UBC Theses and Dissertations

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UBC Theses and Dissertations

The microwave and infra-red spectra of some unstable gaseous molecules Jemson, Helen Margaret 1986

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THE MICROWAVE AND INFRA-RED SPECTRA OF SOME UNSTABLE GASEOUS MOLECULES By HELEN MARGARET JEMSON B.Sc. ( H o n s . ) , The U n i v e r s i t y o f Otago, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (De p a r t m e n t 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 c o n 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 December 1986 ® H e l e n M a r g a r e t Jemson, 1986 In p resen t i ng this thesis in part ial fu l f i lment o f the requ i remen ts for an a d v a n c e d d e g r e e at t he Un ivers i ty o f Br i t ish C o l u m b i a , I agree that the Library shal l m a k e it f reely avai lable for re fe rence and s tudy . I fur ther agree that pe rm iss ion for ex tens i ve c o p y i n g o f this thesis for scho la r l y p u r p o s e s may b e g ran ted by the h e a d o f m y depa r tmen t o r by his o r her representa t i ves . It is u n d e r s t o o d that c o p y i n g o r pub l i ca t i on of this thesis fo r f inanc ia l ga in shal l no t b e a l l o w e d w i t h o u t m y wr i t t en p e r m i s s i o n . D e p a r t m e n t o f f£.y T h e Un ivers i ty o f Bri t ish C o l u m b i a 1956 M a i n M a l l V a n c o u v e r , C a n a d a V 6 T 1Y3 Da te tf t>ec DE-6(3 /81 ) A B S T R A C T The microwave s p e c t r a o f t h r e e u n s t a b l e m o l e c u l e s , bromine i s o c y a n a t e (BrNCO), i o d i n e i s o c y a n a t e (INCO), and b r o m i n e t h i o c y a n a t e ( B r S C N ) , have been o b s e r v e d and a n a l y z e d i n the f r e q u e n c y r a n g e 16-54 GHz. The i n f r a - r e d s p e c t r u m o f a m i n o d i f l u o r o b o r a n e ( B F 2 N H 2 ) has b e en i n v e s t i g a t e d i n t h e r e g i o n 3700-400 c m - 1 , and one band, the 2j v i b r a t i o n a l b and has been r e c o r d e d a t a r e s o l u t i o n o f 0.004 c m - 1 , and the r o t a t i o n a l s t r u c t u r e a n a l y z e d . BrNCO: BrNCO was g e n e r a t e d from th e f l o w r e a c t i o n o f B r 2 w i t h s i l v e r c y a n a t e . The s p e c t r a o f two i s o t o p i c s p e c i e s were o b s e r v e d : 7 9 B r N C O and 8 1 B r N C 0 . They c o n t a i n s t r o n g a - t y p e t r a n s i t i o n s as w e l l as some weaker b - t y p e t r a n s i t i o n s w h i c h c o u l d n o t i n i t i a l l y be a s s i g n e d . I n a d d i t i o n , t h e t r a n s i t i o n s show b o t h Br and N 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 n o v e l method has b e en d e v e l o p e d w h i c h u s e s p e r t u r b a t i o n s i n the Br s t r u c t u r e t o e v a l u a t e a l l the r o t a t i o n a l c o n s t a n t s , as w e l l as t h e Br q u a d r u p o l e t e n s o r , e n t i r e l y f r o m a - t y p e R b r a n c h t r a n s i t i o n s u s i n g a g l o b a l 1 e a s t - s q u a r e s f i t t i n g programme. T h i s has a l l o w e d some b - t y p e t r a n s i t i o n s to be a s s i g n e d . The m o l e c u l e has b e en shown to be p l a n a r and a p a r t i a l r Q s t r u c t u r e was d e t e r m i n e d . The p r i n c i p a l v a l u e s o f the Br q u a d r u p o l e t e n s o r have been e v a l u a t e d and have p r o v i d e d some i n f o r m a t i o n a b o u t the t y p e o f b o n d i n g i n v o l v e d i n the Br-N bond. INCO: INCO was o b s e r v e d i n the f l o w r e a c t i o n o f I 2 w i t h s i l v e r c y a n a t e . Many s t r o n g a_-type t r a n s i t i o n s were o b s e r v e d as w e l l as some v e r y weak b_-type t r a n s i t i o n s . These t r a n s i t i o n s showed I and N 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 ; many p e r t u r b a t i o n s i n the I s t r u c t u r e were o b s e r v e d . The method d e v e l o p e d i n t h e a n a l y s i s o f the s p e c t r u m o f BrNCO u s i n g s u c h p e r t u r b a t i o n s to o b t a i n o t h e r w i s e u n o b t a i n a b l e r o t a t i o n a l c o n s t a n t s was e x t e n d e d to i n c l u d 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 . The p l a n a r i t y o f INCO has been c o n f i r m e d and a p a r t i a l r 0 s t r u c t u r e was d e t e r m i n e d . The p r i n c i p a l v a l u e s o f the I q u a d r u p o l e t e n s o r have b e e n e v a l u a t e d and have p r o v i d e d some i n f o r m a t i o n a b o u t the t y p e o f b o n d i n g i n v o l v e d i n the I-N bond . BrSCN: BrSCN was g e n e r a t e d i n the f l o w r e a c t i o n o f B r 2 w i t h s i l v e r t h i o c y a n a t e . The s p e c t r a c o n t a i n e d b o t h a- and b-t y p e t r a n s i t i o n s , a l l o f w h i c h showed Br 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 . 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 g a l d i s t o r t i o n c o n s t a n t s were o b t a i n e d f o r two i s o t o p i c s p e c i e s : 7 9 B r S C N and 8 1 B r S C N . The r o t a t i o n a l c o n s t a n t s c o n f i r m t h e t h i o c y a n a t e c o n f i g u r a t i o n , and a p a r t i a l r Q s t r u c t u r e has been o b t a i n e d . A l s o , the p r i n c i p a l v a l u e s o f t h e Br q u a d r u p o l e t e n s o r were e v a l u a t e d w h i c h show t h a t the Br-S bond i s e s s e n t i a l l y c o v a l e n t , w i t h s m a l l amounts o f n and i o n i c c h a r a c t e r . B F 2 N H 2 : B F 2 N H 2 was g e n e r a t e d by h e a t i n g s o l i d B F 3 NH 3 . The wavenumbers o f 7 o f the v i b r a t i o n a l f u n d a m e n t a l s have been i v o b t a i n e d , and f r o m t h e a n a l y s i s o f t h e 2j band, an a c c u r a t e s e t o f r o t a t i o n a l 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 o f the g r o u n d v i b r a t i o n a l s t a t e have been o b t a i n e d and the r o t a t i o n a l 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 o f the 2 1 l e v e l have b e e n e v a l u a t e d . A l s o a C o r i o l i s t y p e p e r t u r b a t i o n was o b s e r v e d , p r o b a b l y due to the c o m b i n a t i o n l e v e l v1 + v l x , w h i c h has p r o v i d e d an e s t i m a t e o f the wavenumber o f t h e v x x f u n d a m e n t a l w h i c h has n o t y e t been o b s e r v e d . V TABLE OF CONTENTS C h a p t e r Page I. I n t r o d u c t i o n 1 B i b l i o g r a p h y 8 I I . T h e o r y 2.1 I n t r o d u c t i o n 10 2.2 The R i g i d R o t o r 11 2.3 R i g i d R o t o r S e l e c t i o n R u l e s 15 2.4 C e n t r i f u g a l D i s t o r t i o n 17 2.5 S t r u c t u r a l D a t a 21 2.6 N u c l e a r S p i n S t a t i s t i c s 25 2.7 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 26 2.8 S t a r k E f f e c t 32 2.9 The Harmonic O s c i l l a t o r 37 2.10 V i b r a t i o n S e l e c t i o n R u l e s 39 2.11 C o r i o l i s P e r t u r b a t i o n s 41 B i b l i o g r a p h y 46 I I I . E x p e r i m e n t a l Methods 3.1 The Mi c r o w a v e S p e c t r o m e t e r 48 3.2 The FT -IR I n t e r f e r o m e t r i c S p e c t r o m e t e r 52 B i b l i o g r a p h y 59 IV. The Mi c r o w a v e S p e c t r u m o f Bromine I s o c y a n a t e , BrNCO 4.1 I n t r o d u c t i o n 60 4.2 E x p e r i m e n t a l Methods 60 4.3 I n i t i a l A s s i g n m e n t s 61 4.4 D e t e r m i n a t i o n o f A 65 4.5 A n a l y s i s o f a - t y p e T r a n s i t i o n s 68 4.6 b - t y p e T r a n s i t i o n s 69 4.7 The S t r u c t u r e o f BrNCO 101 4.8 Br and H N Q u a d r u p o l e C o u p l i n g 105 4.9 D i s c u s s i o n 111 B i b l i o g r a p h y 113 V. The Mi c r o w a v e S p e c t r u m o f I o d i n e I s o c y a n a t e , INCO 5.1 I n t r o d u c t i o n 115 5.2 E x p e r i m e n t a l Methods 116 5.3 A n a l y s i s o f a - t y p e T r a n s i t i o n s 117 5.4 A n a l y s i s o f b - t y p e T r a n s i t i o n s 121 5.5 S t r u c t u r e o f INCO 145 5.6 i 2 7 j a n d 1 4 N Q u a d r u p o l e C o u p l i n g 148 5.7 D i s c u s s i o n 150 B i b l i o g r a p h y 155 v i T a b l e o f C o n t e n t s ( C o n t i n u e d ) C h a p t e r Page V I . The M i c r o w a v e S p e c t r u m o f Bromine T h i o c y a n a t e , BrSCN 6.1 I n t r o d u c t i o n 155 6.2 E x p e r i m e n t a l Methods 156 6.3 A n a l y s i s o f t h e Microwave S p e c t r u m 158 6.4 The S t r u c t u r e o f BrSCN 182 6.5 Bromine Q u a d r u p o l e C o u p l i n g 185 6.6 D i s c u s s i o n 189 B i b l i o g r a p h y 191 V I I . The I n f r a - R e d S p e c t r u m o f A m i n o d i f l u o r o b o r a n e , B F 2 N H 2 7.1 I n t r o d u c t i o n 193 7.2 E x p e r i m e n t a l Methods 194 7.3 A n a l y s i s o f the I n f r a - r e d S p e c t r u m 196 7.4 A n a l y s i s o f the R o t a t i o n a l S t r u c t u r e o f the 2 1 Band 199 7.5 D i s c u s s i o n 224 B i b l i o g r a p h y 226 v i i L I ST OF TABLES T a b l e Page 4.1 S p e c t r o s c o p i c c o n s t a n t s o f BrNCO from a^-type t r a n s i t i o n s . 7 0 4.2 C o r r e l a t i o n c o e f f i c i e n t s o f the s p e c t r o s c o p i c c o n s t a n t s o f BrNCO d e r i v e d from a - t y p e t r a n s i t i o n s o n l y . 71 7 9 4.3 S p e c t r o s c o p i c c o n s t a n t s o f BrNCO. 78 4.4 S p e c t r o s c o p i c c o n s t a n t s o f 8 1 B r N C 0 . 79 4.5 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 7 9 B r N C 0 . 80 4.6 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 8 1 B r N C 0 . 86 4.7 O b s e r v e d h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s i n (MHz) o f 7 9 B r 1 4 N C O b - t y p e t r a n s i t i o n s . 92 4.8 O b s e r v e d h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s i n (MHz) o f 8 1 B r 1 A N C 0 b - t y p e t r a n s i t i o n s . 97 4.9 Bromine 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 i n p r i n c i p a l i n e r t i a l a x e s . 101 4.10 1 *N 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 i n p r i n c i p a l i n e r t i a l a x e s . 102 4.11 S t r u c t u r a l p a r a m e t e r s o f b r o m i n e i s o c y a n a t e . 103 4.12 C o m p a r i s o n o f s t r u c t u r a l p a r a m e t e r s o f BrNCO w i t h v a l u e s i n o t h e r m o l e c u l e s . 104 4.13 P r i n c i p a l v a l u e s o f the b r o m i n e q u a d r u p o l e c o u p l i n g t e n s o r . 107 4.14 C o m p a r i s o n o f e x p e r i m e n t a l l y d e t e r m i n e d 1 A N 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 w i t h v a l u e s c a l c u l a t e d u s i n g t h e o r e t i c a l c a l c u l a t i o n s . I l l 5.1 S p e c t r o s c o p i c c o n s t a n t s o f 1 2 7 I N C O from a_-type t r a n s i t i o n s o n l y . 123 5.2 C o r r e l a t i o n c o e f f i c i e n t s o f the s p e c t r o s c o p i c c o n s t a n t s o f 1 2 7 INCO c a l c u l a t e d f r o m a^-type t r a n s i t i o n s . 125 5.3 S p e c t r o s c o p i c C o n s t a n t s o f 1 2 7 I N C 0 . 128 v i i i L i s t o f T a b l e s ( C o n t i n u e d ) T a b l e Page 5.4 C o r r e l a t i o n c o e f f i c i e n t s o f t h e s p e c t r o s c o p i c c o n s t a n t s o f 1 2 7 I N C O . . 129 5.5 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f INCO. 131 5.6 O b s e r v e d h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s ( i n MHz) o f 1 2 7 I 1 4 N C O b - t y p e Q b r a n c h t r a n s i t i o n s . 139 5.7 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 1 4 N i n p r i n c i p a l i n e r t i a l a x e s . 145 5.8 S t r u c t u r a l p a r a m e t e r s o f INCO. 146 5.9 C o m p a r i s o n o f s t r u c t u r a l p a r a m e t e r s o f INCO w i t h o t h e r m o l e c u l e s . 147 12 7 5.10 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 I i n p r i n c i p a l i n e r t i a l a x e s . 148 5.11 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 1 2 7 l i n p r i n c i p a l q u a d r u p o l e a x e s . 148 5.12 C o m p a r i s o n o f 1 4 N 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 b t a i n e d e x p e r i m e n t a l l y w i t h t h e o r e t i c a l l y c a l c u l a t e d v a l u e s . 150 5.13 I o n i c bond c h a r a c t e r o f the h a l o g e n i s o c y a n a t e s . 153 6.1 The r o t a t i o n a l c o n s t a n t s o f b r o m i n e t h i o c y a n a t e and b r o m i n e i s o t h i o c y a n a t e c a l c u l a t e d f r o m model s t r u e t u r e s. 15 9 6.2 S p e c t r o s c o p i c c o n s t a n t s o f b r o m i n e t h i o c y a n a t e . 164 6.3 C l o s e s t n e a r d e g e n e r a c i e s h a v i n g the c o r r e c t symmetry to c a u s e p e r t u r b a t i o n s i n h y p e r f i n e s t r u c t u r e i n the s p e c t r u m o f b r o m i n e t h i o c y a n a t e . 166 6.4 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 7 9 BrSCN. 167 6.5 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 8 1 B r S C N . 175 6.6 C o m p a r i s o n o f the measured r o t a t i o n a l c o n s t a n t s o f b r o m i n e t h i o c y a n a t e w i t h t h o s e c a l c u l a t e d f r o m model s t r u c t u r e s . 183 I X L i s t o f T a b l e s ( C o n t i n u e d ) T a b l e Page 6.7 S t r u c t u r a l p a r a m e t e r s o f b r o m i n e t h i o c y a n a t e . 183 6.8 C o m p a r i s o n o f s t r u c t u r a l p a r a m e t e r s o f BrSCN w i t h s t r u c t u r e s o f o t h e r m o l e c u l e s . 184 6.9 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 b r o m i n e t h i o c y a n a t e i n the p r i n c i p a l i n e r t i a l axes s y s tem. 18 6 6.10 P r i n c i p a l v a l u e s o f the b r o m i n e q u a d r u p o l e c o u p l i n g t e n s o r o f b r o m i n e t h i o c y a n a t e . 186 7.1 V i b r a t i o n a l f r e q u e n c i e s o f B F 2 N H 2 ( i n c m - 1 ) . 200 7.2 V i b r a t i o n a l F r e q u e n c i e s o f B F 2 NH 2 ( i n c m - 1 ) . 201 7.3 R o t a t i o n a l c o n s t a n t s o f t h e 2 1 l e v e l o f 1 1 B F 2 N H 2 . 206 7.4 R o t a t i o n a l c o n s t a n t s o f the 2 1 l e v e l o f 1 1 B F 2 NH 2 . 207 7.5 O b s e r v e d i n f r a r e d t r a n s i t i o n s o f 1 1BF,NH,. 209 X LIST OF FIGURES F i g u r e Page 3.1 B l o c k d i a g r a m showing b a s i c d e s i g n o f microwave s p e c t r o m e t e r . 49 3.2 S c h e m a t i c d e s i g n o f i n t e r f e r o m e t e r . 54 4.1 B r o a d b a n d s c a n o f the microwave s p e c t r u m o f BrNCO i n the f r e q u e n c y r a n g e 32.7-38.6 GHz. 63 4.2 J = 6 «- 5 a - t y p e R b r a n c h o f BrNCO i n t h e f r e q u e n c y r a n g e 24.8 - 26.2 GHz. 64 4.3 R o t a t i o n a l e n e r g y l e v e l s o f 8 1 B r N C O . 73 4.4 The e n e r g y l e v e l s o f the 1 1 0 l l - 10 Q 1 0 t r a n s i t i o n s o f 8 1 B r N C 0 . ' ' 72 4.5 H y p e r f i n e s p l i t t i n g p a t t e r n s o f some K a= 0 t r a n s i t i o n s o f 8 1 B r N C 0 . 74 4.6 The 1 7 1 1 6 - 1 7 0 > 1 7 t r a n s i t i o n s o f 7 9 B r N C 0 showing b o t h 7 9 B r and 1 4 N n u c l e a r q u a d r u p o l e e f f e c t s . 76 4.7 The atoms o f BrNCO i n i t s p r i n c i p a l i n e r t i a l a x i s s y s t e m a c c o r d i n g to s t r u c t u r e I I ( T a b l e 4 . 1 1). 104 5.1 B r o a d b a n d s c a n o f the J = 9 «- 8 a^-type R b r a n c h o f INCO i n t h e f r e q u e n c y range 29.68 - 30.71 GHz. 118 5.2 The 1 2 0 ( 1 2 - 1 1 0 1 1 t r a n s i t i o n s o f INCO. 120 5.3 The r o t a t i o n a l e n e r g y l e v e l s o f INCO showing s e v e r a l i m p o r t a n t n e a r - d e g e n e r a c i e s . 122 5.4 The e n e r g y l e v e l s o f 1 7 2 > 1 5 and 19X 1 9 o f INCO. 127 5.5 The r e l a t i v e p o s i t i o n s o f the atoms o f INCO i n i t s p r i n c i p a l i n e r t i a l a x i s s y s t e m ( f r o m s t r u c t u r e I I i n T a b l e 5.8). 147 6.1 P r e p a r a t i o n o f BrSCN. 157 6.2 The t r a n s i t i o n 1 3 2 X 1 - 131 1 2 f o r 7 9 B r S C N and 8 1 B r S C N . ' ' 162 X 1 L i s t o f F i g u r e s ( C o n t i n u e d ) F i g u r e Page 6.3 B r o a d b a n d s c a n o f t h e s p e c t r u m o f BrSCN from 31 .57 - 31 .87 GHz. 163 6.4 The p o s i t i o n s o f the atoms o f BrSCN r e l a t i v e t o i t s p r i n c i p a l i n e r t i a l a x i s s y s t e m . 185 7.1 The c o n f i g u r a t i o n o f the atoms o f B F 2 NH 2 . 197 7 .2 L o w - r e s o l u t i o n t r a n s m i t t a n c e s p e c t r u m o f gaseous B F 2 NH 2 i n the r e g i o n 750- 3700 c m - 1 . 198 7.3 Medium r e s o l u t i o n t r a n s m i t t a n c e s p e c t r u m o f the uz f u n d a m e n t a l o f gaseous B F 2 N H 2 . 202 7 .4 H i g h r e s o l u t i o n a b s o r b a n c e s p e c t r u m o f a p o r t i o n o f t h e P P b r a n c h s i d e o f the 2j band o f g aseous B F 2 NH 2 . 204 7.5 H i g h r e s o l u t i o n a b s o r b a n c e s p e c t r u m o f a p o r t i o n o f the P P b r a n c h s i d e o f the 2j band o f B F 2 N H 2 i n d i c a t i n g a s m a l l C o r i o l i s p e r t u r b a t i o n . 208 7 . 6 R e l a t i v e p o s i t i o n s o f the K 2 1 and p e r t u r b i n g l e v e l f o r v a l u e o f J . s t a c k s o f the a p a r t i c u l a r 223 x i i ACKNOWLEDGEMENT I w o u l d l i k e to thank my s u p e r v i s o r Dr. M.C.L. G e r r y f o r h i s g u i d a n c e , encouragement and a p p r o a c h a b i l i t y t h r o u g h o u t my time a t U.B.C . I w o u l d a l s o l i k e to thank Dr. W. L e w i s - B e v a n and Dr. N.P.C. Westwood f o r t h e i r many h e l p f u l d i s c u s s i o n s . F i n a l l y , I w o u l d l i k e t o thank my h u s b a n d James f o r h i s s u p p o r t and en c o u r a g e m e n t . 1 CHAPTER I: INTRODUCTION E v e r y m o l e c u l e p o s s e s s e s a u n i q u e s e t o f e n e r g y l e v e l s . T hese e n e r g y l e v e l s , a s s o c i a t e d w i t h the m o t i o n s o f t h e n u c l e i and e l e c t r o n s i n the m o l e c u l e , depend on su c h f a c t o r s as a t o m i c masses, i n t e r a t o m i c d i s t a n c e s , the e l e c t r o n d i s t r i b u t i o n and i n t e r p a r t i c l e f o r c e s . M o l e c u l a r s p e c t r o s c o p i c s t u d i e s examine the a b s o r p t i o n or e m i s s i o n o f e l e c t r o m a g n e t i c r a d i a t i o n a r i s i n g f r o m t r a n s i t i o n s between t h e s e e n e r g y l e v e l s . The f r e q u e n c y o f the r a d i a t i o n depends on the t y p e o f t r a n s i t i o n . Pure r o t a t i o n a l t r a n s i t i o n s , between l e v e l s i n the same e l e c t r o n i c and v i b r a t i o n a l s t a t e , u s u a l l y o c c u r i n t h e microwave r e g i o n w h i c h e x t e n d s from a p p r o x i m a t e l y 1 GHz to 1000 GHz, w h i l e i n f r a - r e d r a d i a t i o n i s u s u a l l y u s e d to d e t e r m i n e the f r e q u e n c y o f t r a n s i t i o n s between v i b r a t i o n a l s t a t e s . The r a p i d t e c h n o l o g i c a l a d v a n c e s a s s o c i a t e d w i t h the d e v e l o p m e n t o f r a d a r d u r i n g W o r l d War I I p r o v i d e d t h e i n s t r u m e n t a t i o n f o r s p e c t r o s c o p i c a l l y a n a l y z i n g m o l e c u l e s i 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 s p e c t r u m . S i n c e t h e n , the a v a i l a b l e f r e q u e n c y r a n g e has expanded and t h e s e n s i t i v i t y and r e s o l u t i o n have i m p r o v e d c o n s i d e r a b l y . I n s t e a d o f d o i n g l a b o r i o u s c a l c u l a t i o n s u s i n g e x p l i c i t e n e r g y f o r m u l a s , or u s i n g p e r t u r b a t i o n t h e o r y to a c c o u n t f o r c e n t r i f u g a l d i s t o r t i o n , q u a d r u p o l e c o u p l i n g o r o t h e r e f f e c t s , c omputers have a l l o w e d i n c r e a s i n g l y complex f o r m u l a t i o n s to be u s e d to a n a l y z e microwave s p e c t r a i n o r d e r to f i n d e x a c t s o l u t i o n s f o r t h e 2 e n e r g i e s a s s o c i a t e d w i t h r o t a t i o n a l m o t i o n . From t h e a n a l y s i s o f m i c r o w a v e s p e c t r a we c a n o b t a i n , i n a d d i t i o n to t h e r o t a t i o n a l c o n s t a n t s o f m o l e c u l e s , 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 , s t r u c t u r a l i n f o r m a t i o n and f o r c e f i e l d d e t e r m i n a t i o n s ( 1 ) . The s p e c t r o s c o p i c c o n s t a n t s o f the g r o u n d v i b r a t i o n a l s t a t e o f a m o l e c u l e o b t a i n e d f r o m m i c r o w a v e s p e c t r a c a n be u s e f u l when a s s i g n i n g r o t a t i o n a l s t r u c t u r e i n v i b r a t i o n a l t r a n s i t i o n s . N o t o n l y h a v e a l a r g e number o f g a s e o u s s t a b l e m o l e c u l e s b e e n i n v e s t i g a t e d u s i n g m i c r o w a v e s p e c t r o s c o p y , b u t a l s o t h e s p e c t r a o f many u n s t a b l e g a s e s h a v e b e e n a n a l y z e d , and more r e c e n t l y , g a s e o u s f r e e r a d i c a l s and m o l e c u l a r i o n s h a v e b e e n s t u d i e d s p e c t r o s c o p i c a l l y . The a p p l i c a t i o n s o f t e c h n i q u e s u s i n g m i c r o w a v e r a d i a t i o n a r e n u m e r o u s . F o r e x a m p l e , m i c r o w a v e - m i c r o w a v e d o u b l e r e s o n a n c e , i n v o l v i n g a s i m u l t a n e o u s i r r a d i a t i o n w i t h two f r e q u e n c i e s , i s u s e f u l i n a s s i g n i n g t r a n s i t i o n s i n c o m p l e x s p e c t r a , and i s a l s o u s e f u l i n s t u d y i n g m o l e c u l a r c o l l i s i o n p r o c e s s e s ( 2 ) . One e x t r e m e l y i n t e r e s t i n g use o f m i c r o w a v e s p e c t r o s c o p y i s t h e o b s e r v a t i o n o f s p e c t r a l l i n e s o f a v a r i e t y o f m o l e c u l a r f r e e r a d i c a l s , i o n s and s t a b l e m o l e c u l e s i n i n t e r s t e l l a r s p a c e ( 3 ) . I n f r a - r e d s p e c t r o s c o p y has l o n g b e e n u s e d as a t o o l f o r i n v e s t i g a t i n g t h e p h y s i c a l and c h e m i c a l p r o p e r t i e s o f m o l e c u l e s i n t h e g a s e o u s , l i q u i d and s o l i d p h a s e s . The i n f r a - r e d r e g i o n e x t e n d s f r o m a p p r o x i m a t e l y 2-50 fim. T r a n s i t i o n s o f g a s e o u s 3 m o l e c u l e s i n t h i s r e g i o n i n v o l v e s i m u l t a n e o u s changes i n r o t a t i o n a l and v i b r a t i o n a l quantum numbers, and a n a l y s e s o f t h e s e t r a n s i t i o n s p r o v i d e s p e c t r o s c o p i c c o n s t a n t s f o r b o t h the g r o u n d and e x c i t e d v i b r a t i o n a l l e v e l s , w h i l e t h e f r e q u e n c i e s o f the f u n d a m e n t a l v i b r a t i o n s can be u s e d i n f o r c e - f i e l d c a l c u l a t i o n s . D i s p e r s i v e t e c h n i q u e s , i n v o l v i n g the use o f a monochromator, have been s u p e r s e d e d f o r many a p p l i c a t i o n s by the t e c h n i q u e o f F o u r i e r - T r a n s f o r m I n f r a - R e d S p e c t r o s c o p y ( 4 ) . Such a p p l i c a t i o n s i n c l u d e the measurement o f e x t r e m e l y h i g h -r e s o l u t i o n s p e c t r a , t h e measurement o f weak bands and the s t u d y o f s h o r t - l i v e d s p e c i e s . T h i s t h e s i s r e p o r t s the s p e c t r o s c o p i c s t u d i e s o f some u n s t a b l e g a s e o u s m o l e c u l e s : b r o m i n e i s o c y a n a t e , i o d i n e i . s o c y a n a t e , b r o m i n e t h i o c y a n a t e and d i f l u o r o a m i n o b o r a n e . T h i s f o l l o w s a g e n e r a l theme t h a t has b een f o l l o w e d w i t h i n t h i s r e s e a r c h group i n r e c e n t y e a r s where s e v e r a l u n s t a b l e m o l e c u l e s have been s t u d i e d u s i n g b o t h microwave and i n f r a - r e d s p e c t r o s c o p y . Each o f the f o u r m o l e c u l e s i n v e s t i g a t e d i s s u f f i c i e n t l y u n s t a b l e t h a t i t was g e n e r a t e d and s t u d i e d i n a f l o w s y s t e m . The microwave s p e c t r a o f the f i r s t t h r e e m o l e c u l e s , BrNCO, INCO and BrSCN were a n a l y z e d i n o r d e r t o d e t e r m i n e t h e i r r o t a t i o n a l c o n s t a n 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 and 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 q u a d r u p o l a r n u c l e i i n the m o l e c u l e s , and to d e t e r m i n e some s t r u c t u r a l i n f o r m a t i o n . 4 Thes e m o l e c u l e s a l l b e l o n g to a c l a s s o f m o l e c u l e s known as the p s e u d o h a l i d e s , w h i c h have s i m i l a r c h e m i c a l p r o p e r t i e s to the h a l i d e s . O t h e r examples o f p s e u d o h a l i d e s a r e the a z i d e s , c y a n i d e s and c y a n a m i d e s . The s t r u c t u r e s o f many p s e u d o h a l i d e m o l e c u l e s have been s t u d i e d i n t h e gas phase u s i n g b o t h e l e c t r o n d i f f r a c t i o n and microwave s p e c t r o s c o p y ( 5 - 1 9 ) . Many i n t e r e s t i n g f e a t u r e s have been f o u n d . M o l e c u l e s c o n t a i n i n g the NCO group a r e e i t h e r c y a n a t e s or i s o c y a n a t e s d e p e n d i n g on whether the r e s t o f t h e m o l e c u l e i s l i n k e d v i a t h e oxygen or n i t r o g e n atom r e s p e c t i v e l y . The s t r u c t u r e s o f a l l t h e c y a n a t e m o l e c u l e s w h i c h have been s t u d i e d so f a r i n t h e gas phase , have been shown, w i t h one e x c e p t i o n , to be l i n k e d v i a the n i t r o g e n atom, and a r e t h e r e f o r e i s o c y a n a t e s (XNCO) ( 6 - 1 1 ) . O n l y F 5SeOCN has been d e m o n s t r a t e d to have a c y a n a t e s t r u c t u r e ( 1 2 ) . The X-N-C a n g l e i n the i s o c y a n a t e s i s f o u n d t o v a r y w i d e l y , d e p e n d i n g on t h e s u b s t i t u e n t X; f o r example i t i s e f f e c t i v e l y 180° i n t h e g r o u n d s t a t e o f S i H 3 N C 0 ( 6 ) , -124° i n HNCO (7) and -118° f o r C1NC0 ( 8 , 9 ) . U n t i l the s t r u c t u r e o f C1NC0 was d e t e r m i n e d , t h e -NCO c h a i n was assumed to be l i n e a r i n a l l i s o c y a n a t e m o l e c u l e s ; however i n C1NC0 i t was f o u n d t h a t i t i s i n f a c t n o n - l i n e a r , w i t h the 0 atom b e n t away from t h e N-C bond a x i s by -9° i n a t r a n s c o n f i g u r a t i o n to C l ( 8 , 1 0 ) . The 0 atom has s i n c e a l s o b e en shown to l i e s l i g h t l y o f f the N-C a x i s i n HNCO as w e l l as i n o t h e r i s o c y a n a t e m o l e c u l e s ( 7 , 1 1 ) . T hese s t r u c t u r a l v a r i a t i o n s a r e n o t u n i q u e . The i s o c y a n a t e 5 m o l e c u l e s a r e i s o e l e c t r o n i c w i t h t h e a z i d e m o l e c u l e s (XN 3) ( 1 3 , 1 4 ) . The a z i d e s e x h i b i t r a t h e r s i m i l a r s t r u c t u r a l t r e n d s , a l t h o u g h the X-N-N a n g l e s a r e somewhat s m a l l e r t h a n t h e c o r r e s p o n d i n g X-N-C a n g l e s o f t h e i s o c y a n a t e s ( e . g . i n C1N 3 i t i s - 109° ( 1 3 ) ) . T h e r e i s a l s o a s l i g h t t i l t o f the N-N-N group w i t h <(N-N-N)=171.9° i n C1N 3, a l m o s t i d e n t i c a l w i t h t h e NCO a n g l e i n C1NC0. The t h i o c y a n a t e s a r e a l s o a r a t h e r i n t e r e s t i n g group o f m o l e c u l e s . They c o n t a i n the -SCN group, w h i c h i s a m b i d e n t a t e , meaning t h a t i t c a n bond a t e i t h e r the N atom or the S atom to form b o t h i s o t h i o c y a n a t e s (XNCS) and t h i o c y a n a t e s (XSCN). T h e r e seems to be no p r i o r i n d i c a t i o n as to whether a m o l e c u l e has the i s o t h i o c y a n a t e o r t h i o c y a n a t e c o n f i g u r a t i o n , and i n f a c t , the m e t h y l d e r i v a t i v e has been f o u n d to e x i s t i n b o t h f o r m s : CH 3SCN and CH 3NCS ( 1 5 ) . The i s o t h i o c y a n a t e s , f o r example S i H 3 N C S (16) and t h e p a r e n t a c i d HNCS ( 1 7 ) , show t h e same t r e n d s i n the v a r i a t i o n o f t h e X-N-C a n g l e as do the i s o c y a n a t e s , a l t h o u g h on a v e r a g e t h e X-N-C a n g l e i s -7° w i d e r . On t h e o t h e r hand, the t h i o c y a n a t e s , f o r example NCSCN (18) and C1SCN (19) do n o t show s u c h t r e n d s and the X-S-C a n g l e i s -99° i n a l l c a s e s . Of the h a l o g e n p s e u d o h a l i d e s , the microwave s p e c t r a and t h e r e f o r e the gas phase s t r u c t u r e s o f the c h l o r i n e d e r i v a t i v e s have been a n a l y z e d , eg. C1NC0 ( 8 , 9 ) , C1SCN ( 1 9 ) , and C1N 3 ( 1 3 ) . However few o f t h e brom i n e and i o d i n e c o n t a i n i n g p s e u d o h a l i d e s have been examined s p e c t r o s c o p i c a l l y . T h i s may be p a r t l y due to t h e d i f f i c u l t y i n a n a l y z i n g t h 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 6 i n the microwave s p e c t r a o f s u c h m o l e c u l e s . Bromine and i o d i n e have l a r g e q u a d r u p o l e moments, and i n many c a s e s , t h i s c a u s e s the h y p e r f i n e s t r u c t u r e n o t to f o l l o w a s i m p l e f i r s t o r d e r p a t t e r n . T h i s makes t h e s p e c t r a o f m o l e c u l e s c o n t a i n i n g t h e s e atoms d i f f i c u l t to a n a l y z e . The microwave s p e c t r a o f BrNCO, INCO and BrSCN have n o t been i n v e s t i g a t e d p r i o r to the s t u d i e s r e p o r t e d h e r e . I n f a c t , l i t t l e i s known ab o u t t h e s e m o l e c u l e s i n t h e gaseous p h a s e . A l l t h r e e m o l e c u l e s were e x p e c t e d to show non f i r s t - o r d e r q u a d r u p o l e h y p e r f i n e s p l i t t i n g due to the h a l o g e n n u c l e i . However a computer programme had been w r i t t e n , w h i c h u s e s the e x a c t q u a d r u p o l e H a m i l t o n i a n , to s i m u l t a n e o u s l y e v a l u a t e the r o t a t i o n a l , c e n t r i f u g a l d i s t o r t i o n and 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 a m o l e c u l e ( 2 0 ) . T h i s was e x p e c t e d to a i d c o n s i d e r a b l y i n t h e a n a l y s i s o f the s p e c t r a o f t h e s e m o l e c u l e s . The i n f r a - r e d s p e c t r u m o f B F 2 N H 2 was examined i n the r e g i o n 3700-400 c m - 1 u s i n g F o u r i e r T r a n s f o r m i n f r a - r e d s p e c t r o s c o p y . B F 2 N H 2 b e l o n g s to the e x t e n s i v e group o f i n o r g a n i c m o l e c u l e s c o n t a i n i n g a b o r o n - n i t r o g e n bond. The p r o p e r t i e s o f t h e s e m o l e c u l e s a r e o f i n t e r e s t b e c a u s e t h e y a r e i s o e l e c t r o n i c w i t h h y d r o c a r b o n s c o n t a i n i n g a C-C l i n k a g e s u c h as a l k e n e s , a l k y n e s and b e n z e n e s . F o r example, b o r a z i n e , N 3 B 3 H 6 , w h i c h has a r i n g s t r u c t u r e , i s i s o e l e c t r o n i c w i t h b e n z e n e , and i n f a c t i t has been c a l l e d the ' i n o r g a n i c b e n z e n e ' ( 2 1 , 2 2 ) . The a m i n e b o r a n e s , e.g. R 3N:BR 3, a r e c o - o r d i n a t i o n compounds o f an amine w i t h a b o r a n e and a r e the B-N a n a l o g u e s o f the 7 a l k a n e s . They a r e , however, much l e s s s t a b l e t h a n t h e i r a l i p h a t i c c o u n t e r p a r t s b e c a u s e o f the n a t u r e o f the v e r y p o l a r d onor - a c c e p t o r b o n d i n g , and t h e y decompose e a s i l y to more s t a b l e compounds, w h i c h i n c l u d e a m i n o b o r a n e s . The a m i n o b o r a n e s , e.g. R 2N-BR 2, a r e i s o e l e c t r o n i c w i t h the a l k e n e s . W h i l e s t r u c t u r a l l y t h e y a r e f o u n d t o be p l a n a r , w i t h C 2 v symmetry l i k e t h e i r o r g a n i c a n a l o g u e s , the d o u b l e bond c h a r a c t e r o f t h e B-N bond i s c o n s i d e r a b l y l e s s t h a n i n the C=C bond i n e t h y l e n e , r e f l e c t i n g the d i f f e r e n t n a t u r e o f the b o n d i n g (23 - 2 5 ) . The 7r b o n d i n g i n the a m i n o b o r a n e s a r i s e s from the t r a n s f e r o f l o n e p a i r o f e l e c t r o n s f r o m t h e n i t r o g e n atom to the empty p o r b i t a l on t h e b o r o n . C o n s e q u e n t l y t h e s e m o l e c u l e s a r e c o n s i d e r a b l y l e s s s t a b l e t h a n the h y d r o c a r b o n s and have a t e n d e n c y to p o l y m e r i z e ( 2 6 ) . The p a r e n t compound, am i n o b o r a n e , BH 2NH 2, has been c h a r a c t e r i z e d i n t h e gas phase by microwave s p e c t r o s c o p y ( 2 3 ) , and more r e c e n t l y an e x t e n s i v e i n f r a - r e d s t u d y , w h i c h i s s t i l l i n p r o g r e s s , has been r e p o r t e d ( 2 7 ) . I t was t h e r e f o r e d e c i d e d to i n v e s t i g a t e t h e i n f r a - r e d s p e c t r u m o f B F 2 N H 2 to d e t e r m i n e the wavenumbers o f t h e f u n d a m e n t a l v i b r a t i o n s . A h i g h r e s o l u t i o n s t u d y o f t h e i / 2 f u n d a m e n t a l was a l s o c a r r i e d o u t . B i b l i o g r a p h y 1. W. Gordy, R.L. Cook, "Microwave M o l e c u l a r S p e c t r a , " 3 r d ed. i n " T e c h n i q u e s o f C h e m i s t r y " (A. W e i s s b e r g e r , E d . ) , V o l . 18, W i l e y , New Y o r k , 1984. 2. J.G. B a k e r , " M i c r o w a v e - M i c r o w a v e D o u b l e R e s o n a n c e , " pp. 65-122, i n "Modern A s p e c t s o f Mi c r o w a v e S p e c t r o s c o p y , "(G.W. C h a n t r y , E d . ) , Ac a d e m i c , London, 1979. 3. G. W i n n e w i s s e r , E. C h u r c h w e l l , C.M. Walmsley, " A s t r o p h y s i c s o f I n t e r s t e l l a r M o l e c u l e s " , pp. 313-503, i n "Modern A s p e c t s o f M i c r o w a v e S p e c t r o s c o p y " , (G.W. C h a n t r y , E d . ) , Ac a d e m i c , London, 1979. 4. P.R. G r i f f i t h s , " C h e m i c a l I n f r a r e d F o u r i e r T r a n s f o r m S p e c t r o s c o p y " , W i l e y , New Y o r k , 1975. 5. C. G l i d e w e l l , I n o r g . Chem. A c t a , 11, 257-282, ( 1 9 7 4 ) . 6. J.A. D u c k e t t , A.G. R o b i e t t e , M.C.L. G e r r y , J . M o l . S p e c t r o s c . 90., 374-393, ( 1 9 8 1 ) . 7. K. Yamada, J . M o l . S p e c t r o s c , 79., 323-344, ( 1 9 8 0 ) . 8. W.H. H o c k i n g , M.C.L. G e r r y , J . M o l . S p e c t r o s c . 42., 547-566, ( 1 9 7 2 ) . 9. W.H. H o c k i n g , M.L. W i l l i a m s , M.C.L. G e r r y , J . M o l . S p e c t r o s c . 58., 250- 260, ( 1 9 7 5 ) . 10. H. Oberhammer, Z. N a t u r f o r s c h , a2_6, 280 - 286, ( 1 9 7 1 ) . 11. H. Oberhammer, K. S e p p e l t , R. Mews, J . M o l . S t r u c t . 101. 325 - 331, (1983 ) . 12. K. S e p p e l t , H. Oberhammer, I n o r g . Chem. 2A, 1227-1229, (1985 ) . 13. R.L. Cook, M.C.L. G e r r y , J . Chem. Phys . 53., 2525 -2528, (1970) . 14. M. W i n n e w i s s e r , R.L. Cook, J . Chem. Phys. 4_1, 999- 1004, ( 1 9 6 4 ) . 15. R.G. L e t t , W.H. F l y g a r e , J . Chem. Phys. 47., 4730-4750, ( 1 9 6 7 ) . 16. D.R. J e n k i n s , R. Kewley, T.M. Sugden, T r a n s . F a r a d a y Soc. 58., 1284- 1290, ( 1962) . 9 17. K. Yamada, M. W i n n e w i s s e r , G. W i n n e w i s s e r , L.B. S z a l a n s k i , M.C.L. G e r r y , J . M o l . S p e c t r o s c . 7_9, 295 - 313, ( 1 9 8 0 ) . 18. L. P i e r c e , R. N e l s o n , C H . Thomas, J . Chem. Phys. 43, 3423-3431, ( 1 9 6 7 ) . 19. R . J . R i c h a r d s , R.W. D a v i s , M.C.L. G e r r y , J . Chem. Soc. Chem. Comm., 915-916, ( 1 9 8 0 ) . 20. M.C.L. G e r r y , W. L e w i s - Bevan, N.P.C. Westwood, J . Chem. Phys. 7_9, 4655-4663, ( 1 9 8 3 ) . 21. N. N i e d e n z u , J.W. Dawson, " B o r o n - N i t r o g e n Compounds", Ac a d e m i c P r e s s , New Yo r k , 1965. 22. E.L. M u e t t e r t i e s , "The C h e m i s t r y o f B o r o n and i t s Compounds", W i l e y , New Y o r k , 1967. 23. M. S u g i e , H. Takeo, C. Matsumura, Chem. Phys. L e t t . , 6U, 573-575, ( 1 9 7 4 ) . 24. F . J . L o v a s , D.R. J o h n s o n , J . Chem. Phys. 59., 2347 - 2353 (1973 ) . 25. F.B. C l i p p a r d , L.S. B a r t e l l , I n o r g . Chem., 9_, 2439 -2442, ( 1 9 7 0 ) . 26. S.Y. P u s a t c i o g l u , H.A. McGee, A.L. F r i c k e , J . C. H a s s l e r , J . A p p l . S c i . 21, 1561-1567, ( 1 9 7 7 ) . 27. M.C.L. G e r r y , W. L e w i s - B e v a n , A . J . M e r e r , N.P.C. Westwood, J . M o l . S p e c t r o s c , 110 . 153 - 163, (1985 ). 1 0 CHAPTER I I : THEORY 2 . 1 I n t r o d u c t i o n M a t h e m a t i c a l models d e s c r i b i n g t h e m o t i o n o f the e l e c t r o n s and n u c l e i i n a m o l e c u l e a r e u s e d f o r the a n a l y s i s o f m o l e c u l a r s p e c t r a . T h i s e n a b l e s us to f i n d s o l u t i o n s f o r t h e e n e r g y l e v e l s a s s o c i a t e d w i t h t h e s e m o t i o n s . The a s s i g n m e n t o f the quantum numbers i n v o l v e d i n the t r a n s i t i o n s between l e v e l s , and the d e r i v e d e n e r g y e x p r e s s i o n s f o r t h e s e l e v e l s , a l l o w v a r i o u s p a r a m e t e r s to be o b t a i n e d w h i c h c an be i n t e r p r e t e d i n terms o f m o l e c u l a r p r o p e r t i e s . A s s u m p t i o n s a r e o f t e n made t o s i m p l i f y t h e m a t h e m a t i c s . I n i n t e r p r e t i n g v i b r a t i o n a l and r o t a t i o n a l s p e c t r a i n p a r t i c u l a r , t h e e n e r g i e s a s s o c i a t e d w i t h the v i b r a t i o n a l and r o t a t i o n a l m o t i o n s a r e u s u a l l y much d i f f e r e n t i n m a g n i t u d e and c a n be t r e a t e d i n d e p e n d e n t l y . T h i s a l l o w s them t o be c a l c u l a t e d s e p a r a t e l y . The two b a s i c models a d o p t e d f o r v i b r a t i o n and r o t a t i o n a r e the h a r m o n i c o s c i l l a t o r and r i g i d r o t o r r e s p e c t i v e l y . These models, however, do n o t e x a c t l y r e p r o d u c e the r o t a t i o n a l and v i b r a t i o n a l e n e r g i e s , and c o r r e c t i o n s must be made to a l l o w f o r o t h e r f a c t o r s s u c h as a n h a r m o n i c i t y i n the c a s e o f v i b r a t i o n a l e n e r g i e s , and f o r n o n - r i g i d i t y o f bonds when c a l c u l a t i n g r o t a t i o n a l e n e r g i e s . Sometimes even the a s s u m p t i o n t h a t the v i b r a t i o n a l and r o t a t i o n a l e n e r g i e s c an be c a l c u l a t e d i n d e p e n d e n t l y b r e a k s down. I n a d d i t i o n , t r a n s i t i o n s may have 1 1 o b s e r v a b l e s p l i t t i n g s due t o f a c t o r s s u c h as n u c l e a r q u a d r u p o l e moments, or e x t e r n a l m a g n e t i c or e l e c t r i c f i e l d s . These f a c t o r s a l l r e q u i r e c o r r e c t i o n s to the H a m i l t o n i a n . Once the c o r r e c t model i s c h o s e n , a l e a s t - s q u a r e s f i t t i n g p r o c e d u r e i s u s e d to f i t the o b s e r v e d f r e q u e n c i e s , g i v i n g p a r a m e t e r s s u c h as v i b r a t i o n a l f r e q u e n c i e s , moments o f i n e r t i a and 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 . These s p e c t r o s c o p i c c o n s t a n t s can t h e n i n t u r n be u s e d to c a l c u l a t e m o l e c u l a r p r o p e r t i e s s u c h as s t r u c t u r e s , b o n d i n g c h a r a c t e r i s t i c s s u c h as e s t i m a t e s o f i o n i c or d o u b l e bond c h a r a c t e r , and d i p o l e moments. 2 . 2 The R i g i d R o t o r The c o a r s e f e a t u r e s o f the m o l e c u l e can be a c c o u n t e d f o r r e model. The H a m i l t o n i a n f o r t h i s p r i n c i p a l axes o f i n e r t i a o f the H = B J 2 + B J 2 + B J 2 r x x y y z z r o t a t i o n a l s p e c t r u m o f a a s o n a b l y w e l l by the r i g i d r o t o r model, r e f e r r e d to the m o l e c u l e , i s g i v e n by: ( 2 . 1 ) where J x , J y and J z a r e the components o f t h e r o t a t i o n a l a n g u l a r momentum a b o u t e a c h o f the p r i n c i p a l axes o f i n e r t i a . B x , B y and B z a r e t h e r o t a t i o n a l c o n s t a n t s o f the m o l e c u l e w h i c h a r e r e l a t e d to t h e p r i n c i p a l moments o f i n e r t i a by: B a = h a = x, y, z ( 2 . 2 ) 8 * 2 I a The n o n - z e r o m a t r i x e l e m e n t s o f t h i s H a m i l t o n i a n ( i n 12 f r e q u e n c y u n i t s ) a r e : <J,K,M|H r|J,K,M> = j-( B x+B y ) J (J + l ) + [ B z - £-( B x +B y ) ] K 2 (2.3) <J,K+2,M|H r|J,K,M> = f ( B x - B y ) { [ J ( J + 1 ) - K ( K + 1 ) ] X [ J ( J + l ) - ( K + l ) ( K + 2 ) ] } 1 / 2 (2.4) By c o n v e n t i o n , J z i s c h o s e n as the component o f the a n g u l a r momentum f o r w h i c h t h e r e e x i s t s i m u l t a n e o u s e i g e n s t a t e s w i t h J 2 . J i s t h e r o t a t i o n a l quantum number r e p r e s e n t i n g the t o t a l r o t a t i o n a l a n g u l a r momentum o f t h e m o l e c u l e , K i s the quantum number r e p r e s e n t i n g t h e component o f J a l o n g t h e p r i n c i p a l z-a x i s w i t h v a l u e s J , ( J - l ) (-J+1), - J , and the quantum number M g i v e s the component o f the t o t a l a n g u l a r momentum a l o n g the s p a c e - f i x e d Z a x i s . The p r i n c i p a l axes o f a m o l e c u l e a r e u s u a l l y l a b e l l e d a, b, and c w i t h I a < I b < I c . The a, b and c axes c an be i d e n t i f i e d w i t h the x, y and z a x i s a c c o r d i n g to v a r i o u s r e p r e s e n t a t i o n s . The t h r e e r i g h t - h a n d e d r e p r e s e n t a t i o n s a r e ( 8 ) : I r x - » b ; y - > c ; z - + a I I r x ->• c ; y ->• a ; z b I I I r x - > a ; y - > - b ; z - > - c (2.5) The I r r e p r e s e n t a t i o n i s the one most commonly u s e d . F o r some s p e c i a l t y p e s o f m o l e c u l e s , the H a m i l t o n i a n has d i a g o n a l m a t r i x e l e m e n t s o n l y , and s i m p l e e x p r e s s i o n s f o r the 13 r i g i d r o t o r e n e r g y can be d e r i v e d : (a) S p h e r i c a l Top: I f l = I b = I c E r - h B J ( J + l ) (2.6) (b) L i n e a r M o l e c u l e s : I b = I c ; I a = 0 E r = h B J ( J + l ) ( 2 . 7 ) ( c ) Symmetric Top : ( i ) p r o l a t e r o t o r s : ^ b ^ c ^ a E r = h [ B J ( J + l ) + ( A - B ) K 2 ] (2.8) ( i i ) o b l a t e r o t o r s : I =I.<I x ' a D c E r = h [ B J ( J + 1 ) + ( C - B ) K 2 ] (2.9) Most m o l e c u l e s , however, f a l l i n t o t h e c l a s s o f a s y m m e t r i c r o t o r s w i t h I a < I b < I c . F o r t h e s e m o l e c u l e s , the o f f - d i a g o n a l m a t r i x e l e m e n t s o f the H a m i l t o n i a n a r e n o n - z e r o . T h e r e a r e no e x p l i c i t 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 , e x c e p t a t low J , and the r e s u l t i n g s p e c t r a c an be q u i t e complex. The c o m p l e t e H a m i l t o n i a n must be d i a g o n a l i s e d i n o r d e r to d e t e r m i n e the e x a c t e n e r g y . T h i s p r o c e d u r e c a n be c o n s i d e r a b l y s i m p l i f i e d by f i r s t u s i n g the Wang t r a n s f o r m a t i o n (9) to i n t r o d u c e a new s e t o f b a s i s f u n c t i o n s : | J , 0 +> = |J,0> |J,K +> = [|J,K> + |J,-K>] (K>0) |J,K"> = T - i - [|J,K> - |J,-K>] (K>0) (2.10) 14 B e c a u s e t h e r e a r e no K+l terms to c o n n e c t odd and even K m a t r i x e l e m e n t s , and f o l l o w i n g the Wang t r a n s f o r m a t i o n t h e r e a r e no e l e m e n t s c o n n e c t i n g | J , K + > and | J,K"> t e r m s , t h e m a t r i x can be c o n v e r t e d t o f o u r s m a l l e r s u b m a t r i x e s d e s i g n a t e d E + , E", 0 + and 0". These s m a l l e r s u b m a t r i c e s a r e t h e n d i a g o n a l i s e d to f i n d t h e e n e r g i e s . W h i l e the m a t r i c e s a r e d i a g o n a l i n J , t h e y a r e non-d i a g o n a l i n K. K i s no l o n g e r a 'good' quantum number. The n o t a t i o n t h a t i s most commonly u s e d to d e s c r i b e the e n e r g y l e v e l s o f an a s y m m e t r i c r o t o r i s J K a , K c ( 8 ) , where K a r e p r e s e n t s t h e K quantum number i n t h e p r o l a t e s y m m e t r i c t o p l i m i t and K c i s t h e K quantum number i n the o b l a t e s y m m e t r i c top l i m i t . V a r i o u s p a r a m e t e r s can be u s e d as measures o f how c l o s e a m o l e c u l e i s to b e i n g a s y m m e t r i c t o p . One c o n v e n i e n t p a r a m e t e r i s Ray's asymmetry p a r a m e t e r K ( 1 0 ) : K = 2B-A-C (2.11) A-C The l i m i t i n g v a l u e s o f K are -1 and +1 c o r r e s p o n d i n g to p r o l a t e and o b l a t e s y m m e t r i c t o p s r e s p e c t i v e l y . A n o t h e r s u c h p a r a m e t e r i s Wang's asymmetry p a r a m e t e r b p (9) , where: b p = C - B w i t h -1 < bp < 0 (2.12) 2A-B-C bp = 0 i n t h e p r o l a t e l i m i t and b p = -1 i n the o b l a t e l i m i t . E x p r e s s i o n s f o r the e n e r g y l e v e l s o f an a s y m m e t r i c top have been d e r i v e d i n terms o f the asymmetry p a r a m e t e r s e.g.: = h{±-(B + C) J ( J + l ) [A-±-(B + C) ]W(b p) } 15 (2.13) W(b p) i s c a l l e d t h e r e d u c e d e n e r g y . I t i s u s u a l l y o b t a i n e d by d i a g o n a l i s i n g t h e H a m i l t o n i a n . F o r a n e a r s y m m e t r i c top i t can be e x p r e s s e d a p p r o x i m a t e l y as a power s e r i e s i n b p : W(b p) = K 2 + C.bp + C 2 b p 2 + (2.14) 2 . 3 R i g i d R o t o r S e l e c t i o n R u l e s R o t a t i o n a l t r a n s i t i o n s a r e i n d u c e d by the i n t e r a c t i o n o f the e l e c t r i c f i e l d component o f e l e c t r o m a g n e t i c r a d i a t i o n w i t h the permanent e l e c t r i c d i p o l e moment o f a m o l e c u l e . B e c a use the mic r o w a v e s a r e p l a n e p o l a r i s e d , w i t h the e l e c t r i c f i e l d E ( t ) a l o n g the sp a c e f i x e d Z a x i s , p e r p e n d i c u l a r to t h e i r d i r e c t i o n o f p r o p a g a t i o n , the r a d i a t i o n i n t e r a c t s w i t h the component o f the m o l e c u l a r d i p o l e moment a l o n g t h i s d i r e c t i o n : H ( t ) - -fi. E ( t ) = - M z E z ( t ) (2.15) F o r a t r a n s i t i o n t o be a l l o w e d , the m a t r i x e l e m e n t <J ' K ' M ' | fiz | J , K , M> must be n o n - z e r o . \iz i s r e l a t e d to t h e m o l e c u l e - f i x e d axes by d i r e c t i o n c o s i n e s ( < ^ z g ) : = g ^ z g g=a,b,c (2.16) In a s y m m e t r i c t o p , where t h e d i p o l e moment l i e s a l o n g the 16 d i r e c t i o n o f t h e symmetry a x i s , the f o l l o w i n g s e l e c t i o n r u l e s c a n be d e r i v e d : K>0; AJ = 0 , ±1 ; AK=0 ; AM=0 K=0; AJ = ±1 ; AK=0 ; AM=0 (2.17) A s y m m e t r i c r o t o r s e l e c t i o n r u l e s a r e more complex. The d i p o l e moment i s n o t n e c e s s a r i l y a l i g n e d a l o n g any o f the p r i n c i p a l axes o f i n e r t i a , and t h e r e f o r e t h e r e i s a p o s s i b i l i t y o f a.-, b- and c - t y p e t r a n s i t i o n s , d e p e n d i n g on whether the component o f the d i p o l e moment a l o n g e ach o f t h e s e axes i s non-z e r o . The e x p r e s s i o n : <j\r ' \<t>Ze \J,r> where r = K a - K c (2.18) must t r a n s f o r m a c c o r d i n g to the t o t a l l y s y m m e t r i c r e p r e s e n t a t i o n A i n t h e D 2 p o i n t group w h i c h i s the symmetry group o f the as y m m e t r i c r o t o r e i g e n f u n c t i o n s . The e i g e n f u n c t i o n s a r e c l a s s i f i e d a c c o r d i n g to one o f t h e symmetry s p e c i e s A , B a , B b , B 0 o f t h i s g r o u p . The s e l e c t i o n r u l e s a r e : AJ = 0, ±1 ; AM=0 K ' K ' K_ K „ a c a c a_-type na ^ 0 ee # eo oe oo b_-type uh ^ 0 ee * oo e o ** o e c_-type nc f 0 ee •»• oe oo **• eo 17 (2.19) e and o r e f e r t o the even or odd n a t u r e o f K and K a c 2 . 4 C e n t r i f u g a l D i s t o r t i o n W h i l e r i g i d r o t o r t h e o r y p r o v i d e s a r e a s o n a b l e a p p r o x i m a t i o n o f o b s e r v e d r o t a t i o n a l s p e c t r a , many d i s c r e p a n c i e s a r e o b s e r v e d between measured and c a l c u l a t e d f r e q u e n c i e s , p a r t i c u l a r l y f o r l i g h t e r m o l e c u l e s , and a t h i g h v a l u e s o f J and K. R e a l m o l e c u l e s a r e n o t r i g i d . F l e x i b l e bonds and a n g l e s r e s u l t i n c e n t r i f u g a l d i s t o r t i o n s i n m o l e c u l e s as t h e y r o t a t e . C o r r e c t i o n s t o the r i g i d - r o t o r H a m i l t o n i a n , w h i c h i n v o l v e h i g h e r o r d e r a n g u l a r momentum terms, must be made ( 1 1 ) . H d ~ f s Ta0is J« J / 3 J 7 Js a.fi.y.S, - x,y, z (2.20) The p a r a m e t e r s fa^ s can be d i r e c t l y i n t e r p r e t e d i n terms o f t h e i n v e r s e h a r m o n i c f o r c e c o n s t a n t s : 3 N - 6 3 N - 6 rap,s = 1 S S d l a p d l l 5 ( f 1 ) ^ a R i a R j (2.21) R A and R^  b e l o n g t o the s e t o f 3N-6 i n t e r n a l d i s p l a c e m e n t co-o r d i n a t e s w h i l e ( f _ 1 ) i j i s an el e m e n t o f the i n v e r s e f o r c e c o n s t a n t m a t r i x where a f o r c e c o n s t a n t i s d e f i n e d i n the h a r m o n i c p o t e n t i a l e n e r g y by: 18 V - f 2 f\ . R, R. (2.22) Symmetry r e s t r i c t i o n s and c ommutation r e l a t i o n s r e d u c e the number o f p o s s i b l e r ' s to 21. Many o f t h e s e a r e e q u i v a l e n t , w h i c h l e a v e o n l y 6 r ' s : r ' a a o , r ', . . , , r'„ „„„, r ' , r ' a a a a ' b b b b 1 c c c c ' a a b b 1 b b c c a n d ' ' a a c c ( 1 2 ) . H ' d = T 2 r ' a a ^ J „ 2 J / (2.23) a/8 However t h e s e 6 r ' s c a n n o t a l l be d e t e r m i n e d s i m u l t a n e o u s l y from e x p e r i m e n t a l d a t a ( 1 3 , 1 4 ) . Watson (15,16) has s o l v e d t h i s i n d e t e r m i n a c y p r o b l e m s t a r t i n g from the s t a n d a r d form o f the r o t a t i o n a l H a m i l t o n i a n as a power s e r i e s i n the components o f a n g u l a r momentum: H «. = S h ( J P J q J r + J r J q J p ) (2 24) r o t p q r ^ x y z x y 2 ' \ ^ • ' - ^ ) I n p r a c t i c e t h i s power s e r i e s c o n v e r g e s r a p i d l y . B e c a u s e o f v a r i o u s p h y s i c a l p r o p e r t i e s and symmetry c o n s i d e r a t i o n s o f the H a m i l t o n i a n , o n l y a c e r t a i n number o f terms o f e a c h d e g r e e a r e p o s s i b l e . Once a g a i n , f o r an a s y m m e t r i c r o t o r , t h i s means t h e r e w i l l be 6 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 4 t h d e g r e e . The i n d e t e r m i n a c y i s removed by f u r t h e r r e d u c i n g the number o f p a r a m e t e r s by a u n i t a r y t r a n s f o r m a t i o n o f t h e H a m i l t o n i a n . T h i s i s a n a l o g o u s to the r i g i d r o t o r p r o b l e m where a r o t a t i o n o f the axes d i a g o n a l i z e s the i n e r t i a t e n s o r . The number o f 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 i s 19 t h u s r e d u c e d to f i v e and a s m a l l v i b r a t i o n a l c o r r e c t i o n i s i n t r o d u c e d i n t o the r o t a t i o n a l c o n s t a n t s . T h e r e i s no u n i q u e r e d u c t i o n . However, t h e r e a r e two t h a t a r e commonly u s e d . I n c l u d i n g the 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 ( t e r m s i n t h e a n g u l a r momentum to the s i x t h d e g r e e ) t h e s e a r e The A r e d u c t i o n i s the most commonly u s e d r e d u c t i o n . The m a t r i x e l e m e n t s o f the H a m i l t o n i a n a r e a l l o f the form AK = 0, AK = ± 2 , thu s p r e s e r v i n g t h e same s t r u c t u r e o f t h e s u b m a t r i c e s as f o r a r i g i d a s y m m e t r i c t o p . I n f r e q u e n c y u n i t s : <J,K|H A|J,K> = |-( B + C ) J ( J + l ) + [A - i-(B + C ) ] K 2 - A J J 2 ( J + 1 ) 2 - A J K J ( J + 1 ) K 2 - A KK* + $ j J 3 ( J + l ) 3 + $ J K J 2 ( J + 1 ) 2 K 2 + $ K J J ( J + 1 ) K 4 (17) : ( i ) A s y m m e t r i c top (A) r e d u c t i o n + $ V K 6 (2.25) < J , K ± 2 | H A | J , K > = { f ( B - C ) - 5 a J ( J + l ) - f f i K [ ( K ± 2 ) 2 + K 2 ] + ^ J 2 ( J + 1 ) 2 + ^ J K J ( J + 1) [ ( K ± 2 ) 2 + K 2 ] + i - ^ K [ ( K ± 2 ) A + K * ] } { [ J ( J + 1 ) - K ( K ± 1 ) ] x [ J ( J + 1 ) - ( K ± l ) ( K ± 2 ) ] } 1 / 2 (2.26) The d i s a d v a n t a g e becomes i n d e t e r m i n a t e t h i s c a s e t h e S - r e d u c t o f t h i s r e d u c t i o n f o r an a c c i d e n t a l i o n i s u s e d . i s t h a t t h e c o n s t a n t n e a r - s y m m e t r i c t o p . In 20 ( i i ) Symmetric top (S) r e d u c t i o n I n t h e sym m e t r i c top r e d u c t i o n t h e r e i s no J z - dependence i n t h e o f f - d i a g o n a l m a t r i x e l e m e n t s . The r e s u l t i s t h a t the m a t r i x e l e m e n t s a r e o f the form AK=0, ± 2 , ± 4 , ± 6 . I n f r e q u e n c y u n i t s: <J,K|H S|J,K> = j-( B + C ) J ( J + l ) + [ A - j-( B + C ) ] K 2 - D j J 2 ( J + l ) 2 - D J K J ( J + 1 ) K 2 - D KK 4 - H j J 3 ( J + l ) 3 + H J K J 2 ( J + l ) 2 K 2 + H K j J ( J + 1 ) K A + H KK 6 (2.27) < J , K ± 2 | H s | J , K > = ( f ( B - C ) + d x J ( J + l ) + h 1 J 2 ( J + l ) 2 } x{ [ J ( J + l ) - K ( K ± 1 ) ] [ J ( J + l ) - ( K ± l ) ( K ± 2 ) ] } 1 / 2(2.28) < J , K ± 4 | H s |J,K> = ( d 2 + h 2 J ( J + l ) } { [ J ( J + l ) - K ( K ± 1 ) ] x [ J ( J + l ) - ( K ± l ) ( K ± 2 ) ] [ J ( J + 1 ) - ( K + 2 ) ( K + 3 ) ] x [ J ( J + l ) - ( K + 3 ) ( K + 4 ) ] }1I 2 (2.29) < J , K ± 6 | H s | J , K > = h 3 { [ J ( J + l ) - K ( K ± 1 ) [ J ( J + l ) - ( K ± l ) ( K ± 2 ) ] x [ J ( J + l ) - ( K ± 2 ) ( K ± 3 ) ] [ J ( J + l ) - ( K ± 3 ) ( K ± 4 ) ] x [ J ( J + l ) - ( K ± 4 ) ( K ± 5 ) ] [ J ( J + l ) - ( K ± 5 ) ( K ± 6 ) ] 1 1 2 (2.30) The d i s a d v a n t a g e o f t h i s r e d u c t i o n i s t h a t t h e d i a g o n a l i z a t i o n p r o c e d u r e t a k e s l o n g e r b e c a u s e o f the g r e a t e r number o f o f f - d i a g o n a l m a t r i x e l e m e n t s . I n a l l the s p e c t r o s c o p i c s t u d i e s r e p o r t e d i n t h i s t h e s i s , Watson's A-21 r e d u c t i o n i n t h e I r r e p r e s e n t a t i o n i s u s e d . I n many e a r l i e r p a p e r s the e f f e c t s o f d i s t o r t i o n a r e o f t e n r e p o r t e d i n terms o f the r ' s . However 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 f r o m Watson's A - r e d u c t i o n a r e s i m p l y r e l a t e d to the r ' s . I n the I r r e p r e s e n t a t i o n ( 1 6 , 1 8 ) : c c c c A J - " F " l ' ' b b b b + T ' A = — f r ' + r ' } - — IT' + T ' + T ' '\ U J K 8 1 ' b b b b ' c c o o ' 4 1 ' c c a a ' b b a a T b b c c ' A K = ~T~ ' 7 ' b b b b + T ' c c c c + 7 ' a a a a ' + T" { 7 " ' c c a a + T ' b b c c + r ' a a b b ) = " T T ^ ' b b b b " T ' c c c c ) « K = F ^ ' b b b b ( B - A ) / ( B - C ) + f r ' c c c c ( C - A ) / ( B - C ) + f ^ ' c c a a - ' ' b b a a + ^ ' b b c o ( 2 A - B - C ) / ( B - C ) } ' 9 9 9 T 1 = r a a b b + T b b c c + r c c a a T'2 = ( A / S ) r ' b b c c + ( B / S ) r ' a a c e + ( C / S ) r ' a a b b (S = A+B + C) (2.31) 2 . 5 S t r u c t u r a l Data In t h e gas phas e , s t r u c t u r e s o f m o l e c u l e s c a n be c a l c u l a t e d u s i n g b o t h e l e c t r o n d i f f r a c t i o n and microwave s p e c t r o s c o p y . The s t r u c t u r a l p a r a m e t e r s e x t r a c t e d from s u c h s t u d i e s a r e o f p a r t i c u l a r i m p o r t a n c e , as t h e y c an be c o n s i d e r e d f r e e o f i n t e r m o l e c u l a r f o r c e s . T r e n d s i n bond l e n g t h s and a n g l e s o v e r a s e r i e s o f s i m i l a r m o l e c u l e s g i v e i n s i g h t s i n t o t h e n a t u r e o f the c h e m i c a l bonds i n v o l v e d i n c o n n e c t i n g the atoms o f a m o l e c u l e . I n f o r m a t i o n may be d e r i v e d s u c h as i o n i c c h a r a c t e r and d o u b l e bond c h a r a c t e r . 22 S t r u c t u r a l i n f o r m a t i o n i s c o n t a i n e d i n t h e moments o f i n e r t i a c a l c u l a t e d f r o m the s p e c t r o s c o p i c r o t a t i o n a l c o n s t a n t s A, B and C ( s e e e q u a t i o n 2 . 2 ). The moments o f i n e r t i a a r e s i m p l y r e l a t e d to the masses o f the atoms i n a m o l e c u l e and t h e i r c o - o r d i n a t e s i n the p r i n c i p a l i n e r t i a l a x e s : I x x - S » i (7iZ + Z i 2 ) i I y y = S m, ( z , 2 + X i 2 ) i I z z - S m± ( x , 2 + Y i 2 ) (2.32) However, the a c c u r a c y o f the bond l e n g t h s and a n g l e s o b t a i n e d f r o m the moments o f i n e r t i a i s n o t as p r e c i s e as the u n c e r t a i n t i e s i n t h e r o t a t i o n a l c o n s t a n t s w o u l d s u g g e s t . T h i s i s b e c a u s e t h e d i m e n s i o n s o f a m o l e c u l e a r e a f f e c t e d by i t s z e r o p o i n t m o t i o n . T h e r e f o r e the moments o f i n e r t i a i n the g r o u n d s t a t e , o b t a i n e d by r o t a t i o n a l s p e c t r o s c o p y , a r e o n l y d i r e c t l y r e l e v a n t t o t h e g r o u n d v i b r a t i o n a l s t a t e s t r u c t u r a l p a r a m e t e r s . S e v e r a l d i f f e r e n t t y p e s o f s t r u c t u r e c an be c a l c u l a t e d from the a v a i l a b l e d a t a . The s t r u c t u r e t h a t w o u l d be the most i d e a l to d e t e r m i n e i s the e q u i l i b r i u m o r r e s t r u c t u r e , w h i c h i s t h e c o n f i g u r a t i o n o f the m o l e c u l e a t the minimum o f the v i b r a t i o n a l p o t e n t i a l s u r f a c e ; however i t s c a l c u l a t i o n r e q u i r e s a knowledge o f the r o t a t i o n a l c o n s t a n t s f o r enough i s o t o p e s i n a l l t h e e x c i t e d v i b r a t i o n a l s t a t e s , w h i c h a r e n o t known f o r many m o l e c u l e s . 23 The e f f e c t i v e s t r u c t u r e , r o , i s o b t a i n e d d i r e c t l y from the gr o u n d s t a t e s p e c t r o s c o p i c moments o f i n e r t i a v i a the moment o f i n e r t i a and f i r s t moment e q u a t i o n s . F o r a p l a n a r a s y m m e t r i c r o t o r t h e s e a r e : I„= = 2 m.b,2 I,. = S m. a, 2 I . = I,, a = S m, a,b. = 0 aa i l b b 1 1 ab b a i l l i i i S m ia i=0 £ m.b.=0 (2.33) i i O b v i o u s l y more i n f o r m a t i o n t h a n the moments o f i n e r t i a o f a s i n g l e i s o t o p i c s p e c i e s would be r e q u i r e d to c o m p l e t e l y d e t e r m i n e t h e s t r u c t u r e o f a m o l e c u l e . To be a b l e to s o l v e the above e q u a t i o n s f o r a l l s t r u c t u r a l p a r a m e t e r s , i s o t o p i c s u b s t i t u t i o n must be u s e d . These s t r u c t u r a l p a r a m e t e r s must be assumed to r e m a i n c o n s t a n t w i t h i s o t o p i c s u b s t i t u t i o n w h i c h i s no t a l w a y s a good a s s u m p t i o n , e s p e c i a l l y f o r l i g h t e r atoms. A common r e p r e s e n t a t i o n o f the s t r u c t u r e o f a m o l e c u l e i s the s u b s t i t u t i o n s t r u c t u r e , r s , w h i c h i s c a l c u l a t e d u s i n g e q u a t i o n s d e v e l o p e d by K r a i t c h m a n ( 1 9 ) . These e q u a t i o n s c a l c u l a t e t h e c o o r d i n a t e s o f ea c h atom i n a m o l e c u l e u s i n g the changes i n t h e moments o f i n e r t i a upon the i s o t o p i c s u b s t i t u t i o n o f the atom. C o s t a i n (20) has shown t h a t the r s s t r u c t u r e i s c l o s e r t o t h e r e s t r u c t u r e t h a n the r Q one i s , b e c a u s e some o f the g r o u n d - s t a t e v i b r a t i o n a l e f f e c t s have been a v e r a g e d o u t . The d i s a d v a n t a g e o f the r s s t r u c t u r e i s t h a t i s l a c k s a w e l l - d e f i n e d p h y s i c a l meaning. One s t r u c t u r e , however, t h a t can be r e a d i l y compared to e l e c t r o n d i f f r a c t i o n d a t a i s the ground-24 s t a t e a v e r a g e or r z s t r u c t u r e , w h i c h r e p r e s e n t s the a v e r a g e c o n f i g u r a t i o n o f the atoms. A knowledge o f the h a r m o n i c f o r c e c o n s t a n t s i s r e q u i r e d to c a l c u l a t e r z and t h e s e a r e n o t always a v a i l a b l e b e c a u s e t h e i r c a l c u l a t i o n r e q u i r e s v i b r a t i o n a l f r e q u e n c i e s , and o t h e r d a t a s u c h as 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 f o r more t h a n one i s o t o p i c s p e c i e s . I f an r z s t r u c t u r e i s o b t a i n e d t h e n i t may i n t u r n be u s e d to o b t a i n an a p p r o x i m a t i o n f o r the e q u i l i b r u m s t r u c t u r e ( 2 1 , 2 2 ) . An i m p o r t a n t p a r a m e t e r u s e d f o r t e s t i n g t h e p l a n a r i t y o f a m o l e c u l e i s the i n e r t i a l d e f e c t . A » I c ° " I a ° " I b ° (2.34) F o r a p l a n a r m o l e c u l e 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 , A would be z e r o . However, A i s u s u a l l y a s m a l l p o s i t i v e number, l a r g e l y b e c a u s e o f i n - p l a n e v i b r a t i o n a l e f f e c t s , b u t i t a l s o c o n t a i n s some c o n t r i b u t i o n f r o m o u t - o f p l a n e v i b r a t i o n a l e f f e c t s and e l e c t r o n i c and c e n t r i f u g a l e f f e c t s ( 2 3 ) . I n e r t i a l d e f e c t s can a l s o be u s e f u l i n o b t a i n i n g an e s t i m a t e o f a r o t a t i o n a l c o n s t a n t i n c a s e s when o n l y two o f them can be d e t e r m i n e d : eg. o n l y B and C a r e o r d i n a r i l y d e t e r m i n a b l e i f a m o l e c u l e e x h i b i t s a s t r o n g a^ -t y p e R b r a n c h s p e c t r u m o n l y . A knowledge o f A f r o m s i m i l a r m o l e c u l e s c o u l d be u s e d to e s t i m a t e a v a l u e o f A. H e r s c h b a c h and L a u r i e (24) have d e v e l o p e d a s i m p l e a p p r o x i m a t i o n f o r the r e l a t i o n s h i p between the i n e r t i a l d e f e c t 25 and t h e f r e q u e n c y o f the l o w e s t i n - p l a n e b e n d i n g v i b r a t i o n : A~ ^ (2.35) w i t h co i n cm" 1 and K = h / 8 7 r 2 . T h i s v i b r a t i o n a l f r e q u e n c y c o u l d a l s o be e s t i m a t e d f r o m the i n t e n s i t i e s o f v i b r a t i o n a l s a t e l l i t e s i f t h e e x c i t e d v i b r a t i o n a l s t a t e s a r e s u f f i c i e n t l y p o p u l a t e d a t t h e t e m p e r a t u r e o f the e x p e r i m e n t . 2.6 N u c l e a r S p i n S t a t i s t i c s A number o f m o l e c u l e s c o n t a i n two or more i d e n t i c a l n u c l e i , i . e . n u c l e i t h a t c a n be e x c h a n g e d by a r o t a t i o n o f the m o l e c u l e by l e s s t h a n 2n d e g r e e s a b o u t a symmetry a x i s , so t h a t the c o n f i g u r a t i o n i s i n d i s t i n g u i s h a b l e from the o r i g i n a l . F o r such an exchange o f n u c l e i the o v e r a l l w a v e - f u n c t i o n must e i t h e r r e m a i n u n c h a n g e d ( s y m m e t r i c ) or e l s e change s i g n o n l y ( a n t i s y m m e t r i c ) . F o r Bose p a r t i c l e s ( i n t e g r a l or z e r o s p i n ) the o v e r a l l wave f u n c t i o n s a r e s y m m e t r i c , w h i l e f o r F e r m i p a r t i c l e s ( h a l f - i n t e g r a l s p i n ) the o v e r a l l w a v e - f u n c t i o n s a r e a n t i s y m m e t r i c w i t h r e s p e c t to an o p e r a t i o n w h i c h e x c h a n g e s i d e n t i c a l p a r t i c l e s ( 2 5 ) . A s y m m e t r i c r o t o r s o f t e n c o n t a i n one o r more p a i r s o f i d e n t i c a l n u c l e i . F o r m o l e c u l e s w i t h one p a i r o f s u c h n u c l e i the r e l a t i v e w e i g h t o f the s y m m e t r i c to 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 i s (1 + 1) (21 + 1) : I ( 2 1 + 1) . F o r a m o l e c u l e i n i t s g round e l e c t r o n i c and v i b r a t i o n a l s t a t e ( s y m m e t r i c ) , the p a r i t y o f the 26 r o t a t i o n a l wave f u n c t i o n w i t h r e s p e c t to the symmetry a x i s i s i m p o r t a n t e.g. i f the symmetry a x i s i s the b - a x i s t h e r o t a t i o n a l wave f u n c t i o n s w i t h K a K c = ee or oo a r e sym m e t r i c w i t h r e s p e c t to the b - a x i s , w h i l e t h e f u n c t i o n s w i t h K a K c = eo or oe a r e a n t i s y m m e t r i c . T h e r e f o r e the r e l a t i v e i n t e n s i t i e s o f b - t y p e t r a n s i t i o n s o f a m o l e c u l e o b e y i n g Bose s t a t i s t i c s i s ee»oo: eo •oe - (21+1)(1+1):1(21+1) I f a m o l e c u l e has more t h a n one p a i r o f i d e n t i c a l n u c l e i the r e s u l t a n t s t a t i s t i c s and 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 a r e d e r i v e d by c o n s i d e r i n g t h e s i m u l t a n e o u s exchange o f e a ch p a i r . F o r example, f o r the s i m u l t a n e o u s exchange o f two p a i r s o f e q u i v a l e n t f e r m i o n s , t h e t o t a l w a v e f u n c t i o n i s s y m m e t r i c . 2.7 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 An i m p o r t a n t h y p e r f i n e i n t e r a c t i o n i n r o t a t i o n a l s p e c t r o s c o p y i s t h e i n t e r a c t i o n between t h e q u a d r u p o l e moment o f a n u c l e u s and t h e e l e c t r i c f i e l d g r a d i e n t a t t h e n u c l e u s due to the e l e c t r o n c h a r g e d i s t r i b u t i o n . A l l atoms w i t h a n u c l e a r s p i n g r e a t e r t h a n 1/2 have a q u a d r u p o l e moment. Because the e l e c t r i c f i e l d g r a d i e n t , and t h e r e f o r e t h e ma g n i t u d e o f the i n t e r a c t i o n , depends upon the r o t a t i o n a l s t a t e o f the m o l e c u l e , the i n t e r a c t i o n e f f e c t i v e l y c o u p l e s t h e r o t a t i o n a l a n g u l a r momentum and the n u c l e a r s p i n . The r e s u l t a n t new t o t a l a n g u l a r momentum i s d e s i g n a t e d F. 27 J + I = F (2.36) The r o t a t i o n a l e n e r g y l e v e l s a r e s p l i t i n t o components w h i c h have d i f f e r e n t v a l u e s o f F where F = J + I, J + I- l , . . . . | J - I | . The s p e c t r o s c o p i c c o n s e q u e n c e o f t h i s c o u p l i n g i s t h e h y p e r f i n e s p l i t t i n g o f a l l 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 t o t h e a d d i t i o n a l s e l e c t i o n r u l e s AF = 0, ± 1 . The most i n t e n s e h y p e r f i n e components a r e t h o s e w i t h AF = A J . The q u a d r u p o l e i n t e r a c t i o n a r i s e s from the s e c o n d non-v a n i s h i n g term i n the m u l t i p o l e e x p a n s i o n o f the e l e c t r o s t a t i c i n t e r a c t i o n between a n u c l e u s and the v a r i o u s e l e c t r o n s s u r r o u n d i n g i t . The q u a d r u p o l e H a m i l t o n i a n i s Q and VE a r e s e c o n d - r a n k t e n s o r s where Q i s the e l e c t r i c q u a d r u p o l e moment o p e r a t o r ( d e p e n d e n t on the n u c l e a r co-o r d i n a t e s ) and VE r e f e r s to the g r a d i e n t o f the e l e c t r i c f i e l d . The m a t r i x e l e m e n t s o f t h i s H a m i l t o n i a n a r e d i a g o n a l i n F b u t o f f - d i a g o n a l i n J and K. E x a c t q u a d r u p o l e e n e r g i e s must t h e r e f o r e be c a l c u l a t e d by d i a g o n a l i z i n g m a t r i c e s w i t h d i m e n s i o n s (2F+1)(2I+1) x (2F+1)(2I+1) w h i c h c a n r a p i d l y become l a r g e a t h i g h v a l u e s o f J . However, q u a d r u p o l e e n e r g i e s a r e i n g e n e r a l s m a l l compared to t h e o v e r a l l r o t a t i o n a l e n e r g y and a f i r s t - o r d e r a p p r o x i m a t i o n , d i a g o n a l i n J , a c c u r a t e l y p r e d i c t s most h y p e r f i n e Q VE (2.37) 2 8 s t r u c t u r e . I n t h i s c a s e t h e g e n e r a l i z e d e x p r e s s i o n f o r the f i e l d g r a d i e n t o p e r a t o r i s : V ( E i j ) - q a [§-(J± J d + J j JL ) - S±i J 2 ] i , j - X,Y,Z (2.38) J ( 2 J - 1 ) where q3 = <J,Mj = J | V E Z z |J,Mj =J> (2.39) qj i s t h e f i e l d g r a d i e n t c o u p l i n g c o n s t a n t . S i m i l a r l y : Q i j = eQ [f- ( I . I . + I . I . ) - 5 i d I 2 ] i , j = X,Y,Z (2.40) 1(21-1) where eQ = <I,M I=I|Q Z Z|I,M I=I> (2.41) Q i s d e f i n e d as the q u a d r u p o l e moment o f the n u c l e u s . A s i m p l i f i c a t i o n o f terms y i e l d s t h e more compact form o f the q u a d r u p o l e e n e r g y : E Q = eQq a [ f- C ( C + l ) - J ( J + l ) I ( 1 + 1) ] (2.42) 2 J ( 2 J - 1 ) I ( 2 I - 1 ) where C = F ( F + l ) - J ( J + l ) - 1 ( 1 + 1) (2.43) Because the q u a n t i t y q j i s d e f i n e d i n the s p a c e - f i x e d r e f e r e n c e s y s t e m , i t must be t r a n s f o r m e d i n t o a m o l e c u l e - f i x e d a x i s s y s t e m u s i n g t h e d i r e c t i o n c o s i n e s . The p r i n c i p a l i n e r t i a l axes a r e c h o s e n even t h o u g h i n g e n e r a l t h e y a r e n o t the p r i n c i p a l q u a d r u p o l a r a x e s . I n terms o f d i r e c t i o n c o s i n e s : 29 V E Z Z " 1 a a ^ a 2 + t l b b ^ b 2 + q c c ^ c 2 + 2 q a b ^ a ^ b + 2 ( l b c ^ b ^ c + 2 ( l a ^ Z a ^ c (2.44) The l a s t 3 terms make no c o n t r i b u t i o n to t h e f i r s t - o r d e r q u a d r u p o l e e n e r g y . U s i n g L a p l a c e ' s r e l a t i o n s h i p : X a a + 4 b + X c c - 0 ( X s s = e Q ( l S g > (2.45) w h i c h i n d i c a t e s t h a t o n l y two 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 ( X g g ) c a n be i n d e p e n d e n t l y d e t e r m i n e d , t o g e t h e r w i t h the e x p r e s s i o n : < J , r , M j = J | ^ Z g 2 | J , r , M j = J > = 2 <J,r | J g 2 | J , r > + 1 ( J + l ) ( 2 J + 3 ) (2J+3) (2.46) the f i r s t o r d e r q u a d r u p o l e e n e r g y may c o n v e n i e n t l y be e x p r e s s e d i n terms o f t h e r e d u c e d e n e r g y and x a a and X b b ' ^ c o • Eg = 3C(C+1) - 4 I ( I + 1 ) J ( J + 1 ) { [ 3 < J 2 > - J ( J + l ) ] x « 8 1 ( 2 1 - 1 ) J ( 2 J - 1 ) ( J + l ) ( 2 J + 3 ) + ( l / b p ) [ < J 2 > - W ( b p ) ] ( X b b - X c c ) ) (2.47) Once v a l u e s f o r Xaa , Xhb a n < ^ o have been o b t a i n e d , t h e y can be t r a n s f o r m e d i n t o the p r i n c i p a l q u a d r u p o l e axes s y s t e m to f i n d x z z . X y y and x x x • These q u a n t i t i e s c a n g i v e v a l u a b l e i n f o r m a t i o n a b o u t t h e n a t u r e o f t h e c h e m i c a l b o n d i n g i n a 3 0 m o l e c u l e e.g. c o v a l e n t or i o n i c c h a r a c t e r , or 7r b o n d i n g c h a r a c t e r . The a s s u m p t i o n t h a t o n l y the f i r s t - o r d e r q u a d r u p o l e e n e r g y i s s i g n i f i c a n t b r e a k s down f o r m o l e c u l e s t h a t have r e l a t i v e l y l a r g e q u a d r u p o l e e n e r g i e s , i n p a r t i c u l a r , b r o m i n e and i o d i n e c o n t a i n i n g m o l e c u l e s . I n t h i s c a s e , s e c o n d - o r d e r p e r t u r b a t i o n t h e o r y must a l s o be c o n s i d e r e d . The r e s u l t i n g c o r r e c t i o n terms a r e u s u a l l y v e r y s m a l l b u t t h e y may become a p p r e c i a b l e , p a r t i c u l a r l y i f n e a r - d e g e n e r a c i e s o f the c o r r e c t symmetry o c c u r ( s e e C h a p t e r I V ) . When a m o l e c u l e has more t h a n one q u a d r u p o l e c o u p l i n g n u c l e u s , t h e r e l a t i v e m a g n i t u d e s o f the c o u p l i n g due to each n u c l e u s d e t e r m i n e s the c o u p l i n g scheme ( 2 7 ) . F o r example, i f t h e r e a r e two n u c l e i w i t h s i m i l a r c o u p l i n g ; the c o u p l i n g scheme i s : 1 J + I 2 " I = F (2.48) A t o t a l n u c l e a r s p i n I i s f o r m e d by t h e c o u p l i n g o f I x and I 2 . I t h e n c o u p l e s to the r o t a t i o n a l a n g u l a r momentum J to g i v e a t o t a l a n g u l a r momentum F. A much s i m p l e r two n u c l e i c a s e i s where one n u c l e u s c o u p l e s much more s t r o n g l y t h a n the o t h e r . The c o u p l i n g scheme i s : 31 J + I F l * 1 + I, = F (2.49) The s t r o n g l y c o u p l i n g n u c l e u s I 1 c o u p l e s w i t h the r o t a t i o n a l a n g u l a r momentum J to form a r e s u l t a n t F X to w h i c h the s p i n o f the s e c o n d n u c l e u s I 2 c o u p l e s . The t o t a l r e s u l t a n t i s F. The a s s o c i a t e d quantum numbers a r e : F x = ( J + I1 ) , ( J + I x -1) , | J - I1 | and F - ( F x + I 2 ) , ( F x + I 2 - 1) |F, - I 2 | (2.50) I f H Q x r e p r e s e n t s the i n t e r a c t i o n o f 11 and J , and H Q 2 r e p r e s e n t s the H a m i l t o n i a n f o r the i n t e r a c t i o n o f I 2 and J , w i t h the sum o f t h e s e H a m i l t o n i a n s r e p r e s e n t i n g the o v e r a l l i n t e r a c t i o n , t h e n i n the f i r s t o r d e r a p p r o x i m a t i o n , H Q x has the same e i g e n v a l u e s as t h e H a m i l t o n i a n f o r a s i n g l e c o u p l i n g n u c l e u s ( e q u a t i o n 2.46), w h i l e H Q 2 i s t r e a t e d as a p e r t u r b a t i o n on H Q 1 . The o v e r a l l q u a d r u p o l e e n e r g y i s the sum o f the e n e r g i e s r e s u l t i n g from each H a m i l t o n i a n : E Q = <F,F 1 | H Q 1 ( I , , J ) + H Q 2 ( I 2 , J ) I F . F , > _ 3 A 0 ( A 0 + 1 ) - 4 I 1 ( I 1 + 1 ) J ( J + 1 ) { [ 3 < J a 2 > - J ( J + l ) ] X a a (1)+ 8 I 1 ( 2 I 1 - l ) J ( 2 J - l ) ( J + l ) ( 2 J + 3 ) a/bp) [ < J a 2 > - w ( b p ) H x b b ( D - x c c ( i ) } + 32 [3A1(A1+1)-4I2(I2+1)F1(F1+1)][3A2(A2+1)-4J(J+1)F1(F1+1)] x 16 I 2 ( 2 I 2 - 1 ) J ( J + 1) ( 2 J - 1 ) ( 2 J + 3 ) F , ( 2 F , - 1 ) ( F , + l ) ( 2 F , + 3 ) { [ 3 < J a 2 > - J ( J + l ) ] X a a ( 2 ) + ( l / b p ) [ < J a 2 > - W ( b p ) ] ( X b b ( 2 ) - X c c ( 2 ) ) } (2.51) A 0 = F1(F1 + 1 ) - I 1 ( I 1 + 1 ) - J ( J + 1) A, = F ( F + 1 ) - I 2 ( I 2 + l)-F1(F1 + 1) A 2 = 1,(1, + 1 ) - J ( J + 1)-F1(F1 + 1) (2.52) The r e s u l t i n g r o t a t i o n a l s p e c t r u m can become e x t r e m e l y c o m p l i c a t e d even i n t h i s s i m p l e s t c a s e . 2 . 8 S t a r k E f f e c t The S t a r k e f f e c t i s i n d u c e d when an e x t e r n a l e l e c t r i c f i e l d i n t e r a c t s w i t h t h e d i p o l e moment o f a m o l e c u l e . The i n t e r a c t i o n l i f t s or p a r t i a l l y l i f t s the d e g e n e r a c y i n M - t h e quantum number r e p r e s e n t i n g t h e component o f t h e t o t a l a n g u l a r momentum a l o n g the s p a c e - f i x e d Z a x i s . 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: Hs = -fi.E (2.53) fj, i s the permanent d i p o l e moment o f a m o l e c u l e , d e f i n e d i n terms o f the m o l e c u l e - f i x e d a x es, and E i s an e x t e r n a l e l e c t r i c f i e l d w h i c h i s k e p t c o n s t a n t i n m a g n i t u d e , and by c o n v e n t i o n l i e s a l o n g t h e d i r e c t i o n o f the s p a c e - f i x e d Z a x i s . I n terms o f 33 d i r e c t i o n c o s i n e s : H s = -E E M g ^ Z g g = x , y , z (2.54) g A l t h o u g h e x a c t S t a r k e n e r g i e s c a n be c a l c u l a t e d , t h e y a r e r e l a t i v e l y s m a l l , and p e r t u r b a t i o n t h e o r y i s g e n e r a l l y u s e d to c a l c u l a t e b o t h the f i r s t and s e c o n d o r d e r S t a r k e n e r g i e s w i t h s u f f i c i e n t a c c u r a c y to d e s c r i b e the i n t e r a c t i o n . I n t h e c a s e o f a s y m m e t r i c top m o l e c u l e t h e f i r s t o r d e r S t a r k e n e r g y i s E s< 1> = <J,K,Mj |HS |J,K,Mj > = -AtEKMj (2.55) J ( J + l ) The M d e g e n e r a c y i s c o m p l e t e l y l i f t e d and the e n e r g y i s l i n e a r i n t h e e l e c t r i c f i e l d s t r e n g t h . When K = 0 f o r a s y m m e t r i c t o p , the f i r s t o r d e r S t a r k e f f e c t becomes z e r o and t h e s e l i n e s e x h i b i t a s e c o n d o r d e r S t a r k e f f e c t o n l y , as do the t r a n s i t i o n s o f l i n e a r m o l e c u l e s i n 1 E s t a t e s . The s e c o n d o r d e r S t a r k e n e r g y i s g i v e n by: E s ( 2 > - u2E2 { [ ( J 2 - K 2 ) ( J 2 - M 2 ) / [ J 3 (2J + 1) ( 2 J - 1 ) ] 2hB - [ ( J + l ) 2 - K 2 ] [ ( J + l ) 2 - M 2 ] / [ ( J + l ) 3 ( 2 J + 1 ) ( 2 J + 3 ) ] } (2.56) The M - d e g e n e r a c y i s o n l y p a r t i a l l y l i f t e d and the e n e r g y i s q u a d r a t i c i n /zE. 34 When th e e l e c t r i c f i e l d i s p a r a l l e l to the d i r e c t i o n o f the e l e c t r i c v e c t o r o f t h e m i c r o w a v e s , the s e l e c t i o n r u l e i s AMj=0. The e x p r e s s i o n f o r the S t a r k e n e r g y o f an a s y m m e t r i c r o t o r i s much more c o m p l i c a t e d b e c a u s e o f the p o s s i b i l i t y o f components o f t h e d i p o l e moment a l o n g e a c h o f the p r i n c i p a l a x e s . G o l d e n and W i l s o n (28) have d e v e l o p e d the t h e o r y f o r the S t a r k e n e r g y o f an a s y m m e t r i c r o t o r . E x c e p t f o r the s p e c i a l c a s e o f a n e a r - d e g e n e r a c y , symmetry r e s t r i c t i o n s p r e c l u d e the p o s s i b i l i t y o f a f i r s t o r d e r S t a r k e f f e c t f o r a s y m m e t r i c r o t o r s ; the S t a r k e n e r g y i s s e c o n d o r d e r . The e n e r g y s h i f t f o r each component o f t h e d i p o l e i s ( E ( 2 M = a 2 E 2 ( J 2 - M 2 ) S | < J , r \ 4 , I J H , r ' > | 2 4 J 2 ( 4 J 2 - 1 ) E° - E ^ , JLl S | <J,r \<f,ZR \J,T>\Z 4 J 2 ( J + l ) : ' z g ' ( J + l ) 2 - M 2 S | <J,r\<j> | J + l , r ' > | 2 4 ( J + 1 ) 2 (2J + 1 ) ( 2 J + 3) T ' V ° . F ' J , T J + l , T (2.57) When the M de p e n d e n t and i n d e p e n d e n t terms a r e f a c t o r e d out a g e n e r a l e x p r e s s i o n i s : ( E g ( 2 ) ) J r M - 2 M g 2 E 2 [ A J > r + M 2 B J > T ] (2.58) A + C T h i s i s a s e c o n d o r d e r S t a r k e f f e c t 35 I n a s y m m e t r i c r o t o r s , n e a r - d e g e n e r a c i e s a r e q u i t e common; b o t h n e a r - s y m m e t r i c r o t o r d e g e n e r a c i e s and a c c i d e n t a l n e a r -d e g e n e r a c i e s o f v a r i o u s t y p e s can o c c u r . C o n s e q u e n t l y , u s i n g t h e Van V l e c k t r a n s f o r m a t i o n ( 2 9 ) , a 2 x 2 s u b m a t r i x i n v o l v i n g m a t r i x e l e m e n t s due o n l y to the two i n t e r a c t i n g l e v e l s needs to be d i a g o n a l i z e d to f i n d the S t a r k e n e r g y : H n - W H 1 2 H 1 2 H 2 2 -W = 0 (2.59) H j , and H 2 2 r e f e r to the two e n e r g i e s o f the d e g e n e r a t e or n e a r -d e g e n e r a t e l e v e l s : H = E (°) + E < 2 ) n i i D i i T ^ i i (2.60) where E A A ( 2 5 i s t h e s e c o n d - o r d e r c o n t r i b u t i o n o f the r e m a i n i n g n o n - d e g e n e r a t e l e v e l s . The o f f - d i a g o n a l term d i f f e r s f o r v a r i o u s k i n d s o f n e a r -d e g e n e r a c y . G o l d e n and W i l s o n (28) have g i v e n e x p r e s s i o n s f o r the v a r i o u s c a s e s . I f i t i s a n e a r - d e g e n e r a c y between the members o f an asymmetry d o u b l e t , t h e n the e x p r e s s i o n f o r H 1 2 i s |H 1 ; = |<J,r,M|H s | J , r 5 M>| - E 2 M |<J,r \<t>Zg \ J,r>\ (2.61) 4 J 2 ( J + l ) : where g = a o r c d e p e n d i n g on t h e symmetry o f the two l e v e l s 36 The dependence o f the e n e r g y on the e l e c t r i c f i e l d s t r e n g t h depends on t h e r e l a t i v e s i z e o f the d i f f e r e n c e i n e n e r g y between the two i n t e r a c t i n g l e v e l s compared to t h e m a g n i t u d e o f the o f f -d i a g o n a l e l e m e n t s . When the l e v e l s a r e v e r y c l o s e t o g e t h e r w i t h | H 1 2 | » | ( H 1 : L " H 2 2 ) I ' a f i r s t o r d e r S t a r k dependence i s i n t r o d u c e d : w = T < E J \ T + Ej°,r') ± ^ g E |M| <J,r | ^ Z g | J , r ' > ( 2 . 6 2 ) 2 J ( J + l ) T h i s i s a l i n e a r f u n c t i o n o f the e l e c t r i c f i e l d . When the two l e v e l s a r e r e a s o n a b l y f a r a p a r t w i t h | ( H 1 ; L - H 2 2 ) > > H 1 2 | , the e n e r g y e x p r e s s i o n r e d u c e s to the sec o n d -o r d e r e x p r e s s i o n . The S t a r k e f f e c t c a n be e x t r e m e l y u s e f u l i n a i d i n g the a s s i g n m e n t o f r o t a t i o n a l t r a n s i t i o n s . F o r example, the number of r e s o l v e d S t a r k l o b e s ( f o r low J l i n e s ) g i v e s t h e v a l u e o f the s m a l l e r o f t h e two J v a l u e s i n v o l v e d i n the t r a n s i t i o n . A l s o , t h e i n t e n s i t y p a t t e r n o f the S t a r k l o b e s d i f f e r s f o r Q and R b r a n c h e s , where the S t a r k l o b e i n t e n s i t y i n c r e a s e s w i t h M f o r re-b r a n c h l i n e s and d e c r e a s e s f o r R b r a n c h l i n e s . I n a d d i t i o n , t h e dependence on the f i e l d s t r e n g t h f o r any g i v e n t r a n s i t i o n c a n p r o v i d e c l u e s as to the a s s i g n m e n t o f t h i s t r a n s i t i o n . F o r example, f o r a p r o l a t e r o t o r , the S t a r k e f f e c t may be u s e d to d i s t i n g u i s h t r a n s i t i o n s w i t h i n an a.-type R b r a n c h group o f l i n e s h a v i n g the same v a l u e o f J . The K a = 0 3 7 t r a n s i t i o n w i l l have a t y p i c a l s e c o n d - o r d e r e f f e c t , w h i l e any d e g e n e r a t e or n e a r - d e g e n e r a t e asymmetry p a i r w i l l e x h i b i t a f i r s t o r d e r S t a r k e f f e c t and the S t a r k l o b e s w i l l move away from t h e u n s p l i t t r a n s i t i o n f r e q u e n c y v e r y r a p i d l y w i t h an i n c r e a s e i n f i e l d s t r e n g t h . Asymmetry p a i r s a t low K a, w h i c h have r e l a t i v e l y l a r g e asymmetry s p l i t t i n g s a l s o show a s e c o n d - o r d e r e f f e c t , a l t h o u g h i n g e n e r a l t h e y a r e m o d u l a t e d more q u i c k l y t h a n the K a = 0 t r a n s i t i o n . The most i m p o r t a n t c h e m i c a l a p p l i c a t i o n o f the S t a r k e f f e c t i s the measurement o f d i p o l e moments from t h e d i s p l a c e m e n t s o f t h e S t a r k components as a f u n c t i o n o f the f i e l d s t r e n g t h . The S t a r k e f f e c t i s a l s o i m p o r t a n t when m e a s u r i n g r o t a t i o n a l s p e c t r a . Z e r o - b a s e d square-wave S t a r k m o d u l a t i o n i s one o f the most commonly u s e d m o d u l a t i o n t e c h n i q u e s to improve s e n s i t i v i t y ( s e e S e c t i o n 3.1). 2 . 9 The Harmonic O s c i l l a t o r The v i b r a t i o n a l H a m i l t o n i a n i n terms o f the n o r m a l co-o r d i n a t e s i s : 3 N - 6 3 N - 6 H v 1 2 S P i2 + i - 2 A I Q I 2 (2.63) i =1 i = 1 where i s t h e n o r m a l c o - o r d i n a t e , P ± i s the momentum c o n j u g a t e to Q ± (P, = - i ^ ( 3 / 3 Q i ) ) , and A ± i s a c o n s t a n t r e l a t e d to the f r e q u e n c y vL (A, = 4?r2 v L 2 ) . 38 S u b s t i t u t i n g t h i s i n t o the quantum m e c h a n i c a l S c h r o e d i n g e r e q u a t i o n g i v e s : 3 N - 6 ziL2 S [ ( a 2 ^ v / 3 Q 2 ) + i - A. 2 Q. 2 V v - E v V v ] = 0 (2.64) 8?r2 i = i A s s u m i n g t h a t t h e m o l e c u l e i s a h a r m o n i c o s c i l l a t o r , t h e v i b r a t i o n s ( n o r m a l c o - o r d i n a t e s ) a r e i n d e p e n d e n t , so t h a t V v i - s j u s t t h e p r o d u c t o f the i n d i v i d u a l ^6(Q i) f o r t h e n o r m a l modes. 3 H - 6 V>v - n (Q. ) (2.65) and t h e o v e r a l l e n e r g y i s the sum o f the e n e r g i e s o f each o f the n o r m a l modes. 3 N - 6 E v = 2 E V ( Q ± ) (2.66) i =1 where E v (Q. ) = ( v ± + ^hco. v ± =0 , 1 , 2 . . . . (2.67) v, i s the v i b r a t i o n a l quantum number f o r the i t h n o r m a l mode and w4 i s the f u n d a m e n t a l f r e q u e n c y o f the i t h n o r m a l mode. The n o r m a l modes a r e numbered a c c o r d i n g to t h e i r symmetry p r o p e r t i e s . E ach o f the 3N-6 n o r m a l modes has the same symmetry p r o p e r t i e s as one o f the i r r e d u c i b l e r e p r e s e n t a t i o n s o f the p o i n t group to w h i c h t h e m o l e c u l e b e l o n g s . The l o w e s t numbers 39 a r e g i v e n to t h e n o r m a l modes w h i c h have t h e h i g h e s t symmetry, and f o r n o r m a l modes h a v i n g the same symmetry p r o p e r t i e s , the l o w e s t number goes to the v i b r a t i o n w i t h t h e h i g h e s t f r e q u e n c y . 2.10 V i b r a t i o n S e l e c t i o n R u l e s I f a v i b r a t i o n a l t r a n s i t i o n i s to o c c u r , a change i n the d i p o l e moment i n some d i r e c t i o n i s r e q u i r e d . The d i p o l e moment can be w r i t t e n i n terms o f i t s 3 s p a c e -f i x e d components: A* = ux + f i y + nz (2.68) C o n s i d e r i n g one o f t h e s e components o n l y (nF : F = X, Y, Z ) , i t s T a y l o r e x p r e s s i o n i n terms o f the n o r m a l c o - o r d i n a t e s i s : 3 N - 6 M F = /ip + S ( a r t F / a Q i ) 0 Q A + (2.69) i = 1 The t r a n s i t i o n moment m a t r i x e l e m e n t f o r t h i s component o f the d i p o l e moment i s : 3 N - 6 ( M F ) m n ~ <m|At F°|n> + S < m| (8fxF/dQi ) Q Q i | n> + .... (2.70) i = 1 The wave f u n c t i o n s c an be s e p a r a t e d i n t o t h e i r v i b r a t i o n a l and r o t a t i o n a l p a r t s and can be w r i t t e n i n terms o f i t s 4 0 components a l o n g t h e m o l e c u l e - f i x e d a x e s . 0 F ) m n = S = x , y , z { < V m l ^ g ° l V n > < r m I ^ F g l r n > + ? ( 3 A * 8 / a Q i ) 0 < v m I Q i | v n > < r m | ^ F g | r n > } (2.71) The f i r s t p a r t o f t h i s e x p r e s s i o n i s s t r i c t l y a p u r e o r o t a t i o n a l term b e c a u s e < v m | £ « g | v n > = 0 u n l e s s m = n ( i . e . no change i n v i b r a t i o n a l s t a t e ) . F o r t h e s e c o n d term to be n o n - z e r o , ( 3 y i i g / 3 Q i ) 0 must be non-z e r o ; t h e r e must be a change i n a t l e a s t one component o f the d i p o l e moment w i t h v i b r a t i o n . The e x p r e s s i o n < v m | Q i | v n > l e a d s to t h e s e l e c t i o n r u l e s f o r a h a r m o n i c o s c i l l a t o r : < v m i Q i i v n > = <^ r i^ r > < v - 2 m i ^ 2 n > - • - ^ i " 1 1 Q± i v - i n > . . . . . . < ^ N - 6 l ^ N - 6 > <i>im I Qi I V>in> = 0 u n l e s s A v i = ± l <V>jm | t f j n > = 5 m n /. A v . ( i ^ j ) = 0 (2.72) Each n o r m a l c o o r d i n a t e t h e r e f o r e a b s o r b s r a d i a t i o n i n d e p e n d e n t l y . The r o t a t i o n a l p a r t o f t h e e x p r e s s i o n g i v e s the same s e l e c t i o n r u l e s as f o r a pu r e r o t a t i o n a l p r o b l e m , e x c e p t t h a t i t i s t h e d i r e c t i o n o f (d/j.g/dQi)0 t h a t d e t e r m i n e s the a- , b_- or c_-t y p e s e l e c t i o n r u l e s . R e a l m o l e c u l e s a r e an h a r m o n i c o s c i l l a t o r s so t h a t the s t r i c t s e l e c t i o n r u l e s o f a h a r m o n i c o s c i l l a t o r b r e a k down. 41 O v e r t o n e s a r e a l l o w e d w i t h Av t = +1, +2, + 3 , each w i t h d i m i n i s h i n g i n t e n s i t y . O v e r t o n e s a r e n o t e x a c t m u l t i p l e s o f the f u n d a m e n t a l f r e q u e n c y b e c a u s e o f the a n h a r m o n i c i t y . C o m b i n a t i o n bands a r e a l s o a l l o w e d . These i n v o l v e the s i m u l t a n e o u s changes i n the v i b r a t i o n a l quantum numbers o f more t h a n one n o r m a l mode . 2 . 1 1 C o r i o l i s P e r t u r b a t i o n s W h i l e i n most c a s e s the r o t a t i o n and v i b r a t i o n terms i n the o v e r a l l r o t a t i o n - v i b r a t i o n H a m i l t o n i a n c an be c o n s i d e r e d s e p a r a t e l y , t h e s i t u a t i o n c a n a r i s e when a 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 term becomes s i g n i f i c a n t . T h i s i s the c a s e when t h e r e a r e d e g e n e r a t e modes o f v i b r a t i o n , or when two v i b r a t i o n a l l e v e l s h a v i n g the a p p r o p r i a t e symmetry a r e n e a r - d e g e n e r a t e . P e r t u r b a t i o n s i n t h e r o t a t i o n a l s t r u c t u r e a r e o b s e r v e d . The o v e r a l l r o t a t i o n - v i b r a t i o n H a m i l t o n i a n c a n be w r i t t e n : H " f HV+^Q 2 . ) + ( J x - P x ) 2 + ( J y " P y ) 2 + ( J Z - P z ) 2 ( 2 - 7 3 ) 2lT T h i s i s j u s t t h e sum o f a p u r e v i b r a t i o n a l term and a r o t a t i o n a l term. p a i s the component o f v i b r a t i o n a l a n g u l a r momentum a b o u t t h e a a x i s , and i n terms o f t h e n o r m a l c o o r d i n a t e s i s d e f i n e d by: 21. 21. = 2 2 r s > r ^ r , s L s r J (2.74) 42 The z e t a c o n s t a n t s (f™ g ) r e l a t e a p a i r o f n o r m a l c o o r d i n a t e s t h r o u g h r o t a t i o n a b o u t one o f t h e axes a, e.g.: N r ? > 8 = 2 ( 3 q x j / a Q r ) ( a q y j / a Q s ) - ( a q x j / a Q s ) ( a q y j / a Q r ) ( 2 . 7 5 ) j =1 The q a j a r e the mass w e i g h t e d C a r t e s i a n d i s p l a c e m e n t c o o r d i n a t e s o f atom j . The o v e r a l l H a m i l t o n i a n c a n be s e p a r a t e d i n t o a r i g i d r o t o r H a m i l t o n i a n , a h a r m o n i c o s c i l l a t o r H a m i l t o n i a n and a p e r t u r b a t i o n term. H = H R + H V + H ' ( 2 . 7 6 ) - P X J X " P y J y - P z J z + P x 2 + P y ' + P z " (2 . 77 ) ~hT ~TT 2l7 2I7 2T7 The p a 2 terms have no r o t a t i o n a l dependence and g e n e r a l l y make a v e r y s m a l l c o n t r i b u t i o n ; t h e r e f o r e i t i s the p a J a terms t h a t a r e r e s p o n s i b l e f o r t h e C o r i o l i s p e r t u r b a t i o n . J a and p a commute; J a o p e r a t e s o n l y on the r o t a t i o n a l wave f u n c t i o n s and p a o p e r a t e s o n l y on t h e v i b r a t i o n a l wave f u n c t i o n s . T h e r e f o r e the m a t r i x e l e m e n t s f o r t h e f i r s t t h r e e terms o f t h e p e r t u r b a t i o n H a m i l t o n i a n c a n be f a c t o r i z e d : < v ' , r ' | - ( p a J a ) / I a | v , r > - - d / I a ) < V | P a |v><r' I J a |r> ( 2 . 78 ) |v> and |r> a r e the v i b r a t i o n a l and r o t a t i o n a l wave f u n c t i o n s 43 r e s p e c t i v e l y . ( i ) V i b r a t i o n a l p a r t < v ' | p a | v > The v i b r a t i o n a l wave f u n c t i o n s a r e a s s u m e d to be s i m p l e p r o d u c t s o f t h e h a r m o n i c o s c i l l a t o r f u n c t i o n s i n t h e n o r m a l c o o r d i n a t e s . v a n d v ' must d i f f e r o n l y i n two o f t h e i r v i b r a t i o n a l q u a n t u m numbers (v a n d v ) . I n a d d i t i o n t h e s e two q u a n t u m numbers must v a r y o n l y by one u n i t b e t w e e n t h e two s t a t e s . T h i s g i v e s m a t r i x e l e m e n t s o f two t y p e s : (a ) < v r + l , v s | p a | v r , v s + l > (b) < v r + l , v s + l | p a | v r , v s > ( 2 . 7 9 ) O n l y t e r m s o f t y p e (a) a r e i m p o r t a n t s i n c e t h e y c o n n e c t l e v e l s w h i c h may h a v e s i m i l a r e n e r g y , w h i l e t e r m s o f t y p e (b) a r e o n l y l i k e l y to c o n n e c t l e v e l s w h i c h h a v e d i f f e r e n t e n e r g i e s . E v a l u a t i o n o f t e r m (a) g i v e s : < v E + l , v 8 | p a | v E , v 8 + l > - i h ri>s A r , s [ ( v r + l ) ( v B + l ) J 1 ' 2 ° r , s = [ < « r / « B ) 1 / 2 + ( " s / " r > W 2 1 ( 2 . 8 0 ) An i m p o r t a n t s p e c i a l c a s e r e l a t e s t h e f i r s t e x c i t e d s t a t e s o f 2 d i f f e r e n t n o r m a l modes : < i , o | P a | o , i > - - i h r ? > s n r > s ( v r = v s = o ) ( 2 . 8 1 ) 44 F o r m a t r i x e l e m e n t s o f p a to be n o n - z e r o t h e y must be t o t a l l y s y m m e t r i c . T h e r e f o r e <v r, v^ | v r , v s > must have the same symmetry as p a w h i c h has the symmetry p r o p e r t i e s o f a r o t a t i o n a b o u t t h e a a x i s ( R a ) . When t h i s c o n d i t i o n i s met f o r two v i b r a t i o n a l l e v e l s , and t h e e n e r g y l e v e l s a r e c l o s e i n e n e r g y , t h e n a n g u l a r momentum i s i n d u c e d a b o u t the a - a x i s . ( i i ) R o t a t i o n a l p a r t < r ' | J |r> The n o n - z e r o m a t r i x e l e m e n t s f o r the components o f the t o t a l a n g u l a r momentum a r e g i v e n by the s t a n d a r d f o r m u l a e , a s s u m i n g t h a t t h e m o l e c u l e i s a s y m m e t r i c t o p : < J , K | J z | J , K > = Kft < J , K | J x ± i J y | J , K ± 1 > = h[J(J+l)-K(K±1)]1'2 (2.82) These e q u a t i o n s a r e a good enough a p p r o x i m a t i o n when d e t e r m i n i n g t h e symmetry o f a C o r i o l i s p e r t u r b a t i o n i n a n e a r -s y m m e t r i c r o t o r . The p e r t u r b a t i o n has the symmetry o f a r o t a t i o n a bout one o f t h e axes ( R x , R y or R z ) . The symmetry s p e c i e s o f e a c h o f t h e s e i s d e t e r m i n e d by the p o i n t group to w h i c h the m o l e c u l e b e l o n g s . The symmetry s p e c i e s o f t h e p e r t u r b i n g mode i s e a s i l y d e t e r m i n e d f rom the r e l a t i o n s h i p : r ( v ) x r ( v - ) = r ( R a ) (2.83) 45 F o r a C o r i o l i s i n t e r a c t i o n i n d u c i n g a n g u l a r momentum about the z - a x i s , t h e s e l e c t i o n r u l e i s AK = 0, w h i l e AK = ± 1 f o r a n g u l a r momentum i n d u c e d a b o u t t h e x or y a x i s . AJ = 0 f o r a l l t h r e e c a s e s . 46 B i b 1 i o g r a p h y W. Gordy, R.L. Cook, "Microwave M o l e c u l a r S p e c t r a , " 3 r d . ed., i n " T e c h n i q u e s o f C h e m i s t r y " (A. W e i s s b e r g e r , E d . ) , V o l . 18, W i l e y , New Yo r k , 1984. 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 , " W i l e y , London, 1975 . J . E . 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 , " A c a d e m i c P r e s s , New Y o r k , 1967. C.H. Townes, 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 Yo r k , 1955. T.M. Sugden, C.N. Kenny, "Microwave S p e c t r o s c o p y o f Gas e s , " Van N o s t r a n d , London, 1965. G. H e r z b e r g , " I n f r a r e d and Raman S p e c t r a o f P o l y a t o m i c M o l e c u l e s . " , Van N o s t r a n d , New Y o r k , 1945. H. C. A l l e n , 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 , " W i l e y , New Yo r k , 1963. (1943) . Wang, Phys. Rev., 3_4, 243- 252, (1929) Ray, Z. P h y s i k , 78., 74- 91, (1983 ). W i l s o n , J.B. Howard. J . Chem. Phys., 4, 260-268, (1936) . 12. D. K i v e l s o n , E.B. W i l s o n , J . Chem. Phys., 20., 1575 - 1579, (1952) . 13. H. D r e i z l e r , G.Z. D e n d l , Z. N a t u r f o r s h , 20a. 30-37, (1 9 6 5 ) . 14. H. D r e i z l e r , H.D. R u d o l p h , Z. N a t u r f o r s h , 20a. 749-751, (1965) . 15. J.K.G. Watson, J . Chem. Phys. 46, 1935-1949, ( 1 9 6 7 ) . 16. J.K.G. Watson, J . Chem Phys. 48., 4517-4524, ( 1 9 6 8 ) . 17. J.K.G. Watson, " A s p e c t s o f Q u a r t i c and S e x t i c C e n t r i f u g a l E f f e c t s on R o t a t i o n a l E n e r g y L e v e l s " , 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 , J.R. D u r i g , Ed., V o l . 6, M a r c e l D ekker, New Y o r k , ( 1 9 7 7 ) . 8 . G . W 42, 9 . S . C 10 . B . S 11 . E . B 47 18. W. K i r c h h o f f , J . M o l . S p e c t r o s c , 41, 333-380, ( 1 9 7 2 ) . 19. J . K r a i t c h m a n , Am. J . Phys.. 21, 17-24, ( 1 9 5 3 ) . 20. C. C o s t a i n , J . Chem Phys., 29., 864-874, ( 1 9 5 8 ) . 21. K. K u c h i t s u , J . Chem. Phys., 49, 4456-4462, ( 1 9 6 8 ) . 22. K. K u c h i t s u , T. Fukuyama, Y. M o r i n o , J . M o l . S t r u c t . , 1., 463-479, ( 1 9 6 8 ) ; J M o l . S t r u c t . , 4, 41-50, ( 1 9 6 9 ) . 23. T. Oka, Y. M o r i n o , J . M o l . S p e c t r o s c , 6_, 472-482, ( 1 9 6 1 ) . 24. D.R. H e r s c h b a c h , V.W. L a u r i e , J . Chem. Phys. 40., 3142-3153, ( 1 9 6 4 ) . 25. E. B r i g h t W i l s o n , J r . , J . Chem. Phys., 3_, 276 - 285, ( 1 9 3 5 ) . 26. J.K. B r a g g , Phys. Rev., 7_5, 735 - 738, ( 1 9 4 9 ) . 27. J . B a r d e e n , C H . Townes , Phys. Rev. 7_3, 97- 105, ( 1 9 4 8 ) . 28. S. G o l d e n , E.B. W i l s o n , J . Chem. Phys., 16., 669 - 685, (1948) . 29. J.H. Van V l e c k , Phys. Rev. 3_3, 467 - 506, ( 1929). 30. I.M. M i l l s . , Pure and A p p l . Chem., 2, 325-344, ( 1 9 6 5 ) . 48 CHAPTER I I I : E X P E R I M E N T A L METHODS 3.1 The M i c r o w a v e S p e c t r o m e t e r M i c r o w a v e s p e c t r o m e t e r s have t h r e e b a s i c components. These a r e a s o u r c e o f microwave r a d i a t i o n , an a b s o r p t i o n c e l l w h i c h c o n t a i n s the gas b e i n g s t u d i e d and a l l o w s the m i c r o w a v e s to pass t h r o u g h i t , and a means t o d e t e c t and d i s p l a y the a b s o r p t i o n s i g n a l . The b a s i c d e s i g n o f the microwave s p e c t r o m e t e r u s e d to s t u d y t h e r o t a t i o n a l s p e c t r a o f BrNCO, INCO and BrSCN i s shown i n F i g u r e 3.1. In the microwave r e g i o n , s o u r c e s o f r a d i a t i o n a r e e l e c t r o n i c a l l y g e n e r a t e d and a r e t u n a b l e and e s s e n t i a l l y m o n o c h r o m a t i c . In the e a r l y days o f microwave t e c h n o l o g y r e f 1 e x - k l y s t r o n s were u s e d as s o u r c e s . O t h e r t u b e - t y p e s o u r c e s f o l l o w e d , s u c h as backward-wave o s c i l l a t o r s , w h i c h a l l o w e d f o r a w i d e r e l e c t r o n i c t u n i n g r a n g e . Nowadays, s o l i d s t a t e d e v i c e s , microwave f r e q u e n c y s y n t h e s i z e r s , may be u s e d . F o r a l l t h r e e m o l e c u l e s s t u d i e d i n t h e microwave r e g i o n , t h e f u n d a m e n t a l s o u r c e u s e d was a W a t k i n s J o h n s o n 1291A M icrowave S y n t h e s i z e r w h i c h o p e r a t e s between 8-18 GHz and a l l o w s s t e p s i z e s as s m a l l as 10 Hz. Measurements were r e f e r e n c e d to a c r y s t a l i n the s y n t h e s i s e r o f a c c u r a c y 1 i n 1 0 1 0 . H i g h e r f r e q u e n c i e s were o b t a i n e d by m u l t i p l y i n g the o u t p u t o f t h e s y n t h e s i z e r w i t h a H o n e y w e l l - S p a c e Kom 14-27 d o u b l e r and a T - K a l t r i p l e r to g i v e a t o t a l f r e q u e n c y r a n g e o f 8-54 GHz. To vacuum line DETECTOR S T A R K C E L L S a m p l e input _ J " ATTENUATOR P R E -A M P SQUARF.-WAVE GENERATOR L O C K - I N A M P L I F I E R SOURCE DSCILLOSCOPE CHART RECORDER F i g u r e 3.1 B l o c k d i a g r a m showing b a s i c d e s i g n o f microwave s p e c t r o m e t e r 50 The a b s o r p t i o n c e l l u s e d was a 6 - f t . H e w l e t t - P a c k a r d X-band S t a r k c e l l w h i c h was a t t a c h e d to a vacuum l i n e and s e a l e d a t e i t h e r end w i t h m i c a windows w h i c h a r e t r a n s p a r e n t to microwave r a d i a t i o n . Between t h e microwave s o u r c e and the c e l l t h e r e was an a t t e n u a t o r to p r e v e n t power s a t u r a t i o n . F o r f r e q u e n c y r a n g e s o t h e r t h a n X-band, the ends o f the c e l l were t a p e r e d a t e i t h e r end t o t h e c o r r e c t waveguide d i m e n s i o n s f o r the f r e q u e n c y . The d e t e c t o r s u s e d were d i o d e c r y s t a l r e c t i f i e r s . In t he microwave r e g i o n , a b s o r p t i o n c o e f f i c i e n t s a r e v e r y s m a l l , w i t h l e s s t h a n =0.1% o f t h e i n c i d e n t power b e i n g a b s o r b e d . Any a b s o r p t i o n s i g n a l s would t h e r e f o r e be swamped w i t h o u t some form o f m o d u l a t i o n , by s u c h f a c t o r s as v a r i a t i o n s i n t h e power o u t p u t o f the s o u r c e w i t h f r e q u e n c y , v a r i a t i o n s i n t r a n s m i s s i o n due t o r e f l e c t i o n s i n the wave g u i d e and t h e r m a l n o i s e i n the d e t e c t o r . A l t h o u g h s e v e r a l methods o f m o d u l a t i o n may be u s e d , S t a r k m o d u l a t i o n i s the most common one, and was u s e d i n a l l t h e work d e s c r i b e d i n t h i s t h e s i s . I t makes use o f the s h i f t i n the a b s o r p t i o n f r e q u e n c y upon a p p l i c a t i o n o f an e x t e r n a l e l e c t r i c f i e l d . A f l a t m e t a l s t r i p o r septum i s p l a c e d h a l f w a y between and p a r a l l e l to the b r o a d f a c e s o f t h e c e l l . I t i s h e l d i n p l a c e by s t r i p s o f t e f l o n w h i c h i n s u l a t e the septum from t h e r e s t o f the c e l l . A 0 - 2 0 0 0 v o l t z e r o - b a s e d square-wave v o l t a g e i s a p p l i e d b etween the septum and wave g u i d e , and b e c a u s e the a p p l i e d e l e c t r i c f i e l d i s p a r a l l e l to the e l e c t r i c v e c t o r o f the e l e c t r o m a g n e t i c r a d i a t i o n , o n l y t r a n s i t i o n s w i t h AM = 0 o c c u r 51 when t h e f i e l d i s on. T h i s e l e c t r i c f i e l d i s t u r n e d on and o f f a t a f r e q u e n c y o f 30 - 100 kHz above w h i c h m o d u l a t i o n b r o a d e n i n g ca n become a p r o b l e m . F o r t h e s p e c t r o m e t e r u s e d i n t h i s s t u d y a 100 kHz square-wave g e n e r a t o r was u s e d . The s i g n a l p a s s e s t h r o u g h a p r e - a m p l i f i e r to t h e l o c k - i n a m p l i f i e r . A r e f e r e n c e s i g n a l f r o m the square-wave g e n e r a t o r a l s o goes t o t h e l o c k - i n a m p l i f i e r , so t h a t o n l y t h o s e s i g n a l s w h i c h a r e o s c i l l a t i n g a t t h i s r e f e r e n c e f r e q u e n c y a t the c o r r e c t phase a r e s e l e c t e d . B a c k g r o u n d c h a r a c t e r i s t i c s a r e i g n o r e d ; the r a d i a t i o n i s m o d u l a t e d o n l y when a m o l e c u l a r r e s o n a n c e o c c u r s . The r e s u l t i n g s i g n a l d i s c r i m i n a t e s between a f i e l d - f r e e t r a n s i t i o n and i t s S t a r k components w h i c h a r i s e when the e l e c t r i c f i e l d i s on. The u n s p l i t t r a n s i t i o n and i t s S t a r k components a r e d i s p l a y e d 180° out o f phase w i t h each o t h e r . The s i g n a l was d i s p l a y e d on an o s c i l l o s c o p e o r , f o r a more permanent r e c o r d , i t was r e c o r d e d on c h a r t p a p e r u s i n g an X-Y c h a r t r e c o r d e r ; th e X component o f the t r a c e comes from a v o l t a g e ramp ou t o f the W a t k i n s - J o h n s o n s y n t h e s i z e r and the Y component comes from the l o c k - i n a m p l i f i e r . F r e q u e n c i e s were swept u s i n g the m i c r o p r o c e s s o r i n the W a t k i n s - J o h n s o n S y n t h e s i z e r . F o r the work on BrNCO and INCO the sweeps were c o n t r o l l e d u s i n g the f r o n t p a n e l c o n t r o l s o f the s y n t h e s i z e r , and a l l t h e t r a n s i t i o n f r e q u e n c i e s were measured by t r a c i n g e a c h i n d i v i d u a l l i n e o n t o p a p e r and i n t e r p o l a t i n g the f r e q u e n c y o f t h e c e n t r e o f the peak from f r e q u e n c y m a r k e r s p l a c e d on e i t h e r s i d e o f the peak. 52 I n t h e work on the microwave s p e c t r u m o f BrSCN, the W a t k i n s J o h n s o n F r e q u e n c y S y n t h e s i z e r was i n t e r f a c e d to a M i c r o PDP 11/23+ m i c r o c o m p u t e r v i a a G e n e r a l P u r p o s e I n t e r f a c e Bus (GPIB IEEE-488 1975 s t a n d a r d ) w h i c h c o n t r o l s the f u n c t i o n s o f the S y n t h e s i z e r . The computer i s i n t e r r u p t d r i v e n so t h a t d a t a a c q u i s i t i o n and the s t e p p i n g o f t h e f r e q u e n c y can t a k e p l a c e i n r e a l t i m e . The s i g n a l f r o m t h e o u t p u t o f t h e l o c k - i n a m p l i f i e r i s s h a r e d w i t h t h e o s c i l l o s c o p e , c h a r t r e c o r d e r , and the computer t h r o u g h an A/D c o n v e r t e r w h i c h i s c o n n e c t e d to a b u f f e r a m p l i f i e r . The o p e r a t i n g s y s t e m o f the m i c r o c o m p u t e r was RSX-11M and s o f t w a r e programmes have been w r i t t e n i n F o r t r a n - 7 7 and Macro-11 w h i c h s i g n a l a v e r a g e , o v e r s a m p l e , s t o r e and d i s p l a y t h e s i g n a l , and a i d the measurement o f t h e t r a n s i t i o n f r e q u e n c i e s . Each measured l i n e was r e c o r d e d u s i n g sweeps b o t h up and down i n f r e q u e n c y , and the a v e r a g e o f the two were t a k e n to remove the e f f e c t s o f d i f f e r e n t t i m e c o n s t a n t s i n t h e s y s t e m . The measurement a c c u r a c y f o r a l l t h e m easured t r a n s i t i o n s was ±0.03 MHz. 3 . 2 The FT -IR I n t e r f e r o m e t r i c S p e c t r o m e t e r A l t h o u g h t h e M i c h e l s o n I n t e r f e r o m e t e r was d e s i g n e d by M i c h e l s o n i n t h e l a t e n i n e t e e n t h c e n t u r y , i t has t a k e n the t e c h n o l o g i c a l a d v a n c e s o f more r e c e n t t i m e s , p a r t i c u l a r l y i n computer t e c h n o l o g y , f o r F o u r i e r t r a n s f o r m i n f r a - r e d 5 3 s p e c t r o s c o p y t o r e a c h i t s p o t e n t i a l as a h i g h - r e s o l u t i o n s p e c t r o s c o p i c t e c h n i q u e . The b a s i c i n t e r f e r o m e t e r d e s i g n i s shown i n F i g u r e 3.2. I t c o n s i s t s o f an i n f r a - r e d s o u r c e d i r e c t e d a t a b e a m s p l i t t e r which i s d e s i g n e d to t r a n s m i t 50% o f the i n c o m i n g r a d i a t i o n and r e f l e c t the r e s t . The b e a m s p l i t t e r i s commonly made from a f i l m o f germanium s u p p o r t e d on a s i n g l e c r y s t a l s u c h as KC1 or C s l . At l o w e r wavenumbers, u n s u p p o r t e d M y l a r o f d i f f e r e n t t h i c k n e s s e s c a n be u s e d . One o f the beams i s r e f l e c t e d b a c k to the b e a m s p l i t t e r from a s t a t i o n a r y m i r r o r , w h i l e the s e c o n d beam i s r e f l e c t e d b a c k from a moving m i r r o r . The two beams r e c o m b i n e c o n s t r u c t i v e l y or d e s t r u c t i v e l y a t the beam s p l i t t e r , d e p e n d i n g on the d i f f e r e n c e i n d i s t a n c e each beam has t r a v e l l e d to and from the moving and s t a t i c m i r r o r s . I f the i n c o m i n g r a d i a t i o n i s m o n o c h r o m a t i c , t h e n a s i n u s o i d a l p l o t o f i n t e n s i t y v e r s u s the o p t i c a l r e t a r d a t i o n ( t w i c e t h e d i s p l a c e m e n t o f t h e moving m i r r o r ) w i l l r e s u l t . When a b r o a d band r a d i a t i o n s o u r c e i s u s e d , the i n t e r f e r e n c e p a t t e r n s e e n a t the d e t e c t o r i s much more complex, b e i n g t h e sum o f the i n t e r f e r e n c e p a t t e r n s due to a l l w a v e l e n g t h s . T h i s i s c a l l e d an i n t e r f e r o g r a m . The i n t e n s i t y o f the d e t e c t o r s i g n a l i s g i v e n by: (3.1) where i s t h e i n t e n s i t y o f the s o u r c e as a f u n c t i o n o f 54 F i g u r e 3.2 S c h e m a t i c d e s i g n o f i n t e r f e r o m e t e r . 5 5 f r e q u e n c y v , and S i s the p a t h d i f f e r e n c e . One p a r t o f t h i s e q u a t i o n i s a c o n s t a n t ; the o t h e r i s a m o d u l a t e d component w h i c h i s i m p o r t a n t s p e c t r o s c o p i c a l l y . Thus t h e e q u a t i o n f o r t h e i n t e r f e r o g r a m i s g i v e n by: B (v) t a k e s i n t o a c c o u n t s u c h f a c t o r s as b e a m s p l i t t e r e f f i c i e n c y , d e t e c t o r r e s p o n s e and a m p l i f i e r c h a r a c t e r i s t i c s . E q u a t i o n (3.2) can be t r a n s f o r m e d m a t h e m a t i c a l l y to t h e more c o n v e n t i o n a l f o r m o f the s p e c t r u m by a F o u r i e r t r a n s f o r m a t i o n : T h i s e x p r e s s i o n i m p l i e s t h a t the m i r r o r must be moved an i n f i n i t e d i s t a n c e to o b t a i n the c o m p l e t e s p e c t r u m , and the F o u r i e r t r a n s f o r m i n v o l v e s a c o n t i n u o u s i n t e g r a t i o n o v e r the i n t e r f e r o g r a m f u n c t i o n . I n s t e a d , the s p e c t r u m i s a p p r o x i m a t e d by a summation o f a f i n i t e s e t o f d i s c r e t e p o i n t s m u l t i p l i e d by t h e c a l c u l a t e d c o s i n e v a l u e s p e r f o r m e d u s i n g a h i g h s p e e d computer. A l s o , b e c a u s e the m i r r o r o n l y moves a f i n i t e d i s t a n c e , the i n t e r f e r o g r a m i s e f f e c t i v e l y t r u n c a t e d (known as b o x c a r t r u n c a t i o n ) . The n e t r e s u l t i s the b r o a d e n i n g o f a l l the s p e c t r a l f e a t u r e s w h i c h a r e a c c o m p a n i e d by s i d e l o b e s , w h i c h ( 3 . 2 ) ( 3 . 3 ) 56 o s c i l l a t e w i t h d i m i n i s h i n g f r e q u e n c i e s away from t h e c e n t r a l f r e q u e n c y . T h i s e f f e c t i s c a l l e d r i n g i n g . Such b a s e l i n e i r r e g u l a r i t i e s c a n be r e d u c e d by u s i n g an a p o d i z a t i o n f u n c t i o n w h i c h s c a l e s t h e ends o f the i n t e r f e r o g r a m so t h a t i t goes s m o o t h l y to z e r o . A number o f d i f f e r e n t a p o d i z a t i o n f u n c t i o n s c a n be u s e d . However, w h i l e r e d u c i n g the r i n g i n g e f f e c t s , t h e y w i l l a l s o s e r v e t o r e d u c e the r e s o l u t i o n . W h i l e t h e c o a r s e s p e c t r a l f e a t u r e s come from p a r t s o f the i n t e r f e r o g r a m c l o s e to the c e n t r e b u r s t ( a t z e r o p a t h d i f f e r e n c e ) , t h e h i g h e r r e s o l u t i o n i n f o r m a t i o n comes f r o m t h e wings o f t h e i n t e r f e r o g r a m so t h a t the f u r t h e r t h e moving m i r r o r t r a v e l s , t h e h i g h e r the a t t a i n a b l e r e s o l u t i o n . T h e o r e t i c a l l y , t h e l i m i t o f r e s o l u t i o n f o r a s p e c t r o m e t e r i s : A(u) = l / 2 x c m - 1 ( 3 . 4 ) where x i s t h e maximum d i s p l a c e m e n t o f t h e m i r r o r . I n m e a s u r i n g a h i g h r e s o l u t i o n s p e c t r u m , i t i s e x t r e m e l y i m p o r t a n t t h a t t h e e x a c t p o s i t i o n o f t h e moving m i r r o r i s m o n i t o r e d . T h i s i s a c h i e v e d by p a s s i n g a s t a b i l i z e d He-Ne l a s e r beam t h r o u g h the c e n t r e o f the IR beam. B e i n g a m o n o c h r o m a t i c s o u r c e , the r e s u l t i n g s i n u s o i d a l i n t e r f e r o g r a m a l l o w s a p r e c i s e measurement o f t h e m i r r o r p o s i t i o n . T y p i c a l l y a b a c k g r o u n d s p e c t r u m i s t a k e n as w e l l as the sample s p e c t r u m , so t h a t the two c a n be r a t i o e d to g i v e the f a m i l i a r t r a n s m i t t a n c e s p e c t r u m . • 57 The a d v a n t a g e s o f FTIR o v e r the c o n v e n t i o n a l d i s p e r s i v e t e c h n i q u e a r e w e l l - k n o w n . The best-known i s F e l l g e t ' s a d v a n t a g e , or the m u l t i p l e x a d v a n t a g e , and a r i s e s b e c a u s e the i n t e r f e r o m e t e r d e t e c t s and measures a l l w a v e l e n g t h s s i m u l t a n e o u s l y r a t h e r t h a n s u c c e s s i v e l y as f o r d i s p e r s i v e s p e c t r o s c o p y . I t r e s u l t s i n much f a s t e r d a t a a c q u i s i t i o n i n FTIR, or a b e t t e r s i g n a l to n o i s e r a t i o f o r the same s o u r c e and d e t e c t o r o p e r a t i n g f o r the same measurement t i m e . The J a c q u i n o t or t h r o u g h p u t a d v a n t a g e r e f e r s to the amount o f e n e r g y r e a c h i n g t h e d e t e c t o r . I n a d i s p e r s i v e s p e c t r o m e t e r , the e n t r a n c e and e x i t s l i t s o f the monochromator, w h i c h must be v e r y n a r r o w f o r h i g h r e s o l u t i o n s p e c t r a , r e s t r i c t t h e amount o f l i g h t r e a c h i n g t h e d e t e c t o r . I n an i n t e r f e r o m e t r i c s y s t e m , the amount o f l i g h t r e a c h i n g the d e t e c t o r i s l i m i t e d s o l e l y by the e f f i c i e n c y o f t h e beam s p l i t t e r and the s i z e o f the s o u r c e a p e r t u r e , r e s u l t i n g i n a much g r e a t e r e f f i c i e n c y i n u t i l i z a t i o n o f the l i g h t s o u r c e . A t h i r d and v e r y i m p o r t a n t a d v a n t a g e i s Connes a d v a n t a g e w h i c h a r i s e s f r o m the use o f the He-Ne l a s e r t o r e f e r e n c e the p o s i t i o n o f t h e moving m i r r o r . The a c c u r a c y o f t h e f r e q u e n c y i s f a r s u p e r i o r to t h a t o f the d i s p e r s i v e i n s t r u m e n t . To measure t h e i n f r a - r e d s p e c t r u m o f B F 2 N H 2 , a Bomem DA3.002 i n t e r f e r o m e t r i c s p e c t r o p h o t o m e t e r was u s e d . S p e c t r a were r e c o r d e d between 400 and 3700 c m - 1 a t v a r y i n g r e s o l u t i o n s . The r a d i a t i o n s o u r c e was a G l o b a r w h i c h i s a b l a c k - b o d y c o n t i n u u m s o u r c e . A KC1 b e a m s p l i t t e r was u s e d down to 550 c m - 1 58 be l o w w h i c h a M y l a r b e a m s p l i t t e r was u s e d . The c e l l was a m u l t i p l e r e f l e c t i o n c e l l w h i c h was s e t t o g i v e a p a t h l e n g t h o f 8.25 m. Above 1900 c m - 1 a l i q u i d n i t r o g e n - c o o l e d InSb d e t e c t o r was u s e d , from 700-1800 c m - 1 a l i q u i d n i t r o g e n - c o o l e d HgCdTe d e t e c t o r was u s e d , w h i l e below 700 c m - 1 , the d e t e c t o r u s e d was a l i q u i d h e l i u m c o o l e d Ge:Cu d e t e c t o r . D i g i t a l and o p t i c a l f i l t e r s were u s e d to r e s t r i c t the a m p l i f i e r band w i d t h so t h a t o n l y t h e r a n g e o f i n t e r e s t was c o l l e c t e d . B o t h b a c k g r o u n d and sample s p e c t r a were r e c o r d e d , b o t h o f w h i c h were t r a n s f o r m e d and t h e n r a t i o e d t o g i v e a t r a n s m i t t a n c e s p e c t r u m w h i c h i n t u r n c o u l d be c o n v e r t e d to a b s o r b a n c e . Bibliography 59 1. 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 , " pp. 250-256, W i l e y , London, 1975. 2. T.M. Sugden, C.N. Kenny, "Microwave S p e c t r o s c o p y o f Gases," pp. 191-242, Van N o s t r a d , 1965. 3. W.D. P e r k i n s , J . Chem. Ed., 63., A5 - 10, ( 1 9 8 6 ) . 4. G. H o r l i c k , A p p l . S p e c t r o s c o p y , 22., 617 - 626, ( 1968 ). 5. P.R. G r i f f i t h s , " C h e m i c a l I n f r a r e d F o u r i e r T r a n s f o r m S p e c t r o s c o p y " , W i l e y , New Y o r k , 1975. 60 CHAPTER IV: THE MICROWAVE SPECTRUM OF BROMINE ISOCYANATE, BrNCO 4.1 I n t r o d u c t i o n Bromine i s o c y a n a t e , BrNCO, was f i r s t p r e p a r e d i n the gas phase by G o t t a r d i , i n the r e a c t i o n o f B r 2 v a p o u r w i t h s o l i d AgNCO a t 150°C ( 1 ) , and a l s o by the vacuum t h e r m o l y s i s o f t r i b r o m o i s o c y a n u r i c a c i d ( 2 ) . The i n f r a - r e d s p e c t r a o f BrNCO i n b o t h t h e s o l i d and gas phase have been r e p o r t e d ( 2 ) , as has the H e ( I ) p h o t o e l e c t r o n s p e c t r u m o f gaseous BrNCO ( 3 ) . No s t r u c t u r a l d a t a a r e a v a i l a b l e f o r BrNCO; however the s i m i l a r i t y o f the p h o t o e l e c t r o n s p e c t r a o f C1NC0 and BrNCO (3) makes i t l i k e l y t h a t t h e i r s t r u c t u r e s w i l l be s i m i l a r . Of the h a l o g e n i s o c y a n a t e s , o n l y C1NCO has p r e v i o u s l y been 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 ( 4 , 5 ) . The aim o f t h i s s t u d y was t h e r e f o r e to a n a l y s e the microwave s p e c t r u m o f BrNCO i n o r d e r to d e r i v e i t s r o t a t i o n a l and o t h e r s p e c t r o s c o p i c c o n s t a n t s , to deduce some s t r u c t u r a l i n f o r m a t i o n f r o m t h e s e cons t a n t s . 4.2 E x p e r i m e n t a l Methods BrNCO was p r e p a r e d i n a f l o w s y s t e m by p a s s i n g B r 2 v a p o u r o v e r h e a t e d s i l v e r c y a n a t e a t -150°C a t a p r e s s u r e o f =30 mTorr. AgNCO ( s ) + B r 2 ( g ) ->• BrNCO(g) + A g B r ( s ) (4.1) The AgNCO was p r e v i o u s l y p r e p a r e d by m i x i n g AgN0 3 and KNCO. 61 The r e s u l t i n g p r e c i p i t a t e was washed and t h e n d r i e d t h o r o u g h l y u n d e r vacuum a t 150°C f o r s e v e r a l h o u r s b e f o r e u s e . T h i s s t e p i s e x t r e m e l y i m p o r t a n t b e c a u s e BrNCO t e n d s t o h y d r o l y s e e a s i l y ( 2 ) . I n d e e d , l i n e s due to b o t h NH3 and HNCO, w h i c h a r e p r o d u c t s o f t h e h y d r o l y s i s o f BrNCO, were u s u a l l y o b s e r v e d b e f o r e the s p e c t r u m o f BrNCO s t a r t e d to a p p e a r . F o r o b s e r v a t i o n s o f the a_-type t r a n s i t i o n s , the c e l l was k e p t a t room t e m p e r a t u r e . However, to h e l p r e s o l v e t h e n i t r o g e n h y p e r f i n e s p l i t t i n g i n the b - t y p e l i n e s , t h e c e l l was c o o l e d s l i g h t l y u s i n g d r y i c e under the c e l l , a l t h o u g h c a r e had to be t a k e n n o t to c o o l the c e l l c o m p l e t e l y down to d r y i c e t e m p e r a t u r e b e c a u s e the BrNCO gas c o n d e n s e s . 4 . 3 I n i t i a l A s s i g n m e n t s T h e r e a r e two i s o t o p i c s p e c i e s o f b r o m i n e i n n a t u r a l a bundance: 7 9 B r and 8 1 B r . They a r e i n a p p r o x i m a t e l y e q u a l abundance; t h e s p e c t r a o f 7 9 B r N C 0 and 8 1 B r N C 0 t h e r e f o r e have a p p r o x i m a t e l y e q u a l i n t e n s i t i e s . I n i t i a l c a l c u l a t i o n 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 f b o t h i s o t o p e s were made u s i n g s t r u c t u r a l p a r a m e t e r s t r a n s f e r r e d from C1NC0 (4,5) and a s h o r t e n e d Br-N bond l e n g t h from BrNO ( 6 ) . Bromine 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 were e s t i m a t e d u s i n g 4p-o r b i t a l p o p u l a t i o n s from a CNDO c a l c u l a t i o n i n t h e e q u a t i o n s o f Townes and D a i l e y (7) ( s e e s e c t i o n 4 . 8 ) , and by a s s u m i n g t h a t t h e Br-N bond i s a p r i n c i p a l a x i s o f t h e Br q u a d r u p o l e t e n s o r . BrNCO was p r e d i c t e d to be a p l a n a r n e a r - s y m m e t r i c p r o l a t e 62 r o t o r h a v i n g b o t h a- and b - t y p e t r a n s i t i o n s . A p r e l i m i n a r y i n s p e c t i o n o f t h e s p e c t r u m showed o n l y a s e r i e s o f e q u a l l y s p a c e d g r o u p s o f l i n e s ( F i g u r e 4 . 1 ) . These a r e t h e a - t y p e R b r a n c h t r a n s i t i o n s w h i c h a r e s p a c e d by =(B+C). No b - t y p e l i n e s were e v i d e n t i n t h e s e e a r l y o b s e r v a t i o n s . W h i l e t h e s p e c t r a o f the two i s o t o p e s a r e o v e r l a p p e d , (B+C) f o r e ach i s o t o p e a r e s u f f i c i e n t l y d i f f e r e n t t h a t the c l u s t e r s o f l i n e s f o r e a c h c o u l d be e a s i l y d i s t i n g u i s h e d , w i t h t h o s e o f 8 1 B r N C 0 to l o w e r f r e q u e n c y . The s p e c t r u m was a d d i t i o n a l l y c o m p l i c a t e d by the p r e s e n c e o f l i n e s c o r r e s p o n d i n g to t r a n s i t i o n s w i t h i n e x c i t e d v i b r a t i o n a l s t a t e s o f the m o l e c u l e . Each t r a n s i t i o n was a l s o s p l i t i n t o a q u a r t e t s t r u c t u r e b e c a u s e o f t h e q u a d r u p o l e c o u p l i n g o f t h e b r o m i n e n u c l e u s (I = 3/2 f o r b o t h i s o t o p e s ) . No 1 k N (1=1) h y p e r f i n e s p l i t t i n g was o b s e r v e d f o r any o f t h e a - t y p e t r a n s i t i o n s . The f i r s t t r a n s i t i o n s to be a s s i g n e d were from the J = 6 «- 5 a.-type R b r a n c h , w h i c h i s shown i n F i g u r e 4.2. The asymmetry s p l i t K a = 1 t r a n s i t i o n s were e a s i l y d i s t i n g u i s h e d to the h i g h and low f r e q u e n c y s i d e s o f the main c l u s t e r o f l i n e s f o r b o t h the g r o u n d s t a t e , and f o r a t l e a s t two e x c i t e d v i b r a t i o n a l s t a t e s . The K a = 0 t r a n s i t i o n was i d e n t i f i e d by i t s d i s t i n c t i v e S t a r k e f f e c t ( s e e s e c t i o n 2 . 8 ) . K = 1 and K = 0 t r a n s i t i o n s f o r o t h e r v a l u e s o f J were a a s i m i l a r l y a s s i g n e d . The asymmetry s p l i t t i n g i s d e p e n d e n t on ( B - C ) ; t h e r e f o r e p r e l i m i n a r y v a l u e s o f B and C c o u l d be c a l c u l a t e d . F o r most t r a n s i t i o n s , the b r o m i n e h y p e r f i n e B r N C O 32.7 - 3 8 . 6 6 H z fa ifA/^n^ft n'>iHiKi«"yi><4tti.^ 4»lil > <m J 500 MHz HNCO J=8-7 J = 9-8 F i g u r e 4 . 1 Broadband s c a n o f the microwave s p e c t r u m o f BrNCO i n the f r e q u e n c y range 32.7-38.6 GHz. ' BrNCO J = 6 - 5 24.8 - 26.2 GHz v = 0 1 2 K Q = 1 K Q = 0 K Q = 1 8 1 B r N C 0 K Q = 1 K Q = 0 K Q = 1 7 9 B r N C O F i g u r e 4.2 J = 6 «- 5 a - t y p e R b r a n c h o f BrNCO i n t h e f r e q u e n c y range 24.8 - 26.2 GHz. K a = 0 and K = 1 t r a n s i t i o n s f o r b o t h i s o t o p e s i n the g r o u n d and two e x c i t e d v i b r a t i o n a l s t a t e s a r e i n d i c a t e d . ON •P-6 5 s p l i t t i n g p a t t e r n s were s y m m e t r i c q u a r t e t s as p r e d i c t e d from f i r s t - o r d e r t h e o r y . However, some t r a n s i t i o n s had anomalous s p l i t t i n g p a t t e r n s w h i c h c o u l d n o t i n i t i a l l y be e x p l a i n e d . The d e t e r m i n a t i o n o f an a c c u r a t e v a l u e o f A was a p r o b l e m . An a p p r o x i m a t e v a l u e o f A can sometimes be o b t a i n e d from a_-t y p e R b r a n c h e s a l o n e , f r o m the K a = 2 asymmetry s p l i t t i n g s . However, t h e s e s p l i t t i n g s were v e r y s m a l l f o r BrNCO ( ~ 2 0 MHz f o r J = 8 <- 7 f o r 8 1 B r N C O ) . They were a l s o d i f f i c u l t to a s s i g n u n a m b i g u o u s l y b e c a u s e o f t h e i r l a r g e p r e d i c t e d q u a d r u p o l e s p l i t t i n g s , and t h e y were d i f f i c u l t to measure b e c a u s e o f l i n e s h a p e d i s t o r t i o n by the S t a r k components. A c o u l d n o t be o b t a i n e d v i a t h i s r o u t e . A c a n u s u a l l y be d e t e r m i n e d by a s s i g n i n g b_-type t r a n s i t i o n s . However, t h e y were i m p o s s i b l e to a s s i g n a t t h i s s t a g e o f the s t u d y b e c a u s e t h e y were v e r y weak compared to the a^-type t r a n s i t i o n s . I n a d d i t i o n , t h e y had l a r g e p r e d i c t e d Br q u a d r u p o l e s p l i t t i n g , t h e s p e c t r a o f the two i s o t o p e s were o f e q u a l i n t e n s i t y , and t r a n s i t i o n s w i t h i n e x c i t e d v i b r a t i o n a l s t a t e s were p r e s e n t . I t was the a n o m a l i e s o f the h y p e r f i n e s t r u c t u r e o f the a.-t y p e t r a n s i t i o n s t h a t p r o v i d e d the r o u t e to an a c c u r a t e d e t e r m i n a t i o n o f A. 4 . 4 D e t e r m i n a t i o n o f A F o r m o l e c u l e s c o n t a i n i n g n u c l e i t h a t p r o d u c e r e l a t i v e l y l a r g e q u a d r u p o l e s p l i t t i n g s , s u c h as i o d i n e or b r o m i n e 66 c o n t a i n i n g m o l e c u l e s , th e f i r s t o r d e r a n a l y s i s o f the q u a d r u p o l e c o u p l i n g due to a s i n g l e n u c l e u s g i v e n i n s e c t i o n 2.7 i s u s u a l l y i n a d e q u a t e to d e s c r i b e the o b s e r v e d h y p e r f i n e s p l i t t i n g p a t t e r n s ( 8 ) . Sometimes, even m o l e c u l e s c o n t a i n i n g a n u c l e u s w i t h much s m a l l e 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 , s u c h as c h l o r i n e , have a s m a l l number o f t r a n s i t i o n s w h i c h do n o t f i t the p r e d i c t e d p a t t e r n ( 9 , 1 0 ) . I n t h i s c a s e , s e c o n d - o r d e r p e r t u r b a t i o n t h e o r y c o u l d be u s e d to g e t a c l o s e r a p p r o x i m a t i o n o f t h e a c t u a l q u a d r u p o l e e n e r g i e s . B e t t e r s t i l l , the c o m p l e t e q u a d r u p o l e H a m i l t o n i a n c o u l d be d i a g o n a l i z e d t o d e t e r m i n e th e e x a c t e n e r g i e s . I have d e v e l o p e d a p r o c e d u r e w h i c h u s e s non f i r s t - o r d e 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 to c a l c u l a t e an a c c u r a t e v a l u e o f the r o t a t i o n a l c o n s t a n t A s o l e l y f r o m a_-type R b r a n c h s p e c t r a . F o r p l a n a r m o l e c u l e s c o n t a i n i n g a s i n g l e q u a d r u p o l e n u c l e u s , the f i e l d g r a d i e n t t e n s o r can be w r i t t e n : V E Z Z = S a a ^ a + q b b b + q c o ^ I c + 2 c U b ^ Z a ^ Z b ( 4 - 2 ) The f i r s t 3 terms c o n t r i b u t e to f i r s t o r d e r and u s u a l l y a c c o u n t f o r most o f the h y p e r f i n e s t r u c t u r e . However the f o u r t h term, w h i c h c o n t r i b u t e s to h i g h e r o r d e r , may have a s i g n i f i c a n t e f f e c t . T h i s o c c u r s when x a b , the o f f d i a g o n a l term i n the q u a d r u p o l e t e n s o r , i s l a r g e . F o r x a b t 0 be l a r S e > t w o c o n d i t i o n s must be met. The f i r s t i s t h a t t h e q u a d r u p o l e moment o f th e q u a d r u p o l a r n u c l e u s s h o u l d be l a r g e , w h i c h i s t r u e f o r 67 b r o m i n e . The s e c o n d c o n d i t i o n i s t h a t t h e p r i n c i p a l q u a d r u p o l e axes s h o u l d be a t a l a r g e a n g l e t o t h e p r i n c i p a l i n e r t i a l a x e s . I n BrNCO the a n g l e between the z - a x i s o f the q u a d r u p o l e t e n s o r and t h e a - i n e r t i a l a x i s i s c a l c u l a t e d to be ~28° ( s e e s e c t i o n 4 . 7 ) . The e f f e c t o f a l a r g e x a b ^ s p a r t i c u l a r l y s i g n i f i c a n t , and can p r o d u c e r e l a t i v e l y l a r g e p e r t u r b a t i o n s i n t h e h y p e r f i n e s t r u c t u r e , when n e a r - d e g e n e r a c i e s o f t h e c o r r e c t t y p e o c c u r . The s e l e c t i o n r u l e s f o r t h e s e n e a r - d e g e n e r a c i e s f o r a p l a n a r m o l e c u l e l i k e BrNCO a r e AF=0; AJ=0, ± 1 , ±2 and K a K c = ee * oe or eo +• oo . S i n c e t h e s e n e a r - d e g e n e r a c i e s depend on a l l t h r e e r o t a t i o n a l c o n s t a n t s , and to a l e s s e r e x t e n t on 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 , d e v i a t i o n s from f i r s t - o r d e r h y p e r f i n e s t r u c t u r e can p r o v i d e e x t r a i n f o r m a t i o n on t h e s e c o n s t a n t s , as w e l l as on x a b• T h e r e f o r e i n p r i n c i p l e , i t s h o u l d be p o s s i b l e to use t h e s e p e r t u r b a t i o n s to d e t e r m i n e c o n s t a n t s t h a t would n o t o t h e r w i s e be d e t e r m i n a b l e f r o m the o b s e r v e d t r a n s i t i o n s . F o r example, i t s h o u l d be p o s s i b l e to e v a l u a t e A from a - t y p e R b r a n c h e s a l o n e f o r m o l e c u l e s where t h e r e a r e s e v e r a l n e a r -d e g e n e r a c i e s o f t h e c o r r e c t symmetry and a q u a d r u p o l a r n u c l e u s w i t h a l a r g e x a b• BrNCO would seem to be an i d e a l c a n d i d a t e . T h i s method has p r e v i o u s l y b een p r o p o s e d f o r t r a n s - 1 -bromopropene ( 1 0 ) ; and i n p r o p a d i e n o n e , an anomalous S t a r k e f f e c t , c a u s e d by n e a r - d e g e n e r a c i e s , gave A by an a n a l o g o u s method ( 1 2 ) . However, an e x a c t t r e a t m e n t had n o t b een c a r r i e d out b e f o r e . A computer programme has been w r i t t e n w h i c h does a 6 8 s i m u l t a n e o u s l e a s t - s q u a r e s f i t to the r o t a t i o n a l , c e n t r i f u g a l d i s t o r t i o n and 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 a m o l e c u l e c o n t a i n i n g a s i n g l e q u a d r u p o l a r n u c l e u s ( 9 ) . The m a t r i x e l e m e n t s f o r the q u a d r u p o l e H a m i l t o n i a n a r e t h o s e o f Benz e_t al_ ( 1 3 ) . The m a t r i x e l e m e n t s i n v o l v i n g the o f f - d i a g o n a l term xa^ are o f the form <J'K±l|H Q|J,K>; t h e r e f o r e , a f t e r the Wang t r a n s f o r m a t i o n , the m a t r i x can no l o n g e r be b r o k e n down i n t o 4 s m a l l e r s u b m a t r i c e s f o r a g i v e n v a l u e o f F. The c o m p l e t e m a t r i x has to be d i a g o n a l i z e d to f i n d the e n e r g i e s , w i t h e a c h m a t r i x b e i n g d i a g o n a l i n F and o f the o r d e r o f ( 2 F + 1 ) ( 2 1 + 1 ) . These m a t r i c e s r a p i d l y become l a r g e , and the f i t t i n g p r o c e d u r e r e q u i r e s a g r e a t d e a l o f c o m p u t i n g t i m e . C o n s e q u e n t l y , t h e s e g l o b a l l e a s t - s q u a r e s f i t s were done u s i n g the CRAY-1 V e c t o r Computer o f t h e A t m o s p h e r i c E n v i r o n m e n t S e r v i c e o f E n v i r o n m e n t C anada. 4 . 5 A n a l y s i s o f a - t v p e T r a n s i t i o n s V a l u e s f o r A Q and x a b w e r e e s t i m a t e d as d e s c r i b e d e a r l i e r . They were t h e n u s e d to p r e d i c t the h y p e r f i n e s p l i t t i n g p a t t e r n s o f some p e r t u r b e d t r a n s i t i o n s . A s s i g n m e n t s o f t r a n s i t i o n s were made on a t r i a l and e r r o r b a s i s ; and by an i t e r a t i v e p r o c e d u r e , v a l u e s o f the c o n s t a n t s from one f i t were u s e d to p r e d i c t the f r e q u e n c i e s o f more t r a n s i t i o n s , w h i c h were t h e n measured and i n c l u d e d i n t h e n e x t l e a s t s q u a r e s f i t to f u r t h e r r e f i n e the c o n s t a n t s . K = 0 and K = 1 l i n e s were measured f o r J = 3 to a a 13. V a l u e s o b t a i n e d f o r A„ and v . were w e l l - d e t e r m i n e d f o r o ^ a D 69 b o t h i s o t o p e s , and t h e y a r e e s s e n t i a l l y n o t c o r r e l a t e d w i t h each o t h e r o r w i t h any o t h e r c o n s t a n t ( s e e T a b l e 4 . 2 ) . The a c c u r a c y o f A Q w i t h i n one s t a n d a r d d e v i a t i o n i s l e s s t h a n 0.4 MHz. T h i s i s s e v e r a l o r d e r s o f m a g n i t u d e b e t t e r t h a n i s n o r m a l l y o b t a i n e d f o r m o l e c u l e s h a v i n g s p e c t r a w i t h a - t y p e R b r a n c h e s o n l y ( 1 4 ) . B, C, Aj , A j K , Sj, as w e l l as x a a and Xhh-Xcc f o r b r o m i n e were a l s o w e l l d e t e r m i n e d ( s e e T a b l e 4 . 1 ) . An e n e r g y l e v e l d i a g r a m f o r 8 1 B r N C 0 i s shown i n F i g u r e 4.3. I t shows two o f the c l o s e s t n e a r - d e g e n e r a c i e s w h i c h c a u s e p e r t u r b a t i o n s i n the h y p e r f i n e s t r u c t u r e . T hese a r e between 10 Q 1 0 and 9, 8 w h i c h a r e 426.34 MHz a p a r t and t h e 5 Q 5 and 3, 3 l e v e l s w h i c h a r e 844.13 MHz a p a r t . A n o t h e r s i g n i f i c a n t n e a r -d e g e n e r a c y i s between the 14, , 3 and 12 2 l e v e l s w h i c h a r e 2159.37 MHz a p a r t . These c a u s e the l a r g e s t s h i f t s i n f r e q u e n c y from a f i r s t o r d e r c a l c u l a t i o n ; however, much s m a l l e r s h i f t s can be d e t e c t e d f o r t r a n s i t i o n s i n v o l v i n g t h e 8 0 8 and 7, 6 l e v e l s , e v en t h o u g h t h e y a r e 6983 MHz a p a r t . I n f a c t , n o t one o f the m e asured K a = 0 t r a n s i t i o n s , w h i c h a r e p r e d i c t e d to a p p e a r as a d o u b l e t o f b a r e l y r e s o l v a b l e d o u b l e t s , was u n p e r t u r b e d . The s h i f t s i n f r e q u e n c y r a n g e from 0.5 MHz f o r 8 0 8 - 7 0 7 to 33 MHz f o r one o f the h y p e r f i n e components o f the 10 0 1 0 - 9„ g t r a n s i t i o n ( s e e F i g u r e s 4.4 & 4 . 5 ) . 4 . 6 b - t y p e T r a n s i t i o n s The c o n s t a n t s d e r i v e d from the a.-type l i n e s were u s e d to p r e d i c t the p o s i t i o n s o f some K a = 1 <- 0 b_-type t r a n s i t i o n s . 70 T a b l e 4.1 S p e c t r o s c o p i c c o n s t a n t s o f BrNCO from a - t y p e t r a n s i t i o n s P a r a m e t e r 7 9 B r N C O 8 1 B r N C 0 R o t a t i o n a l C o n s t a n t s (MHz) A D 4 1 1 8 8 . 7 1 ( 2 3 ) 1 41142.57(39) B Q 2175.6311(13) 215 9.5035(13) C D 2063.1025(11) 2048.4716(10) 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) L J K 1 172 0 1366(22) 72(16) 1692(29) 1 . 1258 (23 ) 171.00(12) 0.1690(26) Bromine 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 (MHz) X a a 608.16(48) 508.40(47) X b h - X c c 279.4(11) 230.8(11) Xab 549.85(11) 458.30(22) Number o f R o t a t i o n a l T r a n s i t i o n s 26 29 S t a n d a r d D e v i a t i o n o f f i t (MHz) 0.028 0.029 Numbers i n p a r e n t h e s e s a r e one s t a n d a r d d e v i a t i o n 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 . 71 T a b l e 4 . 2 C o r r e l a t i o n c o e f f i c i e n t s o f the s p e c t r o s c o p i c c o n s t a n t s o f BrNCO d e r i v e d from a_-type t r a n s i t i o n s o n l y 7 9 B r N C 0 A o 1 .00 B D 0 . 1 0 1 .00 C 0 - 0 . 1 3 - 0 . 7 3 1 .00 Aj - 0 . 0 3 0 . 4 8 0 . 1 5 1 .00 A j K 0 . 0 6 0 . 0 0 0 . 0 5 - 0 . 2 7 1 .00 Sj 0 . 1 1 0 .88 - 0 . 8 4 0 . 2 7 - 0 . 0 6 1 .00 X a a - 0 . 0 5 - 0 . 1 0 - 0 . 0 4 - 0 . 1 4 0 . 0 3 0 .02 1 .00 * b b - X c c ° - 2 6 ° - 2 5 - 0 . 2 9 0 . 0 1 0 . 0 1 0 . 2 3 - 0 . 1 9 1 .00 X a b 0 . 3 0 0 . 0 9 0 .16 0 . 0 5 - 0 . 0 3 - 0 . 1 1 - 0 . 2 8 - 0 . 1 6 1 .00 8 1BrNC0. A Q 1 .00 B Q 0 . 1 1 1 .00 C o - 0 . 0 5 - 0 . 7 0 1 .00 A j 0 . 0 7 0 . 5 7 0 . 0 8 1 .00 A j K 0 . 0 9 0 . 1 0 0 . 1 0 - 0 . 1 0 1 .00 Sj 0 . 0 9 0 . 8 8 - 0 . 7 9 0 . 4 4 - 0 . 0 5 1 .00 X a a - 0 . 1 3 - 0 . 1 3 - 0 . 0 1 - 0 . 1 4 - 0 . 0 3 - 0 . 0 5 1 .00 X b b - X c c ° - 2 6 ° - 2 6 - ° - 3 0 ° - 0 2 ° - 0 2 - 0 . 2 3 - 0 . 1 4 1 .00 X a b - 0 . 8 8 - 0 . 1 1 0 . 1 0 - 0 . 0 5 - 0 . 0 6 - 0 . 1 1 - 0 . 1 2 - 0 . 1 6 1 .00 72 3 0 0 12 0,12 "11 1 , 1 0 -1 I 1.11 •8 2,6 2,7 11 0.11 :K>!:I90 .72,5 ' 2,6 N X o >-o LU LU 2 0 0 -10o. 10 '0,9 8 426.34 MHz Ql.B •'1,9 8 17 71,6 ' 17 •2,4 >2.5 32,4 . / 2,2 2,3 J 2,2 92.0 - Z-2,1 0,8 100 -0 J 7o; 6o.( 5o.. 3o. 2o. 1o, 844.13 MHz T A ; 0 0 , o g1.5 16 5!-1,4 1.5 / 1.3 A 1,4 J1,3 -,1,1 ^1,2 11.0 1 1.1 F i g u r e 4.3 R o t a t i o n a l e n e r g y n e a r - d e g e n e r a c i e s l e v e l s o f 8 1 B r N C 0 . a r e i n d i c a t e d . Two i m p o r t a n t .100 0 -100 J K Q K C 11O.II-N X >-o U J 2 : u W •100 > cr 0 --100 -10 o.io--23/2 -21/2 OBS. •25/2 -19/2 S/2-17/2 25/2-23/2 exact 21/2 19/2 -21/2 -19/2 -17/2 "23/2 10 MHz CA 1st order (i) (ii) (iii) (a) 462200 MHz (b) F i g u r e 4 . 4 The e n e r g y l e v e l s o f the 11( l l 10 0 , 1 0 t r a n s i t i o n s o f 8 1 B r N C 0 . (a) The energy l e v e l s : ( i ) the h y p o t h e t i c a l u n s p l i t r o t a t i o n a l e n e r g i e s ; ( i i ) p r e d i c t e d f i r s t - o r d e r bromine q u a d r u p o l e e n e r g y l e v e l s ; ( i i i ) bromine q u a d r u p o l e e n e r g y l e v e l s d e r i v e d f r o m the e x a c t H a m i l t o n i a n , (b) The o b s e r v e d t r a n s i t i o n s compared w i t h the c a l c u l a t e d f i r s t - o r d e r and e x a c t p a t t e r n s . CO Ka=0 Calculated first order split t ing pattern Examples of some perturbed Ka=0 transitions ! I 46216 4 MHz t 42052.7 MHz F i g u r e 4.5 H y p e r f i n e s p l i t t i n g p a t t e r n s o f some K a = 0 t r a n s i t i o n s o f 8 1 B r N C 0 . * 75 T h e s e l i n e s were much weaker t h a n the a_-type l i n e s and c o u l d n o t i n i t i a l l y be a s s i g n e d . A l l the t r a n s i t i o n s were f o u n d w i t h i n 1 MHz o f t h e i r p r e d i c t e d f r e q u e n c i e s . Thus, the v a l u e o f A 0 was c o n f i r m e d . B o t h R and Q b r a n c h l i n e s were measured f o r J up to 2 0 . 1 4 A l l t h e b - t y p e l i n e s showed N q u a d r u p o l e s p l i t t i n g . An example i s g i v e n i n F i g u r e 4 . 6 . The e f f e c t o f t h e n i t r o g e n q u a d r u p o l e s p l i t t i n g had to be s u b t r a c t e d f r o m t h e s e t r a n s i t i o n s b e f o r e t h e b r o m 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 and t h e o t h e r s p e c t r o s c o p i c c o n s t a n t s c o u l d be f u r t h e r r e f i n e d . T h i s was done u s i n g a programme w h i c h f i t s the c o u p l i n g c o n s t a n t s o f two q u a d r u p o l a r n u c l e i . The c o u p l i n g scheme u s e d was ( J + I B r = F,; Fj_ + I N = F) . T h i s i s a good a p p r o x i m a t i o n f o r BrNCO, b e c a u s e the n i t r o g e n 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 much s m a l l e r t h a n t h o s e f o r b r o m i n e . The programme f i t s to the d i f f e r e n c e s b e tween f r e q u e n c i e s o f the h y p e r f i n e components o f the same t r a n s i t i o n . Xaa and X b b ' X c c f ° r t n e n i t r o g e n n u c l e u s were d e t e r m i n e d by i n c l u d i n g i n the f i t o n l y t h e s p l i t t i n g s o f l i n e s h a v i n g t h e same v a l u e o f F, b u t d i f f e r e n t v a l u e s o f F. These s p l i t t i n g s a r e i n d e p e n d e n t o f the b r o m 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 , w h i c h were h e l d c o n s t a n t i n the f i t . The 1 4 N 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 f o r b o t h i s o t o p e s a r e i n c l u d e d i n T a b l e s 4 .3 and 4 . 4 . The e f f e c t o f the n i t r o g e n q u a d r u p o l e c o u p l i n g was s u b t r a c t e d from the b - t y p e t r a n s i t i o n s . A l l the t r a n s i t i o n s , b o t h a and b_-type, were t h e n i n c l u d e d i n a g l o b a l l e a s t - s q u a r e s f i t to 7 9 B r N C O 17i/i6-17o,i7 F i g u r e 4.6 The 17 x 1 6 - 17 0 1 7 t r a n s i t i o n s o f 7 9 B r N C 0 showing b o t h 7 B B r and 1 4N n u c l e a r q u a d r u p o l e e f f e c t s . ON 77 d e t e r m i n e t h e f i n a l r o t a t i o n a l , c e n t r i f u g a l d i s t o r t i o n and b r o m 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 . These a r e shown i n T a b l e 4.3 f o r 7 9 B r N C 0 and T a b l e 4.4 f o r 8 1 B r N C 0 , a l o n g w i t h a c o m p a r i s o n w i t h t h e c o n s t a n t s d e r i v e d from the a - t y p e t r a n s i t i o n s o n l y . Watson's A - r e d u c t i o n i n the I r r e p r e s e n t a t i o n i s u s e d t h r o u g h o u t . U n f o r t u n a t e l y o n l y A j , A J K and Sj and $ K j c o u l d be d e t e r m i n e d b e c a u s e o f the l i m i t e d number o f b r a n c h e s a v a i l a b l e . The measured f r e q u e n c i e s , a l o n g w i t h t h e r e s i d u a l s w h i c h a r e c a l c u l a t e d w i t h xab i n c l u d e d and o m i t t e d , a r e shown i n T a b l e s 4.5 and 4.6. The e f f e c t o f xab i-s c l e a r . 78 T a b l e 4 . 3 7 9 S p e c t r o s c o p i c C o n s t a n t s o f BrNCO Parame t e r a_-type T r a n s i t i o n s A l l T r a n s i t i o n s R o t a t i o n a l C o n s t a n t s (MHz) B„ 41188 .71(23) 1 2175.6311(13) 2063.1025(11) 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) A T J K 1 .1366 ( 22 ) 172.72(16) 0 . 1692 ( 29) K J 41189 2175 2063 1 173 0 -0 . 506 ( 25) . 63391 (52) .09857(53) .1370(19) .97(14) .17367(26) .248(19) Bromine 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 (MHz) X a a %bb Xc c 608 . 16 (48) 279.4(11) 549 .85 (11) 608 280 549 41(52) 086(64) 67(12) N i t r o g e n 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 (MHz) ^ a a — ^ b b ^ c c — I n e r t i a l d e f e c t (a.m.u. A 2 ) Number o f R o t a t i o n a l T r a n s i t i o n s 26 S t a n d a r d D e v i a t i o n o f D i s t o r t i o n F i t (MHz) 0.028 09(78) 811(19) 0 . 400 43 0.032 Numbers i n p a r e n t h e s e s a r e one s t a n d a r d d e v i a t i o n 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 . 79 T a b l e 4 . 4 8 1 S p e c t r o s c o p i c C o n s t a n t s o f BrNCO P a r a m e t e r a_-type T r a n s i t i o n s A l l T r a n s i t i o n s R o t a t i o n a l C o n s t a n t s (MHz) B. 41142.57 (39) 1 2159 . 5035(13) 2048.4716(10) 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) A T J K 1.1258(23) -171.00(12) 0 .1690 (26 ) K J 41141.914(29) 2159.50429(53) 2048.47014(55) 1 . 1281(18) 172.23(14) 0.17004(31) -0.214(19) Bromine 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 (MHz) X • a a ^ b b Xc c ^ a b 508.40(47) 230.8(11) 458 . 30 (22) 508.49(52) 233 . 311 (70) 458 .60(12) N i t r o g e n 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 (MHz) X a a — Xb b c — o I n e r t i a l d e f e c t (a.m.u. A 2 ) Number o f R o t a t i o n a l T r a n s i t i o n s 29 S t a n d a r d D e v i a t i o n o f D i s t o r t i o n F i t (MHz) 0.029 4.75(51) 1 . 912(12) 0 . 401 46 0 . 034 Numbers i n p a r e n t h e s e s a r e one s t a n d a r d d e v i a t i o n 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 . 80 T a b l e 4.5 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 7 9 B r N C O T r a n s i t i o n F' - F" N o r m a l i s e d 1 Weight O b s e r v e d 2 R e s i d u a l s 3 F r e q u e n c y W i t h o u t xab Wit h xab 4 , « .1 1/2 9/2 5/2 7/2 5 , 5 13/2 1 1/2 7/2 9/2 5 o 5 9/2 1 1/2 1 3/2 7/2 5 ! a 1 3/2 7/2 1 1/2 9/2 6 1 6 1 5/2 1 3/2 9/2 11/2 6 0 6 1 3/2 15/2 9/2 1 1/2 9/2 7/2 3/2 5/2 1 1/2 9/2 5/2 7/2 7/2 9/2 1 1/2 5/2 1 1/2 5/2 9/2 7/2 1 3/2 1 1/2 7/2 9/2 1 1/2 1 3/2 7/2 9/2 .000 .000 .000 .000 000 000 000 000 .000 .000 .000 .000 000 000 000 000 000 000 000 000 0, 0, 1, 1, 100 100 000 000 16697.064 16725.798 16732.136 16747.530 20907.007 20914.295 20915.140 20922.857 21174.479 21185.088 21185.088 21187.013 21470.377 21474.140 21477.657 21482.051 25090.043 25094.279 25096.468 25100.904 25420.588 25420.588 25436.877 25451.129 •23.577 -9 .839 -0 .012 -0 .162 0.769 0.519 0.011 -0 .036 •20.928 -0 .136 0.077 -8 .273 0. 1 97 -0 .019 -0 .015 0. 1 28 0.275 0. 1 62 0.020 -0 .003 -0 .183 0.094 9.568 23.585 •0.082 0.001 •0.006 •0.065 0.039 0.028 0.029 0.028 •0.058 •0.028 0.052 0.041 0.004 •0.005 •0.010 •0.037 0.036 0.002 0.040 0.044 •0.010 0.073 •0.068 0.062 Measurements were w e i g h t e d a c c o r d i n g to l/o2 , where a i s the u n c e r t a i n t y i n the measurements. U n i t w e i g h t c o r r e s p o n d e d to an u n c e r t a i n t y o f 0.03 MHz. N i t r o g e n h y p e r f i n e s p l i t t i n g has been s u b t r a c t e d from the b-ty p e t r a n s i t i o n s . O b s e r v e d 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 the c o n s t a n t s i n T a b l e 4.3 81 T a b l e 4 . 5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s ed We i gh t Ob s e r v e d F r e q u e n c y Re s i d u a l s W i t h o u t x a b W i t h x a b 6 1 5 15/2 • 9/2 • 13/2 • 11/2 • - 13/2 - 7/2 - 1 1/2 9/2 5 1 a 1 .000 1 .000 1 .000 1 .000 25766.036 25769.092 25770.035 25773.916 0.310 -0 .051 -0 .016 0.312 -0 .009 -0.031 -0 .016 -0 .016 7 , 7 17/2 -15/2 • 11/2 -13/2 -- 15/2 - 13/2 9/2 - 11/2 6 i e 1 .000 1 .000 1 .000 1 .000 29272.172 29274.880 29277.094 29279.874 0.151 0.099 -0 .042 -0 .082 0.030 0.018 -0.021 -0 .045 7 0 7 17/2 -15/2 -11/2 -13/2 -- 15/2 - 13/2 9/2 - 1 1/2 6 0 6 1 .000 1 .000 0. 1 00 0. 100 29654.116 29654. 116 29658.081 29658.504 0.048 -0 .286 -0 .854 -0 .744 0.030 . 0.018 -0 .010 -0 .030 7 , 6 17/2 -11/2 -15/2 -13/2 -- 15/2 9/2 - 13/2 - 1 1/2 6 5 1 . 0 0 0 1 .000 1 .000 1 .000 30060.726 30062.800 30062.800 30066.356 0.660 -0 .048 -0 .013 0.686 -0 .007 -0 .023 -0 .024 -0.041 8 , 8 19/2 -17/2 -13/2 -15/2 -- 17/2 - 15/2 - 11/2 - 13/2 7 71 .000 1 .000 1 .000 1 .000 33453.349 33455.203 33457.276 33459.210 0.067 0.039 -0 .020 -0 .004 -0 .007 -0 .010 0.002 0.029 8 o 8 17/2 -19/2 -13/2 -15/2 -- 15/2 - 17/2 - 1 1/2 - 13/2 7 0 7 0. 100 0. 100 1 .000 1 .000 33885.400 33885.612 33888.327 33889.384 -0 .578 0.023 -0 .918 -0 .238 0.076 0.006 -0.011 0.002 8 , 7 17/2 -13/2 • 19/2 -15/2 -- 15/2 - 1 1/2 - 17/2 - 13/2 7 1 6 0.100 0.100 0. 100 1 .000 34355.372 34355.688 34355.688 34360.044 0.081 0.014 2.272 2.450 0.018 0.043 -0 .080 -0 .044 9 1 9 21/2 • 19/2 • 15/2 • 17/2 • - 19/2 - 17/2 - 13/2 - 15/2 8 1 8 1 .000 1 .000 1 .000 1 .000 37633.739 37635.076 37636.850 37638.241 0.091 0.069 -0.021 -0 .012 0.041 0.035 0.003 0.020 82 T a b l e 4 . 5 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t O b s e r v e d F r e q u e n c y Res i d u a l s W i t h o u t x a b W i t h x a b 9 0 9 19/2 21 /2 15/2 1 7 /2 9 1 8 17/2 21 /2 1 9/2 15/2 10 , 23 /2 21 /2 1 7/2 19/2 10 o 23 /2 19/2 21 /2 17/2 10 , 17/2 21 /2 23 /2 19/2 11 1 25/2 23 /2 19/2 21 /2 11 o 19/2 23/2 25/2 21 /2 1 o i o 1 i i 1 17/2 19/2 13/2 1 5/2 15/2 19/2 1 7 /2 13/2 2 1 / 2 19/2 15/2 1 7 /2 2 1 / 2 1 7 /2 19/2 15/2 15/2 19/2 2 1 / 2 17/2 2 3 / 2 2 1 / 2 1 7 /2 19/2 10 1 7 /2 2 1 / 2 2 3 / 2 19/2 10 000 ,100 100 000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 8 1 .000 1 .000 1 .000 1 .000 1 0 1 000 000 000 000 1 0 1 .000 1 .000 1 .000 1 .000 38112.998 38114.961 38114.961 38117.988 38617 .849 38626.908 38646.382 38647 .578 41813 .185 41814.197 41815.738 41816.788 42341 .688 42345 .109 42361.038 42375.034 42938 .775 42938 .775 42949 .302 42962 .772 45991 .765 45992 .565 45993.878 45994 .713 46544.577 46554 .253 46565 .779 46567.612 - 2 . 3 0 4 0.101 - 2 . 7 4 6 - 0 . 1 5 3 •31.213 •18.916 - 0 . 8 0 0 - 0 . 0 9 7 0.051 0 .032 - 0 . 0 3 5 -0 .031 0 .033 0 .686 18.890 31 .099 -0 .031 0 .473 12.032 22 .914 0 .049 0 .034 - 0 . 0 3 5 - 0 . 0 2 6 •23.029 •12.030 0 .039 - 0 . 5 3 4 0.038 0 .086 •0. 150 0 .023 0 .0 0 .007 •0.054 •0.063 0.01.5 0 .009 •0.006 0 .003 0 .019 0 .009 •0.042 •0.037 0 .014 •0.023 •0.026 •0.030 0.021 0 .016 0 .0 0 .014 0 .014 0.021 0 .027 0 .010 11 i 23 /2 19/2 25 /2 21 /2 i o 2 1 / 2 17/2 2 3 / 2 19/2 10 0. 100 0 . 100 0 .100 1 .000 47228 .576 47228.888 47228.888 47231.377 0 .060 - 0 . 100 1 . 192 1 .555 0 .030 •0.032 •0.023 0 .012 83 T a b l e 4 . 5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s e d We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x a b W i t h xab 12 , 1 2 • -27/2 - 25/2 25/2 - 23/2 21/2 - 19/2 23/2 — 21/2 12 o 1 2 -25/2 - 23/2 21/2 - 19/2 27/2 - 25/2 23/2 — 21/2 12 a 1 1 -27/2 - 25/2 25/2 - 23/2 21/2 - 19/2 23/2 — 21/2 12 3 1 0 -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 — 21/2 12 3 9 -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 — 21/2 12 , 1 1 -27/2 - 25/2 25/2 - 23/2 21/2 - 19/2 23/2 — 21/2 13 , 1 2 -27/2 - 27/2 25/2 - 25/2 29/2 - 29/2 23/2 — 23/2 14 , 1 3 -29/2 - 29/2 27/2 - 27/2 31/2 - 31/2 25/2 - 25/2 11 11 11 11 11 11 13 1 4 i 1 1 .000 1 .000 1 .000 1 .000 1 1 0. 100 0.100 0. 100 1 .000 1 0 1 .000 1 .000 1 .000 1 .000 000 100 000 100 0. 100 1 .000 0. 100 1 .000 1 0 0, 0, 0, 1, 100 100 100 000 1 3 1 .000 1 .000 1 .000 1 .000 1 « 1 .000 1 .000 1 .000 1 .000 50169.384 50170.039 50171.143 50171.830 50786.288 50786.863 50786.863 50788.988 50858.400 50860.909 50862.154 50864.420 50900.357 50900.950 50905.033 50905.691 50900.950 50901.565 50905.691 50906.313 51517.502 51517.724 51518.023 51519.258 44441.733 44445.392 44482.980 44486.143 45314.448 45320.417 45355.799 45361.203 0.031 0.017 •0.066 •0.056 •1 . 180 •1 .567 •0.012 •0.033 •2.650 •2.348 •0.063 •0.040 0.058 •0.006 0.055 •0.020 •0.007 •0.051 0.066 •0.047 0.474 0.018 •0. 104 0.443 •0.997 •1 .927 0.613 •2.094 •0.808 0.871 •0.496 0.569 0.009 0.005 •0.015 0.002 0.028 0.087 •0.023 0.033 0.001 0.038 •0.056 •0.035 0.049 •0.003 0.048 •0.016 •0.016 •0.048 0.059 0.043 0.012 0.017 0.025 0.014 0.019 0.001 0.044 0.042 0.019 •0.062 0.019 0.020 84 T a b l e 4.5 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x a b With x a b 15 31/2 29/2 33/2 27/2 1 i « 31/2 29/2 33/2 27/2 15 1 5 1 .000 1 .000 1 .000 1 .000 46261.617 46266.069 46303.187 46307.165 -0.690 •0.277 •0.428 •0.533 •0.030 •0.020 •0.007 0.012 16 , 33/2 31/2 35/2 29/2 1 5 33/2 31/2 35/2 29/2 16 1 e 1 .000 1 .000 1 .000 1 .000 47285.651 47289.727 47327.565 47331.196 •0.631 •0.382 •0.372 •0.607 •0.049 •0.033 0.018 •0.001 17 , 1 6 35/2 -33/2 -37/2 -31/2 -1 7 1 B 18 , 35/2 39/2 33/2 19 , 37/2 41/2 35/2 20 , 1 9 41/2 -39/2 -43/2 -37/2 -35/2 33/2 37/2 31/2 1 7 35/2 39/2 33/2 18 - 19 37/2 41/2 35/2 - 20 41/2 39/2 43/2 37/2 1 7 1 .000 1 .000 1 .000 1 .000 1 8 1 .000 1 .000 1 .000 1 9 1 .000 1 .000 1 .000 2 0 1 .000 1 .000 1 .000 1 .000 48389.145 48392.993 48431.442 48434.850 49578.252 49617.344 49620.528 50848.120 50887.846 50890.884 52201.741 52205.209 52245.672 52248.464 •0.530 •0.327 •0.299 •0.572 •0.292 •0.243 •0.582 •0.327 0.245 •0.627 •0.566 •0.298 -0.237 •0.677 0.009 0.024 0.005 0.036 0.042 0.023 0.029 •0.011 -0.010 0.002 0.001 •0.002 •0.026 •0.002 21 1 2 0 41/2 -21 0 2 1 41/2 0.010 53652.430 -0. 186 0.093 14 o 29/2 27/2 31/2 25/2 1 a 27/2 25/2 29/2 23/2 13 , 1 3 1 .000 1 .000 1 .000 1 .000 24966.261 24970.004 24993.737 24999.436 0.964 0.270 0.032 1 .343 0.002 •0.017 0.011 0.009 15 o 31/2 29/2 33/2 27/2 1 5 14 29/2 27/2 31/2 25/2 i 1 u 1 .000 1 .000 1 .000 1 .000 29-875.048 29878.788 29902.383 29907.698 0.837 0.545 0.004 1 .330 0.030 0.018 •0.011 •0.020 85 T a b l e 4.5 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x a D W i t h x a b 16 o 33/2 31/2 35/2 29/2 17 o 35/2 33/2 37/2 31/2 18 o 37/2 35/2 39/2 33/2 19 o 39/2 37/2 41/2 35/2 i e 1 7 1 8 1 9 31/2 29/2 33/2 27/2 15 33/2 31/2 35/2 29/2 16 17 35/2 33/2 37/2 31/2 37/2 35/2 39/2 33/2 18 1 1 5 1 .000 0.0 1 .000 0.0 1 16 1 .000 1 .000 1 .000 1 .000 1 7 1 1 1 1 000 000 000 000 1 1 8 1 .000 1 .000 1 .000 1 .000 34816.506 34823.144 34843.644 34850.568 39787.743 39789.729 39814.522 39817.797 44785.796 44787.977 44812.050 44815.420 49807.390 49809.383 49833.206 49836.343 0.721 3.680 0.025 3.310 0.624 •0.756 •0.014 0.070 0.611 •0.294 •0.067 0.249 0.544 •0.253 •0.028 0.337 0.018 0.305 0.016 0. 1 34 •0.004 0.057 •0.020 0.017 0.038 0.082 •0.071 0.047 0.013 •0.003 •0.029 0.025 86 T a b l e 4.6 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 8 1 B r N C O T r a n s i t i o n N o r m a l i s e d 1 O b s e r v e d 2 R e s i d u a l s 3 F' - F" Weight F r e q u e n c y W i t h o u t x a b W i t h x a b 4 1 A — 3 i 3 11/2 - 9/2 1 .000 16590.877 -11 .334 -0.006 9/2 - 7/2 0. 100 16609.323 -5.455 0. 147 5/2 - 3/2 1 .000 16611.856 -0.020 -0.016 7/2 - 5/2 1 .000 16624.686 -0.142 -0.074 5 , 5 13/2 - 1 1/2 4 1 ai.000 20757.792 0.560 0.022 1 1/2 - 9/2 1 .000 20763.937 0.389 0.028 7/2 - 5/2 1 .000 20764.629 -0.057 -0.045 9/2 - 7/2 1 .000 20771.106 -0.055 -0.010 5 o 5 9/2 - 7/2 4 0 V 100 21031.080 -9.510 -0.034 11/2 - 9/2 0.100 21031.924 -0.127 -0.053 13/2 - 1 1/2 0. 1 00 21031.924 0.053 0.035 7/2 - 5/2 0. 100 21035.953 -4.522 -0.003 5 , 4 13/2 - 1 1/2 4 1 31.000 21313.553 0.119 -0.012 7/2 - 5/2 1 .000 21316.760 -0.050 -0.041 11/2 - 9/2 1 .000 21319.707 -0.011 -0.007 9/2 - 7/2 1 .000 21323.394 0.109 -0.004 6 1 6 - 5 1 5 15/2 - 1 3/2 1 .000 24910.652 0.191 0.018 13/2 - 1 1/2 1 .000 24914.219 0.114 -0.001 9/2 - 7/2 1 .000 24916.049 -0.009 0.005 11/2 - 9/2 1 .000 24919.733 -0.046 -0.013 6 o 6 - 5 0 5 13/2 - 1 1/2 0. 100 25236.625 -0. 169 -0.052 15/2 - 1 3/2 0. 100 25236.625 0.061 0.046 9/2 - 7/2 1 .000 25247.673 5.400 -0.064 11/2 - 9/2 1 .000 25253.866 11.392 0.044 Measurements were w e i g h t e d a c c o r d i n g to l / a 2 , where a i s the u n c e r t a i n t y i n the measurements. U n i t w e i g h t c o r r e s p o n d e d to an u n c e r t a i n t y o f 0.03 MHz. 2 N i t r o g e n h y p e r f i n e s p l i t t i n g has been s u b t r a c t e d from the b-typ e t r a n s i t i o n s . 3 O b s e r v e d 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 the c o n s t a n t s i n T a b l e 4.4 87 T a b l e 4 . 6 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s e d W e i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t xab W i t h x a b 6 , 5 1 5/2 9/2 3/2 1/2 7/2 5/2 1/2 3/2 0 7 7/2 5/2 1/2 3/2 7/2 1/2 5/2 3/2 1 8 9/2 7/2 3/2 5/2 7/2 9/2 3/2 5/2 2 7 9/2 3/2 7/2 5/2 2 6 9/2 3/2 7/2 5/2 3/2 7/2 1/2 9/2 5/2 3/2 9/2 1/2 5/2 3/2 9/2 1/2 5/2 9/2 3/2 1/2 7/2 5/2 1/2 3/2 5/2 7/2 1/2 3/2 7/2 1/2 5/2 3/2 7/2 1/2 5/2 3/2 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 0. 100 0. 1 00 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 0. 100 0.100 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 25577.458 25580.091 25580.857 25584.055 29062.671 29064.944 29066.810 29069.148 29439.508 29439.508 29442.917 29443.243 29840.398 29842.269 29842.269 29845.134 33213.759 33215.310 33217.031 33218.628 33640.279 33640.279 33642.755 33643.526 33666.139 33667.381 33672.197 33673.552 33686.085 33687.347 33691.803 33693.217 0.215 0.039 0.012 0.203 0. 122 0.084 •0.024 •0.039 0.075 •0.202 •0.594 •0.530 0.436 0.039 0.004 0.471 0.035 0.011 0.055 0.058 0.364 •0.043 •0.630 •0. 1 72 0.041 0.0 0.049 0.003 •0.017 •0.069 0.019 •0.038 0.0 •0.025 •0.012 •0.018 0.035 0.026 •0.009 •0.013 0.062 0.003 0.004 •0.003 0.004 0.023 •0.003 0.012 •0.018 •0.025 •0.040 •0.036 0.067 •0.054 •0.018 0.0 0.013 0.004 0.028 0.010 •0.038 •0.066 0.034 •0.033 88 T a b l e 4.6 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i ght O b s e r v e d F r e q u e n c y Res i d u a l s W i t h o u t x a b W i t h * a b 8 3 6 13/2 -19/2 -15/2 -17/2 -1 1/2 17/2 13/2 1 5/2 7 3 0.010 0.010 0.010 0.010 33681.647 33682.607 33695.368 33696.133 0.062 0.078 0.074 0. 1 28 0.065 0.073 0.079 0. 1 25 8 3 5 13/2 -19/2 -15/2 -17/2 -1 1/2 1 7/2 13/2 15/2 7 3 " o . o i o 0.010 0.010 0.010 33681.647 33682.607 33695.368 33696.133 -0.019 -0.002 -0.004 0.050 -0.016 -0.008 0.0 0.048 8 1 7 17/2 -19/2 -13/2 -15/2 -15/2 1 7/2 1 1/2 13/2 7 1 60.100 0. 100 0. 1 00 1 .000 34103.358 34103.358 34103.581 34106.842 0.028 1 .599 -0.081 1 .578 -0.011 0.141 -0.061 -0.007 9. 1 9 21/2 -19/2 -15/2 -17/2 -19/2 1 7/2 1 3/2 15/2 8 1 81.000 1 .000 1 .000 1 .000 37364.100 37365.212 37366.723 37367.891 0.044 0.019 -0.031 -0.017 0.009 -0.005 -0.015 0.005 9 o 9 19/2 -21/2 -15/2 -17/2 -17/2 19/2 13/2 1 5/2 8 0 81.000 1 .000 1 .000 1 .000 37838.013 37839.125 37839.817 37841.727 -1.379 0.098 -1.597 -0.046 0.072 0.087 0.061 0.074 9 1 8 17/2 -21/2 -19/2 -15/2 -15/2 19/2 1 7/2 1 3/2 8 1 ?1.000 1 .000 1 .000 1 .000 38332.348 38344.933 38363.036 38364.182 -33.029 -17.728 -0.762 -0.038 -0.037 0.059 -0.019 -0.014 10 , 1 0 23/2 -21/2 -17/2 -19/2 -21/2 19/2 1 5/2 17/2 9 1 91.000 . 1.000 1 .000 1 .000 41513.589 41514.434 41515.728 41516.617 0.043 0.027 -0.027 -0.010 0.018 0.010 -0.008 0.013 10 o 10 23/2 -19/2 -21/2 -17/2 -21/2 1 7/2 19/2 15/2 9 0 91.000 1 .000 1 .000 1.000 42035.331 42038.338 42053.495 42070.174 0.005 0.698 17.763 32.937 -0.004 0.005 -0.030 -0.001 89 T a b l e 4 . 6 ( C o n t i n u e d ) T r a n s i t i o n F ' - F " N o r m a l i s ed We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t xab W i t h xab 10 , 1 7 / 2 2 1 / 2 2 3 / 2 1 9 / 2 11 1 2 5 / 2 2 3 / 2 1 9 / 2 2 1 / 2 1 i 1 5 / 2 1 9 / 2 2 1 / 2 1 7 / 2 2 3 / 2 2 1 / 2 1 7 / 2 1 9 / 2 10 0 , 0 , 1 , 1 , i o 1 , 1 , 1 , 1 , 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 6 2 3 . 9 8 3 4 2 6 2 3 . 9 8 3 4 2 6 3 5 . 6 9 7 4 2 6 5 2 . 0 8 9 4 5 6 6 2 . 2 2 5 4 5 6 6 2 . 8 8 6 4 5 6 6 4 . 0 0 6 4 5 6 6 4 . 6 9 7 0 . 0 5 3 0 . 4 8 3 1 3 . 0 6 0 2 7 . 2 8 2 0 . 0 6 2 0 . 0 4 2 0 . 0 0 3 0 . 0 0 6 0 . 0 8 4 0 . 0 8 9 • 0 . 0 3 6 0 . 0 0 4 0 . 0 4 2 0 . 0 3 0 0 . 0 2 8 0 . 0 3 4 11 o 1 9 / 2 2 3 / 2 2 5 / 2 2 1 / 2 1 1 1 7 / 2 2 1 / 2 2 3 / 2 1 9 / 2 10 1 o 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 4 6 2 0 3 . 1 8 1 4 6 2 1 6 . 3 4 1 4 6 2 2 9 . 0 3 0 4 6 2 3 0 . 4 1 4 • 2 7 . 3 6 8 • 1 3 . 0 9 0 0 . 0 4 6 - 0 . 5 8 0 • 0 . 0 4 1 0 . 0 0 1 0 . 0 3 8 0 . 0 2 6 11 i 2 3 / 2 2 5 / 2 1 9 / 2 2 1 / 2 12 , 2 7 / 2 2 5 / 2 2 1 / 2 2 3 / 2 12 o 2 5 / 2 2 7 / 2 2 1 / 2 2 3 / 2 12 2 2 7 / 2 2 5 / 2 2 1 / 2 2 3 / 2 i o 1 2 1 2 1 1 2 1 / 2 2 3 / 2 1 7 / 2 1 9 / 2 10 2 5 / 2 2 3 / 2 1 9 / 2 2 1 / 2 1 1 1 1 2 3 / 2 2 5 / 2 1 9 / 2 2 1 / 2 2 5 / 2 2 3 / 2 1 9 / 2 2 1 / 2 1 1 0 . 1 0 0 0 . 1 0 0 0 . 1 0 0 1 . 0 0 0 1 1 1 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 1 0 , 0 , 0 , 1, 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 4 6 8 8 2 . 3 3 4 4 6 8 8 2 . 5 8 9 4 6 8 8 2 . 5 8 9 4 6 8 8 4 . 5 5 7 4 9 8 0 9 . 8 7 9 4 9 8 1 0 . 4 1 7 4 9 8 1 1 . 3 4 6 4 9 8 1 1 . 8 8 7 5 0 4 1 9 . 3 5 6 5 0 4 1 9 . 7 8 7 5 0 4 1 9 . 7 8 7 5 0 4 2 1 . 5 1 0 5 0 4 9 0 . 1 6 9 5 0 4 9 2 . 2 2 1 5 0 4 9 3 . 3 1 6 5 0 4 9 5 . 2 1 8 0 . 0 2 4 0 . 9 6 5 • 0 . 1 2 2 1 . 1 5 1 0 . 0 1 7 • 0 . 0 0 3 • 0 . 0 7 0 • 0 . 0 9 3 - 0 . 8 9 9 0 . 0 2 0 -1 . 2 8 4 - 0 . 0 4 7 • 2 . 2 2 9 • 2 . 0 2 3 0 . 0 6 4 • 0 . 0 3 3 0 . 0 0 1 0 . 0 3 1 0 . 0 7 7 • 0 . 0 4 5 0 . 0 0 1 0 . 0 1 3 • 0 . 0 3 6 0 . 0 5 5 0 . 0 3 0 0 . 0 1 2 • 0 . 0 2 9 0 . 0 0 2 0 . 0 0 4 0 . 0 3 5 • 0 . 0 5 9 • 0 . 0 2 9 12 3 2 7 / 2 2 1 / 2 2 5 / 2 2 3 / 2 i o 1 1 2 5 / 2 1 9 / 2 2 3 / 2 2 1 / 2 1 . 0 0 0 0 . 1 0 0 1 . 0 0 0 0 . 1 0 0 5 0 5 3 1 . 2 5 3 5 0 5 3 1 . 7 5 6 5 0 5 3 5 . 1 4 7 5 0 5 3 5 . 6 7 5 0 . 1 0 0 0 . 0 4 6 0 . 0 7 8 0 . 0 0 5 0 . 0 9 4 0 . 0 4 8 0 . 0 7 3 • 0 . 0 0 2 90 T a b l e 4 . 6 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l ! s e d W e i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x a b W i t h xab 12 3 9 -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 — 21/2 12 , 1 1 -27/2 - 25/2 25/2 - 23/2 21/2 - 19/2 23/2 — 21/2 13 , 1 3 -29/2 - 27/2 27/2 - 25/2 23/2 - 21/2 25/2 — 23/2 13 , 1 2 -27/2 - 27/2 25/2 - 25/2 29/2 - 29/2 23/2 — 23/2 14 , 1 3 -29/2 - 29/2 27/2 - 27/2 31/2 - 31/2 25/2 — 25/2 15 , 1 a -31/2 - 31/2 29/2 - 29/2 33/2 - 33/2 27/2 — 27/2 16 , 1 5 -33/2 - 33/2 31/2 - 31/2 35/2 - 35/2 29/2 — 29/2 17 , 1 6 -35/2 - 35/2 33/2 - 33/2 37/2 - 37/2 31/2 - 31/2 11 11 1 2 1 3 1 4 1 5 16 1 7 0. 100 1 .000 0. 100 1 .000 i o 0, 0, 0, 1, 100 100 1 00 000 1 1 2 1 .000 1 .000 0.100 1 .000 O 1 3 1 .000 1 .000 1 .000 1 .000 o i a 1 .000 1 .000 1 .000 1 .000 O 1 5 1 .000 1 .000 1 .000 1 .000 1 6 1 1 1 1 1 7 1 1 1 1 000 000 000 000 000 000 000 000 50531.756 50532.268 50535.675 50536.229 51139.918 51140.147 51140.415 51141.417 53956.629 53957.085 53957.794 53958.365 44338.710 44341.957 44373.009 44375.878 45198.833 45203.962 45233.165 45237.912 46132. 138 46135.813 46166.698 46170.031 47141.155 47144.494 47175.957 47179.023 48228.193 48231.347 48263.357 48266.234 •0.030 -0.076 -0.018 -0.075 0.371 0.034 •0.057 0.372 0.040 0.023 •0.124 0.031 0.730 •1 .300 0.447 •1 .433 0.535 1 .027 •0.359 0.787 •0.488 •0.171 •0.301 •0.356 •0.399 •0.240 0.253 -0.395 •0.394 -0.268 0.222 -0.398 •0.036 •0.074 •0.023 •0.073 0.029 0.032 0.027 0.025 0.027 0.016 0.067 0.035 •0.003 0.009 0.024 0.026 0.027 -0.067 0.009 -0.030 •0.021 0.008 0.002 0.011 0.011 0.0 •0.002 0.026 •0.015 •0.023 •0.007 0.025 91 T a b l e 4 . 6 ( C o n t i n u e d ) T r a n s i t i o n N o r m a l i s e d O b s e r v e d R e s i d u a l s F ' F" We i gh t F r e q u e n c y W i t h o u t x a b W i t h X a b 18 , 1 7 - 18 0 1 8 37/2 - 37/2 1 .000 49395.853 -0.380 -0.015 35/2 - 35/2 1 .000 49398.883 -0.248 -0.013 39/2 - 39/2 1 .000 49431.438 -0.170 0.018 33/2 — 33/2 1 .000 49434.146 -0.383 0.041 20 , 1 9 - 20 0 2 0 41/2 - 41/2 1 .000 51983.271 -0.401 -0.011 43/2 - 43/2 1 .000 52019.775 -0.151 -0.002 37/2 — 37/2 1 .000 52022.159 -0.447 0.018 14 o 1 a - 13 i 1 3 27/2 - 25/2 0. 100 24515.044 0.276 0.083 31/2 - 29/2 0.100 24534.742 -0.024 -0.039 25/2 — 23/2 0. 1 00 24539.294 0.864 -0.074 15 o 1 5 - 14 i i a 31/2 - 29/2 0. 100 29382.081 0.538 -0.033 29/2 - 27/2 0. 1 00 29385.286 0.383 0.041 33/2 - 31/2 1 .000 29405.051 0.004 -0.006 27/2 — 25/2 1 .000 29409.292 0.915 -0.015 16 o 1 6 - 15 i 1 5 33/2 - 31/2 1 .000 34285.015 0.511 0.014 31/2 - 29/2 1 .000 34289.226 1 .655 0.096 35/2 - 33/2 1 .000 34307.728 -0.008 -0.015 29/2 — 27/2 1 .000 34312.549 1 .774 0.015 17 o 1 7 - 16 1 1 6 35/2 - 33/2 1 .000 39217.570 0.447 0.003 33/2 - 31/2 1 .000 39219.283 -0.648 -0.001 37/2 - 35/2 1 .000 39240.010 -0.006 -0.010 31/2 — 29/2 1 .000 39242.688 -0.111 -0.006 18 o 1 8 - 17 i 1 7 37/2 - 35/2 1 .000 44176.871 0.425 0.021 35/2 - 33/2 1 .000 44178.762 -0.260 0.018 39/2 - 37/2 1 .000 44198.933 -0.009 -0.011 33/2 — 31/2 1 .000 44201.684 0. 189 -0.007 19 o 1 9 - 18 i 1 8 37/2 - 35/2 1 .000 49161.623 -0. 136 0.045 41/2 - 39/2 1 .000 49181.401 -0.056 -0.057 35/2 - 33/2 1 .000 49183.967 0. 177 -0.073 92 T a b l e 4 . 7 O b s e r v e d h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s i n (MHz) o f 7 9 B r 1 4 N C O b - t y p e t r a n s i t i o n s T r a n s i t i o n O b s e r v e d Fj. ' F' - F1" F" F r e q u e n c y 13 -i 12 1 3 o T 3 2 7 / 2 2 7 / 2 - 2 7 / 2 2 7 / 2 4 4 4 4 1 . 4 7 2 2 7 / 2 2 5 / 2 - 2 7 / 2 2 5 / 2 4 4 4 4 1 . 8 6 3 2 7 / 2 2 9 / 2 - 2 7 / 2 2 9 / 2 4 4 4 4 1 . 8 6 3 2 5 / 2 2 5 / 2 - 2 5 / 2 2 5 / 2 4 4 4 4 5 . 1 2 8 2 5 / 2 2 3 / 2 - 2 5 / 2 2 3 / 2 4 4 4 4 5 . 5 2 4 2 5 / 2 2 7 / 2 - 2 5 / 2 2 7 / 2 4 4 4 4 5 . 5 2 4 2 9 / 2 2 9 / 2 - 2 9 / 2 2 9 / 2 4 4 4 8 2 . 6 9 9 2 9 / 2 2 7 / 2 - 2 9 / 2 2 7 / 2 4 4 4 8 3 . 1 2 0 2 9 / 2 3 1 / 2 - 2 9 / 2 3 1 / 2 4 4 4 8 3 . 1 2 0 2 3 / 2 2 3 / 2 - 2 3 / 2 2 3 / 2 4 4 4 8 5 . 8 8 3 2 3 / 2 2 1 / 2 - 2 3 / 2 2 1 / 2 4 4 4 8 6 . 2 7 3 2 3 / 2 2 5 / 2 - 2 3 / 2 2 5 / 2 4 4 4 8 6 . 2 7 3 14 , , 3 " 1 4 o , 4 2 9 / 2 2 9 / 2 - 2 9 / 2 2 9 / 2 4 5 3 1 4 . 1 7 6 2 9 / 2 2 7 / 2 - 2 9 / 2 2 7 / 2 4 5 3 1 4 . 5 8 4 2 9 / 2 3 1 / 2 - 2 9 / 2 3 1 / 2 4 5 3 1 4 . 5 8 4 2 7 / 2 2 7 / 2 - 2 7 / 2 2 7 / 2 4 5 3 2 0 . 1 5 6 2 7 / 2 2 5 / 2 - 2 7 / 2 2 5 / 2 4 5 3 2 0 . 5 4 8 2 7 / 2 2 9 / 2 - 2 7 / 2 2 9 / 2 4 5 3 2 0 . 5 4 8 3 1 / 2 3 1 / 2 - 3 1 / 2 3 1 / 2 4 5 3 5 5 . 5 4 8 3 1 / 2 2 9 / 2 - 3 1 / 2 2 9 / 2 4 5 3 5 5 . 9 2 4 3 1 / 2 3 3 / 2 - 3 1 / 2 3 3 / 2 4 5 3 5 5 . 9 2 4 2 5 / 2 2 5 / 2 - 2 5 / 2 2 5 / 2 4 5 3 6 0 . 9 5 9 2 5 / 2 2 3 / 2 - 2 5 / 2 2 3 / 2 4 5 3 6 1 . 3 2 5 2 5 / 2 2 7 / 2 - 2 5 / 2 2 7 / 2 4 5 3 6 1 . 3 2 5 15 i 1 4 - 1 5 o , 5 3 1 / 2 3 1 / 2 - 3 1 / 2 3 1 / 2 4 6 2 6 1 . 3 5 3 3 1 / 2 2 9 / 2 - 3 1 / 2 2 9 / 2 4 6 2 6 1 . 7 4 9 3 1 / 2 3 3 / 2 - 3 1 / 2 3 3 / 2 4 6 2 6 1 . 7 4 9 2 9 / 2 2 9 / 2 - 2 9 / 2 2 9 / 2 4 6 2 6 5 . 8 0 1 2 9 / 2 2 7 / 2 - 2 9 / 2 2 7 / 2 4 6 2 6 6 . 2 0 3 2 9 / 2 3 1 / 2 - 2 9 / 2 3 1 / 2 4 6 2 6 6 . 2 0 3 3 3 / 2 3 3 / 2 - . 3 3 / 2 3 3 / 2 4 6 3 0 2 . 9 0 2 3 3 / 2 3 1 / 2 - 3 3 / 2 3 1 / 2 4 6 3 0 3 . 3 2 9 3 3 / 2 3 5 / 2 - 3 3 / 2 3 5 / 2 4 6 3 0 3 . 3 2 9 2 7 / 2 2 7 / 2 - 2 7 / 2 2 7 / 2 4 6 3 0 6 . 8 8 8 2 7 / 2 2 5 / 2 - 2 7 / 2 2 5 / 2 4 6 3 0 7 . 3 0 3 2 7 / 2 2 9 / 2 - 2 7 / 2 2 9 / 2 4 6 3 0 7 . 3 0 3 T a b l e 4 . 7 ( C o n t i n u e d ) 93 T r a n s i t i o n F ' F " Ob s e r v e d F r e q u e n c y 16 , 33/2 33/2 33/2 31/2 31/2 31/2 35/2 35/2 35/2 29/2 29/2 29/2 17 , 35/2 35/2 35/2 33/2 33/2 33/2 37/2 37/2 37/2 31/2 31/2 31/2 18 , 35/2 35/2 35/2 39/2 39/2 39/2 33/2 33/2 33/2 1 5 33/2 31/2 35/2 31/2 29/2 33/2 35/2 33/2 37/2 29/2 27/2 31/2 1 e 35/2 33/2 37/2 33/2 31/2 35/2 37/2 35/2 39/2 31/2 29/2 33/2 1 7 35/2 33/2 37/2 39/2 37/2 41/2 33/2 31/2 35/2 16 o 33/2 33/2 33/2 31/2 31/2 31/2 35/2 35/2 35/2 29/2 29/2 29/2 17 o 35/2 35/2 35/2 33/2 33/2 33/2 37/2 37/2 37/2 31/2 31/2 31/2 18 o 35/2 35/2 35/2 39/2 39/2 39/2 33/2 33/2 33/2 1 6 33/2 31/2 35/2 31/2 29/2 33/2 35/2 33/2 37/2 29/2 27/2 31/2 1 7 35/2 33/2 37/2 33/2 31/2 35/2 37/2 35/2 39/2 31/2 29/2 33/2 1 8 35/2 33/2 37/2 39/2 37/2 41/2 33/2 31/2 35/2 47285 47285 47285 47289 47289 47289 47327 47327 47327 47330 47331 47331 48388 48389 48389 48392 48393 48393 48431 48431 48431 48434 48434 48434 49577 49578 49578 4961 7 49617 49617 49620 49620 49620 .376 .789 .789 .460 .860 .860 .280 .708 .708 .917 .335 .335 .886 .274 .274 .722 .128 .128 .154 .557 .557 .573 .988 .988 .931 .402 .402 .061 .485 .485 .243 .671 .671 19 , 37/2 37/2 37/2 41/2 41/2 41/2 1 8 37/2 35/2 39/2 41/2 39/2 43/2 19 o 37/2 37/2 37/2 41/2 41/2 41/2 37/2 35/2 39/2 41/2 39/2 43/2 50847.848 50848.256 50848.256 50887.560 50887.989 50887.989 T a b l e 4 . 7 ( C o n t i n u e d ) 94 T r a n s i t i o n F ' - F , F " Ob s e r v e d F r e q u e n c y 19 , 3 5 / 2 3 5 / 2 3 5 / 2 2 0 , 4 1 / 2 4 1 / 2 4 1 / 2 3 9 / 2 3 9 / 2 3 9 / 2 4 3 / 2 4 3 / 2 4 3 / 2 3 7 / 2 3 7 / 2 3 7 / 2 21 , 4 3 / 2 4 3 / 2 4 3 / 2 14 o 2 9 / 2 2 9 / 2 2 9 / 2 2 7 / 2 2 7 / 2 2 7 / 2 3 1 / 2 3 1 / 2 3 1 / 2 2 5 / 2 2 5 / 2 2 5 / 2 15 o 3 1 / 2 3 1 / 2 3 1 / 2 2 9 / 2 2 9 / 2 2 9 / 2 3 3 / 2 3 3 / 2 3 3 / 2 1 8 3 5 / 2 3 3 / 2 3 7 / 2 1 9 4 1 / 2 3 9 / 2 4 3 / 2 3 9 / 2 3 7 / 2 4 1 / 2 4 3 / 2 4 1 / 2 4 5 / 2 3 7 / 2 3 5 / 2 3 9 / 2 2 0 4 3 / 2 4 1 / 2 4 5 / 2 1 4 2 9 / 2 2 7 / 2 3 1 / 2 2 7 / 2 2 5 / 2 2 9 / 2 3 1 / 2 2 9 / 2 3 3 / 2 2 5 / 2 2 3 / 2 2 7 / 2 1 5 3 1 / 2 2 9 / 2 3 3 / 2 2 9 / 2 2 7 / 2 3 1 / 2 3 3 / 2 3 1 / 2 3 5 / 2 19 o 3 5 / 2 3 5 / 2 3 5 / 2 2 0 o 4 1 / 2 4 1 / 2 4 1 / 2 3 9 / 2 3 9 / 2 3 9 / 2 4 3 / 2 4 3 / 2 4 3 / 2 3 7 / 2 3 7 / 2 3 7 / 2 21 o 4 3 / 2 4 3 / 2 4 3 / 2 13 , 2 7 / 2 2 7 / 2 2 7 / 2 2 5 / 2 2 5 / 2 2 5 / 2 2 9 / 2 2 9 / 2 2 9 / 2 2 3 / 2 2 3 / 2 2 3 / 2 14 , 2 9 / 2 2 9 / 2 2 9 / 2 2 7 / 2 2 7 / 2 2 7 / 2 3 1 / 2 3 1 / 2 3 1 / 2 1 9 3 5 / 2 3 3 / 2 3 7 / 2 2 0 4 1 / 2 3 9 / 2 4 3 / 2 3 9 / 2 3 7 / 2 4 1 / 2 4 3 / 2 4 1 / 2 4 5 / 2 3 7 / 2 3 5 / 2 3 9 / 2 2 1 4 3 / 2 4 1 / 2 4 5 / 2 1 3 2 7 / 2 2 5 / 2 2 9 / 2 2 5 / 2 2 3 / 2 2 7 / 2 2 9 / 2 2 7 / 2 3 1 / 2 2 3 / 2 2 1 / 2 2 5 / 2 1 4 2 9 / 2 2 7 / 2 3 1 / 2 2 7 / 2 2 5 / 2 2 9 / 2 3 1 / 2 2 9 / 2 3 3 / 2 5 0 8 9 0 . 5 7 5 5 0 8 9 1 . 0 3 9 5 0 8 9 1 . 0 3 9 5 2 2 0 1 . 4 7 3 5 2 2 0 1 . 8 7 5 5 2 2 0 1 . 8 7 5 5 2 2 0 4 . 9 6 6 5 2 2 0 5 . 3 3 1 5 2 2 0 5 . 3 3 1 5 2 2 4 5 . 4 2 5 5 2 2 4 5 . 7 9 5 5 2 2 4 5 . 7 9 5 5 2 2 4 8 . 1 8 9 5 2 2 4 8 . 6 0 2 5 2 2 4 8 . 6 0 2 5 3 6 5 2 . 1 2 1 5 3 6 5 2 . 5 8 5 5 3 6 5 2 . 5 8 5 2 4 9 6 6 2 4 9 6 6 2 4 9 6 6 2 4 9 6 9 2 4 9 7 0 2 4 9 7 0 2 4 9 9 3 2 4 9 9 3 2 4 9 9 3 2 4 9 9 9 2 4 9 9 9 2 4 9 9 9 2 9 8 7 4 2 9 8 7 5 2 9 8 7 5 2 9 8 7 8 2 9 8 7 8 2 9 8 7 8 2 9 9 0 2 2 9 9 0 2 2 9 9 0 2 . 0 7 9 . 3 4 3 . 3 4 3 . 8 4 1 . 0 8 6 . 0 8 6 . 5 6 9 . 8 2 1 . 8 2 1 . 2 9 7 . 5 0 6 . 5 0 6 . 8 7 6 . 1 34 . 1 3 4 . 5 8 8 . 8 8 8 . 8 8 8 . 2 1 1 . 4 6 9 . 4 6 9 T a b l e 4 . 7 ( C o n t i n u e d ) 95 T r a n s i t i o n F ' - F , F" Ob s e r v e d F r e q u e n c y 15 o 2 7 / 2 2 7 / 2 2 7 / 2 16 o 3 3 / 2 3 3 / 2 3 3 / 2 3 1 / 2 3 1 / 2 3 1 / 2 3 5 / 2 3 5 / 2 3 5 / 2 2 9 / 2 2 9 / 2 2 9 / 2 17 o 3 5 / 2 3 5 / 2 3 5 / 2 3 3 / 2 3 3 / 2 3 3 / 2 3 7 / 2 3 7 / 2 3 7 / 2 3 1 / 2 3 1 / 2 3 1 / 2 18 o 3 7 / 2 3 7 / 2 3 7 / 2 3 5 / 2 3 5 / 2 3 5 / 2 3 9 / 2 3 9 / 2 3 9 / 2 3 3 / 2 3 3 / 2 3 3 / 2 2 7 / 2 2 5 / 2 2 9 / 2 1 6 3 3 / 2 3 1 / 2 3 5 / 2 3 1 / 2 2 9 / 2 3 3 / 2 3 5 / 2 3 3 / 2 3 7 / 2 2 9 / 2 2 7 / 2 3 1 / 2 1 7 3 5 / 2 3 3 / 2 3 7 / 2 3 3 / 2 3 1 / 2 3 5 / 2 3 7 / 2 3 5 / 2 3 9 / 2 3 1 / 2 2 9 / 2 3 3 / 2 1 8 3 7 / 2 3 5 / 2 3 9 / 2 3 5 / 2 3 3 / 2 3 7 / 2 3 9 / 2 3 7 / 2 4 1 / 2 3 3 / 2 3 1 / 2 3 5 / 2 14 , 2 5 / 2 2 5 / 2 2 5 / 2 15 , 3 1 / 2 3 1 / 2 3 1 / 2 2 9 / 2 2 9 / 2 2 9 / 2 3 3 / 2 3 3 / 2 3 3 / 2 2 7 / 2 2 7 / 2 2 7 / 2 16 , 3 3 / 2 3 3 / 2 3 3 / 2 3 1 / 2 3 1 / 2 3 1 / 2 3 5 / 2 3 5 / 2 3 5 / 2 2 9 / 2 2 9 / 2 2 9 / 2 17 , 3 5 / 2 3 5 / 2 3 5 / 2 3 3 / 2 3 3 / 2 3 3 / 2 3 7 / 2 3 7 / 2 3 7 / 2 3 1 / 2 3 1 / 2 3 1 / 2 i a 2 5 / 2 2 3 / 2 2 7 / 2 1 5 3 1 / 2 2 9 / 2 3 3 / 2 2 9 / 2 2 7 / 2 3 1 / 2 3 3 / 2 3 1 / 2 3 5 / 2 2 7 / 2 2 5 / 2 2 9 / 2 1 6 3 3 / 2 3 1 / 2 3 5 / 2 3 1 / 2 2 9 / 2 3 3 / 2 3 5 / 2 3 3 / 2 3 7 / 2 2 9 / 2 2 7 / 2 3 1 / 2 1 7 3 5 / 2 3 3 / 2 3 7 / 2 3 3 / 2 3 1 / 2 3 5 / 2 3 7 / 2 3 5 / 2 3 9 / 2 3 1 / 2 2 9 / 2 3 3 / 2 2 9 9 0 7 . 5 2 5 2 9 9 0 7 . 7 8 4 2 9 9 0 7 . 7 8 4 3 4 8 1 6 3 4 8 1 6 3 4 8 1 6 3 4 8 2 2 3 4 8 2 3 3 4 8 2 3 3 4 8 4 3 3 4 8 4 3 3 4 8 4 3 3 4 8 5 0 3 4 8 5 0 3 4 8 5 0 3 9 7 8 7 3 9 7 8 7 3 9 7 8 7 3 9 7 8 9 3 9 7 8 9 3 9 7 8 9 3 9 8 1 4 3 9 8 1 4 3 9 8 1 4 3 9 8 1 7 3 9 8 1 7 3 9 8 1 7 4 4 7 8 5 4 4 7 8 5 4 4 7 8 5 4 4 7 8 7 4 4 7 8 8 4 4 7 8 8 4 4 8 1 1 4 4 8 1 2 4 4 8 1 2 4 4 8 1 5 4 4 8 1 5 4 4 8 1 5 . 3 3 8 . 5 9 0 . 5 9 0 . 9 6 7 . 2 3 2 . 2 3 2 . 4 5 9 . 7 3 6 . 7 3 6 . 3 8 3 . 6 6 0 . 6 6 0 . 5 8 1 . 8 2 4 . 8 2 4 . 5 8 1 . 8 0 3 . 8 0 3 . 3 6 1 . 6 0 2 . 6 0 2 . 6 3 9 . 8 7 6 . 8 7 6 . 6 3 8 . 8 7 5 . 8 7 5 . 7 5 6 . 0 0 8 . 0 0 8 . 8 7 2 . 1 3 9 . 1 3 9 . 2 5 9 . 5 0 0 . 5 0 0 96 T a b l e 4 . 7 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d F ' F " F r e q u e n c y 19 o 39/2 1 9 18 , 1 8 39/2 - 37/2 37/2 49807.225 39/2 37/2 - 37/2 35/2 49807.472 39/2 41/2 - 37/2 39/2 49807.472 37/2 37/2 - 35/2 35/2 49809.219 37/2 35/2 - 35/2 33/2 49809.465 37/2 39/2 - 35/2 37/2 49809.465 41/2 41/2 - 39/2 39/2 49833.029 41/2 39/2 - 39/2 37/2 49833.294 41/2 43/2 - 39/2 41/2 49833.294 35/2 35/2 - 33/2 33/2 49836.161 35/2 33/2 - 33/2 31/2 49836.434 35/2 37/2 - 33/2 35/2 49836.434 97 T a b l e 4 . 8 O b s e r v e d h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s i n (MHz) o f 8 1 B r 1 4 N C 0 b - t y p e t r a n s i t i o n s T r a n s i t i o n O b s e r v e d F1' F' - F1" F" F r e q u e n c y 1 3 i i 2 ~ 1 3 o ! 3 2 7 / 2 2 7 / 2 - 2 7 / 2 2 7 / 2 4 4 3 3 8 . 4 5 6 2 7 / 2 2 5 / 2 - 2 7 / 2 2 5 / 2 4 4 3 3 8 . 8 3 7 2 7 / 2 2 9 / 2 - 2 7 / 2 2 9 / 2 4 4 3 3 8 . 8 3 7 2 5 / 2 2 5 / 2 - 2 5 / 2 2 5 / 2 4 4 3 4 1 . 6 8 6 2 5 / 2 2 3 / 2 - 2 5 / 2 2 3 / 2 4 4 3 4 2 . 0 9 2 2 5 / 2 2 7 / 2 - 2 5 / 2 2 7 / 2 4 4 3 4 2 . 0 9 2 2 9 / 2 2 9 / 2 - 2 9 / 2 2 9 / 2 4 4 3 7 2 . 7 5 6 2 9 / 2 2 7 / 2 - 2 9 / 2 2 7 / 2 4 4 3 7 3 . 1 3 6 2 9 / 2 3 1 / 2 - 2 9 / 2 3 1 / 2 4 4 3 7 3 . 1 3 6 2 3 / 2 2 3 / 2 - 2 3 / 2 2 3 / 2 4 4 3 7 5 . 6 0 7 2 3 / 2 2 1 / 2 - 2 3 / 2 2 1 / 2 4 4 3 7 6 . 0 1 3 2 3 / 2 2 5 / 2 - 2 3 / 2 2 5 / 2 4 4 3 7 6 . 0 1 3 14 i 13 " 14 O 14 2 9 / 2 2 9 / 2 - 2 9 / 2 2 9 / 2 4 5 1 9 8 . 5 7 9 2 9 / 2 2 7 / 2 - 2 9 / 2 2 7 / 2 4 5 1 9 8 . 9 6 0 2 9 / 2 3 1 / 2 - 2 9 / 2 3 1 / 2 4 5 1 9 8 . 9 6 0 2 7 / 2 2 7 / 2 - 2 7 / 2 2 7 / 2 4 5 2 0 3 . 7 0 6 2 7 / 2 2 5 / 2 - 2 7 / 2 2 5 / 2 4 5 2 0 4 . 0 9 0 2 7 / 2 2 9 / 2 - 2 7 / 2 2 9 / 2 4 5 2 0 4 . 0 9 0 3 1 / 2 3 1 / 2 - 3 1 / 2 3 1 / 2 4 5 2 3 2 . 8 8 8 3 1 / 2 2 9 / 2 - 3 1 / 2 2 9 / 2 4 5 2 3 3 . 3 0 3 3 1 / 2 3 3 / 2 - 3 1 / 2 3 3 / 2 4 5 2 3 3 . 3 0 3 2 5 / 2 2 5 / 2 - 2 5 / 2 2 5 / 2 4 5 2 3 7 . 6 4 6 2 5 / 2 2 3 / 2 - 2 5 / 2 2 3 / 2 4 5 2 3 8 . 0 4 5 2 5 / 2 2 7 / 2 - 2 5 / 2 2 7 / 2 4 5 2 3 8 . 0 4 5 15 1 1 4 - 1 5 o , 5 3 1 / 2 3 1 / 2 - 3 1 / 2 3 1 / 2 4 6 1 3 1 . 8 8 7 3 1 / 2 2 9 / 2 - 3 1 / 2 2 9 / 2 4 6 1 3 2 . 2 6 5 3 1 / 2 3 3 / 2 - 3 1 / 2 3 3 / 2 4 6 1 3 2 . 2 6 5 2 9 / 2 2 9 / 2 - 2 9 / 2 2 9 / 2 4 6 1 3 5 . 5 4 0 2 9 / 2 2 7 / 2 - 2 9 / 2 2 7 / 2 4 6 1 3 5 . 9 5 0 2 9 / 2 3 1 / 2 - 2 9 / 2 3 1 / 2 4 6 1 3 5 . 9 5 0 3 3 / 2 3 3 / 2 - 3 3 / 2 3 3 / 2 4 6 1 6 6 . 4 3 3 3 3 / 2 3 1 / 2 - 3 3 / 2 3 1 / 2 4 6 1 6 6 . 8 3 0 3 3 / 2 3 5 / 2 - 3 3 / 2 3 5 / 2 4 6 1 6 6 . 8 3 0 2 7 / 2 2 7 / 2 - 2 7 / 2 2 7 / 2 4 6 1 6 9 . 7 5 1 2 7 / 2 2 5 / 2 - 2 7 / 2 2 5 / 2 4 6 1 7 0 . 1 7 1 2 7 / 2 2 9 / 2 - 2 7 / 2 2 9 / 2 4 6 1 7 0 . 1 7 1 98 T a b l e 4 . 8 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d F , ' F ' - F , " F" F r e q u e n c y 1 6 1 i 5 1 6 o 1 6 33/2 33/2 - 33/2 33/2 47140.884 33/2 31/2 - 33/2 31/2 47141.290 33/2 35/2 - 33/2 35/2 47141.290 31/2 31/2 - 31/2 31/2 47144.231 31/2 29/2 - 31/2 29/2 47144.625 31/2 33/2 - 31/2 33/2 47144.625 35/2 35/2 - 35/2 35/2 47175.688 35/2 33/2 - 35/2 33/2 47176.091 35/2 37/2 - 35/2 37/2 47176.091 29/2 29/2 - 29/2 29/2 47178.762 29/2 27/2 - 29/2 27/2 47179.153 29/2 31/2 - 29/2 31/2 47179.153 17 1 1 s ~ 1 7 o , 735/2 35/2 - 35/2 35/2 48227.944 35/2 33/2 - 35/2 33/2 48228.317 35/2 37/2 - 35/2 37/2 48228.317 33/2 33/2 - 33/2 33/2 48231.028 33/2 31/2 - 33/2 31/2 48231.480 33/2 35/2 - 33/2 35/2 48231.480 37/2 37/2 - 37/2 37/2 48263.076 37/2 35/2 - 37/2 35/2 48263.497 37/2 39/2 - 37/2 39/2 48263.497 31/2 31/2 - 31/2 31/2 48265.959 31/2 29/2 - 31/2 29/2 48266.369 31/2 33/2 - 31/2 33/2 48266.369 18 1 1 7 _ 18 o 1 8 37/2 37/2 - 37/2 37/2 49395.589 37/2 35/2 - 37/2 35/2 49395.985 37/2 39/2 - 37/2 39/2 49395.985 35/2 35/2 - 35/2 35/2 49398.620 35/2 33/2 - 35/2 33/2 49399.015 35/2 37/2 - 35/2 37/2 49399.015 39/2 39/2 - 39/2 39/2 49431.171 39/2 37/2 - 39/2 37/2 49431.572 39/2 41/2 - 39/2 41/2 49431.572 33/2 33/2 - 33/2 33/2 49433.866 33/2 31/2 - 33/2 31/2 49434.286 33/2 35/2 - 33/2 35/2 49434.286 T a b l e 4 . 8 ( C o n t i n u e d ) 99 T r a n s i t i o n F ' F" O b s e r v e d F r e q u e n c y 20 , 41/2 41/2 41/2 43/2 43/2 43/2 37/2 37/2 37/2 14 o 27/2 27/2 31/2 31/2 25/2 25/2 15 o 31/2 31/2 29/2 29/2 33/2 33/2 33/2 27/2 27/2 27/2 16 o 33/2 33/2 33/2 31/2 31/2 31/2 35/2 35/2 35/2 29/2 29/2 29/2 1 9 41/2 39/2 43/2 43/2 41/2 45/2 37/2 35/2 39/2 1 4 25/2 29/2 29/2 33/2 23/2 27/2 1 5 29/2 33/2 27/2 31/2 33/2 31/2 35/2 27/2 25/2 29/2 1 6 33/2 31/2 35/2 31/2 29/2 33/2 35/2 33/2 37/2 29/2 27/2 31/2 20 o 41/2 41/2 41/2 43/2 43/2 43/2 37/2 37/2 37/2 13 , 25/2 25/2 29/2 29/2 23/2 23/2 14 , 29/2 29/2 27/2 27/2 31/2 31/2 31/2 25/2 25/2 25/2 15 , 31/2 31/2 31/2 29/2 29/2 29/2 33/2 33/2 33/2 27/2 27/2 27/2 2 0 41/2 39/2 43/2 43/2 41/2 45/2 37/2 35/2 39/2 1 3 23/2 27/2 27/2 31/2 21/2 25/2 1 4 27/2 31/2 25/2 29/2 31/2 29/2 33/2 25/2 23/2 27/2 1 5 31/2 29/2 33/2 29/2 27/2 31/2 33/2 31/2 35/2 27/2 25/2 29/2 51982 51983 51 983 52019 52019 52019 52021 52022 52022 .974 .420 .420 .489 .918 .918 .875 .301 .301 24515.015 24515.015 24534.838 24534.838 24539.391 24539.391 29382, 29382, 29385, 29385, 29404, 29405, 29405, 29409, 29409, 29409, 1 76 1 76 379 379 897 1 29 1 29 1 24 377 377 34284 34285 34285 34289 34289 34289 34307 34307 34307 34312 3431 2 34312 .843 .101 .101 .066 .307 .307 .549 .818 .818 .372 .628 .628 T a b l e 4 . 8 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d F , ' F ' - F , " F" F r e q u e n c y 17 o 1 7 16 , 35/2 35/2 33/2 35/2 33/2 33/2 35/2 37/2 33/2 33/2 33/2 31/2 33/2 31/2 31/2 33/2 35/2 31/2 37/2 37/2 35/2 37/2 35/2 35/2 37/2 39/2 35/2 31/2 31/2 29/2 31/2 29/2 29/2 31/2 33/2 29/2 18 o 18 17 , 37/2 37/2 35/2 37/2 35/2 35/2 37/2 39/2 35/2 35/2 35/2 33/2 35/2 33/2 33/2 35/2 37/2 33/2 39/2 39/2 37/2 39/2 37/2 37/2 39/2 41/2 37/2 33/2 33/2 31/2 33/2 31/2 31/2 33/2 35/2 31/2 19 o 1 9 18 , 37/2 37/2 35/2 37/2 35/2 35/2 37/2 39/2 35/2 41/2 41/2 39/2 41/2 39/2 39/2 41/2 43/2 39/2 35/2 35/2 33/2 35/2 33/2 33/2 35/2 37/2 33/2 33/2 39217.392 31/2 39217.659 35/2 39217.659 31/2 39219.118 29/2 39219.365 33/2 39219.365 35/2 39239.819 33/2 39240.106 37/2 39240.106 29/2 39242.507 27/2 39242.779 31/2 39242.779 135/2 44176.713 33/2 44176.950 37/2 44176.950 33/2 44178.596 31/2 44178.845 35/2 44178.845 37/2 44198.763 35/2 44199.018 39/2 44199.018 31/2 44201.493 29/2 44201.780 33/2 44201.780 ^5/2 49161.454 33/2 49161.708 37/2 49161.708 39/2 49181.244 37/2 49181.480 41/2 49181.480 33/2 49183.806 31/2 49184.084 35/2 49184.048 101 4 . 7 The S t r u c t u r e o f BrNCO The s t r u c t u r a l i n f o r m a t i o n t h a t can be d e r i v e d f r o m BrNCO i s somewhat l i m i t e d b e c a u s e r o t a t i o n a l c o n s t a n t s were measured f o r o n l y two i s o t o p i c s p e c i e s : 7 9 B r N C 0 and 8 1 B r N C 0 . However some r e a s o n a b l e d e d u c t i o n s c a n be made. The i n e r t i a l d e f e c t , w h i c h i s t h e same f o r b o t h i s o t o p e s , i s a s m a l l , p o s i t i v e number (s e e T a b l e s 4.3 and 4 . 4 ) . T h i s i m p l i e s t h a t BrNCO i s p l a n a r ( s e e s e c t i o n 2 . 5 ) . F u r t h e r m o r e , the r a t i o s o f the o u t o f p l a 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 xcc ( 8 1 B r N C 0 ) / X 0 0 ( 7 9 B r N C 0 ) = 0.835. T h i s i s c l o s e to t h e r a t i o o f t h e q u a d r u p o l e moments o f t h e b r o m i n e atoms (0.8354) w h i c h s u p p o r t s the c o n c l u s i o n t h a t BrNCO i s p l a n a r . T a b l e 4 . 9 Bromine 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 i n P r i n c i p a l I n e r t i a l Axes 7 9 B r N C 0 8 1 B r N C 0 Xaa (MHz) 608.41(52) 508.49(52) X b b (MHz) -164.16(26) -137.59(26) X c c (MHz) -444.25(26) -370.90(26) The 1 4 N 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 c o n s i s t e n t w i t h the c o n f i g u r a t i o n BrNCO r a t h e r t h a n BrOCN. I f the s t r u c t u r e were BrOCN, the C-N bond would p r o b a b l y be a p r i n c i p a l a x i s i n the 102 n i t r o g e n q u a d r u p o l e t e n s o r . I n t h i s c a s e Xzz w o u l d be = -4 MHz ( 1 5 ) . A s s u m i n g c y l i n d r i c a l symmetry x c c w o u l d t h e r e f o r e be — 2 MHz. Even w i t h a l a r g e asymmetry a b o u t the C-N bond, Xcc w o u l d s t i l l be e x p e c t e d to be p o s i t i v e . T a b l e 4.10 shows t h a t Xcc f o r b o t h i s o t o p e s i s i n f a c t n e g a t i v e , hence the c o n f i g u r a t i o n i s p r o b a b l y BrNCO. T a b l e 4.10 1 4 N 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 i n P r i n c i p a l I n e r t i a l Axes 9 B r N C 0 8 1 B r N C 0 5.09(78) 4.75(51) 1.64(39) -1.41(26) 3.45(39) -3.33(26) X a a (MHz) X b b (MHz) Xcc (MHz) A l e a s t s q u a r e s f i t was u s e d to f i t t h e r o t a t i o n a l c o n s t a n t s to t h e s t r u c t u r a l p a r a m e t e r s . Because o f the l i m i t e d number o f c o n s t a n t s a v a i l a b l e , some o f the s t r u c t u r a l p a r a m e t e r s had to be h e l d f i x e d . The N-C and C-0 bond l e n g t h s were h e l d f i x e d a t t h e i r v a l u e s i n C1NC0(4). T h i s i s a r e a s o n a b l e a s s u m p t i o n b e c a u s e t h e s e p a r a m e t e r s do n o t change v e r y much w i t h i n the group o f i s o c y a n a t e m o l e c u l e s whose s t r u c t u r e s have been d e t e r m i n e d ( 1 6 , 1 7 ) . The N-C-0 a n g l e was h e l d f i x e d a t v a l u e s v a r y i n g between 9.13° as i n C1NC0, and 0° w h i c h c o r r e s p o n d s to a l i n e a r NCO g r o u p . T h r e e f i t s were done to d e t e r m i n e v a l u e s f o r the Br-N bond l e n g t h and the Br-N-C a n g l e . The r e s u l t i n g 103 T a b l e 4.11 S t r u c t u r a l p a r a m e t e r s o f b r o m i n e i s o c y a n a t e I I I I I I r ( B r - N ) / A 1.836 1 . 847 1.863 r (N-C) V A 1.225 1 . 225 1 . 225 r ( C - 0 ) V A 1 . 162 1 . 162 1 .162 <(BrNC) 121.59° 119.44° 116 . 74° < ( N C 0 ) 2 o 0 o 4 9.13° < ( B r - N - a ) 3 28.5° 28.65° 28.8° 1 V a l u e f i x e d a t t h a t o f C1NC0 ( 5 ) . 2 V a l u e f i x e d f o r each s t r u c t u r a l d e t e r m i n a t i o n . 3 A n g l e between Br-N bond and a - i n e r t i a l a x i s . p a r a m e t e r s a r e shown i n T a b l e 4.11. T a b l e 4.12 shows some c o m p a r i s o n s w i t h o t h e r m o l e c u l e s . The BrNC a n g l e i s r e a s o n a b l e when compared w i t h the C1NC a n g l e i n C1NC0. A l s o , the Br-N bond l e n g t h a g r e e s w e l l w i t h the Br-N bond l e n g t h s i n o t h e r m o l e c u l e s . F o r a more d e f i n i t i v e s t r u c t u r a l d e r i v a t i o n , moments o f i n e r t i a o f o t h e r i s o t o p i c s p e c i e s o f BrNCO w i l l have to be d e t e r m i n e d . The c o n f i g u r a t i o n o f BrNCO r e l a t i v e to i t s p r i n c i p a l i n e r t i a l axes i s shown i n F i g u r e 4.7. 104 T a b l e 4.12 C o m p a r i s o n o f S t r u c t u r a l P a r a m e t e r s o f BrNCO W i t h V a l u e s i n O t h e r M o l e c u l e s r ( B r - N ) ( A ) BrNCO 1 1.85 CH 3C(0)NHBr (18) 1.82 C 6 H 5 C ( 0 ) N H B r (19) 1.82 B r N ( C 0 C H 2 ) 2 (19) 1.84 BrNO (11) 2.14 Sum o f s i n g l e bond r a d i i (20) 1.84 <(XNC) BrNCO 1 119° C1NC0(4,5) 118° ' V a l u e s t a k e n from S t r u c t u r e I I F i g u r e 4 . 7 The atoms o f BrNCO i n i t s p r i n c i p a l i n e r t i a l a x i s s y s t e m a c c o r d i n g to s t r u c t u r e I I ( T a b l e 4.11). 105 4 . 8 Br and 1 4 N Q u a d r u p o l e C o u p l i n g The 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 a n u c l e u s i n a m o l e c u l e c o n t a i n i n f o r m a t i o n a b o u t t h e d i s t r i b u t i o n o f c h a r g e s i n the m o l e c u l e ; t h e r e f o r e s o m e t h i n g c a n be l e a r n e d a b o u t the n a t u r e o f t h e c h e m i c a l b o n d i n g i n v o l v e d . F i r s t , h o w e v e r , t h 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 i n the i n e r t i a l a x i s s y s t e m n e e d to be t r a n s f o r m e d i n t o t h e p r i n c i p a l q u a d r u p o l e axes s y s t e m . The m e a s u r e m e n t o f x a b has e n a b l e d us to do t h i s . F o r a p l a n a r m o l e c u l e t h i s u n i t a r y t r a n s f o r m a t i o n i s : x' - u x U"1 . 1 _ X z z 0 0 u = X a b 0 c o s l s i n ( 0 X x x 0 Xab Xb b 0 s i n ( c o s ( 0 0 X 0 0 X c 0 0 1 y y ( 4 . 3 ) where & z a i s the a n g l e b e t w e e n the a - i n e r t i a l a x i s and the z -p r i n c i p a l q u a d r u p o l e a x i s , and X z z , X x x a n d Xyy a r e t h e p r i n c i p a l v a l u e s o f t h e b r o m i n e q u a d r u p o l e c o u p l i n g t e n s o r . The y - a x i s i s d e f i n e d to be p e r p e n d i c u l a r to t h e p l a n e o f the 106 m o l e c u l e . The r e s u l t i n g e q u a t i o n s a r e : X z z Xy y X a a c o s 2 ( ? z a + 2 X a b c o s 6 z a s i n 6 z a + x b b s i n 2 S : a - 2 * a b c o s 0 2 a s i n « z a + x b b c o s 2 0 (4.4) F o r many m o l e c u l e s x a b ^ s n o t d e t e r m i n e d . However, x z z and Xxx c a n s t i l l be c a l c u l a t e d u s i n g the 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 i s o t o p i c a l l y s u b s t i t u t e d m o l e c u l e s , or by a s s u m i n g t h a t t h e p r i n c i p a l q u a d r u p o l e a x i s l i e s a l o n g t h e bond c o n t a i n i n g t h e q u a d r u p o l e n u c l e u s g i v i n g a v a l u e f o r 9za . However, i n BrNCO, xao i s w e 1 1 - d e t e r m i n e d and 8za c a n be c a l c u l a t e d from th e r e l a t i o n s h i p : t a n 2 0 z a = 2 * a b (4.5) Xa a - Xb b C o m p a r i s o n o f 8za w i t h t h e a n g l e between the b r o m i n e -n i t r o g e n bond a x i s and the a - a x i s shows t h a t the z - a x i s does i n d e e d l i e a l o n g t h e bond a x i s ( s e e T a b l e 4.11). The =1° d i f f e r e n c e i s p r o b a b l y n o t s i g n i f i c a n t b u t f u r t h e r r e f i n e m e n t o f the s t r u c t u r a l p a r a m e t e r s i s r e q u i r e d to c o n f i r m t h i s . The p r i n c i p a l v a l u e s o f t h e b r o m i n e q u a d r u p o l e c o u p l i n g t e n s o r a r e g i v e n i n T a b l e 4.13. The i n t e r p r e t a t i o n o f t h e s 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 i n terms o f t h e t y p e o f c h e m i c a l b o n d i n g between the b r o m i n e and 107 T a b l e 4.13 P r i n c i p a l V a l u e s o f the Bromine Q u a d r u p o l e C o u p l i n g T e n s o r 7 9 B r S C N 8 1 B r S C N X z z ( M H z ) 8 9 3 . 9 5 C 4 6 ) 1 746.41(46) X x x ( M H z ) -449.70(36) -375.51(31) X y y ( M H z ) -444.25(26) -370.90(26) 0za (deg ) 27.45(1) 27.42(1) 1 U n c e r t a i n t i e s a r e one s t a n d a r d d e v i a t i o n 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 . 2 9za i s t h e a n g l e between the z - p r i n c i p a l q u a d r u p o l e a x i s i n the a - i n e r t i a l a x i s . n i t r o g e n n u c l e i r e q u i r e s t h a t s e v e r a l a s s u m p t i o n s a r e made, such as n e g l e c t o f o r b i t a l o v e r l a p , and s and p o r b i t a l h y b r i d i z a t i o n . D e r i v e d q u a n t i t i e s s u c h as i o n i c bond c h a r a c t e r s h o u l d n o t be t a k e n to be e x a c t , b u t r a t h e r as i n d i c a t i o n s o f the r e l a t i v e c o n t r i b u t i o n s o f each p o s s i b l e r e s o n a n c e form. One o f t h e main a s s u m p t i o n s i s t h a t t h e p a r t i a l l y f i l l e d p o r b i t a l s a r e p r i m a r i l y r e s p o n s i b l e f o r t h e e l e c t r i c f i e l d g r a d i e n t s a r o u n d a q u a d r u p o l a r n u c l e u s ( 7 ) . These f i e l d g r a d i e n t s c a n t h e r e f o r e be r e l a t e d to the number or f r a c t i o n a l number o f e l e c t r o n s i n the v a l e n c e p o r b i t a l s . The e q u a t i o n s o f Townes and D a i l e y (7) a r e : * S g = e Q ( l s = "< UP> 8 eQ cInim g = x, y, z (4.6) < V x - r ( * y + n z ) " n x ( U p ) y - f ( n z + n x ) - n y ( U p ) z = H n x + n y ) - n z (4.7) 108 n x , n y and n z r e p r e s e n t the number o f e l e c t r o n s i n the p x , p y and p z o r b i t a l s . F o r a s i n g l e b r o m i n e atom q n l m = q 4 1 0 = - q z and q x = q y = " l / 2 q z • When t h e b r o m i n e atom i s bound to a n o t h e r atom, t h e e l e c t r i c f i e l d g r a d i e n t s a b o u t the n u c l e u s a r e m o d i f i e d , so t h a t c o m p a r i s o n s o f e x p e r i m e n t a l 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 w i t h t h o s e o f a f r e e b r o m i n e atom w i l l g i v e some measure o f the typ e o f bond i n v o l v e d , e.g. the d e g r e e o f TT b o n d i n g or the i o n i c o r c o v a l e n t c h a r a c t e r . The t h r e e most l i k e l y r e s o n a n c e forms c o n t r i b u t i n g to the o v e r a l l s t r u c t u r e o f BrNCO a r e : Br B r + B r + \ X N=C=0 "N=C=0 N-C ^0 I I I I I Form I I I shows a r e s o n a n c e form o f BrNCO w i t h an o u t - o f - p l a n e TT bond between t h e Br and N n u c l e i . The d i f f e r e n c e i n x x  a n d Xyy i s d i r e c t l y r e l a t e d to t h e number or f r a c t i o n a l number o f e l e c t r o n s l o s t from Br as a r e s u l t o f TT b o n d i n g . The d o u b l e bond c h a r a c t e r i s d e n o t e d TT and i s g i v e n by (20) : Xy y ) 3 e Q q B r (4.8) 7T a l s o r e p r e s e n t s the f r a c t i o n a l c o n t r i b u t i o n o f form I I I to the o v e r a l l s t r u c t u r e o f BrNCO. xx x a n c ^ Xyy a ^ e v e r y c l o s e ; n I m p l y i n g t h a t t h e Br-N bond i s e s s e n t i a l l y c y l i n d r i c a l l y s y m m e t r i c . In C1NC0 the amount o f n c h a r a c t e r was c a l c u l a t e d to be f r o m 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 ( 4 ) . The r e s o n a n c e form f o r n b o n d i n g i n C1NC0 i s C1 + 0 T h i s i s c o n s i s t e n t w i t h the 9.13° bend i n t h e NCO group i n C1NC0 w i t h t h e 0 atom t r a n s to the C l atom. The NCO group may be c l o s e r t o b e i n g l i n e a r i n BrNCO b u t no c o n c l u s i o n s can be drawn b e f o r e a f u r t h e r s t r u c t u r a l i n v e s t i g a t i o n i s c a r r i e d o u t . A measure o f t h e i o n i c c h a r a c t e r o f the Br-N bond can be c a l c u l a t e d u s i n g the V a l e n c e Bond t h e o r y p r o p o s e d by Townes and D a i l e y . The w e i g h t e d c o n t r i b u t i o n s o f a l l p o s s i b l e r e s o n a n c e s t r u c t u r e s a r e c o n s i d e r e d . Here o n l y forms I and I I need to be c o n s i d e r e d ; the c o n t r i b u t i o n o f form I I I may be n e g l e c t e d . Form I I r e p r e s e n t i n g a t o t a l l y i o n i c BrNCO i s shown w i t h the p o s i t i v e p o l e on the b r o m i n e atom s i n c e \xzz | ^ | X B r | • The c o n t r i b u t i o n o f t h i s r e s o n a n c e s t r u c t u r e i s i and t h a t o f form I i s ( 1 - i ) . The p o r b i t a l p o p u l a t i o n s o f each o f t h e s e s t r u c t u r e s a r e : 109 -0.5% =4% n x = n y = 2 ; n z = 1 ( U p ) 2 = 1 I I n x = n y = 2 ; n z = 0 < U P > Z = 2 (4.9) 110 The i o n i c c h a r a c t e r i s o b t a i n e d from: Xzz - e Q q B r + 2 i ( l + e ) ] (4.10) The c o n t r i b u t i o n o f form I I must be m u l t i p l i e d by a f a c t o r (1+e) to a c c o u n t f o r the d e c r e a s e d s c r e e n i n g e f f e c t a t the Br n u c l e u s by t h e " e l e c t r o n s . e = 0.15 f o r the h a l o g e n s ( 2 2 ) . In BrNCO i = 12% and the s i n g l e bond c h a r a c t e r =87%. The i o n i c c h a r a c t e r o f BrNCO i s l a r g e r t h a n i n C1NC0 w h i c h a g r e e s w i t h the l o w e r e l e c t r o n e g a t i v i t y o f Br compared to C l . I t must be e m p h a s i z e d t h a t t h e c a l c u l a t e d c o n t r i b u t i o n o f e a c h o f t h e r e s o n a n c e s t r u c t u r e s i s o n l y v e r y r o u g h i n v i e w o f the a p p r o x i m a t i o n s made. An a t t e m p t was made to r e p r o d u c e the e x p e r i m e n t a l l y e v a l u a t e d 1 A N 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 u s i n g a t h e o r e t i c a l c a l c u l a t i o n . A m o d i f i e d CNDO c a l c u l a t i o n (CNDO/BW) was u s e d to e s t i m a t e the p o p u l a t i o n s o f t h e 2p o r b i t a l s o f n i t r o g e n a l o n g the d i r e c t i o n o f each o f the i n e r t i a l a x e s . These p o p u l a t i o n s were t h e n u s e d i n e q u a t i o n s 4.6 and 4.7 to c a l c u l a t e t h e n i t r o g e n 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 . e Q q 2 x 0 ( 1 *N) = -10MHz ( 2 3 ) . The t h e o r e t i c a l p - o r b i t a l p o p u l a t i o n s a r e : n a = 0.8770; n b = 1.3553; n c = 1.6776. A c o m p a r i s o n o f t h e e x p e r i m e n t a l and t h e o r e t i c a l n i t r o g e n 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 4.14. The t h e o r e t i c a l c a l c u l a t i o n s r e p r o d u c e t h e e x p e r i m e n t a l l y d e t e r m i n e d v a l u e s o n l y m o d e r a t e l y w e l l . T h i s may be b e c a u s e Br I l l T a b l e 4.14 C o m p a r i s o n o f e x p e r i m e n t a l l y d e t e r m i n e d 1 4 N 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 w i t h v a l u e s c a l c u l a t e d u s i n g t h e o r e t i c a l c a l c u l a t i o n s E x p e r i m e n t a l . T h e o r e t i c a l 7 9 B r N C O 8 1 B r N C O X a a ( M H z ) 5.09(78) 4.75(51) 6.39 X b b ( M H z ) -1.64(39) -1.42(26) -0.78 v (MHz) -3.45(39) -3.33(26) -5.61 and N have s i m i l a r e l e c t r o n e g a t i v i t i e s , d e m o n s t r a t i n g the need f o r i m p r o v e d t h e o r e t i c a l c a l c u l a t i o n s , p a r t i c u l a r l y when d e a l i n g w i t h m o l e c u l e s c o n t a i n i n g heavy atoms s u c h as b r o m i n e . 4.9 D i s c u s s i o n T h i s i s t h e f i r s t d e t a i l e d a n a l y s i s o f a s p e c t r u m o f b r o m i n e i s o c y a n a t e i n the gas phas e , a s i d e from t h e p h o t o e l e c t r o n s t u d y ( 3 ) . U n f o r t u n a t e l y o n l y t h r e e o f the f i v 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 one 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 c o u l d be measured, p a r t l y b e c a u s e t h e b - t y p e t r a n s i t i o n s were v e r y weak w h i c h p r e v e n t e d any b r a n c h e s o t h e r t h a n the K a = 1 <- 0 R and Q b r a n c h e s to be measured. T h i s a n a l y s i s , however, has amply d e m o n s t r a t e d the w o r t h o f our g l o b a l l e a s t - s q u a r e s f i t t i n g p r o c e d u r e . F o r the f i r s t time an a c c u r a t e v a l u e o f A Q has been e v a l u a t e d s o l e l y f r o m the 112 a n a l y s i s o f a.-type R b r a n c h t r a n s i t i o n s . T h i s method has the p o t e n t i a l to be a p p l i e d to a l a r g e number o f o t h e r m o l e c u l e s , a l t h o u g h i t s a p p l i c a t i o n i s r e s t r i c t e d to m o l e c u l e s c o n t a i n i n g n u c l e i w i t h l a r g e q u a d r u p o l e moments (eg Br and I ) , w i t h the a d d i t i o n a l l i m i t a t i o n t h a t 8za l i e s between =20° and 7 0 ° . The p r e c i s i o n o f the c o n s t a n t s d e r i v e d u s i n g t h i s method w i l l be d e p e n d e n t on the number o f n e a r - d e g e n e r a c i e s o f t h e c o r r e c t symme t r y . S e v e r a l 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 i n the s p e c t r u m o f BrNCO. R e l a t i v e i n t e n s i t y measurements p r o v i d e an e s t i m a t e o f t h e l o w e s t v i b r a t i o n a l f r e q u e n c y o f BrNCO a t - 116 ± 40 c m - 1 . T h i s i s p r o b a b l y the Br-N-C i n p l a n e b e n d i n g v i b r a t i o n . The i n e r t i a l d e f e c t ( s e e S e c t i o n 2.5) was a l s o u s e d to c a l c u l a t e t h i s f r e q u e n c y a t = 168cm _ 1 w h i c h i s s l i g h t l y h i g h e r t h a n the i n t e n s i t y measurements. A p a r t i a l r Q s t r u c t u r e has a l s o been d e t e r m i n e d f o r BrNCO. More i s o t o p i c d a t a w i l l be r e q u i r e d to o b t a i n a f u l l s u b s t i t u t i o n s t r u c t u r e . A l s o , b e c a u s e the i n f r a - r e d d a t a (2) a r e i n c o m p l e t e , and o n l y t h r e e out o f f i v 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 have been d e t e r m i n e d i n t h i s s t u d y f o r each i s o t o p e , t h e r e a r e i n s u f f i c i e n t d a t a to make a f o r c e - f i e l d d e t e r m i n a t i o n f o r t h i s m o l e c u l e , w h i c h w o u l d e n a b l e an r z s t r u c t u r e t o be c a l c u l a t e d . F i n a l l y , an a n a l y s i s o f the 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 BrNCO has shown the Br-N bond to be c o v a l e n t , w i t h a s m a l l amount o f i o n i c c h a r a c t e r . B i b l i o g r a p h y 113 1. W. G o t t a r d i , Angew Chem. I n t l . Ed. 10., 416, ( 1 9 7 1 ) . 2. W. G o t t a r d i , Monatsh. 103, 1150-1157, ( 1 9 7 3 ) . 3. D.C. F r o s t , C B . MacDonald, C A . Mc D o w e l l , N.P.C Westwood, Chem. Phys. 47., 111-124 ( 1 9 8 0 ) . 4. W.H. H o c k i n g , M.C.L. G e r r y , J . M o l . S p e c t r o s c . 42., 547-566 ( 1 9 7 2 ) . 5. W.H. H o c k i n g , M.L. W i l l i a m s , M.C.L. G e r r y , J . M o l . S p e c t r o s c . 58., 250 - 260 ( 1 9 7 5 ) . 6. D.J. M i l l e n , D. M i t r a , T r a n s F a r a d a y S o c , 66., 2414-2419 (1970) . 7. W. Gordy, R.L. Cook, "Microwave M o l e c u l a r S p e c t r a , " 3 r d . ed., i n " T e c h n i q u e s o f C h e m i s t r y " (A W e i s s b e r g e r , E d . ) , V o l . 18, pp. 725-802, W i l e y , New Y o r k , 1984. 8. See f o r example C. F l a n a g a n , L. P i e r c e , J . Chem. Phys. 3 8, 2963-2969, ( 1 9 6 3 ) ; W. Gordy, J.W. Simmons, A.G. Smith , Phys. Rev. 7_4, 243-249, ( 1 9 4 8 ) . 9. M.C.L. G e r r y , W. L e w i s - Bevan, N.P.C. Westwood, J . Chem. Phys. 79., 4655-4663, ( 1 9 8 3 ) . 10. J.A. Howe, J . Chem. Phys. 34., 1247-1249, ( 1 9 6 1 ) . 11. R.A. B e a u d e t , J . Chem. Phys. 50., 2002 - 2011 ( 1 9 6 9 ) . 12. R.D. Brown, P.D. G o d f r e y , R. Champion, D. McNaughton, J . Am. Chem. Soc. 103. 5715-5719, ( 1 9 8 1 ) . 13. H.P. Benz, A. Bauder, Hs. H. G u n t h a r d , J . M o l . S p e c t r o s c . 21. 156-164 ( 1 9 6 6 ) . 14. R. Kewley, K.V.L.N. S a s t r y , M. W i n n e w i s s e r , J . M o l . S p e c t r o s c . 10., 418 -441, ( 1 9 6 3 ) . 15. W.B. M o n i z , H.S. Gutowsky, J . Chem. Phys. 3_8, 1155- 1162, ( 1963) . 16. K. Yamada, J . M o l . S p e c t r o s c . 79., 323- 344 ( 1 9 8 0 ) . 17. H. Oberhammer, K. S e p p e t t , R. Mews, J . M o l . S t r u c t . 101. 325 - 331, (1983) . 114 18. R.J. Dubey, A c t a C r y s t , B. 2_7, 23 - 25 ( 1971 ). 19. 0. J a b e y , H. P r i t z o w , J . J a n d e r , Z. N a t u r f o r s c h . 3 2b. 1416-1420 , (1977) . 20. L. P a u l i n g . "The C h e m i c a l Bond." C o r n e l l U n i v e r s i t y P r e s s , I t h a c a , New Yo r k , 1960. 21. J.H. G o l d s t e i n , J . Chem Phys. 24,, 106 - 109 ( 1 9 5 6 ) . 22. C.H. Townes, A.L. Schawlow, "Microwave S p e c t r o s c o p y " , pp. 225-247, McGraw H i l l I n c . , New Y o r k , ( 1 9 5 5 ) . 23. E.A.C. L u c k e n , T r a n s . F a r a d a y S o c , 57., 729 - 734, ( 1 9 6 1 ) . 115 CHAPTER V: THE MICROWAVE SPECTRUM OF IODINE ISOCYANATE, INCO 5.1 I n t r o d u c t i o n I o d i n e i s o c y a n a t e i s t h e n e x t i n t h e s e r i e s o f h a l o g e n i s o c y a n a t e s . A f t e r the s u c c e s s i n u s i n g the l e a s t - s q u a r e s f i t t i n g p r o c e d u r e t o d e t e r m i n e s i m u l t a n e o u s l y t h e r o t a t i o n a l , c e n t r i f u g a l d i s t o r t i o n and 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 BrNCO, i t was d e c i d e d to a p p l y t h e same method to INCO. INCO i s e x p e c t e d to have a s i m i l a r s t r u c t u r e to BrNCO and C1NC0, and t h e r e f o r e s h o u l d a l s o be a n e a r - s y m m e t r i c p r o l a t e r o t o r . A l s o , b e c a u s e i o d i n e i s a r e l a t i v e l y h e a v y atom i t s h o u l d have a p r e d o m i n a t e l y s t r o n g a_-type R b r a n c h s p e c t r u m and t h i s , c o u p l e d w i t h the f a c t t h a t the i o d i n e n u c l e u s has a l a r g e q u a d r u p o l e moment, means t h a t INCO i s an i d e a l c a n d i d a t e f o r the method u s e d to a n a l y s e the s p e c t r u m o f BrNCO. The p r e p a r a t i o n o f INCO i n s o l u t i o n was f i r s t r e p o r t e d i n the 1930's by B i r c k e n b a c h and L i n h a r d ( 1 ) . S i n c e t h e n i t has commonly b e e n u s e d i n s o l u t i o n as a r e a g e n t u n d e r g o i n g e l e c t r o p h i l i c s t e r e o s p e c i f i c t r a n s a d d i t i o n to a l k e n e s : NCO I I INCO + >C = C< - C - C - (5.1) INCO c a n be g e n e r a t e d i n s i t u as a r e a c t i o n i n t e r m e d i a t e i n an e t h e r s o l u t i o n c o n t a i n i n g i o d i n e , s i l v e r c y a n a t e and an u n s a t u r a t e d compound. I t i s , however, s u f f i c i e n t l y s t a b l e t h a t i t c a n be u s e d from a p r e f o r m e d s o l u t i o n . The r e a c t i o n between 116 INCO and a l k e n e s p r o d u c e s i o d o i s o c y a n a t e s w h i c h c a n t h e n be t r e a t e d to f o r m a v a r i e t y o f m o l e c u l e s c o n t a i n i n g C - N b o n d s e . g . c a r b a m a t e s , u r e a s and amine h y d r o c h l o r i d e s ( 2 ) . O t h e r u s e s o f INCO i n s o l u t i o n i n c l u d e t h e m o d i f i c a t i o n o f u n s a t u r a t e d p o l y m e r s (3) and t h e o x i d a t i v e a d d i t i o n o f INCO to o r g a n o m e t a l 1 i c c o m p l e x e s ( 4 ) . The o n l y p r e v i o u s r e p o r t o f INCO i n t h e g a s e o u s p h a s e was o f i t s H e ( I ) p h o t o e l e c t r o n s p e c t r u m ( 5 ) , where i t was p r e p a r e d i n a f l o w s y s t e m by a m e t h o d s i m i l a r to t h e p r e p a r a t i o n o f B r N C O . The p h o t o e l e c t r o n s p e c t r a o f C 1 N C 0 , BrNCO and INCO a r e a l l s i m i l a r , and i t t h e r e f o r e seems l i k e l y t h a t INCO w i l l have a s i m i l a r s t r u c t u r e to t h e o t h e r h a l o g e n i s o c y a n a t e s . 5 . 2 E x p e r i m e n t a l M e t h o d s I o d i n e i s o c y a n a t e was p r e p a r e d by p a s s i n g I 2 v a p o u r a t a p r e s s u r e o f - 3 0 m T o r r o v e r s i l v e r c y a n a t e a t 1 5 0 - 1 9 0 ° C . I 2 ( g ) + A g N C O ( s ) INCO(g) + A g l c s ) ( 5 . 2 ) The s i l v e r c y a n a t e , w h i c h was p r e p a r e d as i n s e c t i o n 4 . 2 , h a d p r e v i o u s l y b e e n d r i e d by h e a t i n g t h e s a m p l e t o - 1 5 0 ° C f o r =24 h o u r s . T h i s i s c r u c i a l b e c a u s e INCO a p p e a r s to be e v e n more s u s c e p t i b l e t o h y d r o l y s i s t h a n B r N C O . H o w e v e r , d e s p i t e c a r e f u l d r y i n g , t h e p r o d u c t s o f h y d r o l y s i s , N H 3 and HNCO, were o b s e r v e d i n i t i a l l y . INCO was g e n e r a t e d i n a f l o w s y s t e m , b u t i t i s s u f f i c i e n t l y s t a b l e t h a t i t c o u l d be k e p t i n t h e m i c r o w a v e c e l l 117 f o r s e v e r a l m i n u t e s w i t h o u t a n o t i c e a b l e d e c r e a s e i n the i n t e n s i t y o f t h e s p e c t r u m . To r e s o l v e the n i t r o g e n h y p e r f i n e s p l i t t i n g i n the b - t y p e Q b r a n c h t r a n s i t i o n s , the c e l l was c o o l e d s l i g h t l y u s i n g d r y i c e , a l t h o u g h c a r e had to be t a k e n as INCO c o n d e n s e s a t d r y i c e t e m p e r a t u r e s . A l l o t h e r measurements were made a t room t e m p e r a t u r e . 5 .3 A n a l y s i s o f a - t v p e T r a n s i t i o n s I n i t i a l e s t i m a t 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 made u s i n g t h e bond l e n g t h s and a n g l e s t r a n s f e r r e d f r o m C1NC0(6,7), as w e l l as the I-N bond l e n g t h i n I N 3 ( 8 ) . The e s t i m a t e d c o n s t a n t s p r e d i c t e d INCO to be a n e a r - s y m m e t r i c p r o l a t e r o t o r w i t h t h e p o s s i b i l i t y o f b o t h a- and b - t y p e t r a n s i t i o n s . The 12 7 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 f o r I were e s t i m a t e d by a s s u m i n g t h a t t h e r a t i o o f xzz f o r I i n INCO to xzz f o r Br i n BrNCO i s the same as t h e r a t i o o f t h e q u a d r u p o l e moments o f the n u c l e i . The I-N bond was i n i t i a l l y t a k e n to be c y 1 i n d r i c a l l y s y m m e t r i c . As f o r BrNCO, th e i n i t i a l o b s e r v a t i o n o f t h e microwave s p e c t r u m o f INCO was o f a s e r i e s o f s t r o n g a - t y p e R b r a n c h t r a n s i t i o n s . F i g u r e 5.1 shows a t y p i c a l a - t y p e R b r a n c h group ( J = 9 <- 8) . The asymmetry s p l i t K a = 1 t r a n s i t i o n s a r e e a s i l y d i s t i n g u i s h e d on e i t h e r s i d e o f the main group o f l i n e s , b o t h f o r t h e g r o u n d s t a t e and f o r a t l e a s t f o u r e x c i t e d v i b r a t i o n a l s t a t e s . The K a = 0 l i n e s were much more d i f f i c u l t to i d e n t i f y b e c a u s e many o f them a r e p a r t i a l l y o v e r l a p p e d by o t h e r l i n e s . 118 INCO J = 9—8 29.68-30.71 GHz v= 0 1 2 34 Ka = 1 v= 0 1 2 3 4 Ka = 1 30100 MHz F i g u r e 5.1 Broadband s c a n o f the J = 9 <- 8 a_-type R b r a n c h of INCO i n the f r e q u e n c y r a n g e 29.68 - 30.71 GHz. The K a = 1 t r a n s i t i o n s f o r the g r o u n d s t a t e and f o r f o u r e x c i t e d v i b r a t i o n a l s t a t e s a r e i n d i c a t e d . 119 A l s o , b e c a u s e 1 2 7 l has a s p i n o f 5/2, e a c h t r a n s i t i o n showed q u a d r u p o l e h y p e r f i n e s p l i t t i n g w i t h 6 s t r o n g components, many o f w h i c h a p p e a r e d t o be s i g n i f i c a n t l y p e r t u r b e d . No h y p e r f i n e s p l i t t i n g due to t h e n i t r o g e n n u c l e u s was o b s e r v e d i n the a_-type t r a n s i t i o n s . A s s i g n m e n t s were made on a t r i a l and e r r o r b a s i s f o r some of the l e s s p e r t u r b e d K a = 1 and K a = 0 l i n e s , as w e l l as the more h i g h l y p e r t u r b e d t r a n s i t i o n 12 0 1 2 - 1 1 0 1 1 . The h y p e r f i n e components o f t h i s t r a n s i t i o n were p e r t u r b e d by as much as 49 MHz to l o w e r f r e q u e n c y b u t were n o t o v e r l a p p e d by o t h e r l i n e s . I t i s shown i n F i g u r e 5.2. U s i n g the same method t h a t was u s e d to f i t t h e a - t y p e R - b r a n c h e s o f BrNCO, the i n i t i a l a s s i g n m e n t s were p u t i n t o a l e a s t s q u a r e s f i t t o s i m u l t a n e o u s l y d e t e r m i n e t h e r o t a t i o n a l and I 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 p e r t u r b a t i o n s i n t h e h y p e r f i n e s t r u c t u r e a l l o w e d v a l u e s o f A Q and X a b to be d e t e r m i n e d a l o n g w i t h B Q , C Q , x a a and X b b - X o c -These c o n s t a n t s were t h e n u s e d to p r e d i c t and a s s i g n f u r t h e r a--t y p e l i n e s w i t h K a = 0 and K a = 1 f o r J between 5 and 15 i n the ra n g e 18-54 GHz. No a s s i g n m e n t s f o r t r a n s i t i o n s w i t h K a > 1 c o u l d be made b e c a u s e o f the o v e r l a p p i n g h y p e r f i n e s t r u c t u r e . The two r e q u i r e m e n t s f o r the s u c c e s s o f the l e a s t s q u a r e s f i t t i n g programme i n f i n d i n g a c c u r a t e v a l u e s o f A Q from a - t y p e R b r a n c h e s a r e met i n INCO. The f i r s t , t h a t i s the r e q u i r e m e n t t h a t xab s h o u l d be l a r g e , i s met b e c a u s e the q u a d r u p o l e moment of the n u c l e u s i s l a r g e and the a n g l e between the p r i n c i p a l q u a d r u p o l a r z - a x i s and t h e i n e r t i a l a - a x i s i s -24° ( s e e s e c t i o n INCO 12o.i2-11o.ii F split split (a) (i) (ii) (in) (b) F i g u r e 5 . 2 The 120 1 2 - 110 1 1 t r a n s i t i o n s o f INCO. (a) The a s s o c i a t e d e n e r g y l e v e l s a r e shown: ( i ) the h y p o t h e t i c a l u n s p l i t r o t a t i o n a l e n e r g i e s ; ( i i ) the p r e d i c t e d f i r s t o r d e r I q u a d r u p o l e e n e r g y l e v e l s ; ( i i i ) t h e I q u a d r u p o l e e n e r g y l e v e l s d e r i v e d from the e x a c t H a m i l t o n i a n . (b) The o b s e r v e d t r a n s i t i o n s a r e compared w i t h the c a l c u l a t e d f i r s t o r d e r and e x a c t H a m i l t o n i a n p a t t e r n s . 121 5 . 5 ) . The s e c o n d c o n d i t i o n , w h i c h a r i s e s b e c a u s e xab has o n l y a h i g h - o r d e r e f f e c t , i s t h a t t h e r e i s a number o f n e a r -d e g e n e r a c i e s w i t h t h e a p p r o p r i a t e s y m m e t r y . S e v e r a l o f t h e s e i n v o l v e r o t a t i o n a l e n e r g y l e v e l s w h i c h t a k e p a r t i n t r a n s i t i o n s i n t h e f r e q u e n c y r a n g e s t u d i e d . A n e n e r g y l e v e l d i a g r a m i s shown i n F i g u r e 5 . 3 . Some o f t h e c l o s e s t n e a r - d e g e n e r a c i e s , w h i c h p r o d u c e t h e l a r g e s t p e r t u r b a t i o n s i n t h e h y p e r f i n e s t r u c t u r e , a r e i n d i c a t e d ; t h o s e t h a t i n v o l v e m e a s u r e d a_-type t r a n s i t i o n s a r e b e t w e e n K a = 0 and K a = 1 l e v e l s . Some h y p e r f i n e c o m p o n e n t s were p e r t u r b e d by r e l a t i v e l y l a r g e a m o u n t s . F o r 1 2 l j : L 1 - 111 1 0 and 13 Q 1 3 -1 2 0 1 2 , t h e s e s h i f t s were as l a r g e as 100 MHz. From t h e s e a-t y p e t r a n s i t i o n s a l o n e , v a l u e s f o r A Q , B Q , C Q , A j , A J K and Sj, as w e l l as f o r x a a , X h h - X c c and xah f o r 1 271 , were w e l l -d e t e r m i n e d . T h e s e a r e shown i n T a b l e 5 . 1 . The c o r r e l a t i o n c o e f f i c i e n t s i n T a b l e 5 .2 show t h a t a l l t h e c o n s t a n t s , i n c l u d i n g A Q a n d x a b , a r e e s s e n t i a l l y u n c o r r e l a t e d . As i n t h e a n a l y s i s o f t h e s p e c t r u m o f B r N C O , an a c c u r a t e v a l u e o f A Q was e v a l u a t e d f o r INCO s o l e l y f r o m a_-type R b r a n c h t r a n s i t i o n s . The a c c u r a c y o f A Q to w i t h i n one s t a n d a r d d e v i a t i o n i s ~ 0 . 5 MHz. T h i s a l l o w e d us to p r e d i c t , w i t h a g r e a t d e a l o f a c c u r a c y t h e f r e q u e n c i e s o f some K a = 1 «- 0 b - t y p e t r a n s i t i o n s . 5 .4 A n a l y s i s o f b - t y p e T r a n s i t i o n s R a n d Q B r a n c h K a = 1 «- 0 b - t y p e t r a n s i t i o n s were p r e d i c t e d u s i n g t h e c o n s t a n t s i n T a b l e 5 . 1 . The a c c u r a c y o f t h e / 1 2 2 7 0 0 - 20o.2o . . . 45 6.54 MH 2 19!:!? , , 7 $ 600 19o.i 18!-" 16'-" 18o,18 120616 MHz 1 7 1 . 1 6 } 1 5 2 . K ' ' 1 . 17 500 • 170 16 1/2.12 U 2 . 1 3 N o 400 • 16g.l6 1.15 t e l . ' * " ' 1 , 1 5 1.1 ,,2.11 132.12 1 7 2.10 11 2 9 1 12.10 o LU UJ 3 0 0-200 • 1 00-Ho.H 13o.,3 12o.i 11 0.11 10o.io 8 0,8 7o.7 5o,s 40,4 3 0.3 10.1 1304 67 MHz • 1848.56 MHz n 1 . 1 2 '^1,12 1 ,1.10 ' ' 1.11 10!;,9o Q1.8 '1 ,9 Ql.7 °1.8 7I.6 ' 1 . 7 fi1-5  b1.6 8]« 52,3 32.4 Z.2 2 ?2|0 Oao F i g u r e 5.3 The r o t a t i o n a l e n e r g y l e v e l s o f INCO showing s e v e r a l i m p o r t a n t n e a r - d e g e n e r a c i e s between ( i ) K a l e v e l s 0 and 1 l e v e l s and ( i i ) K 1 and 2 123 T a b l e 5.1 S p e c t r o s c o p i c C o n s t a n t s o f 1 ^ ' INCO from a_-type t r a n s i t i o n s o n l y P a r a m e t e r R o t a t i o n a l C o n s t a n t s (MHz) A D 4 0 5 9 1 . 5 9 ( 5 3 ) ! B 0 1704.9870(19) C Q 1633.9090(17) 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) Aj 0.7571(20) A J K -155.80(45) 6j 0.0941(25) 12 7 I 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 (MHz) X a a -2235.2(16) X b b - X c c " 740.8(40) X a b -1671.95(25) Numbers i n p a r e n t h e s e s a r e one s t a n d a r d d e v i a t i o n 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 . 124 T a b l e 5.2 C o r r e l a t i o n c o e f f i c i e n t s o f t h e s p e c t r o s c o p i c c o n s t a n t s o f 1 2 7 I N C O c a l c u l a t e d f r o m a_-type t r a n s i t i o n s C c A . A J K 1 . 00 0.03 1.00 0.12 -0.67 1.00 0.04 0.43 0.27 1.00 0.17 0.22 0.13 0.03 1.00 Sj -0.04 0.88 -0.84 -0.14 0.07 1.00 X a a -0.09 -0.04 -0.17 -0.20 -0.05 0.04 1.00 * b b - X c c - 0 • 1 5 -0.20 -0.05 0.08 0.16 -0.01 1.00 X a b -0.42 -0.03 0.06 0.06 -0.04 -0.41 -0.18 0.06 1.00 p r e d i c t i o n was l i m i t e d by the u n c e r t a i n t y i n ( x b b - X c c ) - Many o f t h e s e t r a n s i t i o n s , w h i c h were much weaker t h a n the a - t y p e t r a n s i t i o n s and d i f f i c u l t to d e t e c t , were measured t o w i t h i n a few MHz o f the p r e d i c t e d f r e q u e n c i e s . Some t r a n s i t i o n s were not so e a s i l y i d e n t i f i e d f r o m t h i s e a r l y p r e d i c t i o n b e c a u s e t h e y were o v e r l a p p e d w i t h a - t y p e l i n e s , a l t h o u g h t h e i r a s s i g n m e n t s were c o n f i r m e d a f t e r a f u r t h e r r e f i n e m e n t o f t h e c o n s t a n t s . T h e r e was, however, an o b v i o u s anomaly. When the h y p e r f i n e components o f t h e t r a n s i t i o n 17 1 is'^-^o n w e r e i n c l u d e d i n a l e a s t s q u a r e s f i t , w h i c h i n c l u d e d o n l y t h o s e c o n s t a n t s t h a t were u s e d t o f i t the a_-type t r a n s i t i o n s , 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 f r e q u e n c i e s were as l a r g e as 3 MHz. T h i s was n o t due to a m i s a s s i g n m e n t b e c a u s e t h e r e were no o t h e r l i n e s o v e r l a p p i n g t h i s t r a n s i t i o n . However, from th e e n e r g y l e v e l d i a g r a m , i t was f o u n d t h a t the l e v e l 17 x 1 6 was =1200 MHz away from th e 1 5 2 1 4 l e v e l . N o r m a l l y f o r A K to be d e t e r m i n e d i n d e p e n d e n t l y o f A Q , t r a n s i t i o n s w i t h K a = 2 «- 1 a r e r e q u i r e d . I n BrNCO, no s u c h t r a n s i t i o n s were measured and A K was a s s i m i l a t e d i n t o A Q . I n INCO, however, b e c a u s e the h i g h - o r d e r s h i f t s o f the h y p e r f i n e components o f t h e 17 1 1 6 and 15 2 1 4 l e v e l s a r e c r i t i c a l l y d e p e n d e n t on the m a g n i t u d e o f the n e a r -d e g e n e r a c y , t h e y depend n o t o n l y on the m a g n i t u d 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 , b u t a l s o on the m a g n i t u d e s o f 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 . T h e r e f o r e t h e s i z e s o f the p e r t u r b a t i o n s a r e d e p e n d e n t on the v a l u e o f A K . Hence, i t was p o s s i b l e t h a t A Q and A K c o u l d be s e p a r a t e d . When A K was i n c l u d e d i n t h e . l e a s t s q u a r e s f i t , a r e a s o n a b l e v a l u e was o b t a i n e d , and the c a l c u l a t e d f r e q u e n c i e s f o r the h y p e r f i n e components o f the 17 x 1 6 - 1 7 0 1 7 t r a n s i t i o n f e l l w i t h i n the r.m.s. e r r o r o f the o b s e r v e d f r e q u e n c i e s . A K was s t i l l h i g h l y c o r r e l a t e d w i t h A Q . However, the v a l u e o f A K e s t i m a t e d from 17 1 x 6 - 17 0 1 7 was u s e d to p r e d i c t the f r e q u e n c i e s o f t h e h y p e r f i n e components o f the t r a n s i t i o n 20 Q 2 0 - 1 9 j i g . T h i s i s a p a r t i c u l a r l y i n t e r e s t i n g c a s e . The u n s p l i t e n e r g y l e v e l d i f f e r e n c e between 19.^  i g and 17 2 1 5 i s o n l y =420 MHz. T h i s i s the s m a l l e s t n e a r - d e g e n e r a c y i n v o l v i n g 126 t r a n s i t i o n s i n the f r e q u e n c y range s t u d i e d . The two l e v e l s a r e i n f a c t so c l o s e , t h a t o f the f o u r F components t h a t i n t e r a c t ( i . e . t h e y have the same F v a l u e ) , t h r e e o f t h e 19 x 1 9 l e v e l s l i e b e l o w th e c o r r e s p o n d i n g l e v e l s o f 17 2 1 5 and a r e p e r t u r b e d to l o w e r e n e r g y , w h i l e the f o u r t h , w i t h F=15/2, l i e s above and i s s h i f t e d to h i g h e r e n e r g y . T h i s i s shown i n F i g u r e 5.4. W i t h the i n c l u s i o n o f t h i s t r a n s i t i o n i n t o the l e a s t - s q u a r e s f i t , A K was now w e l l - d e t e r m i n e d and i n d e p e n d e n t o f A Q . 1 4 B e c a u s e th e N q u a d r u p o l e s t r u c t u r e was v e r y s m a l l , n i t r o g e n h y p e r f i n e s p l i t t i n g c o u l d be r e s o l v e d o n l y f o r the Q - b r a n c h b-t y p e t r a n s i t i o n s . U s i n g the same method as was u s e d f o r BrNCO, Xbb~Xcc f o r n i t r o g e n was c a l c u l a t e d i n a f i t u s i n g the q u a d r u p o l e H a m i l t o n i a n o f 2 n u c l e i u s i n g the c o u p l i n g scheme: ( J + I z = Fj_ ; Fj_ + I N = F) . x a a a n d Xbb-Xcc f o r i o d i n e were h e l d c o n s t a n t a l o n g w i t h Xaa f ° r n i t r o g e n w h i c h was n o t d e t e r m i n a b l e from t h e s e t r a n s i t i o n s . I t was c a l c u l a t e d by a s s u m i n g t h a t x c c i s t h e same as the a v e r a g e v a l u e o f x c c i n 7 9 8 1 1 4 BrNCO and BrNCO. The e f f e c t s o f t h e N q u a d r u p o l e c o u p l i n g were s u b t r a c t e d from the b - t y p e Q - b r a n c h f r e q u e n c i e s b e f o r e the f i n a l v a l u e s o f the o t h e r c o n s t a n t s were measured. The f i n a l c o n s t a n t s , d e r i v e d from the g l o b a l l e a s t - s q u a r e s f i t t o a l l the measured t r a n s i t i o n s , b o t h a_ and b t y p e , a r e shown i n T a b l e 5.3 a l o n g w i t h a c o m p a r i s o n w i t h t h e c o n s t a n t s m e asured from a,-type l i n e s a l o n e , where A K was a s s i m i l a t e d i n t o A o . U n f o r t u n a t e l y , b e c a u s e the number o f b r a n c h e s t h a t c o u l d be o b s e r v e d was l i m i t e d , 5 K c o u l d n o t be d e t e r m i n e d . T a b l e 5.4 F i g u r e 5 . 4 The e n e r g y l e v e l s o f 1 7 2 1 5 and 1 9 1 > 1 9 o f INCO showing ( i ) t h e h y p o t h e t i c a l u n s p l i t r o t a t i o n a l l e v e l s ; ( i i ) t h e c a l c u l a t e d f i r s t o r d e r s p l i t t i n g s and ( i i i ) t h e e x a c t s p l i t t i n g s . F o r 1 9 i . i 9 t h e l e v e l s w i t h F - 35/2, 37/2 and 39/2 a r e p u s h e d t o l o w e r e n e r g y by the c o r r e s p o n d i n g l e v e l s o f 1 7 2 1 5 , w h i l e t h e l e v e l w i t h 33/2 o f 191 1 9 i s p u s h e d to h i g h e r e n e r g y . 1 2 8 T a b l e 5 . 3 S p e c t r o s c o p i c C o n s t a n t s o f 1 2 7 I N C O P a r a m e t e r a-Types Only- A l l T r a n s i t i o n s R o t a t i o n a l C o n s t a n t s (MHz) C, 4 0 5 9 1 . 5 9 ( 5 3 ) 1 1 7 0 4 . 9 8 7 0 ( 1 9 ) 1 6 3 3 . 9 0 9 0 ( 1 7 ) 4 0 6 0 1 . 4 8 5 ( 3 3 ) 1 7 0 4 . 9 8 9 5 3 ( 4 4 ) 1 6 3 3 . 9 0 6 0 0 ( 3 9 ) 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) * J K 0 . 7 5 7 1 ( 2 0 ) - 1 5 5 . 8 0 ( 4 5 ) 0 . 0 9 4 1 ( 2 5 ) 0 . 7 5 2 6 ( 1 1 ) - 1 5 5 . 6 0 5 ( 7 9 ) 1 0 9 4 8 ( 1 5 ) - 0 . 0 9 6 9 5 ( 1 2 ) 12 7 I 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 (MHz) X a a X b b X c c X a b 2 2 3 5 . 2 ( 1 6 ) 7 4 0 . 8 ( 4 0 ) 1 6 7 1 . 9 5 ( 2 5 ) 2 2 3 8 . 3 3 ( 7 5 ) 7 3 4 . 8 3 0 ( 8 0 ) 1 6 7 1 . 8 1 ( 1 4 ) l 4 N 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 (MHz) X b b X c c 5 . 2 2 1 . 4 9 6 ( 1 8 ) Number o f R o t a t i o n a l T r a n s i t i o n s 2 7 4 7 S t a n d a r d D e v i a t i o n o f f i t (MHz) 0 . 0 5 8 0 . 0 3 8 1 Numbers i n p a r e n t h e s e s a r e one s t a n d a r d d e v i a t i o n 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 . 2 X a a w a s c a l c u l a t e d by a s s u m i n g t h a t x Q C ^ s the s a m e a s the a v e r a g e v a l u e o f x c c i n 7 9 B r N C O and 8 * BrNCO. 129 T a b l e 5 . 4 C o r r e l a t i o n c o e f f i c i e n t s o f the s p e c t r o s c o p i c c o n s t a n t s o f 1 2 7 I N C O A D 1.00 B Q 0.41 1.00 C D 0.82 -0.01 1.00 A-, 0.84 0.16 0.94 1.00 Aj K 0.81 0.70 0.56 0.73 1.00 A K -0.09 0.67 -0.27 -0.17 0.09 1.00 Sj -0.55 -0.77 -0.01 -0.22 -0.72 -0.24 1.00 Xaa 0.22 0.35 -0.26 -0.22 -0.11 0.77-0.01 1.00 Xbb-Xcc ° - 0 0 -0.10 0.05 0.03 0.05 -0.09 0.06 -0.05 1.00 Xah -0.10 -0.25 0.02 -0.03 -0.18 -0.07 0.15 0.03 -0.04 1.00 shows t h a t none o f the c o n s t a n t s , i n p a r t i c u l a r A Q and A K, a r e c o r r e l a t e d . I t i s n o t e w o r t h y t h a t A K was measured from t h e s e t r a n s i t i o n s . We have n o t o n l y b e en a b l e to d e t e r m i n e an a c c u r a t e A Q s o l e l y f r o m a - t y p e R b r a n c h t r a n s i t i o n s b o t h i n the a n a l y s i s o f the microwave s p e c t r u m o f BrNCO and i n the i n i t i a l a n a l y s i s o f INCO, b u t a l s o t h i s method has been e x t e n d e d so t h a t A K was d e t e r m i n e d from t r a n s i t i o n s from w h i c h i t would n o t n o r m a l l y be o b t a i n a b l e . Some o f t h e e n e r g i e s o f t h e K a = 1 l e v e l s i n K a = 1 <- 0 b - t y p e t r a n s i t i o n s were p e r t u r b e d by n e a r d e g e n e r a c i e s o f the t y p e K a 2 <- 1 , w h i c h a l l o w e d A K to be s e p a r a t e d from A Q . No K a = 2 <- 1 t r a n s i t i o n s c o u l d be measured. The r e l e v a n t n e a r - d e g e n e r a c i e s a r e shown i n t h e e n e r g y l e v e l d i a g r a m i n F i g u r e 5.3. T a b l e 5.5 g i v e s t h e m e a s u r e d f r e q u e n c i e s as w e l l as t h e c a l c u l a t e d r e s i d u a l s , w i t h x a b i n c l u d e d and o m i t t e d to show the m a g n i t u d e o f t h e h i g h - o r d e r s h i f t s . 131 T a b l e 5 5 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f INCO T r a n s i t i o n N o r m a l i s e d 1 F' - F" Weight O b s e r v e d 2 F r e q u e n c y Res i d u a l s 3 W i t h o u t x a b W i t h x a b 6 0 6 9/2 -11/2 -7/2 -1 3/2 -1 7/2 -15/2 -" 5 o 7/2 9/2 5/2 1 1/2 15/2 13/2 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 19978.071 19982.765 20003.661 20012.940 20038.666 20044.658 -20.546 -23.761 -9.042 -13.967 0. 1 23 -0.460 -0.004 -0.014 0.037 0.007 0.009 -0.004 7 , 7 11/2 -1 3/2 -9/2 -15/2 -17/2 -19/2 -" 6 , 9/2 1 1/2 7/2 13/2 15/2 1 7/2 61.000 1 .000 1 .000 1 .000 1 .000 1 .000 23101.368 23104.899 23116.751 23119.941 23135.731 23136.812 -0.021 0.382 0.002 1 .095 1 .809 1 .486 0.042 0.058 0.025 0.050 0.064 0.049 7 0 7 9/2 -19/2 -11/2 -17/2 -1 3/2 -15/2 -" 6 o 7/2 1 7/2 9/2 15/2 1 1/2 13/2 61.000 1 .000 1 .000 1 .000 1 .000 1 .000 23366.374 23372.965 23376.151 23377. 189 23391 .934 23393.259 12.010 0.047 31.713 -0.653 41.411 28.031 0.042 -0.053 0.027 -0.013 0.026 0.032 7 , 6 11/2 -13/2 -15/2 -9/2 -17/2 -19/2 -6 , 9/2 1 1/2 13/2 7/2 15/2 17/2 51.000 1 .000 1 .000 1 .000 1 .000 1 .000 23606.211 23606.717 23615.948 23617.646 23627.395 23631.369 0.979 0.421 -0.069 -0.071 0.225 0.993 0.006 -0.026 -0.021 -0.055 -0.030 -0.009 1 Measurements were w e i g h t e d a c c o r d i n g to l / a 2 , where a i s the u n c e r t a i n t y i n the measurements. U n i t w e i g h t c o r r e s p o n d e d to an u n c e r t a i n t y o f 0.03 MHz. 2 N i t r o g e n h y p e r f i n e s p l i t t i n g has been s u b t r a c t e d f r o m the b-t y p e Q b r a n c h t r a n s i t i o n s . 3 O b s e r v e d 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 the c o n s t a n t s i n T a b l e 5.3 132 T a b l e 5 . 5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F " No r m a l i s e d W e i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t xab W i t h x a b 1/2 3/2 9/2 5/2 9/2 7/2 1/2 3/2 9/2 5/2 9/2 7/2 1/2 3/2 5/2 9/2 7/2 9/2 3/2 5/2 1/2 7/2 21/2 9/2 3/2 5/2 1/2 7/2 1/2 9/2 5/2 3/2 1/2 7/2 9/2 21/2 1 8 1 .000 1 .000 1 .000 1 .000 0. 1 00 0. 100 .000 .000 .000 .000 .000 .000 .000 .000 .100 .100 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 0. 100 0. 1 00 1 .000 1 .000 1 .000 1 .000 26409.229 26412.527 26420.444 26424.204 26435.761 26435.761 26681.085 26684.285 26690.587 26695.709 26707.287 26710.014 26983.957 26984.656 26991.501 26991.501 27000.306 27003.029 29715.095 29718.030 29723.605 29727.382 29735.782 29736.293 30022.047 30026.278 30027.800 30034.914 30040.998 30042.335 131 131 30361 30361 30364.818 30365.946 30373.029 30375.840 •0.049 0. 1 63 025 530 738 838 •0 0 0, 0, •4, •6, 2 •5, 0 •0, 0, 0 1 , 2 •1 , •2, •1 , 0, •1 , 657 252 587 948 120 -0 .924 1.614 0.857 1 1 2 095 313 525 0.072 0.012 •0.054 0.245 0.451 0.474 102 718 1 77 789 082 510 591 1 20 048 032 620 785 021 053 .006 066 0.083 0.015 0 0 0 0 0 0 0 •0 0 0 007 012 005 001 031 019 0.017 0.005 •0.113 0. 1 38 •0.049 •0.025 0.004 •0.019 •0.016 •0.006 0.076 •0.007 0.012 •0.016 •0.021 •0.019 0.003 •0.011 •0, 0, 0, •0, •0, 0, 1 43 091 012 041 007 039 133 T a b l e 5 . 5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s ed We i g h t O b s e r v e d F r e q u e n c y Res i d u a l s W i t h o u t X a b W i t h x a b 10 , 1 7 / 2 1 9 / 2 1 5 / 2 2 1 / 2 2 5 / 2 2 3 / 2 10 o 1 7 / 2 1 5 / 2 1 9 / 2 2 1 / 2 2 3 / 2 2 5 / 2 10 , 1 5 / 2 1 9 / 2 2 1 / 2 1 7 / 2 2 3 / 2 2 5 / 2 11 i I 9 / 2 2 1 / 2 1 7 / 2 2 3 / 2 2 7 / 2 2 5 / 2 I I o 1 9 / 2 1 7 / 2 2 1 / 2 2 3 / 2 2 5 / 2 2 7 / 2 1 o 1 1 1 7 / 2 2 3 / 2 2 5 / 2 2 1 / 2 2 7 / 2 1 9 / 2 1 o 1 1 1 1 1 1 o 1 5 / 2 1 7 / 2 1 3 / 2 1 9 / 2 2 3 / 2 2 1 / 2 1 5 / 2 1 3 / 2 1 7 / 2 1 9 / 2 2 1 / 2 2 3 / 2 1 3 / 2 1 7 / 2 1 9 / 2 1 5 / 2 2 1 / 2 2 3 / 2 1 7 / 2 1 9 / 2 1 5 / 2 2 1 / 2 2 5 / 2 2 3 / 2 10 1 7 / 2 1 5 / 2 1 9 / 2 2 1 / 2 2 3 / 2 2 5 / 2 10 1 5 / 2 2 1 / 2 2 3 / 2 1 9 / 2 2 5 / 2 1 7 / 2 10 1 8 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 0 . 100 0 . 100 0 . 1 00 1 . 0 0 0 0 0 0 0 0 0 , 0 0 0 , 1 0 0 , 1 0 0 , 1 0 0 3 3 0 1 9 . 5 9 4 3 3 0 2 2 . 2 2 5 3 3 0 2 6 . 2 9 3 3 3 0 2 9 . 9 0 8 3 3 0 3 6 . 1 5 9 3 3 0 3 6 . 9 3 8 3 3 3 5 7 . 9 9 0 3 3 3 6 1 . 7 4 0 3 3 3 6 2 . 6 0 4 3 3 3 6 9 . 2 2 8 3 3 3 7 3 . 5 0 0 3 3 3 7 3 . 9 8 8 3 3 7 3 7 . 8 4 6 3 3 7 3 8 . 4 5 3 3 3 7 3 9 . 6 1 2 3 3 7 4 0 . 1 9 2 3 3 7 4 5 . 9 4 0 3 3 7 5 0 . 9 2 0 3 6 3 2 2 . 9 0 3 3 6 3 2 5 . 2 4 4 3 6 3 2 8 . 2 7 2 3 6 3 3 1 . 6 0 5 3 6 3 3 6 . 5 1 1 3 6 3 3 7 . 3 7 7 3 6 6 8 9 . 8 6 3 3 6 6 9 0 . 7 5 7 3 6 6 9 6 . 6 5 0 3 6 7 0 1 . 3 0 1 3 6 7 0 1 . 5 5 7 3 6 7 0 5 . 9 9 2 3 7 1 1 0 . 4 3 7 3 7 1 1 3 . 7 5 7 3 7 1 2 3 . 3 2 0 3 7 1 3 3 . 9 5 8 3 7 1 4 3 . 7 5 0 3 7 1 5 4 . 8 0 3 - 0 . 0 5 1 0 . 0 1 3 - 0 . 0 0 9 0 . 2 0 3 0 0 0, 7, 1 , 6, 3 0 7 3 4 3 - 2 . 3 8 2 - 3 . 3 7 6 - 0 . 8 9 8 - 1 . 2 7 8 - 2 . 6 9 7 0 . 0 8 3 - 0 . 0 8 0 4 . 4 1 5 2 9 5 6 2 6 4 5 5 2 4 4 - 0 . 1 3 6 - 0 . 0 8 5 - 0 . 1 2 6 0 . 0 2 0 0 . 163 0 . 1 9 5 - 4 . 8 7 2 - 7 . 9 5 9 - 0 . 6 5 9 - 1 . 7 6 3 - 6 . 1 7 1 0 . 0 5 9 - 0 . 0 6 5 1 . 7 6 3 7 . 1 2 1 2 6 . 3 9 6 2 7 . 6 0 0 4 8 . 6 0 8 0 . 0 3 0 0 . 0 2 2 0 3 5 0 5 6 0 6 3 0 2 8 • 0 . 0 1 7 • 0 . 0 1 1 • 0 . 0 2 9 • 0 . 0 0 8 0 . 0 0 4 0 . 0 1 2 •0 •0 0 •0 0 0 0 4 0 0 2 021 0 0 7 0 0 3 0 . 0 1 6 0 . 0 4 8 • 0 . 0 4 9 • 0 . 0 7 6 • 0 . 0 6 6 • 0 . 0 0 9 • 0 . 0 2 6 0 . 0 5 2 • 0 . 0 7 0 0 . 0 8 8 0 . 0 6 4 0 . 0 1 5 • 0 . 0 0 6 0 . 0 2 6 • 0 . 0 5 3 • 0 . 0 7 6 0 . 0 0 7 0 . 0 9 0 • 0 . 0 2 1 1 3 4 T a b l e 5 . 5 ( C o n t i n u e d ) T r a n s i t i o n N o r m a l i s e d Ob s e r v e d F ' - F " We i gh t F r e q u e n c y 12 , 1 2 " 11 1 i i 21/2 - 19/2 1 .000 39625.450 23/2 - 21/2 1 .000 39627.502 1 9/2 - 17/2 1 .000 39629.865 25/2 - 23/2 1 .000 39632.897 29/2 - 27/2 1 .000 39636.822 27/2 — 25/2 1 .000 39637.682 12 o 1 2 " 11 0 1 1 19/2 - 17/2 1 .000 39982.019 21/2 - 19/2 1 .000 40000.702 27/2 - 25/2 1 .000 40010.776 25/2 - 23/2 1 .000 40026.890 23/2 - 21/2 1 .000 40027.370 29/2 27/2 1 .000 40036.962 12 , 1 1 " 11 1 1 0 21/2 - 19/2 0. 100 40375.057 29/2 - 27/2 1 .000 40389.220 23/2 - 21/2 1 .000 40417.708 27/2 - 25/2 1 .000 40465.533 25/2 - 23/2 1 .000 40478.924 19/2 — 1 7/2 1 .000 40482.417 13 , 1 3 - 12 , 1 2 23/2 - 21/2 1 .000 42927.130 25/2 - 23/2 1 .000 42928.972 21/2 - 19/2 1.000 42930.875 27/2 - 25/2 1 .000 42933.616 31/2 - 29/2 1 .000 42936.822 29/2 — 27/2 1 .000 42937.644 13 o 1 3 - 12 o 1 2 25/2 - 23/2 1 .000 43364.895 31/2 - 29/2 1 .000 43366.541 27/2 - 25/2 1 .000 43385.969 23/2 - 21/2 0.100 43420.583 21/2 - 19/2 1 .000 43465.088 29/2 — 27/2 0.100 43465.697 13 , 1 2 " 12 , 1 1 21/2 - 19/2 0. 100 43853.888 27/2 - 25/2 0. 100 43856.716 29/2 - 27/2 1 .000 43865.600 25/2 - 23/2 1 .000 43867.346 23/2 - 21/2 1 .000 43872.824 31/2 - 29/2 1 .000 43895.390 Res i d u a l s W i t h o u t x a b W i t h x a b -0 .086 -0 .069 -0 .082 0.028 0. 1 60 0. 179 -48 .785 -26.671 -27 .457 -7 .429 -2 .136 0. 126 -1 03.942 -98 .109 -62 .537 -21 .969 -5 .089 -0 .123 - 0 . 108 -0 .075 -0 .062 0.029 0. 1 40 0. 1 55 4 0 21 62 1 03 98 792 075 783 256 738 1 60 - 0 . 108 1 .325 7.267 15.194 21.798 37.286 0.014 •0.008 •0.023 •0.015 0.032 0.016 0 0 0 0. 0, 0 0, •0, 0 •0, 0, •0, 071 023 016 022 010 068 065 056 059 015 006 013 0.010 0.015 0.007 0.022 0.041 0.031 •0.038 0.021 0.018 •0.070 •0.039 0.073 0. 0 •0 •0. •0 0 033 017 046 026 022 017 135 T a b l e 5 . 5 ( C o n t i n u e d ) T r a n s i t i o n N o r m a l i s e d O b s e r v e d F' F" Weight F r e q u e n c y W i t h o u t 14 , 1 4 - 13 1 1 3 25/2 - 23/2 1 .000 46228.027 -0.175 27/2 - 25/2 1 .000 46229.708 -0. 104 23/2 - 21/2 1 .000 46231.267 -0.088 29/2 - 27/2 1 .000 46233.761 0.017 33/2 - 31/2 1 .000 46236.475 0. 152 31/2 - 29/2 1 .000 46237.204 0. 128 14 o 1 4 " 13 O 1 3 31/2 - 29/2 1 .000 46658.210 -37.280 23/2 - 21/2 1 .000 46668.225 -22.073 25/2 - 23/2 1.000 46672.091 -15.491 29/2 - 27/2 1 .000 46685.082 -7.489 27/2 - 25/2 1 .000 46687.479 -1 .585 33/2 - 31/2 1 .000 46694.714 0.023 14 , 1 3 " 13 1 1 2 23/2 - 21/2 1 .000 47224.639 -0.188 29/2 - 27/2 0. 100 47226.213 0.097 27/2 - 25/2 0.100 47226.602 3.298 25/2 - 23/2 1 .000 47227.535 5.243 31/2 - 29/2 1 .000 47230.022 1 .388 33/2 - 31/2 1 .000 47235.438 7.051 Res i d u a l s W i t h X a b • a b •0.020 0.027 0.001 0.047 0.072 0.032 •0.042 0.010 0.014 0.023 •0.028 0.026 0.009 •0.013 •0.024 •0.016 •0.046 •0.023 15 , 1 5 " 14 , 1 4 27/2 - 25/2 1 .000 49528.210 -0.243 29/2 - 27/2 1 .000 49529.663 -0.226 25/2 - 23/2 1 .000 49531.029 -0.151 31/2 - 29/2 1 .000 49533.219 -0.107 35/2 - 33/2 1 .000 49535.589 0.071 33/2 - 31/2 1 .000 49536.301 0.093 15 o 15 - 14 o 1 4 27/2 - 25/2 1 .000 50011.379 -3.714 25/2 - 23/2 1 .000 50011.952 -5.624 33/2 - 31/2 1 .000 50014.908 -7.047 29/2 - 27/2 1 .000 50015.927 -0.402 31/2 - 29/2 1 .000 50017.802 -1.571 35/2 - 33/2 1 .000 50021.470 0.082 15 , " 14 , 1 3 29/2 - 27/2 0.100 50594.701 1 .000 27/2 - 25/2 0.100 50594.701 1 .908 25/2 - 23/2 0. 100 50594.701 -0.289 31/2 - 29/2 1 .000 50595.926 -0.237 33/2 - 31/2 0.100 50598.962 0.617 35/2 - 33/2 0. 100 50601.151 3.048 •0.030 •0.027 •0.030 •0.027 0.006 0.018 •0.022 0.010 •0.002 •0.007 0.007 0.037 0.038 •0.066 0.038 0.012 0.033 0.070 136 T a b l e 5 . 5 ( C o n t i n u e d ) T r a n s i t i o n N o r m a l i s e d O b s e r v e d R e s i d u a l s F ' - F" W e i g h t F r e q u e n c y W i t h o u t x a b W i t h x a b 13 , 1 2 - 13 0 1 3 2 1 / 2 - 2 1 / 2 1 . 000 42183 .411 - 3 7 . 7 1 3 3 1 / 2 - 3 1 / 2 1 . 000 4 2 2 1 6 . 0 8 4 - 1 6 . 6 1 0 2 3 / 2 - 2 3 / 2 1 . 000 4 2 2 3 9 . 3 4 0 - 4 0 . 6 7 0 2 9 / 2 - 2 9 / 2 1 . 000 4 2 2 4 3 . 3 8 6 - 5 7 . 9 0 8 2 5 / 2 - 2 5 / 2 1 . 000 4 2 3 0 4 . 5 1 5 - 1 2 . 8 8 8 2 7 / 2 — 2 7 / 2 1 . 000 4 2 3 1 3 . 8 3 3 - 1 3 . 0 3 6 14 , 1 3 - 14 0 1 a 2 3 / 2 - 2 3 / 2 1 . 000 4 2 7 3 9 . 8 1 0 - 1 5 . 8 4 3 3 3 / 2 - 3 3 / 2 1 . 000 4 2 7 5 6 . 8 1 5 - 9 . 5 7 5 2 5 / 2 - 2 5 / 2 1 . 000 4 2 7 9 4 . 8 1 7 - 1 9 . 9 0 3 3 1 / 2 - 3 1 / 2 1 . 000 4 2 8 1 5 . 2 1 7 - 1 9 . 2 2 2 2 7 / 2 - 2 7 / 2 1 . 0 0 0 4 2 8 4 3 . 6 2 5 - 8 . 0 1 8 2 9 / 2 — 2 9 / 2 1 . 000 4 2 8 5 4 . 9 4 8 - 5 . 4 6 6 15 , i a - 15 0 1 5 2 5 / 2 - 2 5 / 2 1 . 000 4 3 3 2 2 . 6 3 8 - 1 0 . 4 2 9 3 5 / 2 - 3 5 / 2 1 . 0 0 0 4 3 3 3 6 . 4 6 3 - 6 . 6 4 3 2 7 / 2 - 2 7 / 2 1 . 000 4 3 3 7 8 . 1 8 2 - 1 4 . 2 3 7 3 3 / 2 — 3 3 / 2 1 . 000 4 3 3 9 9 . 2 1 6 - 1 1 . 6 1 3 16 , 1 5 - 16 0 1 6 3 5 / 2 - 3 5 / 2 1 . 0 0 0 44023 .091 - 8 . 3 4 1 3 1 / 2 — 3 1 / 2 1 . 000 4 4 0 4 3 . 5 3 5 - 6 . 9 7 7 17 , 1 6 - 17 0 1 7 2 9 / 2 - 2 9 / 2 1 . 000 44599 .201 - 2 1 . 5 5 5 3 9 / 2 - 3 9 / 2 1 . 0 0 0 4 4 6 2 5 . 6 6 3 - 4 . 0 2 8 3 1 / 2 - 3 1 / 2 1 . 000 4 4 6 4 8 . 4 9 2 - 3 2 . 4 3 2 3 7 / 2 - 3 7 / 2 1 . 0 0 0 44690 .701 - 6 . 5 7 4 3 3 / 2 - 3 3 / 2 1 . 000 4 4 6 9 2 . 4 4 5 - 2 4 . 7 3 9 3 5 / 2 — 3 5 / 2 1 . 000 4 4 7 1 2 . 0 0 3 - 1 2 . 4 5 5 18 , 1 7 - 18 0 1 8 3 1 / 2 - 3 1 / 2 1 . 000 4 5 3 3 0 . 1 7 7 - 3 . 0 5 9 4 1 / 2 - 4 1 / 2 1 . 0 0 0 4 5 3 3 8 . 3 7 6 - 3 . 3 5 2 3 3 / 2 - 3 3 / 2 1 . 000 4 5 3 9 1 . 3 5 5 - 2 . 5 5 8 3 9 / 2 - 3 9 / 2 1 . 0 0 0 4 5 4 0 3 . 9 4 6 - 5 . 4 9 4 3 5 / 2 - 3 5 / 2 1 . 000 4 5 4 3 2 . 3 3 8 2 .211 3 7 / 2 — 3 7 / 2 1 . 0 0 0 4 5 4 3 8 . 5 7 6 1 . 540 19 , 1 8 - 19 0 1 9 3 3 / 2 - 3 3 / 2 1 . 000 4 6 0 8 9 . 5 4 0 - 3 . 4 7 1 4 3 / 2 - 4 3 / 2 1 . 000 4 6 0 9 8 . 2 7 2 - 2 . 8 4 3 3 5 / 2 - 3 5 / 2 1 . 000 4 6 1 5 0 . 4 7 2 - 3 . 7 8 1 4 1 / 2 - 4 1 / 2 1 . 000 4 6 1 6 4 . 2 9 4 - 4 . 7 6 7 3 7 / 2 - 3 7 / 2 1 . 000 4 6 1 9 0 . 4 2 4 - 0 . 0 6 3 3 9 / 2 - 3 9 / 2 1 . 0 0 0 4 6 1 9 7 . 0 2 0 - 0 . 0 5 5 •0 .044 •0 .080 0.001 •0 .004 0 . 0 3 9 0 . 0 2 5 •0. •0. 0 0. 0 060 069 003 012 029 0 . 0 1 9 0 . 0 6 7 • 0 . 0 6 9 0 . 0 0 2 •0 .008 0 . 0 1 7 0 . 0 5 6 • 0 . 0 3 6 •0 .052 •0 .010 0 . 0 0 8 0.021 0 . 0 3 5 009 058 01 1 01 1 060 0 . 0 1 6 • 0 . 0 0 5 •0.041 0 . 0 4 8 • 0 . 0 0 9 0 . 0 1 3 0 . 0 137 T a b l e 5.5 ( C o n t i n u e d ) T r a n s i t i o n N o r m a l i s e d O b s e r v e d R e s i d u a l s F ' - F " W e i g h t F r e q u e n c y W i t h o u t x a b W i t h x a b 20 , 1 9 - 20 0 2 0 45/2 - 45/2 1 .000 46906.578 -2.465 -0.033 37/2 - 37/2 1 .000 46959.334 -3.803 0.047 43/2 - 43/2 1 .000 46973.087 -4.225 0.038 39/2 - 39/2 1 .000 46998.937 -0.510 0.052 41/2 — 41/2 1 .000 47005.355 -0.399 0.021 21 , 2 0 - 21 0 2 1 47/2 - 47/2 1 .000 47764.570 -2.167 -0.022 45/2 - 45/2 1 .000 47831.497 -3.910 0.018 41/2 - 41/2 1 .000 47857.554 -0.675 0.036 43/2 — 43/2 1 .000 47863.753 -0.533 0.032 22 , 2 1 - 22 0 2 2 39/2 - 39/2 1 .000 48665.105 -3.166 0.044 49/2 - 49/2 1 .000 48673.524 -1.930 -0.014 41/2 - 41/2 1 .000 48727.954 -3.532 0.001 47/2 - 47/2 1 .000 48740.840 -3.753 -0.039 43/2 - 43/2 1 .000 48767.260 -0.826 -0.074 45/2 — 45/2 1 .000 48773.279 -0.639 0.006 23 , 2 2 - 23 0 2 3 43/2 - 43/2 1 .000 49690.140 -3.363 0.038 45/2 - 45/2 1 .000 49729.556 -0.748 0.004 47/2 — 47/2 1 .000 49735.222 -0.706 0.003 24 , 2 3 - 24 0 2 4 53/2 - 53/2 1 .000 50649.544 -1 .546 0.031 45/2 - 45/2 1 .000 50706.054 -3.339 -0.021 47/2 - 47/2 1 .000 50745.651 -0.716 0.017 49/2 — 49/2 1 .000 50750.848 -0.840 -0.052 25 ! 2 4 - 25 0 2 5 45/2 - 45/2 1 .000 51710.642 -3.393 0.043 55/2 - 55/2 1 .000 51719.163 -1.449 -0.001 47/2 - 47/2 1 .000 51776.247 -3.241 0.046 53/2 - 53/2 1 .000 51787.779 -3.712 -0.024 49/2 - 49/2 1 .000 51816.052 -0.723 -0.009 51/2 — 51/2 . 1.000 51821.258 -0.855 -0.008 26 ! 2 5 - 26 0 2 6 57/2 - 57/2 1 .000 52845.021 -1.327 0.012 49/2 - 49/2 1 .000 52902.935 -3.327 0.014 55/2 - 55/2 1 .000 52913.936 -3.960 -0.031 51/2 - 51/2 1 .000 52943.130 -0.713 -0.024 53/2 - 53/2 1 .000 52948.001 -1.018 -0.048 T a b l e 5 . 5 (Cont inued) 138 T r a n s i t i o n N o r m a l i s e d Observed R e s i d u a l s F ' - F" Weight Frequency Without x a b With X a b 20 o 2 0 - 19 1 1 9 35/2 - 33/2 1 .000 33838.242 -67.392 -0.009 45/2 - 43/2 0. 100 33913.537 -0.035 0.104 43/2 - 41/2 •1 .000 33964.972 4. 166 -0.034 41/2 - 39/2 1 .000 33995.752 16.966 0.012 39/2 - 37/2 1 .000 34011.441 38.889 0.069 37/2 — 35/2 1 .000 34018.275 71 .534 -0.022 21 o 2 1 - 20 1 2 0 37/2 - 35/2 1 .000 37828.243 1 .715 0.015 47/2 - 45/2 1 .000 37833.826 -0.094 0.046 39/2 - 37/2 1 .000 37865.109 -2.224 0.035 45/2 - 43/2 1 .000 37884.237 3.804 0.008 41/2 - 39/2 1 .000 37888.182 -4.459 -0.034 43/2 — 41/2 1 .000 37896.723 -1.725 -0.068 22 o 2 2 - 21 1 2 1 39/2 - 37/2 1 .000 41767.255 2.346 0.005 49/2 - 47/2 1 .000 41771.756 -0.054 0.085 41/2 - 39/2 1 .000 41804.838 -0.483 -0.071 47/2 - 45/2 1 .000 41821.010 3.458 -0.023 43/2 - 41/2 1 .000 41828.062 -2.052 -0.061 45/2 — 43/2 1 .000 41835.421 -0.115 -0.055 23 o 2 3 - 22 1 2 2 41/2 - 39/2 1 .000 45721.705 2.486 0.054 51/2 - 49/2 1 .000 45725.596 -0.087 0.050 43/2 - 41/2 0.100 45759.169 0.016 -0.098 49/2 - 47/2 1 .000 45773.882 3.274 0.042 45/2 - 43/2 1 .000 45782.108 -1.310 -0.060 47/2 — 45/2 1 .000 45788.752 0.256 -0.103 24 o 2 4 - 23 1 2 3 43/2 - 41/2 1 .000 49690.163 2.494 0.049 53/2 - 51/2 1 .000 49693.957 0.017 0.151 45/2 - 43/2 1 .000 49727.240 0.249 -0.091 51/2 - 49/2 1 .000 49741.133 3. 127 0.096 47/2 - 45/2 1 .000 49749.800 -0.980 -0.081 139 T a b l e 5 .6 O b s e r v e d h y p e r f i n e t r a n s i t i o n f r e q u e n c i e s ( i n MHz) o f 1 2 7 I 1 A N C 0 b - t y p e Q b r a n c h t r a n s i t i o n s T r a n s i t i o n O b s e r v e d F x ' F' - F j " • F" F r e q u e n c y 12 t , , - 12 o i 2 29/2 29/2 - 29/2 29/2 41686.998 29/2 27/2 - 29/2 27/2 41687.308 29/2 31/2 - 29/2 31/2 41687.308 13 1 i 2 ~ 13 o 1 3 21/2 21/2 - 21/2 21/2 42183.259 21/2 19/2 - 21/2 19/2 42183.488 21/2 23/2 - 21/2 23/2 42183.488 31/2 31/2 - 31/2 31/2 42215.884 31/2 29/2 - 31/2 29/2 42216.185 31/2 33/2 - 31/2 33/2 42216.185 23/2 23/2 - 23/2 23/2 42239.187 23/2 21/2 - 23/2 21/2 42239.417 23/2 25/2 - 23/2 25/2 42239.417 29/2 29/2 - 29/2 29/2 42243.161 29/2 27/2 - 29/2 27/2 42243.499 29/2 31/2 - 29/2 31/2 42243.499 25/2 25/2 - 25/2 25/2 42304.329 25/2 23/2 - 25/2 23/2 42304.609 25/2 27/2 - 25/2 27/2 42304.609 27/2 27/2 - 27/2 27/2 42313.642 27/2 25/2 - 27/2 25/2 42313.929 27/2 29/2 - 27/2 29/2 42313.929 14 , 1 3 - 14 o 23/2 23/2 - 23/2 23/2 42739.633 23/2 21/2 - 23/2 21/2 42739.900 23/2 25/2 - 23/2 25/2 42739.900 33/2 33/2 - 33/2 33/2 42756.630 33/2 31/2 - 33/2 31/2 42756.909 33/2 35/2 - 33/2 35/2 42756.909 25/2 25/2 - 25/2 25/2 42794.621 25/2 23/2 - 25/2 23/2 42794.916 25/2 27/2 - 25/2 27/2 42794.916 31/2 31/2 - 31/2 31/2 42814.998 31/2 29/2 - 31/2 29/2 42815.327 31/2 33/2 - 31/2 33/2 42815.327 27/2 27/2 - 27/2 27/2 42843.416 27/2 25/2 - 27/2 25/2 42843.730 27/2 29/2 - 27/2 29/2 42843.730 29/2 29/2 - 29/2 29/2 42854.765 29/2 27/2 - 29/2 27/2 42855.040 29/2^ 3J/2 - 29/2 31 /2 _^2Q55.0AO T a b l e 5 . 6 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d F1' F ' - F1" F" F r e q u e n c y 1 5 , , 4 - 15 o i s 25/2 25/2 - 25/2 25/2 43322.317 25/2 23/2 - 25/2 23/2 43322.638 25/2 27/2 - 25/2 27/2 43322.638 35/2 35/2 - 35/2 35/2 43336.245 35/2 33/2 - 35/2 33/2 43336.572 35/2 37/2 - 35/2 37/2 43336.572 27/2 27/2 - 27/2 27/2 43377.983 27/2 25/2 - 27/2 25/2 43378.282 27/2 29/2 - 27/2 29/2 43378.282 33/2 33/2 - 33/2 33/2 43399.060 33/2 31/2 - 33/2 31/2 43399.295 33/2 35/2 - 33/2 35/2 43399.295 1 6 , j 5 - 1 6 o t 6 35/2 35/2 - 35/2 35/2 44022.898 35/2 33/2 - 35/2 33/2 44023.188 35/2 37/2 - 35/2 37/2 44023.188 31/2 31/2 - 31/2 31/2 44043.308 31/2 29/2 - 31/2 29/2 44043.649 31/2 33/2 - 31/2 33/2 44043.649 1 7 l 1 6 — 1 7 O 1 7 29/2 29/2 - 29/2 29/2 44599.001 29/2 27/2 - 29/2 27/2 44599.302 29/2 31/2 - 29/2 31/2 44599.302 39/2 39/2 - 39/2 39/2 44625.469 39/2 37/2 - 39/2 37/2 44625.760 39/2 41/2 - 39/2 41/2 44625.760 31/2 31/2 - 31/2 31/2 44648.230 31/2 29/2 - 31/2 29/2 44648.589 31/2 33/2 - 31/2 33/2 44648.589 37/2 37/2 - 37/2 37/2 44690.483 37/2 35/2 - 37/2 35/2 44690.810 37/2 39/2 - 37/2 39/2 44690.810 33/2 33/2 - 33/2 33/2 44692.221 33/2 31/2 - 33/2 31/2 44692.557 33/2 35/2 - 33/2 35/2 44692.557 35/2 35/2 - 35/2 35/2 44711.831 35/2 33/2 - 35/2 33/2 44712.089 35/2 37/2 - 35/2 37/2 44712.089 T a b l e 5 .6 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d T1' F ' - ¥ 1 " F " F r e q u e n c y 18 , 1 7 - 18 o 31/2 31/2 - 31/2 31/2 29/2 - 31/2 31/2 33/2 - 31/2 41/2 41/2 - 41/2 41/2 39/2 - 41/2 41/2 43/2 - 41/2 33/2 33/2 - 33/2 33/2 31/2 - 33/2 33/2 35/2 - 33/2 39/2 39/2 - 39/2 39/2 37/2 - 39/2 39/2 41/2 - 39/2 35/2 35/2 - 35/2 35/2 33/2 - 35/2 35/2 37/2 - 35/2 37/2 37/2 - 37/2 37/2 35/2 - 37/2 37/2 39/2 — 37/2 19 1 1 a - 19 o 33/2 33/2 - 33/2 33/2 31/2 - 33/2 33/2 35/2 - 33/2 43/2 43/2 - 43/2 43/2 41/2 - 43/2 43/2 45/2 - 43/2 35/2 35/2 - 35/2 35/2 33/2 - 35/2 35/2 37/2 - 35/2 41/2 41/2 - 41/2 41/2 39/2 - 41/2 41/2 43/2 - 41/2 37/2 3 7/2 - 37/2 37/2 35/2 - 37/2 37/2 39/2 - 37/2 39/2 39/2 - 39/2 39/2 37/2 - 39/2 39/2 41/2 — 39/2 20 , 1 9 - 20 o 45/2 45/2 - 45/2 45/2 43/2 - 45/2 45/2 47/2 - 45/2 37/2 37/2 - 37/2 37/2 35/2 - 37/2 37/2 39/2 - 37/2 31/2 45329.974 29/2 45330.279 33/2 45330.279 41/2 45338.181 39/2 45338.474 43/2 45338.474 33/2 45391.148 31/2 45391.451 35/2 45391.451 39/2 45403.765 37/2 45404.037 41/2 45404.037 35/2 45432.145 33/2 45432.435 37/2 45432.435 37/2 45438.399 35/2 45438.665 39/2 45438.665 133/2 46089.349 31/2 46089.636 35/2 46089.636 43/2 46098.062 41/2 46098.378 45/2 46098.378 35/2 46150.272 33/2 46150.572 37/2 46150.572 41/2 46164.076 39/2 46164.404 43/2 46164.404 37/2 46190.242 35/2 46190.516 39/2 46190.516 39/2 46196.838 37/2 46197.111 41/2 46197.111 245/2 46906.392 43/2 46906.676 47/2 46906.676 37/2 46959.082 35/2 46959.460 39/2 46959.460 T a b l e 5 .6 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d F x ' F ' - F x " F" F r e q u e n c y 20 , 19 20 o 43/2 43/2 43/2 43/2 41/2 43/2 43/2 45/2 43/2 39/2 39/2 39/2 39/2 37/2 39/2 39/2 41/2 39/2 41/2 41/2 41/2 41/2 39/2 41/2 41/2 43/2 41/2 21 , 2 0 21 o 47/2 47/2 47/2 47/2 45/2 47/2 47/2 49/2 47/2 45/2 45/2 45/2 45/2 43/2 45/2 45/2 47/2 45/2 41/2 41/2 41/2 41/2 39/2 41/2 41/2 43/2 41/2 43/2 43/2 43/2 43/2 41/2 43/2 43/2 45/2 43/2 22 , 2 1 ' 22 o 39/2 39/2 39/2 39/2 37/2 39/2 39/2 41/2 39/2 49/2 49/2 49/2 49/2 47/2 49/2 49/2 51/2 49/2 41/2 41/2 41/2 41/2 39/2 41/2 41/2 43/2 41/2 47/2 47/2 47/2 47/2 45/2 47/2 47/2 49/2 47/2 43/2 43/2 43/2 43/2 41/2 43/2 43/2 45/2 43/2 45/2 45/2 45/2 45/2 43/2 45/2 45/2 47/2 45/2 43/2 46972.851 41/2 46973.205 45/2 46973.205 39/2 46998.731 37/2 46999.040 41/2 46999.040 41/2 47005.155 39/2 47005.456 43/2 47005.456 *47/2 47764.358 45/2 47764.677 49/2 47764.677 45/2 47831.272 43/2 47831.610 47/2 47831.610 41/2 47857.340 39/2 47857.662 43/2 47857.662 43/2 47863.549 41/2 47863.856 45/2 47863.856 239/2 48664.877 37/2 48665.220 41/2 48665.220 49/2 48673.310 47/2 48673.632 51/2 48673.632 41/2 48727.734 39/2 48728.065 43/2 48728.065 47/2 48740.616 45/2 48740.953 49/2 48740.953 43/2 48767.203 41/2 48767.513 45/2 48767.513 45/2 48773.066 43/2 48773.386 47/2 48773.386 T a b l e 5 .6 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d F 1 ' F ' - F1" F " F r e q u e n c y 23 , 2 2 23 o 2 3 43/2 43/2 43/2 43/2 49689. 953 43/2 41/2 43/2 41/2 49690. 234 43/2 45/2 43/2 45/2 49690. 234 45/2 45/2 45/2 45/2 49729. 369 45/2 43/2 45/2 43/2 49729. 650 45/2 47/2 45/2 47/2 49729. 650 47/2 47/2 47/2 47/2 49735. 010 47/2 45/2 47/2 45/2- 49735. 328 47/2 49/2 47/2 49/2 49735. 328 24 , 2 3 - 24 o 2 4 53/2 53/2 53/2 53/2 50649. 327 53/2 51/2 53/2 51/2 50649. 653 53/2 55/2 53/2 55/2 50649. 653 45/2 45/2 45/2 45/2 50705. 806 45/2 43/2 45/2 43/2 50706. 179 45/2 47/2 45/2 47/2 50706. 179 47/2 47/2 47/2 47/2 50745. 420 47/2 45/2 47/2 45/2 50745. 767 47/2 49/2 47/2 49/2 50745. 767 49/2 49/2 49/2 49/2 50750. 622 49/2 47/2 49/2 47/2 50750. 961 49/2 51/2 49/2 51/2 50750. 961 25 , 2 4 25 o 2 5 45/2 45/2 45/2 45/2 51710. 422 45/2 43/2 45/2 43/2 51710. 753 45/2 47/2 45/2 47/2 51710. 753 55/2 55/2 55/2 55/2 51718. 925 55/2 53/2 55/2 53/2 51719. 283 55/2 57/2 55/2 57/2 51719. 283 47/2 47/2 47/2 47/2 51776. 031 47/2 45/2 47/2 45/2 51776. 355 47/2 49/2 47/2 49/2 51776. 355 53/2 53/2 53/2 53/2 51787. 543 53/2 51/2 - 53/2 51/2 51787. 898 53/2 55/2 - . 53/2 55/2 51787. 898 49/2 49/2 49/2 49/2 51815. 820 49/2 47/2 49/2 47/2 51816. 169 49/2 51/2 49/2 51/2 51816. 169 51/2 51/2 51/2 51/2 51821 . 028 51/2 49/2 51/2 49/2 51821 . 373 51/2 53/2 51/2 53/2 51821 . 373 144 T a b l e 5 . 6 ( C o n t i n u e d ) T r a n s i t i o n O b s e r v e d F ' F " F r e q u e n c y 26 , 2 5 26 o 2 6 57/2 57/2 57/2 57/2 52844.797 57/2 55/2 57/2 55/2 52845.133 57/2 59/2 57/2 59/2 52845.133 49/2 49/2 49/2 49/2 52902.691 49/2 47/2 49/2 47/2 52903.057 49/2 51/2 49/2 51/2 52903.057 55/2 55/2 55/2 55/2 5 2 9 1 3 . 6 8 9 55/2 53/2 55/2 53/2 5 2 9 1 4 . 0 5 9 55/2 57/2 55/2 57/2 5 2 9 1 4 . 0 5 9 51/2 51/2 51/2 51/2 52942.871 51/2 49/2 51/2 49/2 5 2 9 4 3 . 2 5 9 51/2 53/2 51/2 53/2 5 2 9 4 3 . 2 5 9 53/2 53/2 53/2 53/2 52947.791 53/2 51/2 53/2 51/2 52948.106 53/2 55/2 53/2 55/2 5 2 9 4 8 . 1 0 6 145 5 .5 The S t r u c t u r e o f INCO The moments o f i n e r t i a o f o n l y one i s o t o p e o f INCO have been 127 14 12 16 measured i n t h i s s t u d y : I N C O . Hence, t h e r e i s o n l y l i m i t e d s t r u c t u r a l i n f o r m a t i o n a v a i l a b l e . The i n e r t i a l d e f e c t f o r the g r o u n d s t a t e i s 0.448 a.m.u. o 2 A ; INCO i s t h e r e f o r e a l m o s t c e r t a i n l y p l a n a r . A l t h o u g h o n l y one o f the n i t r o g e n 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 was d e t e r m i n a b l e , the c o n s t a n t s g i v e n i n T a b l e 5.7 a r e s i m i l a r i n m a g n i t u d e t o t h o s e o f BrNCO and a r e t h e r e f o r e c o n s i s t e n t w i t h t h e c o n f i g u r a t i o n INCO r a t h e r t h a n IOCN ( s e e s e c t i o n 4 . 7 ) . T a b l e 5 . 7 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 1 4 N i n P r i n c i p a l I n e r t i a l Axes X a a ( M H z ) Xbb(MHz) X c c ( M H z ) 5 . 2 1 1 . 852 (18) 3.348 1 Xaa was c a l c u l a t e d a v e r a g e v a l u e o f x c c d e t e r m i n e d f r o m t h e s p e c t r u m was by a s s u m i n g t h a t i n 7 9 B r N C O and *b b x9 8 1 i s the same as the BrNCO. What was X r r - 1.496(18)MHz. A s t r u c t u r e c o n s i s t e n t w i t h the measured r o t a t i o n a l c o n s t a n t s can be d e r i v e d f o r INCO o n l y by f i x i n g some o f the s t r u c t u r a l p a r a m e t e r s . The N-C and C-0 bond l e n g t h s were f i x e d a t C1NC0 v a l u e s ( 6 , 7 ) . The N-C-0 a n g l e was v a r i e d between 0 ° ( l i n e a r ) and 9.13°(<N-C-0 i n C1NC0), and v a l u e s f o r the I-N 146 b o n d l e n g t h a n d I - N - C a n g l e were c a l c u l a t e d ( T a b l e 5 . 8 ) . The I - N b o n d l e n g t h i s c o m p a r a b l e w i t h o t h e r I - N b o n d l e n g t h s and t h e I - N - C a n g l e i s r e a s o n a b l e when c o m p a r e d w i t h t h e X - N - C a n g l e s i n t h e o t h e r h a l o g e n i s o c y a n a t e s (See T a b l e 5 . 9 ) . When c o m p a r e d w i t h t h e sum o f t h e s i n g l e b o n d r a d i i , t h e I - N b o n d l e n g t h c a l c u l a t e d f o r t h e v a r i o u s N - C - 0 a n g l e s ( T a b l e 5 . 8 ) i s more c o n s i s t e n t w i t h a b e n t N - C - 0 c h a i n . The p o s i t i o n o f t h e atoms r e l a t i v e t o t h e i n e r t i a l axes i s shown i n F i g u r e 5 . 5 . T a b l e 5 .8 S t r u c t u r a l p a r a m e t e r s o f INCO I I I I I I r ( I - N ) / A 2 . 005 2 . 0 1 6 2 .032 r ( N - C ) 1 / A 1 .225 1 .225 1 .225 r ( C - 0 ) V A 1.162 1 . 162 1 . 162 < ( I N C ) 124 . 2 2 ° 1 2 2 . 0 7 ° 1 1 9 . 4 2 ° 2 o o o <(NC0) 0 4 9 . 13 < ( I - N - a ) 3 2 5 . 0 3 ° 2 5 . 2 0 ° 2 5 . 3 4 ° 1 C o n s t r a i n e d t o C1NC0 v a l u e s . 2 Cons t r a i n e d . 3 A n g l e b e t w e e n t h e I - N b o n d a x i s and t h e a - i n e r t i a l a x i s . 147 T a b l e 5 .9 C o m p a r i s o n o f s t r u c t u r a l p a r a m e t e r s o f INCO w i t h o t h e r m o l e c u l e s . r ( I - N ) INCO 2 . 0 2 A I 2 N C H 0 ( 9 ) 2 . 0 4 A Sum o f s i n g l e b o n d r a d i i ( l O ) 2 . 0 2 A < ( X - N - C ) INCO 122 BrNCO 119' C 1 N C 0 ( 6 , 7 ) 118' F i g u r e 5 .5 The r e l a t i v e p o s i t i o n s o f t h e atoms o f INCO i n p r i n c i p a l i n e r t i a l a x i s s y s t e m ( f r o m s t r u c t u r e i n T a b l e 5 . 8 ) . i t s I I 148 5 . 6 I and 1 4 N Q u a d r u p o l e C o u p l i n g The p r o c e d u r e u s e d to a n a l y z e the 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 b r o m i n e i n BrNCO was a l s o f o l l o w e d i n INCO. The q u a d r u p o l e t e n s o r was d i a g o n a l i z e d to f i n d i t s p r i n c i p a l v a l u e s . T hese a r e g i v e n i n T a b l e 5.11. 0 z a , w h i c h i s the a n g l e between the z - p r i n c i p a l q u a d r u p o l e a x i s and the a - i n e r t i a l a x i s a g r e e s to w i t h i n =1° w i t h t h e a n g l e between the I-N bond and the a--i n e r t i a l a x i s ( s e e T a b l e 5.8). The d i f f e r e n c e i s p r o b a b l y n o t s i g n i f i c a n t ; hence the z - p r i n c i p a l q u a d r u p o l e a x i s and t h e r e f o r e t h e maximum e l e c t r o n d e n s i t y o f the I-N bond l i e s a l o n g t h e I-N bond a x i s . T a b l e 5.10 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 P r i n c i p a l I n e r t i a l axes 12 7 I i n X a a ( M H z ) Xbb(MHz) X c c ( M H z ) X a b ( M H z ) 751.75(41) 1486.58(41) -1671.81(14) - 2238 .33 (75) T a b l e 5.11 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 1 2 7 I i n P r i n c i p a l Q u a d r u p o l e Axes X z z ( M H z ) X x x ( M H z ) X y y ( M H z ) * z a ( d e g ) - 2986 . 1 (15) 1499.5(12) 1486.58(41) 24.097(7) 149 The d i f f e r e n c e between v T T and v i s v e r y s m a l l . T h e r e f o r e x x y y t h e c o n t r i b u t i o n o f a ir-bonded r e s o n a n c e s t r u c t u r e to t h e o v e r a l l s t r u c t u r e o f INCO i s n e g l i g i b l e (=0.4%). The I-N bond i s e s s e n t i a l l y c y l i n d r i c a l l y s y m m e t r i c , as was assumed i n i t i a l l y . The two r e s o n a n c e forms w h i c h c o n t r i b u t e most to the o v e r a l l I-N bond a r e p r o b a b l y : N = C = 0 ( I ) N"= C = 0 ( I D The p o s i t i v e c h a r g e i s on the i o d i n e i n form ( I I ) w h i c h r e p r e s e n t s an i o n i c I-N bond b e c a u s e \xzz l> l eQqi I • The c o n t r i b u t i o n o f t h i s r e s o n a n c e form i s e s t i m a t e d t o be =23% ( c a l c u l a t e d as f o r BrNCO i n s e c t i o n 4 . 8 ) . As i n BrNCO, an a t t e m p t was made to r e p r o d u c e t h e 1 A N 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 from p - o r b i t a l p o p u l a t i o n s c a l c u l a t e d i n a semi - e m p i r i c a l CNDO c a l c u l a t i o n . The p o r b i t a l p o p u l a t i o n s were c a l c u l a t e d to be: n a = 0.9061, n b = 1.3821, n c = 1.6795. The 1 *N 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 i n the i n e r t i a l a x i s s y s t e m were c a l c u l a t e d u s i n g e q u a t i o n s 4.4 and 4.5. A c o m p a r i s o n o f t h e c a l c u l a t e d c o n s t a n t s w i t h t h o s e o b t a i n e d e x p e r i m e n t a l l y i s g i v e n i n T a b l e 5.12. Once, a g a i n the t h e o r e t i c a l l y c a l c u l a t e d c o n s t a n t s do n o t r e p r o d u c e the e x p e r i m e n t a l v a l u e s v e r y w e l l . T h i s f u r t h e r d e m o n s t r a t e s the 150 n e e d f o r i m p r o v e d t h e o r e t i c a l c a l c u l a t i o n s , p a r t i c u l a r l y f o r m o l e c u l e s c o n t a i n i n g h e a v y a t o m s . T a b l e 5 .12 C o m p a r i s o n o f 1 4 N 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 b t a i n e d e x p e r i m e n t a l l y w i t h t h e o r e t i c a l l y c a l c u l a t e d v a l u e s E x p e r i m e n t a l C a l c u l a t e d 1 X a a ( M H z ) 5 . 2 2 6 . 2 4 7 X b b ( M H z ) - 1 . 8 5 2 ( 1 8 ) - 0 . 8 9 3 v (MHz) - 3 . 3 4 8 2 - 5 . 3 5 4 1 C a l c u l a t e d u s i n g p - o r b i t a l p o p u l a t i o n s f r o m CNDO c a l c u l a t i o n . 2 See t e x t to see how o b t a i n e d . 5 . 7 D i s cus s i o n I n C h a p t e r I V , p e r t u r b a t i o n s i n t h 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 i n t h e m i c r o w a v e s p e c t r u m o f BrNCO were d e m o n s t r a t e d to be u s e f u l i n e v a l u a t i n g a l l t h r e e r o t a t i o n a l c o n s t a n t s where o t h e r w i s e t h e y may n o t h a v e a l l b e e n d e t e r m i n a b l e . The same m e t h o d was a l s o u s e d f o r a n a l y z i n g t h e m i c r o w a v e s p e c t r u m o f I N C O , a n d A Q was c a l c u l a t e d s o l e l y f r o m t h e a n a l y s i s o f a - t y p e R b r a n c h t r a n s i t i o n s , u s i n g K a = 1 •»• 0 n e a r - d e g e n e r a c i e s . T h i s s t u d y h a s f u r t h e r d e m o n s t r a t e d t h e u s e f u l n e s s o f u s i n g t h e ' e x a c t ' H a m i l t o n i a n to f i t t h e r o t a t i o n a l , c e n t r i f u g a l d i s t o r t i o n a n 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 o f a m o l e c u l e . The e n e r g i e s a r e so s e n s i t i v e to t h e m a g n i t u d e s o f t h e n e a r -151 d e g e n e r a c i e s , t h a t n o t o n l y can the p e r t u r b a t i o n s i n the q u a d r u p o l e s t r u c t u r e be u s e d to e v a l u a t e r o t a t i o n a l c o n s t a n t s , b u t a l s o 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 n be d e t e r m i n e d , i n t h i s c a s e A K . A K w o u l d n o r m a l l y r e q u i r e K = 2 •»• 1 t r a n s i t i o n s to be measured; t h i s was i m p o s s i b l e f o r INCO. I n s t e a d , p e r t u r b a t i o n s i n K a = 1 <- 0 b - t y p e t r a n s i t i o n s , c a u s e d by K a = 2 «*• 1 n e a r - d e g e n e r a c i e s c o n t a i n e d enough i n f o r m a t i o n f o r A K to be e v a l u a t e d s e p a r a t e l y from A Q . T h i s was a s i g n i f i c a n t e x t e n s i o n o f t h e method d e v e l o p e d to a n a l y z e the s p e c t r u m o f BrNCO. W h i l e n o t o f g e n e r a l a p p l i c a b i l i t y , the method o f u s i n g p e r t u r b a t i o n s i n the 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 i n the m icrowave s p e c t r u m o f a m o l e c u l e to e v a l u a t e o t h e r w i s e u n d e t e r m i n a b l e r o t a t i o n a l and c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s , w i l l be u s e f u l when a n a l y z i n g t h e s p e c t r a o f m o l e c u l e s c o n t a i n i n g b r o m i n e and i o d i n e , p a r t i c u l a r l y when the s p e c t r u m has p r e d o m i n a n t l y a^-type R b r a n c h t r a n s i t i o n s . I n f a c t , the microwave s p e c t r a o f o t h e r m o l e c u l e s s u c h as v i n y l i o d i d e a r e a l r e a d y b e i n g a n a l y z e d u s i n g t h i s method ( 1 1 ) . The major r e q u i r e m e n t f o r the u s e f u l n e s s o f t h i s method i s t h a t none o f t h e a n g l e s between the bond a x i s , c o n t a i n i n g the q u a d r u p o l a r n u c l e u s and t h e atom to w h i c h i t i s a t t a c h e d , and t h e i n e r t i a l axes i s s m a l l , b e c a u s e Xab would be r e l a t i v e l y s m a l l . The o n l y o t h e r l i m i t a t i o n i s the r e l a t i v e m a g n i t u d e o f the r o t a t i o n a l c o n s t a n t s , w h i c h w i l l d e t e r m i n e the number o f n e a r - d e g e n e r a c i e s w i t h t h e c o r r e c t symmetry r e l e v a n t to the a v a i l a b l e f r e q u e n c y 152 r a n g e . I f t h e r e a r e o n l y a few n e a r - d e g e n e r a c i e s , t h e n the a c c u r a c y o f the c o n s t a n t s o b t a i n e d by t h i s method w i l l be l i m i t e d . I n t h i s microwave s t u d y , the r o t a t i o n a l c o n s t a n t s o f INCO have been measured, a l o n g w i t h 4 out o f 5 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 r o t a t i o n a l c o n s t a n t s have been u s e d to d e t e r m i n e a p a r t i a l r o s t r u c t u r e f o r INCO w h i c h i s c o n s i s t e n t w i t h t h e o t h e r h a l o g e n i s o c y a n a t e s t r u c t u r e s . I n t h e microwave s p e c t r u m o f INCO, s e v e r a l 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 , the r e l a t i v e i n t e n s i t i e s o f w h i c h p r o v i d e an e s t i m a t e o f the l o w e s t v i b r a t i o n a l f r e q u e n c y o f INCO a t = 130 ± 30cm" 1. T h i s a g r e e s q u i t e w e l l w i t h the f r e q u e n c y o f the l o w e s t i n p l a n e b e n d i n g v i b r a t i o n e s t i m a t e d from the i n e r t i a l d e f e c t ( e q u a t i o n 2.35) to be = 1 5 0 c m - 1 , p r o b a b l y c o r r e s p o n d i n g t o t h e I-N-C b e n d i n g v i b r a t i o n . I n a d d i t i o n , an a n a l y s i s o f the 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 1 2 7 i have e s t a b l i s h e d t h a t t h e r e i s a p p r o x i m a t e l y 23% i o n i c c h a r a c t e r i n the I-N bond. T a b l e 5.13 summarises t h e i o n i c bond c h a r a c t e r o f t h e h a l o g e n - n i t r o g e n bond i n the h a l o g e n i s o c y a n a t e s . The t r e n d o f d e c r e a s i n g e l e c t r o n e g a t i v i t y from C l to I i s r e f l e c t e d i n the i n c r e a s i n g i o n i c c h a r a c t e r o f t h e h a i o g e n - n i t r o g e n bond. T h i s t r e n d a l s o a p p a r e n t l y f o l l o w s t h e s t a b i l i t y o f the h a l o g e n i s o c y a n a t e s w i t h C1NC0 b e i n g much l e s s s t a b l e t h a n INCO. 153 T a b l e 5.13 I o n i c bond c h a r a c t e r o f the h a l o g e n i s o c y a n a t e s % I o n i c C h a r a c t e r % 7r B o n d i n g % S i n g l e Bond C h a r a c t e r C1NC0 9.0 4.0 87.0 BrNCO 12.4 0.5 87.1 INCO 23.3 0.4 76.3 154 B i b l i o g r a p h y 1. L. B i r c k e n b a c h , M. L i n h a r d , B e r . 63., 2544- 2558, ( 1 9 3 0 ) ; 64, 961-968, ( 1 9 3 1 ) . 2. S. Rosen, D. Swern, A n a l . Chem. 3_8, 1392 - 1397, ( 1966). 3. C G . G e b e l e i n , J . Macromol. S c i . -Chem. A5_, 433 -442 (19 7 1 ) . 4. J . Macazaga, S. D e l g a d o , J.R. Masaguer, J . O r g a n o m e t a l l i c . Chem. 259. 233-236 ( 1 9 8 3 ) . 5. D.C. F r o s t , C B . MacDonald, C.A. Mc D o w e l l , N.P.C. Westwood, Chem. Phys. 47., 111-124 ( 1 9 8 0 ) . 6. W.H. H o c k i n g , M.C.L. G e r r y , J . Mol S p e c t r o s c . 42, 547-566 (1972) . 7. W.H. H o c k i n g , M.L. W i l l i a m s , M.C.L. G e r r y , J . Mol S p e c t r o s c . 58., 250- 260 ( 1 9 7 5 ) . 8. J . J a n d e r , Adv. I n o r g . Chem. Radiochem. 19., 1- 63 ( 1 9 7 6 ) . 9. H. P r i t z k o w , Monatsh. 105. 621-628 ( 1 9 7 4 ) . 10. L. P a u l i n g . "The N a t u r e o f t h e C h e m i c a l Bond" 3 r d ed., C o r n e l l U n i v e r s i t y P r e s s , I t h a c a , N.Y., 1960. 11. D. Cramb, P r i v a t e C o m m u n i c a t i o n . 155 CHAPTER V I : THE MICROWAVE SPECTRUM OF BROMINE THIOCYANATE, BrSCN 6.1 I n t r o d u c t i o n The c h e m i s t r y o f bromi n e t h i o c y a n a t e , an u n s t a b l e i n t e r m e d i a t e , has b een s t u d i e d i n s o l u t i o n ( 1 - 4 ) . I n common w i t h the o t h e r h a l o g e n t h i o c y a n a t e s , i t can be p r e p a r e d i n a m i x t u r e o f the h a l o g e n and the p s e u d o h a l o g e n ( S C N ) 2 , w h i c h has p r e v i o u s l y b e en p r e p a r e d by m i x i n g P b ( S C N ) 2 and a s o l u t i o n o f b r o m i n e : * ( i ) P b ( S C N ) 2 + B r 2 -» ( S C N ) 2 + P b B r 2 ( i i ) ( S C N ) 2 + X 2 -> 2XSCN X = C l , Br , I (6.1) I n s o l u t i o n , BrSCN u n d e r g o e s a d d i t i o n r e a c t i o n s w i t h a l k e n e s . However, t h e r e a c t i o n p r o d u c t s a r e n o t u n i q u e , w i t h b o t h b r o m o t h i o c y a n a t o and dibromo d e r i v a t i v e s b e i n g f o r m e d ( 2 ) . I t has a l s o b e i n g u s e d as a r e a g e n t i n t h i o c y a n a t i o n r e a c t i o n s (8, 9) . B o t h i n f r a - r e d s o l u t i o n s t u d i e s and c h e m i c a l s t u d i e s o f t h e s e h a l o g e n t h i o c y a n a t e s (1-7) c o n f i r m t h a t t h e h a l o g e n i s l i n k e d v i a the S atom. The o n l y p r e v i o u s g a s - p h a s e s t u d y o f BrSCN was o f i t s H e ( I ) p h o t o e l e c t r o n s p e c t r u m by F r o s t e t a l (10) . I t was for m e d by the gas phase t i t r a t i o n o f ( S C N ) 2 w i t h B r 2 . S i n c e the c o n f i g u r a t i o n o f c h l o r i n e t h i o c y a n a t e i n the g a s - p h a s e has been shown i n a microwave s t u d y to be C1SCN ( 1 1 ) , i t seems l i k e l y , 156 e s p e c i a l l y s i n c e the p h o t o e l e c t r o n s p e c t r u m o f BrSCN d i r e c t l y p a r a l l e l s t h a t o f C1SCN, t h a t BrSCN a l s o has a t h i o c y a n a t e s t r u c t u r e . A c c o r d i n g l y , the aim o f t h i s microwave s t u d y was to a s s i g n the g r o u n d s t a t e r o t a t i o n a l s p e c t r u m o f b r o m i n e t h i o c y a n a t e and to d e t e r m i n e w h e t h e r the m o l e c u l e has a t h i o c y a n a t e or i s o t h i o c y a n a t e s t r u c t u r e . 6.2 E x p e r i m e n t a l M e t h o d s BrSCN was p r e p a r e d a c c o r d i n g to the method o f F r o s t e_t a_l (10, 1 2 ) . S i l v e r t h i o c y a n a t e was p r e p a r e d by m i x i n g aqueous s o l u t i o n s o f p o t a s s i u m t h i o c y a n a t e and s i l v e r n i t r a t e . The r e s u l t i n g p r e c i p i t a t e was f i l t e r e d , washed, and t h e n d r i e d i n the a i r and s t o r e d i n the d a r k u n t i l u s e . AgSCN was l o o s e l y p a c k e d u s i n g g l a s s wool i n t o a U-shaped t u b e , and d r i e d t h o r o u g h l y u n d e r vacuum f o r s e v e r a l h o u r s w h i l e b e i n g h e a t e d to 100°C. The s o l i d sample was t h e n c o o l e d to room t e m p e r a t u r e and gaseous b r o m i n e was p a s s e d o v e r i t . The r e a c t i o n p r o d u c t s depended on t h e p r e s s u r e o f the B r 2 and t h e way i t came i n c o n t a c t w i t h the s o l i d . I f the B r 2 was s i m p l y p a s s e d t h r o u g h the s o l i d sample, ( F i g u r e 6.1 ( a ) ) the s p e c t r u m o f S ( C N ) 2 r e s u l t e d , a l o n g w i t h some l i n e s o f S 0 2 and HNCS. No l i n e s b e l o n g i n g to ( S C N ) 2 c o u l d be i d e n t i f i e d , a l t h o u g h t h i s was the major r e a c t i o n p r o d u c t e x p e c t e d ( 1 2 ) . However, when the b r o m i n e was m e r e l y p a s s e d o v e r t h e AgSCN a t low p r e s s u r e , i n su c h a way t h a t the gaseous 157 r e a c t i o n p r o d u c t s r e a c t e d w i t h more b r o m i n e , the s p e c t r u m o f BrSCN a p p e a r e d a l m o s t i m m e d i a t e l y . (See F i g u r e 6.1 ( b ) ) I t s f o r m a t i o n i s e n t i r e l y a n a l o g o u s w i t h i t s f o r m a t i o n i n s o l u t i o n : ( i ) 2 A g N C S ( s ) + B r 2 ( g ) -> ( S C N ) 2 ( g ) + 2 A g B r ( s ) ( i i ) ( S C N ) 2 ( B ) + B r 2 ( 8 ) -» 2BrSCN(g) (6.2) T h r o u g h o u t t h e microwave s t u d y , BrSCN was p r o d u c e d s o l e l y i n a f l o w s y s t e m , and the c e l l was k e p t a t room t e m p e r a t u r e . F i g u r e 6.1 P r e p a r a t i o n o f BrSCN: (a) S t o p c o c k s 1 and 2 were open, s t o p c o c k 3 was c l o s e d . Gaseous B r 2 was p a s s e d t h r o u g h the s o l i d AgSCN. the r e s u l t i n g microwave s p e c t r u m p r e d o m i n a n t l y showed l i n e s o f S ( C N ) 2 . (b) S t o p c o c k 1 was c l o s e d , s t o p c o c k s 2 and 3 were open. Gaseous B r 2 was p a s s e d o v e r the AgSCN and the gaseous r e a c t i o n p r o d u c t s r e a c t e d w i t h f u r t h e r b r o m i n e . The microwave s p e c t r u m p r e d o m i n a t e l y showed t r a n s i t i o n s o f BrSCN. 158 6.3 A n a l y s i s o f t h e Microwave S p e c t r u m The r o t a t i o n a l c o n s t a n t s o f b r o m i n e t h i o c y a n a t e were p r e d i c t e d f o r b o t h i s o t o p e s o f b r o m i n e and f o r b o t h p o s s i b l e c o n f i g u r a t i o n s : BrSCN and BrNCS. The f o r m e r a r r a n g e m e n t o f atoms was more l i k e l y i n a n a l o g y to C1SCN, a l t h o u g h the l a t t e r c o n f i g u r a t i o n c o u l d n o t i n i t i a l l y be r u l e d o u t . F o r BrSCN the s t r u c t u r e was assumed by t r a n s f e r r i n g the Br-S bond l e n g t h from S 2 B r 2 ( 1 3 ) and t h e S-C and C-N bond l e n g t h s and the S-C-N a n g l e from S ( C N ) 2 ( 1 4 ) . The Br-S-C a n g l e was t a k e n to be t h e same as t h e C-S-C a n g l e i n S ( C N ) 2 . F o r BrNCS, the Br-N bond l e n g t h was t r a n s f e r r e d f r o m BrNCO. The Br-N-C a n g l e was t a k e n to be t h a t o f BrNCO, b u t i n c r e a s e d by 7° i n k e e p i n g w i t h o t h e r i s o c y a n a t e s and i s o t h i o c y a n a t e s ( 1 5 , 1 6 ) . The p a r a m e t e r s o f t h e N-C-S c h a i n were t r a n s f e r r e d f r o m HNCS ( 1 6 ) . The p r e d i c t e d r o t a t i o n a l c o n s t a n t s f o r b o t h p o s s i b l e c o n f i g u r a t i o n s a r e shown i n T a b l e 6.1. F o r b o t h p o s s i b l e c o n f i g u r a t i o n s , the m o l e c u l e was p r e d i c t e d to be a p l a n a r n e a r - s y m m e t r i c p r o l a t e r o t o r h a v i n g b o t h a_- and b - t y p e t r a n s i t i o n s . However, the s p e c t r u m p r e d i c t e d f o r e a c h c o n f i g u r a t i o n was q u i t e d i f f e r e n t . The a - t y p e t r a n s i t i o n s o f BrNCS would be much more c l o s e l y s p a c e d t h a n f o r t h e BrSCN i s o m e r , w h i l e the m a g n i t u d e o f A Q f o r BrNCS i s much l a r g e r t h a n t h a t p r e d i c t e d f o r BrSCN, and c o n s e q u e n t l y i t would be e x p e c t e d t o have f a r fewer b - t y p e t r a n s i t i o n s i n t h e a v a i l a b l e f r e q u e n c y r a n g e . The o b s e r v e d s p e c t r u m was s i m i l a r to the s p e c t r a o f BrNCO and INCO i n t h a t t h e r e was a s e r i e s o f s t r o n g a - t y p e R b r a n c h 159 T a b l e 6.1 The r o t a t i o n a l c o n s t a n t s o f b r o m i n e t h i o c y a n a t e and b r o m i n e i s o t h i o c y a n a t e c a l c u l a t e d from model s t r u c t u r e s . BrSCN BrNCS 7 g B r A D(MHz) 9888 . .716 41482. . 906 B D(MHz) 1882 . . 847 1187 , . 136 C D(MHz) 1581 . .688 1154 . . 109 " B r A 0(MHz) 9872 . . 200 41412. .436 B 0(MHz) 1866 . .279 1176 , .730 C o(MHz) 1569 . .562 1144 . .217 c l u s t e r s t h r o u g h o u t t h e s p e c t r u m ; however, w h i l e t h e b - t y p e t r a n s i t i o n s were e x t r e m e l y weak i n t h e s p e c t r a o f BrNCO and INCO so as to be v e r y d i f f i c u l t to a s s i g n , t h e y were r e a s o n a b l y i n t e n s e i n t h e s p e c t r u m o f BrSCN. C o n s e q u e n t l y , t h e i r a s s i g n m e n t was much more s t r a i g h t f o r w a r d . The s p a c i n g o f the a-t y p e R b r a n c h c l u s t e r s was f o u n d to be =3500 MHz, w h i c h was i n r e a s o n a b l e agreement w i t h the p r e d i c t e d (B+C) o f BrSCN. A l s o , the p a t t e r n o f the p r e d i c t e d b - t y p e t r a n s i t i o n s f o r t h i s c o n f i g u r a t i o n c o r r e s p o n d e d q u i t e c l o s e l y to t h o s e o b s e r v e d i n the s p e c t r u m . I t f o l l o w e d t h a t t h i s c o n f i g u r a t i o n was most l i k e l y to be the c o r r e c t one. A l l the t r a n s i t i o n s showed h y p e r f i n e s p l i t t i n g due to q u a d r u p o l e c o u p l i n g o f the b r o m i n e n u c l e u s (I = 3/2). Rough 160 v a l u e s f o r t h 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 h e b r o m i n e n u c l e u s i n BrSCN were c a l c u l a t e d by s i m p l y t a k i n g the r a t i o o f X a a i n BrSCN to xa a i n C1SCN (11) to be the same as t h e r a t i o o f the q u a d r u p o l e moments o f the br o m i n e and c h l o r i n e n u c l e i . ( X b b - X 0 c ) was s i m i l a r l y e s t i m a t e d . These c o n s t a n t s were t h e n u s e d to p r e d i c t t h e f i r s t o r d e r h y p e r f i n e s p l i t t i n g p a t t e r n s o f b o t h t h e a- and b - t y p e t r a n s i t i o n s t o f a c i l i t a t e t he a s s i g n m e n t o f t h e s p e c t r u m . U n f o r t u n a t e l y no h y p e r f i n e s p l i t t i n g due to the q u a d r u p o l e c o u p l i n g o f the n i t r o g e n n u c l e u s was r e s o l v e d f o r any t r a n s i t i o n . Not a l l t h e t r a n s i t i o n s showed the p r e d i c t e d s y m m e t r i c a l s p l i t t i n g p a t t e r n s . Some o f t h e h y p e r f i n e s t r u c t u r e was i n f a c t s i g n i f i c a n t l y p e r t u r b e d , i n d i c a t i n g a h i g h e r o r d e r e f f e c t from the c o n t r i b u t i o n o f the o f f - d i a g o n a l term i n 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 , x a b• F o r BrSCN, x a b• c a l c u l a t e d by as s u m i n g t h a t the Br-S bond i s a p r i n c i p a l a x i s o f the q u a d r u p o l e t e n s o r , was p r e d i c t e d t o be l a r g e : the q u a d r u p o l e moment o f the Br atom i s l a r g e , and 6za , t h e a n g l e between the z - a x i s i n the p r i n c i p a l q u a d r u p o l e t e n s o r and the a - i n e r t i a l a x i s was c a l c u l a t e d t o be — 33° ( s e e S e c t i o n 6.4). A l s o , s e v e r a l n e a r - d e g e n e r a c i e s o f the ty p e AF = 0, AJ = 0, ± 1 , ± 2 , AK aK c = ee * oe , oo **• eo, were l i k e l y , and t r a n s i t i o n s i n v o l v i n g any o f t h e s e e n e r g y l e v e l s were p r e d i c t e d t o be s i g n i f i c a n t l y s h i f t e d from t h e i r f i r s t o r d e r p r e d i c t i o n . The c o m p l e t e a n a l y s i s o f t h e s p e c t r u m o f BrSCN t h e r e f o r e r e q u i r e d use o f the g l o b a l l e a s t - s q u a r e s f i t t i n g p r o c e d u r e to o b t a i n s i m u l t a n e o u s l y the r o t a t i o n a l , c e n t r i f u g a l d i s t o r t i o n and 161 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 , i n c l u d i n g the o f f - d i a g o n a l term Xab- T h i s was p r e v i o u s l y s u c c e s s f u l l y employed i n the a n a l y s i s o f BrNCO and INCO, w h i c h a l s o have l a r g e p e r t u r b a t i o n s i n t h e i r h y p e r f i n e s t r u c t u r e . However, u n l i k e the a n a l y s e s o f t h e s e s p e c t r a , where the b - t y p e t r a n s i t i o n s were r e l a t i v e l y weak, the e x i s t e n c e o f s t r o n g , e a s i l y a s s i g n a b l e , Q - b r a n c h b - t y p e l i n e s i n the s p e c t r u m o f BrSCN, p r e c l u d e d the n e c e s s i t y o f u s i n g p e r t u r b a t i o n s i n the h y p e r f i n e s t r u c t u r e o f t h e a_-type R b r a n c h t r a n s i t i o n s to f i n d the r o t a t i o n a l c o n s t a n t A . o F i r s t , B Q and C Q were c a l c u l a t e d f r o m a - t y p e R b r a n c h K a = 0 and t h e asymmetry s p l i t K a = 1 t r a n s i t i o n s , w h i c h were e i t h e r u n p e r t u r b e d or showed o n l y s m a l l p e r t u r b a t i o n s i n t h e i r h y p e r f i n e s t r u c t u r e . W i t h the s i z e o f t h e asymmetry o f the m o l e c u l e (K = - 0 . 9 2 6 3 ) , t h e s e l i n e s were w e l l s e p a r a t e d from the main c l u s t e r o f l i n e s . T r a n s i t i o n s from one asymmetry b r a n c h o f the K a = 2 «- 1 b - t y p e Q -branch ( J 2 ( J _ 2 ) " J i ( j - i ) ) w e r e a s s i g n e d , to p i n p o i n t a v a l u e o f A o . These were a s s i g n e d from t h e i r h y p e r f i n e s p l i t t i n g p a t t e r n s . F i g u r e 6.2 shows the 1 3 2 1 : L - 12 t r a n s i t i o n s f o r b o t h i s o t o p e s . T hese t r a n s i t i o n s were u s e d to f i t v a l u e s o f A „ , B„, C , o ' o ' o 1 *aa> (*bb " * c c ) > a n d X a b . s o t h a t f u r t h e r t r a n s i t i o n s c o u l d be a s s i g n e d and t h e s e c o n s t a n t s r e f i n e d 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 m easured. K a = 0 and 1 a - t y p e R b r a n c h t r a n s i t i o n s were measured f o r J = 6 to 12. S e v e r a l K a = 2 and 3 asymmetry d o u b l e t s f r o m t h e s e b r a n c h e s were a l s o measured. As w e l l as s e v e r a l K a = 2 <- 1 Q -branch t r a n s i t i o n s o f the t y p e m e n t i o n e d , l i n e s f r o m the l o w e r asymmetry s u b - b r a n c h e s o f t h e 162 BrSCN 13211 - 1 3 i i 2 21.93-22.09 GHz 8 1 BrSCN 12 MHz < > 7 9 B r S C N F i g u r e 6 .2 The t r a n s i t i o n 1 3 2 1 X - 131 1 2 f o r 7 9 B r S C N a n d 8 1 B r S C N . K a = 3 «- 2 ( J 3 > ( j - 3 , " J 2 , ( J . - 2 ) ) a n d K a " 4 - 3 ( J A , ( J - A ) -J 3 ( j - 3 ) ) Q b r a n c h e s were a s s i g n e d . T h e s e were e a s i l y i d e n t i f i e d a t t h e p o i n t where t h e s e s u b - b r a n c h e s c h a n g e d i r e c t i o n to h i g h e r f r e q u e n c y . T h i s i s i l l u s t r a t e d i n F i g u r e 6 . 3 . A few l i n e s o f t h e o t h e r a s y m m e t r y s u b - b r a n c h o f the K a = 3 *- 2 Q b r a n c h ( J 3 ( J - 2 ) " ( J - i ) ) a n < * some K a = 1 «- 0 a n d K a = 0 <- 1 R b r a n c h t r a n s i t i o n s were m e a s u r e d to c o m p l e t e t h e a n a l y s i s . The f i n a l c o n s t a n t s a r e shown i n T a b l e 6 . 2 . As w e l l as the B r S C N U U aii Br 31.57-31.87 GHz 79 B r 193.16-192.17 203.17-202.18 L _ 183,15 -182,16 15 MHz < > F i g u r e 6.3 Broadband s c a n o f the s p e c t r u m o f BrSCN from 31.57 - 31.87 GHz . The t r a n s i t i o n s 18 3 1 5 - 18 2 1 6 , 19 3 1 6 1.92 > l 7 and 20 3 1 7 20 2 a r e shown f o r b o t h i s o t o p e s O l 164 T a b l e 6 .2 S p e c t r o s c o p i c c o n s t a n t s o f b r o m i n e t h i o c y a n a t e Parame t e r 7 9 B r S C N 8 1 B r S C N R o t a t i o n a l C o n s t a n t s (MHz) C. 10092 . 2012 ( 6 8 ) 1 1 9 4 4 . 4 0 5 4 1 ( 1 3 ) 1627 . 94999 (11) 1 0 0 7 4 . 4 7 3 1 ( 7 8 ) 1 9 2 7 . 4 5 0 9 5 ( 1 3 ) 1615 . 5 8 9 1 4 ( 1 0 ) 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 ( k H z ) * J K 0 . 8477 (18) - 1 3 . 6 9 0 ( 4 3 ) 1 0 4 . 2 ( 1 2 ) 0 . 2 3 9 5 6 ( 4 3 ) 2 . 0 1 0 ( 3 9 ) B r o m 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 (MHz) A a a X b b X c c * a b 4 0 2 . 6 2 ( 7 7 ) 366 . 20 (16) 478 . 4 1 ( 2 3 ) 0. 8271 ( 22) - 1 3 . 5 1 7 ( 5 4 ) 102 . 7 ( 1 5 ) 0 . 2 3 5 3 0 ( 5 5 ) 1 . 989 (52) 336 . 4 ( 1 2 ) 3 0 4 . 4 2 ( 2 0 ) 397 . 7 4 ( 3 8 ) I n e r t i a l d e f e c t ( a . m . u . A2) A 0 . 4 4 8 Number o f R o t a t i o n a l T r a n s i t i o n s 56 0 . 449 55 S t a n d a r d D e v i a t i o n o f f i t (MHz) 0 . 044 0 . 0 5 5 1 Numbers i n p a r e n t h e s e s a r e one s t a n d a r d d e v i a t i o n 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 . 165 r o t a t i o n a l c o n s t a n t s and t h e b r o m 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 , a l l f i v 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 were measured. The f r e q u e n c i e s o f a l l the measured t r a n s i t i o n s a r e g i v e n i n T a b l e s 6.4 and 6.5. The t r a n s i t i o n s have been w e i g h t e d a c c o r d i n g t o t h e i r r e s o l v a b i l i t y and wh e t h e r t h e y a r e p a r t i a l l y o v e r l a p p e d by o t h e r t r a n s i t i o n s . The c o m p a r i s o n o f the r e s i d u a l s , w i t h x ab i n c l u d e d i n t h e c a l c u l a t i o n o f the e x a c t f r e q u e n c i e s , and w i t h x a b o m i t t e d , w h i c h a p p r o x i m a t e s a f i r s t o r d e r c a l c u l a t i o n , i n d i c a t e s t h a t t h e r e a r e s e v e r a l i m p o r t a n t ne a r - de gene r ac i e s , p r i m a r i l y a f f e c t i n g the measured a_-type t r a n s i t i o n s . These a r e a l l o f t h e t y p e K a = 2 **• 1 and K a = 3 2 . The c l o s e s t n e a r - d e g e n e r a c y s e p a r a t e s t h e h y p o t h e t i c a l u n s p l i t r o t a t i o n a l e n e r g y l e v e l s 9X g and 82 7 by =265 MHz i n t h e c a s e o f 7 9 B r S C N and =407 MHz i n 8 1 B r S C N . T h i s p r o d u c e s s h i f t s i n t h e h y p e r f i n e s t r u c t u r e o f measured t r a n s i t i o n s w h i c h i n v o l v e the 9X g l e v e l , from a f i r s t - o r d e r p a t t e r n by as much as 30 MHz i n 7 9 B r S C N and up to =13 MHz i n 8 1 B r S C N . T a b l e 6.3 i n d i c a t e s some o f the c l o s e s t n e a r -d e g e n e r a c i e s . 166 T a b l e 6 .3 C l o s e s t n e a r d e g e n e r a c i e s h a v i n g the c o r r e c t symmetry to cause p e r t u r b a t i o n s i n h y p e r f i n e s t r u c t u r e i n the s p e c t r u m o f bromine t h i o c y a n a t e . E n e r g y L e v e l s D i f f e r e n c e i n E n e r g y (MHz) 7 9 B r S C N 8 1 B r S C N 6 1 , 5 " 5 2 , 3 -590 . , 84 - 79 3 . 51 V 9 " 8 2 , , 7 - 265 , .13 -406, , 54 1 0 1 . , 9 " 9 2 , , 8 1584 , . 16 1439 , .67 X 1 2 , , 9 " 1 ° 3 , 7 1645 , . 41 1247 , .23 1 2 2 , . 1 1 " 1 X 3 , , 9 -694, . 41 -976 . 20 1 3 2 , , 1 2 " 1 2 3 , , 1 0 2165 , . 01 1872 . 17 167 T a b l e 6 .4 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 7 9 B r S C N T r a n s i t i o n N o r m a l i s e d 1 O b s e r v e d R e s i d u a l s 2 F' - F" Weight F r e q u e n c y W i t h o u t xah W i t h x a b 7 , 7 17/2 -15/2 -11/2 -13/2 -15/2 13/2 9/2 11/2 6 i 1 .000 1 .000 1 .000 1 .000 23786.693 23789.286 23790.086 23793.610 0.053 -0.376 -0.559 -0.092 0.016 -0.003 -0.068 0.018 7 0 7 17/2 -11/2 -15/2 -13/2 -1 5/2 9/2 13/2 11/2 6 0 61.000 1 .000 1 .000 1 .000 24518.481 24520.856 24523.468 24526.252 0.052 -0.290 -0.129 -0.070 0.008 0.007 0.026 -0.028 7 1 6 17/2 -13/2 -11/2 -15/2 -1 5/2 11/2 9/2 1 3/2 6 i 51.000 1 .000 0. 100 0. 100 25981.968 25987.525 25997.999 25997.999 0. 172 1.319 15.313 12.732 0.053 0.080 0.123 -0.057 8 , 8 19/2 -17/2 -13/2 -15/2 -17/2 15/2 11/2 13/2 7 i 71.000 0.500 0.500 1 .000 27148.453 27149.908 27150.324 27153.938 0.035 -1.042 -1.199 -0.139 0.005 0.049 -0.002 -0.043 8 0 8 19/2 -13/2 -17/2 -15/2 -1 7/2 11/2 1 5/2 13/2 7 0 71.000 1 .000 1 .000 1 .000 27869.916 27871.645 27875.241 27877.345 0.047 -0.209 -0.044 0.043 0.011 -0.018 0.059 0.061 8 , 7 13/2 -19/2 -17/2 -15/2 -11/2 17/2 15/2 13/2 7 i 60.500 0.500 1 .000 1 .000 29638.808 29639.418 29641 .682 29643.412 -1.297 0.028 -0.930 0.054 -0.018 -0.057 -0.055 0.036 9 1 9 19/2 -15/2 -21/2 -17/2 -1 7/2 13/2 19/2 15/2 8 i 81.000 1 .000 1 .000 1 .000 30474.460 30488.289 30498.014 30502.019 -25.762 -12.151 0.045 -0.688 -0.050 0.007 0.019 -0.003 1 Measurements were w e i g h t e d a c c o r d i n g to l / a 2 , where a i s the u n c e r t a i n t y i n the measurements. U n i t w e i g h t c o r r e s p o n d e d to an u n c e r t a i n t y o f 0.03 MHz. 2 O b s e r v e d 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 the c o n s t a n t s i n T a b l e 6.2. 168 T a b l e 6.4 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x ab W i t h x a b 9 o 9 2 1 / 2 -1 5 / 2 -1 9 / 2 -1 7 / 2 -9 , 8 2 1 / 2 -1 5 / 2 -1 9 / 2 -1 7 / 2 -10 , 2 3 / 2 1 9 / 2 1 7 / 2 2 1 / 2 10 o 2 3 / 2 1 7 / 2 2 1 / 2 1 9 / 2 10 2 1 7 / 2 2 3 / 2 2 1 / 2 1 9 / 2 10 3 1 7 / 2 2 3 / 2 2 1 / 2 1 9 / 2 10 3 2 3 / 2 1 9 / 2 1 7 / 2 2 1 / 2 10 2 2 1 / 2 1 7 / 2 1 9 / 2 2 3 / 2 1 o t o 1 9 / 2 1 3 / 2 1 7 / 2 1 5 / 2 1 9 / 2 1 3 / 2 1 7 / 2 1 5 / 2 2 1 / 2 1 7 / 2 1 5 / 2 1 9 / 2 2 1 / 2 1 5 / 2 1 9 / 2 1 7 / 2 1 5 / 2 2 1 / 2 1 9 / 2 1 7 / 2 1 5 / 2 2 1 / 2 1 9 / 2 1 7 / 2 2 1 / 2 1 7 / 2 1 5 / 2 1 9 / 2 1 9 / 2 1 5 / 2 1 7 / 2 2 1 / 2 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 0 , 0 , 1 , 1 , 1 0 0 1 0 0 0 0 0 0 0 0 1 . 0 0 0 1 . 0 0 0 0 . 5 0 0 1 . 0 0 0 1 . 0 0 0 0 . 7 6 8 1 . 0 0 0 1 . 0 0 0 8 0 . 1 0 0 0 . 1 0 0 1 . 0 0 0 1 . 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 1 . 0 0 0 0 0 0 5 0 0 5 0 0 , 5 0 0 3 1 1 7 9 . 5 1 8 3 1 1 8 0 . 7 7 9 3 1 1 8 4 . 8 3 1 3 1 1 8 6 . 4 6 6 3 3 2 7 1 . 8 7 0 3 3 2 7 1 . 8 7 0 3 3 2 7 4 . 7 0 8 3 3 2 7 5 . 6 5 6 3 3 8 3 5 . 4 0 1 3 3 8 4 0 . 2 6 3 3 3 8 5 5 . 8 4 8 3 3 8 6 8 . 1 0 5 3 4 4 5 4 . 4 1 1 3 4 4 5 5 . 3 2 5 3 4 4 5 9 . 3 0 3 3 4 4 6 0 . 8 7 8 3 5 4 9 3 . 1 4 0 3 5 4 9 3 . 1 4 0 3 5 4 9 6 . 0 6 6 3 5 4 9 8 . 4 8 3 3 5 8 6 3 . 9 1 2 3 5 8 6 4 . 9 1 6 3 5 8 6 9 . 0 4 6 3 5 8 6 9 . 7 9 9 3 5 9 8 2 . 8 9 2 3 5 9 8 5 . 2 9 9 3 5 9 8 8 . 3 5 7 3 5 9 9 1 . 8 0 0 3 6 7 5 1 . 0 3 1 3 6 7 5 3 . 3 1 7 3 6 7 5 3 . 3 1 7 3 6 7 5 3 . 6 5 3 0 . 0 5 6 - 0 . 1 9 5 - 0 . 0 3 6 - 0 . 0 0 4 0 . 1 0 0 - 0 . 5 2 7 - 0 . 3 0 2 - 0 . 0 0 5 0 . 0 0 9 0 . 7 7 5 1 8 . 4 4 5 3 0 . 6 3 8 0 . 0 4 0 0 . 0 9 6 • 0 . 0 5 4 • 0 . 0 1 1 • 0 . 192 1 . 3 2 2 0 . 1 8 9 2 . 1 3 7 • 0 . 2 7 8 0 . 9 9 7 0 . 1 1 8 0 . 5 1 4 • 5 . 5 0 8 • 7 . 2 4 6 0 . 4 4 3 0 . 2 6 4 •1 . 1 5 2 •1 . 3 4 8 0 . 0 0 4 0 . 0 7 7 0 . 0 2 6 • 0 . 0 6 2 0 . 0 3 8 0 . 0 0 5 0 . 0 3 6 • 0 . 1 2 8 • 0 . 0 3 0 • 0 . 0 5 5 • 0 . 0 1 2 • 0 . 0 4 2 • 0 . 1 0 7 • 0 . 0 3 8 0 . 0 1 4 0 . 0 0 1 0 . 0 0 4 • 0 . 0 0 4 0 . 1 5 4 • 0 . 0 5 4 0 . 0 3 3 0 . 0 2 0 0 . 0 4 9 0 . 0 1 3 0 . 0 1 4 0 . 0 4 4 0 . 0 3 6 • 0 . 0 0 8 • 0 . 1 3 1 • 0 . 0 7 5 0 . 0 8 5 0 . 0 6 7 • 0 . 0 3 1 • 0 . 0 1 3 169 T a b l e 6 . 4 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s e d We i g h t Ob s e r v e d F r e q u e n c y Res i d u a l s W i t h o u t x ab W i t h x a b 10 , 23/2 17/2 21/2 19/2 11 1 19/2 25/2 23/2 21/2 11 o 25/2 19/2 23/2 21/2 11 2 19/2 25/2 23/2 21/2 11 3 19/2 23/2 25/2 21/2 11 3 19/2 23/2 25/2 21/2 11 2 21/2 25/2 23/2 19/2 11 i 25/2 19/2 23/2 21/2 1 1 1 i i o 1 o 21/2 15/2 19/2 1 7/2 17/2 23/2 21/2 19/2 23/2 17/2 21/2 19/2 10 1 7/2 23/2 21/2 19/2 10 10 1 7/2 21/2 23/2 19/2 10 1 7/2 21/2 23/2 19/2 10 19/2 23/2 21/2 17/2 23/2 1 7/2 21/2 19/2 10 1 8 0.500 0.500 1 .000 1 .000 i i o 1 .000 1 .000 1 .000 1 .000 o 1 o 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 0 1 1 1 100 0-00 000 000 1 .000 1 .000 1 .000 1 .000 1 .000 .1 .000 1 .000 1 .000 0 0 0 0 100 100 500 500 36874.089 36874.089 36877.300 36877.877 37160.568 37161.104 37161.668 37164.620 37703.711 37705.567 37709.293 37709.698 38985.034 38985.679 38987.672 38990.044 39464.936 39468.320 39472.350 39475.583 39664.034 39665.671 39666.155 39669.494 40563.801 40564.123 40568.213 40571.828 40440.946 40440.946 40444.394 40444.779 0.093 0.266 •0.112 0.089 •2.205 •0.002 •1 .385 •0. 106 •0.035 •0.098 0.014 0.033 •0.805 0.405 •0.725 0.557 •0.039 •0.036 7.727 6.809 •0. 1 45 0.057 2.528 3.270 0.233 0.042 5.578 6.844 0. 1 79 •0. 129 •0.067 -0.004 0.044 •0.064 0.026 0.043 •0.043 •0.020 •0.019 •0.027 •0.057 •0.007 0.042 0.016 0.039 •0.044 0.015 0.013 0.074 0.035 0.037 0.002 •0.029 0.029 •0.038 •0.025 0.027 •0.020 0.002 •0.014 0. 140 •0.004 0.019 •0.043 170 T a b l e 6.4 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x ab W i t h x a b 12 , 1 2 -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 — 21/2 12 o 1 2 . -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 — 21/2 12 2 1 1 -21/2 - 19/2 25/2 23/2 27/2 - 25/2 23/2 — 21/2 12 3 1 0 -27/2 - 25/2 23/2 - 21/2 21/2 - 19/2 25/2 — 23/2 12 3 9 -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 — 21/2 12 2 1 0 -25/2 - 23/2 21/2 - 19/2 23/2 - 21/2 27/2 — 25/2 12 , 1 1 -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 — 21/2 12 , 1 2 -27/2 - 25/2 21/2 - 19/2 25/2 - 23/2 23/2 - 21/2 11 1 1 1 11 11 11 11 11 11 11 1 .000 1 .000 1 .000 1 .000 1 1 1 .000 1 .000 1 .000 1 .000 1 0 1 .000 0.500 1 .000 1 .000 1 .000 1 .000 1 .000 1 .000 0. 100 0. 100 0.100 1 .000 1 .000 1 .000 1 .000 1 .000 1 0 1 .000 1 .000 0.500 0.500 10.100 0. 100 0.100 0.100 40475.840 40476.624 40477.225 40479.106 40936.990 40937.318 40941.081 40942.039 42455.891 42457.166 42462.373 42465.999 43051.182 43054.541 43063.601 43065.805 43366.981 43366.981 43366.981 43368.254 44368.265 44369.292 44371.522 44372.018 43966.862 43966.862 43970.747 43970.993 42646.644 42646.644 42659.909 42659.909 0.029 -0.623 -0.428 0.010 0.089 -0.255 -0.001 -0.209 -6.872 -7.934 0.238 0. 1 52 •1 2. 1 24 •1 2. 1 24 -0.110 -0.395 0.528 -0.092 -0. 186 0.425 •2.548 •3.444 0.039 0.009 0.112 •0. 102 •0.034 0.018 0.085 0.592 0.498 0.285 0.013 0.0 •0.001 0.045 0.071 •0.083 0.031 0.001 0.017 •0.001 0.015 0.025 0.015 •0.072 0.006 •0.099 0. 1 22 0.036 •0.114 0.027 •0.004 0.068 0.004 •0.037 0.081 •0.016 0.028 •0.050 0.060 •0. 1 76 •0.072 0.209 171 T a b l e 6 . 4 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t Ob s e r v e d F r e q u e n c y Res i d u a l s W i t h o u t X a b W i t h x a b 13 , 1 3 - 12 0 1 2 2 9 / 2 - 2 7 / 2 1 . 0 0 0 2 3 / 2 - 2 1 / 2 1 . 0 0 0 2 7 / 2 - 2 5 / 2 0 . 5 0 0 2 5 / 2 — 2 3 / 2 0 . 5 0 0 14 , 1 a - 13 0 1 3 3 1 / 2 - 2 9 / 2 1 . 0 0 0 2 5 / 2 - 2 3 / 2 1 . 0 0 0 2 9 / 2 - 2 7 / 2 0 . 5 0 0 2 7 / 2 — 2 5 / 2 0 . 5 0 0 15 , 1 5 - 14 0 1 4 3 3 / 2 - 3 1 / 2 1 . 0 0 0 2 7 / 2 - 2 5 / 2 1 . 0 0 0 3 1 / 2 - 2 9 / 2 0 . 1 0 0 2 9 / 2 — 2 7 / 2 0 . 1 0 0 12 o 1 2 - 1 1 1 1 1 2 5 / 2 - 2 3 / 2 1 . 0 0 0 2 3 / 2 - 2 1 / 2 1 . 0 0 0 2 7 / 2 - 2 5 / 2 1 . 0 0 0 2 1 / 2 — 19/2 0 . 5 0 0 13 o 1 3 - 12 1 1 2 2 7 / 2 - 2 5 / 2 1 . 0 0 0 2 5 / 2 - 2 3 / 2 1 . 0 0 0 2 9 / 2 2 7 / 2 1 . 0 0 0 2 3 / 2 — 2 1 / 2 1 . 0 0 0 15 o 1 5 - 14 1 1 4 3 1 / 2 - 2 9 / 2 1 . 0 0 0 2 9 / 2 - 2 7 / 2 1 . 0 0 0 3 3 / 2 - 3 1 / 2 1 . 0 0 0 2 7 / 2 — 2 5 / 2 1 . 0 0 0 16 o 1 6 - 15 1 1 5 3 3 / 2 - 3 1 / 2 1 . 0 0 0 3 1 / 2 - 2 9 / 2 0 . 1 0 0 3 5 / 2 - 3 3 / 2 0 . 1 0 0 2 9 / 2 — 2 7 / 2 1 . 0 0 0 13 2 1 1 - 13 1 1 2 2 7 / 2 - 2 7 / 2 1 . 0 0 0 2 5 / 2 - 2 5 / 2 1 . 0 0 0 2 9 / 2 - 2 9 / 2 1 . 0 0 0 2 3 / 2 - 2 3 / 2 0 . 5 0 0 4 5 4 9 0 . 0 4 4 4 5 4 9 0 . 7 8 7 4 5 5 0 0 . 9 6 4 4 5 5 0 0 . 9 6 4 4 8 4 0 4 . 3 0 8 4 8 4 0 4 . 7 9 5 4 8 4 1 2 . 8 4 1 4 8 4 1 2 . 8 4 1 5 1 3 8 3 . 5 5 4 5 1 3 8 4 . 1 5 8 5 1 3 9 0 . 3 7 3 5 1 3 9 0 . 3 7 3 3 8 7 5 8 . 3 3 4 3 8 7 6 1 . 4 0 9 3 8 7 6 6 . 2 0 3 3 8 7 6 7 . 2 5 3 4 2 4 4 6 . 6 8 7 4 2 4 4 9 . 2 0 3 4 2 4 5 2 . 1 3 0 4 2 4 5 3 . 3 9 2 4 9 5 8 5 . 9 4 8 4 9 5 8 7 . 4 9 5 4 9 5 8 8 . 4 3 8 4 9 5 8 9 . 2 8 2 5 3 0 5 8 . 8 4 3 5 3 0 6 0 . 2 0 2 5 3 0 6 0 . 2 0 2 5 3 0 6 1 . 0 6 4 2 2 0 4 3 . 0 6 4 2 2 0 4 5 . 1 7 1 2 2 0 6 4 . 7 0 3 2 2 0 6 7 . 5 3 0 0 . 0 3 5 0 . 6 9 5 0 . 4 6 6 0 . 2 2 5 0 . 0 5 3 0 . 3 1 6 0 . 3 1 6 • 0 . 0 4 2 0 . 0 2 2 0 . 2 8 0 0 . 3 2 4 • 0 . 1 1 6 0 . 9 9 0 0 . 3 1 1 0 . 0 5 0 • 1 . 5 1 4 • 0 . 6 0 3 0 . 0 2 6 0 . 0 2 7 • 0 . 7 7 9 • 0 . 3 5 1 • 0 . 0 5 5 0 . 0 4 7 • 0 . 4 2 8 • 0 . 2 4 0 0 . 0 8 0 0 . 0 7 7 • 0 . 3 0 8 0 . 2 9 4 0 . 0 3 6 0 . 0 1 6 0 . 3 5 8 • 0 . 0 5 5 0 . 0 5 7 0 . 0 7 0 • 0 . 0 4 1 0 . 0 3 6 • 0 . 0 1 8 0 . 0 1 9 0 . 0 3 1 0 . 0 0 9 0 . 0 1 6 0 . 0 9 1 - 0 . 1 1 4 0 . 0 3 9 0 . 0 1 0 0 . 0 4 1 0 . 0 4 8 0 . 0 1 9 0 . 0 5 2 - 0 . 0 3 6 0 . 0 3 2 • 0 . 0 3 3 • 0 . 0 3 5 0 . 0 3 8 • 0 . 0 2 0 0 . 0 0 4 0 . 0 9 5 • 0 . 0 8 5 0 . 0 0 3 0 . 0 2 5 • 0 . 0 1 3 0 . 0 1 2 0 . 0 1 4 172 T a b l e 6.4 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x ab W i t h xab 14 2 29/2 27/2 31/2 25/2 15 2 31/2 29/2 33/2 27/2 16 2 33/2 31/2 35/2 29/2 17 2 35/2 33/2 37/2 31/2 18 2 37/2 35/2 39/2 33/2 17 3 35/2 33/2 37/2 31/2 18 3 39/2 33/2 37/2 35/2 18 3 37/2 35/2 39/2 33/2 1 2 1 3 1 4 1 S 1 6 1 5 1 5 1 6 29/2 27/2 31/2 25/2 1 4 31/2 29/2 33/2 27/2 15 33/2 31/2 35/2 29/2 16 1 7 35/2 33/2 37/2 31/2 37/2 35/2 39/2 33/2 18 1 1 3 1 .000 1 .000 1 .000 1 .000 1 1 4 1 .000 1 .000 1 .000 1 .000 1 1 5 1 .000 1 .000 1 .000 1 .000 1 1 6 1 .000 1 .000 1 .000 1 .000 1 1 7 1 .000 0.500 1 .000 1 .000 1 7 35/2 33/2 37/2 31/2 39/2 33/2 37/2 35/2 18 37/2 35/2 39/2 33/2 18 1 6 0, 0, 0, 1, 1 6 0, 0, 0, 0, 500 500 500 000 500 500 100 100 1 7 1 .000 1 .000 1 .000 1 .000 23100.077 23102.644 23126.847 23129.906 24522.033 24524.821 24553.501 24556.832 26323.997 26327.378 26360.322 26363.405 28513.068 28516.505 28553.209 28556.745 31083.442 31086.835 31127.053 31130.490 48953.793 48954.258 48979.983 48984.696 31796.927 31796.927 31798.831 31798.831 50483.824 50485.479 50512.093 50515.192 0. 1 92 •0.031 0.045 0.235 0. 1 39 •0.040 0.019 0.090 0. 1 37 0.022 0.114 0.074 0. 103 0.021 0.010 0. 1 28 0.117 0.128 0.060 0.013 1 .748 0.202 0.193 2.073 0.033 0.387 0.458 0.107 0.644 0.062 0.075 0.649 •0.010 •0.004 0.032 0.043 •0.012 •0.016 •0.002 0.035 0.015 0.009 0.087 •0.044 •0.006 0.035 •0.044 0.091 0.016 0.087 0.020 •0.046 0.0 •0. 120 •0.135 0.004 0.030 0.067 0. 185 0. 138 0.004 0.007 •0.042 •0.053 1 7 3 T a b l e 6.4 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d We i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x ab W i t h xab 19 3 39/2 37/2 41/2 35/2 19 3 37/2 41/2 35/2 20 3 41/2 39/2 43/2 37/2 22 3 45/2 43/2 47/2 41/2 23 3 47/2 45/2 49/2 43/2 24 3 49/2 47/2 51/2 45/2 26 4 49/2 55/2 51/2 53/2 27 , 57/2 51/2 53/2 55/2 1 6 19 1 7 1 7 1 9 2 0 2 1 2 2 2 3 39/2 37/2 41/2 35/2 " 19 2 37/2 41/2 35/2 - 20 2 41/2 39/2 43/2 37/2 - 22 2 45/2 43/2 47/2 41/2 - 23 2 47/2 45/2 49/2 43/2 " 24 2 49/2 47/2 51/2 45/2 - 26 3 49/2 55/2 51/2 53/2 " 27 3 57/2 51/2 53/2 55/2 0.500 0.500 1 .000 1 .000 1 8 1 .000 1 .000 0.500 1 8 1 .000 1 .000 1 .000 1 .000 2 0 1 .000 1 .000 1 .000 1 .000 2 1 1 .000 1 .000 1 .000 1 .000 2 2 1 .000 1 .000 1 .000 1 .000 2 3 0.500 0.500 0. 100 0. 100 2 4 0.500 0.500 0.500 0.500 31633.001 31633.001 31635.683 31636.091 52186.309 52213.579 52215.793 31810.444 31810.820 31817.705 31818.401 33333.022 33334.111 33349.587 33350.487 34727.587 34728.833 34748.251 34749.638 36562.329 36563.859 36587.216 36588.710 42280.139 42280.139 42284.232 42284.232 41864.304 41864.304 41864.616 41864.616 0.223 0.013 0.024 0.191 •0.011 0.039 0.464 0. 1 30 •0.017 •0.004 0.119 0.070 •0.060 0.055 •0.026 0.141 •0.001 •0.043 0.053 0.048 0.003 0.014 0.008 0. 155 •0.064 0.200 •0.047 0.056 0.048 0.026 •0.023 0.057 •0.002 0.017 0.0 0.043 0.056 0. 1 25 0.016 •0.029 •0.014 •0.007 0.002 •0.039 0.040 0.069 0.077 0.012 •0.062 0.014 •0.012 0.016 •0.007 •0.023 0.056 •0.073 0. 1 76 •0. 1 27 0.046 •0.046 •0.018 •0.084 174 T a b l e 6 .4 ( C o n t i n u e d ) T r a n s i t i o n N o r m a l i s e d O b s e r v e d R e s i d u a l s F ' - F" W e i g h t F r e q u e n c y W i t h o u t x a b W i t h x a b 28 ( 2« " 28 3 2 5 5 9 / 2 - 5 9 / 2 1 . 0 0 0 4 1 8 4 2 . 0 2 5 0 . 0 7 8 0 . 0 6 7 5 3 / 2 - 5 3 / 2 1 . 0 0 0 4 1 8 4 2 . 7 1 5 - 0 . 0 0 2 - 0 . 0 4 3 5 5 / 2 - 5 5 / 2 0 . 5 0 0 4 1 8 3 8 . 7 2 7 0 . 1 2 1 0 . 1 1 8 5 7 / 2 - 5 7 / 2 0 . 5 0 0 4 1 8 3 9 . 3 0 1 0 . 0 1 4 - 0 . 0 4 1 175 T a b l e 6 . 5 M e a s u r e d r o t a t i o n a l t r a n s i t i o n s ( i n MHz) o f 8 1 B r S C N T r a n s i t i o n N o r m a l i s e d 1 O b s e r v e d R e s i d u a l s 2 F' - F" W e i g h t F r e q u e n c y W i t h o u t x a b W i t h x a h 7 , 7 17/2 -15/2 -1 1/2 -13/2 -15/2 13/2 9/2 11/2 6 1 1 .000 1 .000 1 .000 1 .000 23600.994 23603.280 23603.993 23606.793 0.017 -0.207 -0.332 -0.067 -0.011 0.035 -0.005 0.008 7 O 7 17/2 -1 1/2 -15/2 -13/2 -15/2 9/2 13/2 11/2 6 0 61.000 1 .000 1 .000 1 .000 24327.058 24329.117 24331.202 24333.615 0.026 -0.199 -0.084 0.041 -0.002 0.011 0.027 0.073 7 , 6 17/2 -13/2 -11/2 -15/2 -15/2 11/2 9/2 13/2 6 t 51.000 1 .000 0.100 0.100 25764.780 25769.026 25774.304 25774.304 0.084 0.654 8.842 6.733 0.0 -0.042 0.245 -0.100 8 , 8 19/2 -17/2 -13/2 -15/2 -17/2 15/2 11/2 13/2 7 1 7i.000 0.500 0.500 1 .000 26937.043 26938.539 26938.944 26941.625 0.008 -0.596 -0.686 -0.121 -0.016 0.081 0.080 -0.059 8 o 8 19/2 -13/2 -17/2 -15/2 -17/2 11/2 15/2 13/2 7 0 ?1.000 1 .000 1 .000 1 .000 27654.686 27656.179 27659.074 27660.763 0.021 -0.156 -0.059 -0.061 -0.002 -0.020 0.015 -0.045 8 i 7 13/2 -19/2 -17/2 -15/2 -11/2 17/2 15/2 13/2 7 1 60.500 0.500 1 .000 1 .000 29392.619 29392.907 29394.885 29396.091 -0.871 0.032 -0.649 -0.080 0.095 -0.027 0.017 -0.088 9 1 9 19/2 -15/2 -21/2 -17/2 -17/2 13/2 19/2 15/2 8 1 81.000 1 .000 1 .000 1 .000 30253.948 30256.989 30261.182 30264.830 -9.082 -6.240 0.018 -0.275 -0.045 -0.009 -0.002 0.015 Measurements were w e i g h t e d a c c o r d i n g t o l / a 2 , where a i s the u n c e r t a i n t y i n t h e measurements.. U n i t w e i g h t c o r r e s p o n d e d to an u n c e r t a i n t y o f 0.03 MHz. 2 O b s e r v e d 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 the c o n s t a n t s i n T a b l e 6.2. 176 T a b l e 6.5 ( C o n t i n u e d ) T r a n s i t i o n F' - F" N o r m a l i s e d Weight O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x ab W i t h xab 9 o 9 - 8 21/2 - 19/2 15/2 - 13/2 19/2 - 17/2 17/2 - 15/2 9 1 8 - 8 21/2 - 19/2 15/2 - 1 3/2 19/2 - 17/2 17/2 - 15/2 10 , 1 0 - 9 23/2 - 21/2 19/2 - 17/2 17/2 - 1 5/2 21/2 - 19/2 10 0 10 - 9 23/2 - 21/2 17/2 - 1 5/2 21/2 - 19/2 19/2 - 17/2 10 2 9 - 9 17/2 - 1 5/2 23/2 - 21/2 21/2 - 19/2 19/2 - 17/2 10 3 8 - 9 17/2 - 1 5/2 23/2 - 21/2 21/2 - 19/2 19/2 - 1 7/2 10 3 7 - 9 23/2 - 21/2 19/2 - 17/2 17/2 - 15/2 21/2 - 19/2 10 2 8 - 9 21/2 - 19/2 19/2 - 17/2 17/2 - 15/2 23/2 - 21/2 1 .000 1 .000 1 .000 1 .000 000 000 500 500 000 000 000 000 1 .000 1 .000 1 .000 1 .000 0, 0 1, 1, 100 100 000 000 000 000 500 500 1 .000 1 .000 1 .000 1 .000 1 .000 0.100 0.100 0.100 30941.085 30942.180 30945.499 30946.853 32996.687 32996.687 32999.105 32999.573 33573.369 33577.213 33585.911 33587.745 34192.997 34193.776 34197.107 34198.349 35206.758 35206.758 35209.164 35211.150 35567.891 35568.498 35572.237 35572.610 35682.658 35684.728 35687.130 35690.004 36434.114 36435.943 36435.943 36435.943 0.050 -0. 132 -0.013 0.006 0.025 -0.360 -0.222 0.024 -0.058 0.381 10.803 12.601 0.063 •0.095 •0.033 0.0 0.131 1 .048 •0. 1 45 1 .690 •0.234 0.612 0. 162 0.233 •4.473 •5.900 •0.338 •0.229 -0.698 0. 183 -0.937 -0.019 0.032 •0.035 0.041 0.016 •0.020 •0.070 •0.024 •0.014 •0.076 •0.009 • 0 . 0 1 1 -0.016 0.049 •0.018 0.005 0.008 0.095 •0.080 •0.011 0.056 0.045 0.060 0.125 0.032 •0.044 0.0 •0.075 •0.082 0.019 0. 153 •0.083 •0.083 177 T a b l e 6 .5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s e d We i g h t O b s e r v e d F r e q u e n c y Res i d u a l s W i t h o u t x ab W i t h y a b 10 , 23 /2 17 /2 21/2 19/2 2 1 / 2 1 5 / 2 1 9 / 2 17 /2 1 8 0 . 100 0 . 1 0 0 1 .000 1 .000 3 6 5 7 1 . 4 4 4 3 6 5 7 1 . 4 4 4 3 6 5 7 4 . 0 1 4 3 6 5 7 4 . 7 1 7 0 . 1 69 0 . 2 9 7 0 . 0 6 6 •0 .020 0 . 1 34 •0 . 1 55 0 . 0 3 3 0 . 0 4 9 1 1 , 1 9 / 2 2 5 / 2 2 3 / 2 2 1 / 2 i 1 1 7 / 2 2 3 / 2 2 1 / 2 1 9 / 2 10 i o 0 . 100 0 . 1 00 0 . 100 1 .000 3 6 8 7 4 . 0 1 0 3 6 8 7 4 . 0 1 0 3 6 8 7 4 . 7 0 3 3 6 8 7 7 . 2 0 9 •1 . 5 8 9 •0 . 1 95 •1 .114 0 . 0 0 6 0 . 0 9 8 •0.211 • 0 . 0 1 7 0 .051 11 o 2 5 / 2 1 9 / 2 2 3 / 2 2 1 / 2 11 2 19/2 2 5 / 2 2 3 / 2 2 1 / 2 11 3 1 9 / 2 2 3 / 2 2 5 / 2 2 1 / 2 1 i 1 o 2 3 / 2 17 /2 2 1 / 2 19 /2 10 1 7 / 2 2 3 / 2 2 1 / 2 1 9 / 2 10 1 7 / 2 2 1 / 2 2 3 / 2 1 9 / 2 10 1 o 1 , 1 , 0, 0, 000 000 500 500 0 . 5 0 0 0 . 5 0 0 1 .000 1 .000 000 100 100 000 3 7 4 1 9 . 2 3 2 3 7 4 2 0 . 6 2 9 3 7 4 2 3 . 6 8 4 3 7 4 2 4 . 0 4 9 3 8 6 7 1 . 8 1 8 3 8 6 7 2 . 0 8 8 3 8 6 7 3 . 9 2 8 38675 .751 3 9 1 3 9 . 0 0 0 3 9 1 4 2 . 0 9 9 3 9 1 4 2 . 0 9 9 3 9 1 4 5 . 6 5 6 0 . 0 5 2 •0 .077 0 . 0 0 6 0 . 108 • 0 . 4 6 3 0 . 2 7 3 0 . 4 6 5 0 . 4 2 9 0 . 0 9 7 0 . 1 7 3 3 . 2 9 7 3.391 0.041 • 0 . 0 3 4 0 . 0 3 8 • 0 . 0 9 3 0 . 0 6 4 • 0 . 0 5 9 •0 .012 • 0 . 0 0 4 • 0 . 0 1 7 0 . 2 2 2 0 . 0 3 6 0 . 1 1 2 11 3 19 /2 2 3 / 2 2 5 / 2 2 1 / 2 11 2 2 1 / 2 2 5 / 2 2 3 / 2 19 /2 17 /2 2 1 / 2 2 3 / 2 1 9 / 2 10 1 9 / 2 2 3 / 2 2 1 / 2 1 7 / 2 10 1 .000 1 .000 1 .000 0 . 5 0 0 0 . 100 0 . 100 1 .000 1 .000 3 9 3 2 9 . 9 9 8 3 9 3 3 1 . 2 3 0 3 9 3 3 2 . 0 8 4 3 9 3 3 4 . 9 0 2 4 0 2 1 3 . 2 7 8 4 0 2 1 3 . 2 7 8 40216 .691 4 0 2 1 9 . 7 4 3 • 0 . 0 0 5 • 0 . 0 1 5 2 . 5 4 5 3 . 1 52 0 . 3 1 4 •0 .112 4 . 5 1 3 5 . 5 8 8 0 . 0 7 7 •0 .057 0 . 0 6 5 •0 .068 0 . 1 54 •0 . 1 57 0.061 • 0 . 0 0 9 11 1 2 5 / 2 19 /2 2 3 / 2 2 1 / 2 i o 2 3 / 2 1 7 / 2 2 1 / 2 19 /2 10 0 . 100 0 . 100 0 . 5 0 0 0 . 5 0 0 4 0 1 1 1 . 6 5 3 4 0 1 1 1 . 6 5 3 4 0 1 1 4 . 5 3 7 4 0 1 1 4 . 8 6 3 0 . 0 7 4 0 . 1 9 5 •0 .070 • 0 . 0 2 3 0 . 0 4 7 •0 . 106 •0 .008 • 0 . 0 4 9 1 7 8 T a b l e 6 .5 ( C o n t i n u e d ) T r a n s i t i o n N o r m a l i s e d O b s e r v e d R e s i d u a l s F ' - F" W e i g h t F r e q u e n c y W i t h o u t xab W i t h x 12 , 1 2 - 1 1 1 1 1 27/2 - 25 /2 1 .000 21/2 - 19/2 1 .000 25 /2 - 2 3 / 2 1 .000 23 /2 — 2 1 / 2 1 .000 12 o 1 2 - 1 1 0 1 1 27/2 - 25 /2 0 .500 21 /2 - 19/2 0 .500 25 /2 - 2 3 / 2 1 .000 23/2 — 2 1 / 2 1 .000 12 2 1 1 - 1 1 2 1 0 21/2 - 1 9/2 1 .000 25/2 - 23 /2 1 .000 27/2 - 25 /2 1 .000 23 /2 — 21 /2 1 .000 12 3 1 0 - 11 3 9 27/2 - 2 5 / 2 1 .000 23/2 - 2 1 / 2 1 .000 21/2 - 19/2 1 .000 25 /2 — 2 3 / 2 1 .000 12 3 9 - 1 1 3 8 27/2 - 2 5 / 2 0 . 100 21/2 - 19/2 0 . 100 25/2 - 2 3 / 2 0 . 100 23/2 — 21 /2 1 .000 12 2 1 0 - 1 1 2 9 25/2 - 2 3 / 2 1 .000 21/2 - 19/2 1 .000 23/2 - 2 1 / 2 1 .000 27/2 — 2 5 / 2 1 .000 12 , 1 1 - 1 1 1 1 0 27/2 - 2 5 / 2 0 .500 21/2 - 1 9/2 0 .500 25/2 - 2 3 / 2 0 . 100 23/2 — 2 1 / 2 0 . 100 12 , 1 2 - 1 1 0 1 1 27/2 - 2 5 / 2 0 .500 21/2 - 19/2 0 .500 23/2 - 2 1 / 2 0 .100 25 /2 - 23 /2 0 .100 40164 .185 0 .028 0 .013 40164 .895 - 0 . 4 6 9 - 0 . 0 1 6 40165 .308 - 0 . 3 7 5 - 0 . 0 5 7 40166 .910 0 .018 0 .040 40628 .925 0.051 0 .043 40629 .218 - 0 . 1 9 8 - 0 . 0 9 6 40632 .326 - 0 . 0 2 1 0 .0 40633.231 - 0 . 1 0 0 -0 .021 42119 .239 - 3 . 2 7 4 0 .066 42120 .968 - 3 . 4 7 0 - 0 . 0 3 7 42122 .147 0 .167 0 .004 42125 .199 0 .139 0 .006 42701 .442 -6 .461 0 .078 42703 .598 - 7 . 1 1 0 0 .072 42708 .194 - 0 . 0 5 5 0 .023 42710 .197 - 0 . 1 2 4 0 .045 42999 .136 0 .464 0.151 42999 .136 - 0 . 0 5 4 0 .032 42999 .136 - 0 . 1 8 3 - 0 . 1 3 7 43000 .226 0 .359 0 .010 43985 .660 - 2 . 4 8 9 - 0 . 0 2 5 43986.501 - 3 . 2 8 5 - 0 . 0 0 5 43988 .768 - 0 . 0 1 3 0 .037 43989 .128 -0 .041 - 0 . 0 7 4 43612 .402 0 .030 0 .008 43612 .402 - 0 . 1 6 1 - 0 . 1 0 0 43615 .752 0 .077 0.121 43615 .752 - 0 . 1 2 4 - 0 . 1 4 6 42376 .320 0 .110 0 .028 42376 .320 0 .548 - 0 . 0 9 0 42387.484 0 .235 0 .122 42387 .484 0 .404 - 0 . 1 2 3 179 T a b l e 6 .5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s e d We i g h t O b s e r v e d F r e q u e n c y Re s i d u a l s W i t h o u t x a h W i t h • a b 13 , 1 3 -29/2 - 27/2 23/2 - 21/2 27/2 - 25/2 25/2 — 23/2 14 , 1 4 -31/2 - 29/2 25/2 - 23/2 29/2 - 27/2 27/2 — 25/2 15 , 1 5 -33/2 - 31/2 27/2 - 25/2 31/2 - 29/2 29/2 — 27/2 12 o 1 2 -25/2 - 23/2 23/2 - 21/2 27/2 - 25/2 21/2 — 19/2 13 o 1 3 -27/2 - 25/2 25/2 - 23/2 29/2 - 27/2 23/2 — 21/2 15 o 1 5 -31/2 - 29/2 29/2 - 27/2 33/2 - 31/2 27/2 — 25/2 16 o 1 6 -33/2 - 31/2 31/2 - 29/2 35/2 - 33/2 29/2 — 27/2 13 2 1 1 -27/2 - 27/2 25/2 - 25/2 29/2 - 29/2 23/2 - 23/2 1 2 13 1 4 1 1 1 2 1 4 15 13 1 2 0.500 0.500 1 .000 1 .000 10.500 0.500 0.500 0.500 1 4 0, 0, 0, 0, 500 500 100 100 i 1 1 0.500 1 .000 1 .000 1 .000 1 1 2 1 .000 1 .000 1 .000 1 .000 1 4 1 1 1 1 000 000 000 000 1 1 5 1 .000 0. 100 0. 100 1 .000 1 1 2 1 .000 1 .000 1 .000 1 .000 45191.522 45191.891 45200.618 45200.618 48076.846 48077.207 48084.042 48084.042 51027.030 51027.401 51032.750 51032.750 38410.064 38412.821 38416.798 38417.818 42077.895 42079.944 42082.530 42083.585 49176.783 49178.124 49178.942 49179.644 52629.383 52630.518 52630.518 52631.243 21955.197 21-956.873 21972.735 21975.046 0.031 0.394 0.283 0. 106 0.060 0.241 0.222 •0.056 0.046 0. 133 0.213 •0. 1 38 •0.886 •0. 1 53 •0.023 •1 . 1 90 •0.472 •0.013 •0.051 •0.676 •0.370 0.086 •0.065 •0.469 •0. 197 0.061 •0. 148 •0.338 0.296 •0.010 0.038 0.336 •0.057 •0. 1 34 •0.119 •0.077 •0.036 •0. 1 20 •0.119 •0. 1 28 •0.062 •0. 1 96 •0.098 •0.231 0.020 0.061 0.035 0.003 0.096 0.073 0.017 0.016 0.003 0.023 0.027 •0.036 0. 1 42 0. 1 82 •0.039 0.045 0.063 0.007 0.036 0.082 180 T a b l e 6 .5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F" N o r m a l i s e d W e i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t xab W i t h xab 14 2 29/2 27/2 31/2 25/2 1 2 29/2 27/2 31/2 25/2 1 4 1 .000 1 .000 1 .000 1 .000 22970.004 22972.062 22991.750 22994.208 0. 183 •0.037 •0.019 0.111 0.038 •0.018 •0.027 0.029 15 2 31/2 29/2 33/2 27/2 1 3 31/2 29/2 33/2 27/2 15 i 1 a 1 .000 1 .000 1 .000 1 .000 24342.389 24344.708 24368.156 24370.858 0. 1 22 •0.021 0.022 0. 1 02 0.015 •0.004 0.008 0.012 16 2 33/2 31/2 35/2 29/2 i a 33/2 31/2 35/2 29/2 16 1 1 5 1 .000 1 .000 1 .000 1 .000 26088.090 26090.776 26117.835 26120.347 0. 139 •0.049 0.080 0.053 0.052 •0.048 0.061 •0.025 17 2 35/2 33/2 37/2 31/2 1 5 35/2 33/2 37/2 31/2 17 1 1 6 1 .000 1 .000 1 .000 1 .000 28214.886 28217.702 28247.880 28250.666 0.048 •0.051 •0.021 •0.030 •0.029 •0.009 •0.045 •0.054 18 2 37/2 35/2 39/2 33/2 1 6 37/2 35/2 39/2 33/2 18 1 1 7 1 .000 1 .000 1 .000 1 .000 30718.746 30721.620 30754.684 30757.595 0.023 •0.087 0.013 0.031 •0.047 •0.058 •0.014 0.007 17 3 35/2 33/2 37/2 18 3 35/2 37/2 39/2 33/2 1 5 1 5 35/2 33/2 37/2 17 35/2 37/2 39/2 33/2 18 0.500 1 .000 1 .000 1 6 1 .000 1 .000 0.500 0.500 48760.444 48761.000 48782.276 31832.303 31832.654 31830.840 31 830.840 1 .370 •0.071 0.062 0.045 0.229 0. 1 26 0.271 •0.131 •0.013 •0.018 0.030 0.024 0. 125 0.029 18 3 37/2 35/2 39/2 33/2 1 6 37/2 35/2 39/2 33/2 18 1 7 1 .000 1 .000 1 .000 0.500 50257.717 50259.092 50281.177 50283.626 0.468 •0. 108 •0.051 0.435 •0.026 •0.059 •0.025 •0. 109 181 T a b l e 6 .5 ( C o n t i n u e d ) T r a n s i t i o n F ' - F " N o r m a l i s e d W e i g h t O b s e r v e d R e s i d u a l s F r e q u e n c y W i t h o u t x ab W i t h x a b 19 3 39/2 37/2 41/2 35/2 19 3 37/2 41/2 35/2 20 3 41/2 39/2 43/2 37/2 22 3 45/2 43/2 47/2 41/2 24 3 49/2 47/2 51/2 45/2 26 a 49/2 55/2 51/2 53/2 27 , 57/2 51/2 53/2 55/2 28 , 55/2 57/2 59/2 53/2 1 6 1 7 1 7 1 9 2 1 2 2 2 3 2 a 39/2 37/2 41/2 35/2 19 19 37/2 41/2 35/2 - 20 2 41/2 39/2 43/2 37/2 - 22 2 45/2 43/2 47/2 41/2 ~ 24 2 49/2 47/2 51/2 45/2 - 26 3 49/2 55/2 51/2 53/2 " 27 3 57/2 51/2 53/2 55/2 - 28 3 55/2 57/2 59/2 53/2 1 7 1 , 1 , 0, 0, 1 s 0, 0, 1 , 1 , 2 2 1 , 1 , 1 , 1 , 2 3 0, 0, 0, 0, 000 000 500 500 1 8 0.500 0.500 0.500 500 500 000 000 2 0 1 .000 1 .000 1 .000 1 .000 000 000 000 000 500 500 100 100 2 a 1 .000 1 .000 0.500 0.500 2 5 1 .000 1 .000 0.100 0. 100 31626.135 31626.135 31627.936 31628.167 51924.463 51947.175 51949.413 31752.252 31752.527 31757.655 31758. 181 33141.743 33142.585 33154.851 33155.562 36202.721 36203.810 36222.795 36223.924 42384.580 42384.580 42388.465 42388.465 41902.265 41902.265 41903.148 41903.148 41796.875 41796.875 41799.153 41799.153 0. 159 0.023 0.093 0. 168 0.099 0.059 0.401 0. 1 69 0.046 •0.015 0.082 0. 129 0.024 0.027 •0.006 0. 122 •0.058 0.056 •0.029 0. 149 •0.068 0.098 0. 138 0.010 0.046 0.014 •0.054 •0.007 0.025 0. 129 •0.077 0.036 0.012 0.089 0.027 0. 1 38 0.072 0. 133 0.086 0.038 •0.022 •0.010 0.078 •0.003 0.017 •0.032 0.080 •0.048 0.043 •0.051 0.077 •0.074 0.081 •0. 196 0.003 •0.014 •0.007 •0.098 •0.007 0.011 0.121 0.107 182 6 . 4 The S t r u c t u r e o f B r S C N 7 9 D e s p i t e o n l y h a v i n g r o t a t i o n a l c o n s t a n t s f o r BrSCN and 8 1 BrSCN, some d e d u c t i o n s c a n be made ab o u t t h e s t r u c t u r e o f the m o l e c u l e . I t i s most p r o b a b l y p l a n a r , as i n d i c a t e d by the i n e r t i a l d e f e c t w h i c h i s s m a l l and p o s i t i v e , and i s e s s e n t i a l l y the same f o r b o t h i s o t o p e s ( s e e S e c t i o n 2 . 5 ) . T h i s i s c o n f i r m e d by t h e r a t i o o f the o u t - o f - p l a 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 8 1 7 9 Xcc ( Br) / x c c ( B r ) = 0 . 8 3 3 5 , w h i c h i s c l o s e to the r a t i o o f the q u a d r u p o l e moments o f the br o m i n e n u c l e i ( 0 . 8 3 5 3 ) . As was m e n t i o n e d p r e v i o u s l y , t h e measured r o t a t i o n a l c o n s t a n t s c o n f i r m t h a t the c o r r e c t c o n f i g u r a t i o n o f br o m i n e t h i o c y a n a t e i s BrSCN r a t h e r t h a n BrNCS. A c o m p a r i s o n o f the p r e d i c t e d r o t a t i o n a l c o n s t a n t s f o r ea c h o f t h e s e c o n f i g u r a t i o n s w i t h the measured c o n s t a n t s a r e shown i n T a b l e 6 . 6 . A f i t o f t h e r o t a t i o n a l c o n s t a n t s to t h e s t r u c t u r a l p a r a m e t e r s o f BrSCN was made. The S-C and C-N bond l e n g t h s were h e l d f i x e d a t t h e i r v a l u e s i n S ( C N ) 2 ( 1 4 ) . The SCN a n g l e was f i x e d a t 5 ° w i t h the N atom i n a t r a n s c o n f i g u r a t i o n t o the Br atom. T h i s i s t h e d e v i a t i o n from l i n e a r i t y i n the S-C-N group i n S ( C N ) 2 . T h i s S-C-N a n g l e was a l s o u s e d i n c a l c u l a t i n g a p a r t i a l r o s t r u c t u r e f o r C1SCN ( 1 1 ) , g i v i n g r e a s o n a b l e v a l u e s f o r t he s t r u c t u r a l p a r a m e t e r s . V a l u e s f o r the Br-S bond l e n g t h and the Br-S-C a n g l e were f o u n d i n the l e a s t s q u a r e s f i t ( T a b l e 6 . 7 ) . C o m p a r i s o n s o f t h e s e v a l u e s w i t h t h o s e i n s i m i l a r m o l e c u l e s , and w i t h the sum o f the s i n g l e bond r a d i i , show t h a t t h e y a r e r e a s o n a b l e ( T a b l e 6 . 8 ) . The Br-S bond l e n g t h i s s i m i l a r to t h a t f o u n d i n o t h e r m o l e c u l e s , w h i l e the BrSC a n g l e 183 T a b l e 6 .6 C o m p a r i s o n o f the measured r o t a t i o n a l c o n s t a n t s o f bro m i n e t h i o c y a n a t e w i t h t h o s e c a l c u l a t e d f r o m model s t r u c t u r e s C a l c u l a t e d E x p e r i m e n t a l BrSCN BrNCS 7 9 Br A Q (MHz) 9888 . , 716 41482. . 906 10092. . 2012 (68 ) (MHz) 1882 . . 847 1187 . . 136 1944 . .40541(13) Co (MHz) 1581 . .688 1154 . . 109 1627 , . 94999(11) 8 1 Br A 0 (MHz) 9872 . . 200 41412. . 436 10074. .4731(78) B D (MHz) 1866 . .279 1176 . 730 1927 .45095(13) Co (MHz) 1569 , .562 1144 .217 1615 .58914(10) T a b l e 6 .7 S t r u c t u r a l p a r a m e t e r s o f br o m i n e t h i o c y a n a t e r ( B r - S ) r ( S - C ) 1 r ( C - N ) 1 <(Br-S-C) < ( S - C - N ) 1 < ( B r - S - a ) 2 2 . 18 A 1.701 A 1.156 A 9 9 . 7 5 ° 5 . 0 ° 3 4 . 4 ° C o n s t r a i n e d to v a l u e s t r a n s f e r r e d f r o m S ( C N ) 2 (11) The a n g l e between the Br-S bond and the a - i n e r t i a l a x i s . 184 T a b l e 6 .8 C o m p a r i s o n o f s t r u c t u r a l p a r a m e t e r s o f BrSCN w i t h s t r u c t u r e s o f o t h e r m o l e c u l e s r ( B r - S ) / A BrSCN 2.18 S 2 B r 2 ( 1 3 ) 2.237 S 0 B r 2 ( 1 7 ) 2.27 S 0 2 B r F (18) 2.155 B r S F 5 ( 1 9 ) 2.190 Sum o f s i n g l e bond r a d i i (20) 2.162 <(X-S-C)/deg BrSCN o 99.75 C1SCN (8) 99.8 S ( C N ) 2 ( 1 4 ) 98.4 CH 3SCN (15) 99.9 185 i s = 9 9 ° i n common w i t h o t h e r m o l e c u l e s c o n t a i n i n g t h e - S C N g r o u p w i t h t h e t h i o c y a n a t e c o n f i g u r a t i o n . The p o s i t i o n o f the atoms r e l a t i v e to t h e p r i n c i p a l axes a r e shown i n F i g u r e 6 . 4 . F i g u r e 6 . 4 The p o s i t i o n s o f t h e atoms o f B r S C N r e l a t i v e to i t s p r i n c i p a l i n e r t i a l a x i s s y s t e m . 6 .5 B r o m i n e Q u a d r u p o l e C o u p l i n g The 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 f o r t h e b r o m i n e n u c l e u s i n B r S C N i n t h e i n e r t i a l a x i s s y s t e m a r e g i v e n i n T a b l e 6 . 9 . U n f o r t u n a t e l y no n i t r o g e n q u a d r u p o l e c o u p l i n g c o u l d be r e s o l v e d a t a l l . Once a g a i n , the B r q u a d r u p o l e t e n s o r s were d i a g o n a l i z e d , to g i v e t h e p r i n c i p a l v a l u e s o f t h e b r o m i n e q u a d r u p o l e c o u p l i n g t e n s o r s , as w e l l as 0 z a , t h e a n g l e b e t w e e n t h e z - p r i n c i p a l a x i s and t h e a . - i n e r t i a l a x i s ( T a b l e 6 . 1 0 ) . 186 T a b l e 6.9 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 brom i n e t h i o c y a n a t e i n the p r i n c i p a l i n e r t i a l axes s y s t e m 7 9 8 1 BrSCN BrSCN X a a ( M H z ) X b b ( M H z ) X c c ( M H z ) X a b ( M H z ) 402 . 62 (77) - 18.21(39) -384.41(39) 478.41(23) 336 .4( 12) -16 .00 (20) -320.42(62) 397.74(38) T a b l e 6.10 P r i n c i p a l v a l u e s o f the b r o m i n e q u a d r u p o l e c o u p l i n g t e n s o r o f b r o m i n e t h i o c y a n a t e 7 9 8 1 BrSCN BrSCN X z z ( M H z ) 714.85(63) 595.2(10) X x x ( M H z ) -330.44(26) -274.82(71) X y y ( M H z ) -384.41(39) -320.42(62) 0 z a ( d e g ) 33.12(2) 33.05(4) A c o m p a r i s o n o f 9za w i t h the a n g l e between t h e Br-S bond a x i s and t h e a - i n e r t i a l a x i s ( s e e T a b l e 6.7) i n d i c a t e s t h a t p r i n c i p a l z a x i s e s s e n t i a l l y l i e s a l o n g the Br-S bond, i . e . , i t i s n o t a b e n t bond ( t h e maximum e l e c t r o n d e n s i t y l i e s a l o n g t h e Br-S b o n d ) . I t i s i n t e r e s t i n g t h a t 8za i s =1° l e s s t h a n < ( B r - S - a ) , i n common w i t h t h e c o r r e s p o n d i n g c o m p a r i s o n s i n BrNCO and INCO. 187 T h i s t r e n d has a l s o been o b s e r v e d i n o t h e r m o l e c u l e s ( 2 1 ) . No t h e o r y has b een p r o p o s e d w h i c h w o u l d a c c o u n t f o r t h i s ; however the e f f e c t p r o b a b l y a r i s e s b e c a u s e t h e e l e c t r o n s i n the bond between th e q u a d r u p o l a r n u c l e u s and the atom to w h i c h i t i s a t t a c h e d a r e n o t i n d e p e n d e n t o f the o t h e r e l e c t r o n s i n the m o l e c u l e . The amount o f 7r c h a r a c t e r i n the Br-S bond i s c a l c u l a t e d from t h e d i f f e r e n c e between y v v and v „, r e f l e c t i n g a d i f f e r e n c e i n the p - o r b i t a l p o p u l a t i o n s a l o n g t h e s e d i r e c t i o n s ( s e e e q u a t i o n 4 . 6 ) . The c o n t r i b u t i o n o f a n bonded r e s o n a n c e s t r u c t u r e to the o v e r a l l s t r u c t u r e i s c a l c u l a t e d to be =4.6%. Hence, t h e r e i s more e l e c t r o n i c c h a r g e i n the p y ( o u t o f p l a n e ) o r b i t a l t h a n i n the p x o r b i t a l . I t c a n n o t be a s c e r t a i n e d w hether t h i s ir b o n d i n g c h a r a c t e r i s o u t - o f - p l a n e , w i t h e l e c t r o n d e n s i t y d o n a t e d from the s u l f u r atom towards the b r o m i n e atom, or w h e t h e r t h e r e i s -K c h a r a c t e r i n t h e p l a n e o f the m o l e c u l e , w i t h the p x o r b i t a l o f t h e Br atom s h a r i n g i t s e l e c t r o n s w i t h an o r b i t a l o f t h e s u l f u r atom. The c o r r e s p o n d i n g r e s o n a n c e forms a r e : Br N S + - C ^ N K a ) Br" \ S" - C = N K b ) U s i n g the t h e o r y o f Townes and D a i l e y , as d e s c r i b e d i n S e c t i o n 4.8, t h e c o n t r i b u t i o n o f the v a r i o u s p o s s i b l e r e s o n a n c e forms to the Br-S bond can be c a l c u l a t e d . The two o t h e r p o s s i b l e r e s o n a n c e forms a f f e c t i n g the n a t u r e o f the Br-S bond 188 B r " S + - C = N I I I Form I I shows a t o t a l l y c o v a l e n t B r - S b o n d , w h i l e f o r m I I I i n d i c a t e s a t o t a l l y i o n i c B r - S b o n d , w i t h t h e n e g a t i v e p o l e on t h e b r o m i n e atom b e c a u s e \xzz | < | e Q q B r | . The c o n t r i b u t i o n o f f o r m I I I , r e p r e s e n t i n g t h e i o n i c c h a r a c t e r o f t h e B r - S b o n d , i s d e s i g n a t e d i , and i s c a l c u l a t e d by c o m p a r i n g xzz a n d e Q q B r : X 2 Z - - e Q q B r [ ( U p ) ^ (1-i-TT) + K U p ) 1 1 1 * T r C U p ) 1 ] I n f o r m I I I , t h e i o n i c c h a r a c t e r p r o d u c e s a c l o s e d s h e l l on t h e b r o m i n e , so t h a t i t has z e r o c o u p l i n g ( ( U p ) 1 1 1 = 0 ) . B e c a u s e i t i s u n c e r t a i n w h e t h e r f o r m 1 ( a ) o r f o r m 1 ( b ) i s t h e c o r r e c t r e s o n a n c e s t r u c t u r e r e p r e s e n t i n g TT b o n d i n g , v a l u e s f o r i were c a l c u l a t e d f o r b o t h p o s s i b i l i t i e s . F o r t h e f o r m e r i ~ 5%, and f o r t h e l a t t e r i ~ 9%. H e n c e , w h i c h e v e r j r - b o n d e d r e s o n a n c e s t r u c t u r e i s t h e c o r r e c t o n e , t h e B r - S b o n d i s p r e d o m i n a t e l y c o v a l e n t , w h i c h a g r e e s w i t h t h e c o m p a r i s o n o f t h e B r - S b o n d l e n g t h w i t h t h e sum o f t h e c o v a l e n t r a d i i o f t h e B r a n d S atoms ( s ee T a b l e 6 . 8 ) . a r e B r ^ S - C s N I I 189 6 . 6 D i s c u s s i o n B r S C N h a s o n l y p r e v i o u s l y b e e n s t u d i e d i n t h e g a s e o u s p h a s e i n a p h o t o e l e c t r o n s t u d y ( 1 2 ) . A n a l y s i s o f t h e m i c r o w a v e s p e c t r u m o f B r S C N h a s y i e l d e d v a l u e s f o r a l l t h r e e r o t a t i o n a l c o n s t a n t s , as w e l l as a l l f i v 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 f o r b o t h i s o t o p i c s p e c i e s . B o t h a . - type R b r a n c h t r a n s i t i o n s a n d b - t y p e t r a n s i t i o n s f r o m s e v e r a l d i f f e r e n t b r a n c h e s were m e a s u r e d . Many l i n e s due to t r a n s i t i o n s w i t h i n e x c i t e d v i b r a t i o n a l s t a t e s o f t h e m o l e c u l e were a l s o o b s e r v e d . R e l a t i v e i n t e n s i t y m e a s u r e m e n t s i n d i c a t e t h a t t h e l o w e s t e x c i t e d v i b r a t i o n a l s t a t e l i e s =154 ± 30 c m " 1 above t h e g r o u n d s t a t e . T h i s i s i n e x c e l l e n t a g r e e m e n t w i t h t h e f r e q u e n c y o f t h e 1 o w e s t - i n - p 1 a n e b e n d i n g v i b r a t i o n w h i c h was c a l c u l a t e d , u s i n g t h e i n e r t i a l d e f e c t i n e q u a t i o n 2 . 3 5 , to be =150 c m " 1 . I t was u n f o r t u n a t e t h a t I c o u l d n o t d e t e c t any t r a n s i t i o n s o f t h e p s e u d o h a l o g e n ( S C N ) 2 . T h i s was p r o b a b l y p a r t l y due to t h e i n s t a b i l i t y o f t h e m o l e c u l e , w i t h any ( S C N ) 2 t h a t was f o r m e d d e c o m p o s i n g b e f o r e i t c o u l d be d e t e c t e d . A l s o , b e c a u s e t h e d i p o l e moment o f S ( C N ) 2 , t h e t r a n s i t i o n s o f w h i c h were o b s e r v e d s p e c t r o s c o p i c a l l y when s e a r c h i n g f o r t r a n s i t i o n s o f ( S C N ) 2 , i s r e l a t i v e l y l a r g e , t h e m u l t i t u d e o f i n t e n s e l i n e s due to t h i s m o l e c u l e may h a v e o b s c u r e d t r a n s i t i o n s o f any ( S C N ) 2 t h a t m i g h t o t h e r w i s e h a v e b e e n d e t e c t e d . The m e c h a n i s m f o r t h e f o r m a t i o n o f S ( C N ) 2 i s n o t known. T h i s s t u d y h a s a l l o w e d us to d e t e r m i n e t h a t B r S C N does i n d e e d h a v e a t h i o c y a n a t e c o n f i g u r a t i o n r a t h e r t h a n an 190 i s o t h i o c y a n a t e one. A p a r t i a l r o s t r u c t u r e was c a l c u l a t e d to g i v e r e a s o n a b l e v a l u e s f o r the Br-S- bond l e n g t h and Br-S-C a n g l e . No e q u i l i b r i u m or a v e r a g e s t r u c t u r e was c a l c u l a t e d f o r BrSCN. However the d i s t o r t i o n c o n s t a n t s measured i n t h i s s t u d y , c o u p l e d w i t h the s o l u t i o n v i b r a t i o n a l f r e q u e n c i e s (4), a l t h o u g h i n c o m p l e t e , may e n a b l e a f o r c e f i e l d c a l c u l a t i o n to be done w h i c h w o u l d a l l o w a g r o u n d s t a t e a v e r a g e s t r u c t u r e t o be c a l c u l a t e d . T h i s avenue was n o t p u r s u e d a t t h i s t i m e b e c a u s e a f u l l s t r u c t u r e r e q u i r e s a c o m p l e t e s e t o f i s o t o p i c d a t a . I n a d d i t i o n , the 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 f o r the b r o m i n e n u c l e u s have been measured, i n c l u d i n g the o f f - d i a g o n a l term, Xab , w h i c h was a v a i l a b l e b e c a u s e o f t h e l a r g e number o f p e r t u r b a t i o n s i n t h e h y p e r f i n e s t r u c t u r e . The Br-S bond has b e e n d e m o n s t r a t e d to be e s s e n t i a l l y c o v a l e n t w i t h s m a l l amounts o f i o n i c and TT bonded c h a r a c t e r . B i b l i o g r a p h y 191 1. C. Raby, J . C l a u d e , J . Bux e r a u d , B u l l . Soc. Pharm. Bo r d e a u x 114. 147-152, ( 1 9 7 5 ) . 2. C. Raby, J . C l a u d e , J . Bu x e r a u d , B u l l . Soc. Pharm. Bo r d e a u x 115. 153-161, ( 1 9 7 6 ) . 3. C. Raby, J . Bux e r a u d , C. Moesch, J . C l a u d e , B u l l . Soc. Pharm. B o r d e a u x 120. 33-38, ( 1 9 8 1 ) . 4. M.J. N e l s o n , A.D.E. P u l l i n . J . Chem. Soc. 604-612, ( 1 9 6 0 ) . 5. A.B. Angus, R.G.R. Bacon, J . Chem. Soc. 774-778, ( 1 9 5 8 ) . 6. R.G.R. Bacon, R.S. I r w i n , J . Chem. Soc. 778-784, ( 1 9 5 8 ) . 7. C. Raby, J . Bux e r a u d , J . C l a u d e , J . Ann Chim., 1_, 65-7, (1976) . 8. K. Yamane , K. F u j i m o r i , S. I c h i k a w a , S. M i y o s h i , K. Hashizume; H e t e r o c y c l e s . 20., 1263 - 1266 (1983 ). 9. K. F u j i m o r i , N. H i r a k o , K. Yamane, B u l l . Chem. Soc. J p n . 56., 1247 -1248 , (1983) . 10. D.C. F r o s t , C B . MacDonald, C A . Mc D o w e l l , N.P.C. Westwood, J . Am. Chem. Soc. 103. 4423-4427, ( 1 9 8 1 ) . 11. R.J. R i c h a r d s , R.W. D a v i s , M.C.L. G e r r y , J . Chem. Soc. Chem., Comm., 915-916 ( 1 9 8 0 ) . 12. D.C. F r o s t , C. K i r b y , W.M. Lau, C B . MacDonald, C A . Mc D o w e l l , N.P.C. Westwood, Chem. Phys. L e t t . , 69., 1-6, (1980) . 13. R. K n i e p , L. K o r t e , D. Mootz, Z. N a t u r f o r s c h , b38_, 1-6, ( 1 9 8 3 ) . 14. L. P i e r c e , R. N e l s o n , C H . Thomas, J . Chem. Phys. 43., 3423- 3431, (1965) . 15. R . C L e t t , W.H. F l y g a r e , J . Chem. Phys. 4_7_, 4730-4750, (1976) . 16. K. Yamada, M. W i n n e w i s s e r , G. W i n n e w i s s e r , L.B. S z a l a n s k i , M.C.L. G e r r y , J . Mol S p e c t r o s c . 79., 295 - 313, ( 1 9 8 0 ) . 192 17. J . B r u n v o l l , I . H a r g i t t a i , B. R o z s o n d a i , J . M o l . S t r u c t . 84, 153-155, ( 1 9 8 2 ) . 18. J . R a l e y , J . E . W o l l r a b , R.W. L o v e j o y , J . M o l . S p e c t r o s c . 48., 100-106, ( 1 9 7 3 ) . 19. R. J u r e k , P. G o u l e t , C. V e r r y , A. P o i n s o t , Can. J . Phys. 61 . 1405-1415 ( 1 9 8 3 ) . 20. L. P a u l i n g . "The C h e m i c a l Bond" 3 r d ed., C o r n e l l U n i v e r s i t y P r e s s , I t h a c a , New Yo r k , 1960. 21. M.C.L. G e r r y , W. Lewis - Bevan, N.P.C. Westwood, J . Chem. Phys. 79., 4655-4663, ( 1 9 8 3 ) . 193 CHAPTER V I I : THE INFRA-RED SPECTRUM OF AMINODIFLUOROBORANE, B F 2 N H 2 7.1 I n t r o d u c t i o n The a m i n o b o r a n e s c a n o f t e n be p r e p a r e d by the p y r o l y s i s o f b o r a n e - a m i n e c o m p l e x e s , e.g.: R 3 N:BRg ^ R 2 N - B R 2 + R-R' (7.1) F o r example, the p a r e n t compound, BH 2NH 2, the i n o r g a n i c a n a l o g u e o f e t h y l e n e , i s r e p o r t e d to be p r e p a r e d by t h e t h e r m a l d e c o m p o s i t i o n o f B H 3 N H 3 ( 1 ) . S i m i l a r l y , g a s e o u s a m i n o d i f l u o r o b o r a n e , B F 2 N H 2 , w h i c h i s the i n o r g a n i c a n a l o g u e o f 1 , 1 - d i f l u o r o e t h y l e n e , may be p r e p a r e d by h e a t i n g ammonia-boron t r i f l u o r i d e , B F 3NH 3 . E a r l y s t u d i e s of the p r o d u c t s o f h e a t i n g BF 3NH 3 s u g g e s t e d t h a t the d e c o m p o s i t i o n o f the a d d u c t above 125° too k p l a c e a c c o r d i n g to ( 2 ) : 4 B F 3 N H 3 -• 3NH+BFA" + BN (7.2) However, i t was l a t e r shown t h a t no b o r o n n i t r i d e i s p r e s e n t i n the d e c o m p o s i t i o n p r o d u c t s , w h i c h do however c o n t a i n s e v e r a l H-N-B-F s p e c i e s ( 3 ) . The mass s p e c t r u m o f the v o l a t i l e d e c o m p o s i t i o n p r o d u c t s o f t h e p y r o l y s i s o f B F 3NH 3 a t 185° has been m o n i t o r e d c a r e f u l l y by R o t h g e r y e_t a l . ( 4 ) , showing t h a t p r i m a r i l y B F 2 N H 2 i s formed, a l o n g w i t h some t r i f l u o r o b o r a z i n e , ( B F N H ) 3 . The v a p o u r c an a l s o be c o n d e n s e d to form p o l y m e r i c 194 a m i n o d l f l u o r o b o r a n e ( 4 , 5 ) . L o v a s and J o h n s o n (6) have s t u d i e d t h e microwave s p e c t r u m o f B F 2 N H 2 , w h i c h was p r o d u c e d i n a s i m p l e gas phase r e a c t i o n o f a m i x t u r e o f NH 3 and BF 3 , and l a t e r by the r e v a p o r i z a t i o n o f the c o n d e n s a t i o n p r o d u c t s o f t h i s r e a c t i o n by h e a t i n g to 140°C. The measurement o f the r o t a t i o n a l c o n s t a n t s o f 6 i s o t o p i c s p e c i e s c o n f i r m e d the e t h y l e n e - 1 i k e p l a n a r s t r u c t u r e o f the m o l e c u l e . The work a l s o p r o d u c e d g r o u n d s t a t 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 and a v a l u e f o r the d i p o l e moment. No i n f r a - r e d d a t a i s a v a i l a b l e i n the l i t e r a t u r e f o r B F 2 N H 2 . The aim o f t h i s s t u d y was t h e r e f o r e t o measure the i n f r a - r e d s p e c t r u m o f t h i s m o l e c u l e i n t h e gas p h a s e , and to e v a l u a t e t h e wavenumbers o f the f u n d a m e n t a l v i b r a t i o n s . The r o t a t i o n a l s t r u c t u r e o f the 2j band was a l s o i n v e s t i g a t e d a t h i g h r e s o l u t i o n to improve the a c c u r a c y o f t h e g r o u n d s t a t e c o n s t a n t s , and to measure f o r the f i r s t time r o t a t i o n a l p a r a m e t e r s o f the 2 1 l e v e l . 7 . 2 E x p e r i m e n t a l Methods B F 2 N H 2 was p r e p a r e d by h e a t i n g s o l i d B F 3NH 3 : B F 3 N H 3 ( s ) ^ B F 2 N H 2 ( g ) + HF< 8) (7.3) The a d d u c t was p r e p a r e d by p a s s i n g a s t r e a m o f ammonia a s t i r r e d s o l u t i o n o f b o r o n t r i f l u o r i d e e t h e r a t e (BDH C h e m i c a l s ) , w h i c h was d i l u t e d w i t h t w i c e i t s volume o f gas o v e r d i e t h y l 195 e t h e r ( 7 ) . A w h i t e p r e c i p i t a t e , w h i c h was B F 3 N H 3 , was formed. I t was t h e n washed w i t h d i e t h y l e t h e r and d r i e d u n d e r vacuum. Care was t a k e n to keep the r e a c t i o n f l a s k f l u s h e d w i t h n i t r o g e n b e c a u s e B F 3 N H 3 h y d r o l y s e s e a s i l y . B F 3 N H 3 was t h e n l o o s e l y p a c k e d i n a 20 cm p y r e x tube and was h e a t e d t o between 125° and 140°C. The r e a c t i o n p r o d u c t s were f l o w e d t h r o u g h the l o n g p a t h c e l l w i t h p a t h l e n g t h 8.25 m. I n i t i a l l y o n l y r e s i d u a l s o l v e n t , d i e t h y l e t h e r was p r o d u c e d , b u t g r a d u a l l y t h e s p e c t r u m o f B F 2 N H 2 was d e t e c t e d , a l t h o u g h some d i e t h y l e t h e r was s t i l l p r e s e n t c o n t a m i n a t i n g the s p e c t r u m . When t h e B F 3 N H 3 was h e a t e d to h i g h e r t e m p e r a t u r e s , t h e s p e c t r u m o f t h e more s t a b l e t r i f l u o r o b o r a z i n e , ( B F N H ) 3 , s t a r t e d t o a p p e a r , and above = 1 8 0 ° , t h e sample decomposed r a t h e r r a p i d l y and the s p e c t r u m d i s a p p e a r e d . V e r y l i t t l e v a p o u r p r e s s u r e c o u l d be m a i n t a i n e d , p r o b a b l y b e c a u s e t h e a m i n o d i f l u o r o b o r a n e was p o l y m e r i z i n g i n t h e c e l l . T h e r e f o r e t h e s p e c t r a o b t a i n e d were n o t v e r y i n t e n s e . H i g h and low r e s o l u t i o n s p e c t r a were r e c o r d e d a t low p r e s s u r e s (-20-50 m i c r o n s ) , some o f w h i c h was due to d i e t h y l e t h e r . P o r t i o n s o f the s p e c t r u m between 400 and 3700 c m - 1 were r e c o r d e d a t 0.05 and 0.01 c m - 1 r e s o l u t i o n to i d e n t i f y the f u n d a m e n t a l s , and one band, t h e 2j band n e a r 1608 c m - 1 , was r e c o r d e d a t 0.004 cm" 1 r e s o l u t i o n . F o r t h i s band, a t o t a l o f 90 i n t e r f e r o g r a m s was co-added f o r t h e f i n a l i n t e r f e r o g r a m . 10 i n t e r f e r o g r a m s were c o l l e c t e d a t a t i m e , w i t h each s c a n t a k i n g —3^- m i n u t e s , between w h i c h a low r e s o l u t i o n s c a n was t a k e n to e n s u r e the c o n t i n u e d 196 p r e s e n c e o f B F 2 N H 2 . The empty c e l l was a l s o s c a n n e d to g i v e a b a c k g r o u n d s p e c t r u m . No a p o d i z a t i o n f u n c t i o n was u s e d ( b o x c a r t r u n c a t i o n ) , and t h e i n t e r f e r o g r a m s were c o n v e r t e d by the F o u r i e r t r a n s f o r m a t i o n o p e r a t i o n to t o t a l i n t e n s i t y s p e c t r a , and t h e n r a t i o e d to g i v e a t r a n s m i t t a n c e s p e c t r u m . F i n a l l y the s p e c t r u m was c o n v e r t e d to a b s o r b a n c e . A Bomem s o f t w a r e peak-f i n d i n g programme, w h i c h d i f f e r e n t i a t e s t h e p e a k s , was u s e d to f i n d the l i n e p o s i t i o n s . A d e u t e r a t e d sample, B F 2 N D 2 , was a l s o p r e p a r e d by h e a t i n g B F 3ND 3 w h i c h was p r e p a r e d as above u s i n g g aseous ND 3 (MSD i s o t o p e s , 99.2 atom %D). Low r e s o l u t i o n (0.05 c m - 1 ) s p e c t r a were r e c o r d e d , as above. 7 .3 A n a l y s i s o f t h e I n f r a - r e d S p e c t r u m B F 2 N H 2 i s a p l a n a r , o b l a t e n e a r - s y m m e t r i c r o t o r (K = 0.8326) ( 6 ) . The a l i g n m e n t o f the p r i n c i p a l i n e r t i a l axes i s shown i n F i g u r e 7.1. The m o l e c u l e has C 2 v symmetry and 3N - 6 = 12 v i b r a t i o n a l d e g r e e s o f freedom, w h i c h t r a n s f o r m under t h e symmetry o p e r a t i o n s o f t h i s p o i n t group a c c o r d i n g t o : r ( v i b ) - 5 A 1 + A 2 + 2 B 1 + 4 B 2 (7-4) The f u n d a m e n t a l s w i t h Ax symmetry g i v e A - t y p e bands, t h o s e w i t h Bj^ symmetry have C - t y p e s p e c t r a , B - t y p e bands c o r r e s p o n d to B 2 symmetry, w h i l e the v i b r a t i o n w i t h A 2 symmetry c o r r e s p o n d s to th e t o r s i o n and i s i n f r a - r e d i n a c t i v e . ( F i g u r e 7.1 The c o n f i g u r a t i o n o f the atoms o f B F 2 NH 2 . The d i r e c t i o n o f the p r i n c i p a l i n e r t i a l axes i s i n d i c a t e d . U n f o r t u n a t e l y the i n f r a - r e d s p e c t r u m o f B F 2 N H 2 c o u l d not be c o m p l e t e l y a s s i g n e d i n t h i s s t u d y . Some bands were too weak to be o b s e r v e d w h i l e o t h e r s were o v e r l a p p e d . The bands w h i c h were o b s e r v e d have been a s s i g n e d from the band c o n t o u r s ( 8 ) , by a n a l o g y w i t h the f r e q u e n c i e s o f the f u n d a m e n t a l s o f NH 2BH 2 ( 1 , 9 ) and HBF 2 ( 1 0 , 1 1 ) , and from the f r e q u e n c i e s c a l c u l a t e d u s i n g ab-i n i t i o SCF c a l c u l a t i o n s ( 1 2 ) . The d e u t e r a t e d s p e c t r u m was even weaker, and i t p r o v i d e d v e r y l i m i t e d i n f o r m a t i o n , a l t h o u g h i t d i d h e l p to a s s i g n one band ( s e e b e l o w ) . A low r e s o l u t i o n s p e c t r u m o f B F 2 N H 2 , from 800 to 3700 cm" 1 i s shown i n F i g u r e 7.2. The p a i r o f f u n d a m e n t a l s a t =3500 cm" 1 i s a s s i g n e d to the N-H s y m m e t r i c and a s y m m e t r i c s t r e t c h i n g v i b r a t i o n s vl , and i / g , by a n a l o g y w i t h BH 2 NH 2 . The band c o n t o u r s i n d i c a t e t h a t the band a t 3576 cm""1 i s a B - t y p e band 198 V — 1 BF2NH2 1 1 1 E /cm-1 1 3000 2000 1000 F i g u r e 7.2 L o w - r e s o l u t i o n t r a n s m i t t a n c e s p e c t r u m o f gaseous B F 2 N H 2 i n the r e g i o n 750-3700 c m - 1 . and t h e r e f o r e c o r r e s p o n d s to 1/g , w h i l e the band a t 3487 c m - 1 i s an A - t y p e band and i s the vx f u n d a m e n t a l . The A - t y p e band a t =1608 c m - 1 i s the NH 2 symmetric b e n d i n g v i b r a t i o n , a g a i n f o l l o w i n g BH 2NH 2. T h e r e a r e a t l e a s t two o v e r l a p p i n g f u n d a m e n t a l s between 1360 and 1460 c m - 1 . T h i s r e g i o n was i n v e s t i g a t e d a t 0.01 c m - 1 r e s o l u t i o n i n o r d e r to make an a s s i g n m e n t . A B- t y p e band c o n t o u r c o u l d be d i s t i n g u i s h e d w i t h a band c e n t r e a t = 1339 c m - 1 . T h i s i s p r o b a b l y the B F 2 asymmetric s t r e t c h i n g mode. A t e n t a t i v e a s s i g n m e n t f o r the B-N s t r e t c h i n g v i b r a t i o n was made a t 1406 c m - 1 , w h i c h c o r r e s p o n d s to the most i n t e n s e p o r t i o n o f t h i s r e g i o n . Two bands were o b s e r v e d below 700 c m - 1 . One, a C- t y p e band c e n t r e d a t 661 c m - 1 was a s s i g n e d 199 to the B F 2 o u t - o f - p l a n e b e n d i n g m o t i o n f o l l o w i n g the t h e o r e t i c a l c a l c u l a t i o n s . A l s o , t h i s was the o n l y band i d e n t i f i e d i n the d e u t e r a t e d s p e c t r u m . I t s f r e q u e n c y d i d n o t change much upon d e u t e r a t i o n ; i t must t h e r e f o r e c o r r e s p o n d t o the BF Z o u t - o f -p l a n e b e n d i n g m o t i o n and n o t the NH 2 o u t - o f - p l a n e b e n d i n g m o t i o n . The o t h e r l i e s a t 439 c m - 1 and c o r r e s p o n d s to the BF 2 s y m m e t r i c bend. T h i s a g r e e s e x t r e m e l y w e l l w i t h t h e r o u g h a p p r o x i m a t i o n o f the f r e q u e n c y o f t h e l o w e s t i n - p l a n e b e n d i n g v i b r a t i o n c a l c u l a t e d by Lovas and J o h n s o n u s i n g the i n e r t i a l d e f e c t to be =440 c m - 1 . A summary o f t h e s e a s s i g n m e n t s i s g i v e n i n T a b l e 7.1 a l o n g w i t h any 1 0 B F 2 N H 2 band c e n t r e s t h a t c o u l d be i d e n t i f i e d and a c o m p a r i s o n w i t h the ab- i n i t i o c a l c u l a t i o n s w h i c h a r e c o n s i s t e n t l y h i g h e r t h a n the measured f r e q u e n c i e s , f o r b o t h B F 2 N H 2 , and f o r BH 2NH 2 f o r w h i c h f r e q u e n c i e s were a l s o c a l c u l a t e d ( 1 0 ) . T a b l e 7.2 g i v e s a c o m p a r i s o n o f t h e f u n d a m e n t a l s o f BH 2NH 2 w i t h the c o r r e s p o n d i n g f r e q u e n c i e s o f the f u n d a m e n t a l s o f B F 2 NH 2 and HBF 2 . 7 .4 A n a l y s i s o f t h e R o t a t i o n a l S t r u c t u r e o f t h e 2g B a n d . The v2 f u n d a m e n t a l a t 1608 c m - 1 i s a s s i g n e d to be due p r e d o m i n a n t l y to the NH 2 s y m m e t r i c b e n d i n g m o t i o n . I t was r e c o r d e d a t =0.004 c m - 1 r e s o l u t i o n . I t i s an A - t y p e band o f a n e a r - o b l a t e a s y m m e t r i c r o t o r w i t h s e l e c t i o n r u l e s : AJ = 0,±1, AK a = 0, ±2 and AK C = ±1 , ±3 The s p e c t r u m a t 0.05 c m - 1 r e s o l u t i o n i s shown i n F i g u r e 7.3. I t shows two i n t e n s e c e n t r a l Q b r a n c h f e a t u r e s b e l o n g i n g to the o v e r l a p p i n g Q 200 T a b l e 7.1 V i b r a t i o n a l f r e q u e n c i e s o f B F 2 N H 2 ( i n c m - 1 ) Symmetry 1 1 B F 2 N H 2 1 0 B F 2 N H 2 1 1 B F 2 N D 2 C a l c u l a t e d 1 A l " l 3 4 87 2 3629 1608 1619 1793 ( 1 4 0 6 ) 3 1590 vk - 940 439 464 488 A 2 I.R. i n a c t i v e 553 B l Vl 661 687 684 713 " 8 - 562 U9 3576 3736 "10 1339 1663 " l l - 1061 "12 - 417 From r e f e r e n c e 12. U n c e r t a n t i e s a r e ±1 c m - 1 . E s t i m a t e d f r o m most i n t e n s e p o r t i o n o f s p e c t r u m . T a b l e 7.2 V i b r a t i o n a l F r e q u e n c i e s o f BF 2 N H 2 ( i n c m - 1 ) 1 1 B F 2 NH 2 1 1 BH 2NH 2 1 H 1 1 B F 2 2 Type o f M o t i o n 3487 3451 - NH symm. s t r e t c h 1608 1617 - NH 2 symm. bend ( 1 4 0 6 ) 3 1337 - BN s t r e t c h - - 1167 BF symm. s t r e t c h 439 - 544 B F 2 symm. bend I.R. i n a c t i v e 830 T o r s i o n 661 - - B F 2 o u t - o f - p l a n e - 1005 - NH 2 o u t - o f - p l a n e 3576 3534 - NH asymm. s t r e t c h 1339 - 1404 BF asymm. s t r e t c h - 1122 - NH 2 asymm. bend - - - B F 2 asymm. bend From r e f e r e n c e ( 1 , 9 ) . From r e f e r e n c e (10, 11) E s t i m a t e d from most i n t e n s e p o r t i o n o f s p e c t r u m . 11 B F i g u r e 7 .3 Medium r e s o l u t i o n t r a n s m i t t a n c e s p e c t r u m o f the v2 f u n d a m e n t a l o f g a s e o u s BF 2NH 2 The 1 o X 1 B s h i f t i s i n d i c a t e d , o r o 203 b r a n c h l i n e s o f 1 1 B F 2 N H 2 and 1 0 B F 2 N H 2 . The r e l a t i v e i n t e n s i t i e s o f t h e s e f e a t u r e s do n o t e x a c t l y r e f l e c t t h e r e l a t i v e abundances o f e a c h i s o t o p e ( 1 X B =* 80% and 1 0 B = 20%) p r o b a b l y b e c a u s e o f u n d e r l y i n g R b r a n c h t r a n s i t i o n s i n t h e c a s e o f 1 0 B Q-branch s p i k e . On e i t h e r s i d e o f the band c e n t r e l i e c l u s t e r s o f a p p r o x i m a t e l y e q u a l l y s p a c e d R- and P- b r a n c h t r a n s i t i o n s . The g r o u p i n g t o g e t h e r o f t r a n s i t i o n s i s common i n o b l a t e n e a r -s y m m e t r i c r o t o r s when the r o t a t i o n a l c o n s t a n t s do n o t change much upon v i b r a t i o n a l e x c i t a t i o n and C - |-(A + B) ( 1 3 ) . Each c l u s t e r has a d i f f e r e n t v a l u e o f ( 2 J - K 0 ) and t h e y a l t e r n a t e between even and odd K c. W i t h i n each c l u s t e r , the l o w e r s t a t e quantum numbers o f t h e t r a n s i t i o n s a r e ( J , K c = J ) , ( J - l , K c = J - 2 ) , . . . down to ( ( J + l ) / 2 , K c .- 1) or ( J / 2 , K c = 0 ) . The s p e c t r u m t h e r e f o r e becomes more dense away from the band c e n t r e , b o t h to h i g h and low f r e q u e n c y . A s e c t i o n o f the P b r a n c h s i d e i s shown i n F i g u r e 7.4. F o r a m o l e c u l e w i t h two e q u i v a l e n t H's and two e q u i v a l e n t F's the r e l a t i v e i n t e n s i t i e s o f asymmetry s p l i t t r a n s i t i o n s g i v e n by the s p i n s t a t i s t i c s a r e : 5 ( K a K c = ee or e o ) : 3 ( K a K c = oo or o e ) . However, b e c a u s e o n l y a few asymmetry s p l i t t r a n s i t i o n s c o u l d be a s s i g n e d b e c a u s e o f t h e m u l t i t u d e o f o v e r l a p p e d l i n e s , i t was d i f f i c u l t to see the e x a c t i n t e n s i t y a l t e r n a t i o n . A s s i g n m e n t o f the quantum numbers o f the P P and r R b r a n c h t r a n s i t i o n s , w h i c h were the s t r o n g e s t l i n e s i n t h e s p e c t r u m , were made u s i n g c o m b i n a t i o n d i f f e r e n c e s . The d i f f e r e n c e i n f r e q u e n c y between p a i r s o f r R and P P b r a n c h t r a n s i t i o n s , h a v i n g F i g u r e 7 .4 H i g h r e s o l u t i o n a b s o r b a n c e s p e c t r u m o f a p o r t i o n o f t h e P P b r a n c h s i d e o f the 2j b a n d o f g a s e o u s B F 2 N H 2 . The v a l u e o f 2 J - K C f o r t h e g r o u n d s t a t e f o r e a c h c l u s t e r o f l i n e s i s i n d i c a t e d . T h i s i s a l s o the v a l u e o f J a n d K c f o r the peak to the l o w e s t f r e q u e n c y s i d e o f e a c h c l u s t e r . J d e c r e a s e s by 1 and K c d e c r e a s e s by 2 t o w a r d s to h i g h e r f r e q u e n c y . 205 common u p p e r s t a t e b u t d i f f e r e n t g r o u n d s t a t e r o t a t i o n a l e n e r g y l e v e l s , were c a l c u l a t e d and compared w i t h t h e f r e q u e n c y o f the c o r r e s p o n d i n g t r a n s i t i o n p r e d i c t e d u s i n g the microwave c o n s t a n t s o f L o v a s and J o h n s o n ( 6 ) . Once c o r r e c t a s s i g n m e n t s were made f o r s e v e r a l l i n e s , as d e t e r m i n e d by a good agreement o f the c o m b i n a t i o n d i f f e r e n c e s and t h e p r e d i c t e d f r e q u e n c i e s , the r e m a i n d e r o f t h e a s s i g n m e n t s were c l e a r f r o m the s p e c t r a l p a t t e r n s . An i n f r a - r e d l e a s t s q u a r e s f i t t i n g p r o c e d u r e was u s e d to d e t e r m i n e t h e r o t a t i o n a l 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 o f b o t h the gro u n d and 2 1 1eve I s . B o t h the microwave t r a n s i t i o n s , measured by Lo v a s and J o h n s o n ( 6 ) , and the c o m b i n a t i o n d i f f e r e n c e s , were u s e d to improve t h e d e t e r m i n a t i o n o f the g r o u n d s t a t 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 . These were l i m i t e d i n a c c u r a c y i n the microwave s t u d y b e c a u s e p r i m a r i l y o n l y \x& Q b r a n c h t r a n s i t i o n s c o u l d be measured i n the f r e q u e n c y range s t u d i e d . The microwave d a t a were g i v e n u n c e r t a i n t i e s =100 ti m e s s m a l l e r t h a n t h e c o m b i n a t i o n d i f f e r e n c e s ; the w e i g h t s a r e p r o p o r t i o n a l to ( u n c e r t a i n t y ) - 2 . The r e s u l t s a r e g i v e n i n T a b l e 7.3, a l o n g w i t h a c o m p a r i s o n w i t h the microwave c o n s t a n t s w h i c h were c o n v e r t e d from MHz i n t o c m - 1 . The microwave d i s t o r t i o n c o n s t a n t s were c o n v e r t e d from the r ' s u s i n g the e q u a t i o n s g i v e n i n S e c t i o n 2.4. F i n a l l y , a l e a s t s q u a r e s f i t was made to t h e e x c i t e d s t a t e c o n s t a n t s u s i n g the measured t r a n s i t i o n f r e q u e n c i e s . The gro u n d 206 T a b l e 7 .3 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 1 1 B F 2 N H 2 P a r a m e t e r T h i s work 1 M i c r o w a v e d a t a 2 R o t a t i o n a l C o n s t a n t s (cm ) A 0.33421379(34) 0.3342132(17) B 0.31990223(32) 0.3199009(17) C 0.16320694(31) 0.1632092(17) 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 m - 1 ) 1 0 6 A j 0.17560(23) 0.188(24) 1 0 7 A J K 0.335(10) 1 0 6 A K 0.2067(14) 0.233(58) 1 0 7 5 j 0.7669(16) 0.688(12) 1 0 6 5 K 0.21307(41) C a l c u l a t e d f r o m c o m b i n a t i o n d i f f e r e n c e s o f the 2 1 band and the microwave d a t a from r e f e r e n c e ( 6 ) . 2 C o n v e r t e d from MHz to c m - 1 ( u s i n g c = 2.99792458 x 10 8 m s - 1 ) from v a l u e s g i v e n i n r e f e r e n c e ( 6 ) . s t a t e c o n s t a n t s were h e l d f i x e d a t the v a l u e s c a l c u l a t e d as above. The r o t a t i o n a l 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 o f t h e 2 1 l e v e l a r e g i v e n i n T a b l e 7.4. No c a l i b r a t i o n o f the s p e c t r u m was done; however the band o r i g i n was c o r r e c t e d u s i n g the a v e r a g e s h i f t o f the peak p o s i t i o n s o f some l i n e s o f H 20 (0.00109(50) c m - 1 ) . The wavenumbers o f t h e o b s e r v e d t r a n s i t i o n s a r e g i v e n i n T a b l e 7.5. The s t a n d a r d d e v i a t i o n o f the l e a s t s q u a r e s f i t was 0.0005 c m - 1 207 T a b l e 7 . 4 R o t a t i o n a l c o n s t a n t s o f t h e 2 1 l e v e l o f 1 1 B F 2 N H 2 P a r a m e t e r R o t a t i o n a l C o n s t a n t s (cm 1 ) A 0 . 3 3 4 2 4 4 8 ( 1 3 ) B 0 . 3 1 9 6 9 0 8 ( 1 1 ) C 0 . 1 6 3 0 3 4 8 6 ( 1 2 ) 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 m - 1 ) 1 0 6 A j 0 . 1 7 7 2 5 ( 2 3 ) 1 0 7 A J K 0 . 4 1 8 ( 5 2 ) 1 0 6 A K 0 . 1 8 2 8 ( 6 5 ) 1 0 7 5 j 0 . 7 7 4 4 ( 4 4 ) 1 0 6 S K 0 . 2 2 0 3 ( 1 8 ) Band C e n t r e ( c m - 1 ) T Q 1 6 0 8 . 7 0 6 9 1 ( 5 0 ) w h i c h a l s o c o r r e s p o n d s to u n i t w e i g h t . Some t r a n s i t i o n s were g i v e n l e s s t h a n u n i t w e i g h t b e c a u s e t h e y were s l i g h t l y o v e r l a p p e d w i t h o t h e r t r a n s i t i o n s . Not a l l t h e t r a n s i t i o n s c o u l d be f i t t e d to t h i s m o d e l . The r o t a t i o n a l s t r u c t u r e o f t h e i>2 f u n d a m e n t a l i s s i g n i f i c a n t l y p e r t u r b e d by a C o r i o l i s i n t e r a c t i o n . T h i s i s c l e a r l y i l l u s t r a t e d i n F i g u r e 7 . 5 ; a gap a p p e a r s i n b o t h t h e P and R b r a n c h c l u s t e r s a t t h e same v a l u e o f K c . C e r t a i n r o t a t i o n a l l e v e l s o f t h e 2 1 s t a t e a r e s h i f t e d , w i t h t h e l a r g e s t s h i f t s f o r K = 3 1 . The s h i f t s , w h i c h a r e c a l c u l a t e d f r o m t h e c ' F i g u r e 7 . 5 H i g h r e s o l u t i o n a b s o r b a n c e s p e c t r u m o f a p o r t i o n o f t h e ?P b r a n c h s i d e o f the 2j band o f B F 2 N H 2 i n d i c a t i n g a s m a l l C o r i o l i s p e r t u r b a t i o n . The v a l u e o f 2 J - K C f o r t h e 2 1 l e v e l i s i n d i c a t e d f o r e a c h c l u s t e r as w e l l as t h e v a l u e o f K f o r the p e a k s on e i t h e r s i d e o f the gap i n t h e r o t a t i o n a l s t r u c t u r e . o CO T a b l e 7 . 5 O b s e r v e d i n f r a r e d t r a n s i t i o n s o f 1 1 B F 2 N H 2 O b s e r v e d N o r m a l i s e d J ' K . ' K c ' - J " K . " K c " Wavenumber D e v i a t i o n 1 W e i g h t 2 ( cm" 1 ) ( c m " 1 ) 7 6 1 - 7 6 2 1609.00673 0.00100 1 .0 10 8 2 - 10 8 3 1609.29112 0.00032 1 .0 12 10 2 - 12 10 3 1609.15716 0.0001 1 1.0 13 12 2 - 13 10 3 1609.97330 -0.00100 0.5 17 15 2 - 17 15 3 1608.83798 -0.00028 1 .0 10 7 3 - 10 7 4 1609.77828 0.00035 0.5 13 10 3 - 13 10 4 1609.63400 -0.00000 0.5 16 14 3 - 16 12 4 1610.05792 0.00088 1.0 17 14 3 - 17 14 4 1609.30626 -0.00040 1.0 19 16 3 - 19 16 4 1609.12325 0.00039 1 .0 23 20 3 - 23 20 4 1608.82741 0.00073 1 .0 19 1 6 4 - 19 14 5 1610.20539 0.00069 1.0 15 10 5 - 15 10 6 1610.44284 -0.00059 0.5 19 14 5 - 19 14 6 1610.34129 0.00006 1.0 29 24 5 - 29 24 6 1609.34159 -0.00034 0.5 33 27 6 - 33 27 7 1609.60739 0.00048 0.0 17 10 7 - 17 10 8 1611.10592 -0.00004 0.5 28 22 7 - 28 20 8 1610.94038 -0.00057 0.5 24 16 8 - 24 16 9 1611.36479 -0.00068 1.0 29 22 8 - 29 20 9 1611.27539 0.00037 1 .0 24 16 9 - 24 14 10 1611.70709 -0.00053 0.5 25 16 9 - 25 16 10 1611.69498 -0.00014 1 .0 26 18 9 - 26 16 10 1611.68094 -0.00063 1.0 27 18 9 - 27 18 10 1611.66652 -0.00000 1.0 2B 20 9 - 28 18 10 1611.65000 -0.00054 1.0 29 20 9 - 29 20 1 0 1611.63268 0.00043 1 .0 24 14 10 - 24 14 1 1 1612.04264 -0.00089 0.5 25 16 10 - 25 14 1 1 161.2.03246 -0.00043 1 .0 26 16 10 - 26 16 1 1 1612.02122 -0.00012 1 .0 27 18 10 - 27 16 1 1 1612.00893 0.00009 1 .0 28 18 10 - 28 18 1 1 1611.99491 -0.00037 1 .0 29 20 10 - 29 18 1 1 1611.98168 0.00102 0.5 25 14 1 1 - 25 14 12 1612.36605 -0.00048 1.0 26 16 1 1 - 26 14 1 2 1612.35576 -0.00058 1.0 27 16 1 1 - 27 16 12 1612.34431 -0.00106 0.5 29 18 1 1 - 29 18 12 1612.32105 0.00016 1.0 30 20 1 1 - 30 18 12 1612.30719 -0.00009 1 .0 25 1 4 12 - 25 12 1 3 1612.69739 -0.00027 1 .0 26 14 12 - 26 14 13 1612.68763 -0.00075 0.5 27 16 12 - 27 14 1 3 1612.67850 0.00006 1.0 28 16 12 - 28 16 1 3 1612.66795 0.00013 1.0 29 18 12 - 29 16 13 1612.65698 0.00052 1.0 1 The d e v i a t i o n r e p r e s e n t s the d i f f e r e n c e between the o b s e r v e d wavenumber and t h a t 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 i n T a b l e s 7.3 and 7.4. 2 Measurements were w e i g h t e d a c c o r d i n g t o 1/cr 2 where a i s the u n c e r t a i n t y i n the measurements. U n i t w e i g h t c o r r e s p o n d e d to an u n c e r t a i n t y o f 0.0005 c m - 1 . O b s e r v e d N o r m a l i s e d J ' K „ ' K c ' - J " K . " K c " Wavenumber D e v i a t i o n W e i g h t ( c m " 1 ) ( c m " 1 ) 33 22 12 - 3 3 20 13 1 6 1 2 . 6 0 2 4 1 - 0 . 0 0 0 4 8 1 . 0 34 22 12 - 34 22 13 1 6 1 2 . 5 8 7 3 3 0 . 0 0 0 1 2 0 . 0 28 16 13 - 28 14 14 1 6 1 2 . 9 9 9 2 8 - 0 . 0 0 0 1 9 1 . 0 3 0 18 13 - 3 0 16 14 1 6 1 2 . 9 7 7 7 5 - 0 . 0 0 0 2 0 1 . 0 33 2 0 13 - 33 2 0 14 1 6 1 2 . 9 4 0 0 5 - 0 . 0 0 0 3 4 1 . 0 34 22 13 - 34 2 0 14 1 6 1 2 . 9 2 5 5 0 - 0 . 0 0 0 8 2 1 . 0 2 7 14 14 - 2 7 12 15 1 6 1 3 . 3 3 8 0 8 - 0 . 0 0 0 5 2 1 . 0 28 14 14 - 28 14 15 1 6 1 3 . 3 3 0 0 1 0 . 0 0 0 6 3 1 . 0 2 9 16 14 - 2 9 14 15 1 6 1 3 . 3 2 0 2 3 0 . 0 0 0 6 3 0 . 5 2 9 14 15 - 2 9 14 16 1 6 1 3 . 6 4 8 9 7 0 . 0 0 0 2 0 1.0 3 0 16 15 - 3 0 14 16 1 6 1 3 . 6 3 8 9 1 - 0 . 0 0 0 0 5 1.0 31 16 15 - 31 16 16 1 6 1 3 . 6 2 8 8 3 0 . 0 0 0 2 2 1 . 0 32 18 15 - 32 16 16 1 6 1 3 . 6 1 7 5 9 - 0 . 0 0 0 1 1 1 . 0 33 18 15 - 33 18 16 1 6 1 3 . 6 0 6 3 1 0 . 0 0 0 1 1 1 . 0 34 2 0 15 - 34 .18 16 1 6 1 3 . 5 9 4 2 9 0 . 0 0 0 1 9 1 . 0 2 9 14 16 - 2 9 12 17 1 6 1 3 . 9 7 6 4 4 - 0 . 0 0 0 5 0 1 . 0 31 16 16 - 31 14 17 1 6 1 3 . 9 5 6 5 0 - 0 . 0 0 1 1 2 1.0 32 16 16 - 32 16 17 1 6 1 3 . 9 4 6 2 3 - 0 . 0 0 0 9 8 1 . 0 3 3 18 16 - 33 16 17 1 6 1 3 . 9 3 5 1 7 - 0 . 0 0 1 1 0 1 . 0 34 18 16 - 34 18 17 1 6 1 3 . 9 2 4 0 2 - 0 . 0 0 0 7 6 1 . 0 3 5 20 16 - 3 5 18 17 1 6 1 3 . 9 1 2 5 0 - 0 . 0 0 0 2 3 1 . 0 36 2 0 16 - 36 2 0 17 1 6 1 3 . 9 0 0 9 6 0 . 0 0 0 8 7 0 . 0 3 7 22 18 - 37 2 0 17 1 6 1 3 . 8 B 7 7 3 0 . 0 0 0 8 9 0 . 0 28 12 17 - 28 10 18 1 6 1 4 . 3 1 1 9 8 - 0 . 0 0 1 0 7 0 . 5 2 9 12 17 - 2 9 12 18 1 6 1 4 . 3 0 3 9 7 - 0 . 0 0 0 4 0 0 . 5 30 14 17 - 3 0 12 18 1 6 1 4 . 2 9 3 9 2 - 0 . 0 0 1 3 3 0 . 5 31 14 17 - 31 14 18 1 6 1 4 . 2 8 5 0 8 - 0 . 0 0 0 6 0 1 . 0 32 16 17 - 32 14 18 1 6 1 4 . 2 7 4 4 6 - 0 . 0 0 1 1 8 0 . 5 3 3 16 17 - 33 16 18 1 6 1 4 . 2 6 4 0 2 - 0 . 0 0 1 1 0 1 . 0 38 22 17 - 38 2 0 18 1 6 1 4 . 2 0 5 0 3 0 . 0 0 0 3 7 0 . 0 2 7 10 18 - 27 8 19 1 6 1 4 . 6 4 7 5 4 - 0 . 0 0 0 3 0 1 . 0 3 0 12 18 - 3 0 12 19 1 6 1 4 . 6 2 1 7 2 - 0 . 0 0 0 6 4 1 . 0 31 14 18 - 31 12 19 1 6 1 4 . 6 1 2 2 7 - 0 . 0 0 0 7 7 1 . 0 32 14 18 - 32 14 19 1 6 1 4 . 6 0 2 2 0 - 0 . 0 0 1 0 8 0 . 5 3 3 16 18 - 33 14 19 1 6 1 4 . 5 9 3 0 4 - 0 . 0 0 0 0 3 1 . 0 3 0 12 19 - 30 10 2 0 1 6 1 4 . 9 4 9 4 8 0 . 0 0 0 4 8 0 . 5 31 12 19 - 31 12 2 0 1 6 1 4 . 9 3 9 3 4 - 0 . 0 0 0 5 2 1 . 0 32 14 19 - 32 12 2 0 1 6 1 4 . 9 2 9 9 5 - 0 . 0 0 0 3 6 1 . 0 33 14 19 - 33 14 2 0 1 6 1 4 . 9 2 0 0 6 - 0 . 0 0 0 2 8 1 . 0 34 16 19 - 34 14 2 0 1 6 1 4 . 9 0 9 9 0 - 0 . 0 0 0 0 3 1 . 0 3 5 16 19 - 3 5 16 2 0 ' 1 6 1 4 . 8 9 9 0 5 - 0 . 0 0 0 0 2 1 . 0 3 6 18 19 - 36 16 20 1 6 1 4 . 8 8 8 2 6 0 . 0 0 0 5 0 1 . 0 3 7 18 19 - 37 18 20 1 6 1 4 . 8 7 6 9 4 0 . 0 0 0 9 7 0 . 0 37 18 2 0 - 37 16 21 1 6 1 5 . 2 0 3 0 2 - 0 . 0 0 0 6 5 1 . 0 38 18 20 - 38 18 21 1 6 1 5 . 1 9 1 7 3 0 . 0 0 0 0 2 0 . 0 2 7 6 21 - 27 6 22 1 6 1 5 . 6 2 6 2 9 0 . 0 0 0 4 3 0 . 5 32 12 21 - 32 10 22 1 6 1 5 . 5 8 3 8 5 0 . 0 0 0 7 4 0 . 5 3 6 16 21 - 36 14 22 1 6 1 5 . 5 4 2 7 8 0 . 0 0 0 7 4 0 . 5 3 7 16 21 - 37 16 22 1 6 1 5 . 5 3 1 6 7 0 . 0 0 0 9 2 0 . 5 38 18 21 - 38 16 22 1 6 1 5 . 5 1 8 6 3 - 0 . 0 0 0 3 9 1 . 0 3 9 18 21 - 39 18 22 1 6 1 5 . 5 0 7 4 4 0 . 0 0 0 6 0 0 . 0 8 8 0 - 9 8 1 1 6 0 3 . 3 7 5 7 1 - 0 . 0 0 0 2 7 0 . 5 9 9 0 - 10 9 1 1 6 0 2 . 8 1 7 5 1 0 . 0 0 0 3 9 1 . 0 10 10 0 - 11 10 1 1 6 0 2 . 2 6 3 3 0 0 . 0 0 0 6 6 1 . 0 18 18 0 - 19 18 1 1 5 9 7 . 7 9 1 8 2 - 0 . 0 0 0 8 3 0 . 5 6 6 1 - 7 6 2 1 6 0 4 . 7 6 6 2 4 - 0 . 0 0 0 4 0 0 . 5 15 14 1 - 16 14 2 1 5 9 9 . 2 3 5 8 7 0 . 0 0 0 3 2 1 . 0 17 16 1 - 18 16 2 1 5 9 8 . 1 4 4 5 4 - 0 . 0 0 0 2 8 1 . 0 7 6 2 - 8 6 3 1 6 0 4 . 3 2 3 1 7 - 0 . 0 0 0 6 2 0 . 5 10 9 2 - 11 9 3 1 6 0 2 . 4 3 5 2 1 - 0 . 0 0 0 0 0 1 . 0 1 1 10 2 - 12 10 3 1 6 0 1 . 8 1 9 0 0 0 . 0 0 0 3 7 1 . 0 13 11 2 - 14 1 1 3 1 6 0 0 . 2 3 8 9 9 0 . 0 0 0 8 3 0 . 5 13 12 2 - 14 12 3 1 6 0 0 . 6 0 5 6 5 - 0 . 0 0 0 2 3 0 . 5 O b s e r v e d N o r m a l i s e d J ' K . ' K c ' - J " K . " K c " Wavenumber D e v i a t i o n W e i g h t ( c n - 1 ) ( c m " 1 ) 15 14 2 - 16 14 3 1599.41808 -0.00064 0.5 16 14 2 - 17 14 3 1598.41023 0.00041 1.0 22 20 2 - 23 20 3 1595.10937 0.00002 1.0 9 7 3 - 10 7 4 1603.30966 -0.00001 0.5 10 7 3 - 11 7 4 1602.60527 -0.00096 0.5 11 8 3 - 12 8 4 1601.92746 0.00083 0.5 12 10 3 - 13 10 4 1601.36698 -0.00072 1.0 13 10 3 - 14 10 4 1600.55169 0.00056 1.0 14 12 3 - 15 12 4 1600.09526 0.00008 1.0 15 12 3 - 16 12 4 1599.17484 0.00106 1 .0 16 14 3 - 17 14 4 1598.84750 0.00012 0.5 17 14 3 - 18 14 4 1597.82735 -0.00076 0.5 19 16 3 - 20 16 4 1596.54118 -0.00077 0.5 20 18 3 - 21 18 4 1596.43331 -0.00089 0.5 23 20 3 - 24 20 4 1594.19396 0.00076 0.5 24 21 3 - 25 21 4 1593.64794 0.00038 0.5 15 12 4 - 16 12 5 1599.69470 0.00070 1.0 17 14 4 - 18 14 5 1598.39590 -0.00008 1.0 18 14 4 - 19 14 5 1597.53961 -0.00074 1.0 18 15 4 - 19 15 5 1597.75292 -0.00040 1.0 19 15 4 - 20 15 5 1596.83960 0.00057 0.5 19 16 4 - 20 16 5 1597.11611 0.00002 1.0 20 16 4 - 21 16 5 1596.14045 -0.00008 1.0 21 18 4 - 22 18 5 1595.86125 0.00051 1.0 21 17 4 - 22 17 5 1595.44954 -0.00017 0.5 24 20 4 - 25 20 5 1593.46417 -0.00066 1.0 23 18 5 - 24 18 6 1594.52632 0.00059 0.5 28 22 6 - 29 22 7 1591.51025 0.00101 0.5 29 22 7 - 30 22 8 1591.33304 0.00026 1.0 20 4 16 - 21 4 17 1600.32007 -0.00021 0.5 21 6 16 - 22 6 17 1599.66282 -0.00033 0.5 20 4 17 - 21 4 18 1600.64480 0.00005 0.5 21 4 17 - 22 4 18 1599.98748 -0.00008 0.5 22 6 17 - 23 6 18 1599.32997 -0.00033 0.5 24 8 17 - 25 8 18 1598.01515 -0.00043 1.0 25 8 17 - 26 8 18 1597.35787 -0.00026 1 .0 21 4 18 - 22 4 19 1600.31146 -0.00038 0.5 22 4 18 - 23 4 19 1599.65418 -0.00033 0.5 23 6 18 - 24 6 19 1598.99750 0.00038 0.5 24 6 18 - 25 6 19 1598.33981 0.00013 1.0 25 8 18 - 26 8 19 1597.68200 -0.00018 1.0 27 10 18 - 28 10 19 1596.36656 -0.00046 1.0 28 10 18 - 29 10 19 1595.70925 -0.00011 0.5 29 12 18 - 30 12 19 1595.05179 0.00014 0.5 34 16 18 - 35 16 19 1591.76233 -0.00003 0.5 21 2 19 - 22 2 20 1600.63588 -0.00014 1 .0 22 4 19 - 23 4 20 1599.97904 0.00043 1.0 23 4 19 - 24 4 20 1599.32120 0.00006 1.0 24 6 19 - 25 6 20 1598.66342 -0.00020 1.0 25 6 19 - 26 6 20 1598.00569 -0.00036 0.5 26 8 19 - 27 8 20 1597.34822 -0.00022 1.0 27 8 19 - 28 8 20 1596.69041 -0.00037 1.0 28 10 19 - 29 10 20 1596.03249 -0.00060 1.0 29 10 19 - 30 10 20 1595.37557 0.00021 1.0 30 12 19 - •31 12 20 1594.71765 0.00006 0.5 31 12 19 - 32 12 20 1594.06014 0.00035 0.5 33 14 19 - 34 14 20 1592.74380 -0.00028 0.5 22 2 20 - 23 2 21 1600.30249 -0.00011 0.5 23 4 20 - 24 4 21 1599.64479 -0.00025 1.0 24 4 20 - 25 4 21 1598.98732 -0.00011 1 .0 25 6 20 - 26 6 21 1598.32988 0.00010 1.0 26 6 20 - 27 6 21 1597.67210 0.00001 1.0 27 8 20 - 28 8 21 1597.01414 -0.00023 1.0 212 O b s e r v e d N o r m a l i s e d - J " K a " K c " Wavenumber D e v i a t i o n W e i g h t ( c m - 1 ) ( c m - 1 ) 28 8 20 - 2 9 8 21 1 5 9 6 . 3 5 6 3 2 - 0 . 0 0 0 2 9 1 . 0 2 9 10 20 - 30 10 21 1 5 9 5 . 6 9 8 7 3 - 0 . 0 0 0 1 0 1 . 0 30 10 20 - 31 10 21 1 5 9 5 . 0 4 0 9 0 - 0 . 0 0 0 1 2 1 . 0 31 12 2 0 - 32 12 21 1 5 9 4 . 3 8 2 9 7 - 0 . 0 0 0 2 2 1 . 0 32 12 2 0 - 33 12 21 1 5 9 3 . 7 2 5 0 3 - 0 . 0 0 0 3 1 0 . 5 33 14 2 0 - 34 14 21 1 5 9 3 . 0 6 7 4 2 - 0 . 0 0 0 0 4 1 . 0 22 2 21 - 2 3 2 22 1 6 0 0 . 6 2 6 5 9 0 . 0 0 0 0 8 1 . 0 23 2 21 - 24 2 22 1 5 9 9 . 9 6 8 8 4 - 0 . 0 0 0 0 0 1 . 0 24 4 21 - 2 5 4 22 1 5 9 9 . 3 1 1 1 3 - 0 . 0 0 0 0 1 1 . 0 25 4 21 - 26 4 22 1 5 9 8 . 6 5 3 0 9 - 0 . 0 0 0 3 0 1 . 0 26 6 21 - 27 6 22 1 5 9 7 . 9 9 5 5 1 - 0 . 0 0 0 1 0 1 . 0 27 6 21 - 28 6 22 1 5 9 7 . 3 3 8 0 5 0 . 0 0 0 2 5 1 . 0 28 8 21 - 2 9 8 22 1 5 9 6 . 6 7 9 7 0 - 0 . 0 0 0 2 7 1 . 0 2 9 8 21 - 30 8 22 1 5 9 6 . 0 2 2 3 4 0 . 0 0 0 2 3 1 . 0 30 10 21 - 31 10 22 1 5 9 5 . 3 6 4 1 1 - 0 . 0 0 0 1 3 1 . 0 31 1 0 21 - 32 10 22 1 5 9 4 . 7 0 6 7 9 0 . 0 0 0 4 4 1 . 0 32 1 2 21 - 33 12 22 1 5 9 4 . 0 4 9 0 2 0 . 0 0 0 5 7 1 . 0 33 12 21 - 34 12 22 1 5 9 3 . 3 9 0 8 5 0 . 0 0 0 3 1 1 . 0 36 16 21 - 37 16 22 1 5 9 1 . 4 1 7 0 8 0 . 0 0 0 3 0 1 . 0 23 2 22 - 24 2 23 1 6 0 0 . 2 9 2 6 1 0 . 0 0 0 0 3 1 . 0 24 2 22 - 2 5 2 23 1 5 9 9 . 6 3 4 8 0 0 . 0 0 0 0 4 1 . 0 2 5 4 22 - 2 6 4 23 1 5 9 8 . 9 7 7 0 6 0 . 0 0 0 1 5 1 . 0 26 4 22 - 2 7 4 23 1 5 9 8 . 3 1 9 1 5 0 . 0 0 0 1 3 1 . 0 27 6 22 - 28 6 23 1 5 9 7 . 6 6 1 2 7 0 . 0 0 0 1 6 1 . 0 28 6 22 - 2 9 6 23 1 5 9 7 . 0 0 3 3 3 0 . 0 0 0 1 5 1 . 0 29 8 22 - 30 8 23 1 5 9 6 . 3 4 5 4 2 0 . 0 0 0 1 8 1 . 0 30 8 22 - 31 8 23 1 5 9 5 . 6 8 7 8 0 0 . 0 0 0 5 2 0 . 5 31 10 22 - 32 10 23 1 5 9 5 . 0 2 9 7 1 0 . 0 0 0 4 0 1 . 0 32 10 22 - 3 3 10 23 1 5 9 4 . 3 7 1 8 3 0 . 0 0 0 4 8 1 . 0 33 1 2 22 - 34 12 23 1 5 9 3 . 7 1 3 5 6 0 . 0 0 0 1 8 0 . 5 34 12 22 - 35 12 23 1 5 9 3 . 0 5 5 8 9 0 . 0 0 0 4 8 1 . 0 23 0 2 3 - 24 0 24 1 6 0 0 . 6 1 6 3 8 0 . 0 0 0 1 3 1 . 0 24 2 2 3 - 2 5 2 24 1 5 9 9 . 9 5 8 3 2 0 . 0 0 0 0 1 1 . 0 2 5 2 2 3 - 26 2 24 1 5 9 9 . 3 0 0 4 0 0 . 0 0 0 0 6 1 . 0 26 4 2 3 - 27 4 24 1 5 9 8 . 6 4 2 2 8 - 0 . 0 0 0 0 7 1 . 0 27 4 2 3 - 28 4 24 1 5 9 7 . 9 8 4 3 8 0 . 0 0 0 0 5 1 . 0 28 6 2 3 - 2 9 6 24 1 5 9 7 . 3 2 6 5 3 0 . 0 0 0 2 4 1 . 0 29 6 2 3 - 30 6 24 1 5 9 6 . 6 6 8 8 0 0 . 0 0 0 5 6 0 . 5 30 8 23 - 31 8 24 1 5 9 6 . 0 1 0 9 0 0 . 0 0 0 7 2 1 . 0 31 8 23 - 32 8 24 1 5 9 5 . 3 5 2 5 7 0 . 0 0 0 4 5 1 . 0 32 10 23 - 33 10 24 1 5 9 4 . 6 9 4 4 8 0 . 0 0 0 4 2 1 . 0 33 10 23 - 34 10 24 1 5 9 4 . 0 3 6 3 2 0 . 0 0 0 3 1 1 . 0 34 12 23 - 3 5 12 24 1 5 9 3 . 3 7 8 5 2 0 . 0 0 0 5 5 1 . 0 35 1 2 23 - 36 12 24 1 5 9 2 . 7 2 0 8 3 0 . 0 0 0 8 9 1 . 0 36 1 4 23 - 37 1 4 24 1 5 9 2 . 0 6 2 0 4 0 . 0 0 0 1 1 1 . 0 37 1 4 23 - 38 14 24 1 5 9 1 . 4 0 4 5 9 0 . 0 0 0 6 5 1 . 0 24 0 24 - 2 5 0 2 5 1 6 0 0 . 2 8 1 7 0 - 0 . 0 0 0 1 1 1 . 0 2 5 2 24 - 26 2 25 1 5 9 9 . 6 2 3 6 2 - 0 . 0 0 0 1 0 1 . 0 26 2 24 - 2 7 2 25 1 5 9 8 . 9 6 5 8 0 0 . 0 0 0 2 0 1 . 0 27 4 24 - 28 4 2 5 1 5 9 8 . 3 0 7 9 5 0 . 0 0 0 4 9 1 . 0 28 4 24 - 2 9 4 2 5 1 5 9 7 . 6 4 9 9 3 0 . 0 0 0 6 3 1 . 0 2 9 6 24 - 30 6 2 5 1 5 9 6 . 9 9 1 6 9 0 . 0 0 0 5 5 1 . 0 30 6 24 - 31 6 2 5 1 5 9 6 . 3 3 3 5 3 0 . 0 0 0 5 6 0 . 5 31 8 24 - 32 8 25 1 5 9 5 . 6 7 5 3 9 0 . 0 0 0 5 9 1 . 0 32 8 24 - 3 3 8 2 5 1 5 9 5 . 0 1 6 9 1 0 . 0 0 0 2 7 1 . 0 33 10 24 - 34 10 25 1 5 9 4 . 3 5 9 0 2 0 . 0 0 0 5 3 1 . 0 34 10 24 - 3 5 10 25 1 5 9 3 . 7 0 0 6 0 0 . 0 0 0 2 5 1 . 0 35 12 24 - 36 12 25 1 5 9 3 . 0 4 2 6 8 0 . 0 0 0 4 4 1 . 0 37 1 4 24 - 38 14 2 5 1 5 9 1 . 7 2 6 4 2 0 . 0 0 0 3 3 1 . 0 25 0 2 5 - 26 0 26 1 5 9 9 . 9 4 7 3 7 0 . 0 0 0 3 3 1 . 0 26 2 2 5 - 27 2 26 1 5 9 9 . 2 8 9 2 6 0 . 0 0 0 4 7 1 . 0 O b s e r v e d N o r m a l i s e d J ' K . ' K c ' - J " K . " K c " Wavenumber D e v i a t i o n W e i g h t ( c m - 1 ) (cm""1) 27 2 2 5 - 28 2 2 6 1 5 9 8 . 6 3 1 0 5 0 . 0 0 0 5 2 1 . 0 28 4 2 5 - 2 9 4 26 1 5 9 7 . 9 7 2 8 7 0 . 0 0 0 6 3 1 . 0 2 9 4 2 5 - 3 0 4 26 1 5 9 7 . 3 1 4 9 4 0 . 0 0 0 9 9 0 . 5 30 6 2 5 - 31 6 26 1 5 9 6 . 6 5 5 9 8 0 . 0 0 0 3 2 1 . 0 31 6 2 5 - 32 6 2 6 1 5 9 5 . 9 9 7 8 0 0 . 0 0 0 4 3 1 . 0 32 8 2 5 - 33 8 26 1 5 9 5 . 3 3 9 0 4 - 0 . 0 0 0 0 5 1 . 0 33 8 2 5 - 34 8 26 1 5 9 4 . 6 8 1 2 7 0 . 0 0 0 4 4 1 . 0 35 10 2 5 - 36 10 26 1 5 9 3 . 3 6 4 6 3 0 . 0 0 0 2 6 1 . 0 38 14 2 5 - 3 9 14 2 6 1 5 9 1 . 3 9 0 2 7 0 . 0 0 0 3 6 1 . 0 26 0 2 6 - 27 0 27 1 5 9 9 . 6 1 1 7 1 - 0 . 0 0 0 2 3 1 .0 27 2 2 6 - 28 2 27 1 5 9 8 . 9 5 3 6 3 0 . 0 0 0 0 9 1 .0 2 8 2 2 6 - 2 9 2 2 7 1 5 9 8 . 2 9 5 4 3 0 . 0 0 0 3 1 1 . 0 2 9 4 26 - 3 0 4 27 1 5 9 7 . 6 3 7 1 1 0 . 0 0 0 4 1 1 . 0 30 4 26 - 31 4 27 1 5 9 6 . 9 7 9 1 5 0 . 0 0 0 8 7 0 . 5 31 6 2 6 - 32 6 27 1 5 9 6 . 3 2 0 3 8 0 . 0 0 0 5 2 1 . 0 32 6 26 - 3 3 6 27 1 5 9 5 . 6 6 1 7 1 0 . 0 0 0 2 6 1 . 0 33 8 26 - 34 8 2 7 1 5 9 5 . 0 0 3 1 7 0 . 0 0 0 1 1 1 . 0 34 8 26 - 3 5 8 2 7 1 5 9 4 . 3 4 5 2 8 0 . 0 0 0 5 8 1 . 0 3 5 10 26 - 3 6 10 2 7 1 5 9 3 . 6 8 7 1 2 0 . 0 0 0 7 6 0 . 5 36 10 2 6 - 3 7 10 2 7 1 5 9 3 . 0 2 8 7 3 0 . 0 0 0 6 7 1 . 0 3 7 12 26 - 38 12 2 7 1 5 9 2 . 3 7 0 8 7 0 . 0 0 1 0 8 1 . 0 27 0 2 7 - 28 0 28 1 5 9 9 . 2 7 6 6 6 0 . 0 0 0 1 5 1 . 0 28 2 27 - 2 9 2 28 1 5 9 8 . 6 1 8 3 7 0 . 0 0 0 4 2 1 . 0 2 9 2 27 - 30 2 28 1 5 9 7 . 9 6 0 0 1 0 . 0 0 0 6 2 1 . 0 30 4 27 - 31 4 28 1 5 9 7 . 3 0 1 5 7 0 . 0 0 0 7 4 1 . 0 31 4 27 - 32 4 28 1 5 9 6 . 6 4 3 3 0 0 . 0 0 1 0 3 0 . 5 32 6 27 - 3 3 6 28 1 5 9 5 . 9 8 4 6 4 0 . 0 0 0 9 1 1 . 0 33 6 27 - 34 6 28 1 5 9 5 . 3 2 5 7 6 0 . 0 0 0 5 6 0 . 5 34 8 27 - 3 5 8 28 1 5 9 4 . 6 6 7 2 2 0 . 0 0 0 5 1 1 . 0 3 5 8 2 7 - 36 8 28 1 5 9 4 . 0 0 9 0 1 0 . 0 0 0 7 7 1 . 0 38 12 27 - 3 9 12 28 1 5 9 2 . 0 3 3 6 1 0 . 0 0 0 5 2 1 . 0 41 14 27 - 4 2 14 28 1 5 9 0 . 0 5 9 2 7 0 . 0 0 0 8 6 1 . 0 28 0 28 - 2 9 0 2 9 1 5 9 8 . 9 4 0 7 3 - 0 . 0 0 0 0 2 1 . 0 2 9 2 28 - 30 2 2 9 1 5 9 8 . 2 8 2 1 1 0 . 0 0 0 0 7 1 . 0 31 4 28 - 32 4 2 9 1 5 9 6 . 9 6 5 4 1 0 . 0 0 0 7 8 1 . 0 32 4 28 - 33 4 2 9 1 5 9 6 . 3 0 6 6 2 0 . 0 0 0 6 8 1 . 0 33 6 28 - 34 6 2 9 1 5 9 5 . 6 4 8 0 9 0 . 0 0 0 8 2 0 . 5 34 6 28 - 3 5 6 2 9 1 5 9 4 . 9 8 9 4 4 0 . 0 0 0 8 1 0 . 5 3 5 8 28 - 3 6 8 2 9 1 5 9 4 . 3 3 0 6 6 0 . 0 0 0 6 3 0 . 5 36 8 28 - 3 7 8 2 9 1 5 9 3 . 6 7 2 9 8 0 . 0 0 1 5 2 0 . 0 3 7 10 28 - 38 10 2 9 1 5 9 3 . 0 1 4 3 8 0 . 0 0 1 4 4 0 . 0 39 12 28 - 4 0 12 2 9 1 5 9 1 . 6 9 6 9 4 0 . 0 0 0 8 8 1 . 0 2 9 0 2 9 - 30 0 30 1 5 9 8 . 6 0 5 0 1 0 . 0 0 0 3 5 1 . 0 3 0 2 2 9 - 31 2 30 1 5 9 7 . 9 4 6 0 5 0 . 0 0 0 2 5 1 . 0 31 2 2 9 - 32 2 3 0 1 5 9 7 . 2 8 7 5 3 0 . 0 0 0 5 9 1 . 0 32 4 2 9 - 33 4 3 0 1 5 9 6 . 6 2 9 2 3 0 . 0 0 1 1 3 0 . 0 3 3 4 2 9 - 34 4 3 0 1595 .97035 0 . 0 0 1 0 6 0 . 0 34 6 2 9 - 3 5 6 3 0 1 5 9 5 . 3 1 2 0 2 0 . 0 0 1 5 2 0 . 0 3 5 6 2 9 - 3 6 6 30 1 5 9 4 . 6 5 3 2 7 0 . 0 0 1 5 3 0 . 0 36 8 2 9 - 3 7 8 30 1 5 9 3 . 9 9 4 7 8 0 . 0 0 1 7 5 0 . 0 37 8 2 9 - 38 8 3 0 1 5 9 3 , 3 3 5 7 6 0 . 0 0 1 4 0 0 . 0 3 9 10 2 9 - 4 0 10 3 0 1 5 9 2 . 0 1 9 9 2 0 . 0 0 2 7 3 0 . 0 38 10 2 9 - 3 9 10 30 1 5 9 2 . 6 7 8 0 9 0 . 0 0 2 3 4 0 . 0 4 0 12 2 9 - 41 12 30 1 5 9 1 . 3 6 1 8 3 0 . 0 0 3 1 2 0 . 0 41 12 2 9 - 42 12 30 1 5 9 0 . 7 0 3 0 7 0 . 0 0 2 7 8 0 . 0 42 14 2 9 - 4 3 14 30 1 5 9 0 . 0 4 6 4 5 0 . 0 0 4 5 0 0 . 0 4 3 14 2 9 - 4 4 14 3 0 1 5 8 9 . 3 8 5 8 8 0 . 0 0 2 1 9 0 . 0 30 0 30 - 31 0 31 1 5 9 8 . 2 6 8 5 8 0 . 0 0 0 3 4 0 . 0 31 2 3 0 - 32 2 31 1 5 9 7 . 6 1 0 0 4 0 . 0 0 0 8 1 0 . 0 32 2 30 - 3 3 2 31 1 5 9 6 . 9 5 1 0 4 0 . 0 0 0 8 1 0 . 0 33 4 30 - 34 4 31 1 5 9 6 . 2 9 2 7 2 0 . 0 0 1 4 7 0 . 0 34 4 3 0 - 3 5 4 31 1 5 9 5 . 6 3 4 2 1 0 . 0 0 1 9 0 0 . 0 3 5 6 3 0 - 3 6 6 31 1 5 9 4 . 9 7 5 3 9 0 . 0 0 2 0 0 0 . 0 214 O b s e r v e d N o r m a l i s e d J " K a " K c " Wavenumber D e v i a t i o n W e i g h t ( c m - 1 ) ( c m - 1 ) 36 6 3 0 - 3 7 6 31 1 5 9 4 . 3 1 7 0 8 0 . 0 0 2 5 6 0 . 0 3 7 8 3 0 - 38 8 31 1 5 9 3 . 6 5 8 3 0 0 . 0 0 2 6 0 0 . 0 38 8 30 - 3 9 8 31 1 5 9 2 . 9 9 9 7 8 0 . 0 0 2 8 4 0 . 0 3 9 10 30 - 4 0 10 31 1 5 9 2 . 3 4 1 3 0 0 . 0 0 3 0 7 0 . 0 42 12 30 - 4 3 12 31 1 5 9 0 . 3 6 5 2 1 0 . 0 0 2 6 6 0 . 0 31 0 31 - 32 0 32 1 5 9 7 . 9 3 3 6 8 0 . 0 0 2 1 9 0 . 0 32 2 31 - 33 2 32 1 5 9 7 . 2 7 6 3 9 0 . 0 0 4 0 6 0 . 0 33 2 31 - 34 2 32 1 5 9 6 . 6 1 9 1 4 0 . 0 0 5 9 5 0 . 0 34 4 31 - 3 5 4 32 1 5 9 5 . 9 6 1 1 1 0 . 0 0 7 0 3 0 . 0 3 5 4 31 - 36 4 32 1 5 9 5 . 3 0 2 5 0 0 . 0 0 7 5 0 0 . 0 3 6 6 31 - 3 7 6 32 1 5 9 4 . 6 4 3 7 6 0 . 0 0 7 7 9 0 . 0 37 6 31 - 38 6 32 1593 .98398 0 . 0 0 7 0 0 0 . 0 38 8 31 - 39 8 32 1593 .32618 0 . 0 0 8 1 2 0 . 0 39 8 31 - 4 0 8 32 1 5 9 2 . 6 6 8 1 6 0 . 0 0 8 9 7 0 . 0 4 0 10 31 - 41 10 32 1 5 9 2 . 0 0 9 8 3 0 . 0 0 9 4 3 0 . 0 41 10 31 - 42 10 32 1 5 9 1 . 3 5 1 2 1 0 . 0 0 9 5 3 0 . 0 43 12 31 - 44 12 32 1 5 9 0 . 0 3 4 5 1 0 . 0 1 0 0 1 0 . 0 44 14 31 - 4 5 14 32 1 5 8 9 . 3 7 5 7 8 0 . 0 0 9 7 4 0 . 0 32 0 32 - 33 0 33 1 5 9 7 . 5 9 4 1 2 - 0 . 0 0 0 2 9 0 . 0 3 3 2 32 - 34 2 33 1 5 9 6 . 9 3 3 6 8 - 0 . 0 0 1 4 2 0 . 0 34 2 32 - 3 5 2 33 1 5 9 6 . 2 7 4 0 8 - 0 . 0 0 1 7 4 0 . 0 3 5 4 32 - 36 4 33 1 5 9 5 . 6 1 3 7 7 - 0 . 0 0 2 8 1 0 . 0 3 6 4 32 - 3 7 4 33 1 5 9 4 . 9 5 3 2 5 - 0 . 0 0 4 1 2 0 . 0 3 7 6 32 - 38 6 33 1 5 9 4 . 2 9 3 3 8 - 0 . 0 0 4 8 4 0 . 0 38 6 32 - 39 6 33 1593 .63370 - 0 . 0 0 5 4 2 0 . 0 3 9 8 32 - 4 0 8 33 1 5 9 2 . 9 7 3 2 3 - 0 . 0 0 6 8 6 0 . 0 4 0 8 32 - 41 8 33 1 5 9 2 . 3 1 3 1 2 - 0 . 0 0 8 0 1 0 . 0 3 3 0 33 - 34 0 34 1 5 9 7 . 2 5 6 9 4 - 0 . 0 0 0 0 7 0 . 0 34 2 3 3 - 3 5 2 34 1 5 9 6 . 5 9 7 1 4 - 0 . 0 0 0 4 1 0 . 0 3 5 2 33 - 36 2 34 1 5 9 5 . 9 3 6 6 2 - 0 . 0 0 1 5 1 0 . 0 3 6 4 33 - 37 4 34 1 5 9 5 . 2 7 7 3 4 - 0 . 0 0 1 4 1 0 . 0 37 4 33 - 38 4 34 1 5 9 4 . 6 1 7 5 1 - 0 . 0 0 1 9 1 0 . 0 3 9 6 33 - 40 6 34 1 5 9 3 . 2 9 7 9 5 - 0 . 0 0 2 9 9 0 . 0 4 0 8 33 - 41 B 34 1 5 9 2 . 6 3 8 8 6 - 0 . 0 0 2 9 4 0 . 0 41 8 33 - 42 8 34 1 5 9 1 . 9 7 9 9 4 - 0 . 0 0 2 8 1 0 . 0 42 10 33 - 4 3 10 34 1 5 9 1 . 3 2 0 6 3 - 0 . 0 0 3 1 4 0 . 0 4 3 10 33 - 44 10 34 1 5 9 0 . 6 6 0 9 4 - 0 . 0 0 3 9 5 0 . 0 4 5 12 33 - 46 12 34 1 5 8 9 . 3 4 2 3 2 - 0 . 0 0 5 1 1 0 . 0 34 0 34 - 3 5 0 35 1 5 9 6 . 9 1 9 2 6 - 0 . 0 0 0 0 2 1 . 0 3 5 2 34 - 3 6 2 3 5 1 5 9 6 . 2 5 9 3 6 - 0 . 0 0 0 3 1 1 .0 3 6 2 34 - 37 2 3 5 1 5 9 5 . 5 9 9 6 8 - 0 . 0 0 0 4 3 1 .0 3 7 4 34 - 38 4 3 5 1 5 9 4 . 9 3 9 5 6 - 0 . 0 0 1 0 4 0 . 5 38 4 34 - 3 9 4 3 5 1 5 9 4 . 2 8 0 4 0 - 0 . 0 0 0 7 5 0 . 5 3 9 6 34 - 4 0 6 35 1 5 9 3 . 6 2 0 4 5 - 0 . 0 0 1 3 1 0 . 0 4 0 6 34 - 41 6 35 1 5 9 2 . 9 6 0 9 9 - 0 . 0 0 1 4 5 0 . 0 41 8 34 - 42 8 3 5 1 5 9 2 . 3 0 1 2 7 - 0 . 0 0 1 9 3 0 . 0 42 8 34 - 43 8 3 5 1 5 9 1 . 6 4 2 3 6 - 0 . 0 0 1 6 8 0 . 0 3 5 0 3 5 - 36 0 36 1 5 9 6 . 5 8 1 1 5 - 0 . 0 0 0 0 7 1 . 0 3 6 2 3 5 - 3 7 2 36 1 5 9 5 . 9 2 1 5 5 0 . 0 0 0 0 8 1 . 0 3 7 2 3 5 - 38 2 36 1 5 9 5 . 2 6 1 4 5 - 0 . 0 0 0 3 2 1 .0 38 4 3 5 - 3 9 4 36 1 5 9 4 . 6 0 1 0 8 - 0 . 0 0 1 0 5 0 . 5 3 9 4 3 5 - 40 4 36 1 5 9 3 . 9 4 2 1 2 - 0 . 0 0 0 4 3 0 . 5 4 0 6 3 5 - 41 6 36 1 5 9 3 . 2 8 2 0 6 - 0 . 0 0 0 9 8 0 . 5 41 6 3 5 - 42 6 36 1 5 9 2 . 6 2 2 1 6 - 0 . 0 0 1 4 5 0 . 0 42 8 3 5 - 4 3 8 36 1 5 9 1 . 9 6 2 6 2 - 0 . 0 0 1 6 5 0 . 0 4 3 8 3 5 - 44 8 36 1 5 9 1 . 3 0 3 3 4 - 0 . 0 0 1 6 8 0 . 0 44 10 3 5 - 4 5 10 36 1 5 9 0 . 6 4 3 9 3 - 0 . 0 0 1 9 4 0 . 0 4 5 10 35 - 46 10 36 1 5 8 9 . 9 8 4 4 1 - 0 . 0 0 2 4 2 0 . 0 3 6 0 36 - 37 0 37 1 5 9 6 . 2 4 2 6 4 - 0 . 0 0 0 1 9 1 . 0 37 2 36 - 38 2 37 1 5 9 5 . 5 8 2 5 9 - 0 . 0 0 0 3 5 1 . 0 38 2 36 - 3 9 2 37 1 5 9 4 . 9 2 2 4 8 - 0 . 0 0 0 6 2 1 . 0 3 9 4 3 6 - 4 0 4 37 1 5 9 4 . 2 6 2 7 4 - 0 . 0 0 0 5 9 1 . 0 4 0 4 36 - 41 4 37 1 5 9 3 . 6 0 2 6 3 - 0 . 0 0 1 0 0 1 . 0 215 O b s e r v e d N o r m a l i s e d Wavenumber D e v i a t i o n W e i g h t ( c m - 1 ) ( c m " 1 ) 41 6 36 - 42 6 37 1592.94294 -0.00106 0.0 42 6 36 - 43 6 37 1592.28334 -0.00113 0.0 37 0 37 - 38 0 38 1595.90409 -0.00003 0.5 38 2 37 - 39 2 38 1595.24418 0.00010 1.0 39 2 37 - 40 2 38 1594.58351 -0.00060 1.0 40 4 37 - 41 4 38 1593.92362 -0.00059 1.0 41 4 37 - 42 4 38 1593.26357 -0.00082 1.0 42 6 37 - 43 6 38 1592.60332 -0.00133 0.0 43 6 37 - 44 6 38 1591.94385 -0.00115 0.0 44 8 37 - 45 8 38 1591.28440 -0.00106 0.0 46 10 37 - 47 10 38 1589.96646 -0.00024 0.0 47 10 37 - 48 10 38 1589.30685 -0.00066 0.0 38 0 38 - 39 0 39 1595.56485 -0.00023 1.0 40 2 38 - 41 2 39 1594.24415 -0.00064 1.0 41 4 38 - 42 4 39 1593.58425 -0.00052 1.0 42 4 38 - 43 4 39 1592.92373 -0.00109 1.0 43 6 38 - 44 6 39 1592.26385 -0.00112 0.5 44 6 38 - 45 6 39 1591.60425 -0.00097 1.0 46 8 38 - 47 8 39 1590.28629 0.00024 1.0 39 0 39 - 40 0 40 1595.22524 -0.00047 1.0 40 2 39 - 41 2 40 1594.56548 0.00009 1.0 41 2 39 - 42 2 40 1593.90493 -0.00023 1.0 42 4 39 - 43 4 40 1593.24452 -0.00048 1.0 43 , 4 39 - 44 4 40 1592.58417 -0.00077 1.0 44 6 39 - 45 6 40 1591.92414 -0.00083 0.5 48 10 39 - 49 10 40 1589.28591 -0.00036 1.0 40 0 40 - 41 0 41 1594.88587 -0.00015 1.0 41 2 40 - 42 2 41 1594.22503 -0.00053 1.0 42 2 40 - 43 2 41 1593.56496 -0.00023 1.0 43 4 40 - 44 4 41 1592.90423 -0.00068 1.0 48 8 40 - 49 8 41 1589.60503 -0.00012 1.0 41 0 41 - 42 0 42 1594.54602 0.00002 1.0 42 2 41 - 43 2 42 1593.88563 0.00022 1.0 43 2 41 - 44 2 42 1593.22485 -0.00006 1.0 44 4 41 - 45 4 42 1592.56491 0.00040 0.5 45 4 41 - 46 4 42 1591 .90381 -0.00040 1.0 46 6 41 - 47 6 42 1591.24436 0.00034 1.0 47 6 41 - 48 6 42 1590.58346 -0.00050 1 .0 49 8 41 - 50 8 42 1589.26424 0.00001 1.0 42 0 42 - 43 0 43 1594.20587 0.00021 1.0 43 2 42 - 44 2 43 1593.54482 -0.00012 1.0 44 2 42 - 45 2 43 1592.88446 0.00016 1.0 45 4 42 - 46 4 43 1592.22396 0.00018 1.0 46 4 42 - 47 4 43 1591.56354 0.00018 1.0 48 6 42 - 49 6 43 1590.24314 0.00024 1 .0 49 8 42 - 50 8 43 .1589.58309 0.00021 1 .0 43 0 43 - 44 0 44 1593.86509 0.00009 1.0 44 2 43 - 45 2 44 1593.20427 0.00013 1.0 45 2 43 - 46 2 44 1592.54358 0.00020 1.0 46 4 43 47 4 44 1591.88305 0.00032 1.0 47 4 43 - 48 4 44 1591.22264 0.00044 1.0 48 6 43 - 49 6 44 1590.56199 0.00019 1.0 44 0 44 - 45 0 45 1593.52379 -0.00022 1.0 45 2 44 - 46 2 45 1592.86300 -0.00001 0.5 46 2 44 - 47 2 45 1592.20244 0.00031 1 .0 49 6 44 - 50 6 45 1590.22041 0.00020 1.0 50 6 44 - 51 6 45 1589.56021 0.00037 1.0 45 0 45 - 46 0 46 1593,18309 0.00039 1.0 46 2 45 - 47 2 46 1592.52195 0.00038 1 .0 47 2 45 - 48 2 46 1591.86149 0.00093 1.0 46 0 46 - 47 0 47 1592.84179 0.00072 1.0 47 2 46 - 48 2 47 1592.17943 -0.00037 1.0 48 2 46 - 49 2 47 1591.51888 0.00022 1.0 O b s e r v e d N o r m a l i s e d j ' K . ' K c ' - J " K a " K e " Wavenumber D e v i a t i o n W e i g h t ( c m " 1 ) ( c m - 1 ) 50 4 46 - 51 4 47 1590.19618 -0.00061 1.0 5) 6 46 - 52 6 47 1589.53530 -0.00078 1.0 47 0 47 - 48 0 48 1592.49958 0.00047 1.0 48 2 47 - 49 2 48 1591.83852 0.00080 1.0 49 2 47 - 50 2 48 1591.17661 0.00016 1.0 50 4 47 - 51 4 48 1590.51491 -0.00042 1.0 48 0 48 - 49 0 49 1592.15737 0.00054 1.0 49 2 48 - 50 2 49 1591.49548 0.00017 1.0 50 2 48 - 51 2 49 1590.83461 0.00069 1.0 51 4 48 - 52 4 49 1590.17190 -0.00078 1.0 52 4 48 - 53 4 49 1589.51201 0.00041 1.0 49 0 49 - 50 0 50 1591.81513 0.00090 1.0 50 2 49 - 51 2 50 1591.15258 0.00000 1.0 51 2 49 - 52 2 50 1590.49083 -0.00024 1.0 51 2 50 - 52 2 51 1590.81059 0.00106 1.0 53 4 50 - 54 4 51 1589.48647 0.00003 1.0 4 2 2 - 4 4 1 1608.12462 -0.00019 1.0 6 4 2 - 6 6 1 1607.99243 0.00003 1.0 8 6 3 - 8 6 2 1607.99243 0.00001 1.0 9 7 3 - 9 7 2 1608.03995 0.00101 0.5 1 1 9 3 - 1 1 9 2 1608.15255 -0.00010 0.5 9 6 4 - 9 6 3 1607.58534 -0.00063 1.0 19 16 4 - 19 16 3 1608.19593 0.00079 1.0 17 12 5 - 17 14 4 1607.19255 -0.00106 0.5 20 16 5 - 20 16 4 1607.62740 0.00109 0.5 21 16 5 - 21 18 4 1606.96913 -0.00085 0.5 24 20 5 - 24 20 4 1608.02499 -0.00032 1 .0 26 22 5 - 26 22 4 1608.21528 -0.00002 1 .0 17 12 6 - 17 12 5 1606.93483 0.00001 1 .0 18 13 6 - 18 13 5 1606.95311 0.00005 0.5 20 15 6 - 20 15 5 1607.01411 0.00079 1.0 22 16 6 - 22 18 5 1606.87952 0.00067 1.0 23 17 6 - 23 19 5 1606.84906 -0.00019 1.0 24 18 6 - 24 20 5 1606.80500 0.00022 1.0 25 20 6 - 25 20 5 1607.37524 -0.00056 1 .0 30 24 6 - 30 26 5 1606.03838 0.00047 1.0 31 26 6 - 31 26 5 1608.06097 0.00009 1.0 22 16 7 - 22 16 6 1606.62164 -0.00050 1.0 24 18 7 - 24 18 6 1606.67338 -0.00046 1.0 29 23 7 - 29 23 6 1607.00411 0.00019 1.0 29 22 8 - 29 22 7 1606.36646 0.00031 1.0 13 12 1 - 12 12 0 1616.24304 0.00109 0.5 1 5 14 1 - 14 14 0 1617.35769 0.00098 1.0 4 2 2 - 3 2 1 1610.85716 -0.00023 1.0 6 4 2 - 5 4 1 1612.17960 -0.00014 0.5 8 6 2 - 7 6 1 1613.47157 0.00099 0.5 9 7 2 - 8 7 1 1614.09878 -0.00018 1.0 10 9 2 - 9 9 1 1614.43123 -0.00093 0.5 12 10 2 - 1 1 10 1 1615.90077 -0.00072 1.0 12 11 2 - 1 1 1 1 1 1615.60060 0.00037 1.0 5 2 3 - 4 2 2 1611.16120 0.00098 1.0 8 5 3 - 7 5 2 1613.16121 0.00064 0.5 9 6 3 - 8 6 2 1613.83466 0.00031 0.5 1 1 8 3 - 10 8 2 1615.17602 0.00080 1.0 12 9 3 - 1 1 9 2 1615.83481 0.00009 1.0 13 10 3 - 12 10 2 1616.48335 0.00066 0.5 13 11 3 - 12 1 t 2 1616.17436 -0.00037 1.0 14 11 3 - 13 11 2 1617.11643 -0.00049 1.0 15 12 3 - 14 12 2 1617.73611 0.00023 1.0 16 13 3 - 15 13 2 1618.33884 0.00026 1.0 4 0 4 - 3 0 3 1610.17152 -0.00053 1.0 12 8 4 - 1 1 8 3 1615.44846 -0.00018 0.5 O b s e r v e d N o r m a l i s e d J ' K a ' K c ' - J " K . " K c " Wavenumber D e v i a t i o n W e i g h t ( c m - 1 ) ( c m - 1 ) 20 16 4 - 19 16 3 1620.75200 -0.00018 1 .0 26 22 4 - 25 22 3 1624.13973 -0.00063 0.5 5 0 5 - 4 0 4 1610.49661 -0.00018 0.5 14 9 5 - 13 9 4 1616.38916 0.00009 0.5 15 10 5 - 14 10 4 1617.05440 -0.00034 1.0 16 11 5 - 15 11 4 1617.72660 0.00064 0.5 17 12 5 - 16 12 4 1618.40338 0.00011 1.0 6 0 6 - 5 0 5 1610.82188 0.00067 0.5 18 13 6 - 17 13 5 1618.64555 0.00001 1 .0 19 14 6 - 18 14 5 1619.29583 -0.00023 1 . 0 20 14 6 - 19 14 5 1619.99592 0.00003 1.0 23 18 6 - 22 18 5 1621.87527 -0.00096 1.0 21 14 7 - 20 14 6 1620.27792 0.00057 1.0 23 17 7 - 22 17 6 1621.57296 . 0.00058 1.0 15 8 8 - 14 8 7 1616.02859 0.00000 1.0 18 10 8 - 17 10 7 1617.98033 -0.00044 1.0 20 12 8 - 19 12 7 1619.28183 -0.00065 1.0 26 19 8 - 25 19 7 1623.19022 0.00005 1.0 19 10 9 - 18 10 8 1618.30107 0.00082 1.0 21 12 9 - 20 12 8 1619.60058 0.00057 1.0 16 6 10 - 15 6 9 1616.02094 -0.00003 0.5 17 8 10 - 16 8 9 1616.67074 -0.00030 0.5 18 8 10 - 17 8 9 1617.32080 -0.00008 1.0 19 10 10 - 18 10 9 1617.97023 -0.00028 1.0 21 12 10 - 20 12 9 1619.26895 -0.00027 1.0 22 12 10 - 21 12 9 1619.91821 -0.00013 1.0 24 14 10 - 23 14 9 1621.21626 0.00002 1.0 16 6 1 1 - 15 6 10 1615.69181 -0.00036 0.5 17 6 1 1 - 16 6 10 1616.34129 -0.00088 0.5 18 8 1 1 - 17 8 10 1616.99164 -0.00027 1.0 19 8 1 1 - 18 8 10 1617.64092 -0.00047 1.0 20 10 1 1 - 19 10 10 1618.29044 -0.00018 1.0 23 12 1 1 - 22 12 10 1620.23659 -0.00033 0.5 24 14 1 1 - 23 14 10 1620.88559 0.00033 0.5 25 14 1 1 - 24 14 10 1621.53303 ^0.00038 1 .0 26 16 1 1 - 25 16 10 1622.18116 -0.00024 1 .0 27 16 1 1 - 26 16 10 1622.82947 0.00023 1.0 18 6 12 - 17 6 11 1616.66246 -0.00059 0.5 19 8 12 - 18 8 11 1617.31244 -0.00004 . 1 .0 23 12 12 - 22 12 11 1619.90708 -0.00035 1.0 24 12 12 - 23 12 11 1620.55591 0.00043 1 .0 25 14 12 - 24 14 1 1 1621.20332 0.00003 1.0 26 14 12 - 25 14 11 1621.85033 -0.00051 1.0 27 16 12 - 26 16 11 1622 . 49815 -0.00001 1.0 18 6 13 - 17 6 12 1616.33368 -0.00045 1.0 19 6 13 - 18 6 12 1616.98305 -0.00054 0.5 20 8 13 - 19 8 12 1617.63267 -0.00007 1.0 21 8 13 - 20 8 12 1618.28146 -0.00012 1 .0 23 10 13 - 22 10 12 1619.57856 0.00021 0.5 24 12 13 - 23 12 12 1620.22594 -0.00034 1.0 25 12 13 - 24 12 12 1620.87375 -0.00016 1.0 26 14 13 - 25 14 12 1621.52123 -0.00002 1.0 27 14 13 - 26 14 12 1622.16851 0.00021 1 .0 28 16 13 - 27 16 12 1622.81603 0.00097 0.5 29 16 13 - 28 16 12 1623.46160 0.00006 1.0 18 4 14 - 17 4 13 1616.00555 0.00046 0.5 19 6 14 - 18 6 13 1616.65379 -0.00081 0.5 20 6 14 - 19 6 13 1617.30363 -0.00016 1 .0 21 8 14 - 20 8 13 1617.95277 0.0001 1 1.0 22 8 14 - 21 8 13 1618.60139 0.00018 1.0 23 10 14 - 22 10 13 1619.24947 0.00004 1.0 24 10 14 - 23 10 13 1619.89708 -0.00024 1.0 O b s e r v e d J ' K 0 ' K c ' - J " K . " K c " Wavenumber ( cm" 1 ) N o r m a l i s e d D e v i a t i o n W e i g h t ( cm" 1 ) 25 12 14 - 24 12 13 1 6 2 0 . 5 4 4 8 5 - 0 . 0 0 0 0 4 1 . 0 26 12 14 - 2 5 12 13 1 6 2 1 . 1 9 1 3 2 - 0 . 0 0 0 8 1 1 . 0 27 1 4 14 - 26 14 1 3 1 6 2 1 . 8 3 8 2 7 - 0 . 0 0 0 7 8 1 . 0 2 9 16 14 - 28 16 13 1 6 2 3 . 1 3 1 1 8 - 0 . 0 0 0 7 3 1 . 0 18 4 15 - 17 4 1 4 1 6 1 5 . 6 7 6 3 0 0 . 0 0 0 4 3 0 . 5 19 4 15 - 18 4 14 1 6 1 6 . 3 2 5 4 8 0 . 0 0 0 0 2 0 . 5 20 6 15 - 19 6 14 1 6 1 6 . 9 7 4 0 3 - 0 . 0 0 0 6 9 0 . 5 21 6 15 - 2 0 6 14 1 6 1 7 . 6 2 3 2 2 - 0 . 0 0 0 4 2 .0 22 8 15 - 21 8 1 4 1 6 1 8 . 2 7 2 3 5 0 . 0 0 0 1 1 . 0 25 10 15 - 24 10 1 4 1 6 2 0 . 2 1 5 7 4 - 0 . 0 0 0 2 5 . 5 26 12 15 - 2 5 12 14 1 6 2 0 . 8 6 2 8 9 - 0 . 0 0 0 3 2 . 0 27 12 15 - 26 12 1 4 1 6 2 1 . 5 0 9 6 8 - 0 . 0 0 0 4 1 . 0 29 14 15 - 28 14 14 1 6 2 2 . 8 0 2 7 8 - 0 . 0 0 0 0 1 . 5 30 16 15 - 2 9 16 14 1 6 2 3 . 4 4 9 2 7 0 . 0 0 0 6 5 . 0 31 16 15 - 30 16 14 1 6 2 4 . 0 9 4 1 6 0 . 0 0 0 0 7 . 0 19 4 16 - 18 4 15 1 6 1 5 . 9 9 6 4 2 0 . 0 0 0 3 0 . 5 21 6 16 - 20 6 15 1 6 1 7 . 2 9 4 1 6 - 0 . 0 0 0 3 2 . 0 22 6 16 - 21 6 15 1 6 1 7 . 9 4 2 9 4 - 0 . 0 0 0 2 1 . 0 23 8 16 - 22 8 15 1 6 1 8 . 5 9 1 2 9 - 0 . 0 0 0 1 8 . 0 24 8 16 - 2 3 8 15 1 6 1 9 . 2 3 9 5 7 0 . 0 0 0 1 2 . 0 2 5 10 16 - 24 10 15 1619 .88687 - 0 . 0 0 0 2 0 . 0 26 10 16 - 2 5 10 15 1 6 2 0 . 5 3 3 9 7 - 0 . 0 0 0 3 6 . 0 27 12 16 - 26 12 15 1 6 2 1 . 1 8 0 6 5 - 0 . 0 0 0 5 8 . 0 28 12 16 - 27 12 15 1 6 2 1 . 8 2 7 6 6 - 0 . 0 0 0 1 0 . 0 2 9 1 4 16 - 28 14 15 1 6 2 2 . 4 7 4 1 5 0 . 0 0 0 2 3 . 0 30 1 4 16 - 2 9 14 15 1 6 2 3 . 1 1 9 8 3 0 . 0 0 0 1 3 . 0 19 2 17 - 18 2 16 1 6 1 5 . 6 6 6 2 4 - 0 . 0 0 0 3 3 . 0 20 4 1 7 - 19 4 1 6 1 6 1 6 . 3 1 5 5 1 - 0 . 0 0 0 5 0 . 0 21 4 17 - 20 4 1 6 1 6 1 6 . 9 6 4 4 7 - 0 . 0 0 0 6 5 . 0 22 6 17 - 21 6 1 6 1 6 1 7 . 6 1 3 2 0 - 0 . 0 0 0 6 8 . 0 23 6 17 - 22 6 16 1 6 1 8 . 2 6 2 2 4 - 0 . 0 0 0 0 6 . 5 2 5 8 17 - 24 8 16 1 6 1 9 . 5 5 7 5 8 - 0 . 0 0 0 4 7 . 0 26 10 17 - 2 5 10 16 1 6 2 0 . 2 0 6 2 8 0 . 0 0 0 9 0 . 5 27 10 17 - 26 10 16 1 6 2 0 . 8 5 2 2 8 - 0 . 0 0 0 0 6 . 0 28 12 17 - 27 12 16 1 6 2 1 . 4 9 8 7 5 - 0 . 0 0 0 1 6 . 0 2 9 12 17 - 28 12 16 1 6 2 2 . 1 4 4 7 2 - 0 . 0 0 0 3 9 . 0 30 14 17 - 2 9 14 16 1 6 2 2 . 7 9 1 0 5 0 . 0 0 0 1 3 . 0 31 14 17 - 30 14 16 1 6 2 3 . 4 3 6 6 8 0 . 0 0 0 3 5 . 0 32 16 17 - 31 16 16 1 6 2 4 . 0 8 1 5 2 0 . 0 0 0 1 7 . 0 20 2 18 - 19 2 17 1 6 1 5 . 9 8 6 3 1 - 0 . 0 0 0 0 3 . 0 21 4 18 - 20 4 17 1 6 1 6 . 6 3 5 1 3 - 0 . 0 0 0 4 2 . 0 22 4 18 - 21 4 17 1 6 1 7 . 2 8 3 9 1 - 0 . 0 0 0 5 1 . 0 23 6 18 - 22 6 17 1 6 1 7 . 9 3 2 5 5 - 0 . 0 0 0 3 9 . 0 24 6 18 - 23 6 17 1 6 1 8 . 5 8 1 2 3 0 . 0 0 0 1 4 .0 25 8 18 - 24 8 17 1 6 1 9 . 2 2 8 8 6 - 0 . 0 0 0 0 2 . 0 26 8 18 - 25 8 17 1 6 1 9 . 8 7 6 4 0 0 . 0 0 0 1 0 . 0 27 10 18 - 26 10 17 1 6 2 0 . 5 2 3 3 8 0 . 0 0 0 0 4 . 0 28 10 18 - 27 10 17 1 6 2 1 . 1 7 0 0 1 0 . 0 0 0 0 1 . 0 2 9 12 18 - 28 12 17 1 6 2 1 . 8 1 7 2 2 0 . 0 0 0 9 5 . 5 30 12 18 - 2 9 12 17 1 6 2 2 . 4 6 1 6 0 - 0 . 0 0 0 5 4 . 0 31 14 18 - 30 14 17 1 6 2 3 . 1 0 7 5 2 - 0 . 0 0 0 0 8 . 0 20 2 19 - 19 2 18 1 6 1 5 . 6 5 6 6 9 0 . 0 0 0 2 7 . 0 21 2 19 - 20 2 18 1 6 1 6 . 3 0 5 5 4 - 0 . 0 0 0 2 1 . 0 22 4 19 - 21 4 18 1 6 1 6 . 9 5 4 7 4 0 . 0 0 0 0 1 . 0 23 4 19 - 22 4 18 1 6 1 7 . 6 0 3 1 0 - 0 . 0 0 0 2 6 . 0 24 6 19 - 23 6 18 1 6 1 8 . 2 5 1 6 8 0 . 0 0 0 0 5 . 0 25 6 19 - 24 6 18 1 6 1 8 . 8 9 9 7 8 0 . 0 0 0 2 5 . 0 27 8 19 - 26 8 18 1 6 2 0 . 1 9 4 5 2 0 . 0 0 0 3 2 . 0 28 10 19 - 27 10 18 1 6 2 0 . 8 4 0 8 3 - 0 . 0 0 0 1 3 . 0 2 9 10 19 - 28 10 18 1 6 2 1 . 4 8 7 1 3 - 0 . 0 0 0 1 9 . 0 30 12 19 - 2 9 12 18 1 6 2 2 . 1 3 3 7 8 0 . 0 0 0 5 0 . 0 31 12 19 - 30 12 18 1 6 2 2 . 7 7 8 3 5 - 0 . 0 0 0 4 7 0 . 5 Observed J ' K . ' K c ' - J " K . " K c " Wavenumber (cm" 1) Normalised Dev ia t ion Weight (cm" 1) 33 14 19 - 32 14 18 1624.06889 0.00022 0.5 21 2 20 - 20 2 19 1615.97572 0.00002 1.0 22 2 20 - 21 2 19 1616.62481 0.00001 0.5 23 4 20 - 22 4 19 1617.27271 -0.00084 1.0 24 4 20 - 23 4 19 1617.92169 -0.00025 1.0 25 6 20 - 24 6 19 1618.57002 0.00006 1.0 27 8 20 - 26 8 19 1619.86492 0.00005 1.0 28 8 20 - 27 8 19 1620.51237 0.00063 1 .0 29 10 20 - 28 10 19 1621.15864 0.00043 1.0 30 10 20 - 29 10 19 1621.80491 0.00063 1.0 31 12 20 - 30 12 19 1622.45015 0.00021 1.0 32 12 20 - 31 12 19 1623.09517 0.00000 1.0 21 0 21 - 20 0 20 1615.64556 0.00016 1.0 22 2 21 - 21 2 20 1616.29439 -0.00023 1.0 23 2 21 - 22 2 20 1616.94317 -0.00033 1.0 24 4 21 - 23 4 20 1617.59193 -0.00008 1.0 25 4 21 - 24 4 20 1618.24005 -0.00011 1.0 26 6 21 - 25 6 20 1618.88796 0.00002 1.0 27 6 21 - 26 6 20 1619.53531 -0.00002 1.0 28 8 21 - 27 8 20 1620.18251 0.00019 1.0 29 8 21 - 28 8 20 1620.82955 0.00063 1.0 30 10 21 - 29 10 20 1621.47573 0.00062 1 .0 31 10 21 - 30 10 20 1622.12117 0.00028 0.5 32 12 21 - 31 12 20 1622.76640 0.00016 1.0 34 14 21 - 33 14 20 1624.05524 -0.00041 0.5 22 0 22 - 21 0 21 1615.96437 0.00019 1.0 23 2 22 - 22 2 21 1616.61305 -0.00014 1 .0 24 2 22 - 23 2 21 1617.26166 -0.00017 1.0 25 4 22 - 24 4 21 1617.90972 -0.00040 1.0 26 4 22 - 25 4 21 1618.55778 -0.00024 1.0 27 6 22 - 26 6 21 1619.20540 -0.00015 1.0 28 6 22 - 27 6 21 1619.85267 -0.00001 1.0 29 8 22 - 28 8 21 1620.49969 0.00027 1.0 30 8 22 - 29 8 21 1621.14545 -0.00029 1.0 31 10 22 - 30 10 21 1621.79191 0.00026 1.0 32 10 22 - 31 10 21 1622.43753 0.00039 1.0 33 12 22 - 32 12 21 1623.08147 -0.00072 0.5 34 12 22 - 33 12 21 1623.72659 -0.00022 1.0 23 0 23 - 22 0 22 1616.28288 0.00027 1.0 24 2 23 - 23 2 22 1616.93116 -0.00023 1.0 25 2 23 - 24 2 22 1617.57930 -0.00051 1.0 26 4 23 - 25 4 22 1618.22776 -0.00010 1.0 27 4 23 - 26 4 22 1618.87558 0.00005 1.0 28 6 23 - 27 6 22 1619.52277 -0.00003 1.0 29 6 23 - 28 6 22 1620.17005 0.00037 1.0 30 8 23 - 29 8 22 1620.81700 0.00085 1.0 31 8 23 - 30 8 22 1621.46230 0.00010 1.0 32 10 23 - 31 10 22 1622.10788 0.00005 1.0 33 10 23 - 32 10 22 1622.75357 0.00054 1.0 35 12 23 - 34 12 22 1624.04243 0.00034 1.0 24 0 24 - 23 0 23 1616.60077 0.00009 1.0 25 2 24 - 24 2 23 1617.24888 -0.00036 1.0 26 2 24 - 25 2 23 1617.89719 -0.00024 1.0 27 4 24 - 26 4 23 1618.54519 -0.00005 1 .0 28 4 24 - 27 4 23 1619.19215 -0.00052 1.0 29 6 24 - 28 6 23 1619.83970 0.00001 1.0 30 6 24 - 29 6 23 1620.48644 0.00013 1.0 31 8 24 - 30 8 23 1621.13344 0.00093 0.5 32 8 24 - 31 8 23 1621.77831 0.00002 1.0 34 10 24 - 33 10 23 1623.06868 0.00013 1.0 36 12 24 - 35 12 23 1624.35703 0.00002 1.0 25 0 25 - 24 0 24 1616.91852 0.00013 1.0 O b s e r v e d N o r m a l i s e d Wavenumber D e v i a t i o n Weight ( c m - 1 ) ( c n T 1 ) 26 2 2 5 - 25 2 24 1 6 1 7 . 5 6 6 6 2 - 0 . 0 0 0 1 1 1 . 0 27 2 2 5 - 2 6 2 24 1 6 1 8 . 2 1 4 4 0 - 0 . 0 0 0 2 9 1 . 0 28 4 2 5 - 27 4 24 1 6 1 8 . 8 6 2 2 6 - 0 . 0 0 0 0 0 1 .0 2 9 4 2 5 - 28 4 24 1 6 1 9 . 5 0 8 5 9 - 0 . 0 0 0 8 5 0 . 5 30 6 25 - 2 9 6 24 1 6 2 0 . 1 5 6 0 1 - 0 . 0 0 0 2 1 1 . 0 31 6 25 - 30 6 24 1 6 2 0 . 8 0 2 9 8 0 . 0 0 0 4 0 1 . 0 32 8 2 5 - 31 8 24 1 6 2 1 . 4 4 8 2 3 - 0 . 0 0 0 2 9 0 . 5 34 10 2 5 - 33 10 24 1 6 2 2 . 7 4 0 1 0 0 . 0 0 1 0 1 0 . 5 35 10 2 5 - 34 10 24 1 6 2 3 . 3 8 4 1 9 0 . 0 0 0 4 8 1 . 0 36 12 2 5 - 3 5 12 24 1 6 2 4 . 0 2 8 6 6 0 . 0 0 0 7 9 1 . 0 26 0 26 - 2 5 0 25 1 6 1 7 . 2 3 5 2 9 - 0 . 0 0 0 4 5 1 . 0 27 2 26 - 26 2 25 1 6 1 7 . 8 8 3 7 2 - 0 . 0 0 0 1 4 1 . 0 28 2 26 - 2 7 2 25 1 6 1 8 . 5 3 1 7 6 0 . 0 0 0 1 7 1 . 0 2 9 4 26 - 28 4 25 1 6 1 9 . 1 7 8 7 0 - 0 . 0 0 0 2 2 1 . 0 30 4 26 - 2 9 4 25 1 6 1 9 . 8 2 6 2 2 0 . 0 0 0 3 6 1 . 0 31 6 26 - 30 6 25 1 6 2 0 . 4 7 2 6 2 0 . 0 0 0 2 4 1 .0 32 6 26 - 31 6 25 1621 . 1 . 1 8 6 3 0 . 0 0 0 1 5 1 . 0 33 8 26 - 32 8 25 1 6 2 1 . 7 6 4 5 8 0 . 0 0 0 4 3 1 . 0 34 8 26 - 33 8 25 1 6 2 2 . 4 1 0 2 9 0 . 0 0 0 9 0 1 . 0 35 10 26 - 34 10 25 1 6 2 3 . 0 5 4 6 6 0 . 0 0 0 4 8 1 . 0 36 10 26 - 3 5 10 25 1 6 2 3 . 6 9 9 2 2 0 . 0 0 0 7 1 1 . 0 37 12 26 - 36 12 25 1 6 2 4 . 3 4 1 7 5 - 0 . 0 0 0 6 2 0 . 5 27 0 27 - 26 0 26 1 6 1 7 . 5 5 2 5 8 - 0 . 0 0 0 1 5 1 . 0 28 2 27 - 27 2 26 1 6 1 8 . 2 0 0 3 9 - 0 . 0 0 0 2 3 1 . 0 30 4 27 - 2 9 4 26 1 6 1 9 . 4 9 5 3 4 0 . 0 0 0 1 2 0 . 5 31 4 27 - 30 .4 26 1 6 2 0 . 1 4 2 0 8 0 . 0 0 0 1 7 1 . 0 32 6 27 - 31 6 26 1 6 2 0 . 7 8 8 8 8 0 . 0 0 0 7 0 0 . 5 33 6 27 - 32 6 26 1621 . 4 3 4 3 0 0 . 0 0 0 2 8 1 . 0 28 0 28 - 27 0 27 1 6 1 7 . 8 6 9 1 1 - 0 . 0 0 0 2 6 1 . 0 2 9 2 28 - 28 2 27 1 6 1 8 . 5 1 7 1 4 0 . 0 0 0 1 1 1 . 0 30 2 28 - 2 9 2 27 1 6 1 9 . 1 6 4 7 5 0 . 0 0 0 4 5 1 . 0 32 4 28 - 31 4 27 1 6 2 0 . 4 5 8 2 5 0 . 0 0 0 6 5 1 . 0 34 6 28 - 33 6 27 1 6 2 1 . 7 4 9 7 1 0 . 0 0 0 5 2 0 . 5 3 5 8 28 - 34 8 27 1 6 2 2 . 3 9 5 2 0 0 . 0 0 0 8 7 0 . 5 36 8 28 - 35 8 27 1 6 2 3 . 0 4 0 5 7 0 . 0 0 1 5 5 0 . 0 37 10 28 - 36 10 27 1 6 2 3 . 6 8 5 4 4 0 . 0 0 2 2 0 0 . 0 38 10 28 - 37 1 0 27 1 6 2 4 . 3 2 7 9 3 0 . 0 0 0 9 4 0 . 0 2 9 0 2 9 - 28 0 28 1 6 1 8 . 1 8 6 3 2 0 . 0 0 0 6 8 0 . 5 31 2 2 9 - 3 0 2 28 1 6 1 9 . 4 8 0 3 9 0 . 0 0 0 2 8 0 . 5 32 4 2 9 - 31 4 28 1 6 2 0 . 1 2 7 4 6 0 . 0 0 0 7 4 0 . 5 33 4 2 9 - 32 4 28 1 6 2 0 . 7 7 3 7 7 0 . 0 0 0 8 5 0 . 5 34 6 2 9 - 33 6 28 1 6 2 1 . 4 1 9 8 5 0 . 0 0 1 17 0 . 0 35 6 2 9 - 34 6 28 1 6 2 2 . 0 6 5 2 6 0 . 0 0 1 2 6 0 . 0 39 10 2 9 - 38 10 28 1 6 2 4 . 6 4 3 5 7 0 . 0 0 2 8 9 0 . 0 40 12 2 9 - 3 9 12 28 1 6 2 5 . 2 8 6 0 1 0 . 0 0 2 3 5 0 . 0 30 0 30 - 2 9 0 2 9 1 6 1 8 . 5 0 2 1 1 0 . 0 0 0 5 6 0 . 0 32 2 30 - 31 2 2 9 1 6 1 9 . 7 9 6 7 4 0 . 0 0 1 19 0 . 0 33 4 30 - 32 4 29 1 6 2 0 . 4 4 3 1 0 0 . 0 0 1 1 7 0 . 0 34 4 30 - 33 4 29 1 6 2 1 . 0 8 9 6 3 0 . 0 0 1 7 5 0 . 0 3 5 6 30 - 34 6 2 9 1 6 2 1 . 7 3 5 4 3 0 . 0 0 2 0 5 0 . 0 36 6 30 - 35 6 2 9 1 6 2 2 . 3 8 0 3 1 0 . 0 0 1 8 7 0 . 0 37 8 30 - 36 8 2 9 1 6 2 3 . 0 2 5 6 9 0 . 0 0 2 6 5 0 . 0 3 9 10 30 - 38 10 2 9 1 6 2 4 . 3 1 4 0 1 0 . 0 0 3 1 8 0 . 0 31 0 31 - 30 0 30 1 6 1 8 . 8 2 0 3 7 0 . 0 0 3 2 7 0 . 0 32 2 31 - -31 2 30 1619 .46854 0 . 0 0 4 4 6 0 . 0 33 2 31 - 32 2 30 1 6 2 0 . 1 1 6 2 0 0 . 0 0 5 5 6 0 . 0 34 4 31 - 33 4 30 1 6 2 0 . 7 6 2 9 8 0 . 0 0 6 2 1 0 . 0 3 5 4 31 - 34 4 30 1 6 2 1 . 4 0 9 5 7 0 . 0 0 7 1 0 0 . 0 36 6 31 - 3 5 6 30 1 6 2 2 . 0 5 5 4 3 0 . 0 0 7 7 1 0 . 0 39 8 31 - 38 8 30 1 6 2 3 . 9 8 9 7 1 0 . 0 0 9 0 1 0 . 0 40 10 31 - 3 9 10 30 1 6 2 4 . 6 3 3 6 9 0 . 0 0 9 6 2 0 . 0 41 10 31 - 4 0 10 30 1 6 2 5 . 2 7 6 6 0 0 . 0 0 9 6 5 0 . 0 N o r m a l i s e d O b s e r v e d J ' K a ' K c ' - J " K s " K e " Wavenumber D e v i a t i o n W e i g h t ( c m - 1 ) ( c m - 1 ) 33 2 32 - 32 2 31 1619.77745 -0.00158 0.0 34 2 32 - 33 2 31 1620.42337 -0.00198 0.0 35 4 32 - 34 4 31 1621.06865 -0.00259 0.0 36 4 32 - 35 4 31 1621.71346 -0.00323 0.0 37 6 32 - 36 6 31 1622.35763 -0.00405 0.0 38 6 32 - 37 6 31 1623.00096 -0.00526 0.0 39 8 32 - 38 8 31 1623.64302 -0.00726 0.0 40 8 32 - 39 8 31 1624.28581 -0.00804 0.0 34 2 33 - 33 2 32 1620.09305 -0.00057 0.0 35 2 33 - 34 2 32 1620.73902 -0.00069 0.0 36 4 33 - 35 4 32 1621.38413 -0.00122 0.0 37 4 33 - 36 4 32 1622.02880 -0.00175 0.0 39 6 33 - 38 6 32 1623.31682 -0.00273 0.0 40 8 33 - 39 8 32 1623.96018 -0.00316 0.0 41 8 33 - 40 8 32 1624.60333 -0.00331 0.0 34 0 34 - 33 0 33 1619.76108 -0.00048 1.0 35 2 34 - 34 2 33 1620.40740 -0.00045 1.0 36 2 34 - 35 2 33 1621.05327 -0.00042 1.0 37 4 34 - 36 4 33 1621.69855 -0.00054 0.5 38 4 34 - 37 4 33 1622.34329 -0.00074 0.5 39 6 34 - 38 6 33 1622.98678 -0.00173 0.0 40 6 34 - 39 6 33 1623.63147 -0.00104 0.0 41 8 34 - 40 8 33 1624.27381 -0.00222 0.0 35 0 35 - 34 0 34 1620.07519 -0.00047 1.0 36 2 35 - 35 2 34 1620.72176 0.00005 1.0 37 2 35 - 36 2 34 1621.36683 -0.00048 0.5 38 4 35 - 37 4 34 1622.01215 -0.00032 1.0 39 4 35 - 38 4 34 1622.65676 -0.00039 0.0 40 6 35 - 39 6 34 1623.29972 -0.00165 0.0 41 6 35 - 40 6 34 1623.94379 -0.00131 0.0 42 8 35 - 41 8 34 1624.58705 -0.00130 0.0 43 8 35 - 42 8 34 1625.22958 -0.00151 0.0 36 0 36 - 35 0 35 1620.38889 -0.00050 1.0 37 2 36 - 36 2 35 1621.03509 -0.0001 1 1.0 38 2 36 - 37 2 35 1621 .68107 0.00050 1.0 39 4 36 - 38 4 35 1622.32486 -0.00061 0.0 40 4 36 - 39 4 35 1622.96886 -0.00104 0.0 42 6 36 - 41 6 35 1624.25641 -0.00092 0.0 41 6 36 - 40 6 35 1623.61266 -0.00120 1.0 37 0 37 - 36 0 36 1620.70260 -0.00015 1.0 38 2 37 - 37 2 36 1621.34833 0.00000 1.0 39 2 37 - 38 2 36 1621.99305 -0.00040 1.0 40 4 37 - 39 4 36 1622.63748 -0.00063 1.0 41 4 37 - 40 4 36 1623.28162 -0.00066 1.0 38 0 38 - 37 0 37 1621.01538 -0.00036 1.0 39 2 38 - 38 2 37 1621.66084 -0.00025 1.0 41 4 38 - 40 4 37 1622.95074 0.00037 1.0 43 6 38 - 42 6 37 1624.23707 -0.00065 1 .0 44 6 38 - 43 6 37 1624.88004 -0.00061 1.0 39 0 39 - 38 0 38 1621.32850 0.00013 1.0 40 2 39 - 39 2 38 1621.97374 0.00026 1.0 41 2 39 - 40 2 38 1622.61799 -0.00012 1.0 43 4 39 - 42 4 38 1623.90537 -0.00056 1.0 44 6 39 - 43 6 38 1624.54860 -0.00050 1.0 45 6 39 - .44 6 38 1625.19169 -0.00006 1.0 46 8 39 - 45 8 38 1625.83349 -0.00040 1.0 40 0 40 - 39 0 39 1621.64058 -0.00005 1.0 41 2 40 - 40 2 39 1622.28565 0.00015 1.0 42 2 40 - 41 2 39 1622.92955 -0.00034 1.0 44 4 40 - 43 4 39 1624.21725 0.00005 1.0 41 0 41 - 40 0 40 1621.95258 0.00006 1.0 43 2 41 - 42 2 40 1623.24142 0.00013 1.0 222 O b s e r v e d N o r m a l i s e d J ' - J " K c " Wavenumber D e v i a t i o n We i g ' ( c m " 1 ) ( c m ' 1 ) 44 4 41 - 43 4 40 1623.88416 -0.00078 1.0 45 4 41 - 44 4 40 1624.52847 0.00038 1.0 46 6 41 - 45 6 40 1625.17085 0.00013 1.0 47 6 41 - 46 6 40 1625.81239 -0.00045 1.0 42 0 42 - 41 0 41 1622.26400 -0.00005 1.0 43 2 42 - 42 2 41 1622.90866 0.00023 1 .0 45 4 42 - 44 4 41 1624.19558 -0.00014 1 .0 46 4 42 - 45 4 41 1624.83828 -0.00033 1.0 43 0 43 - 42 0 42 1622.57502 -0.00018 1 .0 d i f f e r e n c e b e t w e e n the o b s e r v e d and c a l c u l a t e d f r e q u e n c i e s and a r e r e l a t i v e l y s m a l l (<= 0 . 0 1 c m - 1 ) , were f o u n d to be r o u g h l y p r o p o r t i o n a l t o [ J ( J + 1 ) - K c ( K c l l ) ] 1 f o r v a l u e s o f K c = 29 to 33 . F o r a m o l e c u l e w i t h C 2 v s ymmetry t h i s means t h a t : Tu2 ( A , ) x r ( p e r t u r b i n g , = A 2 o r B , ( 7 . 5 ) T h e r e f o r e t h e p e r t u r b i n g mode must h a v e t h e s y m m e t r y s p e c i e s A 2 o r B1. F u r t h e r m o r e , t h e d i r e c t i o n o f t h e s h i f t s i n d i c a t e t h a t i t i s a A K C = -1 i n t e r a c t i o n w i t h a mode l y i n g j u s t b e l o w the uz f u n d a m e n t a l . A r o u g h e s t i m a t e o f the f r e q u e n c y o f t h e p e r t u r b i n g mode was made. The l e v e l w i t h t h e l a r g e s t s h i f t ( K 0 = 31) was a s s u m e d to l i e e q u a l i n e n e r g y to t h e l e v e l w i t h K c = 30 i n t h e p e r t u r b i n g mode f o r the same v a l u e o f J ( s ee F i g u r e 7 . 6 ) . When s y m m e t r i c t o p r i g i d r o t o r e n e r g i e s a r e a s sumed and t h e r o t a t i o n a l c o n s t a n t s a r e t a k e n to be t h e same f o r b o t h 223 21 level per tu rb ing level K c K 29 28 ^ 30 29 cn CD LU 3! 30 > 1 32 31 rr 33 32 •34 33 F i g u r e 7 .6 R e l a t i v e p o s i t i o n s o f t h e K s t a c k s o f t h e 2 1 and p e r t u r b i n g l e v e l f o r a p a r t i c u l a r v a l u e o f J . 2 2 4 l e v e l s , t h e p e r t u r b i n g l e v e l i s f o u n d to l i e b e l o w t h e 2 1 l e v e l b y : T ( i / 2 ) - T ( i / p ) « [ J - ( A + B ) - C ] [ ( 3 1 ) 2 - ( 3 0 ) 2 ] ( 7 . 6 ) = 1 0 c m " 1 The p e r t u r b i n g l e v e l c a n n o t be a f u n d a m e n t a l : t h e s h i f t s a r e too s m a l l , t h e r e a r e no b a n d s o v e r l a p p i n g vz and i t i s h i g h l y u n l i k e l y t h a t t h e t o r s i o n w i l l l i e a t s u c h a h i g h f r e q u e n c y . A l s o , s i n c e i t c a n n o t be an o v e r t o n e , w h i c h w o u l d h a v e symmetry kx , i t must t h e r e f o r e be a c o m b i n a t i o n l e v e l . U n f o r t u n a t e l y , b e c a u s e n o t a l l t h e f r e q u e n c i e s o f t h e f u n d a m e n t a l s h a v e b e e n i d e n t i f i e d , i t i s u n c e r t a i n w h i c h c o m b i n a t i o n o f f u n d a m e n t a l s p r o d u c e s t h e p e r t u r b a t i o n . One p o s s i b i l i t y , a l t h o u g h u n l i k e l y b e c a u s e i t w o u l d l i e a t t o o low a f r e q u e n c y i s 2 i / 5 + u7 ( = 1 5 4 0 c m - 1 ) w h i c h h a s Bj^  s y m m e t r y . U s i n g t h e c a l c u l a t e d f r e q u e n c i e s ( 1 2 ) f o r b a n d s w h i c h h a v e n o t y e t b e e n i d e n t i f i e d ( s ee T a b l e 7 . 1 ) , o t h e r p o s s i b i l i t i e s f o r t h e p e r t u r b i n g c o m b i n a t i o n b a n d a r e v4 + i / ? a n d i / 7 + i / n w h i c h h a v e Bx and A 2 s y m m e t r i e s r e s p e c t i v e l y . The l a t t e r i s more l i k e l y as t h e c a l c u l a t e d f r e q u e n c i e s a r e h i g h when c o m p a r e d to t h e c o r r e s p o n d i n g e x p e r i m e n t a l f r e q u e n c i e s . 7 . 5 D i s c u s s i o n F o r t h e f i r s t t i m e , t h e i n f r a - r e d s p e c t r u m o f B F 2 N H 2 has b e e n i n v e s t i g a t e d . The wavenumbers o f 7 o f t h e 1 1 i n f r a - r e d a c t i v e f u n d a m e n t a l s h a v e b e e n e v a l u a t e d . The o t h e r f u n d a m e n t a l s 225 may have been t o o weak to d e t e c t , e s p e c i a l l y s i n c e o n l y a low v a p o u r p r e s s u r e o f B F 2 N H 2 c o u l d be m a i n t a i n e d , or t h e y may have b e e n o b s c u r e d by o t h e r bands, p a r t i c u l a r l y bands o f t h e i m p u r i t y d i e t h y l e t h e r . I n a d d i t i o n , one o f the f u n d a m e n t a l s , the 2j band, has been examined i n g r e a t e r d e t a i l and the r o t a t i o n a l 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 f o r the g r o u n d and t h e f i r s t e x c i t e d s t a t e have been c a l c u l a t e d . 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 o r the g r o u n d s t a t e were i m p r o v e d i n a c c u r a c y o v e r t h o s e c a l c u l a t e d s o l e l y from microwave t r a n s i t i o n s ( 6 ) . T h e r e i s a l s o a s m a l l C o r i o l i s p e r t u r b a t i o n i n t h i s band; i t i s u n c e r t a i n w h i c h c o m b i n a t i o n band i s c a u s i n g the p e r t u r b a t i o n , t h o u g h i t i s l i k e l y to be u7 + i / u . T h i s l e v e l i s e s t i m a t e d to l i e =10 c m - 1 below the 2 1 l e v e l w h i c h w o u l d mean t h a t the f r e q u e n c y o f vlx i s =937 c m - 1 . 226 B i b l i o g r a p h y 1. M.C.L. G e r r y , W. L e w i s - B e v a n , A . J . M e r e r , N.P.C. Westwood, J . M o l . S p e c t r o s c . 110, 153-163, ( 1 9 8 5 ) . 2. A.W. L a u b e n g a y e r , G.F. C o n d i k e , J . Am. Chem. Soc. 7_0, 2274-2276, ( 1 9 4 8 ) . 3. I.G. R y s s , N.G. Parkhomenko, Russ. J . I n o r g . Chem. (Eng. T r a n s l . ) 11_, 55 - 59 (1966) 4. E.F. R o t h g e r y , H.A. McGee, J r . , S. P u s a t c i o g l u , I n o r g . Chem. L4, 2236-2239, ( 1 9 7 5 ) . 5. S.Y. P u s a t c i o g l u , H.A. McGee J r . , A.L. F r i c k e , J.C. H a s s l e r , J A p p l . Polym. S c i . 2JL, 1561- 1567, ( 1 9 6 7 ) . 6. F . J . L o v a s , D.R. J o h n s o n , J . Chem. Phys. 59., 2347 - 2353, ( 1973 ). 7. H.J. B e c h e r , "Handbook o f P r e p a r a t i v e I n o r g a n i c C h e m i s t r y " , Ed. G. B r a u e r . , V o l . 1., Ac a d e m i c , New Y o r k , 1963. 8. G. H e r z b e r g . " I n f r a r e d and Raman S p e c t r a o f P o l y a t o m i c M o l e c u l e s " , pp. 469-484, Van N o s t r a n d , New Y o r k , 1945. 9. Work i n p r o g r e s s a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r . 10. M. P e r e c , L.N. Becka, J . Chem. Phys., 43., 721 - 727 ( 1 9 6 5 ) . 11. A.G. R o b i e t t e , M.C.L. G e r r y , J . M o l . S p e c t r o s c . 80_, 403-410 (1980) . 12. T.-K. Ha, J . M o l . S t r u c t . (Theochem) 136. 165-176, ( 1 9 8 6 ) . 13 W. L e w i s - B e v a n , A . J . Mer e r , M.C.L. G e r r y , P.B. D a v i e s , A . J M o r t o n - J o n e s , P.A. H a m i l t o n , J . M o l . S p e c t r o s c . 113. 458 -471, ( 1 9 8 5 ) . 

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