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UBC Theses and Dissertations

The microwave spectra of sulphur dichloride, dichlorosilane and propiolyl chloride Davis, Robert Wellington 1980

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THE MICROWAVE SPECTRA OF SULPHUR DICHLORIDE, DICHLOROSILANE AND PROPIOLYL CHLORIDE by Robert W e l l i n g t o n D a v i s B . S c , Memorial U n i v e r s i t y o f Newfoundland, 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department o f C h e m i s t r y ) We a c c e p t t h i s t h e s i s as con f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA D e c e m b e r 1 9 8 0 Q R o b e r t W e l l i n g t o n D a v i s , 1 9 8 0 I n 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 t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e 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 t h e L i b r a r y s h a l l m a k e 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 a n d s t u d y . I f u r t h e r a g r e e 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 m a y b e g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r 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 n o t b e 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 . D e p a r t m e n t o f T h e 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 2 0 7 5 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V 6 T 1W5 -fi t?/lQ\ i i ABSTRACT The microwave s p e c t r a and s t r u c t u r e s o f t h r e e m o l e c u l e s have been i n v e s t i g a t e d ; t h e s e a r e : s u l p h u r d i c h l o r i d e (SCI 2)» d i c h l o r o s i l a n e ( S i H 2 C l 2 ) and p r o p i o l y l c h l o r i d e (H-C=C-C0C1). 32 35 S u l p h u r D i c h l o r i d e : The microwave s p e c t r a o f S C l 2 i n the ground and v 2 = 1 e x c i t e d v i b r a t i o n a l s t a t e s , and o f S Cl C l i n the ground s t a t e have been measured i n t h e 1 2 - 4 0 GHz f r e q u e n c y r e g i o n . The s p e c t r a o f the ground s t a t e s p e c i e s have been a n a l y s e d t o y i e l d v a l u e s f o r t h e r o t a t i o n a l c o n s t a n t s , t he q u 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 c o n s t a n t s and a p a r t i a l s e t o f s e x t i c c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s . P r e c i s e r o t a -t i o n a l c o n s t a n t s have been o b t a i n e d f o r t h e v 2 = 1 e x c i t e d s t a t e o f 32 35 S Cl2« A complete s e t o f harmonic f o r c e c o n s t a n t s has been d e t e r m i n e d from the q u 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 c o n s t a n t s and the v a r i a t i o n o f the i n e r t i a l d e f e c t w i t h v i b r a t i o n a l s t a t e . The wavenumbers o f the t h r e e v i b r a t i o n a l fundamentals o f s u l p h u r d i c h l o r i d e have been p r e d i c t e d , and a r e i n e x c e l l e n t agreement w i t h the o b s e r v e d v a l u e s . An e f f e c t i v e and a p a r t i a l s u b s t i t u t i o n s t r u c t u r e f o r s u l p h u r d i c h l o r i d e have been e v a l u a t e d from the ground s t a t e r o t a t i o n a l c o n s t a n t s . The harmonic f o r c e c o n s t a n t s 32 35 have been used t o o b t a i n t he average s t r u c t u r e s o f S C l 2 i n the ground and v 2 = 1 s t a t e s . The ground s t a t e average s t r u c t u r a l parameters o f 3 2 S 3 5 C 1 2 a r e : r ( S - C l ) = 2.01525 + 0.00008 A and <(C1-S-C1) = 102.730 + 0.005° The e q u i l i b r i u m s t r u c t u r e o f s u l p h u r d i c h l o r i d e has a l s o been e s t i m a t e d . D i c h l o r o s i l a n e : The microwave s p e c t r a o f 2 8 S i H 2 3 5 C l 2 , 2 8 S i H 2 3 5 C l 3 7 C l and 29 35 S i H 2 C l 2 have been measured i n the 8 - 4 0 GHz f r e q u e n c y range. The i i i s p e c t r a have been a n a l y s e d t o y i e l d v a l u e s f o r the r o t a t i o n a l c o n s t a n t s , q u 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 c o n s t a n t s and c h l o r i n e 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 , as w e l l as the m o l e c u l a r d i p o l e moment, 1.129 +0.020 Debye. The m o l e c u l e has been shown t o have C 2 v symmetry. E f f e c t i v e and p a r t i a l s u b s t i t u t i o n s t r u c t u r e s have been o b t a i n e d f o r d i c h l o r o s i l a n e u s i n g t he e x p e r i m e n t a l v a l u e s f o r the r o t a t i o n a l c o n s t a n t s . F u r t h e r , t he q u 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 c o n s t a n t s have been combined w i t h e x i s t -i n g v i b r a t i o n a l d a t a t o d e t e r m i n e a harmonic f o r c e f i e l d w h i c h, i n t u r n , has been used t o d e r i v e the ground s t a t e average s t r u c t u r a l parameters o f ^ ^ S i H g ^ ^ C l g • These a r e : r (S1-C1) = 2.0352 + 0.0003 A , < ( C 1 - S i - C l ) = 109.68 + 0.03° r z ( S i - H ) = 1.4726 + 0.0025 A , <(H-Si-H) = 1 1 2 . 4 4 + 0 . 2 8 ° The e q u i l i b r i u m s t r u c t u r e o f d i c h l o r o s i l a n e has a l s o been e s t i m a t e d . P r o p i o l y l C h l o r i d e : The microwave s p e c t r a o f HCCC0 3 5C1, HCCC0 3 7C1, 35 37 DCCC0 C l . a n d DCCC0 CI have been measured i n the ground and, e x c e p t 37 f o r DCCC0 C I , the v g = 1 v i b r a t i o n a l s t a t e s . The s p e c t r a have y i e l d e d v a l u e s f o r the r o t a t i o n a l c o n s t a n t s , q u 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 c o n s -t a n t s and c h l o r i n e 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 , as w e l l as the m o l e c u l a r d i p o l e moment, 2.717 + 0.035 Debye. The q u 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 c o n s t a n t s have been combined w i t h e x i s t i n g v i b r a t i o n a l d a t a t o d e t e r m i n e an approximate harmonic f o r c e f i e l d . Having assumed a r e a s o n a b l e s t r u c t u r e f o r the e t h y n y l group, the f o r c e f i e l d was used t o o b t a i n t h e ground s t a t e average s t r u c t u r e o f p r o p i o l y l c h l o r i d e . These r e s u l t s s u g g e s t t h a t the carbon c h a i n i n p r o p i o l y l c h l o r i d e has a d e v i a t i o n from l i n e a r i t y o f l e s s than one degree. i v TABLE OF CONTENTS CHAPTER PAGE 1. INTRODUCTION 1 1.1 Energy L e v e l s o f the Asymmetric Rot o r 3 1.2 N u c l e a r Quadrupole C o u p l i n g 10 1.3 The Asymmetric Rot o r S t a r k E f f e c t 14 1.4 M o l e c u l a r S t r u c t u r e s from R o t a t i o n a l S p e c t r a 16 1.5 C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s and t h e Harmonic F o r c e F i e l d 23 B i b l i o g r a p h y 25 2. EXPERIMENTAL METHODS 28 2.1 The Microwave S p e c t r o m e t e r 29 2.2 The Microwave S t a r k C e l l s 32 2.3 D i p o l e Moment Measurements 32 2.4 O r i g i n o f Samples and Running C o n d i t i o n s 33 B i b l i o g r a p h y 36 3. THE MICROWAVE SPECTRUM OF SULPHUR DICHLORIDE 37 3.1 Observed Spectrum and Assignment 40 3.2 A n a l y s i s o f the S u l p h u r D i c h l o r i d e S p e c t r a 47 3.3 The Harmonic P o t e n t i a l F u n c t i o n o f S u l p h u r D i c h l o r i d e . 60 3.4 The M o l e c u l a r S t r u c t u r e o f S u l p h u r D i c h l o r i d e 73 3.5 Comments on the S u l p h u r D i c h l o r i d e P o t e n t i a l F u n c t i o n . 81 3.6 Comments on the M o l e c u l a r S t r u c t u r e o f S u l p h u r D i c h l o r i d e 91 B i b l i o g r a p h y 95 V TABLE OF CONTENTS CHAPTER PAGE 4. THE MICROWAVE SPECTRUM OF DICHLOROSILANE 99 4.1 Assignment o f the D i c h l o r o s i l a n e Spectrum 100 4.2 A n a l y s i s o f the D i c h l o r o s i l a n e Spectrum 102 4.3 The D i p o l e Moment o f D i c h l o r o s i l a n e 119 4.4 The E f f e c t i v e and S u b s t i t u t i o n S t r u c t u r e s o f D i c h l o r o s i l a n e 124 4.5 The Harmonic F o r c e F i e l d o f D i c h l o r o s i l a n e 132 4.6 The Average S t r u c t u r e o f D i c h l o r o s i l a n e 139 4.7 The E q u i l i b r i u m S t r u c t u r e o f D i c h l o r o s i l a n e 143 4.8 Comments on the S t r u c t u r e and F o r c e F i e l d o f D i c h l o r o s i l a n e 143 B i b l i o g r a p h y 150 5. THE MICROWAVE SPECTRUM OF PROPIOLYL CHLORIDE 152 5.1 Assignment o f the S p e c t r a 155 5.2 D e t e r m i n a t i o n o f the R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s 157 5.3 N u c l e a r Quadrupole C o u p l i n g i n P r o p i o l y l C h l o r i d e . . . 173 5.4 The D i p o l e Moment o f P r o p i o l y l C h l o r i d e 179 5.5 The E f f e c t i v e S t r u c t u r e o f P r o p i o l y l C h l o r i d e 191 i 5.6 The Harmonic F o r c e F i e l d o f P r o p i o l y l C h l o r i d e . . . . 195 5.7 The Average S t r u c t u r e o f P r o p i o l y l C h l o r i d e 206 5.8 Comments on the S t r u c t u r e o f P r o p i o l y l C h l o r i d e . . . . 209 B i b l i o g r a p h y 212 v i TABLE OF CONTENTS APPENDIX PAGE 1. A R e p r i n t o f a Report o f the Microwave Spectrum o f P r o p i o l y l F l u o r i d e 215 2. A R e p r i n t o f a Report o f the Microwave Spectrum o f P r o p i o l i c A c i d 225 3. A R e p r i n t o f a Report o f the Microwave Spectrum o f Formic A c i d 232 4. A R e p r i n t o f a R e p o r t o f t h e Microwave Spectrum o f P y r r o l e - 2 - c a r b o n i t r i l e 250 5. A R e p r i n t o f a Report o f t h e Microwave Spectrum o f D i f l u o r o s i l a n e 256 v i i LIST OF TABLES TABLE PAGE 3.1 Examples o f H y p e r f i n e S t r u c t u r e i n T r a n s i t i o n s o f 3 2 S 3 5 C 1 3 7 C 1 44 3.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f S u l p h u r D i c h l o r i d e 49 3.3 Observed R o t a t i o n a l T r a n s i t i o n s (MHz) o f S u l p h u r D i c h l o r i d e 51 3.4 R e l a t i o n s h i p s Between Q u 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 C o n s t a n t s 62 32 35 3.5 A l t e r n a t e Ground S t a t e M o l e c u l a r C o n s t a n t s o f S C l 2 . . 65 32 35 3.6 V a l u e s o f Watson's Q u a r t i c P l a n a r i t y Sum f o r S C l 2 . . . 66 3.7 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s 32 35 o f ° ^ S J 3 C 1 2 O b t a i n e d from V a r i o u s F i t s , 6 8 3.8 Q u a d r a t i c P o t e n t i a l C o n s t a n t s , V i b r a t i o n a l Fundamentals and C o r i o l i s C o u p l i n g C o n s t a n t s o f S u l p h u r D i c h l o r i d e 71 3.9 P r i n c i p a l Moments o f I n e r t i a and I n e r t i a l D e f e c t s o f °2 V a r i o u s S u l p h u r D i c h l o r i d e S p e c i e s (uA ) 74 3.10 E f f e c t i v e , P a r t i a l S u b s t i t u t i o n and Average S t r u c t u r e s f o r 3 2 S 3 5 C 1 2 77 3.11 The E q u i l i b r i u m Bond Lengths i n S u l p h u r D i c h l o r i d e and R e l a t e d M o l e c u l e s 79 3.12 Summary o f P r e s e n t and P r e v i o u s S u l p h u r D i c h l o r i d e P o t e n t i a l F u n c t i o n s and R e l a t e d E x p e r i m e n t a l Data 83 3.13 Observed and C a l c u l a t e d I s o t o p e S h i f t s f o r the S t r e t c h i n g Fundamentals o f S u l p h u r D i c h l o r i d e 89 3.14 The S-Cl Bond Lengths and x z z ( 3 5 C l ) V a l u e s f o r S u l p h u r D i c h l o r i d e and R e l a t e d M o l e c u l e s 92 v i i i LIST OF TABLES TABLE PAGE 3.15 E s t i m a t e d S t r e t c h i n g F o r c e C o n s t a n t s o f Some S u l p h u r C h l o r i n e Bonds 94 4.1 C h l o r i n e 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 (MHz) o f D i c h l o r o s i l a n e 104 4.2 Some R e p r e s e n t a t i v e T r a n s i t i o n s (MHz) o f 2 8 S i H 2 3 5 C l 2 Showing N u c l e a r Quadrupole H y p e r f i n e S t r u c t u r e 106 4.3 Observed R o t a t i o n a l T r a n s i t i o n s (MHz) o f D i c h l o r o s i l a n e . . 110 4.4 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f D i c h l o r o s i l a n e 117 4.5 S t a r k S h i f t s i n D i c h l o r o s i l a n e : 2 8 S i H 2 3 5 C l 2 121 4.6 S t a r k C o e f f i c i e n t s o f D i c h l o r o s i l a n e : 2 8 S i H 2 3 5 C l 2 123 4.7 I n e r t i a l Parameters o f D i c h l o r o s i l a n e 126 4.8 The E f f e c t i v e S t r u c t u r e o f D i c h l o r o s i l a n e 127 28 35 ° 4.9 S u b s t i t u t i o n C o o r d i n a t e s o f D i c h l o r o s i l a n e : S i H 2 C l 2 (A) 130 4.10 The S u b s t i t u t i o n S t r u c t u r e o f D i c h l o r o s i l a n e 131 4.11 I n t e r n a l C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f D i c h l o r o s i l a n e 133 4.12 The Harmonic F o r c e F i e l d o f D i c h l o r o s i l a n e 136 4.13 Observed and C a l c u l a t e d V i b r a t i o n a l Wavenumbers (cm~^) o f D i c h l o r o s i l a n e 137 4.14 Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s (kHz) o f D i c h l o r o s i l a n e 138 4.15 Parameters D e s c r i b i n g t he I s o t o p i c V a r i a t i o n i n the Average Bond Lengths o f D i c h l o r o s i l a n e 140 4.16 Average R o t a t i o n a l C o n s t a n t s o f D i c h l o r o s i l a n e and Average S t r u c t u r e o f 2 8 S i H „ 3 5 C l 0 142 i x LIST OF TABLES TABLE PAGE 4.17 The E q u i l i b r i u m S t r u c t u r e o f D i c h l o r o s i l a n e 144 4.18 A Comparison o f the D e r i v e d S t r u c t u r e s o f D i c h l o r o s i l a n e . 146 4.19 A Comparison o f Bond Lengths and S t r e t c h i n g F o r c e C o n s t a n t s i n t h e F l u o r o s i l a n e s and C h l o r o s i l a n e s 148 5.1 Observed R o t a t i o n a l T r a n s i t i o n s (MHz) o f P r o p i o l y l C h l o r i d e 159 5.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f P r o p i o l y l C h l o r i d e 169 5.3 R e p r e s e n t a t i v e P r o p i o l y l C h l o r i d e T r a n s i t i o n s (MHz) used i n t h e N u c l e a r Quadrupole C o u p l i n g A n a l y s e s . . . 175 5.4 C h l o r i n e 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 P r o p i o l y l C h l o r i d e 178 5.5 S t a r k S h i f t s i n C a r b o n y l S u l p h i d e : 1 6 0 1 2 C 3 2 S 184 5.6 C e l l C a l i b r a t i o n w i t h C a r b o n y l S u l p h i d e : 1 6 0 1 2 C 3 2 S . . . . 185 5.7 S t a r k S h i f t s i n P r o p i o l y l C h l o r i d e : HCCC0 3 5C1 186 5.8 S t a r k C o e f f i c i e n t s o f P r o p i o l y l C h l o r i d e : HCCC0 3 5C1 . . . . 189 5.9 The D i p o l e Moment o f P r o p i o l y l C h l o r i d e 190 5.10 Ground S t a t e I n e r t i a l Parameters o f P r o p i o l y l C h l o r i d e . . 192 5.11 The E f f e c t i v e S t r u c t u r e o f P r o p i o l y l C h l o r i d e 194 5.12 I n t e r n a l C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f P r o p i o l y l C h l o r i d e 196 5.13 The Harmonic F o r c e F i e l d o f P r o p i o l y l C h l o r i d e 198 5.14 Observed and C a l c u l a t e d V i b r a t i o n a l Wavenumbers ( c n f ^ ) o f P r o p i o l y l C h l o r i d e 201 5.15 Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s (kHz) o f P r o p i o l y l C h l o r i d e . 203 oo 5.16 Observed and C a l c u l a t e d I n e r t i a l D e f e c t s (uA ) o f P r o p i o l y l C h l o r i d e 205 X LIST OF TABLES TABLE PAGE 5.17 Ground S t a t e Average R o t a t i o n a l C o n s t a n t s (MHz) o f P r o p i o l y l C h l o r i d e 207 5.18 The Average S t r u c t u r e o f P r o p i o l y l C h l o r i d e 208 5.19 The S t r u c t u r e s o f P r o p i o l y l C h l o r i d e and R e l a t e d M o l e c u l e s . 211 x i LIST OF FIGURES FIGURE PAGE 3.1 The K = 2 «- 1 Q-Branch T r a n s i t i o n s o f S C I 0 46 a c 4.1 An Example o f N u c l e a r Quadrupole H y p e r f i n e S t r u c t u r e i n t h e Spectrum o f D i c h l o r o s i l a n e 108 x i i ACKNOWLEDGEMENTS The i n v e s t i g a t i o n s d e s c r i b e d i n t h i s t h e s i s were c a r r i e d o u t under the d i r e c t i o n o f Dr. M.C.L. G e r r y a t the U n i v e r s i t y o f B r i t i s h Columbia. I would l i k e v e r y much t o thank Dr. G e r r y f o r p r o v i d i n g a s t i m u l a t i n g i n t r o d u c t i o n t o the f i e l d o f M o l e c u l a r S p e c t r o s c o p y and f o r h i s i n v a l u a b l e a s s i s t a n c e and encouragement. As w e l l , I would l i k e to e x p r e s s my g r a t i t u d e t o Dr. G e r r y f o r a l l o w i n g me c o n s i d e r a b l e l a t i t u d e i n the c h o i c e o f r e s e a r c h t o p i c s and f o r h e l p i n g i n many ways t o make my s t a y a t U.B.C. an e n j o y a b l e one. I f u r t h e r extend my thanks t o s e v e r a l c o l l e a g u e s a t U.B.C. f o r s p e c i f i c c o n t r i b u t i o n s t o t h i s work. The C h e m i s t r y Department E l e c t r o n i c s Shop and e s p e c i a l l y Z o l Germann a r e acknowledged f o r t h e i r p a t i e n t e f f o r t s i n taming a somewhat r e c a l c i t r a n t a p p a r a t u s . Dr. R. Green and Dr. A.G. R o b i e t t e a f f o r d e d i l l u m i n a t i n g d i s c u s s i o n s o f v i b r a t i o n a l problems and Gary L i t t l e p r o v i d e d an asymmetric top l i n e s t r e n g t h program. F i n a l l y , I am d e e p l y g r a t e f u l to my p a r e n t s f o r the s u p p o r t which they have g i v e n me t h r o u g h o u t my s t u d i e s . In no s m a l l measure they a r e r e s p o n s i b l e f o r any s u c c e s s e s which I might have a c h i e v e d . 1 C h a p t e r 1 I n t r o d u c t i o n The microwave r e g i o n o f the e l e c t r o m a g n e t i c spectrum l i e s between the r a d i o r e g i o n and the f a r i n f r a r e d , encompassing a f r e q u e n c y range o f r o u g h l y 1-1000 GHz. A c c o r d i n g t o the wavelength o f t h e r a d i a -t i o n t h i s r e g i o n i s f u r t h e r d i v i d e d i n t o the c e n t i m e t e r , m i l l i m e t e r and s u b m i l 1 i m e t e r r a n g e s . S p e c t r o s c o p i c i n v e s t i g a t i o n s , though, have l a r g e l y been c o n f i n e d to f r e q u e n c i e s below 40 GHz, because microwave hardware becomes i n c r e a s i n g l y s o p h i s t i c a t e d and c o s t l y a t s h o r t e r w a v e l e n g t h s . A l t h o u g h a v a r i e t y o f atomic and m o l e c u l a r phenomena can g i v e r i s e t o microwave s p e c t r a , the s t u d i e s made a t t h e s e f r e q u e n c i e s have almos t e x c l u s i v e l y been o f t r a n s i t i o n s between m o l e c u l a r s t a t e s h a v i n g d i f f e r e n t r o t a t i o n a l e n e r g i e s . T h i s i s t r u e t o such an e x t e n t t h a t the terms Microwave S p e c t r o s c o p y and R o t a t i o n a l S p e c t r o s c o p y have come t o be v i r t u a l l y synonymous. In s p i t e o f t h i s the f i r s t o b s e r v e d microwave spectrum, o b t a i n e d by C l e e t o n and W i l l i a m s ( 1 ) , i n v o l v e d a s t u d y o f t h e ground v i b r a t i o n a l s t a t e i n v e r s i o n spectrum o f ammonia. They used a low r e s o l u t i o n g r a t i n g s p e c t r o g r a p h and an ammonia gas sample c o n t a i n e d i n a r u b b e r bag. S u b s e q u e n t l y , i n t e r e s t i n r a d a r t e c h n o l o g y l e d t o t h e development o f the e l e c t r o n i c i n s t r u m e n t a t i o n used i n modern s p e c t r o -meters. S i n c e m o l e c u l a r r o t a t i o n i s t o t a l l y randomized i n l i q u i d s and i s u s u a l l y quenched i n s o l i d s pure r o t a t i o n a l s p e c t r a a r e s t u d i e d o n l y f o r the gas phase. Very low gas p r e s s u r e s a r e used t o o b t a i n maximum 2 r e s o l u t i o n and measurement a c c u r a c y . A t a p r e s s u r e o f 0.5 Pa, f o r example, i t i s o f t e n p o s s i b l e to r e s o l v e l i n e s s e p a r a t e d by l e s s than 0.5 MHz and t o measure them w i t h an a c c u r a c y o f b e t t e r than 50 kHz. A t the f r e q u e n c i e s o f the p r e s e n t s t u d y t h i s c o r r e s p o n d s t o a measurement g p r e c i s i o n o f about 1 p a r t i n 10 . Modern microwave t e c h n i q u e s e n a b l e a t l e a s t some t r a n s i t i o n s t o be seen f o r a l m o s t a l l m o l e c u l e s which e x h i b i t pure r o t a t i o n a l s p e c t r a . E x c e p t i o n s a r e t h e f i r s t row element monohydrides such as HF and OH. T h i s l a t t e r m o l e c u l e , however, does have a A - d o u b l i n g spectrum i n t h e microwave r e g i o n , f i r s t seen by Dousmanis, Sanders and Townes ( 2 ) . T h i s i n i t i a l microwave s t u d y o f a f r e e r a d i c a l s t i m u l a t e d s u c c e s s f u l s e a r c h e s f o r r o t a t i o n a l t r a n s i t i o n s o f o t h e r f r e e r a d i c a l s p e c i e s ( 3 ) . As w e l l , i t l e d i n d i r e c t l y t o s t u d i e s o f the r o t a t i o n a l s p e c t r a o f i n t e r s t e l l a r m o l e c u l e s by r a d i o a s t r o n o m y , c u r r e n t l y an a r e a o f v i g o r o u s i n v e s t i g a t i o n ( 4 ) . Microwave s p e c t r a have been used t o p r o v i d e a c c u r a t e i n f o r m a -t i o n about a wide v a r i e t y o f m o l e c u l a r p r o p e r t i e s . P r i m a r i l y they have been used as a t o o l f o r d e t e r m i n i n g p r e c i s e m o l e c u l a r s t r u c t u r e s . The r o t a t i o n a l c o n s t a n t s , which d e f i n e t h e m o l e c u l a r s t r u c t u r e i n terms o f the p r i n c i p a l moments o f i n e r t i a , a r e a f u n c t i o n o f t h e v i b r a t i o n a l s t a t e . As a r e s u l t , i t i s o f t e n p o s s i b l e t o c h a r a c t e r i z e t he changes i n m o l e c u l a r s t r u c t u r e which r e s u l t from v i b r a t i o n a l e x c i t a t i o n s . The a n a l y s i s o f a r o t a t i o n a l spectrum can a l s o y i e l d v a l u e s f o r c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s , C o r i o l i s c o u p l i n g c o n s t a n t s and o t h e r v i b r a t i o n -r o t a t i o n parameters which a r e used t o e v a l u a t e i n t r a m o l e c u l a r f o r c e f i e l d s ; f o r some v e r y s i m p l e m o l e c u l e s complete p o t e n t i a l f u n c t i o n s have been o b t a i n e d u s i n g microwave d a t a o n l y . I n f o r m a t i o n about t h e e l e c t r o n i c 3 s t r u c t u r e o f a m o l e c u l e can be o b t a i n e d from t h e S t a r k and Zeeman e f f e c t s and from the v a l u e s o f 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 . T h i s t h e s i s r e p o r t s microwave i n v e s t i g a t i o n s o f s e v e r a l m o l e c u l e s , namely the i s o e l e c t r o n i c s u l p h u r d i c h l o r i d e and d i c h l o r o s i l a n e and, as w e l l , p r o p i o l y l c h l o r i d e . The s p e c i f i c aims i n i n v e s t i g a t i n g the v a r i o u s i n d i v i d u a l m o l e c u l e s a r e d i s c u s s e d a t the b e g i n n i n g o f the r e l e v a n t c h a p t e r s . The b a s i c t h e o r y r e q u i r e d t o i n t e r p r e t microwave r o t a t i o n a l s p e c t r a i s not d e v e l o p e d here s i n c e i t i s e x t e n s i v e l y documen-t e d i n s e v e r a l good t e x t s (5, 10). P a r t i c u l a r l y u s e f u l i s the book by Gordy and Cook (9). Only the p e r t i n e n t e q u a t i o n s and n o t a t i o n a r e c o n s i d e r e d i n t h i s c h a p t e r . 1.1 Energy L e v e l s o f the Asymmetric Rotor The r o t a t i o n a l H a m i l t o n i a n f o r a r i g i d r o t o r can be w r i t t e n as H = A P 2 + BP^ + C P 2 (1.1) where P , P b , and P c ( i n u n i t s o f h/2ir) a r e t h e components, r e f e r r e d t o m o l e c u l e f i x e d axes, o f the t o t a l r o t a t i o n a l a n g u l a r momentum P_. The p r i n c i p a l i n e r t i a l axes a, b and c have been l a b e l l e d i n such a way t h a t the r o t a t i o n a l c o n s t a n t s f o l l o w t h e o r d e r A >_ B >_ C. The r o t a t i o n a l c o n s t a n t s a r e r e l a t e d t o t h e c o r r e s p o n d i n g p r i n c i p a l moments o f i n e r t i a I a , I b and I c by I x A = I , x B = I x C = h/8-rr2 (1.2) a u c R i g i d r o t o r s can be c l a s s i f i e d i n t o s e v e r a l d i s t i n c t t y p e s a c c o r d i n g t o r e l a t i o n s among th e moments o f i n e r t i a o r r o t a t i o n a l c o n s t a n t s . Thus one has 4 (1) L i n e a r m o l e c u l e s I = 0, I. = I a b c (2) S p h e r i c a l tops I = I b = I (3) P r o l a t e symmetric tops I < I b = I (4) O b l a t e symmetric tops I = I. < I a D C (5) Asymmetric t o p s I < 1^ < I Except f o r the asymmetric top case t he r i g i d r o t o r H a m i l t o n i a n can be e x p l i c i t l y d i a g o n a l i z e d t o g i v e c l o s e d form e x p r e s s i o n s f o r the r o t a t i o n a l e n e r g i e s ( 1 1 ) . F or p r o l a t e symmetric t o p s , f o r example, one o b t a i n s E = B J ( J + 1) + (A - B ) K 2 (1.3) w h i l e f o r o b l a t e symmetric tops E = B J ( J + 1) + (C - B ) K 2 (1.4) Here J i s the quantum number d e n o t i n g t he t o t a l r o t a t i o n a l a n g u l a r momentum and K g i v e s t he m o l e c u l e f i x e d component; a t h i r d quantum number M, which g i v e s t he space f i x e d component o f the t o t a l r o t a t i o n a l a n g u l a r momentum, w i l l l a t e r be needed t o d e s c r i b e t h e e l e c t r i c f i e l d dependence o f t h e r o t a t i o n a l e n e r g i e s . The symmetric top w a v e f u n c t i o n s a r e u s u a l l y denoted as |JKM> where J can assume any p o s i t i v e i n t e g r a l v a l u e ; K and M range from - J t o +J. The symmetric top r o t a t i o n a l e n e r g i e s a r e , however, independent o f M a t z e r o f i e l d and, as w e l l , do not depend on the s i g n o f K. The i n t r o d u c t i o n o f asymmetry s p l i t s the symmetric top l e v e l s which a r e dou b l y d e g e n e r a t e , t h a t i s , t h o s e w i t h |K| ? 0. However, t h e H a m i l t o n i a n m a t r i x f o r the asymmetric top can s t i l l be c o n s t r u c t e d u s i n g a b a s i s s e t o f symmetric r o t o r w a v e f u n c t i o n s . The non-zero m a t r i x elements a r e , i n the I r r e p r e s e n t a t i o n (12) u s u a l l y chosen f o r p r o l a t e asymmetric tops 5 <JKM| H |JKM> = h(B + C ) J ( J + 1) + [A -%(B + C ) ] K 2 ( 1 . 5 ) <JK ± 2M| H |JKM> = Js(B - C ) { [ J ( J + 1) - K(K ± 1 ) ] x [ J ( J + 1) - (K ± 1 ) ( K ± 2)l)k S i n c e t h e r e a r e no m a t r i x elements c o n n e c t i n g even and odd K the H a m i l t o n i a n m a t r i x b l o c k s i m m e d i a t e l y i n t o two t r i d i a g o n a l s u b m a t r i c e s . F u r t h e r f a c t o r i z a t i o n i n t o an u l t i m a t e f o u r independent s u b m a t r i c e s i s p o s s i b l e through a p p l i c a t i o n o f the Wang t r a n s f o r m a t i o n ( 1 3 ) . Because f o r an asymmetric top K i s no>longer a good quantum number the l e v e l s a r e l a b e l l e d by „ . Here K and K a r e the |K| v a l u e s which o b t a i n a c a c i n t he l i m i t i n g p r o l a t e and o b l a t e symmetric l i m i t r e s p e c t i v e l y . The asymmetric r o t o r f u n c t i o n s , o b t a i n e d as a l i n e a r c o m b i n a t i o n o f the symmetric top w a v e f u n c t i o n s a f t e r d i a g o n a l i z a t i o n o f the H a m i l t o n i a n m a t r i x , a r e denoted by |JTM> where T = KFL - K C -The r i g i d r o t o r H a m i l t o n i a n can be r e c a s t i n o t h e r forms through the i n t r o d u c t i o n o f s o - c a l l e d asymmetry parameters. One has the Ray asymmetry parameter K (14) and the Wang asymmetry parameter b p (15) where K = 2B - A - C (1.6) A - C and b p = C - B (1.7) 2A - B - C The v a l u e o f K v a r i e s from -1 i n the p r o l a t e symmetric l i m i t t o +1 i n the o b l a t e symmetric l i m i t ; b v a r i e s c o r r e s p o n d i n g l y from 0 t o - 1 . U s i n g t he Wang asymmetry parameter, f o r example, the r i g i d r o t o r H a m i l t o n i a n t a k e s the form (13) H R = Js(B + C ) P 2 + [A - %(B + C)]H(b ) (1.8) 6 U s i n g t h e known m a t r i x elements o f H(bp) the H a m i l t o n i a n i s d i a g o n a l i z e d to o b t a i n (13) E R = JsCB + C ) J ( J + 1) + [A - 3s(B + C)]W 0 (b ) (1.9) where Wj (b ) i s the Wang reduced energy, a d i m e n s i o n l e s s q u a n t i t y . The Wang reduced energy Wj (b ) can be r e g a r d e d as the r o t a t i o n a l energy o f a r i g i d r o t o r h a v i n g the r o t a t i o n a l c o n s t a n t s 1, -b and +b . p p The s i m p l e r i g i d r o t o r H a m i l t o n i a n can o f t e n be used s u c c e s s -f u l l y to f i t t r a n s i t i o n s i n v o l v i n g low J s t a t e s . A t h i g h e r v a l u e s o f J c e n t r i f u g a l f o r c e s become i m p o r t a n t . E s s e n t i a l l y t h e y cause d i s t o r t i o n s o f the m o l e c u l a r s t r u c t u r e which a r e , i n t u r n , r e f l e c t e d by changes o f the i n s t a n t a n e o u s moments o f i n e r t i a . The r o t a t i o n a l t r a n s i t i o n s a c c o r d -i n g l y a r e s h i f t e d from t h e i r r i g i d r o t o r p o s i t i o n s . T h i s problem was c o n s i d e r e d i n d e t a i l by W i l s o n and co-workers (16,17,18). They d e v e l o p e d a n o n - r i g i d r o t o r H a m i l t o n i a n which f o r an asymmetric t o p has the form H - A'P a 2 • B 'P„ 2 + C P C 2 + k r ^ M P b z P B 2 (1.10) where the T' o d a r e q u 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 c o n s t a n t s and t h e CXCXpp r o t a t i o n a l c o n s t a n t s A", B' and C a r e d i s t i n c t from t h o s e o f the r i g i d r o t o r as they now have absorbed s m a l l c e n t r i f u g a l terms. The v a r i o u s x 1 s a r e d i r e c t l y r e l a t e d t o the harmonic f o r c e f i e l d ( 1 8 ) . A l t h o u g h e q u a t i o n 1.10 c o n t a i n s s i x T'' (= x' . T 1.,,,, X' „ . x' .., aaBB aaaa bbbb c c c c aabb T T ' k k ^ ^ ) > i t w a s shown by Watson t h a t o n l y f i v e c o m b i n a t i o n s o f aacc D D C C them can be determined from a r o t a t i o n a l spectrum (19,20). Of the many p o s s i b l e c o m b i n a t i o n s which can be w r i t t e n , one o f the s i m p l e s t t o use, and which was used t h r o u g h o u t t h i s work, i s the s o - c a l l e d A r e d u c t i o n (20,21). In t h i s c a s e the r o t a t i o n a l H a m i l t o n i a n , now i n c l u d i n g h i g h e r degree terms, i s w r i t t e n (20,21): 7 H = H R + H D + HD,. (1.11) HR = A P a 2 + B P b 2 + C P c 2 HD " ~ A / ~ AJK PV " A K P a 4 " 2 6 0 PV " ^  " 6 K { P a 2 ( P b 2 " P c 2 ) + ( R b 2 " P c 2 ) P a 2 } HD' = » / + HJK PV + HKJ PV + ^ K P a ^ + 2 h / ( P b 2 - P c 2 ) + h J K P 2 { P a 2 ( P b 2 - P c 2 ) + ( P , 2 - P c 2 ) P a 2 } + h K { P a 4 ( R b 2 " P c 2 ) + ( R b 2 " PcV} The r o t a t i o n a l c o n s t a n t s s t i l l c o n t a i n s m a l l c o r r e c t i o n terms, and the q u a r t i c d i s t o r t i o n c o n s t a n t s A j , A J K , A^, 6J and 6K a r e c o m b i n a t i o n s o f t h e T' d o g i v e n e a r l i e r (20) . The s o - c a l l e d s e x t i c c o n s t a n t s H., CtOtpp J Hj|^, HJ^J, HK, h j , h j ^ and h^, a r e r e l a t e d t o the c u b i c p a r t o f t h e i n t r a m o l e c u l a r f o r c e f i e l d (21) . I t s h o u l d be emphasized t h a t t h i s i s an e f f e c t i v e H a m i l t o n i a n f o r a g i v e n v i b r a t i o n a l s t a t e ; because o f v i b r a t i o n a l a v e r a g i n g e f f e c t s t h e v a l u e s o f a l l o f t h e c o n s t a n t s a r e exp e c t e d t o v a r y from one v i b r a t i o n a l s t a t e t o t h e next. The m a t r i x elements o f H R have a l r e a d y been g i v e n . The a d d i t i o n a l m a t r i x e l e m e n t s , t h o s e o f Hp and H^,, have t h e same form and can be e v a l u a t e d u s i n g the same t e c h n i q u e s . A g a i n i n t h e I r r e p r e s e n t a t i o n t h e y a r e : <JKM| Hp + HD,|JKM> = - A j J 2 ( J + I ) 2 - A J K J ( J + 1)K 2 (1.12) - A K K 4 + H j J 3 ( J + I ) 3 + H J K J 2 ( J + 1 ) 2 K 2 + H K J J ( J + 1)K 4 + H KK 6 <JK + 2M|HD + H D, |JKM> = {-6jJ(J + 1) - ^ [ ( K 1 2 ) 2 + K 2 ] + h j J 2 ( J + l ) 2 + % h J K ( J + 1 ) [ ( K + 2 ) 2 + K 2 ] + Jsh K[(K + 2 ) 4 + K 4 ] } x { [ J ( J + 1) - K(K + 1 ) ] [ J ( J + 1) - (K + 1)(K + 2 ) ] } % 8 D i a g o n a l i z a t i o n o f t h i s H a m i l t o n i a n a g a i n g i v e s the asymmetric r o t o r f u n c t i o n s |JTM> as l i n e a r c o m b i n a t i o n s o f the symmetric r o t o r wave-f u n c t i o n s . The s i m p l e t r i d i a g o n a l m a t r i x o f the A r e d u c t i o n H a m i l t o n i a n can u s u a l l y be c o n s t r u c t e d and d i a g o n a l i z e d f a s t e r than the h e p t a d i a g o n a l m a t r i x o f the a l t e r n a t i v e S r e d u c t i o n ( 2 1 ) ; the S r e d u c t i o n i s , however, t h e n e c e s s a r y c h o i c e f o r m o l e c u l e s which a r e o n l y s l i g h t l y asymmetric ( 2 1 ) . The most e l e g a n t way o f f i t t i n g r o t a t i o n a l s p e c t r a i s to use the e i g e n v e c t o r s o b t a i n e d from the e x a c t d i a g o n a l i z a t i o n o f Watson's reduced H a m i l t o n i a n t o ge n e r a t e t he r e q u i r e d J a c o b i a n s 8E/3A = <P a 2>, = <P b 2>, .... 9E/9A K = <Pg 4>» ••• e t c . I n i t i a l l y , o f c o u r s e , e s t i m a t e d v a l u e s o f the r o t a t i o n a l c o n s t a n t s were used to be g i n the f i t t i n g p r o c e s s . L i n e a r v a r i a t i o n s o f the r o t a t i o n a l c o n s t a n t s and any chosen s e t o f q u a r t i c and s e x t i c c o n s t a n t s were s u b s e q u e n t l y a l l o w e d . Because t he v a r i o u s J a c o b i a n s a r e not q u i t e independent o f the v a l u e s o f A , B, C, A J } A J K ... an i t e r a t i v e approach was r e q u i r e d to determine the f i n a l s p e c t r o s c o p i c c o n s t a n t s ; t h r e e i t e r a t i o n s u s u a l l y produced convergence o f the f i t . F i t t i n g c o n s i d e r a t i o n s a r e d i s c u s s e d i n d e t a i l by K i r c h h o f f (22) who a l s o d i s c u s s e s schemes f o r d e t e c t i n g m i s a s s i g n e d t r a n s i t i o n s . In the e a r l i e r f i t s , however, the c e n t r i f u g a l d i s t o r t i o n was t r e a t e d as a p e r t u r b a t i o n on the r i g i d r o t o r e n e r g i e s as o u t l i n e d by Helmi n g e r , Cook and De L u c i a ( 2 3 ) . I t i s p o s s i b l e to w r i t e a f i r s t o r d e r e x p r e s s i o n f o r t he r o t a t i o n a l e n e r g i e s as E = E R + E D + E D . (1.13) where E R = % ( B + C ) J ( J + 1) + [A - ia(B + C)]Wj (b ) E D = - A / ( J + I ) 2 - A J K J ( J + l ) < P a 2 > - A K<P a 4> 9 - 2 6 j a J ( J + l ) [ W j (b ) - <P a 2>] T - 2 6 K a [Wj (b ) <P a 2> - <P a 4>] T r E D , = H j J 3 ( J + l ) 3 + H J K J 2 ( J + l ) 2 < P a 2 > + H K J J ( J + D<P a 4> + H„<P 6> + 2 h , o J 2 ( J + 1) 2[W, ( b j - <P 2>] l\ a 0 J p a + 2ah K J ( J + l ) [ W j (b )<P a 2> - <P 4 > ] + 2 o h K C W J ( b p ) < P a 4 > " < P a 6 > ] Here o = - l / b ; W, (b ), the Wang reduced energy, has been p r e v i o u s l y P J T P d i s c u s s e d . In u s i n g t he f i r s t o r d e r energy e x p r e s s i o n the ob s e r v e d f r e q u e n c i e s were i n i t i a l l y f i t t o the q u 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 c o n s t a n t s and t o changes i n the r o t a t i o n a l c o n s t a n t s . In each c a s e , a f t e r the f i r s t i t e r a t i o n where the t r i a l v a l u e s used f o r the r o t a t i o n a l c o n s t a n t s were e i t h e r guessed v a l u e s o r t h o s e o b t a i n e d from a r i g i d r o t o r a n a l y s i s , changes i n the r o t a t i o n a l c o n s t a n t s were small but s i g n i f i c a n t . As v a r i a t i o n s i n the r o t a t i o n a l c o n s t a n t s a f f e c t the v a l u e s o b t a i n e d f o r the d i s t o r t i o n c o n s t a n t s an i t e r a t i v e approach was a g a i n used t o a r r i v e a t t h e f i n a l r e s u l t s ; the r o t a t i o n a l c o n s t a n t s d e r i v e d from the most r e c e n t f i t s e r v e d i n each c a s e as t r i a l v a l u e s i n the next sequence o f the i t e r a t i o n . The convergence was s w i f t w i t h changes b e i n g i n s i g n i f i c a n t a f t e r the second i t e r a t i o n . U n f o r t u n a t e l y , h i g h e r o r d e r d i s t o r t i o n e f f e c t s can be i m p o r t a n t when t h i s f i r s t o r d e r energy e x p r e s s i o n i s employed. E s s e n t i a l l y t h i s i s because the v a r i o u s e x p e c t a t i o n v a l u e s 2 2 <P g > = 3E/8A, <P b > = 9E/8B, ... e t c . have been c a l c u l a t e d u s i n g the e i g e n v e c t o r s o f the r i g i d r o t o r H a m i l t o n i a n and not the complete r o t a t i o n a l H a m i l t o n i a n . To ac c o u n t f o r h i g h e r o r d e r d i s t o r t i o n e f f e c t s t he r o t a t i o n a l c o n s t a n t s and c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s d e t e r m i n e d u s i n g the above p r o c e d u r e were i n s e r t e d i n t o the complete H a m i l t o n i a n , 10 e q u a t i o n 1.11, which was then n u m e r i c a l l y d i a g o n a l i z e d t o y i e l d a s e t o f "e x a c t " t r a n s i t i o n f r e q u e n c i e s . The d i f f e r e n c e s between t h e s e e x a c t f r e q u e n c i e s and t h o s e c a l c u l a t e d u s i n g t he f i r s t o r d e r energy e x p r e s s i o n r e p r e s e n t the h i g h e r o r d e r d i s t o r t i o n c o n t r i b u t i o n . These f r e q u e n c i e s were s u b t r a c t e d from t he ob s e r v e d f r e q u e n c i e s and the r e s u l t a n t f r e q u e n -c i e s ' O b s e r v e d " v H i g h e r O r d e r ' w e r e r e f i t u s i n g t h e f i r s t o r d e r e n e r g y e x p r e s s i o n . T h i s p r o c e d u r e i s u s u a l l y employed o n l y when hi g h J l i n e s have been i n c l u d e d i n the f i t . In such c a s e s s e v e r a l i t e r a t i o n s may be needed t o a t t a i n c o n v e r g e n c e ; t h a t i s , b e f o r e the h i g h e r o r d e r c o r r e c t i o n s a c h i e v e a c o n s t a n t v a l u e . Here two t o f o u r i t e r a t i o n s were r e q u i r e d . When deemed n e c e s s a r y t he f i t t i n g p r o c e d u r e was expanded t o i n c l u d e t h e s e x t i c d i s t o r t i o n c o n s t a n t s ; a g a i n i t was n e c e s s a r y t o a c c o u n t f o r h i g h e r o r d e r e f f e c t s . The s p e c t r o s c o p i c c o n s t a n t s o b t a i n e d u s i n g e i t h e r o f t h e two p o s s i b l e f i t t i n g p r o c e d u r e s were i n each c a s e , o f c o u r s e , u l t i m a t e l y i d e n t i c a l . 1.2 N u c l e a r Quadrupole C o u p l i n g A n u c l e u s w i t h a s p i n quantum number g r e a t e r than 1/2 p o s s e s s e s a n u c l e a r e l e c t r i c q u a d r u p o l e moment which can i n t e r a c t w i t h the e l e c t r i c f i e l d g r a d i e n t produced a t t h a t n u c l e u s by the m o l e c u l e ' s e x t r a q u a d r u p o l a r c h a r g e s . In e f f e c t t h e n u c l e a r s p i n a n g u l a r momentum I_ c o u p l e s w i t h t he r o t a t i o n a l a n g u l a r momentum J_ t o g i v e a net a n g u l a r momentum F_ F = I + J (1.14) where F ranges from J + I t o |J - I | . The e f f e c t o f the i n t e r a c t i o n i s t o s p l i t a r o t a t i o n a l l e v e l i n t o 21 + 1 l e v e l s and, i n t u r n , t o i n t r o d u c e h y p e r f i n e s t r u c t u r e i n t o t he r o t a t i o n a l spectrum. A l l o f the h y p e r f i n e s t r u c t u r e o b s e r v e d i n t h e p r e s e n t s t u d y c o u l d be t r e a t e d w i t h a f i r s t o r d e r H a m i l t o n i a n ; t h a t i s , a H a m i l t o n i a n d i a g o n a l i n J . 11 The q u a d r u p o l e H a m i l t o n i a n f o r a m o l e c u l e c o n t a i n i n g one quad-r u p o l a r n u c l e u s can be w r i t t e n (24) HQ = eQqj [ 3 ( I - J ) 2 + | I_-J - I _ 2 J 2 ] (1.15) 2 J ( 2 J - 1)1(21 - 1) where eQ i s the cha r g e - w e i g h t e d n u c l e a r q u a d r u p o l e moment, a c o n s t a n t f o r a g i v e n n u c l e u s , and q j i s a c o u p l i n g c o n s t a n t o b s e r v e d f o r the maximum p r o j e c t i o n o f J_ a l o n g a s p a c e - f i x e d a x i s , t h a t i s f o r the s t a t e w i t h M = J . For an asymmetric r o t o r q j = <JTM = J | 3 2V / 9 Z 2 |JTM = J> (1.16) where V i s the e l e c t r i c f i e l d a t the q u a d r u p o l a r n u c l e u s and Z d e f i n e s the s p a c e - f i x e d a x i s . A l t e r n a t i v e l y one can w r i t e E ( * J = 2 Z X G G < P G 2 > (1.17) ( J + 1 ) ( 2 J + 3 ) g = a,b,c where x g g i s c a l l e d a 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 . As a consequence o f La P l a c e ' s e q u a t i o n t h e r e a r e o n l y two independent x a a ' s yy s i n c e *aa + *bb + * c c ' 0 0 . 1 8 ) And, f o r a p r o l a t e asymmetric t o p a 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 asymmetry paramter, n» i s d e f i n e d by n = ( x b b - x c c ) / x a a 0 . 1 9 ) The two independent c o n s t a n t s which can be dete r m i n e d from a f i r s t o r d e r a n a l y s i s o f a spectrum h a v i n g n u c l e a r q u a d r u p o l e h y p e r f i n e s t r u c t u r e a re u s u a l l y chosen as x , and n. I t i s then p o s s i b l e t o w r i t e a f i r s t o r d e r aa e x p r e s s i o n f o r the quad r u p o l e energy as (25) (1.20) E Q = f(I»J,F) (3<P a 2> - J ( J + 1) +• {<P a 2> - Wj (b )}.n/b )X J ( J + 1) T 12 where f ( I , J , F ) , C a s i m i r ' s f u n c t i o n , i s d e f i n e d by f ( I , J , F ) = 3C(C + l ) / 4 - 1 ( 1 + 1 ) J ( J + 1) 21(21 - 1 ) ( 2 J - 1 ) ( 2 J + 3) wi t h C = F( F + 1) - J ( J + 1) - 1(1 + 1) A g a i n , t h e Wang reduced energy Wj (b ) has been used p r e v i o u s l y i n d i s c u s s i n g t h e r i g i d asymmetric r o t o r problem. I t i s , o f c o u r s e , p o s s i b l e f o r a m o l e c u l e t o e x h i b i t p l u r a l 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 . The s i m p l e s t p o s s i b l e c a s e i n v o l v e s two qu a d r u p o l a r n u c l e i where one c o u p l e s much more s t r o n g l y than t he o t h e r . In t h i s c a s e i t i s p o s s i b l e to d e r i v e a f i r s t o r d e r e x p r e s s i o n f o r the qu a d r u p o l e e n e r g i e s s i m i l a r t o t h a t a l r e a d y g i v e n f o r t he one n u c l e u s c a s e ; the t h e o r y has been o u t l i n e d by Bardeen and Townes (2 6 ) . In the case where two n u c l e i have equal o r n e a r l y equal c o u p l i n g s , however, i t i s n e c e s s a r y t o d i a g o n a l i z e t h e H a m i l t o n i a n m a t r i x o f Hg. When a m o l e c u l e p o s s e s s e s two q u a d r u p o l a r n u c l e i h a v i n g n u c l e a r s p i n a n g u l a r momenta o f Lj and Ir, r e s p e c t i v e l y t h e r e a r e two p o s s i b l e c o u p l i n g schemes. F o r example one can have — + —1 = ^ 1 (1.21) —1 + —2 = — where a g a i n J_ i s the r o t a t i o n a l a n g u l a r momentum and F_ i s the t o t a l a n g u l a r momentum. Then F^ and F can assume the v a l u e s J + 1^, J + 1^ - 1, |J - I-|| and F^ + I 2 , F^ + I 2 - 1, ... | F-j - I 2 | r e s p e c t i v e l y . A l t e r n a t i v e l y one can use the scheme -1 + -2 = -(1.22) I + J = F In t h i s case the quantum number I which d e s c r i b e s t he t o t a l n u c l e a r 13 s p i n a n g u l a r momentum can have the v a l u e s I-| + I g , I-| + I 2 - 1, .... , |I-| - I^I and F c o v e r s the range J + I, J + I - 1 , | J - I | . The second o f t h e s e two schemes i s the most u s e f u l s i n c e i t a l l o w s one t o d e t e r m i n e by i n s p e c t i o n the symmetry o f the n u c l e a r s p i n w a v e f u n c t i o n s . T h i s i s t h e d e s i r e d c o u p l i n g scheme f o r a m o l e c u l e which c o n t a i n s i d e n t i -c a l n u c l e i s i n c e i n t h i s c a s e the r e q u i r e m e n t s o f n u c l e a r s p i n p e r m u t a t i o n symmetry d i c t a t e t h a t the s t a t i s c a l w e i g h t s o f the v a r i o u s s p i n f u n c t i o n s 32 35 a r e d i f f e r e n t . In c a s e s such as t h a t o f S C l g s t a t i s t i c a l w e i g h t s o f z e r o a r e p o s s i b l e . O nly t h i s l a t t e r c ase w i l l be c o n s i d e r e d here. In p r a c t i c e , however, the former scheme was sometimes used f o r the i n e q u i v a -l e n t n u c l e i c a s e ; the r e q u i r e d computer program was w r i t t e n by Robert L. Cook u s i n g the m a t r i x elements i n the form g i v e n by Cook and De L u c i a (27), P l u r a l 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 was o b s e r v e d i n t h i s s t u d y onliy f o r m o l e c u l e s c o n t a i n i n g two c h l o r i n e atoms. For t h i s case I-j = Ig = 3/2. The r e q u i r e d m a t r i x elements o f ( H g ) j 0 t a ] where (Vlota l " \ + % have been e v a l u a t e d by F l y g a r e and Gwinn i n t h e i r landmark s t u d y o f methylene c h l o r i d e ( 2 8 ) . As a f i r s t o r d e r t r e a t m e n t was s u f f i c i e n t f o r the p r e s e n t s t u d y o n l y the elements d i a g o n a l i n J were r e q u i r e d . The m a t r i x elements have the form < I 1 I 2 I ' J ' F | H Q i + H Q 2 | I 1 I 2 I J F > = <HQt> (1.24) = <3 3 i ' j ' F | H n + H n I3- I IJF> 71 1 Q1 Q212 2 S p e c i f i c a l l y one has f o r the v a r i o u s c a s e s (28) 1. J ' = J and I' = I <H Q > = 3 / ( 1 + 3 ) ( I - 2) [A(A + 1) - I 1(1 + 1 ) J ( J + 1 ) ] T 1 6 J ( 2 J - 1 ) ( 2 I - 1 ) ( 2 I + 3) 14 w i t h A = F(F + 1) - 1(1 + 1) - J ( J + 1) 2. J ' = J and I 1 = I + 1 <H Q > = x " [ I ( I + 2) + J ( J + 1) - F ( F + 1 ) ]  T 1 6 J ( 2 J - 1) (I + 5 ) ( - I + 3) (21 + 1) (21 + 3) x.[(F + I + J + 2 ) ( F - I + J ) ( F + I - J + 1 ) ( - F + I + J + 1 ) ] ' 3. J 1 = J and 1 1 = I + 2 + (I + 6 ) ( I + 5 ) ( - I + 3 ) ( - I + 2 ) ( F + I + J + 3) (21 + 5)(21 + 1) 32 J ( 2 J - 1 ) ( 2 I + 3) x (F + I + J + 2 ) ( F + I - J + 2 ) ( F + I - J + 1 ) ( - F + I + J + 2) x.(- F + I + J + 1 ) ( F - I + J ) ( F - I + J - 1) where the c o u p l i n g c o n s t a n t s x + and x~ a r e g i v e n i n terms o f p r e v i o u s l y d e f i n e d c o n s t a n t s by X + = (eQ + (eQ ) 2 i f I' = I o r I' = I ± 2 and x" = (eQ. ), - (eQ ) 2 1f I' = I ± 1 (1.25) (1.26) For a m o l e c u l e c o n t a i n i n g two c h l o r i n e s , 1-j = I 2 = |. , i t i s a s i m p l e m a t t e r to c o n s t r u c t and d i a g o n a l i z e t he 16 x 16 H a m i l t o n i a n m a t r i x o f H n + H n . No l e a s t squares f i t s though were made u s i n g t h i s H a m i l t o n i a n . g l g 2 1.3 The Asymmetric R o t o r S t a r k E f f e c t The S t a r k e f f e c t o f an asymmetric r o t o r has been d e s c r i b e d by Golden and W i l s o n ( 2 9 ) . When a m o l e c u l e i s p l a c e d i n a u n i f o r m e l e c t r i c f i e l d E ( d i r e c t e d a l o n g t he s p a c e - f i x e d Z - a x i s ) i t e x p e r i e n c e s a t o r q u e which p e r t u r b s t he r o t a t i o n a l e n e r g i e s o f the m o l e c u l e . The S t a r k H a m i l t o n i a n i s g i v e n by (1.27) H s = - u - E Z , u g = a,b,c Zg g 15 where i s the d i r e c t i o n c o s i n e between the s p a c e - f i x e d Z - a x i s and the zg m o l e c u l e - f i x e d g - a x i s . I f t h e r e a r e no near d e g e n e r a t e l e v e l s then the S t a r k energy f o r a g i v e n l e v e l J i s M dependent and i s g i v e n by t h e second o r d e r p e r t u r b a t i o n sum ( J 2 - M2) 4 J 2 ( 4 J 2 1) E | <JT I * Y R I | J - l,x'> 1 , - Z g — CO _ po X (1.28) M 4 J 2 ( J + I ) 2 T ' + ( J + I ) 2 - M 2 j ^ i i * Z g i J i ^ . r T X 4 ( J + 1 T ( 2 J + 1 ) ( 2 J + 3) x' I l < J T [ $ Z g l J + 1 , t ' >|' J + 1 2 C2 x u g E where E°j i s t h e r o t a t i o n a l energy o f the l e v e l |Jx> i n the absence o f T an e l e c t r i c f i e l d . The d i r e c t i o n c o s i n e m a t r i x elements can be e x p r e s s e d i n terms o f the l i n e s t r e n g t h s * g ( J T '> J u s i n g | < J x | * 7 n | J + 1,T'>| 2 = 4 ( J + l ) x g ( d x ; J + 1,T') fZg' ^Zgl | < j T | * 7 n | J T ' > r = 4 J ( J + 1) X g ( J t ; J T') 2J + 1 (1.29) | < J x | $ Z g | J - 1,T'>|^ = 40 X g ( J x ; J - 1,T') The l i n e s t r e n g t h s X ( J x ; J'x') depend o n l y on the degree o f asymmetry 9 o f a m o l e c u l e and have been t a b u l a t e d as a f u n c t i o n o f K, the asymmetry parameter o f Ray (1 4 ) . The use o f t h e s e t a b l e s (30) may r e q u i r e i n t e r -p o l a t i o n between a p p r o p r i a t e v a l u e s o f K. A l t e r n a t i v e l y the l i n e s t r e n g t h s can be e s t i m a t e d u s i n g the e i g e n v e c t o r s o f the asymmetric r o t o r H a m i l t o n i a n and the r e l a t i o n (31) 16 X g ( J x ; J V ) = Z j g j M , | < J x M | $ Z g |J'T'M'>| 2 ( 1 . 3 0 ) The e i g e n v e c t o r s o f the r i g i d r o t o r H a m i l t o n i a n a r e u s u a l l y adequate as St a r k e f f e c t measurements a r e almos t always made u s i n g low J t r a n s i t i o n s . The e x p r e s s i o n used above t o c a l c u l a t e the S t a r k e n e r g i e s f o r a pure second o r d e r o r q u a d r a t i c S t a r k e f f e c t , w h i l e adequate to d e s c r i b e the s h i f t s measured h e r e , i s not g e n e r a l l y a p p l i c a b l e . A l t e r n -a t i v e t r e a t m e n t s may be r e q u i r e d i f t h e r e a r e near d e g e n e r a t e r o t a t i o n a l l e v e l s o r i f a t r a n s i t i o n e x h i b i t s n u c l e a r q u a d r u p o l e h y p e r f i n e s t r u c t u r e . T h i s l a t t e r problem i s d i s c u s s e d f o r p r o p i o l y l c h l o r i d e i n Ch a p t e r 5. Near d e g e n e r a c i e s a r e most f r e q u e n t l y o f the approximate symmetric r o t o r t y p e . Very f a s t S t a r k e f f e c t s can then o c c u r p r o v i d e d t h a t t he a p p r o p r i a t e d i p o l e moment component i s non-zero. 1.4 M o l e c u l a r S t r u c t u r e s from R o t a t i o n a l S p e c t r a Both o f the methods commonly used t o deter m i n e t he m o l e c u l a r s t r u c t u r e s o f gaseous m o l e c u l e s , namely microwave s p e c t r o s c o p y and e l e c t r o n d i f f r a c t i o n , have i n h e r e n t l i m i t a t i o n s . In microwave i n v e s t i -g a t i o n s , f o r example, s e v e r a l i s o t o p i c s p e c i e s must o f t e n be s t u d i e d i n o r d e r t o s p e c i f y the m o l e c u l a r geometry; i n a d d i t i o n , t h e r e a r e d i f f i c u l t -i e s i n d e t e r m i n i n g a c c u r a t e l y t he c o o r d i n a t e s o f atoms which a r e s i t u a t e d near i n e r t i a l axes. Problems a r i s e w i t h the e l e c t r o n d i f f r a c t i o n method because o f i n a d e q u a t e l y r e s o l v e d r a d i a l d i s t r i b u t i o n c u r v e s , sample i m p u r i t i e s and complex c o n f o r m a t i o n a l e q u i l i b r i a . In both c a s e s , however, the a c c u r a c y o f the s t r u c t u r a l d e t e r m i n a t i o n s i s o f t e n l i m i t e d by an inad e q u a t e t r e a t m e n t o f v i b r a t i o n a l e f f e c t s . In p a r t because the e f f e c t s o f v i b r a t i o n a r e m a n i f e s t e d d i f f e r e n t l y i n the two expe r i m e n t s s e v e r a l t y p e s o f s t r u c t u r a l parameters a r e used. Here o n l y those parameters n o r m a l l y d e r i v e d from r o t a t i o n a l s p e c t r a w i l l be c o n s i d e r e d ; a more 17 d e t a i l e d d i s c u s s i o n i s g i v e n by Gordy and Cook ( 3 2 ) . Good o v e r v i e w s o f the t h e o r y r e q u i r e d to r e l a t e s p e c t r o s c o p i c and d i f f r a c t i o n s t r u c t u r e s a r e g i v e n by R o b i e t t e (33) and by K u c h i t s u and C y v i n ( 3 4 ) . To a f i r s t a p p r o x i m a t i o n a m o l e c u l e can be thought o f as a c o l l e c t i o n o f r i g i d p o i n t masses, m., h a v i n g p r i n c i p a l a x i s c o o r d i n a t e s a.-, b.j and . Then t h e e q u a t i o n s d e f i n i n g t h e p r i n c i p a l moments o f i n e r t i a I a , 1^ and I can be w r i t t e n : I a = ?m. ( b . 2 + c . 2 ) I b = zm 1 ( a . 2 + C i 2 ) (1.31) I c = ?m. ( a i 2 + b i 2 ) For a r i g i d p l a n a r m o l e c u l e t h e r e a r e o n l y two independent moments o f i n e r t i a s i n c e a l l o f the c^ a r e i d e n t i c a l l y z e r o and I c - I a - I b = 0 (1.32) Real m o l e c u l e s a r e n o t r i g i d , however, and do not conform to t h i s i d e a l i z e d p i c t u r e . As a r e s u l t a g i v e n moment o f i n e r t i a ( o r r o t a t i o n a l c o n s t a n t ) i s a f u n c t i o n o f the v i b r a t i o n a l s t a t e o f the m o l e c u l e . A p a r t i c u l a r consequence o f t h i s i s the o b s e r v a t i o n o f s o - c a l l e d i n e r t i a ! d e f e c t s f o r p l a n a r m o l e c u l e s ; f o r a v i b r a t i o n a l s t a t e , v, c h a r a c t e r i z e d V Vi ' V by t h e o b s e r v e d p r i n c i p a l moments I f i , 1^ and I ' the i n e r t i a ! d e f e c t A v i s d e f i n e d by V"- J b V = A v H.33) The i n e r t i a l d e f e c t depends m a i n l y on the harmonic p a r t o f the i n t r a -m o l e c u l a r f o r c e f i e l d b u t , as i s the ca s e w i t h t he p r i n c i p a l moments, t h e r e a r e sm a l l c o n t r i b u t i o n s from c e n t r i f u g a l terms and from e l e c t r o n -r o t a t i o n i n t e r a c t i o n s . U s u a l l y one w r i t e s (35) 18 = A V i b + A c e n t + A e l e c (1.34) v The ground s t a t e i n e r t i a l d e f e c t , A , i s o b t a i n e d from the o b s e r v e d ground s t a t e moments I °, I b ° and I c ° u s i n g For a p l a n a r m o l e c u l e the ground s t a t e i n e r t i a l d e f e c t s a r e u s u a l l y small and p o s i t i v e . In f a c t , such an o b s e r v a t i o n i s o f t e n taken as p r o o f o f a p l a n a r m o l e c u l a r s t r u c t u r e , e s p e c i a l l y i f the i n e r t i a l d e f e c t e x h i b i t s o n l y s l i g h t i s o t o p i c v a r i a t i o n . S t r i c t l y the o b s e r v e d i n e r t i a l d e f e c t s s h o u l d be compared w i t h t h o s e c a l c u l a t e d from a good harmonic f o r c e f i e l d (35, 36) but o f t e n t h i s i s i m p o s s i b l e . The most meaningful s t r u c t u r a l parameters a r e t h o s e which c h a r a c t e r i z e the geometry o f a m o l e c u l e i n i t s h y p o t h e t i c a l v i b r a t i o n l e s s s t a t e o r e q u i l i b r i u m c o n f i g u r a t i o n . W i t h i n the l i m i t a t i o n s o f the Born-Oppenheimer a p p r o x i m a t i o n the e q u i l i b r i u m o r r g s t r u c t u r e has the i m p o r t a n t p r o p e r t y o f b e i n g i s o t o p i c a l l y i ndependent ( 3 7 ) . As w e l l , t h i s i s :the s t r u c t u r e which i s c a l c u l a t e d by db initio methods. To o b t a i n an r g s t r u c t u r e the c o r r e s p o n d i n g e q u i l i b r i u m v a l u e s o f the r o t a t i o n a l c o n s t a n t s a r e needed. F o r d i a t o m i c m o l e c u l e s the. r o t a t i o n a l c o n s t a n t s can be e x p r e s s e d as a f u n c t i o n o f the v i b r a t i o n a l quantum number v u s i n g a q u i c k l y c o n v e r g i n g power s e r i e s Here B i s the e q u i l i b r i u m r o t a t i o n a l c o n s t a n t and a and y a r e c o n s t a n t s e which g i v e the v i b r a t i o n a l dependence o f the r o t a t i o n a l c o n s t a n t . Three s i m i l a r e q u a t i o n s can be w r i t t e n f o r the g e n e r a l p o l y a t o m i c m o l e c u l e . Keeping o n l y t h o s e terms l i n e a r i n the v i b r a t i o n a l quantum number we have (1.36) 19 3N - 6 r G = G - Z a b(v • + d./2) (1.37) V e i = 1 i 1 1 Here V. a r e the v i b r a t i o n a l quantum numbers f o r the 3N - 6 normal modes which s p e c i f y t h e s t a t e v, d^ i s the degeneracy o f the i t h normal mode and G i s e i t h e r A, B or C. I f a l l o f the v i b r a t i o n - r o t a t i o n c o n s t a n t s a. a r e known the e q u i l i b r i u m v a l u e s o f the r o t a t i o n a l c o n s t a n t s can be o b t a i n e d from the ground s t a t e c o n s t a n t s u s i n g a s i m p l i f i e d form o f the above e q u a t i o n , namely 3N - 6 r G e = G o + . E ] «i V 2 ( 1- 3 8 ) Here G i s e i t h e r A , B o r C . T h i s method o f e x t r a p o l a t i n g t o o b t a i n o 0 0 0 r a the e q u i l i b r i u m r o t a t i o n a l c o n s t a n t s and thus t h e r g s t r u c t u r e i s u s u a l l y i m p r a c t i c a l , however. Even f o r a si m p l e m o l e c u l e such as a bent XYZ t r i a t o m i c two i s o t o p i c s p e c i e s a r e need to o b t a i n a s t r u c t u r e ; t h e r e f o r e s i x ground s t a t e and e i g h t e e n e x c i t e d s t a t e r o t a t i o n a l c o n s t a n t s must be dete r m i n e d . The s i t u a t i o n i s much worse f o r more complex m o l e c u l e s . F u r t h e r , i t i s o f t e n i m p o s s i b l e to o b s e r v e e x c i t e d s t a t e r o t a t i o n a l s p e c t r a because o f u n f a v o u r a b l e Boltzmann f a c t o r s a l t h o u g h the i n c r e a s e d use o f i n f r a r e d microwave doubl e resonance (38) may somewhat a l l e v i a t e t h i s problem; the a n a l y s i s o f t h e s e e x c i t e d s t a t e s p e c t r a i s o f t e n c o m p l i c a t e d by h i g h e r o r d e r v i b r a t i o n - r o t a t i o n i n t e r a c t i o n s . For a p l a n a r m o l e c u l e one e e e can check t h a t the e q u i l i b r i u m p r i n c i p a l moments I , 1^ and I have been c o r r e c t l y c a l c u l a t e d s i n c e t h e s e must s a t i s f y the r e l a t i o n ^ " - V • A e " 0 ( ' - 3 9 ) A second p h y s i c a l l y w e l l - d e f i n e d s t r u c t u r e i s the average s t r u c t u r e which, f o r a g i v e n v i b r a t i o n a l s t a t e v, g i v e s the mean p o s i t i o n s o f the atoms. T h i s i s u s u a l l y denoted by an r z o r <r> f o r the ground s t a t e and by r z f o r a n e x c i t e d v i b r a t i o n a l s t a t e v. The c o r r e c t i o n s r e q u i r e d 20 to o b t a i n the average r o t a t i o n a l c o n s t a n t s depend o n l y on the harmonic Q p a r t o f the i n t r a m o l e c u l a r f o r c e f i e l d ( 3 9 ) . S i n c e the o .^ c o n s t a n t s used p r e v i o u s l y can be s e p a r a t e d i n t o harmonic and anharmonic p a r t s as P P p a.. = a.. (Harmonic) + ou (Anharmonic) (1.40) one can w r i t e e q u a t i o n s analagous t o t h o s e used t o d e f i n e the e q u i l i b r i u m r o t a t i o n a l c o n s t a n t s . For example 3N - 6 r G z = G Q + E d . a . b ( H a r m o n i c ) (1.41) Here G z i s any one o f the ground s t a t e average r o t a t i o n a l c o n s t a n t s A z , B z o r C z and G Q and d.. have been d e f i n e d p r e v i o u s l y . The a.. (Harmonic) a r e r e a d i l y c a l c u l a t e d i f a good harmonic f o r c e f i e l d i s a v a i l a b l e ( 4 0 ) . A d i f f i c u l t y w i t h average s t r u c t u r e s i s t h a t a l t h o u g h they a r e p h y s i c a l l y w e l l - d e f i n e d , because o f anharmonic e f f e c t s , t h e y a r e n o t i s o t o p i c a l l y i n v a r i a n t . S t r i c t l y , t h e r e f o r e , f o r complex m o l e c u l e s one needs to be a b l e t o c a l c u l a t e the i s o t o p i c v a r i a t i o n o f the average s t r u c t u r e consequent on i s o t o p i c s u b s t i t u t i o n b e f o r e the average s t r u c t u r e o f a g i v e n i s o t o p i c s p e c i e s can be d e t e r m i n e d . T h i s problem has been c o n s i d e r -ed by K u c h i t s u and co-workers (41, 42). They have su g g e s t e d t h a t the i s o t o p i c v a r i a t i o n s o f the bond l e n g t h s a r e most i m p o r t a n t . They have c a l c u l a t e d t h e s e and a l s o e s t i m a t e d the e q u i l i b r i u m bond d i s t a n c e s u s i n g the e q u a t i o n s r z = r e + 3 au 2/2 - K (1.42) and <Srz = 3 a 6 ( u 2 ) / 2 - K (1.43) Here r g and r z a r e the e q u i l i b r i u m and average bond l e n g t h s , u i s the z e r o - p o i n t mean square a m p l i t u d e o f the bond i n q u e s t i o n , K i s the c o r r e s p o n d i n g p e r p e n d i c u l a r a m p l i t u d e c o r r e c t i o n (both u and K a r e 21 r e a d i l y c a l c u l a t e d from the harmonic f o r c e f i e l d ( 4 3 ) ) , and a i s the Morse a n h a r m o n i c i t y parameter; where p o s s i b l e v a l u e s o f a a r e o b t a i n e d from t he c o r r e s p o n d i n g d i a t o m i c m o l e c u l e . When no c o r r e c t i o n s f o r v i b r a t i o n a l e f f e c t s a r e p o s s i b l e the s t r u c t u r a l parameters a r e u s u a l l y a d j u s t e d t o f i t the e f f e c t i v e ground s t a t e moments o f i n e r t i a I °, I . 0 and I °. The r e s u l t i n g r . s t r u c t u r e a b c 3 o has a v e r y nebulous p h y s i c a l meaning f o r p o l y a t o m i c m o l e c u l e s because o f C o r i o l i s e f f e c t s . e q u a t i o n s ,of Kraitchman ( 4 4 ) . In t h i s method the c o o r d i n a t e s o f an atom ar e c a l c u l a t e d from t h e changes i n the moments o f i n e r t i a c aused by i s o -t o p i c s u b s t i t u t i o n o f t h a t atom. C o s t a i n has s u g g e s t e d t h a t the r g method g i v e s an improvement o v e r the r Q s t r u c t u r e because when d i f f e r e n c e s i n the moments o f i n e r t i a a r e used v i b r a t i o n a l c o n t r i b u t i o n s t o the I's ar e l a r g e l y c a n c e l l e d ( 4 5 ) . F or a p l a n a r asymmetric top Kraitchman's e q u a t i o n s have a p a r t i c u l a r l y s i m p l e form. The a g and b g c o o r d i n a t e s o f the s u b s t i t u t e d atom a r e o b t a i n e d from where the I and I a r e the p r i n c i p a l moments o f i n e r t i a o f the unsub-9 9 s t i t i i t e d and s u b s t i t u t e d s p e c i e s r e s p e c t i v e l y . The reduced mass y i s d e f i n e d by F i n a l l y t h e r e i s the s u b s t i t u t i o n o r r g s t r u c t u r e based on the 2 (1.44) >y = MAm (1.45) M + Am 22 where M and M + Am r e s p e c t i v e l y a r e the masses o f the u n s u b s t i t u t e d and s u b s t i t u t e d m o l e c u l e s . The u n s u b s t i t u t e d s p e c i e s i s c a l l e d t h e p a r e n t m o l e c u l e . S u b s t i t u t i o n o f each atom i n t u r n e n a b l e s a l l o f the r s c o o r d i n a t e s t o be de t e r m i n e d . The c o o r d i n a t e s o f atoms such as f l u o r i n e , phosphorus and i o d i n e cannot be c a l c u l a t e d i n t h i s way because t h e y have o n l y one s t a b l e i s o t o p e . In a d d i t i o n , C o s t a i n has shown (46) t h a t atomic o c o o r d i n a t e s s m a l l e r than about 0.15 A cannot be r e l i a b l y e s t i m a t e d u s i n g the s u b s t i t u t i o n method. Both o f t h e s e l a t t e r d i f f i c u l t i e s can be m i t i -gated by use o f t h e c e n t e r o f mass c o n d i t i o n s E1-miai = z..m..b.. = E..m..c.. = 0 (1.46) o r the p r o d u c t o f i n e r t i a c o n d i t i o n s E.m.a.b. = z.m.a.c. = E.m.b.c. = 0 (1.47) l i i i i i i i I I I I V ' For o v e r - d e t e r m i n e d systems Watson has shown t h a t an r s t r u c t u r e m o b t a i n e d from I = 21 - I (1.48) m s o i s i n many cases an e x c e l l e n t a p p r o x i m a t i o n t o the r g s t r u c t u r e ( 4 7 ) . 23 1.5 C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s and t h e Harmonic F o r c e F i e l d The q u 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 c o n s t a n t s p r o v i d e u s e f u l i n f o r m a t i o n about the harmonic f o r c e f i e l d . They can be used e i t h e r t o check the v a l i d i t y o f a proposed f o r c e f i e l d o r to p r o v i d e d a t a , u s u a l l y a d d i t i o n a l t o t h a t o f t h e v i b r a t i o n a l wavenumbers, f o r the e v a l u a t i o n o f f o r c e c o n s t a n t s . For a C g v t r i a t o m i c , however, the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s can be used t o d e t e r m i n e c o m p l e t e l y the harmonic f o r c e f i e l d . S t r i c t l y t h e e q u i l i b r i u m v a l u e s o f the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s s h o u l d be used f o r f o r c e c o n s t a n t d e t e r m i n a t i o n but t h e s e a r e seldom a v a i l a b l e . The q u 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 c o n s t a n t s a r e r e l a t e d t o the elements o f the i n v e r s e harmonic f o r c e c o n s t a n t m a t r i x . The T ' S o f W i l s o n and Howard (16) can be w r i t t e n i n terms o f t h e i n v e r s e f o r c e c o n s t a n t s u s i n g t h e e q u a t i o n (18) V Y 6 = " ^ R E ( J a 0 6 ) k ( r l ) k l ( J Y 6 } l (1.49) 66 YY Here A,A a r e r o t a t i o n a l c o n s t a n t s i n MHz; I n„,I a r e p r i n c i p a l moments 66 YY °2 17 o f i n e r t i a i n uA ; R = 2h x 10 w i t h h i n e r g - s e c . The q u a n t i t i e s o ( J a ^ ) k = ( 9 l a g / 9 S ) 0 a r e t h e p a r t i a l d e r i v a t i v e s o f the components o f t h e i n e r t i a t e n s o r w i t h r e s p e c t t o t h e k=th i n t e r n a l c o o r d i n a t e , a n d a r e g i v e n by o (a) The i - t h atom has mass m. and c o o r d i n a t e s a . , y.; t h e p . . ' a r e 1 1 1 1 K1 a components o f t h e i - t h atom o f P o l o ' s p - v e c t o r f o r the k-th i n t e r n a l 24 c o o r d i n a t e ( 4 9 ) . I f the i n e r t i a l d e r i v a t i v e s have u n i t s o f uA and uA ra d " ^ f o r a s t r e t c h and a bend, r e s p e c t i v e l y , and the f o r c e c o n s t a n t s O _ "I o have u n i t s o f mdyn A" , mdyn A r a d and mdyn r a d f o r a s t r e t c h , a bend and a s t r e t c h bend i n t e r a c t i o n , r e s p e c t i v e l y , then t he T „ r a r e i n MHz. The e x p e r i m e n t a l A J S A J K , A K, 6J and 6 K can be o b t a i n e d as l i n e a r c o m b i n a t i o n s o f t h e T'S u s i n g e q u a t i o n s due t o Watson ( 2 0 ) ; t h e r e l e v a n t e q u a t i o n s f o r Watson's A r e d u c t i o n H a m i l t o n i a n (21) i n the I r r e p r e s e n t a t i o n a r e g i v e n i n T a b l e 3.4. 25 B i b l i o g r a p h y 1. C.E. C l e e t o n and N.H. W i l l i a m s , Phys. Rev. 45, 234 (1934). 2. G.C. Dousmanis, T.M. Sanders and C.H. Townes, Phys. Rev. 100, 1735 (1955). 3. A. C a r r i n g t o n , Microwave S p e c t r o s c o p y o f F r e e R a d i c a l s , Academic P r e s s , London, 1974. 4. G. Winnewisser, N a t u r w i s s e n s c h a f t e n 62^ 200 (1975). 5. C.H. Townes and A.L. Schawlow, Microwave S p e c t r o s c o p y , M c G r a w - H i l l , New York, 1955. 6. T.M. Sugden and C.N. Kenney, Microwave S p e c t r o s c o p y o f Gases, Van N o s t r a n d , London, 1965. 7. H.C. A l l e n , J r . and P.C. C r o s s , M o l e c u l a r V i b - R o t o r s , John W i l e y and Sons, I n c . , New York, 1963. 8. J.B. W o l l r a b , R o t a t i o n a l S p e c t r a and M o l e c u l a r S t r u c t u r e , Academic P r e s s , New York, 1967. 9. W. Gordy and R.L. Cook, Microwave M o l e c u l a r S p e c t r a , I n t e r s c i e n c e P e b l i s h e r s , New York, 1970. 10. H.W. K r o t o , M o l e c u l a r R o t a t i o n S p e c t r a , John W i l e y and Sons, London, 1975. 11. see f o r example: K r o t o , op_. c i t . , C h a p t e r 3. 12. G.W. K i n g , R.M. H a i n e r and P.C. C r o s s , J . Chem. Phys. 11_, 27 (1943). 13. A l l e n and C r o s s , op_. c i t . , C h a p t e r 2. 14. B.S. Ray, Z. P h y s i k . 78, 74 (1932). 15. S.C. Wang, Phys. Rev. 34, 243 (1929). 16. E.B. W i l s o n , J r . and J.B. Howard, J . Chem. Phys. 4, 260 (1936). 17. E.B. W i l s o n , J r . , J . Chem. Phys. 4, 526 (1936). 18. D. K i v e l s o n and E.B. W i l s o n , J r . , J . Chem. Phys. 21_, 1229 (1953). 19. J.K.G. Watson, J . Chem. Phys. 45, 1360 (1966). 20. J.K.G. Watson, J . Chem. Phys. 46_, 1935 (1967). 21. J.K.G. Watson, i n V i b r a t i o n a l S p e c t r a and S t r u c t u r e , a S e r i e s o f  Advances (J.R. D u r i g , E d . ) , V o l . 6, pp. 1-89, E l s e v i e r , New York, 1977. 26 22. W.H. K i r c h h o f f , J . Mol. S p e c t r o s c . 41, 333 (1972). 23. P. Helminger, R.L. Cook and F.C. De L u c i a , J . Mol. S p e c t r o s c . 40, 125 (1971). 24. Gordy and Cook, op_. c i t . , pp. 246-251. 25. J.K. Bragg and S. Gol d e n , Phys. Rev. 75_, 735 (1949). 26. J . Bardeen and C.H. Townes, Phys. Rev. 73_, 97 (1948). 27. R.L. Cook and F.C. De L u c i a , Amer. J . Phys. 39, 1433 (1971). 28. W.H. F l y g a r e and W.D. Gwinn, J . Chem. Phys. 36, 787 (1962). 29. S. Golden and E.B. W i l s o n , J r . , J . Chem. Phys. J_6, 669 (1948). 30. R.H. Schwendeman and V.W. L a u r i e , T a b l e o f L i n e S t r e n g t h s f o r Rota- t i o n a l T r a n s i t i o n s o f Asymmetric R o t o r M o l e c u l e s , Pergamon P r e s s , London, 1958. 31. Gordy and Cook, op_. c i t . , pp. 193-195. 32. Gordy and Cook, op_. c i t . , C h a p t e r 13. 33. A.G. R o b i e t t e , i n M o l e c u l a r S t r u c t u r e by D i f f r a c t i o n Methods, a  S p e c i a l i s t P e r i o d i c a l R e p o r t , V o l . 1, pp. 160-197, The Chemical S o c i e t y , London, 1973. 34. K. K u c h i t s u and S.J. C y v i n , i n M o l e c u l a r V i b r a t i o n s and S t r u c t u r e  S t u d i e s ( S . J . C y v i n , E d . ) , E l s e v i e r , Amsterdam, 1972. 35. T. Oka and Y. Morino, J . Mol. S p e c t r o s c . 6_, 472 (1961). 36. D.R. Herschbach and V.W. L a u r i e , J . Chem. Phys. 40, 3142 (1964). 37. P.R. Bunker, J . Mol. S p e c t r o s c . 42_, 478 (1972). 38. H. J o n e s , i n Modern A s p e c t s o f Microwave S p e c t r o s c o p y (G.W. C h a n t r y , E d . ) , C h a p t e r 3, Academic P r e s s , London, 1979. 39. T. Oka, J . Phys. Soc. Japan 1_5, 2274 (1960). 40. I.M. M i l l s , i n M o l e c u l a r S p e c t r o s c o p y : Modern R e s e a r c h , (K.N. Rao and C.W. Mathews, E d i t o r s ) , pp. 115-140, Academic P r e s s , New York, 1972. 41. K. K u c h i t s u , J . Chem. Phys. 49, 4456 (1968). 42. K. K u c h i t s u , T. Fukuyama and Y. Morino, J . Mol. S t r u c t . 4, 41 (1969). 43. R. S t 0 1 e v i k , H.M. S e i p and S.J. C y v i n , Chem. Phys. L e t t . 1_5, 263 (1972). 27 44. J . Kraitchman, Amer. J . Phys. 21_, 17 (1953). 45. C C . C o s t a i n , J . Chem. Phys. 29, 864 (1958). 46. C C . C o s t a i n , T r a n s . Am. C r y s t a l l o g r a p h i c A s s o c . 2_, 157 (1966). 47. J.K.G. Watson, J . Mol. S p e c t r o s c . 48, 479 (1973). 48. C R . P a r e n t and M.C.L. G e r r y , J . Mol. S p e c t r o s c . 49, 343 (1974). 49. S.R. P o l o , J . Chem. Phys. 24, 1133 (1956). 28 C h a p t e r 2 E x p e r i m e n t a l Methods A l t h o u g h the i n s t r u m e n t a t i o n and t e c h n i q u e s used i n t h i s work were q u i t e c o n v e n t i o n a l a b r i e f a c c o u n t o f the e x p e r i m e n t a l p r o c e d u r e s i s g i v e n here. In microwave s p e c t r o s c o p y h i g h s p e c t r a l r e s o l u t i o n and a c c u r a t e f r e q u e n c y measurement a r e r e a d i l y a c h i e v e d . E x p e r i m e n t a l l i m i -t a t i o n s r e l a t e m o s t l y t o t h e i n h e r e n t weakness o f the s i g n a l s which i s u s u a l l y a r e s u l t o f s m a l l p o p u l a t i o n d i f f e r e n c e s between t h e r o t a t i o n a l l e v e l s o r a s m a l l d i p o l e moment. O f t e n s i g n a l s a r e so weak t h a t t h e y a r e e a s i l y l o s t i n the d e t e c t o r n o i s e o r masked by power f l u c t u a t i o n s caused by r e f l e c t i o n s i n t h e c e l l . A p a r t i c u l a r l y s i m p l e method o f enhancing the s e n s i t i v i t y o f a microwave s p e c t r o m e t e r i s the S t a r k m o d u l a t i o n t e c h n i q u e s u g g e s t e d by Hughes and W i l s o n ( 1 ) . The a b s o r p t i o n c e l l i s c u s t o m a r i l y a l o n g s e c t i o n o f r e c t a n g u l a r waveguide having a t h i n metal s t r i p o r septum mounted a t the c e n t e r . A r a d i o f r e q u e n c y e l e c t r i c f i e l d i s a p p l i e d t o t h e c e l l by c o n n e c t i n g the septum t o a z e r o - b a s e d square-wave g e n e r a t o r . When t h e f i e l d i s on, t h e r o t a t i o n a l t r a n s i t i o n i s s p l i t i n t o a s e r i e s o f S t a r k components which a r e s h i f t e d away from the z e r o f i e l d l i n e . The use o f a phase s e n s i t i v e d e t e c t o r thus a l l o w s one s e l e c t i v e l y t o modulate t h e r o t a t i o n a l t r a n s i t i o n s and a l m o s t e l i m i n a t e t h e e f f e c t s o f r e f l e c t e d power. The second i m p o r t a n t b e n e f i t o f S t a r k m o d u l a t i o n r e s u l t s from t h e f a c t t h a t t h e n o i s e power o f the s o l i d s t a t e d e t e c t o r s g e n e r a l l y used i s i n v e r s e l y p r o p o r t i o n a l t o the m o d u l a t i o n f r e q u e n c y . Thus, d e t e c t o r n o i s e 29 i s r e a d i l y r e d u c e d by u s i n g h i g h f r e q u e n c y m o d u l a t i o n . T y p i c a l m o d u l a t i o n f r e q u e n c i e s a r e i n the range 5 - 100 kHz; a t h i g h e r f r e q u e n c i e s l i n e b r o a d e n i n g becomes an a p p r e c i a b l e and u n d e s i r a b l e f a c t o r ( 2 ) . The S t a r k m o d u l a t i o n t e c h n i q u e i s s i m p l e and w e l l s u i t e d f o r centimeter-wave s t u d i e s but s e v e r a l a l t e r n a t i v e s , r a n g i n g from s o u r c e m o d u l a t i o n t o F o u r i e r t r a n s f o r m s p e c t r o m e t e r s , a r e a v a i l a b l e . A b r i e f d e s c r i p t i o n o f the v a r i o u s types o f microwave s p e c t r o m e t e r s and components has been g i v e n by Roussy and C h a n t r y (3) t o g e t h e r w i t h a b i b l i o g r a p h y o f the r e l a t e d l i t e r a t u r e . In the m i l l i m e t e r - w a v e and submil1imeter-wave r e g i o n s r a d i a t i o n i s u s u a l l y produced by harmonic g e n e r a t i o n , o r from high f r e q u e n c y backward wave o s c i l l a t o r s . The e x p e r i m e n t a l a s p e c t s o f t h e s e methods have been d i s c u s s e d by De L u c i a ,(:4) and Krupnov (5) r e s p e c t i v e l y . 2.1 The Microwave S p e c t r o m e t e r The e s s e n t i a l elements o f a c o n v e n t i o n a l microwave s p e c t r o m e t e r a r e a t u n a b l e s o u r c e o f microwave r a d i a t i o n , a f r e q u e n c y measurement system, an a b s o r p t i o n c e l l and a d e t e c t o r . In t h i s work a S t a r k modulated i n s t r u m e n t o f the Hughes-Wilson t y p e (1) was used; i t employed a commer-c i a l microwave s o u r c e . The r e c e n t monograph o f Varma and Hrubesh (6) d e s c r i b e s a v e r y s i m i l a r s p e c t r o m e t e r , the Hewlett Packard Model 8460 A, i n some d e t a i l . T h i s l a t t e r i n s t r u m e n t f e a t u r e s a microwave b r i d g e and a more s o p h i s t i c a t e d sweeping system. The s o u r c e o f microwave r a d i a t i o n f o r a l l o f t h e experiments d e s c r i b e d here was a H e w l e t t P a c k a r d 8400 B p h a s e - s t a b i l i z e d microwave s p e c t r o s c o p y s o u r c e . T h i s c o n s i s t e d o f an HP H81-8690 A sweep o s c i l l a t o r , an HP 8466 A r e f e r e n c e o s c i l l a t o r , an HP 8467 B power a m p l i f i e r and an HP 8709 A s y n c h r o n i z e r . Most o f the 8 - 4 0 GHz f r e q u e n c y range c o u l d be 30 c o v e r e d w i t h an a p p r o p r i a t e backward wave o s c i l l a t o r p l u g - i n u n i t . In the X-band (8 - 12.4 GHz), P-band (12.4 - 18 GHz) and R-band (26.5 - 40 GHz) ranges r e s p e c t i v e l y microwave power was o b t a i n e d u s i n g HP H81 - 8694 B, HP H81 - 8695 A and HP 8697 A p l u g - i n u n i t s . D u r i n g o p e r a t i o n o f the microwave s o u r c e the s y n c h r o n i z e r was used t o l o c k the sweep o s c i l l a t o r t o a harmonic o f t h e r e f e r e n c e o s c i l l a -t o r . To a c h i e v e a s t a b l e p h a s e - l o c k i t was o f t e n n e c e s s a r y , e s p e c i a l l y a t R-band, f i r s t t o r o u t e the o u t p u t o f the r e f e r e n c e o s c i l l a t o r t h r o u g h t h e power a m p l i f i e r . An HP 5246 L e l e c t r o n i c c o u n t e r was used t o d e t e r m i n e the f r e q u e n c y o f the microwaves. A l t h o u g h the c o u n t e r measured the r a d i o f r e q -uency o u t p u t o f t h e r e f e r e n c e o s c i l l a t o r i t had been m o d i f i e d t o d i s p l a y d i r e c t l y the microwave f r e q u e n c y o f t h e sweep o s c i l l a t o r p l u g - i n when t h e c o r r e c t l o c k p o i n t was chosen. The p r o p e r harmonic l o c k p o i n t was s e l e c t e d u s i n g a c a l i b r a t e d s c a l e on t h e sweep o s c i l l a t o r . The S t a r k c e l l s used f o r t h e measurements a r e d e s c r i b e d i n the next s e c t i o n . The sweep o s c i l l a t o r was mated t o one end o f the chosen c e l l u s i n g a p p r o p r i a t e waveguide t r a n s i t i o n s e c t i o n s and, when r e q u i r e d , l e n g t h s o f f l e x i b l e waveguide. A power a t t e n u a t o r and a f e r r i t e i s o l a t o r were a l s o i n s e r t e d between the sweep o s c i l l a t o r and t h e c e l l . The i s o l a t o r was needed t o p r e v e n t r e f l e c t e d power from r e a c h i n g t h e s o u r c e - a phenomenon which o f t e n l e d t o l e s s s t a b l e p h a s e - l o c k i n g . The d e t e c t o r s used a t X-band and P-band were HP H06-X422A and HP H06-P422 A back d i o d e s r e s p e c t i v e l y w h i l e an HP 11586 A p o i n t c o n t a c t d i o d e was employed a t R-band. Waveguide t r a n s i t i o n s e c t i o n s were a g a i n used t o j o i n t h e s e d e t e c t o r s t o the c e l l . A s i m p l e p h a s e - s e n s i t i v e d e t e c t i o n system was used t o m o n i t o r t h e a b s o r p t i o n l i n e s . An I n d u s t r i a l Components I n c o r p o r a t e d 100 kHz s q u a r e wave g e n e r a t o r was used t o a p p l y a h i g h v o l t a g e t o the septum o f t h e S t a r k c e l l and a r e f e r e n c e s i g n a l t o a P r i n c e t o n A p p l i e d Research Model 120 l o c k - i n a m p l i f i e r . 31 The d e t e c t o r s i g n a l was f i r s t passed t h r o u g h a p r e a m p l i f i e r and then t o the l o c k - i n a m p l i f i e r . The o u t p u t o f the l o c k - i n s e r v e d as t h e y - a x i s i n p u t f o r e i t h e r an o s c i l l o s c o p e o r an HP 680 s t r i p c h a r t r e c o r d e r ; t he x - a x i s i n p u t was taken from the sweep o s c i l l a t o r . For c h a r t p r e s e n t a t i o n t he microwave f r e q u e n c y was m o n i t o r e d u s i n g an HP 8429 A marker system. A l t h o u g h c a r e was taken t o a v o i d s a t u r a t i n g any t r a n s i t i o n s t he power l e v e l i n t h e c e l l was seldom measured. T y p i c a l d e t e c t o r b i a s c u r r e n t s , however, were 40 ya a t R-band and 80 ya a t X-band and P-band. The s p e c t r a were m o n i t o r e d u s i n g both a u t o m a t i c and manual sweeps. S i n c e S t a r k m o d u l a t i o n was used both t he f i e l d on and f i e l d o f f l i n e s were d i s p l a y e d s i m u l t a n e o u s l y on o p p o s i t e s i d e s o'f t h e base l i n e . The p o s i t i o n s o f most l i n e s were measured by ma n u a l l y t u n i n g t o the a b s o r p t i o n maximum u s i n g an o s c i l l o s c o p e d i s p l a y and r e a d i n g d i r e c t l y t h e c o u n t e r f r e q u e n c y . Weaker l i n e s were d i s p l a y e d on c h a r t r e c o r d i n g s and measured by i n t e r p o -l a t i n g between f r e q u e n c y markers. Measurement a c c u r a c y was e s t i m a t e d t o be 50 kHz o r b e t t e r f o r most s i g n a l s and 100 kHz o r b e t t e r f o r weak l i n e s . 32 2.2 The Microwave S t a r k C e l l s Two d i f f e r e n t S t a r k c e l l s , both c o n s t r u c t e d from l e n g t h s o f r e c t a n g u l a r b r a s s waveguide, were used i n t h i s s t u d y . The f i r s t was an X-band c e l l h aving o u t e r c r o s s - s e c t i o n a l d i m e n s i o n s o f 1.00 i n x 0.50 i n . The c o r r e s p o n d i n g d i m e n s i o n s o f the l a r g e r S-band c e l l were 3.00 i n x 1.50 i n ; both c e l l s were 10 f t i n l e n g t h . Measurements below 40 GHz were made u s i n g t he X-band c e l l w h i l e a t h i g h e r f r e q u e n c i e s t he S-band c e l l was employed. Each S t a r k c e l l c o n t a i n e d a t h i n copper septum o r i e n t e d p a r a l l e l t o t h e l a r g e r f a c e o f t h e waveguide. The s e p t a were h e l d i n p l a c e a t the c e n t e r o f each c e l l and i n s u l a t e d from the b r a s s waveguide w i t h t h i n , s l o t t e d t e f l o n r u n n e r s . The S t a r k c e l l s were mated t o a c o n v e n t i o n a l g l a s s vacuum system equipped w i t h mechanical and d i f f u s i o n pumps. Each c e l l had a b r a s s vacuum p o r t a t both ends t o f a c i l i t a t e r a p i d pumping and t o e n a b l e samples to be f l o w e d t h r o u g h them; the ends o f t h e c e l l s were s e a l e d u s i n g 0 - r i n g s and t h i n s h e e t s o f mica. Measurements were made a t room temperature but more o f t e n w i t h t he c e l l s wrapped w i t h s t y r o f o a m t r o u g h s f i l l e d w i t h d r y i c e . P r e s s u r e s were measured w i t h a Norton Model 801 thermocouple gauge. 2.3 D i p o l e Moment Measurements A t h i g h v o l t a g e s t he waveform produced by the I n d u s t r i a l Compo-nents I n c o r p o r a t e d square wave g e n e r a t o r was q u i t e d i s t o r t e d . T h i s had the e f f e c t o f bro a d e n i n g S t a r k components and making a c c u r a t e measure-ment o f the S t a r k f i e l d i m p o s s i b l e . For p r e c i s e S t a r k measurements t h e r e f o r e a s m a l l square wave m o d u l a t i o n v o l t a g e was f l o a t e d on t o p o f a l a r g e a c c u r a t e l y known DC b i a s p o t e n t i a l . T h i s was done u s i n g a v o l t a g e mixer c o n s t r u c t e d by C R . P a r e n t (7) a c c o r d i n g t o a d e s i g n by Muenter ( 8 ) . 33 The DC b i a s p o t e n t i a l was o b t a i n e d from a John F l u k e M a n u f a c t u r i n g Company Model 412 B DC power s u p p l y . The c a l i b r a t i o n a c c u r a c y and r e s e t a b i l i t y o f t h i s s u p p l y were g i v e n as + 0.25% and + 0.05% r e s p e c t i v e l y . For t h e s e measurements the m o d u l a t i o n v o l t a g e was d e t e r m i n e d u s i n g an o s c i l l o s c o p e . 2.4 O r i g i n o f Samples and Running C o n d i t i o n s a. S u l p h u r D i c h l o r i d e A sample o f s u l p h u r d i c h l o r i d e , o b t a i n e d c o m m e r c i a l l y from Matheson, Coleman and B e l l , was f u r n i s h e d by P r o f e s s o r N.L. Paddock o f t h e C h e m i s t r y Department, U n i v e r s i t y o f B r i t i s h Columbia. The i n v e s t i g a t i o n o f t h i s m o l e c u l e was b e s e t by s e v e r a l d i f f i c u l t i e s due t o sample decomp-o s i t i o n . The sample was s t o r e d under vacuum a t room te m p e r a t u r e i n a 250 ml round bottom f l a s k . B e f o r e making each s e t o f measurements a 15 - 20 ml sample was taken and f r a c t i o n a t e d i n o r d e r t o remove the more v o l a t i l e c h l o r i n e formed by d e c o m p o s i t i o n o f t h e sample and a l s o a s m a l l amount o f s u l p h u r d i o x i d e , whose microwave spectrum i s e x t r e m e l y s t r o n g r e l a t i v e t o s u l p h u r d i c h l o r i d e . Even t h e n , u s i n g a d r y i c e wrapped a b s o r p t i o n c e l l i t was not p o s s i b l e t o see any s i g n a l s u n t i l t h e sample had been f l o w e d t h r o u g h the c e l l a t a p r e s s u r e o f about 5 Pa f o r s e v e r a l hours; f u r t h e r f l o w i n g was r e q u i r e d t o o b t a i n good s i g n a l s . As w e l l , on s e v e r a l o c c a s i o n s , a f t e r rewarming t o room temperature i t was found t h a t the c e l l c o m p l e t e l y a t t e n u a t e d microwave r a d i a t i o n . I t was then n e c e s s a r y t o d i s m a n t l e the c e l l and c l e a n i t as w e l l as t o r e p l a c e the mica windows. E v e n t u a l l y the copper vacuum p o r t s c o n n e c t e d t o t h e c e l l became c l o g g e d and i t was n e c e s s a r y t o p l a c e t h e s e i n an u l t r a s o n i c c l e a n e r f o r s e v e r a l days t o c l e a n s e them o f a b l a c k , g r a n u l a r m a t e r i a l . A l l measurements f o r s u l p h u r d i c h l o r i d e were made w i t h the gas 34 f l o w i n g s l o w l y t h r o u g h the S t a r k c e l l a t p r e s s u r e s o f 0.4 - 4.0 Pa. Once good s i g n a l s had been o b t a i n e d runs i n e x c e s s o f t h i r t y hours c o u l d be made. None o f the d e c o m p o s i t i o n p r o d u c t s gave r i s e t o d e t e c t a b l e s i g n a l s . One o f the p r o b a b l e d e c o m p o s i t i o n p r o d u c t s i s d i s u l p h u r d i c h l o r i d e ( 9 ) . 2 S C 1 2 -y S 2 C 1 2 + C l 2 However, S 2 C 1 2 i s too i n v o l a t i l e a t dr y i c e temperature t o g i v e s i g n a l s and c h l o r i n e has no microwave spectrum. No attem p t was made t o i d e n t i f y t h e b l a c k s u b s t a n c e which formed i n th e waveguide and vacuum p o r t s . b. D i c h l o r o s i l a n e A sample o f normal d i c h l o r o s i l a n e was p r o v i d e d by Dr. R.A.N. McLean, Dr. N.P.C. Westwood and Dr. D.C. F r o s t o f th e C h e m i s t r y Department, U n i v e r s i t y o f B r i t i s h Columbia. The sample was s t o r e d a t l i q u i d n i t r o g e n temperature when no t i n use. A l l s p e c t r a were run a t d r y i c e t e m p e r a t u r e u s i n g p r e s s u r e s o f 0.2 - 3.0 Pa. Under t h e s e c o n d i t i o n s t h e sample was s t a b l e f o r about an hour a f t e r which the i n t e n s i t y o f th e d i c h l o r o s i l a n e l i n e s was a p p r e c i a b l y d i m i n i s h e d but no new s i g n a l s were a p p a r e n t . In p r a c t i c e t h i s sample d e t e r i o r a t i o n p r o v i d e d no d i f f i c u l t i e s . c. P r o p i o l y l C h l o r i d e Samples o f normal p r o p i o l y l c h l o r i d e and p r o p i o l y l c h l o r i d e - d were both s u p p l i e d by Dr. W.J. B a l f o u r , C h e m i s t r y Department, U n i v e r s i t y o f V i c t o r i a . These m o l e c u l e s were p r e p a r e d by r e a c t i n g phosphorus p e n t a -c h l o r i d e w i t h normal p r o p i o l i c a c i d and p r o p i o l i c a c i d - d 2 r e s p e c t i v e l y a c c o r d i n g t o th e method o f B a l f o u r , G r i e g and V i s a i s o u k ( 1 0 ) . HCECCOOH + P C 1 5 HCECCOCI + P0C1 3 + HC1 As p r o p i o l y l c h l o r i d e r e a d i l y decomposes a t room te m p e r a t u r e t h e samples, s t o r e d i n a pyrex tube, were kept immersed i n l i q u i d n i t r o g e n when not i n 35 use. For m a n i p u l a t i o n s on t h e vacuum l i n e t he s t o r a g e v e s s e l s were m a i n t a i n e d i n a Dewar f i l l e d w i t h d r y i c e . A l l r o t a t i o n a l s p e c t r a o f p r o p i o l y l c h l o r i d e were measured w i t h the S t a r k c e l l wrapped i n d r y i c e . P r e s s u r e s used were i n the range 0.3 - 3.0 Pa. Under t h e s e c o n d i t i o n s t h e sample was q u i t e s t a b l e i n the a b s o r p t i o n c e l l ; broad band sweeps r e q u i r i n g about an hour t o complete were c a r r i e d out w i t h o u t n o t i c e a b l e sample d e t e r i o r a t i o n . A l t h o u g h the i n f r a r e d and Raman s p e c t r a o f t h e s e samples showed the p r e s e n c e o f a P0C1^ i m p u r i t y ( 1 1 ) , under t h e e x p e r i m e n t a l c o n d i t i o n s used, the v o l a t i l i t y o f t h i s m o l e c u l e was too low f o r i t t o be d e t e c t e d i n the microwave spectrum. 36 B i b l i o g r a p h y 1. R.H. Hughes and E.B. W i l s o n , J r . , Phys. Rev. 71_, 562 (1947). 2. W. Gordy and R.L. Cook, Microwave M o l e c u l a r S p e c t r a , pp. 50-53, I n t e r s c i e n c e P u b l i s h e r s , New York, 1970. 3. G. Roussy and G.W. C h a n t r y , i n Modern A s p e c t s o f Microwave Spec- t r o s c o p y , (G.W. C h a n t r y , E d . ) , pp. 1-63, Academic P r e s s , London, 1979. 4. F.C. De L u c i a , i n M o l e c u l a r S p e c t r o s c o p y : Modern R e s e a r c h , (K.N. Rao, E d . ) , V o l . I I , pp. 69-92, Academic P r e s s , New York, 1976. 5. A.F. Krupnov, i n Modern A s p e c t s o f Microwave S p e c t r o s c o p y , (G.W. Ch a n t r y , E d . ) , pp. 217-256, Academic P r e s s , London, 1979. 6. R. Varma and L.W. Hrubesh, Chemical A n a l y s i s by Microwave Rota- t i o n a l S p e c t r o s c o p y , pp. 35-39, John W i l e y and Sons, New York, 1979. 7. C R . P a r e n t , Ph.D. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 1972. 8. J.S. Muenter, Ph.D. T h e s i s , S t a n f o r d U n i v e r s i t y , 1962. 9. A.H. Spong, J . Chem. Soc. 1283 (1934). 10. W.J. B a l f o u r , C.C. G r i e g and S. V i s a i s o u k , J . Org. Chem. 39_, 725 (1974). 11. W.J. B a l f o u r , R.H. M i t c h e l l and S. V i s a i s o u k , S p e c t r o c h i m . A c t a A 31, 967 (1975). 37 C h a p t e r 3 The Microwave Spectrum o f S u l p h u r D i c h l o r i d e The r o t a t i o n a l s p e c t r a o f v e r y s i m p l e m o l e c u l e s have l o n g h e l d a s p e c i a l a t t r a c t i o n f o r s p e c t r o s c o p i s t s . These have been o f i n t e r e s t not o n l y as a s o u r c e o f p r e c i s e m o l e c u l a r c o n s t a n t s but a l s o as fundamental t e s t s o f v i b r a t i o n - r o t a t i o n t h e o r y . For microwave s t u d i e s asymmetric top t r i a t o m i c s a r e p a r t i c u l a r l y s u i t a b l e because, f o r non-h y d r i d e s a t l e a s t , t r a n s i t i o n s i n v o l v i n g a l a r g e range o f J v a l u e s a r e a c c e s s i b l e . Such s p e c t r a have been a n a l y s e d t o p r o v i d e v a l u e s f o r a v a r i e t y o f m o l e c u l a r c o n s t a n t s , i n c l u d i n g r o t a t i o n a l c o n s t a n t s , q u a r t i c and h i g h e r o r d e r c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s , 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 , d i p o l e moments and bond l e n g t h s and bond a n g l e s . As w e l l , i n f o r m a t i o n about the i n t r a m o l e c u l a r p o t e n t i a l f u n c t i o n has o f t e n been o b t a i n e d ; i n a few f a v o u r a b l e c a s e s the c u b i c as w e l l as the harmonic p o t e n t i a l c o n s t a n t s have been d e t e r m i n e d . For m o l e c u l e s o f C 2 v symmetry, where t h e p o t e n t i a l f u n c t i o n has a v e r y s i m p l e form t h i s has been done f o r , amongst o t h e r s , t h e m o l e c u l e s S 0 2 ( 1 , 2 ) , S e 0 2 ( 3 ) , 0 F 2 ( 4 ) , S F 2 (5) and 0 3 ( 6 , 7 ) . The p r e s e n t s t u d y o f s u l p h u r d i c h l o r i d e was undertaken w i t h two p a r t i c u l a r aims i n mind. The f i r s t was t o o b t a i n a harmonic poten-t i a l f u n c t i o n f o r the m o l e c u l e u s i n g r o t a t i o n a l d a t a a l o n e . T h i s seemed wo r t h w h i l e as the v a r i o u s p u b l i s h e d p o t e n t i a l f u n c t i o n s (8-15) show an u n a c c e p t a b l e v a r i a t i o n . For example, v a l u e s o f t h e s t r e t c h i n g f o r c e 38 °-l °-1 c o n s t a n t r a n g i n g from 1.8 mdyn'A (14) t o 2.64 mdyn A (15) have been r e p o r t e d . T h i s s i t u a t i o n i s t h e r e s u l t o f an a m b i g u i t y i n t h e assignment o f the s t r e t c h i n g fundamentals and o f i n s u f f i c i e n t d a t a t o deter m i n e u n i q u e l y the p o t e n t i a l c o n s t a n t s . The most commonly quoted v a l u e s f o r the v i b r a t i o n a l fundamentals a r e t h o s e o f Stammreich e t a l . , ( 8 ) , namely 514, 208 and 535 cnf^ f o r v - j , and Vg r e s p e c t i v e l y . With o n l y t h r e e p i e c e s o f dat a a v a i l a b l e t o s p e c i f y t he f o u r q u a d r a t i c p o t e n t i a l c o n s t a n t s , some assumptions were r e q u i r e d and t h e subsequent v a r i a t i o n s o b s e r v e d a r e h a r d l y s u r p r i s i n g . As w e l l , i n a more r e c e n t and d e t a i l e d study S a v o i e and Tremblay (15) sug g e s t e d t h a t t he 535 cm ^ band p r e v i o u s l y a s s i g n e d as Vg o f s u l p h u r d i c h l o r i d e (8) might have been caused by a d i s u l p h u r d i c h l o r i d e (SgClg) i m p u r i t y . T h e i r r e s u l t s d i d not a l l o w an unambiguous assignment o f t h e s t r e t c h i n g fundamentals and Vg a l t h o u g h p o l a r i z a t i o n d a t a ( f o r t h e l i q u i d o n l y ) and f o r c e c o n s t a n t r e f i n e m e n t s f a v o u r e d t he c h o i c e Vg > . Because, i n the harmonic o s c i l l a t o r a p p r o x i m a t i o n , t he d e s i r e d q u a d r a t i c f o r c e c o n s t a n t s can be e x p r e s s e d e x p l i c i t l y i n terms o f the q u 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 c o n s t a n t s , an attempt t o o b t a i n a c c u r a t e v a l u e s f o r the d i s t o r t i o n c o n s t a n t s appeared to be w a r r a n t e d . In the o n l y p r e v i o u s microwave i n v e s t i g a t i o n , t h a t o f Murray, L i t t l e , W i l l i a m s and Weatherly ( 1 6 ) , the data o b t a i n e d 32 35 were l i m i t e d t o seven low J l i n e s o f the S C l 2 s p e c i e s i n i t s ground v i b r a t i o n a l s t a t e . From t h i s l i m i t e d d a t a s e t v a l u e s f o r the r o t a t i o n a l c o n s t a n t s o n l y were d e t e r m i n a b l e . Murray ejt a l _ . , d i d , however, measure t h e m o l e c u l a r d i p o l e moment and o b t a i n a c c u r a t e v a l u e s f o r t h e c h l o r i n e 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 . T h e i r s t u d y , l i k e t h e p r e s e n t i n v e s t i g a t i o n , was pla g u e d by sample d e c o m p o s i t i o n . 39 The second aim o f t h e p r e s e n t s t u d y was a r e f i n e m e n t o f the m o l e c u l a r s t r u c t u r e . T h e r e have been t h r e e e l e c t r o n d i f f r a c t i o n i n v e s t i -g a t i o n s o f the s u l p h u r d i c h l o r i d e m o l e c u l e - two v e r y e a r l y s t u d i e s by Stevenson and Beach (17) and by Palmer (18) and the seldom quoted work o o f M o rino, Murata, I t o and Nakamura ( 1 4 ) . The r g bond l e n g t h o f 2.006 A (4) o b t a i n e d from t h i s l a s t s t u d y i s somewhat s h o r t e r than the r Q o v a l u e o f 2.014 ',(5) A d e r i v e d from the microwave r e s u l t s o f Murray e t a l . ( 1 5 ) . I t was f e l t t h a t a d d i t i o n a l i s o t o p i c , and, i f p o s s i b l e , e x c i t e d s t a t e , d a t a would en a b l e a s t r u c t u r e d e t e r m i n a t i o n o f much improved p r e c i s i o n . In t h e p r e s e n t s t u d y r o t a t i o n a l t r a n s i t i o n s o f the most abundant 32 35 i s o t o p i c s p e c i e s , S C l 2 , have been measured up t o J = 60 i n the ground v i b r a t i o n a l s t a t e and up t o J = 14 i n the v 2 = 1 e x c i t e d s t a t e . F o r t h e op oc oy S Cl C l s p e c i e s , ground s t a t e l i n e s o n l y were a s s i g n e d ; t h e s e measure-ments extended up to J = 40. The d a t a have been a n a l y s e d t o y i e l d v a l u e s f o r the r o t a t i o n a l c o n s t a n t s , q u 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 c o n s t a n t s and a p a r t i a l s e t o f s e x t i c d i s t o r t i o n c o n s t a n t s . A harmonic p o t e n t i a l f u n c t i o n has been d e r i v e d which i s c o n s i s t e n t w i t h a l l o f t h e a v a i l a b l e s p e c t r o s c o p i c d a t a , i n c l u d i n g v i b r a t i o n a l wavenumbers, q u 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 c o n s t a n t s and i n e r t i a l d e f e c t s . U s i n g o n l y the microwave r e s u l t s e f f e c t i v e , p a r t i a l s u b s t i t u t i o n and average s t r u c t u r e s have been deter m i n e d . F u r t h e r , w i t h some ass u m p t i o n s , t h e e q u i l i b r i u m m o l e c u l a r s t r u c t u r e has been e s t i m a t e d . 40 3.1 Observed Spectrum arid Ass igiiment In t h e i r s t u d y o f s u l p h u r d i c h l o r i d e Murray e t al_. (16) noted t h a t the o b s e r v e d spectrum c o n s i s t e d o f b-type t r a n s i t i o n s o n l y . T h e r e f o r e the K K s e l e c t i o n r u l e s a r e e e ^ o o and eo-^>oe where e and o a c r e s p e c t i v e l y denote even and odd v a l u e s o f K and K ( 1 9 ) ; as w e l l , a C the usual AJ=0,±1 s e l e c t i o n r u l e a p p l i e s . In a d d i t i o n , many o f the l i n e s e x h i b i t e d n u c l e a r q u a d r u p o l e h y p e r f i n e s t r u c t u r e due t o the p r e s e n c e o f the two s p i n 3/2 c h l o r i n e n u c l e i . In the p r e s e n t i n v e s t i -g a t i o n the h y p e r f i n e s t r u c t u r e was a n a l y s e d u s i n g the methods o u t l i n e d i n C h a p t e r 1. Because o f the m o l e c u l a r symmetry s p i n s t a t i s t i c s were i m p o r t a n t . For s p e c i e s c o n t a i n i n g e q u i v a l e n t c h l o r i n e n u c l e i i t was r e q u i r e d t h a t the t o t a l w a v e f u n c t i o n - the p r o d u c t o f e l e c t r o n i c , v i b r a t i o n a l , r o t a t i o n a l and n u c l e a r s p i n w a v e f u n c t i o n s - be a n t i -symmetric w i t h r e s p e c t t o i n t e r c h a n g e o f the two c h l o r i n e atoms by r o t a t i o n about the C^ v symmetry a x i s ( 2 0 ) . For a l l s p e c i e s s t u d i e d here the e l e c t r o n i c and v i b r a t i o n a l w a v e f u n c t i o n s were symmetric. The r o t a t i o n a l w a v e f u n c t i o n s were symmetric f o r J „ and J l e v e l s and J ee oo a n t i s y m m e t r i c f o r JQQ and J Q e l e v e l s ( 2 1 ) . Thus o n l y symmetric s p i n f u n c t i o n s had to be c o n s i d e r e d f o r eo^oe r o t a t i o n a l t r a n s i t i o n s and a n t i s y m m e t r i c s p i n f u n c t i o n s f o r ee*->oo r o t a t i o n a l t r a n s i t i o n s . The ee«-»oo l i n e s were e s p e c i a l l y s i m p l e , b e i n g t r i p l e t s w i t h a s t r o n g c e n t r a l component a t the u n s p l i t l i n e p o s i t i o n . These c o n s i d e r a t i o n s have been d i s c u s s e d by Murray e t a l . (16) but the n o t a t i o n they used i s somewhat d i f f e r e n t . The p r e s e n t i n v e s t i g a t i o n was begun by p r e d i c t i n g r i g i d r o t o r 32 35 f r e q u e n c i e s and h y p e r f i n e p a t t e r n s f o r the S C l g s p e c i e s u s i n g the c o n s t a n t s o f Murray e t ' a l , ( 1 6 ) . The L, + L, = J_, J_ + J_ = £ c o u p l i n g 41 scheme was used whenever a v a l u e o f I was r e q u i r e d ; the n u c l e a r s p i n w a v e f u n c t i o n s were symmetric f o r I = 1 o r 3 and a n t i s y m m e t r i c f o r I = 0 or 2. F i v e o f the seven p r e v i o u s l y measured t r a n s i t i o n s were a c c e s s i b l e u s i n g the H e w l e t t - P a c k a r d s p e c t r o m e t e r . An e x a m i n a t i o n o f th e s e l i n e s q u i c k l y c o n f i r m e d the p r e v i o u s assignment and the p r e c i s i o n o f the r e p o r t e d 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 . A d d i t i o n a l low J l i n e s s u f f i c i e n t t o b e g i n a b o o t s t r a p assignment p r o c e s s were r e a d i l y f ound. Prominent among t h e s e were Q-branch l i n e s o f the s e r i e s J 2 j _ 2 J-j > which formed a bandhead a t a p p r o x i m a t e l y 29.9 GHz. These l i n e s were f i t u s i n g the H a m i l t o n i a n o f e q u a t i o n 1.11, now i n c l u d i n g the q u 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 c o n s t a n t s , and the r e s u l t i n g c o n s t a n t s were used t o p r e d i c t f u r t h e r t r a n s i t i o n f r e q u e n c i e s . The p r o c e s s o f measuring w e l l -p r e d i c t e d l i n e s , f i t t i n g the dat a and p r e d i c t i n g a d d i t i o n a l t r a n s i t i o n f r e q u e n c i e s was r e p e a t e d s e v e r a l times w i t h t he measurements g r a d u a l l y b e i n g extended t o h i g h J . The low v a l u e o f the d i p o l e moment, 0.36D ( 1 6 ) , made many l i n e s d i f f i c u l t to modulate. T h i s was t r u e e s p e c i a l l y o f the weak and v e r y h i g h f i e l d low K P- and R- branch l i n e s such as a the 21-j 2 i -> 2 0 2 -jg t r a n s i t i o n . These c o u l d be measured o n l y from c h a r t r e c o r d i n g s . 32 35 Subsequent t o the assignment o f the S C l 2 ground s t a t e l i n e s a s e a r c h was made f o r v i b r a t i o n a l s a t e l l i t e s . The l - ^ «- Ogg and J l J - l ^  Jo J t r a n s i t i o n s a l l had h i g h f r e q u e n c y s a t e l l i t e s which e x h i b i t e d t he same s p i n s t a t i s t i c s as the ground s t a t e l i n e s . T h e i r i n t e n s i t y a t d r y i c e temperature was r o u g h l y 20% o f the ground s t a t e l i n e s . They were t h e r e f o r e a s s i g n e d t o the v 2 = 1 o r (010) e x c i t e d s t a t e . A f t e r a r i g i d r o t o r f i t some f u r t h e r low J l i n e s were f o u n d . A s e a r c h f o r l i n e s o f a d d i t i o n a l i s o t o p i c s p e c i e s was attempted 32 35 37 next . T r a n s i t i o n s o f the S Cl Cl s p e c i e s were e a s i l y l o c a t e d u s i n g 42 r o t a t i o n a l c o n s t a n t s c a l c u l a t e d from the e f f e c t i v e s t r u c t u r e o f Murray e t al_. ( 1 6 ) . A f t e r e s t i m a t i n g the r o t a t i o n o f the m o l e c u l e i n the p r i n c i p a l i n e r t i a l a x i s system consequent on i s o t o p i c s u b s t i t u t i o n the c o u p l i n g c o n s t a n t s o f 3 2 S 3 5 C 1 2 were t r a n s f o r m e d to the 3 2 S 3 5 C 1 3 7 C 1 i n e r t i a l a x i s system. For t h i s c a l c u l a t i o n the f o l l o w i n g e q u a t i o n s -and t h e i r i n v e r s e s (22) - were needed: _ x a a c o s 9 Z a * * b b s i n 9 Z a x z z 2 . 2 cos e Z a - s i n e Z a x _ * a a s i n 2 e Z a - x b b c o s 2 6 Z a xx 2 2 s i n e Z a - cos e Z a x y y x c c Here x x x » x y y and x z z a r e the p r i n c i p a l v a l u e s o f the q u a d r u p o l e c o u p l i n g t e n s o r and e Z a i s the a n g l e between the 1 p r i n c i p a l a x i s o f the quad-r u p o l e t e n s o r ( t a k e n to be c o i n c i d e n t w i t h the S-Cl bond) and the a_ i n e r -t i a l a x i s ; x „ , •> X K K and x „ „ a r e the components o f the q u a d r u p o l e t e n s o r aa DD cc r e f e r r e d t o the p r i n c i p a l i n e r t i a l a x i s system. I t was t h e n assumed t h a t 37 i n the bond a x i s system the Cl c o u p l i n g c o n s t a n t s c o u l d be o b t a i n e d by d i v i d i n g the Cl v a l u e s by 1.2688 (th e r a t i o o f the q u a d r u p o l e moments o f 3 5 C 1 and 3 7 C 1 ( 2 3 ) ) . T h i s c a l c u l a t i o n gave X a a = -37.85 MHz aa and n = 1.529 f o r t h e 3 5 C 1 n u c l e u s and x = -31.61 MHz and n = 1.386 aa 37 f o r the Cl n u c l e u s . Because o f the l o s s o f symmetry no s p i n f u n c t i o n s 32 35 37 o f S Cl Cl had a z e r o s t a t i s t i c a l w e ight. The r e s u l t i n g h y p e r f i n e p a t t e r n s were thus more complex and measurement d i f f i c u l t i e s were o f t e n caused by S t a r k components o v e r l a p p i n g the z e r o f i e l d l i n e s - e s p e c i a l l y 43 a t low J . The J 2 J ^ J l J - l Q'branch l i n e s were a g a i n prominent w i t h 32 35 a bandhead near 29.8 GHz, v e r y c l o s e t o t h a t o f the S C l g s p e c i e s . F i g u r e 3.1 i l l u s t r a t e s the bandheads f o r the ground s t a t e s o f the 3 2 S 3 5 C 1 2 and 3 2 S 3 5 C 1 3 7 C 1 s p e c i e s t o g e t h e r w i t h the r e l a t e d J £ J_ 1 «- J ] j t r a n s i t i o n s . A b o o t s t r a p assignment p r o c e s s e n a b l e d f u r t h e r l i n e s up t o J = 40 t o be l o c a t e d . A summary o f t h e o b s e r v e d and c a l c u l a t e d h y p e r f i n e s t r u c t u r e i s g i v e n f o r two o f t h e s e ' i n T a b l e 3.1 where the J_ + Lj  = L\> F_-j + J_2 = F_ c o u p l i n g scheme has been used. In a l l c a s e s the d i f f e r e n c e s between the c a l c u l a t e d and o b s e r v e d f r e q u e n c i e s a r e l e s s than the measure-ment e r r o r . I t s h o u l d be mentioned f i n a l l y t h a t t r a n s i t i o n s i n v o l v i n g m o l e c u l e s i n the v-j = 1 and Vg = 1 e x c i t e d s t a t e were too weak to 34 d e t e c t . T h i s was t r u e as w e l l f o r ground s t a t e l i n e s o f S s u b s t i t u t e d 32 37 s p e c i e s . T r a n s i t i o n s o f the S C l g s p e c i e s were v i s i b l e on c h a r t r e c o r d i n g s but few were a s s i g n e d as t h e y were weak and p r o v i d e d no a d d i t i o n a l s t r u c t u r a l i n f o r m a t i o n . 44 T a b l e 3.1 Examples o f H y p e r f i n e S t r u c t u r e i n T r a n s i t i o n s o f •=\ F' F ] F a C a l c u l a t e d ( M H z ) Observed(MHz) Frequency Frequency 15(2,13) 15(1,14) 13.5 12 13.5 12 35763.38 35763.44 13.5 15 13.5 15 35763.78 35763.85 16.5 15 16.5 15 35763.90 35763.85 16.5 18 16.5 18 35764.26 35764.21 14.5 13 13.5 13 35767.23 35767.25 13.5 14 13.5 14 35767.63 35767.73 16.5 16 16.5 16 35767.77 35767.73 15.5 17 16.5 17 35768.14 b 13.5 13 14.5 13 35768.54 b 14.5 16 14.5 16 35768.89 35768.92 15.5 14 15.5 14 35769.00 35768.92 16.5 17 15.5 17 35769.38 35769.42 14.5 14 14.5 14 35772.40 35772.46 14.5 15 14.5 15 35772.73 35772.81 15.5 15 15.5 15 35772.88 35772.81 15.5 16 15.5 16 35773.25 35773.27 45 T a b l e 3.1 Examples o f H y p e r f i n e S t r u c t u r e i n T r a n s i t i o n s o f 3 2 S 3 5 C 1 3 7 C 1 ( c o n t i n u e d ) F [ F 1 F ] F a C a l c u l a t e d ( M H z ) Observed(MHz) Frequency Frequency 16(2,14) «- 16(1,15) 14.5 13 14.5 13 38553.71 38553.73 14.5 16 14.5 16 38554.14 38554.24 17.5 16 17.5 16 38554.27 38554.24 17.5 19 17.5 19 38554.65 38554.66 15.5 14 14.5 14 38558.10 38558.13 14.5 15 14.5 15 38558.54 38558.67 17.5 17 17.5 17 38558.68 38558.67 16.5 18 17.5 18 38559.07 b 14.5 14 15.5 14 38559.60 b 15.5 17 15.5 17 38559.97 38560.03 16.5 15 16.5 15 38560.09 38560.03 17.5 18 16.5 18 38560.51 38560.57 15,5 15 15.5 15 38564.01 38564.06 15.5 16 15.5 16 38564.37 38564.46 16.5 16 16.5 16 38564.52 38564.46 16.5 17 16.5 17 38564.92 38564.93 Data i s g i v e n o n l y f o r t h o s e h y p e r f i n e components w i t h an i n t e n s i t y g r e a t e r than 2% o f the t o t a l i n t e n s i t y t h a t i s , t he (2I-|+1 ) ( 2 I 2 + 1 ) s t r o n g e s t components. Unprimed and primed F l a b e l s r e f e r r e s p e c t i v e l y t o t he i n i t i a l and f i n a l s t a t e s . Observed but o v e r l a p p e d by i n t e r f e r i n g S t a r k components. 1 1 1 1 1 1 1 1 1 1 1 1 — ~ — \ 29 30 31 32 33 34 35 36 37 38 39 40 41 F i g u r e 3.1 The Kfl = 2 +- 1 Q-Branch T r a n s i t i o n s o f S C I 2 y ( GHz) '— 47 3.2 A n a l y s i s o f the S u l p h u r D i c h l o r i d e S p e c t r a A f t e r p r e l i m i n a r y c e n t r i f u g a l d i s t o r t i o n a n a l y s e s had y i e l d e d good v a l u e s f o r the r o t a t i o n a l c o n s t a n t s , t he h y p o t h e t i c a l u n s p l i t l i n e f r e q u e n c i e s o f a l l t r a n s i t i o n s were c a l c u l a t e d u s i n g 32 35 f o r t h e S C l g s p e c i e s t he qu 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 Murray e t a l . ( 1 6 ) , namely x „ a = -38.98 MHz and n = 1.458, and f o r aa S CI CI the v a l u e s d e r i v e d i n the p r e v i o u s s e c t i o n . The A r e d u c -t i o n o f Watson's H a m i l t o n i a n i n the I r r e p r e s e n t a t i o n , e q u a t i o n 1.11, was used t o f i t t he u n s p l i t l i n e f r e q u e n c i e s . I n i t i a l a n a l y s e s 32 35 o f t h e S CI2 ground s t a t e d a t a were made u s i n g t he r o t a t i o n a l c o n s t a n t s and the f i v e q u a r t i c d i s t o r t i o n c o n s t a n t s o n l y . In t h i s way t h e d a t a c o u l d be f i t a d e q u a t e l y i f no t r a n s i t i o n s w i t h J g r e a t e r than r o u g h l y 30 were used. A t t h i s p o i n t good v a l u e s had been o b t a i n e d f o r a l l o f the q u a r t i c c o n s t a n t s a l t h o u g h 6^ , was d e t e r m i n e d r a t h e r l e s s p r e c i s e l y than the o t h e r s . The a d d i t i o n o f f u r t h e r d a t a t o h i g h e r J r e s u l t e d i n a s t e a d i l y i n c r e a s i n g s t a n d a r d d e v i a t i o n o f the f i t ; a maximum v a l u e o f 0.56 MHz was reached a t J = 60. A c c o r d i n g l y the s e x t i c c o n s t a n t s were i n t r o d u c e d i n t o t he r e f i n e m e n t p r o c e s s . The r e s u l t o f a f i t made w i t h a l l s e x t i c c o n s t a n t s i n c l u d e d i s shown i n T a b l e 3.2 as F i t 1; most o f the s e x t i c c o n s t a n t s a r e i n d e t e r m i n a t e . When h K , the " c o r r e c t i o n " t o t h e most p o o r l y d e t e r m i n e d q u a r t i c c o n s t a n t , and s u b s e q u e n t l y Hj were removed the o n l y r e m a i n i n g i n d e t e r m i n a t e c o n s t a n t was H^; the removal o f H^ gave the r e s u l t s shown i n T a b l e 3.2 as F i t 2. U n f o r t u n a t e l y the c h o i c e o f s e x t i c c o n s t a n t s t o be r e t a i n e d was s u b j e c t i v e ; r e f i n e m e n t s e s s e n t i a l l y as good as t h o s e o f F i t 2 can be had i f e i t h e r H J K , H^, hj and h K o r H J K > h J S h J K and h K a r e kept. In a l l c a s e s , however, the v a l u e s o f t h e q u a r t i c c o n s t a n t s agreed 48 w i t h i n the e s t i m a t e d s t a n d a r d d e v i a t i o n s . A l s o g i v e n a r e the r e s u l t s o f a r e f i n e m e n t , F i t 3, made u s i n g o n l y the d a t a up t o J = 30 and e x c l u d i n g a l l s e x t i c c o n s t a n t s . 32 35 A few comments s h o u l d be made about t h e v a r i o u s S C l 2 r e f i n e m e n t s . With the p o s s i b l e e x c e p t i o n o f the p o o r l y determined 6^ c o n s t a n t a l l o f the q u a r t i c d i s t o r t i o n c o n s t a n t s show o n l y a s l i g h t v a r i a t i o n from one f i t t o the next. T h i s o f c o u r s e i s e s s e n t i a l i f t h e r e s u l t s a r e t o be used t o d e r i v e a m e a n i n g f u l p o t e n t i a l f u n c t i o n . As w e l l , i t i s e v i d e n t t h a t l i t t l e has been g a i n e d by e x t e n d i n g the measurements beyond J = 30. T h i s would not have been the c a s e i f a more v a r i e d d a t a s e t had been o b t a i n e d . In p a r t i c u l a r , Q branch t r a n s i t i o n s a t h i g h e r v a l u e s o f J and K and P and R branch l i n e s a t a the same o r h i g h e r J but w i t h lower Kfl v a l u e s would have been u s e f u l . No a d d i t i o n a l Q branch l i n e s were a c c e s s i b l e , however, and t h e P and R branch l i n e s were e i t h e r too weak t o measure or i m p o s s i b l e t o modulate. The d a t a f o r S Cl C l were f i t t e d u s i n g the same s e t o f 32 35 d i s t o r t i o n c o n s t a n t s as were r e t a i n e d f o r F i t 2 o f t h e S C l ^ l i n e s . The r e s u l t i n g c o n s t a n t s a r e a l s o g i v e n i n T a b l e 3.2. F i n a l l y , f o r the 32 35 v 2 = 1 e x c i t e d s t a t e o f S C l 2 o n l y a few low J l i n e s were measured and t h e c e n t r i f u g a l d i s t o r t i o n c o n t r i b u t i o n s were assumed equal t o t h o s e o f the ground s t a t e . A summary o f the o b s e r v e d and c a l c u l a t e d u n s p l i t l i n e f r e q u e n c i e s o f the v a r i o u s s u l p h u r d i c h l o r i d e s p e c i e s i s g i v e n i n 32 35 T a b l e 3.3. For the ground s t a t e o f S C l 2 the c a l c u l a t e d f r e q u e n c i e s were o b t a i n e d u s i n g the F i t 2 c o n s t a n t s o f T a b l e 3.2. 49 T a b l e 3.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f S u l p h u r D i c h l o r i d e 3 2 S 3 5 C 1 2 (Ground S t a t e ) F i t l a F i t 2 F i t 3 A(MHz) 14613.5966(59) b 14613.5968(52) 14613.5985(67) B(MHz) 2920.8703(13) 2920.8702(11) 2920.8694(15) C(MHz) 2430.6943(12) 2430.6943(10) 2430.6930(13) A j ( k H z ) 1.3249(46) 1.3249(25) 1.3232(35) A J K ( k H z ) -14.597(55) -14.604(37) -14.516(48) A K ( k H z ) 138.012(83) 138.027(70) 137.808(85) 6j(kHz) 0.33991(82) 0.33968(50) 0.34120(44) 6 K ( k H z ) 3.913(59) 3.927(24) 3.811(21) Hj(Hz) -0.0007(98) c c H J K ( H z ) -0.15(16) -0.209(14) c H K J ( H z ) 0.12(50) 0.345(22) c H K(Hz) 0.48(172) c c h j ( H z ) -0.0023(13) -0.00282(33) c h J K ( H z ) 0.14(25) 0.198(29) c h K ( H z ) 1.3(45) c c JMax 60 60 30 S t d . D e v i a t i o n o f F i t (MHz) 0.048 0.047 0.052 50 T a b l e 3.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f S u l p h u r D i c h l o r i d e ( c o n t i n u e d ) 3 2 S 3 5 C 1 3 7 C 1 (Ground S t a t e ) 3 2 S 3 5 C U {yz = 1 S t a t e ) A(MHz) 14490.169(21) 14732.830(10) B(MHz) 2841.1929(47) 2918.3174(34) C(MHz) 2371.9634(35) 2426.1032(34) •A'j(kHz) 1.239(13) d A J K ( k H z ) -14.40(13) d A K ( k H z ) 135.68(18) d 6 j ( k H z ) 0.3168(35) d 6 K ( k H z ) 3.62(21) d H J K ( H z ) -0.256(68) d H K J ( H z ) 0.36(13) d h j ( H z ) -0.0050(22) d h K ( H z ) 0.27(10) d JMax 40 17 S t d . D e v i a t i o n o f F i t (MHz) 0.035 0/063 a The v a r i o u s f i t s a r e d i s c u s s e d i n t h e t e x t , k E r r o r s c i t e d a r e s t a n d a r d e r r o r s . c C o n s t a n t was c o n s t r a i n e d t o z e r o . ^ C e n t r i f u g a l d i s t o r t i o n c o r r e c t i o n s assumed t o equal t h o s e o f t h e ground s t a t e . 51 T a b l e 3.3 Observed R o t a t i o n a l T r a n s i t i o n s (MHz) o f S u l p h u r D i c h l o r i d e T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n .S C l 9 (ground v i b r a t i o n a l s t a t e ) ' l . i - ° o , o 17044.19 -0.10 0.00 21,1 " 20,2 12688.11 -0.09 0.03 2 - 2 ^2,0 ^1,1 35091.60 -1.77 0.10 3 1 , 3 " 20,2 26527.86 -0.01 0.09 3 - 3 J2,2 J l , 3 37291.67 -1.64 0.05 4 - 4 V 3 40,4 14573.30 -0.10 -0.05 4 2 s 2 " 4 1 , 3 33615.87 -1.04 0.03 5 1 , 5 " 40,4 35143.10 0.05 -0.02 6 1 , 5 " 60,6 17881.46 -0.54 0.11 62,4 " 6 1 , 5 31828.24 0.12 0.05 8 0 , 8 " 71,7 35128.04 -3.28 -0.02 8 1 , 7 " 7 2 , 6 15253.30 -4.52 -0.06 8 2 , 6 " 7 3 , 5 -14560.68 1.95 0.01 8 2 , 6 " 8 1 , 7 30370.45 1.31 -0.05 92,7 " 91,8 29983.31 1.65 -0.04 1 0 2 , 8 " 1 0 1 , 9 29930.42 1.60 -0.11 1 0 1 , 9 " 9 2 , 8 29837.68 -10.12 " -0.02 1 0 1 , 9 - 1 0 0 , 1 0 30046.23 -6.01 -0.02 1 2 2 , 1 0 " 1 2 1 , 1 1 31088.97 -0.52 0.01 1 2 2 , 1 0 " ^ 3 , 9 13435.39 -16.20 0.11 52 T a b l e 3 . 3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n _S C l ? (ground v i b r a t i o n a l s t a t e ) 1 2 3 , 9 " ' " 4 . 8 - 1 7 3 8 4 . 2 4 2 . 1 6 - 0 . 0 2 1 3 3 , n " 1 2 4 , 8 - 1 3 4 2 9 . 9 3 0 . 1 5 - 0 . 0 2 1 32,11 " 1 3 1 , 1 2 32406 .93 - 3 . 0 9 - 0 . 0 3 1 4 2,12 " 1 4 1 . 1 3 34274 .37 - 7 . 0 3 0.01 , 4 4,11 " 1 3 5 , 8 - 3 1 5 5 2 . 9 6 17 .99 0 .02 1 6 2 , H " 1 6 1 , 1 5 39766 .13 - 2 0 . 1 2 - 0 . 0 0 1 7 4,14 " 1 6 5 , 1 1 - 1 4 8 0 8 . 7 4 - 5 . 2 6 - 0 . 0 4 1 7 4,13 " 1 6 5 . 1 2 - 1 3 9 0 8 . 3 8 - 9 . 2 9 - 0 . 0 0 , 7 2 ,16 " 1 6 3 , 1 3 12849.70 5 .12 - 0 . 0 3 1 7 1,17 " 1 6 2 , 1 4 -14716 .81 4 0 . 6 8 0.01 1 8 5,13 " 1 7 6 , 1 2 - 3 3 4 6 0 . 0 9 2 2 . 3 6 0 . 0 8 , 9 3 ,17 " 1 8 4 , 1 4 15710.32 - 2 5 . 5 5 0 . 0 0 19 I Y 2 , 1 8 " 1 8 3 . 1 5 12867.07 24 .86 0.01 2 1 1 , 2 1 " — 2 , 1 8 - 3 6 1 1 0 . 0 7 9 7 . 9 3 - 0 . 0 1 2 1 5 , 1 7 " 2 0 6 , 1 4 - 1 6 5 5 3 . 8 3 - 1 5 . 1 1 0 . 0 3 2 1 5 , 1 6 " 2 0 6 , 1 5 - 1 6 2 1 6 . 5 7 - 1 7 . 9 7 0 . 0 7 2 2 4 , 1 9 " 2 1 5 , 1 6 12753.01 - 5 5 . 4 9 - 0 . 0 4 2 2 6 , 1 6 " 2 1 7 , 1 5 - 3 5 5 0 9 . 1 0 25 .32 0 . 0 4 2 2 6 , 1 7 " 2 1 7 , 1 4 -35535.71 2 5 . 6 2 0.01 2 3 3 , 2 1 " 2 2 4 , 1 8 27811 .12 - 6 . 4 5 - 0 . 0 1 53 T a b l e 3.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n S C l ? (ground v i b r a t i o n a l s t a t e ) 2 3 6 , 1 7 " 2 2 7 , 1 6 -29835.67 7.98 0.01 2 3 4 , 2 0 " 2 2 5 , 1 7 17982.04 -65.03 0.02 2 4 4 , 2 0 " 2 3 5 , 1 9 34379.69 -159.28 -0.03 2 5 4 , 2 2 " 2 4 5 , 1 9 27800.80 -78.94 -0.09 2 6 6 , 2 0 " 2 5 7 , 1 9 -12501.47 -54.89 -0.04 2 6 5 , 2 1 " 2 5 6 , 2 0 14795.95 -131.99 0.01 2 6 6 , 2 1 " 2 5 7 , 1 8 -12691.58 -51.95 0.05 2 7 3 , 2 5 " 2 6 4 , 2 2 28319.52 102.47 0.02 2 7 4 , 2 4 " 2 6 5 , 2 1 36337.36 -79.02 0.01 2 7 5 , 2 3 " 2 6 6 , 2 0 17932.92 -119.05 0.00 2 8 5 , 2 3 " 2 7 6 , 2 2 28694.74 -207.84 -0.03 2 9 5 , 2 4 " 2 8 6 , 2 3 36136.75 -255.82 0.03 3 0 7 , 2 4 " 2 9 8 , 2 1 -14652.50 -80.96 0.02 3 0 5 , 2 6 " 2 9 6 , 2 3 34598.95 -170.63 -0.00 3 1 8 , 2 3 " 3 0 9 , 2 2 -33867.00 -10.98 -0.04 3 1 8 , 2 4 ~ 3 0 9 , 2 1 -33872.14 -10.82 0.00 3 1 6 , 2 6 " 3 0 7 , 2 3 16668.24 -184.59 0.01 3 2 8 , 2 4 " 3 1 9 , 2 3 -28158.19 -44.64 -0.08 3 2 8 , 2 5 " 3 1 9 , 2 2 -28166.70 -44.37 -0.02 3 3 6 , 2 7 " 3 2 7 , 2 6 31414.74 -313.44 -0.04 54 T a b l e 3.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n S C l 0 (ground v i b r a t i o n a l s t a t e ) 3 3 6 , 2 8 " 3 2 7 , 2 5 28529.79 -245.73 0.05 3 4 8 , 2 7 " 3 3 9 , 2 4 -16653.32 -118.28 -0 .00 3 4 6 , 2 9 " 3 3 7 , 2 6 34429.35 -276.29 -0 .02 3 4 8 , 2 6 ' 3 3 9 , 2 5 -16631.11 -119.06 -0.01 3 5 7 , 2 9 " 3 4 8 , 2 6 14852.58 -260.67 0.00 3 5 9 , 2 7 " 3 4 1 0 , 2 4 -35876.03 -29 s61 -0.01 35 • " 7 , 2 8 34 ^ 8 , 2 7 15381.94 -277.61 - 0 . 1 0 3 6 9 , 2 8 " 3 5 1 0 , 2 5 -30172.34 -72 .19 -0.11 3 7 7 , 3 1 3 6 8 , 2 8 26923.09 -347.30 0.02 3 8 7 , 3 2 " 3 7 8 , 2 9 32997.62 -392.99 - 0 . 0 0 3 9 8 , 3 1 " 3 8 9 , 3 0 13003.43 -356.76 - 0 . 0 3 3 9 9 , 3 1 " 3 8 1 0 , 2 8 -12873.02 -215.65 - 0 .02 3 9 9 , 3 0 " 3 8 1 0 , 2 9 -12861.39 -216.26 0.01 3 9 8 , 3 2 " 3 8 9 , 2 9 12816.52 -348.18 0.01 4 0 1 0 , 3 0 " 3 9 1 1 , 2 9 -32184.14 -108.67 0.10 4 0 1 0 , 3 1 ' 3 9 1 1 , 2 8 -32185.13 -108.61 0.02 4 2 8 , 3 4 " 41 ^ ' 9 , 3 3 31591.85 -550.46 0.09 4 3 1 0 , 3 3 - 42 ^ 1 1 , 3 2 -14914.83 -284.32 0.04 4 3 1 0 , 3 4 " 4 2 n , 3 i -14918.62 -284.06 0.03 4 3 8 , 3 5 " 4 2 9 , 3 4 37984.19 -627.84 0.08 55 T a b l e 3.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n S C l ? (ground v i b r a t i o n a l s t a t e ) 4 3 8 , 3 6 " 4 2 9 , 3 3 37162.20 -582.86 0.02 4 4 9 , 3 6 " 4 3 1 0 , 3 3 16697.03 -515.61 -0.01 4 4 9 , 3 5 " 4 3 1 0 , 3 4 16792.23 -521.91 - 0 . 0 3 4 6 9 , 3 8 " 45 H O 1 0 , 3 5 28823.14 -660.03 0.04 4 6 9 , 3 7 - 4 5 1 0 , 3 6 29027.53 -674.74 0.03 4 7 1 1 , 3 6 " 4 6 1 2 , 3 5 -16974.70 -365 .33 0.03 4 7 9 , 3 9 " 4 6 1 0 , 3 6 34954.22 -737.81 - 0 . 0 3 4 7 9 , 3 8 " 4 6 1 0 , 3 7 35249.19 -759.89 -0.01 4 8 1 0 , 3 8 " 4 7 n , 3 7 14550.75 -646.84 - 0 . 0 3 4 8 1 0 , 3 9 " 4 7 1 1 , 3 6 14518.69 -644.01 -0 .04 5 0 1 0 , 4 0 " 4 9 1 1 , 3 9 26635.54 -822.33 -0 .00 5 0 1 0 , 4 1 " 4 9 1 1 , 3 8 26565.42 -815.61 0.00 5 110,41 " 5 0 1 1 , 4 0 32755.91 -918.91 - 0 . 0 8 5 6 1 1 , 4 6 " 5 5 1 2 , 4 3 36412.35 -1208.95 0.03 5 6 n , 4 5 " 5 5 1 2 , 4 4 36462.65 -1215.69 -0.01 5 7 1 4 5 4 3 " 5 6 1 5 , 4 2 -34645.95 -468.92 0.01 5 7 1 2 , 4 5 " 5 6 1 3 , 4 4 16059.53 -1066.87 -0.01 5 7 1 2 , 4 6 " 5 6 1 3 , 4 3 16054.41 -1066.08 0.00 5 8 1 4 , 4 5 " 5 7 1 5 , 4 2 -28944.96 -580.21 -0 .06 5 9 1 2 , 4 7 " 5 8 1 3 , 4 6 28017.72 -1307.84 0.02 56 T a b l e 3.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n F requency C o r r e c t i o n op OC S C l 0 (ground v i b r a t i o n a l s t a t e ) 5 9 1 2 , 4 8 " 5 8 1 3 , 4 5 28006.35 -1305.96 0.03 6 0 1 4 , 4 7 " 5 9 1 5 , 4 4 -17483.10 -815.62 0.04 6 0 1 2 , 4 8 " 5 9 1 3 , 4 7 34052.96 -1436.90 -0.04 6 0 1 2 , 4 9 " 5 9 1 3 , 4 6 34036.27 -1434.04 -0.00 3 2 S 3 5 C 1 3 7 C 1 (ground v i b r a t i o n a l s t a t e ) 8 2 , 6 " 81,7 30324.62 1.34 -0.05 92,7 " 91,8 29897.89 1.74 -0.01 1 0 2 , 8 " 1 0 1 , 9 29778.18 1.79 -0.02 1 ] 2 , 9 " " l . l O 30031.16 1.31 0.08 1 2 2 , 1 0 " 1 2 1 , 1 1 30712.71 0.08 0.01 1 4 2 , 1 2 " 1 4 1 , 1 3 33545.53 -5.65 -0.01 1 5 2 , 1 3 " 1 5 1 , 1 4 35768.34 -10.68 -0.01 1 6 2 , 1 4 " 1 6 1 , 1 5 38559.36 -17.49 0.01 1 7 4 , 1 3 " 1 6 5 , 1 2 -16009.25 -7.30 -0.03 1 9 3 , 1 7 " 1 8 4 , 1 4 13894.23 -25.69 0.03 2 2 5 , 1 8 " 2 1 6 , 1 5 -13477.44 -26.58 -0.01 2 2 5 , 1 7 " 2 1 6 , 1 6 -13041.75 -30.52 -0.01 2 2 4 , 1 8 " 2 1 5 , 1 7 15504.54 -88.87 0.01 T a b l e 3.3 ( c o n t i n u e d ) 57 T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n S^cr'ci (ground v i b r a t i o n a l s t a t e ) 2 3 6 , 1 7 " 2 2 7 , 1 6 -32495.98 11.42 0.04 2 3 6 , 1 8 " 2 2 7 , 1 5 -32531.56 11.85 0.02 2 3 4 , 2 0 " 2 2 5 , 1 7 15316.52 -62.87 0.02 2 4 6 , 1 9 " 2 3 7 , 1 6 -27005.38 -5.86 -0.08 2 6 6 , 2 0 " 2 5 7 , 1 9 -15694.40 -48.03 0.01 2 6 6 , 2 1 " 2 5 7 , 1 8 -15845.02 -45.76 0.01 2 7 7 , 2 1 " 2 6 8 , 1 8 -35007.09 7.20 0.02 2 7 7 , 2 0 " 2 6 8 , 1 9 -34995.32 6.98 0.04 2 8 7 , 2 2 " 2 7 8 , 1 9 -29471.72 -17.11 -0.02 2 8 7 , 2 1 " 2 7 8 , 2 0 -29452.33 -17,51 -0.06 3 0 5 , 2 6 " 2 9 6 , 2 3 30936.25 -165.74 -0.05 3 1 7 , 2 5 " 3 0 8 , 2 2 -12655.17 -101.16 0.01 3 1 6 , 2 6 " 3 0 7 , 2 3 12663.09 -172.70 0.03 3 5 8 , 2 7 " 3 4 9 , 2 6 -15122.18 -143.36 0.02 3 5 8 , 2 8 " 3 4 9 , 2 5 -15147.84 -142.42 0.02 3 5 6 , 3 0 " 3 4 7 , 2 7 35707.97 -292.54 0.02 3 6 7 , 3 0 " 3 5 8 , 2 7 16144.68 -282.52 0.01 3 6 7 , 2 9 " 3 5 8 , 2 8 16735.47 -302.06 -0.03 3 7 9 , 2 9 " 3 6 1 0 , 2 6 -28874.54 -99.69 -0.01 3 7 9 , 2 8 " 3 6 1 0 , 2 7 -28871.30 -99.84 0.00 58 T a b l e 3.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n S ° ° C 1 0 / C l (ground v i b r a t i o n a l s t a t e ) 3 9 9 , 3 0 " 3 8 1 0 , 2 9 -17651.92 -193.33 0.00 3 9 9 , 3 1 " 3 8 1 0 , 2 8 -17660.11 -192,91 0.00 3 9 7 , 3 3 " 3 8 8 , 3 0 33832.47 -414.50 -0.00 3 9 7 , 3 2 " 3 8 8 , 3 1 35523.78 -478.78 0.00 4 0 8 , 3 2 " 3 9 9 , 3 1 13806.35 -382.95 -0.01 4 0 8 , 3 3 " 3 9 9 , 3 0 13603.10 -373.35 0.01 3 2 S 3 5 C 1 „ ( v 0 = 1 e x c i t e d v i b r a t i o n a l s t a t e ) °0,0 17158.90 -0.11 0.08 21,1 " 20,2 12813.97 -0.09 0.06 22,0 " 2 i . i 35456.89 -1.77 0.06 32,2 " 3 1 , 3 37666.03 -1.64 -0.11 4 1 , 3 " 40,4 14705.97 -0.10 -0.04 51,5 " 40,4 35214.68 0.05 0.01 8 2 , 6 " 8 1 , 7 30697.11 1.32 -0.03 80,8 ' 71,7 34980.00 -3.28 -0.02 9 2 , 7 " 91,8 30299.14 1.65 0.03 1 0 2 , 8 • " 1 0 1 , 9 30234.66 1.60 -0.03 1 0 1 , 9 ' " 1 0 0 , 1 0 30225.48 -6.01 -0.04 1 4 2 , 1 2 - 1 4 1 , 1 3 34532.63 -7.03 0.07 59 T a b l e 3.3 ( c o n t i n u e d ) a The " o b s e r v e d " f r e q u e n c i e s g i v e n i n t h i s T a b l e a r e t h e h y p o t h e t i c a l u n s p l i t l i n e f r e q u e n c i e s . The h y p e r f i n e s t r u c t u r e o f the measured t r a n s i t i o n s was s u b t r a c t e d u s i n g t h e methods o u t l i n e d i n s e c t i o n s 3.1 and 3.2. k The c e n t r i f u g a l c o r r e c t i o n s were c a l c u l a t e d u s i n g the c o n s t a n t s o f 32 35 T a b l e 3.2. The c o r r e c t i o n s f o r the v 2 = 1 s t a t e o f S C l 2 were assumed t o be equal t o tho s e o f the c o r r e s p o n d i n g ground s t a t e l i n e s . "Observed" u n s p l i t l i n e f r e q u e n c y minus the f r e q u e n c y c a l c u l a t e d u s i n g t he c o n s t a n t s o f T a b l e 3.2. 60 3.3 The Harmonic P o t e n t i a l F u n c t i o n o f S u l p h u r D i c h l o r i d e A fundamental d i f f i c u l t y i n the d e t e r m i n a t i o n o f harmonic p o t e n t i a l f u n c t i o n s from v i b r a t i o n a l d a t a a l o n e i s t h a t t h e wavenumbers o f the v i b r a t i o n a l fundamentals c o n t a i n c o n t r i b u t i o n s from anharmonic terms and sometimes a r e p e r t u r b e d by v i b r a t i o n a l r e s o n a n c e s . In g e n e r a l i t i s not p o s s i b l e t o make the c o r r e c t i o n s n e c e s s a r y t o o b t a i n the d e s i r e d harmonized or e q u i l i b r i u m wavenumbers. S i m i l a r c o n s i d e r a t i o n s a p p l y t o t h e q u a r t i c d i s t o r t i o n c o n s t a n t s o b t a i n e d from r o t a t i o n a l s p e c t r a . In what f o l l o w s i t has been n e c e s s a r y t o use the o b s e r v e d o r e f f e c t i v e v a l u e s o f t h e s e c o n s t a n t s d i r e c t l y . From the f i t s d e s c r i b e d i n the p r e v i o u s s e c t i o n v a l u e s have been o b t a i n e d f o r the f i v e q u a r t i c d i s t o r t i o n c o n s t a n t s o f Watson's H a m i l t o n i a n . These c o n s t a n t s c o u l d have been used d i r e c t l y t o s p e c i f y the f o r c e f i e l d . However i t has been shown by Dowling t h a t f o r a p l a n a r asymmetric r o t o r i n i t s e q u i l i b r i u m c o n f i g u r a t i o n t h e r e a r e o n l y f o u r independent q u a r t i c c o n s t a n t s ( 2 4 ) . The use o f f o u r q u a r t i c c o n s t a n t s g r e a t l y s i m p l i f i e s the problem and t h i s approach has been f o l l o w e d here. For t h i s purpose t h e f o u r c o n s t a n t s T_, . T,,,, , T aaaa DDDD c c c c and T A L ) A B o f W i l s o n and Howard (25) c o n s t i t u t e d the most u s e f u l c h o i c e . A C 2 v t r i a t o m i c such as s u l p h u r d i c h l o r i d e has t h r e e v i b r a t i o n a l f u n d a m e n t a l s . Of t h e s e , two, the symmetric s t r e t c h and symmetric bend a r e o f s p e c i e s A^ and the t h i r d , the asymmetric s t r e t c h , i s o f s p e c i e s . A p o t e n t i a l f u n c t i o n w r i t t e n i n terms o f symmetry c o o r d i n a t e s t h e r e f o r e has f o u r f o r c e c o n s t a n t s . The elements o f the i n v e r s e p o t e n t i a l c o n s t a n t m a t r i x can be e x p r e s s e d i n terms o f x , aaaa T b b b b ' T c c c c a n d T a b a b u s l n 9 r e l a t i o n s r e a d i l y d e r i v e d from t h o s e o f H e r b e r i c h , J a c k s o n and M i l 1 en (26) by use o f Dowling's e q u a t i o n s ( 2 4 ) . 61 (The relations of Herberich et-al_.(26) follow directly from equation 1.49 after some extensive but straightforward manipulations). These are: - 1 2. 2, (F~ ).J.J = -R sin 4> cos <ft A cot <j>-B x a a a a B tan+-A T , . .. AB t —— - — aaaa + 1— bbbb cccc A 3 B 3 C 4 (3.2) - 1 ,_2. . . .2 . r (F" ) 2 2 = -R s i n ^ cos^ -1 2 2 (F )^2 = -R sin $ cos <fr (A+B) raaaa + Tbbbb _ ^ Tcccc A 3 B 3 J C 4 (3.3) 2(2)' B(tan<f> - cot<|>) - 2A cot<{> T aaaa + A(tan(j> - cot<|)) + 2B tan<|> T H K H H L _ AB tan<j> - cot<|) T B 3 bbbb - ~ ,T. 'cccc ( F - , ) 3 3 = : R _ m x 2M 1 + 2m sin <j> m Tabab AB (3.4) (3.5) These relations have been written for the general C 2 v triatomic of formula XY2. Here R = r 2 x 1 0 ' 1 7 , with r the X-Y bond length; <f> is one-half the Y-X-Y bond angle; M is the molecular weight with M = mx + 2mY. With Planck's constant h in erg seconds and r in Angstroms the potential constants F ^ , F^ 2, F 2 2 and F 3 3 obtained by inverting o the matrix calculated above are in mdyn/A. Again i t should be em-phasized that while these relations are strictly valid only for the equilibrium values of the molecular constants a good approximation can be obtained using the observed ground state values. Before using equations 3.2 - 3.5 to determine a potential function the values of x a a a a » f ^ k , , T C C c c ' T l a n c l T2 m a y b e c a l c u l a t e d 62 TABLE 3.4 R e l a t i o n s h i p s Between Q u 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 C o n s t a n t s 9 E v a l u a t i o n o f Watson's d e t e r m i n a b l e parameters (I r e p r e s e n t a t i o n ) T a a a a = " ^ J + A J K + V T b b b b = " 4 < A J + 2 6 J > T c c c c = - 4 < A J " 2 V T l = T ' a a b b + T , a a c c + T , b b c c = - 4 ( A J K + 3 A J ^ T 2 = A V b b c c + B V a a c c + C V a a b b = 4 ( 2 6 J + 2 6 K - a A j ) + ^ [ f ^ r j P l a n a r R e l a t i o n s T a c a c T b c b c Laabb A 2 B 2 aaaa A 4 •bbbb c c c c - n 2 r 2  T a a c c ^-4f- aaaa Tbbbb c c c c - R 2 r 2  T b b c c " aaaa lbbbb c c c c a B y d e f i n i t i o n T ' ^ = + 2-r,. £ J f f g g f f g g f g f g 63 as linear combinations of the experimentally determined quartic constants using relations given in Table 3.4. The potential constants of species Ap that i s , F^-j, F^ and F22,were obtained directly from the values of x,, . x . . . . and x„„„„ thus derived. In other cases aaaa bbbb cccc similar methods have provided good predictions for the corresponding vibrational fundamentals, to within 5% or better for the very light molecules H20 (27) and H2S (28) and rather better for heavier molecules such as C120 (26). The Fg^ force constant for the vibration was not so easily evaluated. It is related by equation 3.5 to t a b a b , which is not one of Watson's determinable parameters. A value for T a b a b can be calculated in a number of ways (27, 29-31) from x^ and/or x 2 using Dowling's planar relations (24), which are also given in Table 3.4. Unfortunately x-| and x 2 are not very sensitive to the value of T a b a b ; that is , T a b a b does not make a large contribution to either x-| or x 2 . Because of experimental uncertainty and vibrational effects the values of T a b a b thus obtained vary widely, depending on the method used to determine them. As a result the derived value of F 3 3 is rather un-certain, and the prediction of the B-j fundamental is usually much worse than those of the A-j fundamentals. 32 35 The five determinable parameters of S C l 2 in its ground state, calculated from the experimental distortion constants using the equations of Table 3.4, are given in Table 3.5. The constants T=,==> tkkkk> and x, were obtained directly. To evaluate x Q aaaa D D D D cccc i c the rotational constants A ' , B' and C of Kivelson and Wilson (32) were required; these are related to Watson's constants by (27) 6 4 A' = A - 16Rg B' = B + 16Rg (A1 - C'y(B' - C ) C = C - 16Rg (A' - B ' K B ' - C ) (3.6) The quartic constant Rg = -(4Aj + t b b c c ) / 3 2 was defined by Nielsen (33). For l ight molecules such as HgO where the corrections involved are very large these equations must be solved i terat ively (27); for sulfur dichloride this was not the case. Having calculated i " b b c c from the planar relations the values of A ' , B1 and C given in Table 3.5 were derived; these d i f fer by at most 0.012 MHz from the experimental A,B,C. Four different methods were used to calculate x , . for abab o p OC S C l 2 . These were: (i) from the value of and a l l of Dowling's planar relat ions; ( i i ) from the value of x 2 and al l of the planar relat ions; ( i i i ) from the planar relations for x , x , x, , and r aabb' acac bcbc Tbbcc a n d s - i m L | l t a n e o u s solution of the equations for x-| and x 2 - The values determined show a f a i r l y wide range and accordingly are of dubious value for a force constant determination. The T a b a b values obtained from Fi t 3 (see Table 3.2) form a more self -consistent set than those derived using the Fi t 2 results even though the standard errors are smaller for the lat ter set. (The T a b a b values calculated using the Fit 1 results are essential ly identical to those obtained from the F i t 2 constants and hence are not given in Table 3.5). Several authors have considered the problem of choosing the correct value for T a b a b without, in general, throwing much l ight on the subject. (See for example Yamada and Winnewisser (30)). Watson has shown that for the equilibrium values of the molecular constants (34) 65 TABLE 3.5: A l t e r n a t e Ground S t a t e M o l e c u l e C o n s t a n t s o f J £ S C l g F i t 2 a F i t 3 Watson's D e t e r m i n a b l e Parameters W k H z > - 4 9 8 . 9 9 ( 3 2 ) b -498.46(39) W k H z > -8.017(11) -8.023(14) W k H z > -2.582(11) -2.563(14) x-, (kHz) 42.51(15) 42.18(19) x 2 (MHz) 2 58.866(42) 57.829(53) K i v e l s o n - W i l s o n R o t a t i o n a l C o n s t a n t s and R g A' (MHz) 14613.5973(52) 14613.5990(67) B' (MHz) 2920.8586(11) 2920.8577(15) C' (MHz) 2430.7054(10) 2430.7042(13) R 6 (kHz) -0.0292 -0.0294 Val u e s o f T A B A B C a l c u l a t e d by D i f f e r e n t Methods (KHz) Method (1) -5.98(20) -6.62(25) Method ( i i ) -5.80(22) -6.56(28) Method ( i i i ) -6.89(65) -6.96(82) Method ( i v ) -6.02(22) -6.64(28) D i s t o r t i o n C o n s t a n t s E v a l u e d U s i n g the P l a n a r R e l a t i o n s T a a b b ( k H z > 42.92(30) 43.47(38) ^bbcc < k H z> -4.365( 8) -4.353(10) T a a c c < k H z> 15.92(21) 16.31(26) Calculated from the constants of Table 3.2. bErrors cited are standard errors. 66 zplanar = 4 C A J " { * ~ C ) AJK " 2(2A +B +C)6j + 2(B-C)6 K = 0 (3.7) The effective ground state values do not satisfy this expression; these so-called planar sums derived using the results of Fit 2 and Fit 3 are given in Table 3.6. The magnitude of E is smaller for Fit 3 than for Fit 2 and accounts for the more self-consistent set of fgk^k, values obtained using the Fit 3 results; this reflects mostly the different estimates of 6 j and <5^  derived from Fit 2 and Fit 3. If the results of Table 3.6 are taken to indicate that the quartic constants of Fit 3 constitute the more reasonable set then the sextic constants of Fit 2 must be regarded with suspicion. With all of the data being f i t only one set of sextic constants - H K J , HK and hj - was found whose use would give values for the quartic constants essentially identical to those of Fit 3 (albeit at the expense of a slightly higher standard deviation of the f i t ) . However TABLE 3.6 Values of Watson1 s Quartic Planarity Sum for 3 2 S 3 5 C 1 2 Refinement Value3 Fit 2 0.400(53) MHz^  Fit 3 0.120(56) MHz2 Calculated using equation 3.7 and the constants of Table 3.2 there was no process of logical and sequential elimination of other sextic constants which would lead to H^j, H^  and hj being retained. Again, whereas x,,, . x k k k k , x„„„„ were insensitive to the data set aaaa D D D D C C C C and the details of the refinement procedure the values of T a b a k , > though imprecise, varied widely. 67 32 35 In a f inal refinement of the S C l^ ground state data Dowling's planarity relations (24) were used to eliminate one of the f ive quartic distortion constants, and a f i t was made to four constants, chosen to be r a a a a , T f a b b b , x a a b b and T a b a b . Similar analyses have been made for the F 20 (35) and Cl^O (26) molecules amongst others. The f i t was a f i r s t order f i t in a r ig id asymmetric rotor basis, and the rotational constants used in the planar relations were the effective ground state constants obtained ear l ier . Only transitions with J < 25 were used in this refinement as possible sextic distortion contributions were ignored. The standard deviation of the f i t was 0.055 MHz with an average deviation of 0.044 MHz. The results of this refinement, F i t 4, are compared to those of previous analyses, Fits 2 and 3, in Table 3.7. Excellent agreement is observed for the direct ly determinable constants A ' , B 1 , C , T , , , , and T . . . . . The values of aaaa bbbb T cccc a n c * Taabb n a v e b e e n c o m P a r e c ' u s i n 9 the planar relations of Table 3.4, the agreement here is less satisfactory with the values of Taabb o b t a i n e d f r o n i F i t 2 and Fi t 4 di f fer ing by more than the sum of their standard errors. F ina l ly , the values of t a b a b have been compared. For Fi t 2 and F i t 4 the agreement is very poor; the discrepancies between the Fit 3 and F i t 4 x a b a b values are rather smaller. Because the differences between the various values of i " a b a b are large this constant was not used to determine F^. The three A-j species force constants were calculated using the values of T „ . T, . . . and T from Table 3.7 in equations 3.2 -aaaa bbbb cccc ^ 3.4; the results are given in Table 3.8. The uncertainties given in Table 3.8 were derived assuming the errors in T„„ . T. . and T 3 aaaa' bbbb cccc to be those given in Table 3.7 and the errors in the rotational 68 TABLE 3.7 Rotational and Centrifugal Distortion Constants of S CI Obtained from Various Fits Parameter F i t 2 a F i t 3 b Fit 4 C A' (MHz) 14613.5973(52) 14613.5990(67) 14613.6041(73) B'(MHz) 2920.8586(11) 2920.8577(15) 2920.8598(18) C'(MHz) 2430.7054(10) 2430.7042(13) 2430.7054(18) -498.99(32) -498.46(39) -498.47(26) W k H z > -8.017(11) -8.023(14) -8.050(24) Tcccc< k H z> -2.582(11) -2.563(14) -2.574(13) W k H z > 42.92(30) 43.47(38) 43.55(15) , -5.98(20) -6.62(25) W K H z > \ -5.80(22) I -6.56(28) -6.858(76) ) -6.89(65) i -6.96(82) ' -6.02(22) ' -6.64(28) The i n i t i a l fit was made using Watson's Hamiltonian. A l l quartic constants and all sextic constants except H,, H„ and h., were included. See Tables 3.2 and 3.5. 0 K h Refinement was made using Watson's Hamiltonian with a l l quartic but no sextic terms included. See Tables 3.2 and 3.5. c F i t was made to A", B', C , T a a a a , T b b b b , T Q a b b and x ^ . 69 constants to be the differences between the effective ground state values and.those calculated from the average ground state moments of inert ia of Table 3.9. These lat ter errors are several orders of magnitude larger than the experimental uncertainties but should give some indication of the model error. The potential constants derived using the various f i t s are in good agreement although the value of F^ -j obtained from F i t 2 is s l ight ly smaller than those calculated from Fits 3 and 4. As has been already mentioned, because of the range of experimental values for T b ^ i t was not used to calculate the force constant F^g- Instead inert ia l defect data was used for this purpose. The inert ia l defects of a l l species studied are given in Table 3.9. The fact that the ground state inert ia l defects are small positive numbers showing sl ight isotopic variation is consistent with the molecule having a planar structure. The inert ia l defects determined experimentally are the sum of v ibrat ional , centrigual and electronic contributions of which the vibrational part is usually by far the largest (36). The vibrational 32 35 contributions to the inert ia l defects of S C l 2 in the ground or (000) state and the = 1 or (010) state depend only upon the harmonic part of the potential function (36, 37) and are given by (1, 3) A(000) = 4 K  A Vib ™ = (010) _ (000) = 4  A2 A Vib A Vib ^ ^2 ^2 + a ) 3 - J - \ c ) 2 (3.8) (3.9) Here c13 and ^3 (s t r ic t ly cj'^  and c|^)are Cor io l is coupling co-70 e f f i c i e n t s ; , w 2 and wg a r e the e q u i l i b r i u m v i b r a t i o n a l wavenumbers (assumed here t o d i f f e r n e g l i g i b l y from v 1, v 2 and v 3) and t h e f a c t o r K = h/8TT 2c has the v a l u e 16.85763 uA 2 cm" 1. In e q u a t i o n 3.9 A 2 i s the d i f f e r e n c e between the ground and v 2 = 1 s t a t e i n e r t i a l d e f e c t s . The c e n t r i f u g a l c o n t r i b u t i o n to the K i v e l s o n - W i l s o n c o n s t a n t s i s gi v e n by A c e n t = " W<3IV4C,> + ^ V28'* + d'a^'J^ ( 3 J 0 ) Where I' , I ' k and I' a r e the p r i n c i p a l moments o f i n e r t i a o b t a i n e d a D c from A', B' and C r e s p e c t i v e l y . In w r i t i n g e q u a t i o n 3.9 i t has been assumed t h a t the s m a l l e l e c t r o n i c and c e n t r i f u g a l c o n t r i b u t i o n s a r e the same f o r t h e ground and v 2 = 1 s t a t e s . Because o f the c a n c e l l a t i o n o f the e l e c t r o n i c and c e n t r i f u g a l c o n t r i b u t i o n s and because A 2 i s more s e n s i t i v e than t o the v a l u e o f a ^ , and hence F^, i t has been used t o c a l c u l a t e F 3 3 . B e f o r e u s i n g A 2 to o b t a i n w 3 i t was f i r s t n e c e s s a r y to c a l c u l a t e v a l u e s f o r , o>2> ?-|3 and c 2 3- V a l u e s o f and u>2 were 2 2 2 o b t a i n e d from t h e r o o t s x. = 4n c u . o f t h e A^ b l o c k o f t h e u s u a l s e c u l a r e q u a t i o n (38) |FG - XE| = 0 (3.11) T h i s was c o n s t r u c t e d u s i n g t h e f o r c e c o n s t a n t s o f T a b l e 3.8 and the G m a t r i x i n the form s p e c i f i e d by C a l i f a n o ( 3 9 ) . The e q u a t i o n s o f Meal and P o l o (40) were used t o c a l c u l a t e t h e C o r i o l i s c o u p l i n g c o n s t a n t s . F o r an XY 2 m o l e c u l e (C 1 3 ) 2 - [X-, - F 1 1/(G " 1 ) 1 ] ] / ( X 1 - X2) (3.11b) 71 TABLE 3.8 Quadratic Potential Constants, Vibrational Fundamentals and Coriol is Coupling Constants of Sulphur Dichloride Potential Constant F i t 2 a Fit 3 Fi t 4 F n(mdyn/A) 2.913(90) 2.994(95) 2.986(96) F 1 2(mdyn/A) 0.0926(55) 0.0913(55) 0.0891(57) F 2 2(mdyn/A) 0.2624(21) 0.2611(21) 0.2606(23) F3 3(mdyn/A) 2.421(41) 2.479(45) 2.470(44) Vibrational Fundamental oo-j (cm 1 ) 514.8(84) 521.9(88) 521.6(89) a> 2 (cm 1 ) 206.9( 7) 206.5( 8) 206.2( 8) u>2 (cm 1 ) 523.8(62) 530.0(68) 529.0(66) Coupling Constants ^13>2 0.3241(26) 0.3221(28) 0.3231(27) ( c 2 3 ) 2 0.6759(26) 0.6779(28) 0.6769(27) a F i t s are described in Table 3.7. The errors are discussed in the text. 72 u13)2 + u23)2 = 1 <3-12) An expression for (G'^-J-J has been given by Polo ( 4 1 ) . These equations were solved in an i terat ive manner using i n i t i a l l y the effective structural parameters and f ina l ly the average parameters discussed in Section 3.4. A value of F.^ was thus obtained for each set of A.| species force constants (F-J-J. F 1 2 and F 2 2 ) given in Table 3.8. These results as well as the corresponding values of ^ , u > 2 , ojg, ( C i 3 ) 2 are also given in Table 3.8. The experimental A 2 value of o 2 0.52198 (38) uA is very precise; the errors quoted for F 3 3 and ref lect almost entirely the estimated uncertainties in u>2 and U23) The errors quoted for the A-| species force constants, A^ vibrational wavenumbers and Cor io l is coupling constants are roughly twice what would be obtained i f only the experimental uncertainties in the distortion constants had been considered; the largest contributions to these errors come from the uncertainties assigned the rotational constants. Table 3.8 shows that the potential functions derived using the F i t 3 and F i t 4 results are almost ident ica l ; the potential function derived from Fi t 2 has s l ight ly lower values for the stretching force constants F i n and F o 0 . 73 3.4 The M o l e c u l a r S t r u c t u r e o f S u l p h u r D i c h l o r i d e The e f f e c t i v e p r i n c i p a l moments o f i n e r t i a and i n e r t i a l d e f e c t s o f t h e v a r i o u s s u l p h u r d i c h l o r i d e s p e c i e s s t u d i e d a r e c o l l e c t e d i n T a b l e 3 . 9 ; t h e s e parameters were d e r i v e d u s i n g the r o t a t i o n a l c o n s t a n t s o f T a b l e 3 . 2 . The ground s t a t e e f f e c t i v e s t r u c t u r a l p a r a m e t e r s , r Q and 9 Q , 32 35 were c a l c u l a t e d u s i n g the p r i n c i p a l moments o f the S C l 2 s p e c i e s . Because the i n e r t i a l d e f e c t i s non-zero, somewhat d i f f e r e n t r e s u l t s were o b t a i n e d when the t h r e e p o s s i b l e p a i r s o f moments I , , I. ; I I and I, , a D a c D I c were used. These r e s u l t s a r e summarized i n T a b l e 3 . 1 0 ; t h e mean ground s t a t e e f f e c t i v e s t r u c t u r e i s i d e n t i c a l t o t h a t o f Murray e t a l • ( 1 6 ) . A s i m i l a r c a l c u l a t i o n has y i e l d e d v a l u e s f o r t h e e x c i t e d s t a t e e f f e c t i v e parameters r (Q-JQ) a n d 0 ( o i 0 )* ^ e c a u s e t n e i n e r t i a l d e f e c t i s l a r g e r f o r t he e x c i t e d s t a t e the r e s u l t s o b t a i n e d u s i n g d i f f e r e n t p a i r s o f p r i n c i p a l moments show a w i d e r v a r i a t i o n than the ground s t a t e v a l u e s . A p a r t i a l s u b s t i t u t i o n s t r u c t u r e has a l s o been o b t a i n e d f o r t h e ground s t a t e . E q u a t i o n s 1.44 and 1.45 were used t o c a l c u l a t e t he a_ and 32 35 ib c o o r d i n a t e s o f c h l o r i n e u s i n g S Cl,, as t h e p a r e n t s p e c i e s . The c e n t e r o f mass c o n d i t i o n , E nub. = 0 , gave the b_ c o o r d i n a t e o f s u l p h u r ; i t s a_ c o o r d i n a t e i s z e r o by symmetry. D i f f e r e n t s t r u c t u r e s c o r r e s p o n d i n g t o changes i n t h e t h r e e p o s s i b l e p a i r s o f p r i n c i p a l moments were c a l c u l a t e d . These r g parameters a r e a l s o p r e s e n t e d i n T a b l e 3.10 and a r e seen t o be more s e l f c o n s i s t e n t than the e f f e c t i v e v a l u e s . 74 T a b l e 3.9 P r i n c i p a l Moments o f I n e r t i a and I n e r t i a l D e f e c t s o f op V a r i o u s S u l p h u r D i c h l o r i d e S p e c i e s (uA ) S ^ C 1 2 3 2 $ 3 5 c l 3 7 Ground S t a t e v~ = 1 S t a t e Ground S t a t e E f f e c t i v e V a l u e s 9 34.58279(1) 34.30291(2) 34.87737(5) 173.. 02344(7) 173.17479(20) 177.87564(30) 207.91549(9) 208.30895(30) 213.06357(32) 0.30926(11) 0.83125(35) 0.31056(44) Average Values' 3 'a 34.7366 34.5889 173.3086 173.8166 I z c 208.0466 208.4068 A z 0.0014 0.0013 a C a l c u l a t e d u s i n g the r o t a t i o n a l c o n s t a n t s o f T a b l e 3.2 and the °p 32 35 c o n v e r s i o n f a c t o r 505379.0 uA . F o r t h e ground s t a t e o f S C l 2 t h e F i t 2 r e s u l t s were used. b C a l c u l a t e d u s i n g e q u a t i o n s 3.13-3.15 and the F i t 2 f o r c e c o n s t a n t s o f T a b l e 3.8. 75 As w e l l , the p h y s i c a l l y w e l l - d e f i n e d average s t r u c t u r e s (42, 32 35 43) o f S C l 2 have been c a l c u l a t e d f o r both the ground and (010) v i b r a -t i o n a l s t a t e s . For a C 2 v t r i a t o m i c such as SCI^ one has ( 4 3 ) : I A Z = I A V + 3 K [ ( 2 V i + 1) s i n 2 X + ( 2 v 2 + !) c o s 2 x + ( 2 v 3 + 1 ) H A / I c l l L u l w 2 u 3 J (3.13) V = lb v + 3K [ ( 2 V , + 1) c o s 2 x + ( 2 v 2 + 1) s i n 2 x + ( 2 v 3 + 1 )Hb/lcL I u l u 2 w 3 (3.14) I c Z = I c V + 3 K [ ( 2 v 1 + 1 ) / W l + ( 2 v 2 + l ) / u 2 + ( 2 v 3 + l ) / w 3 ] - 4K (2 v ] + 1) ( o 3 3 ? 1 3 2 + ( 2 v 2 + 1) '23 • t 2 Z\ u-j ( w 3 -OJ-| ; ( 2 v 3 + l ) i 2 2 \ J 3 ( c o 3 ~ w l ) t 2 2^ r 2 2^ a) 2(o> 3 - u 2 ) '23 (3.15) where I z e t c . and I v e t c . a r e the average and e f f e c t i v e moments o f a a i n e r t i a , r e s p e c t i v e l y , f o r the v i b r a t i o n a l s t a t e i n q u e s t i o n , and 2 K (='h/8ir c) has been e v a l u a t e d e a r l i e r . The parameter x i s d e t e r m i n e d from the e q u a t i o n (43) (3.16) c o s 2 x + 2 ? 2 3 ( I b / I c ) ! l C 0 S x + C 2 3 2 " ( I a / I c ) = 0 '23 Here ? 2 3 i s n e g a t i v e by c o n v e n t i o n ( 4 4 ) . In e q u a t i o n s 3.13-3.15 Oka's I z n o t a t i o n (42) has been used i n s t e a d o f the I * o f Herschbach and L a u r i e ( 4 3 ) . In ge n e r a l the use o f e q u a t i o n s 3.13-3.15 r e q u i r e s t h a t (tog-cu-j) and (co3-co2) be f a i r l y l a r g e . Here t h i s i s not the case s i n c e u>3 and <o-j a r e a p p r o x i m a t e l y e q u a l . For the groundJand v 2 = 1 s t a t e s , however, the e q u a t i o n s a r e v a l i d because f a c t o r s o f (u>3-u)-|) a l l c a n c e l . The r e s u l t i n g average moments o f i n e r t i a and i n e r t i a ! d e f e c t s a r e a l s o p r e s e n t e d i n 76 T a b l e 3.9; the average i n e r t i a l d e f e c t s a r e e f f e c t i v e l y z e r o , as r e q u i r e d . In the average moment c a l c u l a t i o n s t he v a l u e s o f , u ^ , w ^ , and were t h o s e p r e d i c t e d u s i n g t he F i t 2 f o r c e c o n s t a n t s o f T a b l e 3.8; , e s s e n t i a l l y i d e n t i c a l average moments were c a l c u l a t e d when the F i t 3 o r F i t 4 f o r c e c o n s t a n t s were used. In the c a l c u l a t i o n o f the average moments the n e g l i g i b l e c e n t r i f u g a l c o r r e c t i o n s and n e c e s s a r i l y the unknown e l e c t r o n i c c o r r e c t i o n s have been i g n o r e d . The small v a l u e s o f A z o b t a i n e d f o r both v i b r a t i o n a l 32 35 s t a t e s o f S demon s t r a t e , however, t h a t the e l e c t r o n i c c o n t r i b u t i o n s cannot be l a r g e and a r e , i n f a c t , on the o r d e r o f o r s m a l l e r than the u n c e r t a i n t i e s i n the v i b r a t i o n a l c o r r e c t i o n s . The average bond l e n g t h s and a n g l e s , o b t a i n e d u s i n g the average p r i n c i p a l moments o f T a b l e 3.9, a r e g i v e n i n T a b l e 3.10. For both the ground and v^ = 1 v i b r a t i o n a l s t a t e s t he s t r u c t u r e s c a l c u l a t e d u s i n g the t h r e e p o s s i b l e p a i r s o f p r i n c i p a l moments a r e v e r y s e l f - c o n s i s t e n t . As might be e x p e c t e d f o r d i f f e r e n t s t a t e s o f a bending v i b r a t i o n , t he average bond l e n g t h i s e s s e n t i a l l y c o n s t a n t w h i l e the average bond a n g l e i s s l i g h t l y l a r g e r i n the e x c i t e d s t a t e . I t i s w o r t h w h i l e , i n p a r t i c u l a r , e s t i m a t i n g t he r e l i a b i l i t y o f t he ground s t a t e average s t r u c t u r e . U s i n g t he F i t 2 r e s u l t s o f T a b l e 3.8 the e r r o r s i n the harmonic v i b r a t i o n a l c o r r e c t i o n s I z - I °, • a a I z - I , 0 and I z - I 0 were c a l c u l a t e d t o be 0.6%, 0.5% and 1.1% b b c c r e s p e c t i v e l y . The s u g g e s t e d u n c e r t a i n t i e s i n a s t r u c t u r e d e r i v e d from I z and I. z a r e t h e r e f o r e 0.00002 & and 0.001° f o r r and 6, r e s p e c t i v e l y ; a D z z th e s e e r r o r s seem r a t h e r s m a l l . Even i f both I z - I 0 and I , z - I . 0 a a b b a r e assumed t o be i n e r r o r by 3%, however, then r z and e z can change by a t most 0.00008 A and 0.005° from t he I z , I. z s t r u c t u r e o f T a b l e 3.10. 77 T a b l e 3.10 E f f e c t i v e , P a r t i a l S u b s t i t u t i o n and Average S t r u c t u r e s f o r 3 2 S 3 5 C 1 2 Ground V i b r a t i o n a l S t a t e r0(A) e Q ( D e g . ) rs(A) e s ( D e g . ) rz(A) e z (Deg.) Vo = 1 E x c i t e d S t a t e '(010) '(010) (A) (Deg.) ( o i o ) ( A ) e (010) (Deg.) " a - V ('a- 'c> Mean 2.0125 2.0136 2.0160 2.0140 102.81 102.86 102.56 102.74 2.0138 2.0135 2.0151 2.0141 102.66 102.70 102.56 102.64 2.01524 2.01524 2.01526 2.0 1 5 2 5 ( 8 ) a 102.730 102.730 102.729 1 0 2 . 7 3 0 ( 5 ) a 2.0099 2.0128 2.0193 2.0140 103.06 103.19 102.39 102.88 2.01537 2.01538 2.01538 2.01538 102.931 102.931 102.930 102.931 a E s t i m a t e d o u t s i d e l i m i t s o f e r r o r . See t e x t . 78 These a r e r e a s o n a b l e o u t s i d e e r r o r l i m i t s f o r the ground s t a t e average s t r u c t u r e . F i n a l l y , the e q u i l i b r i u m v a l u e o f the s u l p h u r - c h l o r i n e bond d i s t a n c e was e s t i m a t e d . The r g bond l e n g t h was p r e d i c t e d u s i n g e q u a t i o n 1.42; v a l u e s o f u , the z e r o - p o i n t mean square a m p l i t u d e o f the S-Cl bond, and K, the c o r r e s p o n d i n g p e r p e n d i c u l a r a m p l i t u d e c o r r e c t i o n were c a l c u l a t e d u s i n g the F i t 2 f o r c e c o n s t a n t s o f T a b l e 3.8. The magnitude o f a ( S - C l ) , t he Morse a n h a r m o n i c i t y parameter, was taken as the mean o f the v a l u e s g i v e n f o r the and C l g m o l e c u l e s ( 4 5 ) . The same c a l c u l a t i o n has been performed f o r s e v e r a l m o l e c u l e s whose e q u i l i b r i u m s t r u c t u r e s a r e known; i n a l l c a s e s the v a l u e o f a was c a l c u l a t e d u s i n g the a v a i l a b l e r e s u l t s f o r d i a t o m i c m o l e c u l e s ( 4 5 ) . The e r r o r a s s i g n e d t o each o f the r g v a l u e s c a l c u l a t e d u s i n g e q u a t i o n 1.42 was the d i r e c t sum o f the e x p e r i m e n t a l u n c e r t a i n t y i n r 2 and one q u a r t e r o f the r - r d i f f e r e n c e . T h i s somewhat s u b j e c t i v e e r r o r was chosen because i n a l l c a s e s i t exceeds the d i f f e r e n c e between the s p e c t r o s c o p i c o r o b s e r v e d r g v a l u e and t h a t c a l c u l a t e d u s i n g e q u a t i o n 1.42. The d e v i a t i o n s a r e , i n f a c t , on the o r d e r o f the e x p e r i -mental e r r o r f o r t h e m o l e c u l e s w i t h s i n g l y bonded atoms. For the o x i d e s the agreement i s p o o r e r ; t h i s r e f l e c t s the f a c t t h a t the v a l u e o f the Morse a n h a r m o n i c i t y parameter d e r i v e d from the c u b i c f o r c e c o n s t a n t s o f ozone, f o r example, i s s l i g h t l y h i g h e r than t h a t found f o r the m o l e c u l e ( 6 ) . 79 T a b l e 3.11 The E q u i l i b r i u m Bond Lengths i n S u l p h u r D i c h l o r i d e and R e l a t e d M o l e c u l e s Parameter S C l g SFg SOg u 2(fl 2) 0.00195 0.00173 0.00123 K(A) 0.00060 0.00062 0.00059 a(A_1) 1.71 2.06 2.07 r (A) 2.0153(1) 1.5921(1) 1 . 4 3 4 9 ( 1 ) a r e(Calc . ) (A) b 2.0109(12) 1.5874(13) 1.4317(9) r e(0bs.)(A) c - 1.5875(1) 1.4308(2) R e f e r e n c e T h i s work (5) (1) 80 T a b l e 3.11 The E q u i l i b r i u m Bond Lengths i n S u l p h u r D i c h l o r i d e and R e l a t e d M o l e c u l e s ( c o n t i n u e d ) Parameter 0 F 2 0^ S i F 2 u 2(A 2) 0.00225 0.00191 0.00172 K(A) 0.00076 0.00067 0.00069 a ( A - 1 ) 2.45 2.48 1.88 r (A) 1 . 4 1 2 4 ( 1 ) a 1.2792(1) 1.5946(2) r e ( C a l c . ) ( A ) b 1.4049(20) 1.2728(17) 1.5904(14) r e ( 0 b s . ) ( A ) C 1.4053(4) 1.2717(2) 1.5901(1) Re f e r e n c e (4) (6) (29, 46) a No e r r o r was g i v e n . T h i s i s a r e a s o n a b l e u n c e r t a i n t y . b C a l c u l a t e d from r z u s i n g e q u a t i o n 1.42. c The s p e c t r o s c o p i c a l l y d e r i v e d r g bond l e n g t h : 81 3.5 Comments on the S u l p h u r D i c h l o r i d e P o t e n t i a l F u n c t i o n The harmonic p o t e n t i a l f u n c t i o n o b t a i n e d i n t h i s i n v e s t i g a t i o n has been based e n t i r e l y on microwave d a t a . In a s s e s s i n g i t s v a l i d i t y two o b v i o u s q u e s t i o n s s h o u l d be answered. F i r s t , i s t h e p o t e n t i a l f u n c t i o n c o n s i s t e n t w i t h a l l o f the v i b r a t i o n a l as w e l l as the r o t a t i o n a l data? Second, i s i t p o s s i b l e to r e f i n e the p o t e n t i a l f u n c t i o n f u r t h e r by u s i n g a c o m b i n a t i o n o f r o t a t i o n a l and v i b r a t i o n a l r e s u l t s ? As w e l l one s h o u l d i n q u i r e whether the p r e s e n t f o r c e f i e l d i s demonstrably b e t t e r than those p r e v i o u s l y o b t a i n e d . D e s p i t e the f a c t t h a t s e v e r a l s t u d i e s o f the v i b r a t i o n a l spectrum o f s u l p h u r d i c h l o r i d e have been made, d i f f i c u l t i e s a r i s e i n c h o o s i n g a p p r o p r i a t e v a l u e s f o r the v i b r a t i o n a l wavenumbers. In a l l c a s e s though v a l u e s quoted f o r are i n the range 202-211 cm ^ and those f o r v-j and l i e between 514 cm ^ and 535 cm ^ ( n e g l e c t i n g r e s u l t s f o r c r y s t a l l i n e s u l p h u r d i c h l o r i d e (15) which show e v i d e n c e o f v i b r a t i o n a l c o u p l i n g ) . A lthough the p r e s e n t r e s u l t s do n o t a l l o w i t , . i d e a l l y one would l i k e t o 32 35 have gas phase v a l u e s f o r the v a r i o u s fundamentals o f the S C l 2 s p e c i e s . The v q r e g i o n o f the i n f r a r e d spectrum o f the gas, f o r example, shows o n l y one band w i t h a complex c o n t o u r (15) due a t l e a s t p a r t l y to the f a c t t h a t the s t r e t c h i n g fundamentals a r e o v e r l a p p e d and the i s o t o p i c s t r u c t u r e o f the band i s u n r e s o l v e d ; i t i s a l s o p o s s i b l e t h a t the r o t a t i o n a l s t r u c t u r e o f t h i s band might be a f f e c t e d by a C o r i o l i s p e r t u r b a t i o n . The i n f r a r e d spectrum o f m a t r i x i s o l a t e d s u l p h u r d i c h l o r i d e p r o b a b l y g i v e s the b e s t e s t i m a t e f o r the s t r e t c h i n g f undamentals; i n t h i s case t h e i r i s o t o p i c s t r u c t u r e i s a t l e a s t p a r t i a l l y r e s o l v e d ( 1 5 ) . A g a i n , however, the assignment o f v-j and i s u n c e r t a i n . F r a n k i s s and H a r r i s o n (47) a s c r i b e a gas phase Raman band a t 528 cm ^ to v q 82 but do n o t reproduce the spectrum o r d e s c r i b e the bandshape; S a v o i e and Tremblay found an asymmetric band i n the Raman spectrum o f t h e l i q u i d a t 519 cm~^ (15) and i n t e r p r e t e d t he p o l a r i z a t i o n p r o p e r t i e s as i n d i c a t i n g the i n t e n s i t y a r o s e m a i n l y from the v q fundamental. The e a s i l y a s s i g n e d v 2 fundamental has been o b s e r v e d i n the Raman spectrum o f the l i q u i d as an asymmetric band a t 211 cm - 1 (15) .and i n the gas a t 205 cm - 1 (47) a l t h o u g h the l a t t e r r e p o r t a g a i n does n o t d e s c r i b e t he bandshape. F u r t h e r , the v£ fundamental has been o b s e r v e d i n an argon m a t r i x a t 208 cm ^ ( 4 8 ) . In T a b l e 3.12 the p o t e n t i a l f u n c t i o n s d e r i v e d i n t h i s work a r e compared w i t h those o f S a v o i e and Tremblay (15) and Oka and Morino ( 1 1 ) . A l s o g i v e n a r e the c a l c u l a t e d and e x p e r i m e n t a l v a l u e s f o r t h e c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s , ground and e x c i t e d s t a t e i n e r t i a l d e f e c t s and v i b r a t i o n a l wavenumbers. The e s t i m a t e d e q u i l i b r i u m wavenumbers ^ were p r e d i c t e d u s i n g e f f e c t i v e microwave d a t a ; t h e s e have been compared d i r e c t l y w i t h the e x p e r i m e n t a l e f f e c t i v e wavenumbers . A l l o f t h e p o t e n t i a l f u n c t i o n s g i v e good p r e d i c t i o n s f o r the v i b r a t i o n a l f u n d a m e n t a l s . Only the microwave-based r e s u l t s , however, a r e c o n s i s t e n t w i t h both the r o t a t i o n a l and v i b r a t i o n a l d a t a . The f o r c e c o n s t a n t s o f S a v o i e and Tremblay ( 1 5 ) , which a r e based on the most comprehensive v i b r a t i o n a l d a t a , p r o v i d e b e t t e r p r e d i c t i o n s f o r the d i s t o r t i o n c o n s t a n t s and i n e r t i a l d e f e c t s than any p r e v i o u s p o t e n t i a l f u n c t i o n ( 8 - 1 5 ) ; even i n t h i s case though, t h e agreement between the c a l c u l a t e d and e x p e r i m e n t a l v a l u e s o f the d i s t o r t i o n c o n s t a n t s and i n e r t i a l d e f e c t s i s poor. The p r e s e n t e s t i m a t e s f o r the p o t e n t i a l c o n s t a n t s a r e c l e a r l y a more r e p r e s e n t a t i v e s e t ; they v a r y from t h o s e p r e v i o u s l y o b t a i n e d i n h a v i n g a l a r g e r v a l u e f o r the s t r e t c h i n g f o r c e c o n s t a n t , F q - j , a s m a l l e r v a l u e f o r the bending c o n s t a n t , F 9 9 , and a p o s i t i v e r a t h e r than n e g a t i v e v a l u e f o r t h e 83 T a b l e 3.12 Summary o f P r e s e n t and P r e v i o u s S u l p h u r D i c h l o r i d e P o t e n t i a l F u n c t i o n s and R e l a t e d E x p e r i m e n t a l Data. C a l c u l a t e d Values F i t 2 F i t 3 F i t 4 F ] 1(mdyn/A) 2.913 2.994 2.986 F ] 2(mdyn/A) 0.0926 0.0913 0.0891 o F 2 2(mdyn/A) 0.2624 0.2611 0.2606 F 3 3(mdyn/A) 2.421 2.479 2.470 x (kHz) aaaa -499.0 -498.5 -498.5 ^ b b b b ( k H z > -8.017 -8.023 -8.050 T (kHz) c c c c v ' -2.582 -2.563 -2.574 <abab< k H z> -6.728 -6.571 -6.595 0.3241 0.3221 0.3231 U 2 3 ) 2 0.6759 0.6779 0.6769 0)^ (cm 1 ) 514.8 -> 521.9 521 .6 u 2 ( c m " 1 ) 206.9 206.5 206.2 a)3(.cm 1 ) 523.8 530.0 529.0 0.3086 0.3081 0.3084 A 2 ( u A 2 ) 0.5220 0.5220 0.5220 A l : ° 1 0 > ( u A 2 > f 0.8306 0.8301 0.8304 84 T a b l e 3.12 Summary o f P r e s e n t and P r e v i o u s S u l p h u r D i c h l o r i d e P o r e n t i a l F u n c t i o n s and R e l a t e d E x p e r i m e n t a l D a t a . ( c o n t i n u e d ) C a l c u l a t e d Values S a v o i e and Oka and E x p e r i m e n t a l Tremblay (15) Morino (11) F^Cmdyn/A) 2.641 2.52 -F 1 2(mdyn/A) -0.029 -0.055 -F 2 2(mdyn/A) 0.303 0.305 -F 3 3(mdyn/A) 2.433 2.52 -^ a a a a ( K H z ) -404 -397 -498.6a ^ b b b b ( K H z > -8.22 -8.52 -8.0263 T - . . (KHz) c c c c -2.88 -3.04 -2.574a W K H Z > -6.69 -6.46 -6.58b ^ 1 3 > 2 0.415 0.440 -U 2 3 ) 2 0.585 0.560 -oi-jCcm 1) 517.1 514 518.0° o ) 2 ( c m - 1 ) 211 208 d e 20 5 ° , 2 i r u 3 ( c m " 1 ) 525.3 535 525.5° A ( ° 0 0 ) ( u A 2 ) f 0.290 0.287 0.3077 f A 2 ( u A 2 ) 0.446 0.427 0.5220 A ( ° 1 0 ) ( u A 2 ) f 0.736 0.714 0.8297 f 85 T a b l e 3.12 Summary o f P r e s e n t and P r e v i o u s S u l p h u r D i c h l o r i d e P o t e n t i a l F u n c t i o n s and R e l a t e d E x p e r i m e n t a l Data ( c o n t i n u e d ) C a l c u l a t e d Values  F i n a l ' P o t e n t i a l C onstants E x p e r i m e n t a l o F 1 1(mdyn/A) 2.949 — F 1 2(mdyn/A) 0.0916 -o F 2 2(mdyn/A) 0.2618 -F 3 3(mdyn/A) 2.439 -T a a a a ( : k H z > -498.6 -498.6a T b b b b ( k H z ) -8.023 -8.0263 W k H z ) -2.575 -2.574a ^ b a b ( k H z > -6.679 -6.58b ^ l / 0.3234 -0.6766 -a)-| ( c m - 1 ) 518.0 518.0° w 2(cm 1 ) 206.7 d e 20 5 ° , 2 i r u> 3(cnf 1) 525.7 525.5 C 4< 0 0 0 »(uA 2 ) 0.3085 0.3077 f i 2 ( " A 2 ) 0.5222 0.5220 S < 0 1 0 >CuA 2 ) f 0.8307 0.8297 f 86 Footnotes t o T a b l e 3.12 a Weighted average o f the t h r e e v a l u e s i n T a b l e 3.7. Weights g i v e n were i n v e r s e l y p r o p o r t i o n a l to the quoted e r r o r s . b Mean o f the F i t 4 v a l u e and the average F i t 2 and F i t 3 v a l u e s o f T a b l e 3.7. T h i s c o n s t a n t i s o n l y p o o r l y d e t e r m i n e d . M a t r i x v a l u e from S a v o i e and Tremblay ( 1 5 ) . Gas phase v a l u e from F r a n k i s s and H a r r i s o n ( 4 7 ) . ' L i q u i d phase v a l u e from S a v o i e and Tremblay ( 1 5 ) . F Values f o r the K i v e l s o n - W i I s o n A',B',C' as g i v e n i n T a b l e 3.7. The e x p e r i m e n t a l v a l u e o f &^010^ i s h i g h e r than A ^ 0 0 0 ^ by 0.5220 uA 2 r e g a r d l e s s o f whether Watson o r K i v e l s o n - W i I s o n c o n s t a n t s a r e used. The Watson v a l u e s o f A ^ 0 0 0 ^ and A ^ 0 1 0 ) a r e 0.3093 uA 2 and 0,8313 uA 2 r e s p e c t i v e l y ( f r o m T a b l e 3.8). 87 i n t e r a c t i o n c o n s t a n t , F ^ -F i n a l l y , the q u e s t i o n a r i s e s as to whether a c o m b i n a t i o n o f microwave and v i b r a t i o n a l data would improve the a c c u r a c y o f the f o r c e c o n s t a n t s . Any meaningful r e f i n e m e n t i s u n l i k e l y s i n c e the d i f f e r e n c e s between the o b s e r v e d and c a l c u l a t e d wavenumbers a r e l e s s than the s h i f t s o b s e r v e d upon a change o f phase from, f o r example, l i q u i d to s o l i d ( 1 5 ) . N e v e r t h e l e s s one notes t h a t the F i t 2 f o r c e c o n s t a n t s p r e d i c t v a l u e s f o r the s t r e t c h i n g fundamentals which a r e s l i g h t l y low when 32 35 compared to the m a t r i x data f o r S C l 2 w h i l e the p r e d i c t i o n s o b t a i n e d from F i t 3 and F i t 4 a r e s l i g h t l y h i g h . A minor adjustment o f the f o r c e c o n s t a n t s g i v e s the r e s u l t s l i s t e d i n T a b l e 3.12,under the h e a d i n g " F i n a l P o t e n t i a l C o n s t a n t s " . T h i s p o t e n t i a l f u n c t i o n i s e s s e n t i a l l y i d e n t i c a l to t h a t which would be o b t a i n e d through the use o f the w e i g h t e d -average v a l u e s f o r the d i s t o r t i o n c o n s t a n t s , as g i v e n i n T a b l e 3.12. No attempt has been made t o reproduce the gas phase v a l u e f o r v 2- I f the measured v a l u e o f 205.(1) cm ^ i s assumed to c o r r e s p o n d to the " c e n t e r o f 32 35 g r a v i t y " o f the v 2 band, however, then the p r e d i c t e d S C l 2 fundamental i s e s t i m a t e d to o c c u r a t 206.2 (10) cm~\ i n good agreement w i t h the p r e d i c t i o n s o f T a b l e 3.12. The a c c u r a c y o f the p r e s e n t p o t e n t i a l f u n c t i o n i s a l s o c o n f i r m e d by the m a t r i x i s o l a t i o n data o f S a v o i e and Tremblay ( 1 5 ) , where the i s o t o p i c s t r u c t u r e o f the s t r e t c h i n g fundamentals v q and was m o s t l y r e s o l v e d . In T a b l e 3.13 the o b s e r v e d i s o t o p e s h i f t s are compared t o those c a l c u l a t e d u s i n g the " F i n a l P o t e n t i a l C o n s t a n t s " o f T a b l e 3.12. The agreement i s a g a i n very good a l t h o u g h the p r e s e n t i n t e r p r e t a t i o n o f the s t r u c t u r e o f the v q band i s somewhat d i f f e r e n t from t h a t g i v e n e a r l i e r . S a v o i e and Tremblay (15) a s s i g n e d a v e r y weak f e a t u r e ~10 cm ^ 88 32 35 away from the S C l 2 peak as b e i n g due t o the symmetric s t r e t c h o f 34 35 the S CT^ s p e c i e s . The microwave r e s u l t s , however, s u g g e s t t h a t the 32 37 34 35 symmetric s t r e t c h i n g fundamentals o f the S C l 2 and S C l 2 s p e c i e s a r e o v e r l a p p e d . I t i s o f some i n t e r e s t to note t h a t f o r the asymmetric s t r e t c h the i s o t o p i c s h i f t s o f the C 2 v s p e c i e s can be used t o e s t i m a t e the C l - S - C l bond a n g l e through the e q u a t i o n (49) where a i s h a l f the C l - S - C l «.3lY =-i s nigi ( f £ ' ± J ^ l * ™ ^ ) (3-16) - + 2m--,sin a ' "3 ' m S m C l X m S + ""ci bond a n g l e . U s i n g the data o f T a b l e 3.13 the e s t i m a t e d bond a n g l e i s 105.2° 32-37,,, . L : j i . i i n j iro - 4.1 34—35, us i n g the S C l 2 s h i f t and 104.5° u s i n g the S C l 2 s h i f t . These e s t i m a t e s agree very w e l l w i t h the microwave v a l u e o f 1 0 2 . 7 ° , because an u n c e r t a i n t y o f even 0.1 cm ^  i n the measured s h i f t s i n t r o d u c e s an e r r o r o f a p p r o x i m a t e l y 2.0° i n the bond a n g l e . In c o n c l u s i o n , i n the p r e s e n t work an improved p o t e n t i a l f u n c t i o n has been d e r i v e d which i s c o n s i s t e n t w i t h a l l o f t h e r e l a t e d e x p e r i m e n t a l data i n c l u d i n g i n e r t i a l d e f e c t s , c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s , v i b r a t i o n a l wavenumbers and i s o t o p i c s h i f t s i n the v i b r a t i o n a l fundamentals. While i t has n o t been p o s s i b l e to demonstrate t h a t f o r the gas phase vg > v-|,both the microwave and m a t r i x i s o l a t i o n data are c o n s i s t e n t . w i t h t h i s c h o i c e . T h i s i s s u e c o u l d be s e t t l e d unambiguously by measuring the microwave spectrum o f t h e v-j = 1 and/or the Vg = 1 e x c i t e d s t a t e s because, as f o r S F 2 ( 5 ) , the i n e r t i a l d e f e c t s would be very s e n s i t i v e to the d i f f e r e n c e W g - ^  . For S F 2 the microwave r e s u l t s showed c o n c l u s i v e l y t h a t Wg > ( 5 ) ; c o r r o b o r a t i o n has been p r o v i d e d by 89 T a b l e 3.13 Observed and C a l c u l a t e d I s o t o p e S h i f t s For the S t r e t c h i n g Fundamentals o f S u l p h u r D i c h l o r i d e . Symmetric S t r e t c h S p e c i e s C a l c u l a t e d V a l u e ! C a l c u l a t e d ; Shi f t Observed S h i f t 3 2 s 3 5 c i 2 518.0 0.0 0.0 3 2 S 3 5 C 1 3 7 C 1 a 513.3 4.7 ' 4.5 3 2 s 3 7 c i 2 511.0 7.0 7.5 3 4 s 3 5 c i 2 510.3 7.7 7.5 Asymmetric S t r e t c h S p e c i e s C a l c u l a t e d Value C a l c u l a t e d S h i f t Observed S h f i t 3 2 s 3 5 c i 2 525.7 0.0 0.0 3 2 S 3 5 C 1 3 7 C 1 a 523.8 1.9 3.2 32 37 J V c i 2 519.6 6.1 6.0 3 4 s 3 5 c i 2 516.8 8.9 9.0 a The r e q u i r e d G m a t r i x elements f o r the S CI CI s p e c i e s (C symmetry) are g i v e n by C a l i f a n o ( 3 3 ) . 90 m a t r i x i s o l a t i o n d a t a f o r "^SFg and J H S F 2 ( 5 0 ) . I n i t i a l i n f r a r e d r e s u l t s f o r s u l p h u r d i b r o m i d e and s u l p h u r d i i o d i d e have been t a k e n t o s u g g e s t , however, t h a t i n both c a s e s v^ > v-j ( 4 8 ) . T h e r e f o r e i t i s h a r d l y s u r p r i s -i n g t h a t Vg and v^ i n S C I 2 a r e n e a r l y d e g e n e r a t e . In f a c t f o r a l l f o u r s u l p h u r d i h a l i d e s t h e two s t r e t c h i n g fundamentals l i e w i t h i n 2% o f t h e i r average v a l u e . 91 3.6 Comments on the M o l e c u l a r S t r u c t u r e o f S u l p h u r D i c h l o r i d e In T a b l e 3.14 the v a r i o u s s u l p h u r - c h l o r i n e bond l e n g t h s d e r i v e d i n t h i s s t u d y a r e compared t o the p r e v i o u s e s t i m a t e s . The microwave r , r o ' r s a n c' r e v a l u e s a r e a " q u i t e s i m i l a r and a r e c l e a r l y more p r e c i s e than the e a r l y e l e c t r o n d i f f r a c t i o n r e s u l t s o f Palmer (18) and o f Stevenson and Beach ( 1 7 ) . A s l i g h t e r r o r i n the e l e c t r o n d i f f r a c t i o n r e s u l t s o f Morino e t ' a l _ . (14) must a l s o be s u s p e c t e d because the r g d i s t a n c e i s e x p e c t e d to exceed the r z o r r g bond l e n g t h ( 5 1 ) . The r Q e s t i m a t e o f t h e S-Cl bond l e n g t h i s i d e n t i c a l t o t h a t g i v e n by Murray e t al_. ( 1 6 ) . A l s o g i v e n i n T a b l e 3.14 a r e the S-Cl bond l e n g t h s d e t e r m i n e d f o r some r e l a t e d m o l e c u l e s . Except f o r S0 2C1F (52) t h e s e d i s t a n c e s a l l have quoted e r r o r s o f l e s s than 0.010 A* and o n l y f o r NSC! (53) i s the o b s e r v e d bond l e n g t h v e r y d i f f e r e n t from the sum o f P a u l i n g ' s s i n g l e o bond r a d i i (2.03 A) ( 6 6 ) . The e s t i m a t e d p r i n c i p a l v a l u e o f the c h l o r i n e 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 t e n s o r , x z z > "is p r e s e n t e d as w e l l f o r each o f t h e s e m o l e c u l e s ; where n e c e s s a r y , x z z has been c a l c u l a t e d by d o u b l i n g the NQR f r e q u e n c y ( 6 7 ) . These numbers s h o u l d be r e g a r d e d w i t h some d e t a c h -ment as the v a r i a t i o n s to a l a r g e e x t e n t r e f l e c t changes i n the h y b r i d i -z a t i o n o f the s u l p h u r atom ( 6 3 ) . N e v e r t h e l e s s , f o r d i v a l e n t s u l p h u r an i n c r e a s e i n the S-Cl bond l e n g t h i s p a r a l l e d by a d e c r e a s e i n the magnitude o f the c o u p l i n g c o n s t a n t x Z 2 - T h i s i s i l l u s t r a t e d by the r e s u l t s f o r S C 1 2 , CHgSCl and S 2 C 1 2 where bond l e n g t h s o f 2.015 A, 2.030 A o and 2.057 A a r e a s s o c i a t e d w i t h x z z v a l u e s o f -91.9 MHz, -78.9 MHz and -71.6 MHz r e s p e c t i v e l y . The f i r s t o f t h e s e v a l u e s i n p a r t i c u l a r i s q u i t e c l o s e to t h a t o f t h e c h l o r i n e atom (109.74 MHz (68)) and p r o v i d e s s t r o n g e v i d e n c e f o r p r i m a r i l y c o v a l e n t s i n g l e bond c h a r a c t e r ( 6 9 ) . 92 T a b l e 3.14 The S-Cl Bond Lengths and x- ( J 0 C 1 ) V a l u e s f o r S u l p h u r D i c h l o r i d e and R e l a t e d M o l e c u l e s M o l e c u l e r ( S - C l ) ( A ) X Z z ( M H z ) a R e f e r e n c e SCI 2 r z 2 . 0 1 5 2 5 ( 8 ) b T h i s work r s 2.0141(10) T h i s work r o 2.014(2) -91.9 T h i s work r e 2.0109(12) T h i s work r o 2.014(5) -89.9 (16) r g 2.006(4) (14) r g 2.00(2) (17) r g 1.99(2) (18) s o 2 c i 2 r g 2.011(4) -75.4 (54, 55) S0 2C1F r o 1.985(15) -74.7(7) (52) s 2 c i 2 r g 2.057(2) -71.6 (56, 57) r s 2.055(1) (58) CHgSCl r s 2.030(1) -78.9(14) (59) SF 5C1 r s 2.0392(2) -85.4 (60) r z 2.045(3) (61) CH 3S0 2C1 r g 2.046(4) -66.5 (62, 63) C 6 H 5 S 0 2 C 1 r g 2.047(8) -66.0 (64, 63) s o c i 2 r g 2.077(6) -64.0 (54,63) NSC1 r s 2.161 -43.4 (53) r g 2.159(3) (65) a P r i n c i p a l v a l u e , p a r a l l e l t o t h e S-Cl bond. b The quoted e r r o r l i m i t s have d i f f e r e n t meanings f o r t h e v a r i o u s m o l e c u l e s . 93 I t i s i n t e r e s t i n g as w e l l t o compare t h e S-Cl bond d i s t a n c e s and t h e r e l a t e d s t r e t c h i n g f o r c e c o n s t a n t s . F o r S C I 2 t h e r e q u i r e d v a l e n c e f o r c e c o n s t a n t i s s i m p l y t he mean o f and F ^ . A g a i n t h e most mean-i n g f u l comparisons i n v o l v e m o l e c u l e s where s u l p h u r e x h i b i t s t he same h y b r i d i z a t i o n . T h e r e a r e s u r p r i s i n g l y few good d a t a a v a i l a b l e f o r t h i s purpose. A l t h o u g h s e v e r a l e s t i m a t e s o f the S-Cl s t r e t c h i n g f o r c e c o n s t a n t s a r e p r e s e n t e d i n T a b l e 3.15 i n a l l c a s e s e x c e p t t he p r e s e n t i t was n e c e s s a r y t o make c o n s t r a i n t s i n e v a l u a t i n g t h e p o t e n t i a l f u n c t i o n . 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S u t h e r s and T. H e n s h a l l , Z. Anorg. A l l g . Chem. 388, 257 (1972). 73. A. M u l l e r , N. Mohan, S.J. C y v i n , N. Weinstock and 0. Glemser, J . Mol. S p e c t r o s c . 59^, 161 (1976). 99 CHAPTER 4 The Microwave Spectrum o f D i c h l o r o s i l a n e A l t h o u g h t h e r e have been many microwave i n v e s t i g a t i o n s o f v a r i o u s halomethanes and h a l o s i l a n e s , t h e s e s t u d i e s have been l i m i t e d m o s t l y t o symmetric top s p e c i e s . Whereas p r i o r to t h i s s t u d y r o t a t i o n a l s p e c t r a had been o b s e r v e d f o r d i f l u o r o m e t h a n e ( 1 ) , d i c h l o r o m e t h a n e (2,3) and dibromomethane (4) the q u 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 con-s t a n t s had been measured o n l y f o r d i f l u o r o m e t h a n e ; even f o r d i f l u o r o -methane, however, the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s were n o t used i n a f o r c e f i e l d r e f i n e m e n t . More s u r p r i s i n g l y , the spectrum o f o n l y one d i h a l o s i l a n e , namely d i f l u o r o s i l a n e , had been s t u d i e d (5) and a g a i n no c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s were d e t e r m i n e d . For t h e s e s i m p l e C^ v m o l e c u l e s the d i s t o r t i o n c o n s t a n t s can be combined w i t h v i b r a t i o n a l d a t a to e v a l u a t e the f o r c e f i e l d w hich, i n t u r n , can be used t o r e f i n e the m o l e c u l a r s t r u c t u r e . The p r e s e n t s t u d y o f d i c h l o r o s i l a n e was undertaken p r i m a r i l y to determine a p r e c i s e m o l e c u l a r s t r u c t u r e , to complement the e a r l i e r work on c h l o r o s i l a n e (6) and t r i c h l o r o s i l a n e (7,8) and, h o p e f u l l y , to p i n p o i n t any s y s t e m a t i c v a r i a t i o n s i n the s t r u c t u r e s o f t h e s e m o l e c u l e s . A l t h o u g h d i c h l o r o s i l a n e has not been p r e v i o u s l y s t u d i e d u s i n g microwave s p e c t r o s c o p y , i t has been the s u b j e c t o f s e v e r a l o t h e r s p e c t r o s c o p i c and s t r u c t u r a l i n v e s t i g a t i o n s . I t s bond l e n g t h s and a n g l e s were d e t e r m i n e d i n an e a r l y e l e c t r o n d i f f r a c t i o n s t u d y ( 9 ) . S e v e r a l s t u d i e s o f i t s v i b r a t i o n a l spectrum have been made (10-12) and 100 t h e s e d a t a have been used to dete r m i n e f o r c e f i e l d s (13-17) f o r the m o l e c u l e . R e c e n t l y t he p h o t o e l e c t r o n spectrum o f d i c h l o r o s i l a n e , a l o n g w i t h t h o s e o f o t h e r h a l o s i l a n e s , has been i n v e s t i g a t e d (18) and used t o p r o v i d e e v i d e n c e f o r (p^d)-rr back bonding t o s i l i c o n . The n u c l e a r q u a d r u p o l e resonance spectrum o f d i c h l o r o s i l a n e i s a l s o known (19) and s u g g e s t s as w e l l t h a t t he bonding i n the halomethanes and h a l o s i l a n e s i s q u i t e d i f f e r e n t . In t he p r e s e n t s t u d y t h r e e i s o t o p i c s p e c i e s o f d i c h l o r o s i l a n e , namely, 2 8 S i H 0 3 5 C l 2 , 2 8 S i H 2 3 5 C l 3 7 C l and 2 9 S i H 2 3 5 C l 2 have been i n v e s t i -g a t e d . The a c c u r a t e v a l u e s o b t a i n e d f o r the r o t a t i o n a l c o n s t a n t s have been used t o d e t e r m i n e e f f e c t i v e and s u b s t i t u t i o n m o l e c u l a r s t r u c t u r e s . V a l u e s have a l s o been o b t a i n e d f o r the c h l o r i n e 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 , the m o l e c u l a r d i p o l e moment and the q u 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 c o n s t a n t s . The d i s t o r t i o n c o n s t a n t s have been combined w i t h e x i s t i n g v i b r a t i o n a l d a t a t o e v a l u a t e the harmonic f o r c e f i e l d and s u b s e q u e n t l y t he average m o l e c u l a r s t r u c t u r e . Because o f the l a r g e r number o f f o r c e c o n s t a n t s and s t r u c t u r a l parameters t h i s p r o c e d u r e was more complex than t h a t o u t l i n e d f o r s u l p h u r d i c h l o r i d e i n C h a p t e r 3. 4.1 Assignment o f the D i c h l o r o s i l a n e Spectrum The r o t a t i o n a l spectrum o f d i c h l o r o s i l a n e was found t o be q u i t e dense w i t h many l i n e s h a v i n g complex h y p e r f i n e s t r u c t u r e . To f a c i l i t a t e the assignment o f the spectrum r i g i d r o t o r t r a n s i t i o n f r e q u e n c i e s were p r e d i c t e d f o r the low J l i n e s u s i n g a model m o l e c u l a r s t r u c t u r e . S p e c i -f i c a l l y , C 2 v symmetry was assumed w i t h s i l i c o n - c h l o r i n e and s i l i c o n -hydrogen bond d i s t a n c e s equated to t h e i r v a l u e s i n c h l o r o s i l a n e ( 6 ) ; a l l bond a n g l e s were assumed to be e q u a l . These c a l c u l a t i o n s i n d i c a t e d t h a t o n l y b^type l i n e s s h o u l d be seen. A p r e d i c t i o n o f the n u c l e a r 101 q u a d r u p o l e h y p e r f i n e s t r u c t u r e was a l s o r e q u i r e d . Indeed, the o b s e r v e d h y p e r f i n e p a t t e r n s e v e n t u a l l y p r o v i d e d the means o f making the a s s i g n -ment. I n i t i a l l y t he s i l i c o n - c h l o r i n e bond was assumed t o be the p r i n c i p a l a x i s o f a symmetric qua d r u p o l e t e n s o r h a v i n g x z z = - 2 x x x = - 2 x V y = 35 -40 MHz f o r C l (the c o r r e s p o n d i n g v a l u e f o r c h l o r o s i l a n e i s -39 .7 MHz 28 35 ( 6 ) ) . T h e r e f o r e u s i n g e q u a t i o n 3.1 one o b t a i n s f o r S i H 2 C l 2 (assuming t e t r a h e d r a l a n g l e s ) the v a l u e s X a a = - x c c = _ 2 0 MHz and xbk,=0 MHz. The hyper-f i n e p a t t e r n s were c a l c u l a t e d u s i n g the Lj + L, = J_, £ + J_ = £ c o u p l i n g 32 35 scheme because, as f o r S C l 2 , s p i n s t a t i s t i c s were i m p o r t a n t . Whereas 32 35 f o r S C l 2 some s p i n w a v e f u n c t i o n s had a s t a t i s t i c a l w e i g h t o f z e r o 28 35 t h i s was not the case f o r S i H 2 C l 2 because o f the p r e s e n c e o f a second p a i r o f e q u i v a l e n t f e r m i o n s , the hydrogen atoms. These gave the even and odd I h y p e r f i n e components s t a t i s t i c a l w e i g h t s o f 1 and 3 r e s p e c t i v e l y f o r K K =ee«->oo t r a n s i t i o n s and the r e v e r s e f o r K K'=eo^oe a c a c t r a n s i t i o n s . The same s i t u a t i o n has been o b s e r v e d i n methylene c h l o r i d e ( 2 ) . The model spectrum i n d i c a t e d t h a t the h y p e r f i n e p a t t e r n s o f the low J t r a n s i t i o n s o f the s e r i e s 0-j j j s h o u l d be e s p e c i a l l y complex and i r r e g u l a r . In a c a r e f u l e x a m i n a t i o n o f the 14-18 GHz r e g i o n t h r e e t r a n s i t i o n s were found whose h y p e r f i n e p a t t e r n s a l m o s t e x a c t l y matched t h o s e c a l c u l a t e d f o r the J=5,6 and 7 members o f t h i s s e r i e s ; t h e s e 29 30 37 t r a n s i t i o n s were too s t r o n g t o belong t o a symmetric S i , S i o r Cl s p e c i e s . As w e l l , near 16 GHz a s e r i e s o f u n s p l i t l i n e s w i t h s i n g l e h i g h f r e q u e n c y S t a r k components were found. The s t r o n g e s t o f t h e s e 28 35 l i n e s was a s s i g n e d as the l i n e o f the S i H 2 C l 2 s p e c i e s . 28 35 A s s i g n i n g the Q-branch l i n e s as w e l l t o the S i H 2 C l 2 s p e c i e s e n a b l e d a r i g i d r o t o r f i t to be made which a c c u r a t e l y p r e d i c t e d the p o s i t i o n s o f 102 many o t h e r t r a n s i t i o n s w i t h J<10; i n a l l ca s e s t he o b s e r v e d h y p e r f i n e s t r u c t u r e was c o n s i s t e n t w i t h the p r e d i c t e d s p l i t t i n g s . A s u f f i c i e n t number o f t h e s e low J t r a n s i t i o n s were measured to beg i n the usual b o o t s t r a p c e n t r i f u g a l d i s t o r t i o n a n a l y s i s which r e s u l t e d i n s u c c e s s i v e l y 28 35 h i g h e r J l i n e s b e i n g a s s i g n e d . F or S i H 2 CI,, t r a n s i t i o n s h a v i n g a maximum J v a l u e o f 34 were measured a l t h o u g h h i g h e r J l i n e s were seen. 28 35 Having made the assignment f o r S i H 2 C l 2 (46.6% f r a c t i o n a l abundance) the l i n e s o f a d d i t i o n a l i s o t o p i c s p e c i e s were sought. The 28 35 37 S i H 2 CI CI s p e c i e s (30.4% f r a c t i o n a l abundance) was s t u d i e d f i r s t and i t s l i n e s were e a s i l y i d e n t i f i e d ; because the two c h l o r i n e n u c l e i were now n o t e q u i v a l e n t s l i g h t l y more complex h y p e r f i n e p a t t e r n s were o b s e r v e d . T r a n s i t i o n s h a v i n g a maximum J v a l u e o f 29 were measured 28 35 37 f o r S i H 2 CI C I . U s i n g t h i s i s o t o p i c d a t a the m o l e c u l a r s t r u c t u r e was r e f i n e d and l i n e s o f the S i H 2 C l 2 s p e c i e s (2.37% f r a c t i o n a l abundance) were s e a r c h e d f o r . A g a i n t h e s e were q u i c k l y l o c a t e d ; t he assignment was c o n f i r m e d by the r e l a t i v e i n t e n s i t i e s o f the t r a n s i t i o n s compared t o thos e o f S i H 2 C l 2 , t h e h y p e r f i n e s p l i t t i n g s , s p i n s t a t i s t i c s and the S t a r k e f f e c t o f the l-|-|"«-0oo l i n e . Only e i g h t 29 35 t r a n s i t i o n s w i t h a maximum J v a l u e o f 17 were measured f o r S i H 2 CI.,. 28 37 T r a n s i t i o n s f o r f u r t h e r i s o t o p i c s p e c i e s , s p e c i f i c a l l y S i H 2 C l 2 and 30 35 S i H 2 C l 2 , were o b s e r v e d . These were n o t measured, however, because th e y p r o v i d e d no a d d i t i o n a l i n f o r m a t i o n . No attempt was made t o a s s i g n e x c i t e d s t a t e l i n e s . 4-2 A n a l y s i s o f the D i c h l o r o s i 1 a h e Spectrum a. N u c l e a r Quadrupole C o u p l i n g 28 35 In an i n i t i a l a n a l y s i s o f the S i H 2 C l ^ d a t a the h y p o t h e t i c a l u n s p l i t l i n e f r e q u e n c i e s o f the v a r i o u s t r a n s i t i o n s were c a l c u l a t e d 103 u s i n g the model 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 the p r e v i o u s s e c t i o n . A c e n t r i f u g a l d i s t o r t i o n a n a l y s i s then y i e l d e d p r e l i m i n a r y v a l u e s f o r the r o t a t i o n a l c o n s t a n t s and c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s . The model c o u p l i n g c o n s t a n t s , however, d i d n o t p r e c i s e l y p r e d i c t the o b s e r v e d h y p e r f i n e s t r u c t u r e . For t h e 6-j5"*~^06 t r a n s i t 1 0 n > f o r example, the r e l a t i v e s p a c i n g o f the h y p e r f i n e components was al m o s t p e r f e c t l y p r e d i c t e d but t h e a b s o l u t e s p l i t t i n g s were about f i v e per c e n t s m a l l e r than the o b s e r v e d s p l i t t i n g s . 35 P r e c i s e v a l u e s f o r the CI 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 con-P R 35 s t a n t s o f S i H 2 C l 2 were o b t a i n e d by comparison o f the o b s e r v e d h y p e r f i n e p a t t e r n s w i t h t h o s e o b t a i n e d from a s e r i e s o f guessed v a l u e s . T h i s was done by d i a g o n a l i z i n g the c o u p l i n g H a m i l t o n i a n f o r two quad-r u p o l a r n u c l e i as d e s c r i b e d i n s e c t i o n 1.2 o f Cha p t e r 1; the r o t a t i o n a l c o n s t a n t s used f o r t h i s purpose were the v a l u e s o b t a i n e d from the p r e l i m i n a r y r o t a t i o n a l a n a l y s i s . To ac c o u n t f o r t h e s p i n s t a t i s t i c s t h e c o u p l i n g scheme L| + = J_, J_ + J_ = IF had t o be used. In d e t e r -m i n i n g the v a l u e s o f the c o u p l i n g c o n s t a n t s , however, t h i s was used i n t e r c h a n g e a b l y w i t h the Lj + J_ = £ p F^ + L, = F_ scheme because o n l y t h o s e o b s e r v e d f r e q u e n c i e s which c o r r e s p o n d e d t o i s o l a t e d h y p e r f i n e components were used f o r comparison p u r p o s e s ; thus o n l y the e i g e n v a l u e s o f the q u a d r u p o l a r H a m i l t o n i a n were needed. In a more s o p h i s t i c a t e d a n a l y s i s one might attempt t o make use o f the d a t a c o n t a i n e d i n the p a r t i a l l y r e s o l v e d p o r t i o n s o f the a b s o r p t i o n l i n e s ; t h i s would n e c e s s i t a t e a l i n e s h a p e s i m u l a t i o n , i n which c a s e the s t a t i s t i c a l w e i g h t s o f the v a r i o u s components would have t o be acc o u n t e d f o r . The b e s t v a l u e s o f the c o u p l i n g c o n s t a n t s o b t a i n e d by v a r y i n g x a a and n(=(xkib-xcc)/xaa) t 0 r e p r o d u c e the h y p e r f i n e s t r u c t u r e o f the po OC S i H ? C l ? s p e c i e s a r e g i v e n i n T a b l e 4.1; the e r r o r l i m i t s r e p r e s e n t 104 T a b l e 4.1 C h l o r i n e 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 (MHz) o f D i c h l o r o s i l a n e 2 8 S i H 2 3 5 C l 2 x - 2 1 . 1 3 ( 3 5 ) a ad X b b - x c c -20.88(30) 2 8 S i H 2 3 5 C l 3 7 C l X a a ( 3 5 C l ) -20.70 b X a a ( 3 7 C D -16.99 b a E s t i m a t e d o u t s i d e e r r o r l i m i t s . . pp or O b t a i n e d by t r a n s f o r m i n g t he S i H ? C l ? v a l u e s t o t h e pp OK 0 7 S i H , C l C l p r i n c i p a l i n e r t i a l axes system and u s i n g x z z ( 3 ^ C l ) = 1.2688 X Z Z ( 3 7 C 1 ) . 105 e s t i m a t e d o u t s i d e l i m i t s o f e r r o r . Some r e p r e s e n t a t i v e o b s e r v e d pp or t r a n s i t i o n s f o r S i H 2 C l 2 > a l o n g w i t h t h e i r assignments and the s p l i t t i n g s c a l c u l a t e d u s i n g the d e r i v e d 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 , a r e g i v e n i n T a b l e 4.2. One o f t h e s e , the 615-<-606 t r a n s i t i o n , i s a l s o shown i n F i g u r e 4.1 a l o n g w i t h the c a l c u l a t e d h y p e r f i n e p a t t e r n . 29 35 To a n a l y s e t he d a t a f o r S i H 2 C l 2 the c o u p l i n g c o n s t a n t s 29 35 d e r i v e d above were used; the h y p e r f i n e s p l i t t i n g s f o r S i H 2 C l 2 and 28 35 S i H 2 C l 2 were s l i g h t l y d i f f e r e n t , however, because the r o t a t i o n a l pp or 07 c o n s t a n t s a r e i s o t o p i c a l l y dependent. For S i H 2 C l C l , a f t e r e s t i m a t i n g t h e r o t a t i o n o f the m o l e c u l e i n the p r i n c i p a l i n e r t i a l a x i s system consequent on i s o t o p i c s u b s t i t u t i o n , the c o u p l i n g c o n s t a n t s o f 2 8 S i H 2 3 5 C l 2 were t r a n s f o r m e d t o the 2 8 S i H 2 3 5 C l 3 7 C l i n e r t i a l a x i s 37 system. I t was assumed t h a t i n the bond a x i s system t he Cl c o u p l i n g 35 c o n s t a n t s c o u l d be o b t a i n e d by d i v i d i n g the Cl v a l u e s by 1.2688 ( t h e 35 37 r a t i o o f the quad r u p o l e moments o f Cl and Cl ( 2 0 ) ) . T h i s c a l c u l a t i o n 35 gave x, =-20.70 MHz and n=1.029 f o r the 3C1 n u c l e u s and X a =-16.99 MHz aa aa 37 and n=0.948 f o r t h e Cl n u c l e u s . The h y p e r f i n e p a t t e r n s o b s e r v e d f o r 28 35 37 the S i H 2 Cl Cl s p e c i e s were a c c u r a t e l y p r e d i c t e d u s i n g t h e s e v a l u e s f o r t h e c o u p l i n g c o n s t a n t s , b. R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s A f t e r t h e h y p e r f i n e s t r u c t u r e was acco u n t e d f o r i t was s u b t r a c t e d from each r o t a t i o n a l t r a n s i t i o n . The r e s u l t i n g u n s p l i t l i n e f r e q u e n c i e s were used t o c a l c u l a t e t he r o t a t i o n a l c o n s t a n t s and q u 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 c o n s t a n t s . The A r e d u c t i o n o f Watson's H a m i l t o n i a n i n t h e I r r e p r e s e n t a t i o n , e q u a t i o n 1.11, was a g a i n used. No s e x t i c d i s t o r t i o n c o n s t a n t s were r e q u i r e d t o f i t t he d a t a f o r e i t h e r 2 8 S i H 2 3 5 C l 2 o r 2 8 S i H 2 3 5 C l 3 7 C l . The d a t a s e t o b t a i n e d f o r 2 9 S i H 2 3 5 C l 2 was too l i m i t e d 106 T a b l e 4.2 Some R e p r e s e n t a t i v e T r a n s i t i o n s (MHz) o f " s i H g CI showing N u c l e a r Quadrupole H y p e r f i n e S t r u c t u r e I a F a C a l c u l a t e d O b s e r v e d 0  Frequency Frequency 6(1,5) - 6(0,6) 3 C 3 15706.64 15706.67 0 6 15707.57 15707.57 1 6 15707.57 15707.57 3 9 15708.31 15708.29 3 4 15709.22 15709.16 3 5 15710.73 15710.97 1 7 15710.98 15710.97 2 8 15711.15 15710.97 2 7 15711.15 15710.97 2 5 15711.15 15710.97 2 4 15711.15 15710.97 3 8 15712.57 15712.60 1 5 15713.90 15714.17 3 6 15714.22 15714.17 2 6 15714.73 15714.17 3 7 15715.32 15715.31 1,6) - 7 ( 0 , 7 ) 3 4 17200.83 -0 7 17201.64 17201.63 1 7 17201.64 17201.63 3 10 17202.30 17202.31 3 5 17204.67 17205.26 3 6 17204.98 17205.26 1 8 17205.14 17205.26 2 9 17205.28 17205.26 2 8 17205.28 17205.26 2 6 17205.28 17205.26 2 5 17205.28 17205.26 3 9 17206.56 17206.56 1 6 17208.17 17208.94 3 7 17208.53 17208.94 2 7 17208.93 17208.94 3 8 17209.48 17208.94 107 Table 4.2 (continued) a The I and F labels are the same for both rotational levels. b Repeated frequencies indicate unresolved hyperfine structure. 0 Strictly, I is not a good quantum number; i t can , however, be used to specify the symmetries of the various hyperfine levels. 108 ' ^ iH 2 3 5 Cl 2 6i 5-~ 6o6 R e c o r d e r t r a c i n g C a l c u l a t e d p a t t e r n 3 MHz-15711.16 MHz ( u n s p l i t l i n e f r e q u e n c y ) F i g u r e 4.1 An Example o f N u c l e a r Quadrupole H y p e r f i n e S t r u c t u r e i n the Spectrum o f D i c h l o r o s i l a n e 109 / t o e n a b l e t h e q u 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 c o n s t a n t s t o be d e t e r m i n e d . 29 35 For S i H 2 C l 2 > t h e r e f o r e , two approaches were t r i e d . In an i n i t i a l r e f i n e m e n t , F i t 1, the d i s t o r t i o n on each t r a n s i t i o n was assumed t o be 28 the same as f o r S i H 2 C l 2 and was s u b t r a c t e d from t he measured f r e q u e n c i e s ; t he r e s u l t i n g f r e q u e n c i e s were then f i t t o the t h r e e r o t a t i o n a l c o n s t a n t s . In a subsequent a n a l y s i s , F i t 2, t h e q u a r t i c 29 35 c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s o f S i H 2 C l 2 were c o n s t r a i n e d t o v a l u e s c a l c u l a t e d u s i n g the harmonic f o r c e f i e l d o f T a b l e 4.12. Both o f t h e s e r e f i n e m e n t s gave v e r y s i m i l a r v a l u e s f o r the r o t a t i o n a l c o n s t a n t s a l t h o u g h t he s t a n d a r d d e v i a t i o n o f the f i t was s m a l l e r f o r F i t 2. A summary o f the t r a n s i t i o n s measured f o r 2 8 S i H 2 3 5 C l 2 , 2 8 S i H 2 3 5 C l 3 7 C l and S i H 2 C l 2 , w i t h h y p e r f i n e s t r u c t u r e removed, i s g i v e n i n T a b l e 4.3. The r o t a t i o n a l c o n s t a n t s and q u 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 c o n s t a n t s c a l c u l a t e d u s i n g t h i s d a t a a r e g i v e n i n T a b l e 4.4. 110 T a b l e 4.3 Observed R o t a t i o n a l T r a n s i t i o n s (MHz) o f D i c h l o r o s i l a n e T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n 2 8 S i H 0 3 5 C l 2 : '1,1 - °0,0 16367.54 -0.11 0.03 22,1 " 21,2 35705.26 -1.88 -0.04 31,2 " 3 12787.20 -0.03 -0.01 32,1 " 31,2 34213.14 -1.51 -0.00 42,2 " 4 1 , 3 33615.07 -1.08 -0.06 4 1 , 4 " 3 J 0 , 3 29269.93 0.06 0.04 51,4 " 50,5 14494.45 -0.04 -0.01 52,4 " 5 1,5 37780.27 -1.06 0.01 50,5 " 4 1,4 13763.52 -0.77 0.02 5 1 , 5 " 4 0 , 4 33266.36 0.12 0.01 5 1 , 4 " 42,3 -8654.58 0.56 0.04 6 1 , 5 " 6 0 , 6 15711.15 -0.19 -0.02 6 2 , 5 " 6 1 , 6 38826.71 -0.75 0.01 6 1 , 6 " 50,5 37140.59 0.16 0.01 7 1 , 6 " 70,7 17205.28 -0.51 0.04 7 2 , 5 : 7 1 , 6 31449.25 0.91 -0.06 8 2 , 6 " 8 1 , 7 30753.37 1,71 -0.00 8 0 , 8 " 71,7 30170.15 -2.99 0.02 92,7 " 91,8 30154.89 2.47 -0.04 9 0 , 9 " 8 1 , 8 35644.41 -4.04 0.05 Ill T a b l e 4 .3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n 2 8 S i H 2 3 5 C l 2 : 1 0 2 , 8 " ' 1 0 1 , 9 29705.41 3.09 -0.01 " l . l O " " 0 . 1 1 26424.00 -5 .54 0.00 "2.9-• " i . i o 29453.38 3.43 - 0 . 0 3 " l . l O " 1 0 2 , 9 28014.83 -11 .62 0.06 1 2 i , n " 1 2 0 , 1 2 29596.24 - 8 . 2 3 -0 .04 1 2 2 , 1 0 " 1 2 1 , 1 1 29443.01 3.36 0.02 1 3 1 , 1 2 " 1 3 0 , 1 3 33101.16 -11 .64 -0 .04 13 " 1 3 1 , 1 2 29713.18 2.68 0.02 1 4 2 , 1 2 " 1 4 1 , 1 3 30297.99 1.22 0.03 1 4 2 , 1 2 " 1 3 3 , 1 1 16682.58 -24 .19 . 0.08 1 4 3 , 1 2 " 1 3 4 , 9 -14378.03 -2.24 0.05 1 4 3 , 1 1 " 1 3 4 , 1 0 -13158.87 - 5 .19 0.05 1 5 2 , 1 3 " 1 5 1 , 1 4 31227.00 -1 .27 0.01 1 6 2 , 1 4 " 1 6 1 , 1 5 32525.80 -5 .00 0.03 1 6 2 , 1 5 " 1 5 3 , 1 2 11425.18 - 9 . 9 3 0.03 1 7 2 , 1 5 " 1 7 1 , 1 6 34215.43 -10 .23 ••: 0.02 1 7 2 , 1 5 " 1 6 3 , 1 4 37379.40 -51 .44 0.03 1 8 2 , 1 6 " 1 8 1 , 1 7 36311.53 -17 .15 - 0 . 0 3 1 8 4 , 1 5 " 1 7 5 , 1 2 -17999.50 -7.11 0.02 1 8 4 , 1 4 " 1 7 5 , 1 3 -17643.17 - 9 .02 0.01 112 T a b l e 4.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n 2 8 S i H 2 3 5 C l 2 : 1 9 2 , 1 7 - 1 9 1 , 1 8 38822.66 -26.02 0.01 1 9 3 , 1 6 - 1 8 4 , 1 5 15781.69 -56.55 0.02 1 9 4 , 1 6 - 1 8 5 , 1 3 -13015.99 -16.34 0.02 1 9 4 , 1 5 - 1 8 5 , 1 4 -12473.76 -19.53 -0.02 2 0 3 , 1 8 - 1 9 4 , 1 5 13432.88 -35.42 -0.01 2 1 3 , 1 9 - 2 0 4 , 1 6 17632.81 -39.97 -0.00 2 1 3 , 1 8 - 2 0 4 , 1 7 29008.99 -91.27 -0.01 2 1 5 , 1 6 - 2 0 6 , 1 5 -26846.69 -1.82 0.01 2 2 3 , 1 9 - 2 1 4 , 1 8 36023.77 -112.23 -0.07 2 3 5 , 1 9 - 2 2 6 , 1 6 -16873.55 -28.56 -0.04 2 4 3 , 2 2 - 2 3 4 , 1 9 28781.05 -44.05 -0.03 2 4 4 , 2 1 - 2 3 5 , 1 8 11837.58 -72.12 0.01 2 4 5 , 2 0 - 2 3 6 , 1 7 -11823.35 -43.86 -0.06 2 4 5 , 1 9 - 2 3 6 , 1 8 -11599.51 -46.46 -0.02 2 4 6 , 1 9 - 2 3 7 , 1 6 -35886.15 11.36 -0.03 25 " 4 , 2 2 - 2 4 5 , 1 9 16713.56 -84.21 -0.05 2 5 6 , 2 0 - 2 4 7 , 1 7 -30897.89 -5.90 0.04 2 5 6 , 1 9 - 2 4 7 , 1 8 -30882.65 -6.13 -0.01 2 6 1 , 2 6 - 2 5 2 , 2 3 -30404.24 157.07 -0.00 2 8 5 , 2 3 - 2 7 6 , 2 2 9555.52 -131.34 -0.07 113 T a b l e 4.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n __S_i_H 2__C_12 L 2 8 6 , 2 3 " 2 7 7 , 2 0 -15801.15 -65.70 -0.03 2 8 6 , 2 2 " 2 77,21 -15742.85 -66.81' -0.05 2 9 5 , 2 4 " 2 8 6 , 2 3 15071.88 -159.23 -0.05 2 9 6 , 2 4 " 2 8 7 , 2 1 -10721.06 -88.50 -0.02 2 9 6 , 2 3 " 2 8 7 , 2 2 -10633.01 -90.29 -0.03 33 - 32 J J 6 , 2 8 ^ 7 , 2 5 9851.46 -195.21 0.03 3 3 7 , 2 7 " 3 2 8 , 2 4 -14760.28 -122.39 0.02 3 3 7 , 2 6 " 3 2 8 , 2 5 -14738.05 -123.08 0.01 34 - 33 J^6,29 -"7,26 15054.40 -225.78 0.03 34 - 33 ^ 6 , 2 8 J J 7 , 2 7 15612.68 -241.05 0.05 34 - 33 ^ 7 , 2 8 ""8,25 -9668.23 -154.08 0.04 34 - 33 ^ 7 , 2 7 J J 8 , 2 6 -9634.73 -155.18 0.04 2 8 S i H „ 3 5 C l 3 7 C l : ^ , 1 " °0,0 16212.28 -0.11 0.05 22,1 " 21,2 35567.21 -1.85 0.03 4 1 , 3 " 40,4 13409.58 -0.00 -0.01 5 0 , 5 " 41,4 13130.49 -0.72 00.04 6 1 , 5 ~ 6 0 , 6 15488.80 -0.15 -0.04 71,6 " 70,7 16909.15 -0.45 0.03 114 T a b l e 4.3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n 2 8 S i H 2 3 5 C 1 3 7 C 1 : 7 2 . 5 " 7 1 , 6 31454.12 0.86 -0.02 92,7 " 91,8 30159.00 2.42 0.04 9 2 , 7 " 8 3 , 6 -14665.44 0.88 -0.04 1 0 2 , 8 " " 1 0 1 , 9 29687.33 3.08 -0.03 1 0 2 , 9 " ' 93,6 -12496.89 0.45 0.05 " 2 . 9 - • " i . i o 29395.50 3.49 -0.02 1 2 2 , 1 0 " 1 2 1 , 1 1 29325.82 3.53 -0.00 1 3 2 , 1 1 " 1 3 1 , 1 2 29516.01 3.02 0.00 1 4 2 , 1 2 " 1 4 1 , 1 3 29999.17 1.78 0.02 1 4 3 , 1 2 " 1 3 4 , 9 -15855.35 -1.67 0.03 1 6 2 , 1 4 " 1 6 1 , 1 5 31956.06 -3.76 -0.02 1 7 2 , 1 5 " 1 7 1 , 1 6 33476.11 -8.52 -0.00 1 7 2 , 1 6 " 1 6 3 , 1 3 13058.87 -9.86 -0.03 1 8 2 , 1 6 " 1 8 1 , 1 7 35380.84 -14.89 0.02 1 9 3 , 1 6 " 1 8 4 , 1 5 13095.86 -52.51 -0.03 1 9 4 , 1 6 " 1 8 5 , 1 3 -15101.44 -14.54 0.05 1 9 4 , 1 5 " 1 8 5 , 1 4 -14639.54 -17.19 0.02 2 0 3 , 1 8 " 1 9 4 , 1 5 11406.02 -34.45 -0.00 2 4 4 , 2 1 " 2 3 5 , 1 8 9137.21 -68.73 -0.02 2 4 4 , 2 0 " 2 3 5 , 1 9 11889.25 -92.57 -0.02 115 T a b l e 4 .3 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n 2 8 S i H 2 3 5 C l 3 7 C l : 2 4 5 , 2 0 " 2 3 6 , 1 7 -14507.72 -39 .79 -0 .04 2 4 5 , 1 9 " 2 3 6 , 1 8 -14324.44 -41 .88 -0.01 25 - 24 " 5 , 2 0 ^ 6 , 1 9 -9305.05 -58 .90 - 0 . 02 2 9 2 , 2 8 " 2 8 3 , 2 5 9246.21 200.75 0.00 2 9 5 , 2 5 " 2 8 6 , 2 2 10307.50 -129.18 0.02 2 9 5 , 2 4 " 2 8 6 , 2 3 11444.95 -147.55 0.03 2 9 S i H 0 3 5 C l 2 :° ^ l " °o ,o 16114.23 -0.11 0.18 5 1 , 5 " 4 0 , 4 32947.58 0.12 -0 .04 1 0 2 , 8 " 1 0 1 , 9 29016.89 3.09 -0 .04 ] 1 2 , 9 " ] 1 1 , 1 0 28814.00 3.43 -0 .06 1 2 2 , 1 0 " 1 2 1 , 1 1 28866.79 3.36 0.01 1 3 2 , 1 1 " 1 3 1 , 1 2 29214.36 2.68 0.04 1 5 2 , 1 3 " 1 5 1 , 1 4 30925.93 -1 .27 0.04 1 7 2 , 1 5 " 1 7 1 , 1 6 34167.56 -10 .23 - 0 . 0 3 116 T a b l e 4.3 ( c o n t i n u e d ) a The " o b s e r v e d " f r e q u e n c i e s g i v e n i n t h i s T a b l e a r e t h e h y p o t h e t i c a l u n s p l i t l i n e f r e q u e n c i e s . The h y p e r f i n e s t r u c t u r e o f the measured t r a n s i t i o n s was s u b t r a c t e d u s i n g t he 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 T a b l e 4.1. b 29 35 For t he S i H 2 s p e c i e s the d i s t o r t i o n c o r r e c t i o n s were assumed 28 35 t o be equal t o tho s e o f the S i H 2 s p e c i e s . The d e v i a t i o n s from the o b s e r v e d f r e q u e n c i e s were c a l c u l a t e d u s i n g the F i t 1 c o n s t a n t s o f T a b l e 4.4. 117 T a b l e 4.4 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f D i c h l o r o s i l a n e 2 8 S i H 2 3 5 C l 2 2 8 S i H 2 3 5 C l 3 7 C 1 A(MHz) B(MHz) C(MHz) A j ( k H z ) A J K ( k H z ) A K ( k H z ) 6 j ( k H z ) 6 K ( k H z ) S t d . D e v i a t i o n o f F i t (MHz) 14135.0061(41) a 2573.58084(80) 2232.61326(80) 1.0223(18) -15.464(27) 142.107(54) 0.24100(20) 3.117(16) 0.036 14034.3404(73) 2504.4799(16) 2177.9966(13) 0.9691(29) -14.912(43) 139.46(11) 0.23335(35) 2.490(59) 0.033 No. o f T r a n s i t i o n s 72 32 118 T a b l e 4.4 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f D i c h l o r o s i l a n e 29 35 " S 1 H 2 J C l 2 F i t 1 F i t 2 A(MHz) 13887.8035(182) 13887.9255(94) B(MHz) 2573.6076(97) 2573.6278(50) C(MHz) 2226.3566(93) 2226.3496(48) A j ( k H z ) b 1.016 C A J K ( k H z ) b -15.02 A K ( k H z ) b 138.7 6j ( k H z ) b 0.2470 c c c c 6 K ( k H z ) b 2.895 S t d . D e v i a t i o n 0.092 0.048 o f F i t (MHz) No. o f T r a n s i t i o n s 8 8 E r r o r s c i t e d a r e s t a n d a r d e r r o r s C e n t r i f u g a l d i s t o r t i o n c o r r e c t i o n s assumed t o be equal t o pp oc t h o s e o f the S i H 2 C l 2 s p e c i e s . These c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s have been c a l c u l a t e d from the f o r c e f i e l d g i v e n i n T a b l e 4.12. 119 4.3 The D i p o l e Moment o f D i c h l o r o s i l a n e 28 35 The e l e c t r i c d i p o l e moment o f S i H 2 C l 2 , because o f the m o l e c u l a r symmetry, c o i n c i d e s w i t h t h e b _ - p r i n c i p a l i n e r t i a l a x i s . Thus the d i p o l e moment can be det e r m i n e d by measuring S t a r k s h i f t s f o r j u s t one S t a r k component. The S t a r k e f f e c t on the l ^ O ^ t r a n -po o c s i t i o n o f S i H 2 C l 2 was used t o measure the d i p o l e moment because both the z e r o - f i e l d and S t a r k - s h i f t e d l i n e s showed no e v i d e n c e o f h y p e r f i n e s t r u c t u r e . As w e l l , t h e S t a r k e f f e c t o f t h i s t r a n s i t i o n , though s e c o n d - o r d e r , was m o d e r a t e l y f a s t . The f r e q u e n c y o f the S t a r k component was measured up t o f i e l d s o f about 1000 V cm" 1 i n t h e c e l l . U n f o r t u n a t e l y t he p r e c i s i o n o f t h e f r e q u e n c y measurements was g r e a t l y degraded by i n t e r m i t t e n t s h o r t i n g i n the S t a r k c e l l which caused d r i f t i n g i n the p o s i t i o n o f the S t a r k l o b e ; i t was not p o s s i b l e t o r e p e a t t h e s e measurements l a t e r . In a d d i t i o n the s h o r t i n g made i t i m p o s s i b l e t o o b t a i n t he h i g h f i e l d s n e c e s s a r y t o c a l i b r a t e t he c e l l . However, the c e l l had been p r e v i o u s l y c a l i b r a t e d i n a d i p o l e moment measurement f o r p r o p i o l y l c h l o r i d e ( s e e s e c t i o n 5.4 o f C h a p t e r 5 ) ; the e l e c t r o d e s p a c i n g o f 0.4689(4) cm det e r m i n e d i n t h a t e x p e r i m e n t was used h e r e . The c a l i b r a t i o n p r o c e d u r e i s d i s c u s s e d i n d e t a i l i n C h a p t e r 5 a l o n g w i t h t h e d e t e r m i n a t i o n o f t h e a p p l i e d e l e c t r i c f i e l d from the s i m u l t a n e o u s l y impressed DC and m o d u l a t i o n v o l t a g e s . Here i t i s noted o n l y t h a t a m o d u l a t i o n v o l t a g e , 2V^ C, o f 30 v o l t s was used 28 35 th r o u g h o u t . The o b s e r v e d S i H 2 C l 2 f r e q u e n c i e s a r e g i v e n t o g e t h e r w i t h the square o f the a p p l i e d S t a r k v o l t a g e s i n T a b l e 4.5; t h i s T a b l e a l s o c o n t a i n s t he r e s i d u a l s from a l i n e a r l e a s t squares a n a l y s i s o f t h e d a t a . The r e s u l t s o f T a b l e 4.5 show t h a t t h e S t a r k e f f e c t f o r the 120 1-jl 0 g 0 t r a n s i t i o n o f ^SiH^CI^ i s second o r d e r . The second o r d e r e x p r e s s i o n f o r the S t a r k energy has been found u s i n g e q u a t i o n 1.28 t o be A v ( l i r M = 0 +• 0 Q 0 >M=0) = 1.8229 x 1 0 ~ 5 y 2 E 2 (4.1) where Av i s the f r e q u e n c y s h i f t and E i s the e l e c t r i c f i e l d i n V c m - 1 . L i n e a r l e a s t s q u a r e s a n a l y s i s o f t h e S t a r k d a t a gave the r e s u l t s p r e s e n t e d i n T a b l e 4.6. The s l o p e A v/V 2 = 1.056(12) x 1 0 " 4 MHz V o l t " 2 p _c has been c o n v e r t e d t o the r e q u i r e d hv/E v a l u e o f 2.322(26) x 10 MHz -2 -2 V o l t cm u s i n g the e l e c t r o d e s p a c i n g o f 0.4689(4) cm. T h i s g i v e s 2 ? f o r y b and y k r e s p e c t i v e l y v a l u e s o f 1.274(15) D and 1.129(7) D. The v a l u e f i n a l l y adopted f o r y ^ i s 1.129(20) D where t h e e r r o r , c o r r e s -ponding t o t h r e e s t a n d a r d e r r o r s , has been i n c r e a s e d s u b j e c t i v e l y t o r e f l e c t p o s s i b l e s y s t e m a t i c e r r o r s i n the d e t e r m i n a t i o n . T h i s v a l u e f o r t h e d i p o l e moment ag r e e s e x t r e m e l y w e l l w i t h t he p r e v i o u s v a l u e o f 1.173 D, o b t a i n e d u s i n g d i e l e c t r i c measurements ( 9 ) . 121 pp gc T a b l e 4.5 S t a r k S h i f t s i n D i c h l o r o s i l a n e : S i H 2 C l 2 T r a n s i t i o n 1 ^ , M=0<-0 , M=0 1 0 ~ 2 x V 2 Observed F r e q u e n c y 9 0 b s . - C a l c . b 0.00 16367.54 -0.23 27.25 16367.86 -0.20 102.25 16368.75 -0.11 227.25 16370.15 -0.02 402.25 16372.16 0.13 508.50 16373.08 -0.07 627.25 16374.67 0.27 758.50 16375.75 -0.04 902.25 16377.70 0.39 1058.50 16378.84 -0.12 1227.25 16381.16 0.42 1408.50 16382.38 -0.27 122 T a b l e 4.5 S t a r k S h i f t s i n D i c h l o r o s i l a n e : S i H 2 C l 2 10 x V Observed Frequency O b s . - C a l c . 1602.25 16385.18 0.48 1808.50 16386.47 -0.41 2027.25 16389.62 0.43 2164.50 16390.00 -0.63 a Given i n MHz. b C a l c u l a t e d f r e q u e n c i e s a r e o b t a i n e d u s i n g t he c o n s t a n t s o f T a b l e 4.6. 123 T a b l e 4.6 S t a r k C o e f f i c i e n t s o f D i c h l o r o s i l a n e : SiH« CI T r a n s i t i o n 1 n,, M=0^0 . M=0 v o = A v / V 2 = 16367.77(14)MHz 1.056(12) x 1 0 " 4 MHz V " 2 124 4.4 The E f f e c t i ve and Subs t i t u t i on S t r u c t u r e s o f D i c h l o r o s i 1 ane I t i s c o n v e n i e n t t o d i s c u s s t he e v a l u a t i o n o f e f f e c t i v e and p a r t i a l s u b s t i t u t i o n s t r u c t u r e s f o r d i c h l o r o s i l a n e b e f o r e c o n s i d e r i n g the d e t e r m i n a t i o n o f the harmonic f o r c e f i e l d . The f o r c e f i e l d d e s c r i b e d i n the next s e c t i o n has, however, been used here t o h e l p s p e c i f y t h e c o o r d i n a t e s o f t h e hydrogen atoms. S u f f i c i e n t i s o t o p i c d a t a have been o b t a i n e d t o c a l c u l a t e a l l o f t he s t r u c t u r a l parameters o f the m o l e c u l e . The r o t a t i o n a l con-s t a n t s o f T a b l e 4.4 have been c o n v e r t e d t o the p r i n c i p a l moments o f i n e r t i a , which a r e g i v e n a l o n g w i t h some r e l a t e d parameters i n T a b l e 4.7. A l t h o u g h the e f f e c t o f the s p i n s t a t i s t i c s on the h y p e r f i n e s t r u c -t u r e has a l r e a d y c o n f i r m e d t he ex p e c t e d C 2 v m o l e c u l a r symmetry, a d d i t i o n a l c o r r o b o r a t i o n i s p r o v i d e d by the r e s u l t s o f T a b l e 4.7. The d i s t a n c e o f the hydrogen atoms from t he S i C l 2 p l a n e , c ^ , i s g i v e n by W " 'a + lb " 'c < 4- 2> and, n e g l e c t i n g s m a l l z e r o - p o i n t v i b r a t i o n a l e f f e c t s , s h o u l d be c o n s t a n t f o r a l l t h r e e s p e c i e s . As w e l l , f o r the two a x i a l l y symmetric s p e c i e s , 28 35 29 35 S i H 2 C l 2 and S i H 2 C l 2 , t he d i s t a n c e o f t h e c h l o r i n e atoms from the S i H 2 p l a n e , a c i , i s g i v e n by 4 m C l a C l = lb + lc - *a ( 4 ' 3 ) and s h o u l d a l s o be e s s e n t i a l l y c o n s t a n t f o r t h e s e two s p e c i e s . C l e a r l y the r e s u l t s o f T a b l e 4.7 s a t i s f y both o f t h e s e r e q u i r e m e n t s . F i n a l l y , 28 35 C 2 v symmetry would r e q u i r e t h a t 1^ be c o n s t a n t f o r the S i H 2 C l 2 and 29 35 S i H 2 C l 2 s p e c i e s s i n c e i n t h e s e two c a s e s t he s i l i c o n atom must l i e on t he b - i n e r t i a l a x i s ; t h i s r e q u i r e m e n t i s a l s o met. Thus, t h e mole-125 c u l a r symmetry i s w e l l e s t a b l i s h e d . The s i m p l e s t m o l e c u l a r s t r u c t u r e t o c a l c u l a t e i s t h e e f f e c t i v e o r r Q s t r u c t u r e . T h i s s t r u c t u r e was s u b s e q u e n t l y employed i n t h e f o r c e f i e l d d e t e r m i n a t i o n ; i t s use e n s u r e s t h a t t h e t h e o r e t i c a l moments o f i n e r t i a used i n c a l c u l a t i n g the d i s t o r t i o n c o n s t a n t s r e p r o d u c e as c l o s e l y as p o s s i b l e the ground s t a t e moments. In the p r e s e n t case a l e a s t s quares f i t t o f o u r i ndependent s t r u c t u r a l parameters was made, namely, the S i - H and Si-CI bond d i s t a n c e s and the H-Si-H and C l - S i - C l bond a n g l e s . The d a t a used were the n i n e independent r o t a t i o n a l c o n s t a n t s o f T a b l e 4.4. The r e s u l t s o f t h i s f i t a r e g i v e n i n T a b l e 4.8. 29 35 In d e r i v i n g t h i s s t r u c t u r e the S i H 2 CI,, r o t a t i o n a l c o n s t a n t s o f F i t 1 were used. When the F i t 2 v a l u e s were used i n s t e a d the f i t t e d s t r u c t u r e was i n s i g n i f i c a n t l y d i f f e r e n t - the S i - H d i s t a n c e , f o r example, i n -o o c r e a s e d t o 1.4599 A and the Si-CI d i s t a n c e d e c r e a s e d t o 2.0334 A. The s t a n d a r d e r r o r s o b t a i n e d from t h e l e a s t s q u a r e s f i t a r e n o t quoted i n the t a b l e as t h e y a r e t hought t o u n d e r e s t i m a t e the u n c e r t a i n t y i n t h e s e p a rameters. For the Si-CI and S i - H d i s t a n c e s , f o r example, o o the s t a n d a r d e r r o r s were ±0.0003 A and ±0.0022 A r e s p e c t i v e l y . The s m a l l s t a n d a r d d e v i a t i o n o f the f i t , 0.032 MHz, a l m o s t c e r t a i n l y r e f l e c t s the f a c t t h a t z e r o - p o i n t v i b r a t i o n s s i m i l a r l y c o n t r i b u t e t o the r o t a t i o n a l c o n s t a n t s o f the v a r i o u s i s o t o p i c s p e c i e s s t u d i e d . T h i s would c e r t a i n l y not be the c a s e f o r a d e u t e r a t e d s p e c i e s . 126 4.7 I n e r t i a l Parameters o f D i c h l o r o s i l a n e 3 Parameter 2 8 S i H 2 3 5 C l 2 2 8 S i H 2 3 5 C l 3 7 C l 'a 3 5 . 7 5 3 7 2 ( 1 ) b 36.01017(2) ! b 196.37192(6) 201.79000(13) lc 226.36209(8) 232.03847(14) 4 m H c H 2 5.76354(10) 5.76170(20) 4 m C l a C 1 386.98029(10) 2 9 S i H 2 3 5 C l 2 ( F i t 1) 2 9 S i H 2 3 5 C l 2 ( F i t 2) h 36.39013(5) 36.38981(3) 196.36987(74) 196.36833(38) 226.99823(95) 226.99894(49) 4 m H c H 2 5.7618(12) 5.7592(6) 4 n b a C l 386.9780(12) 386.9775(6) 3 C a l c u l a t e d c o n v e r s i o n i n uA2. from t he r o t a t i o n a l c o n s t a n t s f a c t o r o f 505379.0 MHz uA 2. o f T a b l e 4.4 u s i n g a A l l parameters g i v e n a r e E r r o r s quoted a r e s t a n d a r d e r r o r s . 127 T a b l e 4.8 The E f f e c t i v e S t r u c t u r e o f D i c h l o r o s i l a n e Parameter Value r Q ( S i - C l ) 2.0336 A r Q ( S i - H ) 1.4590 A < ( C l - S i - C l ) 109.76° < (H-Si-H) 110.05° 128 The s u b s t i t u t i o n s t r u c t u r e o f d i c h l o r o s i l a n e was i n v e s t i g a t e d n e x t . Because no d e u t e r a t e d s p e c i e s were s t u d i e d a complete sub-s t i t u t i o n s t r u c t u r e c o u l d not be o b t a i n e d . N e v e r t h e l e s s , t h e heavy atom c o o r d i n a t e s were a c c u r a t e l y d e t e r m i n e d . The p a r e n t s p e c i e s 28 35 adopted f o r t h e s u b s t i t u t i o n c o o r d i n a t e c a l c u l a t i o n s was S i r ^ C ^ . Because t h e c h l o r i n e atoms l i e i n a symmetry p l a n e and have z e r o c_ c o -o r d i n a t e s t h e i r a_ and b_ c o o r d i n a t e s were d e t e r m i n e d u s i n g t h e method o u t l i n e d f o r p l a n a r m o l e c u l e s i n C h a p t e r 1 ( e q u a t i o n 1.44). And, because s i l i c o n has both z e r o a_ and c_ c o o r d i n a t e s i t s b_ c o o r d i n a t e can be o b t a i n e d from where n has i t s u s u a l meaning ( 2 1 ) . These v a r i o u s c o o r d i n a t e s a r e g i v e n i n T a b l e 4.9. The hydrogen atoms had to be l o c a t e d by a l t e r -n a t i v e methods. The lb c o o r d i n a t e was c a l c u l a t e d u s i n g t h e c e n t e r o f mass c o n d i t i o n , z m.b. = 0. A c c u r a t e v a l u e s o f the c_ c o o r d i n a t e o f hydrogen were h a r d e r t o o b t a i n . T h r e e methods were t r i e d . In Method 1 t h e y were c a l c u l a t e d u s i n g e q u a t i o n 4.2, and were thus r Q c o o r d i n a t e s , h a v i n g nebulous p h y s i c a l meaning. They a r e a l s o g i v e n i n T a b l e 4.8, and a g r e e o n l y p o o r l y w i t h t h e c o r r e s p o n d i n g v a l u e s f o r d i f l u o r o s i l a n e , ±1.220 A ( 5 ) . In Method 2 an attempt was made t o improve t h e p h y s i c a l meaning o f t h e s e c o o r d i n a t e s by u s i n g the average moments o f i n e r t i a d e r i v e d u s i n g the f o r c e f i e l d o f T a b l e 4.12. One has 4 ™ H < C H > 2 * ll + >b " ll <4-5' These average c o o r d i n a t e s , however, a r e u s u a l l y l a r g e r than t h e 129 c o r r e s p o n d i n g s u b s t i t u t i o n v a l u e s . In the r e l a t e d S i H o F , , (22) and C H 2 C 1 2 (23) m o l e c u l e s , f o r example, the s u b s t i t u t i o n v a l u e s f o r the o c H c o o r d i n a t e s a r e i n each case 0.002 A s m a l l e r than the average v a l u e s . In Method 3 t h e r e f o r e t he p r e f e r r e d e s t i m a t e s f o r the c ^ c o o r d i n a t e s o have been o b t a i n e d by a p p l y i n g t h i s 0.002 A c o r r e c t i o n . The r e s u l t s g i v e n i n T a b l e 4.9 have been o b t a i n e d u s i n g the ground s t a t e moments OA or* o f i n e r t i a f o r S i H 2 C l 2 c o r r e s p o n d i n g to F i t 1 (see T a b l e 4.4). Us i n g i n s t e a d the F i t 2 v a l u e s changes o n l y the ^ c o o r d i n a t e s o f s i l i c o n and hydrogen t o 0.8017 A and -1.6399 A. The " l a r g e " jump i n the b R c o o r d i n a t e r e s u l t s from the use o f the f i r s t moment c o n d i t i o n . In ge n e r a l t he a c c u r a c y w i t h which an atom can be p l a c e d u s i n g a f i r s t moment c o n d i t i o n v a r i e s i n v e r s e l y as i t s mass; a sm a l l change i n the s i l i c o n c o o r d i n a t e causes a much l a r g e r s h i f t i n the hydrogen p o s i t i o n . The s u b s t i t u t i o n s t r u c t u r e o b t a i n e d from the c o o r d i n a t e s o f T a b l e 4.9 29 35 i s g i v e n i n T a b l e 4.10. U s i n g the F i t 2 v a l u e s f o r S i H 2 C l 2 would o r e s u l t i n an S i - C l d i s t a n c e s h o r t e n e d by 0.0001 A from t he v a l u e g i v e n o and an S i - H d i s t a n c e i n c r e a s e d by 0.0016 A. 130 T a b l e 4.9 S u b s t i t u t i o n C o o r d i n a t e s o f D i c h l o r o s i l a n e : S i H 9 C1,(A) Atom C o o r d i n a t e Method 1 Method 2 Method 3 CI S i a b c a b c a b c ±1.6622 0.3680 0.0000 0.0000 -0.8019 0.0000 0.0000 -1.6372 ±1.1957 ±1.6622 0.3680 0.0000 0.0000 -0.8019 0.0000 0.0000 -1.6372 ±1.2240 ±1.6622 0.3680 0.0000 0.0000 -0.8019 0.0000 0.0000 -1.6372 ±1.222 131 T a b l e 4.10 The S u b s t i t u t i o n S t r u c t u r e o f D i c h l o r o s i l a n e 3 Parameter V a l u e r s ( S i - C l ) 2.0326 A r s ( S i - H ) 1.4802 A < ( C l - S i - C l ) 109.72 < (H-Si-H) 111.29 o o 3 O b t a i n e d u s i n g the Method 3 c o o r d i n a t e s o f T a b l e 4.9. 132 4.5 The Harmonic F o r c e F i e l d o f D i c h l o r o s i l a n e S e v e r a l f o r c e f i e l d s have been p u b l i s h e d f o r d i c h l o r o s i l a n e (13-17) o f which the most d e t a i l e d and c o n v i n c i n g i s t h a t o f C h r i s t e n s e n and N i e l s e n ( 1 7 ) . They had a v a i l a b l e a complete s e t o f v i b r a t i o n a l wavenumbers f o r the normal s p e c i e s ( c h l o r i n e i s o t o p e e f f e c t s were not r e s o l v e d ) and a p a r t i a l s e t f o r the s i n g l y and d o u b l y d e u t e r a t e d s p e c i e s ( 1 2 ) . However, as C h r i s t e n s e n and N i e l s e n p o i n t e d o u t , not a l l o f the v i b r a t i o n a l wavenumbers were independent; i n a d d i t i o n they were f o r c e d t o use an assumed m o l e c u l a r s t r u c t u r e . I t t h e r e f o r e seemed wo r t h w h i l e a t t e m p t i n g a new f o r c e f i e l d r e f i n e m e n t u s i n g the p r e s e n t microwave s t r u c t u r e and the a d d i t i o n a l d a t a p r o v i d e d by the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s . The f o r c e f i e l d r e f i n e m e n t program used here was one d e v e l o p e d i n t he C h e m i s t r y Department, U n i v e r s i t y o f Reading and k i n d l y s u p p l i e d by Dr. A. 6. R o b i e t t e . I t had a v e r y f l e x i b l e weighted l e a s t s quares f i t t i n g r o u t i n e which a l l o w e d the use o f any number o f v i b r a t i o n a l wavenumbers o r c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s as d a t a ( 2 4 ) . Refinements were i n terms o f v a l e n c e f o r c e c o n s t a n t s u s i n g the EQ m a t r i x method o f W i l s o n ( 2 5 ) . The f o r c e f i e l d r e f i n e m e n t f o r d i c h l o r o s i l a n e was c a r r i e d o u t i n terms o f nonredundant symmetry c o o r d i n a t e s . These symmetry co-o r d i n a t e s , which t r a n s f o r m as 4A-| + A 2 + 2B-j + 2 B 2 i n the p o i n t group C 2 v , a r e g i v e n i n terms o f the i n t e r n a l d i s p l a c e m e n t c o o r d i n a t e s i n T a b l e 4.11. These a r e e s s e n t i a l l y the symmetry c o o r d i n a t e s used by C h r i s t e n s e n and N i e l s e n (17) e x c e p t t h a t the c o e f f i c i e n t s o f the i n t e r n a l c o o r d i n a t e s i n S 3 and S^ have been changed t o be c o n s i s t e n t w i t h the microwave r s t r u c t u r e . 133 T a b l e 4.11 I n t e r n a l C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f D i c h l o r o s i l a n e I n t e r n a l C o o r d i n a t e s : 9 r . = r ( S i - H . ) = 1.459 A ; R, = r ( S i - C l , ) = 2.034 A a = <H-Si-H = 110.05° g = <C1-Si-Cl = 109.76° 6 , , = <:H.-Si-Cl, = 109.25° Symmetry C o o r d i n a t e s : b l o c k S l ( l/^CA^+Aro) S 2 = (1//2 ) (AR 1 +AR 2 ) . S b ^3 = mAa-n (A9-| -j +A6 ^ 2 + A 0 2 1 + A 0 2 2 ^ S C  5 4 = d A e - e ( A 6 1 1 + A 0 1 2 + A e 2 1 + A e 2 2 ) b l o c k S 5 = (1 /2) ( - A 6 - J 1 + A 6 1 2 + A 6 2 i _ A e 2 2 ^ B l b l o c k S 6 = ( l / v ^ ) ( A r r A r 2 ) S 7 = ( l / 2 ) ( - A e 1 1 - A e 1 2 + A e 2 i + A e 2 2 ) b l o c k S 8 ( l / 2 ) ( A R r A R 2 ) S 9 - ( l / 2 ) ( - A 6 1 1 + A e 1 2 - A 6 2 1 + A e 2 2 ) The m o l e c u l a r s t r u c t u r e used i s the r 0 s t r u c t u r e o f T a b l e 4.8. T h i s ensures t h a t t h e t h e o r e t i c a l moments o f i n e r t i a used i n c a l c u l a t i n g t he d i s t o r t i o n c o n s t a n t s a r e as c l o s e as p o s s i b l e t o the ground s t a t e moments. b So i s d e f i n e d as a pure HSiH bending c o o r d i n a t e w i t h no change i n C l S i C l . The c o e f f i c i e n t s , c a l c u l a t e d from t h e assumed geometry, remove t he f i r s t o r d e r redundancy between the s i x a n g l e s and n o r m a l i z e 53. T h e i r v a l u e s a r e : m = 0.8947 n = 0.2234 c S4 i s d e f i n e d as a pure C I S j C l bending c o o r d i n a t e w i t h no change i n HSiH. The c o e f f i c i e n t s , c a l c u l a t e d from the assumed s t r u c t u r e , remove the f i r s t o r d e r redundancy between the s i x a n g l e s and n o r m a l i z e 54. T h e i r v a l u e s a r e : d = 0.8956 e = 0.2229 134 Because no heavy atom i s o t o p e e f f e c t s were r e s o l v e d f o r d i c h l o r o s i l a n e the ob s e r v e d wavenumbers o f the normal, d o u b l y d e u t e r a t e d and s i n g l y d e u t e r a t e d m o l e c u l e s were a s s i g n e d t o the 2 8 S i H 2 3 5 C l 2 , 2 8 S i D 2 3 5 C l 2 and 2 8 S i H D 3 5 C l 2 s p e c i e s r e s p e c t i v e l y . The v i b r a t i o n a l wavenumbers were a l l a s s i g n e d u n c e r t a i n t i e s o f 1% i n the 28 35 weighted l e a s t squares f i t . No SiHD C l 2 wavenumbers were used i n t h e f i t because t h i s s p e c i e s has C s symmetry and, i n any c a s e , p r o v i d e s no a d d i t i o n a l i n f o r m a t i o n . The c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s o f 28 35 S i H 2 C l 2 o n l y were i n c l u d e d i n the f i t ; t h e s e were a l s o a s s i g n e d u n c e r t a i n t i e s o f 1% e x c e p t f o r which was a s s i g n e d an u n c e r t a i n t y o f 3% as i t i s r e l a t i v e l y p o o r l y d e t e r m i n e d . A l l d a t a were weighted i n t he f i t a c c o r d i n g t o the r e c i p r o c a l s o f the squares o f t h e i r u n c e r t a i n t i e s . In a n . i n i t i a l r e f i n e m e n t t he d i a g o n a l f o r c e c o n s t a n t s were f i t t e d t o t h e v i b r a t i o n a l wavenumbers a l o n e ; t he t r i a l v a l u e s f o r t h e s e f o r c e c o n s t a n t s were taken from C h r i s t e n s e n and N i e l s e n ( 1 7 ) . I t was found a t once t h a t a non-zero v a l u e o f F 8 Q was r e q u i r e d t o rep r o d u c e v g and Vg f o r the two i s o t o p i c s p e c i e s . The d i s t o r t i o n c o n s t a n t s were then i n c l u d e d as d a t a , and t h e o f f - d i a g o n a l f o r c e c o n s t a n t s were g r a d u a l l y i n t r o d u c e d . The b e s t f i t s were o b t a i n e d i n c l u d i n g F 2 3 , F 2 4 , F 3 4 and F g 9 ; F 1 2 , F 1 3 , F 1 4 and F 5 6 were i n d e t e r -minate and were c o n s t r a i n e d t o z e r o . In f a c t a l l t he i n t e r a c t i o n c o n s t a n t s between the S i - H ( S i D) s t r e t c h i n g c o o r d i n a t e s and the r e m a i n i n g symmetry c o o r d i n a t e s have been c o n s t r a i n e d t o z e r o . S i n c e even the Si-D s t r e t c h i n g modes a r e a t l e a s t 900 cm - 1 h i g h e r than any o t h e r s t he i n t e r a c t i o n s can p l a u s i b l y be e x p e c t e d t o be s m a l l . The f o r c e f i e l d o b t a i n e d i s g i v e n i n T a b l e 4.12; a l l o f the f o r c e c o n s t a n t s 135 appear t o have r e a s o n a b l e magnitudes and s i g n s . T a b l e s 4.13 and 4.14 demonstrate how w e l l t he f o r c e f i e l d r e p r o d u c e s the o b s e r v e d d a t a . These t a b l e s g i v e t he o b s e r v e d v i b r a t i o n a l wavenumbers o r d i s t o r t i o n c o n s t a n t s and t h e i r a s s i g n e d u n c e r t a i n t i e s , t o g e t h e r w i t h t he d e v i a t i o n s between t h e observed v a l u e s and t h o s e c a l c u l a t e d from the f o r c e f i e l d . T a b l e 4.13 shows t h a t the f i t f o r the v i b r a t i o n a l wavenumbers i s s a t i s f a c t o r y , and, f u r t h e r m o r e , t he f o r c e c o n s t a n t s g i v e e x c e l l e n t p r e d i c t i o n s o f the wavenumbers o f S i H D C l 2 which were not used i n the r e f i n e m e n t . The d e v i a t i o n o b s e r v e d f o r t h e S i - H ( S i - D ) s t r e t c h i n g fundamentals i s h a r d l y s u r p r i s i n g i n view o f the f a c t t h a t no c o r r e c t i o n s f o r a n h a r m o n i c i t y have been made. T a b l e 4.14 shows t h a t the f i t i s a l s o v e r y good f o r the d i s t o r t i o n c o n s t a n t s , a l t h o u g h f o r 6j and 6^  t he d e v i a t i o n s a r e s l i g h t l y l a r g e r than the e s t i m a t e d u n c e r t a i n t i e s . I t i s seen as w e l l t h a t t he f o r c e f i e l d 28 35 37 g i v e s good p r e d i c t i o n s f o r the d i s t o r t i o n c o n s t a n t s o f the S i H 2 CI CI s p e c i e s . 136 T a b l e 4.12 The Harmonic F o r c e F i e l d o f D i c h l o r o s i l a n e S p e c i e s F o r c e C o n s t a n t s 9 A ] 2 . 8 9 1 ( 3 9 ) b A 2 0.418(8) B ] 2.862(38) 3.231(45) -0.188(87) 0.180(52) 0.547(28) -0.357(83) 0.814(70) 0.723(10) B 2 2.871(43) -0.283(26) 0.607(11) a °-l Bond s t r e t c h i n g f o r c e c o n s t a n t s i n mdyn A ; s t r e t c h - b e n d i n t e r a c t i o n f o r c e c o n s t a n t s i n mdyn r a d " ' ; a n g l e bending f o r c e c o n s t a n t s i n mdyn A r a d - 2 . b Numbers i n b r a c k e t s a r e s t a n d a r d d e v i a t i o n s i n u n i t s o f the l a s t s i g n i f i c a n t f i g u r e s . c These f o r c e c o n s t a n t s were c o n s t r a i n e d t o z e r o 137 T a b l e 4.13 Observed and C a l c u l a t e d V i b r a t i o n a l Wavenumbers ( c m - 1 ) o f D i c h l o r o s i l a n e 2 8 S 1 H 9 3 5 C 1 * 2 8 S i D 3 5 C 1 / 2 8 S i H D 3 5 C l b V i b r a t i o n c c c Obs. c Dev. d Obs. c Dev. d Obs. c Dev. d A ] V ] 2224 -9.9 1608 7.4 2231 ' -10.4 v 2 954 0.9 695 -0.7 885 2.0 v 3 527 -2.5 519 0.6 v 4 188 0.8 187 0.7 A 2 v 5 710 -0.2 B, v c 2237 -11.7 1637 8.6 1621 6.5 1 6 v ? 602 -0.3 466 0.1 B 2 v 8 876 -1.2 663 0.8 818 0.0 v g 590 0.0 566 1.1 599 -0.1 Wavenumbers f o r t h e s e i s o t o p e s were used t o det e r m i n e the harmonic f o r c e f i e l d . In the l e a s t squares f i t s u n c e r t a i n t i e s were taken t o be 1% o f the measured v a l u e . These wavenumbers were not used i n the l e a s t squares f i t s . S i n c e t h i s s p e c i e s , has C s symmetry the v i b r a t i o n s t r a n s f o r m as A(=Ai+B] i n t h e symmetric m o l e c u l e s ) and A"(=A2+B2 i n the symmetric m o l e c u l e s ) . Taken from C h r i s t e n s e n and N i e l s e n ( 1 2 ) . Observed v a l u e minus v a l u e c a l c u l a t e d u s i n g t he f o r c e c o n s t a n t s o f T a b l e 4.12. 138 T a b l e 4.14 Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s (kHz) o f D i c h l o r o s i l a n e Parameter Observed Value' U n c e r t a i n t y D e v i a t i o n 2 8 S i H 2 3 5 C l 2 1.022 -15.46 142.1 0.2410 3.117 0.010 0.15 1.4 0.0024 0.093 0.0014 -0.14 -0.49 -0.0032 0.18 28 S i H 2 3 5 C l 3 7 JK cr 0.969 -14.91 139.5 0.2334 2.490 -0.003 -0.02 1.1 0.0045 -0.34 a Taken from T a b l e 4.4. b E s t i m a t e d u n c e r t a i n t i e s used i n the f o r c e c o n s t a n t f i t . c Observed v a l u e minus v a l u e c a l c u l a t e d from t he f o r c e f i e l d o f T a b l e 4.12. ^ V a l u e s f o r t h i s i s o t o p e were not used i n t h e f o r c e f i e l d r e f i n e m e n t . 139 4.6 The Average S t r u c t u r e o f D i c h l o r o s i l a n e The harmonic f o r c e f i e l d o f T a b l e 4.12 has been used t o e v a l u a t e the ground s t a t e average s t r u c t u r e o f d i c h l o r o s i l a n e . In C h a p t e r 3 the average s t r u c t u r e o f s u l p h u r d i c h l o r i d e was e v a l u a t e d ; because t h i s s t r u c t u r e c o u l d be d e t e r m i n e d u s i n g the r o t a t i o n a l c o n s t a n t s o f o n l y one i s o t o p i c s p e c i e s i t was p o s s i b l e to i g n o r e i s o t o p i c v a r i a t i o n s i n t h e average bond l e n g t h s . For d i c h l o r o s i l a n e , however, a t l e a s t two i s o t o p i c s p e c i e s a r e r e q u i r e d t o e v a l u a t e the m o l e c u l a r s t r u c t u r e ; t h e r e f o r e the i s o t o p i c v a r i a t i o n o f the bond d i s t a n c e s were c a l c u l a t e d u s i n g e q u a t i o n 1.43.The v a l u e s used f o r the Morse a n h a r m o n i c i t y parameter a were a ( S i H ) = 1.75 A" and O "I a ( S i C l ) = 1.56 A , both taken from K u c h i t s u and Morino ( 2 6 ) . The c a l c u l a t e d i s o t o p i c changes i n the average bond l e n g t h s a r e g i v e n i n 2 T a b l e 4.15 t o g e t h e r w i t h the c o r r e s p o n d i n g v a l u e s o f 6<u >, the change i n the mean square a m p l i t u d e o f v i b r a t i o n o f the bond i n q u e s t i o n , and 6K, t h e c o r r e s p o n d i n g change i n the mean square p e r p e n d i c u l a r a m p l i t u d e c o r r e c t i o n . In a l l c a s e s the i s o t o p i c v a r i a t i o n s i n the bond d i s t a n c e s -5° a r e e x t r e m e l y s m a l l , l e s s than 4 x 10 A; a more t y p i c a l s e t o f <Srz v a l u e s has been g i v e n f o r f o r m i c a c i d ( 2 7 ) . The average v a l u e s o f t h e r o t a t i o n a l c o n s t a n t s A z , B z and C z a r e g i v e n f o r the v a r i o u s i s o t o p i c s p e c i e s o f d i c h l o r o s i l a n e i n T a b l e 4.16. 29 35 For S i H 2 C l 2 t h e s e have been c a l c u l a t e d u s i n g the F i t 2 c o n s t a n t s o f T a b l e 4.4; f o r t h i s f i t B z i s l a r g e r than the c o r r e s p o n d i n g v a l u e f o r 28 35 the S i H 2 C l 2 s p e c i e s by 0.047 MHz, i n good agreement w i t h the 0.076 MHz p r e d i c t e d u s i n g t h e 6 r z v a l u e s o f T a b l e 4.15. The m o l e c u l a r s t r u c t u r e o b t a i n e d by a l e a s t squares f i t t o t h e s e average r o t a t i o n a l 140 Table 4.15 Parameters Describing the Isotopic Variation Average Bond Lengths of Dichlorosilane in the Parameter 9 2 8 S i H 2 3 5 C l 2 - > 2 8 S i H 2 3 5 C l 3 7 C l 2 8 S i H ; 2 3 5 C l 2 - > 2 9 S i H 2 3 5 C l 2 6<u2>(SiH) 0.0 -0.4 6<u 2>(Si 3 5Cl) 0.0 -1.7 6<u 2>(Si 3 7Cl) -2.4 -6.K(SiH) 0.9 1.3 dK ( S i 3 5 C l ) 1.0 -1.0 <SK(Si 3 7Cl) -2.0 -6r z(SiH) -0.9 -2.4 6 r z ( S i 3 5 C l ) -1.0 -3.0 6 r z ( S i 3 7 C l ) -3.6 — 9 Parameters give values for substituted species minus the value for the parent or 2 8 S i H 2 3 5 C l 2 species. The units of <5<u2>, 6K and 6 r z are respectively 10" 5A 2, 10"5A and 10" 5 A. 141 c o n s t a n t s , w i t h a l l o w a n c e made f o r t h e i s o t o p i c bond l e n g t h v a r i a t i o n s i s a l s o g i v e n i n T a b l e 4.16. A n e g l i g i b l y d i f f e r e n t s t r u c t u r e was 29 35 o b t a i n e d when the average r o t a t i o n a l c o n s t a n t s f o r S i h ^ were i n s t e a d c a l c u l a t e d u s i n g t he F i t 1 v a l u e s o f T a b l e 4.4. When the 6 r z v a l u e s were o m i t t e d from t he f i t a s l i g h t l y d i f f e r e n t s t r u c t u r e was o b t a i n e d ; the s i l i c o n - h y d r o g e n and s i l i c o n - c h l o r i n e bond l e n g t h s , o o f o r example, i n c r e a s e d and d e c r e a s e d by 0.0037 A and 0.0004 A r e s p e c t i v e l y . The e r r o r s quoted f o r t h e average s t r u c t u r a l parameters a r e t h e s t a n d a r d e r r o r s o b t a i n e d from t h e l e a s t squares f i t and a l m o s t c e r t a i n l y u n d e r e s t i m a t e t h e t o t a l e r r o r i n t h e s e parameters. The r e l i a b i l i t y o f the v a r i o u s d i c h l o r o s i l a n e s t r u c t u r e s i s d i s c u s s e d i n s e c t i o n 4.8. 142 T a b l e 4.16 Average R o t a t i o n a l C o n s t a n t s o f D i c h l o r o s i l a n e and Average S t r u c t u r e o f 2 8 S i H 2 3 5 C l 2 Parameter 2 8 S i H 3 5 C 1 ? 2 8 S i H 3 5 C 1 3 7 C 1 2 9 S T H 3 5 C 1 * A z(MHz) 14082.142 13982.115 13836.076 B2 ( M H z ) 2570.078 2501.117 2570.120 C z(MHz) 2231.376 2176.795 2225.130 r z ( S 1 - C l ) r 2 ( S 1 - H ) < ( C 1 - S i - C l ) <(H-Si-H) 2.0352(3) A ° 1.4726(25) A 109.68(3)° 112.44(28)° O b t a i n e d u s i n g t he F i t 2 v a l u e s o f T a b l e 4.4. E r r o r s quoted a r e s t a n d a r d e r r o r s . These p r o b a b l y u n d e r e s t i m a t e the t o t a l e r r o r f o r t h e s e parameters. 143 4.7 The E q u i l i b r i u m S t r u c t u r e o f D i c h l o r o s i l a n e Having e v a l u a t e d t h e average m o l e c u l a r s t r u c t u r e o f d i c h l o r o -s i l a n e , i t seemed o f i n t e r e s t t o c a l c u l a t e as w e l l a c r u d e e q u i l i b r i u m s t r u c t u r e . T h i s was done u s i n g e q u a t i o n 1.42 and the f o r c e f i e l d o f T a b l e 4.12 t o g e t h e r w i t h the r e s u l t s o f the p r e v i o u s s e c t i o n ; t he c a l c u l a t e d e q u i l i b r i u m v a l u e s o f t h e S i - H and S i - C l bond l e n g t h s a r e g i v e n i n T a b l e 4.17. I t was not p o s s i b l e t o e s t i m a t e t he e q u i l i b r i u m v a l u e s o f the bond a n g l e s ; r e s u l t s f o r methylene f l u o r i d e (28) s u g g e s t , however, t h a t t h e s e can be a p p r e c i a b l y d i f f e r e n t from t h e a v e r a g e v a l u e s . The e q u i l i b r i u m s t r u c t u r e and o t h e r d i c h l o r o s i l a n e s t r u c t u r e s a r e compared i n s e c t i o n 4.8. 4.8 Comments on t h e S t r u c t u r e and F o r c e F i e l d o f D i c h l o r o s i l a n e The v a r i o u s m o l e c u l a r s t r u c t u r e s d e r i v e d f o r d i c h l o r o s i l a n e have been compared i n T a b l e 4.18. I t i s seen t h a t the s i l i c o n - h y d r o g e n bond l e n g t h and bond a n g l e show a wide v a r i a t i o n from one s t r u c t u r e t o the ne x t ; the s i l i c o n - c h l o r i n e p a r a m e t e r s , on t h e o t h e r hand, show o n l y s l i g h t v a r i a t i o n s and, i n f a c t , the s i l i c o n - c h l o r i n e bond l e n g t h s f o l l o w the r >r >r >r t r e n d t y p i c a l o f d i a t o m i c m o l e c u l e s ( 2 1 ) . The r e s u l t s z o s e J r o f T a b l e 4.18 a r e i n a c c o r d w i t h t he g e n e r a l o b s e r v a t i o n t h a t t he n e g l e c t o f v i b r a t i o n a l e f f e c t s w i l l i n t r o d u c e t he g r e a t e s t e r r o r i n the c o o r d i n a t e s o f hydrogen atoms. I t i s easy t o u n d e r s t a n d why t h e r (S i - H ) bond l e n g t h i n p a r t i c u l a r s h o u l d have a nebulous meaning. U s i n g t h e r e s u l t s o f T a b l e s 4.7, 4.16 and 4.18, and n e g l e c t i n g any 144 T a b l e 4.17: The E q u i l i b r i u m S t r u c t u r e o f D i c h l o r o s i l a n e 3 Parameter V a l u e u 2 ( S i - H ) ( A 2 ) 0.00773 u 2 ( S i - C l ) ( A 2 ) 0.00190 K ( s i - H ) ( A ) 0.01493 K ( S i - C l ) ( A ) 0.00076 a ( S i - H ) ( A _ 1 ) 1.75 a ( S i - C l ) ( A - 1 ) 1.56 r z ( S i - H ) ( A ) 1.4726 r z ( S i - C l ) ( A ) 2.0352 r e ( S i - H ) ( A ) 1.4672 r e ( S i - C l ) ( A ) 2.0315 3 C a l c u l a t i o n f o r 2 8 S i H 0 C l 0 . V a l u e s o f u 2 and K were c a l c u l a t e d u s i n g t h e f o r c e f i e l d o f T a b l e 4.12. V a l u e s o f a and were take n from the p r e v i o u s s e c t i o n . 145 anharmonic e f f e c t s , the c o n t r i b u t i o n made t o 1^, f o r example, by the c h l o r i n e atoms, the hydrogen atoms and the z e r o - p o i n t v i b r a t i o n a l e f f e c t s a r e , f o r 2 8 S i H 2 3 5 C l 2 , c a l c u l a t e d t o be 193.62 u i \ 2 (= 2 m c ] ( a ^ ) 2 ) , 3.02 uA 2 (= 2 m H ( c z | ) 2 ) and -0.27 uA 2 (= 1° - I z ) r e s p e c t i v e l y . C l e a r l y t h e z e r o -p o i n t v i b r a t i o n a l e f f e c t s can produce a l a r g e u n c e r t a i n t y i n t h e hydrogen c o o r d i n a t e s . For the example g i v e n one might e x p e c t the e f f e c t i v e a 0 ^ and c^ c o o r d i n a t e s t o d i f f e r from t h e i r c o r r e s p o n d i n g w e l l - d e f i n e d o o average v a l u e s by a t most 0.0012 A and 0.056 A r e s p e c t i v e l y ; t h e o b s e r v e d o o d e v i a t i o n s a r e 0.0005 A and 0.029 A. I t i s o b v i o u s then t h a t comparing the r Q ( S i - H ) bond l e n g t h s o f d i f f e r e n t h a l o s i l a n e s would be a m e a n i n g l e s s e x e r c i s e . L o o k i n g next a t the s u b s t i t u t i o n and average s t r u c t u r e s o f d i c h l o r o s i l a n e , i t i s seen t h a t the r s ( S i - H ) bond l e n g t h , which was e s t i -mated u s i n g t h e c e n t e r o f mass c o n d i t i o n ( s e e s e c t i o n 1.4), i s a p p a r e n t l y l a r g e r than r z ( S i - H ) . In d i f l u o r o m e t h a n e ( 2 8 ) , d i c h l o r o m e t h a n e (23) and d i f l u o r o s i l a n e ( 2 2 ) , however, the r s ( C - H ) and r s ( S i - H ) bond l e n g t h s , o b t a i n e d u s i n g d e u t e r a t e d s p e c i e s d a t a , a r e a l l s m a l l e r t h a n t h e c o r r e s -ponding average bond l e n g t h s . In t h i s r e g a r d i t has been p o i n t e d o u t t h a t hydrogen atom c o o r d i n a t e s c a n n o t , i n g e n e r a l , be a c c u r a t e l y s p e c i f i e d u s i n g a c e n t e r o f mass c o n d i t i o n ( 2 1 ) ; w i t h o u t d e u t e r a t e d s p e c i e s d a t a t h e r e i s , however, l i t t l e a l t e r n a t i v e . I t becomes c l e a r then t h a t o n l y the w e l l - d e f i n e d a verage s t r u c t u r e g i v e s an a c c u r a t e e s t i m a t e f o r the s i l i c o n - h y d r o g e n bond l e n g t h and bond a n g l e . Whereas average s t r u c t u r e s have not been e v a l u a t e d f o r o o t h e r c h l o r o s i l a n e s , the r z ( S i - H ) d i s t a n c e o f 1.4723 A found f o r d i f l u o r o s i l a n e (22) i s i n e x c e l l e n t agreement w i t h the v a l u e g i v e n i n T a b l e 4.18. Because the d i f f e r e n c e between t h e r n ( S i - C l ) bond l e n g t h 146 T a b l e 4.18 A Comparison o f the D e r i v e d S t r u c t u r e s o f D i c h l o r o s i l a n e 3 r ( S i - X ) ( A ) <(X-Si-X)(Deg.) r o S i H 1.4590 110.05 S i C l 2.0336 109.76 r s S i H b 1.4802 111.29 S i C l 2.0326 109.72 r z S i H 1.4726(75)° 112.44(84) S i C l 2.0352(9) 109.68(9) r e S i H 1 .4672(89) d _e S i C l 2.0315(18) e 3 The r Q , r s > r z and r g s t r u c t u r e s a r e t a k e n from T a b l e s 4.8, 4.10, 4.16 and 4.17 r e s p e c t i v e l y . b S t r i c t l y , the s i l i c o n - h y d r o g e n parameters g i v e n a r e not s u b s t i t u t i o n v a l u e s . No d e u t e r a t e d d i c h l o r o s i l a n e s p e c i e s were s t u d i e d . See s e c t i o n 4.4. c E r r o r s c i t e d f o r the r z parameters a r e e s t i m a t e d o u t s i d e l i m i t s o f e r r o r . See t e x t . ^ E r r o r s c i t e d a r e the d i r e c t sums o f t h e e r r o r s i n the r z v a l u e s p l u s one q u a r t e r o f the a p p r o p r i a t e r z - r g d i f f e r e n c e . e No e s t i m a t e o f t h e s e a n g l e s o b t a i n e d . See t e x t . 147 and the r z ( S i - C l ) d i s t a n c e i s o n l y 0.0016 A and the f o r m e r s t r u c t u r e t a k e s no_ a c c o u n t o f v i b r a t i o n a l e f f e c t s , i t seems e v i d e n t t h a t the o u n c e r t a i n t y i n r z ( S i - C l ) must be l e s s than 0.001.A. The u n c e r t a i n t i e s a s s i g n e d the average s t r u c t u r e i n T a b l e 4.18 a r e t h r e e t imes the l e a s t s quares s t a n d a r d e r r o r s o f T a b l e 4.16; t h e s e c o n s t i t u t e r e a s o n a b l e o u t s i d e l i m i t s o f e r r o r . The f i n a l s e t o f s t r u c t u r a l parameters g i v e n i n T a b l e 4.18 a r e t h e r e ( S i - H ) and r e ( S i - C l ) d i s t a n c e s . E r r o r s have been a s s i g n e d t o t h e s e parameters u s i n g t h e approach o u t l i n e d p r e v i o u s l y f o r s u l p h u r d i c h l o r i d e ( s ee s e c t i o n 3.4); t h a t i s , the t o t a l u n c e r t a i n t y i n each r g v a l u e was taken as the d i r e c t sum o f the u n c e r t a i n t y i n the c o r r e s p o n d i n g r z v a l u e p l u s one q u a r t e r o f the r z - r g d i f f e r e n c e . A c c e p t i n g the r g d i s t a n c e s a t f a c e v a l u e and assuming t h a t the a verage and e q u i l i b r i u m bond a n g l e s a r e i d e n t i c a l , one can c a l c u l a t e t h a t t h e anharmonic c o n t r i -o °2 b u t i o n o f the z e r o - p o i n t v i b r a t i o n s t o 1^, f o r example, i s 0.72(37) uA , °2 somewhat l a r g e r than the -0.27 uA harmonic c o n t r i b u t i o n e s t i m a t e d e a r l i e r . These r e l a t i v e magnitudes and s i g n s a r e c o n s i s t e n t w i t h r e s u l t s f o r d i f l u o r o m e t h a n e ( 2 8 ) . F i n a l l y , i n T a b l e 4.19, t h e s i l i c o n - h a l o g e n bond l e n g t h s and s t r e t c h i n g f o r c e c o n s t a n t s o f the f l u o r o s i l a n e s and c h l o r o s i l a n e s have been compared; where p o s s i b l e c o n s i s t e n t bond l e n g t h d e f i n i t i o n s have been used. For t h e f l u o r o s i l a n e s t h e r e i s a s t r o n g i n v e r s e c o r r e l a t i o n between the s t r e t c h i n g f o r c e c o n s t a n t s and the bond l e n g t h s ( 2 2 ) . The r e s u l t s f o r the c h l o r o s i l a n e s a r e l e s s c l e a r - c u t . In p a r t i c u l a r , t h e s t r e t c h i n g f o r c e c o n s t a n t o f t r i c h l o r o s i l a n e appears t o be too s m a l l ; t h i s may s u g g e s t t h a t the t r i c h l o r o s i l a n e f o r c e f i e l d r e q u i r e s f u r t h e r a t t e n t i o n . However, w i t h the p o s s i b l e e x c e p t i o n o f the t e t r a h a l o s i l a n e s , t h e r e i s a 148 T a b l e 4.19 A Comparison o f Bond Lengths and S t r e t c h i n g Force' C o n s t a n t s i n t h e F l u o r o s i l a n e s and C h l o r o s i l a n e s , (a) F l u o r o s i l a n e s F R (Si-F)(mdyn A " 1 ) r ( S i - •F)(A) R e f e r e n c e s S i H 3 F 5.31 r e = 1.591 (24) S i H 2 F 2 5.83 r e = 1.576 (22) STHF 3 6.01 r e = 1.562 (29) S i F 4 6.52 r a = 1.552 (30,31) (b) C h l o r o s i l a n e s F R (Si-CI)(mdyn A " 1 ) r ( S i --C1)(A) R e f e r e n c e s S i H 3 C l 2.98 's = 2.048 (32,6) S i H 2 C l 2 3.05 r s = 2.033 T h i s work S i H C l 3 2.92 r s = 2.020 (33,8) S i C l 4 3.37 r g = 2.019 (34,35) 149 d e f i n i t e s y s t e m a t i c s h o r t e n i n g o f the s i l i c o n - h a l o g e n bond as the number o f halogen atoms i n c r e a s e s . 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Japan 38, 104 (1965). 152 C h a p t e r 5 The Microwave Spectrum o f P r o p i o l y l C h l o r i d e The a c i d h a l i d e d e r i v a t i v e s o f s i m p l e c a r b o x y l i c a c i d s have been e x t e n s i v e l y s t u d i e d u s i n g microwave s p e c t r o s c o p y . The m o l e c u l e s which have been i n v e s t i g a t e d i n c l u d e the a c i d f l u o r i d e s and a c i d c h l o r i d e s o f f o r m i c a c i d ( 1 , 2 ) , a c e t i c a c i d ( 3 , 4 ) , c y c l o p r o p a n e -c a r b o x y l i c a c i d (5,6) and p r o p i o n i c a c i d ( 7 , 8 ) . The c o r r e s p o n d i n g d e r i v a t i v e s o f p r o p i o l i c ( p r o p y n o i c ) a c i d have not been p r e v i o u s l y examined. In f a c t , t h e p r e p a r a t i o n o f the p r o p i o l y l h a l i d e s has o n l y r e c e n t l y been a c c o m p l i s h e d . As p r o p i o l i c a c i d i s one o f t h e two s i m p l e s t p l a n a r c a r b o x y l i c a c i d s a s t u d y o f t h e p r o p i o l y l h a l i d e s seemed worth-w h i l e . These m o l e c u l e s a r e o f e s p e c i a l i n t e r e s t as t h e p a r e n t p r o p i o l i c a c i d has a v e r y l a r g e a c i d d i s s o c i a t i o n c o n s t a n t (9,10) compared t o t h o s e o f a l i p h a t i c , o l e f i n i c o r a r o m a t i c c a r b o x y l i c a c i d s . A t 20°C, f o r example, t h e a c i d d i s s o c i a t i o n c o n s t a n t s o f the t h r e e - c a r b o n p r o p i o n i c -5 -2 -1 and p r o p i o l i c a c i d s a r e 1.35 x 10 and 1.36 x 10 mole l i t e r r e s p e c t i v e l y . T h i s d i f f e r e n c e has been a t t r i b u t e d t o the s t r o n g e l e c -t r o n w i t h d r a w i n g p r o p e r t i e s o f the e t h y n y l group (11) r e l a t i v e t o t h o s e o f o t h e r hydrocarbon s u b s t i t u e n t s . As w e l l , the p r o p i o l y l h a l i d e s a r e the s i m p l e s t a c i d h a l i d e s i n which the c a r b o n y l bond i s c o n j u g a t e t o a c a r b o n - c a r b o n t r i p l e bond. T h e r e f o r e i t would not be s u r p r i s i n g i f t h e -COX groups i n t h e p r o p i o l y l h a l i d e s had somewhat d i f f e r e n t s t r u c t u r e s from t h o s e found f o r o t h e r a c i d h a l i d e s . 153 T h i s c h a p t e r d e a l s w i t h the microwave spectrum and s t r u c t u r e o f one such d e r i v a t i v e : p r o p i o l y l c h l o r i d e . S e v e r a l r e c e n t r e p o r t s have d e a l t w i t h i t s s y n t h e s i s and w i t h o t h e r s p e c t r o s c o p i c i n v e s t i g a t i o n s . Augdahl ejt aj_. (12) p r e p a r e d p r o p i o l y l c h l o r i d e from t he p a r e n t a c i d by h a l o g e n a t i o n w i t h 1,1 d i c h l o r o d i m e t h y l e t h e r , r e c o r d e d t h e i n f r a r e d and Raman s p e c t r a and a s s i g n e d a l l v i b r a t i o n a l f u n d a m e n t a l s . B a l f o u r , G r i e g and V i s a i s o u k d e s c r i b e d a s y n t h e s i s from p r o p i o l i c a c i d and phosphorus p e n t a c h l o r i d e ( 1 3 ) . S u b s e q u e n t l y B a l f o u r e t al_. a n a l y s e d the v i b r a t i o n a l spectrum o f p r o p i o l y l c h l o r i d e - d (14) and ob s e r v e d t he near u l t r a v i o l e t s p e c t r a o f the normal and d e u t e r a t e d s p e c i e s ( 1 5 ) . Two r a t h e r i n c o m p l e t e normal c o o r d i n a t e a n a l y s e s have been made f o r p r o p i o l y l c h l o r i d e . In t h e f i r s t s t u d y t he mean a m p l i t u d e s o f v i b r a t i o n were r e p o r t e d w i t h o u t d e t a i l s o f the c o r r e s p o n d i n g f o r c e f i e l d ( 1 6 ) . A second a n a l y s i s gave v a l u e s f o r the f o r c e c o n s t a n t s but u n f o r t u n a t e l y d i d not use non-redundant symmetry c o o r d i n a t e s ( 1 7 ) . The r o t a t i o n a l s p e c t r a o f a few m o l e c u l e s s t r u c t u r a l l y s i m i l a r t o p r o p i o l y l c h l o r i d e have been i n v e s t i g a t e d . The c o r r e s p o n d i n g a l d e h y d e , p r o p y n a l , was f i r s t s t u d i e d by Howe and G o l d s t e i n (18) who a s s i g n e d a few low J l i n e s o f the normal i s o t o p i c s p e c i e s and measured t h e d i p o l e moment. A complete s t r u c t u r e f o r p r o p y n a l was l a t e r d e t e r m i n e d by C o s t a i n and Morton ( 1 9 ) . T h e i r microwave r e s u l t s showed t h a t t he carbon c h a i n i n pro p y n a l has a bend o f a p p r o x i m a t e l y 1.5 d e g r e e s . T h i s r e s u l t has s i n c e been c o n f i r m e d by a c o m b i n a t i o n o f the microwave r e s u l t s w i t h e l e c t r o n d i f f r a c t i o n d a t a ( 2 0 ) . The d e v i a t i o n from l i n e a r i t y , i f any, o f the carbon c h a i n s o f o t h e r p r o p i o l y l - t y p e m o l e c u l e s i s an i n t e r e s t i n g problem which has not p r e v i o u s l y r e c e i v e d a t t e n t i o n . Other r e l a t e d microwave s t u d i e s 154 i n c l u d e t h o s e o f p r o p i o l i c a c i d , which L i s t e r and T y l e r (21) showed t o be p l a n a r , and 2- c h l o r o b u t e n - 3 - y n e (22) which i s i n e r t i a l l y s i m i l a r t o and i s o e l e c t r o n i c w i t h p r o p i o l y l c h l o r i d e . In t h e p r e s e n t s t u d y o f p r o p i o l y l c h l o r i d e f o u r i s o t o p i c s p e c i e s have been i n v e s t i g a t e d . T h e i r s p e c t r a have been a n a l y s e d t o y i e l d v a l u e s f o r t h e r o t a t i o n a l c o n s t a n t s , q u 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 c o n s t a n t s and 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 . The m o l e c u l a r d i p o l e moment has a l s o been o b t a i n e d . U s i n g an assumed s t r u c t u r e f o r t h e e t h y n y l group th e r e m a i n i n g s t r u c t u r a l parameters have been c a l c u l a t e d from t h e ground s t a t e e f f e c t i v e moments o f i n e r t i a . F u r t h e r , t he c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s have been combined w i t h e x i s t i n g v i b r a t i o n a l d a t a t o d e t e r m i n e an approximate f o r c e f i e l d . A g a i n , h a v i n g assumed a s t r u c t u r e f o r t h e e t h y n y l group, the average r o t a t i o n a l c o n s t a n t s have been used t o c a l -c u l a t e t he average s t r u c t u r e i n the ground v i b r a t i o n a l s t a t e . 155 5.1 Assignment o f the S p e c t r a The g e n e r a l method used t o a s s i g n the spectrum o f p r o p i o l y l c h l o r i d e was v e r y s i m i l a r t o t h o s e used f o r s u l p h u r d i c h l o r i d e and d i c h l o r o s i l a n e . F i r s t a model s t r u c t u r e based on the known ge o m e t r i e s o f pr o p y n a l (19) and a c e t y l c h l o r i d e (4) was used t o p r o v i d e e s t i m a t e s f o r the r o t a t i o n a l c o n s t a n t s ; t h e s e c o n s t a n t s , i n t u r n , were used to make an approximate p r e d i c t i o n o f the spectrum, and e s p e c i a l l y o f some key t r a n s i t i o n s which c o u l d be used f o r i n i t i a l a s s i g n m e n t s . A major d i f f e r e n c e was e x p e c t e d , however, between the spectrum o f p r o p i o l y l c h l o r i d e and the p r e v i o u s two m o l e c u l e s . L i k e p r o p y n a l , p r o p i o l y l c h l o r i d e was e x p e c t e d t o be p l a n a r , w i t h C $ symmetry, and thus to have non-zero components o f i t s d i p o l e moment a l o n g two o f i t s p r i n c i p a l i n e r t i a l axes. Thus, i n c o n t r a s t t o S C I 2 and S i H o C l g , which have o n l y b_-type t r a n s i t i o n s , p r o p i o l y l c h l o r i d e s h o u l d have both a- and b_-type s p e c t r a . (The K K s e l e c t i o n r u l e s f o r a-type t r a n s i t i o n s a r e ee -<—*• eo and a c — oe « — • oo where a g a i n (see s e c t i o n 3.1) e and o r e s p e c t i v e l y denote even and odd v a l u e s o f K and K ( 2 3 ) ) . The a-type s p e c t r a f o l l o w a r e l a t i v e l y a C s i m p l e p a t t e r n , the most prominent p a r t o f which i s a s e r i e s o f e q u a l l y spaced R branch l i n e s . F or the t r a n s i t i o n s ( J + 1) *• J , t h e s e groups s h o u l d be a t a f r e q u e n c y ^ ( B + C ) ( J + 1 ) . They s h o u l d , f u r t h e r m o r e , have h i g h l y c h a r a c t e r i s t i c S t a r k p a t t e r n s ; i n p a r t i c u l a r the c e n t r a l p a r t s o f the groups, and v e r y l i t t l e e l s e i n the spectrum, s h o u l d be o b s e r v a b l e a t v e r y low S t a r k f i e l d s . They s h o u l d thus be u s e f u l f o r i n i t i a l a s s i g n m e n t s . An i n i t i a l sweep o f the spectrum o f normal p r o p i o l y l c h l o r i d e i n t he f r e q u e n c y range 26.5-40 GHz a t h i g h S t a r k f i e l d s showed i t t o be v e r y r i c h and complex, w i t h e v i d e n c e o f c h l o r i n e q u a d r u p o l e h y p e r f i n e s t r u c t u r e , but no w e l l r e s o l v e d S t a r k p a t t e r n s . T h i s was i n k e e p i n g w i t h i n i t i a l p r e d i c t i o n s . A t v e r y low m o d u l a t i o n f i e l d s , t y p i c a l l y 20-40 v o l t 156 cm , the d e n s i t y o f l i n e s was g r e a t l y reduced. Under t h e s e c o n d i t i o n s two clumps o f l i n e s were found a t ^ 31.5-32.5 GHz and a t 37.0-38.2 GHz, a f r e q u e n c y r a t i o o f ^6:7. They were a p p a r e n t l y t he a_-type R branches J = 6 + 5 and 7 6 r e s p e c t i v e l y . C l o s e r i n s p e c t i o n r e v e a l e d t h a t each clump c o n t a i n e d two groups o f l i n e s : a s t r o n g h i g h f r e q u e n c y group and an almos t i d e n t i c a l group w i t h one t h i r d the i n t e n s i t y a t lower f r e q u e n c y . They 35 37 were e a s i l y a s s i g n e d as a_-type R branches o f HCCCO Cl and HCCCO C l , r e s p e c t i v e l y , and the o v e r a l l assignment was taken as c o n f i r m e d . I t was a l s o r e l a t i v e l y easy to a s s i g n i n d i v i d u a l l i n e s i n s i d e a g i v e n group u s i n g t h e i r S t a r k e f f e c t s , and r e l a t i v e i n t e n s i t i e s i n comparison w i t h t he o r i g i n a l p r e d i c t i o n s . F i r s t to be a s s i g n e d were the hig h K a t r a n s i t i o n s 7 g «*- 6 g, 7 g 6 g , 7^ «- 6 4 3 , 7 4 3 <- 6 4 2 , 6 5 <- 5 5 , 6 4 3 -«- 5 4 2 and 6 4 2 5 ^ , which were then used i n a f i t t o the r o t a t i o n a l c o n s t a n t s , which i n t u r n gave new p r e d i c t i o n s f o r f u r t h e r t r a n s i t i o n s . The b o o t s t r a p p r o c e d u r e which had e a r l i e r been used f o r S C I 2 and S i H 2 C l 2 was now employed t o a s s i g n an i n c r e a s i n g number o f t r a n s i t i o n s , f i r s t a_-type and then b_-type, f o r both i s o t o p i c s p e c i e s . Most t r a n s i t i o n s showed to some degree c h l o r i n e q u a d r u p o l e h y p e r f i n e s t r u c t u r e , from which i t was p o s s i b l e t o e v a l u a t e t he c o u p l i n g c o n s t a n t s ( s e c t i o n 5.3). T h i s h y p e r f i n e s t r u c t u r e c o n f i r m e d the r o t a t i o n a l a s s i g n m e n t s . The r e l a t i v e i n t e n s i t i e s o f t he a- and b_-type t r a n s i t i o n s were v e r y s i m i l a r , s u g g e s t i n g t h a t the u and y, d i p o l e moment components were o f n e a r l y equal magnitude, a D The spectrum o f p r o p i o l y l c h l o r i d e - d was a l s o examined w i t h 35 37 t r a n s i t i o n s o f the DCCCO Cl and DCCCO Cl s p e c i e s b e i n g a s s i g n e d . The c h l o r i n e 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 the two d e u t e r a t e d s p e c i e s were f i r s t e s t i m a t e d u s i n g the normal s p e c i e s r e s u l t s . These v a l u e s o f the c o n s t a n t s p r e d i c t e d the o b s e r v e d h y p e r f i n e p a t t e r n s w e l l and g r e a t l y f a c i l i t a t e d 'the assignment, which f o l l o w e d a c o u r s e s i m i l a r t o t h a t 157 p r e v i o u s l y d e s c r i b e d f o r t h e normal s p e c i e s . F i n a l l y , v i b r a t i o n a l s a t e l l i t e s were o b s e r v e d f o r the h i g h K a l i n e s o f the J = 6 5 and J = 7 -«- 6 a_-type R branch groups. These were measured f o r s p e c i f i c i s o t o p i c s p e c i e s and en a b l e d some f u r t h e r a s s i g n -ments t o be made. From the r e l a t i v e i n t e n s i t i e s o f the ground and e x c i t e d s t a t e l i n e s a t d r y i c e temperature a v i b r a t i o n a l fundamental was p r e d i c t e d a t 150 +_ 50 cm" 1. T h i s agrees v e r y w e l l w i t h the measured f r e q u e n c y o f t h e v g fundamental a t 157 cm" 1 ( 1 2 ) . No o t h e r fundamental l i e s w i t h i n the p r e d i c t e d range a l t h o u g h a t 224 cm" 1 i s f a i r l y c l o s e ( 1 2 ) . No attempt was made t o a s s i g n any l i n e s o f o t h e r e x c i t e d s t a t e s . 5.2 D e t e r m i n a t i o n o f the R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n  C o n s t a n t s The h y p e r f i n e s t r u c t u r e o f the v a r i o u s p r o p i o l y l c h l o r i d e t r a n s i t i o n s was ac c o u n t e d f o r u s i n g t h e c h l o r i n e 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 T a b l e 5.4. A f t e r t he h y p e r f i n e s t r u c t u r e was s u b t r a c t e d from each r o t a t i o n a l t r a n s i t i o n the r e s u l t i n g u n s p l i t l i n e f r e q u e n c i e s were used t o c a l c u l a t e the r o t a t i o n a l c o n s t a n t s and q u 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 c o n s t a n t s . The A r e d u c t i o n o f Watson's H a m i l t o n i a n i n the I r r e p r e s e n t a t i o n , e q u a t i o n 1.11, was a g a i n used; no s e x t i c c o n s t a n t s were r e q u i r e d t o f i t the d a t a . For most s p e c i e s s t u d i e d the data were used t o o b t a i n v a l u e s f o r the r o t a t i o n a l c o n s t a n t s and a l l f i v e q u a r t i c c e n t r i f u -07 OC gal d i s t o r t i o n c o n s t a n t s . F or the HCCCO Cl and DCCCO C l e x c i t e d s t a t e s , however, t h e r e were i n s u f f i c i e n t d a t a a v a i l a b l e t o per f o r m c e n t r i f u g a l d i s t o r t i o n a n a l y s e s . In t h e s e l a t t e r two c a s e s t he d i s t o r t i o n on each l i n e was assumed t o be the same as t h a t c a l c u l a t e d f o r the c o r r e s p o n d i n g ground s t a t e t r a n s i t i o n , and was s u b t r a c t e d from the measured f r e q u e n c i e s ; t he r e s u l t i n g f r e q u e n c i e s were f i t t o the t h r e e r o t a t i o n a l c o n s t a n t s . 158 A summary o f the " o b s e r v e d " u n s p l i t l i n e f r e q u e n c i e s o f the measured t r a n s i t i o n s i s p r e s e n t e d i n T a b l e 5.1 t o g e t h e r w i t h t h e c a l c u l a t e d t r a n s i t i o n f r e q u e n c i e s and c e n t r i f u g a l d i s t o r t i o n c o r r e c t i o n s . The d e t e r m i n e d r o t a t i o n a l c o n s t a n t s and c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s a r e g i v e n i n T a b l e 5.2. 159 T a b l e 5.1 Observed R o t a t i o n a l T r a n s i t i o n s (MHz) o f P r o p i o l y l C h l o r i d e T r a n s i t i o n O b s e r v e d 3 D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n HCCCO CI (ground v i b r a t i o n a l s t a t e ) 3 0 , 3 " 2 ^0,2 15422.13 -0.08 -0.00 5 1 , 4 - 4 1 , 3 28253.37 -0.63 -0.05 53,3 " 43,2 27062.95 -0.24 0.04 6 1 , 6 - 51,5 28261.22 -0.28 -0.04 6 1 , 5 " 51,4 33278.70 -0.91 0.02 6 2 , 5 " 52,4 31341.46 -0.58 -0.02 62,4 " 5 °2,3 34666.16 -1.33 -0.07 6 3 , 4 " 5 °3,3 32497.22 -0.62 -0.02 6 3 , 3 " 53,2 33252.92 -0.90 -0.03 6 1 , 6 - 5 0 , 5 29075.06 -0.12 0.01 7 1 , 6 - 61,5 37944.99 -1.14 0.04 7 2 , 6 " 6 2 , 5 36214.00 -0.89 0.01 7 3 , 5 " 63,4 37873.60 -1.14 -0.02 73,4 " 7 2 , 5 17312.08 0.20 0.04 7 4 , 3 " 73,4 29105.35 -1.34 0.02 8 0 , 8 " 70,7 37251.45 -0.56 0.03 8 1 , 8 " 7 1 , 7 37140.16 -0.59 -0.06 8 1 , 8 " 70,7 37355.33 -0.47 0.04 8 1 , 7 " 72,6 38796.04 -2.33 0.04 8 2 , 6 " 7 3 , 5 31381.27 -4.12 0.01 160 T a b l e 5.1 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n HCCCO CI (ground v i b r a t i o n a l s t a t e ) 81,7 ' 80,8 29541.94 -2.90 -0.02 8 3 , 6 " 82,7 28813.10 -1.85 -0.04 8 3 , 5 " 8 2 , 6 16954.97 -0.11 0.02 8 4 , 5 " 8 3 , 6 32032.24 -2.16 -0.04 8 4 , 4 " 8 3 , 5 27423.15 -0.12 0.04 9 2 , 8 " 9 1 , 9 35659.32 -2.68 0.00 93,7 " 92,8 31534.94 -2.77 -0.02 93,6 " 92,7 17688.25 -1.30 0.04 1 0 1 , 9 " 1 0 1 , 1 0 39198.13 -4.41 0.01 1 0 2 , 8 - 1 0 1 , 9 29159.19 -7.33 0.01 1 ] 2 , 9 " " l . l O . 34607.49 -9.36 -0.00 1 ] 4 , 8 " ] 1 3 , 9 36028.24 -4.17 0.01 "5.6 ""4.7 35100.25 1.50 0.00 1 2 4 , 8 " "5.7 34666.84 -14.20 0.01 1 2 3 , 9 " 1 2 2 , 1 0 27689.11 -12.11 0.05 1 3 5 , 8 " 1 3 4 , 9 30293.78 6.19 0.01 1 4 3 , 1 1 " 1 4 3 , 1 2 38123.23 -23.72 -0.03 1 4 3 , 1 1 " 1 4 2 , 1 2 38913.77 -21.48 0.01 1 4 5 , 9 " 1 4 4 , 1 0 28405.37 5.62 0.02 1 5 4 , 1 1 " 1 5 3 , 1 2 31099.80 -22.69 0.01 161 T a b l e 5.1 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n HCCCO C l (ground v i b r a t i o n a l s t a t e ) 1 5 5 , 1 0 " 1 5 4 , 1 1 27570.16 1.46 0.01 1 5 6 , 9 " 1 4 7 , 8 27673.54 -9.29 0.05 1 6 4 , 1 2 ~ 1 6 3 , 1 3 36529.52 -32.50 0.03 1 6 5 , 1 1 " 1 6 4 , 1 2 28174.53 -6.97 -0.01 1 7 5 , 1 2 " 1 7 4 , 1 3 30418.62 -19.81 -0.01 1 7 6 , 1 1 " 1 7 5 , 1 2 34636.11 15.24 -0.00 1 8 5 , 1 3 " 1 8 4 , 1 4 34294.39 -36.16 -0.02 1 8 6 , 1 2 " 1 8 5 , 1 3 32962.61 9.42 -0.02 1 8 7 , 1 1 " 1 7 8 , 1 0 36321.78 -21.78 -0.03 2 0 6 , 1 4 " 2 0 5 , 1 5 34165.71 -24.00 0.00 HCCC0 3 5C1 (v« = 1 e x c i t e d v i b r a t i o n a l s t a t e ) j 6 1 , 5 _ 51,4 33332.71 -0.83 0.03 62,4 " 52,3 34753.68 -1.25 -0.03 6 3 , 3 " 53,2 33337.35 -0.81 0.02 7 2 , 6 " 6 2 , 5 36267.03 -0.77 -0.03 73,4 " 7 2 , 5 17265.02 0.17 0.00 8 0 , 8 " 70,7 37279.27 -0.52 -0.00 81,8 " 71,7 37170.36 -0.55 -0.04 8 1 , 8 " 70,7 37380.14 -0.43 0.05 8 3 , 5 ' 8 2 , 6 16939.57 -0.15 0.01 n 4 , 8 " 1 ] 3 , 9 36094.39 -4.11 0.00 162 T a b l e 5.1 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n HCCCCT 3 5 C 1 (v, = 1 e x c i t e d v i b r a t i o n a l s t a t e ) 1 3 5 . 8 " , 3 4 , 9 30126 .37 6 . 0 5 -o.o-j 1 5 5 , 1 0 " 1 5 4 . 1 1 27527 .17 0 . 9 6 0 . 0 0 1 6 5 , 1 1 " 1 6 4 , 1 2 28243 .55 - 7 . 6 4 - 0 . 0 4 1 7 5 , 1 2 " 1 7 4 , 1 3 30619 .49 - 2 0 . 5 3 0 . 0 3 1 7 6 , 1 1 " 1 7 5 , 1 2 34426 .43 14 .64 - 0 . 0 0 1 8 6 , 1 2 ' 1 8 5 , 1 3 32842 .36 8 . 3 9 0 .02 1 9 6 , 1 3 " 1 9 5 , 1 4 32717 .54 - 5 . 0 6 0 . 0 0 2 0 6,14 - 2 0 5 , 1 5 34340.11 - 2 5 . 6 8 - 0 . 0 1 HCCCO 37 CI (ground v i b r a t i o n a l s t a t e ) 5 1 , 4 - 4 1 , 3 27716 .53 - 0 . 6 2 - 0 . 0 3 6 0 , 6 " 5 0 , 5 - 28149.22 - 0 . 2 8 0 . 0 5 6 1 , 6 - 5 1 , 5 27757 .83 - 0 . 2 9 - 0 . 0 2 6 1 , 5 " 51,4 32666 .33 - 0 . 9 1 - 0 . 0 1 6 2 , 5 " 5 2 , 4 30755 .84 - 0 . 5 6 0 .04 6 2 , 4 " 5 2 , 3 33963.76 - 1 . 3 0 - 0 . 0 1 6 3 , 4 " 5 ° 3 , 3 31863 .00 - 0 . 5 6 0 . 0 9 6 1 , 6 " 5 0 , 5 28596 .52 - 0 . 1 1 0 .02 7 0 , 7 " 6 0 , 6 32361 .13 - 0 . 4 0 0 . 0 4 7 1 , 7 " 6 1 , 6 32140 .30 - 0 . 4 3 - 0 . 0 3 163 T a b l e 5.1 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n HCCCO Cl (ground v i b r a t i o n a l s t a t e ) 7 1 , 6 - 6 1 , 5 37270.77 -1.14 0.04 7 2 , 6 " 6 2 , 5 35546.13 -0.87 0.02 73,4 " 6 3 , 3 38558.10 -1.75 0.08 7 0 , 7 - 6 1 , 6 31913.76 -0.56 0.01 7 U 6 - 6 2 , 5 31928.92 -1.96 -0.02 73,4 " 7 2 , 5 17281.11 0.31 0.04 74,4 ' 7 3 , 5 31376.17 -2.27 ' 0.00 74,3 " 73,4 29048.37 -1.34 0.11 8 0 , 8 " 70,7 36600.92 -0.57 -0.13 8 1 , 8 " 71,7 36485.07 -0.61 -0.02 8 4 , 5 " 8 3 , 6 31797.02 -2.04 0.01 84,4 " 8 3 , 5 27430.51 -0.05 -0.07 8 0 , 8 " 71,7 36374.41 -0.71 -0.06 8 1 , 8 " 70,7 36711.66 -0.47 -0.01 8 1 , 7 " 7 2 , 6 37959.35 -2.40 -0.04 9 1 , 8 - 9 0 , 9 33757.47 -3.53 -0.03 92,8 " 91,9 35015.11 -2.51 -0.03 9 3 , 7 " 9 2 , 8 31055.48 -2.53 -0.00 " 2 . 9 - " " 1 . 1 0 33741.53 -9.24 -0.03 1 2 4 , 8 " N 5 , 7 33076.32 -14.04 0.03 164 T a b l e 5.1 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n HCCCCO CI (ground v i b r a t i o n a l s t a t e ) 1 3 3 , 1 0 " 1 3 2 , 1 1 32125.13 -16.72 0.02 1 5 4 , 1 1 " 1 5 3 , 1 2 30143.61 -21.48 0.02 1 6 4 , 1 2 " 1 6 3 , 1 3 35329.74 -31.54 0.02 1 7 5 , 1 2 " 1 7 4 , 1 3 29721.53 -17.05 -0.04 1 8 5 , 1 3 " 1 8 4 , 1 4 33242.33 -33.35 -0.03 1 8 6 , 1 2 ' 1 8 5 , 1 3 33008.99 12.98 0.00 1 9 6 , 1 3 " 1 9 5 , 1 4 32450.44 1.04 0.02 2 0 6 , 1 4 " 2 0 5 , 1 5 33520.17 -18.48 0.00 HCCC0 3 7C1 ( v n = 1 e x c i t e d v i b r a t i o n a l s t a t e ) j 71,7 " 6 1 , 6 32168.07 -0.42 -0.05 70,7 " 6 0 , 6 32385.71 -0.44 0.04 8 0 , 8 " 70,7 36628.65 -0.57 -0.04 8 1 , 8 " 71,7 36514.92 -0.62 0.02 80,8 " 71,7 36407.26 -0.72 0.03 DCCCO CI (ground v i b r a t i o n a l s t a t e ) 6 0 , 6 " 50,5 27220.32 -0.29 0.01 6 1 , 5 " 51,4 31431.45 -0.87 -0.04 6 2 , 5 " 52,4 29565.57 -0.57 -0.03 165 T a b l e 5.1 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n DCCCO Cl (ground v i b r a t i o n a l s t a t e ) 62,4 " 52,3 32426.90 -1.20 -0.09 70,7 " 60,6 31286.97 -0.42 0.02 7 1 , 7 " 61,6 31028.19 -0.45 0.02 7 1 , 6 - 61,5 35957.32 -1.15 0.04 7 2 , 6 " 62,5 34205.01 -0.88 0.03 73,4 _ 63,3 36737.71 -1.63 0.06 7 1 , 7 " 60,6 31578.78 -0.30 0.02 7 2 , 6 " 71,7 26517.39 -1.20 -0.00 73,4 " 72,5 17897.98 0.03 0.04 7 0 , 7 " 61,6 30736.36 -0.57 0.01 80,8 " 70,7 35376.25 -0.61 0.02 81,8 " 71,7 35233.36 -0.64 -0.05 80,8 _ 71,7 35084.42 -0.74 0.01 81,8 " 70,7 35525.23 -0.51 0.01 9 y0,9 80,8 39489.08 -0.85 -0.09 9 2 , 7 " 83,6 35045.08 -5.15 0.05 9 3 , 7 " 92,8 30367.90 -2.62 0.01 9 5 , 4 " 94,5 39408.38 -4.19 0.01 1 22,10 " 1 2 i . n 36649.99 -10.56 -0.01 1 55,10 " 1 54,11 28519.27 4.02 0.00 166 T a b l e 5.1 ( c o n t i n u e d ) T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n DCCCO CI (ground v i b r a t i o n a l s t a t e ) 1 6 4 , 1 2 " 1 6 4 , 1 3 32007.70 -25.29 -0.02 1 6 5 , i l l _ 1 6 4 , 1 2 27899.78 -0.72 0.01 1 7 5 , 1 2 " 1 7 4 , 1 3 28608.40 -9.35 0.01 1 7 6 , 1 1 " 1 7 5 , 1 2 37485.52 13.51 -0.01 1 8 5 , 1 3 " 1 8 4 , 1 4 30801.18 -21.96 -0.02 , 8 6 , 1 2 _ 1 8 5 , 1 3 35031.99 13.26 -0.00 1 9 5 , 1 4 " 1 9 4 . 1 5 34464.80 -37.75 0.00 1 9 6 , 1 3 " 1 9 5 , 1 4 33415.47 7.53 -0.01 2 0 6 . 1 4 " 2 0 5 , 1 5 33059.76 -4.69 0.02 DCCCO 3 5 CI (v„ - 1 e x c i t e d v i b r a t i o n a l s t a t e ) 6 0 , 6 " 5 J 0,5 27242.71 -0.29 0.06 6 2 , 5 " 5 2,4 29616.06 -0.57 -0.01 63,4 " 5 3,3 30589.93 -0.63 -0.10 70,7 " 6 0,6 31311.83 -0.43 0.02 72,6 " 6 2,5 34258.96 -0.88 0.03 73,4 - 6 3,3 36841.02 -1.63 0.05 8 0 , 8 " 7 0,7 35404.30 -0.61 -0.01 8 1 , 8 " 7 1,7 35264.57 -0.64 -0.03 8 1 , 8 " 7 0,7 35548.60 -0.51 -0.01 167 Table 5.1 (continued) Transition Observed Distortion Deviation Frequency Correction DCCCO Cl (ground vibrational state) 6 0 , 6 ' 50,5 26753.09 -0.22 0.06 6 1 , 5 " 5 1 ,4 30861.99 -0.79 -0.01 6 2 , 5 " 52,4 29026.61 -0.46 -0.02 6 2 , 4 " 52,3 31796.35 -1.08 0.00 6 3 , 3 " 53,2 30477.66 -0.65 -0.06 7 0 , 7 - 6 0 , 6 30749.08 -0.31 0.00 7 1 , 7 -6 1 , 6 30486.19 -0.34 0.03 7 2 , 6 - 62,5 33587.34 -0.72 0.02 73,5 " 63,4 34930.36 -0.89 -0.02 73,4 ' 6 3 , 3 36013.11 -1.38 0.05 8 0 , 8 ' 70,7 34766.45 -0.44 0.06 8 1 , 8 " 71,7 34619.95 -0.48 -0.04 8 1 , 8 ' 70,7 34921.53 -0.33 -0.10 8 3 , 5 " 8 2 , 6 17089.68 0.05 0.01 9 3 0 , 9 8 0 , 8 38806.98 -0.62 0.03 9 1 , 9 " 8 1 , 8 38729.39 -0.65 -0.03 9 0 , 9 " 81,8 38651.73 -0.73 0.02 1 0 3 , 8 " " 1 0 2 , 9 32634.75 -3.47 -0.04 1 2 2 , 1 0 " 1 2 1 . 1 1 35816.05 -10.38 -0.02 1 4 3 , n " 1 4 2 , 1 2 33761.33 -18.81 0.06 T a b l e 5.1 ( c o n t i n u e d ) 168 T r a n s i t i o n Observed D i s t o r t i o n D e v i a t i o n Frequency C o r r e c t i o n DCCCO CI (ground v i b r a t i o n a l s t a t e ) 1 4 5 , 9 " ' 1 4 4 , 1 0 30153.18 6.19 0.05 1 5 4 , n " 1 5 3 , 1 2 27043.66 -15 .00 0.01 1 5 5 , 1 0 " 1 5 4 , 1 1 28446,86 5.31 0.01 1 7 5 , 1 2 " 1 7 4 , 1 3 28191.16 -7 .20 - 0 . 0 3 1 7 6 , 1 1 " 1 7 5 , 1 2 37565.51 14.86 -0 .06 1 8 5 , 1 3 " 1 8 5 , 1 4 30130.00 -19 .56 -0.01 1 8 6 , 1 2 ' 1 8 5 , 1 3 35074.66 15.54 0.00 1 9 6 , 1 3 " 1 9 5 , 1 4 33328.16 10.79 0.07 2 0 5 , 1 5 " 2 0 4 , 1 6 38179.02 -52 .89 -0 .00 2 0 6 , 1 4 " 2 0 5 , 1 5 32754.35 - 0 . 58 - 0 . 0 3 a H y p o t h e t i c a l u n s p l i t l i n e f r e q u e n c i e s . 169 T a b l e 5.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f P r o p i o l y l C h l o r i d e HCCC0 3 5C1 Ground S t a t e Vg = 1 S t a t e A(MHz) B(MHz) C(MHz) A j ( k H z ) A J K ( k H z ) A K ( k H z ) 6 j ( k H z ) 6 K ( k H z ) S t d . D e v i a t i o n o f F i t (MHz) No. o f T r a n s i t i o n s 7190.0143(30) a 3149.2440(10) 2186.7459(11) 1.2066(69) -4.790(28) 22.69(11) 0.4948(21) 2.325(30) 0.031 50 7190.3397(90) 3158.1194(85) 2188.0389(66) 1.171(60) -5.30(39) 24.0(15) 0.463(19) 2.91(33) 0.033 18 170 T a b l e 5.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f P r o p i o l y l C h l o r i d e ( c o n t i n u e d ) HCCC0 3 7C1 Ground S t a t e v g = 1 S t a t e A(MHz) 7111.7135(87) 7113.41(79) B(MHz) 3084.7668(30) 3093.18(21) C(MHz) 2148.3505(20) 2149.635(30) A j(kHz) 1.197(15) b A J K ( k H z ) -5.338(81) b A K ( k H z ) 23.86(41) b 6 j ( k H z ) 0.4837 b 6 K ( k H z ) 2.19(10) b S t d . D e v i a t i o n o f F i t (MHz) 0.050 0.061 No. o f T r a n s i t i o n s 38 5 171 T a b l e 5.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f P r o p i o l y l C h l o r i d e ( c o n t i n u e d ) DCCC0 J JC1 Ground S t a t e v n = 1 S t a t e A(MHz) 7075.1763(54) 7072.40(21) B(MHz) 2943.0992(34) 2951.8115(82) C(MHz) 2075.4480(26) 2076.8132(55) A j ( k H z ) 1.080(23) b A J K ( k H z ) -3.413(58) b A K ( k H z ) 20.73(25) b 6 j ( k H z ) 0.4174(44) b 6 K ( k H z ) 2.501(70) b S t d . D e v i a t i o n o f F i t (MHz) 0.038 0.056 No. o f T r a n s i t i o n s 32 9 172 T a b l e 5.2 R o t a t i o n a l C o n s t a n t s and C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s o f P r o p i o l y l C h l o r i d e ( c o n t i n u e d ) D C C C 0 o / C l Ground S t a t e A(MHz) 6990.1164(88) B(MHz) 2885.5642(39) C(MHz) 2039.4673(30) A j ( k H z ) 0.99(25) A J K ( k H z ) -4.30(14) A K ( k H z ) 24.06(68) 6j ( k H z ) 0.4042(62) 6 K ( k H z ) 2.45(11) S t d . D e v i a t i o n 0.047 o f F i t (MHz) No. o f T r a n s i t i o n s 30 a E r r o r s c i t e d a r e s t a n d a r d e r r o r s . b C e n t r i f u g a l d i s t o r t i o n c o r r e c t i o n s assumed t o be equal t o t h o s e o f th e c o r r e s p o n d i n g ground s t a t e . 173 5.3 N u c l e a r Quadrupole C o u p l i n g i n P r o p i o l y l C h l o r i d e The n u c l e a r q u a d r u p o l e h y p e r f i n e s t r u c t u r e observed i n the r o t a t i o n a l spectrum o f p r o p i o l y l c h l o r i d e was a n a l y s e d u s i n g e q u a t i o n 1.20, which g i v e s , t o f i r s t o r d e r , the n u c l e a r q u a d r u p o l e energy o f a p r o l a t e asymmetric r o t o r h a v i n g one q u a d r u p o l a r n u c l e u s . When good v a l u e s f o r the r o t a t i o n a l c o n s t a n t s had been o b t a i n e d , t h i s e q u a t i o n was used t o p r e d i c t t he dependence o f t h e ob s e r v e d s p l i t t i n g s on x„, aa and nx„, = X K K " x„„- As t h e s p l i t t i n g s o f some t r a n s i t i o n s depended aa DD CC a l m o s t e x c l u s i v e l y on e i t h e r x,, o r x kk " x„„ rough v a l u e s f o r t h e s e aa D D c c parameters were r e a d i l y e s t i m a t e d . These e n a b l e d assignments o f F quantum numbers and s u b s e q u e n t l y l e a s t squares f i t s t o be made. An a n a l y s i s o f the h y p e r f i n e s t r u c t u r e was performed f o r the ground v i b r a t i o n a l s t a t e o f each o f t h e f o u r i s o t o p i c s p e c i e s s t u d i e d . No l i n e s which e x h i b i t e d v e r y small s p l i t t i n g s - t y p i c a l l y l e s s than 0.30 MHz - were used t o de t e r m i n e the c o u p l i n g c o n s t a n t s as i n t h e s e c a s e s i t was i m p o s s i b l e t o d e f i n e t he magnitude o f the s p l i t -t i n g s a c c u r a t e l y . F or the t r a n s i t i o n s used i n the a n a l y s e s t h e s t r o n g e s t h y p e r f i n e components were the f o u r w i t h AF = aJ; none o f t h e weaker AF = AJ + 1 components were o b s e r v e d . E q u a t i o n 1.20 shows t h a t f o r t h e expect e d q u a r t e t t he s e p a r a t i o n o f the f i r s t and t h i r d components s h o u l d equal t h a t o f the second and f o u r t h . N e g l e c t i n g i n t e n s i t y v a r i a t i o n s t h e h y p e r f i n e p a t t e r n s can t h e r e f o r e be c o n s i d e r e d as c o n s i s t i n g o f two p a i r s o f s t a g g e r e d , e q u a l l y spaced d o u b l e t s . F or f i t t i n g p u r p o s e s , when a " d o u b l e t " was ob s e r v e d because o f i n c o m p l e t e l y r e s o l v e d h y p e r f i n e s t r u c t u r e , t h e s t a g g e r i n g o f the p a i r s o f components was i g n o r e d . T h i s i s e q u i v a l e n t t o assuming t h a t t he measured s p l i t t i n g s h o u l d equal t he s e p a r a t i o n o f say the f i r s t and t h i r d h y p e r f i n e components. As a l t e r n a n t 174 components o f the ob s e r v e d t r a n s i t i o n s had near equal i n t e n s i t i e s t h i s was a r e a s o n a b l e p r a c t i c e . In T a b l e 5.3 t h e o b s e r v e d h y p e r f i n e component f r e q u e n c i e s , F quantum numbers and ob s e r v e d and c a l c u l a t e d s p l i t t i n g s a r e g i v e n f o r s e v e r a l t r a n s i t i o n s used i n the f i t s . The v a l u e s o b t a i n e d f o r t he 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 a r e p r e s e n t e d i n T a b l e 5.4. A p l a n a r m o l e c u l a r s t r u c t u r e f o r p r o p i o l y l c h l o r i d e r e q u i r e s t h a t x c c be one o f the p r i n c i p a l v a l u e s o f the q u a d r u p o l e t e n s o r . C o n s e q u e n t l y i t s v a l u e must be i n v a r i a n t t o the i s o t o p i c s u b s t i t u t i o n o f any atom e x c e p t or 07 c h l o r i n e . F u r t h e r , the r a t i o x c c ( C l ) / X ( CI) must equal the r a t i o o f the q u a d r u p o l e moments o f the two c h l o r i n e n u c l e i (= 1.269 ( 2 4 ) ) . The OC d a t a o f T a b l e 5.4 s a t i s f y t h e s e c r i t e r i a ( e x p e r i m e n t a l l y x ( C I ) / 37 X c c ( CI) = 1.279) and, i n f a c t , p r o v i d e s t r o n g e v i d e n c e f o r a p l a n a r m o l e c u l a r s t r u c t u r e . 175 T a b l e 5.3 R e p r e s e n t a t i v e P r o p i o l y l C h l o r i d e T r a n s i t i o n s (MHz) used i n the N u c l e a r Quadrupole C o u p l i n g A n a l y s e s a a F F Observed Observed C a l c u l a t e d Frequency S p l i t t i n g S p l i t t i n g HCCC0 3 5C1 : Ground V i b r a t i o n a l S t a t e  5 3 3 " 4 3 2 5.5 4.5 27061.58 -1.39 -1.39 4.5 3.5 27062.35 -0.62 -0.62 6.5 5.5 27063.75 0.78 0.79 3.5 4.5 27064.55 1.58 1.56 5 3 2 " 431 5.5 4.5 27365.95 -1.21 -1.22 4.5 3.5 27366.65 -0.51 -0.52 6.5 5.5 27367.85 0.69 0.68 3.5 4.5 27368.52 1.36 1.38 8 1 7 ~ 8 0 8 6.5 6.5 29539.16 -2.78 -2.76 9.5 9.5 29540.01 -1.93 -1.94 7.5 7.5 29543.79 1.85 1.84 8.5 8.5 29544.62 2.68 2.67 8 3 6 ' 8 2 7 6.5 6.5 28811.38 -1.72 -1.72 9.5 9.5 28811.90 -1.20 -1.20 7.5 7.5 28814.24 1.14 1.14 8.5 8.5 28814.76 1.66 1.66 a 1 Here F and F are the l a b e l s f o r the i n i t i a l and f i n a l s t a t e s r e s p e c t i v e l y . 176 T a b l e 5.3 R e p r e s e n t a t i v e P r o p i o l y l C h l o r i d e T r a n s i t i o n s (MHz) used i n the N u c l e a r Quadrupole C o u p l i n g A n a l y s e s F F Observed Observed C a l c u l a t e d Frequency S p l i t t i n g S p l i t t i n g 9 - 9 y 2 8 y 1 9 7.5 7.5 35657.13 -2.19 -2.21 10.5 10.5 35657.72 -1.61 -1.61 8.5 8.5 35660.86 1.54 1.55 9.5 9.5 35661.46 2.14 2.14 1 0 1 9 " 1 0 1 , 1 0 8.5 8.5 39196.00 -2.13 -2.13 11.5 11.5 39196.51 -1.62 -1.60 9.5 9.5 39199.70 1.57 1.55 10.5 10.5 39200.22 2.09 2.08 HCCC0 3 7C1 : Ground V i b r a t i o n a l S t a t e 9 - 9 y 1 8 y 0 9 7.5 7.5 33755.71 -1.82 -1.83 10.5 10.5 33756.16 -1.37 -1.33 8.5 8.5 33758.81 1.28 1.28 9.5 9.5 33759.33 1.80 1.78 9 2 8 " 9 1 9 7.5 7.5 35013.41 -1.71 -1.68 10.5 10.5 35013.91 -1.21 -1.22 8.5 8.5 35016.32 1.20 1.17 9.5 9.5 35016.74 1.62 1.63 177 T a b l e 5.3 R e p r e s e n t a t i v e P r o p i o l y l C h l o r i d e T r a n s i t i o n s (MHz) used i n the N u c l e a r Quadrupole C o u p l i n g A n a l y s e s Observed Frequency Observed S p l i t t i n g C a l c u l a t e d S p l i t t i n g DCCC0 3 5C1 Ground V i b r a t i o n a l S t a t e 26 17 5.5 8.5 6.5 5.5 1 2 2 , 1 0 - 1 2 10.5 13.5 11.5 12.5 1,11 5.5 8.5 6.5 5.5 10.5 13.5 11.5 12.5 26514.49 26515.41 26519.25 26520.14 36647.90 36648.29 36651.63 36652.04 -2.90 -1.98 1.86 2.75 -2.08 -1.69 1.65 2.06 -2.91 1.95 1.82 2.78 •2.09 -1.65 1.61 2.06 DCCC0 3 7C1 Ground V i b r a t i o n a l S t a t e 10 12 38 8.5 11.5 9.5 10.5 2,10 " 10.5 13.5 11.5 12.5 10 29 12 1,11 8.5 11.5 9.5 10.5 10.5 13.5 11.5 12.5 32633.46 32633.76 32635.71 32636.01 35814.49 35814.80 35817.27 35817.57 -1.29 -0.99 0.96 1.26 -1.56 -1.25 1.22 1.52 -1.29 -0.97 0.94 1.26 -1.56 -1.23 1.20 1.54 178 T a b l e 5.4 C h l o r i n e 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 P r o p i o l y l C h l o r i d e S p e c i e s X a a ( M H z ) X b b ( M H z ) X c c ( M H z ) HCCC0 3 5C1 - 2 0 . 5 6 ( 6 ) a -3.21(8) 23.77(8) HCCC0 3 7C1 -16.80(12) -1.68(13) 18.48(13) DCCC0 3 5C1 -16.43(15) -7.20(18) 23.63(18) DCCC0 3 7C1 -14.43(32) -4.14(33) 18.57(33) a E r r o r s c i t e d a r e s t a n d a r d e r r o r s . 179 5.4 The D i p o l e Moment o f P r o p i o l y l C h l o r i d e A d e t e r m i n a t i o n o f t h e d i p o l e moment o f an asymmetric r o t o r by means o f the S t a r k e f f e c t r e q u i r e s t h e measurement o f S t a r k s h i f t s depen-dent on a l l non-zero d i p o l e moment components. For p r o p i o l y l c h l o r i d e t h e o b s e r v a t i o n o f s t r o n g a_- and b_-type t r a n s i t i o n s i n d i c a t e d t h a t y Q and y^ were both non-zero. The y c component o f the d i p o l e moment i s n e c e s s a r i l y z e r o , however, because o f the m o l e c u l e ' s p l a n a r s t r u c t u r e . When measuring the d i p o l e moment o f a m o l e c u l e c o n t a i n i n g a q u a d r u p o l a r n u c l e u s i t i s d e s i r a b l e t o use t r a n s i t i o n s whose h y p e r f i n e s p l i t t i n g i s sm a l l compared t o t h e o b s e r v e d S t a r k s h i f t s and a l s o t o the s e p a r a t i o n between i n d i v i d u a l S t a r k components. Because i n t e r f e r e n c e between the S t a r k components o f n e i g h b o u r i n g l i n e s s h o u l d a l s o be a v o i d e d , t h e r e were few s u i t a b l e c a n d i d a t e s f o r S t a r k e f f e c t measurements i n t h e dense p r o p i o l y l c h l o r i d e spectrum. The 3^ <- 2 ^ and 6^ t r a n s i t i o n s , which have S t a r k s h i f t s s t r o n g l y dependent on both y , and a y ^ , were s e l e c t e d f o r t h i s p u rpose; t h e low f r e q u e n c y component o f t h e *• 2Q2 t r a n s i t i o n and t h e two s t r o n g e s t 6 2 4 6^ components were measured. The S t a r k e f f e c t can be q u i t e c o m p l i c a t e d when a n u c l e u s w i t h q u a d r u p o l e c o u p l i n g i s p r e s e n t . T h i s i s t r u e e s p e c i a l l y when the S t a r k and q u a d r u p o l e e n e r g i e s a r e s i m i l a r , i n which c a s e s e c u l a r e q u a t i o n s must be s o l v e d (25). These d i f f i c u l t i e s a r e l a r g e l y a l l e v i a t e d when t h e qua d r u p o l e energy i s sm a l l compared t o the S t a r k energy; i n t h i s s t r o n g f i e l d l i m i t n u c l e a r s p i n - r o t a t i o n d e c o u p l i n g i s o b s e r v e d and the hyper-180 f i n e s p l i t t i n g can be t r e a t e d as a p e r t u r b a t i o n on t h e S t a r k e n e r g i e s . Howe and F l y g a r e have d i s c u s s e d t he e v a l u a t i o n o f t h e q u a d r u p o l e e n e r g i e s i n the h i g h f i e l d l i m i t ( 2 6 ) ; th e y showed t h a t t h e S t a r k components may be s p l i t t o g i v e h y p e r f i n e components f o r each p o s s i b l e v a l u e o f Mj, where Mj i s the s p a c e - f i x e d component o f J_. F u r t h e r , f o r the I = 3/2 c a s e , t he average o f the Mj = +_ 1/2 and Mj = 3/2 h y p e r f i n e component f r e q u e n c i e s i s t h a t which would be obs e r v e d f o r a m o l e c u l e ^ w i t h o u t q u a d r u p o l e c o u p l i n g . T h e r e f o r e , t h e s e average f r e q u e n c i e s , when e x t r a p o l a t e d t o z e r o f i e l d , g i v e the h y p o t h e t i c a l u n s p l i t l i n e f r e q u e n c y o f the t r a n s i t i o n s t u d i e d . T h i s s t r o n g f i e l d c a s e o b t a i n e d f o r a l l measured p r o p i o l y l c h l o r i d e S t a r k s h i f t s ; no h y p e r f i n e s t r u c t u r e was o b s e r v e d f o r any o f t h e S t a r k components. The S t a r k d a t a were t h e r e f o r e t r e a t e d as i f no q u a d r u p o l a r n u c l e u s were p r e s e n t . When p e r f o r m i n g S t a r k e f f e c t measurements the e l e c t r o d e s p a c i n g and t h e a p p l i e d v o l t a g e must both be measured p r e c i s e l y . The e l e c t r o d e s p a c i n g can be determined by o b s e r v i n g the S t a r k e f f e c t o f a m o l e c u l e whose d i p o l e moment i s a c c u r a t e l y known; u s u a l l y c a r b o n y l s u l p h i d e i s chosen. Very a c c u r a t e measurements o f the e l e c t r i c d i p o l e moment o f c a r b o n y l s u l p h i d e have been made by Muenter (27) and by R e i n a r t z and Dymanus (28) u s i n g m o l e c u l a r beam e l e c t r i c r esonance s p e c t r o s c o p y ; the v a l u e o f Muenter (0.71521 (20) Debye) was used h e r e . For t he S t a r k measurements a p o t e n t i a l V was o b t a i n e d by m i x i n g a l a r g e DC v o l t a g e and a s m a l l , f l o a t i n g AC v o l t a g e as d e s c r i b e d i n Chapter 2. The AC v o l t a g e was a 100 kHz square wave o f peak t o peak 181 amplitude 2V^; the signal observed for each Stark component therefore, consisted of two lobes (having opposite phases) at potentials of V Q C + V A C and v"DC - V A C respectively. If d i s the electrode spacing then the 2 value of E which corresponds to the mean frequency of these two lobes i s given by: E 2 = (Vp2. + V A 2 ) / d 2 = V 2/d 2 (5.1) The use of these mean frequency s h i f t s obviated the need for a precise determination of V^c because the modulation voltage required to produce a strong signal was always small compared to the DC bias voltage. The second order Stark energy of a l i n e a r molecule such as OCS i s given by (29): E = H2!2. J(J+D - 3M2 (5.2) S 2hB J(J+l)(2J-l)(2J+3) where B i s the rotational constant. The Stark s h i f t of the lone M=0 component of the J=l«-0 tr a n s i t i o n i s thus 2 2 Av = (0.50348) 2 4]L_ V (5.3) 15B d^ With B in MHz,y in Debye, d in cm and V i n volts the conversion factor 0.50348 MHz Debye - 1 v o l t " 1 cm gives Av in MHz; th i s value gives con-sistency with the results of Muenter (27). Therefore, a plot of Av 2 versus V should give a straight l i n e passing through the o r i g i n or, 2 al t e r n a t i v e l y , a plot of the observed frequencies versus V should give a l i n e with the identical slope but with the intercept at the zero f i e l d frequency v n . The carbonyl sulphide c a l i b r a t i o n data are collected 182 i n T a b l e 5.5; V A C was kept a t 20 v o l t s f o r a l l measurements. A l i n e a r l e a s t s q u a r e s f i t o f t h i s d a t a gave t h e r e s u l t s o f T a b l e 5.6. The c a l c u l a t e d i n t e r c e p t i s i n e x c e l l e n t agreement w i t h the p u b l i s h e d z e r o f i e l d f r e q u e n c y o f 12162.979(1) MHz ( 3 0 ) . U s i n g t h e v a l u e o f 6081.49 MHz (31) f o r B, the e l e c t r o d e s p a c i n g c a l c u l a t e d from t h e l e a s t squares s l o p e i s 0.46890(40) cm. The p r o p i o l y l c h l o r i d e S t a r k d a t a a r e c o l l e c t e d i n T a b l e 5.7; a g a i n , V ^ c was kept c o n s t a n t a t 20 v o l t s . In a l l c a s e s second o r d e r S t a r k s h i f t s were o b s e r v e d . The assignment o f M v a l u e s f o r t h e 6 2 4 *• 6 ^ t r a n s i t i o n was im m e d i a t e l y o b v i o u s because f o r a Q branch t r a n s i t i o n t h e i n t e n s i t y o f a g i v e n M component i s p r o p o r t i o n a l t o M ( 3 2 ) . To a s s i g n t h e s i n g l e 3 Q 3 «- 2 Q 2 component as t h e M = 0 t r a n s i t i o n , however, i t was f i r s t n e c e s s a r y t o e v a l u a t e t h e second o r d e r e x p r e s s i o n s f o r t he S t a r k e n e r g i e s o f a l l t h r e e 3 Q 3 *- 2 Q 2 components. The r e s u l t s o f l i n e a r l e a s t squares a n a l y s e s o f the data o f T a b l e 5.7 a r e g i v e n i n T a b l e 5.8. The poo r e r d a t a o b t a i n e d f o r p r o p i o l y l c h l o r i d e can, i n r e t r o s p e c t , be l a r g e l y a s c r i b e d t o the use o f an e x c e s s i v e m o d u l a t i o n v o l t a g e , which u n n e c e s s a r i l y broadened the S t a r k l o b e s . The second o r d e r e x p r e s s i o n s f o r t he p r o p i o l y l c h l o r i d e S t a r k e n e r g i e s , e v a l u a t e d u s i n g e q u a t i o n 1.28, a r e : Av(3 Q 3,M=0 <- 2 Q 2,M=0) = (-1.2769 x 1 0 ~ 6 y 2 - 3.3736 x 1 0 ~ 7 y 2 ) E 2 Av(6 2 4,M=5 + 6 ] 5,M=5) = ( 1.1322 x 1 0 ~ 6 y 2 + 4.6451 x 1 0 ~ 6 y 2 ) E 2 (5.4) Av(6 2 4,M=6 «• 6 ] 5,M=6) = ( 1.8425 x 1 0 " 6 y 2 + 7.1915 x 1 0 " 6 y 2 ) E 2 Because the l a s t two e x p r e s s i o n s a r e a l m o s t l i n e a r i l y dependent, o n l y two good s o l u t i o n s t o t h e s e e q u a t i o n s a r e p o s s i b l e ; t h e s e a r e o b t a i n e d by 183 s o l v i n g s i m u l t a n e o u s l y the f i r s t and e i t h e r o f t h e two r e m a i n i n g e q u a t i o n s . For t h i s purpose m u l t i p l y i n g the s l o p e s o f T a b l e 5 .8 2 2 by t h e f a c t o r d gave the a p p r o p r i a t e v a l u e s o f Av/E . The d e r i v e d mean v a l u e s o f u and y, were 2 .044 (3 ) Debye and 1 .790(14) Debye a D r e s p e c t i v e l y . The s i m i l a r y = v a l u e s r e s u l t from t h e f a c t t h a t o n l y a 2 the 3Q2, M=0 2Q2> M = 0 S t a r k e n e r g i e s depend p r i m a r i l y on y . The sp r e a d o f t h e y^ v a l u e s i s a b e t t e r i n d i c a t i o n o f t h e e x p e r i m e n t a l e r r o r ; the somewhat a r b i t r a r y but r a t h e r l a r g e r e r r o r l i m i t s a s s i g n e d t o both y f l and y b a r e + 0 .025 Debye g i v i n g 2 .717 (35 ) Debye f o r t h e 2 t o t a l d i p o l e moment y. A summary o f t h e e x p e r i m e n t a l v a l u e s o f Av/E t o g e t h e r w i t h t h o s e c a l c u l a t e d u s i n g the d e r i v e d v a l u e s o f y and y, a D i s g i v e n i n T a b l e 5 . 9 . I t s h o u l d be emphasized t h a t o n l y the magnitudes o f y = and y, have been d e t e r m i n e d from the S t a r k e f f e c t ; t h e a D r e s u l t s a r e i n agreement w i t h the r e l a t i v e i n t e n s i t i e s o f the a_- and b^ -t y p e s p e c t r a . 184 T a b l e 5.5 S t a r k S h i f t s i n Carbonyl S u l p h i d e : 1 6 0 1 2 c 3 2 s T r a n s i t i o n : J = 1 0 -2 2 10 c x r Observed Frequency a O b s . - C a l c . f r e q u e n c y 0 12162.970 -0.016 29 12163.070 0.009 104 12163.260 0.005 229 12163.580 0.001 404 12164.035 0.004 904 12165.330 0.006 1604 12167.135 0.001 2504 12169.460 0.002 3604 12172.305 -0.001 4765 12175.290 -0.019 6088 12178.695 -0.035 7573 12182.605 0.035 9220 12182.605 0.061 11029 12186.890 -0.047 a Given i n MHz . C a l c u l a t e d u s i n g t h e c o n s t a n t s o f T a b l e 5.6 . 185 T a b l e 5.6 C e l l C a l i b r a t i o n w i t h Carbonyl S u l p h i d e : 0' C S T r a n s i t i o n : J = 1 0 A v / V 2 2.5860(21) a x 1 0 ' 5 MHz V " 2 V 0 12162.986(10) MHz d 0.46890(40) cm a E r r o r s c i t e d a r e s t a n d a r d e r r o r s . 186 T a b l e 5.7 S t a r k S h i f t s i n P r o p i o l y l C h l o r i d e : HCCCO^Cl T r a n s i t i o n 3n?, M = 0 «- 2 n o , M = 0 7 7 a b 10 x V Observed Frequency O b s . - C a l c . Frequency 0 15422.13° 0.07 2504 15414.93 0.18 3029 15413.24 0.02 3604 15411.34 -0.20 4036 15410.28 0.00 4100 15410.06 -0.04 4493 15408.79 -0.16 4904 15407.68 -0.07 5333 15406.49 -0.01 5644 15405.59 0.00 6277 15403.78 0.03 6565 15402.94 0.04 6943 15401.91 0.11 7400 15400.51 0.04 187 T a b l e 5.7 S t a r k S h i f t s i n P r o p i o l y l C h l o r i d e : HCCCO^Cl T r a n s i t i o n 6 9 / 1, M = 5 6 , M = 5 10" x V Observed F r e q u e n c y 3 O b s . - C a l c . Frequency 0 12947.82° -0.23 2029 12966.05 0.11 2213 12967.65 0.07 2504 12970.35 0.20 2605 12971.09 0.05 2920 12973.88 0.06 3029 12974.83 0.04 3253 12976.65 -0.11 3604 12979.88 0.02 4229 12985.48 0.10 4904 12991.05 -0.28 188 T a b l e 5.7 S t a r k S h i f t s i n P r o p i o l y l C h l o r i d e : HCCC0 3 5C1 T r a n s i t i o n 6 0 „ , M = 6 *• 6 1 f-, M = 6 10 x V Observed F r e q u e n c y 3 O b s . - C a l c . Frequency 0 12947.82° -0.02 1604 12970.61 0.12 1768 12972.89 0.09 1940 12975.10 -0.13 2120 12977.83 0.05 2504 12982.82 -0.38 2708 12986.35 0.27 a Given i n MHz . D C a l c u l a t e d u s i n g t he c o n s t a n t s o f T a b l e 5.8 . ° H y p o t h e t i c a l u n s p l i t - l i n e f r e q u e n c y o f the z e r o - f i e l d t r a n s i t i o n . 189 35 T a b l e 5.8 S t a r k C o e f f i c i e n t s o f P r o p i o l y l C h l o r i d e : HCCCO CI 3 2 a b T r a n s i t i o n 10 x Av/V v Q 3 Q 3 , H = 0 + 2 Q 2 , M = 0 - 2 . 9 1 8 ( 1 4 ) C 15422.06(7) 6 2 4 , M = 5 -^ 6 1 5 , M = 5 8.826(39) 12948.05(12) 6 2 4 , M = 6 «- 6 1 5 , M = 6 14.12(1 ) 12947.84(21) a Measured i n MHz v o l t Given i n MHz E r r o r s c i t e d a r e s t a n d a r d e r r o r s 190 T a b l e 5.9 The D i p o l e Moment o f P r o p i o l y l C h l o r i d e 5 2 10° x A v / E ^ T r a n s i t i o n Observed C a l c u l a t e d 3 0 3 ' M = 0 ^ 2 0 2 ' M = 0 • 0 . 6 4 2 ( 3 )b -0, .642 6 2 4 ' M = 5 + 6 1 5 ' M = 5 1.941(9) 1, ,961 6 2 4 , M = 6 ^ 6 1 5 ' M = 6 3.104(23) 3, .074 y a = 2 . 0 4 4 ( 2 5 ) C Debye y f a = 1.790(25) Debye y = 2.717(35) Debye a Measured i n MHz v o l t " cm' S t a n d a r d e r r o r s A s s i g n e d e r r o r s . See t e x t 191 5.5 The E f f e c t i v e S t r u c t u r e o f P r o p i o l y l C h l o r i d e The ground s t a t e p r i n c i p a l moments o f i n e r t i a and i n e r t i a l d e f e c t s o f the f o u r i s o t o p i c s p e c i e s o f p r o p i o l y l c h l o r i d e s t u d i e d a r e g i v e n i n T a b l e 5.10. The ground s t a t e i n e r t i a l d e f e c t s a r e s m a l l p o s i t i v e numbers which show o n l y s m a l l i s o t o p i c v a r i a t i o n s and t h e r e -f o r e c o n f i r m t h a t the m o l e c u l e has a p l a n a r s t r u c t u r e . The l i m i t e d i s o t o p i c d a t a o b t a i n e d f o r p r o p i o l y l c h l o r i d e p r e c l u d e d the c a l c u l a t i o n o f a s u b s t i t u t i o n s t r u c t u r e . T h e r e f o r e , i n an i n i t i a l s t r u c t u r a l r e f i n e m e n t , a c r u d e ground s t a t e e f f e c t i v e geometry was c a l c u l a t e d . V a l u e s f o r f i v e bond l e n g t h s and f o u r a n g l e s a r e r e q u i r e d t o d e f i n e the s t r u c t u r e o f p r o p i o l y l c h l o r i d e ; t h e f o u r a n g l e s can be chosen as < ( H - C E C ) , <(C=C-C), <(C-C=0) and <(C-C-C1). As no d e v i a t i o n from l i n e a r i t y has been found f o r an e t h y n y l group i t i s r e a s o n a b l e t o assume t h a t < ( H - C E C ) = 180°; t h i s r e d u c e s the number o f s t r u c t u r a l parameters t o be d e t e r m i n e d t o e i g h t . T a b l e 5.10 c o n t a i n s v a l u e s f o r t w e l v e ground s t a t e p r i n c i p a l moments o f i n e r t i a . Because the p r o p i o l y l c h l o r i d e m o l e c u l e i s p l a n a r , however, o n l y e i g h t o f t h e s e (two f o r each i s o t o p e ) a r e i n d e p e n d e n t . T h e r e f o r e f u r t h e r assumptions were r e q u i r e d t o d e r i v e a m e a n i n g f u l s t r u c t u r e . S i n c e t h e C - H and C E C d i s t a n c e s have been found t o be n e a r l y i d e n t i c a l i n a wide range o f a c e t y l e n i c m o l e c u l e s (19,33-44) v a l u e s o f 1.057+0.002A and 1.206+0.003A were i n i t i a l l y assumed f o r t h e s e bond l e n g t h s ; o n l y f o r f l u o r o a c e t y l e n e (34) do t h e C - H and C=C d i s t a n c e s l i e o u t s i d e t h e s e r a n g e s . U s i n g the assumed e t h y n y l group geometry a s e r i e s o f e f f e c t i v e s t r u c t u r e s were c a l c u l a t e d f o r p r o p i o l y l c h l o r i d e . The c h o i c e o f " b e s t " s t r u c t u r e was s u b j e c t i v e , however,because d i f f e r e n t r e s u l t s were o b t a i n e d when e i t h e r the A and B o r , a l t e r n a t i v e l y , t h e B and C r o t a t i o n a l c o n s t a n t s 192 T a b l e 5.10 Ground S t a t e I n e r t i a l P a r a m e t e r s 9 o f P r o p i o l y l C h l o r i d e Parameter HCCC0 3 5C1 HCCC0 3 7C1 Ia° 7 0 . 2 8 9 0 1 ( 3 ) b 71.06290(9) l 0b 160.47629(5) 163.83053(16) 231.11006(12) 235.24048(22) A o 0.34477(13) 0.34704(29) DCCC0 3 5C1 DCCC0 3 7C1 <a° 71.42988(5) 72.29908(9) *°b 171.71660(20) 175.14045(24) *l 243.50357(31) 247.79951(36) A o 0.35709(37) 0.35998(44) a C a l c u l a t e d from the r o t a t i o n a l c o n s t a n t s o f T a b l e 5.2 u s i n g a op op c o n v e r s i o n f a c t o r o f 505379.0 uA . A l l parameters g i v e n a r e i n uA . b E r r o r s quoted a r e s t a n d a r d e r r o r s . 193 were used i n t h e f i t . T h e r e f o r e the e f f e c t i v e s t r u c t u r e g i v e n i n T a b l e 5.11 s h o u l d be r e g a r d e d w i t h detachment; i t was o b t a i n e d u s i n g the ground s t a t e A and B r o t a t i o n a l c o n s t a n t s and assuming f u r t h e r t h a t <(CEC-C) = 180° and r ( C - C ) = 1.435 A. When o n l y the geometry o f t h e e t h y n y l group was c o n s t r a i n e d somewhat d i f f e r e n t r e s u l t s were o b t a i n e d . For example, by f i t t i n g t h e A and B r o t a t i o n a l c o n s t a n t s r ( C - C ) , r(C=0) and r ( C - C l ) d i s t a n c e s o f 1.430 A, 1.200 A and 1.764 A r e s u l t e d ; the c o r r e s p o n d i n g v a l u e s d e r i v e d from a f i t t o the B and C r o t a t i o n a l o o o c o n s t a n t s were 1.450 A, 1.188 A and ii..760 A. F u r t h e r c a l c u l a t i o n s showed t h a t , w i t h the p r e s e n t d a t a s e t , the r ( C - C ) and r(C=0) d i s t a n c e s a r e h i g h l y c o r r e l a t e d ; i s o t o p i c s u b s t i t u t i o n o f t h e c a r b o n y l group would p r o b a b l y a l l e v i a t e t h i s d i f f i c u l t y . In both o f t h e s e l a t t e r r e f i n e m e n t s v e r y s i m i l a r v a l u e s were o b t a i n e d f o r the <(C=C-C) - 179.4° from t h e f i t t o the A and B r o t a t i o n a l c o n s t a n t s and 179.3° from the f i t t o the B and C c o n s t a n t s ( ( here an a n g l e l e s s than 180° i n d i c a t e s t h a t the e t h y n y l group i s bent away from t h e C-Cl bond and towards the C=0 bond whereas i n p r o p y n a l t h e o p p o s i t e was o b s e r v e d (19) ). I t was f e l t t h a t a f o r c e f i e l d r e f i n e m e n t and average s t r u c t u r e c a l c u l a t i o n would be u s e f u l t o determine whether t h i s a p p a r e n t bend o f the c a r b o n c h a i n was an a r t i f a c t caused by z e r o p o i n t v i b r a t i o n a l e f f e c t s . These c a l c u l a t i o n s a r e d e s c r i b e d i n the f o l l o w i n g two s e c t i o n s o f t h i s c h a p t e r . 194 T a b l e 5.11 The E f f e c t i v e S t r u c t u r e o f P r o p i o l y l C h l o r i d e 3 Parameter Value r Q ( C - H ) ( A ) b 1.056 r 0 ( C = C ) ( A ) D 1.208 r 0 ( C - C ) ( A ) b 1.435 r 0 ( O 0 ) ( A ) 1.207 r Q ( C - C l ) ( A ) 1.753 <(H-C=C)(Deg.) b 180.0 <(C E C - C ) ( D e g . ) b 180.0 <(C-C=0)(Deg.) 124.9 <(C-C-Cl)(Deg.) 113.0 3 O b t a i n e d by f i t t i n g t h e ground s t a t e A and B r o t a t i o n a l c o n s t a n t s o f T a b l e 5.2. b Assumed. 195 5.6 The Harmonic Fo r c e F i e l d o f P r o p i o l y l C h l o r i d e The f o r c e f i e l d r e f i n e m e n t f o r p r o p i o l y l c h l o r i d e proceeded i n a manner analogous to t h a t d e s c r i b e d p r e v i o u s l y f o r d i c h l o r o s i l a n e (see Chapter 4 ) . A g a i n , the d a t a p r o v i d e d by the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s were used to augment the a v a i l a b l e v i b r a t i o n wavenumbers. The chosen nonredundant symmetry c o o r d i n a t e s , which t r a n s f o r m as 9A 1 + 3A" i n the p o i n t group C s , a r e g i v e n i n terms o f the i n t e r n a l d i s p l a c e m e n t c o o r d i n a t e s i n T a b l e 5.12; the t r e a t m e n t o f the a n g u l a r redundancy a t the c a r b o n y l carbon f o l l o w s t h a t used f o r f o r m i c a c i d ( 4 5 ) . From the i n f r a r e d spectrum o f the gas (12) a complete s e t o f v i b r a t i o n a l wavenumbers was a v a i l a b l e f o r normal p r o p i o l y l c h l o r i d e a l t h o u g h the assignment o f (H-CEC i n p l a n e bend) was c o n s i d e r e d u n c e r t a i n . Except f o r v^, which showed a complex hot band s t r u c t u r e , t h e s e wavenumbers were used d i r e c t l y w i t h no c o r r e c t i o n s f o r a n h a r m o n i c i t y b e i n g made; the Raman l i q u i d v a l u e was adopted f o r v^. U n f o r t u n a t e l y , t h e r e s u l t s f o r p r o p i o l y l c h l o r i d e - d were l e s s c l e a r c u t , p a r t l y because a weaker spectrum was o b t a i n e d . For t h i s s p e c i e s v-|0 was not ob s e r v e d and gas phase v a l u e s f o r vg and were u n a v a i l a b l e ( 1 4 ) . Because the c o r r e s p o n d i n g gas and l i q u i d v a l u e s f o r the normal s p e c i e s were q u i t e d i f f e r e n t the Vg Raman l i q u i d v a l u e f o r p r o p i o l y l c h l o r i d e - d was d i s -c a r d e d ; i n s t e a d , a v a l u e was taken from the u l t r a v i o l e t spectrum ( 1 5 ) . A d d i t i o n a l l y , V | 2 f o r t n e d e u t e r a t e d s p e c i e s was taken to be 2 cm - 1 lower i n the gas than i n the l i q u i d ( o b s e r v e d s h i f t f o r the normal s p e c i e s i s 3 c m - 1 ) and, as f o r the normal s p e c i e s , t he Raman l i q u i d v a l u e was adopted f o r v 7 . Except f o r v f i (D-CEC i n p l a n e bend) the 196 T a b l e 5.12 I n t e r n a l C o o r d i n a t e s and Symmetry C o o r d i n a t e s o f P r o p i o l y l C h l o r i d e I n t e r n a l C o o r d i n a t e s : 3 A' b l o c k r l = r(C-H) = 1.056 A ; r 2 = r(CEC) = 1 .208 A r 3 = r ( C - C ) = 1.435 A ; r 4 = r(C=0) = 1 .207 A r 5 = r ( C - C l ) = 1.752 A ; e i = <(H-C=C) = 180° 9 2 = <(CEC-C) = 180° ' 6 3 = <(C-C=0) = 124.9° 6 4 = <(0=C-C1) = 113.0° ; 9 5 = <(C-C-C1) = 122.2° A" b l o c k a l = 6 ( C C 0 C l ) b ; a 2 = <(H-C=C) = 180° a 3 = <(C=C-C) = 180° Symmetry C o o r d i n a t e s : A' b l o c k S l = A r l S 2 = A r 2 S 3 = A r 4 S 4 = A r 3 S 5 = A r 5 S 6 = A9 1 S 7 = ( l / v ^ " ) ( A 6 3 - A 0 5 ) S 8 = ( l / v ^ " ) ( 2 A 6 4 - A 0 3 -, A 9 5 ) S 9 = A 6 2 A" b l o c k S 1 0 = : A a ^ S l l = : A a ] , S 1 2 = : A a 3 The m o l e c u l a r s t r u c t u r e i s the e f f e c t i v e s t r u c t u r e o f T a b l e 5.11. The i n t e r n a l c o o r d i n a t e a-j d e f i n e s t h e A" d e f o r m a t i o n o f t h e CC0C1 group. 197 wavenumbers used f o r the r e m a i n i n g p r o p i o l y l c h l o r i d e - d fundamentals were the r e p o r t e d gas i n f r a r e d v a l u e s ( 1 4 ) . The p r e v i o u s assignment o f vg t o a band a t 522 cm" 1 (14) seemed u n l i k e l y f o r s e v e r a l r e a s o n s . F i r s t l y , t h i s band showed no a p p r e c i a b l e gas to l i q u i d f r e q u e n c y s h i f t whereas f o r normal p r o p i o l y l c h l o r i d e (12) and pro p y n a l (46) the Raman l i q u i d v a l u e s a r e 20-25 cm - 1 h i g h e r than the gas i n f r a r e d v a l u e s . As w e l l , the f o r c e f i e l d c a l c u l a t i o n s suggested t h a t vg and v ^ ( D - C = C out o f p l a n e bend) s h o u l d be n e a r l y d e g e n e r a t e and s h o u l d o c c u r a t a somewhat h i g h e r f r e q u e n c y . N o t a b l y , a gas i n f r a r e d band o b s e r v e d a t 547 cm - 1 ( a s s i g n e d to v ^ ) i s seen i n the l i q u i d a t 570 c m - 1 . No o t h e r band shows t h i s b e h a v i o u r ; t e n t a t i v e l y t h e r e f o r e Vg and v-^ have been taken to be d e g e n e r a t e . The f o r c e c o n s t a n t s o b t a i n e d i n the p r e s e n t a n a l y s i s a r e g i v e n i n T a b l e 5.13. Because o f the l i m i t e d d a t a a v a i l a b l e the v a l u e s o f s e v e r a l f o r c e c o n s t a n t s were f i x e d and o t h e r s were c o n s t r a i n e d t o z e r o . In a d d i t i o n , the c o r r e s p o n d i n g f o r c e c o n s t a n t s d e f i n i n g the i n p l a n e and out o f p l a n e H - C E C arid C E C - C d e f o r m a t i o n s were assumed to be e q u a l . The v a l u e s o b t a i n e d f o r the v a r i o u s f o r c e c o n s t a n t s appear r e a s o n a b l e i n l i g h t o f r e s u l t s f o r the r e l a t e d m o l e c u l e s a c e t y l e n e ( 4 7 ) , propyne ( 4 8 ) , phosgene (49) and f o r m i c a c i d (45,50); the v a l u e o b t a i n e d f o r F 4 4 ( C - C s t r e t c h i n g f o r c e c o n s t a n t ) does, however, appear low i n comparison to the o_l c o r r e s p o n d i n g 5.50 mdyn A v a l u e o b t a i n e d f o r propyne ( 4 8 ) . T a b l e s 5.14 and 5.15 demonstrate how w e l l the p r e s e n t f o r c e f i e l d r e p r o d u c e s the ob s e r v e d d a t a . T a b l e 5.14 shows t h a t the f i t f o r the v i b r a t i o n a l wavenumbers, w i t h the p o s s i b l e e x c e p t i o n o f v Q , i s 198 T a b l e 5.13 The Harmonic F o r c e F i e l d o f P r o p i o l y l C h l o r i d e S p e c i e s F o r c e C o n s t a n t s A' A" F l l • 5 . 9 4 3 ( 9 4 ) b F22 = 15.79(29) F33 = 12.70 C ' r 3 4 =1.50 ; F 3 5 = F44 = 4.66(13) ; F 4 5 = 0.15 ; F 4 8 = F55 = 3.03 F66 = 0 . 2 6 3 ( 6 ) d ' F 6 9 = 0 . 0 9 6 ( 2 0 ) d F77 = 0.844(27) ' r 7 9 = 0.040(8) F 8 8 = 1.249(22) ; F 8 9 =-0.093(9) F 9 9 = 0 . 2 1 8 ( 9 ) d F10,10 = ° - 2 6 3 ( 6 ) 5 F10.12 ' ° - 0 9 6 ( 2 0 ) F 1 ^ = 0.689(15) F!2,12 • ° - 2 1 8 ( 3 ) °-l Bond s t r e t c h i n g f o r c e c o n s t a n t s i n mdyn A ; s t r e t c h - b e n d i n t e r a c t i o n f o r c e c o n s t a n t s i n mdyn r a d " ^ ; a n g l e bending f o r c e c o n s t a n t s i n mdyn A r a d c. U n c e r t a i n t i e s c i t e d a r e s t a n d a r d e r r o r s i n u n i t s o f t h e l a s t s i g n i f i -c a n t f i g u r e s . 199 T a b l e 5.13 ( c o n t i n u e d ) c No e r r o r c i t e d i n d i c a t e s a c o n s t r a i n e d f o r c e c o n s t a n t . F o r c e c o n s t a n t s not c i t e d were c o n s t r a i n e d t o z e r o . d The c o r r e s p o n d i n g f o r c e c o n s t a n t s d e f i n i n g t h e A 1 and A" H-C=C and CEC-C d e f o r m a t i o n s were assumed t o be e q u a l . S p e c i f i c a l l y , t h e c o n s t r a i n t s made were: F g 6 = F ] ( M 0 ; F g g = F ] ( M 2 and F g g = F 1 2 J 2 . 200 s a t i s f a c t o r y . T a b l e 5.15 shows t h a t t he f i t i s a l s o v e r y good f o r the c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s . F i n a l l y , a good harmonic f o r c e f i e l d s h o u l d a c c u r a t e l y p r e d i c t t he v a l u e s o f t h e ground and e x c i t e d s t a t e i n e r t i a l d e f e c t s ; t he r e s u l t s o f T a b l e 5.16 show t h a t t h i s i s the c a s e here and, f u r t h e r , t h a t t he i s o t o p i c dependence o f the ground s t a t e i n e r t i a l d e f e c t s i s w e l l a c c o u n t e d f o r . A l t h o u g h t he r e s u l t s o b t a i n e d a r e v e r y p l e a s i n g t he f o r c e f i e l d g i v e n i n T a b l e 5.13 s h o u l d be re g a r d e d as a p r e l i m i n a r y r e s u l t ; w i t h the many assumptions made, i n c l u d i n g t he n e g l e c t o f a n h a r m o n i c i t y , i t i s e v i d e n t t h a t t h e u n c e r t a i n t i e s g i v e n i n T a b l e 5.13 u n d e r e s t i m a t e t h e t o t a l e r r o r s i n th e s e parameters. 201 T a b l e 5.14 Observed and C a l c u l a t e d V i b r a t i o n a l Wavenumbers (cm" ) o f P r o p i o l y l C h l o r i d e V i b r a t i o n HCCCO .35C1 DCCC0 3 5C1 O b s e r v e d 9 D e v i a t i o n Observed b D e v i a t i o n A 1 v} 3326 -11.1 2609 7.8 v 2 2131 -8.2 2000 8.9 v 3 1767 -3.6 1772 1.6 v 4 1003 0.0 994 -5.9 v 5 696 -3.3 653 3.9 v 6 655 -1.4 547 -0.6 v 7 478 2.1 472 1.1 v 8 414 3.6 404 -1.2 v 9 157 5.2 147 2.8 703 3.2 ( 6 6 4 ) C -v l l 665 1.4 547 3.8 v i 2 224 -2.3 214 -2.2 9 Taken from Augdahl ejt al_. ( 1 2 ) . The o b s e r v e d wavenumbers a r e gas i n f r a r e d v a l u e s e x c e p t f o r v 7 which i s a Raman l i q u i d v a l u e . In th e f i t s t h e u n c e r t a i n t y o f was taken t o be 1.5%; a l l o t h e r fundamentals were g i v e n u n c e r t a i n t i e s o f 1% o f t h e measured v a l u e . 202 T a b l e 5.14 ( c o n t i n u e d ) The o b s e r v e d wavenumbers a r e m o s t l y gas i n f r a r e d v a l u e s ( 1 4 ) ; i s a Raman l i q u i d v a l u e and v - ^ i s an e s t i m a t e d gas phase v a l u e ( 216 cm - 1 i n the Raman spectrum o f the l i q u i d ( 1 4 ) ) . A v a l u e f o r v g was taken from t he u l t r a v i o l e t spectrum ( 1 5 ) . In the f i t s Vg and ^ were assumed t o be d e g e r a t e but were g i v e n low w e i g h t s ; see t e x t . In t h e f i t s v^, Vg and were g i v e n u n c e r t a i n t i e s o f 2%, 5% and 5% r e s p e c t i v e l y ; a l l o t h e r fundamentals were a s s i g n e d u n c e r t a i n t i e s o f 1% o f the measured v a l u e . c C a l c u l a t e d v a l u e . No e x p e r i m e n t a l v a l u e was a v a i l a b l e . 203 T a b l e 5.15 Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s (kHz) o f P r o p i o l y l C h l o r i d e ci b e Parameter Observed C a l c u l a t e d U n c e r t a i n t y HCCC0 3 5C1 A j 1.207 1.212 0.021 A J K -4.790 -4.717 0.084 A K 22.69 22.61 0.33 6 j 0.4948 0.4911 0.0063 6 K 2.325 2.195 0.090 DCCC0 3 5C1 A j 1.080 1.022 0.092 A J K -3.41 -3.408 0.23 A K 20.7 21.28 1.0 S j 0.417 0.4082 0.018 6 K 2.50 2.424 0.28 204 T a b l e 5.15 Observed and C a l c u l a t e d C e n t r i f u g a l D i s t o r t i o n C o n s t a n t s (kHz) o f P r o p i o l y l C h l o r i d e ( c o n t i n u e d ) Parameter Observed C a l c u l a t e d U n c e r t a i n t y HCCC0 3 7C1 A J 1.197 1.201 0.060 A J K -5.34 -5.164 0.32 A K 23.9 23.12 1.6 6 J 0.484 0.4859 0.029 6 K 2.19 2.006 0.40 DCCC0 3 7C1 A J 0.99 1.020 1.00 A J K -4.30 -3.933 0.56 A K 24.1 21.89 2.7 6 J 0.404 0.4072 0.025 2.45 2.172 0.44 a E x p e r i m e n t a l v a l u e s from T a b l e 5. 2. b V a l u e s c a l c u l a t e d u s i n g t h e f o r c e f i e l d o f T a b l e 5.13, c U n c e r t a i n t i e s used i n t h e f o r c e f i e l d r e f i n e m e n t . F or HCCC0 3 5C1 t h e c i t e d u n c e r t a i n t i e s a r e t h r e e s t a n d a r d e r r o r s ; f o r t h e o t h e r i s o t o p e s the a s s i g n e d u n c e r t a i n t i e s r e p r e s e n t f o u r s t a n d a r d e r r o r s . 205 T a b l e 5.16 Observed and C a l c u l a t e d I n e r t i a l D e f e c t s (uA ) o f P r o p i o l y l C h l o r i d e S p e c i e s Observed C a l c u l a t e d D e v i a t i o n Ground V i b r a t i o n a l S t a t e HCCC0 3 5C1 HCCC0 3 7C1 DCCC0 3 5C1 DCCC0 3 7C1 HCCC0 3 5C1 HCCC0 3 7C1 DCCC0 3 5C1 0.3448(1)' 0.3470(3) 0.3571(4) 0.3600(4) 0.3436 0.3460 0.3560 0.3587 _Vg = 1 E x c i t e d S t a t e 0.662(1) 0.669(14) 0.676(2) 0.652 0.668 0.683 0.0012 0.0011 0.0011 0.0013 0.010 0.001 -0.007 a C a l c u l a t e d from the r o t a t i o n a l c o n s t a n t s o f T a b l e 5.2. The v i b r a t i o n a l p a r t o f t h e i n e r t i a l d e f e c t c a l c u l a t e d u s i n g t he f o r c e f i e l d o f T a b l e 5.13. c E r r o r s c i t e d a r e s t a n d a r d e r r o r s . 206 5.7 The Average S t r u c t u r e o f P r o p i o l y l C h l o r i d e The harmonic f o r c e f i e l d o f T a b l e 5.13 was used t o c a l c u l a t e the ground s t a t e average r o t a t i o n a l c o n s t a n t s o f t h e f o u r i s o t o p i c s p e c i e s s t u d i e d ; t h e s e a r e g i v e n i n T a b l e 5.17. Because the i n e r t i a l d e f e c t s c a l c u l a t e d u s i n g t h e s e A z , B z and C z v a l u e s a r e e s s e n t i a l l y z e r o (see T a b l e 5.16) a l l t w e l v e r o t a t i o n a l c o n s t a n t s were used t o d e t e r m i n e t h e ground s t a t e average s t r u c t u r e . A g a i n , s i n c e o n l y e i g h t o f t h e s e were independent, i t was n e c e s s a r y to assume a s t r u c t u r e f o r t h e e t h y n y l o group. The r(C-H) bond l e n g t h was taken t o be 1.055 A ( r and r z v a l u e s o o f o r p r o p y n a l a r e 1.055 A (19) and 1.054 A (20) r e s p e c t i v e l y ) and t h e o r(CEC) l e n g t h was t a k e n t o be 1.207 A ( r and r z v a l u e s f o r p r o p y n a l o o a r e 1.209 A (19) and 1.205 A (20) r e s p e c t i v e l y ). The r e s u l t s o f a l e a s t squares f i t t o the ground s t a t e average r o t a t i o n a l c o n s t a n t s a r e g i v e n i n T a b l e 5.18. In the s t r u c t u r a l r e f i n e m e n t s the <(C-CEC) was not o c o n s t r a i n e d and r ( C - C ) was v a r i e d by t r i a l and e r r o r ( a t 0.0005 A i n c r e m e n t s ) t o f i n d the b e s t f i t ; i s o t o p i c v a r i a t i o n s i n t h e bond l e n g t h s were i g n o r e d . The s t a n d a r d d e v i a t i o n o f the f i t t o t h e t w e l v e r o t a t i o n a l c o n s t a n t s o f T a b l e 5.17 was 0.008 MHz, not s i g n i f i c a n t l y l a r g e r than the e r r o r s quoted f o r t h e e f f e c t i v e ground s t a t e c o n s t a n t s o f T a b l e 5.2; i n view o f the l i m i t e d i s o t o p i c data a v a i l a b l e , however, t h i s s m a l l s t a n d a r d d e v i a t i o n may not be m e a n i n g f u l . As w e l l , because p o s s i b l e s y s t e m a t i c e r r o r s have been i g n o r e d the l e a s t squares s t a n d a r d e r r o r s a l m o s t c e r t a i n l y u n d e r e s t i m a t e the t o t a l e r r o r s i n t h e s t r u c t u r a l p a r a m e t e r s ; t h e u n c e r t a i n t i e s quoted i n T a b l e 5.18 r e p r e s e n t f i v e s t a n d a r d e r r o r s but do not i n d i c a t e o u t s i d e l i m i t s o f e r r o r . 207 T a b l e 5.17 Ground S t a t e Average R o t a t i o n a l C o n s t a n t s (MHz) o f P r o p i o l y l C h l o r i d e HCCC0 3 5C1 HCCC0 3 7C1 7175.153 3145.260 2186.696 7097.163 3080.869 2148.287 DCCC0 3 5C1 DCCC0 3 7C1 7060.482 2939.564 2075.455 6975.728 2882.102 2039.460 a O b t a i n e d u s i n g t he e f f e c t i v e ground s t a t e r o t a t i o n a l c o n s t a n t s o f T a b l e 5.2 and the f o r c e f i e l d o f T a b l e 5.13. \ 208 T a b l e 5.18 The Average S t r u c t u r e o f P r o p i o l y l C h l o r i d e Parameter V a l u e r z ( C - H ) ( A ) a 1.055 r z ( C E C ) ( A ) a 1.207 r z ( C - C ) ( A ) b 1.4415 r z ( C = 0 ) ( A ) 1.1988(40)° r z ( C - C l ) ( A ) 1.7587(37) < ( H - C E C ) ( D e g . ) a 180.0 <(CEC-C)(Deg.) 1 7 9 . 5 8 ( 2 2 ) d <(C-C=0)(Deg.) 125.19(30) <(C-C-Cl)(Deg.) 112.42(23) a Assumed. b V a l u e found by t r i a l and e r r o r . See t e x t . E r r o r s quoted a r e f i v e s t a n d a r d e r r o r s . These a r e a r b i t r a r y e r r o r l i m i t s and may u n d e r e s t i m a t e t h e t o t a l e r r o r i n t h e s e p a r a m e t e r s . d The e t h y n y l group i s bent away from t h e C-Cl bond. 209 5.8 Comments on the S t r u c t u r e o f P r o p i o l y l C h l o r i d e A l t h o u g h the p r e s e n t r e s u l t s f o r p r o p i o l y l c h l o r i d e a r e not d e f i n i t i v e i t i s n e v e r t h e l e s s i n t e r e s t i n g t o compare the s t r u c t u r e s o f p r o p i o l y l c h l o r i d e and some r e l a t e d m o l e c u l e s ; t h i s has been done i n T a b l e 5.19. The r e s u l t s o f T a b l e 5.19 s u g g e s t t h a t the C O bond i n p r o p i o l y l c h l o r i d e i s s h o r t e r than t h a t i n p r o p y n a l . T h i s i s r e a s o n a b l e i n view o f r e s u l t s f o r H 2C0 ( 5 2 ) , HC0C1 (2) and C1 2C0 (53) where C=0 bond l e n g t h s o f 1.207 A ( r 2 ) , 1.188 A ( r ) and 1.179 A ( r z ) have been o b t a i n e d ; as w e l l , f o r CHgCHO (54) and CHgCOCl (51) the c o r r e s p o n d i n g v a l u e s a r e 1.207 A ( r z ) and 1.185 A ( r z ) . T h e r e f o r e t h e C=0 bond i n o p r o p i o l y l c h l o r i d e might be e x p e c t e d t o be 0.010 - 0.020 A s h o r t e r than t h a t i n p r o p y n a l ; t h e r e s u l t s o f T a b l e 5.19, a l b e i t i m p r e c i s e , s u p p o r t t h i s h y p o t h e s i s . More marked a r e the v a r i a t i o n s i n t h e C-Cl l e n g t h s ; e s s e n t i a l l y i d e n t i c a l bond d i s t a n c e s have been d e t e r m i n e d f o r fo r m y l c h l o r i d e and p r o p i o l y l c h l o r i d e w h i l e t h a t found f o r a c e t y l c h l o r i d e i s r a t h e r l o n g e r . K a g a r i s e (55) s u g g e s t e d t h a t e l e c t r o n e g a t i v e s u b s t i t u e n t s s h o u l d lower the c o n t r i b u t i o n o f nonbonded res o n a n c e s t r u c t u r e s such as RC0 +C1"; t h e r e f o r e the l o n g e s t C-Cl bond would be e x p e c t e d f o r a c e t y l c h l o r i d e due t o the p r e s e n c e o f the " e l e c t r o n d o n a t i n g " methyl group. S i m i l a r arguments have been used t o e x p l a i n t h e t r e n d i n t h e a c i d d i s s o c i a t i o n c o n s t a n t s o f the p a r e n t c a r b o x y l i c a c i d s ( 1 1 ) . On t h i s b a s i s one might e x p e c t the C-Cl bond i n p r o p i o l y l c h l o r i d e t o be s l i g h t l y s h o r t e r than t h a t found i n fo r m y l c h l o r i d e ; t h i s v e r y s i m p l e argument n e g l e c t s , however, p o s s i b l e c o n j u g a t i v e e f f e c t s i n p r o p i o l y l c h l o r i d e . The r e m a i n i n g bond l e n g t h s i n p r o p i o l y l c h l o r i d e and p r o p y n a l a r e appar-e n t l y n e a r l y e q u a l . 210 Lo o k i n g a t the bond a n g l e s i n a c e t y l c h l o r i d e and p r o p i o l y l c h l o r i d e i t i s seen t h a t the <(C-C-C1) i s e s s e n t i a l l y i d e n t i c a l i n both m o l e c u l e s ; t he <(C-C=0) i s i n each case about 14° l a r g e r . A p p a r e n t l y t he car b o n c h a i n i n p r o p i o l y l c h l o r i d e i s more n e a r l y l i n e a r t h a n t h a t f o u n d i n p r o p y n a l . A l t h o u g h t h i s may be an e x p e r i m e n t a l a r t i f a c t the r Q s t r u c t u r e c a l c u l a t i o n s o u t l i n e d i n s e c t i o n 5.5 l e a d t o t h e same c o n c l u s i o n . Less ambiguous s t r u c t u r a l r e s u l t s f o r p r o p i o l y l c h l o r i d e would r e q u i r e a d d i t i o n a l i s o t o p i c d a t a . In t h i s r e g a r d i t i s worth n o t i n g t h a t v e r y r e c e n t s y n t h e t i c work has p r o v i d e d a v i a b l e r o u t e t o o b t a i n i n g 13 18 C and 0 l a b e l l e d p r o p i o l i c a c i d ( 5 6 ) . T h e r e f o r e i t s h o u l d be p o s s i b l e t o c o r r e s p o n d i n g l y l a b e l p r o p i o l y l c h l o r i d e . 211 T a b l e 5.19 The S t r u c t u r e s o f P r o p i o l y l C h l o r i d e and R e l a t e d M o l e c u l e s 3 Parameter HCCC0C1 b HCCCHO HC0C1 CH 3C0C1 r ( C - H ) ( A ) 1.055 1.054(7) r(C=C)(A) 1.207 1.205(6) r ( C - C ) ( A ) 1.442 1.449(2) r(C=0)(A) 1.199(4) 1.212(5) 1.188(2) 1.185(3) r ( C - C l ) ( A ) 1.759(4) 1.760(2) 1.796(2) <(C-C=0)(Deg.) 125.2(3) 124.2(2) 127.2(6) <(C-C-C1)(Deg.) 112.4(2) 111.6(6) <(CEC-C)(Deg.) 1 7 9 . 6 ( 2 ) C 1 7 8 . 6 ( 3 ) d R e f e r e n c e T h i s work (20) (2) (51) The HC0C1 s t r u c t u r e i s an r s t r u c t u r e . The o t h e r s t r u c t u r e s a r e r z s t r u c t u r e s . S t r u c t u r e taken from T a b l e 5.18. Et h y n y l group bent away from C-Cl bond. E t h y n y l group bent away from C=0 bond. 212 B i b l i o g r a p h y 1. R.F. M i l l e r and R.F. C u r l , J r . , J . Chem. Phys. 34, 1847 (1961). 2. H. Takeo and C. Matsumura, J . Chem. Phys. 64, 4536 (1976). 3. L. P i e r c e and L.C. K r i s h e r , J . Chem. Phys. 31_, 875 (1959). 4. K.M. S i n n o t t , J . Chem. Phys. 34, 851 (1961). 5. H.N. V o l l t r a u e r and R.H. Schwendeman, J . Chem. Phys. 54, 268 (1971). 6. K.P.R. N a i r and J . E . Boggs, J . Mol. S t r u c t . 33, 45 (1976). 7. O.L. S t i e f v a t e r and E.B. W i l s o n , J r . , J . Chem. Phys. 50, 5385 (1969). 8. H. K a r l s s o n , J . Mol. S t r u c t . 33, 227 (1976). 9. 6.H. M a n s f i e l d and M.C. W h i t i n g , J . Chem. Soc. 4761 (1956). 10. J . G u i l l e m e and B. Wojtkowiak, B u l l . Soc. Chim. F r a n c e 3007 (1969). 11. C K . 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T s u c h i y a , J . Mol. S p e c t r o s c . 44, 88 (1972). 55. R.E. K a r g a r i s e , J . Am. Chem. Soc. 77_, 1377 (1955). 56. W.H. Dawson and R.B. Dunlap, J . Lab. Comp. Radiopharm. 1_6, 335 (1979). J 215 Appendix 1 A R e p r i n t o f a Report o f the Microwave Spectrum o f P r o p i o l y l F l u o r i d e 216 JOURNAL OF MOLECULAR SPECTROSCOPY 57, 118-126 (1975) The Microwave Spectrum, Structure, and Dipole Moment of Propiolyl Fluoride R. WELLINGTON DAVIS A N D M. C. L. GERRY Department of Chemistry, University of British Columbia, Vancouver, V6T 1W5, Canada The microwave spectrum of propiolyl fluoride has been observed in the frequency region 12.5-40 GHz. Rotational transitions have been assigned for the ground and two excited vibrational states of the normal isotopic species and for the ground vibrational state of the deuterated species. In each case, values for the rotational constants and centrifugal distortion constants have been obtained. The molecule has been shown to be planar and structural cal-culations suggest no anomalies in any of the internuclear parameters. Stark effect measure-ments have yielded a value of 2.98 ± 0.02 Debyes for the dipole moment. INTRODUCTION A simple method for the preparation of propiolyl fluoride, along with its vibrational spectrum, has recently been reported (i). The microwave spectra of the corresponding aldehyde (2), acid (3) and acid chloride (4) have been previously investigated. The present study was undertaken to determine the rotational constants and centrifugal distortion constants of propiolyl fluoride and hopefully to reveal any unusual structural features. A number of both a-type and considerably weaker b-type transitions have been measured up to / = 40 and the desired spectroscopic constants have been evaluated. Another recent report has presented an estimate for the dipole moment of propiolyl fluoride based on molecular orbital calculations (5). The dipole moment of propiolyl fluoride has been measured for purposes of comparison with this calculated value and with the measured dipole moments of structurally similar molecules. E X P E R I M E N T A L M E T H O D S The samples of normal and deuterated propiolyl fluoride were kindly prepared (/) and supplied by Balfour, Klapstein, and Visaisouk. Transitions were measured in the frequency regions 12.5-18 GHz and 26.5-40 GHz, using a 100 kHz Stark modulated spectrometer having a 10 ft. X-band cell. The source was a phase stabilized Hewlett-Packard 8400 B Microwave Spectroscopy Source. All measurements were made at dry ice temperature, at which propiolyl fluoride has an appreciable vapor pressure. After initial conditioning of the cell, broad band frequency sweeps requiring up to ninety minutes to complete could be obtained without noticeable sample decomposition. Sample pressures were typically 10-15 microns for broad band sweeps and Stark effect measurements, and 0-5 microns when measuring zero-field line 118 Copyright © 1975 by Academic Press, Inc. All rights of reproduction in any form reserved. 217 MICROWAVE SPECTRUM OF PROPIOLYL FLUORIDE 119 Table I. Observed and calculated rotational transitions of propiolyl fluoride (in MHz) Transition Observed Frequency Calculated Frequency Distortion Correction First High Order Order HCCC(0)F (Ground vibrational state) 2( 0, 2)-2( 1, 2)-2( 1, 1)-2( 2,. 1)-4( 2, 3)-4( 0, 4)-4( 1, 4)-4( 1, 3)-4( 2, 3)-2) -D-3) -4) -4)-4)-K 0, 1) K l , 1) 1 ( 1, 0) K i , o ) 4( 0, 4) 3( 0, 3) 3( 1, 3) 3( 1, 3( 2, 2) 2) 3( 2, 1) 3( 3, 4( 1, 3( 0, 5( 1, 5( 0, 5( 0, 5)- 4(0, 4) 5( 5( 5( 5( 5( 3, 3) 5( 3, 2) 5)-4)-4)-3)-5( 0, 4) -5) -5) -6) -3)-6)-6)-4( 1 4( 1 4( 4( 4( 4( 5( 1 4) 3) 3) 2) 2) 1) 5) 4( 0, 4) 4( 1 5( 1 6( H H 3, 4)-7( 2, 8( 2, 8( 3, 2, 3, 9( 9( 10( 10( I K IH 2, 2, 3, 3, 12( 3, 9) 13( 3,10) 5) -6) -5) -7) -6) -8)-8)-8). 8)-4) 5) 4) 7) 7( 0, 7) 7( 2, 5) 6( 3, 4) 8( 2 8( 2 9( 1, 9( 2, 10( 2 10( 1 11( 3 7) 6) 8) 7) 9) 9) 9) H( 2, 9) 12( 13( 10) 11) Deviation 14384.72 14384. .72 0 .00 0, .00 0.00 13401.54 13401 .49 -0. .05 0, .00 0.05 15584.98 15584, .98 -0 .16 0 • DO 0.00 38555.97 38556. .94 -0 .33 0. .00 0.03 34289.88 34289 .89 -1 .79 0. .00 -0.01 27959.53 27959 .58 0 .01 0 .00 -0.05 26604.68 26604. .66 -0. .09 0. .00 0.02 30931.10 30931. .10 -0 .36 0, .00 0.00 28901.27 28901. .21 -0. .78 0 .00 0.06 29927.76 29927. .82 -0. .93 0. .00 -0.06 29223.60 29223. .65 -1 .86 0. .00 -0.05 30245.73 30245, .74 -1 .55 0. .00 -0.01 32003.73 32003. .73 -0. .23 0 .00 0.00 16188.96 16188, ,93 -0. .99 0, .00 0.03 3H956.80 35956. .77 -2. .73 0, .00 0.03 34324.36 34324, .33 -0. .02 0 .00 0.03 33094.22 33094, .15 -0. .11 0, .00 0.07 38412.89 38412. .97 -0. .49 0 .00 -0.08 35991.24 35991. ,21 -0. .96 0 .00 0.03 37897.07 37897, .16 -1 .21 0. .00 -0.09 36538.47 36538. 34 -2. .31 0. .00 0.13 36678.00 36678. .09 -2. .36 0 .00 -0.09 33142.82 33142. .80 -2 .39 0. .00 0.02 37138.33 37138. 30 -0. .36 0. .00 0.03 30280.18 30280. 17 0. ,23 0. .00 0.01 39505.68 39505. 74 -0, .16 0. .00 -0.06 36917.14 36917. 16 -4. .07 0. .00 -0.02 29235.80 29235. 76 -2. .09 0. .00 .0.04 30374.31 30374. 23 -2. .51 0. .00 0.08 34920.37 34920. 38 -5. .68 0. .00 -0.01 17667.52 17667. 43 2. .05 0. .00 0.03 15863.74 15863. 74 -2. .01 0. ,00 0.00 32990.48 32990. 39 -7. .46 0. .00 0.09 28468.48 28468. 44 -5. .82 0. .00 0.04 31544.50 31544. 48 -9. .31 0. .00 0.02 29349.36 29349. 35 -4. ,04 0. .00 0.01 33669.58 33669. 56 -6. .97 0. .00 0.02 13536.49 13536. 52 -2. ,35 0, ,00 -0.03 31597.19 31597. 24 -12. ,80 0. ,00 -0.05 33624.19 33624. 22 -14. ,33 0, ,00 -0.03 26740.57 26740. 55 -4. ,55 0, .00 0.02 frequencies. The estimated uncertainty of the measurements was better than ±0.10 MHz. ANALYSIS OF OBSERVED SPECTRA The assignment of the ground state spectra of propiolyl fluoride was facilitated by the very well-resolved nature of the Stark effect. Broad band frequency sweeps obtained at low modulation voltages over the range 26.5-40 GHz revealed several pairs of lines having the characteristic Stark effects of near degeneracies (<5). They were easily assigned as the K = 2 and 3 asymmetry doublets of the a-type J — 3 —> 4 and 4 —»5 transitions. After they were fitted to three rotational constants the rigid rotor frequencies of other low J lines, both a and b type, were predicted and assigned. The Stark effect was used to verify assignments. These new transitions were included in the fits, and the pro-218 120 DAVIS AND GERRY Table I (Continued) Transition Observed Calculated Distortion Correction Deviation Frequency Frequency First High Order Order 13( 3,10)- 13( 2,1.1) 37175 07 37175 17 -15 69 0 00 -0 10 14( 3,11)- 14( 3,12) 34839 48 34839 50 -6 43 0 00 -0 02 15( 4,11)- 15( 4,12) 15696 72 15696 79 -1 91 0 00 -0 07 17( 4,13)- 17( 4,14) 30253 99 30254 04 -3 74 0 01 -0 05 18( 4,14)- 18( 4,15) 39181 72 30181 79 -6 05 0 01 -0 07 19( 5,14)- 19( 5,15) 17244 76 17244 84 1 73 0 01 -0 08 21( 5,16)- 21( 5,17) 32906 34 32906 37 2 46 0 02 -0 03 25( 6,19)- 25( 6,20) 34834 10 34833 98 17 32 0 07 0 12 28( 7,21)- 28( 7,22) 26731 46 26731 44 35 84 0 16 0 02 30( 8,22)- 30( 8,23) 13087 71 13087 69 32 82 0 19 0 02 32( 8,24)- 32( 8,25) 27217 70 27217 65 68 64 0 37 0 05 34( 9,25)- 34( 9,26) 13130 29 13130 26 55 33 0 41 0 03 36( 9,27)- 36( 9,28) 27349 39 27349 32 114 69 0 76 0 07 40(10,30)- 40(10,31) 27189 44 27189 55 175 12 1 53 -0 11 DCCC(0)F (Ground vibrational state) 2( 0, 2)- 1( 0, 1) 13376 28 13376 24 0 00 0 00 0 04 4( 1, 3J- 3( 1, 2) 28627 24 28627 30 -0 33 0 00 -0 06 4( 1, 4)- 3( 0, 3) 30848 95 30848 98 -0 22 0 00 -0 03 4( 2, 3)- 3( 2, 2) 26847 97 26847 95 -0 74 0 00 0 02 4( 2, 2)- 3( 2, 1) 27604 67 27604 72 -0 87 0 00 -0 05 4( 3, 2)- 3( 3, 1) 27054 40 27054 33 -1 73 0 00 0 07 4( 3, l i - 3( 3, OJ 27079 03 27078 98 -1 74 0 00 0 05 Sf 0, 5)- 4( 0, 4) 32203 91 32203 92 0 00 0 00 -0 01 5( 1, 4)- 4( 1, 3) 35607 60 35607 62 -0 44 0 00 -0 02 5( 1, 5)- 4( 0, 4) 35668 96 35668 97 -0 34 0 00 -0 01 5( 1, 5)- 4( 1, 4) 30972 96 30973 01 -0 10 0 00 -0 05 5( 2, 4J- 4( 2, 3) 33461 75 33461 68 -0 90 0 00 0 07 5( 2, 3)- 4( 2, 2) 34893 65 34893 72 -1 12 0 00 -0 07 5( 3, 2)- 4( 3, 1) 33950 96 33951 05 -2 21 0 00 -0 09 5( 3, 3)- 4( 3, 2) 33865 68 33865 60 -2 17 0 00 0 08 5( 1, 4)- 5( 0, 5) 17511 19 17511 18 -1 25 0 00 0 01 5( 1, 4)- 5( 1, 5) 14046 16 14046 12 -0 91. 0 00 0 04 5( 2, 4)- 5( 1, 5) 32726 78 32726 80 -2 27 0 00 -0 02 6 0, 6 - 5( 0, 5) 38060 16 38060 15 -0 05 . 0 00 0 01 6( 0, 6)- 5( 1, 5) 34595 12 34595 10 0 29 0 00 0 02 6( 1, 6)- 5( 1, 5) 37007 99 37007 98 -0 14 0 00 0 01 6( 3, 3)- 6( 2, 4) 39108 18 39108 15 -3 86 0 00 0 03 7( 2, 6)- 7( 1, 7) 39231 86 39231 87 -4 24 0 00 -0 01 7( 3, 4)- 7( 2, 5) 37349 93 37349 96 -5 39 0 00 -0 03 7( 1, 6)- 6( 2, 5) 32859 39 32859 37 1 12 0 00 0 02 8( 1, 7)- 8( 0, 8) 33246 67 33246 65 -3 02 0 00 0 02 8( 1, 7)- 8( 1, 8) 32226 07 32226 07 -2 56 0 00 0 00 8( 3, 5)- 8( 2, 6) 35448 11 35448 12 -7 12 0 00 -0 01 9( 1, 8)- 9( 1, 9) 39134 16 39134 09 -3 41 0 00 0 07 9( 2, 7)- 9( 2, 8) 17659 50 17659 50 -2 44 0 00 0 00 cedure was repeated several times, gradually adding more transitions, up to / = 40. As / increased it was found necessary to fit as well to five quartic centrifugal distortion constants, besides the rotational constants. For (?-branch transitions above / = 10 the frequency fit was most important in making the assignments. The a-type lines were observed to be much stronger than the b-types and in some cases intensities were useful in initially selecting between several candidates. Two prominent and several much weaker vibrational satellites were observed for many low J lines. In the case of the normal isotopic species, the relative intensities of the two strongest vibrational satellites were about 0.20 and 0.25 that of the ground state lines suggesting vibrational frequencies of 218 ± 25 cm - 1 and 188 ± 25 cm-1. These 219 MICROWAVE SPECTRUM OF PROPIOLYL FLUORIDE Table I (Continued) 1 2 1 Transition Observed Calculated Distortion Correction Deviation Frequency Frequency First High Order Order 9( 3, 6)- 9( 2, 7) 33708. 25 33708 17 -8 99 0.00 0 08 10( 2, 8)- 10 ( 1, 9) 29990 66 29990 68 -6 71 0.00 -0 02 10( 3, 7)- 10 ( 2, 8) 32462 88 32462 86 -10 89 0.00 0 02 11( 2, 9)- 11 ( 2,10) 30595 86 30595 89 -4 55 0.00 -0 03 11( 2, 9)- 11 ( 1,10) 34992 68 34992 70 -7 87 0.00 -0 02 11( 3, 8)- 11 ( 2, 9) 32015 65 32015 67 -12 73 0.00 -0 02 12( 3, 9)- 11 ( 4, 8) 34691 51 34691 51 -12 67 0.00 0 00 12( 2,10)- 12 ( 2,11) 37988 67 37988 63 -6 09 0.00 0 04 12( 3, 9)- 12 ( 2,10) 32607 33 32607 37 -14 45 0.00 -0 04 12( 3, 9)- 12 ( 3,10) 13789 41 13789 42 -2 57 0.00 -0 01 13( 3,10)- 13 ( 2,11) 34408 98 34408 98 -16 01 0.00 0 00 14( 3,11)- 14 ( 2,12) 37520 78 37520 82 -17 39 0.00 -0 04 15( 3,12)- 15 ( 3,13) 33459 08 33459 09 -6 36 0.00 -0 01 16( 4,12)- 16 ( 4,13) 14052 22 14052 24 -1 88 0.00 -0 02 18( 4,14)- 18 ( 4,15) 26738 09 26738 13 -3 02 0.01 -0 04 19( 4,15)- 19 ( 4,16) 34636 74 34636 80 -4.59 0.01 -0 06 20( 5,15)- 20 ( 5,16) 13578 33 13578 35 1 35 0.01 -0 02 23( 5,18)- 23 ( 5,19) 34462 63 34462 65 3 62 0.03 -0 02 27( 6, 21)- 27 ( 6,22) 33230 98 33230 94 20 44 0.09 0 04 31( 7,24)- 31 ( 7,25) 31215 60 31215 56 46 82 0.22 0 04 35( 8,27)- 35 ( 8,28) 28670 94 28670 85 82 08 0.48 0 09 36( 8,28)- 36 ( 8,29) 37875 29 37875 28 101 08 0.56 0 01 40( 9,31)- 40 ( 9,32) 34642 05 34642 13 158 36 1 .14 -0 08 HCCC(0)F 1) 2( 0, 2)- H 0, 1) 14427 04 14427 04 -0 01 0.00 0 00 2( 1, 2)- H 1, 1) 13433 35 13433 22 -0 06 0.00 0 13 2( 1, 1 )- 1( 1, 0) 15648 02 15648 08 -0 16 0.00 -0 06 4( 0, 4)- 3( 0, 3) 28009 86 28009 88 -0 04 0.00 -0 02 4( 1, 4)- 3( 1, 3) 26659 43 26659 38 -0 14 0.00 0 05 4( 1, 3)- 3( 1, 2) 31045 22 31045 29 -0 40 0.00 -0 07 4( 2, 3)- 3( 2, 2) 28992 09 28992 03 -0 80 0.00 0 06 4( 2, 2)- 3( 2, 1) 30063 01 30063 08 -0 95 0.00 -0 07 5( 0, 5)- 4( 0, 4) 34367 76 34367 75 -0 11 0.00 0 01 5( 1, 5)- 4( 1, 4) 33156 26 33156 21 -0 20 0.00 0 05 5( 1, 4)- 4( 1, 3) 38542 36 38542 34 -0 57 0.00 0 02 5( 2, 3)- 4( 2, 2) 38078 94 38079 04 -1 27 0.00 -0 10 5( 1, 4)- 5( 1, 5) 16409 31 16409 26 -0 96 0.00 0 .05 6( 1, 6)- 5( 1, 5) 39573 06 39573 04 -0 31 0.00 0 .02 7( 3, 4)- 7( 2, 5) 34074 74 34074 76 -4 45 0.00 -0 02 8( 2, 6)- 8( 2, 7) 16357 83 16357 81 -2 06 0.00 0 .02 8( 3, 5)- 8( 2, 6) 32184 .40 32184 39 -6 16 0.00 0 .01 9( 3, 6)- 9( 2, 7) 30841 36 30841 35 -7 .96 0.00 0 .01 11( 3, 8) - H( 3, 9) 14278 .33 14278 .34 -2 .76 0.00 -0 .01 r e s u l t s a r e i n g o o d a g r e e m e n t w i t h m e a s u r e d f r e q u e n c i e s o f 2 2 9 c m - 1 a n d 1 8 9 c m - 1 a s s i g n e d t o t h e i> 9 a n d vu f u n d a m e n t a l s o f p r o p i o l y l fluoride (1). T h e s p e c t r a w e r e a n a l y z e d u s i n g t h e " r e d u c e d " H a m i l t o n i a n o f W a t s o n ( 7 ) i n c l u d i n g a l l q u a r t i c b u t n o s e x t i c c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s . F o r a n e a r p r o l a t e s e m i r i g i d a s y m m e t r i c r o t o r t h i s c a n b e w r i t t e n i n t h e Ir r e p r e s e n t a t i o n (8) a s 3C = KR + KD, XB = UB + C)P2 + [A - i(B + C)]iY + UB- C)(/V - iV), ( 1 ) ( 2 ) XD = - AjP* - AJKP'PJ - AKPa4 + ( P i , 2 - Pc%- hP* - 8KP<?1 + J > &JP2 - ?>KPa23(Pl? - Pc2). (3) 220 122 DAVIS AND GERRY Table I (Concluded) Transition Observed Calculated Distortion Correction Deviation Frequency Frequency First High Order Order i 5 ( 4,ni- 1 5 ( 4 , 1 2 ) 1 6 8 8 5 . 9 8 1 6 8 8 6 01 - 3 46 0 0 0 - 0 0 3 u t 4 , 1 3 ) - 1 7 ( 4 , 1 4 ) 3 2 0 3 8 . 7 2 3 2 0 3 8 73 - 6 70 0 01 - 0 01 1 8 ( 5 , 1 3 ) - 1 8 ( 5 , 1 4 ) 1 2 8 1 9 . 7 5 1 2 8 1 9 74 -1 91 0 01 0 01 2 1 ( 5,16)- 2 1 ( 5 , 1 7 ) 3 5 4 0 8 . 9 5 3540£, 94 - 4 52 0 0 2 0 01 2 4 ( 6 , 1 8 ) - 2 4 ( 6 , 1 9 ) 2 8 5 8 6 . 0 4 2 8 5 8 6 03 4 44 0 05 0 01 2 5 ( 6 , 1 9 ) - 2 5 ( 6 , 2 0 ) 3 8 1 1 6 . 8 1 3 8 1 1 6 8 2 3 84 0 06 - 0 01 2 8 ( 7 , 2 1 ) - 2 8 ( 7 , 2 2 ) 3 0 1 7 7 . 3 7 3 0 1 7 7 38 18 96 0 13 - 0 01 HCCC(0 )F ( v 1 2 = i ) 2 ( 0 , 2 ) - 1 ( 0 , 1 ) 1 4 4 3 3 . 0 7 1 4 4 3 3 02 0 00 0 0 0 0 05 2 ( 1 , 2 ) - 1( 1 , 1 ) 1 3 4 4 6 . 2 5 1 3 4 4 6 18 - 0 06 0 0 0 0 07 2 ( 1 , D- K 1 , 0 ) 1 5 6 3 4 . 5 5 1 5 6 3 4 58 - 0 18 0 0 0 - 0 0 3 4 ( 0 , 4 ) - 3 ( 0 , 3 ) 2 8 0 6 3 . 3 5 2 8 0 6 3 33 - 0 01 0 0 0 0 02 4 ( 1 , 4 ) - 3 ( 1 , 3 ) 2 6 6 9 5 . 9 4 2 6 6 9 5 90 - 0 12 0 0 0 0 04 4 ( 1 , 3 ) - 3 ( 1 , 2 ) 3 1 0 3 2 . 9 8 3 1 0 3 3 09 - 0 42 0 0 0 - 0 11 4 ( 2 , 3 ) - 3( 2 , 2 ) 2 8 9 9 6 . 3 9 2 8 9 9 6 33 - 0 87 0 0 0 0 06 4 ( 2 , 2 ) - 3 ( 2 , l ) 3 0 0 1 3 . 4 2 3 0 0 1 3 4 8 -1 04 0 0 0 - 0 06 5 ( 0 , 5 ) - 4 ( 0 , 4 ) 3 4 4 5 6 . 8 6 3 4 4 5 6 8 8 - 0 07 0 0 0 - 0 02 5 ( 1 , 5 ) - 4 ( 1 , 4 ) 3 3 2 0 9 . 4 7 3 3 2 0 9 39 - 0 17 0 0 0 0 0 8 5 ( 1 , 4 ) - 4 ( 1 , 3 ) 3 8 5 4 3 . 6 7 3 8 5 4 3 67 - 0 58 0 0 0 0 0 0 5 ( 2 , 4 ) - 4 ( 2 , 3 ) 3 6 1 1 1 . 5 0 36111 51 -1 09 0 00 - 0 01 5 ( 2 , 3 ) - 4 ( 2 , 2 ) 3 8 0 0 2 . 7 6 3 8 0 0 2 84 -1 36 0 00 - 0 0 8 5 ( 1 , 4 ) - 5 ( 1 , 5 ) 1 6 2 3 0 . 0 7 1 6 2 3 0 04 -1 0 8 0 0 0 0 0 3 6 ( 1 , 6 ) - 5 ( 1 , 5 ) 3 9 6 4 5 . 2 5 3 9 6 4 5 22 - 0 26 0 00 0 0 3 8 ( 2 , 6 ) - 8 ( 2 , 7 ) 1 5 7 9 1 . 6 1 15791 61 - 2 16 0 0 0 0 0 0 8 ( 3 , 5 J - 8( 2 , 6 ) 3 3 5 9 3 . 9 7 3 3 5 9 3 99 - 8 47 0 0 0 - 0 02 9 ( . 3 , 6 ) - 9 ( 2 , 7 ) 3 2 0 9 6 . 7 1 3 2 0 9 6 69 - 1 0 46 0 00 0 02 1 0 ( 3 , 7 ) 1 0 ( 2 , 8 ) 3 1 4 5 7 . 2 2 3 1 4 5 7 22 - 1 2 4 0 0 00 0 00 11( 3 , 8 ) - H ( 3 , 9 ) 1 3 3 4 8 . 6 9 1 3 3 4 8 64 - 2 4 0 0 0 0 0 05 15( 4 , 1 1 ) - 15 ( 4 , 1 2 ) 1 5 3 5 1 . 4 2 15351 4 5 -1 66 0 00 - 0 03 17( 4 , 1 3 ) - 17 ( 4 , 1 4 ) 2 9 7 7 7 . 5 0 2 9 7 7 7 53 - 3 32 0 01 - 0 03 18( 4 , 1 4 ) - 1 8 ( 4 , 1 5 ) 3 8 6 7 7 . 5 0 3 8 6 7 7 45 - 5 65 0 01 0 05 19( 5 , 1 4 ) - 19 ( 5 , 1 5 ) 1 6 7 2 2 . 6 2 1 6 7 2 2 59 2 72 0 02 0 0 3 2 1 ( 5 , 1 6 ) - 2 1 ( 5 , 1 7 ) 3 2 1 b 7 . 2 9 3 2 1 6 7 36 4 29 0 03 - 0 07 2 5 ( 6 , 1 9 ) - 2 5 ( 6 , 2 0 ) 3 3 8 0 6 . 8 8 3 3 8 0 6 86 21 70 0 0 8 0 02 2 9 ( 7 , 2 2 ) - 2 9 ( 7 , 2 3 ) 3 4 8 1 2 . 7 2 3 4 8 1 2 72 52 38 0 22 0 0 0 The effective rotational constants A, B, C differ from the usual ones by a small cen-trifugal term; Pa, Pb, Pc are the components of the angular momentum P along the a-, b-, and c-inertial axes, respectively. A least-squares fit was made to the five distortion constants using the first-order energy expression for a semirigid prolate rotor in a rigid asymmetric rotor basis (P); linear variations of the rotational constants were allowed. The parameters thus obtained were inserted into the complete Hamiltonian and used to calculate the transition frequencies. The difference between those frequencies and the first order frequencies represented the higher order distortion contributions; these were subtracted from the observed frequencies and the resulting values were refit using the first-order expression. Changes in any of these parameters were insignificant after two iterations. Expanding the fitting procedure to include all the sextic distortion constants resulted in no significant values being obtained for any of these parameters. Accordingly no sextic distortion constants were included in the final fit. The observed frequencies and their assignments along with calculated frequencies and the distortion contributions are given in Table I. Table II gives the spectroscopic constants calculated in the analyses. 221 MICROWAVE SPECTRUM OF PROPIOLYL FLUORIDE 123 T a b l e I I . R o t a t i o n a l c o n s t a n t s 3 a n d c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s 3 o f p r o p i o l y l f l u o r i d e GROUND V I B R A T I O N A L S T A T E S H C C C ( 0 ) F D C C C ( 0 ) F A 11826 . 6 1 0 ± 0 . 0 0 6 ° 1 1 8 2 6 . 1 7 3 i 0 . 0 0 5 B 4 1 6 9 . 2 3 6 4 0 . 0 0 4 3 8 3 5 . 8 0 5 ± 0 . 0 0 2 C 3 0 7 7 . 4 3 4 4 0 . 0 0 4 2 8 9 1 . 7 1 7 4 0 . 0 0 2 A j x 1 0 4 5 . 4 9 4 0 . 7 3 4 . 3 6 4 0 . 1 3 A J K x 1 0 2 2 . 2 4 3 4 0 . 0 1 4 2 . 1 4 9 4 0 . 0 0 8 A K x 1 0 2 - 1 . . 0 5 2 i 0 . 0 8 7 - 0 . 9 9 0 ± 0 . 0 6 2 Sj x 1 0 4 1. . 7 9 8 4 0 . 0 3 5 1 . 3 6 7 ± 0 . 0 2 0 « K x 1 0 2 1 . 2 4 4 4 0 . 0 0 9 1 . 1 9 9 4 0 . 0 0 6 E X C I T E D V I B R A T I O N A L S T A T E S OF H C C C ( 0 ) F v < r-1 1 v 1 2 = 1 A 1 1 6 9 6 . 2 0 3 4 0 . 0 2 0 1 1 9 6 3 . 8 2 2 4 0 . 0 2 0 B 4 1 8 8 . 9 3 0 4 0 . 0 0 6 4 1 8 2 . 2 5 7 ± 0 . 0 0 6 C 3 0 8 1 . 4 4 8 4 0 . 0 0 6 3 0 8 7 . 9 9 3 4 0 . 0 0 6 A j x 1 0 4 7 . 4 4 1 . 2 6 . 8 4 1.1 A J K x l O 2 2 . 15 4 0 . 0 5 2 . 4 4 0 . 0 5 A K X 1 0 2 - 2 . 5 4 0 . 4 - 0 . 5 6 0 . 3 8 6 j x 1 0 4 2 . 10 4 0 . 1 1 1 . 9 3 ± 0 . 0 9 6 K x 1 0 2 1 . 11 4 0 . 0 3 1 . 3 5 4 0 . 0 3 a i n MHz b E r r o r s a r e s t a n d a r d e r r o r s THE STRUCTURE OF PROPIOLYL FLUORIDE Table III gives values for the principal moments of inertia and inertial defects of all species studied. The ground vibrational state inertial defects are small positive numbers varying little with isotopic substitution, and thus suggest a planar structure. An attempt was then made to obtain the bond lengths and angles. Several assumptions were necessary to derive them with the limited isotopic data available. The C-H and C=C distances were taken to be the same as those in propynal (2) and the C = O distance the same as that found in acetyl fluoride (10) and formyl fluoride (11). A linear carbon chain was also assumed. The a- and b-coordinates of hydrogen were determined using Kraitchman's equations (12) for a planar rigid molecule; the b-coordinate was unfortunately small, and probably rather inaccurate. The remaining structural parameters were found using the five available equations, namely, the center-of-mass conditions ^irmdi = 0, = 0; the product of inertia condition X>wt f f l^> = u> 222 124 DAVIS AND GERRY T a b l e I I I . Momen ts o f i n e r t i a 3 a n d i n e r t i a l d e f e c t s 3 o f p r o p i o l y l f l u o r i d e GROUND V I B R A T I O N A L S T A T E S H C C C ( 0 ) F D C C C ( 0 ) F J A 4 2 . 7 3 3 37 4 2 . 7 3 4 95 ! b 1 2 1 . 2 1 9 1 1 3 1 . 7 5 6 2 1° 1 6 4 . 2 2 4 8 1 7 4 . 7 7 1 9 A 0 . 2 7 2 3 0 . 2 8 0 8 E X C I T E D S T A T E S OF H C C C ( 0 ) F v g = l v 1 2 - 1 ! A 4 3 . 2 0 9 8 3 4 2 . 2 4 3 27 J B 1 2 0 . 6 4 9 2 1 2 0 . 8 4 1 7 ' c 1 6 4 . 0 1 0 9 1 6 3 . 6 6 3 2 A 0 . 1 5 1 9 0 . 5 7 8 3 a i n amu A ' and the principal moments of inertia in the ground vibrational state: I A0 = £>w;&i2 and IB° = 23>wia«2- The derived bond lengths and angles are shown in Table IV; reasonable values were obtained in all cases. T a b l e I V . S t r u c t u r a l p a r a m e t e r s o f p r o p i o l y l f l u o r i d e a n d r e l a t e d m o l e c u l e s H - C = C - C ( 0 ) F C H 3 - C ( 0 ) F ( 1 0 ) H C ( 0 ) F ( 1 J _ ) H-CFC-C(0)C1 (14_) r ( H - C ) (A ) 1 . 0 5 5 3 1 . 0 5 7 - 0 . 0 0 4 3 r ( C n C ) ( A ) 1 . 2 0 9 3 1 . 2 0 7 i 0 . 0 0 4 3 r ( C - C ) ( A ) 1 . 4 5 4 1 . 4 2 4 i 0 . 0 1 6 r ( C = 0 ) (A ) 1 . 1 8 1 3 1 . 1 8 1 ± 0 . 0 1 0 1 . 1 8 H 0 . 0 0 5 1 . 2 0 9 i 0 . 0 1 4 r ( C - F ) ( A ) 1 .331 1 . 3 4 8 + 0 . 0 1 5 1 . 3 3 8 ± 0 . 0 0 5 < ( H - C - C ) 1 8 0 ° a < ( C - C - C ) 1 8 0 ° 3 < ( C - C - 0 ) 1 2 7 . 2 1 ° 1 2 8 ° 2 1 ' i l ° 1 2 5 . 9 i 0 . 6 ° < ( C - C - F ) 1 0 9 . 6 3 ° 1 1 0 ° 1 8 ' ± 1 ° < ( 0 - C - F ) 1 2 3 . 1 6 ° 1 2 1 ° 2 1 ' 1 2 2 ° 4 6 ' ± 3 0 ' 3 A s s u m e d 223 MICROWAVE SPECTRUM OF PROPIOLYL FLUORIDE 125 T a b l e V . T h e d i p o l e moment o f p r o p i o l y l f l u o r i d e — ~ 2 2 2 5 T r a n s i t i o n C o m p o n e n t A v / E MH2(V / c m ) x 10 O b s e r v e d C a l c u l a t e d  2 m . l n l M = 0 - 4 . 3 B 8 - 4 . 3 7 3 U ' U M = 1 3 . 9 9 0 3 . 9 9 4 2 , , - l l n M = 0 3 . 4 5 6 3 . 4 3 8 " w M = 1 - 4 5 . 4 4 - 4 5 . 4 4 y a = 2 . 9 1 5 ± 0 . 0 2 0 Debye M f a = 0 . 6 3 0 ± 0 . 0 8 0 D e b y e v = 2 . 9 8 ± 0 . 0 2 D e b y e DIPOLE MOMENT Stark effect measurements were made on the 2o2~loi and 2n-lio transitions of the normal isotopic species. The cell was calibrated using the J = 0—* 1 transition of OCS and adopting the value of 0.71521 Debye for its dipole moment (13). After estimating approximate values for the dipole moment, the experimentally observed frequencies of the M = 1, 2U-110 transition were "deperturbed" to allow for the near degeneracy of the In and lio levels (14). Least-squares analysis of all the data obtained gave the results presented in Table V. The component pa is much larger than nb, in agreement with the relative intensities of the a- and b-type transitions. T a b l e V I . C o m p a r i s o n o f o b s e r v e d a n d c a l c u l a t e d d i p o l e momen ts ( i n D e b y e s ) o f p r o p i o l y l f l u o r i d e a n d r e l a t e d m o l e c u l e s . v _a v_h M o l e c u l e O b s e r v e d o b s . C a l c . ( 5 1 O h s . C a l c . ( 5 ) H C C C ( 0 ) F 2. . 9 8 2. . 9 1 5 H C ( 0 ) F n , 0 2 a 0. . 5 9 5 C H 3 C ( 0 ) F 2 . 9 6 b 2 . 83 H C C C ( 0 ) H 2 . 4 6 c 2 . 39 3 . 0 4 0 . 6 3 C 0 . 8 1 0 . 3 8 1 . 9 3 4 1 . 8 3 — 0 . 8 8 — 2 . 2 8 0 . 6 0 1 . 2 7 a R e f . ( T 5 ) b R e f . (1_0) c R e f . 0 6 ) 224 126 DAVIS A N D G E R R Y DISCUSSION Because of the lack of isotopic data, which requires us to assume some of the struc-tural parameters, the structure given in Table IV, though very reasonable, is one of several possible. Nevertheless, when it is compared with those of related molecules, also in Table IV, essential agreement between corresponding values is obtained, and we conclude that propiolyl fluoride shows no structural anomalies. It is perhaps noteworthy, however, that the C-C single bond is rather longer in propiolyl fluoride than in propiolyl chloride, consistent with the C-C stretching frequency being lower in the fluoride than the chloride (2). The estimated values of the dipole moment components are compared to those of similar molecules and to the predicted values (5) in Table VI. The predicted values are a little higher than the measured values for both propynal and propiolyl fluoride. The measured dipole moments of propiolyl and acetyl fluoride are very similar. A C K N O W L E D G M E N T S The support of the National Research Council of Canada is gratefully acknowledged. We also wish to thank Walter J. Balfour, Dieter Klapstein and Somyong Visaisouk for supplying samples and details of the preparation. RECEIVED: January 15, 1975 R E F E R E N C E S 1. W A L T E R J . B A L F O U R , D I E T E R K L A P S T E I N , A N D SOMYONG VISAISOUK, Spectrochimica Acta, in press. 2. C . C . COSTAIN A N D J . R . M O R T O N , / . Chem. Phys. 31, 389 (1959). 3. D . G . L I S T E R AND J . K . T Y L E R , Spectrochimica Acta 28A, 1423 (1972). 4. R . W . D A V I S , M . C L . G E R R Y , SOMYONG VISAISOUK, AND W A L T E R J . B A L F O U R , Chem. Phys. Lett. 26, 561 (1974). 5. D . W . D A V I E S A N D R O G E R E L V I N , / . Chem. Soc, Farad. Trans. II 70, 727 (1974). 6. W A L T E R GORDY A N D R O B E R T L . C O O K , "Microwave Molecular Spectra," Interscience, New York, 1970. 7. J . K . G . W A T S O N , / . Chem. Phys. 46, 1935 (1967). 8. H . C . A L L E N AND P . C . CROSS, "Molecular Vib-Rotors," Wiley, New York, 1963. P. P . HELMINGER, R. L . COOK, AND F. C D E L U C I A , J. Mol. Spectrosc. 40, 125 (1971). 10. L . P I E R C E AND L . C . KRISHER, J. Chem. Phys. 31, 875 (1959). 11. R . F . M I L L E R A N D R . F . C U R L , JR . , / . Chem. Phys. 34, 1847 (1961). 12. J . K R A I T C H M A N , Amer. J. Phys. 29, 864 (1958). 13. J . S. M U E N T E R , / . Chem. Phys. 48, 4544 (1968). 14. S. G O L D E N AND E . B . WILSON, J. Chem. Phys. 16, 669 (1948). 15. O. H . L E B L A N C , JR. , V. W. L A U R I E , A N D W. D. G W I N N , / . Chem. Phys. 33, 598 (1960). 16. J O H N A. H O W E AND J . H . GOLDSTEIN, J. Chem. Phys. 23, 1223 (1955). 225 Appendix 2 A R e p r i n t o f a Report o f the Microwave Spectrum o f P r o p i o l i c A c i d 226 JOURNAL OF MOLECULAR SPECTROSCOPY 59, 407-412 (1976) The Microwave Spectrum and Centrifugal Distortion Constants of Propiolic Acid R. WELLINGTON DAVIS A N D M . C. L . GERRY Department of Cliemistry, The University of British Columbia, 2075 Wesbrook Place, Vancouver, B. C, Canada V6T 1W5 The microwave spectra of propiolic acid and propiolic acid-<2 have been measured up to J — 30. These have enabled accurate evaluation of the rotational and centrifugal distortion constants for each species. The measured frequencies are presented, along with some pre-dictions of transitions unmeasured in the present work, but of potential use in radioastronomy. INTRODUCTION There has been one previous study of the microwave spectrum of propiolic acid (i). The spectra of three isotopic species were assigned, and from them were obtained the rotational constants and some structural information. The molecule was shown to be planar, and had nonzero dipole moment components along the a- and 6-inertial axes. Both these components were measured, and the latter was found to be rather the larger of the two. The spectra were assigned, however, only to low values of J, and although an attempt was made to account for centrifugal distortion, the authors recognized that they had insufficient data to evaluate accurate distortion constants (/). Several fragments and molecules related to propiolic acid have been observed in interstellar space. These have included formic acid (2), propiolonitrile (3), the ethynyl radical H C C (4), and methyl acetylene (5). Propiolic acid is thus also a candidate for such observation. This requires, however, an accurately known spectrum, including accurate distortion constants. In the present work we have measured the spectra of two isotopic species, HC2COOH and HC2COOD, to high values of J, and have been able to obtain the necessary distortion constants. These are all presented in this article, along with predictions of some further, unmeasured, transitions, which should also be of interest to radioastronomers. EXPERIMENTAL DETAILS Spectra were observed between 12.5 and 40 GHz using the 100 kHz Stark modulated spectrometer described previously (6). It used a Hewlett-Packard 8400 C Microwave Spectroscopy Source. The sample of propiolic acid was obtained from the Aldrich Chemical Company and was used without further purification. The deuterated species was initially obtained by mixing the acid with D2O in the cell. Later it was found more profitable to prepare it by mixing the acid with an excess of D2O, extracting the resulting 407 Copyright © 1976 by Academic Press, Inc. All rights of reproduction in any form reserved. 227 DAVIS AND GERRY Table 1. Observed and Calculated Transition Frequencies {MHz) of Propiolic Acid ( H C 2 C 0 O H ) . Transition Observed Calculated CentH- Devi-Frequency Frequency fugal ation Dist-ortion 21 2 . 1 ) _ 21 1, 2 ) 2 7 0 7 6 . 2 8 2 7 C 7 6 . 25 - C . 3 5 0 . 0 3 31 2 , 2) - 31 1, 3) 2 8 7 2 8 . 87 2 8 7 2 8 . 88 - 0 . 8 5 - 0 . 0 1 31 I* 3) - 2 1 0 . 21 27C41 . 06 2 7 0 4 1 . 02 - C . 1 3 0 . 0 4 3( 0 , 3) - 2 1 1 , 2 1 1 4 3 0 2 . 49 1 4 3 C 2 . 48 C . C 6 0 .01 4( 0 . 41 - 31 0 , 3 ) 2 7 9 8 0 . 26 2 7 9 8 0 . 24 C . C O 0 . 0 2 4( 1, 4) - 31 1. 3) 2 6 6 1 8 . 2 9 2 6 6 1 8 . 30 - C . C 9 - 0 . 0 1 '.I 1 , 3 1 - 3 1 1, 2 > 308 3 2 . 9 9 3 C 8 3 3 . CO - C . 3 5 - 0 . 0 1 4( 2 , 3) - 31 ?, 2 ) 2 8 H 4 7 . 4 8 2 8 8 4 7 . 49 - C . 7 5 - 0 . 0 1 41 2 , 2) - 31 2 . 1 ) 2 9 7 9 2 . 4V 2 9 7 9 2 . 52 - 0 . 8 9 - 0 . 0 3 41 3 , 2) - 31 3 . 1 ) 2 9 1 C 6 . 43 2 9 1 C 6 . 36 - 1 . 7 5 0 . 0 7 41 t . 3) - 41 0 , 4 ) 1 4 9 5 9 . 93 1 4 9 5 9 . e9 - C . 8 3 0 . 0 4 41 2 , 31 - 41 1. 4 > 3 0 9 5 8 . 06 3 0 9 5 8 . 07 - 1 . 5 0 - 0 . 0 1 41 I t 4) - 3( 0 . 3) 3 2 3 5 6 . 89 3 2 3 5 6 . "9 - C . 23 C O O 51 0 , 5) - 4 1 0 , 4 ) 3 4 3 b 7 . 36 3 4 3 8 7 . 3 5 - C . C 3 0 .01 51 I. 5) - 41 It 4 ) 3 3 1 2 2 . 86 3 3 1 2 2 . 85 - 0 . 1 3 0 .01 51 1, 4) - 4 1 1. 3! 3 8 3 1 4 . 21 3 8 3 1 4 . 29 - C . 48 - 0 . 0 8 5( 2 , 41 - 4 ( 2 , 3 1 359 3 5 . 56 3 5 9 3 5 . 5 3 - C . 9 3 0 . C 3 51 2 . 3) - 41 2 , 2 1 3 7 7 0 2 . 79 3 7 7 0 2 . 76 - 1 . 17 0 . 0 3 51 2 , 4) - 51 1 . 5 1 3 3 7 7 0 . 71 3 3 7 7 0 . 75 - 2 . 31 - C . 0 4 5( 0 , 51 - 4 1 1, 4] 300 10. 73 3 C C 1 0 . 70 C . 2C 0 . 0 3 61 1 , 6) - 5 < 1 , 5 ) 3 9 5 5 3 . 52 3 9 5 5 3 . 54 - C . 18 - 0 . 02 61 0 , 6) - 51 It 5) 3 7 4 7 3 . 67 3 7 4 7 3 . 73 0 .21 - C . C 6 61 1, 51 - 5 I 2t 4 1 2 7 6 1 7 . 72 2 7 6 1 7 . 7 0 C . 71 C . 0 2 61 2 , 5 ) - 6 1 1 , 6) 37 160 . 18 3 7 1 6 C . IB - 3 . 2 3 o . c o 6( 3 . 31 - 6( 2 , 4) 3 8 6 1 3 . 33 3 B 6 1 3 . 30 - 3 . 9 7 0 . 0 3 7 ( 1, 61 - b ! 2 . 5 ) 3 7 3 4 7 . ,69 3 7 3 4 7 . 72 C . 9 7 - 0 . 0 3 7( 1 , 6) - 7 [ 0 , 7) 2 9 9 1 3 . 06 2 9 9 1 3 . 'J9 - 2 . 4 C - 0 . 0 1 7( 3 , 4) - 71 2 , 5 ) 3 6 6 4 5 . ,58 3 6 6 4 5 . 55 - 5 . 4 9 0 . 0 3 71 2 . 5) - 6( 3 , 4 ) 1 5 6 * 9 . .96 1 5 6 2 9 . 98 2 . 0 2 - 0 . 0 2 61 1 , 7) - 6 1 0 , 8 ) 366 19 .91 3 6 6 1 9 . 94 - 3 . C9 - 0 . 0 3 B( 3 . 5) - 81 2 , 6) 3 4 6 5 6 . ,86 3 4 6 5 6 . 86 - 7 . 19 - O . C O 91 2» 7) - 9( 1. 8 ) 2 6 1 9 6 . . 12 2 6 1 9 6 . C9 - 5 . 6 4 0 . 0 3 VI 3 . 61 - 91 2 , 7) 3 3 C 3 4 . .73 3 3 0 3 4 . 7 4 - 8 . 97 - 0 . 0 1 91 2 , 7) - 81 3 . 6 ) 3 7 2 0 6 . .08 3 7 2 0 6 . ,C5 3 . SH 0 . 0 3 10< 2, 8) - 10< 1 , 9) 3 3 0 2 5 . .67 3 3 0 2 5 . , (,4 - 6 . 76 0 . 0 3 ID ( 3 , 7) - 101 2 , fct) 32 163. .9C 3 2 1 6 3 . ,92 - I C . 7 7 - C . 0 2 111 2 , 9) - 11 1 2 , 10 ) 3 5 6 2 6 . .28 35626 . , ?0 - 5 . 18 - 0 . 0 2 111 3 , 8) - 101 4 , 7 ) 3 2 0 4 7 , ,96 3 2 0 9 7 . ,9fc 9 . 8 0 - 0 . 0 2 111 2 . 9) - 111 1, 10 ) 3 9 0 4 1 . .13 3 9 C 4 1 . , 11 - 7 . 99 0 .02 1 1 ( 3 , 8) - 1 L 1 2 , 9 1 3<i3b5. ,02 3 2 3 6 5 . ,G3 - 1 2 . 4 6 - C . 0 1 121 3 , 9) - 121 2 , 10 ) 33B 71 , .83 33871 . . 84 - 1 4 . C 6 - 0 . C 1 121 4 , 8) - 1 1 1 5 , 7 ) 161d7 , .95 16187. ,93 14 . 1 3 0 . 0 2 131 3 , 10) - 13 1 2 , 1 1 ) 3 6 8 3 0 . 5 9 36830 , .•37 - 1 5 . 5 4 0 . 0 2 13( 3 , 11 ) - 12 1 4 . 8 ) 2 8 4 1 8 , .29 2841B, . 30 1 9 . 5 5 - 0 . 0 1 141 3* 11 ) - 141 i . 12 ) 32322 . .43 32322 . .43 - 5 . 9 3 - 0 . 0 0 141 3 . 12) - 13 1 4 , 9 ) 3 0 9 3 9 . 8 3 30939 , .h3 2 3 . 22 - 0 . 0 0 141 4 , 11 ) - 131 5 . B) 2 7 4 o 8 . .16 27468 . .23 2 4 . 7 9 - 0 . 0 7 141 4 , 10) - 13( 5 , 9 ) 36787 , .46 36787. .48 2 2 . 6 6 - 0 . 0 2 141 5 , 9) - 131 6 , 8) 125B3, .93 12583, . p a 2 2 . 9 3 0 . 0 5 151 3 , 13) - 141 4 , 10 ) 31656, . 46 3 1 6 5 6 . 4 6 2 6 . 8C O.CO 15< 4 , 12) - 141 5 , 9 ) 3 3 9 J 7 , . 0 7 33937 , .05 3 0 . 0 7 0 . 0 2 16 1 3 . 141 - 151 4 , 1 1 ) 30389, . 6 3 3C389. .65 3 C . 2 6 - 0 . 0 2 161 5 , 12) - 15 1 6 • 9 ) 2 7 3 8 0 . 4 6 27380 , . 4 5 3 6 . 5 8 0 . 0 1 161 5 , 11 I - 151 6 , 10) 3C969 , . 88 30969 , .90 3 5 . 4 3 - 0 . 0 2 171 3 , 15) - 16 1 4 , 12) 271C7 . 2 3 27107 , . 2 3 3 3 . 7 7 - C O O 17< 5 , 13) - 161 6 . IC ) 35093, . 9 3 35C93, . P9 4 3 . 67 0 . 0 4 171 6 . 12) - 161 7, , 9 ) 1 7612 . 7 5 17612 . fl 4 2 . 6 9 0 . 0 4 18( 4 * 1 4 ) - 181 4 . 15) 35331 .32 35331, . 34 - 5 . 4 3 - 0 . 0 2 l B t 6 . 12) - 17 1 7 , 11 ) 2 6 9 7 0 . 9 3 26970 . 9 4 5 C . 91 - 0 . 0 1 1 9 1 1 0 , 10) - 1 8 ( 1 1 , , 7) - 3 8 3 5 1 . 4 9 - 38351 . 5 2 3 2 . 16 0 . 0 3 19( 6 , • 13) - 181 7, .12 ) 36166 . 0 4 36166 . 0 5 6 0 . 4 6 - 0 . 0 1 191 7 , ,131 - 1R( 6, .10) 1 5408 . 0 9 15408 . 1 0 5 8 . B4 - 0 . 0 1 19( 7 , 12) - 181 8, , 11 ) 15583 .54 1 5 5 8 3 . 4 9 58 .61 0 . 0 5 191 6, i 14) - 18 ( 7 , .11) 33993 .88 33993 . 8 5 6 1 . 1 2 0 . 0 3 20( 10, i l l ) - 19111 , . 8) - 3 0 6 9 0 . 4 9 - 3 0 6 9 0 . 4 3 4 5 . 9 1 - 0 . 0 6 211 5, . 16) - 211 5, , 17) 28254 . 2 9 28254 . 32 1 . 5 6 - 0 . 0 3 211 7, . 15) - 101 8, . 12 ) 31957 . 1 1 31957 . 14 82 . 11 - 0 . 0 3 211 7, . 14) - 201 8 . 1 3 ) 32640 . 5 5 32640 . 5 5 8 1 . 7 0 0 . 0 0 221 5, , 17) - 221 5, , 18) 37221 . 1 6 37221 .14 o . 5 e 0 . 0 2 231 B. r 15) - 221 9, , 1 4 ) 29825 . 0 7 29825 .01 1 0 6 . 9 4 0 . 0 6 231 6. . 16) - 22 1 9 • 13 ) 29625 . 5 4 29625 . 56 1 0 7 . 1 5 - 0 . 0 2 24112 , r 12) - 23113 . 11 ) - 3 5 0 6 5 . 4 6 - 3 5 0 6 5 . 4 3 8 1 . 7 3 - 0 . 0 3 241 e , • 16) - 231 9, . 1 5 ) 38437 . 2 9 3B437 . 30 1 2 2 . 6 7 - 0 . 0 1 24( 8, , 17) - 231 9 • 14 ) 38051 . 4 5 38051 . 5 ^ 1 2 2 . 9 0 - 0 . 0 7 251 9, r 17) - 24 (10 . 14 ) 27245 . 3 9 2 7 2 4 5 . 4 1 1 3 6 . 6 0 - 0 . 0 2 2 6 ( 1 3 . . 14) - 25114 . 11 1 - 3 7 2 4 6 . 2 3 - 3 7 2 4 6 . 2 7 1 0 5 . c e 0 . 0 4 261 9, , 18) - 25 (10 .151 35614 . 7 8 35614 • 79 155. 45 - 0 . 0 1 261 9, . 17) - 25( 10 , 1 6 ) 3 5 7 2 5 . 3 9 35725 . 3 3 1 5 5 . 3 3 0 . 0 6 271 13, r 15) - 26( 14 . 1 2 ) - 2 9 5 1 5 . 6 0 - 2 9 5 1 5 . 5 9 1 2 9 . 6 8 - 0 . 0 1 29114 , • 15) - 28( 15 . 14) - 3 1 6 8 7 . 1 7 - 3 1 6 8 7 . 16 1 6 1 . O C - 0 . 0 1 408 deuterated sample with diethyl ether and drying with magnesium sulfate. The fre-quencies were measured with the sample at room temperature at pressures of about 25 nm and are accurate to better than 0.1 M H z . 2 2 8 MICROWAVE SPECTRUM OF PROPIOLIC ACID 409 Table 2. Observed and Calculated Transition Frequencies (MHz) of Propio-lic Acid-<2 ( H C 2 C O O D ) . Transition Observed Calculated Centr i - Devi-Frequency Frequency fugal ation Dist-ortion 21 2. 1 1 1 1 1 , 01 38570.56 3e570.58 -0.35 -0.00 21 2, , 11 - 2 1 1, 1 2) 265d8.18 26588.19 -C. 35 -0.01 31 2, , 21 - 31 1 . 31 281 73.71 28173.7? -0.8C -0.01 41 0, , 41 - 31 0, . 3) 27156.83 27156.80 -0.00 0.03 4< 1. , 3) - 3 ( 1, 21 29881.88 29881.87 -0. 33 0.01 41 2 , . 31 - <• ( 1 • , 4 1 30312.09 30312. 11 -1.39 -0.02 4 1 1 , , 41 - 31 0. , 3) 3 15 30 . 9 1 31530.92 -0.20 -0.01 51 0, 51 - 4 1 0, > 4 1 33389.19 33389.21 -0.04 -0.02 51 1 , 41 - 4 ( 1, 3 ) 3714C.43 37140.42 -0.46 0.01 5( 1, . 51 - 4 1 < , 4 ) 32150.58 32150.55 -C12 0.03 5( 0. 51 - 4 1 1 r 4 1 29015.11 29015.09 0.16 0.02 51 11 5 ) - 4( 0, , 4) 36524.71 36524.66 -0. 32 0.05 5( 2, 41 - 5 1 1, 5 I 33010.35 33010.35 -2.11 -0.00 51 2. 4) - 4 I 2, , 31 34848.78 34848.79 -0.64 -0.01 51 2, 3) - 41 2, 2) 36513.85 36513.85 -1. 07 0.00 6! 0 , 61 - 5 1 0. r 5 1 394 18.83 39418.76 -0. 12 0.07 61 0, 61 - 5( 1 , , 5 1 36283.23 36283.30 0.16 -0.07 61 2, 5 1 - 61 1, 61 36262.92 36262. 96 -2. 96 -0.04 7( 1, 61 - 61 2 , , 5 1 35B17.14 35817.14 0.61 0.00 7( 1, 6) - 7( 0, . 7 1 28856.55 28856.54 -2.25 0.01 7( 3, 41 - 71 2, . 51 36214.43 36214.4S -5. 00 -0.02 B( 1, 7 1 - tt 1 0,, 8 1 35319.00 35319.00 -2. 92 0.00 6 I 3, 51 - 81 2, 6) 34269.52 34269.53 -6.49 -0.01 9( 2, 71 - ei 3, - 6) 35249.03 35249.08 3.38 -0.05 91 71 - 9 ( 1, 8 ) 27281.61 27281.59 -5. 19 0.02 91 3. 61 - 9 ( 2 , , 7 1 32638.63 32638.64 -8.08 -0.01 10( 2, 81 - 101 1 , , 9 1 3 ie<:8 .48 31828.44 -6.30 0.04 10( 3, 71 - 10 1 2, 8 1 31690.49 31690.52 -9.70 -0.03 111 2, 91 - 11 1 1 , ,10 1 37535.16 37535.13 -7.53 0.03 1 1 ( 3,8) - 11 1 2 , , 9 1 31738.30 31738.30 -11.29 -0.00 121 3, 91 - 121 2, 10) 33014.51 33014.49 -12.83 0.02 131 3 , 101 - 13 1 2, 111 35669.65 35669.64 -14. 31 0.01 141 3, 111 - 141 2 , ,12 1 39762.61 39762.63 -15.76 -0.02 141 4, 101 - 13( 5, 91 34098.57 34098.59 20.21 -0.02 15 1 4, 121 - 14 ( 5, 9 1 32012.60 32012.64 27. 13 -0.04 161 4, 131 - 15 ( 5 , ,101 37624.32 37624.32 31.99 -0.00 161 5, 111 - 15( 6 1 ,01 28341.18 28341.17 32.11 0.01 171 3, 15 1 - 161 4, 12 I 27122.15 27122.14 31.76 0.01 171 5, 131 - 16 ( 6 , 10 ) 32687.64 32687.85 39.68 -0.01 17( 5, 121 - 16( 6, HI 38138.26 38138.27 38.16 -0.01 lei 5, 141 - 171 9, 1 1 1 39918.95 39918.93 46. 35 0.02 19( 6, 131 - 181 7, 12) 33137.96 33137.94 54. 81 0.02 19( 6 , 141 - 181 7 , ,11 ) 31265.19 31265.16 55.65 0.03 211 7, 151 - 20( e, 12) 28999.78 28999.81 75. 36 -0.03 211 7, 141 - 20 ( 8, 131 29573.89 29573.88 74. 91 0.01 22111, 12) - 21 ( 12, 91 -34668.92 -34668.91 70.35 -0.01 221 7, 16) - 21 1 8, 131 37131.69 37131.68 86. 36 0.01 22( 7, 15 1 - 21 ( e. 14) 38198.54 38198.55 e5. 88 -0.01 23(11. 121 - 22(12, 11 1 -27198.95 -27198.96 85.81 0.01 23( 8, 151 - 221 9, 14) 26645.92 26645.93 98.95 -0.01 25(12, 141 - 24(13, 11) -29555.90 -29555.90 110.44 0.00 261 6, 20) - 26 1 6t 21 ) 34564.28 34564.28 8.64 0.00 OBSERVED SPECTRA AND THEIR ANALYSIS Both a- and 6-type transitions were observed for the two species, up to J = 29 and Ka = 15 for HC2COOH, and up to / = 26 and Ka = 13 for HC2COOD. Assignment was made using the bootstrap procedure we have used previously (6, 7). Transitions having low values of / were initially predicted using Lister and Tyler's rotational con-stants (1), and these predictions, along with the Stark effect, enabled further unmea-sured transitions to be assigned easily. These were included in a frequency fit to the rotational constants and centrifugal distortion constants, and from it further transitions were predicted and measured, and used in a new fit. The procedure was repeated up to / ~ 30. At higher values of J the frequency fit was the chief criterion for the assign-ment, though some transitions involved degenerate pairs of levels, and had a first-order Stark effect which was useful in confirming these assignments. 229 410 DAVIS AND GERRY Table 3. Spectroscopic Constants 3 of P r o p i o l i c Acid HC2C00H HCjCOOD A 12110.0172 • 0.0046 b 11858.4445 ± 0.0050 B 4146.9388 i 0.0014 4015.7137 1 0.0015 C 3084.4861 1 0.0012 2995.5965 ± 0.0011 4 J * 1 1 ) 4 5.376 ± 0.146 5.205 1 0.140 A J K x 10 2 2.132 t 0.010 1.891 t 0.015 A K X 1 0 3 -7.715 » 0.045 -4.026 t 0.070 6 j x 10 4 1.605 t 0.043 1.593 ± 0.070 6 K x 10 2 1.219 ± 0.013 1.106 + 0.016 Hj x 10 7 -2.20 1 0.63 -0.73 ± 0.81 »JK * 1 0 6 6.88 ± 1.50 4.99 • 2.64 H K J x 10 5 -1.99 ± 0.41 -1.27 + 0.65 H K x 1 0 5 1.37 i 0.29 0.94 1 0.49 hj x 10 7 1.17 ± 0.31 0.76 ; 0.56 h J K x 10 6 -5.90 ± 1.36 -2.91 • 2.21 hj x 10 5 5.86 • 1.19 3.95 + 1.93 a In MHz ^ M l errors one standard deviation. The fitting procedure has also been described earlier (6, 7). The Hamiltonian used was that of Watson (<?), including terms up to the sixth degree in the angular momentum: 3C = 3CR + X D + 3CD', (1) 3CR = \(B + C)P* + [A - \{B + C)IJ/V + i(B - C)(iV - A 2 ) , (2) Table 4. Comparison of the Spectroscopic Constants (in MHz) of Propiolic Acid with Earlier Values (I) Parameter HC2' C00H HC2C00D present e a r l i e r present e a r l i e r value value value value A(MHz) 12110.017(5) a 12110.09 11858.445(5) 11858.32 B 4146.939(1) 4146.94 4015.714(2) 4015.69 C 3084.486(1) 3084.49 2995.597(1) 2995.58 ^aaaa*'" 2 -5.656(45) -14.76 -6.162(66) -1.72 'bbbb x'° 3 -3.434(68) -7.6 -3.357(79) +1.3 -8.66(68) -25 -8.08(79) +28 a Numbers i n parentheses are the standard d e v i a t i o n s i n terms of the l a s t quoted f i g u r e s of the constant. Note. (MHz) should not appear beside A in column 1. 230 MICROWAVE SPECTRUM OF PROPIOLIC ACID 411 Table 5. Some Predicted Transition Frequencies of Propiolic Acid (HC.COOH) Transition Frequency (MHz) Standard Deviation (MHz) 1(0, 1) • 0(0, 0) 7231.42 0.00 1(1, 0) • 1 ( 1 , 1 ) 1062.40 0.00 1(1, 0) • 1(0, 1) 9025.47 0.00 1 ( 1 , 1 ) • 0(0, o) 151 M.49 0.01 2(0, 2) • 1(0, 1) 14363.47 0.00 2(1, 2) • 1 (1 ,1 ) 13400.35 0.00 2(1, 1) • 1(1, 0) 15525.15 0.00 2(1, 1) • 2(1, 2) 3187.20 0.00 2(1, 1) • 2(0, 2) 10187.14 0.00 2(1, 2) • 1(0, 1) 21363.42 0.01 2(0, 2) • 1(1, 1) 6400.40 0.00 3(0, 3) • 2(0, 2) 21302.42 0.00 3(1, 3) 2(1, 2) 20041.08 0.01 3(1, 2) 2(1, 1) 23222.42 0.01 3(1, 2) 3(1, 3) 6368.54 0.01 3(1, 2) 3(0, 3) 12107.14 0.01 4(1, 3) 4(1. 4) 10583.25 0.01 4(0, 4) 3(1, 3) 22241.65 0.01 5(1, 4) - 5(1, 5) 15774.69 0.01 5(1, 4) - 5(0, 5) 18886.84 0.01 5(1, 5) - 4(0, 4) 37499.50 0.01 6(1, 5) - 6(1. 6) 21834.90 0.01 6(1, 5) - 6(0, 6) 23914.72 0.01 6(1. 6) - 5(0, 5) 42665.69 0.01 7(1. 6) - 7(1, 7) 28591.72 0.01 7(1, 7) - 6(0, 6) 47995.99 0.01 7(0, 7) - 6(1, 6) 44594.81 0.01 8(1, 7) - 8(1, 8) 35812.61 0.02 8(1, 8) - 7(0, 7) 53542.66 0.02 8(0, 8) - 7(1, 7) 51413.95 0.01 9(1, 8) - 9(0, 9) 43715.76 0.03 10(1,9) - 10(0,10) 50911.10 0.05 11(1,11) - 10(0,10) 71190.75 0.04 11(0,11) - 10(1,10) 70755.13 0.04 12(1,12) - 11(0,11) 77260.95 0.07 12(0,12) - 11(1,11) 77014.21 0.07 13(1,12) - 13(0,13) 71660.35 0.22 13(1,13) - 12(0,12) 83371.99 0.10 13(0,13) - 12(1,12) 83234.11 0.10 14(1,13) - 14(0,14) 78234.73 0.36 14(1,14) - 13(0,13) 89507.19 0.16 14(0,14) - 13(1,13) 89431.00 0.16 150,14) - 15(0,15) 84693.21 0.54 15(1,15) - 14(0,14) 95656.32 0.24 15(0,15) - 14(1,14) 95614.62 0.24 3CD = —AjP4 - AJKP*P2 - AKPa* - (iV - Po2)LSjP2 + 5KPa2l -IhP2 + 5KiY](P<? - Pc2), (3) 3CD' = HjP* + HJKP'P* + HKJP2Pa' + HKPa* + (Pi2 - Pc2) XlhjP* + hjKpPa2 + hKPa^ + LhjP* + hJKP2Pa2 + hKP^ X(P<?-Pc2). (4) 231 412 D A V I S AND G R A Y In these equations the angular momentum P has components Pa, Pb, Pc; A, B, C are the rotational constants; Aj, AJK, AR, &J, SK are the quartic distortion constants; and Hj, HJK, HRJ, HR, hj, hjK, ha are the sextic constants. A first-order fit was made to the rotational and distortion constants, and the frequencies were predicted in this approximation. The frequencies were also calculated exactly, and the differences be-tween these and the first-order frequencies, which represented high-order contributions, were substracted from the measured values. The resulting frequencies were refit to the first-order expression, and the procedure was repeated until the process converged. The measured frequencies, along with their assignments and centrifugal distortion contributions, are given in Tables 1 and 2. In only a few cases did we repeat the earlier measurements (1); in general there is fair agreement, though in some cases there are substantial discrepancies, of a few hundred kilohertz. The derived molecular constants are given in Table 3 ; they have been obtained using only the frequencies measured in the present work. Good values have been obtained for the rotational and quartic distor-tion constants. In addition, fairly good values have been obtained for all the sextic coefficients of the normal species; they are only poorly determined in the deuterated species. However, most of the sextic coefficients are highly correlated (|p| > 0.9) among themselves. DISCUSSION The molecular constants are compared with the earlier values in Table 4. In this table the distortion constants have been converted to the "determinable" coefficients using the equations of Watson (<?). Our rotational constants agree with those of Lister and Tyler (1), but our distortion constants in general do not, as they anticipated (/). It is noteworthy that the quartic distortion constants are very similar to those of propiolyl fluoride (6); this is not surprising, however, in view of the similar molecular structures and masses of the atoms (9). In Table 5 we give the predicted frequencies and standard deviations of some transi-tions unmeasured in the present work, but which should be of interest in radioastronomy; some of these are transitions measured earlier (i). Since nb is much bigger than ju<. (i), the predictions are mainly of i-type transitions, though we include some a-type transi-tions at very low / . The maximum value of / = 15 and of frequency = 100 GHz. ACKNOWLEDGMENT Support of the National Research Council of Canada is gratefully acknowledged. RECEIVED : June 30, 1975 REFERENCES 1. D. G . LISTER AND J. K. T Y L E R , Spectrochim. Acta A 28, 1423 (1972). 2. B . ZDCKERMAN, J. A. B A L L , AND C A. GOTTLIEB, Astrophys. J. 163, L41 (1971). 3. B . E. T U R N E R , Astrophys. J. 163, L3S (1971). 4. K. D. TU C K E R, M. L. K U T N E R , AND P. TH A D D E U S , Astrophys. J. 193, L115 (1974). 5. L. E. SNYDER AND D. B K U L , Bull. Amer. Astron. Soc. 3, 388 (1971). 6. R. W. DAVIS AND M. C L. GE R R Y , / . Mol. Spectrosc. 57, 118 (1975). 7. M. C. L. GE R R Y , / . Mol. Spectrosc. 45, 71 (1973); M. C L. G E R R Y AND G . WINNEWISSER, / . Mol. Spectrosc, 48, 1 (1973). 8. J. K. G . WA T S O N , / . Chem. Phys. 46, 1935 (1967); 48, 4517 (1968). 9. R. L. C O O K , J. Mol. Struct. 26, 126 (1975). 232 Appendix 3 A R e p r i n t o f a Report o f the Microwave Spectrum o f Formic A c i d 233 J O U R N A L O F M O L E C U L A R S P E C T R O S C O P Y 81, 93-109 (1980) Microwave Spectra and Centrifugal Distortion Constants of Formic Acid Containing 1 3 C and 1 8 0 : Refinement of the Harmonic Force Field and the Molecular Structure 1 R. WELLINGTON DAVIS , A . G. ROBIETTE, 2 AND M . C . L . GERRY Department of Chemistry, The University of British Columbia, Vancouver, V6T 1W5 Canada AND E . B j A R N O V 3 A N D G. W l N N E W I S S E R Physikalisch-Chemisches Institut, Justus Liebig-Universitdt Giessen and Max-Planck-Institut fur Radioastronomie, Bonn, Germany Pure rotational spectra of H13COOH, HC18OOH, and HCO'8OH have been measured in the frequency region 8-185 GHz. Analysis of the spectra has given improved rotational constants and quartic and sextic centrifugal distortion constants. The quartic distortion constants have been combined with previously published distortion constants of four other isotopic species, and with the vibrational wavenumbers of seven isotopic species, to produce a refined harmonic force field. An improved substitution structure and the ground state average structure have been obtained. Some unmeasured transi-tion frequencies which may be of importance in radioastronomy are also presented. INTRODUCTION Although the microwave spectrum of the more stable rotamer of formic acid has been the subject of a very large number of studies (7) the spectra of the species containing 1 3 C and l s O have received relatively little attention. The earliest re-ports of the spectrum of H 1 3 C O O H were those of Lerner, Dailey, and Friend (2), who observed the 101 <— 0 0 0 and 2 1 2 <— l n transitions. Subsequently Bellet et al. (3) measured a substantial number of a-type Q and R branch transitions extending into the millimeter wave region and derived improved rotational con-stants along with four quartic centrifugal distortion constants. Most recently Willemot et al. (4) have published refined rotational constants, but did not present the data from which they were obtained. The only reported measure-ments for H C 1 8 O O H and H C 0 1 8 O H are those of Kwei and Curl (5), who measured five a-type transitions for each species, and used their rotational constants to calculate a substitution structure. Somewhat different, and apparently improved, 1 This work was supported by the Natural Sciences and Engineering Research Council of Canada, the Deutsche Forschungsgemeinschaft, and the North Atlantic Treaty Organization. 2 On leave from Department of Chemistry, The University of Reading, England. 3 Present address: Department of Chemistry, Michigan State University, East Lansing, Michigan. 93 0022-2852/80/050093-17$02.00/0 Copyright © 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. 234 94 DAVIS ET AL. rotational constants have also been reported recently by Willemot et al., again without any measured frequencies (4). The present work was initiated for several reasons. The first was to clarify the molecular structure, concerning which there is some controversy. In their deter-mination of their substitution structure Kwei and Curl noted that four coordinates are very small and could not determine them accurately by the substitution method (6). Since their rotational constants are relatively imprecise by present day standards it might be expected that a more extensive study would clarify the situation by producing more accurate values. Later, Bellet et al. (3) published a considerably different structure, based on their isotopic measurements. Their rotational constants for H I 3 C O O H are also relatively imprecise, however, because of the lack of b-type transitions, and a more extensive measurement of this spec-trum was therefore in order. Stiefvater (7), in the course of his study of propionic acid, has also published a structure which is in substantial agreement with that of Kwei and Curl . Besides a substitution structure it should also be possible to obtain the ground state average structure. Such a determination requires a knowledge of the harmonic force field (8). There have been many force fields published for formic acid, of which the most detailed is the recent work of Redington (9) from the vibrational wavenumbers of 24 different isotopic species. He also reviews the earlier literature. H a , Meyer, and Giinthard (10) obtained a modified force field consistent with ab initio force constants and the same vibrational data. N o force field, however, has made use of the additional experimental information con-tained in the quartic centrifugal distortion constants, largely because accurate values have not been available. It would thus be desirable to measure the dis-tortion constants of as many isotopic species as possible for this purpose. Finally, formic acid is a known interstellar molecule. It was first reported by Zuckerman et al. (11), who observed the l i o - l n emission of the normal species at 1638 M H z in Sgr B2; this was confirmed by Whiteoak and Gardner (12) in Sgr A and Sgr B2. Winnewisser and Churchwell (13) provided additional confirmation with their measurement of the 2 n - 2 , 2 transition, also in Sgr B2. Since several interstellar molecules containing I 3 C and 1 8 0 are known, the possibility exists that corresponding species of formic acid might also be ob-served. Such observations require detailed knowledge of the rotational spectrum, which was not previously available. In the present paper we report extensive measurements of the microwave spectra of H 1 3 C O O H , H C 1 8 O O H , and H C O , 8 O H , along with the rotational con-stants and centrifugal distortion constants derived from these spectra. For H 1 3 C O O H the constants are somewhat improved over those of Willemot et al. (4), while for H C 1 8 O O H and H C O , 8 O H we present the first reported distortion constants. The quartic distortion constants have been combined with those of other isotopic species (4), as well as the vibrational data of Redington (9), to refine the force field. Both an improved substitution structure and the ground state aver-age structure of H C O O H are reported. Finally we present a table of transitions unmeasured in the present work, but of potential interest in radioastronomy. 235 SPECTRUM AND STRUCTURE OF FORMIC ACID 95 EXPERIMENTAL DETAILS The rotational spectra of H 1 3 C O O H , H C 1 8 O O H , and H C 0 1 8 O H were measured in the frequency region 8-185 G H z . The isotopically enriched samples were ob-tained commercially as follows: H 1 3 C O O H (90 atom% 1 3 C) from Merck Sharp & Dohme Canada Limited, and , 8 0 - H C O O H (-40 atom% 1 8 0) from Stohler Isotope Chemicals (Massachusetts). They were used without further purification. The transitions were measured using several spectrometers. At the University of British Columbia a conventional 100-kHz Stark modulated instrument was used, in the frequency range 8-80 G H z . Between 8 and 40 G H z the source was an appropriate backward wave oscillator (BWO) in a Hewlett-Packard 8400 C microwave spectroscopy source, or, at K band, an O K I 20V10 or 24V10 klystron. Power above 40 G H z was obtained by doubling the corresponding lower frequency source. At the Justus Liebig-Universitat spectra were measured in the 8-53 G H z region with a Hewlett-Packard 8460 A M R R spectrometer, modulated at 33.3 k H z . The X, P, and K bands (8-26.5 G H z ) were covered with an ap-propriate B W O , while between 26.5 and 53 G H z power was obtained by doubling the P- or /C-band B W O frequency. Above 80 G H z the millimeter wave spectrom-eter at the Justus Liebig-Universitat was used (14). Al l measurements were made at room temperature at pressures s l 5 mTorr; they are estimated to be accurate to better than ± 5 0 k H z . ASSIGNMENTS AND ANALYSIS OF THE OBSERVED SPECTRA Initial predictions of the spectra of the various isotopic species were made using previously published data. For H 1 3 C O O H only the 1971 work of Bellet et al. (3) was available as the present work was started. We measured a large number of new a-type Q and R branches predicted from their constants, and also re-measured many of their reported transitions. Analysis of these spectra gave im-proved rotational constants which permitted identification of several of the weaker low K„ b-type transitions. These were included in a new fit, from which further assignments could be made. This procedure was repeated up to high values of J and Ka. The frequency fit and line intensities were the chief criteria for assign-ment, confirmed where possible by the Stark effect. A similar bootstrap procedure was used to assign the spectra of the 1 8 0 species, starting this time from the rotational constants of Kwei and Curl (5). The frequency fits, intensities, and Stark effects were again the chief criteria for assignment. Because the isotopic enrichment was much lower here than in the 1 3 C species, and was distributed over two positions in the molecule, the data sets were correspondingly smaller for these species. Rotational and centrifugal distortion constants were calculated using Watson's reduced Hamiltonian in the A reduction (15) and the P representation (76): at — alR T" eftjj ~r OLQ' S€R = API + BPl + CP\ (1) (2) 236 DAVIS ET AL. TABLE I Measured and Calculated Transition Frequencies (in MHz) of H13COOH, HC18OOH,a and HC0 1 8OH b T r a n s i t i o n Observed C a l c u l a t e d D i s t o r t i o n D i f f . Freouency Frequency C o r r e c t i o n H COOH 1 ( 0 . 1) - 0 ( 0 , 0) 22432. 52 22432. 52 - 0 . 0 4 -0 .00 2( 0, 2) - 1 ( 0, 1) 44832. 15 44832. 14 -0 .31 0.01 2( 1, 2) - 1 ( 1. 1) 43190.82 43190.81 0. 25 0.0 1 2 ( 1. 1) - 1 ( 1, 0) 46539. 46 46539.48 -0 .21 -0 .02 3( 0. 3) - 2 ( 0, 2) 67166.06 67166.07 -1 .01 - 0 . 0 1 3 ( 1. 2) - 2 ( 1. 1) 69787.90 69787.90 -1 .01 - 0 . 0 0 3( 1, 3) - 2 ( 1, 2) 64765.53 64765.53 - 0 . 08 O.CO 3 ( 2 . 1) - 2 ( 2 . 0) 67429.16 67429.19 0.91 - 0 . 0 3 3( 2. 2) - 2( 2, 1) 67298.69 67298.65 0.97 0.04 5 { 1, 5) - 4 ( 1. 4) 107835. 07 107835.03 - 2 . 5 4 0.04 6( 2, 6) - 7( 2, 5) 181688.70 181688.70 - 17. 32 - 0 . 0 0 8 ( 3 , 6) - 7 ( 3 , 5) 179795. 46 179795.45 - 8 . 2 3 0.01 8[ 3. 5) - 7( 3, 4) 179895.11 179395.10 - 8 . 4 3 0.0 1 8 ( 4 . 4) - 7 ( 4, 3) 179691.89 17969 1.91 1.21 - 0 . 02 8( 5, 3) - 7 ( 5, 2) 179633.52 179633.54 13. 20 -0 .02 8 ( 6 , 3) - 7 ( 6, 2) 17961 1. 63 179611.65 27.93 - 0 . 0 2 8( 7, 1) - 7( 7, 0) 179607.30 179607.29 45. 14 0.01 3( 1. 2) - 3 ( 1, 3) 10045.45 10045.44 - 1 . 5 6 0.01 «( 1. 3) - 4 ( 1. 4) 16739.65 16739.64 - 3 . 26 0.0 1 5 ( 1, 4) - 5 ( 1, 5) 25101. 31 25101.31 - 6 . 0 7 O.CO 6( 1. 5) - 6( 1, 6) 35122.04 35122.04 - 10.47 0.0 0 8( 2 . 7) - 7 ( 2, 6) 179047.81 179047.79 - 1 3 . 8 8 0.02 9( 2, 7) - 9( 2, 8) 10388.91 10388.89 - 12 .77 0.02 10 ( 2 , 8) - 10 ( 2. 9) 15326. 19 15326.15 - 2 1 . 7 2 0.04 11( 2. 9) - 11 ( 2, 10) 21679.27 21679.27 -34 .99 0.00 12 ( 2.10) - 12 I 2, 11) 29590.22 29590.21 - 5 3 . 75 0.01 13( 2. 11) - 13( 2, 12) 39164.68 39164.b8 - 7 9 . 2 3 - 0 . 0 0 16 ( 3.13) - 16 ( 3,14) 10079.42 10079.42 - 49. 82 o.co 17( 3. 14) - 17 ( 3, 15) 14130.73 14130.79 - 7 b . 5 6 - 0 . 0 6 19 ( 3.16) - 19 I 3.17) 25896.09 25896.10 -164 .74 - 0 . 0 1 20 ( 3. 17) - 20 ( 3, 18) 33962.75 33962.76 - 2 3 1 . 52 -0 .0 1 23 ( 4.19) - 23 ( 4,20) 8060. 45 8060.44 -104.71 0.01 2<4( 4. 20) - 24| 4,21) 11072.21 1 1072. 21 -153 .85 0.00 25 ( 4.21) - 25( 4,22) 14959.59 14959.6 1 -221 .28 -0 .02 28( 4.24) - 28( 4,25) 33632.43 33632.43 -582 . 35 O.CO 32 { 5.27) - 32 ( 5,28) 10671. 27 10671.27 -321.91 - 0 . 0 0 33( 5.28) - 33| 5,29) 14142.71 14142.71 -447 .23 - 0 . 0 0 36 ( 5.31) - 36 I 5,32) 30696.59 30696.57 -1094 .60 0.02 40{ 6,34) - 4C| 6,35) 9530.55 9530.55 -536 .38 - O . C O "1 I 6,35) - 41 I • 6,36) 12480.07 12480.09 -729 .63 -0 .02 42 ( 6,36) - 0 2 I 6,37) 16189.72 16189.71 -980 .78 0.0 1 44 | 6.38) - 44 I 6,39) 26498. 52 26498.54 -1709 .44 - 0 . 0 2 49 ( 7.4 2) - 49( 7,43) 10478.86 10478.87 -10 30. 46 - 0 . 0 1 50 ( 7.43) - 50 I 7.44) 1350 1.98 13502.00 -1368 .68 - 0 . 0 2 51( 7,44) - 51 ( 7.45) 17263.94 17263.92 -1800.28 0.02 4 ( 0 , «) - 3 ( 1, 3) 29917.99 29917.93 - 2 . 44 0.06 2( 1. 1) - 2( 0. 2) 66907.58 66907.59 - 1 . 50 -0 .01 3 < 1, 2) - 3 ( o. 3) 69529.44 69529.43 - 1 . 4 9 0.01 4| 1. 3) - 4| 0. 4) 73137.72 73137.70 - 1 . 7 7 0.02 5 j 1 , 4) - 5 ( o. 5) 77825.78 77825.79 - 2 . 6 2 -0.01 7{ 1. 6) - 6( 2. 5) -13343 .87 -13343 . 89 - 5 . 7 5 0.02 8 1, 7) - 7 2. 6) 15322. 22 15322.26 - 19.89 -0 .04 9( 1. 9) - 8 2. 6) -37012.37 -3701 2.35 8. 14 -0 .02 10 ( 1,10) - 9 2, 7) -27220.77 -27220 .80 8.49 0.03 12 l 1. 12) - 111 2, 9) - 14404.77 -14404.77 20.88 O.CO 13 1.13) - 12 2,10) -1 1685. 11 - 1 1 6 8 5 . 13 35.89 0.02 14( 1, 14) - 13( 2, 11) -11560.80 -11560.77 58. 86 - 0 . 0 3 15 1.15) - 14 2,12) -14078.16 - 14078. 15 91.35 -0.01 12{ 2, 10) - 1 1 3. 9) -30628 .62 -30628.67 - 4 4 . 56 0.05 0 a t the c a r b o n y l oxygen 'o a t the hydroxy l oxygen 237 S P E C T R U M A N D S T R U C T U R E O F F O R M I C A C I D T A B L E I—Continued Transition Observed Calculated Distortion Diff. Frequency Frequency Correction H COOH (continued) 1U( 2,12) - 13 ( 3,11) 28973. 80 28973.85 -143 .70 - 0 . 0 5 15 ( 2,13) - 14 3,12) 60402. 55 60402. 59 - 2 0 6 . 97 -0 .04 18 ( 2. 17) - 17| 3,14) 33121.56 33121.56 - 3 2 . 7 1 0.00 28 ( 2,27) - 27 3,24) 14730.30 14730.29 1295. 01 0.01 30 ( 2,29) - 29 l 3, 26) -21127.36 -21127.39 1925.65 0.03 31 ( 2,30) - 30 3,27) -42481 . 73 -4248 1. 70 2285. 00 - 0 . 0 3 20 { 3, 17) - 19 l 4, 16) 33138.66 33138.63 -418 .36 0.03 17 ( 3.15) - 16 i 4,12) -66946.81 -66946 . 83 - 26.12 0.02 21{ 3, 19) - 20 ( 4,16) 17535.35 17535.35 -212 .50 -o.co 22 < 3,20) - 21 ( 4, 17) 36938.70 36938. 74 - 2 5 0 . 00 - 0 . 0 4 23( 3,21) - 22( 4,18) 55333.67 55333.67 -278 . 10 -O.CO 22 ( U,18) - 21 ( 5.17) -71229.04 -71229.06 - 1 9 6 . 2 5 0.02 26 ( 4.22) - 25( 5.21) 36162.16 36 16 2. 12 -847 .52 0.04 23 ( « , 2 0 ) - 22 5,17) -53880 .93 -53880 .93 - 2 1 6 . 5 2 0.00 26 ( 4, 23) - 25( 5,20) 15239.88 15239.90 -515 .36 - 0 . 0 2 30 ( 5,25) - 29 ( 6,24) -1 1985. 76 -11985 .73 -927 .44 - 0 . 0 3 31( 5,2b) 30 ( 6,25) 14219.23 14219.24 -1176 .50 - 0 . 0 1 33 ( 5,28) - 32 6.27) 68638. 33 68638. 29 - 1 7 7 7 . 95 0.04 28 ( 5, 24) - 27( 6,21) -66003.26 -66003.25 -431 .80 - 0 . 0 1 37 ( 6,32) - 36 ( 7,29) 17620.64 17620.65 -1733 .93 -0 .01 39 ( 7,32) 38( 0,31) -69211.07 -69211.08 -1453 .82 0.0 1 HC1800H 1 ( 0, 1) - 0( 0, 0) 21301.76 21301.76 - 0 . 0 4 0.00 2 ( 0, 2) - 1 ( 0 , 1) 42577. 97 42577.95 - 0 . 2 8 0.02 2( 1. 2) - 1 ( 1, 1) 41111.43 41111.42 0. 25 0.0 1 2 ( 1. 1) - 1 ( 1, 0) 44095. 84 44095.84 - 0 . 1 7 0.00 3( 1. 2) - 2 ( 1. 1) 66127. 16 66127.15 - 0 . 88 0.01 3( 1. 2) - 3 ( 1. 3) 8952. 86 8952.82 - 1 . 4 3 0.04 4< 1. 3) - 4 ( 1. 4) 14919.41 14919.40 - 2 . 9 3 0.0 1 5 ( 1. « ) - 5 ( 1, 5) 22373. 38 22373. 37 - 5 . 4 0 0.01 6( 1, 5) - 6( 1. 6) 31308.96 31308.99 - 9 . 25 - 0 . 0 3 10( 2, 8) - 10 ( 2, 9) 12037.20 12037.17 - 16.92 0.03 11( 2. 9) - 11( 2.10) 17101. 10 17101.09 - 2 7 . 3 9 0.0 1 2 { 2,10) - 12 ( 2,11) 23458.87 23458.87 - 4 2 . 3 5 - 0 . 0 0 13( 2, 11) - 13( 2,12) 31222.73 31222.77 - 6 2 . 8 8 - 0 . 0 4 17 ( 3.11) - 17 ( 3,15) 9753. 26 9753.23 - 5 2 . 2 7 0.03 18< 3. 15) - 18( 3,16) 13425.03 13425.04 - 7 8 . 4 8 - 0 . 0 1 19 ( 3.16) - 19 ( 3,17) 18092. 03 18092.03 -114 .60 0.00 20 ( 3. 17) - 20 ( 3, 18) 23906.76 23906.77 -163 .00 - 0 . 0 1 21 ( 3,18) - 21 ( 3,19) 31015. 10 31015. 10 -226 .14 0.00 2( 0, 2) - 1 ( 1. 1) -22550.01 -22549.98 1. 15 - 0 . 0 3 4 ( 0 , « ) - 3( 1. 3) 23442. 59 23442.59 - 2 . 1 4 0.00 2( 1. D - 2( 0, 2) 68138.10 68138.07 - 1 . 49 0.03 3 ( 1. 2) - 3( 0, 3) 70462.06 70462.14 - 1 . 4 4 - 0 . 0 8 7{ 1, 6) - 6( 2, 5) -28175.20 -28175.21 - 3 . 3 2 0.00 9 ( 1, 8) - 8 ( 2. 7) 26254. 33 26254.33 - 3 2 . 6 4 - 0 . 0 0 11< 1, 11) - 10( 2, 8) -26750 .13 -26750.10 6. 94 - 0 . 0 3 2( 1,12) - 11 ( 2 . 9) -20 129. 35 -20129 . 37 11.98 0.02 13( 1, 13) - 12( 2, 10) -15647.54 -15647.54 22.08 -O .CO 17 ( 1.17) - 16 ( 2.14) -20697. 15 -20697 . 16 141.43 0.01 19 ( 1, 19) - 18( 2,16) -37186.98 -37186.97 267.23 - 0 . 0 1 13 < 2,11) - 12 ( 3,10) -29355.38 -29355 . 37 - 6 9 . 0 0 -0 .01 15( 2, 13) - I'M 3,12) 27368.71 27368.69 -173.44 0.02 1«( 2,13) - 13 ( 3,10) -44066.22 -44066 . 22 - 19.41 0.01 5  2, 14) - 11 ( 3.11) -27131.02 -27131.01 - 3 5 . 56 - O . C O 19 ( 2,18) - 18 ( 3,15) 28323. 45 28323. 47 -52 .51 - 0 . 0 2 20 ( 2, 19) - 19( 3,16) 38214. 19 38214. 18 -32 .94 0.0 1 21 ( 3,18) - 20 ( 4,17) 18498. 18 18498. 18 - 4 4 6 . 17 - 0 . 0 0 21( 3. 19) - 20( 4, 16) -14178.77 -14178.77 -203. 17 0.00 23 < 3,21) - 22( 4,10) 24099.97 24099.97 - 2 9 1 . 8 5 0.00 238 98 DAVIS ET AL. TABLE I—Continued Transition Observed Calculated Distortion Diff. Frequency Frequency Correction H C 0 ' ° 0 H 1 ( 0 , 1) - 0 ( 0 , 0) 21209.69 21289.69 - 0 . 0 4 0.00 2 ( 0. 2) - 1 i 0, 1) 42554.55 42554.56 - 0 . 28 -0 .01 2( 1, 2) - 1 i 1, 1) 4 1101.87 41101.88 0. 25 - 0 . 0 1 2 I 1. 1) - 1 i 1, 0) 44057. 11 44057.11 - 0 . 1 6 - 0 . 0 0 3| 1. 3) - 2( 1. 2) 6 1637. 10 61637.14 - 0 . 0 4 -0 .04 3 | 1. 2) - 2 i 1. 1) 66069.56 66069.53 - 0 . 8 7 0.03 11 1. 3) - 4 1 1, «) 14773.62 14773.58 - 2 . 89 0.04 5 I 1. 4) - 5 ( 1. 5) 22154.91 22154.90 - 5 . 3 4 0.01 6| 1. 5) - 6{ 1, 6) 31003.69 31003.73 - 9 . 14 - 0 . 0 4 11 I 2 , 9) - 11 1 2. 10) 16631. 16 16631. 15 - 2 6 . 6 C 0.01 12 I 2. 10) - 12| 2,11) 22829.24 22829.24 - 4 1 . 18 - 0 . 0 0 13 1 2.11) - 13 i 2. 12) 30407.27 30407.28 - 6 1 . 2 2 -0.01 14( 2. 12) - 14( 2. 13) 39450.87 39450.90 - 8 7 . 83 - 0 . 0 3 18 | 3,15) - 18 1 3,16) 128 11.57 1281 1.59 - 7 4 . 8 0 - 0 . 0 2 19( 3, 16) - 19| 3,17) 17279.35 17279.34 -109 .38 0.0 1 20 ( 3.17) - 20 I 3, 18) 22854.45 22854. 4 1 -155 .84 0.04 : i ( 3, 18) - 21 ( 3,19) 29681.63 29681.65 -216 .6 1 - 0 . 0 2 2 | 0. 2) - 1 ( 1. 1) -2326 1. 52 . -2326 1. 52 1. 17 - 0 . 0 0 4 ( 0,- 4) - 3 ( 1. 3) 22680.43 22680.41 - 2 . 12 0.02 11 1. 0) - 1 I 0 , 1) 67293. 74 67293. 74 - 1 . 6 2 0.00 2( 1) - 2( 0, 2) 68796.26 63796.29 - 1 . 51 - 0 . 0 3 3 ( "1. 2) - 3 | 0 , 3) 7 1095. 96 71095.95 - 1 . 4 6 0.01 » ( 1. 3) - 1 ( 0, 4) 74247.16 74247.12 - 1 . 6 2 0.04 5 ( 1. 4) - 5 ( 0, 5) 78320. 80 78J20. 80 - 2 . 2 3 - 0 . 0 0 7( 1, 6) - 6( 2, 5) -30489.34 -30489.34 - 2 . 87 0.0 1 9 ( 1. 8) - 8 1 2 , 7) 238 18. 49 23818.49 - 3 2 . 13 0.00 10( 1, 10) - 9( 2. 7) -36862.94 -36862.93 5. 32 - 0 . 0 1 11 ( 1,11) - 10 ( 2, 8) -28050.41 -28050 .42 6.28 0.01 12( 1. 12) - 11 ( 2, 9) -21206.85 -21206.84 10.05 - 0 . 0 1 13( 1,13) - 12 ( 2. 10) -16466 .79 - 16466.80 20.33 0.01 17( 1, 17) - 16( 2 , 1 « ) -20181.70 -20181.69 135.62 - 0 . 0 1 18 ( 1.18) - 17 ( 2,15) -26902. 20 -26902.20 190.62 0.00 13( 2. 11) - 12( 3,10) -33504.32 -33 50 4.31 - 6 6 . 3 1 - 0 . 0 1 15 ( 2,13) - I t ( 3,12) 22909. 95 22909.93 -170 .05 0.02 15( 2, 11) - I'M 3, 11) -30179.38 -30 179.37 - 3 5 . 7 9 - 0 . 0 1 16 ( 2.15) - 15 ( 3,12) -14140.31 -14140.31 - 5 0 . 0 5 -0.01 18( 2, 17) - 17( 3,14) 1 4209. 81 14209.02 - 6 3 . 62 -O .CO 19 ( 2,18) - 18 ( 3,15) 26 166. 03 26166.03 - 5 8 . 3 0 0.01 20 ( 2. 19) - 19( 3, 16) 36399.70 36399.70 - 4 1 . 24 - 0 . 0 0 19 ( 3.16) - 18 ( 4,15) -41614. 52 -41614.51 -217 .42 - 0 . 0 0 20 ( 3, 17) - 19( 4, 16) -15145.76 -15145.76 -3 17. 84 O.CO 22 ( 3,19) - 21 ( 4,18) 40818. 30 40818.30 - 5 6 9 . 4 8 - 0 . 0 0 20 ( 3, 18) - 19( 4,15) -39042.70 -39042.71 -152 . 32 0.00 21 ( 3,19) - 20 ( 4.16) -18927.38 - 18927. 37 -202 .33 - 0 . 0 0 23( 3,2 1) - 22( 4,18) 19610.76 19610.76 -294 .70 - 0 . 0 1 24 ( 3,22) - 23 ( 4,19) 37783.95 37783.95 - 3 3 2 . 1 5 0.00 % = -AjP4 - AJKP2P2 - AKP40 - 2SjP\Pl - PI) - 8KiH(H - H) + (H - H)P2a] O ) 3ifD. = HjP« + HJKP*P2 + HKJP2H + HKP% + [hjP4 + hJKP2P2 + hKfi*](Pl - P2) + [PI - P2c)[hjP4 + hJKP2P\ + hKPt}. (4) In these equations the angular momentum P has components Pa, P„, Pc; A, B, C are the rotational constants; AJt AJK, AK, Sj, 8K are the quartic centrifugal dis-tortion constants; and Hj, HJK, HKJ, HK, hj, hJK, hK are the sextic constants. The 239 SPECTRUM AND STRUCTURE OF FORMIC ACID 99 spectroscopic constants were obtained using the iterative least-squares procedure described earlier (17). Only a partial set of sextic constants could be determined from the available data, and the indeterminate constants were omitted from the fits. In all calculations double precision (16 digit) arithmetic was used. Table I contains the frequencies and assignments of the measured transitions of the various isotopic species, along with calculated frequencies and distortion corrections. The values obtained for the rotational constants and centrifugal distortion constants are given in Tables II, III, and IV for H 1 3 C O O H , H C , 8 O O H , and H C O ' 8 O H , respectively, in comparison with earlier values. Clear improve-ments are evident for all species in the present work. FORCE FIELD AND STRUCTURE CALCULATIONS (a) Harmonic Force Field For the interconversion of various types of structure parameters we required a good harmonic force field. We found, however, that the recent experimentally based force field of Redington (9), which was refined to fit the wavenumbers of numerous isotopic species, predicted distortion constants in poor agreement with experiment. For this reason we adjusted the force field in an attempt to make use of the new information supplied by the distortion constants. TABLE II Comparison of the Spectroscopic Constants of H13COOH Obtained in the Present Work with Those of Earlier Work Parameter Present Willemot et al_. Bel let et a l . Work (ref. (4j) (ref. 7T)T Rotational Constants (KHz) A 75580.8474(57) a 75580.80(7) a 75580.58 b B 12053.56428(86) 12053.566(3) 12053.47 C 10378.99597(74) 10378.998(3) 10379.09 Centrifugal Distortion Constants (kHz) A j 9.9134(22) 9.91(1) 9.862d A J K -85.013(33) -84.79(5) -84.51 d A K 1673.66(19) 1655(1) 1601 d 6j 1.98138(22) 1.978(1) 1.981d « K 41.928(36) 42.2(2) 40.13 d H K J x 102 -1.494(51 ) - c - e HK x 10 1.656(65) h j x 106 4.82(17) h K x 102 1.84(12) o(MHz) 0.0247 Numbers in parentheses are one standard deviation in units of the last significant figures. ^ No uncertainties given. c Not determined d Calculated from the T ' S of ref. (3). 240 100 DAVIS ET AL. TABLE III Comparison of the Spectroscopic Constants of HC18OOHa Obtained in the Present Work with Those of Earlier Work Parameter Present Willemot et a l . Kwei and Curl Work (ref. (?J)— (ref. (5)) Rotational Constants (MHz) A 76526.465(15) b 76635(108) b 76521(100) C B 11397.1065(25) 11397.15(2) 11396.91(30) C 9904.6859(20) 9904.70(2) 9904.76(30) Centrifugal Distortion Constants (kHz) 4j 8.9757(338) d d 4 J K -82.560(687) - -4 K 1674.5(39) — -6j 1.6934(21) - -6 K 39.36(23) - — H K J x 102 -1.32(104) - -HK X 10 1.7(21) — — hj x 106 2.2(30) — -hK x 102 2.8(17) — --a(MHz) 0.0251 a 18 0 at the carbonyl oxygen. b Numbers in parentheses are one standard deviation i in units of the last significant figures. c Numbers in parentheses are stated uncertainties in units of the last significant figures. d Not determined. The data used were the vibrational wavenumbers and distortion constants of seven isotopic species: H C O O H , H C O O D , D C O O H , D C O O D , H 1 3 C O O H , H C 1 8 O O H , and H C 0 1 8 O H . The vibrational data, taken unchanged from Redington (9), were each given an uncertainty of 1% of their values (apart from vs of D C O O H and v2 of D C O O D which, following Redington, were excluded from the fit). The distortion constants were assigned uncertainties ranging from 1 to 5%, as quoted in Table V , depending on their experimental errors and our estimates of possible zero-point averaging effects. A l l data were weighted as the inverse squares of these uncertainties in the force field calculation. Initially the distortion constants of H C O O D were included as data. Later, however, it was found that the planarity sum 2, defined by X = 4 C A , - (B - C)AJK - 2(2A + B + C)8j + 2(5 - C)5A., (5) was anomalous for this species (see Table V) and it seemed preferable to exclude these distortion constants. The value of 2 should be zero for the equilibrium rotational and distortion constants of a planar molecule, as shown by Watson (15). We were not successful in finding a set of force constants which would give a good fit to the distortion constants while preserving the wavenumber fit achieved by Redington (9). For our best compromise, quoted in Table V I , the 241 SPECTRUM AND STRUCTURE OF FORMIC ACID 101 TABLE IV Comparison of the Spectroscopic Constants of HC0 1 8OH a Obtained in the Present Work with Those of Earlier Work Parameter Present Willemot et al_. Kwei and Curl Work (ref. (|J) (ref. (5)) Rotational Constants (MHz) A 77201.3076(88) b 77283(111) b 72206(100) C B 11383.7761(18) 11383.82(2) 11383.58(30) C 9905.9491(12) 9905.94(2) 9906.06(30) Centrifugal Distortion Constants (kHz) A J "JK *K 4 J -MM x 10' HK x 10 h, x 106  J 2 hK x 10 8.9674(245) -82.823(465) 1701.5(25) 1.6723(12) 38.95(17) -1.68(55) 2.5(10) 3.3(21) 2.3(14) o(MHz) 0.0194 0 at the hydroxyl oxygen. b Numbers in parentheses are one standard deviation in units of the last significant figures. c Numbers in parentheses are stated uncertainties in units of the last significant figures. d Not determined. rms relative error (Av/v) is 0.89% for 48 vibrational data in the A' block. This should be compared with values of better than 0.5% achieved for 163 vibrational data from 24 isotopic species by the A' force field of Redington, or 0.6% by H a , Meyer, and Giinthard. On the other hand, a fit to better than 1% is still quite reasonable for vibrational data which are not corrected for anharmonicity. Our A" force constants are essentially identical to those of Redington. This is expected, as the calculated distortion constants do not depend on the A" block. The fit to the distortion constants is shown in Table V . Here the unweighted rms relative error is 3.3% for 30 observations. This is also reasonable. The experimental values of the planarity sum 2 are about 3 to 4 M H z 2 in most cases: this is about 2% of the AJK or the dK contribution to 2 (we pick out AJK and 8A as these have the largest experimental uncertainties of the four distortion con-stants involved in 2 and thus attract the largest residuals in the least-squares fit). Even if the force field were ideal in all other respects, therefore, the use of experi-mental distortion constants which do not obey the planarity conditions would imply an error of the order of 2% in at least one constant. In conclusion, it should be pointed out that we found the combined fit to vibra-tional data and distortion constants to be poorly conditioned. We were able to 2 4 2 DAVIS ET AL. TABLE V Fit to the Centrifugal Distortion Constants of Seven Isotopic Species of Formic Acid3 4 J AJK 4K { J h Ic HCOOH obs. 9.989 -86.25 1702.3 1.949 42.60 3 .10 0 0.099 0.86 17.0 0.019 0.85 £ -0.127 -0.42 -15.9 0.000 2.41 HCOOD b obs. 10.18 -59.67 988.0 2.146 44.7 10 .80 e (-0.26) (-6.75) (4.4) (-0.012) (1.55) DCOOH obs. 9.40 -39.52 755.0 2.224 37.7 3 .03 0.14 0.59 11.3 0.033 1.9 e -0.15 2.18 -13.3 -0.005 2.9 DCOOD obs. 9.64 -34.0 497.0 2.420 35.17 3. .77 o 0.14 0.5 9.9 0.036 1.06 E -0.24 -2.6 -1.9 -0.009 1.11 H13C00H obs. 9.913 -85.01 1673.6 1.981 41.93 4. 48 o 0.099 0.85 16.7 0.020 0.84 e -0.138 -0.74 -14.3 -0.002 2.45 HC18O0H obs. 8.975 -82.57 1674.7 1.693 39.35 3. 90 0 0.224 3.30 33.5 0.025 1.57 -0.089 -0.06 -17.0 0.000 2.50 HC0180H obs. 8.968 -82.82 1701.5 1.672 38.94 3. 33 0.135 2.07 25.5 0.025 1.17 t -0.100 -0.09 -15.1 -0.001 2.40 a Observed distortion constants from ref. (4) for HCOOH, HCOOD, DCOOH and DC000; from the present work for the three heavy-atom substituted species. 0 is the uncertainty assigned in the force field least-squares f i t . e is the residual (obs.-calc.). Distortion constants and values of o and c in kHz. b The HCOOD distortion constants were excluded from the f i t (see text), c 2 1 is the planarity sum defined in equation (5), given in units of MHz . refine only a small group of off-diagonal constants in the A' block, keeping the remainder fixed at the ab initio values. Thus our force field should not be con-sidered definitive, but simply an interim result which may be improved upon in the future. It does have the merit of yielding good agreement not only with the distortion constants but also with the inertial defects, as we discuss below. (b) rs Structure As Kwei and Curl noted (5), formic acid is a troublesome molecule for structure determination by microwave spectroscopy since in the H C O O H principal axis system there are four coordinates less than 0.25 A. These are the a 243 SPECTRUM AND STRUCTURE OF FORMIC ACID 103 TABLE VI Force Constants Derived from a Least-Squares Fit to Vibrational Data and Distortion Constants of Seven Isotopic Species of Formic Acid" F n = 7.198(68) aJ A " 2 C F 4 5 = -0.035(22) aJ A" 1 F J 6 - -0.097(17) aJ F 2 2 = 1.759(52) aO A" 2 F 4 g = 0.180(31) aJ A" 1 F 5 ? * -0.076(15) aJ F 3 3 = 13.22(15) aj A" 2 F 4 ? = -0.605(11) aJ A" 1 F f i 6 = 1.138(8) aJ F 4„ = 6.520(69) aJ A" 2 F & 5 = 0.683(13) aJ F 6 ? * 0.054(39) aJ F ? 7 « 0.605(8) aJ A' ' block: F o c = 0.469(10) aj F f l Q = 0.096(18) aJ F g g = 0.168(5) aJ a Symmetry coordinates identical to those of Redington (9_). Geometry r C H = 1.095 A, r c = 0 = 1.201 A, r C Q •= 1.346 A, r Q H = 0.971 A, <(0C0)-O 24.9°, «(HC=0)»124.5'', <(HC-0)'110.6°, <(C0H)=106.2°. This is an "r 0 geometry" refined i.j give a best f i t to AQ and BQ of the seven isotopic species, in order that the theoretical 1^  and IB moments of inertia used in the distortion constant calculation should reproduce the experimental ground state moments as closely as possible. k All interaction constants in the A' block not quoted in the Table were con-strained to the ah initio values of Ha, Meyer and Giinthard (10). c 1 aJ A" 2 = 1 mdyn A" ' . coordinates of the C and H atoms connected by the C - H bond, and the b coordinates of both O atoms. In fact only the hydroxyl H atom has two large coordinates. Table VII lists the results of an rs structure calculation (6) based on the ground-state moments /? and / £ determined in this work for H 1 3 C O O H , H C 1 8 O O H , and H C 0 1 8 O H , along with those given for H C O O H , H C O O D , D C O O H , and D C O O D by Willemot et al. (4). The effective moments were obtained by inverting the values of B and C as denned in E q . (2) (i.e., no centrifugal corrections were applied); the conversion factor used was B x I" = 505379.0 uA2 M H z . Structure calculations were based on IB and Ic for comparability with earlier work (5, 7, 18) and because vibration-rotation contributions are probably proportionally greater in IA than in the two larger moments (this is certainly true of the harmonic parts of the a constants calculated from the harmonic force field). O f the four small coordinates, we have accepted the values of the two oxygen b coordinates given by Kraitchman's equations (19) even though these values are 0.218 and 0.122 A, respectively. Kwei and Curl (5) fixed these coordinates from the first-moment and cross-product conditions 2/77,(7, = 0 and = 0, having determined all other coordinates by appropriate methods. We found that this procedure gave b coordinates differing by less than 0.0015 A from the 244 104 DAVIS ET AL. TABLE VII Principal Axis Coordinates and r, Structural Parameters for HCOOH 0 Atom a(A) b(A) H -0.0668 a -1 .5107 rm.a, = 0 C -0.0966 a -0. .4140 =0 -1 .12)2 0.2176 » i b i = 0.0326 u A -0 1 .1341 0, .1218 H 1 .0124 1 .0863 M i a i b i = -0.0014 u A2 I A 'o - > sA = . •0.0211 u A 2 I B 0 - ' s B 0.0904 u A2 I c ->sC 0.1457 u A 2 r s (CH) 1.097, A <(0C0) = 124.82° r s (00) 1.2036 A <(HO0) = 123.21° r s (00) 1.3424 A <(HC-0)= 111.97° r s (OH) 0.972, A <(C0H) - 106.34° These ^-coordinates were determined by double substitution and f irst moment calculations (see text). The a-coordinate from Kraitchman's equations is imaginary for H and -0.0737 for C. Kraitchman values. Using only the larger of the two Kraitchman coordinates and determining the other by the first-moment condition leads to a slightly larger change, 0.0020 A, in the latter. Since all these variations in the oxygen b coordinates are small, we felt that the simplest procedure was to use the Kraitchman values, and reserve the first-moment and cross-product conditions as checks. The small a coordinates of the C and H atoms are another matter. If the carbon atom is assigned its Kraitchman a coordinate of (-) 0.074 A and the imaginary hydrogen a coordinate is assumed to be zero, 2 / 71 ,0 , becomes 0.34 uA and Lmidjbi becomes -0.22 uA2; or if the hydrogen coordinate is assumed zero and the carbon coordinate is determined from the first-moment condition, the value of the latter is -0.102 A, a shift of almost 0.03 A from the Kraitchman value. Clearly these Kraitchman coordinates should not be used, and we have followed Kwei and Curl (5) in determining the hydrogen coordinate by a double substitution calculation based on H C O O H , H C O O D , D C O O H , and D C O O D , and then determining the carbon coordinate from the first-moment relation 2m,a, = 0. (c) rz Structure Calculation The zero-point average or rz structure (8) was calculated by a direct fit to the Bz and Cz constants of the seven isotopic species considered in the force field calculation. These average structure rotational constants are listed in Table 245 SPECTRUM AND STRUCTURE OF FORMIC ACID 105 TABLE VIII Zero-Point Average Rotational Constants and Srz Bond Length Changes Used in the r 2 Structure Calculation A Z , B 2 , C 2 ,(«Hz) A2(u A 2) CH 6r z(10"4 A) a C=0 C-0 OH HC00H A 77198. 995 -0.0018 0 0 0 0 B 12028. 986 C 10407. 725 HCOOD A 65894.510 -0.0024 -4. 7 -1.4 -2.0 +25. 1 B 11736. 011 C 9962. 252 DCOOH A 57506. 697 -0.0014 -3. 9 -1.7 -1.2 -7. 1 B 12028. 958 C 9948. 345 DCOOD A 50676. 726 -0.0017 -7. .2 -2.6 -2.6 +17. 5 B 11733. .063 C 9527. .550 H13C00H A 75270.381 -0.0017 -1. .1 -0.5 -1.1 -0. 8 B 12027. .564 C 10370.709 HC1800H A 76217 .462 -0.0016 -0. .4 -0.6 -0.3 -0. 7 B 11373 .213 C 9896 .775 HC0180H A 76892 .462 -0.0016 -0 .1 -0.2 -1.3 -0. 3 B 11359 .934 C 9897 .991 a Shifts given are from the parent isotopic species HC00H; e.g. the C-0 r z bond length is 2.0 x 10"4 A shorter in HCOOD than in HC00H. VIII: They were obtained from the ground state constants using the harmonic parts of the a constants as calculated from the force field. It will be seen that the quantity A £ = ( /£ — Ii — / f ) is small and negative for all species. A n alternative expression of this is that while the ground-state inertial defect A 0 is 0.0764 uA2 for the parent species H C O O H , for example, the vibrational contribution A v i D to the calculated inertia defect is 0.0782 uA2. Most of the discrepancy can be accounted for in A e l e c , the electronic contribution. From the work of Kukolich and Flygare (20) we can calculate Aei e c = -0.0023 uA2 for H C O O H . Thus the force field appears to predict A v i b very satisfactorily. Also, the observed values of A 0 range from 0.0764 uA2 in H C O O H to 0.0871 uA2 in D C O O D ; but the variation in A: is less than a tenth of this range, so that the vibrational dependence of A 0 is well reproduced. It is interesting that A* for H C O O D is slightly out of line with the other species. Since the distortion constant 246 DAVIS ET AL. TABLE IX Molecular Structures Obtained for Formic Acid by Various Techniques" rs,MW This workc r s Ref ,MW .(5) rs,HW Ref.(3) ra° ED Ref"(25)b r ,MW z c This work r .MM e c This work r(CH) 1.097 1 .097 1.097 1.096 1.097 1.091 r(O0) 1.204 1 .202 1.228 1.213 1.205 1.201 r(C-O) 1.342 1 .343 1.317 1.357 1.347 1 .340 r(0H) 0.972 0 .972 0.974 0.966 0.966 0.969 <(0C0) 124.82 124. .88 125.00 123.55 124.80 124.80 <(HC=0) 123.21 124. .13 124.58 d 123.26 123.26 <(HC-0) 111.97 110. .79 110.42 d 111.94 111.94 <(C0H) 106.34 106. 32 106.83 d 106.61 106.61 r(0..O) 2.257 2. 257 2.258 2.265 2.262 2.253 ° Interatomic distances in A, angles in degrees. t\t = microwave spectroscopy, •ED = electron diffraction. Converted from r g distances given by Almenningen e_t aj_. (25). 0.25$ was subtracted from the r f l values as a calibration correction - see original reference for details. Estimated uncertainties in the.present work are ±0.005 A for all bond lengths, Jl .5" for *(HC=0) and <(HC-0); ±0.4° for <(0C0) and <(C0H). ^ The ED angles involving hydrogen are in general agreement with those in the spectroscopic structures, but are not sufficiently precise to warrant detailed comparison. planarity sum is also anomalous for this molecule, the two anomalies taken together suggest that the constants for H C O O D may need minor revision. Table VIII also contains values of the isotopic changes in bond lengths, 8rz, consequent on isotopic substitution in H C O O H . These were estimated from an approximate equation due to Kuchitsu and co-workers (21, 22): rz=re + 3au2/2 - K, (6) 8rz = 3a8(u2)/2 - 8K. (7) Here u2 is the zero-point mean square amplitude of the bond in question, K is the corresponding perpendicular amplitude correction (both readily calculated from the harmonic force field (23)), and a is the Morse anharmonicity parameter. We took o C H = 1.97 A" 1 , aco = 2.39 A" 1 , and a0H = 2.32 A" 1 from the diatomic molecules (24). The rz structure obtained is listed in Table IX compared with the rs structure and with other structures obtained for formic acid. We also give a crude re structure obtained by applying corrections based on E q . (6) to the rz structure. (d) Comparisons of Structural Parameters Our rs structure is close to the structure obtained by Kwei and Curl (5) by similar methods, and also to the structure obtained by Stiefvater (7). The 247 SPECTRUM AND STRUCTURE OF FORMIC ACID 107 rs structure obtained by Bellet and coworkers (3) is rather different, apparently because they used the Kraitchman value of the carbon a coordinate. For rea-sons stated above, we regard the use of this coordinate as unacceptable. In addition there are two independent pieces of evidence which favor our structure rather than that of Bellet et al. (i) The C = 0 and C — O bond lengths have been determined with good pre-cision in H C O O H monomer by electron diffraction (25). The ratio of the observed bond lengths i s r a ( C — 0 ) / r „ ( C = 0 ) = 1.118. This ratio is insensitive to the effects of thermal averaging or scale errors in the diffraction experiment and to the fact that the bond length definition is not the same in the two types of experiment: our rs structure yields a ratio of 1.115 in agreement with the electron diffraction work, whereas the ratio from the rs structure of Bellet et al. is 1.072. We comment further on the electron diffraction parameters below. (ii) Even though the force field is still somewhat uncertain, all force fields in the literature agree that the / ( C = 0 ) / / ( C — O ) ratio is approximately 2. From this, bond-length/force-constant correlations (26) predict that the difference between the C — O and C = 0 bond lengths should be about 0.15 A, rather than 0.09 A as found by Bellet et al. In fact, the C = 0 stretching wavenumber and force constant are both slightly higher than in formaldehyde (27), suggesting that the C = 0 bond in formic acid might be a little less than the 1.2070 A (rz), 1.2033 A (re) found in H 2 C O (28). Thus our r s ( C = 0 ) bond length of 1.2036 A seems very reasonable. The rz structure is compared in Table IX with an restructure derived from the electron diffraction (ED) results (25) by techniques which are now standard (21, 22). The rz and r£ structures should be equivalent if there are no systematic errors in either experiment or in the conversions involved. The C = 0 and C — O bond lengths in the r° structure are larger than in the rz structure by —0.8%, which may be a consequence of a scale error in the E D experiment. (No conclusions can be drawn from the C H and O H bond lengths, which superficially appear in good agreement in the r°a and rz structures, as the experimental errors in these bond lengths are —0.02 A in the E D work.) A puzzling feature of the E D results is the O C O angle; we calculate this as 123.55° in the ra structure at 175°C, and the temperature variation of the angle is expected to be very small. The rz structure angle is 124.80°, some 1.25° larger. It is possible that the composition of the sample in the E D experiment was more complex than was realized at the time: although about 9% decomposition to C O and H z O was suggested, the presence of other species may have caused unsuspected systematic errors. At high temperatures, too, the less stable rotamer of formic acid will begin to contribute. In fact the less stable rotamer does have a much smaller O C O angle than the stable rotamer (18), but it does not seem likely that this is the reason for the E D results as at 175°C the less stable form should be present only in a few percent abundance. In conclusion, it is interesting to note that the approximate re structure derived from the spectroscopic rz structure is in good agreement with the rs structure. The rs bond lengths are in each case longer but by less than 0.01 A. The larger difference occurs for the C H bond, where the rs bond length is the longer by 2 4 8 108 DAVIS ET AL. TABLE X Some Predicted Transitions of HI3COOH, HC18OOH, and HC018OH of Potential Astrophysical Interest Transition H'^COOH HC 00H HCO OH 1(1.0) - 1(1,1) 1674 .385(0)a 1492.250(1) 1477.658(1) 2(1.1) - 2(1.2) 5023 .059(1) 4476.668(3) 4432.893(2) 3(1.2) - 3(1,3) 10045 .436(1)b 8952.823(5)c 8865.290(3) 4(0,4) - 3(0,3) 89401 .920(6) 84951.898(16) 84911.074(9) 4(1,4) - 3(1,3) 86315 .989(6) 82171.577(18) 82153.947(10) 4(1,3) - 3(1,2) 93010. .189(6) 88138.150(18) 88082.240(10) 4(2,3) - 3(2,2) 89705. .051(5) 85187.825(29) 85140.147(17) 4(2,2) - 3(2,1) 90030. .830(5) 85440.796(29) 85385.676(17) 4(3,2) - 3(3,1) 89797. .914(5) 85260.669(52) 85210.964(32) 4(3,1) - 3(3,0) 89800. 302(5) 85262.283(52) 85212.500(32) 5(0,5) - 4(0,4) 111508, .611(7) 105999.918(22). 105954.380(12) 5(1,5) - 4(1,4) 107835. .031(7) 102667.477(26) 102646.749(14) 5(1,4) - 4(1,3) 116196. .701(7) 110121.455(25) 110028.063(14) 5(2,4) - 4(2,3) 112008. 775(6) 106451.538(41) 106392.875(24) 5(2.3) - 4(2,2) 112737. 977(6) 106956.076(41) 106882.619(24) 5(3,3) - 4(3,2) 112273. 588(6) 106596.202(71) 106533.458(44) 5(3,2) - 4(3,1) 112281. 940(6) 106601.847(71) 106538.828(44) 5(4,2) - 4(4,1) 112243. 876(5) 106573.89(11) 106511.929(70) 5(4,1) - 4(4,0) 112243. 908(5) 106573.91(11) 106511.947(70) Numbers in parentheses are standard deviations of the predictions in units of the last significant figures. b This transition was measured at 10045.45 MHz. c This transition was measured at 8952.86 MHz 0.006 A. This is perhaps not surprising, as the C and H atoms are the least accurately located by virtue of their small a-coordinates. ASTROPHYSICAL PREDICTIONS The transitions measured in the present work may be useful in searching for formic acid- 1 3 C or - 1 8 0 in interstellar space. For transitions unmeasured in this work the derived spectroscopic constants of Tables I I - I V are accurate enough to give excellent predictions. The frequencies of several unmeasured transitions, along with the standard deviations of the predictions, are given in Table X . They are only a representative sample, however; any others may easily be calculated from the constants. We would be pleased to supply frequencies of any such transitions on request. ACKNOWLEDGMENTS We thank Dr. W. H. Hocking and Dr. H. Mantsch for assistance with some of the initial measure-ments. The former is also thanked for many helpful discussions. 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D U N C A N A N D P. D . M A L L I N S O N , Chem. Phys. Letters 23, 597-599 (1973). 28. J . L . D U N C A N , Mol. Phys. 28, 1177-1191 (1974). 250 Appendix 4 A R e p r i n t o f a Report o f the Microwave Spectrum o f P y r r o l e - 2 - c a r b o n i t r i l e 251 [Reprinted from the Journal of Physical Chemistry, 84,1767 (1980).] Copyright © 1980 by the American Chemical Society and reprinted by permission of the copyright owner. Microwave Spectrum and Structure of Pyrroie-2-carbonitrile R. Wellington Davis and M. C. L. Gerry* Department ol Chemistry, The University of British Columbia, Vancouver, British Columbia V6T 1W5, Canada (Received August 14, 1979) Microwave spectra in the frequency region 26-75 GHz have been obtained for two isotopic species of pyr-role-2-carbonitrile. Rotational constants and centrifugal distortion constants have been obtained for both species. The molecule has been shown to be planar. Strong evidence is presented for distortion of the pyrrole ring at the substituted C 2 atom. Introduction T h e synthesis of pyrrole-2-carbonitrile (I) was first re-•CN I H I ported by Anderson, 1 and since then improved methods have been reported. 2 , 3 It has recently been found as part of the neutral fraction of tobacco smoke condensates. 4 There has been only a l i t t l e spectroscopic study i n both the infrared 5 , 6 and ultraviolet 6 , 7 regions. The electric dipole moment has, however, been measured by dielectric methods and has been found to be equal i n magnitude to the vector sum of the dipole moments of pyrrole and benzonitrile. 8 Pyrrole itself is one of a series of heterocyclic molecules wi t h considerable aromatic character. There is much ev-idence for this, such as its planar structure, the close sim-i l a r i t y of its nominally single and double C C bond lengths (1.417 and 1.382 A, respectively 9), its a b i l i t y to undergo 252 1768 The Journal of Physical Chemistry, Vol. 84, No. 14, 1980 Davis and Gerry Ic A = Ic T A B L E I: Spectrcecopic Constants and Principal Moments of Inertia of Pyrrole-2-carbonitrile pyrrole-2- pyrroles-parameter carbonitrile-7-h carbonitrile-7-d Rotational Constants, MHz A 8 9 4 6 . 6 2 9 7 ( 8 8 ) ° 8367.099(11) B 1988.5936(21) 1988.4938(19) C 1626.5440(16) 1606.2658(16) Quartic Centrifugal Distortion Constants, kHz A j 0.0690(26) 0.0839(33) A J K 2.812(11) 2.734(13) A K indetb indet 6 j 0.0169(26) 0.0150(12) 6 K 1.26(10) 1.461(81) Principal Moments of Inertia, n A 2 56.4882 60.4007 254.1389 254.1517 310.7072 314.6297 - / . - / b 0.0801 0.0773 ° Numbers in parentheses are standard errors in units of the last significant figures. b A K was indeterminate and omitted from the fits. substitution rather than addition reactions, and its very low base dissociation constant.10 Though its bond lengths and angles are all accurately known,9 no attempt has been made to determine the effect of a substitution on the ring structural parameters. Detailed studies of this effect have, however, been conducted on three six-membered aromatic molecules, namely, benzonitrile,11 fluorobenzene,12 and 2,6-difluoropyridine.13 In all three cases the ring was found to be pushed in at the substituted carbon atom with shortening of the ring bonds attached to this atom. Naively one might expect this to occur for substituted five-membered aromatic compounds. Though there has been no previous microwave investi-gation of pyrrole-2-carbonitrile, the spectra of three closely related molecules have been reported. These are furan-2-carbonitrile,14,15 thiophene-2-carbonitrile,16,15 and thiophene-3-carbonitrile.17 In each case the spectrum of only one isotopic species was obtained, giving hardly enough data to do a definitive structural study. Suggested structures were evaluated, however. For furan-2-carbo-nitrile it was felt that the rotational constants were best accounted for with a model in which the furan ring was the same as in furan itself, but with the C-C=N chain possessing a bend at the central C of some 13° toward 0. Several possible structures were suggested for thiophene-2-carbonitrile, with a structure containing a distorted thiophene ring considered the most probable. In addition, in thiophene-3-carbonitrile an asymmetric distortion of the thiophene ring was considered very likely. The present study has been carried out to see what structural information could be obtained for pyrrole-2-carbonitrile, in spite of the several structural interpreta-tions for the related molecules. It is, however, easy to obtain two isotopic species in the present case, so that considerably more information is available which should narrow the possibilities. Experimental Section The spectra were measured with a conventional 100-kHz Stark-modulated spectrometer in the frequency range 26-75 GHz. Because of the low volatility of the molecule (vapor pressure 1.5 torr at 90 °C) the spectra were obtained at room temperature. Even then the samples were difficult to handle and move about in the vacuum line. The sample of pyrrole-2-carbonitrile was kindly provided by Dr. Hugh Anderson of Memorial University of New-J*^ L373\ Vp2 C G N 1382 1 R / 1432 I.I5B / l^370"~ M H \ H * Figure 1. Orientation of the principal inertial axes in pyrrole-2-carbonitrile- 1-h. The numbering of the carbon atoms is given. The ring and substiruerri bond lengths (in A) are those of model t, Table III, and show the shortening of the ring bonds at the substituted C 2 atom. foundland. Pyrrole-2-carbonitrile-/-d (deuterated at the ring N) was prepared by exchange with D20 in the mi-crowave cell. Observed Spectrum and Analysis Initially the spectrum was predicted by using rotational constants calculated from an assumed structure made up from an undistorted pyrrole ring with CN as in benzonitrile attached at the 2 position. Since the dipole moment \i had a magnitude calculable by taking the vector sum of the pyrrole and benzonitrile dipole moments, it was assumed that this also gave the direction of the dipole moment, giving M , ~ 3.4 D and Mb ~ 1-5 D. Accordingly, strong a-type and much weaker b-type transitions were predicted. This general pattern was indeed what was found. However, in spite of the large value of u, the spectrum was rather weak because of the low volatility of the molecule. The a-type groups were very distinct and had partially resolved K, structure. Although the lines were quite broad (~1 MHz), they could not be split to give 14N quadrupole coupling constants. Some transitions of vibrationally ex-cited molecules were also observed but no analysis was carried out. The rotational constants B and C were ac-curately obtained from the measured transitions, along with an approximate value for A. The b-type transitions required to give an accurate value for A were weaker and more difficult to observe, but could be predicted accurately at low K, by using a rigid rotor approximation. Predictions of higher K, transitions were made with the inclusion of quartic distortion effects. A linear least-squares analysis for three rotational con-stants and five quartic centrifugal distortion constants was carried out. Watson's reduced Hamiltonian18 in its A re-duction, P representation, was used, and the analysis used a rigid rotor basis. Because the distortion contributions were very small only first-order contributions were needed. The resulting spectroscopic constants are in Table I. Clearly good values have been obtained for A, B, C, Aj, and AJK- The values of 6j and 6 K are more poorly determined. AK is indeterminate and was omitted from the fits. Table II contains the measured transition frequencies and as-signments, along with the frequencies calculated by using the spectroscopic constants of Table I, and the distortion contributions. Molecular Structure Table I contains, besides the spectroscopic constants, the effective principal moments of inertia and inertial defects of the two isotopic species. Since the two inertial defects are small positive numbers, and are essentially 253 Structure of Pyrrole-2-carbonitrite 77ie Journal of Physical Chemistry, Vol. 84, No. 14, 1980 17S9 T A B L E II: Observed and Calculated Transition Frequencies (MHz) of Pyrrole-2-carbonitrile frequency obsd calcd dis-tortion corr frequency dev transition obsd calcd dis-tortion corr dev PyrTole-2-carbonitrile-i-ri 32290.22 33654.19 32841.47 32602.67 32688.98 32580.10 34403.31 33906.87 35807.39 36588.96 36237.61 8(0,8)-7(0,7) 8(1,8)-7(1,7) 8(5,4)-7(5,3) 8(6,3)-7(6,2) 9(0,9)-8(0,8) 9(1,9)-8(1,8) 9(2,8)-8(2,7) 9(2,7)-8(2,6) 9(3,6)-8(3,5) 9(6,4)-8(6,3) 9(7,2)-8(7,l) 9(8,2)-8(8,l) 10(0,10)-9(0,9) 10(1,10>-9(1,9) 10(2,9)-9(2,8) 10(3,7)-9(3,6) 10(6,5)-9(6,4) 10(7,4)-9(7,3) 10(8,2)-9(8,1) 10(9,2)-9(9,1) 11(0,11)-10(0,10) 11(1,11)-10(1,10) 11(2,10)-10(2,9) 11(10,2)-10(10,l) 16(9,7)-15(9,6) 16(11,6)-15(11,5) 17(1,16)-16(1,15) 17(2,16)-16(2,15) 17(3,15)-16(3,14) 17(4,14)-16(4,13) 17(8,9)-16(8,8) 17(9,9)-16(9,8) 17(10,7)-16(10,6) 17(11,6)-16(11,5) 17(12,6)-16(12,5) 18(8,11)-17(8,10) 18(9,10)-17(9,9) 18(12,6)-17(12,5) 18(13,5)-17(13,4) 18(14,5)-17(14,4) 18(16,3)-17(16,2) 20(9,11)-19(9,10) 20(11,10)-19(11,9) 72485.95 20(13,7)-19(13,6) 72436.62 20(16,5)-19(16,4) 10(l,10)-9(0,9) 11(1,11)-10(0,10) 18(2,16)-18(1,17) 14(3,11 )-14(2,12) 15(3,12)-15(2,13) 27901.48 27901.45 27236.27 27236.25 28987.13 28987.17 28971.32 28971.26 31166.92 31166.88 30578.96 30579.02 32290.15 33654.25 32841.54 32602.68 32589.04 32579.95 34403.32 33906.80 35807.44 36589.04 36237.64 36219.05 36219.10 36206.85 36206.83 36198.12 36198.10 37624.36 37624.25 37220.70 39303.87 39816.01 57988.12 57945.16 60735.24 59811.09 61604.45 62067.67 61668.34 61628.39 61599.45 61577.30 61559.91 37220.79 39303.79 39815.95 57988.12 57945.16 60735.24 59811.10 61604.47 62067.67 61668.27 61628.39 61599.40 61577.36 61559.96 65318.82 65318.78 65271.66 65271.60 65191.01 65174.61 65160.87 65138.16 65191.12 65174.56 65160.70 65138.26 72567.54 72567.51 72486.02 72436.64 72389.21 36018.78 38836.25 34626.71 28153.58 27514.54 72389.20 36018.76 38836.13 34626.69 28153.62 27514.39 -0.09 -0.10 -1.27 -1.79 -0.12 -0.13 -0.34 -0.41 -0.64 -2.04 -2.72 -3.51 -0.17 -0.18 -0.41 -0.76 -2.31 -3.06 -3.94 -4.92 -0.23 -0.23 -0.49 -6.68 -8.41 -12.13 -1.31 -1.28 -1.87 -2.61 -7.37 -9.05 -10.93 -13.01 -15.28 -7.94 -9.72 -16.31 -18.93 -21.75 -28.03 -11.12 -15.77 -21.35 -31.47 -0.28 -0.34 -3.44 -2.66 -3.00 0.03 0.02 -0.04 0.06 0.04 -0.06 0.07 -0.06 -0.07 -0.01 -0.06 0.15 -0.01 0.07 -0.05 -0.08 -0.03 -0.05 0.02 0.02 0.11 -0.09 0.08 0.06 0.00 -0.00 -0.00 -0.01 -0.02 0.00 0.07 -0.00 0.05 -0.06 -0.05 0.04 0.06 -0.11 0.05 0.17 -0.10 0.03 -0.07 -0.02 -0.01 -0.02 -0.12 -0.02 0.04 -0.15 equal, the molecule, like pyrrole itself, furan-2-carbonitrile, and thiophene-2-carbonitrile, is planar. Consequently, for the purposes of structural determination, there are only two independent principal moments of inertia for each species, which can be taken as /„ and It is noteworthy too that only I, changes appreciably with deuteration, implying that this atom is located close to the 6 axis. Any reasonable model calculation will show this; it will show also that the C-C=N chain is near the a axis, so that 7a is rather insensitive to the positions of these atoms. An attempt has been made to obtain further structural information from the available rotational constants, and in particular by reproducing the observed constants with reasonable structures. Since there are some 21 structural parameters, but only four rotational constants, there is clearly an infinite number of possibilities. However, by making some reasonable constraints sensible structural deductions can be made. Since detailed structures of pyrrole9 and of several ni-trites, particularly benzonitrile11 and acrylonitrile19 (which 16(3,13)-16(2,14) 17(3,14)-17(2,15) 18(3,15)-18(2,16) 21(3,18)-21(2,19) 20(4,16)-20(3,17) 24(4,20)-24(3,21) 27181.59 27181.59 27220.06 27220.13 27683.19 27683.16 31964.44 31964.39 38748.85 38748.75 35856.25 35856.26 8(0,8)-7(0,7) 8(1,8)-7(1,7) 8(1,7)-7(1,6) 8(2,7)-7(2,6) 8(2,6)-7(2,5) 8(5,4)-7(5,3) 8(6,2)-7(6,l) 8(7,2)-7(7,l) 9(0,9)-8(0,8) 9(1,9)-8(1,8) 9(1,8)-8(1,7) 9(6,3)-8(6,2) 9(7,3)-8(7,2) 10(1,10)-9(1,9) 10(6,5)-9(6,4) 10(7,3)-9(7,2) 10(8,2)-9(8,1) 11(0,11)-10(0,10) 11(2,10)-10(2,9) 11(7,5)-10(7,4) 11(9,3)-10(9,2) 12(1,12)-11(1,11 17(3,14)-16(3,13 17(8,10)-16(8,9) 17(11,6)-16(11,5 17(12,6)-16(12,5 18(3,16)-17(3,15 18(11,7)-17(11,6 18(14,5)-17(14,4 19(1,19)-18(1,18 11(0,11)-10(1,10 12(0,12)-11(1,11 18(3,15)-18(2,16 19(3,16)-19(2,17 20(3,17)-20(2,18 16(4,12)-16(3,13 18(4,14)-18(3,15 20(4,16)-20(3,17 21(4,17)-21(3,18 23(4,19,-23(3,20 24(4,20>- 24(3,21 25(4,21)-25(3,22 27(4,23,-27(3,24 Pyrrole-2-carbonitrile-i-d 27563.93 26948.86 29895.12 28555.44 29745.92 28838.31 28819.23 28807.68 30769.50 30246.60 33485.84 32433.73 32417.48 33528.09 36052.40 36030.37 36015.63 37126.04 38985.26 39646.57 39613.76 40049.90 63918.65 61367.92 61258.96 61238.63 64642.45 64876.88 64817.27 62640.28 35924.38 39428.88 26665.07 28236.89 30346.91 39459.68 36533.51 34097.00 33327.40 33131.30 33831.51 35118.08 39493.81 27563.92 26948.87 29895.20 28555.35 29745.97 28838.37 28819.22 28807.60 30769.41 30246.55 33485.90 32433.75 32417.38 33528.06 36052.57 36030.28 36015.62 37125.84 38985.30 39646.65 39613.77 40049.88 63918.60 61367.98 61259.04 61238.48 64642.49 64876.98 64817.23 62640.22 35924.44 39429.03 26665.06 28236.81 30346.90 39459.59 36533.61 34096.89 33327.55 33131.31 33831.49 35118.12 39493.82 -3.36 -3.73 -4.13 -5.52 -7.52 -9.76 -0.11 -0.12 -0.21 -0.29 -0.35 -1.28 -1.78 -2.37 -0.16 -0.17 -0.28 -2.04 -2.71 -0.23 -2.31 -3.06 -3.92 -0.30 -0.53 -3.42 -5.43 -0.39 -2.27 -7.45 -13.00 -15.24 -2.28 -13.92 -21.65 -1.55 -0.21 -0.30 -4.04 -4.43 -4.85 -5.07 -6.22 -7.33 -7.85 -8.81 -9.26 -9.71 -10.70 -0.00 -0.07 0.03 0.05 0.10 -0.01 0.01 -0.01 -0.08 0.09 -0.05 -0.06 0.01 0.08 0.09 0.05 -0.06 -0.02 0.10 0.03 -0.17 0.09 0.01 0.20 -0.04 -0.08 -0.01 0.02 0.05 -0.06 -0.08 0.15 -0.04 -0.10 0.04 0.06 -0.06 -0.15 0.01 0.08 0.01 0.09 -0.10 0.11 -0.15 -0.01 0.02 -0.04 -0.01 show similar hybridization to pyrTole-2-carbonitrile), are known, we have taken as starting points structures in which the pyrrole ring is unchanged, and the exocyclic C-C=N chain has the bond lengths and angles of these two nitrites. An immediate problem is encountered in such a procedure, however, in that the principal moments a r e effective moments, whereas the structural parameters are substitution values. By definition the substitution coor-dinates should not reproduce the effective moments, and small corrections were made to the effective moments to account for this. Because the C - C ^ N chain is very close to the a inertial axis, and because pyrrole-2-carbonitrile is inertially very similar to benzonitrile, the corrections have been taken to be the same as those of benzonitrile.11 Table III contains a comparison of the experimental and calculated rotational constants for the two isotopic species, listed according to various "models". Model a contains the effective ground rotational constants, and model b gives the "substitution" values described above. Models c and d have been calculated by assuming the ring has the same 254 1770 The Journal of Physical Chemistry, Vol. 84, No. 14, 1980 T A B L E III: Comparison of Experimental Rotational Constants (MHz) of Pyrrole-2-carbonitrile with those Calculated from Assumed Structures Davis and Gerry model 0-" pyrrol e-2-carbonitrile-i-n pyrrole-2-carbonitrile-/-d Experimental Values 8946.63 1988.593 8367.10 1988.494 9000.16 1992.882 8413.91 1992.782 Calculated Values 9024.89 9024.80 9024.81 9003.28 9027.54 9022.79 1955.566 1975.076 1978.795 1993.141 1978.295 1976.000 8438.38 8438.18 8438.17 8420.42 8450.49 8438.51 1955.445 1974.764 1978.683 1993.158 1978.253 1975.909 a Effective ground-state rotational constants. b "Sub-stitution" rotational constants, obtained from 7 a ° - / s ° = 0.336 uA';Ib° - Ibs = 0.547 «A' . c Ring as in pyrrole. C - C s N as in benzonitrile:11 r(C-C) = 1.451 A ; r(CsN) = 1.158 A. d Ring as in pyrrole. C-C=N as in acryl-onitrile:" r(C-C) = 1.426 A ; r(C=N) = 1.164 A. ' R i n g as in pyrrole. C-C as in acrylonitrile; C=N as in benzo-nitrile. ^Ring: opened at N and Cj by 0.1° ; C , - C , and C j - N shortened by 0.009 A. Chain: C-C = 1.432 A (cf. 1.426 A in acrylonitrile); C s N = 1.158 A (as in benzo-nitrile). 8 Ring as in pyrrole. C, -C 6 =N lengths as in acrylonitrile; chain moved at ring, 2° toward N. h Ring as in pyrrole. C j - C ^ N lengths as in acrylonitrile; bend in chain at C„, 1.5° toward N. structural parameters as i n pyrrole itself and the C - C s N chain has the same bond lengths as i n benzonitrile and acrylonitrile, respectively. Since the uncertainties i n the experimental values are probably £ the differences be-tween the effective and substitution values, apparently neither of the assumed structures reproduces the experi-mental values, though /, is very close. T h e ac r y l o n i t r i l e model d is the better of the two. Some changes w i l l nev-ertheless have to be made to the structures to reproduce the experimental rotational constants. In deducing the adjustments required we have adopted the principle that the most reasonable ones make the smallest possible changes from the above assumed struc-tures. There are five " s o f t " parameters which have been used for this purpose. These are the following: (i) a ri n g distortion similar to those of other substituted aromatics, where the ring is squashed and the bonds to the substi-tuted atoms are shortened; (ii) a change i n the exocyclic C-C length; (iii) a change i n the exocyclic angle of the C N group at the ring; (iv) following the deduction for furan-2-carbonitrile, u a bend i n the C - O ^ N chain at the central C; (v) the C = N length. A brief reflection w i l l reveal that these are really the only simple changes possible, with the last two being probably less likely to adjust the calculated constants enough to reproduce the experimental values. In any adjustment to the structure from either the benzonitrile model c or the acr y l o n i t r i l e model d, the changes necessary must decrease A and increase B, and must be essentially the same for each isotopic species. These requirements can be met by assuming a symmetrical ring distortion similar to those found with other aromatics. Expansion of the ring by 0.1° at C 3 and N, an essentially negligible change, gives a sufficient adjustment to A (cf. models f and c or d). Obtaining the desired effect on B is slightly t r i c k i e r . Although the acrylonitrile model d comes nearest to what is required, the C-C length (1.426 A) is probably a lower li m i t . One can do no more shortening of this bond to reproduce B. Shortening O ^ N to its length i n benzonitrile (1.158 A, probably also a lower li m i t ) is not enough, as is T A B L E IV: Observed and Calculated Rotational Constants (MHz) of Furan-2-carbonitrile model"-" A B 9220.11 9276.97 9290.05 9289.81 2029.262 2033.728 1999.916 2020.727 ° Effective ground state rotational constants, ref 14. 6 "Substitution" rotational constants, from / a ° - 7 A S = 0.336 M A ' ; / b - / b s = 0.547 uA 1 . c Ring as in furan;" C - C s N as in benzonitrile. d Ring as in furan;1 0 C-C=N as in acrylonitrile. e The models parallel exactly those of pyrrole-2-carbonitrile in Table III. seen by comparing models d and e. However, i f the C 2-C 3 and C 2-N ring bonds are both shortened by 0.009 A, sim-i l a r to the six-membered aroma t i c s , 1 1 - 1 3 the requirement is met. M o d e l f gives the rotational constants calculated w i t h this ring distortion, r ( C = N ) = 1.158 A as in benzo-n i t r i l e , and r(C-C) = 1.432 A (slightly longer than i n acrylonitrile). T h i s is clearly a satisfactory model and is shown i n Figure 1. It must be remembered that both these C-C and C = N lengths are at or near their lower limits. These bonds may well be longer, implying an even greater r i n g contraction. T h e effects of the other reasonable st r u c t u r a l changes were also considered. A comparison of models g and d shows the effect of moving the C ^ C ^ N chain about the ring carbon C 2, 2° toward N. (An equal but opposite effect is obtained by the same bend away from N.) T h e trend i n B is reasonable and a bend of ~12° would be enough to reproduce the experimental values. However the change in A is i n the wrong direction, and furthermore, for the deuterated species i t would be some 70 M H z in the wrong direction, considerably more than ~ 2 0 M H z for the H species. T h i s structural change cannot be the only one for this molecule; i f i t were i t must be accompanied by a ring distortion even greater than that proposed above. A comparison of models d and h shows the effect of bending the C 2 - C ^ N chain 1.5° toward the ring N. In both cases there is an increase i n B. However, i n order to reproduce B a linear extrapolation suggests that a bend of ~25° is required, a most unreasonable value. The change of A for the normal species is in the right direction but not for the deuterated species. Once again this cannot be the only parameter to account for the rotational con-stants, but a small bend i n this chain, i n conjunction with other changes, cannot be ruled out. Discussion Although there is an infinity of possible structures which can account for the experimental data, the deductions of the previous section have shown that the simplest model to do so contains a pyrrole ring slightly squashed at the substituted C 2 atom and a linear C - C = N chain w i t h a rather short C-C bond at the same angle as C 2-H i n pyrrole. Other models cannot of themselves do what is required, though our simple model does not preclude other changes occurring to some degree. We feel, however, that we have presented very strong evidence for a ring distor-tion similar to those i n six-membered aromatics and to that considered most l i k e l y for thiophene-2-carbonitrile. A l t hough the structural information was obtained by trying to reproduce the "substitution" rotational constants, model b, i t is worthwhile considering what is required t o reproduce the effective constants, model a. It is apparent from Table III that the same general conclusions must be reached. Expansion of the ring to reproduce A must be even greater than we have shown above. A n d the re-255 quirements to reproduce B are very similar. Finally, in the light of our present deductions, it is in-teresting to reconsider furan-2-carbonitrile, for which a bend of some 13° in the C-C^N angle was deemed to be reasonable.14 Table IV contains the rotational constants of this molecule, exactly paralleling models a-d of Table III. Much the same trends are found for the furan de-rivative as for the pyrrole derivative. Again model d re-produces the experimental rotational constants better than model c, and in fact better than model d in the pyrrole derivative. Clearly similar conclusions can be reached for furan-2-carbonitrile as for pyrrole-2-carbonitrile, and ex-treme structural changes such as the 13° bend in the C-O^N chain are not required. Acknowledgment. We thank Dr. H. J. Anderson for the sample of pyrrole-2-carbonitrile. This work was supported by the Natural Sciences and Engineering Research Council of Canada. References and Notes (1) H. J. Anderson, Can. J. Chem.. 37, 2053 (1959). (2) C. E. Loader and H. J. Anderson. Can. J. Chem., 4», 45 (1971). (3) H. J. Anderson. C. R. Rlche, T. G. Coslello, C. E. Loader, and G. H. 1771 Bamett, Can. J. Chem., 56, 654 (1978). (4) H SHgematsu. R. One Y. Yamashits. and Y. Kaberaki, Agr. Biol. Chem.. 35, 1751 (1971). (5) L. H. Oeady. R. A. Shanks, and R. D. Topsom, Tetrahedron Lett.. 1881 (1973). (6) L. F. Elsom and R. A. Jones. J. Chem. Soc. B, 79 (1970). (7) T. Marey and J. Arriau. C. R. Acad. Sci. Paris, Ser. C, 272. 850 (1971). (6) D. M. Benin. M. Farrier, and C. Uegeois, Bui. Soc. Chim. Fr.. part 1, 2677 (1974). (9) L. Nygaard. J. T. Nielsen. J. Krchheiner. G Mahesen. j . Rastrup-Andersen, and G. O. Serensen. J. Mol. Struct., 3, 491 (1969). (10) See. for example, C. R. Noller, "Chemistry of Organic Compounds", 2nd ed., Saunders. Philadelphia. 1957. (11) J. Casado, L. Nygaard, and G. O. Sftensen, J. Mol. Struct., 8, 211 (1971). (12) L. Nygaard. I. Bolesen, T. Pedersen, and J. Rastrup-Andersen. J. Mol. Struct., 2. 209 (1968). (13) O. SrJefvater, Z. Naturforsch. A, 30, 1765 (1975). (14) L. Engefcrecht and D. H. Sutter, Z. Naturforsch. A. 31. 670(1976). (15) J. Wiese. L. Engelbrechl. and H. Dreizler. Z. Naturforsch. A, 32. 152 (1977). (16) T. K. Avirah, T. B. MaDoy. and R. I Cook. J. Mol Struct.. 29. 47 (1975). (17) J. Wtose and O. H. Sutter. Z. Naturforsch. A. 32, 890 (1977). (18) J. K. G. Watson In "Vibrational Spectra and Structure ", J. R. Durig. Ed., Elsevier, Amsterdam. 1977, p 1. (19) C. C. Costain and B. P. Stoicheft, J. Chem. Phys.. 30, 777 (1959). (20) B. Bak, D. Christensen, W. B. Dixon, L. Hansen-Nygaard. J. Rastr-up-Andersen. and M. SchoWandei, J. Mol. Spectrosc.. 9,124 (1962). 256 Appendix 5 A Repr i n t o f a Report o f t h e Microwave Spectrum o f P i f 1 u o r o s i 1 a n e 257 JOURNAL OF MOLECULAR SPECTROSCOPY 83, 185-201 (1980) The Microwave Spectrum, Centrifugal Distortion Constants, Harmonic Force Field, and Molecular Structure of Difluorosilane1 R. WELLINGTON DAVIS, A. G. ROBIETTE,2 AND M. C . L. GERRY Department of Chemistry, The University of British Columbia, 2075 Wesbrook Malt, Vancouver, British Columbia, V6T 1W5, Canada The rotational spectrum of difluorosilane in the frequency region 8-40 GHz has been examined; transitions have been assigned for the "SiH2F2, MSiH 2F 2, and 3 0SiH 2F 2 species in the ground vibrational state and for 2 8SiH 2F 2 in the v, = 1 excited state. For the ground states of 2 8SiH 2F 2, "SiH2F2, and 3°SiH2F2 the measurements have extended up to J = 50, 37, and 35, respectively, allowing the determination of accurate values for the quartic centrifugal distortion constants. The quartic distortion constants have been combined with the vibrational wavenumbers to obtain a harmonic force field. The rotational constants were used to obtain substitution and average structures and an estimate of the equilibrium struc-ture of the molecule. INTRODUCTION Several aspects of the microwave spectum of difluorosilane, S i H 2 F 2 , were investigated by Laurie (/), over two decades ago, but since then the spectrum has received very little attention. Laurie was able to assign ground vibrational state transitions for the species 2 8 S i H 2 F 2 , 2 9 S i H 2 F 2 , 2 8 S i D 2 F 2 , 2 9 S i D 2 F 2 , and 3 0 S i D 2 F 2 , as well as transitions of the two 2 8Si-containing species in the state v4 = 1. From them he obtained structural parameters and the molecular dipole moment. The reported spectra, especially of the less abundant isotopic species, were, however, rather sparse. Indeed, he obtained no R branch transitions of the less abundant species, and was required to assume the invariance of B0 to 2 8 S i —» 2 9 S i or 2 8 S i —» 3 0 S i substitution to complete the structure determination. N o attempt was made to obtain centrifugal distortion constants. The quartic centrifugal distortion constants of simple molecules are readily related to the quadratic force constants of the molecule (2). In favorable cases they can be used, along with other rotational spectroscopic data such as inertial defects and Coriolis coupling coefficients, to specify the force field completely without using any vibrational data at all (5). While this is not possible for most molecules the distortion constants can instead be combined with vibrational data to evaluate the force field, or be used to check the validity of results obtained from vibrational data alone. The former approach is generally applied, but the latter has 1 Work supported by the Natural Sciences and Engineering Research Council of Canada. * On leave from Department of Chemistry, The University of Reading, Reading RG6 2AD, England. 185 0022-2852/80/090185-17S02.00/0 Copyright © 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. 258 186 DAVIS, ROBIETTE, AND GERRY been followed, for example, for the related molecules difluoromethane, C H 2 F 2 (4, 5), and dichlorosilane, S i H 2 C l 2 (6). The only reported infrared spectrum of difluorosilane was obtained in the gas and solid phases by Cradock et al. (7). Spectra were measured for 2 8 S i H 2 F 2 and 2 8 S i D 2 F 2 , and assignments were made largely through gas-phase band contours and the product rule. Wavenumbers were reported for all nine normal vibrations for each species. These were all easily obtained for the deuterated species, but for the normal species there were several overlapped bands so that certain wavenumbers are only poorly known. N o attempt was made to obtain a force field. In the present paper we present extensive measurements of the microwave spectra of three isotopic species of difluorosilane. In particular, the measurements have been extended to high values of J (—50) and Ka (—22). P and R branches of 2 9 S i H 2 F 2 , as well as the spectrum (including P, Q, and 7? branches) of 3 0 S i H 2 F 2 , are reported for the first time. Centrifugal distortion constants, quartic, sextic, and octic, have been evaluated. The quartic constants, including their isotopic depend-ence, have been combined with the vibrational wavenumbers obtained in the infra-red spectrum (7) to produce a harmonic force field. This in turn has been used to calculate ground state average (r2) structures for 2 8 S i H 2 F 2 and 2 8 S i D 2 F 2 and to obtain an estimate of the equilibrium (re) structure of the molecule. EXPERIMENTAL METHODS The spectra was measured in the frequency region 8-40 G H z using a 100-kHz Stark modulated spectrometer having a 3-m X-band cell. In the frequency regions 8-18 G H z and 26.5-40 G H z the sources were the appropriate backward wave oscillators contained in a Hewlett-Packard 8400 C Microwave Spectroscopy Source. A n O K I 24V10A klystron was used to cover the 22-26 G H z region. For these latter measurements frequency markers were obtained by multiplying the output of a Hewlett-Packard 8466A tunable reference oscillator. The accuracy of the measurements was estimated to be better than ± 0 . 0 5 M H z . Al l measure-ments were made with the sample cell cooled with dry ice and sample pressures in the range 0-20 mTorr. The sample of difluorosilane was kindly provided by D . C . Frost, N . P. C . Westwood, and R. A . N . M c L e a n ; it contained no interfering impurities. ASSIGNMENT OF THE SPECTRUM The spectrum of difluorosilane consisted of fc-type transitions only. Initially, the rotational constants of Laurie (7) were used to predict a rigid rotor spectrum for 2 8 S i H 2 F 2 . While only one additional ()-branch line (the 6,5 <— 6^ transition) could be identified in the available frequency region, sufficient low J /^-branch lines to begin a bootstrap centrifugal distortion analysis were identified by their Stark patterns. Almost all other lines exhibited unresolved moderate field high frequency Stark components and the frequency fit was the chief criterion in their identification. For close-lying asymmetry-split transitions the effects of nuclear spin statistics provided confirmation of assignments. The 7^ and levels have a statistical weight of 10 while the Jeo and Jw levels have a statistical weight of 6. 259 MICROWAVE SPECTRUM OF DIFLUOROSILANE 187 28 19 Si H 2 F2 : K-doubling O,K> 9,13 ( 3 3 4 0 4 . 3 4 ) F I G . 1. Recorder tracing of the 2 3 8 . , 6 - 22 9 . , 3 and 23 8 , i5 -22 9 . 1 4 transitions of 2 aSiH 2 F 2 . Their relative intensities show the effect of nuclear spin statistics. Frequencies shown are in megahertz. A n example of the resultant intensity pattern is seen for the 23 8 , 1 6 -22 9 , ] 3 and 23 8 , 1 5 -22 9 , u transitions in Fig. 1. For almost all transitions measured the centrifugal corrections due to the A A term were largest. On the other hand, for lines of the weak P and R branches having selection rules AJ*V 0 = ± 1 , AKC = ± 3 , the 8j term was most important. A careful bootstrap procedure was required to assign these latter lines, which were rather important for the evaluation of meaningful distortion constants. A similar procedure was used for molecules in the v4 = 1 state, as well as for the two less abundant isotopic species. For 2 9 S i H 2 F 2 , however, it was first necessary to find the 1 „ <— OQO transition; this was fairly easily done using the frequency shift, relative intensity, and the Stark effect. For 3 0 S i H 2 F 2 , for which no transition frequencies had been previously reported, the same criteria applied. ANALYSIS O F THE SPECTRUM The observed line frequencies were analyzed using a fitting procedure that has been described earlier (8). The " A reduction" of Watson's Hamiltonian (9) in the lT representation (10) was used, including terms up to the eighth degree in the angular momentum. ^f R = (\I2)(B + C)P2 + [A - (V2)(B + C)]P2a + (l/2)(B - C)(P2b - P2.), (2) % D = -AjP4 - AjKP2P2a - AKPa - (Pi - P2)[8jP2 + 5KP2a] - [8jP2 + 8KPIKPI - P2), (3) 2lfD = HjP* + HJKP*P% + HKJP2Pt + HKPa + hj[P\Pl - P2) + (P2b - P2)P4] + LKPl (4) Here the angular momentum P has components Pa, P0, Pr; A, B, C are the rota-tional constants; Aj, AJK, A * , 8j, 8K are the quartic distortion constants; Hj, HJK, 260 DAVIS, ROBIETTE, AND GERRY TABLE I Rotational Transitions (MHz) of Difluorosilane T r a n s i t i o n Observed C a l c u l a t e d D i s t o r t i o n Frequency Frequency C o r r e c t i o n SiH^F^ (Rround v i b r a t i o n a l s t a t e ) 1. 1) - 0 0, 0) 31067.71 31067.72 -0.19 -0.01 2i 1. 1) - 2 0. 2) 19824.84 19324.86 -0. 1tt -0.02 2 0. 2) - 1 1. 1) 1 1383. 19 11383.17 -0.08 0.02 31 1. 2) - 3 0, 3) 2225C.00 22250.00 -0. 20 0.00 3 0. 3) - 2 1, 2) 26642. 88 26642.90 -0.92 -0.02 3| 1. 3) - 2. 2. 0) -14676.05 -14S76.04 3.62 -0.0 1 tt 1. 3) - 4 0. «) 25761. 92 25761.88 -0.75 0.04 <tl 1. ?) - 3( 2, 2 10799.01 10798.99 -0.08 0.02 tt 2, 3) - 3 3, 0) -31 395. 71 -31395.72 16.46 0.01 4| 2. 2) - 3( 3, 1) -30117.4B -30117.49 15. 9« 0.0 1 5 1 1. «) - 5 0, 5) 305«8.93 30548.92 -2.28 0.01 5( 1. 1 - 4 2. 3| 26190.01 28189.99 -«.29 0.02 5( 2, ») - tt 3, 1) -17595.02 - 17595.00 13. 00 -0.02 5( 2. 3 - tt| 3. 2) -14659.26 -14659.25 11. 36 -0.01 6 1 1. 5) - 6 i 0. 6) 3676 1. 90 36761.90 -5 03 -0.00 6| 1. 6) - 5( 2, 3) 13489.35 13489.35 0.61 -0.0 0 6 1 3. «) - 5 ( 1. 1) -37484.21 -37484.20 40.83 -0.01 6( 3. 31 - 5{ 1, 2) -37211.49 -37211.47 00.51 -0.0 2 7 | 2, 6) - 6 ( 3, 3) B796.17 8796.17 3.11 0.00 7( 3. 5) - 61 «. 2) -23082.07 -23082.08 32. 87 o.o i 7 | 3, ») - 6 ( «. 3) -22405. 97 -22405.95 31.84 -0.02 8| 1. 8 - 7( 2. 5) 23152.24 23152.22 4. 95 0.02 8 | 2. 6) - 7 I 3, 5) 36840. 95 36840.92 -20.04 0.03 8( 3. 6) - 7( 1. 3) -8684.66 -8684.66 22.82 -0.00 9 1 1. 9) - 8 1 2. 6) 24621.88 24621.92 12.26 -0.04 9{ 2, 8) - 8( 3. 5) 32201.60 32201.62 -7.30 -0.02 9 1 3, 6) - B { <*. 5) 8519. 53 8519.54 3.96 -0.01 9( tt. 6) - 8| 5. 3) -29390.97 -29390.99 68. 13 0.02 9 1 «. 5) - 8 ( 5. «) -29260. 30 -29260. 30 67.71 -.0.00 10( 1. 10) - 9( 2. 7 23812.33 23812.30 20.47 0.03 10 | 3. 7) - 9 ( «. 6) 24990.05 24990.04 -17.61 0.01 10( ». 7) - 9( 5. «) -14764.88 -14764.90 51.09 0.02 10( ». 6) - 9 1 5, 5 -14462.60 - 14»62. 62 49.92 0.02 " ( 3. 9) - 10( 1. 6) 33649.98 33649.98 -18. 13 -0.00 11 < 5. 7) - 10 I 6, »> -35873.59 -35873.61 123.22 0.02 11( 5, 6) - 10( 6, 5) -35850.50 -35850.50 123.09 0.00 12 ( 1.12) - 11 ( 2, 9) 15812.93 15812.94 66.87 -0.01 12( «. 9) - 11( 5, 6) 14708.63 14708.61 7.04 0.02 12 ( «. 8) - 11 ( 5, 7) 15967.30 15967.30 0. 19 -0.00 '3( 1. 13) - 12( 2,10) 9017.48 9017.47 97.75 0.0 1 13 ( «.10) - 12 ( 5, 7) 29H91.96 29491.97 - 19. 91 -0.01 13( ». 9) - 12( 5, 8) 31817.20 31817.2 1 -34.51 -0.0 1 14( 5.10) - 13( 6, 7) 8391.07 8391.08 34. 15 -0.01 1tt( 5. 9) - 13( 6, 8) 8649.96 8649.96 31.77 0.00 14< 6. 9) - 13 ( 7. 6) -27732.18 -27732. 19 167.51 0.01 1«( 6. 8) - 13( 7. 7) -27722.57 -27722.58 167.4 1 0.0 1 15 ( 1.15) - 14 ( 2.12) -8797.39 -8797. »0 176.19 0.01 15{ 5. 11) - 1tt{ 6. 8) 23360.7« 23360.73 -4.96 0.0 1 15 ( 5.10) - 14 ( 6. 9) 23870.66 23870.6 1 - 10.31 0.05 15( 6. 10) - 1tt( 7. 7) -13007.61 -13007.60 127. 52 -0.0 1 15 ( 6. 9) - 14 ( 7, a) -12985. 38 -12985.38 127.25 -0.00 16 ( 5. 12) - 15( 6. 9) 38428. 18 38tt28. 13 -49.07 0.05 16 ( 5.11) - 15 ( 6,10) 39383.10 39383.09 -60.39 0.01 16( 7. 10) - 15( 8. 7) -3K219.82 -34219.83 263.96 0.0 1 16 ( 7. 9) - 15 ( 8, 8) -34218. 24 -3«216.2« 263.94 0.00 17( 1, 17) - 16( 2.14) -29973.87 -29973.87 264.68 -0.00 17 ( 6 12 - 16 ( 7, 9) 16756.93 16756.92 30.45 0.01 17( 6, 11) - 16( 7.10) 16856.83 16856.83 28.84 -0.00 18 ( 6.13) - 17 ( 7.10) 31813.69 31813.71 -27.53 -0.02 18( 6. 12) - 17 ( 7,11) 32010.51 323 10. Stt -31.08 -0.03 19( 2. 18) - 16( 3, 15) 35630.68 35630.70 404. 94 -0.02 19 ( 7.13) - 18 ( 8,10) 10113. 11 10113. 11 89.22 -0.00 19 ( 7, 12) - 18( 8,11) 10131.30 10131. 31 88.80 -0.0 1 20( 7.11) - 19 ( 8,11) 25088.41 25088.tt1 16. 98 -o.oo 20 ( 7. 13) - 19( 8. 12) 25125.71 25125.71 16. 0 2 -0.00 20 ( 8.13) - 19 ( 9,10) -11289.82 -11289.82 254. 0U 0.00 261 MICROWAVE SPECTRUM OF DIFLUOROSILANE 189 TABLE I—Continued Transition Observed Frequency Calculated Frequency Distortion Correction 28 20 ( 21 ( 23( 23 ( 23( 8. 12) 2.20) 2.22) 0,16) . 8,15) 23(10,13) 24( 9, 16) 21< 9.15) 2<t( 10, 15) 25( 2,24) 25( 9 ,17 | 25( 9,16) 26{11, 15) 27{ 3,25) 27( 11, 16) 28(10,19) 28( 10. 18) 28(12,16) 29 ( 3, 27) 31( 3,29) 31(13. 18) 32 ( 3,30) 32(13, 19) 33 (111,20) 34(13, 22) 35( « , 3 2 ) 35( 13, 23) • 36( « , 3 3 ) 36(14,23) 36(15,21) 37 (1 i» , 21) -37(15,22) • 38 { 4,35) • 38(14,25) • 38( 16.23) -39(15,211) -10{ 11,37) -10(15,25) -10(17,211) -11(16,25) -12(17,25) -13(18,26) -14(18,27) -15(17,28) -15(19,26) -16(18,28) -17(18,30) -18 (20,28) -19(20,29) -50(19,32) -50(21, 29) -S i H ? F ; (ground vibrational state)(c - 19( 9,11) - 20 ( 3, 17) - 22( 3,19) - 22( 9,13) - 22( 9,14) - 22(11,12) - 23(10,13) - 23(10,14) - 23(11.12) - 24( 3,21) - 21(1C,14) - 24 (10, 15) - 25(12.11) - 26 ( 4,22) - 26(12,15) - 27(11,16) - 27(11,17) - 27(13,15) - 28( 4,24) - 30 { 4,26) - 30(14,17) " 31 ( 4,27) • 31(14,18) - 32(15.17) • 33(14,19) • 34 ( 5 ,29| 34( 14, 20) • 35( 5,30) 35(15,20) 35(16,20) 36(15,21) 36(16,21) 37( 5, 32) 37 (15,22) 37( 17,70) 38(16,23) 39( 5.34) 39(16,24) 39(18,21) 10 (17,24) 11(18,24) 42 (19,23) 13(19,24) 11 (18,27) 14(20,25) 15 (19,27) 16(19,27) 17 (21,27) 18(21,28) 19 (20,29) 19(22,28) -11288.40 13297. 14 -11457.45 33404. 34 33417.92 -38859.00 11807.12 11808. 25 -21209.3B -35813. 97 26714.63 26717. 01 -30595.51 37029.41 -15930.62 35013.78 35014.62 -36930.57 9011.54 -17669.06 -28623.75 -30019.22 -13995.33 -34885 . 16 15392.87 310 16. 19 30 158.48 16256. 92 8989.85 -26539 .73 23695.76 -11960. 54 -10892.66 38446.30 -32717.58 17303. 28 -34766.03 31992.03 -38828 . 99 10980.67 -9817.67 -30420.96 -15948 .17 33909. 61 -36433.07 13070.17 27618.28 -27987.79 -13588.06 35920. 17 -33891.53 ontlnued) -11288.40 13297. 11 -11457.44 33404.36 334 17. 94 -38858 .98 11807.12 11808.26 -24209.40 -35813 .97 26714.65 26717. 04 -30595.52 37029.42 -15930.51 35013.80 350 14.64 -36930.56 901 1.52 -17669 .05 -28623.76 -30019 .22 -13995.34 - 3 1 8 8 5 . 16 15392.87 31016.20 30158.49 16256.92 8989.86 -26539 .74 23695.76 - 11960. 53 -10892.68 38446. 28 -32717.57 17303.27 -34766 .03 31992.02 -38828.98 10980.64 -9817 .66 -30420 .94 -15948. IB 33909.59 -36433. 06 13070.15 27618.29 -27987 .77 -13588.04 35920.20 -3399 1.56 254.39 608.44 796.58 - 8 . 9 8 -9 .51 660.60 187. 11 187.06 556.26 939.24 73.43 73.31 766.10 1506.67 633. 86 44.88 44. B2 1020.72 1311.74 2003.18 1149.51 2068. 51 963. 51 1182.16 555. 39 3195.31 332. 15 3615.97 814.38 1635.32 565. 26 1386.75 3748.33 301.97 2056.08 848.12 3815.55 556.96 2538.53 1181.69 1914.00 2751.47 2400.99 860.27 3337.04 1651.48 1251. 39 3578.10 3144.96 1252.94 4275. 4 1 -0 .00 0.03 - 0 . 0 1 - 0 . 0 2 - 0 . 0 2 - 0 . 02 0.00 -0 .01 0.02 0.00 - 0 . 0 2 - 0 . 0 3 0.0 1 -0 .01 -0 .01 - 0 . 0 2 - 0 . 0 2 -0 .01 0.02 -0 .01 0.0 1 - 0 . 0 0 0.01 0.00 0.00 -0 .01 - 0 . 0 1 - 0 . 0 0 - 0 . 0 1 0.01 0.00 -0 .01 0.02 0.02 - 0 . 0 1 0.01 - 0 . 0 0 0.01 -0 .01 0.03 - 0 . 0 1 - 0 . 0 2 0.0 1 0.02 - 0 . 0 1 0.02 - 0 . 0 1 - 0 . 0 2 - 0 . 0 2 - 0 . 0 3 0.03 HKJ, HK, hj are sextic constants; and LK is an octic constant. Only a partial set of sextic and octic constants, but one which was sufficient to represent the most extensive data set, is included. Initially, a first-order and then an exact fit were made to the 2 8 S i H 2 F 2 ground state lines with./ < 30 including the quartic distortion constants only; a satisfactory fit of the data was not obtained. Al l seven sextic constants were added and t h e / range of transitions used was gradually extended to 50. Even at this point, however, the sextic constants hJK and hK were indeterminate and were accordingly 262 190 DAVIS, ROBIETTE, AND GERRY TABLE 1—Continued Transition Observed Frequency Calculated Frequency Distortion Correction 28. _S1H„F„ (v - 1 state) 1( 1. 1) 2( 0 . 2) 3( 1. 3) 5( 1, 4) 5( 2, 31 -5( 1. 4 ) 6) 6( 1 6( 1. 5) 7( 2. 5) 8( 2 , 6) 9( 4, 6) 9( 4 , 5) « ( 2, . 10( 3 . 8) 10( it. 6) 10( « . 7) 11( 5. 6) 11 ( 3 , 9) 12( 1.12) 12< » . 9) 12( 4 . 8) 13( 4 , 9) 13( « . 10) 14( 6, 8) 1"( 6. 9) 15( 6. 9) 15( 6, 10) 16 ( 7,10) 16 ( 7. 9) 16( 5,12) 16( 5,11) 17( 6,12) 17( 6,11) 18( 6,12) 18( 6,13) 19( 8 , 1 1 | 19( 8, 12) 20 ( 8,12) 20( 8,13) 21( 7,15) 21 ( 7.14) 22( 8.10) 22 ( 8.15) 24(10,14) 26(11, 16) 26{ 9,18) 26( 9.17) 30(12,16) 31(13, 18) 32(12,21) 35(14,21) 36 (15.22) 37(1 a, 24) 38 (14,25) 40(16, 25) 0( 0, 1( 1. 2( 2. » ( 2 , » ( 3. 5( 0 , 5( 2, 6( 0. 6( 3, 7( 3 . 8( 5. 8( 5. 8) - 8( 3 . 9( 4 , - 9( 5, - 9 ( 5 , - 10( 6, - 10( 4, - H( 2, - 1 1 ( 5 , " 11< 5, - 12( 5, - 12( 5, - 13( 7, • 13( 7. - 1 » ( 7 , • I'M 7. - 15( 8. • 15( 8, - 15( 6, • »5 ( 6, • 16 ( 7. 16( 7. • 17( 7, 17( 7, • 18( 9 , 18( 9 . • 19( 9 , 19( 9 . 20 ( 8, 20 ( 8. 2 1 ( 9 . 21( 9 , 23(11. 25(12, 25(10 , 25(10, 29(13, 30(14, 31(13, 34(15. 35(16, 36(15, 37(15. 39(17. 0) 1) 0) 3) 2) 5) 3) 6) «> 5) 3) 1) 5) 5) 51 1) 5) 6) 9) 6) 7) 8) 7| 7) 6) 8) 7) 7) 3) 9) 10) 9) 10) 11) 10) 10) 9) 11) 10) 12) 13) 13) 12) 13) 13) 15) 16) 17) 17) 18) 20) 19) 21) 22) 22) 31297.6* 11108. 16 -15504. 36 27444.89 -15981.40 30884. 10 12529.44 37135. 26 17403.27 35507.21 -31771.91 -31642. 81 30812.81 17914.92 -16860.63 -17159.34 -38 75 8.73 31759. 42 14248.03 12290.48 13534.96 29364. 70 27064.89 -31169.50 -31 178.84 -16446. 78 -16468 .45 -3818B.87 -38187.34 35456.22 36394.58 13268. 49 13365.96 28 50 4. 27 28312.18 -30519.64 -30520.25 -15805 .53 -15806.90 36139. 30 36210.56 13874. 33 13867.85 -29757.05 -36653.52 36620. 34 36624.94 -14224.74 -35704.54 15244. 22 -13279 . 28 -34625 .53 16064.65 30802. 48 -12216.42 31297.69 11108.17 -15504.36 27444.91 -15981 .39 30884.06 12529.43 37135.26 17403.29 35507.23 -31771.93 -31642 .79 30812.82 17914.93 -16860.63 - 17159. 35 -38758.69 31759.42 14248.03 12290.49 13534.95 29364.71 27064.90 -31169.51 -31178.88 -16446.78 -16468.46 -38188.86 -38187.32 35456.22 36394.57 13268.49 13365.98 28504.28 28312. 16 -30519 .65 -30520.25 -15805 .53 -15806.90 36139.30 36210.55 13874. 28 13867.86 -29757 .05 -36653.55 36620.33 36624.97 - 14224.73 -35704.53 15244.20 -13279.26 -34625 .53 16064.67 30802.47 -12216.44 - 0 . 20 - 0 . 06 3.84 - 4 . 09 12. 24 - 2 . 3 3 0.93 - 5 . 4 9 - 5 . 0 6 - 1 9 . 0 7 73.21 72.80 - 6 . 2 1 - 0 . 5 4 55. 11 56.2 7 132. 34 - 15.44 67. 26 12.46 5.69 - 2 8 . 7 2 - 1 4 . 3 5 182.84 182.95 142.92 143.19 287.57 287.54 - 3 8 . 8 3 -49 .