. Chapter 1 Introduction 2 Great technical improvements in the past thirty years have improved mic rowave spectroscopy both in its range o f measurements and in its sensi t ivi ty and frequency resolution [1-3]. Ba l l e and Flygare developed Fourier transform microwave ( F T M W ) spectroscopy in 1981 [1] as a sensitive technique for the study o f rotational transitions o f weakly bound molecular dimers. Since then many other kinds o f molecules have also been studied [4-7] using this technique, one of them being transition-metal-containing diatomic molecules. The interest in such molecules arises mostly in efforts to understand their bonding. Scandium (Sc) is the first o f the transition metals and therefore has the fewest electrons. In the ground state o f the Sc atom there is only one d electron. A s a result, the scandium monohalides may be considered ideal systems to interpret the nature o f transition metal chemistry and in particular to understand the role of d electrons in chemical bonding[8]. In this thesis, pure rotational spectra of three scandium monohalides, ScF, ScCl and ScBr in their ground ( X ' S ) electronic states, are presented for the first time. For ScF and S c C l there have been several studies o f their electronic spectra [9-14], from wh ich accurate rotational constants have been evaluated for several vibrational states, and the equilibrium bond lengths determined. For ScBr there is very little spectroscopic data in the literature [15], and none at all at high resolution. The present work was prompted by studies o f the spectra o f y t t r ium halides in this laboratory [16-18]. The nuclear quadrupole hyperfine constants o f the halogens in YC1 [16] and Y B r [17] (and, after the present work was started, in Y I as well [18]) indicated very high ionic characters, nearly 100%, for the bonds, in contrast to their relatively small dipole Chapter I Introduction 3 moments [19]. This small dipole moment is beleived to be caused by a lone pair o f electrons in an sp hybrid orbital on Y , pointed away from the halogen, which partially cancels the effect o f the halogen [20]. Comparable quadrupole coupling information on Y would be useful to verify this. Unfortunately, the nuclear spin o f Y is 1/2, so this information is unavailable. Such a restriction does not apply to scandium, since the nuclear spin o f 4 5 S c (100% abundant) is 7/2. The electronic structures of both nuclei in the scandium monohalides can therefore be probed. It was anticipated that the electronic structure o f Sc would also apply, at least approximately, to Y , and that comparisons of the electronic structures o f the scandium and yttrium halides could be made. The primary purpose o f the present work was to measure and interpret the hyperfine structures in the spectra o f scandium halides. This was not observed in the published electronic spectra, even at high resolution. For ScF and S c C l it was not expected that new in fo rma t ion on the geometries cou ld be obtained. F o r S c C l , however , s ign i f i can t disagreement was found between the published rotational constants and those from the present study, so the geometry has been redetermined. For ScBr, where there had been no previous high resolution study, the bond length has been measured for the first time. This thesis is organized in the fo l lowing manner. Chapter two contains theory and background information important to the analysis o f the microwave spectra o f diatomic molecules. The experiments were carried out using a cavity pulsed jet Fourier transform microwave Chapter I Introduction 4 ( F T M W ) spectometer [21]. Chapter three contains information on the theory o f F T M W spectroscopy, and on the instrumentation used to generate and collect spectra. The samples were prepared by ablating scandium metal with a pulsed N d : Y A G laser and treating it with a second precursor gas contained as a small percentage in argon. To obtain their spectra the samples were entrained in pulsed supersonic jets o f the noble gas, in near collision-free conditions, which stablize the molecules. The apparatus for doing this is also described in chapter three. Chapter four contains a description o f the spectra, and the analysis, o f each o f the three molecules studied. For each molecule there is a detailed introduction giving background information, a description o f the particular experimental conditions for that species, and an account o f the measured spectra and their analysis. The derived spectroscopic constants are given, and compared wi th earlier values. The rotational constants were used to derive information about the geometries, and vibration information from the centrifugal distortion constants is also discussed. Chapter five focuses on the interpretation of the hyperfine constants. Information on the electronic structures and bonding is obtained from nuclear quadrupole coupling constants. Interpretation o f two other types of hyperfine constants from the spectra were also given; magnetic shieldings are obtained from nuclear spin-rotation constants, and nuclear spin-spin constants are correlated with the derived geometry. Comparisons are made between the S c X and related molecules. To aid the reader, the tables o f data and results and figures are collected at the end o f each chapter. The references are also separated into every chapter. Chapter I Introduction 5 Bibliography [I] T. J. Bal leand W. H . Flygare, Rev. Sci. Instrum. 52, 33, 1981. [2] T. J. Balle, E . J. Campbell, M . R. Keenan, and W . H . Flygare, J. Chem. Phys. 71, 2723, 1979. [3] H . Dreizler, Mol. Phys. 59, 1, 1986. [4] C. H . Townes, and A . L . Schawlow, Microwave Spectroscopy, Dover Publications, N e w York, 1975. [5] W . Gordy, and R. L . Cook, Microwave Molecular Spectra, John Wi ley & Sons, N e w York, 1984. [6] M . C . L . Gerry , Some things we can do with a cavity pulsed microwave Fourier transform spectroscopy. 9 t h international conference of Fourier transform spectroscopy; Calgary, Aug. , 1993. [7] J . M . H o l l a s , High Resolution Spectroscopy, 2 n d edi t ion, John W i l e y & Sons, Chichester, 1998. [8] S. R. LanghoffandC. W. Bauschlicher, Jr. Annu. Rev. Phys. Chem. 39, 181, 1988. [9] E . A . Shenyavskaya, A . A . Mal'tsev, D . I. Katsev, and L . V . Gurvich, Opt. Spektrosk. 26, 937, 1969. [10] F. Taher, C. Effantin, A . Bernard, J. d'Incan, E . A . Shenyavskaya, and J. Verges, J. Mol. Spectrosc. 179, 223, 1996. [II] F. Taher, A . Bernard, C. Effantin, J. d'Incan, E . A . Shenyavskaya, and J. Verges, J. Mol. Spectrosc. 179, 229, 1996. [12] F. Taher, C. Effantin, A . Bernard, J. d'Incan, E . A . Shenyavskaya, and J. Verges, J. Mol. Spectrosc. 184, 88, 1997. [13] M . - A . Lebeault-Dorget, C. Effantin, A . Bernard, J. d'Incan, J. Chevaleyre, and E . A . Shenyavskaya, J. Mol. Spectrosc. 163, 276, 1994. [14] E . A . Shenyavskaya, J. Verges, A . Topouzkhanian, M . - A . Lebeault-Dorget, J. d'Incan, C. Effantin, and A . Bernard, J. Mol. Spectrosc. 164, 129, 1994. Chapter 1 Introduction [15] D . R. Fischell, H . C. Brayman, and T. A . Cool, J. Chem. Phys. 73, 4260, 1980. [16] K . D . Hensel and M . C. L . Gerry, J. Mol. Spectrosc. 166, 304, 1994. [17] K . A . Walker and M . C. L . Gerry, J. Chem. Phys. 109, 5439, 1998. [18] L . Norman, B . Sc. Thesis, University of British Columbia, 1999. [19] S. R. Langhoff, C. W. Bauschlicher Jr., and H . Partridge, J. Chem. Phys. 89, 396, 1988 [20] B . Simard, A . M . James, and P. A . Hackett, J. Chem. Phys. 96, 2565, 1992. [21] Y . X u , W. Jager, and M . C. L . Gerry, J. Mol. Spectrosc. 151, 206, 1992. Chapter 2 Theory 1 Chapter 2 Theory 2.1 Rotational spectroscopy A complete description of the theory of pure rotational spectroscopy is beyond the scope o f this thesis. For a detailed discussion, please refer to references [1, 2]. This chapter w i l l provide only some background in rotational spectroscopy and hyperfine structures o f diatomic molecules needed in the present work. A l l three molecules studied in this thesis have ' Z + ground electronic states. The Hamiltonian for these systems is H = H r o t + H d l s t o r t + H h y p e r f i n e (2.1) where H r o t , H d i s l o r l and H h y p e r f i n e are the rotational, centrifugal distortion and hyperfine Hamiltonians, respectively. Each o f these contributions is discussed separately. 2.1.1 Born-Oppenheimer Approximation The Hami l ton ian for a diatomic molecule is the sum o f the kinet ic energy T and the potential energy V. In a molecule the kinetic energy T consists o f contributions T e and T n from the motions o f the electrons and nuclei respectively. The potential energy is composed o f three terms. V e e and V n n describe the Coulombic repulsions between the electrons and between the nuclei, respectively, and V e n is the attractive potential between the electrons and nuclei. The Hamiltonian H in this case is Chapter 2 Theory 8 H = T + T + V + V + V (2 2) \" Me * n T ee ' nn * en V*\" \u00E2\u0080\u00A2 ) For fixed nuclei T n = 0 and V m is constant, so that for different molecular geometries there is a series o f electronic wave functions ^ e which satisfy H e Y e =EeVe (2.3) where H e = T e + V e e + V e n (2.4) In the Born-Oppenheimer approximation, proposed in 1927 [3], it is assumed that vibrating nuclei move so slowly compared to the electrons that the electrons adjust instantaneously to any nuclear motion. x \u00C2\u00A5 e and Ee involve the nuclear coordinates as parameters only. Ee can be treated as part o f the potential field in which the nuclei move. The total wave function *F is given by \u00C2\u00A5 = \u00C2\u00A5 e (q ,Q)Y n (Q) (2.5) where q is the coordinate of the electron and *Fe is a function o f the nuclear coordinate Q as well as q. The practical result is that the total energy E is given by E = Ee + En (2.6) and En = Ev + Et (2.7) so that , P = T e ^ v x P r (2.8) where Ev and ET are the vibrational and rotational energies, and x \u00C2\u00A5 v and x \u00C2\u00A5 r are the electronic, vibrational and rotational wave functions, respectively. I f any atom has nuclear Chapter 2 Theory 9 spin then this part of the total wave function can be factorized into *F, and its energy added to E. It is for these reasons that as a first approximation we can treat electronic, vibrational, rotational, and N M R spectroscopy separately. 2.1.2 Rigid Rotor and Centrifugal Distortion Approximation Most stable diatomic molecules have a ' I ground electronic state with no unbalanced electronic angular momentum. Their rotational spectra are quite simple. The r igid rotor approximation provides a straightforward understanding o f the gross rotational spectra o f diatomic molecules. The Hamiltonian for a rigid rotor can be expressed as H, o l = 5 A 2 + \u00C2\u00A5 y 2 + ^ 2 ( 2 9> where x, y, z are the principal inertial axes of the molecule and J x ( y j Z ) is the component o f the rotat ional angular momentum about each o f the p r inc ipa l axes. The rota t ional constant 5 x ( y , z ) (in frequency units) is related to the principal moments o f inertia 7 x ( y z ) by B*=irh->etc (210) For diatomic molecules the r-axis is taken to be along the molecular bond axis. There is no rotational angular momentum about this axis, and the moments o f inertia about the other two axes are equal, so that Ix = Iy= I. Therefore, the Hamiltonian can be expressed as H r o t = 5 f J x 2 + Jy2) = BJ2 (2.11) where BK = By = B. The rotational energy levels obtained from this equation are Em=BJ(J+\) (2.12) Chapter 2 Theory 10 where J = 0, 1, 2 .. . . The selection rule for rotational transitions is A / = \u00C2\u00B1 1 ; thus the transition (J+\)<\u00E2\u0080\u0094J occurs at v= 2B (J+l). The spectrum is a combination o f single lines, equally spaced, with a separation of IB. Real molecules are not rigid, and therefore the rigid rotor model for molecular rotation is only an approximation. The molecule w i l l be distorted i f the interatomic bond stretches as the molecule rotates. This centrifugal distortion increases with increasing rotational angular momentum. The Hamiltonian including this effect can be expressed as \u00E2\u0080\u00A2j \u00E2\u0080\u0094ii i I I -'-'-semirigid -'-'Tot \u00E2\u0080\u00A2'-'\u00E2\u0080\u00A2distort = BJ2-DJ4 (2.13) where D is the centrifugal distortion constant, and is ~\0AB. The rotational energy expression now becomes Evlb.wi-BJ(J+l)-DAJ+\y (2.14) with the same selection rules, AJ = \u00C2\u00B1 1. The rotational transition frequencies are modified slightly to v= 2B(J+l) - 4D(J+l)2. 2.1.3 The E q u i l i b r i u m State The internuclear bond length of a diatomic molecule can be obtained from the determined rotational constant B, which can be expressed as: B = ir4\u00E2\u0080\u0094T- ( 2 1 5 ) where the reduced mass ju is / / = /n,m/(m, + m2) (2.16) For a given vibrational state v the measured rotational constant is designated Bu. Thus the Chapter 2 Theory 11 measured rotational constants in the ground and first excited vibrational states are 5 0 a n d Bu respectively. The bond lengths obtained by direct application o f E q . 2.15 are the effective values o f r0 and r,. For diatomic molecules l ike the scandium halides, the vibrational dependence o f the rotational constant and centrifugal distortion constant can be expressed as where ae, y e , Be are vibration-rotation interaction constants, and Be and De are respectively the equilibrium rotational and centrifugal distortion constants. In particular, to obtain re, the hypothetical internuclear distance at the minimum of the vibrational potential, Be must first be evaluated by measuring rotational constants in several vibrational states, and applying E q . 2.17. This requires that several vibrational levels be populated in the conditions o f the experiment. The population of the v th vibrational level relative to the population N0 o f the zero-point level is given by 5 u = 5 e - a e ( u + ' / 2 ) + Y e ( u + ' / 2 ) 2 +. . . (2.17) and D\u00E2\u0080\u009E = De-fr(o+V2) + ... (2.18) = exp ^ -hv vib ( 2 . 1 9 ) kT J I f the vibra t ional energy hvVib is small enough, vibrat ional levels wi th v > 0 may be appreciably populated. The vibrational energies o f a diatomic molecule are given by Chapter 2 Theory 12 \u00C2\u00A3vib= hve(o +1/2) - hVgKe (v +1/2)2 (2.20) When the energies \u00C2\u00A3 v i b are expressed in cm' 1 , hve is usually replaced by a>e [4 ]. From the equi l ibr ium state rotational constant, we can also estimate the value o f the vibrat ional frequency, co& and the anharmonicity constant, a^ce, using the relations developed by Kratzer [5] and Pekeris [6] 4 W co e= ^ (2.21) r V \6Bl j (2.22) 2.2 Nuclear Hyperf ine Structure Nuclear hyperfine interactions occur via electrostatic and magnetic means. The observed hyperfine structure can be classified into three types \u00E2\u0080\u00A2^ hyperfine -^ quadrupole -Hspin-rotation ^^ spin-spin (2.23) where H q u a d r u p o l e describes the nuclear electric quadrupole interaction, and H s p i n . r o t a t i o n and H s p i n . s p i n describe the magnetic nuclear spin-rotation and nuclear spin-spin interactions respectively. 2.2.1 The Coupl ing Schemes To simplify the discussion up to now, only the total rotational angular momentum J has been used. N o w the coupling of electronic and rotational angular momenta w i l l be considered. A l l the molecules investigated in this work have ' I ground electronic states, for which there is no electron orbital angular momentum, so A = 0, and thus, N , the rotational angular Chapter 2 Theory 13 momentum including electron orbital angular momentum, is the same as R, the rotational angular momentum. For diamagnetic species, the electron spin angular momentum S = 0, and N = J. Thus, J is the total rotational angular momentum in this case. Interactions i nvo lv ing nuclear spin angular momenta, 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, F = I + J (2.24) When there are two coupled nuclei , the simplest coupl ing scheme occurs when the coupling by one nucleus is large compared with that of the other. The spin I, w i l l couple to J to form a resultant F, about which they both precess. ^ = 1 , + ! ; (2.25) then the second nuclear spin, I2, couples to F, to form F. F = I2 + F, (2.26) This is sometimes called the \"series\" scheme. It best describes the hyperfine interactions observed for ScF and ScCl in this thesis. The other scheme is applied when the coupling energies o f the two nuclei are equal or nearly so. It is called the \"parallel\" scheme. The two nuclear spins couple each other to form a resultant nuclear spin angular momentum, I, which then couple to J. I = I, + I2 (2.27) F = I + J (2.28) This \"parallel\" scheme best describes the hyperfine interactions observed for ScBr in this Chapter 2 Theory 14 thesis. 2.2.2 Nuclear Quadrupole Coupl ing The most important hyperfine interaction in the present work is that o f molecular electric field gradients with electric quadrupole moments o f the nuclei. This interaction is found when a nuclear quadrupole moment (due to a nonspherical distribution o f nuclear charge) interacts wi th an electric field gradient due to a non-spherical distribution o f the external charge(due mostly to electrons). I f either the nuclear charge or the external charge distribution is spherically symmetric, no such interaction is observed. Nuclei with spins o f 0 or Vi are spherically symmetric and hence have no quadrupole moments. It is for this reason a quadrupole coupl ing constant for , 9 F (I = 1/2) is not reported in this work . The observed nuclear quadrupole hyperfine structure can provide a measure o f the molecular electric field gradient from which information about molecular electronic structure and chemical bonds can be obtained. The Hamiltonian for the nuclear quadrupole coupling o f a single quadrupolar nucleus can be written as where V y = - V E y , V E is the gradient of the electric field o f the extra nuclear charges and Q is the quadrupole moment of the molecule. Hquadmpoie c a n be written in terms o f observable parameters called nuclear quadrupole coupling constants, eQq. For a diatomic molecule with a quadrupolar nucleus H q u a d r u p o , e is H , quadrupole = -1/6 Q : V E (2.29) Chapter 2 Theory 15 written to first order as eQq IJ) 2+-I J-I2J^ (2.30) quadrupole 27(27-l)/(2/-l) 2 and eQq is the only measurable nuclear quadrupole coupl ing constant. A l though this Hamiltonian is usually adequate to describe the gross features of the quadrupole coupling for a single nucleus, H q u a d r u p o l e has matrix elements off-diagonal in 7 by \u00C2\u00B11 and \u00C2\u00B12 [2]. A t the resolution and accuracy o f the experiments described in this thesis these off-diagonal terms though small must be considered. Full details of these matrix elements are given by Gordy and Cook[2]. The Hamiltonian when there are two quadrupolar nuclei, H q u a d r u p o l e is the sum o f the two terms o f the type in Eq . 2.29, one for each nucleus. The exact form o f the matrix elements depends on the coupling scheme being used (though both, in the end should produce the same eigenvalues) [2]. Each nucleus has a single quadrupole coupl ing constant. The program used to fit the data obtained in this work includes all these considerations [7]. N u c l e a r quadrupole coup l i ng constants can be used to invest igate the e lec t ronic structures o f molecules. For monohalides of the type discussed in this thesis, the bonding can be examined semi-quantitatively using the Townes-Dailey model [8], which relates the molecular nuclear quadrupole coupling constant o f a halogen to the quadrupole coupling constant of a single electron in a halogen wp-orbital (e(2t7nl0(atom)): here \u00C2\u00AB x , nT and nz are orbital populations in the npK, npy and npz orbitals, respectively. The z axis is taken to be the molecular axis, n, I, 0 are the principal, orbital angular momentum, and eQq (mol) = [nz - (nx + ny)/2] eQqnW(aXom) (2.31) Chapter 2 Theory 16 magnetic quantum numbers. Values of e(9<7nio(atom) are the nuclear quadrupole coupling constants for singly occupied atomic halogen np orbitals, which can be found in Ref. 2. For scandium monohalides, the valence shell configuration of halogens is n^np5, thus npx and npy orbitals w i l l be filled. The occupation of the npz orbital depends on its participation o f the corresponding molecular orbital. It must be remembered that Eq . 2.31 applies only to atoms where only /7-orbitals need to be considered (eg. halogens). In the single bonded diatomic molecules like the scandium halides, S c X , the a-bonding orbital can be represented by the linear combination Vc = aVx+bVSc (2.32) And the ionic character of the a bond may be represented by ic = \a2-b2\ (2.33) With normalization ofa2 + b2 = 1, assuming X is the negative pole of the molecule for which a^O.5, it is evident that ic = \2a2-l\ = 2a2-! (2.34) Putting nz = 2a2 into Eq . 2.3l,we get eQq (X) = (2a2 - 2 ) eQqn]0 (X) (2.35) Combining 2.34 and 2.35 gives h=^+eQq0(X)/eQqn]0(X) (2.36) The nuclear quadrupole coupling constants o f Sc in S c X can also be used to understand the orbital hybridisation on scandium. For Sc, the atomic orbitals x \u00C2\u00A5 S c wi l l be Chapter 2 Theory 17 Y S c = a s ^ s 4 - a p V F p + flrd^d (2.37) where a2\, a\, a2& are the fractional weights of the ^ - o r b i t a l , 4/?-orbital and 3; in effect, molecules rotate coherently at . The amplitude of P(t) is dependent on N w 0 , the init ial population difference, and pxl, the transition moment matrix element. It is at its maximum when xt p = (4izpl2e tp)/h = nil ( at the \"7c/2-condition\"). Observed signals w i l l thus be their strongest when the rotational temperature is minimized, and when the product june t p is opt imized. This means that when e, the microwave amplitude, is constant, molecules wi th a larger dipole moment w i l l require a shorter pulse length, and vice versa. A n interesting feature o f E q . 3.1 is that signal strength is proportional to p]2, instead o f its Chapter 3 Experimental Method 23 square as in conventional spectroscopy. This treatment neglects relaxation effects. In practice, the signal decays because the coherence is lost and because the populations return to those at thermal equilibrium. This can be treated phenomenologically by multiplying P(t) in equation 3.1 by an exponential term of the form e\"\u00C2\u00B0\". 3.3 Instrumentation The heart o f the spectrometer is a microwave cavity. It consists o f two spherical a l u m i n i u m mi r ro r s , 28 cm in diameter, 38.4 cm in radius o f curvature and p laced approximately 30 cm apart. One o f the mirrors is fixed; the other is movable so that the cavity can be tuned manually into resonance at the excitation frequency. The microwave excitation pulse is coupled to the cavity via an antenna located at the centre o f the movable mirror . The cavi ty mode is monitored by an osc i l loscope . The size o f the cavi ty is controlled by a micrometer screw to optimise the absorption o f radiation at the excitation frequency. The cavity must be tuned each time the excitation frequency is changed to get the maximum absorption energy. The bandwidth of the cavity is 1 M H z when operating at 10 G H z , thus restr ict ing searching steps to at most 1 M H z . The operating range o f the spectrometer is 4-26 G H z . A schematic diagram of the microwave cavity is given in F ig . 3.1. The microwave source is a Hewlett-Packard 8341A microwave synthesizer, wh ich is referenced to a 10 M H z frequency obtained from a Loran C frequency standard, which is accurate to 1 part in 10 1 2 . The 10 M H z signal is also used to control the t iming o f the experiment and do up- and down- frequency conversion. Once the cavity has been tuned to Chapter 3 Experimental Method 24 the excitation frequency v e x c i u t l 0 n to where v e x c i t a t i o n = v M W - 20 M H z , the synthesizer output frequency is locked at v ^ . This frequency is then mixed with 20 M H z in a single side-band modulator to produce v M W - 20 M H z . The microwave pulse is produced by opening and closing a switch. The pulse then goes through the circulator to the microwave cavity, where it interacts with the gas sample that has been introduced into the cavity. After the microwave pulse, the gas sample emits radiation at the frequencies of the transitions that are off-resonant from v e x c i t a t i o n by a small amount Av . The signal is detected by the antenna on the moving mirror and then coupled out o f the cavity via the circulator. A second switch is used to protect the microwave circuit from getting damaged by the excitation pulse. The signal is then amplified, down-converted to 20 M H z - Av, and then to 5 M H z + Av . This last signal is fed through a 5 M H z bandpass filter to eliminate other signals leaving the R F mixer. The 5 M H z + A v signal is collected by a transient recorder board in the personal computer. A total of 4 K data points during a scan are collected at intervals of 50 ns. The decay signal, obtained by subtracting the cavity-only signal from the cavity-plus-molecular signal, is stored in the computer. Signal averaging is accomplished by addition of successive time-domain signals. A frequency-domain spectrum F(v ) , with both real and imaginary components, is computed from the time-domain signal j\nA.t) using a discrete Fourier transform [4]: ^ ( v ) = l ' / ( \" A / ) e - ' w ' ( 3 .2 ) n= 0 where J%nAt) is the time domain signal consisting of n data points collected with Ar sampling Chapter 3 Experimental Method 25 interval. The spectra are usually displayed as power spectra, which are the sum o f the squared moduli o f the real and imaginary parts of F( v). The sample molecules were studied while entrained as <1% in pulsed supersonic jets o f noble gas. Since they are in an essentially collision-free environment, unstable and reactive molecules are stablized. The supersonic jet was introduced into the cavity using a General Valve Series 9 pulsed nozzle, operated at a backing pressure (noble gas pressure) o f a few atmospheres. The nozzle was mounted slightly off-centre in the fixed mirror, so that the axes o f the jet and o f microwave propagation were essentially para l le l . A s a result each microwave line was split into two components by the Doppler effect. The samples were prepared by vaporizing a Sc metal rod (Goodfellow, 92% scandium, 8% Tantalum) and reacting the metal vapour with a precursor gas present in the backing gas. The rod, 7 mm in diameter, was mounted in a specially designed nozzle cap, based on the design o f Barnes et al. [5,6], and can be translated and rotated inside the cap by a motorized actuator. The Sc rod was ablated using the second harmonic (532 nm) o f a N d : Y A G laser (Continuum Surelite I-10). The laser energy is directed into the chamber through a set o f mirrors. The beam is focused to a spot less than 1mm in diameter. The laser channel and the gas expansion channel are perpendicular to each other, thus the timing o f the laser pulse with respect to the nozzle opening is crucial to the experiment. The best delay between the nozzle being fully open and the laser pulse was found to be -375-425 ps. Because the scandium monohalides investigated in this work are unstable, they require the collision-free environment resulting from a supersonic expansion. The supersonic expansion Chapter 3 Experimental Method 26 converts the molecular rotational degrees of freedom to a directed mass flow, with the result that rotational temperatures are very low, estimated to be less than 3 K . V i b r a t i o n a l temperatures have been approximated to be around 200K. The cavity cell is mounted in a vacuum chamber, and pumped by a diffusion pump which is backed by a rotary pump. To enhance the supersonic cooling the chamber requires a low background pressure (~10 6 torr). This restriction, combined with the low efficiency o f the pumping system, limited the experimental repetition rate to about 1Hz. Observed line widths were -7-10 kHz, full width at half maximum. For unblended lines the transition frequencies were determined by averaging the line positions o f the Doppler components obtained from the power spectrum. For closely spaced or overlapped lines, the frequencies were obtained by fitting directly to the time domain signals [7] to eliminate the effects o f line shape distortion in the power spectra. The accuracy o f the experiment is estimated to be better than \u00C2\u00B11 kHz. Chapter 3 Experimental Method 27 Figure 3.1 Pu lse N o z z l e -with cap and r o d N d : Y A G Lase r (532nm) V a c u u m C h a m b e r I V a c u u m P u m p gure 3.1 Schematic diagram of microwave cavity showing location o f mirrors, nozzle, laser and antennae. Chapter 3 Experimental Method 28 Bibliography [1] T. J. Balle and W . H . Flygare, Rev. Sci. Instrum. 52, 33, 1981. [2] T. J. Balle, E . J. Campbell, M . R. Keenan and W. H . Flygare, J. Chem. Phys. 71, 2723, 1979. [3] H . Dreizler, Mol. Phys. 59, 1, 1986. [4] R. N . Bracewell, The Fourier Transform and Its Applications, 2 n d edition, M c G r a w - H i l l , N e w York, 1986. [5] M . Barnes, M . M . Fraser, P. G. Hajigeorgiou, A . J. Merer and S. D . Rosner, J. Mol. Spectrosc 170, 449, 1995. [6] K . A . Walker, doctoral thesis, Univ. of British Columbia, 1998. [7] J. Haekel and H . Mader, Z Naturforsch. Teil A 43, 203, 1988. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 29 Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 4.1 Pure Rotational Spectrum of Scandium Monofluoride 4.1.1 Introduction Scandium monofluoride (ScF) has one of the best-studied spectra o f the transition metal monohalides. Low-temperature matrix isolation studies [1] demonstrated aXT,+ ground state, whi le high-temperature studies [2] indicated a l o w - l y i n g a 3 A state w h i c h also contributes to the absorption spectrum. The earliest theoretical work [3] by Carlson and Moser considered Xl+ and a 3 A states at the SCF level. They showed that although a 3 A ground state was initially predicted, the Xlf state was predicted to be slightly lower. The dissociation energy o f ScF has been determined from high temperature mass spectroscopic studies [4]. E ight singlet transitions invo lv ing XxYf and AXA states and five tr iplet transitions involv ing the first excited a 3 A state have been rotationally analysed [2, 5-9]. The energies o f the a 3 A , b2U, c 3 E + and A1 A states have been de te rmined [10-14] . Shenyavskaya et al. measured rotational constants in several vibrational states and used the information to evaluate equilibrium bond lengths [12]. However, to our knowledge, there is no previous work on the hyperfine interactions o f ScF, or of its pure rotational spectrum. Accordingly, in this chapter, the first measurements Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 30 and analyses o f this spectrum are presented. The very high resolution and accuracy o f mic rowave spectroscopy have a l lowed the first measurements o f several hyperf ine parameters. The nuclear quadrupole coupling constant for Sc, the nuclear spin-rotation constants for Sc and F, and the nuclear spin-spin constant has been determined. The quadrupole coupling constants have been used to investigate the nature o f the bonding in ScF. 4.1.2 Experimental Details Gas phase scandium monofluoride was prepared by reacting ablated Sc metal with sulfur hexafluoride (SF 6 ) , present as 0.003-0.01% in A r carrier gas. A s was found in the F T M W investigation o f yttrium monohalides [16], a very low concentration (0.05-0.1%) o f the halogen precursor, SF 6 , had to be used to promote the formation o f the monohalide rather than di- and trihalides. The signals obtained for ScF were frustratingly weak compared to those of Y F , even after much care was taken to optimize experimental parameters. There seem to be several possible reasons for this, including greater stability of ScF 3 over ScF, less efficient ablation o f Sc and a particularly uneven surface on the ablation rod. A typical measurement took 3000-5000 averaging cycles to measure the transition lines, which translated into 50-90 minutes in measurement time. 4.1.3 Observed Spectrum and Analysis Rotational transition frequencies o f ScF were predicted using the accurate values o f B0 and D0 available from earlier electronic spectroscopic work [12]. Only the J=1-0 transition was available for study in the frequency range o f the spectrometer. The first transition line Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 31 was found within 5 M H z of the prediction, and consisted basically o f a widely spaced triplet caused by 4 5 S c hyperfine coupling (chiefly nuclear quadrupole coupling). Two lines o f the triplet showed further splitting due to 1 9 F hyperfine coupling. The pattern is shown in Figure 4.1, together with the J= 1-0 spectrum of ScCl for comparison. The coupling scheme I S C + J = F \u00E2\u0080\u009E I F + F , = F (4.1) was used to assign the transitions for ScF. The nuclear spins o f 4 5 S c and 1 9 F are 7/2 and 1/2 respectively. A l l the measured lines and their assignments are listed in Tables 4.1. The specific Hamiltonian can be taken from Chapter 2 [15] H = H r o t + H e l e c q u a d + H m a g n (4.2) where [16] H r o t =B0J2-D0J4 (4.3) H e l e , q u a d = - l / 6 Q S c :VE S c (4.4) FT = IT -}_ I T -^magri -^spin-rotation -^spin-spin = Q(sc)ISc-J + CmIr J + Osc.F (IKScf^rV3lSc-IF) (4.5) The constants are defined in chapter two. The transitions of ScF were fit using Pickett's exact fitting program, SPFIT[17]. Since only the 7=1-0 transition was available for study in the frequency range of the spectrometer, the centrifugal distortion parameter (D0) was fixed to the value from reference 12 in the fit. The resulting constants are listed in Table 4.2, which also contains the results from reference 12 for a comparison. As can be seen, there is a major improvement in the precision o f B0, Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 32 which reflects the accuracy o f the F T M W measurements. The ground state effective bond distance (r0) has been calculated from B0 using E q . 2.15 The resulting value is 1.7902990(8) A. The uncertainty given reflects the accuracy o f the atomic masses and fundamental constants used in the calculation. It is listed in Table 4.14 with the bond lengths of ScCl and ScBr for comparison. 4.2 The Pure Rotational Spectrum of Scandium monochloride 4.2.1 Introduction The spectrum o f scandium monochloride (ScCl) is less extensively studied than that o f ScF. The first spectroscopic work on ScCl was done in the late 1960's by Shenyavskaya et al. [7,18], who observed nine electronic band systems in the 200-900 nm range. Fischell et al. [19] measured radiative lifetimes for three electronic states o f S c C l in 1980. Recently, Taher et al. [20-24] have begun to reinvestigate this molecule with the aim o f improving the knowledge o f a number of states and to characterize as yet unobserved low-lying singlet and triplet states. In particular, they have measured rotational constants in several vibrational states o f the ground state X1!. state, and have used them to obtain an equilibrium geometry. A d a m et al. [25] also reinvestigated the (0,0) \u00C2\u00A3> 1 n-X 1 E transition. Langhoff et al. [26] reported theoretical values of the spectroscopic constants in the Xl and a 1 A states. In this section, the first measurements and analysis o f the pure rotational spectra o f S c C l are presented. The very high resolution and accuracy of microwave spectroscopy have al lowed the first measurements o f several hyperfine parameters. Nuclear quadrupole Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 33 coupling constants and nuclear spin-rotation constants for both nuclei, and the nuclear spin-spin constant, have been determined. The hyperfine parameters have been used to investigate the nature o f the bonding of ScCl . Because a significant difference was found between the B0 value o f S c 3 5 C l determined in the present work and that in the literature [20], transitions were also measured from the first excited vibrational state in order to confirm, and perhaps improve, the equilibrium geometry. 4.2.2 Experimental Details The gas phase scandium monochloride was prepared by reacting ablated Sc metal rod with chlorine (Cl 2 ) , present as 0.003-0.01% in A r carrier gas. As was found for ScF, a very low concentration o f the halogen precursor, C l 2 , had to be used to promote the formation o f the monohal ide rather than d i - and trihalides. The signals obtained for S c C l were again frustratingly weak compared to those of YC1. For some weak transition lines, it took 10000 averaging cycles to measure, which took more than three hours in measurement time. The proposed reasons are similar to those for ScF. 4.2.3 Observed Spectra and Analysis The two lowest frequency rotational transitions of ScCl (X^Tf), 7=1-0 and 7 = 2-1, were available for study in the frequency range of our spectrometer. Since Be values have already been published, the present work initially concentrated on the ground vibrational state. The transition frequencies were predicted using the published values o f B0 and D0 [20]. Again they were found within several M H z o f the prediction. The coupling scheme, Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 34 I S c + J = F \u00E2\u0080\u009E Ia + F , = F (4.6) was used to assign the observed transitions. The nuclear spin o f 4 5 S c is 7/2 and for both 3 5 C1 (75.77%) and 3 7C1 (24.23%), 1=3/2. The J= 1-0 transitions are shown in Figure 4.1 together with those o f ScF for comparison. One Sc hyperfine component o f the J= 1-0 transition o f S c 3 5 C l is shown in Fig . 4.2. This was the most intense transition observed, yet 3000 cycles were required to obtain the signal-to-noise ratio shown. A l l the measured lines and their assignments are listed in Table 4.3. The H a m i l t o n i a n is the same as that used for ScF wi th the add i t ion o f a second quadrupole coupling term: H= H r o t + H e l e c q u a d + H m a g n (4.2) where [16] H r o t = 5 0 J 2 - Z ) 0 J 4 (4.3) H e l e , q u a d = - l / 6 Q S c : V E S c - l / 6 Q c l : V E c , (4.7) I I = I I i II \"magn. -^ spin-rotation s^pin-spin =Q(Sc)Isc'J + Q(Ci)Ic)'J + ^Sc-Cl (^zcsc/zccirl/^lg^la) (4-8) The transitions o f each isotopomer o f S c C l were fit separately using Picke t t ' s exact fitting program, SPFIT [17]. The resulting constants are listed in Tables 4.4. Table 4.4 also contains a comparison of the present spectroscopic constants with the most precisely determined values from electronic spectroscopy (20). The values of B0 are similarly determined and the D0 values are less well determined than those from reference 20. The latter is not surprising considering that transitions involving J as high as 215 (Sc 3 5 Cl) and 165 Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 35 ( S c 3 7 C l ) were reported in reference 20 whereas only the two lowest . / t ransi t ions were measured in present work. On the other hand, the accurate value of B0 reflects the greater resolution and accuracy o f this technique. The ground state effective bond distances (r0) are 2.2331083(9) A and 2.2330595(9) A for S c 3 5 C l and S c 3 7 C l respect ively. A g a i n the measured uncertainties reflect the uncertainties in the atomic masses and fundamental constants. They are listed in Table 4.14 with other bond length values for comparison. The ratios of the hyperfine parameters found for S c 3 5 C l and S c 3 7 C l should be equal to the ratios o f certain nuclear and molecular properties. The ratio o f C, is proportional to the product o f gJ3 [16], while the ratio of the quadrupole coupling constants should be equal to that of the quadrupole moments o f the CI nuclei. These ratios have been calculated for the parameters and are listed in Table 4.5 along with ratios obtained from the literature. The deviation observed in these ratios is due to vibrational effects, because the equilibrium values should really be used to calculate the ratios [27,28]. Unfortunately, lines o f S c 3 7 C l in the first excited vibrational state could not be measured, so that such a comparison could not be made. 4.2.4 The Equilibrium State and Vibration Frequency of Sc 3 S Cl From the data listed in Table 4.4, it is clear that there are differences between the present values o f B0 and the literature values [20]. These differences are w e l l outside the uncertainties determined in this work. It was therefore thought to be worthwhile to examine the first excited vibrational state and make a comparison o f equi l ibr ium results. The transitions o f the first excited state were measured and are listed with their assignments in Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 36 Table 4.6. Their intensities were about one third those observed for the ground state. The spectroscopic constants derived for this state are listed in Table 4.7, with those o f reference 20 for comparison. The information about the equilibrium state was obtained using the B0 and 5 , values in Table 4.4 and 4.7, respectively. The relationship between the equilibrium rotational constant, Be, and the rotational constants Bu can be expressed using Eq . 2.17. B0 = Be - ae(u + K) + r\u00C2\u00A3u+ V2f +... (2.17) where ae and ye are the vibration-rotation constants. Four methods were used to determine these parameters, with Be then used to obtain re using Eq . 2.15. In Method 1, ye was set to zero, and Be and ae were calculated. In Method 2, ye was set to the value from reference 20, and the calculation was repeated. The equilibrium distances re were then calculated from the derived Be values using atomic masses. Two further determinations o f re, ca l led Methods 3 and 4, were then carried out: they used the constants o f Methods 1 and 2, respectively, along with ionic masses for Sc + and CT. This procedure is justified by the ionic character of the ScCl bond, discussed in Section 5.1 below. These results are also in Table 4.8, as are literature values. Significant difference between the equilibrium rotational constants calculated from all four methods and the reference value still exist, similar to that in the ground states. The equilibrium bond lengths are also listed in Table 4.14 together with other values for the ground states and those for the other two molecules studied in this work. The harmonic vibration frequency, coe, and the vibrational anharmonicity constant, o)gXe, of S c 3 5 C l can be estimated using the relations developed by Kratzer (29) and Pekeris (30), respectively, as presented in Eq . 2.21 and 2.22. The results are also listed in Table 4.8 with Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 3 7 reference values. The differences between the calculated values and the experimentally determined ones are 0.56% and 3.5% for oje and a>exe, respectively. These expressions evidently provide reasonable estimates of the desired constants. It is interesting to compare the present Be and ae values with those from reference 20. It is clear from Table 4.4, 4.7 and 4.8 that although the ae values are in excellent agreement, all discrepancies are in the rotational constants. This would also account for the discrepancies be tween the present re va lue and that f rom reference 20 . S ince the m i c r o w a v e measurements are all based on a frequency standard accurate to 1 part o f 10 1 2 , the error then appears to be in the literature constants. Possible reasons for this error might be calibration errors, or errors present in the fitting procedure used. The derived re values differ only marginally whether ye is included or not, or whether atomic or ionic masses are used. The variations are ~10' 6 A . The change from atomic to ionic masses should give a lower limit to how well the Born-Oppenheimer breakdown for transition metal compounds in the literature. A recent study of Z r O and ZrS , in which the Born-Oppenheimer approximation breaks down, found isotopic variations in r e ~ 10\"5 A [31] With the vibrational constants obtained, it is possible to estimate the dissociation energy, De, using the equation from reference 33 The value o f dissociation energy is also listed in Table 4.8. This result agrees wi th the uncertain experimental value from reference 32. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 38 4.3 Pure Rotational Spectrum of Scandium monobromide 4.3.1 Introduction U n l i k e ScF and S c C l , there are no previously determined rotational data available for ScBr. Fischell et al. [19] measured radiative lifetimes and gave rotational constants for three electronic states o f ScBr in 1980. However, their rotational constants for ScF and S c C l were not very accurate, so the same situation was expected for ScBr. Langhoff et al. [26] reported theoretical values o f the spectroscopic constants in the X ' Z and a 1 A states. In this section, the first measurements and analysis o f the pure rotational spectrum of ScBr are presented. Transitions have been measured for two isotopic species, S c 7 9 B r and Sc 8 1 Br , in the ground and first excited vibrational states. From them rotational and centrifugal distortion constants have been determined, and have been used to evaluate the equilibrium bond length, re, and the vibrational wavenumbers. Again the hyperfine constants have been determined and have been used to investigate the nature o f the bonding in the molecule. 4.3.2 Experimental Details Gas phase scandium monobromide was prepared by reacting ablated Sc metal wi th bromine (Br 2 ) , present at a very low percentage in A r carrier gas. The averaging number o f cycles used in the measurements was between 4000-10000 cycles. 4.3.3 Observed Spectra and Analysis The three lowest rotational transitions o f S c B r (X'E + ) , J = 1-0, 2-1 and 3-2, were available for study in the frequency range of the spectrometer. The transition frequencies were predicted using the theoretical values of rt from reference 27. Comparisons were Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 39 made between the constants from the same reference for ScF and S c C l , and a prediction o f the ScBr spectrum was made. Similar comparisons were made when searching for the excited vibrational states. The ratio of the rotational constants, Bv, between the ground and first excited vibrational states o f Y B r was used to estimate that o f ScBr. Two rotational transitions for the first excited states were measured and assigned to both B r isotopes. The assignment was verified by the prediction and measurement of other transitions. A different coupling scheme, the \"parallel\" scheme, I S c + IB r = I, J + I = F (4.10) was used to assign the transitions. This coupling scheme was employed because the eQq value o f B r is of the same order of magnitude as that of Sc. The nuclear spin o f Sc is 7/2, and for both 7 9 B r (50.69%) and 8 1 B r (49.31%) is 3/2. One hyperfine component o f the J = 2-1 transition of S c 8 1 B r is shown in Fig . 4.3. A l l the measured lines and their assignments are listed in Tables 4.9 and 4.10. The Hamiltonian for ScBr was the same as that used for ScCl . The analysis followed the same procedure : the transitions o f both isotopomers of ScBr were fitted separately using Pickett 's exact fitting program, SPFIT [17]. The resulting constants are listed in Tables 4.11. The ground state effective bond distances (r0) from the value of B0 are 2.3833167(9)A and 2.3833042(9) A for S c 7 9 B r and S c 8 1 B r respectively. They are listed in Table 4.14 with those for ScF and ScCl for comparison. The ratio of the hyperfine parameters found for S c 7 9 B r and S c 8 1 B r should be equal to the ratios o f certain nuclear and molecular properties, as discussed in section 4.2.3. These Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 40 ratios have been calculated for the parameters and are listed in Table 4.12 along with ratios obtained from the literature. The deviation observed is due to vibrational effects because e q u i l i b r i u m values should be used to calculate the ratios [27,28]. To examine the vibrational dependence of the nuclear quadrupole coupling constants, an expansion in terms of vibrational contributions was made eQqu = ^ e + \u00C2\u00AB e Q q ( u + ' / 2 ) (4.11) where eQqe is the equilibrium nuclear quadrupole coupling constant and aeQq is the vibration-rotation correction term. Using the nuclear quadrupole coupling constants obtained in the ground and the first excited states, the following two expressions have been derived: eQqu(9Br) = 38.0748(8) + 2.0218(59)( u+V2) eQqu ( 8 1 Br) = 31.8026(8) + 1.6824(71)( v+ V2) The ratio o f the equilibrium nuclear quadrupole coupling constants is also listed in Table 4.12. This value agrees more closely with the literature value than the result obtained for the ground state. Structural information about the equilibrium state has again been obtained using the E q . 2.15. The same four methods were used as for ScCl . The only difference is that since y e has not been obtained experimentally it was estimated using the relation o f a e and y e for S c C l . Methods 1 and 2 used atomic masses to obtain re; Methods 3 and 4 used ionic masses. The results are listed in Table 4.13. The variations in re values between the methods are again very small. For ScBr it is also possible to compare re values between different isotopomers. These variations are also Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 41 ~10\"6 A, an order o f magnitude smaller than those for Z r O and ZrS [31] discussed earlier. Therefore it is safe to say that for S c B r ( and probably also ScF and S c C l ) the B o r n -Oppenheimer approximation holds well. The calculated equilibrium bond distances are also listed in Table 4.14 with the geometry information o f other molecules. The information about the vibrational constants, , F j\u00E2\u0080\u009E F \u00E2\u0080\u009E F\u00E2\u0080\u009E ( M H z ) rMHz) (kHz) 1 5/2 3 0 7/2 4 23605.4962 23605.4962 0.0 1 5/2 2 0 7/2 3 23605.5400 23605.5400 0.0 1 9/2 4 0 7/2 3 23609.8622 23609.8622 0.0 1 9/2 5 0 7/2 4 23609.9341 23609.9341 0.0 1 7/2 3 0 7/2 3 23624.1031 23624.1026 0.5 1 7/2 4 0 7/2 4 23624.1031 23624.1036 -0.5 \"Measured transition frequency, minus that calculated using derived constants. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.2. Molecular constants calculated for ScF in M H z \u00C2\u00B0 46 Parameter This work Literature value* Bo 11806.79620 (24) 11806.8 (4) Do 0.01375 c 0.01375 (4) eQq, (Sc) 74.0861 (51) C,(Sc) 0.019308 (13) Q ( F ) 0.0587(10) -0.0127(19) \"One standard deviation in parentheses, in units of least significant digit. ^Reference 12, CD() fixed at the value from Reference 12. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.3. Measured hyperfine components of ScCl 47 Transition Observed Freq. Calculated Freq. O - C J' F , ' F J\" F,\" F\" (MHz) ( M H z ) (kHz) S c 3 5 C l 1 5/2 3 0 7/2 4 10297.1904 10297.1904 0.0 1 5/2 4 0 7/2 5 10297.3403 10297.3394 0.9 1 5/2 2 0 7/2 3 10297.3724 10297.3719 0.5 1 5/2 1 0 7/2 2 10297.5986 10297.6001 -1.5 1 9/2 5 0 7/2 4 10301.1636 10301.1640 -0.4 1 9/2 4 0 7/2 3 10301.4524 10301.4524 0.0 1 9/2 6 0 7/2 5 10301.6922 10301.6918 0.4 1 9/2 3 0 7/2 2 10301.8716 10301.8716 0.0 1 7/2 2 0 7/2 2 10314.0079 10314.0074 0.5 1 7/2 5 0 7/2 5 10314.3060 10314.3071 -1.1 1 7/2 3 0 7/2 3 10314.7477 10314.7475 0.2 1 7/2 4 0 7/2 4 10315.0182 10315.0178 0.4 2 9/2 6 1 7/2 5 20606.7634 20606.7628 0.6 2 11/2 5 1 9/2 4 20607.9705 20607.9704 0.1 2 11/2 6 1 9/2 5 20608.0885 20608.0881 0.4 2 11/2 4 1 9/2 3 20608.2115 20608.2126 -1.1 2 11/2 7 1 9/2 6 20608.2753 20608.2754 -0.1 Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides 4 8 Sc37Cl 1 5/2 3 0 7/2 4 9984.5495 9984.5502 -0.7 1 5/2 4 0 7/2 5 9984.6793* 9984.6775 1.8 1 5/2 2 0 7/2 3 9984.6793* 9984.6838 -4.5 1 5/2 1 0 7/2 2 9984.8620 9984.8623 -0.3 1 9/2 5 0 7/2 4 9988.5357 9988.5354 0.3 1 9/2 4 0 7/2 3 9988.7397 9988.7401 -0.4 1 9/2 6 0 7/2 5 9988.9484 9988.9486 -0.2 1 9/2 3 0 7/2 2 9989.0846 9989.0843 0.3 1 7/2 2 0 7/2 2 10001.4206 10001.4202 0.4 1 7/2 5 0 7/2 5 10001.6546 10001.6552 -0.6 1 7/2 3 0 7/2 3 10002.0010 10002.0003 0.7 1 7/2 4 0 7/2 4 10002.2160 10002.2165 -0.5 2 9/2 6 1 7/2 5 19981.3108 19981.3103 0.5 2 11/2 5 1 9/2 4 19982.6407 19982.6414 -0.7 2 11/2 6 1 9/2. 5 19982.7128 19982.7125 0.3 2 11/2 7 1 9/2 6 19982.8605 19982.8606 -0.1 \"O-C stands for observed frequency- frequency calculated using the derived constants. *Fit as blended lines-weighted by the ratio of the predicted intensities. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.4. Molecular constants for ScCl in MHz\" 49 Parameter Sc 3 5Cl Literature value* Sc 3 7Cl Literature value* Bo 5152.41543 (21) 5152.6730 4996.06537 (22) 4996.365 Do 0.003097 (36) 0.00308801 0.002891 (39) 0.0029041 eQq, (Sc) 68.2067 (29) 68.2062 (29) eQq0(Cl) -3.7861 (35) -2.9824 (36) Q (Sc) 0.024383 (95) 0.023621 (94) C, (CI) 0.00463 (24) 0.00369 (28) ^ S c - C l -0.00065 (35) -0.00045 (34) \"One standard deviation in parentheses, in units of least significant digit. *Reference 20; there were no uncertainties listed in the reference. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.5. Comparison of hyperfine constants for ScCl 50 C(Sc in Sc 3 5 Cl) / eQq0CCiy C:( 3 7C1) Q(Sc in Sc 3 7 Cl) This work 1.26(12) 1.0322 (58) 1.2695 (19) Li t . Value\" 1.23989 1.0313 1.2688773(15)* \"The literature values are the ratios of gx B0 for Ch and the ratio of the nuclear quadrupole moments for eQq0 [16]. For the spin-rotation constants the uncertainties in the literature values are three to four orders of magnitude smaller than the number of digits given. ^Reference 34. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.6. Measured hyperfine components of the first excited vibrational state of S c 3 5 C l . J. F ; Transition F J\" F , \" F\" Observed Freq. (MHz) Calculated Freq. (MHz) 0 -C\u00C2\u00B0 (kHz) 1 5/2 3 0 7/2 4 10245.1528 10245.1537 -0.9 1 5/2 4 0 7/2 5 10245.3105 10245.3095 1.0 1 9/2 5 0 7/2 4 10249.1156 10249.1159 -0.3 1 9/2 4 0 7/2 3 10249.4409 10249.4411 -0.2 1 9/2 6 0 7/2 5 10249.6898 10249.6888 1.0 1 9/2 3 0 7/2 2 10249.8871 10249.8878 -0.7 1 7/2 5 0 7/2 5 10262.2253 10262.2254 -0.1 1 7/2 3 0 7/2 3 10262.7021 10262.7039 -1.8 1 7/2 4 0 7/2 4 10262.9967 10262.9948 1.9 2 9/2 5 1 7/2 4 20501.9969 20501.9968 -0.1 2 9/2 6 1 7/2 5 20502.7311 20502.7315 -0.4 2 11/2 5 1 9/2 4 20503.8849 20503,8836 1.3 2 11/2 6 1 9/2 5 20504.0219 20504.0226 -0.7 2 11/2 7 1 9/2 6 20504.2245 20504.2248 -0.3 \u00C2\u00B0 0 - C stands for observed frequency minus frequency calculated using derived constants. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.7. Molecular constants calculated for the first excited state of S c 3 5 C l in M H z Parameter This work Literature value b Bx 5126.39924 (24) 5126.6915 A 0.003097 (41) 0.00309620 eQq, (Sc) 67.9957 (35) eQq, (CI) -4.1003 (40) Q (Sc) 0.02525 (11) Q (Ci) 0.00466 (30) \"One standard deviation in parentheses, in units o f least significant digit. bReference 20, there were no uncertainties listed in the reference. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.8. Equalibrium parameters and vibration frequency calculated for S c 3 5 C l . 53 This work \u00E2\u0080\u009E c References Parameter Mr. M 2 f l M 3 a M 4 \" Theo.\" Expt l . c Be ( M H z ) 5165.42352(26) 5165.43049(26) 5165.42352(26) 5165.43049(26) 5165.691 a e ( M H z ) 26.01619(32) 26.03477(32) 26.01619(32) 26.03477(32) 26.02 ' . ( A ) 2.23029467(95) 2.23029317(95) 2.23029079(95) 2.23028928(95) 2.255 2.23026 coe (cm 1 ) 445.0(26) 438 447.523 % ( c m ' ' ) 1.729(14) 1.67025 A(eV) 3.55 4.12 3.4* \" M l , M 2 , M 3 , M 4 stand for Methods 1, 2, 3, 4 discussed in context, estimated uncertainties in parentheses, derived from rotational constants, fundamental constants, and reduced mass. ^Reference 26; no isotope effect specified, average values are used. 'Reference 20; no standard deviations were given. 'Reference 32. Chapter 4 Microwave Spectra and Geomatries of Scandium Monohalides Table 4.9 Measured hyperfine components of Sc79Br 54 Transition u=0 V = 1 J' r F J\" I\" F\" 0\u00C2\u00B0 (MHz) C\u00C2\u00B0 (MHz) o-e (kHz) 0\u00C2\u00B0 (MHz) C\u00C2\u00B0 (MHz) O - C (kHz) 1 5 6 0 5 5 6207.8646 6207.8646 0.0 1 4 5 0 4 4 6211.3141 6211.3122 1.9 1 5 5 0 5 5 6226.6323 6226.6334 -1.1 2 3 5 1 3 4 12419.6103 12419.6097 0.6 12367.6518 12367.6516 0.2 2 2 2 1 2 2 12419.7074 12419.7073 0.1 2 5 6 1 5 5 12420.7110 12420.7110 0.0 12369.0502 12369.0503 -0.1 2 2 3 1 2 2 12420.8852 12420.8865 -1.3 2 5 5 1 5 5 12423.1964 12423.1945 1.9 12371.6096 12371.6088 0.8 2 3 2 1 3 2 12423.4482 12423.4492 -1.0 2 4 4 1 4 4 12423.6809 12423.6812 -0.3 2 5 7 1 5 6 12423.7889 12423.7890 -0.1 12372.1562 12372.1566 -0.4 2 4 5 1 4 4 12424.1428 12424.1436 -0.8 12372.6127 12372.6123 0.4 2 4 6 1 4 5 12425.2268 12425.2281 -1.3 12373.6262 12373.6265 -0.3 2 5 3 1 5 4 12425.4539 12425.4523 1.6 12373.9359 12373.9364 -0.5 2 3 4 1 4 3 12425.6435 12425.6451 -1.6 12374.1421 12374.1424 -0.3 2 2 4 1 2 3 12426.7468 12426.7475 -0.7 12375.1420 12375.1423 -0.3 2 4 5 1 4 5 12431.0992 12431.0975 1.7 2 4 4 1 3 3 12432.0629 12432.0633 -0.4 2 3 4 1 3 4 12433.0153 12433.0097 5.64 2 4 3 1 2 3 12433.0435 12433.0454 1.9* 2 5 5 1 3 4 12433.6452 12433.6456 -0.4 2 3 5 1 5 4 12436.2015 12436.2001 1.4 2 5 4 1 5 4 12437.2037 12437.2031 0.6 Chapter 4 Microwave Spectra and Geomatries of Scandium Monohalides 55 2 5 6 1 5 6 12439.4792 12439.4799 -0.7 12388.1929 12388.1924 0.5 3 5 7 2 5 6 18635.9785 18635.9791 -0.6 18558.5622 18558.5606 1.6 3 5 8 2 5 7 18637.6740 18637.6736 0.4 18560.2612 18560.2618 -0.6 3 4 6 2 4 5 18638.0360 18638.0374 -1.4 18560.6185 18560.6189 -0.4 3 4 7 2 4 6 18638.4430 18638.4418 1.2 18561.0375 18561.0376 -0.1 3 2 5 2 ' 2 4 18638.7390 18638.7387 0.3 3 3 6 2 3 5 18639.2695 18639.2698 -0.3 18561.9651 18561.9655 -0.4 3 5 5 .2 3 4 18639.4763 18639.4756 0.7 \"C stands for frequency calculated from the derived constants; O stands for observed frequency; O-C stands for observed frequency minus frequency calculated using the derived constants. *Lines that were excluded from the final fit program. Chapter 4 Microwave Spectra and Geomatries of Scandium Monohalides Table 4.10 Measured hyperfine components of Sc 8 1 Br 56 Transition u=0 V = 1 J' r F J\" I\" F\" 0\u00C2\u00B0 (MHz) C (MHz) O-C (kHz) 0\u00C2\u00B0 (MHz) C (MHz ) O-C (kHz) 1 5 6 0 5 5 6152.5747 6152.5766 -1.9 2 2 2 1 2 2 12308.8060 12308.8053 0.7 2 3 5 1 3 4 12309.5221 12309.5205 1.6 12258.3306 12258.3305 0.1 2 5 6 1 5 5 12309.7646 12309.7640 0.6 12258.7957 12258.7961 -0.4 2 2 3 1 2 2 12309.9014 12309.9021 -0.7 2 5 5 1 5 5 12311.9484 12311.9471 1.3 12261.0628 12261.0631 -0.3 2 4 4 1 4 4 12312.1661 12312.1667 -0.6 12261.3480 12261.3473 0.7 2 5 7 1 5 6 12312.7074 12312.7084 -1.0 12261.7747 12261.7753 -0.6 2 5 3 1 5 4 12313.9221 12313.9213 0.8 2 4 6 1 4 5 12314.0138 12314.0135 0.3 12263.1191 12263.1182 0.9 2 3 4 1 4 3 12314.0868 12314.0878 -1.0 12263.2824 12263.2828 -0.4 2 2 4 1 2 3 12315.5642 12315.5653 -1.1 2 4 5 1 4 5 12320.2946 12320.2952 -0.6 2 4 3 1 2 3 12320.9695 12320.9698 -0.3 2 4 4 1 3 3 12321.2040 12321.2041 -0.1 2 3 4 1 3 4 12322.0999 12322.0959 4.0* 2 3 5 1 5 4 12323.5476 12323.5461 1.5 2 5 4 1 5 4 12324.8791 12324.8789 0.2 2 5 6 1 5 6 12327.2884 12327.2887 -0.3 12276.6098 12276.6098 0.0 3 5 7 2 5 6 18469.2840 18469.2838 0.2 18392.3972 18392.3962 1.0 3 5 8 2 5 7 18470.9238 18470.9236 0.2 18394.5517 18394.5517 0.0 3 4 6 2 4 5 18471.3057 18471.3047 1.0 18394.9246 18394.9260 1.4 3 4 7 2 4 6 18471.6371 18471.6363 0.8 18395.2826 18395.2816 1.0 Chapter 4 Microwave Spectra and Geomatries of Scandium Monohalides 57 3 2 5 2 2 4 18471.6830 18471.6880 5.0* 18395.3917 18395.3933 -1.6 3 3 6 2 3 5 18472.1819 18472.1844 -2.5 18395.9010 18395.9000 1.0 aC stands for frequency calculated from the derived constants; O stands for observed frequency; O -C stands for observed frequency minus frequency calculated using the derived constants. *Lines that are excluded from the fit program. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.11 Molecular constants for ScBr in M H z a 58 Parameter S c 7 9 B r ( y = 0 ) S c 7 9 B r ( u = l ) Sc 8 1Br(t> = 0) S c 8 1 B r ( y = l ) Bu 3106.49059(11) 3093.59149(18) 3078.68584 (12) 3065.96014 (19) Du 0.001169 (8) 0.001157(12) 0.001148 (11) 0.001178 (12) eQq, (Sc) 65.2558 (32) 65.1345 (103) 65.2597 (38) 65.1424 (87) eQq, (Br) 39.0857 (24) 41.1075 (54) 32.6438 (19) 34.3262 (68) C, (Sc) 0.020478 (62) 0.02161 (15) 0.020244 (61) 0.02118 (23) Q (Br) 0.01706(16) 0.01688 (24) 0.01824(17) 0.01771 (25) ^ S c - B r -0.00175 (54) \"One standard deviation in parentheses, in units of the least significant digit. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.12. Comparison of hyperfine constants for ScBr 59 C,( 7 9 Br)/ C r f B r ) C,(Sc in Sc 7 9 Br)/ C : (Sc in Sc 8 1 Br) eQq0{19Br)l 0.935(12) 1.0116(43) 1.19734(10) v=\ 0.953(19) 1.020(13) 1.19755 (28) Equilibrium 1.19722(4) Li t . Value c 0.939995(2)\u00C2\u00B0 1.0090* 1.19707(3)\u00C2\u00B0 \"Reference 33. ^Inverse ratio of reduced masses of Sc 7 9 Br and Sc 8 1 Br. l i terature values are the ratios of gJ3 for Ch and of the nuclear quadrupole moments for eQq. Chapter 4 Microwave Spectra and Geometries of Scandium Monohalides Table 4.13. Equilibrium parameters and vibration frequency calculated for ScBr. 60 References Parameter M l \" M 2 \" M 3 a M 4 \" Theo* E x p l c ae ( M H z ) 12.8991(2) 12.9077(2) 12.8991(2) 12.9077(2) Be ( M H z ) 3112.94014(15) 3112.94337(15) 3112.94014(15) 3112.94337(15) 2623 re (A) 2.3808465(10) 2.3808453(10) 2.3808435(10) 2.3808515(10) 2.432 2.60 Sc 8 1 Br a e ( M H z ) 12.7257(2) 12.7343(2) 112.7257(2) 12.7343(2) Be ( M H z ) 3085.04869(15) 3085.05192(16) 3085.04869(15) 3085.05192(16) 2623 '.(A) 2.3808451(10) 2.3808439(10) 2.3808423(10) 2.3808504(10) 2.432 2.60 coe (cm 1 ) 338.9(12) 327 275(5) % ( c m - 1 ) 1.099(5) A (eV) 3.24 3.74 \" M l , M 2 , M 3 and M 4 stand for Methods 1, 2, 3 and 4 discussed in the text, M 3 and M 4 use estimated ye, with estimated uncertainties for re parentheses, derived from rotational constants, fundamental constants, and reduced masses. 'Reference 26, no isotope effect specified, average values are used. 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Ref. Data 3, 609, 1974. Chapter 5 Discussion and Conclusions 6 5 Chapter 5 Discussion and Conclusions 5.1 Nuclear Quadrupole Coupling Constants The ionic character o f the S c X bond can be calculated from the halogen nuclear quadrupole coupling constants, eQq0 (X) . I f we assume only the np orbitals of the X atom contribute to eQq(X) [1], the ionic character can be related to the coupling constants using Eq . 2.36: ic=l+eQq0(X)/eQqnWrX) (2.36) where eQqnU) ( X ) is the quadrupole coupling constant for a singly occupied npz orbital o f atomic halogen; eQq3l0 (35C1)=109.74 M H z and eQq4W ( 7 9Br)=-769.76 M H z [1]. The result is /'c = 0.966 for S c 3 5 C l and 0.949 for S c 7 9 B r indicating an almost completely ionic S c X bond. Tables 5.1 and 5.2 compare the ionic characters calculated by this method wi th those o f several alkali and alkaline earth metal monohalides and o f the yttrium halides ( Y X ) . These results fol low the expected periodic trends in electronegativity for S c X and Y X , with S c X being less ionic than Y X . The ionicity values o f ScCl and ScBr are comparable to the other listed species. Unfortunately, since 1 9 F has no quadrupole moment, the same treatment can not be applied to ScF. However, given that the electronegativity of F is greater than that o f CI, ScF can reasonably be expected to be even more ionic than ScCl . Interpreting the 4 5 Sc quadrupole coupling constants is somewhat less straightforward. The Chapter 5 Discussion and Conclusions 66 Townes-Dailey approach [2], modified to include J-orbital contribution [3], predicts that they should be given by Eq . 2.38 Here n4pa, n4pm, n3dm n3dn and n3dS are the total orbital populations ( summed over degenerate orbitals where applicable) of the 4p and 3d orbitals on Sc. The parameters eQqAW and eQq320 are the quadrupole coupling constants of an 4 5 S c atom containing a singly occupied 4p2 and 3dz2 orbitals. In the absence o f experimental values these parameters were evaluated, following Gordy and C o o k [ l ] , using the equation [4] Here Q is the nuclear quadrupole moment in fm 2; for 4 5 S c it is -23.1 fm 2 (ref. 5). Estimates for (r\"3> are available from the literature: 3d=: 1.72 a0\"3(ref. 6,7). These are values for the S c + ion, chosen because o f the ionic characters derived above. The resulting eQqnl0 values are eQq4W = 49.6 M H z and eQq320 = 53.4 M H z . Values for the orbital populations can be obtained from ab initio calculations. Although such calculat ions have been published for ScF and S c C l , no orbital populations were presented [8]. For the related molecules ScO and ScS, similar calculations have yielded orbital populations [9-12]. It might thus be expected that a comparison o f their coupling (5.1) Chapter 5 Discussion and Conclusions 67 constants would be fruitful. The measured 4 5 S c quadrupole coupling constants of several Sc compounds are given in Tab le 5.3. C l e a r l y a l l the values are comparable, thus i m p l y i n g that the e lec t ron arrangements around Sc are essentially the same. It is generally accepted[8,12] that the valence molecular orbitals of all four compounds are approximately l t r ~ n s ( X ) 2CT ~3da(Sc) + npa(X) l ^ - ~ 3 ^ ( S c ) + n/7^(X) 3tr ~ % (Sc) + 4/?cr(Sc) + 3Jcr(Sc)) Figure 5.1 is the schematic diagram of the valence molecular orbital energy levels o f S c C l . The highest occupied molecular orbital ( H O M O ) is 3cr. In ScO and ScS it is singly occupied (and thus sometimes called the S O M O ) . In ScF and ScCl it is doubly occupied. It is largely 45, but has some 4p and 3d character, and is polarized away from X [9]. The four published sets o f orbital population densities o f ScO give very similar values [9-12]. We choose to use the two most recent sets published by Mattar [11] and Knight et al. [12], because they give population densities of relevant individual orbitals (Table 5.4). Using the populations presented in these references and E q . 2.38 the values calculated are 62.5 M H z and 56 .6MHz, respectively. (The U B 3 L Y P results from reference 12 were used). The agreement wi th the experimental value (72.240 M H z ) is only moderate. When an extra Chapter 5 Discussion and Conclusions 68 electron is added to the S O M O the corresponding values for ScF are 69.1 M H z and 70.4 M H z , which are in good agreement with the experimental value of 74.086 M H z . However, in both cases the differences between the ScF and ScO values (6.6 M H z and 13.8MHz) are rather larger than the experimental values (1.846 M H z ) , so the agreement for ScF is to some degree fortuitous. The possible reason for this disagreement may be attributed to the fact that we ignored potential population changes in the bonding orbitals when making the assumption. Since fluorine is more electronegative than oxygen, it is reasonable to think that the 3d and 4p populations o f Sc in bonding orbitals w i l l be less in ScF, thus making the result lower, whi le because o f the additional electron to the valence orbital, the 4p (or possibly 3d ) populat ions w i l l double and thus increase the eQq o f Sc. Judging from the s imi l a r experimental results, these two effects are comparable, with the latter being slightly more significant , wh ich also proves that the valence orbitals o f S c X are largely s orbitals. Nonetheless this treatment makes the small differences between ScF and ScO at least qualitatively understandable. Al though the necessary specific orbital populations are not available to calculate the differences in eQq ( 4 5 Sc) among the monohalides, it is nonetheless reasonably easy to rationalize them qualitatively from the Townes-Dailey model. The lower electronegativities of CI and B r suggest there should be less charge transfer on formation o f an ionic bond. The CI\" and B r ' ion would cause a lower electric field than F , and the electron distribution at Sc would be less polarized. In turn this would mean less 4pa character for the 3 cr orbital, and a lower eQq ( 4 5 Sc). On the other hand, the greater spatial extent of the CI and B r npn orbitals Chapter 5 Discussion and Conclusions 69 over the F 2pn orbitals should increase ^--overlap, and allow a greater covalency, increasing the Sc 2>dn popu la t ion , and its eQq,. E v i d e n t l y the former effect is p redominant . It is perhaps also instructive to compare the experimental difference between eQq o f ScF and ScO wi th those obtained from interpretation o f the experimental magnetic hyperfine parameters o f ScO [13]. In this case it was deduced from the Fermi contact parameter that the3 a orbital has 69% 4s (and thus 31% 4p) character, which is in very good agreement with the recent ab initio results [12]. The difference in eQq, calculated from these values is 13.8 M H z , so a l i t t le more information is needed to interpret the quadrupole coupl ing data completely. It could also be thought that a similar problem might occur in comparing the eQq, values of S c C l and ScS. The interpretation o f both the Fermi contact and dipole-dipole terms for ScS [8] predicts a difference o f - 2 6 M H z . The measured difference is 11 M H z , but the uncertainty in eQq,(Sc) in ScS is \u00C2\u00B118MHz, so the comparison is largely meaningless. There would seem to be a good reason to expect that eQq,(Sc) \u00C2\u00B0 f ScS should be close to that o f ScO, say -68 M H z . Although the published ab initio results for ScO and ScS [10] can not be used to support this idea, however, those for Y O and Y S do support it [14]. A n accurate measurement of eQq,(Sc) in ScS is needed. For comparison purposes a low level ab initio Hartree-Fock (HF) calculation for ScO, ScF and ScCl was carried out by Dr. C. Evans in the laboratory. The orbital populations obtained for ScO agreed quite wel l wi th the other theoretical results. Another Townes-Dai ley analysis, using these results, gave 48.6MHz, 27.5 M H z and 39.5 M H z for the eQq values o f Chapter 5 Discussion and Conclusions 70 Sc for ScO, ScF and ScCl , respectively. The values for ScF and S c C l were much lower due to a significantly lowered 3d population in both molecules. These results did not agree with the experimental values at all. The same calculations,however, produced calculated electric field gradients directly, which were then used to calculate nuclear quadrupole coupl ing constants. This procedure gave the results 81.9MHz, 89.5MHz and 73 .9MHz. These results agreed better with the experimental values o f 72 .2MHz , 7 4 . 1 M H z and 6 8 . 2 M H z both in magnitude and in trend. This led to reconsideration o f the val idi ty o f applying Townes-Dailey model in the analysis of scandium quadrupole coupling constants. It is possible that the assumption that the value of eQgnl0 (Sc) remain the same from oxide to fluoride may not be correct. And we should also question the assumption concerning the orbital populations. To make matters worse, the H F calculation did not show either decreased polarization o f the Sc cr-orbitals in going from ScF to ScCl, or of ;r back-donation to Sc in the same process. On the other hand, fortunately, the Townes-Dailey theory for the halogens does agree with the H F results. A l l the calculated results are listed in Table 5.5. 5.2 Nuclear Spin-rotation Coupling Constants and Nuclear Spin-Nuclear Spin Constants The analysis o f nuclear spin-rotation coupling constants has been reviewed in Chapter 2. Table 5.6 and 5.7 presents the observed and calculated constants. From Table 5.6 we find that the dominant contribution to the nuclear spin-rotation coupling constant is the electronic part. Significant variations can be found for the paramagnetic shieldings of Sc in the halides. The other interesting fact is that the magnetic shieldings of Sc and F in ScF have different Chapter 5 Discussion and Conclusions 71 signs from their counterparts in ScCl and ScBr. From the nuclear spin-spin coupling constants measured for ScF, ScCl and ScBr, the S c - X bond distance can be estimated. The assumption is required that the spin-spin coupling arises main ly from a direct dipole-dipole interaction. The equation can be expressed us ing Eq. 2.47 [21]: \"sc-x = (-3//N 2 gscgx)/ ^ s c - x (247) where / / N is the nuclear magneton and g S c and gx are the nuclear ^-factors for the Sc and F, CI, B r nuclei. Internuclear bond distances of 1.87(9) A, 2.37(43) A, 2.52(63) A and 2.32(7) A were calculated for ScF, S c 3 5 C l , S c 3 7 C l and Sc 7 9 Br, respectively. The large uncertainties in the estimated bond distances are due to uncertainties in the respective constants. The results compare well , within the uncertainties, with the experimental /yvalues of 1.7902990 (8) A for ScF, 2.2331083(9) A for S c 3 5 C l , 2.2330595 (9) A for S c 3 7 C l and 2.3833167(8) A for Sc 7 9 Br. . These results show that the assumption that the direct terms of spin-spin constants are the main contribution is reasonable. 5.4 Conclusions This thesis has presented the first measurements and analysis o f the pure rotational spectra o f three scandium monohalides, ScF, ScCl and ScBr. Transitions have been measured for ScF ( J = 1-0) in its ground vibrational state, for both S c 3 5 C l and S c 3 7 C l (J= 1-0, 2-1) in the ground vibrational state and for S c 3 5 C l (J = 1-0, 2-1) in the first excited state, and both S c 7 9 B r and S c 8 ' B r (J= 1-0, 2-1 and 3-2 for ground vibrational state and J = 2 -1 , 3-2 for the first excited state). Rotational constants, and centrifugal distortion constants are presented for all Chapter 5 Discussion and Conclusions 72 the molecules in al l the states. The quadrupole nuclear coupling constants o f 4 5 S c and both isotopes o f CI and B r have been determined, along with the spin-rotation constants for all the nuclei and the nuclear spin-nuclear spin constants for all the molecules. The rotational constants and major hyperfine constants o f all three molecules are listed in Table 5.8 for comparison. From the derived constants molecular geometries, vibration frequencies, dissociat ion energies and details o f the electronic structure have been obtained. A n y breakdown of the Born-Oppenheimer approximation is marginal at most. A l l these three species have ' E + ground electronic states. From the nuclear quadrupole coupling constants observed for CI and Br, the ionic characters of the S c - X bonds have been evaluated. The overall observed picture is consistent with the results o f a simple ab initio Har t ree-Fock predict ion. A l l three molecules are h ighly ion ic wi th ion ic characters comparable to those o f some alkali and alkaline earth metal monohalides. They are only slightly less ionic than the corresponding yttrium halides, whose spectra were measured recently in this lab. A Townes-Dailey analysis comparing the 4 5 Sc quadrupole coupling constants o f ScO and ScF produced a reasonable rationale for the values for both molecules . The orbi ta l populat ions used were ab initio literature values for ScO. Furthermore, a p laus ib le argument is presented to rationalize the decrease in 4 5 Sc coupling constant in going from ScF to ScCl to ScBr. The Hartree-Fock calculation mentioned above gives reasonable predictions of the 4 5 S c coupling constants for ScO, ScF and ScCl. However, when the orbital populations obtained Chapter 5 Discussion and Conclusions 73 from this calculation are used in the Townes-Dailey analysis the values obtained are very poor. Evidently the assumptions made in the Townes-Dailey analysis are not justified, and great care must be taken in using such a simple approach to interpret nuclear quadrupole coupling constants, particularly for elements with complex electronic structures like transition metals. The nuclear spin-rotation constants have been used to estimate the paramagnetic shieldings and from them the total shieldings, for both atoms in each molecule. Significant variations have been found for the paramagnetic shieldings, especially for 4 5 Sc, between the molecules. The very small nuclear spin-nuclear spin coupling constants, which are barely determined at best, are consistent with a direct dipole-dipole interaction between the nuclei. This work can be considered as continuation of the previous work on yttrium monohalides in this lab. We compare the hyperfine constants of scandium monohalides and yttrium monohalides in Table 5.9 as part of conclusions. To make it a more complete study, it is suggested that we should extend the work to the pure rotational spectra of scandium monoiodide and lanthanum monohalides. Also as stated earlier in this chapter, it would also be necessary to improve the eQq0 o f Sc in scandium sulfide to carry out a similar comparison of ScS and ScCl . Chapter 5 Discussion and Conclusions 74 Figure 5.1 3p la 3s Sc CI Figure 5.1 Schematic diagram (not to scale) of the valence molecular orbital energy levels for ScCl. Chapter 5 Discussion and Conclusions Table 5.1. Comparison of z'c for S c 3 5 C l and some related species. S c 3 5 C l Y 3 5 C 1 \" ' M g 3 5 C f N a 3 5 C l c C a 3 5 C l d e\u00C2\u00A3??o( 3 5Cl)/MHz -3.786 -0.822 -11.62 -5.642 -1.002 / / /% 96.6 99.3 89.4 94.8 99.1 \"Reference 22. *Reference 23. 'Reference 24. \"Reference 25. Tonic character Chapter 5 Discussion and Conclusions Table 5.2. Comparison of ic for Sc 7 9 Br and some related species. Sc 7 9 Br Y 7 9 B r \" Mg 7 9 Br* N a 7 9 B r c C a W e ( M 3 5 C l ) / M H z 39.087 12.935 110.313 58.6080 20.015 / / / % 94.9 98.3 85.7 92.5 97.4 \"Reference 26. ^Reference 27. \"Reference 28. \"Reference 29. Tonic character Chapter 5 Discussion and Conclusions 11 Table 5.3. Comparison of 4 5 Sc quadrupole coupling constants (MHz) in various Sc compounds. ScO\" ScS\" ScF c S c C l c S c B ^ e\u00C2\u00A3??o(Sc) 72.240(5) 57(18) 74.0861(51) 68.2067(29) 65.2558(32) \"Reference 13. ^Reference 8. T h i s work. Chapter 5 Discussion and Conclusions Table 5.4 Orbital populations for Sc in ScO. 4s 4pa 4pn 3ddn Mattar et ala total 0.90 0.25 0.07 0.58 0.78 lcr 0.04 0.12 0.06 2cr 0.02 0.05 0.45 \n 0.07 0.78 3CT 0.84 0.08 0.07 Knigh te / al.b total 0.67 0.17 0.06 0.5.7 0.72 3cr 0.69 0.15 0.10 0.04 \"Reference 11. Reference 12. Chapter 5 Discussion and Conclusions Table 5.5 Comparison of the calculated and experimental eQq, (Sc) in M H z . 79 ScO ScF ScCl H F ( l ) a 48.6 27.5 39.5 H F ( 2 ) 6 81.9 89.5 73.9 experimental 72.2C 74 . \ d 68.2* \"Calculated from orbital populations in H F results using Townes-Dailey theory. *Calculated directly from electric field gradient in H F results. 'Reference 13. \"This work. Chapter 5 Discussion and Conclusions 80 Table 5.6. Nuclear and electronic contributions to the experimental spin-rotation constants and corresponding paramagnetic shieldings in ScX. Sc X 3 C,/kHz C ^ ' / k H z C ^ / k H z Op/ppm C,/kHz C \" u c l /kHz C \" l e c /kHz o-p/ppm ScF 19.308(13) -1.24 20.55(1) -784(1) 58.7(10) -11.19 69.9(12) -689(12) S c 3 5 C l 24.383(95) -0.82 25.20(10) -2203(9) 4.63(24) -0.41 5.04(26) -1093(57) S c 3 7 C l 23.621(94) -0.80 24.42(10) -2201(9) 3.69(28) -0.33 4.02(31) -1080(82) Sc 7 9 Br 20.478(62) -0.95 21.43(6) -3107(9) 17.06(16) -0.59 17.65(17) -2476(23) Sc 8 1 Br 20.244(61) -0.94 21.18(6) -3098(9) 18.24(17) -0.63 18.87(18) -2396(22) X = F, CI, Br. Chapter 5 Discussion and Conclusions Table 5.7. The magnetic shieldings of the nuclei in ScX. 81 Sc X o-p (ppm) o-d (ppm) trav (ppm) Op (PPm) crd (ppm) crav (ppm) ScF -784(1) 1569 785(1) -689(12) 581 -108(2) S c 3 5 C l -2203(9) 1593 -610(2) -1093(57) 1232 139(7) S c 3 7 C l -2201(9) 1593 -608(2) -1080(82) 1231 151(11) Sc 7 9 Br -3107(9) 1659 -1448(4) -2476(23) 3204 728(7) Sc 8 1 Br -3098(9) 1659 -1439(4) -2478(22) 3204 726(5) Chapter 5 Discussion and Conclusions 8 2 Table. 5.8. Comparison of ScF, S c 3 5 C l and Sc 7 9 Br. ScF S c 3 5 C l Sc 7 9 Br B0/MHz eQq0(Sc) / M H z C I ( S c ) / M H z eQq0(X) / M H z C , ( X ) / M H z ic/%a 11806.79620(24) 74.0861(51) 0.019308(13) 0.0587(10) 5152.41543(21) 68.2067(29) 0.024383(95) -3.7861(35) 0.00463(24) 96.6 3106.49059(11) 65.2558(32) 0.020478(62) 39.0857(24) 0.01706(16) 94.9 \"Ionic characters calculated from nuclear quadrupole coupling constants. Chapter 5 Discussion and Conclusions Table 5.9. Comparison of hyperfine parameters of Y X and S c X 83 Y F a ScF Y 3 5 C l b S c 3 5 C l Y 7 5 B r c Sc 7 9 Br e0c7o(X)/MHz -0.8216(43) -3.7861(35) 12.9352(16) 39.0857(24) Cj(X)/kHz 39.6(9) 58.7(10) 2.86(39) 4.63(24) 8.58(12) 17.06(16) egc70(M)/MHz 74.0861(51) 68.2067(29) 65.2558(32) C, (M)/kHz 19.308(13) 24.383(95) 20.478(62) \"Reference 30. \u00E2\u0080\u00A2Reference 22. 'Reference 26. Chapter 5 Discussion and Conclusions 84 Bibl igraphy [1] W . Gordy, and R. L . Cook, Microwave molecular spectra, John Wiley &Sons, N e w York, 1984. [2] C. H . Townes and B . P. Dailey, J. Chem. Phys. 17, 782, 1949. [3] T. L . Brown, Acc. Chem. Research 1, 408, 1974. [4] S. A . Beaton and M . C. L . Gerry, J. Chem. Phys. In press. [5] J. Bieron, I. P. Grant, and C. Froese Fischer, Phys. Rev. A. 56, 316, 1997. [6] L . Young, W. J. Childs, T. Dinneen, C. Kurtz, H . G. Berry, L . Engshdm, and K . T. Cheng, Phys. Rev. A 37, 4213, 1988. [7]T. C. Steimle, A . J. Marr, and D . M . Goodridge, J. Chem. 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"University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "Fourier transform microwave spectroscopy of scandium monohalides"@en . "Text"@en . "http://hdl.handle.net/2429/9345"@en .