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Microwave spectroscopic studies of chloryl fluoride and acetaldehyde-D1 Parent, Charles Robert 1972

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151 ^ MICROWAVE SPECTROSCOPIC STUDIES OF CHLORYL FLUORIDE AND ACETALDEHYDE-D^ by Charles Robert Parent B.S., San Diego State College, 1967; A.M., Harvard U n i v e r s i t y , 1968 A THESIS SUMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Chemistry We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1972 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . The U n i v e r s i t y o f B r i t i s h C Vancouve r 8, Canada Department o f - i i -ABSTRACT The microwave spectra of three i s o t o p i c species of c h l o r y l f l u o r i d e , 3 5 C 1 1 6 0 2 F , 3 7 C 1 1 6 0 2 F , and 3 5C1 1 60 1 80F, have been measured and the t r a n s i t i o n s f i t to Watson's nonrigid rotor reduced Hamiltonian. The r e s u l t i n g r o t a t i o n a l constants have allowed the c a l c u l a t i o n of a molecular structure that features an anomalously long Cl-F bond and unusually short Cl-0 bonds. The nuclear quadrupole coupling constants and e l e c t r i c dipole moment have also been deter-mined and both suggest the withdrawal of considerable e l e c t r o n density from the CIC^ moiety along the Cl - F bond. The molecular structure and i o n i c character of the Cl-F bond are con s i s -tent with a modi f i c a t i o n of the multicentered molecular o r b i t a l bonding theory proposed by Lipscomb and expanded by Spratley and Pimentel. C h l o r y l f l u o r i d e may p r o f i t a b l y be viewed as a molecule created by the formation of a bond be-tween a f l u o r i n e atom and a stable paramagnetic c h l o r i n e dioxide molecule. Q u a l i t a t i v e l y the anomalously long C l - F bond r e s u l t s from overlap of a f l u o r -ine 2p atomic o r b i t a l with a lobe of the highest s i n g l y occupied antibonding molecular o r b i t a l of C l * ^ . The s i g n i f i c a n t c ontraction of the Cl-0 bond i n CIO2F, compared to the bond i n CIC^, suggests that there i s considerable e l e c -tron withdrawal from t h i s CIC^ antibonding o r b i t a l . S i milar bonding p i c t u r e s are used to c o r r e l a t e the anomalous structures of M^F, NOF, NSF, C v ^ ' and S 2 F 2 . The r o t a t i o n a l constants and b a r r i e r to i n t e r n a l r o t a t i o n of the CH^CDO is o t o p i c species of acetaldehyde have been determined. The b a r r i e r i s i n good agreement with b a r r i e r heights of other i s o t o p i c species previously mea-sured, and the r o t a t i o n a l constants are consistent with the recent zero-point average structure reported by Iijiraa and Tsuchiya. - i i i -Summary of Spectroscopic and.Structural Constants of CIC^F a n c* CH^ CDO 3 5 C 1 1 6 0 2 F 3 7 C 1 1 6 0 2 F 3 5 C 1 1 6 0 1 8 0 F CH3CD0 A (MHz) 9635.91 9598.47 9178.21 45009.95 B (MHz) 8275.66 8239.13 8101.02 10158.90 C (MHz) 5019.22 5016.16 4843.20 8731.38 X c c (MHz) 51.8 40.6 52.6 Xbb " Xaa (MHz) 17.7 14.1 16.0 (cal/mo le) 1184 35 Dipole Moment of Cl V ^a = 0.55 D, V = 1.63 D, c p = 1.72 D Structure of Chloryl Fluoride r(Cl-F) = 1.697 8 r(Cl-O) = 1.418 8 Z(0-Cl-0) = 115.23° Z(F-Cl-0) = 101.72° - i v -TABLE OF CONTENTS CHAPTER PAGE 1. INTRODUCTION . . . 1 1.1 Ch l o r y l Fluoride 3 1.2 Acetaldehyde 4 2. MICROWAVE SPECTROSCOPY OF GASES 5 2.1 Rotational Energy Levels of Asymmetric Top Molecules . . . . 5 2.2 Nuclear Quadrupole Hyperfine Interactions . . . . 14 2.3 The Stark E f f e c t i n Molecules with Nuclear Quadrupole Coupling 17 2.4 Ca l c u l a t i o n of Quartic C e n t r i f u g a l D i s t o r t i o n Constants from Molecular Structures and V i b r a t i o n a l Force F i e l d s . . . 22 2.5 Coupling of Internal Torsion and Molecular Rotation . . . . 26 2.6 Determination of Molecular Structures from Spectroscopic Rotational Constants . . 28 3. EXPERIMENTAL PROCEDURES AND EQUIPMENT 32 3.1 Preparation of Samples 32 3.2 100 kHz Stark Modulated Microwave Spectrometer 33 3.3 Microwave C e l l s and Gas Handling Equipment 38 3.4 Double Resonance Modulated Microwave Spectrometer 41 3.5 Stark Voltage Mixer 43 4. THE MICROWAVE SPECTRA OF CHLORYL FLUORIDE . . .45 4.1 Assignment of the Spectra 45 4.2 Determination of the Rotational Constants and the C e n t r i -fugal D i s t o r t i o n Constants from the Microwave Spectra . . . 46 4.3 C a l c u l a t i o n of the C e n t r i f u g a l D i s t o r t i o n Constants of Ch l o r y l Fluoride from the V i b r a t i o n a l Force F i e l d 59 4.4 Determination and Discussion of the Nuclear Quadrupole Coupling Constants of C h l o r y l Fluoride 65 -v-CHAPTER PAGE 5. THE STARK EFFECT IN THE MICROWAVE SPECTRUM OF CHLORYL FLUORIDE . 86 5.1 General Considerations 86 5.2 Calibration of the Stark Cell with Carbonyl Sulphide . . . 87 5.3 The Electric Dipole Moment of 3 5 C 1 1 6 0 2 F 90 35 16 5.4 Nuclear Quadrupole Coupling Constants of Cl 0_F in the High Field Spin-Rotation Uncoupled Limit 102 6. THE MOLECULAR STRUCTURE OF CHLORYL FLUORIDE 104 6.1 Determination of the Internuclear Parameters 104 6.2 • Discussion of the Structure of Chloryl Fluoride and Related Molecules 109 7. THE MICROWAVE SPECTRUM OF ACETALDEHYDE-D^ 119 7.1 Assignment of the Spectrum 119 7.2 Determination of the Rotational Constants and the Barrier to Internal Rotation 120 8. COMMENTS ON THE STRUCTURE OF ACETALDEHYDE 126 APPENDIX REPRINT OF A PRELIMINARY REPORT OF THE MICROWAVE SPECTRUM OF CHLORYL FLUORIDE 132 BIBLIOGRAPHY 134 - v i -LIST OF TABLES TABLE PAGE 4.1 Rotational Constants and Quartic Centrifugal Distortion Constants 35 16 of Cl 0_F from Linear Least Squares Variational Fits to Equa-tion 2.25 . . 48 4.2 Cl 0 2F Transition Frequencies 51 37 1 fi 4.3 Cl 0 2F Transition Frequencies 54 4.4 3 5 C 1 1 6 0 1 8 0 F Transition Frequencies .56 4.5 Rotational Constants and Centrifugal Distortion Constants of Chloryl Fluoride 59 4.6 Structural Parameters of Chloryl Fluoride 60 4.7 Valence Force Constants of Chloryl Fluoride 61 4.8 Quartic Centrifugal Distortion Constants Calculated from the Vibrational Force Field of Chloryl Fluoride 64 35 16 4.9 Nuclear Quadrupole Hyperfine Components of Resolved Cl 0 2F Transitions 66 37 16 4.10 Nuclear Quadrupole Hyperfine Components of Resolved Cl 0 2F Transitions 72 35 16 18 4.11 Nuclear Quadrupole Hyperfine Components of Resolved Cl 0 OF Transitions 75 4.12 Nuclear Quadrupole Coupling Constants of Chloryl Fluoride . . . . 78 4.13 Nuclear Quadrupole Coupling Constants of Cl 0 2F and Cl 0 2 . 82 4.14 SCF-M0-CND0 Chlorine 3p Electron Populations and Nuclear Quadrupole Coupling Constants of C102F and CK>2 84 5.1 Stark Coefficients of the M = 0, J = 1 «- 0, OCS Transition . . . . 90 5.2 Frequencies of the M = 0 Stark Component of the 1.. n ~ 0 n n - _ - - J 1 , U U , 0 Transition of C f OjF 91 5.3 Frequencies of the M T = + 3 Stark Component of the 3_ , _3_ .. Transition of Cl 0 2F 92 5.4 Quadratic Stark Coefficients of the M = 0, 1.. ~-0 and M = + 3, 3_ ..-3. Transitions . . . . . . T'V . J U 97 - v i i -TABLE PAGE 5.5 Higher Order Contributions to the Stark Energies of the 3^ j~^2 i Transition Arising from the Near Degeneracy of the 3„ - and 3, _ States . . . . , U. 98 5.6 The Electric Dipole Moment of Cl 0 2F . 99 35 16 5.7 Nuclear Quadrupole Coupling Constants of Cl O^F in the High and Zero Field Limits 103 6.1 Principal Moments of Inertia of Chloryl Fluoride 104 6.2 The Structure of Chloryl Fluoride with with Complete r Deter-mination of C102 Group Structure 106 6.3 The Structure of Chloryl Fluoride with F, a and c_ and Cl a-Coordinates Determined from Fir s t and Second Moment Conditions . 107 6.4 Proposed Structure of Chloryl Fluoride 108 35 16 6.5 Nuclear Coordinates of Chloryl Fluoride in the Cl 0 2F Principal Inertial Axis System 109 6.6 Structural Parameters and Stretching Force Constants of Chloryl Fluoride and Related Molecules . . 110 6.7 Structural Parameters of Ni t r y l Fluoride and Related Molecules . I l l 6.8 Structural Parameters and Stretching Force Constants of Nitrosyl Fluoride and Related Molecules I l l 6.9 Structural Parameters and Stretching Force Constants of Thionitrosyl Fluoride and Related Molecules . 112 6.10 Structural Parameters and Stretching Force Constants of Dioxygen Difluoride and Related Molecules 112 6.11 Structural Parameters of Sulfur Monofluoride and Related Molecules . . . . . . 113 6.12 Summary of the Anomalous Structures of C102F, N02F, NOF, NSF, 0 2F 2, and S ^ 115 6.13 Sulfur Halogen Bond Lengths in S 2Hal 2 and Related Compounds . . . 117 7.1 Observed and Calculated CH^ CDO Transition Frequencies 121 7.2 Observed and Calculated CH3CD0 Torsional Splitting 124 7.3 Rotational and Torsional Parameters of CH^ CDO 125 8.1 Effective and Zero-Point Average Structures of Acetaldehyde . . . 128 - v i l l -u s ! OF FIGURES FIGURE PAGE 3.1 Components of Double Resonance Modulated Microwave Spectrometer. . 41 3.2 Schematic Diagram of Stark Voltage Mixer 43 4.1 Internal Coordinates of Chloryl Fluoride 61 4.2 Elements of the Matrix (P^) 6 3 4.3 Principal Inertial Axis Systems of Chloryl Fluoride and Chlorine Dioxide 81 5.1 Frequency of the 1 6 0 1 2 C 3 2 S , J = 1 +• 0 Transition 89 35 16 5.2 Frequency of Hyperfine Components of the Cl O 2 F , 1^ Q _ 0 Q Q Transition as a Function of the Square of the Electric Field Strength . . 93 35 16 5.3 Frequency of Hyperfine Components of the Cl O 2 F , Mj = + 3, 3_ -,-3- .. Transition as a Function of the Square of the Electric Field Strength 94 5.4 The Electric Dipole Moment of Chloryl Fluoride in the a_,c_-Plane. . 100 8.1 The Configuration of Acetaldehyde 129 - i x -ACKNOWLEDGEMENT The c h l o r y l f l u o r i d e and acetaldehyde i n v e s t i g a t i o n s reported i n t h i s d i s s e r t a t i o n were completed under the d i r e c t i o n of Professor M.C.L. Gerry at the U n i v e r s i t y of B r i t i s h Columbia and Professor E. Bright Wilson, J r . at Harvard U n i v e r s i t y . I am very pleased and g r a t e f u l to acknowledge the most able supervision and patient encouragement of t h i s work provided by Professors Gerry and Wilson. I also wish to express my thanks to my colleagues i n the microwave groups at UBC and Harvard f o r innumerable assistances and many help-f u l discussions. S p e c i f i c thanks go to Professor F. Aubke for advice and the loan of f a c i l -i t i e s f o r the preparation of c h l o r y l f l u o r i d e , to Dr. Martin Williams for per-forming the CNDO c a l c u l a t i o n s on c h l o r y l f l u o r i d e , to Professor J.L. Wood for the g i f t of a sample of CH^CDO, and to Dr. Ray Green for many enlightening d i s -cussions of the v i b r a t i o n a l problem. My most sincere gratitude goes to the people of Canada and the United States of America f o r f i n a n c i a l assistance during the course of t h i s work i n the form of a National Research Council of Canada bursary and a National S c i -ence Foundation (U.S.A.) Graduate Fellowship. With only a s l i g h t degree of mixed f e e l i n g s , I salute the M i l i t a r y Ser-v i c e s and the Selec t i v e Service System of the United States of America f o r occasioning my return to Canada. Chapter 1 Introduction This d i s s e r t a t i o n i s a report of i n v e s t i g a t i o n s of the microwave spectra of c h l o r y l f l u o r i d e and acetaldehyde. The two studies d i f f e r e d considerably i n scope. Acetaldehyde was a short study designed to further i l l u m i n a t e the structure of a molecule that had been frequently studied before, and c h l o r y l f l u o r i d e was a broader i n v e s t i g a t i o n of a molecule whose structure was un-known. Before discussing the s p e c i f i c s of these studies, there i s some value i n considering the general kinds of information that the a n a l y s i s of the micro-wave spectrum of a molecule can provide. I t i s hoped that t h i s w i l l i l l u s t r a t e the considerable power that t h i s spectroscopic technique has to i l l u m i n a t e what appear to be unusual molecular structures and chemical bonding schemes, and make c l e a r the motivation f o r t h i s work. The molecular t r a n s i t i o n s most frequently observed i n the microwave spec-t r a l region (usually considered to l i e i n the frequency range between 8 and 40 GHz) are between states of d i f f e r e n t r o t a t i o n a l energies. The purely r o -t a t i o n a l energies are determined by the three p r i n c i p a l moments of i n e r t i a of a molecule which i n turn are simple functions of the molecular atomic masses and i n t e r n u c l e a r distances. Therefore, the a n a l y s i s of the microwave spectra of a s u f f i c i e n t number of i s o t o p i c species of a molecule completely determines the molecular structure. On top of the gross energy l e v e l pattern determined by the r o t a t i o n a l states are smaller energy displacements caused by coupling between the o v e r a l l r o t a t i o n a l motion of the molecule and other i n t e r n a l degrees of freedom. A l -- 2 -though these energy displacements are very small compared to r o t a t i o n a l l e v e l separations, the p r e c i s i o n of frequency measurements i n the microwave region ( t y p i c a l l y one part i n 5 x 10"*) allows t h e i r accurate measurement. C e n t r i f u -gal d i s t o r t i o n and C o r i o l i s coupling e f f e c t s a r i s e from the coupling of r o t a -t i o n a l and v i b r a t i o n a l motions, and constants c h a r a c t e r i z i n g t h e i r magnitude can be determined from an a n a l y s i s of the microwave spectrum. These constants are functions of the v i b r a t i o n a l force f i e l d of a molecule and i n a few favor-able cases can be used to completely determine the force f i e l d . C l o s e l y r e l a t e d i s the determination of the b a r r i e r to i n t e r n a l r o t a t i o n i n a molecule with a methyl group from the influence of r o t a t i o n a l - i n t e r n a l t o r s i o n a l coupling on the microwave spectrum. Another frequent b e n e f i t of the analysis of the microwave spectrum i s the determination of nuclear quadrupole coupling constants. These constants are parameters that characterize the magnitude of nuclear s p i n - r o t a t i o n a l coupling through the nuclear quadrupole hyperfine i n t e r a c t i o n . They are r e l a t e d to the e l e c t r o n i c d i s t r i b u t i o n s i n a molecule and provide a valuable probe of the nature of chemical bonds. Further assessment of the e l e c t r o n i c d i s t r i b u t i o n i s provided by the molecular dipole moment which can be measured by observing the Stark e f f e c t i n the microwave spectrum. The body of theory necessary for an understanding of these e f f e c t s as they bear on the microwave spectrum of a molecule i s too w e l l discussed elsewhere to warrant a general review here. However, discussions of the theory as i t applies s p e c i f i c a l l y to the problems considered i n t h i s t h e s i s can be found i n the following chapter. The reader who desires a more thorough dis c u s s i o n of the techniques and a p p l i c a t i o n s of microwave spectroscopy may consult one of the large number of good monographs i n the f i e l d [1], - 3 -1.1 C h l o r y l Fluoride The microwave study of c h l o r y l f l u o r i d e was begun to determine the appar-en t l y anomalous structure of t h i s molecule. C h l o r y l f l u o r i d e , CIG^F, was f i r s t synthesized i n 1942 by Schmitz and Schumacher [2] by the d i r e c t f l u o r i n a t i o n of ch l o r i n e dioxide with f l u o r i n e gas. The compound i s thermally s t a b l e , but i s very v i g o r o u s l y hydrolyzed to chlorate ion. I t s chemistry appears to be dominated by the formation of s a l t -l i k e c h l o r y l complexes [3]. Infrared and Raman v i b r a t i o n a l studies [4, 5] f i r s t suggested unusual features i n the molecular s t r u c t u r e . V i b r a t i o n a l spectra were consistent with the expected d i s t o r t e d t r i g o n a l pyramidal s t r u c t u r e , c h l o r i n e at the apex and f l u o r i n e and the oxygens at the corners. However, force f i e l d c a l c u l a t i o n s using assumed values of the in t e r n u c l e a r parameters i n d i c a t e d that the molecule has an unusually small C l - F s t r e t c h i n g force constant and an unusually large Cl-0 s t r e t c h i n g force constant [5]. The suggestion was made that the C l - F bond has a high degree of i o n i c character and that the Cl-0 bond has consid-erably greater double bond character than found i n e i t h e r the i s o e l e c t r o n i c chlorate ion or the c h l o r i n e dioxide molecule. Recently, Carter, Johnson, and Aubke [ 6 ] have noted that the bonding i n ClO^F appears s i m i l a r to that observed i n the s e r i e s of molecules FNO, FtM^, O^F^, and O 2 F . A l l appear to be characterized by an unusually weak and long f l u o r i n e bond to a stable paramagnetic species. In the l a t t e r four instances formation of the f l u o r i n e bond(s) appears to cause l i t t l e change i n the s t r u c -t u r a l parameters of the parent paramagnetic species. The only v a r i a t i o n from t h i s pattern observed when one contrasts C 1 0 „ F and C 1 0 0 i s the s i g n i f i c a n t - 4 -strengthening of the Cl-0 bond evidenced by the v i b r a t i o n a l spectra. It was hoped that a thorough i n v e s t i g a t i o n of the structure of c h l o r y l f l u o r i d e would help c l a r i f y the nature of the bonding i n t h i s e n t i r e s e r i e s of compounds. 1.2 Acetaldehyde The study of the microwave spectrum of acetaldehyde-d^ was begun with more l i m i t e d o b j e c t i v e s . In 1957 K i l b , L i n , and Wilson [7] reported the microwave spectra of nine i s o t o p i c species of acetaldehyde, but not of CH^CDO. By a l i n -ear l e a s t squares v a r i a t i o n a l f i t of the s t r u c t u r a l parameters of acetaldehyde to the observed r o t a t i o n a l constants, Wilson et. a l . determined the structure of the molecule. Acetaldehyde has also been the subject of several e l e c t r o n d i f f r a c t i o n studies [8, 9, 10]. I i j i m a and Kimura [11] have combined the spec-troscopic and d i f f r a c t i o n data to c a l c u l a t e the average structure of the mol-ecule over the ground v i b r a t i o n a l s t a t e . They were unable, however, to r e l i -ably determine the CHO hydrogen bond angle. Since acetaldehyde i s of some considerable importance as the prototype i n the homologous s e r i e s of a l i p h a t i c aldehydes, when the g i f t of a sample of CH^CDO became a v a i l a b l e i t appeared d e s i r a b l e to analyze the microwave spectrum of t h i s i s o t o p i c species and combine the r e s u l t s of t h i s a n a l y s i s with the ear-l i e r data to improve the calculated structure of the molecule. - 5 -Chapter 2 Microwave Spectroscopy of Gases The purpose of this chapter i s to set down reasonably concisely the body of theory necessary for the interpretation of the microwave spectra of chloryl fluoride and acetaldehyde. Both molecules are asymmetric tops (molecules with no two principal moments of inertia equal), but chloryl fluoride i s a limiting oblate and acetaldehyde i s a limiting prolate rotor. To conform with usual convention equations applicable to an oblate top w i l l be set in the III^ re-presentation and those applicable to a prolate top in the I representation [12]. Because chloryl fluoride was the subject of a more detailed investiga-tion, much of what follows w i l l be developed only for the oblate case. Equa-ls tions applicable in the prolate I representation, however, can be set down merely by interchanging a and c in a l l quantities labeled by the three p r i n c i -pal i n e r t i a l axes. 2.1 The Rotational Energy Levels of Asymmetric Top Molecules The Hamiltonian describing the rotational energy of a r i g i d symmetric top molecule (a molecule with two principal moments of inertia equal) can be easily diagonalized to yield analytic expressions for the energy levels and wave func-tions [13]. Introduction of asymmetry so that no two moments of inertia re-main equal introduces elements into the Hamiltonian that are off diagonal in the symmetric top representation. In cases of small asymmetry these terms can be folded onto the diagonal using perturbation theory [14], or in any case the Hamiltonian matrix can be completely rediagonalized. The latter procedure i s never d i f f i c u l t because the total angular momentum commutes with the rigi d asymmetric top Hamiltonian, and, therefore, the Hamiltonian^is s t i l l diagonal - 6 -i n the t o t a l angular momentum quantum number J . The energy matrix that must be diagonalized for a given J i s square and of order 2J+1. Advantage can be taken of symmetry properties of the Hamiltonian to further reduce the energy matrix f o r a given J to four smaller orthogonal sub-matrices. The c a l c u l a t i o n of r i g i d asymmetric top r o t a t i o n a l energy l e v e l s can be f a c i l i t a t e d by a change i n v a r i a b l e s . Ray [15] introduced a frequently adopted asymmetry parameter K, given by K = (2.1) A, B, and C are the three r o t a t i o n a l constants given by convention i n order of decreasing magnitude. The asymmetry parameter K v a r i e s from -1 f o r a p r o l a t e symmetric top (B = C) to +1 for an oblate symmetric top (B = A). In terms of Ray's asymmetry parameter, the energy expression for a r i g i d asymmetric top i s E = 1/2(A + C ) J ( J + 1) + 1/2(A - C ) E ( K ) (2.2) K - i K i E ( K ) i s a reduced energy that depends on the value of the r o t a t i o n a l constants only through K. The expression J i s the quantum l a b e l f o r a p a r t i c u l a r K - 1 K 1 r o t a t i o n a l s tate introduced by King, Hainer, and Cross [12]. J i s the t o t a l r o t a t i o n a l angular momentum quantum number, and K ^ and are the values of K (the component of J on the molecular axis) of the l i m i t i n g p r o l a t e and oblate symmetric rotor states that c o r r e l a t e with t h i s p a r t i c u l a r asymmetric r o t o r s t a t e . A d i f f e r e n t f a c t o r i z a t i o n of the r i g i d asymmetric rotor energy expression r e s u l t s from the use of an asymmetry parameter introduced by Wang [16]. In the oblate case Wang's asymmetry parameter i s -7-b = A - B (2.3) o 2C - B A Use of this parameter leads to the following energy expression E = 1/2(A + B)J(J + 1) + 1/2(2C - A - B)W(b ) r o (2.4) 2 In the oblate limit W(b ), the Wang reduced energy, goes to K and this ex-pression reduces to the familiar oblate symmetric rotor result [17]. The r i g i d asymmetric rotor model very successfully f i t s the low J rota-tional spectra of most molecules. However, molecules in higher rotational states may be severely distorted by centrifugal forces that tend to increase the instantaneous moments of inertia of molecules in these states and cause large deviations at higher J from a r i g i d rotor model spectrum. It i s , there-fore, necessary to consider the Hamiltonian for a general non-rigid asymmetric top molecule. The quantum theory of the non-rigid asymmetric top molecule i s quite involved; however, i t s development w i l l be sketched in some detail i n order to unify the notation adopted by the several contributors to the theory. The foundations and a large part of the development of the theory were estab-lished by E. B. Wilson and several of his collaborators [18, 19, 20, 21]. Consider a non-linear molecule of N atoms. To f a c i l i t a t e the greatest possible separation of rotation and vibration we w i l l define a molecule fixed axis system that translates with the center of mass of the molecule and rotates with the equilibrium structure of the molecule. Let R_ be the position vector of the center of mass in the space fixed frame (SFF); r_^  i s the instantaneous th position of the i atom in the molecule fixed frame (MFF), and a^ is i t s equil-ibrium position. If to is the angular velocity of the rotating molecule fixed t li axis system, then the volocity of the i atom in the SFF is o -8-V. = R + oixr, + r , (2.5) — i . — 1 — i We need s i x equations to give mathematical d e f i n i t i o n to the MFF ax i s system. Three of these lock the o r i g i n of the MFF system to the center of mass of the molecule. Sm.r. = 0 (2.6) l i l Locking the MFF axes to the r o t a t i o n of the molecule i s l e s s straightforeward. Requiring that the instantaneous angular momentum i s zero i n the MFF (^ m^I^ x r-^ = 0) couples v i b r a t i o n and r o t a t i o n through A more t r a c t a b l e decoupling i s achieved through the use of Eckart's condition [22] which sets the angular mo-mentum i n the MFF to zero only i n the f i r s t approximation. " " i V ^ = 0 (2.7) If R^ i s the p o s i t i o n vector of the i atom i n the SFF, and = _r^ - a_^  i s the v i b r a t i o n a l displacement i n the MFF, the use of equations 2.6 and 2.7 allows us to write the t o t a l k i n e t i c energy as *2 2T = Jm^R. l i i *2 '2 = R £m. + Jm. (coxr.)• (oixr.) + Em.p. + 2o> Em.p.xr. (2.8) l i i i i 1 l i i — l ITL — i The f i r s t term on the r i g h t of the second l i n e i s the t r a n s l a t i o n a l k i n e t i c en-ergy, the second and t h i r d are decoupled r o t a t i o n a l and v i b r a t i o n a l energies, and the fourth i s a r o t a t i o n a l - v i b r a t i o n a l coupling term. Defining the moment 2 of i n e r t i a tensor i n the usual way (.1 = Enu{lr^ - r^r^}) and neglecting the cen-te r of mass t r a n s l a t i o n a l energy, one can rewrite equation 2.8 as t t * "2 2T = ui -I-OJ + 2o) >Zm_, (p.xr.) + Znupt - (2.9) — = — — I i — l — l i i i It i s now convenient to express the c a r t e s i a n displacement vectors, p . , — i -9-i n terms of the normal coordinates that diagonalize the v i b r a t i o n a l Hamiltonian, Q . Introducing mass weighted c a r t e s i a n displacements, £^ = ^nu£^, Q v and are r e l a t e d by the following orthogonal transformation. % = P i v % ( 2' 1 0 ) Following Meal and Polo [23] we can rewrite the i n t e r a c t i o n Hamiltonian that appears i n equation 2.9 as r(a) l n t - £ V ^ - % , " a (2.1D a , i , i * (a) with the introduction of three M matrices that have the e f f e c t of taking t r— x the cross product between column and row vectors. I f ^  has the form (/m^ p^ , /rn^p^, <4^ p^ , v^P**'*' v ^ i j p i P ' t * i e n e a c ^ matrix i s composed of N three by three submatrices along the p r i n c i p a l diagonal. These submatrices have the following form '0 0 M ( X ) = ( 0 0 l | M ( y ) -.0-1 0, (2.12) To complete the reduction of the i n t e r a c t i o n Hamiltonian to functions of the normal coordinates of the molecule we simply rewrite equation 2.11 as T. = V Q tC ( a!Q ,a) (2.13) a,v,v' (a) and note that c o m p a t i b i l i t y between equation 2.13 and 2.11 requires that » the matrix of C o r i o l i s coupling c o e f f i c i e n t s , be given by (°) - V i .^(oO.it i»i -10-Before transcribing the Hamiltonian from i t s present class i c a l non-Hermitian form to quantum mechanical form, i t is necessary to rewrite everything in terms of the momenta conjugate to and Q. P = 8T/9U) = gl 0u)D + EQ tc- ( o t *Q a a g ag g v v w v p = 9T/8Q = Q + EQ t? ( a ) (2.15) v v v a v w The total classical energy, neglecting only the translation of the center of mass, can then be written in the following simple form. H = 1/2 0? - E ^ - l ^ O ? - p_) + 1/2 p v 2 + V(Q) (2.16) where u is the inverse of I' (I' = I - E(? ( a )Q ) 2 ; I' = I a + E ? ( a ) £ ( B ) Q 2) = = aa aa v w v ag ag v w w v and p_ appears as a vibrational contribution to the angular momentum (p^ = ZQtC^CX^p ). V(Q) is the vibrational potential energy. v v v v v ( Transcription of equation 2.16 to quantum mechanical form is well known [24, 25] and the result w i l l be stated here. H = 1/2 y 1 / 4 ( P - p_).u,p- 1 / 2(P - p . ) / ' 2 + 1/2 ^ ^ ~ 1 \ / / 2 + V (2.17) Separation of the purely vibrational terms in equation 2.17 from the remaining rotational and vibrational-rotational terms followed by a Van Vleck transfor-mation [26] which reduces to second order in the vibrational quantum number, v, those vibrational-rotational terms in equation 2.17 that are off-diagonal in v yields the following result. H = H + 1/2 £ a QP P Q + 1/2 Y] T . .P PQP P. (2.18) r aB a B 4r^ r agy6 a B Y <$ a,B a,g,y,6 where H^ i s the r i g i d rotor energy of the molecule frozen at vibrational equil--11-ibrium and x n . are centrifugal distortion constants given by CX8Y<5 x . - 2-r ^ ^ (2.19) Y V'rv hv , w It is seen that the influence of the vibrational-rotational coupling terms that were neglected in the rigid rotor approximation is to add Coriolis terms to the effective rotational constants and to introduce terms quartic in ang-ular momenta to the Hamiltonian. Smaller terms of higher even order in ang-ular momenta are introduced when the Van Vleck transformation is carried to higher order. A consideration of equation 2.18 with the realization that P and P., a 4 $, do not commute suggests that there are 3 or 81 distinct quartic distortion constants. In fact, large numbers of these constants are zero and the coeffi-cients of others may be combined so that for a general asymmetric top there are only five determinable quartic distortion constants [28]. Equation 2.19 shows that the following coefficients are equal to one another TagY<S Ty6a8 T8ay5 Ta86y T8ot6y T 6 Y a 3 TY68a T<5Y3a (2.20) This provides an immediate reduction in the number of coefficients from 81 to 21. A further reduction to nine coefficients is provided by the following argu-ment [27], The x's are evaluated as coefficients of first order matrix elements in the rigid asymmetric rotor representation. The diagonal matrix elements in this representation of the 21 non-equivalent distortion terms a l l transform -12-l i k e one of the i r r e d u c i b l e representations of the group, but only nine be-long to the t o t a l l y symmetric A i r r e d u c i b l e representation. Since the r i g i d asymmetric rotor Hamiltonian commutes with a l l the symmetry operations of the point group, only these t o t a l l y symmetric d i s t o r t i o n constants are non-zero to f i r s t order. The nine non-zero T'S are of the form T , T and T „ „. aaaa aa33 a3a3 The f i n a l reduction to f i v e l i n e a r l y independent f i r s t order q u a r t i c cen-t r i f u g a l d i s t o r t i o n constants i s accomplished by r e l a t i n g q u a r t i c products of angular momenta to quadratic and other q u a r t i c products with the following f i r s t order equations [20,28]. <H 2 > = E 2  x r ' r <H P 2 + P 2H > = 2E J ( J + 1) r r r <(P 2) 2> = J 2 ( J + l ) 2 <H P 2 + P 2H > = 2E <P 2 > r z z r r z i<[H , P P P + P P P ] > = 2 ( Y - X)<P 2P 2 + P 2P 2 + 2P 2 > N r x y z z y x ' x y y x z ' + 2(Z - Y)<P 2P 2 + P 2P 2 + 2P 2 > + 2(X - Z)<P 2P 2• + P 2P 2 + 2P 2 > N y z z y x N z x x z y ' (2.21) The q u a n t i t i e s X, Y, and Z are the r o t a t i o n a l constants associated with the x, y, and z i n e r t i a l axes. A convenient form of the f i r s t order reduced Hamiltonian i s that suggested by Watson [28]. 2 2 2 2 4 2 2 2 H = H r - A j ( P 2 ) 2 - A J R P 2 P z 2 - A KP z* - 6 j ( P x 2 - P y 2 ) P 2 2 2 2 2 2 2 2 2 2 - 6 TP (P - P ) - 6„(P - P )P - 6JP Z ( P Z - P n (2.22) J x y K x y z K z x y where Watson's f i v e q u a r t i c d i s t o r t i o n constants are re l a t e d to Wilson's T'S ( Taaaa = Tactaa/1't 5 Taa63 = (Taa63 + 2 x a 3 a 3 ) / l i ^ b y -13-A = -1/8(T' + T* ) j xxxx yyyy A _ = 3/8(T' + T' ) - 1/4(T' + T' + T' ) JK xxxx yyyy yyzz xxzz xxyy A = -1/4(T' + T' + T' ) + 1/4(T' + T' + x' ) K xxxx yyyy zzzz yyzz xxzz xxyy 6 T = -1/16(T' - T» ) j xxxx yyyy Sv = 1/8 T' I — + 1 / 8 T' | ^ - | + 1 / 8 ( T * - T' + T' ) 2 Z ~ X ~ Y K xxxx X - Y yyyy X - Y yyzz xxzz xxyy X - Y (2.23) The matrix elements of the c o e f f i c i e n t s of the d i s t o r t i o n constants can be determined from the r i g i d r o t o r Wang reduced energy, W(b Q), and the f i r s t 2 4 order expectation values of ( i n the oblate representation) and P £ . Equa-t i o n 2.4 allows us to write to f i r s t order < P q 2 > = 9E r/8A = 1/2J(J + 1) - l/2W(b Q) + l / 2 ( b Q + l)9W(b Q)/9b o < P 2 > = 8E /3B = 1/2J(J + 1) - l/2W(b ) + 1/2(b - l)8W(b )/3b D V O O O O < P 2 > = 3E /8C = W(b ) - b 9W(b )/9b (2.24) N c ' r o o o o If one eliminates 9W(b )/9b from the three equations and substitu t e s the r e -o o 2 2 s u i t i n g expression f or ^ P , - P y into equation 2.22, one gets a r e l a t i o n s h i p D 3. that i s very s u i t a b l e f o r a l i n e a r l e a s t squares v a r i a t i o n a l f i t of the d i s t o r -t i o n constants to the observed spectrum. H = | l / 2 J ( J + 1) - 1/2<P 2 > - l/2a(W(b ) - <TP 2 » U 1 C O C ' c2 > + l/2a(W(b Q) - < P C 2 ^ + < P C 2 > C - J 2 ( J + l ) 2 A j - J ( J + l ) < P c 2 > A J K - < P C 4>A R - 2aJ(J + l)(W(b Q) - < P c 2 » 6 a - 2a « P c 2>W(b Q) - < P C 4 » < S K (2.25 + | l / 2 J ( J + 1) - 1/2<P 2 > + l/2a(W(b ) - < P 2 » | B ' C o c ' The c o e f f i c i e n t a i s -1/b . o Occasionally, p a r t i c u l a r l y f o r l i g h t molecules [29], i t i s necessary to i n -clude s e x t i c and higher terms i n the nonrigid rotor asymmetric top Hamiltonian -14-to achieve a satisfactory f i t between observed and model spectra. Watson [30] has shown that in general there are seven linearly independent sextic distor-tion constants and has suggested a convenient set for use. The dependence of these constants on the structure and force f i e l d of a molecule is expected to be very complex and has not yet been f u l l y determined. S t i l l the sextic co-efficients may be used as f i t t i n g parameters to improve the determination of the quartic coefficients. If one expresses the matrix elements of the sextic distortion coefficients in terms of W(bQ) and f i r s t order expectation values of even powers of P , one finds that the contribution of the sextic terms to the Hamiltonian has the following form. J 3 ( J 3 + l)Hj + J 2 ( J 2 + l ) < P c 2 > H J K + J ( J + 1)<P C 4>HKJ + < * C 6 > \ + 2 a J 2 ( J + l) 2(W(b Q) - < P c 2 » h j + 2aJ(J + 1) (W(b O)<P C 2> - < P c 4 » h J K + 2a(W(b O)<P C 4> - < P c 6 » h K (2.26) 2.2 Nuclear Quadrupole Hyperfine Interactions An adequate description of the microwave spectrum of a molecule requires a consideration of a l l terms in the Hamiltonian that may contribute energies greater than a few hundred kilohertz. Because chloryl fluoride and acetaldehyde have closed shell electronic configurations in their ground electronic states, i t i s easily shown that the effects of magnetic coupling between the various molecular degrees of freedom is below the resolution of conventional microwave experiments. The only zeroth order magnetic moments occuring in chloryl fluoride or acetaldehyde are those associated with the nuclei of fluorine, chlorine, and hydrogen, These moments are smaller approximately by the ratio of the Bohr magneton to the nuclear mag-neton (1836 : 1) than the electronic magnetic moments that cause the magnetic -15-hyperflne interactions in paramagnetic molecules. Since the latter interac-tions typically involve energies in the tens of megahertz, nuclear spin inter-actions may safely by ignored. Such is not the case when one considers the electrostatic interactions be-tween nuclear and electronic charge distributions. If one makes a multipole expansion about the center of charge of a nucleus in the molecule, one finds that the interaction energy between the nucleus and the surrounding electronic charge distribution can be expressed as [31]: E = ZeV + y . V V - f- Q:y2V + . . . (2.27) o —e — o o = •= o The f i r s t term on the right i s the characteristic value of the familiar inter-action energy between a nucleus with point charge Ze inside a scalar potential f i e l d , of value V q at the nucleus, arising from a surrounding electronic charge distribution. This term i s a major part of the electronic Hamiltonian and w i l l not appear in any expression for a pure rotational transition frequency. The second term i s the scalar product between the potential gradient V V q of the electronic charge distribution evaluated at the nucleus, and the nuclear elec-t r i c dipole moment y^. It had frequently been stated that the requirements of inversion symmetry eliminate the possible existence of an inherent ele c t r i c nuclear dipole moment [32], While the observation of CP-nonconserving nuclear decay [33] and the apparent measurement of the electric dipole moment of the neutron [34] have invalidated this argument, i t i s s t i l l true that the nuclear electric dipole moment is far too small for the observation of i t s effects in a conventional microwave experiment [35]. The third term on the right of equation 2.27 represents the interaction energy of the nuclear electric quadrupole moment with the electric f i e l d gra--16-dient of the e l e c t r o n i c charge density at the nucleus. I n t e r a c t i o n terms of t h i s type can involve energies of tens of MHz and are u s u a l l y e a s i l y observed i n microwave experiments. The theory of the coupling of nuclear spin and molecular r o t a t i o n through the nuclear quadrupole i n t e r a c t i o n i n asymmetric top molecules was developed by Bragg [36], Only n u c l e i whose spin quantum number, I, i s 1 or greater possess an e l e c t r i c quadrupole moment. Of the n u c l e i considered i n t h i s report, 35 37 only C l and C l , both of spin 3/2, have a quadrupole moment. To f i r s t order i n an uncoupled nuclear s p i n - r i g i d asymmetric rotor representation, the Hamil-tonian d e s c r i b i n g t h i s i n t e r a c t i o n energy i s given by: H = e Q / - ^ \ <3(I-J) 2 + 3/2<W) - I 2 J 2 } ( , HQ e QV,2/ T 2J(2J - 1)1(21 - 1) The matrix element ( — i s evaluated over the r o t a t i o n a l state M T = J and the the e l e c t r i c f i e l d gradient i s taken with respect to the space f i x e d Z a x i s . Following Bragg and Golden [37] we can rewrite t h i s element i n terms of der-i v a t i v e s along the three MFF p r i n c i p a l i n e r t i a l axes, • ^ / g t D W M ) ^ , , * g g ( p g 2 > < 2 ' 2 9 ) where x> the nuclear quadrupole coupling tensor i s defined by ( 2 - 3 0 > Equation 2.29 can be placed i n a form that i s p a r t i c u l a r l y convenient for a l i n e a r l e a s t squares v a r i a t i o n a l f i t of the nuclear quadrupole coupling con-stants to the experimental quadrupole hyperfine s p l i t t i n g s i n an oblate molecule by e l i m i n a t i n g <P 2)> and <P, ^ with equations 2.24 [38]. -17-\ z ^ J (J + 1)(2J + 3) The nuclear quadrupole coupling asymmetry parameter, TJ, i s defined i n the ob-l a t e case by n = Xbb " X a a ( 2 > 3 2 )  X c c The operator i n brackets i n equation 2.28 i s diagonal i n the coupled r e -presentation defined by the t o t a l angular momentum, F_ = 1^  + J . The quantum number F can take the values J+I, J+ I - l , . . | j - l | . In t h i s representation the c h a r a c t e r i s t i c value of the operator i n brackets i s given by 3/4 C(C + 1 ) - 1(1 + 1 ) J ( J + 1) (2.33) where C = F(F + 1) - 1 ( 1 + 1 ) - J ( J + 1). Assembling the two parts of equation 2.28, one a r r i v e s at the following u s e f u l r e s u l t : HQ = 7 ( 7 ^ <3*c> - J ( J + 1 } + { < P c 2 > - W < V } T l / b o ) x c c ( 2 ' 3 4 ) where the function f ( I , J , F ) , Casimir's function, i s given by F/T T v\ = 3/4 C(C + 1) - 1(1 + 1 ) J ( J + 1) f . r u , J , * ; 21(21 - 1)(2J - 1)(2J + 3) U - ^ ; 2.3 The Stark E f f e c t i n Molecules with Nuclear Quadrupole Coupling In the presence of a uniform e l e c t r i c f i e l d , gaseous molecules with an e l e c t r i c dipole moment experience a torque that adds a term equal to the sca l a r product of the e l e c t r i c f i e l d strength and the molecular dipole moment to the Hamiltonian. In the absence of a molecular e l e c t r i c quadrupole i n t e r a c t i o n -18-thls Stark term in the Hamiltonian can be handled readily with f i r s t or second order perturbation theory. However, i f the molecule contains an atom with a nuclear electric quadrupole moment, Stark precession about the electric f i e l d direction tends to uncouple the nuclear spin and the rotational angular momen-tum, forcing a reconsideration of the quadrupole interaction term in the Ham-iltonian. The Stark effect in a molecule without nuclear quadrupole hyperfine inter-actions w i l l be described f i r s t , before considering the more complicated case that arises when quadrupole hyperfine interactions are present. The total Hamiltonian of a molecule in a uniform electric f i e l d E_ directed along the space fixed Z axis and containing no atom with a nuclear quadrupole moment can be written as: H = H + H, + H (2.36) r d S The f i r s t and second terms on the right are the ri g i d rotor and centrifugal distortion terms previously discussed, and the third term represents the Stark Hamiltonian. The summation in equation 2.37 is over the three principal i n e r t i a l axes; u th is the g electric dipole moment component and $ is the direction cosine element linking the Z space fixed axis (defined by the direction of E) and the molecule fixed principal i n e r t i a l axis. The f i r s t order Stark energy of a non-degenerate asymmetric top rotation-al state i s zero. This i s readily shown because none of the elements of $ -19-transform l i k e the t o t a l l y symmetric i r r e d u c i b l e representation under the oper-ations of the point group, and the asymmetric r i g i d r o t o r Hamiltonian i s t o t a l l y symmetric under the T)^ S r o u P [39]. The second order Stark energy i s cal c u l a t e d i n the usual way, and i s given by the following expression [39]: , m 2 2 V ' JK K » M; J'K« K " M <1i_ ( 2 )> T = Eu V K - 1 K 1 K - 1 K 1 ( 2 . K - 1 K 1 K l l K i The prime on the summation i n equation 2.38 in d i c a t e s that the diagonal e l e -ments of |<^ Zg/| a r e omitted from the summation. i s diagonal i n M (the pro-j e c t i o n of J on the space f i x e d Z axis) and connects eigenfunctions d i f f e r i n g i n J by 0 and + 1 . In the l i m i t i n g symmetric top basis set, connects e i -genf unctions d i f f e r i n g i n K by 0 and + 1. The matrix elements of i n the symmetric top representation are w e l l known [40], so i f the asymmetric top eigenfunctions are ca l c u l a t e d using a l i m i t i n g symmetric top basi s set, the c a l c u l a t i o n indicated i n equation 2.38 i s r e a d i l y performed. Second order Stark energies can also be cal c u l a t e d from tables of l i n e strengths for asymmetric rotors [39]. I f one defines a quantity c a l l e d the l i n e strength by: 8 S - J ' = ^ KOPj M-J- M' ( 2 ' 3 9 ) JK_ 1K 1' J K ^ K ^ F,M,M' ^ J K _ ] K ^ M , J KV^K^ the second order Stark energy may be written as 2 2 K ^ K ^ " g=a,b,c 2J + 1 K^K» 8S E°J ~ E J - 1 JK_ 1K 1 J K ^ K ^ -20-M -1K1 -1 K 1 (J + 1) - M -1K1 -1 K 1 + J(J + 1) po o (J + 1)(2J + 3) po vo J ~ T T J+l -1K1 -1 K 1 -1K1 "1 K 1 (2.40) To this point the consideration has assumed that a l l rotational energy levels are well separated. However, i f a near degeneracy exists between the rotational level under consideration and another level that i s connected to the f i r s t by the Stark Hamiltonian, then the perturbational approach converges badly and i t i s necessary to solve a second order secular equation to determine the Stark energy of the state. If J v i s the state of interest and J' , v , i s K-1 K1 K - 1 K 1 the nearby nearly degenerate state, the total energy W of the state of interest is given by [39]: 2W =[{Hr + HS<2V + • K ^ Y * s i i i K y M " <i«r + K ,M - K + H S ( 2 ) i j . „, ,M>2 + 4151 V ] 1 / 2 (2.41) K-1 K1 K - 1 K 1 If the two nearly degenerate states have the same value of J, £ i s given by: 2 2 2 1*1 = K*Oj M-J M' 2 2 y g K * Z B ^ J M « J M' B J K _ 1 K 1 ' M , J K ^ 1 K , 1 , N 4J Z(J + 1 ) Z 8 8 K ^ K ^ ' V j K 1 » M (2.42) where y i s the dipole moment component connecting the two nearly degenerate (2) states and H in equation 2.41 does not include the second order terms con-necting J and J , , . -1K1 K - 1 K 1 The theory of the Stark effect in asymmetric rotors with electric quadru-pole hyperfine structure has been developed by Mizushima [41] following the -21-work of Fano [42] on the l i n e a r rotor and Low and Townes [43] on the symmetric top. The t o t a l Hamiltonian, equation 2.36, now includes the quadrupole i n t e r -a c t i o n term, H^, of equation 2.28. I t was e a r l i e r stated that H^ i s diagonal i n the coupled iFjJ.I.Mp^ representation. However, the Stark term, H^, i s not diagonal i n the coupled representation. At e l e c t r i c f i e l d strengths where the Stark energy i s much larger than the hyperfine energies, I_ and are i n d i v i d -u a l l y strongly coupled to the Z axis defined by the f i e l d , which destroys the u t i l i t y of F as a good quantum l a b e l . In the region of high e l e c t r i c f i e l d strengths i t i s more na t u r a l to con-side r the problem i n the uncoupled | J,Mj)>| I , r e p r e s e n t a t i o n . The matrix elements of H^ i n the uncoupled representation contain diagonal elements as w e l l as elements o f f diagonal by AMj = + 1, AM^ . = - 1 and AM^ . = + 2, AM^ = ^ 2 [44]. Howe and Flygare [45], however, have pointed out that at very high f i e l d s , where H >> H n , elements of H o f f - d i a g o n a l i n the uncoupled repre-ss Q sentation may be neglected to a good f i r s t order approximation, since a l l e l e -ments of H are dwarfed by the very large diagonal elements of H . The hyper-f i n e energies i n the high f i e l d l i m i t are, therefore, given by the diagonal elements of equation 2.28 i n the uncoupled representation, < H \ = E Q / ^ \ ^2\^i ~ ^ + D H 3 M J 2 " J ( J + D( \ O/high f i e l d l i m i t 2/ ^ ' J 2J(2J - 1)1(21 - 1) (2.43) and the Stark energy remains as c a l c u l a t e d for a molecule without nuclear quad-rupole hyperfine i n t e r a c t i o n s . Equation 2.43 predicts a considerable s i m p l i f i c a t i o n of the hyperfine s p l i t t i n g pattern of a r o t a t i o n a l t r a n s i t i o n when the t r a n s i t i o n has been d i s --22-placed by a strong electric f i e l d . If the hyperfine s p l i t t i n g i s due to the presence of one chlorine atom (I = 3/2), substitution of the possible values of into equation 2.43 demonstrates that in the high f i e l d limit there should be only two hyperfine components (corresponding to M^  = + 1/2 and M^. = + 3/2), whose average frequency is the frequency one would have observed in the ab-sence of a hyperfine interaction. Therefore, an extrapolation of the average of the frequency of the second order Stark shifts of the two hyperfine compo-nents in the high f i e l d limit back down to zero f i e l d strength should yield the unsplit transition frequency. This provides a sensitive test of the attain-ment of the high f i e l d uncoupled l i m i t , because the unsplit transition frequen-cies can be accurately determined from an analysis of the zero f i e l d hyperfine s p l i t t i n g . 2.4 The Calculation of Quartic Centrifugal Distortion Constants from Molecular  Structures and Vibrational Force Fields Equation 2.19 serves as the starting point in the development of a theory constructed by Kivelson and Wilson [21] that relates the quartic centrifugal distortion constants and vibrational force f i e l d of a molecule. In the approx-imation of a harmonic force f i e l d and small vibrational amplitudes, equation 2.19 can be brought into the form, c f 1 ) . . W - -1/2 £ ° B e ° / e ° e (2-44) where (f ^) is the inverse of the force constant matrix. I e is the a*"*1 prin-aa cipal moment of inertia evaluated at vibrational equilibrium, [ J ^ ] is the n ag o e th derivative 91 „/9R. evaluated at equilibrium, and R. is the i internal coord-ag l l inate. Equation 2.44 i s completely consistent with classical arguments. In--23-t e r n a l coordinates associated with small force constants (therefore, e a s i l y d i s t o r t e d ) and large values of 8I/3R ( d i s t o r t i o n producing large instantaneous i n e r t i a l moment changes) should provide the la r g e s t contributions to the d i s -t o r t i o n constants. In general the inve r s i o n of equation 2.44 to allow the determination of a molecular force f i e l d from the microwave derived c e n t r i f u g a l d i s t o r t i o n con-stants i s not po s s i b l e , because the number of force constants u s u a l l y exceeds the number of determinable d i s t o r t i o n constants. The only important exceptions are bent, symmetric, triatomic molecules that have four harmonic force constants and four determinable d i s t o r t i o n constants. The number of determinable c e n t r i -f u g a l d i s t o r t i o n constants i s reduced from f i v e to four i n these molecules by r e s t r i c t i o n s imposed by t h e i r p l a n a r i t y . Complete microwave determinations of harmonic force f i e l d s have been attempted f o r SC^ [46], 0^ [47], and F^O [48]. Only i n the l a s t instance d i d the analysis of the microwave spectrum involve s u f f i c i e n t t r a n s i t i o n s to allow an accurate determination of the d i s t o r t i o n constants and harmonic force constants. Here the experimental v i b r a t i o n a l f r e -quencies were predicted to within 4% by the force f i e l d determined from the microwave data. Where a complete microwave force f i e l d determination i s impossible, d i s t o r -t i o n constants can s t i l l be us e f u l i n r e f i n i n g the usual normal coordinate force f i e l d c a l c u l a t i o n . P i e r c e , Di Cianni, and Jackson [48] i n t h e i r study of 7^0 and Kivelson [46] i n h i s study of SO^ performed such c a l c u l a t i o n s by req u i r i n g the force f i e l d to be completely consistent with the observed fun-damental v i b r a t i o n a l frequencies and as consistent with the microwave d i s t o r -t i o n constants as po s s i b l e . A more systematic approach to the combination of v i b r a t i o n a l and microwave data i n force constant c a l c u l a t i o n s has been des-cribed by M i l l s [49]. Recently Kirchhoff [50] has suggested caution, however, -24-pointing out that model errors in the theory of centrifugal distortion can lead to very large uncertainties in derived force constants, much larger than exper-imental uncertainties in the centrifugal distortion constants themselves would suggest. The evaluation of [J^jp] i - n equation 2.44 can be very tedious i f the inter-nal coordinate displacements 6R^ must be chosen to maintain the center of mass and to satisfy Eckart's conditions. Fortunately Kivelson and Wilson [21] have developed a procedure that allows one to pick a set of internal displacements that do not satisfy Eckart's conditions and to correct 61 for any r i g i d ro-Otp tations or translations that may result from this set of displacements. If , (a) (b) (c) (a) (c).t . ^ * * • J . i = ( P ^ , p k l ' p k l ' pk2 ' * * * pkN 1 S a n y S cartesian displacements in the principal i n e r t i a l axis system that produces a unit increment 6R^ in the kfc^ internal coordinate and leaves the other 3N - 7 internal coordinates un-changes, then 31 [jOO] = _ a b = ^{Ira.a.hm.b.p^ + Em.b Am.a.p,0^ }/l e ab Jo 3 R ^ j j j i i i k i j j j i i i k i cc 31 f J(k) aa = { b (b) + c ( c ) } ( 2 > 4 5 ) aa Jo l i I k i l k i 9 R k (a) The set of cartesian increments, p^ a (k varying over the 3N - 6 internal coor-dinates, a over the N atoms, and a over the three principal i n e r t i a l axes), need not satisfy Eckart's condition's. A set of vectors that do satisfy Eckart's conditions can be obtained from the vectors by adding the r i g i d translations and rotations of the whole molecule necessary to keep the MFF axes stationary. A prescription is given by Kivelson and Wilson for the determination of the 3N - 6 ^ vectors. Another and clearer discussion of the calculation and -25-physical significance of these quantities has been presented by Polo [51]. In the notation of Wilson, Decius, and Cross [52] we can express the inter-nal coordinate in terms of an arbitrary set of mass weighted cartesian displacements, <^  = (v^a^, v^b^, v^c^, y /™2 a2' ' " " k/™N°N^t' D ^ fc^e following transformation, 3N Rk = if 1 \ ± \ or \ = \ 4 A ( 2 - 4 6 ) a=l One can define a particular vector by the equation N % = \ ^ a a i ( 2 ' 4 7 ) a=l where is an N x N matrix with elements ( v ^ , • • • along the principal diagonal. Because the particular set of cartesian increments that define were chosen to produce unit change in and leave the other inter-nal coordinates unchanged, we can write 3N Rj = ±l± V°k - 6jk ( 2- 4 8 ) where q°^ i s the (3N - 6) x 3N matrix constructed from the 3N - 6 row vectors. Equation 2.48 demonstrates that is in fact the matrix D ^. This is of more than comceptual interest. It allows for the proper normalization of the vectors. Formulae for computing j p ^ (neglecting the Eckart condition restraints) can be found in appendix A of Polo's paper [51]. -26-2.5 The Coupling of Internal Torsion and Molecular Rotation The hindered internal torsion of a methyl group relative to the frame of the rest of a molecule i s a large amplitude, low frequency motion that very strong-l y couples to the overall rotation of the molecule. Our concern w i l l be the i treatment of the coupling of molecular and internal rotation in molecules with high barriers to internal rotation (molecules in which the separation of torsion-a l energy levels i s large compared with rotational energy separations). Acetal-dehyde i s such a easel Torsional transitions in such molecules typically l i e in the far-infrared region. However, internal rotation permitted by the quan-tum mechanical tunneling mechanism has a strong effect on the rotational spectra of these molecules and allows a determination of the barrier to internal rota-tion from an analysis of the microwave spectrum. A very thorough review of the subject has been given by Lin and Swalen [53]. The approach that w i l l be adopted here i s the so-called principal axis method developed by Wilson [7, 54] and Herschbach [55]. A l l terms-in the Ham-iltonian are expressed i n the principal i n e r t i a l axis system of the molecule. If one assumes that the only significant component in a Fourier analysis of the internal rotational barrier potential function i s the three-fold barrier term V^, the total Hamiltonian can be expressed as [55]: H = AP 2 + BP, 2 + CP 2 + F(X I P /I + XT P./I, + X I P /I ) 2 a b c a a a a b a b b c a c c + Fp 2 + 1/2 V 3 ( l - cos3a) - 2Fp(X I P /I + X.I-P./I. + X I P /I ) (2.49) a a a a b a b b c a c c where a i s the dihedral angle between the methyl top and an a r b i t r a r i l y defined plane in the frame of the rest of the molecule and p i s the momentum conjugate to a. I i s the moment of inertia about the symmetry axis of the methyl top, th X i s , t h e d i r e c t i o n cosine between the top axis and the g p r i n c i p a l i n e r t i a l g 2 2 ax i s , and F i s a constant given by K /{21 (1 - EX I /I )}, a g g a g The f i r s t l i n e on the r i g h t of equation 2.49 i s the r i g i d r o t o r energy with contributions quadratic i n angular momentum that a r i s e from the t o r s i o n a l motion. The second l i n e represents the decoupled t o r s i o n a l Hamiltonian. The t o r -s i o n a l eigenvalues are labeled by two quantum numbers, v and a. Each t o r s i o n a l state labeled by v i s s p l i t i nto two sublevels, a nondegenerate sublevel that transforms l i k e the A i r r e d u c i b l e representation of the point group (a = 0), and a doubly degenerate sublevel that transforms l i k e the E species (a = + 1). The l a s t l i n e i n equation 2.49 i s the expression for the coupling term between i n t e r n a l and o v e r a l l molecular r o t a t i o n . The coupling terms have e l e -ments that are o f f diagonal i n the t o r s i o n a l quantum number v. These elements can be folded i n t o the diagonal t o r s i o n a l blocks by successive a p p l i c a t i o n s of a Van Vleck transformation. I f one neglects the decoupled t o r s i o n a l term, which does not contribute to an expression f o r the frequency of a r o t a t i o n a l t r a n s i -t i o n , the Hamiltonian can be brought i n t o the following form [55]. H = AP 2 + BP 2 + CP 2 + FZW ( n ){ZX I P /I } n (2.50) a b c n v a g g a g g The e f f e c t i v e Hamiltonian i s a power s e r i e s i n r i g i d asymmetric rotor momentum expectation values m u l t i p l i e d by a c o e f f i c i e n t X^I^/I . Rapid convergence i s , therefore, best attained i n a molecule with a molecular frame that i s heavy compared to the methyl group (1^ > 1^). The perturbation c o e f f i c i e n t s , w"^"^» are functions only of a reduced b a r r i e r parameter, s = 4V^/9F, and have been tabulated by Herschbach [55], Hayashi and Pierce [56], and Wollrab [57]. -28-At the dry ice temperature at which microwave spectra are usually observed only the ground torsional level (v = 0) of molecules with a high barrier to in-ternal rotation is appreciably populated. Selection rules forbid transitions between the two torsional sublevels, A and E, so the presence of hindered inter-nal rotation causes the appearance of two manifolds of rotational transitions with weaker satellite transitions originating in the torsionally excited states (v = 1, 2, . . ). The nature of the Stark effect in molecules with an internal torsional degree of freedom provides a convenient handle for discriminating A from E sub-level rotational transitions. Herschbach [55] has shown that the odd order perturbation expansion terms for the nondegenerate A levels are identically zero. Therefore, the Hamiltonian for the A levels can be expanded in a con-vergent even order power series in momentum expectation values. Because the A torsional sublevel Hamiltonian has the same symmetry properties as the rigid asymmetric rotor Hamiltonian (both commute with the point group), both, in the absence of a near degeneracy, share a characteristic second order Stark effect (see section 2.3). The E symmetry sublevels, on the other hand, usually show some first order Stark behavior [53]. The odd order momentum terms in the E sublevel Hamiltonian do not commute with the group, so there are no longer symmetry restrictions forbidding first order Stark.terms. Frequently, however, for very high barriers the odd order E sublevel torsional terms nearly vanish, and E symmetry transitions then also exhibit a second order Stark effect. 2.6 The Determination of Molecular Structures from Spectroscopic Rotational  Constants The analysis of the microwave spectra of a number of isotopic species of a molecule provides a method for the accurate determination of the internuclear -29-distances in the molecule. In the principal inertial axis system of each in-dividual isotopic species, the nuclear coordinates are related to the three principal moments of inertia by the equations: \ = P V b i 2 + 0 I b - j n i ( a ± 2 + c ± 2) I = Em. ( a . 2 + b.2) (2.51) c x x i x and the principal moments of inertia are simply obtained from the spectroscopic rotational constants through the relation I. x B = h/8Tr 2 (2.52) b If one expresses moments of inertia in amu X2 and rotational constants in MHz 2 o2 the conversion factor h/8ir is 505,309.9 +8.0 amu A MHz, following the fundamen-tal constants of Taylor, Parker, and Langenberg [58]. e Assuming the equilibrium moments of inertia, I , of a sufficient number of isotopic species of a molecule are known, determination of the equilibrium or r g structure is easily accomplished. To a very good approximation isotopic substitution does not change the value of the equilibrium internuclear para-meters [59], Each isotopic species, therefore, provides three pieces of data without introducing new unknowns, so in general analysis of N - 2 isotopic species (less i f the molecule contains any symmetry elements) will determine the 3N - 6 equilibrium internal coordinates. Equilibrium moments of inertia are, however, exceptionally difficult to obtain, and one is virtually always forced to use the moments of inertia calcu-lated from the rotational constants of the ground vibrational state and pro-ceed on the assumption that the internuclear parameters related by equations -30-2.51 to these moments of i n e r t i a are i n v a r i a n t to i s o t o p i c s u b s t i t u t i o n . Mole-cular structures calculated to s a t i s f y e f f e c t i v e ground state moments of i n e r -t i a are conventionally c a l l e d e f f e c t i v e ground state structures or r Q s t r u c -tures. U t i l i z a t i o n of ground state i n e r t i a l moments, unfortunately, introduces severe u n c e r t a i n t i e s into the c a l c u l a t e d s t r u c t u r e s . Where s u f f i c i e n t i s o t o p i c data i s a v a i l a b l e to c a l c u l a t e an r structure from two or more d i f f e r e n t sets o of moments of i n e r t i a , i t has been observed that the r e s u l t i n g structures may have v a r i a t i o n s i n internuclear parameters as large as 0.01 X [60]. This a r i s e s because the r Q coordinates are e f f e c t i v e l y given by r o - (2.53) where the brackets i n d i c a t e an average over the ground state v i b r a t i o n a l motion. Isotopic s u b s t i t u t i o n changes the v i b r a t i o n a l mode over which the inverse square of the nuclear p o s i t i o n s are averaged. Therefore, the r ^ coordinates are not i n v a r i a n t to i s o t o p i c s u b s t i t u t i o n , and the r Q structure one c a l c u l a t e s depends on the p a r t i c u l a r group of i s o t o p i c s u b s t i t u t i o n s made. Costain [61] has shown that much of the d i f f i c u l t y that plagues the c a l c u -l a t i o n and the i n t e r p r e t a t i o n of r Q structures can be removed i f one uses Kraitchman's equations [62] to determine the internuclear parameters. If I represents the moments of i n e r t i a of an i s o t o p i c species of a molecule defined as the parent i s o t o p i c species and I', represents the moments of i n e r t i a of the molecule with one atom i s o t o p i c a l l y s ubstituted, Kraitchman's r e l a t i o n for the x-coordinate of the i s o t o p i c a l l y substituted atom, i f i t l i e s i n a symmetry plane (x,y-plane) of an asymmetric top molecule i s I ' - I 1*1 = A y - v ( 1 + ~—~ ) } i n ( 2- 5 4 ) v y y i _ i x y -31-and f o r the x-coordinate of a generally located atom i n an asymmetric top |x| = {-A (I ' - I ) + (I ' - I ) - (I ' - I )] 2u y y z z x x (I ' - I ) - (I * - I ) + (I * - I ) X U + *• 1 2 _^ 2_, 2(1 - I ) x y (I ' - I ) + (I ' - I ) - (I ' - I ) 1 / 9 X [1 + 2 2 2 ~ ~ ] } 1 / 2 (2.55) 2< Tx " V V 7 h e r e u = MAm/ (M + Am) , with M the mass of the parent molecule and Am the change i n mass r e s u l t i n g from the i s o t o p i c s u b s t i t u t i o n . Relations f o r other components of the nuclear coordinates can be obtained by c y c l i c permutation of the axes. S u b s t i t u t i o n or r structures c a l c u l a t e d from Kraitchman's equations have s two primary advantages over r Q structures. I t has been shown that they do i n general l i e c l o s e r to equilibrium molecular structures than do r Q s t r u c t u r e s . They are also much better determined than r Q structures. • Where i t i s po s s i b l e to c a l c u l a t e two or more independent r structures f o r the same molecule, the s v a r i a t i o n between structures has been 10 to 100 times l e s s than the v a r i a t i o n between p o s s i b l e TQ structures [61]. -32-Chapter 3 Experimental Procedures and Equipment 3.1 Preparation of Samples A sample of CH^CDO (97% purity) was very k i n d l y provided by Dr. John L. Wood, Chemistry Department, Imperial College of Science and Technology, London. The sample was used without further p u r i f i c a t i o n . Samples of c h l o r y l f l u o r i d e of n a t u r a l i s o t o p i c abundances were prepared according to the method of Woolf [63] by the r e a c t i o n of bromine t r i f l u o r i d e with potassium chlorate. 6 KC10 o + 10 BrF 6 KBrF. + 2 Br. + 3 0. + 6 C10 oF 3 3 4 2 2 2 The r e a c t i o n vessel was a thick-walled monel metal c y l i n d e r constructed for the purpose by Dr. F. Aubke [6] and k i n d l y lent to us for the course of t h i s study. The cy l i n d e r had a removable l i d with a t e f l o n r i n g vacuum se a l and could be evacuated through a short length of 1/4 inch O.D. monel metal tubing with a brass Hoke 417M2B bellows valve. In a t y p i c a l synthesis 7.8 g of a n a l y t i c a l reagent grade KCIO^ (Mallinckrodt Chemical Co., 0.064 mole) was placed i n s i d e the r e a c t i o n v e s s e l . The assembly was then sealed and eva-cuated on a vacuum l i n e u n t i l the i n t e r n a l pressure f e l l below 5 microns Hg to insure the removal of a l l traces of moisture. 23.4 g of bromine t r i f l u o r i d e (Matheson Co., 0.171 mole) was then d i s t i l l e d under vacuum through a monel metal vacuum system into the r e a c t i o n v e s s e l , which was kept at a temperature of -190°C over a l i q u i d nitrogen bath. The r e a c t i o n v e s s e l was then sealed and allowed to stand at room temperature for 24 hours. At the end of t h i s period oxygen gas was removed by pumping on the c y l i n d e r at -190°C. The reac-t i o n v e s s e l was then removed to the microwave spectrometer where i t served as -33-the sample storage c y l i n d e r . 18 A sample of 0 enriched c h l o r y l f l u o r i d e was prepared by i s o t o p i c oxy-18 gen exchange between a c i d i c 0 enriched water and potassium chlorate [64]. A n a l y t i c a l reagent grade KCIO^ (Mallinckrodt Chemical Co., 0.9816 g) was sealed 18 with two drops of concentrated U^SO^ and a sample of 62.8 atom % 0 enriched water (Bio Rad Laboratories, 1.1319 g) into a thick-walled pyrex tube and heated at 100°C for 36 hours over a water bath b o i l i n g under r e f l u x . The tube was then opened and the supernatant l i q u i d removed with a micropipette. The 18 c r y s t a l l i n e 0 enriched KCIO^ was then suction f i l t e r e d and the f i l t r a t e combined with the water e a r l i e r removed. 0.8638 g of i s o t o p i c a l l y enriched water and 0.8814 g of i s o t o p i c a l l y enriched KCIO^ were recovered. This procedure was repeated three further times, each time performing the exchange i n the water recovered from the previous synthesis and adding two more 18 drops of concentrated H^SO^. The four samples of 0 enriched KCIO^ were then combined (3.8714 g) and r e c r y s t a l l i z e d from 8 ml of hot water to which 10 drops of concentrated ammonia had been added to prevent further exchange. The r e -18 c r y s t a l l i z e d sample of 0 enriched KCIO^ was dri e d i n a vacuum desiccator 18 (3.8132 g). The synthesis of 0 enriched CIO2F was performed with t h i s sam-ple and 10.9 g of BrF^ i n the manner already described. A comparison of the 35 16 35 16 18 r e l a t i v e i n t e n s i t i e s of the C l O^F and C l 0 OF 0^ Q _ 1 ^ Q t r a n s i t i o n s 18 observed with t h i s sample indicated that an approximate 25 atom % 0 e n r i c h -ment was achieved. 3.2 100 kHz Stark Modulated Microwave Spectrometer The microwave spectra of c h l o r y l f l u o r i d e and acetaldehyde were measured i n Stark modulated microwave spectrometers [65] at the U n i v e r s i t y of B r i t i s h -34-Columbia and Harvard U n i v e r s i t y . The two spectrometers d i f f e r e d s l i g h t l y i n d e t a i l , but the operational p r i n c i p l e s of both were the same. A s e r i e s of r e f l e x k l y s trons or backward wave o s c i l l a t o r s were used as the source of micro-wave power. At U.B.C. the 8 - 1 8 GHz s p e c t r a l region was covered with a phase-s t a b i l i z e d Hewlett-Packard 8400B microwave spectroscopy source while OKI 20V10, 24V10A, 30V10, 35V10, and 35V11 r e f l e x k l y s trons were used to cover the 18 - 37 GHz s p e c t r a l region. At Harvard the region from 8 to 40 GHz was covered-with the following s e r i e s of r e f l e x k l y s t r o n s : Varian X-12 and X-13, EMI R9518 and R9521; and OKI 20V10, 24V10A, and 35V10. A l l klystrons were operated i n a free running mode without phase s t a b i l i z a t i o n . Output powers t y p i c a l l y ranged from 1 to 10 m i l l i w a t t s . Frequencies of the r e f l e x k l y s trons were scanned over small s p e c t r a l ranges (maximum scan width was us u a l l y about 30 MHz) by applying the voltage of a saw-tooth ramp generator to the k l y s t r o n r e p e l l e r . The same waveform drove the x-plates of a dual beam o s c i l l o s c o p e on which the s i g n a l was observed. Radiation was detected with a v a r i e t y of c r y s t a l and back diode detectors. At U.B.C. the 8 - 1 2 GHz and 12 - 18 GHz s p e c t r a l regions were covered with Hewlett-Packard H06-P422A and H06-X422A back diode detectors. 1N26 c r y s t a l s completed the coverage from 18 to 37 GHz. Spectral t r a n s i t i o n s were detected by applying a 100 kHz square wave e l e c t r i c f i e l d across the c e l l and applying the detector s i g n a l through a preamplifier to a Princeton Applied Research Model 120 or 121 phase s e n s i t i v e l o c k - i n a m p l i f i e r f o r r . f . detection [66]. Terminated waveguide c e l l s of the type used i n t h i s study are plagued by r e -f l e c t i o n s that can cause severe frequency-dependent power f l u c t u a t i o n s that may appear as spurious s i g n a l s . The a p p l i c a t i o n of a high-frequency square wave e l e c t r i c f i e l d across the c e l l modulates the frequency of s p e c t r a l t r a n s i t i o n s , -35-but leaves spurious signals r e s u l t i n g from r e f l e c t i o n s unmodulated and, there-fore, undetected. High frequency modulation also reduces k l y s t r o n and c r y s -t a l detector noise. When the Stark modulation f i e l d i s zero based, the s i g n a l observed on an o s c i l l o s c o p e appears as the d i f f e r e n c e between the s p e c t r a l ab-sorption at zero f i e l d and the absorption i n the presence of the Stark f i e l d . The Stark modulation f i e l d was generated by applying the output of an I n d u s t r i a l Components Incorporated 100 kHz square wave generator (0 to 2000 v o l t s peak to peak) to a Stark septum constructed of copper or phosphor bronze and held r i g i d l y i n s i d e the 10 foot long copper X-band waveguide c e l l . The septum was oriented p a r a l l e l to the broad waveguide face and i n the middle of the narrow face with two s l o t t e d t e f l o n spacers. The spacers also served to i n s u l a t e the septum from the e l e c t r i c a l l y grounded waveguide. It i s of some importance that the deviation of the septum from the exact center plane of the waveguide be small. A d e v i a t i o n produces d i f f e r e n t e l e c -t r i c f i e l d strengths on the two sides of the septum which w i l l broaden observ-able Stark lobes. A deviation may also induce mechanical v i b r a t i o n s i n the septum at the modulation frequency which can modulate waveguide r e f l e c t i o n s and produce spurious si g n a l s [67]. In the present study three d i f f e r e n t methods were used to measure the f r e -quencies of observed s p e c t r a l l i n e s . A l l , however, were based upon mixing the frequency of the microwave source with a harmonic of a primary o s c i l l a t o r whose frequency i s accurately known or accurately measurable and detecting the r e s u l t -ing beat frequency. I f i n some way one observes a beat frequency of v, when b th mixing the n harmonic of a primary o s c i l l a t o r of frequency with the micro-wave source r a d i a t i o n , one knows that the microwave frequency, v , i s given o by -36-v = nv ± v, (3.1) o p b Therefore, the determination of v requires the measurement of v and v, , and o p b knowledge of n and whether the + or - sign a p p l i e s . The spectrometer at Harvard u t i l i z e d a Polarad Model 1106 s i g n a l gen-erator, continuously tunable from 1.95 to 4.6 GHz, as the reference o s c i l l a t o r . The output frequency of the s i g n a l generator was d i r e c t l y counted with a Hew-lett-Packard 5245L e l e c t r o n i c counter. Observation with the e l e c t r o n i c counter indicated that the s i g n a l generator had a short term s t a b i l i t y of roughly 0.05 MHz over a one minute period. The Polarad fundamental was m u l t i p l i e d and mix-ed i n a c r y s t a l mixer with microwave power sampled with an H-plane tee. The r . f . beat s i g n a l was then detected with a radio receiver and the radio r e c e i v e r output s i g n a l was placed on the y-plates of the second beam of a dual beam o s c i l l o s c o p e . The f i r s t beam displayed the s p e c t r a l s i g n a l from the l o c k - i n a m p l i f i e r . The radio receiver was t y p i c a l l y tuned to a beat frequency of 5 MHz. To measure the frequency of an observed s p e c t r a l l i n e , one tuned the frequency of the reference o s c i l l a t o r u n t i l two markers separated by 10 MHz appeared on the second trace of the o s c i l l o s c o p e . The reference harmonic producing t h i s s i g n a l could be determined by making a rough microwave frequency measurement with a wavemeter. The accurate t r a n s i t i o n frequency was then determined by alignning each marker with the t r a n s i t i o n center by adjusting the reference os-c i l l a t o r frequency. This was repeated twice, scanning the microwave frequency both to lower and higher frequency. Note that the average of the four r e f e r -ence o s c i l l a t o r frequencies determined i n t h i s way m u l t i p l i e d by the harmonic number gave the t r a n s i t i o n frequency d i r e c t l y . It was not necessary to use an accurately c a l i b r a t e d radio receiver to measure the beat frequency. -37-A Micro-Now Instrument Company Model 101C frequency multiplier chain was used as the reference oscillator over the klystron frequency region in the microwave spectrometer at U.B.C. This instrument produces a 5 MHz fundamental and higher harmonics of high long-term frequency s t a b i l i t y . The fundamental frequency was continuously monitored and adjusted to 5.00000 MHz using a Hew-lett-Packard 5246L electronic counter. Output from the frequency multiplier chain was mixed in a crystal mixer with microwave power sampled with a 20 db cross guide directional coupler. Beat frequencies were detected with an accur-ately calibrated Hammarlund Model SP-600 radio receiver. Output from the radio receiver was again placed on the y-plates of the second beam of a dual beam oscilloscope. With this apparatus beat frequency markers were aligned with an observed spectral line by adjusting the radio receiver frequency rather than adjusting the reference oscillator frequency. Once again, determination of the particular reference oscillator harmonic that one observed was made from a rough microwave frequency measurement with a wavemeter. The microwave frequency of the Hewlett-Packard 8400B microwave spectros-copy source was continuously and automatically recorded with a Hewlett-Packard 5246L electronic counter. The 8400B unit was composed of a HP H81-8690A sweep oscillator with HP H81-8694B X-band and H81-8695A P-band r . f . plug-in units to-gether with a HP 8709A synchronizer and a HP 8466A reference o s c i l l a t o r . The microwave sweep oscillator was phase locked to a harmonic of the reference oscillator with the synchronizer. The counter measured the frequency of the reference oscillator, but a modification.allowed direct microwave frequency readout when the correct harmonic lock point was used. The correct lock point was simply chosen by comparing the counter readout with a roughly calibrated scale on the sweep oscil l a t o r . It i s estimated that a l l frequency measurements have an accuracy of 0.1 -38-16 12 32 MHz. As a c a l i b r a t i o n check, the 0-1 t r a n s i t i o n of 0 C S was measured on several occasions at U.B.C. The agreement with the published t r a n s i t i o n f r e -quency [68] was always within 0.05 MHz. 3.3 The Microwave C e l l s and Gas Handling Equipment The microwave c e l l used i n the acetaldehyde study was of conventional de-sign. C e l l dimensions and Stark septum construction have been described i n the previous se c t i o n . The c e l l had a s i n g l e gas i n l e t port wedded to a glass vac-uum manifold. The c e l l windows were constructed from t h i n sheets of mica. Pressures of roughly 10 microns Hg, measured with a thermocouple vacuum gauge, were used during the acetaldehyde study. When accurate frequency mea-surements were attempted, the pressure was lowered u n t i l l o s s of peak l i n e i n -t e n s i t y began to destroy the advantage of further reducing pressure l i n e broad-ening. A l l measurements were made at a temperature of roughly -78°C (dry i c e i n a covered styrofoam trough). There was no evidence of acetaldehyde decom-p o s i t i o n or i s o t o p i c exchange i n s i d e the c e l l ; one sample s u f f i c i n g f o r a day's observation. The high r e a c t i v i t y of c h l o r y l f l u o r i d e considerably complicated the gas handling system necessary f o r the observation of i t s microwave spectrum. C e l l windows were again constructed from t h i n mica sheets. The gas handling system was constructed from 1/4 inch O.D. s t a i n l e s s s t e e l tubing and s t a i n l e s s s t e e l Whitey 1KS4 valves with t e f l o n packing. Chemically r e s i s t a n t v i t o n 0-rings were used at a l l vacuum se a l s . I n i t i a l l y a si n g l e gas i n l e t port was used to p e r i o d i c a l l y f i l l and f l u s h the c e l l with c h l o r y l f l u o r i d e . The c e l l was always cooled with dry i c e to a temperature of approximately -78°C when c h l o r y l f l u o r -ide was introduced. -39-Intense spectra of chlorine dioxide [69] and the occasional weaker spectra of carbonyl fluoride [70] were observed using this system. However, no trans-itions that could be assigned to chloryl fluoride were seen. Chlorine dioxide was apparently produced by the fluorination of the inner surfaces of the c e l l and the gas handling line. On the occasions that i t was necessary to dismantle the equipment, a layer of metal salts was observed on the inner surfaces of a l l components that had been in contact with chloryl fluoride. Carbonyl fluoride apparently arises from the reaction of chloryl fluoride with teflon in the c e l l . Transitions due to this molecule were also observed during a microwave study of dioxygen difluoride by Jackson [7] who suggested that 0CF£ was produced when teflon in his microwave c e l l was attacked by ^2^2* Two modifications of the apparatus were made in a further attempt, suc-cessful this time, to observe the microwave spectrum of chloryl fluoride. A flow system was constructed by adding a gas exit port to the c e l l and placing a stainless steel Nupro series "S" needle valve (0.031 inch o r i f i c e diameter, 1° stem taper) immediately before the gas entry port. Entry and exit ports were at opposite ends of the c e l l . In operation the c e l l was pumped with rotary and o i l diffusion pumps from the exit port with roughly a 1/4 open turn on the Whitey 1KS4 valve at the exit port. The needle valve was then adjusted to minimize pressure line broadening. The chloryl fluoride sample was stored over an excess of bromine trifluo r i d e in the monel metal cylinder in which i t was synthesized. During measurements the cylinder was kept over a dry ice-trichloroethylene bath (at approximately -65°C) and had a pressure head of 0.5 to 1.0 mm Hg. Since i t appeared that the complete elimination of chlorine dioxide with i t s very intense and dense microwave spectrum was impossible, an attempt was -40-also made to eliminate or at the l e a s t discriminate the t r a n s i t i o n s due to t h i s molecule by inhomogeneous Zeeman broadening. Chlorine dioxide i s one of a small number of stable molecules with an odd number of electrons. It i s , therefore, paramagnetic and possesses a large magnetic dipole moment that strongly i n t e r a c t s with external magnetic f i e l d s . C h l o r y l f l u o r i d e and most other molecules have s i n g l e t e l e c t r o n i c ground states and molecular Zeeman e f f e c t s that are unobservably small at magnetic f i e l d strengths that may be e a s i l y obtained i n the laboratory. E i t h e r a s p a t i a l l y inhomogeneous magnetic f i e l d or a magnetic f i e l d that v a r i e s r a p i d l y over the time taken to scan one l i n e width w i l l , therefore, strongly broaden CIO2 t r a n s i t i o n s and leave CIC^F t r a n s i t i o n s unaffected. A solenoid of 20 AWG magnet wire was wound around the length of the c e l l (approximately 12 turns per centimeter). The solenoid was powered by an auto-transformer operating on ordinary 60 Hz house current. At a microwave frequen-cy scan rate of 10 MHz per minute, an autotransformer s e t t i n g of 20 v o l t s r e -duced the peak i n t e n s i t y of most CIC^ s p e c t r a l l i n e s by better than 50%. At slower scan rates i t was p o s s i b l e to make some CK^ t r a n s i t i o n s disappear. This, of course, provided a very rapid and convenient means of d i s t i n g u i s h i n g CIO2 and CIC^F t r a n s i t i o n s . On a few occasions the Zeeman solenoid served to o b l i t e r a t e a CIO2 absorption allowing the measurement of the frequency of a p a r t i a l l y overlapped CIO2F t r a n s i t i o n that would have been unobtainable other-wise. With these two modifications i t was p o s s i b l e to observe and assign the microwave spectrum of c h l o r y l f l u o r i d e . A f t e r a new sample of CIO2F was pre-pared, i t t y p i c a l l y took several days of continuously flowing the sample through the c e l l before the C10O and C10 F spectra were of comparable i n t e n s i t y . -41-However, a f t e r a period of several weeks of use only the strongest CIC^ trans-i t i o n s s t i l l i n t e r f e r e d . 3.4 Double Resonance Modulated Microwave Spectrometer Microwave-microwave double resonance was observed between the 3Q 2~^1 2 and 2^ 2~^1 1 t r a n s i t : i - o n s °f CH^CDO on the double resonance modulated micro-wave spectrometer described by Woods, Ronn, and Wilson [72], A diagram of the hardware components of the spectrometer can be found i n f i g u r e 3.1. K-band i s o l a t o r low pass f i l t e r ^attenuator -OKI 24V11 k l y s t r o n attenuator harmonic /Or mixer — c r y s t a l detector c e l l tuning stubs harmonic mixer high pass f i l t e r ] R-band i s o l a t o r ttenuator OKI 35V10 k l y s t r o n c r y s t a l detector^ high pass f i l t e r -Figure 3.1 Components of Double Resonance Modulated Microwave Spectrometer The 3 Q y^i 2 t r a n s i t i o n w a s pumped with power from an OKI 24V11 r e f l e x k l y s t r o n whose frequency was modulated by supplying a 100 kHz square wave s i g -nal of approximately 13 v o l t s amplitude to the r e p e l l e r . Pump power was pre--42-vented from reaching the crystal detector by placing a 31.357 GHz cutoff high pass f i l t e r between the microwave c e l l and the crystal. Scanning frequency of the pump klystron was performed by manually adjusting the screw that varied the klystron cavity size. Pump frequency was only roughly measured (to within 20 MHz) with a wavemeter. Signal power was provided by an OKI 35V10 reflex klystron and coupled to the c e l l with a 10 db directional coupler. A K-band isolator and a Sage Labor-atories 18M26MA355 low pass broad band f i l t e r (14.5 to 29.5 GHz band pass) served to prevent reflected signal power from entering the pump klystron. A 26.342 GHz cutoff high pass f i l t e r prevented reflected pump power from entering and modulating the output of the signal klystron. The frequency of the signal klystron could be swept over small frequency ranges by applying a sawtooth vol-tage to the klystron repeller. Accurate measurement of the signal frequency was made by the harmonic beat method described in section 3.2. The 2^ 2 ~ ^ i 1 t r a n s i t l o n °f CH^ CDO had been assigned and i t s frequency accurately measured (36,356.99 GHz) in a previous experiment with the Stark mod-ulated spectrometer. The frequency of the signal klystron was tuned to this transition by applying the output of the 100 kHz square wave generator to the Stark septum of the microwave c e l l and observing the transition in the usual way (see section 3.2). The square wave output was then disconnected from the Stark septum and applied through a specially constructed modulation box [72] to the repeller of the pump klystron. The frequency of the pump klystron was then varied through the frequency range in which the 3^ 2 t r a n s i t l o n w a s expected. A double resonance modulated spectrum of the 2^ 2~^1 1~^0 3~21 2^  transition was observed at a pump frequency of 22.90 GHz measured with a wave-meter. The frequency of the bisector of the symmetrical double resonance s i g --43-n a l was i d e n t i c a l to the frequency of the 2. 9 - l , -, t r a n s i t i o n measured p r e v i -ously by Stark modulation. The exact frequency of the 3 n o~2-, 9 t r a n s i t i o n was determined by scanning the frequency range from 22.75 to 23.15 GHz with the Stark modulated spectro-meter. Only one t r a n s i t i o n , at 22,914.78 MHz, was observed. This l i n e was assigned to the A t o r s i o n a l s ublevel, 3^ 2~21 2 t r a n s i t l o n °f CH^CDO. 3.5 Stark Voltage Mixer A Stark voltage mixer designed to f l o a t a 100 kHz square wave AC p o t e n t i a l on a large accurately measured DC bias p o t e n t i a l f o r accurate Stark e f f e c t mea-surements of c h l o r y l f l u o r i d e was constructed a f t e r a design by Muenter [73]. A schematic diagram of the voltage mixer i s given i n f i g u r e 3.2 2 H 0.01 yf 2 KV 100 Kfi 0.01 yf 3 KV DC input AC input to c e l l Figure 3.2 Schematic Diagram of Stark Voltage Mixer - 44 -The purpose of the 100 K r e s i s t o r i n the DC input l i n e was to protect the DC power supply i n the event of arcing i n the Stark c e l l . Under normal oper-ating conditions the c e l l draws no DC current and there i s no voltage drop across t h i s r e s i s t o r . The source of the DC bias p o t e n t i a l was a John Fluke Manufacturing Co. Model 412B DC power supply with an output of 0 to + 2100 v o l t s DC k i n d l y l e n t to us by Dr. A. J . Merer. The power supply has a stated c a l i b r a t i o n accuracy of ± 0.25% and a r e s e t a b i l i t y of ± 0.05%. Because a l l Stark measurements were c a l i b r a t e d against the dipole moment of OCS and were obtained with the same DC power supply, probably the second f i g u r e represents the c o n t r i b u t i o n of bias p o t e n t i a l uncertainty to the uncertainty i n the measured dipole moment of c h l o r -y l f l u o r i d e . Bias p o t e n t i a l uncertainty probably contributes an uncertainty of about 0.1% to the measured quadratic Stark s h i f t s i n OCS and C I O 2 F . The modulation voltage was provided by an I n d u s t r i a l Components Incorpor-ated 100 kHz square wave generator. The peak to peak square wave voltage was measured with a Heathkit 10W-14 o s c i l l o s c o p e . Because the square of the mod-u l a t i o n voltage was four orders of magnitude smaller that the square of the DC bias voltage i n the high f i e l d range where accurate voltage measurements were needed, no attempt was made to accurately c a l i b r a t e the o s c i l l o s c o p e . -45-Chapter 4 The Microwave Spectra of Chloryl Fluoride 4.1 Assignment of the Spectra Infrared and Raman vibrational studies of chloryl fluoride [4, 5] and microwave investigations of the related molecules CIC^ [69] and C1F [74] allow one to make reasonable predictions of the structure and microwave spectra of ClO^F. The molecule should be an oblate asymmetric top with the a_ and c^iner-t i a l axes lying in a reflection plane containing the Cl and F atoms. Bond electric dipole moment considerations suggested that the spectra should have strong c:-type and weaker a-type transitions. Predictions of the microwave spectra of CIC^F in the 8 to 37 GHz region based on the structure assumed by Smith, Begun, and Fletcher [5] indicated that the most abundant isotopic spe-35 16 37 16 cies, Cl C^F and Cl O^F, would have rich Q-branch microwave spectra with a few weak, low J, R-branch transitions. Electric quadrupole hyperfine s p l i t t i n g of rotational transitions provided 35 a handle for the assignment of the observed low J transitions. Both Cl and 37 Cl possess nuclear electric quadrupole moments which s p l i t rotational absorp-tion lines into several hyperfine components. A prediction of the nuclear quadrupole hyperfine patterns was obtained by making the assumption that the diagonal component of the nuclear quadrupole coupling tensor along the c^-iner-t i a l axis has the same value as the nuclear quadrupole coupling constant of the 35 isoelectronic ^10^ i° n [75]. The small value 0.1 was assumed for the nu-clear quadrupole coupling asymmetry parameter, n, because i t was thought that the electron distribution about the chlorine nucleus would not be greatly dis-torted from C symmetry. Calculations indicated that transitions of J > 3 would be s p l i t into four AF = AJ components that would tend to coalesce at -46-higher J . T r a n s i t i o n s i n v o l v i n g J < 3 would be s p l i t i n t o complex m u l t i p l e t s c h a r a c t e r i s t i c of the p a r t i c u l a r t r a n s i t i o n . T h e Vo^ o.o* YrVi'and 2 2 , i ~ \ i t r a n s i t i o n s o f 3 5 c i 1 6 o 2 F w e r e assigned on the basis of the pattern of t h e i r hyperfine components. The assign-ment of these t r a n s i t i o n s y i e l d e d accurate values of the r o t a t i o n a l constants A and B, but provided no information about C. However, i t was then p o s s i b l e to p r e d i c t the approximate frequencies of a s e r i e s of higher J , £-type, Q-branch t r a n s i t i o n s that did weakly depend on C. Assignment and measurement of these t r a n s i t i o n s led through a refinement i n the value of C to the assignment of a s e r i e s of weaker ja-type t r a n s i t i o n s that allowed the value of C to be accurately determined. The assignments were confirmed on the b a s i s of t h e i r observed nuclear quadrupole patterns and consistency with a n o n - r i g i d r o t o r spectrum. 37 16 35 16 18 The assignment of the C l C^F and C l 0 OF spectra was accomplished i n much the same way, aided, of course, by the more accurate r o t a t i o n a l con-stant and nuclear quadrupole coupling constant p r e d i c t i o n s that the work on the more abundant i s o t o p i c species provided. 4.2 Determination of the Rotational Constants and the C e n t r i f u g a l D i s t o r t i o n  Constants from the Microwave Spectra 35 16 37 The r o t a t i o n a l and c e n t r i f u g a l d i s t o r t i o n constants of C l 0 2F, C l -16 35 16 18 0 2F, and C l 0 OF were determined i n an i t e r a t i v e pattern together with the a n a l y s i s of nuclear quadrupole hyperfine e f f e c t s . This was necessary be-cause the quadrupole a n a l y s i s requires a knowledge of the r o t a t i o n a l constants and the r o t a t i o n a l constants are obtained by f i t t i n g to a model Hamiltonian the u n s p l i t t r a n s i t i o n frequencies (the t r a n s i t i o n frequencies i n the hypothe--47-t i c a l l i m i t of zero chlorine nuclear quadrupole moment) obtained from the quad-rupole a n a l y s i s . The following strategy for the separation of d i s t o r t i o n and nuclear quad-rupole hyperfine e f f e c t s was adopted. In the f i r s t instance, the u n s p l i t t r a n s i t i o n frequencies were approximated by a simple average over the frequen-c i e s of observed hyperfine components. A rough determination of the r o t a t i o n a l and q u a r t i c d i s t o r t i o n constants was then obtained by a l e a s t squares v a r i a t i o n -a l f i t of the parameters i n equation 2.25 to the set of t r a n s i t i o n frequency d i f f e r e n c e s , (v , - v ), where v , was the set of approximate "observed"un-obs r obs s p l i t t r a n s i t i o n frequencies, and was a set of r i g i d rotor frequencies c a l c u -l a t e d from a t r i a l set of r o t a t i o n a l constants. The f i r s t order matrix elements i n equation 2.25 and the r i g i d rotor t r a n s i t i o n frequencies were c a l c u l a t e d from the t r i a l r o t a t i o n a l constants by the continued f r a c t i o n method [76]. The r o t a t i o n a l constants r e s u l t i n g from the f i r s t v a r i a t i o n a l f i t were then used i n the quadrupole coupling a n a l y s i s discussed i n the next section to c a l c u l a t e a set of more accurate "observed" u n s p l i t t r a n s i t i o n frequencies. In the second i t e r a t i o n of the r o t a t i o n a l and d i s t o r t i o n constant l e a s t squares a n a l y s i s , the f i r s t order momentum matrix elements and were c a l c u -l a t e d from the new r o t a t i o n a l constants and the v a r i a t i o n a l f i t was made to the new set of "observed" u n s p l i t t r a n s i t i o n frequencies. A t h i r d i t e r a t i o n pro-duced no further movement of the r o t a t i o n a l and d i s t o r t i o n constants and no s i g n i f i c a n t movement of the "observed" u n s p l i t t r a n s i t i o n frequencies. The r o t a t i o n a l and d i s t o r t i o n constant a n a l y s i s included t r a n s i t i o n s i n -v o l v i n g J as large as 35. Before proceeding further i t was necessary to deter-mine whether the f i r s t order, qu a r t i c c e n t r i f u g a l d i s t o r t i o n Hamiltonian of equation 2.25 was s u f f i c i e n t to f i t and p r e d i c t the frequencies of the higher J -48-transitions. This was done by gathering the unsplit transition frequencies 35 16 of Cl O^F into four overlapping groups; a l l transitions involving J between 0 and 10, 0 and 20, 0 and 30, and 0 and 35; and making separate variational f i t s to each group. Linear least squares analyses of the f i r s t order quartic Hamiltonian with these four groups of data (see table 4.1) showed a systematic and sizable variation in A and in the standard deviation of the f i t . This indicates the necessity of carrying equation 2.25 to a higher order of approx-imation. There was very l i t t l e variation in other constants. The rotational constants in particular showed essentially no variation; so i t was fortunately unnecessary to reconsider the quadrupole analysis in the further refinements of the distortion constant determination. Table 4.1 Rotational Constants and Quartic Centrifugal Distortion Constants 35 16 of Cl 0£F from Linear Least Squares Variational Fits to Equation 2.25 J = 0 - 10 J = 0 - 2 0 J = 0 - 3 0 J = 0 - 3 5 No. of transitions 25 45 59 65 Std. dev. of f i t 3 0.08 0.14 0.16 0.24 A (MHz) 9635.92±0.03 9635.91+0.05 9635.9210.06 9635.9210.09 B (MHz) 8275.67±0.03 8275.6710.05 8275.6710.06 8275.6710.09 C (MHz) 5019.24±0.03 5019.2210.05 5019.2310.06 5019.2310.09 A j (IO" 2 MHz) 1.0010.20 0.9310.33 0.9610.38 0.9610.57 A J K (10~ 3 MHz) -4.53±0.14 -4.5410.12 -4.4410.12 -4.2710.17 A (10~ 3 MHz) -1.7810.33 -2.8310.35 -3.1610.32 -3.8410.45 6 • (10~ 3 MHz) 1.076+0.017 1.053+0.009 1.05110.007 1.052+0.011 8V (10 - 3 MHz) -2.35510.012 -2.33110.011 -2.32610.008 -2.32310.013 MHz units -49-Two modifications are necessary to construct a non-rigid rotor Hamilton-ian that i s of a sufficiently high approximation to f i t the high J chloryl fluoride transition frequencies. F i r s t , the Hamiltonian can be expanded to include the sextic distortion constants of equation 2.26 and, secondly, a l l momentum expectation values in the Hamiltonian (equation 2.25 plus equation 2.26) can be calculated to higher than f i r s t order in the r i g i d asymmetric top representation. The inclusion of the sextic distortion terms considerably improved the standard deviation on the rotational constants and the quartic distortion con-stants. However, the set of experimental transition frequencies was i n s u f f i -cient to evaluate the individual sextic constants. The term involving Hj was immediately excluded because a l l transitions involving J above 3 were Q-branch and had no dependence on H^ . Of the remaining six sextic constants only H^ was determined; the others were a l l highly correlated (correlation coefficients above 0.92) and had standard deviations larger than the calculated constants themselves. Four further sextic terms were, therefore, discarded and least squares variational f i t s were made to the Hamiltonian of equation 2.25 with the inclusion of just the terms involving H^ and h^ from equation 2.26. Variational f i t s to this Hamiltonian satisfactorily evaluated a l l constants and lowered the large deviations previously seen between calculated and observed frequencies of high J transitions, but H and particularly h must be regarded only as f i t -ting parameters. Previous work has suggested that contributions to the total Hamiltonian 4 of P distortion terms that are off-diagonal in the ri g i d asymmetric rotor 6 representation are comparable to the f i r s t order P terms [29]. The effect of these off-diagonal terms on the constants in the Hamiltonian was determined by -50-the r e i t e r a t i v e procedure suggested by Pierce, Di Cianni, and Jackson [48] and rec e n t l y adopted by Helminger e t . a l . [29, 77]. For a given set of r o t a t i o n a l and d i s t o r t i o n constants a set of f i r s t order t r a n s i t i o n frequencies, v f £ r g t order' ° a n b e c a ± c u l a t e c ^ from f i r s t order expressions l i k e equations 2.25 and 2.26. The e n t i r e Hamiltonian may also be set i n the symmetric rotor represen-t a t i o n and numerically diagonalized to y i e l d the set of t r a n s i t i o n frequencies, v . The strategy suggested by Pierce e t . a l . i s to determine a set of higher c X a C t order corrections given simply by the d i f f e r e n c e , v ^ - v r . , , sub-& ir J J > exact f i r s t order t r a c t these corrections from the observed t r a n s i t i o n frequencies, and make a f i r s t order l i n e a r l e a s t squares v a r i a t i o n a l f i t to t h i s d i f f e r e n c e . The new r o t a t i o n a l and d i s t o r t i o n constants are used to determine a new set of higher order corrections and the e n t i r e process i s i t e r a t e d u n t i l the constants con-verge. A v a r i a t i o n a l f i t was f i r s t made of the r o t a t i o n a l and quartic d i s t o r t i o n 35 16 constants to the experimental u n s p l i t t r a n s i t i o n frequencies of C l O^F, *^ 7 1 £ ^ S I f i l f t C l 0 2F, and C l 0 OF in v o l v i n g J l e s s than 20. A set of f i r s t order t r a n s i t i o n frequencies was cal c u l a t e d from the r e s u l t i n g r o t a t i o n a l and q u a r t i c d i s t o r t i o n constants using equation 2.25. The Hamiltonian with the same r o t a -t i o n a l and quar t i c d i s t o r t i o n constants was then numerically diagonalized i n an oblate symmetric rotor basis set on an I.B.M. 360 system using double-pre-c i s i o n arithmetic (16 f i g u r e s ) . A l e a s t squares v a r i a t i o n a l f i t of the e n t i r e Hamiltonian, in c l u d i n g the H and h terms, was then performed to the set of K K frequencies, v , - v, . , , (v, . , , = v - v r . , ), of obs higher order higher order exact f i r s t order a l l assigned t r a n s i t i o n s . This procedure was r e i t e r a t e d u n t i l the higher order c o r r e c t i o n had s t a -b i l i z e d . With the second i t e r a t i o n a f t e r the in t r o d u c t i o n of the two s e x t i c -51-terms, the higher order corrections had varied l e s s than 0.005 MHz, and the c a l c u l a t i o n was terminated. 35 16 37 16 The observed u n s p l i t t r a n s i t i o n frequencies of C l ^ a m * 35 16 18 C l 0 OF and t h e i r assignments can be found i n tables 4.2 through 4.4. The calculated r o t a t i o n a l constants and c e n t r i f u g a l d i s t o r t i o n constants are pre-sented i n table 4.5. A l l quoted u n c e r t a i n t i e s are one standard d e v i a t i o n . Q C -I fi Table 4.2 C l 0 2F T r a n s i t i o n Frequencies (MHz) T r a n s i t i o n Observed 3 Calculated* 5 Q u a r t i c 0 S e x t i c 0 Higher o r d e r c Frequency Frequency Term Term Term 17 911.58 17 911.54 -0.04 0.00 0.00 2 -1 1,1 0,1 34 462.66 34 462.69 -0.22 0.00 0.00 3 -2 1,2 2,0 36 043.12 36 043.69 -0.38 0.00 0.00 3 -3 3,1 2,1 8 104.34 8 104.44 -0.22 0.00 0.00 3 -3 3,0 2,2 17 345.72 17 345.74 -0.54 0.00 0.00 4 -4 4,1 43,1 13 220.26 13 220.38 0.09 0.00 0.00 4 -4 2,2 *2,3 16 496.21 16 496.32 -0.89 0.00 0.00 4 -4 44,0 *3,2 19 685.54 19 685.52 -0.57 0.00 0.00 54,2~53,2 8 247.91 8 247.91 -0.53 0.00 0.00 53,2"53,3 13 929.96 13 929.99 -1.64 0.00 0.00 65,2_64,2 13 555.71 13 555.74 -0.19 0.00 0.00 74,4"72,5 34 376.09 34 375.89 -6.53 0.04 0.00 75,2"74,4, 35 991.52 35 991.51 -9.27 0.01 0.00 76,2"75,2 19 759.37 19 759.27 0.74 0.00 0.00 77,1~76,1 30 571.87 30 571.93 4.75 0.00 0.00 85,4~83,5 34 528.73 34 528.56 -9.64 0.03 0.00 -52-Table 4.2 (continued) Transition Observed Calculated Quartic Sextic Higher Order Frequency Frequency Term Term Term 86,3"85,3 12 753.93 12 753.94 -0.05 0.00 0.00 87,1"86,3 31 609.83 31 609.85 -2.42 0.00 0.00 88,1"87,1 35 978.83 35 978.87 7.95 0.00 0.00 88,0"87,2 36 460.43 36 460.32 7.13 0.00 0.00 9 -9 7,2 y6,4 34 869.43 34 869.42 -11.85 0.01 -0.01 1 07,4- 1 06,4 11 155.62 11 155.63 0.90 0.00 0.00 1 07,3- 1 07,4 8 919.24 8 919.24 -10.49 0.01 -0.01 1 08,2- 1 07,4 36 649.83 36 649.92 -10.74 0.01 -0.01 n6,5- n6,6 36 347.82 36 347.97 -22.79 0.10 -0.01 19 521.82 19 521.87 -19^97 0.04 -0.02 1 27.5- 1 27 , 6 32 315.53 32 315.55 -29.71 0.11 -0.02 1 28,5- 1 27,5 9 130.20 9 130.20 2.63 -0.02 0.01 1 310,4~ 1 39,4 33 157.01 33 156.96 7.57 0.01 0.01 1 39,5- 1 38,5 15 296.08 15 296.11 6.31 -0.02 0.01 14 -14 H10,5 9,5 22 915.33 22 915.28 10.56 -0.02 0.02 1 49,5- U9,6 21 305.43 21 305.40 -42.89 0.12 -0.05 1 510,6" 1 59,6 12 544.98 12 545.01 10.89 -0.05 0.03 1 511,5 _ 1 510,5 31 413.90 31 413.99 14.28 -0.01 0.02 1 611,6~ 1 610,6 19 879.40 19 879.35 18.50 -0.07 0.05 1 711,7" 1 710,7 9 749.03 9 749.05 15.41 -0.11 0.06 1 711,6~ 1 711,7 22 541.51 22 541.46 -79.40 0.28 -0.14 1 812,7" 1 811,7 16 420.54 16 420.55 27.96 -0.16 0.10 19 -19 12,7 12,8 30 831.15 30 831.19 -124.55 0.60 -0.30 -53-Table 4.2 (continued) a b c c c Transition Observed Calculated Quartic Sextic Higher Order Frequency .Frequency Term Term Term 2 013,8-•2012,8 12 910.92 12 910.89 36.69 -0.28 0.18 2 014,7' •2°13,7 34 580.30 34 580.28 50.63 -0.19 0.14 2 013,7-•2013,8 23 296.93 23 296.85 -132.64 0.60 -0.31 2 114,8-"2113,8 20 759.07 20 759.16 58.04 -0.39 0.26 2 214,9" "2213,9 9 683.34 9 683.38 42.25 -0.43 0.29 22 15,8 -22 14,8 30 342.29 30 342.27 77.14 -0.45 0.31 22 Z Z14,8 -22 14,9 31 857.74 31 857.80 -199.60 1.19 -0.62 2 215,9-•2214,9 16 534.19 16 534.29 73.38 -0.65 0.46 2 517,9' •2516,9 36 195.41 36 195.25 131.04 -0.94 0.60 2 516,9--25 16,10 32 400.92 32 401.02 -300.90 2.19 -1.13 2617,10-'2616,10 20 630.48 20 630.50 131.18 -1.34 1.00 2717,11-•2716,11 9 190.01 9 190.03 84.69 -1.20 0.95 27 18,10 •2717,10 30 816.75 30 816.81 176.26 -1.66 1.15 2818,10" "2818,11 32 503.93 32 503.91 -431.46 3.76 -1.85 29 19,10 -2919,11 23 228.55 23 228.50 -416.54 3.51 -1.29 3019,12-•3018,12 11 828.13 11 828.14 150.34 -2.35 2.06 3020,11--3019,11 36 521.02 36 521.08 274.24 -3.05 2.05 31 20,12 -31 J 19,12 19 783.62 19 783.54 242.40 -3.50 2.99 31 20,11 -31 J 20,12 32 209.05 32 209.09 -593.76 6.12 -2.77 32 20,13 -32 19,13 8 455.06 8 455.06 140.98 -2.68 2.47 32 21,12 -32 20,12 30 266.08 30 266.11 335.05 -4.58 3.50 34 22,12 -34 22,13 31 559.80 31 559.76 -789.05 9.52 -3.75 35 23,13 -35 22,13 35 806.38 35 806.34 493.88 -7.75 5.81 -54-Table 4.3 C l O F T r a n s i t i o n Frequencies (MHz) 3. b c c c T r a n s i t i o n Observed Calculated Quartic Sextic Higher Order Frequency Frequency Term Term Term 1i,o"°o,o 17 837.54 17 837.54 -0.05 0.00 0.00 2 -1 1,1 0,1 34 315.49 34 315.49 -0.34 0.00 0.00 2 -1 2,1 37 034.05 37 034.05 -0.48 0.00 0.00 4 -4 2,2 H2,3 16 313.44 16 313.52 -0.89 0.00 0.00 54,2"53,2 8 274.80 8 274.97 -0.55 0.00 0.00 65,2"64,2 13 584.03 13 584.07 -0.22 0.00 0.00 76,2~75,2 19 776.83 19 776.94 0.68 0.00 0.00 86,3"85,3 12 835.30 12 835.27 -0.16 0.00 0.00 86,2"85,4 34 352.12 34 352.12 -11.03 0.02 0.00 87,1~86,3 31 457.38 31 457.39 -2.31 0.00 0.00 9 -9 8,2 *7,2 32 673.48 32 673.44 4.19 0.00 0.00 107,4-106,4 11 288.50 11 288.46 0.69 0.00 0.00 107,3-107,4 8 687.29 8 687.30 -10.10 0.01 -0.01 108,2-107,4 36 431.45 36 431.40 -10.45 0.02 -0.01 17 798.08 17 798.03 2.53 0.00 0.01 119,3~118,3 33 635.21 33 635.11 4.38 0.01 0.00 128,5-127,5 9 301.02 9 301.00 2.33 -0.01 0.01 129,4"128,4 25 335.56 25 335.76 4.80 0.01 0.01 139,5-138,5 15 519.48 15 519.43 5.74 -0.01 0.01 13 -13 iJ10,4 J9,4 33 280.23 33 280.21 6.85 0.02 0.01 1410,5-149,5 23 165.41 23 165.30 9.65 -0.01 0.02 159,6-159,7 34 844.34 34 844.21 -59.16 0.30 -0.09 1510,6-159,6 12 815.90 12 815.88 10.17 -0.05 0.03 -55-Table 4.3 (continued) 3. b C C C Transition Observed Calculated Quartic Sextic Higher Order Frequency Frequency Term Term Term 1 611,6" 1 610,6 20 213.43 20 213.38 17.22 -0.05 0.05 1 610,6- 1 610,7 28 602.50 28 602.42 -69.65 0.30 -0.12 1 711,7- 1 710,7 10 038.77 10 038.75 14.68 -0.10 0.06 1 712,6~ 1 711,6 28 924.95 28 924.96 23.61 -0.04 0.06 1 812,7" 1 811,7 16 814.18 16 814.13 26.47 -0.13 0.10 2 013,8- 2°12,8 13 328.29 13 328.28 35.28 -0.26 0.18 2 014,7- 2°13,7 35 056.68 35 056.81 46.92 -0.12 0.14 21 -21 14,8 13,8 21 296.66 21 296.64 55.22 -0.33 0.26 22 -22 14,9 13,9 10 085.87 10 085.87 41.27 -0.41 0.28 22 -22 Z Z14,8 14,9 30 865.37 30 865.42 -192.89 1.24 -0.60 23 -23 J15,9 J14,9 17 103.90 17 103.90 70.84 -0.59 0.45 25 -25 16,9 "16,10 31 241.72 31 241.86 -289.69 2.23 -1.09 25 -25 ^16,10 15,10 13 141.26 13 141.36 81.32 -0.89 0.69 25 -25 "17,8 J17,9 9 561.51 9 561.58 -153.50 0.77 -0.12 2 617,10" 2 616,10 21 375.66 21 375.64 126.77 -1.21 0.98 27 -27 17,11 16,11 9 687.07 9 687.08 • 84.24 -1.19 0.94 27 -27 18,10 17,10 31 696.08 31 695.98 167.91 -1.42 1.11 18,10 18,11 31 178.66 31 178.81 -413.83 3.76 -1.78 2 8 1 8 , l l " 2 8 1 7 , l l 16 679.72 16 679.80 144.42 -1.78 1.49 29 -29 19,10 19,11 22 060.19 22 060.18 -395.13 3.38 -1.24 30 -30 J 19,12 JU18,12 12 495.49 12 495.50 149.75 -2.31 2.03 31 -31 20,12 19,12 20 720.99 20 721.03 237.68 -3.31 2.90 32 -32 20,13 19,13 9 022.36 9 022.38 142.56 -2.72 2.47 -56-Table 4.3 (continued) 3 b c c c Transition Observed Calculated Quartic Sextic Higher Order Frequency Frequency Term Term Term 32 21,12 •32 20,12 31 422.82 31 422. 97 323.18 -4 .12 3.36 32 21,11 •32 21,12 21 317.01 21 316. 86 -524.79 5 .29 -1.48 33 21,13 -33 20,13 15 778.07 15 778. 11 247.78 -4 .24 3.99 34 22,13 '3421,13 25 280.01 25 279. 79 368.62 -5 .80 5.19 Table 4.4 Cl 0 OF Transition Frequencies (MHz) Transition Observed Calculated Quartic Sextic Higher Order Frequency Frequency Term Term Term 11,0 °0,0 17 279.14 17 279.14 -0.09 0.00 0.00 2 -1 1,1 0,1 33 480.62 33 480.62 -0.65 0.00 0.00 4 -4 4,1 *3,1 10 564.74 10 564.88 0.17 0.00 0.00 55,1"54,1 15 373.40 15 373.37 0.80 0.00 0.00 65,2 _ 64,2 9 940.43 9 940.43 0.64 0.00 0.00 76,2 _ 75,2 14 897.85 14 897.79 1.72 0.00 0.00 75,2 - 75,3 9 531.19 9 531.19 -4.33 0.00 0.00 87,2"86,2 20 433.37 20 433.36 3.25 0.00 0.00 88,1"87,1 30 385.05 30 385.18 5.00 0.00 0.00 9 -9 6,3 6,4 16 020.81 16 020.78 -11.47 0.02 0.00 1 07,3- 1 07,4 12 368.06 12 367.99 -14.15 0.01 0.00 1 09,2- 1 08,2 31 670.00 31 669.86 6.70 0.00 0.00 U8,4- n7,4 10 617.29 10 617.23 8.02 0.01 0.00 8 822.18 8 822.19 -15.92 0.01 0.00 -57-Table 4.4 (continued) 3. b e c c T r a n s i t i o n Observed Calculated Quartic Sextic Higher Order Frequency Frequency Term Term Term 129,4-128,4 16 199.51 16 199.52 13.15 0.02 0.00 128,4-128,5 19 555.56 19 555.43 -29.50 0.05 -0.01 13 -13 J10,4 9,4 22 667.55 22 667.49 18.70 0.03 0.00 139,4-139,5 15 096.41 15 096.35 -34.24 0.04 -0.01 1410,5-149,5 12 839.67 12 839.72 21.31 0.02 0.02 1410,4"1410,5 10 818.56 10 818.59 -36.51 0.03 -0.01 1511,5~1510,5 19 117.54 19 117.57 31.53 0.04 0.02 1510,5~1510,6 22 956.26 22 956.18 -62.10 0.14 -0.03 1611,6"1610,6 9 376.48 9 376.51 28.70 0.01 0.05 1712,6~1711,6 15 002.09 15 002.08 45.77 0.04 0.06 1 712,5 _ 1 712,6 12 769.59 12 769.65 -71.69 0.07 0.01 1813,6"1812,6 21 947.01 21 946.91 63.74 0.09 0.05 1813,5'1813,6 8 500.49 8 500.58 -67.10 . 0.03 0.07 19 -19 *13,7 12,7 10 909.73 10 909.77 56.73 0.01 0.15 2014,7-2013,7 17 121.79 17 121.83 85.95 0.07 0.17 2014,6-2°14,7 14 678.19 14 678.22 -126.67 0.15 0.07 21 -21 14,7 14,8 29 441.70 29 441.73 -194.44 0.60 -0.18 21. _ fi-21-_ _ 15,6 15,7 9 843.15 9 843.24 -116.44 0.07 0.20 22 -22 15,8 14,8 12 430.03 12 430.10 100.64 0.01 0.38 22 -22 15,7 15,8 22 813.49 22 813.56 -208.65 0.46 -0.04 23 -23 16,8 °15,8 19 213.11 19 213.07 147.08 0.11 0.42 23 -23 16,7 16,8 16 543.84 16 543.95 -207.35 0.30 0.21 2 4 1 f i q~24 16,9 1 5 > 9 8 407.58 8 407.64 102.21 -0.08 0.65 24 -24 17,8 16,8 27 430.59 27 430.69 191.33 0.29 0.32 Table 4.4 (continued) 3. b c c c Transition Observed Calculated Quartic Sextic Higher Order Frequency Frequency Term Term Term 2 417,7- 2 417,8 11 162.68 11 162.77 -188.21 0.15 0.52 2 517,9- 2 516,9 13 945.57 13 945.58 165.21 -0.01 0.88 2 618,9 _ 2 617,9 21 288.04 21 288.14 235.04 0.16 0.92 27 -27 18,10 17,10 9 458.54 9 458.56 162.65 -0.17 1.42 27 -27 19,8 'l9,9 12 454.72 12 454.75 -288.06 0.30 1.17 2 819,10~ 2 818,10 15 464.00 15 464.12 255.70 -0.07 1.83 2 819,9 _ 2 819,10 27 617.80 27 617.79 -485.41 1.44 0.10 29 -29 20,10 19,10 23 358.56 23 358.45 356.26 0.20 1.85 30 -30 J U20,11 J U19,11 10 522.71 10 522.78 245.75 -0.32 2.85 3 021,9- 3°21,10 13 714.06 13 714.07 -422.20 0.56 2.40 31 -31 21,11 J i 2 0 , l l 16 993.70 16 993.73 377.91 -0.17 3.56 31 -31 22,9 22,10 8 731.93 8 731.83 -343.39 0.20 3.30 32 -32 J Z22,11 J ^ 2 1 , l l 25 435.12 25 435.06 517.80 0.22 3.49 32 -32 22,10 22,11 21 851.68 21 851.64 -672.37 1.66 2.41 33 -33 22,12 2 ,12 11 605.95 11 605.78 356.31 -0.56 5.35 33 -33 23,10 23,11 14 935.06 14 935.00 -597.45 0.97 4.58 Hypothetical unsplit frequency with hyperfine structure removed. Frequency calculated using the rotational constants and centrifugal distortion constants in table 4.5. Quartic and sextic terms are calculated f i r s t order contributions of the quartic and sextic distortion terms to the transition frequency. Higher order term i s the contribution of terms off-diagonal in the rigid asymmetric rotor representation. Table 4.5 Rotational Constants and C e n t r i f u g a l D i s t o r t i o n Constants of C h l o r y l F l u o r i d e 3 3 5 C 1 1 6 0 2 F 3 7 C 1 1 6 0 2 F 3 5 C l 1 6 o " o F No. of t r a n s i t i o n s 62 52 54 Std. dev. of f i t (MHz) 0.07 0.09 0.07 A (MHz) 9635.91 + 0.03 9598.47 + 0.06 9178.21 + 0.05 B (MHz) 8275.66 + 0.03 8239.13 + 0.06 8101.02 +0.05 C (MHz) 5019.22 + 0.03 5016.16 + 0.06 4843.20 + 0.05 A j (10~ 2 MHz) 0.92 + 0.18 1.35 + 0.79 2.23 + 0.65 A J R (IO" 3 MHz) -4.46 + 0.06 -3.92 + 0.11 -9.26 + 0.09 A R (10~ 3 MHz) -3.08 + 0.14 -4.09 + 0.28 0.68 + 0.27 6j (10~ 3 MHz) 1.060 +0.004 1.050 + 0.008 0.876 + 0.006 6 K (IO" 2 MHz) -2.343 + 0.003 -2.335 + 0.008 -1.486 + 0.007 ^ (IO" 6 MHz) -3.14 + 0.35 -3.83 + 0.70 -6.14 + 0.99 h_ (IO" 7 MHz) K. -1.88 + 1.11 -4.61.+ 2.19 -13.53 + 2.43 Quoted un c e r t a i n t i e s are one standard deviation. 4.3 C a l c u l a t i o n of the Ce n t r i f u g a l D i s t o r t i o n Constants of C h l o r y l Fluoride  from the V i b r a t i o n a l Force F i e l d The i n f r a r e d and Raman spectra of c h l o r y l f l u o r i d e have been extensively investigated by Smith, Begun, and Fletcher [5]. Smith et^.al, (s, B, and F) were unfortunately handicapped by an incomplete knowledge of the molecular structure of C10 2F, but, nevertheless, completed a normal coordinate analysis on the basis of a c a r e f u l l y reasoned assumed stru c t u r e . The s t r u c t u r a l para-meters assumed by S, B, and F are presented together with those reported i n -60-in this work (see chapter 6) in table 4.6. The agreement between the two structures is approximate, but sufficient to put some interest in a comparison of the experimental distortion constants and constants that may be calculated from the S, B, and F force f i e l d . Table 4.6 Structural Parameters of Chloryl Fluoride this work S, B, and F r(Cl-F) (X) 1.697 1.65 r(Cl-O) (X) 1.418 1.46 Z(o-ci-o) 115.23° 108° Z(F-Cl-0) 101.72° 108° The force f i e l d of chloryl fluoride has also been calculated by Robinson, Lavery, and Weller (R, L, and W) [78] using the S, B, and F vibrational data and assumed structure. The calculation of R, L, and W was based upon an approx-imate method of s t l u t i o n of the normal coordinate problem developed by Herranz and Castano [79]. Recently, however, the theoretical j u s t i f i c a t i o n of this approximation technique has come under severe criticism [80]. The valence force constants determined by S, B, and F and by R, L, and W can be found in table 4.7. The set of internal coordinates adopted are defined in figure 4.1. The theory developed by Kivelson and Wilson (see section 2.4) allows one to test the consistency of the vibrational and microwave data. Watson's set of five quartic distortion constants were calculated using equations 2.44 and 35 16 2.23 for the Cl O^F isotopic species from the force constants reported by S, B, and F and by R, L, and W. The £. vectors defining the internal coord--61-Cl CD 0<3> Figure 4.1 Internal Coordinates of Chloryl Fluoride Table 4.7 Valence Force Constants of Chloryl Fluoride' S, B, and F R, L, and W f r 9.07 10.08 fR 2.53 3.34 f /Rr a 0.59 0.62 1.06 1.09 0.00 0.62 f rr -0.12 -0.43 0.38 0.84 -0.10 0.89 ra 0.10 -0.50 fRS / r 0.00 -0.13 0.00 0.37 f /Rr aa 0.13 0.04 f a 3 / r v ^ r - 0.14 0.12 Force constants in units of mdyn/X. -62-b f i s the stretch-bend interaction constant where the retching bond forms one side of the bending angle, and f , i s the interaction constant where the stretching ret bond does not form a side of the bending angle. inates were determined after the method of Polo [51]. There are an i n f i n i t e number of ways of choosing the set of 3N - 6 vectors, differing by a continuous range of resulting r i g i d translations and rotations of the whole molecule. For convenience bond stretches were chosen to involve only motion of the atom bonded to chlorine and bond bends only mo-tion of one of the two atoms bonded to chlorine that define the angle in ques-tion. The set of six internal coordinates defined in figure 4.1 were adopted. (\) = (\> R2, . . R g) = (R, r x , r 2 , a±t a2, B) It i s convenient to rearrange the 3N elements of into a column vector over the N atoms in the molecule. The elements of this vector are themselves the vectorial displacements defining in the principal i n e r t i a l axis system of the N atoms in the molecule. If one numbers the atoms in C102F as done in parentheses in figure 4.1 and defines the following quantities, t i l p_ka - the vectorial displacement of the a atom defining p_^. n - „(<*) n ( Y ) Hka " pka ' pka ' Pka ' e,. - unit vector from atom i to atom i . a possible set of vectors i s given by [51]: *L2 = % 2 fi-la = °' a * 2 £-23 = % 3 f-2a = °» a * 3 -^34 = % 4 fi-3a = °' 3 ^ 4 -63-^43 £•52 % 4 s i n o 1 l r 1 l £ 1 3 « 1 4 ( £ 1 3 x £ 1 2 ) - £ 1 4 s i n a 2 l R | e 1 2 x e 1 3 (£ 1 2 x£i4>-£i3 sine|r 2|£ 1 4xe 1 2 ( £ . 1 4 ^ 1 3 ) . G 1 2 £ ^ a = 0, a j 3 £ 5 a = 0, a t 2 H a = 0, a * 4 The elements of determined from the structure of chloryl fluoride re-ported in table 6.4 and the above relations are presented in figure 4.2. Figure 4.2 Elements of the Matrix (P^)' R Cl F 0 0 /(0, 0, 0) (-0.963, 0,-0.269) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0.329, 0.844, -0.423)(0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0.329, -0.844, -0.423) (0, 0, 0) (0, 0, 0) (1.184, 0, 0.922) (0, 0, 0) (0, 0, 0) (-0.451, 0.984, 1.615.) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (-0.348, -0.760, 1.246)J 35 16 Components are tabulated in the Cl 0 2F principal i n e r t i a l axis system, (a, b, c). The calculation of the five quartic centrifugal distortion constants of 35 16 Cl 0 2F was repeated with three sets of vibrational force constants; the en-t i r e sets reported by S, B, and F and by R, L, and W, and also a set composed just of the S, B, and F diagonal elements. The calculated distortion constants together with the experimental constants derived from the microwave investiga-tion are presented in table 4.8. The data in columns 2 and 3 of table 4.8 provides some confirmation both -64-Table 4.8 Quartic C e n t r i f u g a l D i s t o r t i o n Constants Calculated from the V i b r a t i o n a l Force F i e l d of C h l o r y l F l u o r i d e Experimental I Calculated^ II III A J ( I O - 2 MHz) 0.92 0.846 0.628 0.824 V (10~3 MHz) -4.46 -2.626 0.009 -6.634 \ ( IO" 3 MHz) -3.08 -4.025 -5.129 0.441 ( IO" 3 MHz) 1.060 1.380 0.341 1.150 6 K (1(T2 MHz) -2.343 -2.692 -2.559 -1.366 Constants from column 2 of table 4.3. Calculated from the f u l l force f i e l d reported by S, B, and and F ( I ) , R, L, and W ( I I ) , and the S, B, and F diagonal elements ( I I I ). of the d i s t o r t i o n constant determination reported i n the previous s e c t i o n and of the force constant analysis reported by S, B, and F. Good agreement can-not be expected because the structure assumed by S, B, and F was inaccurate. The worst disagreement between the microwave derived constants and the constants ca l c u l a t e d from the complete S, B, and F force f i e l d i s 70% and the average percentage disagreement i s 31%. The good agreement f or A^ was encouraging because t h i s constant was the l e a s t accurately determined i n the microwave an-a l y s i s . The agreement between columns 2 and' 4 i n table 4.8 i s much l e s s s a t i s f a c -tory. The constants A T and 6 T i n p a r t i c u l a r d i f f e r by large factors from the experimental microwave values. This i n d i c a t i o n of the inaccuracy of the R, L, and W force constant determination i s of some s i g n i f i c a n c e . The value of the Cl-F p r i n c i p a l s t r e t c h i n g force constant i n C10„F reported by S, B, and F i s -65-2.53 mdyn/8. This i s the lowest Cl-F stretching force constant that has yet been reported (see table 6.5) and is considerably lower than the value found in C1F i t s e l f , 4.56 mdyn/8 [78]. Until the present study, this has been the principal evidence suggesting an unusually long and weak Cl-F bond in ClO^F. R, L, and W have calculated a significantly larger stretching constant, 3.34 mdyn/X, and argue that the force constant does not appear to be exceptionally small for a Cl-F bond. The present result i s far more consistent with the S, B, and F force f i e l d and does not support the argument of R, L, and W. The effect of the off-diagonal elements in the chloryl fluoride force f i e l d on the centrifugal distortion constants was tested in the calculation reported in column 5 of table 4.8. It i s seen that neglect of the interaction constants generally worsens the agreement with the experimental distortion con-stants and has a particularly extreme effect on the calculated values of A J K. and A^. It was the values of these two constants that the f u l l S, B, and F force f i e l d was least successful in predicting. This suggests that the exper-imental distortion constants could be effectively used to refine the calcula-tion of the interaction force constants. A similar calculation was performed on vinyl chloride by Gerry [81]. In this instance omission of the off-diagonal force constants worsened the agreement with the observed microwave constants, but not nearly to the extent seen here. 4.4 Determination and Discussion of the Nuclear Quadrupole Coupling Constants  of Chloryl Fluoride The procedure used in the analysis for the chlorine nuclear quadrupole coupling constants of chloryl fluoride was to: (1) calculate the the oblate 2 Wang reduced energy, W(b ), and the f i r s t order expectation values of P o c using the rotational constants yielded by the distortion analysis discussed -66-in section 4.2, (2) use these calculated quantities to determine the c o e f f i -cients of n and Y i n equation 2.34, (3) predict the hyperfine pattern using cc the guessed coupling constants given i n section 4.1, (4) make a tentative assignment of the F quantum number of the upper and lower states of the observed hyperfine components, and f i n a l l y (5) make a linear least squares variational f i t of X c c and n to the frequencies of the observed hyperfine components. Be-cause the quadrupole analysis yielded "observed" unsplit transition frequencies upon which the analysis of the rotational constants and calculation of W(bQ) and ^ rested, i t was necessary to iterate this calculation u n t i l there was no further movement in the value of the unsplit transition frequencies. The iterative procedure i s discussed in greater detail in section 4.2. The frequencies of transitions whose hyperfine structure was resolved can be found in tables 4.9 through 4.11. The calculated nuclear quadrupole coupling constants are reported in table 4.12. Table 4.9 Nuclear Quadrupole Hyperfine Components of Resolved 3 5 C 1 1 6 0 2 F Transitions 3 Transition p» F" Observed ^ Frequency Quadrupole Observed Correction Calculated •"-l.o'Vo 1/2--3/2 17 898.57 -13. 00 -12.96 5/2--3/2 17 908.99 -2. 58 -2.59 3/2--3/2 17 921.98 10. 41 10.36 2 -1 1,1 0,1 1/2--1/2 34 449.53 -13. 13 -12.96 3/2--1/2 34 453.98 -8. 68 -8.69 7/2--5/2 34 459.85 -2. 81 -2.96 5/2--5/2 34 463.84 1. 18 1.31 -67-Table 4.9 (continued) Transition Observed j. Frequency Quadrupole Correction Observed Calculated 3 -3 3,1 2,1 3 -3 3,0 2,2 4 -4 4,1 *3,1 4 -4 2,2 2,3 4 -4 44,0 *3,2 54,2 53,2 3/2-3/2 34 469.58 6.92 6.95 5/2-3/2 34 472.82 10.16 10.00 3/2-3/2 8 100.77 -3.58 -3.53 9/2-9/2 8 102.92 -1.43 -1.47 5/2-5/2 8 105.17 0.82 0.88 7/2-7/2 8 107.35 3.00 2.95 3/2-3/2 17 334.92 -10.80 -10.76 9/2-9/2 17 341.25 -4.47 -4.48 5/2-5/2 17 348.42 2.70 2.69 7/2-7/2 17 354.72 9.00 8.96 5/2-5/2 13 217.13 -3.13 -3.15 11/2-11/2 13 218.64 -1.62 -1.61 7/2-7/2 13 221.50 1.24 1.26 9/2-9/2 13 223.10 2.84 2.81 5/2-5/2 16 489.83 -6.48 -6.43 11/2-11/2 16 493.03 -3.28 -3.27 7/2-7/2 16 498.88 2.57 2.57 9/2-9/2 16 502.09 5.78 5.73 5/2-5/2 19 679.38 -6.16 -6.16 11/2-11/2 19 682.39 -3.15 -3.14 7/2-7/2 19 688.00 2.46 2.46 9/2-9/2 19 691.06 5.52 5.49 7/2-7/2 8 247.07 -0.84 -0.84 -68-Table 4.9 (continued) m . . Observed , Quadrupole Correction Transition F F b * n , , . ,c Frequency Observed Calculated 53,2 53,3 65,2 _ 64,2 77,1"76,1 75,2"74,4 74,4 _ 72,5 76,2 75,2 13/2-13/2 8 247.36 -0.55 -0.51 9/2-9/2 8 248.37 0.46 0.44 11/2-11/2 8 248.70 0.79 0.82 7/2-7/2 13 926.32 -3.64 -3.65 13/2-13/2 13 927.86 -2.10 -2.11 9/2-9/2 13 931.76 1.80 1.83 11/2-11/2 13 933.36 3.40 3.37 9/2-9/2 13 554.64 -1.08 -1.09 15/2-15/2 13 555.00 -0.72 -0.69 11/2-11/2 13 556.38 0.66 0.62 13/2-13/2 13 556.73 1.01 1.03 11/2-11/2 30 569.43 -2.44 -2.51 17/2-17/2 30 570.14 -1.73 -1.68 13/2-13/2 30 573.49 1.62 1.57 15/2-15/2 30 574.20 2.33 2.40 11/2-11/2 35 987.31 -4.21 -4.21 17/2-17/2 35 988.69 -2.83 -2.82 13/2-13/2 35 994.15 2.63 2.63 15/2-15/2 35 995.58 4.06 4.02 11/2-11/2 34 372.33 -3.76 -3.77 17/2-17/2 34 373.65 -2.44 -2.53 13/2-13/2 34 378.42 2.33 2.36 15/2-15/2 34 379.64 3.54 3.61 11/2-11/2" 17/2-17/2 19 758.37 -1.00 -1.01 -69-Table 4.9 (continued) T v a « e - n - i « T , T?' v" Observed , Quadrupole Correction T r a n s i t i o n £ £ _, D „ » -i ._ j c Frequency Observed Calculated 13/2-13/2* 15/2-15/2 19 760.37 1.00 1.01 88,r87,i 13/2-13/2 35 976.63 -2.19 -2.29 19/2-19/2 35 977.12 -1.70 -1.61 15/2-15/2 35 980.42 1.60 1.53 17/2-17/2 35 980.97 2.15 2.21 87,r86,3 13/2-13/2 31 607.75 -2.09 -2.18 19/2-19/2 31 608.27 -1.57 -1.53 15/2-15/2 31 611.33 1.49 1.45 17/2-17/2 31 611.85 2.01 2.10 85,4_83,5 13/2-13/2 34 525.87 -2.86 -2.83 19/2-19/2 34 526.78 -1.95 -1.98 15/2-15/2 34 530.65 1.92 1.88 17/2-17/2 34 531.44 2.71 2.73 86,3"85,3 13/2-13/2' 19/2-19/2 12 753.62 -0.31 -0.31 15/2-15/2' 17/2-17/2 12 754.23 0.30 0.31 88,0"87,2 13/2-13/2' 19/2-19/2 36 457.87 -2.56 -1.96 15/2-15/2 17/2-17/2 36 462.98 2.55 1.96 97,2_96,4 15/2-15/2' 21/2-21/2j 34 867.68 -1.75 -1.83 17/2-17/21 19/2-19/2J 34 871.18 1.75 1.83 107,3-107,4 17/2-17/2' 23/2-23/2 8 918.56 -0.68 -0.69 - 7 0 -Table 4 . 9 (continued) T r a n s i t i o n F' F" Observed Quadrupole Correction D C Frequency Observed Calculated 1 0 8 , 2 - 1 0 7 , 4 1 2 7 , 5 - 1 2 7 , 6 13 -13 1 0 , 4 9 ,4 1 4 9 , 5 - 1 A 9 , 6 1 7 1 1 , 6 - 1 7 1 1 , 7 19 -19 1 2 , 7 1 2 , 8 19/2-19/2 21/2-21/2 17/2-17/2 23/2-23/2 19/2-19/2] 21/2-21/2 J 19/2-19/2" 25/2-25/2 21/2-21/2" 23/2-23/2 19/2-19/2" 25/2-25/2 21/2-21/2 23/2-23/2 21/2-21/2" 27/2-27/2 23/2-23/2" 25/2-25/2 23/2-23/2] 29/2-29/2 j 25/2-25/2" 27/2-27/2 25/2-25/2] 31/2-31/2J 27/2-27/2 ' 29/2-29/2 31/2-31/2 37/2-37/2 33/2-33/2 35/2-35/2 35/2-35/2 ' 41/2-41/2 8 919 .92 36 648 .24 36 651 .41 36 346 .41 36 349 .22 19 520 .85 19 522 .79 32 314 .20 32 316 .86 33 156 .66 33 157 .35 21 304 .62 21 306 .23 22 540 .88 22 542 .13 30 830 .55 0 .68 - 1 . 5 9 1.58 -1.41 1.40 - 0 . 9 7 0 .97 - 1 . 3 3 1.33 - 0 . 3 5 0 .34 -0 .81 0 .80 - 0 . 6 3 0 .62 - 0 . 6 0 0 .69 - 1 . 4 6 1.46 - 1 . 6 0 1.60 - 1 . 0 8 1.08 - 1 . 3 3 1.33 - 0 . 4 3 0 .43 - 0 . 8 7 0 .87 - 0 . 6 7 0 .67 -0 .71 - 7 1 -Table 4 . 9 (continued) T r a n s i t i o n F' F' Observed Quadrupole Correction Frequency Observed C a l c u l a t e d 0 2 0 1 3 , 7 - 2 ° 1 3 , 8 22 -22 " 1 4 , 8 1 4 , 9 25 -25 1 6 , 9 1 6 , 1 0 2 8 1 8 , 1 0 _ 2 8 1 8 , 1 1 29 -29 1 9 , 1 0 19 ,11 31 -31 20 ,11 20 ,12 37/2-37/2] 39/2-39/2 J 37 2-37/2 43/2-43/2 39/2-39/2] 41/2-41/2J 41/2-41/2] 47/2-47/2J 43/2-43/2 45/2-45/2J 47/2-47/2 53/2-53/2 49/2-49/2 51/2-51/2 53/2-53/2 59/2-59/2 55/2-55/2 57/2-57/2 , 55/2-55/2] 61/2-61/2J 57/2-57/2 59/2-59/2 59/2-59/2 65/2-65/2 61/2-61/2 63/2-63/2 30 831 .75 23 296 .40 23 297 .45 31 857 .14 31 858 .33 32 400 .41 32 4 0 1 . 4 3 32 503 .32 32 504 .54 23 228 .24 23 228 .86 32 208 .70 32 2 0 9 . 4 0 0 .60 - 0 . 5 3 0 .52 - 0 . 6 0 0 .59 -0 .51 0 .51 -0 .61 0 .61 -0 .31 0 .31 - 0 . 3 5 0 .35 0 .71 - 0 . 5 7 0 .57 -0 .61 0.61 - 0 . 5 3 0 .53 - 0 . 4 7 0 .47 - 0 . 3 7 0 .37 - 0 . 4 2 0 .42 -72-Table 4.10 Nuclear Quadrupole Hyperfine Components of o y -if. £ Resolved C l 0 2F T r a n s i t i o n s T r a n s i t i o n F' F" Observed ^ Frequency Quadrupole Observed Correction c Calculated -"-l.o'^ o.o 1/2-3/2 17 827.30 -10.24 -10.16 5/2-3/2 17 835.51 -2.03 -2.03 3/2-3/2 17 845.74 8.20 8.13 2 -1 1,1 0,1 1/2-1/2 34 305.26 -10.23 -10.16 7/2-5/2 34 313.21 -2.28 -2.32 5/2-5/2 34 316.54 1.05 ' 1.00 3/2-3/2 34 320.95 5.46 5.48 5/2-3/2 34 323.36 7.87 7.84 2 -1 2,1 ^ . l 7/2-7/2 37 031.68 -2.37 -2.62 3/2-3/2 37 036.65 2.60 2.65 5/2-5/2 37 038.25 4.20 4.23 5/2-3/2 37 041.41 7.36 7.54 4 -4 4,1 *3,1 5/2-5/2 13 203.12 -2.51 -2.52 11/2-11/2 13 204.31 -1.32 -1.28 7/2-7/2 13 206.64 1.01 1.01 9/2-9/2 13 207.90 2.27 2.24 4 -4 *2,2 ^ 2,3 5/2-5/2 16 308.40 -5.04 -5.03 11/2-11/2 16 310.80 -2.64 -2.56 7/2-7/2 16 315.47 2.03 2.01 9/2-9/2 16 317.98 4.54 4.48 65,2_64,2 9/2-9/2 13 583.19 -0.84 -0.88 15/2-15/2 13 583.47 -0.56 -0.56 11/2-11/2 13 584.54 0.51 0.51 -73-Table 4.10 (continued) T r a n s i t i o n F* F" Observed j. Frequency Quadrupole Correction Observed Calculated 13/2-13/2 13 584.82 0.79 0.83 76,2-75,2 11/2-11/2' 17/2-17/2j 19 776.01 -0.82 -0.80 13/2-13/2' 15/2-15/2 19 777.64 0.81 0.80 86,2~85,4 13/2-13/2 19/2-19/2 34 34 349.93 350.44 -2.19 -1.68 -2.31 -1.62 15/2-15/2 34 353.69 1.57 1.54 17/2-17/2 34 354.25 2.13 2.23 87,1_86,3 13/2-13/2 19/2-19/2 31 31 455.73 456.15 -1.65 -1.23 -1.72 -1.21 15/2-15/2 31 458.59 1.20 1.15 17/2-17/2 31 458.94 1.56 1.66 86,3"85,3 13/2-13/2' 19/2-19/2 12 835.04 -0.26 -0.24 15/2-15/2' 17/2-17/2 12 835.55 0.25 0.24 9 -9 8,2 7,2 15/2-15/2' 21/2-21/2 32 672.51 -0.97 • -0.99 17/2-17/2' 19/2-19/2 32 674.44 0.96 0.99 107,3-107,4 17/2-17/2' 23/2-23/2 8 686.75 -0.54 -0.54 19/2-19/2' 21/2-21/2 8 687.82 0.53 0.54 108,2-107,4 17/2-17/2' 23/2-23/2 36 430.31 -1.14 -1.15 19/2-19/2' 21/2-21/2 36 432.59 1.14 1.15 -74-Table 4.10 (continued) Transition F* F" Observed ^ Quadrupole Correction Frequency Observed Calculated U 9 , 3 13-8,3 1 310,4- 1 39,4 19/2-19/2 25/2-25/2 21/2-21/2 23/2-23/2 23/2-23/2' 29/2-29/2 25/2-25/2' 27/2-27/2 33 634.48 33 635.93 33 279.90 33 280.55 -0.73 0.72 -0.33 0.32 -0.60 0.60 -0.34 0.34 1 610,6- 1 610,7 22 -22 14,8 14,9 29/2-29/2 35/2-35/2 31/2-31/2 33/2-33/2, 41/2-41/2 47/2-47/2 43/2-43/2' 45/2-45/2 28 601.94 28 603.05 30 864.89 30 865.85 -0.56 0.55 -0.48 0.48 -0.67 0.67 -0.48 0.48 25 -25 16,9 16,10 47/2-47/2 53/2-53/2, 49/2-49/2 51/2-51/2 31 241.44 31 242.00 -0.28 0.28 -0.42 0.42 Table 4.11 Nuclear Quadrupole Hyperfine Components of 35 16 18 a Resolved Cl 0 OF Transitions m . . _,, „„ Observed v Quadrupole Correction _ Transition F F o c Frequency Observed Calculated 11,0 °0,0 1/2-3/2 5/2-3/2 17 17 265.89 276.45 -13.25 -2.69 -13.14 -2.63 3/2-3/2 17 289.82 10.68 10.51 2 -1 1,1 0,1 7/2-5/2 3/2-3/2 33 33 477.86 487.44 -2.76 6.82 -3.02 6.85 5/2-3/2 33 ,490.50 9.88 10.12 4 -4 4,1 *3,1 5/2-5/2 11/2-11/2 10 10 561.81 563.23 -2.93 -1.51 -2.84 -1.44 7/2-7/2 10 566.05 1.31 1.13 9/2-9/2 10 567.26 2.52 2.53 55,1~54,1 7/2-7/2 13/2-13/2 15 15 370.85 371.89 -2.55 -1.51 -2.62 -1.51 9/2-9/2 15 374.71 1.31 1.31 11/2-11/2 15 375.77 2.37 2.42 65,2 - 64,2 9/2-9/2 ' 15/2-15/2 9 939.75 -0.68 -0.71 11/2-11/2' 13/2-13/2 9 941.10 0.67 0.71 75,2 - 75,3 11/2-11/2' 17/2-17/2 9 530.07 -1.12 -1.14 13/2-13/2' 15/2-15/2 532.30 1.11 1.14 76,2"75,2 11/2-11/2' 17/2-17/2 u 897.03 -0.82 -0.86 13/2-13/2' 15/2-15/2 14 898.67 0.82 0.86 - 7 6 -Table 4 .11 (continued) T r a n s i t i o n F* p" Observed ^ Quadrupole Correction c Frequency Observed Calculated 8 8 , r 8 7 , i 8 7 , 2 " 8 6 , 2 9 -9 6 ,3 6 ,4 1 0 7 , 3 - 1 0 7 , 4 1 0 9 , 2 - 1 0 8 , 2 U 8 f 3 - U 8 , 4 1 2 8 , 4 " 1 2 8 , 5 1 3 9 , 4 " 1 3 9 , 5 13/2-13/2 ' 19/2-19/2 15/2-15/2 ' 17/2-17/2 13/2-13/2] 19/2-19/2J 15/2-15/2 17/2-17/2 15/2-15/2) 21/2-21/2J 17/2-17/2 19/2-19/2 > 17/2-17/2] 23/2-23/2J 19/2-19/2 21/2-21/2 17/2-17/2] 23/2-23/2J 19/2-19/2 21/2-21/2 19/2-19/2] 25/2-25/2J 21/2-21/2 23/2-23/2 21/2-21/2] 27/2-27/2J 23/2-23/2] 25/2-25/2J 23/2-23/2 ' 29/2-29/2 25/2-25/2 27/2-27/2 30 383.51 30 386 .58 20 4 3 2 . 5 0 20 434 .24 16 019 .63 16 021 .98 12 367 .22 12 368 .86 31 668 .89 31 671 .10 8 821 .65 8 822 .71 19 554 .75 19 556 .36 15 095 .75 15 097 .07 - 1 . 5 4 1.53 - 0 . 8 7 0 .87 - 1 . 1 8 1.17 - 0 . 8 4 0 .80 -1 .11 1.10 - 0 . 5 3 0 .53 -0 .81 0 .80 - 0 . 6 6 0 .66 - 1 . 7 4 1.74 - 0 . 9 7 0 .97 - 1 . 1 9 1.19 - 0 . 8 3 0 .83 -1 .11 1.11 - 0 . 5 6 0 .56 - 0 . 9 0 0 .90 - 0 . 6 7 0 .67 - 7 7 -Table 4 .11 (continued) T r a n s i t i o n F' F" Observed Quadrupole Correction Frequency Observed Calculated 14 -14 X 4 1 0 , 4 10 ,5 15 -15 1 0 , 5 1 0 , 6 1 7 1 2 , 5 1 7 1 2 , 6 1 8 1 3 , 5 _ 1 8 1 3 , 6 2 0 1 4 , 6 - 2 0 1 4 , 7 2 1 1 5 , 6 - 2 1 1 5 , 7 22 -22 1 5 , 7 1 5 , 8 23 -23 1 6 , 7 1 6 , 8 25/2-25/2 31/2-31/2 27/2-27/2) 29/2-29/2J 27/2-27/2 33/2-33/2 29/2-29/2] 31/2-31/2J 31/2-31/2 37/2-37/2 33/2-33/2] 35/2-35/2J 33/2-33/2 ' 41/2-41/2 35/2-35/2 ' 37/2-37/2 , 37/2-37/2 43/2-43/2 39/2-39/2 ' 41/2-41/2 39/2-39/2 ' 45/2-45/2 41/2-41/2 ' 43/2-43/2 41/2-41/2 ' 47/2-47/2 43/2-43/2 ' 45/2-45/2 , 43/2-43/2 ' 49/2-49/2 45/2-45/2 ' 47/2-47/2 10 818 .12 10 8 1 9 . 0 0 22 955 .65 22 956 .87 12 769 .21 12 769 .96 8 500 .32 8 500 .66 14 677 .88 14 678 .48 9 842 .89 9 8 4 3 . 4 0 22 813 .23 22 813 .75 16 543 .51 16 544 .16 - 0 . 4 4 0 .44 -0 .61 0.61 - 0 . 3 8 0 .37 - 0 . 1 7 0 .17 -0 .31 0 .31 - 0 . 2 6 0 .25 - 0 . 2 6 0 .26 - 0 . 3 3 0 .32 - 0 . 4 7 0 .47 - 0 . 7 4 0 .74 -0 .41 0 .41 - 0 . 2 3 0 .23 - 0 . 3 7 0 .37 - 0 . 2 6 0 .26 - 0 . 4 5 0 .45 - 0 . 3 4 0 .34 -78-Table 4.11 (continued) Transition F 1 F" Observed ^ Frequency Quadrupole Correction Observed Calculated 24 -24 ^17,7 17,8 27 -27 '19,8 19,9 45/2-45/2' 51/2-51/2 47/2-47/2' 49/2-49/2 51/2-51/2 59/2-59/2 53/2-53/2' 55/2-55/2 11 162.52 11 162.83 12 454.60 12 454.83 -0.16 0.15 -0.12 0.11 -0.24 0.24 -0.22 0.22 a b c Transition frequencies and quadrupole corrections are in MHz. Estimated uncertainty in completely resolved hyperfine component frequencies is + 0.10 MHz, and in par t i a l l y resolved component fre-quencies i s + 0.20 MHz. Frequency shift of hyperfine component from hypothetical unsplit transition frequency calculated from constants in table 4.12. Partially resolved quadrupole corrections were calculated by aver-aging the frequency shifts of the components contributing to the unresolved transition weighted by their line strengths. Table 4.12 Nuclear Quadrupole a b Coupling Constants of Chloryl Fluoride ' 3 5 C 1 1 6 0 2 F 3 7 C 1 1 6 0 2 F 3 5C1 1 60 1 8OF X (MHz) 51.82 + 0.16 40.63 + 0.16 52.56 + 0.36 cc — — — X,, - X (MHz) 17.67 + 0.21 14.12 + 0.23 15.96 + 0.45 bb aa — — — Si Determined by making a linear least squares f i t of the coupling constants to the observed quadrupole corrections of a l l completely resolved hyperfine components in tables 4.9 through 4.11. k Quoted uncertainties are one standard deviation. 35 16 37 16 The r a t i o s of the quadrupole coupling constants of C l O^F and C l C^F 35 37 can be compared to the r a t i o of the C l and C l e l e c t r i c quadrupole moments. Since there i s l i t t l e r o t a t i o n of the p r i n c i p a l i n e r t i a l axes of c h l o r y l f l u o r -ide upon i s o t o p i c chlorine s u b s t i t u t i o n , the three r a t i o s should agree c l o s e l y . 35 37 The r a t i o of the quadrupole moments of C l and C l i s 1.2688 [82]. The r a -t i o s of the C l 0„F and C l 0„F values of Y and Y ^ - X are 1.275 + z z cc bb aa — 0.009 and 1.251 + 0.035 r e s p e c t i v e l y . The c h l o r i n e quadrupole coupling constants are functions of the e l e c t r o n d i s t r i b u t i o n about the ch l o r i n e nucleus and provide a valuable probe of the nature of the Cl-F bond. I f one expands the molecular e l e c t r o n i c wave function i n equation 2.30 i n terms of two-electron LCAO molecular o r b i t a l s , one f i n d s : *gg " " I i ! j <«-» th th where a, . i s the o r b i t a l c o e f f i c i e n t of the i atomic o r b i t a l i n the k k i molecular o r b i t a l , and the k summation i s over a l l occupied molecular o r b i t a l s . The quantity q ^ i s the matrix element of 3 2V/9g 2 between the i t b and j t b atomic o r b i t a l s . Townes and Dailey [83] have made the suggestion, on the basis of a wealth of semiempirical evidence, that terms a r i s i n g from the valence s h e l l p atomic o r b i t a l s on the atom possessing the nuclear quadrupole moment make the only s i g n i f i c a n t contributions to the sum i n equation 4.1. Within the l i m -i t s of t h i s approximation the nuclear quadrupole coupling constants are given simply by: * a a = ( n a " ^ ^ T ^ ^ C l ( 4' 2> where n i s the electron population of the ch l o r i n e 3p o r b i t a l d i r e c t e d along th the g p r i n c i p a l i n e r t i a l a x i s , and q ^ i s the e l e c t r i c f i e l d gradient along the z axis of an electron i n a chlorine 3p or 3p atomic o r b i t a l . The quanti-x y -80-ty eQq . has been experimentally determined from atomic hyperfine spectra as 109.74 MHz [84]. Expressions for the two other principal elements of x can be obtained by a cyclic permutation of the axes' labels. Unfortunately for each isotopic species we have only two observables, x c c and n, and this i s insufficient to determine the three unknowns n^, n^, and n c« However, i t i s possible to make a comparison of the nuclear quadrupole 35 16 35 16 coupling constants of Cl O^F and Cl 0^ that does yield information about the nature of the Cl-F bond. One may choose to view chloryl fluoride as a molecule created by the for-mation of a bond between a fluorine atom and a chlorine dioxide molecule. For-mation of this bond changes the electron population of the chlorine atomic orbitals, particularly the valence shell 3p orbitals, and this causes a change 35 16 in the quadrupole coupling constants. If we express the Cl 0^ quadrupole 35 16 coupling tensor in the Cl O^F principal i n e r t i a l axis system, the change in quadrupole coupling constants i s given by: x(C10 2F, . x(C10 2) . [ 4 „ a . ^ + 4 „ c ) / 2 ] e Q q c i ^ b 1 0 2 " " * b b 1 0 2 > " t A"b " < 4 n a + V ^ ^ c l x £ 1 0 2 F ) - X<fV - [4n c - ( 4 „ a + An b )/21eQ„ c l (4.3) (CIO ^ th X 2 is the g diagonal element of the quadrupole coupling tensor of 88 35 16 35 16 Cl O 2 in the Cl O^F principal i n e r t i a l axis system, and An^ is the change in the electron population of the 3p chlorine atomic orbital upon bond forma-35 16 tion, also expressed in the Cl O^F principal i n e r t i a l axis system. 35 16 The quadrupole coupling constants of Cl 0^ have been determined by Curl et.al. [69, 85]. The principal i n e r t i a l axes and principal quadrupole -81-35 16 coupling tensor axes of C l 0^ are n e c e s s a r i l y c o l i n e a r . Therefore, i f we l a b e l the p r i n c i p a l i n e r t i a l axes of C10_ with a prime, x^"?2^ i s diagonal and can r e a d i l y be transformed by a simple r o t a t i o n to the CIC^F p r i n c i p a l i n e r t i a l axis system. The transformation required to go from the ClO^ axis system to the CIC^F axis system (see f i g u r e 4.3) i s : a-—»-b, b-—>a, c—>c followed by a r o t a t i o n of the a and c axes about b by an angle G equal to 52° 7'. 0 i s the angle between the plane defined by the C l and 0 atoms i n 36 16 C l C^F and the a_,b_-plane (determined from the structure reported i n table 6.4). Therefore: / Y(C10 ) =  Xgg cos© 0 -sinO 0 1 0 sinO 0 cosO 0 \ / cosO 0 sinG^ 0 0 0 X< ? ?2> 0 1 0 -sinQ 0 cosQ (4.4) 35 16 35 16 Values of the C l 0^ and C l 0^$ nuclear quadrupole coupling constants can be found i n table 4.13. Figure 4.3 P r i n c i p a l I n e r t i a l Axis Systems of Chlorine Dioxide and C h l o r y l F l u o r i d e (not drawn to scale) -82-35 16 35 16 ci Table 4.13 Nuclear Quadrupole Coupling Constants of Cl C^F and Cl 0^ .(.') ^ x£?2> xf/V a -34.75 -51.90 31.76 b -17.08 2.28 -51.90 c 51.82 49.62 20.14 Coupling constants are in MHz. The solution of equations 4.3 for 4n &, An^, and An^ is s t i l l indeterminate. However, a resonable approximation that allows us to continue may now be made. The 3p, orbital on chlorine in chloryl fluoride (corresponding to the 3p , D a orbital on chlorine in chlorine dioxide) is not involved in the Cl-F a bond or the CIC^ TT system. It contributes strongly only to the CIO2 a bonding system. The poss i b i l i t y that i t may contribute to a Cl-F TT bond can be reasonably pre-cluded by the unusual length of the Cl-F bond (see chapter 6). It, therefore, appears that the electron population of this 3p chlorine atomic orbital w i l l change upon formation of the Cl-F bond only through the small change in the hybridization of the CIO2 cr frame. If one neglects the contribution of chlor-ine 3d atomic orbitals, An, can be estimated from the observed O-Cl-0 bond angles, b $, with the equation [87]: = _ cos* b cos<J> - 1 The assumption is made that chlorine, in both CIC^ and CIC^F, contributes two electrons to the hybridized valence orbital that goes into the construction of the CIO2 o frame. Using equation 4.5, An^ is calculated to be +0.06. Substi-tution of this value into equations 4.3 yields values of -0.53 and +0.10 for -83-An and An respectively, a c Formation of the Cl-F bond, therefore, removes electron density from the chlorine 3p orbital directed along the a-principal i n e r t i a l axis. Since the Cl-F bond forms a small angle with the a^-axis (15 36' from the structure in• table 6.4), this suggests a d r i f t of roughly one half an electronic charge to the fluorine atom. The interpretation of the chloryl fluoride nuclear quadrupole coupling constants is supported by self consistent f i e l d molecular orbital CNDO calcu-lations of the electronic configurations of CIC^ [88] and CIC^F [89] performed and kindly communicated to us by J. Tait and F. G. Herring, and M. Williams. SCF-MO-CNDO electronic wave functions have enjoyed moderate success in the pre-diction within the Townes and Dailey approximation of the nuclear quadrupole coupling constants of molecules containing chlorine [90]. Calculations on C I O 2 and C I O 2 F were performed using the Pople and Segal C N D 0 / 2 formulation [91]. The atomic orbital basis set included s, p, and d orbitals on chlorine and s and p orbitals on oxygen and, in the C I O 2 F case, fluorine. The calculated chlorine 3p electron populations and nuclear quadrupole coupling constants (evaluated using equation 4 . 2 ) are presented in table 4.14. A l l quantities are evaluated with respect to the principal i n e r t i a l axes of the molecule in ques-tion. A comparison of the CNDO and experimental quadrupole coupling constants in table 4.14 demonstrates that there i s agreement roughly within 1 0 MHz. The interpretation of the nuclear quadrupole coupling constants relied upon the use of equation 4.5 for the calculation of An^. The valid i t y of the assumptions allowing i t s use can now be tested by determining An predicted by the CNDO wave functions of C 1 0 O and C 1 0 . F . If one defines n ^ C 1 ° 2 F \ n ^ C 1 ( V , 2 2 g g and n ^ ^ P as respectively the chlorine 3p electron population of chloryl 6 fluoride in the C I O 2 F principal axis system, of chlorine dioxide in the C I O 2 -84-Table 4.14 SCF-MO-CNDO Chlorine 3p Electron Populations and Nuclear Quadrupole Coupling Constants of ClO^ and CIG^F C10 2F cio 2 n a 0.791 0.936 \ 0.934 1.175 n c 1.269 1.431 X a a ' CNDO (observed) -34 .23 (-34.75) -40.31 (-51. 90) Xbb' .CNDO (observed) -10 .21 (-17.08) -0.83 ( -2. 28) X c c ' CNDO (observed) 44 .43 ( 51.82) 41.17 ( 49. 62) <a Coupling constants i n MHz • p r i n c i p a l axis system, and of chl o r i n e dioxide i n the CK^F p r i n c i p a l axis «-!. A • • - - i t . / (C10.F) (C10-) V system, then An i s given simply by (n 2 - n 2 ). 8 8 8 The determination of n^^2^ requires a transformation of the ch l o r i n e 3p e l e c t r o n populations i n chl o r i n e dioxide from the C10 2 (g' system) into the C10 2F (g system) p r i n c i p a l i n e r t i a l axis system. This i s accomplished i n the following way. The k*"*1 c h l o r i n e dioxide molecular o r b i t a l can be expanded i n the LCAO-MO approximation i n terms of ch l o r i n e 3p atomic o r b i t a l s d i r e c t e d along e i t h e r the C10 2 p r i n c i p a l axes, {g'}, or the C10 2F p r i n c i p a l axes, {g}. In the f i r s t case the c o e f f i c i e n t of the chl o r i n e 3p , atomic o r b i t a l i n the k ch l o r i n e dioxide molecular o r b i t a l i s a, ,, and i n the second case the kg' c o e f f i c i e n t of the chlorine 3p atomic o r b i t a l i s a. . The two sets of c o e f f i -g kg cie n t s are r e l a t e d by the same transformation used i n equation 4.4. akb " a k a ' a, = a,, ,cos0 + a, . sinG ka kb' kc' a, = -a,, .sinO + a, .cosO kc kb' kc' wh ere 0 i s the angle between the C10 2 plane and the a_,b_-plane. The c h l o r i n e 3p population numbers i n C10 2 are, therefore, given by (C10 o) „, |2 „, |2 (CIO.) nb 2 = g'akbl = I'aka'l = V 2 = °'936 n a C 1 0 2 > = £ K f = c o s 2 0 l l a k b ' | 2 + S i n 2 0 l l a k c ' ! 2 + 2 c o s 0 s i n 0 | | a k b , | | a k c , | 2 n (C10 o) . . 2. (C10 o) . = cos Gn,;, 2 + s i n 0n , 2 = 1.334 b' c' n c C 1 ° 2 ) - l K / = S i n 2 0 £ l a k b ' ! 2 + C O S \ K c ^ - 2 0 0 8 9 8 1 ^ 1 0 ^ , 1 1 ^ , 1 = s i n ^ n ^ V + C O S 2 0 J C 1 O 2 > = 1.272 (4.7) where k summations are over a l l occupied molecular o r b i t a l s . The cross terms in the l a s t two equations can be set zero because the ch l o r i n e 3p^, and 3p c, atomic o r b i t a l s do not transform l i k e the same i r r e d u c i b l e representation under the operations of the point group of the ch l o r i n e dioxide molecule, and hence | a k b t | | a k c t | i s always zero. Continuing one finds that the CNDO values of An^, An^, and An £ are -0.543, +0.002, and -0.003. The agreement with the values that r e s u l t e d from the quad-rupole a n a l y s i s , -0.53, +0.06, and +0.10, i s better than could reasonably be expected and must to a large extent be f o r t u i t o u s . The good agreement, however, c e r t a i n l y does suggest that the approximation involved i n the use of equation 4.5 was indeed reasonable. -86-Chapter 5 The Stark E f f e c t i n the Microwave Spectrum of C h l o r y l F l u o r i d e 5.1 General Considerations The e l e c t r i c dipole moment of the n a t u r a l l y most abundant i s o t o p i c species 35 16 of c h l o r y l f l u o r i d e , C l u2^' ^ a s n o n - z e r o components along the a_- and c_-in-e r t i a l axes. The component along b_ i s zero because the b_-axis i s perpendicular to a r e f l e c t i o n plane. The values of the two non-zero components were deter-mined from measurements of the Stark e f f e c t i n the 1^ Q ~ ° Q Q and 3^ ^.~^2 1 t r a n s i t i o n s . Two c r i t e r i a were considered i n the choice of these two t r a n s i -t i o n s : (1) Both t r a n s i t i o n s l i e i n the frequency range of the Hewlett-Packard 8400C spectrometer with i t s attendant s e n s i t i v i t y and s t a b i l i t y advantage over the free-running k l y s t r o n frequency range. (2) Each t r a n s i t i o n i s between low J energy l e v e l s , allowing easier r e s o l u t i o n of the Stark components. Stark components were observed by impressing a large negative DC voltage (100 - 1250 V) on the Stark c e l l septum while modulating the Stark components with a much smaller (5 - 50 V) f l o a t i n g 100 kHz square wave AC voltage [73]. With phase s e n s i t i v e detection a Stark component observed under these conditions appears as two Stark lobes, a (+) lobe and a (-) lobe, d i f f e r i n g i n phase by 180°. The (+) lobe experiences a Stark f i e l d of E + E and the (-) lobe a Q C 3.C f i e l d of E, - E , where E i s the e l e c t r i c f i e l d strength r e s u l t i n g from dc ac ac one h a l f the peak to peak modulation voltage. During measurement, E was set at the minimum value s t i l l producing a c lC strong s i g n a l . At a bias p o t e n t i a l of 1000 V, a 5 V peak to peak square wave was always s u f f i c i e n t to w e l l modulate the t r a n s i t i o n s i g n a l . Lower bias po-t e n t i a l s required higher modulation p o t e n t i a l s . At a bias p o t e n t i a l of 100 V, a 20 V peak to peak AC p o t e n t i a l was necessary to produce a strong s i g n a l to -87-noise r a t i o . If one replaces the expression i n brackets i n equation 2.40 by {C}, the average of the second order Stark s h i f t s of the (+) and (-) lobes i s given by: <H,(2)>r- M = ^ V2^ M-K^M"* M > / 2 V v > S ir K ' S 3 v Y »M is. ^ 1 1 1 1 ? 2 2 Y IX (E , + E n . I ^ _ ^ c a c _ J { c } ( 5 > 1 ) g 2J + 1 -1' 1 35 At the large voltages necessary to uncouple the C l nuclear spin from the 2 r o t a t i o n a l angular momentum, i s greater than four orders or magnitude 2 lar g e r than E . This had two fortunate consequences. I t was not necessary to accurately measure the strength of the modulation f i e l d because i t s c o n t r i -bution to the Stark s h i f t was dwarfed by the e f f e c t of the large s t a t i c f i e l d . Broadening of the Stark lobes caused by the f a i l u r e of the 100 kHz square wave generator to produce a p e r f e c t l y square waveform was also l a r g e l y avoided. 5.2 C a l i b r a t i o n of the Stark C e l l with Carbonyl Sulphide Measurements of precise e l e c t r i c f i e l d strengths i n a Stark c e l l i s poss-i b l e only i f the impressed voltage and the Stark electrode spacing are accur-a t e l y known. To avoid the necessity of p h y s i c a l l y measuring the spacing and also to provide f o r the correct averaging over f i e l d inhomogeneities that always occur i n an X-band Stark c e l l , i t i s common p r a c t i c e to c a l i b r a t e the c e l l by observing the Stark e f f e c t i n carbonyl sulphide. The dipole moment of the molecule under i n v e s t i g a t i o n can then be re l a t e d to the dipole moment of car-bonyl sulphide, whose accurate measurement has been the subject of several stud-ies [92, 93]. -88-The Stark e f f e c t was observed i n the K = 0, J = 1 -«- 0 t r a n s i t i o n of 16 12 32 0 C S. The expression, correct to second order, f o r the Stark energy of a l i n e a r molecule l i k e OCS i s simply [94]: m v u 2 E 2 J ( J + 1) - 3M2 < HS >J K M ( 5 ' 2 ) *> 2hBJ(J + 1) (2J - 1)(2J + 3) where B i s the r o t a t i o n a l constant of the molecule. It i s convenient to define an e f f e c t i v e Stark electrode separation, d, through the equation: E = V/d (5.3) where V i s the impressed Stark voltage and E i s the r e s u l t i n g e l e c t r i c f i e l d strength. The e f f e c t i v e electrode separation can then be determined from the known dipole moment of OCS, ^o^g* a n d from the second order Stark s h i f t of the J = 1 *• 0 OCS t r a n s i t i o n through: 4u 2 d 2- ° C S , (5.4) 15B(Av/V ) 2 The quantity (Av/V ) i s the slope of the average of the frequencies of the (+) and (-), M = 0 Stark lobes of the K = 0 , J = 1 «- 0 t r a n s i t i o n of OCS pl o t t e d 2 2 against (V, + V ), where V, i s the impressed DC bias p o t e n t i a l and V i s G C 3.C Q C c lC one h a l f the peak to peak 100 kHz square wave modulation p o t e n t i a l . Measurement of the frequency of the M = 0, J = 1 -<- 0, OCS Stark lobe over the voltage range from 0 to 1250 V was completed using the technique described i n section 5.1. This and a l l other Stark measurements were made at a c e l l temp-erature of approximately -78°C (dry i c e i n a covered styrofoam trough). A p l o t 2 2 of the frequency as a function of ( V j c + ^ a c ) i s presented i n figu r e 5.1. -89-12205 r 12200 h 12195 h 12190 h 12185 12180 h 12175 r-12170H 12165 h 12160 100 120 140 2 2 2 -4 ®Ao + Va/> <V > x 10 dc ac 16 19 *\0 Figure 5.1 Frequency of the 0 C S, J = 1 «- 0 T r a n s i t i o n 2 2 as a Function of (V, + V ) dc ac -90-The frequency of this transition was f i t t e d by the linear least squares tech-nique to an expression of the form: v - v + (Av/V 2)(V 2 + V 2) + (Av/V4)(V 2 + V 2 ) 2 (5.5) o dc ac dc ac and the results are given in table 5.1. The quartic term was included to account for small polarization and fourth order Stark effects. Table 5.1 Stark Coefficients of the M = 0, J = 1 0, OCS Transition 3 v 12,162.96 +'• 0.01 MHz o — (Av/V2) 2.6065 + 0.0041 x 10 _ 5 MHz/V2 (Av/V4) -4.9 + 2.7 x I O - 1 4 MHz/V4 Quoted uncertainties are one standard deviation. The intercept V q i s in excellent agreement with the published zero f i e l d f r e -quency, 12,162.97 MHz [68]. Adopting Muenter's value of the OCS dipole moment, 0.71521 + 0.00020 D, [93] one may calculate ai. effective electrode separation of 0.4670 + 0.0010 cm. Electric f i e l d strengths necessary for the chloryl fluoride dipole moment de-termination were calculated from this value and equation 5.3. 5.3 The Electric Dipole Moment of Cl OJF Frequencies of the M = 0 Stark component of the 11 n - 0 n n transition and 35 16 the M = + 3 Stark component of the 3_ ,-3 9 1 transition of Cl 0 oF were mea-sured and are presented in tables 5.2 and 5.3. Both transitions have large zero f i e l d hyperfine splittings. Where appropriate, low f i e l d hyperfine com-ponents are labeled by the limiting F quantum numbers, and high f i e l d compo-- 9 1 -nents by the l i m i t i n g quantum numbers. Table 5 . 2 Frequencies of the Mj = 0 Stark Component 3 5 1 6 of the 1 1 Q-OQ Q T r a n s i t i o n of C l 0 2 F „ 2 , „ 2 / T I 2 . 2S nn-h Hyperfine Component Frequency'3 E d c + E a c ( V / C m } X 1 0 I II I I I 4 . 7 4 2 1 7 9 2 2 . 8 2 4 . 8 3 8 1 7 9 0 9 . 8 7 1 8 . 3 7 0 1 7 9 2 5 . 4 1 1 8 . 5 8 2 1 7 9 1 2 . 4 5 4 1 . 2 9 4 1 7 9 3 0 . 0 2 4 1 . 5 1 6 1 7 9 1 6 . 9 0 7 3 . 3 6 0 1 7 9 3 6 . 5 2 7 3 . 5 1 3 1 7 9 2 3 . 2 2 1 1 4 . 6 5 0 1 7 9 3 1 . 7 7 1 7 9 4 1 . 1 1 1 7 9 4 5 . 0 0 1 6 5 . 0 8 1 1 7 9 4 1 . 8 7 1 7 9 5 0 . 2 8 1 7 9 5 5 . 5 0 2 2 4 . 6 8 3 1 7 9 5 3 . 6 0 1 7 9 6 1 . 0 4 1 7 9 6 7 . 8 6 2 9 3 . 4 3 8 1 7 9 6 6 . 2 0 1 7 9 7 4 . 0 8 1 7 9 8 2 . 5 4 3 7 1 . 3 7 0 1 7 9 9 0 . 0 2 1 7 9 9 9 . 1 2 4 5 8 . 4 8 0 1 8 0 0 8 . 1 1 1 8 0 1 7 . 7 9 5 0 5 . 4 7 4 1 8 0 1 7 . 9 0 1 8 0 2 7 . 7 2 5 5 4 . 7 6 0 1 8 0 2 8 . 4 4 1 8 0 3 8 . 3 3 6 0 6 . 3 3 9 1 8 0 3 9 . 5 4 1 8 0 4 9 . 4 0 6 6 0 . 2 1 0 1 8 0 5 1 . 2 2 1 8 0 6 0 . 9 0 7 1 6 . 3 7 3 1 8 0 6 3 . 0 4 1 8 0 7 3 . 1 1 Frequencies are averages of (+) and (-) lobes (see text) i n MHz. At the zero f i e l d l i m i t , hyperfine components I and III c o r r e l a t e with the F'-F" components 5 / 2 - 3 / 2 and 3 / 2 - 3 / 2 r e s p e c t i v e l y , and component II appears to lose a l l i n t e n s i t y . At the high f i e l d l i m i t , components II and III c o r r e l a t e with the = + 1 / 2 and + 3 / 2 components r e s p e c t i v e l y and I loses a l l i n t e n s i t y . Table 5.3 Frequencies of the M = + 3 Stark Component *J of the 3 3 1 ~ 3 2 1 T r a n s i t i o n of C l O^F E, 2 + E 2 (V 2/cm 2) x 10 4 dc ac Hyperfine M = + 3/2 Component = + 1/2 154.244 8072.38 8075.94 181.982 8067.13 8070.58 212.012 8061.52 8045.90 315.858 8042.56 8045.90 363.172 8034.22 8037.65 422.544 8024.04 8027.33 Frequencies are averages of (+) and (-) lobes (see text) i n MHz. Plo t s of the frequencies of the Mj = 0 components of the 1^ Q~0Q Q t r a n s -i t i o n and the M = + 3 components of the 3_ -i - 3 0 , t r a n s i t i o n as a function of 2 2 E, + E are presented i n figures 5.2 and 5 .3 . Analysis the the data sum-Q C c lC marized i n these figures to y i e l d the dipole moment of c h l o r y l f l u o r i d e through equation 5.1 i s possible i f we have c l o s e l y approached the high f i e l d s p i n -r o t a t i o n uncoupled l i m i t . There are three c r i t e r i a f o r the attainment of the high f i e l d uncoupled l i m i t : (1) a quadratic Stark e f f e c t ( i n the absence of a nearby state connected by the Stark Hamiltonian to one of the states involved i n the t r a n s i t i o n ) , (2) the presence of two hyperfine components (M^ . = + 1/2 and M^ = + 3/2) associated with each Stark component and separated by a f r e -quency that may be calculated from equation 2 .43 , and (3) whose average f r e -quency may be extrapolated to zero f i e l d to give the u n s p l i t t r a n s i t i o n f r e -quency . A consideration of fi g u r e 5.2 i n d i c a t e s that the f i r s t two c r i t e r i a f o r the attainment of the high f i e l d uncoupled l i m i t are w e l l s a t i s f i e d by the -93-18060 H 18040h 18020 h 18000h 17980 h 17960h 17940 17920 17900 (E dc + E ~) (V2/cm 2) x 10" ac 35 16 Figure 5.2 Frequency of Hyperfine Components of the C l O^F, 1"! Q~0Q Q T r a n s i t i o n as a Function of the Square of the E l e c t r i c F i e l d Strength -94-8090 r 8 0 8 0 8 0 7 0 8 0 6 0 8 0 5 0 8030 8 0 2 0 100 2 0 0 300 4 0 0 (E, 2 + E 2 ) (V 2/cm 2) x 10" 4 dc ac 35 16 Figure 5.3 Frequency of Hyperfine Components of the C l O2F, Mj = + 3, 3^  "^^ 2 1 T r a n s i t i o n as a Function of the Square of the E l e c t r i c F i e l d Strength - 9 5 -1 ^ Q ~ O Q Q t r a n s i t i o n above f i e l d strengths of 2 5 0 0 V/cm. Over t h i s region the = + 1 / 2 and + 3 / 2 hyperfine components have w e l l defined quadratic Stark s h i f t s . The t h i r d c r i t e r i o n i s l e s s w e l l s a t i s f i e d . The c a l c u l a t e d zero f i e l d u n s p l i t 1 ^ g~0g Q t r a n s i t i o n frequency i s 1 7 , 9 1 1 . 5 8 MHz. The extrapolated zero f i e l d i ntercept of the average of the high f i e l d M^ = + 1 / 2 and + 3 / 2 t r a n s i t i o n frequencies i s 1 7 , 9 1 4 . 2 5 MHz. The disagreement of 2 . 6 7 MHz suggests an uncer-t a i n t y of 2 % i n the slope of the measured quadratic Stark s h i f t of the 1 . . N ~ 1, u 0 Q Q t r a n s i t i o n , a r i s i n g probably from not quite complete high f i e l d uncoupling. The high f i e l d quadratic region of the 1 ^ Q ~ 0 Q Q t r a n s i t i o n was f i t by the l i n e a r l e a s t squares technique to an expression of the form: X - x + ( A v / E 2 y E d c 2 + Eac 2> <5-6> and the r e s u l t s are presented i n table 5 . 4 . The Stark e f f e c t i n the 3 „ - i ~ 3 9 , t r a n s i t i o n i s i n p r i n c i p a l more compli-cated than i n the 1 ^ Q ~ 0 Q Q t r a n s i t i o n , because Mj can take the values 0 , + 1 , + 2 , and + 3 . However, under the conditions of t h i s experiment only the M = J + 3 Stark component was observed. The lower |Mj| Stark lobes were unobserved 2 because the i n t e n s i t y of Q-branch Stark lobes i s p r o p o r t i o n a l to M and be-J cause the lower |M | lobes require higher AC f i e l d strengths to be e f f e c t i v e l y modulated. Unambiguous assignment of the observed Stark lobe to M = + 3 was possible from an analysis of the high f i e l d hyperfine s p l i t t i n g (see sec-t i o n 5 . 4 ) . Figure 5 . 3 suggests that the Stark e f f e c t i n the 3 _ - , - 3 „ - t r a n s i t i o n i s strongly perturbed by a nearby state connected to e i t h e r 3 „ . or 3 9 , by the Stark Hamiltonian. The presence of w e l l defined M^ . = + 1 / 2 and + 3 / 2 hyperfine components i n d i c a t e s that the measurements are w e l l within the high f i e l d un--96-coupled limit, so the deviations observed from a well behaved quadratic Stark shift probably do not arise from incomplete high field spin-rotation uncoupling. The 3_ _ state which lies 1261.84 MHz above the 3 .. state and is connected to j , U J , 1 i t by.the a-component of the dipole moment causes a second order perturbation treatment of the Stark energy of the 3„ T - 3 9 , transition to break down. In order to calculate the a_ and c^-dipole moment components from the observ-ed Stark effects in the 1 n _ 0 n _ and 3_ -,_39 , transitions and account for the near degeneracy of the 3„ . and 3„ n states, the following iterative pro-cedure was adopted. A first approximate evaluation of the dipole moment components, good only to second order in the Stark effect, was made. A linear least squares varia-tional f i t of an expression of the form of equation 5.6 was made to the observed frequencies of the M = + 1/2 and +3/2 hyperfine components of the 3_ 1 -3„ -transition. Results of this f i t can be found in column 3 of table 5.4. Line strengths necessary for the calculation of the quadratic Stark coefficients of the 1^  Q~0Q o and 3^  i~^2 1 t r a n s i t i ° n s were obtained by quadratic interpo-lation between the three entries in the tables of Schwendeman and Laurie [95] 35 16 that best span the asymmetry parameter of Cl C^F. Equations 2.40, set for the 1, _-0_ _ and 3„ ,-3« , transitions, were then solved for u and u . Re-1,00,0 3,12,1 'a c suits of the.calculation were: y = 0.526 D, y = 1.637 D, and y = 1.719 D. Si c The observed frequencies of the 3„ - i~3 9 -. transitions were then corrected for the near degeneracy of the 3^  and 3^  Q states. An exact calculation of the Stark energy of the 3_ 1 state was made using equations 2.41 and 2.42, and a second order calculation of the Stark energy was made using equation 2.40. Both calculations used the "second order" dipole moment components determined above. The difference between the exact aod the second order 3_ - Stark ener-J , 1 -97-gies is a higher order correction that can be subtracted from the observed 3_ - i -3„ , transition frequencies to give a set of effective "deperturbed" trans-J , 1 z , J. i t i o n frequencies. A higher order calculation of the dipole moment was then made by f i t t i n g another expression of the form of equation 5.6 by the linear least squares technique to the effective "deperturbed" 3. 1~3„ , transition fre-j , 1 z , J. quencies. The calculation was iterated twice more, each time using the dipole moment that resulted from the previous iteration. The change in the dipole moment be-tween the last two iterations was less than 0.001 D. Values of the higher or-der correction and effective "deperturbed" 3_ - i~3 7 , transition frequencies that arose from the f i n a l iteration are presented in table 5.5. The electric dipole 35 16 moment of Cl O^ F calculated from the Stark effects observed in the 1^ Q~0Q Q and 3_ -,~39 1 transitions is presented in table 5.6. 5 , i z , J. Table 5.4 Quadratic Stark Coefficients of the M j = 0, l 1 > 0 - 0 b i 0 and M j = + 3, 3 3 f l-3 2 > 1 Transitions 3 ""•l.O^ O.O 33,1" observed •32,1 deperturbed o b " M I = ± 1 / 2 17,910.67 + 0.45 8103.55 + 0.42 8106.95 + 0.06 < A V / E \ - ±1/2 C 2.126 + 0.008 -1.812 + 0.014 -2.108 +0.002 o b V = ±3/2 17,919.19 + 0.25 8099.96 + 0.38 8103.36 + 0.04 < W E \ - ±3/2 C 2.147 + 0.005 -1.806 + 0.013 -2.106 + 0.002 Quoted uncertainties are one standard deviation. In MHz. ° In (MHz cm2/V2) x 10 5. - 9 8 -Table 5.5 Higher Order Contributions to the Stark Energies of the 3^ ^-3 T r a n s i t i o n A r i s i n g from the Near Degeneracy of the 3^ ^ and 3^ Q States 2 2 A E, + E dc ac Higher Order'' Correction Deperturbed 3^ ^~ M = + 1/2 •3_ 1 Frequency'3 z, i. M = + 3/2 154.244 1.48 8074.46 8070.90 181.982 2.01 8068.58 8065.12 212.012 2.66 8062.23 8058.86 315.858 5.57 8040.33 8036.99 363.172 7.19 8030.46 8027.03 422.544 9.49 8017.84 8014.55 3 In (V 2/cm 2) x 10" 4 . b In MHz. The deperturbed or corrected 3» i - 3 9 , t r a n s i t i o n frequencies i n columns 3 and 4 of table 5.5 represent only the second order contributions to the Stark e f f e c t i n the 3_ - i ~ 3 9 , t r a n s i t i o n . The approximation does appear good, be-•5)1. z, J. cause the corrected frequencies p l o t t e d i n figu r e 5.3 (points i n the squares) do vary l i n e a r l y with the square of the e l e c t r i c f i e l d strength. Linear e x t r a -p o l a t i o n to zero f i e l d of the average of the high f i e l d hyperfine component t r a n s i t i o n frequencies, 8105.16 MHz, i s i n acceptable agreement with the zero f i e l d u n s p l i t t r a n s i t i o n frequency, 8104.34 MHz. The disagreement of 0.82 MHz suggests an uncertainty of 1% i n the slope of the quadratic Stark s h i f t of the 3„ i ~ 3 9 ., t r a n s i t i o n . Since t h i s i s roughly ten times the standard deviation of the slope (see table 5 . 4 ) , i t suggests, once again, that we do not have com-plete high f i e l d s p i n - r o t a t i o n uncoupling. The e l e c t r i c dipole moment of c h l o r y l f l u o r i d e was predicted by Williams -99-from a SCF-MO-CNDO c a l c u l a t i o n of the e l e c t r o n i c structure [88]. Results of t h i s c a l c u l a t i o n are presented together with the experimental values of the d i -pole moment determined here i n table 5.6. Table 5.6 The E l e c t r i c Dipole Moment of C l 0~F Experimental CNDO y a (D) 0.551 + 0.020 3 0.438 yb (D) 0 0 y c (D) 1.632 + 0.020 1.182 u (D) 1.722 + 0.020 1.260 Uncertainty includes a p e s s i m i s t i c estimate of the influence of incomplete s p i n - r o t a t i o n uncoupling. There are four p o s s i b l e o r i e n t a t i o n s of the dipole moment of c h l o r y l f l u o r i d e , because the sign of the two non-zero components i s not determined. However, e l e c t r o n e g a t i v i t y considerations and the r e s u l t s of the CNDO c a l c u -l a t i o n i n d i c a t e that the dipole moment i s direc t e d along the c-axis toward the c h l o r i n e atom and toward the oxygen atoms along the a-axis. The dipole 35 16 moment of c h l o r y l f l u o r i d e i n the C l O^F p r i n c i p a l i n e r t i a l axis system i s pl o t t e d i n f i g u r e 5.4 A comparison of the components of the dipole moment of c h l o r y l f l u o r i d e along the Cl-F bond, 1.552 D, and i n the C10 2 plane, 1.539 D, with the dipole moments of the molecules C1F, 0.881 D [74], and C10 2 > 1.785 D [69], i n d i c a t e s that there i s an unusually large d r i f t of e l e c t r o n density i n c h l o r y l f l u o r i d e toward the f l u o r i n e atom (see figure 5.4). -100-F O Figure 5.4 The E l e c t r i c Dipole Moment of C h l o r y l Fluoride i n the a_,£-Plane from the dipole moment of the molecule C10^. This i s apparently a r e s u l t of successful competition by the very electronegative f l u o r i n e atom with the oxy-gen atoms f o r e l e c t r o n density on ch l o r i n e . However, the r e l a t i v e l y small v a l -ue of t h i s change i n dipole moments suggests that the CIC^ molecular o r b i t a l s from which f l u o r i n e i s most successful i n removing e l e c t r o n density are not o r b i t a l s that strongly contribute to the dipole moment of CH^. The component of M C ^ Q F along the Cl-F bond i s nearly twice as large as the dipole moment of C1F (larger by 0.671 D). Naively one might expect t h i s component to be smaller than P^F' because el e c t r o n withdrawal by the oxygen atoms should increase the e l e c t r o n e g a t i v i t y of c h l o r i n e . The observed dipole moment of ClO-F a c t u a l l y would be consistent with such a p i c t u r e i f one were The component of u i n the C10- plane i s reduced s l i g h t l y (by 0.246 D) -101-to change the sign of the a-component. However, this i s completely inconsis-tent with the large amount of ionic character of the Cl-F bond suggested by the quadrupole coupling constants, by the very low Cl-F stretching force con-stant [5], and by the unusually long Cl-F bond (see chapter 6), and directly conflicts with the results of the CNDO calculation. The apparently real, very large value of the component of the dipole mo-ment of chloryl fluoride along the Cl-F bond means that there i s a large d r i f t of electron density from the CIO2 frame toward the fluorine atom. The fact that yCjjj is smaller by roughly half indicates that this electron density d r i f t is significantly larger than that which may be accounted for by differences in the electronegativities of chlorine and fluorine. The percent ionic character of the Cl-F bond in CK^F can be estimated with the equation: component of F along Cl-F % ionic character = 2 i n n x 100 er(Cl-F) The result, 20 percent ionic character, i s in qualitative agreement with the change in 3p electron density, An , of -0.53 determined from the quadrupole 3. SL coupling constant analysis. Note that the angle between the ja-axis and the Cl-F bond is small, 15° 36', so such a comparison is reasonable. Of course, percent ionic character i s a measure of net electron density d r i f t and An^ only of electron density d r i f t out of the chlorine 3p atomic orbital, but the expectation is that the 3p chlorine atomic orbital makes the largest chlorine 3. contribution to the Cl-F bond and to the dipole moment component along the Cl-F bond. -102-35 16 5.4 N u c l e a r Quadrupole C o u p l i n g C o n s t a n t s o f C l O^F i n the H i g h F i e l d  S p i n - R o t a t i o n Uncoupled L i m i t . The magnitude o f the s p l i t t i n g between the h i g h f i e l d h y p e r f i n e compo-n e n t s o f t h e 1^ Q~0Q Q A N C * 3^ ±-^2 ^ t r a n s i t i o n s a l l o w s an independent d e t e r -35 16 m i n a t i o n o f the n u c l e a r q u a d r u p o l e c o u p l i n g c o n s t a n t s o f C l O^F and p r o v i d e s c o n f i r m a t i o n t h a t t h e 3^ i~^2 1 S t a r k component t h a t was o b s e r v e d was i n d e e d t h e Mj = + 3 component. E q u a t i o n s 2.43 and 2.31 a l l o w one to e x p r e s s t h e energy s e p a r a t i o n between = + 3/2 and + 1/2 h i g h f i e l d h y p e r f i n e components o f a p a r t i c u l a r r o t a t i o n a l s t a t e a s : <AE Q> = < E Q > ^ = ± 3 / 2 - < E Q > ^ = ± 1 / 2 [ 3 M / - J ( J + l ) ] [ 3 < P c 2 > - J ( J + 1) + {<P c 2> - w ( b o ) } n / b o ] x c c 2 J ( 2 J - 1 ) ( J + 1 ) ( 2 J + 3) (5.7) The o b s e r v e d s p l i t t i n g between h y p e r f i n e components o f t h e 1^ Q~0Q Q and 3». T-30 1 t r a n s i t i o n s were o b t a i n e d by a v e r a g i n g the d i f f e r e n c e i n h y p e r -f i n e component f r e q u e n c i e s o v e r the h i g h f i e l d r e g i o n . A l l S t a r k measurements o f the 3, -.-39 , t r a n s i t i o n were c o n s i d e r e d t o l i e w i t h i n the h i g h f i e l d r e -3,1 Z , i g i o n and t h o s e measurements o f t h e 1^ Q~0Q Q t r a n s i t i o n above a f i e l d s t r e n g t h of 2500 V/cm. R e s u l t s (Mj = + 3/2 component f r e q u e n c y minus Mj = + 1/2 compo-nent f r e q u e n c y ) were 9.86 + 0.18 MHz and -3.41 + 0.16 MHz f o r the l j Q - 0 0 Q and 3- i ~ 3 9 , t r a n s i t i o n s r e s p e c t i v e l y . S u b s t i t u t i o n o f t h e s e v a l u e s and a p p r o p r i a t e machine c a l c u l a t e d Wang r e -duced e n e r g i e s and momentum e x p e c t a t i o n v a l u e s i n t o e q u a t i o n 5.7 a l l o w s a c a l c -u l a t i o n o f the qua d r u p o l e c o u p l i n g c o n s t a n t s X c c and n. R e s u l t s o f t h i s c a l c --103-u l a t i o n are presented i n table 5.7 with the r e s u l t s of the e a r l i e r zero f i e l d quadrupole a n a l y s i s . There i s s u b s t a n t i a l agreement with the zero f i e l d values providing very strong evidence that the correct assignment of the observed 3_ -,-3„ 1 Stark component i s M = + 3. Equation 5.7 p r e d i c t s no high f i e l d hyperfine s p l i t t i n g f o r the = + 2 Stark component and a s p l i t t i n g roughly 3/5 as large f o r the much weaker Mj = + 1 Stark component. However, the extent of the disagreement between zero and high f i e l d values i s l a r g e r than measure-ment un c e r t a i n t i e s can e a s i l y account f o r and again suggests the incomplete attainment of the high f i e l d l i m i t i n g case. Table 5.7 Nuclear Quadrupole Coupling Constants of C l 0„F Zero F i e l d High F i e l d x c c (tote) 51.82 + 0.16 49.3 + 1.0 n 0.341 + 0.005 0.409 + 0.030 -104-Chapter 6 The Molecular Structure of Chloryl Fluoride 6.1 Determination of the Internuclear Parameters of Chloryl Fluoride Infrared and Raman vibrational studies of chloryl fluoride have reasonably unambiguously shown that the molecule belongs to the C g group [4, 5], This and qualitative chemical bonding arguments suggest a distorted trigonal pyr-amidal molecular structure with chlorine at the apex. A number of aspects of 35 16 37 16 35 16 18 the microwave spectra of Cl O^F, Cl O^F, and Cl 0 OF support this conclusion: (1) The similarity between x c c and the quadrupole coupling constant of ClO^ [75] suggests that the structure of chloryl fluoride does not d i f f e r radically from the structure of this isoelectronic ion. (2) The small changes in the moments of inertia upon isotopic chlorine substitution indicates that chlorine l i e s near the center of mass. (3) The near identity of the quan-35 16 37 16 t i t y I +1 - I, of the Cl 0„F and Cl 0~F isotopic species indicates a c b JL L that the chlorine b_-coordinate is zero. Finally (4), the fact that only one 35 16 18 spectrum could be assigned to a species of molecular formula Cl 0 OF i n d i -cates that the two oxygen positions are equivalent. The moments of inertia de-termined from the ground vibrational state rotational constants of chloryl fluor-ide are presented in table 6.1 Table 6.1 Principal Moments of Inertia of Chloryl Fluoride 3 5 C 1 1 6 0 2 F 3 7 C 1 1 6 0 2 F 3 5 C 1 1 6 0 1 8 0 F I (amu X2) 52.4487 52.6533 55.0642 a t 2 i I (amu X2) 100.6910 100.7517 I b (amu X ) 61.0695 61.3404 62.3861 104.3500 -105-Table 6.1 (continued) 3 5 C 1 1 6 0 2 F 3 7 C 1 1 6 0 2 F 3 5 C 1 1 6 0 1 8 0 F I + I - 92.0701 92.0642 a c The structure of c h l o r y l f l u o r i d e was determined by c a l c u l a t i n g some nu-c l e a r coordinates from Kraitchman's equations and r e q u i r i n g others to s a t i s f y center of mass or moment of i n e r t i a conditions. I t was not p o s s i b l e to de-termine a complete r structure because only one n a t u r a l l y occurring isotope s of f l u o r i n e e x i s t s . Q u a l i t a t i v e aspects of the microwave spectra i n d i c a t e that C l and F l i e i n the a_,c_-plane and that the b_-coordinates of the two 0 atoms are equal i n magnitude and opposite i n sign. S u b s t i t u t i o n coordinates 35 16 of C l were, therefore, c a l c u l a t e d i n the C l 0 2F p r i n c i p a l i n e r t i a l a xis system from equation 2.54, and coordinates of 0 from equation 2.55. An am-b i g u i t y i n sign arose from the use of Kraitchman's equations. However, a r e a -sonable structure was po s s i b l e only i f the a_-coordinates of C l and 0 were as-sumed to have the same sign, and the ^-coordinates opposite signs. The f l u o r i n e a- and c_-coordinates can be ca l c u l a t e d from the two f i r s t moment equations, or by repl a c i n g one or both of these with one or more of the ground v i b r a t i o n a l state p r i n c i p a l i n e r t i a l moment equations, £ mi ai = ^ (6.1a) (6.1b) ! m i ( b i 2 + c i 2 ) " \ (6.1c) -106-lm±(a±2 + c. 2) = I b Zm.(b.2 + a.2) = I 1 1 1 1 c (6.1d) (6.1e) or the off-diagonal i n e r t i a l moment equation, -Sm.a.c. = 0 i i i i (6.If) The fluorine c-coordinate is quite small. Because principal i n e r t i a l mo-ment equations are i l l - s u i t e d for the accurate determination of near axis co-ordinates, equation 6.1b was used for the calculation of the fluorine c-coord-inate. The fluorine a-coordinate, which i s quite large, was calculated in turn by using equations 6.1a, 6.1d, and 6.1e. The resulting molecular struc-35 16 tures and the f i r s t and second Cl O^F i n e r t i a l moments that correspond to these structures are presented in table 6.2. Table 6.2 The Structure of Chloryl Fluoride with Complete r Determination of C10~ Group Structure Equations Used: 6.lb, 6.la 6.1b, 6.1d 6. lb, 6. le r(Cl-F) (X) r(Cl-O) (X) (O-Cl-0) (F-C1-0) l m i \ l m ± C i I (calc) - I (obs)' a. a I, (calc) - I, (obs) b b I (calc) - I (obs)' c c - l : m i a i c i c 1.6652 1.6874 1.6905 1.4220 1.4220 1.4220 114.729° 114.729° 114.729° 102.000° 102.108° 102.123° 0.0 -0.438 -0.500 0.0 0.0 0.0 -0.143 -0.143 -0.143 -1.259 0.0 0.180 -1.438 -0.179 0.0 0.183 0.125 0.117 Equations used to determine the fluorine coordinates, In amu X. C In amu X2, -107-There i s a disturbing lack of consistency between the structures in table 6.2 in which the f i r s t moment condition was used to determine the fluorine a-coordinate and those in which principal i n e r t i a l moment conditions were used. The disagreement unfortunately reflects i t s e l f primarily in the value of the important Cl-F bond length. The origin of the disagreement i s , however, read-i l y isolated and corrected. It i s easily shown that Kraitchman's equations i n -accurately determine near axis coordinates [61]. The smallest non-zero coord-inate in the CIO2 frame of chloryl fluoride is the chlorine a_-coordinate, calc-ulated from Kraitchman's equations to be 0.1760 X. Disagreement between f i r s t and second moment determinations of the fluorine a-coordinate suggests that a near axis a-coordinate in the CIO2 frame of the molecule is inaccurate. The prime suspect i s , of course, the a-coordinate of chlorine. To remove the structural disagreement, the chlorine ^-coordinate calcula-ted from Kraitchman's equation was disregarded, and the fluorine a- and c-co-ordinates and the chlorine ji-coordinate were calculated from the following sets of equations: 6.1a, 6.1b, and 6.Id; 6.1a, 6.1b, and 6.1e; and f i n a l l y 6.1a, 6.1b, and 6.If. Results are presented in table 6.3. Table 6.3 The Structure of Chloryl Fluoride with F, a- and c- and Cl a-Coodinates Determined from Fir s t and Second Moment Conditions Equations Used: 6.1a, b, d 6.1a, b, e 6.1a, b, f r(Cl-F) (£) r(Cl-O) (R) (O-Cl-0) (F-C1-0) 101.737 1.4183 115.198° 1.6956 1.4178 115.264° 101.700° 1.6999 1.4182 115.212° 101.729° 1.6966 0.0 0.0 0.0 0.0 0.0 0.0 -108-Table 6.3 (continued) Equations Used: 6.1a, b, d 6.1a, b, e 6.1a, b, f I (calc) - I (obs)° a a -0.143 -0.143 -0.143 I, (calc) - I, (obs) b b 0.0 0.179 0.038 I (calc) - I (obs)° c c -0.179 0.0 -0.141 _ l m i a i c i c 0.005 -0.020 0.0 Equations used to determine the fluorine a- and c_- and the chlorine ^-coordinates. A l l other coordinates were determined from Kraitch-man's equations. In amu X . In amu X 2 . The agreement between structural parameters and the consistency with the ground vibrational state f i r s t and second moment conditions of the chloryl fluoride structures in table 6 .3 is now very satisfactory. The proposed struc-ture of chloryl fluoride, obtained by averaging the parameters of the structures in table 6 . 3 , is presented in table 6 . 4 . The values of the nuclear coordinates 35 16 in the Cl O^F principal i n e r t i a l axis system are presented in table 6 . 5 . Table 6 .4 Structure of Chloryl Fluoride r(Cl-F) (X ) r(Cl-O) (X ) Z(O-Cl-O) Z(F-Cl-O) 1.697 + 0.003 1.418 + 0.002 115.23 + 0.05° 101.72 + 0.03° -109-Table 6.5 Nuclear Coordinates of C h l o r y l F l u o r i d e 35 16 i n the C l 0 0F P r i n c i p a l I n e r t i a l Axis System a (X) b (X) c (X) C l 0.1877 0.0 0.3240 F -1.4471 0.0 -0.1325 0 0.6542 1.1975 -0.2755 0 0.6542 -1.1975 -0.2755 6.2 Discussion of the Structure of C h l o r y l Fluoride and Related Molecules The inte r n u c l e a r parameters and p r i n c i p a l s t r e t c h i n g force constants of c h l o r y l f l u o r i d e and a few re l a t e d molecules are presented f o r comparison i n table 6.6. I t i s seen that the Cl-F bond i n c h l o r y l f l u o r i d e i s s u b s t a n t i a l l y longer than that observed i n the molecule C 1 F . Of bond lengths between c h l o r -ine and f l u o r i n e that have been determined, only the off-symmetry axis C l - F bond i n CIF^ i s comparable. The long Cl-F bond length suggests an unusually weak bond, and t h i s i s also r e f l e c t e d i n the C 1 F s t r e t c h i n g force constants i n table 6.6. The c h l o r y l f l u o r i d e C 1 F s t r e t c h i n g force constant determined by Smith, Begun, and Fletcher [5] i s the lowest k , yet determined. I t i s , C l r however, nearly equalled by force constants i n CIF^ and ClF,., the l a t t e r sug-gesting that C 1 F , . w i l l also prove to have an unusually long Cl-F bond. I t - i s also observed that the C I O 2 moiety experiences a s i g n i f i c a n t s t r u c -t u r a l change upon formation of the Cl-F bond. The Cl-0 bond i n c h l o r y l f l u o r -ide i s roughly 0.05 X shorter and has a considerably higher s t r e t c h i n g force constant than the Cl-0 bond i n chlorine dioxide, i n d i c a t i n g that Cl-F bond f o r --110-mat ion causes an e l e c t r o n i c rearrangement i n the C10 2 species that consider-ably strengthens the Cl-0 bond. Table 6.6 S t r u c t u r a l Parameters and Stretching Force Constants of C h l o r y l F luoride and Related Molecules r ( C l - F ) a k b  KC1F r ( C l - 0 )a k b  KC10 ^.(O-Cl-O) reference C10 2F 1.697 2.53 1.418 9.07 115° 14' here, 5 cio 2 1.471 6.74 117° 35' 69, 96 C1F 1.628 4.56 74, 78 C1F 3 1.698 ,1.598C 2.92 4.29 C 97, 98 C1F 5 2.57 3.01 d 99 3 InX. b In mdy/X. c Bond on C 2 symmetry a x i s . ^ Bond on C^ symmetry a x i s . Carter, Johnson, and Aubke [6] have suggested on the b a s i s of the v i b r a -t i o n a l spectra and chemistry of c h l o r y l f l u o r i d e that the molecular bonding i n C10 2F i s s i m i l a r to that observed i n NOF [100], N0 2F [101], 0 ^ [102], and 0 2F [103]. To t h i s l i s t might also be added NSF [104], and S ^ [105]. A l l of these molecules appear to be characterized by an unusually long f l u o r i n e bond to a reasonably stable paramagnetic species. Formation of the f l u o r i n e bond u s u a l l y r e s u l t s i n various degrees of shortening and strengthening of the multiple bond(s) of the parent paramagnetic species. The in t e r n u c l e a r parameters and a v a i l a b l e s t r e t c h i n g force constant of N0 2F, NOF, 0,^, S,^, and r e l a t e d molecules are presented i n tables 6.7 through 6.11. - I l l -Table 6.7 Structural Parameters af Ni t r y l and Related Molecules Fluoride r(N-F) (X) r(N-O) (X) reference N02F 1.467 1.180 101 N02 1.197 106 N02C1 1.202 107 HON02 1.180 108 NF 3 1.371 109 cis-N 2F 2 1.384 110 CH3NF2 1.413 111 Table 6.8 Structural Parameters and Stretching Force Constants of Nitrosyl Fluoride and Related Molecules r(N-F) 3 STF13 r(N-0) a reference NOF 1.52 2.09 1.13 15.08 100, 112 NO 1.151 15.5 113, 114 NF 3 1.371 6.14 109 F2NH 1.400 115 cis-N 2F 2 1.384 110 CH3NF2 1.413 111 N0C1 1.17 13.97 116, 117 NOBr 1.15 14.00 117 HN0 1.21 10.5 118 a InX. b In mdy/X. -112-Table 6.9 Structural Parameters and Stretching Force Constants of Thionitrosyl Fluoride and Related Molecules r(S-F) a reference NSF 1.646 2.9 1.446 10.7 104, 119 NS 1.496 8.5 1 2 0 S F4 1.545 1.646C 1 2 1 S F 6 1.58 5.30 1 2 2 , 123 OSF2 1.585 5.18 124, 125 S 0 2 F 2 1.530 5.14 126, 125 N S F 3 1.552 5.6 1.416 12.4 127, 119 a InX. ^ In mdy/X. c Nearly linear F-•S-F bond. Table 6 . 1 0 Structural Parameters and Stretching Force Constants of Dioxygen Difluoride and Related Molecules r(O-F) 3 "OF' C reference °2 F2 1.575 1.50 1.217 10.24 1 0 2 , 128 0 2F 1.43 10.47 103 °2 1.208 11.4 129, 130 F 20 1.412 3.95 48 H 0 2 6.1 131 H2°2 1.48 4.6 132 -113-a InX. In m dy/X. Table 6.11 S t r u c t u r a l Parameters of Sulfur Monofluorlde and Related Molecules (S-F) (X) r(S-S) (X) reference FSSF 1.635 1.888 105 S2 1.889 130 S2 B r2 1.98 133 s 2 c i 2 1.97 133 s2o 1.884 134 H2 S2 2.055 135 S8 2.07 136 SSF 2 1.598 1.860 137, OSF 2 1.585 124 Two qualitative theories have been proposed at various times to account for the anomalous bonding features of these compounds. In a valence bond approach [102, 107, 105] the unusually long fluorine bond can be accounted for by contributions of ionic structures of form II to the resonance hybrid. ~ ; p ' \ . . X ' \ X 7 9 X Jfi-C1+-+ ^ci++ N c i+ + : F : : F : - : F : -I n Such structures are also consistent with the observed shortening of the Cl-0 -114-bond i n c h l o r y l f l u o r i d e when compared to the parent CIC^ molecule. Similar i o n i c structures can account for the observed bond shrinkage i n the frames of NO*2F, NOF, and NSF. In the cases of 0 2 F 2 and S,^ the contributions of p o s s i b i l e i o n i c valence bond structures should r e s u l t i n 0-0 and S-S bond lengths l y i n g somewhere between t y p i c a l s i n g l e and double 0-0 and S-S bonds. In both cases the bond lengths are very near the double bond values which suggests a near 100% c o n t r i b u t i o n from the i o n i c s t r u c t u r e s . Lipscomb [102] has also suggested a multicentered molecular o r b i t a l de-s c r i p t i o n that has been generalized by Spratley and Pimentel [138] i n t o t h e i r (p - i r*)a bonding formalism. C10 2 > NO, NS, 0 2 > and S 2 a l l have one or more s i n g -l y occupied antibonding TT* molecular o r b i t a l . The highest s i n g l y occupied or-b i t a l i n N0 2 > however, i s not c l e a r l y antibonding and may have considerable nonbonding character. Formation of the f l u o r i n e bond i s described by a over-lap of the parent species' TT* o r b i t a l on one atom (presumably the atom with the greatest TT* e l e c t r o n density) with a 2p atomic o r b i t a l on f l u o r i n e . I t was suggested by Spratley and Pimentel [138] that formation of such a bond, at l e a s t when the parent species i s 0 2 or NO, i s accompanied by the release of a very l i t t l e e l e c t r o n density from f l u o r i n e into the parent species' TT* o r b i t a l . The present evidence, however, suggests that such bonds are characterized by the withdrawal of e l e c t r o n density from the TT* o r b i t a l . This m o d i f i c a t i o n of the (p-TT*)o bond theory i s consistent with the observed shortening of the bond(s) i n the parent species, and quite reasonable on the basis of e l e c t r o -n e g a t i v i t y arguments. Because the molecular o r b i t a l that describes the r e -s u l t i n g (p - T r*)a f l u o r i n e bond i s not w e l l l o c a l i z e d between f l u o r i n e and the atom to which i t i s bonded, the bond i s r e l a t i v e l y long and weak. Analysis of the nuclear quadrupole coupling constants and e l e c t r i c dipole -115-moment of chloryl fluoride i s quite consistent with either the qualitative valence bond theory or the present modification of the (p-Tr*)a bond theory. The unpaired electron in chlorine dioxide i s in a b^* orbital which i s anti-bonding between chlorine and oxygen [139]. This orbital has lobes on chlorine that are perpendicular to the CTC^ plane, and bond formation apparently results from overlap of one of these lobes with a fluorine 2p orb i t a l . Because the bj * orbital i s antibonding, i t readily surrenders electron density to the very electronegative fluorine, and hence the large dipole moment component observed along the Cl-F bond (see section 5.3) and the large depopulation of the chlor-ine 3p orbital directed largely along the Cl-F bond (see section 4.4). It i s possible to find some confirmation of this general bonding scheme in the trends observed between the six systems described in tables 6.6 through 6.11. A summary of the observed structural changes of the parent species and the differences between the apparently anomalous fluorine bond lengths and appropriate "normal" bond lengths is presented in table 6.12. Table 6.12 Summary of the Anomalous Structures of CIC^F, NC^F, NOF, NSF, 0 ^ , and S 2F ABF Ar(B-F) a (X) Ar(A-B) b (X) C102F +0.07 -0.05 N02F +0.10 -0.02 NOF +0.15 -0.02 NSF +0.07 -0.05 °2 F2 +0.16 +0.01 S 2F 2 +0.06 0.00 -116-Ar(B-F) i s the d i f f e r e n c e between the observed B-F bond length and a "normal" B-F bond length. The following "normal" bond lengths were assumed: r ( C l - F ) = 1.63 A (C1F), r(N-F) = 1.37 X (NF„), r(S-F) = 1.58 X (SF,), and r(O-F) = 1.41 X ( F 2 0 ) . Ar(A-B) i s the A-B bond length observed i n ABF subtracted from that observed i n the molecule AB i t s e l f . An i n t e r e s t i n g r e s u l t that supports the general v a l i d i t y of a bonding p i c -ture i n v o l v i n g e l e c t r o n withdrawal along a (p - T T*)a bond i s observed i f one l i s t s the s i x systems i n table 6.12 i n order of decreasing values of Ar(B-F) and de-creasing values of Ar(A-B). Ar(B-F): 0,,, NO > N0 2 > C10 2 > NS, S 2 Ar(A-B): S 2 > 0 2 > NO, N0 2 > C10 2 > NS With the exception of the S 2 system that i n e x p l i c a b l y l i e s at opposite extremes i n the two l i s t s , one notes that the ordering i n both l i s t s i s s i m i l a r , and that the ordering, p a r t i c u l a r l y the Ar(B-F) ordering, appears to be c o r r e l a t e d with what one would reasonably expect to be the group e l e c t r o n e g a t i v i t y of the parent species. Some f a i t h i s required to place much s i g n i f i c a n c e i n t h i s ob-servation, because the small s t r u c t u r a l changes i n some cases approach the un-c e r t a i n t y i n the structures themselves. Nevertheless, i t i s noted that the trend i s consistent with a bonding scheme i n v o l v i n g s u b s t a n t i a l e l e c t r o n withdrawal from an antibonding o r b i t a l . The more highly electronegative parent species release l e s s T T* e l e c t r o n density to the very electronegative f l u o r i n e atom. Consequently there i s l e s s bond contraction i n the parent moiety and the f l u o r -ine bond i s weaker and longer. As a c o r o l l a r y , t h i s suggests that molecules formed between one of the s i x parent species i n table 6.12 and one of the l e s s electronegative halogens should not show the same anomalous features, at l e a s t not to the extent seen -117-in the fluorine compounds. Clayton, Williams, and Weatherly [107], however, have reported the opposite observation. A comparison of the N-Halogen bond lengths in N02F and N02C1, and NOF, N0C1, and NOBr with the sum of the appro-priate covalent r a d i i shows that the N-Halogen distances exceed the sum of the covalent r a d i i by greater amounts as one goes through the halogen series from fluorine to bromine. Clayton et.al. were unable to explain this observation in terms of bond structures. It is f e l t that their treatment is not correct because the approximation of the additivity of covalent r a d i i assumed by Clay-ton .et.al. i s not sufficiently accurate to define a "normal" halogen bond length. Unfortunately insufficient structural data exists to well define a "nor-mal" N-Cl or N-Br bond length. However, sufficient evidence to reasonably dispute the treatment of Clayton .et.al.. exists in the S 2Hal 2 series of com-pounds. Table 6.13 Sulfur Halogen Bond Lengths in S„Hal„ and Related Compounds r(S-F) a r ( S - C l ) a r(S-Br) a reference S 2Hal 2 1.635 2.07 2.24 105, 133 0SHal 2 1.585 2.07 2.27 124, 140 Sum of Covalent Radii 1.76 2.03 2.18 141 a In A. If the sum of covalent r a d i i is used to define a "normal" S-Halogen bond length, the S-F bond in S 2F 2 is actually shorter than expected by 0.12 X. The S-Cl and S-Br bonds are then anomalously long by 0.04 X and 0.06 X. This -118-i s the same sort of trend reported by Clayton e t . a l . i n the NO^Hal and NOHal ser i e s of compounds. However, i f we adopt the bond lengths observed i n the t h i o n y l hadides as "normal" S-Halogen bond lengths, the d i f f e r e n c e s , as we run down group VII from F to Br, between the S-Halogen bond lengths of S^Eal^ and the "normal" bond lengths are +0.05, 0.00 , and -0.03 8. This i s i n c l o s e r accord with expectations based on the present work. However, the d i f f e r e n c e s that we are t r y i n g to observe are on the same order of magnitude as the uncer-t a i n t y (+ 0.02 A*) i n the e l e c t r o n diffraction-determined structures of S2CI2, S 2 ^ r 2 ' OSC^, and OSB^. So, although i t i s p o s s i b l e to dispute the treatment of Clayton, Williams, and Weatherly, i t i s not possible to claim that the e v i -dence supports the opposite trend. Another approach i s to compare bond shrinkage i n the parent species when bonded to d i f f e r e n t halogens. Here the l i m i t e d evidence does seem unambiguous-l y to support a bonding p i c t u r e i n v o l v i n g a d r i f t of e l e c t r o n density from an antibonding TT* o r b i t a l toward f l u o r i n e . Kuczkowski [105] has already noted that r(S-S) i n the s e r i e s of compounds S2Hal2 increases as one goes down group VII. The data presented i n tables 6.7 and 6.8 show that the same trend i s apparently observed i n the ISK^Hal and NOHal se r i e s of compounds. F i n a l l y i t should be noted that there i s ample chemical evidence suggest-ing that at l e a s t some of the parent species considered i n table 6.12 do read-i l y surrender an electron from t h e i r s i n g l y occupied o r b i t a l s to form reason-ably stable cations. C h l o r y l , n i t r y l , n i t r o s y l , and dioxygenyl s a l t s have a l l been w e l l characterized [3]. -119-Chapter 7 The Microwave Spectrum of Acetaldehyde-d^ 7.1 Assignment of the Spectrum Acetaldehyde i s a near p r o l a t e asymmetric top molecule with dipole moment components along the a_ and b_-principal i n e r t i a l axes. Assignments have been made by K i l b , L i n , and Wilson (K, L, and W) to the i s o t o p i c species CH^CHO, T O -io 1 T 1 18 CD3CDO, CD3CHO, CH^CHO, CHD2CHO, CH^HO, CH 3 CHO, CH 3 CHO, and CH^ H 0 [7], A reasonably well determined r Q structure of acetaldehyde was ca l c u l a t e d by K, L, and W which allowed a confident p r e d i c t i o n of the microwave spectrum of the CH3CDO i s o t o p i c species. A l l r o t a t i o n a l states i n acetaldehyde are s p l i t into A and E species t o r -s i o n a l sublevels by coupling between the o v e r a l l r o t a t i o n a l motion of the mol-ecule and the i n t e r n a l t o r s i o n a l motion of the methyl group. The b a r r i e r to i n t e r n a l r o t a t i o n has been determined f o r the symmetrical methyl species CH^HO, CD3CDO, CD3CHO, 1 3CH 3CHO, CH^CHO, and 1 3CH 3 1 3CHO [7, 55] and the unsymme-t r i c a l methyl species C^DCHO and CT^HCHO [142]. In a l l cases the b a r r i e r to i n t e r n a l r o t a t i o n was found to l i e within 5% of 1160 cal/mole. This value and the r Q structure determined by K, L, and W allowed reasonable p r e d i c t i o n s of the magnitude of the t o r s i o n a l s p l i t t i n g i n the CH3CD0 i s o t o p i c species. Acetaldehyde i s a molecule with a high b a r r i e r to i n t e r n a l r o t a t i o n . Ro-t a t i o n a l t r a n s i t i o n s i n the A t o r s i o n a l sublevel of such a molecule obey a pseudorigid rotor Hamiltonian [53]. Assignments of CH3CD0 t r a n s i t i o n s within t h i s t o r s i o n a l manifold were, therefore, made on the basis of t h e i r consistency with a r i g i d rotor Hamiltonian, with considerable assistance from p r e d i c t i o n s based on K, L, and W's r Q structure. There was i n i t i a l l y some d i f f i c u l t y i n assigning the b-type, A sublevel t r a n s i t i o n s that depend strongly on the value -120-of the r o t a t i o n a l constant A. The assignment of these t r a n s i t i o n s , however, was r e l i a b l y f i x e d when microwave-microwave modulated double resonance [72] was observed between the 3Q 2~^1 2 A N C * 2 1 2~^~1 1 t r a n s i t i ° n s ( s e e section 3.4). The t o r s i o n a l s p l i t t i n g between A and E sublevel t r a n s i t i o n s was predicted from the previously determined b a r r i e r to i n t e r n a l r o t a t i o n of other i s o t o p i c species using equation 2.50. These p r e d i c t i o n s and the knowledge that the doubly degenerate E sublevel r o t a t i o n a l states have f i r s t order Stark e f f e c t s [53] f a c i l i t a t e d the assignment of the E sublevel r o t a t i o n a l t r a n s i t i o n s . 7.2 Determination of the Rotational Constants and the B a r r i e r to Internal  Rotation Observed A t o r s i o n a l sublevel r o t a t i o n a l t r a n s i t i o n frequencies and the t o r s i o n a l s p l i t t i n g between A and E r o t a t i o n a l t r a n s i t i o n frequencies are presented i n table 7.1. The b a r r i e r to i n t e r n a l r o t a t i o n was ca l c u l a t e d from the observed t o r s i o n -a l s p l i t t i n g s , Av„, by the p r i n c i p a l axis system method developed by Wilson and Herschbach (see section 2.5). The t o r s i o n a l s p l i t t i n g of an observed tr a n s -i t i o n i s r e l a t e d to the b a r r i e r to i n t e r n a l r o t a t i o n through the equation Av_. = FT{W<n> - W^ nh(EA I P /I ) n (7.1) E n 0,±1 0,0 g g a g g where F, A , I and I are parameters defined i n section 2.5 and are functions g a g only of the molecular structure and c e r t a i n fundamental constants. The bar-(n) r i e r dependent terms are the perturbation expansion c o e f f i c i e n t s , W v, a For the purpose of the b a r r i e r c a l c u l a t i o n , the methyl top moment of i n -e r t i a suggested by Laurie a f t e r applying an i n e r t i a l defect c o r r e c t i o n , -121-Table 7.1 Observed and Calculated CH^CDO T r a n s i t i o n Frequencies ( i n MHz) a b T r a n s i t i o n v obs v c a l c Av obs V (cal/mole) 10,1 °0,0 18 891.54 18 891.44 1.44 1233.3 1 i , o " 1 o , i 36 403.07 36 402.82 89.53 1172 2 -1 0,2 0,1 37 740.26 37 739.99 3.75 1169.2 21,2_11,1 36 353.99 36 354.20 -59.43 1179.2 2 -2 1,1 0,2 37 874.19 37 874.38 151.01 1179.7 2 -1 1,1 1,0 39 211.40 39 211.56 65 1182 3 -2 0,3 1,2 22 914.78 22 914.71 3 -3 1,2 J l , 3 8 571.30 8 571.28 -20.72 1190.6 4 -4 1,4 *1,3 14 280.60 14 281.18 -0.96 1201.0 51,4-51,5 21 406.19 21 407.71 16.99 — 61,5-61,6 29 930 89 29 934.90 32.32 — Frequencies c a l c u l a t e d from a r i g i d r o t o r model spectrum with r o t a t i o n a l constants 45,134.19; 10,160.06; and 8,731.38 MHz. b A V E = V E " VA 3.180 amu X 2 , was adopted [143]. The d i r e c t i o n cosines between the methyl top symmetry axis and the p r i n c i p a l i n e r t i a l axes of CH^CDO were c a l c u l a t e d assuming K, L, and W's r Q acetaldehyde str u c t u r e . The angle between the a-p r i n c i p a l i n e r t i a l axis and the methyl top symmetry axis determined i n t h i s way was 23.2°. The b a r r i e r c a l c u l a t i o n was completed by assuming the accuracy of these s t r u c t u r a l parameters and f i t t i n g the t o r s i o n a l s p l i t t i n g of each observed t r a n s i t i o n exactly by varying the value of the b a r r i e r height, V^. The t o r -s i o n a l s p l i t t i n g of each observed t r a n s i t i o n was cal c u l a t e d from equation -122-7.1 for values of the reduced b a r r i e r height, s, that were s u f f i c i e n t to bra-ket the observed t o r s i o n a l s p l i t t i n g . The cal c u l a t e d s p l i t t i n g of a given t r a n s i t i o n was then pl o t t e d versus s and the b a r r i e r height necessary to repro-duce the given observed s p l i t t i n g was obtained by graphical i n t e r p o l a t i o n . The c a l c u l a t i o n was c a r r i e d to fourth order (n = 4) i n the perturbation expan-sion with the neglect of quadratic and higher order cross terms i n angular momentum components. Because acetaldehyde i s a very near pr o l a t e asymmetric 3 r o t o r , only terms in v o l v i n g P and P were included among the odd order con-a a t r i b u t i o n s . Matrix elements of even powers of angular momentum components were evaluated with the computer program TOP i n the l i b r a r y of the microwave group at Harvard U n i v e r s i t y w ritten by Pierce and Dobyns [76, 144]. Odd order momentum expectation values were evaluated with the program LINEAR DPZ written by Beaudet [145]. The necessary perturbation c o e f f i c i e n t s were obtained from Wollrab's extensive tabul a t i o n of perturbation c o e f f i c i e n t s f o r the i n t e r n a l r o t a t i o n problem [57]. The b a r r i e r heights required to reproduce the observed t o r s i o n a l s p l i t t i n g s can be found i n the l a s t column of table 7.1. The t o r s i o n a l s p l i t t i n g s obser-ved i n the J T t r a n s i t i o n s f o r J > 4 could not be f i t by reasonable b a r r i e r heights. Similar disagreement between ca l c u l a t e d and experimental v a l -ues were observed i n the parent i s o t o p i c species and a t t r i b u t e d to d i f f e r e n c e s i n c e n t r i f u g a l d i s t o r t i o n i n the A and E t o r s i o n a l branches of the same r o t a -t i o n a l t r a n s i t i o n [7]. C e n t r i f u g a l d i s t o r t i o n a r i s i n g from the coupling be-tween v i b r a t i o n a l motions and i n t e r n a l r o t a t i o n has been discussed by Kirtman [146]. His semiempirical treatment i n d i c a t e s that a s i z a b l e v i b r a t i o n a l -t o r s i o n a l i n t e r a c t i o n may occur i n near pr o l a t e asymmetric rot o r s p a r t i c u l a r l y for K , = 1 state s . - 1 2 3 -The proposed height of the b a r r i e r to i n t e r n a l r o t a t i o n i n CH^CDO i s the mean of the b a r r i e r s necessary to reproduce the observed t o r s i o n a l s p l i t t i n g s of the following t r a n s i t i o n s : l ^ - O ^ i \ 2 - \ V 2 l f 2 _ 1 l , l ; 2 1 , 1 _ 2 0 , 2 ; 3 . . 9 - 3 1 „; and l\ - 4 , . Because some of the observed t o r s i o n a l s p l i t t i n g s were much l e s s s e n s i t i v e to small changes i n the b a r r i e r height than others, the b a r r i e r heights were weighted by the slope of the ca l c u l a t e d t o r s i o n a l s p l i t t i n g against V ^ . This e f f e c t i v e l y weighted out t r a n s i t i o n s (the 1 ^ ^ " O Q ( t r a n s i t i o n i n p a r t i c u l a r ) i n which a small frequency measurement uncertainty produces a large uncertainty i n the cal c u l a t e d b a r r i e r height. The 1 ^ Q - 1 Q ^ t r a n s i t i o n was neglected because of a maximum i n the ca l c u l a t e d t o r s i o n a l s p l i t t i n g versus near 1 , 1 8 0 cal/mole, and the 2 ^ JT^I Q t r a n s i t i o n was excluded because the E sublevel t r a n s i t i o n frequency could not be accurately measured. The proposed b a r r i e r height to i n t e r n a l r o t a t i o n i n CH^CDO i s 1 , 1 8 4 ± 3 0 cal/mole. This i s i n good agreement with the b a r r i e r f o r acetalde-hyde determined by Herschbach, 1 , 1 6 9 ± 3 0 cal/mole [ 5 5 ] . The c a l c u l a t e d t o r s i o n a l s p l i t t i n g s of the observed CH^CDO t r a n s i t i o n s at a b a r r i e r height of 1 , 1 8 4 cal/mole are presented i n table 7 . 2 for a comparison with the observed values. The s e n s i t i v i t y of the b a r r i e r to i n t e r n a l r o t a t i o n to the angle between the a - p r i n c i p a l i n e r t i a l axis and the methyl top symmetry axis was tested by repeating the c a l c u l a t i o n f o r angles of 2 2 . 7 ° and 2 3 . 7 ° . Although t h i s did a f f e c t the cal c u l a t e d b a r r i e r heights necessary to reproduce a given t o r s i o n a l s p l i t t i n g , i t did not improve the agreement between the cal c u l a t e d b a r r i e r heights and produced no observable change i n the mean c a l c u l a t e d b a r r i e r height. The r o t a t i o n a l constants of CH CDO were determined by f i t t i n g the low J , -124-Table 7.2 Observed and Calculated CH CDO Torsional Splitting Calculated* 3 Observed rransition A (Odd) A V E A v E A V E 0.00 1.73 0.00 1.73 1.44 1i,o~1o,i -91.19 184.15 -4.52 88.41 89.53 2 -1 0,2 0,1 0.00 3.55 -0.02 3.55 3.75 21,2 - 11,1 -59.09 1.72 0.00 -57.36 -59.43 2 -2 1,1 0,2 -32.10 185.76 -4.50 149.13 151.01 2 -1 1,1 i,o 59.09 5.18 -0.01 64.27 65 3 -3 1,2 1,3 -32.28 10.38 -0.03 -21.94 -20.72 4 -4 1,3 *1,4 -19.41 17.32 -0.09 -2.19 -0.96 51,4-51,5 -12.97 25.87 -0.23 12.87 16.99 61,5"61,6 -9.28 36.74 -0.51 26.94 32.32 MHz units. b Calculated from equation 7.1 with a barrier height of 1,184 cal/mo A torsional sublevel transitions to a ri g i d rotor model spectrum and correcting for the contributions to the rotational constants arising from internal rota-tion. Within the A torsional sublevel a l l odd order perturbation expansion coefficients are identically zero. Therefore, the A torsional sublevel rota-tional spectrum obeys a ri g i d rotor model with small fourth order terms that only become significant at higher J. The observed A sublevel transition fre-quencies involving J < 4 were f i t by the linear least squares technique to a rig i d rotor Hamiltonian. The resulting effective rotational constants were A' = 45,134.19 MHz; B' = 10,160.06 MHz; and C = 8,731.38 MHz. -125-The effective ground state rotational constants (A, B, and C in equation 2.50) can be calculated from the effective A torsional sublevel rotational constants (A', B', and C ) with the equations [55]: A = (A' - (A I /I ) V2hcos2$ + (B* - (A, I /I, ) V2hsin2$-a a a 0,0 b a b 0,0 B = {A' - (A I /I ) V2hsin2$ + {B* - (A, I /I ) V^bcos2* a a a 0,0 b a b 0,0 C = C* (7.2) where $ i s given by tan2$ = 2FA, A I V ^ / I I, (A - B) (7.3) b a a 0,U a b Substitution of the assumed structural parameters and the appropriate rotation-a l and barrier parameters (see table 7.3) into equation 7.3 yields an angle $ of 1.3'. The effect of an axis rotation of such small magnitude on the effec-tive rotational constants i s well below experimental uncertainties and $ was, therefore, simply assumed zero. The calculated effective ground state rotation-a l constants of CH^ CDO and other rotational and torsional parameters are sum-marized in table 7.3. Table 7.3 Rotational and Torsional Parameters of CH.CDO A* = 45,134.19 MHz A = 45,009.95 MHz B* = 10,160.06 MHz B = 10,158.90 MHz C = 8,731.38 MHz C = 8,731.38 MHz I a = 11.2315 amu X 2 a F = 211,618 MHz h = 49.7623 amu £2 a V 3 = 1,184 ± 30 cal/mole I c = 57.8982 amu R2 a The conversion factor Bxl = 505531 amu A* MHz was used to maintain consistancy with results of K, L, and W, -126-Chapter 8 Comments on the Structure of Acetaldehyde The molecular structure of acetaldehyde, the prototype of the important homologous series of aliphatic aldehydes, has been the subject of numerous investigations. A few unexplained inconsistencies remain among the structures that have been proposed. The objective of this chapter i s to attempt to re-solve these inconsistencies through a reconsideration of the previous micro-wave and electron diffraction data and the use of the spectroscopic moments of inertia of CH^ CDO that have been measured here. I Kilb, Lin, and Wilson (K, L, and W) reported an r Q structure of the mole-cule based on a microwave study of nine isotopic species. They and later i n -vestigators have made the assumption that the molecule has a plane of symmetry and that the methyl group has a three-fold symmetry axis that is coincident with the C-C bond. The r Q structure was determined by making a linear least squares f i t of the internuclear parameters of acetaldehyde to the observed effective moments of inertia. Several electron diffraction studies have also been reported [8, 9, 10]. The recent electron diffraction structure determined by Kata, Konaka, Iijima, and Kimura [10], a so-called r structure, was not in good agreement with the spectroscopic structure reported by K, L, and W. The suggestion was made that the lack of consistency arose because the spectroscopic and diffraction tech-niques determine internuclear parameters of different physical significances. Iijima and Kimura [11] in an accompanying paper appeared to resolve the dis-agreement by expressing the results of both studies in terms of the average structure over the vibrational ground state (called the zero-point average or -127-r structure by Iijima and Kimura), and proposed an r acetaldehyde structure z z that was most consistent with the spectroscopic and diffraction data. The r^ structure reported by Iijima and Kimura had the advantage of being a physically well defined structure, not an i l l defined effective structure, and, perhaps more important, the inclusion of electron diffraction data had con-siderably constrained the large uncertainties in the microwave determination of r(C-C) and r(C-O) that had arisen because of the small value of the ^-coord-inate of the carbonyl carbon atom. However, in at least one respect the structure reported by Iijima and Kimura was suspect. The zero-point average value of the c-coordinate of the out of plane hydrogen atoms was in poor agreement with earlier work. Hersch-bach and Laurie had calculated an r value of 0.894 A* for this nuclear coord-z inate [147], The value that may be calculated from the zero-point moments of inertia (the moments of inertia of the zero-point average structure which were calculated by correcting the effective moments of inertia determined by K, L, and W) of CH^ CHO reported by Iijima and Kimura i s 0.873 A*. Substitution or r values for this coordinate can also be calculated from the effective mo-s ments of inertia of CD3CH0 and GTTjCHO or CT^CDO and CT^CDO using the extension of Kraitchman's equations to the case of multiple isotopic substitution on a set of symmetrically equivalent atoms developed by Chutjian [148]. The r s value, 0.888 A*, is considerably more consistent with the results of Herschbach and Laurie than with the results of Iijima and Kimura. Average coordinates are in general expected to be somewhat larger than substitution coordinates [149]. While this report was in preparation a recalculation of the zero-point average structure of acetaldehyde by Iijima and Tsuchiya [150] appeared. It -128-was stated in the later paper that the contribution of methyl torsion to the zero-point moments of inertia was incorrectly determined by Iijima and Kimura. This accounted for the anomalously small value of the out of plane coordinate previously reported. A new r^ structure was presented with an out of plane c-coordinate of 0.893 8, in excellent agreement with Herschbach and Laurie's value. The r acetaldehyde structure of K, L, and W and the r structures of o z Iijima and Kimura, and Iijima and Tsuchiya are presented in table 8.1. A sketch of the configuration of the molecule in i t s principal i n e r t i a l axis system i s presented in figure 8.1. Table 8.1 Effective and Zero-Point Average Structures of Acetaldehyde a r o r (I and K)b z r (I and T )C z r(C-C) (X) 1.5005 ± 0.0050 1.515 ± 0.005 1.512 ± 0.004 r(C-O) (8) 1.2155 ± 0.0020 1.207 ± 0.004 1.207 ± 0.004 Z(CC0) 123° 55* ± 6 ' 123° 48' ± 9 ' 124.2° ± 0.5° r(C-H) M e (X) 1.086 + 0.005 1.073 ± 0.002 1.093 ± 0.006 Z(HCH) 108° 16' ± 1 5 ' 108° 52' ±17* 109.6° ± 0.9° r C C - H ) ^ (8) 1.114 ± 0.015 1.114 ± 0.011 1.114 ± 0.009 Z(CCH) A l d 117° 29' ± 45' 117° 29' 115.3° ± 0.3° Reference 7. b Reference 10. c Reference 150. The new structure reported by Iijima and Tsuchiya presents another ano-maly. It was stated by Iijima and Kimura that the angle Z(CCH) could not be reliably determined by f i t t i n g the zero-point moments of inertia. This i s -129-h H / Figure 8.1 Configuration of Acetaldehyde not an unexpected r e s u l t because t h i s angle depends p r i m a r i l y on the small a-coordinates of the carbonyl carbon and hydrogen atoms, and moments of i n e r t i a are quite i n s e n s i t i v e to near-axis coordinates. I i j i m a and Kimura, therefore, set t h i s angle at the r Q value reported by K, L, and W. This may not have been a wise d e c i s i o n because K, L, and W probably were plagued by the same problem i n t h e i r determination of t h i s angle. It i s thought that a better procedure would be to c a l c u l a t e the carbonyl hydrogen a_-coordinate from the center of mass condition along the a-axis. The center of mass r e s t r i c t i o n i s not i n s e n s i t i v e to near-axis coordinates, and a zero-point structure, as a p h y s i c a l l y w e l l defined structure, should s a t i s f y center of mass conditions. The r a-coordinate of the carbonyl carbon atom z — may be ca l c u l a t e d by assuming the accuracy of the structure of the re s t of the molecule. This s u i t a b l y puts the burden of the c a l c u l a t i o n of t h i s coord-inate on the el e c t r o n d i f f r a c t i o n r e s u l t s . In the more recent p u b l i c a t i o n , I i j i m a and Tsuchiya reported no d i f f i c u l t y i n determining a value of 115.3° ± 0.3° f o r the angle Z(CCH) .. , using a proce--130-dure "almost the same" as used i n the study by I i j i m a and Kimura. In view of the e a r l i e r understandable d i f f i c u l t y i n determining t h i s parameter from i n -e r t i a l moments, i t i s d i f f i c u l t to accept t h i s value to the stated uncertainty without f u r t h e r e x p l a i n a t i o n . The value of ZXCCH)... , was investigated i n the following way. Cartesian Aid coordinates i n the p r i n c i p a l axis system of the complete r ^ structure r e -ported by I i j i m a and Tsuchiya were obtained by d i a g o n a l i z i n g the i n e r t i a l ten-sor. The a_ and b_-coordinates of the carbonyl hydrogen atom were then ignored (the c_-coordinate was assumed zero) and r e c a l c u l a t e d by f i t t i n g two f i r s t or second moment conditions. Since t h i s v a r i a t i o n of the carbonyl hydrogen atom p o s i t i o n s l i g h t l y s h i f t s the center of mass and rotates the p r i n c i p a l i n e r t i a l axes, i t was necessary to i t e r a t e the above two steps u n t i l a s t a t i o n a r y struc-ture was obtained. The c a l c u l a t i o n was repeated for the i s o t o p i c species CHgCHO, CD^CHO, and CD^CDO assuming the zero-point moments of i n e r t i a and i s o -t o p i c s h i f t s of r z internuclear parameters reported by I i j i m a and Tsuchiya. When the a-coordinate of the carbonyl hydrogen atom was determined from the center of mass condition along the a-axis and the b_-coordinate by f i t -t i n g 1^ or I ^ z \ an angle Z ( C C H ) A l d of 115.31° ± 0.03° was c a l c u l a t e d . How-(z) (z) ever, when the a-coordinate of the carbonyl hydrogen was f i t to 1^ or I £ , values of 112.93 ± 0.80 were c a l c u l a t e d . Quite c l e a r l y the new set of zero-point moments of i n e r t i a are s t i l l poorly conditioned f o r the determination of Z(CCH)^ l d, and the value reported by I i j i m a and Tsuchiya must have involved the use of the f i r s t moment condition. The r z parameters of the carbonyl hydrogen atom determined by I i j i m a and Tsuchiya were tested by comparing them with parameters c a l c u l a t e d by the sub-s t i t u t i o n method from the e f f e c t i v e moments of i n e r t i a of CH^CHO and CH^CDO. -131-Since the v i b r a t i o n a l amplitudes of the carbonyl hydrogen are probably small ( c e r t a i n l y s i g n i f i c a n t l y smaller than the mean v i b r a t i o n a l amplitudes of the methyl hydrogens) one might expect close agreement between r ^ and r g values of the carbonyl hydrogen internuclear parameters. A hybrid r - r structure was determined by assuming the r structure of s z z the CH^CO frame of acetaldehyde and c a l c u l a t i n g the and b_-coordinates of the carbonyl hydrogen atom from Kraitchman's equations and the e f f e c t i v e moments of i n e r t i a of CH^CHO and CI^CDO [61], The c a l c u l a t i o n was i t e r a t e d i n the manner already described u n t i l a sta t i o n a r y structure was obtained. The r e s u l t s of the c a l c u l a t i o n were r ( C - H ) A 1 J = 1.113 8 and Z(CCH) A 1 J = 115.45° , i n e x c e l -A±d A i d l e n t agreement with the r structure reported by I i j i m a and Tsuchiya. -132-Appendix Reprint of a Preliminary Report of the Microwave Spectrum of Chloryl Fluoride; CR. Parent and M.C.L. Gerry, Chem. Comm., 1972, 285. Microwave Spectrum, Structure, and Nuclear Quadrupole Coupling Constants of Chloryl Fluoride By C. R. PARENT and M. C. L. GERRY* (Department of Chemistry, The University of British Columbia, Vancouver 8, British Columbia, Canada) Summary The structure and nuclear quadrupole coupling constants of chloryl fluoride have been determined from its microwave spectrum. CHLORYL FLUORIDE, FCIO,, is one of several molecules in which a halogen atom is bonded to a stable paramagnetic species. The internuclear parameters of these molecules are of interest because in general the bond from the halogen atom to the remainder of the molecule is very long, usually much longer than the sum of the single bond radii, and because the structural parameters of the paramagnetic species usually change little on bonding with the halogen atom.M Several attempts to account theoretically for these features have been made.*-* We have studied the microwave spectrum of chloryl fluoride to determine its internuclear parameters and thus decide whether it too has the same structural properties. Spectra have been assigned for the two most abundant isotopic species, "F 3*C1 1«0, and "F^Cl^O,, in the ground vibrational state. The spectra are those of a rather asymmetric oblate rotor having components of its dipole TABLB 1 Rotational constants, principal moments of inertia and nuclear quadrupole coupling constants of chloryl fluoride "F"C1"0, "F^CP'O, A (MHz) 963604 9697-97 B (MHz) 8275-69 8239 12 C (MHz) 6019-14 5016-67 J , (Amu A») . . . . 52-448 62-656 7b (Amu A«) . . 61 069 61-340 Ic (Amu A«) . . 100-693 100-742 / . + / « - /b • • .. 92071 92058 (MHz) .. .. 620 ± 0-4 40-9 ± 0-6 Xbb - X»» (MHz) .. 180 ± 0-4 141 ± 0-7 moment along the a- and c-inertial axes. Each transition was clearly resolved by nuclear quadrupole coupling with chlorine, and values of all the coupling constants have been obtained. To obtain accurate rotational constants an analysis for centrifugal distortion using the first-order equation of Watson4 was carried out. Though we have thus far insufficient data to obtain accurate values for all the distortion constants this procedure has been shown to yield good values for the rotational constants.* These are given in Table 1 along with the principal moments of inertia and the nuclear quadrupole coupling constants. The overall spectrum, with a- and c-type transitions, is consistent with a pyramidal configuration with chlorine at the apex of the pyramid, and thus C, molecular symmetry. Such a deduction is supported by (i) the near identity of / a 4- Ic — lb for the two isotopic species, which indicates that the chlorine 6-co-ordinate is zero; (ii) the very small changes in the moments of inertia, particularly J c , on isotopic substitution; (iii) the quadrupole coupling constant Xcc, whose value is similar to that of the isoelectronic chlorate ion.' From the equation 4m 06 0 , = 7 a + Ic — lb an r 0 value for the O-O distance is found to be 2-399 A. The co-ordinates of chlorine were determined using the substitution procedure,7 and the remaining co-ordinates of fluorine and oxygen were calculated using the centre of mass conditions, and by reproducing 7 a and 7C. The T A B L E 2 Structural parameters of chloryl fluoride and related compounds r(F_Cl) (A) r (Cl -O) (A) L (O-C l -O) Z_(F-Cl -0) FCIO, 1-664 ± 0030 1-434 T 0015 113-5 ± 2-0° 103-2 T 1-5° FCI10 1-6281 C1F, " 1-698 1-598* CIO, 1 ' 1-471 117° 35' » The Cl-F bond on the axis of symmetry. resulting internuclear parameters are given in Table 2, together for comparison with those of related molecules. The uncertainties listed arise chiefly from the uncertainty in the rather small a-co-ordinate of chlorine. The difference in the value of 7 a -f- 7C — 7b of the two isotopic species, which may reflect different contributions of vibrational averaging to the effective moments of inertia in the two species, suggests such large uncertainties. The parameters -133-obtained using other methods of calculation, notably using the product of inertia condition to calculate the a-co-ordinate of chlorine, are within the limits given. It is seen from Table 2 that the C l - F bond is evidently somewhat longer than that in C1F, i.e. longer than the sum of the single bond radii , 8 as expected. O n the other hand, the C l - O bond length and (O-Cl -O) angle are somewhat different from those of C102, in contrast to the features found for other molecules of • this assumed type. The changes observed in the CIO, frame can be rationalized within the (p-TT*)a bonding formalism developed by Jack-son 2 and Spratley and Pimentel. 3 The unpaired electron in ClOj is in a bl orbita'l, antibonding between chlorine and oxygen. 1 5 The F - C l bond can be thought as arising from overlap of this orbital with a />-orbital of fluorine. I n contrast to other molecules treated in this way there is evidently withdrawal of antibondiug electron density lrom the 6, orbital of CIO, to the />-orbital of fluorine. This should result in a shortening of the C l - O bond from that of CIO,, as found. Only a small increase in the F - C l bond length over the sum of the single bond radii can be expected, again as found. These deductions are tentative, however, and more definite conclusions must await a more refined determination of structural parameters using further isotopic substitutions. W e thank Dr . F . Aubke for his advice and facilities for preparation of this molecule. W e acknowledge gratefully the support of the National Research Council of Canada in the form of research grants and a bursary (to C . R . P . ) . (Received. 3<MA December 1971; Com. 2211.) 1 A. C. Legon and D . L . MiUen, / . Chem. Soc. (A), 1968, 1736; K . S. Buckton, A . C. Legon, and D. J . Millen. Trans. Faraday Soc. 1969 65 439. 1 R. H . Jackson, / . 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