UBC Theses and Dissertations

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UBC Theses and Dissertations

Vibrations of some aromatic molecules Kydd, Ronald Andrew 1969

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5 v o 2 -THE VIBRATIONS OF SOME AROMATIC MOLECULES b y RONALD ANDREW KYDD B . S c . ( H o n s . ) , 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 , 1963 A THESIS SUBMITTED I N PAR T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e D e 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 a s 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 B R I T I S H COLUMBIA O c t o b e r , 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C olumbia, I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and Study. I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y p u rposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n of t h i s thes.is f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada ABSTRACT The i n f r a r e d s p e c t r a o f s i n g l e c r y s t a l s o f n a p h -t h a l e n e - d g , a n t h r a c e n e - h ^ g a n d a n t h r a c e n e - d ^ g a r e r e p o r t e d w i t h t h e p l a n e o f t h e i n c i d e n t r a d i a t i o n p a r a l l e l t o a l l t h r e e p r i n c i p a l o p t i c a l d i r e c t i o n s o f t h e c r y s t a l s . The p o l a r i z e d m e a s u r e m e n t s e x t e n d down t o 50 cm"'*' and a l l l o w -e n e r g y i n f r a r e d - a c t i v e m o l e c u l a r v i b r a t i o n s a n d many l a t t i c e v i b r a t i o n s h a v e b e e n a s s i g n e d . The l a s e r - e x c i t e d Raman s p e c t r a o f s i n g l e c r y s t a l s o f n a p h t h a l e n e - d g a n d a n t h r a c e n e -d^Q a l s o a r e r e p o r t e d a n d t h i s d a t a was s u p p l e m e n t e d b y d e -p o l a r i z a t i o n r a t i o m e a s u r e m e n t s f r o m s o l u t i o n a n d f r o m t h e m e l t . W i t h t h e new i n f o r m a t i o n a v a i l a b l e f r o m t h e s e s t u d i e s a r e - e v a l u a t i o n o f t h e a s s i g n m e n t s o f t h e m o l e c u l a r f u n d a -m e n t a l s o f t h e s e t h r e e m o l e c u l e s h a s b e e n made. When t h e l i s t o f f u n d a m e n t a l s was as c o m p l e t e as p o s s i b l e , a t t e n t i o n was d i r e c t e d t o t h e f o r c e f i e l d s . The o u t - o f - p l a n e f i e l d o f b e n z e n e was r e c o n s i d e r e d , a n d t h e assump t i o n t h a t i n t e r a c t i o n c o n s t a n t s s h o u l d be as s m a l l as p o s s i b l e was c o m p l e t e l y s u p p o r t e d . T r a n s f e r o f t h e s e f o r c e c o n s t a n t s t o n a p h t h a l e n e was s u c c e s s f u l ; h o w e v e r , i t p r o v e d t o be i m p o s s i b l e t o f i t a l l t h e o b s e r v e d n o n - p l a n a r f r e q u e n c i e s o f a n t h r a c e n e w i t h t h e f o r c e c o n s t a n t s d e v e l o p e d f o r b e n z e n e . An i n - p l a n e m o d i f i e d v a l e n c e f o r c e f i e l d d e s i g n e d f o r b e n z e n e was e x t e n d e d t o n a p h t h a l e n e and a n t h r a c e n e and r e f i n e d t o f i t s i m u l t a n e o u s l y t h e o b s e r v e d f r e q u e n c i e s o f a l l t h r e e m o l e c u l e s a n d t h e i r t h r e e p e r d e u t e r a t e d a n a l o g u e s . The r e s u l t s w e r e c o m p a r e d w i t h t h e r e s u l t s o f a s i m i l a r c a l c u l a t i o n c a r r i e d o u t by N e t o , S c r o c c o and C a l i f a n o and p r e s e n t e d e l s e w h e r e , and c e r t a i n d i f f e r e n c e s w e r e n o t e d , p a r t i c u l a r l y i n t h e a n t h r a c e n e - h ^ g and -d-^g r i n g modes. I n o r d e r t o f i n d o u t how w e l l f o r c e f i e l d s d e v e l o p e d f o r t h e s e m o l e c u l e s w o u l d t r a n s f e r t o r e l a t e d b u t l e s s s i m i l a r m o l e c u l e s , t h e v i b r a t i o n s o f p y r e n e and a c e n a p h t h e n e w e r e c o n s i d e r e d . The i n f r a r e d s p e c t r a o f s i n g l e c r y s t a l s o f p y r e n e -h ^ g , p y r e n e - d ^ g a n d a c e n a p h t h e n e w e r e m e a s u r e d , w i t h empha-s i s on t h e l o w - f r e q u e n c y r e g i o n s n o t p r e v i o u s l y s t u d i e d . The d a t a o b t a i n e d w e r e s u p p l e m e n t e d b y Raman m e a s u r e m e n t s c a r r i e d o u t by o t h e r s i n t h i s l a b o r a t o r y and f a i r l y c o m p l e t e a s s i g n m e n t s o f t h e n o r m a l v i b r a t i o n s w e r e p o s s i b l e . The f u n d a m e n t a l f r e q u e n c i e s o f t h e s e m o l e c u l e s w e r e c a l c u l a t e d w i t h f o r c e f i e l d s s y n t h e s i z e d f r o m t h e two p l a n a r f i e l d s men-t i o n e d e a r l i e r a nd f r o m t h e o u t - o f - p l a n e f i e l d s o f b e n z e n e and ( f o r a c e n a p h t h e n e ) c y c l o p e n t a n e . C o m p a r i s o n o f t h e 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 showed t h a t a l t h o u g h some f a i r l y l a r g e d i s c r e p a n c i e s d i d a r i s e , t h e y w e r e f e w i n number a n d l o c a t e d o n l y i n t h e r e g i o n o f t h e r i n g s t r e t c h i n g i v v i b r a t i o n s ( a b o v e a b o u t 1200 cm "*") . The f i t t o t h e f u n d a -m e n t a l s b e l o w t h a t e n e r g y was m o s t e n c o u r a g i n g , and i n d i -c a t e d t h a t t h e t r a n s f e r o f f o r c e c o n s t a n t s f r o m one m o l e c u l e t o a n o t h e r i n o r d e r t o c a l c u l a t e a p p r o x i m a t e f r e q u e n c i e s was c e r t a i n l y p o s s i b l e . TABLE OF CONTENTS CHAPTER PAGE I . GENERAL INTRODUCTION 1 A. G e n e r a l O u t l i n e 1 1. H i s t o r i c a l B a c k g r o u n d 1 2. A i m o f T h e s i s 7 B. The A s s i g n m e n t o f F u n d a m e n t a l s 8 1. V i b r a t i o n s o f M o l e c u l e s . . 8 2. Symmetry I n f o r m a t i o n f r o m V a p o r , S o l u t i o n and M e l t S p e c t r a 10 a) Symmetry a s s i g n m e n t s f r o m Raman s p e c t r a 11 b) Symmetry a s s i g n m e n t s f r o m v a p o r -p h a s e b a n d c o n t o u r s 12 3. Symmetry I n f o r m a t i o n f r o m C r y s t a l S p e c t r a . 14 a) The o r i e n t e d g a s m o d e l . 14 b) S i n g l e c r y s t a l f l u o r e s c e n c e and p h o s p h o r e s c e n c e . . 16 c) L i m i t a t i o n s o f t h e o r i e n t e d g a s m o d e l . 20 d) The i n t e r a c t i o n o f p l a n e p o l a r i z e d l i g h t w i t h a s i n g l e c r y s t a l . . . . 25 4. C h o o s i n g F u n d a m e n t a l s f r o m t h e Symmetry A s s i g n e d L i n e s . . 28 I I . EXPERIMENTAL . 30 A. P r e p a r a t i o n o f S a m p l e s . 30 1. S o u r c e o f C h e m i c a l s 30 a) N a p h t h a l e n e 30 b) A n t h r a c e n e 30 c) A c e n a p h t h e n e 31 d) P y r e n e . 31 e) S o l v e n t s . 31 v v i CHAPTER PAGE 2. Growth of S i n g l e C r y s t a l s 3 1 B. Spectrometers and Accessories . . 3 3 C. C r y s t a l Data and O p t i c a l P r o p e r t i e s 3 5 1. Naphthalene 35 2. Anthracene 36 3. Acenaphthene 36 4. Pyrene . 39 I I I . THE VIBRATIONS OF NAPHTHALENE 41 A. I n t r o d u c t i o n . . . . . . 41 1. C r i t i c a l Review 41 2. S e l e c t i o n Rules . 42 B. Results 46 1. The Raman Spectra 46 2. The I n f r a r e d Spectra . . . . . 53 C. Assignment of Fundamentals 6 1 1. L a t t i c e V i b r a t i o n s 6 1 2. Raman-active Molecular V i b r a t i o n s . . . . 6 1 3. I n f r a r e d - a c t i v e Molecular V i b r a t i o n s . . 65 ' IV. THE VIBRATIONS OF ANTHRACENE 72 A. I n t r o d u c t i o n 72 1., C r i t i c a l Review 72 2. S e l e c t i o n Rules 73 B. Results 78 v i i CHAPTER PAGE 1. A n t h r a c e n e - h ^ Q I n f r a r e d S p e c t r a a n d A s s i g n m e n t 7 8 a) S p e c t r a . 78 b) A s s i g n m e n t 89 2. A n t h r a c e n e - d ^ g I n f r a r e d S p e c t r a a n d A s s i g n m e n t 99 a) S p e c t r a 99 b) A s s i g n m e n t 106 3. A n t h r a c e n e - d 1 Q Raman S p e c t r u m a nd A s s i g n m e n t . . . . . . 117 a) S p e c t r a . 117 ^ b) A s s i g n m e n t 123 V. CALCULATIONS 128 A. M o l e c u l a r V i b r a t i o n s 128 1. M o t i o n i n C a r t e s i a n C o o r d i n a t e s . . . . . 129 2. M o t i o n i n G e n e r a l i z e d C o o r d i n a t e s . . . . 131 3. M o t i o n i n N o r m a l C o o r d i n a t e s . . . . . . 132 4. M o t i o n i n I n t e r n a l C o o r d i n a t e s 133 5. M o t i o n i n Symmetry C o o r d i n a t e s 135 B. O u t - o f - P l a n e F o r c e F i e l d f o r A r o m a t i c M o l e c u l e s 136 1. B e n z e n e 137 a) Symmetry f o r c e c o n s t a n t s 137 b) I n t e r n a l v a l e n c e - c o o r d i n a t e f o r c e c o n s t a n t s . . . . . . . . . . . 139 2. N a p h t h a l e n e 143 3. A n t h r a c e n e . . 147 4. D i s c u s s i o n o f R e s u l t s 150 v i i i CHAPTER PAGE C. P l a n a r F o r c e F i e l d f o r A r o m a t i c M o l e c u l e s . 152 1. The N e t o , S c r o c c o a n d C a l i f a n o F i e l d . . 153 2. The D u i n k e r - M i l l s F i e l d . . . , 154 3. R e f i n e m e n t o f t h e D u i n k e r - M i l l s F i e l d . . 155 4. R e s u l t s o f t h e R e f i n e m e n t . . . . . , . . 1 6 5 a) N a p h t h a l e n e - d g 173 b) Anthracene-h-^Q. 174 c) A n t h r a c e n e - d i o 175 5. C o n c l u s i o n s 176 V I . THE VIBRATIONS OF PYRENE 179 A. I n t r o d u c t i o n 179 1. C r i t i c a l R e v i e w 179 2. S e l e c t i o n R u l e s . . . . . . . 180 B. R e s u l t s 183 C. C a l c u l a t i o n o f F u n d a m e n t a l s 191 D. A s s i g n m e n t 195 E. C o n c l u s i o n 201 1. O u t - o f - P l a n e A s s i g n m e n t 201 2. I n - p l a n e A s s i g n m e n t 202 V I I . THE VIBRATIONS OF ACENAPHTHENE . . . . . . . . . 203 A. I n t r o d u c t i o n .' . 203 1. C r i t i c a l R e v i e w . . . . . . . 203 2. S e l e c t i o n R u l e s . . 204 B. R e s u l t s 207 i x CHAPTER PAGE C. C a l c u l a t i o n o f F u n d a m e n t a l s 214 D. A s s i g n m e n t 221 1. A^ S p e c i e s 221 2. B 1 S p e c i e s 221 3. B 2 S p e c i e s 222 4. A 2 S p e c i e s 225 E. D i s c u s s i o n 225 V I I I . CONCLUSION . . 227 REFERENCES 233 APPENDIX 240 LIST OF TABLES TABLE PAGE 1. C o r r e l a t i o n t a b l e f o r naphthalene 43 2. The oriented-gas p r e d i c t i o n s of the r e l a t i v e i n t e n s i t i e s of free-molecule Raman l i n e s of naphthalene i n various c r y s t a l c o n f i g u r a t i o n s . . 45 3. The oriented-gas p r e d i c t i o n s of the r e l a t i v e i n t e n s i t i e s of the i n f r a r e d a c t i v e l i n e s of naphthalene along v a r i o u s c r y s t a l axes. . . . . . 46 4. The Raman sp e c t r a near the e x c i t i n g l i n e from c r y s t a l s of naphthalene-dg 50 5. R e l a t i v e l i n e strengths i n the Raman sp e c t r a of naphthalene-dg above 150 cm - 1 51 6. The i n f r a r e d spectrum of naphthalene-dg 57 7. The i n f r a r e d spectrum of naphthalene-h g at low energy 60 8. Planar fundamental v i b r a t i o n s of Naphthalene-dg . 69 9. Non-planar fundamental v i b r a t i o n s of Naphthalene-dg 70 10. C o r r e l a t i o n t a b l e f o r anthracene . 75 11. The oriented-gas p r e d i c t i o n s of the r e l a t i v e i n t e n s i t i e s of the free-molecule Raman l i n e s of anthracene i n various c r y s t a l c o n f i g u r a t i o n s . . . 76 12. The oriented-gas p r e d i c t i o n s of the r e l a t i v e i n t e n s i t i e s of the i n f r a r e d - a c t i v e l i n e s of anthracene along various c r y s t a l axes 77 13. The i n f r a r e d spectrum of anthracene-h^ Q^ 85 14. The a n a l y s i s of the weak i n f r a r e d l i n e s of anthracene-h^g below 600 cm - 1 94 15. The assigned i n f r a r e d - a c t i v e fundamentals of anthracene-h^Q 98 16. The p o l a r i z e d i n f r a r e d spectrum of anthracene-d^Q 107 x x i TABLE ' PAGE 17 . A t e n t a t i v e a s s i g n m e n t o f t h e weak l o w - e n e r g y l i n e s o f a n t h r a c e n e - d ^ g . . . . . . . I l l 1 8 . The a s s i g n e d 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 o f a n t h r a c e n e - d ^ Q . . . . . . . . . 118 19 . The Raman s p e c t r u m o f a n t h r a c e n e - d ^ g 119 20 . The a s s i g n e d R a m a n - a c t i v e f u n d a m e n t a l s o f a n t h r a c e n e 125 2 1 . O u t - o f - P l a n e f o r c e c o n s t a n t s f o r b e n z e n e i n s y m m e t r y c o o r d i n a t e s . . . . . . . . . . . . . . . 138 22. R e l a t i o n s h i p b e t w e e n s y m m e t r y a n d i n t e r n a l c o o r d i n a t e f o r c e c o n s t a n t s f o r b e n z e n e 140 2 3 . The o u t - o f - p l a n e f o r c e c o n s t a n t s o f b e n z e n e , i n mdyn A / r a d i a n ^ . 142 24. O b s e r v e d a nd c a l c u l a t e d n o n - p l a n a r f r e q u e n c i e s o f n a p h t h a l e n e - h g 145 25 . O b s e r v e d a n d c a l c u l a t e d n o n - p l a n a r f r e q u e n c i e s o f n a p h t h a l e n e - d g 146 26. O b s e r v e d a n d c a l c u l a t e d n o n - p l a n a r f r e q u e n c i e s o f a n t h r a c e n e - h ^ g . . . . . 148 27. O b s e r v e d a n d c a l c u l a t e d n o n - p l a n a r f r e q u e n c i e s o f a n t h r a c e n e - d ^ g 149 •28. I n i t i a l a n d f i n a l f o r c e c o n s t a n t s f o r p l a n a r f o r c e - f i e l d . . 162 29. The o b s e r v e d a n d c a l c u l a t e d p l a n a r f r e q u e n c i e s o f b e n z e n e , n a p h t h a l e n e a nd a n t h r a c e n e . . . . . . 166 30. C o r r e l a t i o n t a b l e f o r P y r e n e . 181 3 1 . The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s o f t h e i n f r a r e d a c t i v e l i n e s o f p y r e n e a l o n g v a r i o u s c r y s t a l a x e s . 182 . 3 2 . The l o w - f r e q u e n c y i n f r a r e d s p e c t r a o f p y r e n e - h i n a n d p y r e n e - d , n . . . . . . . . . . . . . . 187 x i i TABLE PAGE 33. O b s e r v e d a n d c a l c u l a t e d u - f u n d a m e n t a l s o f p y r e n e 196 34. O b s e r v e d a n d c a l c u l a t e d g - f u n d a m e n t a l s o f p y r e n e 198 35. C o r r e l a t i o n t a b l e f o r a c e n a p h t h e n e 205 36. The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s o f t h e i n f r a r e d - a c t i v e l i n e s o f a c e n a p h t h e n e a l o n g v a r i o u s c r y s t a l a x e s 206 37. The l o w - e n e r g y i n f r a r e d s p e c t r u m o f a s o l u t i o n o f a c e n a p h t h e n e i n b e n z e n e a n d o f a n a c s e c t i o n o f a n a c e n a p h t h e n e c r y s t a l 211 38. F o r c e c o n s t a n t s f o r a c e n a p h t h e n e c a l c u l a t i o n . . . 219 39. The A^ a n d f u n d a m e n t a l s o f a c e n a p h t h e n e . . . . 2 2 3 40. The a n d B^ f u n d a m e n t a l s o f a c e n a p h t h e n e . . . . 224 4 1 . The o u t - o f - p l a n e symmetry c o o r d i n a t e s o f b e n z e n e . 245 LIST OF FIGURES FIGURE PAGE 1. The aromatic molecules s t u d i e d 9 2. T y p i c a l appearance of type A, B, and C contours f o r an asymmetric r o t o r 13 3. The ab face of a monoclinic c r y s t a l showing the o r i e n t a t i o n of the axes X, Y, Z_ of the i n d i c a t r i x . . 26 4. The anthracene u n i t c e l l 37 5. The acenaphthene u n i t c e l l 38 6. The pyrene u n i t c e l l 39 7. The Raman spectr a obtained from the ac face of naphthalene-dg 47 8. The Raman sp e c t r a obtained from the ab and be' faces of naphthalene-dg . 48 9. Naphthalene-dg i n f r a r e d s p e c t r a above 600 cm ^. . 54 10. Naphthalene-dg low-energy c r y s t a l i n f r a r e d s p e c t r a 56 11. Naphthalene-d_ i n benzene s o l u t i o n low-energy i n f r a r e d spectrum 56 12. Naphthalene-hg low-energy c r y s t a l i n f r a r e d s p e c t r a . 59 13. Anthracene-h.. _ low-frequency i n f r a r e d spectrum; ab face . . 79 14. Anthracene-h,_ low-frequency i n f r a r e d spectrum; be' face. . 7 80 15. Anthracene-h.^ low-frequency i n f r a r e d spectrum; ac face 81 x i i i x i v FIGURE PAGE 16. Anthracene-h^ 0 i n f r a r e d s p e c t r a dDOve 400 cm . . 82 17. Anthracene-d, n low-frequency i n f r a r e d spectrum; ab face 100 18. Anthracene-d, n low-frequency i n f r a r e d spectrum; be' face. . 101 19. Anthracene-d.^ low-frequency i n f r a r e d spectrum; ac face 102 20. Anthracene-d^Q i n f r a r e d spectrum above 500 cm ^; ab face 103 21 . Anthracene-d, n i n f r a r e d spectrum above 500 cm "*"; be' face. . 104 22. Anthracene-d 1 Q i n f r a r e d spectrum above 500 cm 1 ; ac face 105 23. The low-frequency Raman spectrum of p o l y c r y s t a l -l i n e anthracene-d.^ at temperatures near the melti n g p o i n t 122 24. Non-planar i n t e r n a l valence coordinates f o r naphthalene . . . . . . . . . . . . . 1 4 4 25. Non-planar i n t e r n a l valence coordinates f o r anthracene . 1 4 7 26. The planar i n t e r n a l coordinates of benzene. . . . 158 27. The planar i n t e r n a l coordinates of naphthalene. . 159 28. The planar i n t e r n a l coordinates of anthracene . . 160 29. The low-frequency i n f r a r e d s p e c t r a of pyrene-h.^. 184 30. The low-frequency i n f r a r e d s p e c t r a of pyrene-d^g. 186 31. The i n t e r n a l coordinates of pyrene 193 32. The i n f r a r e d s p e c t r a of an ac s e c t i o n of acenaphthene about 45 microns t h i c k 20 8 X V FIGURE PAGE 33. The l o w - f r e q u e n c y i n f r a r e d s p e c t r u m o f a c e n a p h t h e n e i n b e n z e n e s o l u t i o n . . . . . . . . . 210 34. The i n t e r n a l c o o r d i n a t e s o f a c e n a p h t h e n e . . . . . 2 1 6 35 . The a r r a n g e m e n t o f atoms u s e d t o d e f i n e an o u t - o f - p l a n e wag 241 36. The a r r a n g e m e n t o f atoms u s e d t o d e f i n e a t o r s i o n 241 37. The o u t - o f - p l a n e i n t e r n a l c o o r d i n a t e s o f b e n z e n e 242 ACKNOWLEDGMENT I am extremely g r a t e f u l to Dr. A. Bree f o r h i s continued i n t e r e s t and support throughout the course of my graduate s t u d i e s . I would a l s o l i k e to express my appre-c i a t i o n to Dr. R.D. Sp r a t l e y f o r h i s v a l u a b l e a s s i s t a n c e and to other f a c u l t y members and students f o r many h e l p f u l d i s c u s s i o n s . CHAPTER I GENERAL INTRODUCTION A. General O u t l i n e 1. H i s t o r i c a l Background Much work has been done r e c e n t l y to determine the fundamental v i b r a t i o n a l frequencies of aromatic molecules. For benzene and many of i t s deuterated d e r i v a t i v e s , the two 1 2 monumental st u d i e s by Ingold et a l . ' provide almost com-p l e t e assignments. Two c o r r e c t i o n s , f i r s t suggested by Mair 3 4 and Hornig, were confirmed by M i l l e r and by Brodersen and 5 Langseth and are now g e n e r a l l y accepted. Recent s t u d i e s of the i n f r a r e d ^ and Raman^'^' spectra of naphthalene have l e d to a f a i r l y complete understanding of the funda-mental v i b r a t i o n s of naphthalene-hg and a somewhat l e s s c e r t a i n assignment f o r naphthalene-dg. The s i x t y - s i x funda-mental modes of anthracene are known w i t h even l e s s c e r t a i n t y , 15-19 despite much a c t i v e i n t e r e s t i n i t s i n f r a r e d and 14,20-23 Raman ' spe c t r a . The aim of most of t h i s work has been to provide an experimental b a s i s from which c a l c u l a t i o n s can be c a r r i e d 1 2 out to determine a fo r c e f i e l d f o r these aromatic molecules. However, the most general q u a d r a t i c force f i e l d c o n t a i n s , except f o r very simple molecules, more for c e constants than fundamental frequencies. Even when the problem i s reduced to i t s s i m p l e s t form by the use of symmetry coordinates, the number of fundamental v i b r a t i o n s i s not s u f f i c i e n t to de t e r -mine even the symmetry for c e constants e x a c t l y , and approxi-mate p o t e n t i a l f u n c t i o n s must be used. Workers i n the So v i e t Union have tended to use com-p l i a n c e matrices r a t h e r than f o r c e constants f o r the c a l c u -l a t i o n of fundamental v i b r a t i o n s . A compliance matrix i s the inverse of a for c e constant matrix and the element of a compliance matrix connecting any coordinate p a i r has the u s e f u l property t h a t i t i s i n v a r i a n t to any changes i n d e f i -24 n i t i o n of the other i n t e r n a l coordinates. Since f o r c e constants do not have t h i s property, i t would appear t h a t compliance constants are more s u i t e d f o r t r a n s f e r r i n g between 24 molecules. However, Cyvin et a l . have r e c e n t l y shown t h a t i n p r a c t i c e the two methods are roughly e q u i v a l e n t , each having some disadvantages. In p a r t i c u l a r , the compliance method r e q u i r e s t h a t a complete set of i n t e r n a l coordinates be set up i n v o l v i n g no redundancies, and t h i s i s o f t e n awkward with the f a i r l y symmetric aromatic molecules t o be considered. Thus i n t h i s work only the force constant approach i n which redundant coordinates are more e a s i l y t r e a t e d w i l l be used. 3 Three b a s i c types of approximate force f i e l d may be considered; the c e n t r a l force f i e l d , the valence f o r c e f i e l d 25 and the Urey-Bradley force f i e l d . The c e n t r a l f o r c e f i e l d assumes t h a t the forces h o l d i n g atoms i n t h e i r e q u i l i b r i u m p o s i t i o n s e x i s t between every p a i r of atoms and act along the l i n e j o i n i n g t h a t p a i r . When the i n t e r n a l coordinate system i s chosen to be the complete set of i n t e r a t o m i c . d i s t a n c e s , the f o r c e constant matrix i s diagonal. This approximation, which would be true i f the atoms of a molecule were held together only by i o n i c a t t r a c t i o n s , has met w i t h l i t t l e success. The simple valence force f i e l d considers only those forces i n v o l v e d i n the s t r e t c h i n g or t o r s i o n of valance bonds and the bending of valence angles; forces between non-bonded atoms are not considered, nor are i n t e r a c t i o n constants be-tween bonds. The Urey-Bradley f i e l d i s a valence force f i e l d to which have been added some c e n t r a l f o r c e terms as diagonal elements. Of great i n t e r e s t from a chemical viewpoint i s the modified valence force f i e l d , s i nce i t describes the forces i n terms of i n t e r n a l co-ordinates t h a t have chemical s i g n i f i -cance. In t h i s type of f i e l d , i n t e r a c t i o n constants between some i n t e r n a l coordinates are taken i n t o account; t h i s amounts to c o n s i d e r i n g the change i n s t i f f n e s s of one bond or angle r e s u l t i n g from the d i s t o r t i o n of other bonds or angles. The 4 choice of which i n t e r a c t i o n constants to incorporate may be guided by chemical i n t u i t i o n . In order to permit the i n -c l u s i o n of as many i n t e r a c t i o n constants as may be d e s i r a b l e , i t i s necessary to have as much experimental data as p o s s i b l e ; a d d i t i o n a l i n f o r m a t i o n i s provided by the fundamental f r e -quencies of i s o t o p i c a l l y s u b s t i t u t e d molecules. The assump-t i o n t h a t the p o t e n t i a l f u n c t i o n i s unchanged by such i s o t o p i c s u b s t i t u t i o n i s based on the Born-Oppenheimer s e p a r a b i l i t y of e l e c t r o n i c and nuclear coordinates and the assumed harmonic nature of the v i b r a t i o n s . 26 27 M i l l e r and Crawford ' have used both symmetry f a c t o r i z a t i o n and i n f o r m a t i o n from deuterated molecules to 2 8 29 d i s c u s s , w i t h Wilson's technique, ' the complete q u a d r a t i c fo r c e f i e l d of benzene. The number of out-of-plane funda-mentals known should be s u f f i c i e n t to determine the non-2 6 p l a n a r , symmetrized force f i e l d e x a c t l y ; approximations 27 were found to be necessary f o r the in-plane problem. Upon c a r r y i n g out the c a l c u l a t i o n s , however, they found t h a t i n both cases ambiguities s t i l l e x i s t e d due to the appearance of q u a d r a t i c equations f o r which both roots are p h y s i c a l l y rea-sonable. Whiffen^" chose from the a l t e r n a t i v e sets of con-st a n t s on the chemical b a s i s t h a t the simple valence f i e l d i s most important and i n t e r a c t i o n constants added to i t should be as small as p o s s i b l e . 5 Recently two a l t e r n a t i v e modified valence f o r c e f i e l d s have been proposed f o r the planar benzene problem. 31 Scherer converted a Urey-Bradley f i e l d to a modified valence f i e l d , and by r e f i n i n g only nine force constants found a very s a t i s f a c t o r y f i t to the frequencies of benzene and s e v e r a l of 32 i t s c h l o r i n a t e d analogues. Duinker and M i l l s made use of a d d i t i o n a l r e s t r i c t i o n s on the force f i e l d provided by the 33 r e c e n t l y observed C o r i o l i s c o u p l i n g constants and found values f o r c e r t a i n symmetry fo r c e constants d i f f e r i n g markedly from those suggested by Whiffen"^ and by Scherer.'*"'" From these f o r c e constants they developed and r e f i n e d a t h i r t e e n -parameter modified valence f o r c e f i e l d i n v o l v i n g i n t e r a c t i o n constants expected to be s i g n i f i c a n t on the b a s i s of various models (see r e f . 32, p. 428). Several attempts to t r a n s f e r force constants from one aromatic molecule to another have been made. Whiffen's modified valence force f i e l d was a p p l i e d to naphthalene by 34 35 36 Freeman and Ross and by S c u l l y and Whiffen. ' The former authors c a r r i e d out an i t e r a t i v e refinement of the for c e con-sta n t s to f i t the more c e r t a i n frequencies of naphthalene. 37 Scherer t r a n s f e r r e d to naphthalene an e a r l i e r Urey-Bradley 38 39 31 f i e l d ' of benzene although he l a t e r found t h a t a valence force f i e l d could reproduce s u b s t i t u t e d benzene frequencies s i g n i f i c a n t l y b e t t e r than a Urey-Bradley f i e l d . The out-of-30 plane force constants of Whiffen have a l s o been c a r r i e d _ 40 over to anthracene. 6 A d i f f e r e n t approach was used by Neto, Scrocco and 41 C a l i f a n o . Rather than t r a n s f e r a benzene fo r c e f i e l d to l a r g e r aromatic molecules, they assumed the existence of an "aromatic valence force f i e l d " which would simultaneously f i t a number of simple aromatic molecules. They used t h i s method to c a l c u l a t e the planar frequencies of benzene, naphthalene and anthracene, and the f i t w i t h the then a v a i l a b l e data was very good (the average e r r o r was l e s s than 15 cm \ although t h i s value does depend on the choice of experimental a s s i g n -ment) . The i n i t i a l f i e l d used i n the benzene p a r t of t h i s 41 31 c a l c u l a t i o n was almost i d e n t i c a l to t h a t found by Scherer and was probably a l s o the r e s u l t of r e f i n i n g important valence force constants chosen from a Urey-Bradley f i e l d . One of the major d i f f i c u l t i e s encountered i n e v a l u -a t i n g aromatic force f i e l d s has been l o c a t i n g r e l i a b l e v i b r a -t i o n a l assignments. Force constant c a l c u l a t i o n s depend not only on p r e c i s e measurements of the frequency of a normal mode, but a l s o r e q u i r e a knowledge of e x a c t l y how many funda-mentals of the same symmetry l i e higher and lower i n energy. In t h i s sense, fewer frequencies are known d e f i n i t e l y ; when 34 Freeman and Ross c a r r i e d out t h e i r c a l c u l a t i o n s on naph-thalene, they estimated t h a t only ten of the twenty-five i n -plane fundamental v i b r a t i o n s below 2000 cm ^ s a t i s f i e d t h i s requirement. I 7 Many f a c t o r s enter i n t o the experimental problem of a s s i g n i n g the fundamental v i b r a t i o n s . For example, i n the i n f r a r e d , scores of combination and overtone frequencies appear, many w i t h considerable i n t e n s i t y , and l o c a t i n g the fundamentals among them i s extremely d i f f i c u l t . Some of the problems, though, can be overcome by c a r e f u l technique, and others have disappeared as t e c h n o l o g i c a l advances have taken p l a c e . In much of the previous i n f r a r e d work, a t t e n t i o n was l i m i t e d to the r e a d i l y obtained cleavage faces of the c r y s t a l s . Thus incomplete p o l a r i z a t i o n i n f o r m a t i o n was obtained, and although these data were supplemented by s o l u t i o n measurements, the assignment of fundamentals was d i f f i c u l t when the t r a n s i t i o n d i p o l e was not o r i e n t e d near one of the o p t i c a l d i r e c t i o n s of the cleavage face. In a d d i t i o n , low energy molecular v i b r a t i o n s o f t e n f e l l o utside the s p e c t r a l region covered by o l d e r i n f r a r e d spectrometers, and could not be measured. Raman spectra obtained before the advent of the l a s e r were sometimes u n r e l i a b l e , and p o l a r i z e d Raman spectra from s i n g l e c r y s t a l s were extremely d i f f i c u l t to o b t a i n . 2. Aim of Thesis The work undertaken f o r t h i s t h e s i s can be d i v i d e d i n t o two p a r t s . In the experimental s e c t i o n , complete p o l a r i -z a t i o n i n f o r m a t i o n about i n f r a r e d l i n e s was obtained by measuring the spect r a from c r y s t a l faces not p r e v i o u s l y 8 st u d i e d . In a d d i t i o n , a new spectrometer was used to extend the measurements i n t o the f a r i n f r a r e d t o l o c a t e a l l the low-energy molecular v i b r a t i o n s . Raman spect r a were recorded f o r s e v e r a l molecules i n order to re s o l v e d o u b t f u l assignments, wi t h emphasis placed on o b t a i n i n g p o l a r i z e d s p e c t r a from s i n g l e c r y s t a l s . I t was hoped t h a t a l l the inf o r m a t i o n c o l l e c t e d would permit more d e f i n i t e assignments to be made of the fundamental v i b r a t i o n s of s e v e r a l aromatic molecules. When the assignments were as complete as p o s s i b l e , the force f i e l d s were considered. P r e v i o u s l y unobserved fundamentals could be used t o check the accuracy of the p r e d i c t i o n s of various fo r c e f i e l d s . I t was hoped th a t more could be learned about the l e s s - i n t e n s i v e l y s t u d i e d out-of-plane force constants from the new informat i o n about low energy fundamentals. In a d d i t i o n , the a b i l i t y of some forc e f i e l d s to f i t simultaneously the frequencies of benzene, naphthalene and anthracene was considered. A l s o , two r e l a t e d but l e s s s i m i l a r molecules (pyrene and acenaphthene) were st u d i e d to see how w e l l the force constants der i v e d f o r the f i r s t three molecules would t r a n s f e r to other molecules. B. The Assignment of Fundamentals 1. V i b r a t i o n s of molecules When a molecule executes a fundamental or normal v i b r a t i o n , every atom of the molecule v i b r a t e s at the same 9 frequency; the atoms pass through t h e i r e q u i l i b r i u m p o s i t i o n s at the same time and reach t h e i r p o s i t i o n s of maximum d i s -placement at the same time. The t o t a l number of normal v i b r a t i o n s of a n o n - l i n e a r molecule i s 3N-6 where N i s the number of atoms. Each normal v i b r a t i o n has the symmetry of 10 one of 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 of the molecular p o i n t group and the number of v i b r a t i o n s belonging to each repre-s e n t a t i o n can be r e a d i l y determined. The f i r s t step i n as s i g n i n g fundamentals i s to l o c a t e a l l the frequencies at which the molecule v i b r a t e s . The fun-damentals of aromatic molecules l i e i n the energy range between 100 cm and 3200 cm and some v i b r a t i o n s may be observed d i r e c t l y i n the i n f r a r e d and f a r i n f r a r e d s p e c t r a l regions. In a d d i t i o n , other frequencies may a l s o be found as i n t e r v a l s i n Raman and emission (fluorescence and phosphores-cence) s p e c t r a . The second step i n the assignment i s to i d e n t i f y the symmetry type of each observed v i b r a t i o n . 2. Symmetry inf o r m a t i o n from vapor, s o l u t i o n and  melt spectra Some conclusions about the symmetry of the v i b r a -t i o n s of larg e m o l e c u l e s — p a r t i c u l a r l y those modes which are i n f r a r e d or Raman a c t i v e — c a n be made by studying t h e i r s p e c t r a i n the vapor phase, i n s o l u t i o n or i n the melt. Symmetry assignments from fluorescence and phosphorescence are more r e a d i l y made from c r y s t a l s p e c t r a and a d i s c u s s i o n of the r e l e v a n t s e l e c t i o n r u l e s w i l l be made i n the next s e c t i o n . A d i v i s i o n of the v i b r a t i o n s i n t o Raman a c t i v e and i n f r a r e d a c t i v e modes e f f e c t s an i n i t i a l symmetry c l a s s i f i -c a t i o n , since the s e l e c t i o n r u l e s f o r the two processes are 11 d i f f e r e n t . Any v i b r a t i o n which i s i n f r a r e d a c t i v e must belong to a r e p r e s e n t a t i o n of the p o i n t group of the molecule which transforms l i k e a t r a n s l a t i o n along the x, y_ or z_ a x i s . Raman a c t i v e v i b r a t i o n s must have the symmetry of one of the repres e n t a t i o n s which transforms l i k e one of the components of the p o l a r i z a b i l i t y tensor, a . I f the molecule contains a center of symmetry, as s e v e r a l of the aromatic compounds st u d i e d i n t h i s work do, Raman modes are gerade whi l e i n f r a -r e d - a c t i v e v i b r a t i o n s are ungerade. a) Symmetry assignments from Raman spe c t r a . Two techniques are i n use f o r making symmetry assignments from the Raman spectr a of gases, s o l u t i o n s or melts. The f i r s t , used to i d e n t i f y t o t a l l y symmetric v i b r a t i o n s , i s the f a m i l i a r 'Raman d e p o l a r i z a t i o n r a t i o 1 measurement. For the r i g h t -angled viewing arrangement common for.Raman spect r a the sc a t t e r e d r a d i a t i o n corresponding to a non-totally-symmetric v i b r a t i o n has a d e p o l a r i z a t i o n r a t i o p 0 = 3/4 or p = 'I depending on whether the i n c i d e n t l i g h t i s l i n e a r l y p o l a r i z e d ( p . ) or n a t u r a l (p ). The s i g n i f i c a n t r e s u l t i s tha t a l l l i n e s w i t h p l e s s than the maximum value must a r i s e from t o t a l l y symmetric v i b r a t i o n s . For the c o - a x i a l viewing d e p o l a r i z a t i o n r a t i o s are defined by Wilson, Decius and Cross ( r e f . 29, p. 47). 12 arrangement used i n most of t h i s work the maximum value of the d e p o l a r i z a t i o n r a t i o i s 0.75. A l e s s u s e f u l but r a t h e r i n t e r e s t i n g technique used f o r making symmetry assignments from the Raman spectr a of 42 r o t a t i n g molecules was r e c e n t l y demonstrated f o r benzene. The angular dependence of the i n t e n s i t y of Raman s c a t t e r i n g from a l i q u i d (benzene) e x c i t e d by a Helium-neon l a s e r was compared w i t h the i n t e n s i t y d i s t r i b u t i o n p r e d i c t e d (see r e f . 42) by Placzek f o r d i f f e r e n t symmetries. The e x c e l l e n t agreement f o r the few v i b r a t i o n s s t u d i e d served more to demonstrate the method than to assign the modes, whose symmetries were already w e l l e s t a b l i s h e d . This technique has not as yet come i n t o general use, probably because of both the experimental d i f f i c u l t i e s and the p o s s i b i l i t y of making assignments from more standard techniques (e.g. s i n g l e c r y s t a l s p e c t r a ) . b) Symmetry assignments from vapor-phase band  contours. T r a n s i t i o n s observed i n the i n f r a r e d , Raman or emission s p e c t r a of molecules i n the vapor phase and a t t r i -buted to v i b r a t i o n s are i n f a c t due to changes i n both the r o t a t i o n a l and v i b r a t i o n a l quantum numbers. Since the moments of i n e r t i a of aromatic molecules are r e l a t i v e l y l a r g e , the r o t a t i o n a l s t r u c t u r e cannot be r e s o l v e d , and under normal c o n d i t i o n s the band appears as a s i n g l e l i n e . Under higher r e s o l u t i o n , however, the shape of the envelope o f t e n can be 13 found and, by comparison w i t h the contours p r e d i c t e d f o r d i f f e r e n t symmetries, assignments can be made. Although the p r e c i s e shape depends on the molecular dimensions, t y p i c a l contours f o r t r a n s i t i o n s p o l a r i z e d along each of the three p r i n c i p a l axes of an asymmetric r o t o r are shown i n Figure 2. Figure 2. T y p i c a l appearance of type A, B, and C contours f o r an asymmetric r o t o r . A f t e r King^3, p. 374. A type A band has i t s t r a n s i t i o n moment p a r a l l e l to the p r i n -c i p a l a x i s of sm a l l e s t moment of i n e r t i a , type B the i n t e r -mediate moment of i n e r t i a , and type C bands are p o l a r i z e d along the a x i s of l a r g e s t moment of i n e r t i a . Despite the d i f f i c u l t i e s i n v o l v e d ( p a r t i c u l a r l y i n d i s t i n g u i s h i n g between type A and type C contours) symmetries of some bands of the asymmetric r o t o r naphthalene have been found from the v i b r o n i c 44 45 46 6 abs o r p t i o n , ' fluorescence, and i n f r a r e d absorption s p e c t r a . However, t h i s method i s not so u s e f u l f o r a molecule l i k e anthracene which has a much lower vapor pressure and a more crowded spectrum. A B C 14 3. Symmetry Information from C r y s t a l Spectra As shown i n the previous s e c t i o n , some inf o r m a t i o n about the symmetry of molecular v i b r a t i o n s can be gained from a study of the s p e c t r a of molecules when they are able to r o t a t e . Much more inf o r m a t i o n would be a v a i l a b l e , however, i f i t were p o s s i b l e to h o l d a molecule f i x e d i n space and observe the way i t i n t e r a c t s w i t h plane p o l a r i z e d l i g h t . The c l o s e s t approach to t h i s i d e a l experiment i s to study s i n g l e c r y s t a l s , i n which the o r i e n t a t i o n s of the molecules i n the u n i t c e l l are known wit h respect to the c r y s t a l axes. The i n t e r p r e t a t i o n of the s p e c t r a of s i n g l e c r y s t a l s i s u s u a l l y c a r r i e d out under the assumptions of the o r i e n t e d gas model. a) The o r i e n t e d gas model. C r y s t a l s of aromatic molecules, l i k e those of most organic compounds, can be c l a s s i f i e d as molecular c r y s t a l s ; t h a t i s , the i n t e r m o l e c u l a r forces are much weaker than the i n t r a m o l e c u l a r f o r c e s . In a 47 48 u s e f u l approximation, known as the o r i e n t e d gas model, ' the i n t e r m o l e c u l a r forces are neglected completely and the c r y s t a l i s considered to be a r i g i d l y o r i e n t e d system of n o n - i n t e r a c t i n g molecules i n t h e i r e q u i l i b r i u m c r y s t a l l i n e p o s i t i o n s . In t h i s approximation each vapor phase band i s p r e d i c t e d to produce a s i n g l e l i n e at e x a c t l y the same f r e -quency i n the c r y s t a l spectrum, l i n e s which do not appear i n the free-molecule spectrum are expected to have zero i n t e n s i t y 15 i n the c r y s t a l , and the r e l a t i v e i n t e n s i t i e s of Raman l i n e s and of i n f r a r e d l i n e s w i l l depend only on the o r i e n t a t i o n of the molecules i n the u n i t c e l l w i t h respect to the axes along which the i n c i d e n t (and scattered) r a d i a t i o n i s p o l a r i z e d . P o l a r i z a t i o n r a t i o s f o r i n f r a r e d absorption. The t r a n s i t i o n from v i b r a t i o n a l s t a t e i to v i b r a t i o n a l s t a t e j w i l l absorb i n f r a r e d r a d i a t i o n only i f there i s a change i n the e l e c t r i c moment of the molecule i n going from one s t a t e to the other. The i n t e n s i t y of the absorption i s p r o p o r t i o n a l to the square of the t r a n s i t i o n d i p o l e moment. For plane-p o l a r i z e d l i g h t o r i e n t e d at some angle 8 to the vector r e -presenting the e l e c t r i c moment change the i n t e n s i t y of the absorption w i l l vary as cos^e . I f other molecules i n the u n i t c e l l are d i f f e r e n t l y o r i e n t e d w i t h respect to the c r y s t a l axes used, then the t o t a l i n t e n s i t y along each a x i s w i l l be the mean of the c o n t r i b u t i o n s from the i n d i v i d u a l molecules. I n t e n s i t y d i s t r i b u t i o n f o r Raman s c a t t e r i n g i n the  c r y s t a l frame. The d i p o l e moment u_ induced i n an a n i s o t r o p i c molecule i n an e l e c t r i c f i e l d E i s u = a E —xyz =xyz —xyz where a i s the p o l a r i z a b i l i t y tensor. The s u b s c r i p t s em-phasize t h a t the above equation i n v o l v e s only the molecular a x i s frame, x, y, z. However, the experimentally a c c e s s i b l e axes f o r a given c r y s t a l s e c t i o n are not x, y, z but another orthonormal set whose o r i e n t a t i o n i s a property of the c r y s t a l (see s e c t i o n B.3(d)of t h i s c h a pter). 16 The induced d i p o l e P^bc a n c^ ^he e l e c t r i c f i e l d v e c t o r E_akc i n some convenient c r y s t a l a x i s set a, b, c (not n e c e s s a r i l y the c r y s t a l l o g r a p h i c axes) are r e l a t e d by a d i f f e r e n t p o l a r i z a b i l i t y t ensor, ^-abc =abc —abc I f R i s the matrix d e s c r i b i n g the transformation from the molecular to the c r y s t a l axes, then y , = R y and E , = R E —abc = —xyz —abc = —xyz Since x, y, z and a, b, c are both orthonormal bases, the transpose of R equals the inverse of R, and t h e r e f o r e R t y , = y = a R t E , = —abc —xyz =xyz = —abc or, y , = (R a Rfc) E , ' —abc = =xyz — —abc and hence a , = R a .„ R t —abc = =xyz = The above treatment considers only one molecule i n the u n i t c e l l . However, provided the symmetry axes t h a t r e l a t e the molecules i n the u n i t c e l l are contained i n the orthonormal set a, b, c only one molecule need be considered, since the Raman s c a t t e r i n g depends only on the square of the matrix element. b) S i n g l e C r y s t a l fluorescence and phosphorescence. When an aromatic molecule i n the vapor phase (except at very low p r e s s u r e s ) , i n s o l u t i o n or i n a s i n g l e c r y s t a l i s e x c i t e d e l e c t r o n i c a l l y , any energy i n excess of the ground v i b r a t i o n a l 17 l e v e l of the f i r s t e x c i t e d e l e c t r o n i c s t a t e i s r a p i d l y given up as heat to the surrounding molecules. Frequently the remaining energy w i l l then be l o s t w i t h the emission of a quantum of the appropriate frequency; when the higher energy s t a t e i s a s i n g l e t l e v e l , the process i s known as f l u o r e s -cence; the spin-forbidden t r a n s i t i o n from a t r i p l e t l e v e l i s c a l l e d phosphorescence. At low temperature the highest energy quanta emitted a r i s e from the t r a n s i t i o n to the ground v i b r a t i o n a l l e v e l of the ground e l e c t r o n i c s t a t e . Other t r a n s i t i o n s are observed to various v i b r a t i o n a l l e v e l s of the ground s t a t e , and c e r t a i n molecular v i b r a t i o n a l frequencies can be found as energy d i f f e r e n c e s from the o r i g i n band. t e n s i t y of a v i b r o n i c l i n e i n spontaneous emission from s t a t e A to s t a t e B i s p r o p o r t i o n a l to the square of the t r a n s i t i o n moment u A t J , where ^ A and are eigenfunctions of the Hamiltonian f o r s t a t e A and B, P i s the d i p o l e moment operator and the i n t e g r a l i s th over a l l space. The i p a r t i c l e has charge q^ and i t s l o c a t i o n i s determined by the vector r ^ . In the Born-Oppenheimer approximation the e l e c t r o n i c and nuclear coordinates are inde-th pendent. Then the wave f u n c t i o n f o r the i v i b r a t i o n a l th l e v e l of the f e l e c t r o n i c s t a t e can be w r i t t e n as the S e l e c t i o n r u l e s f o r v i b r o n i c t r a n s i t i o n s . The i n --AB P = Z: q.r. — 1 ^ 1 — 1 product ¥ f , i = * f * X f , i 18 where ijj^ i s the e l e c t r o n i c wave f u n c t i o n f o r the e q u i l i b r i u m nuclear c o n f i g u r a t i o n and \ f • i s the v i b r a t i o n a l wave func-t i o n , depending only on the nuclear coordinates. Omission of the r o t a t i o n a l wave f u n c t i o n i m p l i e s neglect of the r o -t a t i o n a l i n t e n s i t y d i s t r i b u t i o n w i t h i n each v i b r o n i c band. I f the d i p o l e moment, operator P can be separated, i n t o components P e f o r the e l e c t r o n s and P_N f o r the n u c l e i , then f o r the t r a n s i t i o n from v i b r a t i o n a l l e v e l i of s t a t e f to v i b r a t i o n a l l e v e l j of s t a t e g, H f i # g j = (*fXfil£el Vgj) + (V<fi'*N 'Vgj) I f the nuclear d i p o l e moment depends only on the v i b r a t i o n a l coordinates then the second term w i l l f a c t o r to give which equals zero s i n c e the wave fun c t i o n s f o r d i f f e r e n t e l e c t r o n i c s t a t e s are orthogonal. Then i f the e l e c t r o n i c wave f u n c t i o n s ^ f r ^ g a r e independent of small changes i n nuclear coordinates the f i r s t term f a c t o r s to give <*f! l * g ) ( X f i I X g j ) Since only d i p o l e - a l l o w e d t r a n s i t i o n s are being considered, the f i r s t term, 19 w i l l be n o n - z e r o o n l y i f t h e d i r e c t p r o d u c t o f t h e g r o u p r e p r e s e n t a t i o n s t o w h i c h % and b e l o n g h a s a component w h i c h t r a n s f o r m s l i k e x , y_ o r £• I n t h i s s i m p l e a p p r o x i m a t i o n , t h e o v e r l a p i n t e g r a l ^ f i ^ g j ^ d e t e r m i n e s how t h e i n t e n s i t y i s p a r t i t i o n e d among t h e v i b r a t i o n a l l e v e l s . I t w i l l be n o n - z e r o o n l y i f t h e d i r e c t p r o d u c t o f t h e r e p r e s e n t a t i o n s o f a n d X ^ j c o n t a i n s t h e 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 . S i n c e , as s t a t e d e a r l i e r , t h e e m i s s i o n p r o c e s s e s c o n s i d e r e d o r i g i n a t e f r o m v i b r a t i o n a l l y n o n - e x c i t e d ( a n d h e n c e s y m m e t r i c ) s t a t e s o n l y t r a n s i t i o n s t o t h e v i b r a t i o n l e s s g r o u n d s t a t e a n d t o s t a t e s e x c i t e d i n t o t a l l y s y m m e t r i c v i b r a t i o n s s h o u l d be s e e n . I n f a c t i n t e r a c t i o n s b e t w e e n e l e c t r o n i c a n d v i b r a -t i o n a l m o t i o n a r e n o t i n s i g n i f i c a n t a n d l i n e s a r i s i n g f r o m n o n - t o t a l l y - s y m m e t r i c v i b r a t i o n s a r e f r e q u e n t l y o b s e r v e d . The t h e o r y i n v o l v e d was f i r s t d i s c u s s e d b y H e r z b e r g a n d 49 T e l l e r a n d c a n be f o u n d i n many s o u r c e s ( e . g . s e e r e f . 4 3 , p. 4 0 5 ) . N o n - t o t a l l y s y m m e t r i c v i b r a t i o n s a p p e a r t h r o u g h m i x i n g w i t h e l e c t r o n i c s t a t e s a t h i g h e r e n e r g y w h i c h b e l o n g t o t h e a p p r o p r i a t e symmetry t y p e . The i n t e n s i t y o f v i b r o n i c b a n d s a r i s i n g f r o m s u c h n o n - t o t a l l y s y m m e t r i c v i b r a t i o n s i s p r o p o r t i o n a l t o t h e i n t e n s i t y o f t h e t r a n s i t i o n f r o m t h e g r o u n d t o t h e p e r t u r b i n g e l e c t r o n i c s t a t e a n d i n v e r s e l y p r o p o r t i o n a l t o t h e s e p a r a t i o n b e t w e e n t h e two i n t e r a c t i n g s t a t e s . The l o w e s t e n e r g y s t a t e s o f a r o m a t i c m o l e c u l e s a l l 20 i n v o l v e IT—TT t r a n s i t i o n s which are p o l a r i z e d i n the molecular plane. Therefore the symmetry of the p e r t u r b i n g v i b r a t i o n i s given as the d i r e c t product of the i r r e d u c i b l e representations spanned by the in-plane t r a n s i t i o n moments. In naphthalene, f o r example, the lowest e x c i t e d s i n g l e t s t a t e has B 2 u symmetry; the other in-plane t r a n s i t i o n has symmetry and so the n o n - t o t a l l y symmetric v i b r a t i o n s which appear most s t r o n g l y i n fluorescence have symmetry B 2 u x B^ u = B3g* I f the t r a n s i t i o n from the f i r s t e x c i t e d e l e c t r o n i c l e v e l to the ground s t a t e i s symmetry allowed and appears s t r o n g l y , t o t a l l y symmetric v i b r a t i o n s dominate the v i b r a t i o n a l s t r u c t u r e ; i f the t r a n s i t i o n appears weakly, then the non-t o t a l l y symmetric v i b r a t i o n s are more e a s i l y found. I f the pure e l e c t r o n i c t r a n s i t i o n i s symmetry forbidden then the v i b r o n i c bands r e s u l t i n g from the p e r t u r b a t i o n appear as f a l s e o r i g i n s , w i t h t o t a l l y symmetric i n t e r v a l s b u i l t upon them. In the event th a t the fluorescence or phosphorescence spectra are obtained from s i n g l e c r y s t a l s , the p o l a r i z a t i o n of the v i b r o n i c band w i t h respect to the c r y s t a l axes can be found and knowing the o r i e n t a t i o n of the molecules i n the c r y s t a l , the symmetry of the v i b r a t i o n i n v o l v e d can be deduced. c) L i m i t a t i o n s of the o r i e n t e d gas model. Although the o r i e n t e d gas model i s very u s e f u l i n i n t e r p r e t i n g the spectr a of s i n g l e c r y s t a l s i t i s only an approximation, and evidence f o r the f a i l u r e of the assumptions upon which i t i s 21 based i s obvious i n a l l s p e c t r a from aromatic s i n g l e c r y s t a l s . The appearance, w i t h appreciable i n t e n s i t y , of fundamentals which are symmetry forbidden i n the f r e e molecule i s not p r e d i c t e d by the o r i e n t e d gas model, although the f a c t t h a t they do appear i s very u s e f u l i n making frequency assignments. Further evidence of the inadequacy of the o r i e n t e d gas assump-t i o n i s the general s h i f t i n v i b r a t i o n a l frequency which occurs i n going to the s o l i d s t a t e , and a l s o the s p l i t t i n g of a non-degenerate vapor phase l i n e i n t o two or more l i n e s i n s i n g l e c r y s t a l s p e c t r a . The i n a b i l i t y of the o r i e n t e d gas model to e x p l a i n these features i s due, of course, to the f a c t t h a t i t neglects the i n t e r a c t i o n s between molecules i n the c r y s t a l . I f , however, the i n t e r m o l e c u l a r forces are small compared wi t h the i n t r a m o l e c u l a r forces the c r y s t a l Hamiltonian can be b u i l t up as a sum of free-molecule Hamiltonians plus an i n t e r a c t i o n p o t e n t i a l . In t h i s case the energy l e v e l s of a c r y s t a l are given by the eigenvalues of the Hamiltonian N H = £ (H + 2 V 0, ) 1.1 k=l K &>k * K t h where H^ i s the Hamiltonian f o r the k molecule and i s the i n t e r a c t i o n operator between two of the N molecules i n the c r y s t a l . The o r i e n t e d gas model corresponds to s e t t i n g V£k ec5ua-'- t o z e r o - T n e wave f u n c t i o n f o r the c r y s t a l when each molecule i s i n i t s ground s t a t e i s given by the product 22 of the molecular ground s t a t e wave f u n c t i o n s . $G = *11*12" * ' *h,N/h X - 2 where h i s the number of molecules i n each u n i t c e l l . t h The zero-order c r y s t a l wave f u n c t i o n when the p th molecule of the i t r a n s l a t i o n a l set i s e x c i t e d to s t a t e r i s given by * i p = *11*12 ' ' - * i p ' ' -*h, N/h I - 3 There are N such wavefunctions, a l l eigenfunctions of EH^ but not of E I V ^ . The eigenfunctions when the p e r t u r b a t i o n i s considered are formed as l i n e a r combinations of the d>. and T i p the c r y s t a l symmetry determines which l i n e a r combinations are appropriate. The symmetry p r o p e r t i e s of c r y s t a l s have been 50 summarized by Winston and H a l f o r d and a p p l i e d to e l e c t r o n i c 51-53 spect r a and to v i b r a t i o n a l spectra (see, f o r example, the 54 summary by Dows ). The b r i e f o u t l i n e given here f o l l o w s the 55 54 treatment of C r a i g and Walmsley and Dows. C r y s t a l symmetry. A l l symmetry operations of a c r y s t a l together form the f i n i t e space group introduced by 50 Winston and H a l f o r d . They can be d i v i d e d i n t o two sub-groups; the t r a n s l a t i o n operations form one subgroup and the f a c t o r group as s o c i a t e d w i t h i t completes the c r y s t a l symmetry operations. The f a c t o r group, o f t e n c a l l e d the u n i t c e l l 23 group, i s isomorphous w i t h one of the t h i r t y - t w o p o i n t groups p o s s i b l e i n c r y s t a l s . I t i s convenient a l s o to d e f i n e the s i t e group, which i s the group of a l l symmetry operations a c t i n g through any p o i n t , or s i t e , i n the c r y s t a l ; when the s i t e i s chosen to c o i n c i d e w i t h a molecular p o s i t i o n i n the c r y s t a l the s i t e group i s a subgroup of the molecular p o i n t group as w e l l as of the f a c t o r group. The c r y s t a l Hamiltonian has the f u l l symmetry of the f i n i t e space group; i t i s the r e f o r e d e s i r a b l e to choose l i n e a r combinations of the ( J K^ (equation 1.3) which have i r r e d u c i b l e symmetry of that group si n c e such combinations w i l l not have any i n t e r a c t i o n terms connecting them. To form combinations i r r e d u c i b l e i n the t r a n s l a t i o n subgroup the b a s i s f u n c t i o n s are p r o j e c t e d i n t o t h i s subgroup to y i e l d .. - * * £ s i - - * i p i k * IT where the phase f a c t o r e contains the wave vector k and the ve c t o r r which defines the s i t e of e x c i t a t i o n . However, the above l i n e a r combinations do not, i n ge n e r a l , form i r r e d u c i b l e representations of the f a c t o r group and i t i s only f o r c e r t a i n values of k tha t f u r t h e r symmetry f a c t o r i z a t i o n i s p o s s i b l e . The value of k of g r e a t e s t i n t e r e s t i n o p t i c a l t r a n s i t i o n s i s k = 0 since conservation of momen-tum demands tha t k = c[ = 0, where c[ i s the wave vec t o r of the i n c i d e n t photon. In t h i s case, r ( 0 ) = & ) h Z <}>.r . 1.5 IP r L i n e a r combinations of the above $^(0) can be found which belong t o 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 of the f a c t o r group; the number of such l i n e a r combinations i s equal to the number of molecules i n the u n i t c e l l . The environment about a molecule i n a c r y s t a l has, as a r u l e , l e s s symmetry than the molecule i t s e l f . Therefore when i n t e r a c t i o n s between a molecule and i t s surroundings are taken i n t o account the molecule r e t a i n s only those symmetry operations which appear i n i t s s i t e group. Wilson, Decius and 29 Cross have ta b u l a t e d c o r r e l a t i o n t a b l e s which r e l a t e the symmetry species of a group to those of i t s subgroups. The c o r r e l a t i o n t a b l e s f o r s p e c i f i c molecular p o i n t groups, f a c t o r groups and s i t e groups w i l l be introduced l a t e r as they are needed. The r e s u l t s p r e d i c t e d by such a f a c t o r group a n a l y s i s are: (1) a non-degenerate l e v e l i n the vapor phase may s p l i t Into 'h 1 l e v e l s i n the c r y s t a l , where h i s the number of molecules i n the u n i t c e l l , and (2) i n a c t i v e molecular funda-mentals and combinations may appear i n the c r y s t a l s p e c t r a by mixing w i t h a c t i v e modes which c o r r e l a t e to the same symmetry species of the f a c t o r group. Together wi t h a s h i f t from the vapor phase frequency a r i s i n g from the e q u i l i b r i u m f i e l d of the c r y s t a l l i n e environment, these two p r e d i c t i o n s c l a r i f y 25 the observations mentioned e a r l i e r i n regard to the break-down of the o r i e n t e d gas model. ^ The i n t e r a c t i o n of plane p o l a r i z e d l i g h t w i t h a s i n g l e c r y s t a l . The p o l a r i z a t i o n p r e d i c t i o n s of the o r i e n t e d gas model have been discussed w i t h reference only to a beam of l i g h t p o l a r i z e d i n an a r b i t r a r y plane. In f a c t the d i r -e c t i o n s of p o l a r i z a t i o n of a beam of l i g h t moving through a c r y s t a l are not a r b i t r a r y , and some knowledge of the o p t i c a l p r o p e r t i e s of s i n g l e c r y s t a l s i s r e q u i r e d i n order to s e t up the experiments and i n t e r p r e t t h e i r r e s u l t s . The aromatic molecules considered i n t h i s work form b i a x i a l c r y s t a l s belonging to the orthorhombic and monoclinic systems. U s u a l l y , a beam of monochromatic l i g h t i n c i d e n t on an a n i s o t r o p i c c r y s t a l w i l l be s p l i t by r e f r a c t i o n at the surface i n t o two rays (the o r d i n a r y and e x t r a o r d i n a r y rays) which t r a v e l i n d i f f e r e n t d i r e c t i o n s and which have t h e i r e l e c t r i c v ectors p o l a r i z e d i n planes at r i g h t angles t o one another. At any p o i n t i n an a n i s o t r o p i c c r y s t a l three mutually perpendicular axes X, Y, Z_ can be constructed, these being the p r i n c i p a l axes of a t r i a x i a l e l l i p s o i d c a l l e d the i n d i c a t r i x . The o r i e n t a t i o n and magnitude of these axes determine the o p t i c a l p r o p e r t i e s of the c r y s t a l . For an orthorhombic c r y s t a l these three d i r e c t i o n s c o i n c i d e w i t h the c r y s t a l l o g r a p h i c axes at a l l wavelengths. In a monoclinic system one of the axes i s c o i n c i d e n t w i t h the symmetry a x i s 26 (b) of the c r y s t a l but the others can l i e anywhere i n the ac plane and must be l o c a t e d e x p e r i m e n t a l l y ; i n a d d i t i o n the p o s i t i o n of the two axes i n the ac plane can change w i t h wavelength. A plane p o l a r i z e d ray normal to a c r y s t a l surface which contains two of the i n d i c a t r i x axes w i l l pass through the c r y s t a l without r e f r a c t i o n . This i d e a l s i t u a t i o n i s l e s s common, p a r t i c u l a r l y f o r monoclinic c r y s t a l s , than the o r i e n -t a t i o n shown i n Figure 3. C 1 Z Figure 3. The ab face of a monoclinic c r y s t a l showing the o r i e n t a t i o n of the axes X, Y, "L_ of the i n d i c a t r i x . The a x i s c' i s defined to be normal to the ab plane. 27 In Figure 3 i s shown a c r y s t a l face c o n t a i n i n g only one (X) of the three p r i n c i p a l axes; the other two axes l i e o b l i q u e l y to the face. L i g h t t r a v e l l i n g along c 1 and p o l a r i z e d p a r a l l e l to b w i l l t r a v e l through the c r y s t a l un-dev i a t e d , g i v i n g r i s e to the or d i n a r y ray. The d i f f i c u l t y a r i s e s when l i g h t propagating i n the same d i r e c t i o n has i t s e l e c t r i c v e c t o r p a r a l l e l to a; t h i s s i t u a t i o n was r e c e n t l y discussed by Rohleder and L u t y ^ who pointed out tha t the a c t u a l path of such a beam through the c r y s t a l was determined by both the o r i e n t a t i o n of Z_ and Y and the magnitudes of the r e f r a c t i v e i n d i c e s i n these d i r e c t i o n s . In c a l c u l a t i n g the t h e o r e t i c a l p o l a r i z a t i o n r a t i o s i n the o r i e n t e d gas approxi-mation the a c t u a l path of such a ray (the e x t r a o r d i n a r y ray) should be determined. U n f o r t u n a t e l y , no informat i o n about the o p t i c a l p r o p e r t i e s of the c r y s t a l s i n the i n f r a r e d s p e c t r a l r egion i s a v a i l a b l e . Due to the p o s s i b i l i t y of d i s p e r s i o n of the i n d i c a t r i x i n monoclinic c r y s t a l s and the probable changes i n the r e f r a c t i v e i n d i c e s f o r a l l c r y s t a l s w i t h wavelength, no p r e d i c t i o n of the e f f e c t on the p o l a r i z a t i o n r a t i o s i n the i n f r a r e d can be made. However, any c o r r e c t i o n a r i s i n g from the d e v i a t i o n of the e x t r a o r d i n a r y ray i s expected t o be small and need be considered only when the p o l a r i z a t i o n r a t i o approaches u n i t y (see, f o r example, the case of pyrene d i s -cussed l a t e r ) . 28 4. Choosing Fundamentals from the Symmetry Assigned L i n e s Once a l l the v i b r a t i o n a l frequencies of a molecule have been l o c a t e d and the a s s o c i a t e d v i b r a t i o n c l a s s i f i e d as to symmetry type the f i n a l step i n making an assignment i s to choose from a l l the l i n e s those which correspond to normal modes. In p r i n c i p l e , i t should be p o s s i b l e to assign a l l l i n e s as being a s s o c i a t e d w i t h e i t h e r a fundamental v i b r a t i o n , an overtone or a combination of fundamentals. In p r a c t i c e , the number of p o s s i b l e combinations and overtones i s u s u a l l y f a r too l a r g e and such a complete assignment i s not p o s s i b l e except at very low frequency. Combination l i n e s appear by s t e a l i n g i n t e n s i t y from nearby fundamentals e i t h e r by an i n t r a m o l e c u l a r i n t e r a c t i o n (e.g. anharmonic terms i n the p o t e n t i a l function) o r , p a r t i c u l a r l y i n the s o l i d s t a t e , by i n t e r m o l e c u l a r i n t e r a c t i o n s . The i n t e r a c t i o n s are small so the s t o l e n i n t e n s i t y w i l l be appreciable only i f the energies of the two s t a t e s i n v o l v e d are n e a r l y i d e n t i c a l . Thus the method of a s s i g n i n g fundamentals i s the f o l l o w i n g : s t a r t i n g at low frequency a l l l i n e s are assigned as fundamentals or combinations u n t i l the number of l i n e s appearing makes t h i s i m p o s s ible. Then fundamentals are chosen on the b a s i s of t h e i r s t r e n g t h and i s o l a t i o n from other strong l i n e s . I t i s , of course, p o s s i b l e t h a t a symmetry allowed fundamental may a c c i d e n t a l l y have no i n t e n s i t y , or t h a t two normal modes may be a c c i d e n t a l l y degenerate, and thus care may be needed i n 29 as s i g n i n g the l a s t fundamentals of a given symmetry type. The T e l l e r - R e d l i c h product r u l e (see r e f . 1) can be used as a guide to i n d i c a t e the energy region i n which to search f o r the l a s t one or two unassigned fundamentals of a symmetry block i f i n f o r m a t i o n i s a v a i l a b l e about the funda-mentals of more than one i s o t o p i c s p e c i e s . Other r u l e s r e l a t i n g the frequencies of i s o t o p i c a l l y s u b s t i t u t e d d e r i v a -57 58 t i v e s e x i s t , ' but only i n f r e q u e n t l y i s s u f f i c i e n t i n f o r -mation a v a i l a b l e to make them u s e f u l . I t i s o c c a s i o n a l l y v a l u a b l e as a check on the f i n a l assignment to use the funda-mental frequencies of the molecule to c a l c u l a t e c e r t a i n thermodynamic f u n c t i o n s (such as the heat c a p a c i t y and entropy) f o r comparison w i t h experimentally determined values. Once again, however, complete experimental i n f o r -mation i s o f t e n not a v a i l a b l e . CHAPTER I I EXPERIMENTAL A. Pr e p a r a t i o n of Samples 1. Source of chemicals a) Naphthalene. The naphthalene-hg used was su p p l i e d by the May and Baker Co., L t d . , England, and was p u r i f i e d by zone r e f i n i n g . The naphthalene-dg used was c e r t i f i e d 99% deuterium content from the S t o h l e r Isotope Chemicals Co., Montreal. I t was subjected to 100 passes on the z o n e - r e f i n e r , during which a dark brown im p u r i t y separated and t r a v e l l e d to the bottom of the column. Mass spectroscopic a n a l y s i s of the remaining sample showed t h a t approximately 20% of the molecules contained one hydrogen atom; i f c I Q D 7 H I -*-S T N E major i m p u r i t y then the f i n a l deuterium c o n t e n t . i s i n f a c t about 98%. b) Anthracene. Eastman-Kodak b l u e - v i o l e t f l u o r -e s cing anthracene-h^Q was used a f t e r zone r e f i n i n g . A lar g e s i n g l e c r y s t a l of h i g h l y - p u r i f i e d anthracene-d^^ was k i n d l y s u p p l i e d by Dr. D.F. Williams of the N a t i o n a l Research C o u n c i l . The monoprotonated i m p u r i t y was found to make up about 22% of the sample, corresponding to a deuterium content of approximately 9 7 . 8 % . 30 31 c) Acenaphthene. Eastman-Kodak w h i t e - l a b e l acen-aphthene was chromatographed according to the method des-59 c r i b e d by Sangster on s i l i c a g e l using petroleum ether as an e l u a n t . d) Pyrene. Eastman-Kodak pyrene-h^g was.chromato-59 graphed by Sangster's method using s i l i c a g e l and petroleum eth e r , and was then subjected to 100 passes on the zone r e -f i n e r . Pyrene-d^g was s u p p l i e d by Merck, Sharp and Dohme of Montreal and was p u r i f i e d by Miss V. V i l k o s ; the sample was e l u t e d onto a s i l i c a g e l column and developed w i t h petroleum eth e r , and then e l u t e d from the column and r e c r y s t a l l i z e d twice i n a 1:4 V/V petroleum ether:benzene mixture. Mass spec t r o s c o p i c a n a l y s i s showed s l i g h t l y l e s s than 17% c i g D 9 H ^ ' e) Solvents. F i s h e r s p e c t r o q u a l i t y benzene and carbon t e t r a c h l o r i d e were used without f u r t h e r p u r i f i c a t i o n , as were Matheson, Coleman and B e l l spectro-grade normal hydrocarbon s o l v e n t s . 2. Growth of s i n g l e c r y s t a l s S i n g l e c r y s t a l s were grown i n a l a r g e , g l a s s - w a l l e d Bridgman furnace by slow sublimation i n vacuum, from s o l u t i o n , o r , when t h i n c r y s t a l s were adequate, by r a p i d s u b l i m a t i o n i n an i n e r t atmosphere of carbon d i o x i d e . The cleavage faces of l a r g e ingots were r e a d i l y l o c a t e d and i d e n t i f i e d by 60 isogyre patterns using o p t i c a l data summarized by W i n c h e l l or a v a i l a b l e i n the l i t e r a t u r e . Often s e c t i o n s normal to a cleavage plane were needed. The i n t e r s e c t i o n of the d e s i r e d face of the c r y s t a l w i t h the cleavage plane was found and the c r y s t a l was cut normal t o the cleavage plane and p a r a l l e l to t h i s face. When such a face was prepared i t was placed on a smooth surface i n a d r i l l e d - o u t d i s k of the req u i r e d thickness (0.15 to 1.0 mm) and held i n place by p l a s t e r of P a r i s . When the p l a s t e r s e t , the u n f i n i s h e d side of the c r y s t a l was slowly ground w i t h f i n e emery paper. F i n a l p o l i s h i n g was c a r r i e d out on a g l a s s p l a t e covered w i t h a s o f t t i s s u e paper and dampened w i t h a s u i t a b l e s o l v e n t , e.g. benzene, acetone, e t c . When p o l i s h i n g was complete the o p t i c a l d i r e c t i o n s of the s e c t i o n were l o c a t e d w i t h a p o l a r i z i n g microscope and the sample was placed on a mount s u i t a b l e f o r the Raman or i n f r a r e d instrument to be used. The transmis s i o n e f f i c i e n c y of p o l a r i z e d l i g h t through a spectrometer v a r i e s with wave-6 2 length and depends on the angle between the e l e c t r i c v e c t o r of the i n c i d e n t l i g h t and the g r a t i n g r u l i n g ; to e l i m i n a t e t h i s e f f e c t a l l c r y s t a l s e c t i o n s were mounted with t h e i r o p t i c a l d i r e c t i o n s at 45° on each side of the v e r t i c a l . 33 B. Spectrometers and Acces s o r i e s I n f r a r e d s p e c t r a were measured on Perkin-Elmer model 301 and 421 i n f r a r e d spectrometers. The model 421 was used f o r the region between 3200 and 400 cm "L. In the region from 700 to 50 cm the model 301 was used; i t has a Golay d e t e c t o r , a globar source f o r energies above 160 cm ^ and a, high-pressure mercury lamp source f o r energies below 160 cm The r o t a t i o n a l spectrum of water below 400 cm ^ contains many strong l i n e s and the a i r i n the model 301 was c i r c u l a t e d continuously through a d r i e r to remove the water vapor. The frequency accuracy of the spectrometers was - 1 cm ^ and wit h the p o s s i b l e e r r o r s i n measurement of the l i n e p o s i t i o n the frequencies reported here were probably accur-ate to w i t h i n * 3 cm The s p e c t r a l s l i t width v a r i e d over the range of i n t e r e s t but was always l e s s than 4 era ^  and below 400 cm was about 1 era \ The i n c i d e n t r a d i a t i o n was p o l a r i z e d with P e r k i n -Elmer gold-wire g r i d p o l a r i z e r s — o n a s i l v e r bromide sub-s t r a t e f o r the region above 300 cm and, on polyethylene f o r the region below 500 cm Low frequency s o l u t i o n measure-ments were made i n an adjus t a b l e path length c e l l (1,5 and 10 mm) f i t t e d w i t h h i g h - d e n s i t y polyethylene windows. The Raman s c a t t e r i n g at r i g h t angles from s i n g l e c r y s t a l s of anthracene-d.^ e x c i t e d by an argon-ion l a s e r was focused i n t o a Spex model 1700-11 (3/4 meter, f/6) spectro-34 meter/spectrograph. An RCA1P2 8 p h o t o m u l t i p l i e r at the e x i t s l i t was attached to a pha s e - s e n s i t i v e d e t e c t o r tuned to the frequency of a chopper i n the l a s e r beam. The l a s e r , model 300 PV of the Orlando Research Corporation, F l o r i d a , was operated at maximum output i n t e n s i t y (nominally 50 mw) at 4879.9A. D i f f i c u l t i e s were experienced due to the high i n -t e n s i t y of the e x c i t i n g r a d i a t i o n s c a t t e r e d from imperfections i n the c r y s t a l s and the i n a b i l i t y of the spectrometer to separate t h i s l i g h t from the Raman-scattered r a d i a t i o n . Another complete set of sp e c t r a of anthracene-d^^ and a l l other Raman measurements were made on a Cary 81 Raman spectro-meter equipped w i t h a Spectrophysics model 125 helium-neon l a s e r . The o p t i c a l system s e l e c t e d l i g h t s c a t t e r e d co-a x i a l l y w i t h the e x c i t i n g beam. The observed frequencies were estimated to be accurate to t 3 cm \ Raman spectr a of molten samples contained under vacuum i n a 6 mm O.D. g l a s s tube were measured. The tube was i n c l i n e d at 45° to the v e r t i c a l so that only a small amount of m a t e r i a l was needed. The lower end had been closed and blown i n such a way as to provide a n e a r l y - f l a t surface p a r a l l e l to the c o l l e c t i n g lens of the instrument. Heating was achieved by applying a s u i t a b l e voltage to chromel heating wire wound around the tube and he l d i n place w i t h Sauereisen cement. Smaller spacings between the wires at the upper end prevented the samples from r e f l u x i n g i n the 35 t u b e . I t was f o u n d t h a t w i t h m o l t e n a n t h r a c e n e (m.p. 217°C) i n t h e t u b e i t s t i p c o u l d be k e p t f o r l o n g p e r i o d s w i t h i n I mm o f t h e s p h e r i c a l l e n s o f t h e s p e c t r o m e t e r w i t h o u t a p p r e c i a b l y h e a t i n g t h e l e n s . C. C r y s t a l D a t a a nd O p t i c a l P r o p e r t i e s 63 1. N a p h t h a l e n e C r y s t a l d a t a U J m.p. 80.2°C; m o n o c l i n i c a = 8.29, b = 5.95, c = 8.68 A, 6= 122.1°. s p a c e g r o u p P 2 i / a ( C ^ h ) ; 2 m o l e c u l e s / u n i t c e l l ; p e r f e c t c l e a v a g e ab p l a n e . 61 O p t i c a l p r o p e r t i e s . The o p t i c a x i a l p l a n e i s a c ; t h e a c u t e b i s e c t r i x , Z_, i s 9.5° f r o m c and c o n t a i n e d w i t h i n t h e o b t u s e m o n o c l i n i c a n g l e . D i r e c t i o n c o s i n e s r e l a t i n g m o l e c u l a r a n d c r y s t a l a x e s a N 0.8410 -0.4350 0.3217 b -0.4428 -0.2128 0.8709 £' = 0.3102 0.8750 0.3718 a* 0.8951 -0.0534 0.4424 c* -0.0477 0.9756 0.2143 X ~ / X Y. z x , y_ a n d z_ a r e d e f i n e d a c c o r d i n g t o t h e i n t e r n a t i o n a l c o n v e n -64 t i o n w i t h y_ and z_ t h e l o n g a n d s h o r t i n - p l a n e a x e s r e s p e c t i v e l y , 36 c' i s the c r y s t a l d i r e c t i o n normal to a and b, and a* and c* are the p r i n c i p a l o p t i c a l d i r e c t i o n s f o r v i s i b l e l i g h t i n the ac plane, a* being the obtuse and c* the acute b i s e c t r i x . 2. Anthracene C r y s t a l d a t a . m . p . 217°C; monoclinic a = 8.561, b = 6.036, c = 11.163 A, 6 = 124°42'. Space group P2 1/a ( C 2 h ) ; 2 molecules/unit c e l l ; P e r f e c t cleavage ab; a secondary 61 cleavage ac was never observed i n t h i s work. 6 i O p t i c a l data. The o p t i c a x i a l plane i s ac w i t h the acute b i s e c t r i x , Z_, almost p a r a l l e l to c, and contained w i t h i n the obtuse monoclinic angle. The angle Z_ A c was found to be about 2° l e s s than the p r e v i o u s l y r e p o r t e d * ^ 7.5°. The a x i s c' i s normal to both a and b and the a x i s a' i s normal to both b and c. D i r e c t i o n cosines r e l a t i n g molecular and c r y s t a l axes f - 1 ' 0.8059 -0.4960 -0.3234V b -0.4347 -0.1248 -0.8919 Z c ' = 0.4020 0.8953 -0.3162 z a' 0.8914 0.0814 -0.4457 c -0.1283 0.9989 -0.0759^ The axes are defined i n Figure 4. 3. Acenaphthene 6 6 C r y s t a l data. m.p. 95°C; orthorhombic a = 8.290, o 2 b = 14.000, c = 7.225 A. The space group i s Pcm2i (C_ ) i n 37 C' Figure 4. The anthracene u n i t c e l l : (a) the ac face showing the axes a' (normal to c) and c' Tnormal to a) and the p r o j e c t i o n of the anthracene molecule. The b a x i s i s normal t o the ac plane; (b) the ab face of the anthracene u n i t c e l l . which a molecular (&—). and a c r y s t a l l o g r a p h i c ( o — ) m i r r o r plane c o i n c i d e . The four molecules i n each u n i t c e l l f a l l i n t o two independent s e t s ; molecules I and I I belong t o one set and I I I and IV to the other. P e r f e c t a£ cleavage, good ab cleavage. 67 O p t i c a l data. The o p t i c a x i a l plane i s be, w i t h the acute b i s e c t r i x , Z = b. 38 D i r e c t i o n cosines r e l a t i n g molecular and c r y s t a l axes Molecular type a 0.0000 0.0000 1.0000 I b = 0 .0000 1.0000 0.0000 c 1.0000 0.0000 0.0000 v -0.8787 0.0000 0.4744 I I I b = O.QOOO 1.0000 0.0000 c 0.4744 0.0000 0.8787 X z x Z z The d i r e c t i o n cosines of molecules I I and IV can be found by c a r r y i n g out the operation corresponding to a screw r o t a t i o n C^ - on the d i r e c t i o n cosines of I and I I I r e s p e c t i v e l y . See Figure 5 f o r the d e f i n i t i o n of molecular axes and numbering. Figure 5. The acenaphthene u n i t c e l l ; molecules I and I I are r e l a t e d by C^/ as are molecules I I I and IV. 39 4. P y r e n e 6 8 C r y s t a l d a t a . m.p. 150°C; m o n o c l i n i c , a = 1 3 . 6 5 , b = 9.26, c = 8.47 A, 3 = 100.28°. S p a c e g r o u p P 2 1 / a ( C ^ ) • 4 m o l e c u l e s / u n i t c e l l ; p e r f e c t ab c l e a v a g e . 69 O p t i c a l d a t a . The o p t i c a x i a l p l a n e i s b e * , w h e r e c * , t h e a c u t e b i s e c t r i x , makes a n a n g l e o f 34.3° w i t h c i n t h e a c p l a n e ( s e e F i g u r e 6) a n d a * , t h e t h i r d p r i n c i p a l o p t i c a l d i r e c t i o n , makes an a n g l e o f 24.0° w i t h a. The a x i s c 1 i s n o r m a l t o b o t h a and b. a' a* F i g u r e 6. (a) The u n i t c e l l o f t h e p y r e n e c r y s t a l , (b) O r i e n t a t i o n o f m o l e c u l a r a x e s a nd o p t i c a l d i r e c t i o n s i n t h e ac p l a n e . 40 D i r e c t i o n c o s i n e s r e l a t i n g t h e m o l e c u l a r a n d  c r y s t a l a x e s f a > '-0.6428 0.5976 0 . 4 8 6 3 N b 0.7466 0.6280 0.2232 c ' = 0.1736 -0.5000 0.8434 a* -0.6572 0.7504 0.0961 c * -0.1084 -0.2089 0.9733 CHAPTER I I I THE VIBRATIONS OF NAPHTHALENE I n t r o d u c t i o n 1. C r i t i c a l r e v i e w 14 A r e c e n t i n v e s t i g a t i o n o f t h e Raman s p e c t r a o b t a i n e d f r o m s i n g l e c r y s t a l s o f n a p h t h a l e n e - h g h a s l e d t o a s e e m i n g l y s e c u r e e x p e r i m e n t a l a s s i g n m e n t o f t h e g e r a d e f u n d a m e n t a l v i b r a t i o n s , a n d t h e i n t e r p r e t a t i o n o f t h e c r o w d e d i n f r a r e d s p e c t r u m h a s b e e n a i d e d b y r e c e n t l y p u b l i s h e d c a l -41 c u l a t i o n s o f t h e p l a n a r f u n d a m e n t a l s . The v i b r a t i o n a l s p e c t r a o f n a p h t h a l e n e - d g h a v e b e e n s t u d i e d i n l e s s d e -t a i l ^ 8,10,12 s e v e r a l d i f f e r e n c e s b e t w e e n t h e e x p e r i m e n t a l 34 35 41 70 a s s i g n m e n t s a n d t h o s e b a s e d o n c a l c u l a t e d f r e q u e n c i e s ' ' ' 7 8 12 h a v e a r i s e n . P r e v i o u s Raman s t u d i e s ' ' o f n a p h t h a l e n e - d g h a v e b e e n c a r r i e d o u t u s i n g m e r c u r y - a r c e x c i t a t i o n a n d h a v e a l l i n v o l v e d s a m p l e s i n t h e m e l t o r i n t h e f o r m o f p o w d e r e d c r y s t a l s . One a i m o f t h e p r e s e n t w o r k h a s b e e n t o m e a s u r e t h e p o l a r i z e d Raman s p e c t r a , u s i n g l a s e r e x c i t a t i o n , f r o m s i n g l e c r y s t a l s o f p e r d e u t e r a t e d n a p h t h a l e n e t o a s s i g n t h e g f u n d a m e n t a l modes. 41 42 The complex i n f r a r e d spectrum has been given various 6 — 10 i n t e r p r e t a t i o n s by d i f f e r e n t authors; the assignments have been made, i n g e n e r a l , from band contours i n the gas 6 6 8 9 phase, from s o l u t i o n s p e c t r a , or from p o l a r i z e d ' ' or even 7 10 u n p o l a r i z e d ' spect r a of the ab face of s i n g l e c r y s t a l s . B 2 u bands are weak i n the ab face and were assigned on the bas i s of t h e i r increased r e l a t i v e strength i n the vapor or l i q u i d phases. Thus a second aim of the present work was to record the p o l a r i z e d i n f r a r e d s p e c t r a from the ac face of naphthalene-dg c r y s t a l s i n an attempt to more f i r m l y l o c a t e the c - p o l a r i z e d B 2 u bands. In a d d i t i o n , the p o l a r i z e d s p e c t r a of both the ac and the ab faces were extended to low frequency to v e r i f y the e a r l i e r assignments based on unpolar-i z e d s p e c t r a " ^ and to l o c a t e the l a t t i c e v i b r a t i o n s . The low frequency i n f r a r e d s p e c t r a of the ab and p r e v i o u s l y un-st u d i e d ac faces of naphthalene-hg were a l s o run. 2. S e l e c t i o n Rules The naphthalene molecular axes were chosen accor-64 ding t o the i n t e r n a t i o n a l convention (see Chapter I I ) . Although the naphthalene molecule may be s l i g h t l y d i s t o r t e d 0 J i n the c r y s t a l , i t i s a s u f f i c i e n t l y c l o s e approximation to assume t h a t i t r e t a i n s i t s f u l l D2n' symmetry. The f a c t o r group i s C 2^ and the naphthalene molecule i s l o c a t e d i n the c r y s t a l at a s i t e having C^ symmetry. 43 T a b l e 1. C o r r e l a t i o n t a b l e f o r n a p h t h a l e n e M o l e c u l a r g r o u p S i t e g r o u p F a c t o r g r o u p D 2h N B a s e s C i '2h B a s e s n 9 x x , y y , z z 3 xy_ B 4 x z B 8 y z B i g 2g 3g I a a , b b , a b , be 4 8 8 4 Y x u B l u B B 2u 3u A u *u J u b a , c 2 1 N i s t h e number o f f u n d a m e n t a l s i n t h e f r e e m o l e c u l e a n d n i s t h e number o f l a t t i c e f r e q u e n c i e s h a v i n g k = 0. F a c t o r g r o u p s ymmetry s p e c i e s a r e d i s t i n g u i s h e d b y t h e u s e o f l o w e r c a s e s y m b o l s . 44 The s e l e c t i o n r u l e s f o r t h e f r e e m o l e c u l e a n d f o r t h e c r y s t a l a r e s u m m a r i z e d i n T a b l e 1. E a c h f r e e m o l e c u l e s t a t e g i v e s r i s e t o two c r y s t a l s t a t e s , b u t b e c a u s e t h e m o l e c u l e s i t s a t a c e n t e r o f symmetry i n t h e c r y s t a l , m i x i n g b e t w e e n g (Raman a c t i v e ) a n d u ( i n f r a r e d a c t i v e ) m o l e c u l a r s t a t e s d o e s n o t o c c u r . An A u s t a t e , i n a c t i v e i n t h e f r e e m o l e c u l e , may m i x w i t h o t h e r u s t a t e s i n t h e c r y s t a l a n d t h u s may a p p e a r i n t h e i n f r a r e d s p e c t r u m w i t h t h e p o l a r i z a t i o n c h a r a c t e r i s t i c s o f t h e s t a t e w i t h w h i c h i t i s i n t e r a c t i n g . The number o f l a t t i c e modes a n d t h e c r y s t a l d i r e c t i o n i n w h i c h t h e y a r e e x p e c t e d a r e a l s o g i v e n i n T a b l e 1. The f a c t o r g r o u p a n a l y s i s i s made f o r t h e c a s e w h e r e t h e wave v e c t o r , k, e q u a l s z e r o . Two CH s t r e t c h i n g modes a r e e x p e c t e d i n e a c h i n -p l a n e s y mmetry b l o c k a n d s o b e l o w 2000 cm 7 A g , 3 B l g r 4 B 2 g ' 6 B 3 g ' 4 A u ' 6 B l u ' 6 B 2 u a n d 4 B 3 u f u n d a m e n t a l v i b r a t i o n s s h o u l d a p p e a r . I n t h e u s u a l o r i e n t e d - g a s a s s u m p t i o n ( s e e C h a p t e r I , s e c t i o n B.3) t h e d i r e c t i o n c o s i n e s ( C h a p t e r I I ) r e l a t i n g t h e m o l e c u l a r a n d c r y s t a l a x e s d e t e r m i n e t h e r e l a t i v e i n t e n -s i t i e s o f a m o l e c u l a r l i n e i n t h e Raman s p e c t r a f r o m t h e v a r i o u s c r y s t a l f a c e s ; t h e r e s u l t s a r e g i v e n i n T a b l e 2. The p r o j e c t e d i n t e n s i t i e s o f t h e i n f r a r e d - a c t i v e modes i n t h e same a p p r o x i m a t i o n a r e l i s t e d i n T a b l e 3. The a n a l y s i s p r e s e n t e d i n t h i s t h e s i s i s b a s e d on t h e a s s u m p t i o n t h a t t h e 45 p o l a r i z a t i o n r a t i o s a r e n o t s o d i s t u r b e d b y t h e c r y s t a l m i x i n g o f m o l e c u l a r s t a t e s as t o be r e v e r s e d . T a b l e 2. The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s o f f r e e - m o l e c u l e Raman l i n e s o f n a p h t h a l e n e i n v a r i o u s c r y s t a l c o n f i g u r a t i o n s I (A C T) I (A_) I ( A a ) I (B1 ) I (B_ ) I (B. ) x x 9 y_y_ g zz <3 gy_ l g x z 2g y_z_ 3g I 0.500 0.036 0.011 0.535 0.293 0.078 aa I . . 0.038 0.002 0.575 0.036 0.595 0.137 D P ^,, c, 0.009 0.586 0.019 0.295 0.053 0.423 I b 0.139 0.009 0.078 0.000 0.348 0.200 I. . 0.018 0.035 0.105 0.206 0.011 0.466 D C a* a* : * *0.000 0.906 0.002 0.009 0.000 0.175 c * c * : * *0.002 0.003 0.009 0.767 0.029 - 0.176 a * c * 0.642 0.000 0.038 0.009 0.627 0.002 46 Table 3. The oriented-gas predictions of the r e l a t i v e i n t e n s i t i e s of the infrared active l i n e s of naphthalene along various c r y s t a l axes B, (z) lu — B 2 u ( ^ B 0 (x) 3u — I a 0.104 0.189 0.707 Z b 0.758 0.045 0.196 v 0.138 0.766 0.096 0.196 0.003 0.801 V 0.046 0.952 0.002 B. Results 1. The Raman Spectra The Raman spectra are shown.in Figures 7 and 8 and the frequencies l i s t e d i n Tables 4 and 5. The weaker li n e s are best seen i n Figure 8 where the detector s e n s i t i v i t y i s about f i v e times greater than i n Figure 7. The spectral s l i t 47 ( 0 * 0 * ) 1 I „ A \. 1 1 1 Ll —l 1 1 1 ( c * c * ) \ « A , / 1 1 1 // 1 ] I A , A 1 l l i I i i l i i i ' i 1 I 1 1 1 1 1 1 1 ] 1 1 1 0 2 0 0 4 0 0 6 0 0 8 0 0 IOOO 1200 I4CO 1600 2 2 0 0 WAVENUMBER (CM-1) Figure 7. The Raman spectr a obtained from the ac face of naphthalene-dg. The n o t a t i o n i s defined i n Table 4. width of the Cary 81 spectrophotometer v a r i e d over the range of observation but was normally l e s s than 5 cm ^ and i n complex regions the spect r a were repeated w i t h considerably narrower s l i t s . I t was found t h a t the 831 and 838 cm-"*" l i n e s , which were separated i n the c r y s t a l , could not be re s o l v e d i n s o l u t i o n . No attempt was made to c o r r e c t f o r var y i n g d e t e c t o r 48 Figure on f o l l o w i n g page. Figure 8. The Raman spectr a obtained from the ab and be' faces of naphthalene-dg. The n o t a t i o n i s d e f i n e d i n Table 4. The d e t e c t o r s e n s i t i v i t y i s approximately f i v e times g r e a t e r than f o r the s p e c t r a shown i n Figure 7. WAVENUMBER (CM"') 50 Table 4. The Raman spectr a near the e x c i t i n g l i n e from c r y s t a l s of naphthalene-dg'f (a*a*) (c*c*) (a*c*) (aa) (bb) (c'c') (ab) (be' ) Sym-metry 43 mw 43 mw bg 49 w 49 s 49 vw 49 ms a g 68 vw 70 ms bg 70 vs 70 w 70 vs a g 102 s 102 mw 102 m 102 m a g 117 mw bg The two c r y s t a l d i r e c t i o n s w i t h i n parentheses at the top of each column define the d i r e c t i o n of p o l a r i z a t i o n of the i n c i d e n t and s c a t t e r e d r a d i a t i o n r e s p e c t i v e l y . T a b l e 5. R e l a t i v e l i n e s t r e n g t h s i n t h e Raman s p e c t r a o f naphthalene-d„ ab o v e 150 cm A v ( c m - 1 ) p+ ( a * a * ) ( c * c * ) ( a * c * ) (aa) (bb) ( c ' c ' ) (ab) (be') Symmetry 162 — — -- — lh 3 — 348 0.75 h 1 2h h 2 h 3 i g B 2 g A g 410 0.8 h h l 2h 0 i 0 494 0.40 43 6 6 5 58 3 14 547 0.80 h 2 lh lh 2 i g 649 h 0 h 0 2g Ag 697 0.23 4 l l 1 17 14 4 3% 761 0.8 h lh 1 0 2 0 2 i g 831 838 0.70 1 8 3 3 10 Z 6 862 0.20 12 35 4 21 35 41 8 8 Ag 884 0 1 967 h 0 h 1175 h h 1214 0 1249 0 1274 0 1295 0.23 0 12 1 h 0 13 h 3 A g 1317 h h T a b l e 5. ( C o n t i n u e d ) Av (cm - ( a * a * ) ( c * c * ) ( a * c * ) (aa) (bb) ( c ' c ' ) fab) (be') Symmetry 1359 h h 1 h 1386 0.33 3h 100 9 13 22 100 9 22 Ag 1418 h 1428 h 1552 0.66 3 5 h 3 20 3 4 6 Ag 1605 ih 0 h 1 3g 2261 2 1 s h I B 7 3g-2276 0.39 1 5 1 2 5 9 2 3 A g 2292 0.07 h 5 1 3 8 1 1 A g 2304 P + + 1 h 1 2 h 0 A g t The d e p o l a r i z a t i o n r a t i o , p, s h o u l d h a v e t h e v a l u e 0.75 f o r n o n -• t o t a l l y s y m m e t r i c modes. p = p o l a r i z e d . 53 s e n s i t i v i t y i n d i f f e r e n t r e g i o n s o f t h e s p e c t r u m b u t a t e a c h f r e q u e n c y t h e s p e c t r a f r o m t h e v a r i o u s f a c e s w e r e m e a s u r e d u n d e r a s n e a r l y t h e same c o n d i t i o n s a s p o s s i b l e . The r e l a t i v e i n t e n s i t y s c a l e s i n T a b l e 5 r u n f r o m 0 t o 100 f o r t h e ab a n d be' f a c e s , a n d f o r t h e a c f a c e i n d e p e n d e n t l y . D e p o l a r i z a t i o n r a t i o s w e r e m e a s u r e d i n b e n z e n e a n d c a r b o n t e t r a c h l o r i d e s o l u t i o n s . E v e n s o , t h e s y m m e t r i e s o f s e v e r a l o f t h e weak l i n e s , p a r t i c u l a r l y i n t h e r e g i o n f r o m 900 t o 1400 cm-"'', c o u l d n o t be d e t e r m i n e d d e f i n i t e l y b e c a u s e i n t h e o n l y s p e c t r a i n w h i c h t h e y a p p e a r e d , ( c 1 c ' ) o r ( c * c * ) , d i s t i n c t i o n b e t w e e n B^g l i n e s a n d Ag l i n e s a l l o w e d t h r o u g h t h e a m o l e c u l a r o p e r a t o r was i m p o s s i b l e . 2. The I n f r a r e d S p e c t r a The p o l a r i z e d i n f r a r e d s p e c t r a i n t h e r e g i o n f r o m 2300 t o 600 cm-"1" o f t h e ab and a c f a c e s o f n a p h t h a l e n e - d g a r e g i v e n a s F i g u r e 9. The ab s p e c t r u m a g r e e s w e l l w i t h t h a t g p r e v i o u s l y p r e s e n t e d a n d i s i n c l u d e d o n l y t o f a c i l i t a t e com-p a r i s o n b e t w e e n t h e d i f f e r e n t f a c e s . S u b l i m a t i o n d u r i n g t h e s c a n was n e g l i g i b l e . The l o w - e n e r g y i n f r a r e d s p e c t r a f r o m t h e ab and a c f a c e s a r e g i v e n as F i g u r e 1 0, a n d may be com-p a r e d w i t h t h e s o l u t i o n s p e c t r u m i n b e n z e n e g i v e n as F i g u r e 7 1 1 . I n a l l s p e c t r a t h e a p p e a r a n c e o f b a n d s a p p a r e n t l y due t o n a p h t h a l e n e - d ^ , h ^ i s o b s e r v e d . The l i n e s o b s e r v e d i n t h e i n f r a r e d s p e c t r u m o f n a p h t h a l e n e - d f i a r e s u m m a r i z e d i n T a b l e 6. 54 Figure on f o l l o w i n g page. Figure 9. Naphthalene-dg i n f r a r e d s p e c t r a above 600 cm : (a) I n c i d e n t l i g h t normal to the ac face; s o l i d l i n e // c*, broken l i n e // a*; c r y s t a l 0.18 mm t h i c k . (b) Incident l i g h t normal to the ab face; s o l i d l i n e // b, broken l i n e // a; c r y s t a l 0.15 mm t h i c k . In both 7 spect r a lxnes due to i s o t o p i c i m p u r i t i e s are marked w i t h arrows. 55 Figure 10. Naphthalene-dg low-energy c r y s t a l i n f r a r e d s p e c t r a : (a) I n c i d e n t l i g h t normal to the ac face; s o l i d l i n e // c*, broken l i n e //a*; c r y s t a l 0.32 mm t h i c k , (b) Incident l i g h t normal to ab face; s o l i d l i n e //b, broken l i n e //a; c r y s t a l 0.45 mm t h i c k below 150 cm~l, 0.25 mm t h i c k above 150 cm~l. 57 Table 6. The i n f r a r e d spectrum of naphthalene-d g v c r y s t a l Symmetry v c r y s t a l Symmetry 63 ms b 82 8 vs B_ u 2u 100 m - a., 836 m B_ u 3u 164 s > 877? s B 0 ? \ B . 2u 178 m ) 3u 879 vs B x 193 ms A u 906 m i s o t o p i c * 328 ms B l u 920 ms i s o t o p i c * 351 w i s o t o p i c ? 954 w B_ ~ 2u 372 vw B_ 964 w B„ ? 2u 2u 392 m? B„ 970 vw B„ 2u 2u 400 ms? i 1045 vw B. > R l u 407 vs S 3u 1053 vw B-3u 425 s i s o t o p i c ? 1085 m B, 447 w B_ ? 1160 vw B 0 3u 2u 2u S,483 vw 1172 w B 2 u 516 vw B„ 1181 mw B„ 2u 2u 538 mw B 2 u 1192 vw 568 mw i s o t o p i c * 1204 mw ^lu 590 ms B 2 u 1217 vw B 2 u 62 8 vs B 3 u 1228 mw B ^ 647 s 1240 mw 658 mw i s o t o p i c * 1249 w B 1 672 s B 3 u 1257 ms B ^ 738 mw B l u 1273 mw B ^ 772 w i s o t o p i c * 1310 mw 'B^ 769 w shoulder 13 41 ms B 2 u 791 s B l u 1393 ms B 2 u 797 vw shoulder 1416 m B ^ 803 w 1425 mw B„ 2u Table 6. (Continued) 5 8 ' c r y s t a l Symmetry v c r y s t a l Symmetry 1439 1452 1542 1550 1562 1570 ms m m mw m m 2u 2u B 7 2u l u 2u 2250-75 vs 2260-90 vs 2288 ms B l u B 2u B l u Ref. 7. The low-frequency, p o l a r i z e d i n f r a r e d s p e c t r a of the ab and ac faces of s i n g l e c r y s t a l s of naphthalene-hg are presented as Figure 12 and the r e l e v a n t data are summarized as Table 7. 59 Figure 12. Naphthalene-hg low-energy c r y s t a l i n f r a r e d spectrum: (a) In c i d e n t l i g h t normal to the ac face; s o l i d l i n e / / c * , broken l i n e / / a * . (b) Incident l i g h t normal to the ab face; s o l i d l i n e //b, broken l i n e / / a . For both Ta) and (b) the c r y s t a l s were 0.4 mm t h i c k above 150 cm~l and 1.5 mm t h i c k below 150 cm - 1. 60 Table 7. The i n f r a r e d spectrum of naphthalene-hg at low energy S o l u t i o n * 181 C r y s t a l 66 ms 100 m 177 vs 19 2 ms Assignment u u B 3u 358 473 210 m 213 s 359 ms 470 s 480 vs u B l u B 3u 507? 562 Benzene 500 sh 510 vw 554 w 572 w 595 vvw 614 ms B 2u B 2u A s o l u t i o n i n benzene 61 C. Assignment of Fund ante nta 1 s 1. L a t t i c e v i b r a t i o n s Three i n f r a r e d - a c t i v e l a t t i c e v i b r a t i o n s are ex-pected, two a u p o l a r i z e d along b and one b u p o l a r i z e d i n the ac plane. The l i n e s at 100 cm 1(//b) and 66 cm "^(//a) i n naphthalene-hg must correspond to the highest energy a u and the bu t r a n s l a t i o n a l modes r e s p e c t i v e l y ; the corresponding l i n e s i n naphthalene-dg l i e at 100 cm~l and 63 cm ^. The l i n e seen at 53 cm ^ i n the protonated molecule by Harada and 71 Shimanouchi and assigned as the lowest a u l a t t i c e v i b r a t i o n was not found. Wyncke et a l . ^ reported an a - p o l a r i z e d t r a n s i t i o n at 54 cm ^ and weak b - p o l a r i z e d l i n e s at 44, 49, 57, 63 and 80 cm i n naphthalene-hg; none of these were observed. S i x Raman-active l a t t i c e v i b r a t i o n s are expected, three belonging to each of the ag and bg c l a s s e s . The l i n e s at 4 3 ( b g ) , 4 9 ( a g ) , 7 0 ( b g ) , 7 0 ( a g ) , 102 (a g) and 117 cm~ 1(b g) i n the naphthalene-dg spectrum correspond to these v i b r a t i o n s ; the agreement w i t h the naphthalene-hg modes reported by 14 Suzuki, Yokoyama and I t o i s good. 2. Raman-active molecular v i b r a t i o n s E i g h t of the nine expected Ag molecular modes can be r e a d i l y i d e n t i f i e d at 494, 6 9 7 , 8 6 2 , 1 2 9 5 , 1386, 1 5 5 2 , 62 2276 a nd 2292 cm ^ f r o m t h e i r s t r e n g t h and d e p o l a r i z a t i o n r a t i o s . The a p p r o x i m a t e l o c a t i o n o f t h e r e m a i n i n g f u n d a -m e n t a l may be c a l c u l a t e d f r o m t h e p r o d u c t r u l e , u s i n g t h e 14 n a p h t h a l e n e - h g f r e q u e n c i e s r e p o r t e d a t 514, 7 6 5 , 1 0 2 1 , 114 8 , 1 3 8 0 , 1 4 6 5 , 1579 and 3058 c m - 1 a n d i n c l u d i n g a s e c o n d CH s t r e t c h i n g f r e q u e n c y a r b i t r a r i l y l o c a t e d a t 3050 cm The e x a c t l o c a t i o n o f t h i s s e c o n d CH s t r e t c h i n g mode i s n o t known, b u t f o r a p r o d u c t r u l e c a l c u l a t i o n t h e e s t i m a t e d f r e -q u e n c y i s s u f f i c i e n t l y a c c u r a t e . The t h e o r e t i c a l v a l u e f o r t h e r a t i o o f t h e p r o d u c t s o f t h e f r e q u e n c i e s o f t h e two m o l -e c u l e s i s 0.250, w h i c h r e q u i r e s t h a t t h e unknown f r e q u e n c y o f t h e r e m a i n i n g Ag mode l i e n e a r 800 cm ^. From t h e Raman s p e c t r u m t h e l i n e s a t 8 3 1 , 838 and 884 a r e t h e o n l y p o s s i b l e 45 c h o i c e s f o r t h i s Ag mode. C r a i g a n d H o l l a s h a v e shown t h a t -1 72 t h e l i n e a t 884 cm i s due t o a v i b r a t i o n , a n d M c C l u r e 3g f o u n d t h a t t h e 831 cm 1 t r a n s i t i o n a l s o b e l o n g s t o t h e B^g c l a s s . ( T h e i r v a l u e s a r e 881 a n d 826 cm 1 r e s p e c t i v e l y ; t h e Raman f r e q u e n c i e s o b s e r v e d i n t h i s w o r k a r e c o n s i s t e n t l y a few wavenumbers a b o v e t h o s e r e p o r t e d i n e a r l i e r p a p e r s . ) Hence t h e l i n e a t 838 cm 1 m u s t mark t h e p r e s e n c e o f t h e r e m a i n i n g Ag f u n d a m e n t a l i n t h e d e u t e r a t e d m o l e c u l e , c o n f i r m -12 i n g t h e a s s i g n m e n t made by L u t h e r e t . a l . The r e s u l t i n g p r o d u c t r u l e r a t i o i s 0.260. The t h r e e B l g f u n d a m e n t a l s o f n a p h t h a l e n e - d g m u s t be a s s o c i a t e d w i t h t h e l i n e s a t 3 4 8 , 547 and 761 c m - 1 , w h i c h 63 a r e t h e o n l y l i n e s s h o w i n g c h a r a c t e r i n t h e e n t i r e s p e c -14 t r u m . The r e p o r t e d f r e q u e n c i e s f o r n a p h t h a l e n e - h g a r e 39 0 , 725 a n d 933 cm "S t h e r e s u l t i n g p r o d u c t r u l e r a t i o i s 0.549, c o m p a r e d w i t h t h e t h e o r e t i c a l v a l u e o f 0.531. O n l y two o f t h e f o u r B 2 g modes c a n be i d e n t i f i e d i n t h e Raman s p e c t r u m o f n a p h t h a l e n e - d g ; t h e s e c o r r e s p o n d t o t h e l i n e s o b s e r v e d a t 410 and 649 cm ^. C o m p a r i s o n w i t h t h e 14 B 2 g f u n d a m e n t a l s o f t h e p r o t o n a t e d m o l e c u l e i n d i c a t e s t h a t t h e two h i g h - e n e r g y modes h a v e n o t b e e n i d e n t i f i e d , a n d t h e s e m u s t e i t h e r be t o o weak t o b e f o u n d o r m u s t be h i d d e n u n d e r s t r o n g e r l i n e s . The B^g symmetry b l o c k i s t h e l e a s t u n d e r s t o o d . 45 C r a i g a n d H o l l a s h a v e shown t h a t one l i n e due t o a B^g v i b r a t i o n l i e s a t 490 cm v e r y c l o s e t o t h e Ag f u n d a m e n t a l w h i c h t h e y p l a c e a t 492 cm 1 and we f i n d a t 494 cm 1 . We w e r e u n a b l e t o r e s o l v e t h e s e two l i n e s . The n e x t two f u n d a -72 45 m e n t a l s i n t h i s b l o c k h a v e b e e n a s s i g n e d ' t o t h e f r e q u e n -c i e s a t 831 a n d 884 cm \ and t h e h i g h e s t - e n e r g y B^g f u n d a -m e n t a l b e l o w t h e CD s t r e t c h i n g r e g i o n i s c l e a r l y a s s o c i a t e d w i t h t h e l i n e a t 1605 cm ^ w h i c h h a s n e v e r b e e n a s s i g n e d a s a f u n d a m e n t a l b e f o r e . The p o s i t i o n s o f t h e two r e m a i n i n g B- modes b e l o w 2000 cm ^ i s u n c e r t a i n . E a c h o f t h e l i n e s 3g o b s e r v e d i n t h e ( c ' c ' ) [ o r ( c * c * ) ] c r y s t a l s p e c t r u m a t 9 6 7 , 1 1 7 5 , 1 2 1 4 , 1 2 4 9 , 1 2 7 4 , 1317 and 1359 c m - 1 c o u l d be due 64 e i t h e r to a B_ fundamental, an A„ combination allowed 3g 9 through the #yy molecular operator, or an impurity molecule such as CgD^H^. The p o s s i b i l i t y that they are combinations of other than Ag symmetry seems very remote. A l l these l i n e s were so weak i n s o l u t i o n t h a t d e p o l a r i z a t i o n r a t i o measure-ments were not p o s s i b l e . Notably absent from e i t h e r c r y s t a l or s o l u t i o n s p e c t r a are the l i n e s v a r i o u s l y reported as 1022 cm i n 72 12 7 -1 mixed c r y s t a l fluorescence and 1030 or 1006 cm i n the melt Raman sp e c t r a e x c i t e d w i t h a mercury lamp; the l i n e at 1 2 - 1 1330 cm seen only i n the Raman s p e c t r a ; and the l i n e at -1 7 12 1573 cm seen weakly i n the melt Raman spectr a ' but 72 assigned as a combination from the fluorescence . Each of these absences i s important since the most recent c a l c u l a t i o n s have been r e f i n e d to f i t fundamentals assigned to these f r e -quencies. The l i n e at 1573 cm ^ may conveniently be replaced i n the assignment by the p r e v i o u s l y mentioned l i n e at 1605 cm-"'". I t i s recognized t h a t a l i n e which i s Raman a c t i v e may be weak i n f l u o r e s c e n c e , and v i c e v e r s a , so t h a t the l i n e reported at 1022 cm ^ may mark the presence of a B^g molecular fundamental i n t r i n s i c a l l y weak i n the Raman spectrum; however, the i s o l a t e d l i n e at 967 cm ^ may a l s o be a contender f o r t h i s p o s i t i o n i n the assignment and a f i n a l d e c i s i o n cannot be made u n t i l more con c l u s i v e experimental i n f o r m a t i o n i s a v a i l a b l e . The l o c a t i o n of the remaining B^g fundamental 41 below 2000 cm ^ must a l s o remain u n c e r t a i n . While we f e e l t h a t the assignment of a fundamental at 1330 cm i s almost c e r t a i n l y i n c o r r e c t , the experimental evidence does not yet permit a choice to be made from the s e v e r a l l i n e s observed near t h a t energy. Two CD s t r e t c h i n g frequencies are expected and the weak l i n e a t 2261 cm w i t h most of i t s strength i n the (c'c') and (c*c*) d i r e c t i o n s probably a r i s e s from one of them. The other i s perhaps hidden under the strong and r a t h e r broad Ag l i n e at 2276 cm ^. The only feature of the Raman spectrum which has not y e t been considered i s the band at 162 cm \ No gerade mode of naphthalene-dg i s expected i n t h i s region and the l i n e i s probably the analogue of the i n f r a r e d - a c t i v e l i n e 163 ( B3 U) a r i s i n g from the presence of a monoprotonated impurity due to the l i f t i n g of the symmetry r e s t r i c t i o n s , and s t e a l i n g i n t e n s i t y from the nearby strong l a t t i c e modes. A simple c a l c u l a t i o n on a-naphthalene-d^h w i t h the out-of-35 36 plane force f i e l d t r a n s f e r r e d from S c u l l y and Whiffen ' i n d i c a t e d t h a t the lowest B^ u mode of naphthalene-dg would s h i f t only 0.3 cm i n the monoprotonated molecule. 3. I n f r a r e d - a c t i v e molecular v i b r a t i o n s Although the i n f r a r e d s p e c t r a of naphthalene-dg have been the subject of even more study than the Raman spec-66 t r a , many p o i n t s of d i f f e r e n c e between the experimental 6 — 10 assignments s t i l l e x i s t . C a l c u l a t i o n s have been c a r r i e d 34 35 41 out ' ' i n an attempt to s e l e c t the c o r r e c t set from the many proposed fundamentals and the various assignments based on these c a l c u l a t i o n s are i n q u i t e good agreement. However, the o r i g i n a l experimental assignments were made e i t h e r ( i ) by analogy w i t h naphthalene-hg or ( i i ) by deducing the appear-ance of the c-axis spectrum from a comparison of the ab c r y s t a l s p e c t r a w i t h the s o l u t i o n spectrum, and i t was f e l t t h a t a more c a r e f u l study could improve the experimental s i t u a t i o n . In order to complete t h i s more accurate assignment, p a r t i c u l a r l y of the B 2 u c - p o l a r i z e d modes, the p o l a r i z e d s p e c t r a of the ab face and the p r e v i o u s l y unstudied ac face have been obtained. I t i s c l e a r (see Figures 9 and 10) t h a t f a r more l i n e s appear i n the sp e c t r a than there are funda-mentals. In order to choose from these many l i n e s , the c a l -c u l a t i o n s were used as a guide to l o c a t e the general region i n which to expect a fundamental. Thus the r e s u l t i n g a s s i g n -ment i s not s t r i c t l y experimental; i n view, however, of the apparent a b i l i t y of the c a l c u l a t i o n s t o f i t at l e a s t approxi-mately the frequencies of naphthalene-hg and the g-modes of naphthalene-dg (see Table 8) i t was f e l t t h a t the p r e d i c t i o n s of the force f i e l d c a l c u l a t i o n s should not be completely ignored. 67 The o n l y A u mode o f n a p h t h a l e n e - d g w h i c h c a n be f i r m l y i d e n t i f i e d i s a s s o c i a t e d w i t h t h e 193 cm ^ (191 cm "*" // b) l i n e a p p e a r i n g t h r o u g h c r y s t a l f o r c e s a n d t e n t a t i v e l y a s s i g n e d b y C h a n t r y e t a l . ^ f r o m t h e i r u n p o l a r i z e d s p e c t r a . The l o w - e n e r g y p o l a r i z e d s p e c t r a p r e s e n t e d i n F i g u r e 10 show t h a t t h e 16 6 cm ^ s o l u t i o n l i n e c l e a r l y s p l i t s i n t o a s t r o n g l i n e a t 164 cm "*" p a r a l l e l t o a i n t h e a c p l a n e a n d a w e a k e r component a t 178 cm ^ p a r a l l e l t o b , c l e a r l y c o n f i r m i n g i t s assignment"*"^ as a B ^ u m o l e c u l a r f u n d a m e n t a l . The r e m a i n i n g B^ f u n d a m e n t a l s a r e f i r m l y e s t a b l i s h e d a t 4 0 6 , 628 a n d 790 c m - 1 . The c o r r e s p o n d i n g e n e r g i e s f o r t h e l o w e s t mode i n n a p h t h a l e n e - h g a r e 177 cm 1 ( a £ p l a n e ) a n d 192 cm 1 ( / / b) and f o r t h e A u f u n d a m e n t a l 210 cm ^ (// b) and 213 cm ^ (ac p l a n e ) . I t i s i n t e r e s t i n g t o n o t e t h a t t h e s e s p l i t t i n g s 73 a g r e e w e l l w i t h t h e p r e d i c t i o n s o f R i c h and Dows b o t h i n m a g n i t u d e a nd s i g n . 41 C a l c u l a t i o n s h a v e p l a c e d t h e h i g h e s t B^ r i n g mode o f n a p h t h a l e n e - d g n e a r 1550 cm \ and t h e 1540 cm "*" l i n e h a s b e e n a s s i g n e d a s t h e o b s e r v e d f r e q u e n c y , a p p a r e n t l y 7 b a s e d on t h e u n p o l a r i z e d s p e c t r u m o f L i p p i n c o t t and O ' R e i l l y . F rom t h e ab s p e c t r u m t h e n e a r b y l i n e a t 1562 cm ^ i s a l s o c l e a r l y o f B ^ u s y m m e t r y , a n d s i n c e i n t h e a c s p e c t r u m i t i s much more c l e a r l y p o l a r i z e d t h a n t h e 1540 cm ^ t r a n s i t i o n , wh i c h shows c o n s i d e r a b l e B 3 u s t r e n g t h , we f e e l i t s h o u l d 68 take the place of 15 40 i n the assignment. The remaining B^ u 41 -1 assignments i n the reg i o n below 2000 cm seem e s s e n t i a l l y c o r r e c t , i f i n f a c t the weak l i n e at 1045 cm i s due to a B^ u fundamental as r e q u i r e d by the c a l c u l a t i o n s . The extremely strong absorption i n the C-D s t r e t -ching region has been v a r i o u s l y i n t e r p r e t e d , and as we have been unable to penetrate t h i s r egion i n the ac spectrum we can only suggest t h a t a l l four fundamentals (two B^ u, two B 2 u) l i e i n the very strong band between 2250 and 2290 cm ^. The B 2 u block i s p o o r l y understood. The highest 41 -1 energy B 2 u r i n g mode i s expected near 1450 cm but from the ab spectrum previous workers have been unable to l o c a t e any properly, p o l a r i z e d l i n e i n t h i s v i c i n i t y . In the ac spectrum, however, i t i s c l e a r t h a t the l i n e s at 1 3 9 3 , 1439 and 1452 cm a l l belong t o the B 2 u c l a s s and, on the b a s i s of s t r e n g t h , the l i n e at 1439 cm ^ may r a t h e r a r b i t r a r i l y be asso c i a t e d w i t h t h i s mode. The next highest fundamental has 41 -1 been placed at 1290 cm but only an extremely weak shoulder occurs at t h a t frequency; the nearest B 2 u l i n e i s the medium str o n g , w e l l - p o l a r i z e d l i n e at 1341 cm and t h i s may be the second B 2 u r i n g mode. The only a l t e r n a t i v e s appear to be the l i n e at 1393 cm (too high i n energy?), the l i n e at 1217 cm ^ (very weak) or the l i n e at 1181 cm (too low i n 41 energy?). The three other B 2 u l i n e s assigned at 5 9 3 , 828 and 1082 cm are confirmed i n the ac spectrum, although the 69 Table 8. Planar fundamental v i b r a t i o n s of Naphthalene-d Symmetry Assigned Previous Work ( t h i s work) Assigned C a l c u l a t e d 2291 2272 2295 2276 2257 2260 1552 1553 1542 1386 1381 1370 A g 1294 1 1293 1288 862 866 852 838 835 830 697 698 695 494 493 484 2278 2282 2232 2249 1562 1545 1543 B, 1257 1260 1245 l u 1045 1050 1045 879 885 840 738 734 749 328 328 336 2299 2293 2258 2256 1439 — 1466 B 2 u 1341 1290 1273 1082 1082 1086 880? 828 837 828 — 803 590 593 606 70 T a b l e 8. ( C o n t i n u e d ) Symmetry A s s i g n e d P r e v i o u s Work ( t h i s w o r k ) A s s i g n e d C a l c u l a t e d 2276? 2302 2275 2261 2257 2246 1605 1574 1598 — 1330 1338 967? 1030 1023 884 881 860 831 828 821 494 490 472 T a b l e 9. N o n - p l a n a r f u n d a m e n t a l v i b r a t i o n s o f N a p h t h a l e n e - d Symmetry A s s i g n e d P r e v i o u s Work ( t h i s w o r k ) A s s i g n e d C a l c u l a t e d — — 829 — 648 — — 511 193 — 185 761 784 751 547 545 528 348 346 316 — 829 812 — 760 754 649 663 665 410 445 429 71 Table 9. (Continued) Symmetry Assigned ( t h i s work) Previous Work 35 Assigned C a l c u l a t e d 791 790 798 B_ 628 628 594 3u 402 408 382 166 160 163 missing fundamental may l i e i n the region near 880 cm where considerable c p o l a r i z e d s t r e n g t h i s seen, r a t h e r than below -1 41 828 cm as suggested by Neto, Scrocco and Calxfano. The proposed fundamentals are summarized i n Tables 8 and 9. CHAPTER IV THE VIBRATIONS OF ANTHRACENE A. I n t r o d u c t i o n 1. C r i t i c a l Review Several assignments of the i n f r a r e d - a c t i v e v i b r a -t i o n s of anthracene"*"^ "^ and anthracene-d.^^' ^  have been made i n recent years. The assignments were reached by com-paring the p o l a r i z e d s p e c t r a obtained from the ab face of the c r y s t a l w i t h the s o l u t i o n or pressed-powder spectrum. B^ u t r a n s i t i o n s had t h e i r maximum strength p a r a l l e l to b and B 3 u t r a n s i t i o n s p a r a l l e l to a; the e s s e n t i a l l y c - p o l a r i z e d B 2 u t r a n s i t i o n s were expected to show greater r e l a t i v e s trength i n s o l u t i o n than i n the ab sp e c t r a . The reported assignments of the i n f r a r e d bands i n the region above 400 cm "*" have shown good agreement. However, the s e l e c t i o n of fundamentals from these many l i n e s has been r a t h e r more a r b i t r a r y and s e v e r a l p o i n t s of d i f f e r e n c e have a r i s e n . One aim of the present work has been to record the s p e c t r a w i t h l i g h t p o l a r i z e d along the c-axis to ass i g n more f i r m l y the B_ bands. The c - p o l a r i z e d spectrum of 72 17 74 anthracene-h 1 0 has already been reported; ' however, the measurements extend only down to 450 cm , and some a s s i g n -ed ments are s t i l l u n c e r t a i n . For anthr a c e n e - d ^ the p o l a r i z 16 17 spe c t r a from the ab face have been recorded ' down to about 400 cm "*"; no c-axis measurements have been reported and no in f o r m a t i o n at a l l i s a v a i l a b l e f o r the region below 400 cm ^. Thus another aim of the present work has been to extend the p o l a r i z e d measurements f o r both c r y s t a l s to the low-energy region where agreement between the anthracene-h^g 19 40 41 75 observed and c a l c u l a t e d ' ' frequencies i s poor. The Raman spectrum of anthracene-h^g has been ex-14 20-23 t e n s i v e l y s t u d i e d ' and the recent i n v e s t i g a t i o n by 14 Suzuki, Yokoyama and I t o using s i n g l e c r y s t a l s and l a s e r e x c i t a t i o n has c l a r i f i e d the experimental s i t u a t i o n consid-e r a b l y . An unp o l a r i z e d Raman spectrum of an anthr a c e n e - d ^ 22 c r y s t a l has been reported and another aim of t h i s work has been to ob t a i n the p o l a r i z e d Raman spectr a of mono-c r y s t a l l i n e anthracene-d^g i n order to improve the a s s i g n -ment of the gerade fundamental v i b r a t i o n s . 2. S e l e c t i o n Rules The anthracene molecular axes have been chosen according to the recommendations of the J o i n t Commission 64 f o r Spectroscopy. The x-a x i s l i e s normal to the molecular plane, the y_-axis i s the long molecular a x i s and the z-axis 74 completes the right-hand s e t . Although the anthracene 6 5 molecule i s very s l i g h t l y buckled i n the c r y s t a l , i t i s a s u f f i c i e n t l y good approximation to assume t h a t i t r e t a i n s i t s f u l l sYmae^-rY • T n e anthracene molecule s i t s at a s i t e of C i symmetry i n the c r y s t a l and the f a c t o r group i s C,,. The s e l e c t i o n r u l e s f o r the f r e e molecule and f o r the 2h c r y s t a l are summarized i n Table 10. Each fr e e molecule s t a t e gives r i s e to two c r y s t a l s t a t e s and, as i n naphthalene, mixing between g (Raman a c t i v e ) and u ( i n f r a r e d a c t i v e ) molecular s t a t e s i s forbidden. The f i v e A^ s t a t e s , i n a c t i v e i n the f r e e molecule, may appear i n the reduced symmetry of the c r y s t a l by mixing w i t h other u s t a t e s . In t h i s event the p o l a r i z a t i o n c h a r a c t e r i s t i c s of the t r a n s i t i o n to the "impure" A u s t a t e are those of the mixed-in component. The number of l a t t i c e modes and the c r y s t a l d i r e c t i o n s i n which they are expected are a l s o given i n Table 10. The r e l a t i v e i n t e n s i t i e s of a molecular l i n e i n the Raman spect r a of the various c r y s t a l faces are deter-mined i n the usual oriented-gas approximation from the 65 d i r e c t i o n cosines r e l a t i n g molecular and c r y s t a l axes and are given i n Table 11. The p r o j e c t e d i n t e n s i t i e s of the i n f r a r e d - a c t i v e modes i n the same approximation are l i s t e d i n Table 12. 75 Table 10. C o r r e l a t i o n t a b l e f o r anthracene* Molecular group S i t e group 2h N Bases Factor group C 2 h Bases n 12 xx, yy, z_z A 4 xy_ B 6 xz B 11 y_z B 5 11 z B 11 Y_ B 6 x . B i g 2g 3g l u 2u u ig aa aa, bb, cc, ac 3 bg ab, be a u b b u £ 3u N i s the number of fundamentals i n the free molecule and n i s the number of l a t t i c e frequencies w i t h k = 0. Factor group species are d i s t i n g u i s h e d by lower case l e t t e r s . 76 T a b l e 1 1 . The o r i e n t e d - g a s p r e d i c t i o n s o f t h e r e l a t i v e i n t e n s i t i e s o f t h e f r e e - m o l e c u l e Raman l i n e s o f a n t h r a c e n e i n v a r i o u s c r y s t a l c o n f i g u r a t i o n s I (A„) I (ACT) I (A„) I (B, ) I (B„ ) I (B 0 ) x x g yy_ a z_z g xy_ v l g x z v 2g v_z 3g I 0.422 0.061 0.011 0.639 0.272 0.103 a a I . . 0.036 0.000 0.633 0.012 0.601 0.050 bb I , , 0.026 0.545 0.010 0.477 0.065 0.295 £ £ I , 0.123 0.004 0.083 0.013 0.334 0.233 ab I, . 0.026 0.012 0.080 0.180 0.049 0.529 be' I , , 0.631 0.000 0.040 0.021 0.632 0.005 a 1 a' I 0.000 0.956 0.000 0.064 0.000 0.023 c c I , 0.013 0.007 0.001 0.759 0.000 0.200 a' c 77 Table 12. The oriented-gas p r e d i c t i o n s of the r e l a t i v e i n t e n s i t i e s of the i n f r a r e d - a c t i v e l i n e s of anthracene along v a r i o u s c r y s t a l axes a' 0.182 0.008 0.811 a 0.104 0.246 0.650 b 0.795 0.016 0.188 c' 0.100 0.746 0.162 c 0.023 0.976 0.001 78 B. Results 1. Anthracene-h-^Q I n f r a r e d Spectra and Assignment a) Spectra., P o l a r i z e d s p e c t r a were recorded w i t h l i g h t i n c i d e n t on the ab, be 1 and ac faces. The s p e c t r a are shown i n Figures 13, 14, and 15, r e s p e c t i v e l y , f o r energies l e s s than 650 cm These samples were of thickness 0.41, 0.47 and 0.98 mm r e s p e c t i v e l y . Spectra measured w i t h l i g h t normal to the ac ( c r y s t a l t hickness 0.27 mm) and be 1 s e c t i o n s ( c r y s t a l t h i c k n e s s 0.14 mm) are shown i n Figure 16 at ener-g i e s above 400 cm The ab s p e c t r a i n t h i s higher-energy 16 — 18 range were i n good agreement w i t h those already reported and are not presented here. The s l o p i n g base l i n e on the spectrum from the be' s e c t i o n (most n o t i c e a b l e i n the 1600-1800 cm ^ region //b) was caused p r i n c i p a l l y by the p o l a r i z e r not being a l i g n e d e x a c t l y at 45° to the g r a t i n g r u l i n g due to the unfortunate d i s p o s i t i o n of the o p t i c a l d i r e c t i o n s of the s e c t i o n i n the r a t h e r elongated c r y s t a l sample used; i t was necessary to l i n e up the c r y s t a l length w i t h the s l i t f o r maximum t r a n s -m i s s i o n . The be' s e c t i o n showed evidence of considerable i n t e r n a l s t r a i n ( i . e . , incomplete e x t i n c t i o n between crossed p o l a r i z e r s ) and the i n t e n s i t i e s of the b - p o l a r i z e d peaks e s p e c i a l l y i n the higher-energy region seem to be d i s t u r b e d . Nonreproducible features i n the s p e c t r a were discounted. i - i 1 * — I 1 1 1 1 « 1 1 1 : r 100 200 300 4 0 0 500 600 cm-' Figure 13. Anthracene-h low-frequency i n f r a r e d spectrum; ab face. S o l i d l i n e // b, broken l i n e // a. — Figure 14. Anthracene-h,- low-frequency i n f r a r e d spectrum; be 1 face. S o l i d l i n e // b, broken l i n e // c'. 82 Figure on f o l l o w i n g page. Figure 16. Anthracene-h^g i n f r a r e d s p e c t r a above 400 cm - 1; (a) i n c i d e n t l i g h t normal to the ac face; s o l i d l i n e / / c , broken l i n e //a 1 . (b) i n c i d e n t l i g h t normal to the be' face; s o l i d l i n e / / c ' , broken l i n e // b. Transmission Transmission 84 There was a sharp drop i n the s i g n a l - t o - n o i s e r a t i o at the extreme low-energy end of the spectrum because of the low i n c i d e n t l i g h t i n t e n s i t y . Table 13 l i s t s the observed frequencies of the bands and t h e i r assignments together w i t h previous a s s i g n -ments i n c l u d e d f o r comparison. The frequencies entered i n the t a b l e were mean frequencies averaged over s e v e r a l samples and p o l a r i z a t i o n s i n such a way tha t measurements p a r a l l e l and perpen d i c u l a r to b were given equal weight. The l i n e p o s i -t i o n s agreed very w e l l w i t h the previous measurements which are, a c c o r d i n g l y , omitted from Table 13. However, n e i t h e r 19 16 IV "~ 1 Chantry et a l . nor we could detect the l i n e ' at 278 cm Indeed, there i s l i t t l e agreement between the low-frequency 17 l i n e s reported by Colombo and those i n t h i s t h e s i s ; our data were repr o d u c i b l e from sample to sample and along the same a x i s i n d i f f e r e n t s e c t i o n s . The low-frequency spec t r a of a 0.08 M s o l u t i o n of anthracene i n benzene and of a saturated s o l u t i o n of anthra-cene i n cyclohexane were measured; the path length was 5 mm. Only two l i n e s at 233 and 467 cm were observed while the presence of a strong l i n e at 180 cm ^ and a weak l i n e at -1 19 362 cm as reported by Chantry et a l . could not be con-firmed. As s o l u t i o n s p e c t r a , of course, permit a c l e a r d i s t i n c t i o n to be made between molecular and l a t t i c e v i b r a -t i o n s , more concentrated s o l u t i o n s were run i n an attempt 85 T a b l e 1 3 . The i n f r a r e d s p e c t r u m o f a n t h r a c e n e - h 10 v c r y s t a l A s s i g n m e n t P r e s e n t w o r k R e f . 15 R e f . 16 R e f . ] 63 m b u 72 w 104 m l 110 s i B 3 u B_ * 3u 107 w b u 126 s a u A * u 166 s 3u B_ * 2u 235 s B l u B-i * l u B o 3u 361 vw 380 w B T l u B_ * 3u 423 s h B o 3u 431 s h B o 2u 456 s h B 7  e 3 u -464 w B o 2u 469 v s 3u Bo B. 3u 3u Bo 3u 493 w B i l u B, l u 515 vw B ? B 3 u ' 536 vw 3u 600 s B o 2u B 3 u B 3 u B 3 u 621 vw B o 3u B ? B 2 u - B 2 u 650 m B i l u B n l u B n l u 689 vw B o 3u B 2 u ' B 3 u 706 ? B„ ? 2u 730 v s B-5 3u B ' B-3u . 3u B o 3u 744 m B 7 l u * A B., u l u B o 3u 775 w B o 3u A u 808 w Bo 2u A' u 86 T a b l e 13. ( C o n t i n u e d ) , , A s s i g n m e n t v c r y s t a l P r e s e n t w o r k R e f . 15 R e f . 16 R e f . 856 m B o 3u A u A u 883 v s 3u B o 3u B o 3u B o 3u 903 s B l u B . l u l u B n l u 915 ? B 2 u 930 ? Bo 3u 954 s B_ 3u Bo 3u Bo 3u B 3 u 977 m B 3 u ? A u A u B 2 u 998 s B 2 u B 2 u B 2 u B 2 u 1012 vw B 3 u 1068 m B 2 u B 2 u B 2 u 1123 m B 2 u B 2 u B 2 u 1145 s B l u B l u B l u B l u 1163 s B 2 u B 2 u B 2 u B 2 u 1200 s h B 2 u 1219 m B 2 u B-, l u 1240 m Bo 3u B . l u B l u B , l u 1270 s l u l u B-, l u Bn l u 1282 m B n l u B l u 1297 m B , l u B l u 1315 s B l u B , l u B l u B l u 1345 m B 2 u B 2 u ' B 3 u B 2 u 1354 w B-, l u B 3 u 1372 vw B 3 u 1392 s B 2 u B 2 u B 2 u B 2 u 1407 vw Bo 3u 1447 s B n l u B l u B l u B l u 1480 vw B 3 u 1495 m B 2 u 17 Table 13. (Continued) 87 v c r y s t a l Present work A s s i g n m e n t Ref. 15 Ref. 16 Ref. 17 1514 m B 2 u 1 5 3 3 3 B 2 u B 2 u B 2 u B 2 u 1561 m B 2 u 1571 m B l u B l u l o 1 6 s B l u B l u B l u B l u 1635 m B l u B l u 1654 vw B 2 u ? 1 6 9 0 5 B2 U B 2 u B 2 u 1713 s B 2 u B 2 u 1 7 2 3 m B l u B l u B l u B l u 1739 m B 2 u 1 7 8 4 m B l u B l u B l u B l u 1793 sh B l u 1806 s B l u B l u B l u B l u 2625 vw B l u 2670 m B l u 2721 w B l u 2745 sh B 2 u 2793 sh B 2 u 2806 vw B l u 2828 w B 2 u 2850 vw B l u 2912 vw B l u B l u 2925 m B 2 u B l u 2950 w B 2 u B l u 2972 sh B l u B l u B 2 u B l u 2988 m B 2 u ? B 2 u B 3 u B 2 u 3010 s h B l u ? B l u B l u B l u 88 Table 13. (Continued) v c r y s t a l Present work A s s i g n Ref. 15 m e n t Ref. 16 Ref. 17 3024 ms B, l u l u l u B n l u 3050 vs B l u ' B 2 u B l u ' B 2 u B l u B l u 3082 sh B l u B 2 u B 2 u B 2 u 3092 m B 2 u 3109 m B. l u B l u B l u B l u 3175 vw B l u 3193 m B 2 u 3248 w B 2 u vs very s t r o n g , s s t r o n g , m medium, w weak, sh shoulder. * data taken from reference 19. 89 to f i r m l y e s t a b l i s h the l o c a t i o n s of the very low energy molecular modes. Un f o r t u n a t e l y , anthracene's s o l u b i l i t y i n the u s e f u l s o l v e n t s proved to be too low and small c r y s t a l s formed i n the s o l u t i o n s . b) Assignment. Of the eleven B^ u, eleven B 2 u , s i x B_ and f i v e A molecular fundamentals three B, and two 3u u l u B 2 u correspond approximately to CH s t r e t c h e s and are expected near 3000 cm The problem now r e s o l v e s i t s e l f i n t o one of s e l e c -t i n g the ungerade fundamentals from the many l i n e s given i n Table 13. In p r i n c i p l e , i t should be p o s s i b l e to account f o r as combinations a l l l i n e s not assigned as fundamentals. In f a c t t h i s proved to be p o s s i b l e only up to about 600 cm ^ where the number of p o s s i b l e combinations became q u i t e l a r g e and incomplete knowledge of the low frequency fundamentals (A u and some g_-modes) was an appreciable inconvenience. Above about 600 cm ^ strong i s o l a t e d l i n e s were u s u a l l y s e l e c t e d as fundamentals; however, a weak l i n e may mark a fundamental, as must s u r e l y be the case f o r the B^ u species of anthracene-d.^ where, as shown l a t e r , no strong l i n e s of the appropriate p o l a r i z a t i o n were found over a wide energy range. The presence of a weak l i n e n e a r l y degenerate w i t h a strong one of a d i f f e r e n t symmetry creates a s p e c i a l problem. Since the two v i b r a t i o n a l s t a t e s may be mixed by 90 c r y s t a l f o r c e s , t h e weak l i n e a c q u i r e s m i x e d s y m m e t r y c h a r -a c t e r i s t i c s a n d i t s a s s i g n m e n t becomes a m b i g u o u s . The l i n e a t 744 cm r e p r e s e n t s s u c h a c a s e a n d i s p r o b a b l y o f B ^ u symmetry w i t h some o f t h e B^u c h a r a c t e r o f t h e l i n e a t 730 cm m i x e d w i t h i t . i ) The l o w - f r e q u e n c y r e g i o n . C l a s s i f i c a t i o n o f c r y s t a l modes i n t o i n t r a - a n d i n t e r - m o l e c u l a r v i b r a t i o n s i s o n l y a p p r o x i m a t e and t h e m i x i n g o f t h e s e s t a t e s i s g r e a t e s t f o r t h e l o w e s t f r e q u e n c i e s o f t h e i s o l a t e d m o l e c u l e . Thus (as shown i n a l a t e r s e c t i o n f o r t h e Raman s p e c t r u m o f a n t h r a c e n e - d ^ Q ) l i n e p o s i t i o n s may s h i f t i n g o i n g f r o m a s o l u t i o n o r m e l t t o t h e c r y s t a l s p e c t r u m . L o w e r c a s e s y m b o l s a r e u s e d h e r e and i n T a b l e 13 f o r l a t t i c e modes t o d i s t i n -g u i s h them f r o m i n t r a m o l e c u l a r v i b r a t i o n s . The l i n e a t 63 cm ^ was p o l a r i z e d a l o n g a a n d s o m u s t mark t h e p r e s e n c e o f t h e o n l y e x p e c t e d ( s e e T a b l e 10) b u l a t t i c e mode. The two a u l a t t i c e f r e q u e n c i e s c o r r e s p o n d t o t h e b - p o l a r i z e d l i n e s a t 126 and 72 cm ^; t h e l a t t e r a s s i g n -ment i s somewhat t e n t a t i v e s i n c e t h e l i n e a t 72 cm was weak and f e l l i n a n o i s y p a r t o f t h e s p e c t r u m . The r e g i o n n e a r 110 cm i s r a t h e r c o m p l e x and i s g i v e n t h e f o l l o w i n g i n t e r p r e t a t i o n . The b - p o l a r i z e d l i n e a t 10 4 cm ^ and t h e s t r o n g e r a c - p o l a r i z e d l i n e a t 110 cm t o g e t h e r f o r m t h e f a c t o r - g r o u p c o m p o n e n t s o f a B, m o l e c u l a r f u n d a m e n t a l . The 91 i n t e n s i t y a l o n g c* i n t h e b e ' s p e c t r u m i s augmen t e d b y t h e s e p a r a t e c - p o l a r i z e d t r a n s i t i o n a t 107 cm ^ ( b e s t s e e n i n t h e a c s p e c t r a ) w h i c h m u s t r e p r e s e n t a c o m b i n a t i o n o f l a t t i c e modes h a v i n g b u symmetry o v e r a l l . The l o w e s t b g l a t t i c e 14 -1 v i b r a t i o n a p p e a r s a t 45 cm f o r a n t h r a c e n e - h ^ g , a v a l u e w h i c h a g r e e s w e l l w i t h t h e v a l u e o f 43 cm f o u n d ( s e e l a t e r s e c t i o n ) f o r t h e c o r r e s p o n d i n g mode o f a n t h r a c e n e - d ^ Q . Thus i t i s a p p a r e n t t h a t t h e 107 cm b u c o m b i n a t i o n c a n n o t i n -v o l v e t h e 72 cm a u v i b r a t i o n , b u t m u s t i n s t e a d i n v o l v e t h e 63 cm ^ b u l a t t i c e mode, w h i c h w o u l d r e q u i r e an ag f u n d a m e n t a l -1 14 n e a r 44 cm . S u z u k i e t a l . h a v e p l a c e d t h e l o w e s t a g mode a t 35 cm "S t h u s t h e r e i s a 9 cm ^ m i s m a t c h i n t h e e n e r g y f i t f o r t h e 107 b u c o m b i n a t i o n . H o w e v e r , o u r Raman s t u d i e s o f a n t h r a c e n e - d - ^ l o c a t e d t h e l o w e s t a g mode o f t h a t c r y s t a l a t 38 cm"''', w h i c h i n d i c a t e s t h a t t h e 35 cm 1 v a l u e 14 -1 o f S u z u k i e t a l . may be 4-5 cm l o w . I n a n y e v e n t , t h e p o s i t i o n o f t h i s i n f r a r e d - a c t i v e c o m b i n a t i o n may be d i s t u r b e d b y t h e s t r o n g a b s o r p t i o n v e r y c l o s e t o i t . The l i n e a t 166 cm ^ p r o b a b l y m a r k s a B ^ u m o l e c u l a r f u n d a m e n t a l s i n c e i t h a s c o m p o n e n t s a l o n g a l l a x e s a , b a n d 19 c w i t h maximum s t r e n g t h a l o n g a. C h a n t r y e t a l . h a v e a s s i g n e d t h i s l i n e a s B 2 u b e c a u s e o f t h e a p p a r e n t l y l a r g e i n t e n s i t y c h a n g e f r o m s o l u t i o n t o c r y s t a l . H o w e v e r , we f i n d no e v i d e n c e o f a c - p o l a r i z e d f u n d a m e n t a l b e l o w 600 cm n o r o f t h e p r e s e n c e o f t h i s b a n d i n t h e weak s o l u t i o n s p e c t r u m . 92 The p o s s i b i l i t y that t h i s l i n e i s due to a combination i n -v o l v i n g l a t t i c e modes cannot be d e f i n i t e l y r u l e d out, and, u n t i l a r e l i a b l e s o l u t i o n spectrum i s a v a i l a b l e , i t s a s s i g n -ment as a molecular fundamental must r e l y on i t s r e l a t i v e i s o l a t i o n and on the f a c t t h a t i t appears along a l l three c r y s t a l axes. The l i n e at 235 cm ^ was q u i t e strong w i t h i t s g r e a t e s t component along b and was assigned as a B ^ u funda-mental . In an e f f o r t to l o c a t e the lowest A u molecular fundamentals, an attempt was made to analyse the weak l i n e s appearing i n the low-energy i n f r a r e d spectrum. The very weak l i n e at 361 cm ^ may s a t i s f a c t o r i l y be explained as a combination of the 110 B 3 u fundamental and the 243 cm 14 -1 B, l i n e . The weak B, band at 380 cm must then i n v o l v e l g l u the same 243 cm ^ B ^ a mode and an A u fundamental a c c o r d i n g l y estimated t o l i e at 137 cm Further experimental evidence f o r the assignment of an A u mode at t h i s energy i s provided by the l i n e at 431 cm ^, seen only i n c - p o l a r i z a t i o n , which 14 may be exp l a i n e d as the combination 137 ( A u ) and 290 ( B 2 g ) . The r a t h e r d o u b t f u l shoulder at 456 cm (very c l o s e to the strong B^u fundamental at 469 cm "*") may be due to 166 ( B 3 u ) + 290 ( f i2g) • T h e n e x t t w o weak l i n e s appear at 464 cm and at 493 cm and again are overlapped by the very strong fundamental at 469 cm "S no simple e x p l a n a t i o n could be 93 f o u n d f o r e i t h e r o f t h e s e l i n e s . The n e x t weak l i n e b e l o w 600 cm \ t h e B ^ u l i n e a t 515 cm ^, h a s a s a t i s f a c t o r y e x -p l a n a t i o n a s t h e c o m b i n a t i o n o f 110 ( B 3 U ) a n d t h e 398 (Ag) 76 77 l i n e known w i t h c e r t a i n t y f r o m t h e f l u o r e s c e n c e s p e c t r u m . ' The 536 ( B g u ) l i n e o n c e a g a i n h a s no s i m p l e e x p l a n a t i o n . F o u r weak l i n e s b e l o w 600 cm h a v e n o t b e e n e x -p l a i n e d a s c o m b i n a t i o n s a n d a n y one o f t h e f o u r may mark t h e p r e s e n c e o f t h e s e c o n d A u f u n d a m e n t a l . T h e s e l i n e s a r e a t 4 2 3 , 464, 493 a n d 536 cm 1 and w i t h o u t f u r t h e r i n f o r m a t i o n t h e c h o i c e o f t h e A u f u n d a m e n t a l f r o m among them i s n o t p o s s i b l e . The o n l y s t r o n g a b s o r p t i o n b e t w e e n 235 a n d 600 cm ^ i s t h e v e r y s t r o n g a - p o l a r i z e d l i n e a t 474 cm \ w i t h i t s b c o mponent a t 464 cm \ w h i c h i s a c c o r d i n g l y a s s i g n e d a s a B_ f u n d a m e n t a l a t 469 cm ^. 3u The a n a l y s i s d e s c r i b e d a b o v e o f t h e weak i n f r a r e d l i n e s b e l o w 600 cm 1 i s s u m m a r i z e d i n T a b l e 14. i i ) B ^ u f u n d a m e n t a l s . The s t r o n g B ^ u l i n e s a t 1 6 1 6 , 1 4 4 7 , 1 3 1 4 , 1 2 7 0 , 1145 and 903 c m - 1 w e r e c h o s e n a s f u n d a m e n t a l s . The one r e m a i n i n g f u n d a m e n t a l b e l o w 2000 cm m u s t be s e l e c t e d f r o m 1 7 8 4 , 744 and 650 cm \ The l i n e a t 744 cm ^ f a l l s i n a r a t h e r c o m p l e x r e g i o n o f t h e s p e c t r u m , l y i n g v e r y c l o s e t o t h e s t r o n g B ^ l i n e a t 724 (JL b) and 736 cm " * " ( / / b) . The v e r y d e t e r m i n a t i o n o f i t s symmetry i s u n c e r t a i n s i n c e i t s i t s on t h e s i d e o f t h e b - p o l a r i z e d 94 T a b l e 14. The a n a l y s i s o f t h e weak i n f r a r e d l i n e s o f a n t h r a c e n e - h •J^Q b e l o w 600 cm" 1 O b s e r v e d l i n e s A s s i g n m e n t 361 vw B 2 u 110 ( B 3 U ) + 243 ( B 1 ) + 8 380 w B l u 137 ( A u ) + 243 ( B l g ) 423 s h B 3 u 431 s h B 2 u 137 ( A u ) + 290 ( B 2 .) + 4 456 s h B 3 u ? 166 (B_ ) + 290 ( B 0 ) ? 3u 2g 464 w B 2 u 493 w l u 515 vw B, ? 3u n o ( B 3 U ) + 398 ( A g ) + 7 536 vw 3u component o f t h e B 3 u l i n e ; t h u s , t h e 744 cm l i n e c a n be t e n t a t i v e l y a s s i g n e d as e i t h e r t h e B ^ u c o m b i n a t i o n 290 (&2q^ 14 + 469 ( B 3 U ) f a s ^ c o m b i n a t i o n i n v o l v i n g one o f t h e m i s s i n g g e r a d e modes, o r as an A u f u n d a m e n t a l . Two c a n d i d a t e s r e m a i n a n d i t i s c l e a r t h a t o n c e one i s c h o s e n as t h e f u n d a m e n t a l , t h e o t h e r m u s t be a c o m b i n a t i o n . P r e s u m a b l y t h e r e a r e many p o s s i b l e B ^ u c o m b i n a t i o n s a t a b o u t 1780 cm 1 ( w h i c h i s p r o -b a b l y t o o h i g h f o r a r i n g mode anyway) s o t h a t t h e p r o b l e m 95 d e v e l o p s i n t o one o f d e c i d i n g w h e t h e r any c o m b i n a t i o n s f a l l n e a r 650 cm 1 . The o n l y a p p a r e n t p o s s i b i l i t y i s 2 43 cm 1 ( B ^ g ) + 423 cm 1 ( A u ) = 666 ( B - ^ u ) w h i c h i s q u i t e u n a p p e a l i n g s i n c e t h e e n e r g y f i t i s n o t g o o d a n d s i n c e t h e r e i s no o t h e r e v i d e n c e t o s u g g e s t t h e 423 cm 1 l i n e i s t h e s e c o n d A u f u n d a -m e n t a l . Hence i t i s s u g g e s t e d t h a t t h e e i g h t h B ^ u f u n d a m e n t a l b e l o w 2000 cm 1 i s a t 650 cm 1 . i i i ) B n „ f u n d a m e n t a l s . The B _ f u n d a m e n t a l s , w i t h — .^u. ^ U t h e i r maximum component a l o n g c , a r e t h e l e a s t u n d e r s t o o d . The l i n e s u n a n i m o u s l y c h o s e n as f u n d a m e n t a l s b y t h e p r e v i o u s w o r k e r s 1 5 - 1 9 a r e t h o s e a t 1 5 3 3 , 1 3 9 2 , 1 1 6 3 , 998 and 621 c m - 1 . E x a m i n a t i o n o f t h e i n t e n s i t y a l o n g c shows t h a t t h e l i n e a t 621 cm 1 i s i n f a c t p f B ^ symmetry a n d t h a t i t i s a l m o s t c e r t a i n l y a c o m b i n a t i o n . H o w e v e r , e v e n w i t h t h e c - p o l a r i z e d s p e c t r u m a v a i l a b l e , t h e p r o b l e m i s n o t e a s i l y r e s o l v e d f o r t h e r e a r e more s t r o n g c - p o l a r i z e d l i n e s t h a n p o s s i b l e f u n d a -m e n t a l s . The s t r o n g l i n e s a t 1 5 3 3 , 1 4 9 5 , 1 3 9 2 , 1 1 6 3 , 1 0 6 8 , 998 a n d 600 cm 1 m u s t mark t h e p r e s e n c e o f B 2 u f u n d a m e n t a l s . I t i s i n t e r e s t i n g t h a t t h i s g r o u p i n c l u d e s t h r e e l i n e s ( 1 4 9 5 , 1068 and 600 c m - 1 ) t h a t h a d n o t b e e n a s s i g n e d a s B 2 u f u n d a -m e n t a l s p r e v i o u s l y ; two o f them ( a t 1495 and 600 cm 1 ) w e r e n o t r e c o g n i z e d as h a v i n g B 2 u s y m m e t r y . The two r e m a i n i n g f u n d a m e n t a l s b e l o w 2000 cm 1 a r e t o be c h o s e n f r o m t h e l i n e s a t 1 6 9 0 , 1 3 4 5 , 1 2 1 9 , 1123 and 808 c m - 1 a n d t h e r e i s no c l e a r way o f m a k i n g t h e c h o i c e . I f a l i n e i s c l e a n l y c - p o l a r i z e d 96 t h e n i t r e p r e s e n t s a t r a n s i t i o n t o a s t a t e w h i c h h a s a t m o s t m i x e d w i t h o t h e r B 2 u s t a t e s ; i f a l i n e i s c l e a n l y c - p o l a r i z e d a nd w e l l s e p a r a t e d i n e n e r g y f r o m o t h e r B 2 u l i n e s t h e n i t p r o b a b l y m a r k s a f u n d a m e n t a l . U s i n g t h i s a p p r o a c h , i t w o u l d a p p e a r t h a t t h e r e m a i n i n g f u n d a m e n t a l s p r o b a b l y l i e a t 1695 and 808 cm" 1. C e r t a i n l y t h e l i n e s a t 1 3 4 5 , 1219 and 1123 c m - 1 show c o n s i d e r a b l e h y b r i d c h a r a c t e r . 41 75 C o m p a r i s o n w i t h t h e c a l c u l a t i o n s , ' h o w e v e r , s u g g e s t s t h e p r e s e n c e b f a B 2 u f u n d a m e n t a l a t 1345 cm 1 r a t h e r t h a n a t 1690 cm 1 , and s o t h e r e l e v a n t d a t a f r o m e x -p e r i m e n t s h o u l d be more c a r e f u l l y c o n s i d e r e d . T h i s l i n e a t 1345 cm 1 i s s t r o n g e r a l o n g b t h a n a i n ab a n d o n l y v e r y s l i g h t l y s t r o n g e r a l o n g c * t h a n a* i n a c . R a t h e r s u r p r i s i n g l y t h e i n t e n s i t y a l o n g c 1 i n b e ' i s s h a r p l y r e d u c e d , v e r y much m o r e , f o r e x a m p l e , t h a n t h e l i n e a t 1392 cm 1 . I t a p p e a r s t h a t w h i l e t h e l i n e a t 1345 cm 1 i s o f medium i n t e n s i t y , a b o u t h a l f t h e s t r e n g t h i s o f B g u c h a r a c t e r . S h o u l d t h e c a l c u l a t i o n s r e q u i r e t h i s l i n e t o be a B 2 u f u n d a m e n t a l , h o w e v e r , d e s p i t e i t s p a r t i a l B^u c h a r a c t e r , i t w o u l d t h e n become n e c e s s a r y t o e x p l a i n t h e 1690 cm 1 b a n d as a c o m b i n a t i o n . S i m i l a r s t r o n g l i n e s i n t h e b e n z e n e 78 79 s p e c t r u m h a v e b e e n e x p l a i n e d ' as c o m b i n a t i o n s i n v o l v i n g t h e CH o u t - o f - p l a n e b e n d i n g v i b r a t i o n s and a n a n a l o g o u s 36 e x p l a n a t i o n h a s b e e n s u g g e s t e d f o r some o f t h e h i g h f r e -q u e n c y b a n d s o f n a p h t h a l e n e . I t i s c l e a r t h a t t h e r e w i l l e x i s t f o r a n t h r a c e n e c o m b i n a t i o n s h a v i n g B 2 u symmetry o v e r a l l 97 w h i c h f a l l n e a r t h e c o r r e c t e n e r g y a n d s o s u c h an e x p l a n a t i o n o f t h e 1690 cm 1 mode i s c e r t a i n l y p o s s i b l e . Thus on t h e b a s i s o f e x p e r i m e n t a l e v i d e n c e a l o n e i t i s i m p o s s i b l e t o make a c o n c l u s i v e a s s i g n m e n t o f t h e p o s i t i o n o f t h e one r e m a i n i n g B_ f u n d a m e n t a l b e l o w 2000 cm 2u — 3 u ^ u n ( ^ a n i e n ^ a l s • The a s s i g n m e n t o f t h e s i x B ^ u f u n d a m e n t a l s i s a u t o m a t i c s i n c e t h e r e a r e o n l y s i x s t r o n g a - p o l a r i z e d l i n e s a t 9 5 4 , 8 8 3 , 7 3 0 , 4 6 9 , 166 a n d 110 c m - 1 . The d i f f i c u l t i e s e n c o u n t e r e d i n a t t e m p t i n g t o o b t a i n a s o l u -t i o n s p e c t r u m o f t h e v e r y l o w - e n e r g y r e g i o n ( b e l o w 200 cm "*") t o v e r i f y t h e m o l e c u l a r c h a r a c t e r o f t h e two l o w e s t b a n d s h a v e a l r e a d y b e e n d e s c r i b e d . F u r t h e r , t h e s e l o w - e n e r g y v i b r a -t i o n s a r e p r o b a b l y p e r t u r b e d b y t h e c r y s t a l e n v i r o n m e n t s o t h a t t h e c o r r e s p o n d i n g v a l u e s i n t h e g a s ( i s o l a t e d m o l e c u l e ) may be somewhat d i f f e r e n t . v) CH s t r e t c h i n g v i b r a t i o n s . I t h a s b e e n s u g -g e s t e d 1 5 ' " ' " ^ t h a t t h e v e r y s t r o n g l i n e a t 3050 cm 1 r e p r e s e n t s two n e a r l y d e g e n e r a t e f u n d a m e n t a l s o f B ^ u a n d B £ U s y m m e t r y . T h i s v i e w h a s b e e n c o n f i r m e d s i n c e t h e l i n e i s s t r o n g l y b - p o l a r i z e d i n a b , c - p o l a r i z e d i n a c a n d e s s e n t i a l l y u n p o l -a r i z e d i n b e 1 . U n f o r t u n a t e l y t h e s p e c t r a l r e g i o n a r o u n d 3000 cm 1 i s d o m i n a t e d b y t h i s v e r y s t r o n g l i n e . The i n t e n -s i t i e s o f n e a r b y l i n e s f a l l o f f a s t h e e n e r g y d i f f e r e n c e s i n c r e a s e , i n a manner c o n s i s t e n t w i t h t h e t r a n s f e r o f i n t e n -s i t y f r o m t h e s t r o n g t o t h e weak l i n e s . The c h o i c e b e t w e e n 98 T a b l e 1 5 . The a s s i g n e d 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 o f a n t h r a c e n e - h ^ Q Symmetry E x p e r i m e n t a l A s s i g n m e n t C a l c u l a t e d T y pe P r e s e n t f l g R e f > 1 ? R e f 1 8 R e f 7 5 R e f . 4 1 Work 235 — 307 490 210 241 650? 743 651 650 627 632 903 907 905 906 922 914 1145 1150 1142 1148 1147 1125 1270 1274 1264 1274 1246 1279 1314 1316 1310 1317 1266 1309 1447 1448 1445 1456 1450 1451 1616 1620 1624 1628 1623 1609 3024? 3022 3028 3008 3051 3030 3050 3049 3050 3020 3062 3079 310 8? 3110 3100 3040 3073 3082 600 615 406 — 591 606 808? — 620 — 808 863 998 999 997 605 1011 1002 1068 1169 1122 1030 1114 1113 1163 — 1163 — 1181 1171 1392 — 1385 1162 1345 1344 1495 1398 1537 1350 1387 1409 1533 1462 1680 1438 1457 1441 1 3 45,1695? 1533 1720 1524 1534 1542 3050 2972 2990 3045 3040 3026 3093? 3079 3080 3079 3062 3081 110 278 287 — 98 96 166 475 470 392 378 383 469 603 600 581 484 504 730 72 8 727 755 743 732 883 886 884 — 916 892 954 957 954 920 959 952^ * c a l c u l a t e d i n r e f e r e n c e 40. weak combinations and weak fundamentals i s r a t h e r an a r b i -t r a r y one but on the b a s i s of strength and near-complete p o l a r i z a t i o n , the remaining fundamentals were chosen at 3108 (B, ), 3093 (B„ ) and 3024 cm~ 1(B 1 ). l u 2u l u A summary of a l l the fundamentals assigned i n t h i s work i s made i n Table 15, which a l s o contains previous experimental and c a l c u l a t e d assignments. 2. Anthracene-d.^ I n f r a r e d Spectra and Assignment a) Spectra. P o l a r i z e d s p e c t r a were recorded w i t h l i g h t i n c i d e n t on the ab, bc_' and ac faces; the spect r a at energies l e s s than 650 cm 1 are shown i n Figures 17, 18 and 19 r e s p e c t i v e l y . Figures 20, 21 and 22 show the spect r a of the same faces at energies between 500 and 1900 cm ^. Because of the higher e x t i n c t i o n c o e f f i c i e n t s a s s o c i a t e d w i t h the CD s t r e t c h i n g v i b r a t i o n s , the c r y s t a l s were almost opaque i n the 2260 cm 1 region and the sp e c t r a are not i n c l u d e d . The ab spect r a f o r the higher-energy region are i n good 16 agreement w i t h those already reported by C a l i f a n o and, to the extent t h a t the ab sample used was r a t h e r t h i c k e r than a subl i m a t i o n f l a k e , the data shown i n Figure 20 complement h i s . On the other hand, the r e s o l u t i o n e x h i b i t e d i n the 17 spectr a of Colombo i s not as good and a correspondence between l i n e s of h i s spect r a and those i n Figure 20 i s not always obvious. IOO 200 300 400 500 600cm Figure 17. Anthracene-^d..Q low-frequency i n f r a r e d spectrum w i t h i n c i d e n t l i g h t normal to ab face; c r y s t a l 0.45 mm t h i c k below 325 c m - l , 0.10 mm t h i c k above 325 cm - 1. S o l i d l i n e // b, broken l i n e / / a . o 1 0 0 200 300 4 0 0 500 600 cm-' Figure 19. Anthracene-d low-frequency i n f r a r e d spectrum w i t h i n c i d e n t l i g h t normal to ac face; c r y s t a l 0.95 mm t h i c k below 85 cm" 1, 0.47 mm t h i c k above 85 cm~^ S o l i d l i n e // a 1 , broken l i n e // c. i , i 1 1 1 1 1 r 600 800 IOOO I200 1400 1600 I800cm~1 Figure 20. Anthracene-d^ i n f r a r e d spectrum, 500-1900 cm - 1, w i t h i n c i d e n t l i g h t normal to ab face. S o l i d l i n e // b, broken l i n e // a. 600 800 IOOO I200 1400 1600 Figure 21. Anthracene-d normal to be 1 face. -1 BOO cm" 1 Q i n f r a r e d spectrum, 500-1900 cm"-1-, wi t h i n c i d e n t l i g h t S o l i d l i n e // b, broken l i n e // c 1 . 106 Table 16 l i s t s the observed band frequencies and t h e i r assignments based on the o r i e n t e d gas assumption (see Table 12) t h a t B^ u l i n e s are most intense along b, B 2 u along c, and along a. The mean frequency of the two f a c t o r -group components was entered i n Table 16. Lines t h a t show a s i g n i f i c a n t factor-group s p l i t t i n g (with components p a r a l l e l and p e r p e n d i c u l a r to b i n parentheses) occur at 102 (100, 103), 397 (393, 401), 560 (564, 557), 722 (724, 720) and perhaps 784 (785, 782) cm 1 . That these are a l l out-of-plane modes i s c o n s i s t e n t w i t h the s i m i l a r behavior observed i n anthra-17 cene-h^g. I t should be noted t h a t Colombo has i n t e r p r e t e d the ab spectrum as showing no f a c t o r group s p l i t t i n g s ; i n Table 16 we have a c c o r d i n g l y omitted Colombo's assignments of what we take to be l e s s intense f a c t o r group components. b) Assignment. Of the eleven B ^ , eleven B 2 u , s i x B_ and f i v e A molecular fundamentals three B, and two 3u u l u B 2 u correspond to CD s t r e t c h e s and are expected near 2250 cm 1. The A u modes appear p r i n c i p a l l y by s t e a l i n g i n t e n s i t y through i n t e r m o l e c u l a r i n t e r a c t i o n s . At low frequencies an attempt was made to assign a l l the l i n e s , both weak and s t r o n g , i n the hope of l o c a t i n g the lowest A u modes; the low energy gerade fundamentals used i n making combinations were found i n the c r y s t a l Raman spectrum of anthracene-d.^, which i s described i n the next s e c t i o n . This a n a l y s i s was not c a r r i e d beyond 500 cm 1 because of ambiguities a r i s i n g from an 107 Table 16. The p o l a r i z e d i n f r a r e d spectrum of anthracene-d 10 v c r y s t a l A s s i g n m e n t Present Ref. 16 Ref. 17 work 60 m b u 71 vw ? a ? u 100 w b u 102 s 3u 118 ms a u 153 m B-, 3u 220 s B n l u 336 mw B-, l u 349 vw 3u 363 sh B 3 u ? 374 w B 2 u 393 m B 2 u 397 vs B, 3u Bo 3u B o 3u 424 s B_ ? 3u B l u 435 w B l u ? B 3 u 451 vw B 2 u 477 vvw B 3 u ? 500 w B 2 u 513 mw B 3 u 531 vw B 2 u 548 vw B 2 u 560 vs B 3 u Bo 3u Bo 3u 575 vs B 2 u Bo 3u B 3 u 601 vw B 3 u B 2 u 619 w B 2 u ? 633 m B 0 3u Bo 3u 665 vw Bo 3u B n l u 689 ms Bo 3u Bo 3u Bo 3u 108 T a b l e 16. ( C o n t i n u e d ) v c r y s t a l A s s i g n m e n t P r e s e n t w o r k R e f . 16 R e f . ] 703 ms B 2 u A u 722 v s B 3 u B - , 3u B 3 u 755 m B 3 u B - , 3u B 3 u 784 v s B 3 u Bo 3u B-3u 805 m B 3 u B o 3u B 0 3u 824 v s B 2 u B l u B 3 u 830. s h B, ? 3u B 2 u B 2 u 860 s h B , l u B n l u B n l u 879 v s B l u l u l u 892 s B 3 u Bo 3u B 3 u 904 ms B 3 u B 2 u 913 s B 3 u B 3 u B 3 u 918 w B 2 u 7 B 2 u 941 m B 2 u 982 ms B 2 u B 2 u 998 vw B 3 u ? 1038 w B 2 u 1046 mw B 3 u Bo 3u 106 2 vw B 2 u B-, l u 1070 vw B l u 1120 mw B 2 u B 2 u B, l u 1175 ms B 2 u 1195 vw B 2 u 1210 vw B 2 u B . l u 1220 ms B T l u B-, l u B n l u 1245 s h B ? B n l u B-, l u 1258 v s B l u B n l u B n l u 1298 s B 2 u 1312 ms B 2 u B n l u 109 Table 16. (Continued) v c r y s t a l Present work A s s i g n m e n t Ref. 16 Ref. 17 1335 s B2u B2u 1348 vw B l u B2u 1380 ms l u B2u 1386 ms B3u B l u B2u 1401 s B2u 1406 ms B l u B l u 1416 ms B2u B-, 3u 1430 m B l u B3u 1455 sh B2u 1468 ms B2u 1493 s B2u B2u B2u 1512 mw B l u B-, l u 1530 ms B2u 1537 vw B. l u B, l u 1556 w B n l u B l u 1584 s B l u B l u 1597 vs B2u B2u B2u 1606 vw B, l u B n l u 1628 m B l u 1647 m B2u B-, l u 1670 mw B„ ? 2u ? 1749 w Bn l u 1785 vw B. l u B2u 1808 vw B l u B l u 1824 ms B2u B2u 110 incomplete knowledge of the g_ fundamentals and because of the increased p r o b a b i l i t y of f i n d i n g above t h i s energy l i n e s due to i s o t o p i c a l l y s u b s t i t u t e d i m p u r i t i e s , such as c ^ 4 D 9 H i « i ) The low frequency r e g i o n . The three t r a n s l a -t i o n a l l a t t i c e modes expected, r e f e r r e d to here and i n Table 16 w i t h lower case symbols, are i d e n t i f i e d w i t h the two a^j ( p o l a r i z e d along b) l i n e s at 71 and 118 cm 1 and the b u ( p o l a r i z e d along a i n the ac plane) l i n e at 60 cm The second b u l i n e , at 100 cm 1 , best seen as a c - p o l a r i z e d l i n e i n the ac spectrum, could be assigned as the combination of the b u mode a t 60 cm 1 w i t h an ag mode observed i n the Raman spectrum at 38 cm These frequencies, as expected, are somewhat l e s s than the corresponding values found f o r the anthracene-h.^ c r y s t a l . The two l i n e s at 103 cm 1 ( p o l a r i z e d i n the ac plane) and 100 cm 1 ( p o l a r i z e d along b) are considered to be the two f a c t o r group components of what was a B 3 u fundamental i n the i s o l a t e d molecule. These l i n e s are completely ana-logous t o the p a i r seen i n anthracene-h^Q at 110 and 104 cm ^, Other molecular fundamentals are seen at 153 cm 1 ( B 3 U ) and 220 cm - 1 (B. ). l u S everal low-frequency l i n e s which appear weakly i n the i n f r a r e d spectrum of anthracene-d^ Q show mixed symmetry c h a r a c t e r i s t i c s , i n d i c a t i n g the presence of c r y s t a l - i n d u c e d i n t e r a c t i o n s between modes of d i f f e r e n t molecular symmetry. Lines which showed mixed and B^ u character were observed I l l a t 3 4 9 , 3 6 3 , 424 a n d 435 cm ^. P r e s u m a b l y t h e B ^ u c h a r a c t e r was s t o l e n f r o m t h e v e r y s t r o n g B . ^ f u n d a m e n t a l a t 397 cm 1 w h i c h d o m i n a t e s t h i s r e g i o n o f t h e s p e c t r u m . B ^ u i n t e n s i t y may be d e r i v e d f r o m t h e more d i s t a n t s t r o n g l i n e a t 220 cm 1 a l t h o u g h t h i s p r o c e s s w o u l d p r o b a b l y be r e l a t i v e l y i n e f f i -c i e n t u n l e s s t h e c o m b i n a t i o n i t s e l f was o f B ^ u s y m m e t r y . A t e n t a t i v e a n a l y s i s o f t h e r e m a i n i n g l o w f r e q u e n c y l i n e s o f a n t h r a c e n e - d ^ g i s s u g g e s t e d i n T a b l e 17. I t s h o u l d be remembered t h a t some o f t h e weak l i n e s may be due t o p r o -t o n a t e d i m p u r i t i e s . T a b l e 17. A t e n t a t i v e a s s i g n m e n t o f t h e weak l o w - e n e r g y l i n e s o f a n t h r a c e n e - d ^ ^ O b s e r v e d l i n e s A s s i g n m e n t 336 B n l u 110 ( A u ) + 228 <v -2 349 B-, 3u 363 B 3 u ? 102 ( B 3 u ) + 261 ( B2g> ? 374 B 2 u 110 ( A u ) + 261 ( B 2 g ) + 3 393 B 2 u 153 ( B3u> + 228 (B ) + 12 424 Bo 3u 153 ( B3u> + 261 ( B 2 g ) + 10? 435 B l u ? 451 B 2 u 220 ( B l u ) + 228 ( B l g ) + 3? 477 B 3 u 102 • ( B3u> + 382 (Ag) - 7 500 B 2 u * The v a l u e s f o r t h e g e r a d e v i b r a t i o n s a r e t a k e n f r o m t h e n e x t s e c t i o n o f t h i s t h e s i s . 112 In Table 17 the presence of an A u fundamental at 110 cm 1 has been p o s t u l a t e d , mainly because of the need f o r such a fundamental t o e x p l a i n the medium weak 336 cm 1 B ^ u l i n e . Although some of the higher-energy l i n e s may be caused by protonated i m p u r i t i e s , such an ex p l a n a t i o n seems u n l i k e l y f o r the 336 cm 1 l i n e , s i n c e i t l i e s q u i t e f a r above any g or u molecular fundamentals of anth r a c e n e - d ^ (see Table 18 or 2 0 , to f o l l o w l a t e r ) and the increase i n frequency of the corresponding modes of the monoprotonated molecule (the p r i n c i p a l impurity) probably i s not l a r g e . I t i s p o s s i b l e t h a t the l i n e i s due to an A u fundamental of anthracene-d^Q, but near the 397 cm 1 fundamental any such molecular-i n a c t i v e mode would be expected to show B 3 u symmetry i n the c r y s t a l . The very weak B^u l i n e at 349 cm 1 may i n f a c t mark the presence of the second lowest A u fundamental of anthracene-d^Q, although i t l i e s q u i t e f a r below the c a l c u -35 l a t e d frequency. Although the a n a l y s i s suggested i n Table 17 i s not unique, others t r i e d seemed l e s s p l a u s i b l e i n at l e a s t one res p e c t , e.g. the p r e d i c t i o n of an an t h r a c e n e - d ^ frequency r a t h e r g r e a t e r than or very much l e s s than the corresponding a n t h r a c e n e - h ^ value, or the p r e d i c t i o n of a fundamental below 250 cm \ e t c . I t i s i n t e r e s t i n g to note t h a t the 220 cm 1 B ^ u fundamental of anthracene-d^g c o i n c i d e s almost e x a c t l y w i t h -1 77 . the 221 cm i n t e r v a l observed i n the fluorescence spectrum 113 o f a n t h r a c e n e - d . ^ i n a f l u o r e n e m a t r i x . P r e s u m a b l y t h e f l u -o r e s c e n c e i n t e r v a l was c a u s e d b y t h e B j , u f u n d a m e n t a l g a i n i n g i n t e n s i t y f r o m t h e f l u o r e n e l a t t i c e t h r o u g h c r y s t a l f o r c e s . i i ) B, f u n d a m e n t a l s . The e i g h t B, f u n d a m e n t a l s — l u v l u e x p e c t e d b e l o w 2000 cm a r e d i f f i c u l t t o i d e n t i f y . O n l y f o u r f a i r l y c e r t a i n a s s i g n m e n t s c a n be made, c o r r e s p o n d i n g t o t h e l i n e s a t 2 2 0 , 879, 1258 a n d 1584 cm" 1. The l i n e o f medium s t r e n g t h a t 1220 cm 1 a n d a t l e a s t one o f t h e t r i o o f l i n e s a t 1 3 8 0 , 1406 a n d 1430 cm 1 may a l s o mark t h e p o s i t i o n o f f u n d a m e n t a l modes. From t h e s e l a t t e r t h r e e t h e l i n e a t 1406 cm 1 h a s r a t h e r a r b i t r a r i l y b e e n c h o s e n a s t h e f u n d a -m e n t a l s i n c e i t p r o b a b l y h a s t h e g r e a t e s t B ^ u i n t e n s i t y ; c e r t a i n l y t h e s t r e n g t h o f t h e l i n e a t 1380 cm 1 i s e x a g g e r a t e d by o v e r l a p w i t h t h e B ^ u l i n e a t 1386 cm ^. I f t h e l i n e a t 1220 cm 1 i s a l s o i n c l u d e d i n t h e a s s i g n m e n t , t h e n t h e p r e s e n c e o f f o u r f u n d a m e n t a l s a b o v e 1200 cm 1 s u g g e s t s t h e r e a r e f o u r r i n g modes o f B ^ u symmetry w h e r e o n l y t h r e e a r e e x p e c t e d ( s e e T a b l e 15 f o r c o m p a r i s o n w i t h t h e modes o f t h e p r o t o n a t e d m o l e c u l e ) . W h i l e t h e s e p a r a t i o n o f t h e v i b r a t i o n s i n t h i s r e g i o n i n t o r i n g modes and CD i n - p l a n e b e n d s i s o n l y an a p p r o x i m a t i o n , i t i s s u r p r i s i n g t h a t t h e c o r r e s p o n d i n g v i b r a t i o n i n c ^ 4 H j o li® s o n l y 50 cm 1 a b o v e t h i s 1220 cm 1 l i n e . The a n t h r a c e n e - d ^ Q s p e c t r u m i s r e m a r k a b l y c l e a r o f s t r o n g b - p o l a r i z e d l i n e s f r o m 1220 t o 879 cm 1 , h o w e v e r ( t h e o n l y B l u l i n e i s t h e v e r y weak b a n d a t 1070 cm 1 ) a n d f o r 114 t h i s r e a s o n t h e a s s i g n m e n t o f t h e l i n e a t 1220 cm 1 i s t e n -t a t i v e l y a c c e p t e d . The a s s i g n m e n t o f t h e two r e m a i n i n g f u n d a m e n t a l s b e l o w 2000 cm 1 i s d e f e r r e d u n t i l t h e CD s t r e t -c h i n g v i b r a t i o n s a r e d i s c u s s e d . A v e r y i n t e n s e b - p o l a r i z e d l i n e c e n t e r e d a t 2264 cm 1 d o m i n a t e s t h i s r e g i o n o f t h e s p e c t r u m a n d i s a s s i g n e d as one B ^ u CD s t r e t c h i n g mode. T h i s l i n e i s f l a n k e d by l i n e s a t 2248 a n d 2283 cm 1 o f l e s s e r s t r e n g t h a n d t h e s e a r e t a k e n as t h e o t h e r CD s t r e t c h i n g f u n d a m e n t a l s i n a g r e e m e n t w i t h t h e , 16,17 p r e v i o u s w o r k e r s . I n an a t t e m p t t o l o c a t e t h e r e m a i n i n g two f u n d a -m e n t a l s i n t h e b l o c k , t h e p r o d u c t r u l e c a l c u l a t i o n s h a v e b e e n u s e d as a g u i d e . The e x p e c t e d v a l u e f o r t h e p r o d u c t r u l e r a t i o i s 0.182. I f t h e l i n e s a l r e a d y a s s i g n e d f o r a n t h r a c e n e - h ^ Q and -d^Q a r e a c c e p t e d a s c o r r e c t , t h e n b o t h u n a s s i g n e d f u n d a m e n t a l s p r o b a b l y l i e b e t w e e n 500 a n d 800 cm 1 . I t i s e v i d e n t f r o m T a b l e 16 a n d f r o m F i g u r e s 20-22 t h a t any B ^ u l i n e s w h i c h may be p r e s e n t i n t h i s r e g i o n , a r e e i t h e r e x t r e m e l y weak o r h i d d e n b y v e r y i n t e n s e B 3 u o r B 2 U b a n d s . I f t h e f u n d a m e n t a l c o r r e s p o n d i n g t o t h e 650 cm 1 v i b r a t i o n o f a n t h r a c e n e - h 1 Q i s assumed t o be h i d d e n u n d e r t h e c o m p l e x s y s t e m a t 560-570 cm 1 t h e n t h e o t h e r i s p r e d i c t e d by t h e p r o d u c t r u l e t o a p p e a r n e a r 740 cm 1 and may be p a r t -1 17 o f t h e s t r o n g a b s o r p t i o n a t 722 cm as s u g g e s t e d by Colombo 115 16 a n d i n a n e a r l y w o r k b y C a l i f a n o , o r i t may be h i d d e n i n t h e s t r o n g b a n d a t 784 cm 1 o r e v e n i n t h e s t r o n g b a n d -1 ' 41 a t 824 cm as s u g g e s t e d b y N e t o , S c r o c c o a n d C a l i f a n o . I f , h o w e v e r , t h e l i n e a t 1220 cm 1 i s n o t a f u n d a -m e n t a l b u t r a t h e r a c o m b i n a t i o n s t e a l i n g i n t e n s i t y f r o m t h e v e r y s t r o n g l i n e a t 1258 cm 1 , and i f t h e t r u e l o c a t i o n o f t h i s mode i s m a r k e d b y t h e v e r y weak 1070 cm 1 l i n e , m e n -t i o n e d e a r l i e r , t h e n a s i m i l a r p r o d u c t r u l e a r g u m e n t w o u l d p l a c e t h e f i n a l B ^ u mode n e a r 840 cm 1 i n s t e a d o f 740 cm S i n c e t h e a v a i l a b l e i n f o r m a t i o n d o e s n o t p e r m i t a c h o i c e t o be made b e t w e e n t h e v a r i o u s a l t e r n a t i v e s , t h e e x p e r i m e n t a l a s s i g n m e n t o f t h e B ^ u s p e c i e s m u s t r e m a i n i n c o m p l e t e . i i i ) B ^ f u n d a m e n t a l s . E l e v e n B 2 u f u n d a m e n t a l s a r e e x p e c t e d , two o f t h e s e a p p e a r i n g a b o v e 2000 cm ^. A v e r y i n t e n s e c - p o l a r i z e d l i n e c e n t e r e d a t a b o u t 2267 cm 1 m u s t mark t h e p r e s e n c e o f a t l e a s t one o f t h e s e two CD s t r e t c h i n g f u n d a m e n t a l s . The s e c o n d was p r o b a b l y a l s o c o n t a i n e d i n t h i s s t r o n g a b s o r p t i o n r e g i o n ( e f f o r t s t o r e d u c e t h e t h i c k -n e s s o f t h e s a m p l e s l e d t o b r e a k a g e ) a n d f o r t h e p u r p o s e o f p r o d u c t r u l e c a l c u l a t i o n s , t h e v a l u e o f 2238 cm 1 s u g g e s t e d 16 17 b y p r e v i o u s a u t h o r s ' i s a c c e p t e d . From t h e c - p o l a r i z e d s p e c t r u m , s i x o f t h e n i n e f u n d a m e n t a l s b e l o w 2000 cm 1 c a n be c h o s e n i m m e d i a t e l y a t 57 5 , 7 0 3 , 824, 9 8 2 , 1335 a n d 1493 c m - 1 . T h e r e h a s b e e n no p r e v i o u s e x p e r i m e n t a l e v i d e n c e t o e s t a b l i s h t h a t t h e l i n e a t 703 c m - 1 h a s B 2 u s y m m e t r y . The s t r o n g l i n e a t 1597 cm 1 116 m u s t c o r r e s p o n d t o t h e l i n e i n a n t h r a c e n e - h . ^ a t 1690 cm 1 a n d t h e same d i f f i c u l t y e x i s t s i n t h e d e u t e r a t e d s p e c i e s i n d e c i d i n g on a n e x p e r i m e n t a l b a s i s b e t w e e n 1597 a n d 1401 cm 1 a s a l t e r n a t i v e s f o r one o f t h e r i n g modes, a n d t h e c h o i c e w i l l be d e l a y e d u n t i l a l a t e r c h a p t e r . A n o t h e r d i f f i c u l t y e x i s t s i n c h o o s i n g b e t w e e n t h e c l e a n l y p o l a r i z e d medium-s t r o n g l i n e a t 1175 cm 1 a n d t h e s t r o n g e r b u t l e s s i s o l a t e d b a n d a t 1298 cm 1 . B e c a u s e o f i t s r e l a t i v e i s o l a t i o n , t h e 1175 cm 1 b a n d h a s t e n t a t i v e l y b e e n c h o s e n and i n s e r t e d i n t h e l i s t o f B 2 U f u n d a m e n t a l s . The a s s i g n m e n t o f a f u n d a m e n t a l a t 982 cm 1 h e l p s t o c l a r i f y t h e e x p e r i m e n t a l s i t u a t i o n i n t h i s r e g i o n c o n s i d e r -17 a b l y . C o l o m b o h a s a s s i g n e d two B 2 U f u n d a m e n t a l s a t 903 and — 1 16 — 1 920 cm . C a l i f a n o h a s named 901 cm and N e t o , S c r o c c o 41 -1 a n d C a l i f a n o h a v e c h o s e n 920 cm . From t h e a c and b e ' s p e c t r a , i t i s c l e a r t h a t t h e 901 cm 1 l i n e i s n o t o f B 2 U s y m m e t r y , b e l o n g i n g i n s t e a d t o t h e B ^ u s p e c i e s , a s d o e s t h e l i n e a t 913 cm 1 . The l i n e a t 918 cm 1 may be o f B 2 U symmetry b u t i n any e v e n t i s r a t h e r weak, a n d t h e 982 cm 1 a s s i g n m e n t i s c l e a r l y p r e f e r a b l e . The r e m a i n i n g f u n d a m e n t a l b e l o w 2000 cm 1 i s e x -41 75 -1 p e c t e d ' b e t w e e n 800 a n d 900 cm and may be h i d d e n i n t h e s t r o n g B ^ u l i n e a t 879 cm 1 w h i c h shows u n e x p e c t e d c -p o l a r i z e d s t r e n g t h . 117 — 3 u ^ u n t ^ a m e n ' t : a l s • A s f ° r a n t h r a c e n e - h ^ Q , t h e c h o i c e o f t h e s i x i n f r a r e d - a c t i v e o u t - o f - p l a n e f u n d a m e n t a l s o f a n t h r a c e n e - d . ^ i s a u t o m a t i c . S t r o n g l i n e s w e r e o b s e r v e d a t 1 0 2 , 1 5 3 , 3 9 7 , 5 6 0 , 722 and 784 c m - 1 and t h e s e c o r r e l a t e v e r y w e l l w i t h t h e a n t h r a c e n e - h ^ g f r e q u e n c i e s . The o b s e r v e d p r o d u c t r u l e r a t i o i s 0.372 w h i c h c o m p a r e s w e l l w i t h t h e -p r e d i c t e d 0.364. A summary o f a l l t h e f u n d a m e n t a l s a s s i g n e d i n t h i s w o r k i s made i n T a b l e 1 8 , w h i c h a l s o c o n t a i n s p r e v i o u s e x -p e r i m e n t a l a n d c a l c u l a t e d a s s i g n m e n t s . 3. A n t h r a c e n e - d . ^ Raman S p e c t r u m a nd A s s i g n m e n t a) S p e c t r a . The d e t a i l s o f t h e Raman s p e c t r a a r e p r e s e n t e d i n T a b l e 19. As f o r t h e n a p h t h a l e n e - d g Raman m e a s u r e m e n t s , no a t t e m p t was made t o c o r r e c t f o r v a r y i n g d e t e c t o r s e n s i t i v i t y i n d i f f e r e n t r e g i o n s o f t h e s p e c t r u m b u t a t e a c h f r e q u e n c y t h e v a r i o u s s p e c t r a w e r e m e a s u r e d u n d e r a s n e a r l y t h e same c o n d i t i o n s as p o s s i b l e . D e p o l a r i z a t i o n r a t i o m e a s u r e m e n t s w e r e a t t e m p t e d i n b e n z e n e a nd c a r b o n t e t r a c h l o r i d e s o l u t i o n s b u t b e c a u s e t h e s o l u b i l i t y o f a n t h r a c e n e was t o o l o w o n l y t h e s t r o n g e s t l i n e s w e r e f o u n d . Somewhat b e t t e r s u c c e s s was o b t a i n e d w i t h t h e m e l t c e l l d e s c r i b e d i n C h a p t e r I I and t h e d e p o l a r i z a t i o n m e a s u r e m e n t s r e p o r t e d h e r e a r e f o r t h e m e l t . I n many c a s e s , a l t h o u g h a l i n e was c l e a r l y p o l a r i z e d (p^g < K 0.75) o r 118 T a b l e 18. The a s s i g n e d 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 o f a n t h r a c e n e - d ^ Q Symmetry t y p e P r e s e n t E x p e r i m e n t a l C a l c u l a t e d w o r k R e f . 16 R e f . 41 R e f . 17 R e f . 41 R e f . 7! 220 — —- 283 199 195 ? (720) 592 592 617 599 ? 822 822 730 825 840 879 881 881 882 861 891 — 981 — 1235 1041 1035 1258 1264 1264 1259 1275 1215 1406? 1389 1389 1400 1380 1357 1584 1583 1583 1515 1582 1603 2248? 2247 2247 2250 2246 2276 2264 2262 2262 2260 2271 2291 2283? 2297 2288 2288 2280 2303 575 580 580 388 588 • 570 703 706 706 562 701 660 824 831 — 830 811 824 879? 901 831 903 840 847 982 — 920 920 943 1007 1175? 1125 1325 1267 1291 1335 1342 1325 1390 1315 1317 1493 1384 1384 1503 1392 1351 1 4 0 1 , 1 5 9 7 ? 1 5 0 0 1500 1595 1487 1506 — 2238 2238 2225 2257 2261 2267 2273 2275 2275 2294 2294 102 236 260 93 153 407 403 333 397 563 566 416 560 577 584 571 722 726 690 753 784 790 758 804 B l u B 2u B 3u Table 19. The Raman spectrum of anthracene-d.^ C r y s t a l (cm-1) I n t e n s i t y D i s t r i b u t i o n ' (aa) (bb) (c'c') (ab) (be 1) (a'a') (cc) (a'c) melt (cm"1) Symmetry 228 1 1 k k 1 0 4 B i g 261 6 18 3 5 k 2 l 1 B 2 g 367 6 5 9 3 6 2 3 3 364 382 11 17 35 6 26 9 50 16 379 P A„ b 415 2 1 9 2 5 1 1 2 407 dp B "? 3g-488 0 0 0 0 502 4 7 8 5 9 3 4 4 502 dp 3g 601 0 0 0 0 0 0 0 Ag? 613 1 k Ik 0 1 k k 1 B-, ? i g 644 k l 0 R 7 2g-651 c k k 0 0 659 k V 709 26 80 34 22 36 6 14 8 707 P Ag6 761 0 k B 2 g ? 777 1 l 2h k 2k 1 1 lk 770 dp B-, 3g 816 5 6 10 4 9 2 3 3 813 dp B 3 g Agb 842 c 20 28 30 12 23 4 20 7 846 P 886 c k k 0 k . 5s B 3 g 942 k 1 1 3 k l 1 B 0 3g A ?b rr 983 k 0 0 t- 1 T a b l e 19. ( C o n t i n u e d ) C r y s t a l I n t e n s i t y D i s t r i b u t i o n 5 m e l t „ . (cm-1) ( i a l ( b b l ( c ' c ' ) ( l b ) (be"1") ( a ' a ' ) (ccl ( i ^ c T (cm" 1) s y m m e t r y 1 0 7 6 c h 1123 h 0 h 0 h 0 1156 1 9 3 3 8 1 3 2 1199 1 0 0 h 0 1233 h h 1 h l 0 % h 1 3 1 0 c h 0 0 h 0 h 0 1338 h 0 0 h 0 h 0 1388 34 100 83 28 81 18 100 33 1402 14 48 19 14 13 5 1419 5 22 7 5 10 2 5 3 1485° 0 1 0 h h 0 0 1534 11 80 20 14 28 5 8 5 1615 3 4 4 3 4 2 4 4 2259 3 16 5 4 ' 7 1 2 2 2266 3 2276 h 1 1 % 2 1 2287 5 18 7 5 7 2 5 3 1153 p 1388 p 1 4 0 2 d p 1534 1610 dp 2259 p 2285 p A b g A „ B 3g A g A b A B A g B_ b 3g B 3g H to o R e l a t i v e i n t e n s i t y s c a l e s f r o m 0 t o 100 f o r t h e ab a n d b e ' f a c e s , a nd f o r t h e a£ f a c e i n d e p e n d e n t l y . b T h i s r e s u l t i s s u p p o r t e d b y t h e p r e v i o u s f l u o r e s c e n c e a s s i g n m e n t . ' 7  c T h i s l i n e i s b r o a d . d T h i s l i n e i s a b s e n t i n t h e m e l t s p e c t r u m ; d a t a e n t e r e d f o r b e n z e n e s o l u t i o n . 121 d e p o l a r i z e d (P o t ) S £ 0.75), a rep r o d u c i b l e numerical value f o r p could not be obtained and so the l i n e s are designated only p (polarized) or dp ( d e p o l a r i z e d ) i n Table 19. A comparison of the observed c r y s t a l s p e c t r a w i t h the expected i n t e n s i t i e s , given i n Table 11, i n d i c a t e s t h a t the p r e d i c t i o n s of the oriented-gas model cannot p r o p e r l y account f o r the observed s p e c t r a . The symmetries of many of the weak l i n e s i n the c r y s t a l spectrum could not be assigned w i t h c e r t a i n t y apparently because of c r y s t a l mixing w i t h adjacent stronger l i n e s ; as shown i n Table 10, a l l gerade molecular modes may mix i n the s i t e symmetry of the molecule i n the c r y s t a l . Some of the d i f f i c u l t y , however, may have been caused by s c a t t e r i n g from imperfections i n the c r y s t a l or at i t s s u r f a c e . The c o a x i a l viewing system used on the Cary 81 spectrophotometer i s p a r t i c u l a r l y s e n s i t i v e to l i g h t s c a t t e r e d from surface i m p e r f e c t i o n s . Another source of i n t e n s i t y p e r t u r b a t i o n a v a i l a b l e i n the c r y s t a l environment a r i s e s from the a r t i f i c i a l s e p a ration of i n t r a - and i n t e r m o l e c u l a r motions. The neglect of i n t e r a c t i o n s between such modes i s not j u s t i f i a b l e f o r a molecule as l a r g e as anthracene whose free-molecule funda-mentals overlap the energy region of the l a t t i c e v i b r a t i o n s , as shown i n e a r l i e r s e c t i o n s of t h i s t h e s i s . In Figure 23 i s shown the change i n i n t e n s i t y of the two lowest molecular modes of anthracene-d, n as a f u n c t i o n of temperature as the 122 6 3 Frequency ( c m - 1 ) Figure 23. The low-frequency Raman spectrum o f . p o l y c r y s t a l l i n e anthracene-d 1 Q at temperatures near the melting p o i n t 123 p o l y c r y s t a l l i n e sample nears the melting p o i n t . I t i s obvious from the spect r a t h a t both l i n e s gain i n t e n s i t y i n the c r y s t a l l i n e environment and tha t the l i n e at 22 8 cm 1 (room temperature c r y s t a l value) gains more than the higher energy mode. I t i s a l s o i n t e r e s t i n g to note t h a t the f r e -quencies of the l a t t i c e modes and molecular modes decrease 14 as the temperature i n c r e a s e s . Suzuki, Yokoyama and I t o have reported f o r anthracene-h-^g t h a t the decrease i n f r e -quency i n going from 4°K to room temperature i s even more marked. Another i n t e r e s t i n g p o i n t i s that the gross i n t e n s i t y changes shown i n Figure 23 begin even before the m e l t i n g p o i n t i s reached. This suggests t h a t at l e a s t the l i b r a -t i o n a l phonon s t r u c t u r e i s l o s t before the c r y s t a l s t r u c t u r e disappears. b) Assignment. The three ag l a t t i c e frequencies were seen at 38, 6 8 and 109 cm 1 and comparison w i t h the 14 corresponding modes i n anthracene-h^g reported at 35, 73, and 121 cm 1 r e v e a l s t h a t there i s probably a minor e r r o r i n the p o s i t i o n of the lowest ag mode i n one or both of the assignments, since an anthracene-d^ v i b r a t i o n i s not expected at higher energy than the corresponding v i b r a t i o n i n anthra-cene-h^g. Since' the energy f i t f o r the 100 cm 1 b u combin-a t i o n of the deuterated molecule i s b e t t e r than the f i t f o r the corresponding combination i n anthracene-h, n (see s e c t i o n 124 14 B.l(b) of thxs chapter) the e r r o r may l i e i n the assignment f o r the protonated molecule. The three bg l a t t i c e v i b r a t i o n s were seen at 43, 63 and 117 cm \ i n good agreement wi t h the 14 -1 anthracene-h^Q assignments at 45, 65 and 125 cm The assignments of the Raman-active molecular fun-damentals of anthracene-d.^ are l i s t e d i n Table 20. Since complete assignments w i t h i n each block could not be made the p o s i t i o n s which the fundamentals occupy i n the block were assigned e i t h e r by comparison w i t h the anthracene-h^g a s s i g n -14 40 41 75 ments or by comparison w i t h the c a l c u l a t i o n s . ' ' The 367 and 415 cm 1 l i n e s were very weak i n the melt but much stronger i n the c r y s t a l spectrum, i n d i c a t i n g t h a t i n the s o l i d they had acquired considerable Ag character by mixing w i t h the strong 3 82 cm 1 l i n e . B, and B_ fundamentals are l g 3g 40 41 expected near t h i s energy ' as w e l l as an Ag fundamental. The 367 cm 1 l i n e may mark the presence of e i t h e r the B^ g fundamental or the combination 153 (Bg u) + 220 ( B l u ) . The 415 cm 1 l i n e appears to have mixed Ag (382 cm and B^g c h a r a c t e r i s t i c s i n the c r y s t a l , and i s taken as the B^g fun-damental. An Ag fundamental at 594 cm 1 was observed i n the 77 fluorescence spectrum; the corresponding i n t e r v a l i n the Raman spectrum may be the l i n e at 601 cm Als o l i s t e d i n Table 20 are the r e s u l t s of some 40 41 75 force f i e l d c a l c u l a t i o n s ' ' and the assigned Raman-active 125 Table 20. The assigned Raman-active fundamentals of Anthracene Symmetry Anthracene-d^g C a l c u l a t e d Anthracene-h Type assignment ' Ref. 75 Ref s. 40,41 assignment"^ 2288 2266 2258 1534 1388 1156 842 709 601 382 2295 2264 2263 1587 1435 1335 1188 884 821 744 600 363 2294 2275 2255 1553 1407 1347 1149 848 819 690 634 356 3056 3027 1557 1481 1402 1261 1163 1007 754 622? 395 B i g 613? 228 780 592 387 207 774 578 403 220 915 2 4 3 B 2g 761? 644,659? 261 927 787 677 665 485 245 910 801 682 602 510 287 978 904 765 622 290 126 Table 20. (Continued) Symmetry Anthracene-d^^ C a l c u l a t e d Anthracene-h Type assignment Ref. 75 Refs. .40,41 assignment+ 2276 2301 2278 3076 — 2278 2247 — 1615 1619 1588 1630 — 1535 1522 — 1233 1266 1244 — — 1044 1027 — 943 929 960 1187 816 878 846 — 777 , 809 810 956 502 479 494 522? 415 339 361 — See t e x t f o r d e s c r i p t i o n of source of anthracene-h assignments. 127 fundamentals of anthracene-h.^. The frequencies l i s t e d f o r the protonated molecule were taken from Suzuki, Yokoyama and 14 22 I t o and from Ting, although the f i n a l assignment does not agree completely w i t h e i t h e r of these authors. The d i f f e r -ences occur p r i m a r i l y i n the Ag and B^^ symmetry blocks and a r i s e to o b t a i n consistency w i t h the p o l a r i z e d fluorescence 77 spectra and w i t h some d e p o l a r i z a t i o n r a t i o s measured f o r a 23 s o l u t i o n and, i n the course of t h i s work, f o r the melt. For example, the e a r l i e r authors have disagreed on the assignments -1 14 of the i n t e r v a l s 1481 and 1505 cm ; Suzuki et a l . assigned 22 them B^ and Ag, while Ting considered them to be Ag and B^g fundamentals, r e s p e c t i v e l y . In the Raman spectrum of the melt, the 1481 cm 1 l i n e was prominant and w e l l p o l a r i z e d while the 1505 cm 1 l i n e was so weakened th a t the d e p o l a r i z a t i o n r a t i o could not be measured. E v i d e n t l y the l a t t e r l i n e i s i n t r i n s i c a l l y weak and gains s t r e n g t h through c r y s t a l e f f e c t s . CHAPTER V CALCULATIONS A. M o l e c u l a r V i b r a t i o n s I n t h e B o r n - O p p e n h e i m e r a p p r o x i m a t i o n t h e p o t e n t i a l f u n c t i o n r e p r e s e n t i n g t h e r e s t o r i n g f o r c e s a c t i n g on t h e n u c l e i when t h e y a r e d i s p l a c e d f r o m t h e i r e q u i l i b r i u m p o s i -t i o n s i s i n d e p e n d e n t o f changes i n t h e e l e c t r o n i c wave f u n c -t i o n . I f t h e m o t i o n o f t h e atoms d u r i n g t h e v i b r a t i o n i s s m a l l , t o a good a p p r o x i m a t i o n t h e t r a n s l a t i o n a l , r o t a t i o n a l and 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 l s o s e p a r a b l e . I n t h e e v e n t t h a t t h e r e s t o r i n g f o r c e s i n t h e m o l e c u l e a r e known, t h e n t h e n u c l e a r d i s p l a c e m e n t s d e t e r m i n e t h e k i n e t i c and p o t e n t i a l e n e r g y w h i c h i n t u r n c a n be u s e d t o f i n d t h e f r e -q u e n c i e s o f v i b r a t i o n and r e l a t i v e a m p l i t u d e s o f t h e v i b r a -t i o n s o f t h e m o l e c u l e . The n o r m a l p r o c e d u r e i s t o u s e t h e known f r e q u e n c i e s o f one m o l e c u l e t o c a l c u l a t e i t s f o r c e c o n s t a n t s w h i c h t h e n c a n be t r a n s f e r r e d t o s i m i l a r m o l e c u l e s t o c a l c u l a t e a p p r o x i m a t e f r e q u e n c i e s . The r e l i a b i l i t y o f t h i s method depends on t h e d e g r e e o f s i m i l a r i t y between t h e m o l e c u l e s ; i n i s o t o p i c s p e c i e s , f o r example, t h e f i t i s e x c e l l e n t . 128 129 1. Motion i n C a r t e s i a n Coordinates A system of N n u c l e i has 3N degrees of freedom of which s i x (only the no n - l i n e a r case i s considered) account f o r the t r a n s l a t i o n s and r o t a t i o n s of the molecule as a whole. I f the 3N mass-weighted C a r t e s i a n displacement co-ordinates {q} are introduced, where q^ = >/m^  • Axj_, q2 = ym^ «Ay^, e t c . then the k i n e t i c energy, T, of the molecule i s given by 2 T = I (q±)2 V . l i o r, i n matrix n o t a t i o n , where q i s the column ve c t o r of the (q ) , . t . • 2 T = g_ 2, V . l a The p o t e n t i a l energy, V, can be expressed as a Taylor s e r i e s i n the displacement coordinates ( q l , i n which a l l sums are over the 3N coordinates, thus: 2 V = 2 V n + 2 E ( ? ) q. + E (^1 , q.q. + ...v. 2 ± 3q. o * i i , j 3 q . 3 q j } o ^ The e q u i l i b r i u m c o n f i g u r a t i o n i s ass o c i a t e d w i t h a minimum i n the p o t e n t i a l energy surface and when i t i s defined to have zero energy the f i r s t two terms i n equation 2 drop out and, i f higher terms are neglected, 2 V = ) q.q*. = f..q.q. V.3 q i q j or 2 V = q^F % V.3a 130 The dependence of the p o t e n t i a l energy only on second order terms i m p l i e s harmonic motions of the atoms; i f the d i s -placements are larg e t h i s approximation i s not v a l i d and higher order terms begin to become important. (The appear-ance of these anharmonic terms i n the force f i e l d r e s u l t s i n i n t e r a c t i o n s between harmonic normal modes.) The motions of the system of n u c l e i are governed by Newton's equations of motion, which are, i n the mass-weighted C a r t e s i a n system and i n Lagrangian form, "It all " 4l " 0 1 1 = 1 3 N ) v-4 where L, the Lagrangian f u n c t i o n , i s given by L = T-V. Since T i s a f u n c t i o n of the q^ and V of the q^, s u b s t i t u t i o n of equations 1 and 3 i n t o 4 gives a set of 3N homogeneous second order d i f f e r e n t i a l equations q' + £ f. . q . = 0 ( i = l , 3N) . V.5 1 j - L J J One p o s s i b l e s o l u t i o n i s q^ = q^ s i n (tj\ + 6) V.6 o where q^ i s the amplitude of the motion, 6 i s a phase f a c t o r and X i s r e l a t e d to the v i b r a t i o n a l frequency. S u b s t i t u t i o n of equation 6 i n t o 5 gives r i s e to a set of 3N l i n e a r homogen-eous equations which have n o n - t r i v i a l s o l u t i o n s only i f the sec u l a r determinant equals zero, i . e . 131 S i x of the 3N values of X s a t i s f y i n g equation 7 are always found to be zero; these correspond to the three molecular r o t a t i o n s and three t r a n s l a t i o n s . The remaining 3N-6 values of X are r e l a t e d to the normal frequencies of> v i b r a t i o n , v -1 2 —2 2 (i n cm ) , by X = 4TT v c ; s u b s t i t u t i o n of these values of A back i n t o equation (6) shows how each of the coordinates q^ v a r i e s w i t h time. The motion of the n u c l e i corresponding to each normal frequency i s known as the normal mode of the v i b r a t i o n . 2. Motion i n g e n e r a l i z e d Coordinates. The normal frequencies and normal modes of v i b r a t i o n are of course independent of the coordinate system used. The above s o l u t i o n i n terms of mass-weighted Cartesians i n v o l v e s force constants which are inconvenient i n two respects; since they cannot be i n t e r p r e t e d i n p h y s i c a l terms they are not immediately t r a n s f e r a b l e between molecules, and a l s o o f f -diagonal terms are not a l l zero. In order to discus s two coordinate systems, each one of which e l i m i n a t e s one of the above d i f f i c u l t i e s , a completely g e n e r a l , u n s p e c i f i e d co-ord i n a t e system w i l l be considered f i r s t . Any set of coordinates can be r e l a t e d to another set by a l i n e a r t ransformation U. In p a r t i c u l a r , the r e l a t i o n between some set {p} and the c a r t e s i a n displacements {q} i s given as 132 q = u p In the coordinates {p} the k i n e t i c energy (from equation la) Is given as 2 T = j ^ t ^ U p V.8 I f the transformation i s orthogonal, then U = U 1 and 2 T = p ^ V.9 S i m i l a r l y , from equation 3a, the p o t e n t i a l energy i s given as 2 V = p_fc U t F U p V.10 3. Motion i n Normal Coordinates The a n a l y s i s of the v i b r a t i o n a l problem would be extremely simple i f a coordinate system could be found f o r which a l l cross-terms between coordinates i n both the p o t e n t i a l and k i n e t i c energy expressions were zero; the mass-weighted Cartesians introduced e a r l i e r have t h i s property only f o r the k i n e t i c energy. Such a system can be d e f i n e d ; a s i n g l e displacement coordinate i n t h i s system describes the motion executed by a l l the atoms when the molecule undergoes a normal v i b r a t i o n . Since there are 3N-6 fundamental v i b r a t i o n s there are 3N-6 of these normal coordinates. In t h i s system the k i n e t i c and p o t e n t i a l energies are given by 2 T = Qfc Q V . l l 133 and 2 V = Q^ A Q V.12 where Q i s a column ve c t o r of the normal coordinates and _A i s a diagonal m a t r i x . The normal coordinates can be v i s u a l i z e d i n terms of the C a r t e s i a n displacement s e t ; i f the t r a n s f o r m a t i o n between the two systems i s L, then a = L Q 4. Motion i n I n t e r n a l Coordinates In the mass-weighted C a r t e s i a n coordinate system used e a r l i e r the elements f ^ j which represent the e f f e c t a change i n coordinate i has on coordinate j are awkward to t r a n s f e r from one molecule to another because they have no d i r e c t chemical i n t e r p r e t a t i o n . This disadvantage can be overcome by s e t t i n g up the problem i n i n t e r n a l coordinates such as the valence coordinates whose a p p l i c a t i o n was summar-8 0 i z e d by Decius. These coordinates measure changes i n bond lengths and angles during v i b r a t i o n s and can be i n t e r p r e t e d chemically i n terms of the strengths of bonds and t h e i r r e s i s t a n c e to d i s t o r t i o n . In the i n t e r n a l coordinates {R}, the p o t e n t i a l energy i s given by 2 V = Rfc F R V. 13 where the elements of F are the f o r c e constants a s s o c i a t e d w i t h the various bond s t r e t c h e s and angle d i s t o r t i o n s . Although F i s diagonal only i n the s i m p l e s t approximation, 134 the f o r c e constants r e l a t e d to bond s t r e t c h e s and d i s t o r -t i o n s of the valence angles should be much l a r g e r than the i n t e r a c t i o n constants. In order to determine the k i n e t i c energy i n the i n t e r n a l coordinate system i t i s necessary to f i n d the transformation from C a r t e s i a n to i n t e r n a l c o o r d i n -a t e s — t h a t i s , the matrix T i n g_ = T_ R V.14 The matrix T i s not r e a d i l y a v a i l a b l e from the mole-c u l a r geometry, however, and i t i s convenient to introduce 2 8 29 the G-matrix elements of Wilson. ' From the molecular geometry the matrix B f o r the inverse t r a n s f o r m a t i o n , R = B q_ V.15 can be c a l c u l a t e d . Since {R} and {q} g e n e r a l l y have d i f f e r -ent dimensions, B i s not square and thus cannot be i n v e r t e d to give T. However, B Bfc i s square and i f the matrix G i s defined as G = B Bfc V. 16 then i t can be shown ( r e f . 29, appendix 7) t h a t the k i n e t i c energy i s given by 2 T = Rfc G _ 1 R V.17 S u b s t i t u t i o n of the expressions f o r T and V i n the Lagrangian gives -2 L = Rfc F R - Rfc G - 1 R V.18 135 which, upon s u b s t i t u t i o n i n t o equation 4, gives r i s e to a set of s e c u l a r equations having n o n - t r i v i a l s o l u t i o n s only i f |F — A G _ 1| = 0 V.19 Equation 19 can be m u l t i p l i e d through by G to give another common form |G F - A EI = 0 V.20 5. Motion i n Symmetry Coordinates The s e c u l a r equation (19 or 20) has dimension of at l e a s t 3N-6 and f o r aromatic molecules i s q u i t e l a r g e ; i n order to f a c t o r i t i n t o s m a l l e r blocks symmetry coordinates are introduced. I n t e r n a l symmetry coordinates are l i n e a r combinations of the i n t e r n a l coordinates formed by p r o j e c t i n g one member of each symmetrically e q u i v a l e n t set of i n t e r n a l coordinates i n t o the p o i n t group of the molecule. Maximum symmetry f a c t o r i z a t i o n i s thus achieved since no i n t e r a c t i o n terms i n the F or G matrices w i l l occur between two co o r d i n -ates of d i f f e r e n t symmetry. I f the G F problem can be solved to give force constants i n terms of the various sym-metry coordinates then from the transformation between the symmetry and i n t e r n a l coordinates the force constants r e l a -t i v e to the i n t e r n a l coordinates can be found. Unfortunately, since there are always more i n t e r n a l force constants than 136 symmetry for c e constants, i t i s not p o s s i b l e to determine a l l the i n t e r n a l constants without making s i m p l i f y i n g assumptions. B. Out-of-Plane Force F i e l d f o r Aromatic Molecules The out-of-plane force f i e l d f o r aromatic molecules, u n l i k e the in-plane f i e l d , has r e c eived l i t t l e a t t e n t i o n i n recent years. There are two reasons f o r t h i s ; l e s s informa-t i o n about the non-planar v i b r a t i o n s has been a v a i l a b l e , and f o r those fundamentals which were known, c a l c u l a t i o n s based 30 on the constants f i r s t suggested by Whiffen f o r benzene i n d i c a t e d t h a t the f i e l d was already q u i t e adequate. The r e c e n t l y a v a i l a b l e i n f o r m a t i o n (see Chapter IV) about anthra-cene, however, shows th a t i n at l e a s t one c a s e — t h e second 40 lowest B 3 u v i b r a t i o n — t h e force f i e l d p r e d i c t s a funda-mental f a r above the observed value. As long as there i s one such large discrepancy between the observed and c a l c u l a t e d f r e q u e n c i e s , the force f i e l d cannot be considered to be secure; i n an e f f o r t to improve the f i t the out-of-plane problem has been considered again i n the course of t h i s work. 137 1. Benzene a) Symmetry for c e constants. The out-of-plane force 26 f i e l d of benzene has been discussed by M i l l e r and Crawford who used Wilson's technique to solve the determinental equation ( i n the form of equation V.20) f o r the force con-s t a n t s . Due to the appearance of q u a d r a t i c equations having two p h y s i c a l l y p o s s i b l e roots the s o l u t i o n i n symmetry co-ordin a t e s i s not unique and converting to i n t e r n a l valence coordinates adds to the u n c e r t a i n t y s i n c e there are then eleven force constants to be evaluated from the e i g h t symmetry 30 constants. Whiffen chose a unique f i e l d from the p o s s i b l e s o l u t i o n s on the b a s i s that i n t e r a c t i o n constants should be as small as p o s s i b l e . In order to permit c o n s i d e r a t i o n of other force f i e l d s , the problem i n terms of symmetry coor-dinates was considered again; the four s o l u t i o n s p o s s i b l e are given i n Table 21. The d e f i n i t i o n of the i n t e r n a l , f o r c e constants and i n t e r n a l coordinates i s the same as that.used 81 by Whiffen (with the t o r s i o n as defined by B e l l ), but f o r the purposes of t h i s work the symmetry force constant 2 6 n o t a t i o n of M i l l e r and Crawford was found more convenient. The i n t e r n a l and symmetry coordinates are defined i n the appendix. The G-matrix elements f o r benzene are a l s o given i n the appendix, along w i t h the d e f i n i t i o n s of the symmetry forc e constants. 138 Out-of-Plane force co symmetry coordinates* ° 2 Force Constant Value (mdyn A/radian ) a .2930 <J> .3600 n -.0400 -.1080 6 .0981 .1661 e .2674 .2186 to .0277^ / N S S S^407 .0277 .3407 9 .0785 .3718 .0785 .3718 a .2930 .3720 .2930 .3720 Set A Set B Set C Set D * The n o t a t i o n f o r t h e ^ g S y m m e t r y force constants i s tha t of M i l l e r and Crawford and i s defined i n the appendix. 139 b) I n t e r n a l valence-coordinate force constants. In order to t r a n s f e r the fo r c e constants to other molecules, i t i s necessary to express them i n terms of i n t e r n a l c o o r d i n -ates. The i n t e r n a l coordinates y a n d <\> have been defined by 30 35 Whiffen or S c u l l y and Whiffen and are a l s o defined i n the appendix. The n o t a t i o n f o r the force constants i s th a t of 30 35 Whiffen and S c u l l y and Whiffen, and can be deduced from the f o l l o w i n g p o t e n t i a l f u n c t i o n i n which the s u b s c r i p t s i n v o l v i n g 'x' determine the p o s i t i o n s of the r e l e v a n t i n t e r n a l coordinates by l o c a t i n g the carbon atoms i n v o l v e d (see the appendix). 2 V = P E Y X 2 + 2 P o E Y X Y x + 1 + 2 p m E Y X Y X + 2 + 2 pp S Y X Y ^ + Q SCc+l + 2 q o Z*x,x+1 *x+l,x+2 + 2 qm E *x,x+l*x+2,x+3 + 2 q P Z * x , x + 1 *x +3,x +4 + 2 fco S Y x * x , x + l - 2 t m E Y cb • - 2 t _ E Y cb , „ , _ . m x Tx+l,x+2 p x Yx+2,x+3 In the equation above, each summation i s over a l l p o s s i b l e i n t e r a c t i o n s of the type i n d i c a t e d by the s u b s c r i p t s . Care must be taken i n choosing the s i g n of the y<)> i n t e r a c t i o n s since y d> , - I = ~ Y C ! ) -I / Y <J> , I , i = - Y <f> ^ a n d 'x Yx,x+l ' x Y x - l , x ' 'x Tx+l,x+2 ' x T x - 2 , x - l Yx*x+2,x+3 = " Yx*x-3,x-2 ' The r e l a t i o n s h i p between the i n t e r n a l and symmetry coordinates f o r benzene i s given i n Table 22. Since there are 140 Table 22. R e l a t i o n s h i p between symmetry and i n t e r n a l coordinate f o r c e constants f o r benzene. a e 0 = 3 6 n 1 1 1 1 2 •2 •1 1 2 2 •1 •1 1 1 1 •1 k 2 k 2 - k 2 - k 2 -2k -2k -2k 1 - 2 2 1 - - -1 -1 -1 1 - - -- - - -2 2 -2 k = 2/ J3 /p N PP Q q o qm q P t o t m 141 eleven force constants i n i n t e r n a l coordinates and only e i g h t i n symmetry coordinates, s o l v i n g f o r the i n t e r n a l constants r e q u i r e s e i t h e r t h a t three of them be f i x e d or t h a t three i n t e r n a l r e l a t i o n s h i p s between them be set up. However t h i s i s done, four sets of i n t e r n a l force constants w i l l be produced corresponding to the four sets of symmetry constants i n Table 21. Whiffen chose s e t A from the symmetry constants and then solved f o r the for c e constants i n i n t e r n a l c o o rdin-ates by s e t t i n g the meta and para t o r s i o n i n t e r a c t i o n con-st a n t s ( q m and q p) and the torsion-wag i n t e r a c t i o n (tp) equal to zero. In an attempt to f i n d a force f i e l d which w i l l reproduce the anthracene B^ u frequencies, s e v e r a l a l t e r n a t i v e force f i e l d s were evaluated, based on the f o l l o w i n g assump-t i o n s about the i n t e r n a l coordinate constants: I - assume, as Whiffen d i d , t h a t q '= q„ = t =. 0; I I - assume t h a t q_ = m^ p p ^o -q = q n and th a t t n = 0; I I I - assume th a t p = q = t _ = 0. m rr ir p p hr The four sets of i n t e r n a l constants produced from the symmetry constants were found under each assumption, and are l i s t e d i n Table 23. Each set of for c e constants w i l l , of course,, r e -produce the frequencies of benzene; the average e r r o r (probably a r i s i n g mainly from anharmonic terms i n the force f i e l d ) i s i n each case l e s s than 1.5 cm 1 f o r CgHg and l e s s than 1.0 cm 1 f o r CgDg, or l e s s than 0.20 percent. The ob-served frequencies of benzene were taken from Brodersen and Langseth.^ o Table 23. The. o u t - o f - p l a n e f o r c e constants of benzene, i n mdyn A / r a d i a n Force Constant A Set I B C A Set I I B C D Set I I I B C D P Po pm P Q Qo q. •m q. t o m 3118 0158 0158 0187 0589 0196 0 0 0160 0040 0 3644 0158 ;0421 0187 6455 2737 0 0 1967 1767 0 .3118 .0280 -.0280 -.0187 -.0091 -.0876 0 0 -.0160 -.0380 0 3644 0280 0542 0187 5775 2057 0 0 1967 1427 0 2943 .0071 0071 ,0013 0818 0033 0033 .0033 ,0160 0040 0 .6077 .1374 .1637 .2620 .3262 .0456 .0456 .0456 ,1967 .1767 0 2338 0010 0110 0592 0931 0146 0146 0146 0160 0380 0 ,5472 ,1194 ,1457 ,2015 3375 0343 ,0343 ,0343 ,1967 1427 0 .2930 .0064 .0064 0 .0870 .0015 .0070 0 .0160 .0040 0 3457 ,0064 0327 0 6735 2947 0070 0 1967 1767 0 2930 0186 0186 0 0190 0666 0070 0 0160 0380 0 .3457 .0186 .0449 0 .6055 .2267 .0070 0 -.1967 .1427 0 143 2. Naphthalene The f i r s t t r a n s f e r of the benzene o u t - o f - p l a n e f o r c e constants to naphthalene was made by S c u l l y and 35 36 Whiffen. ' T h e i r r e s u l t s are l i s t e d i n Tables 24 and 25, along with the most r e c e n t data on naphthalene and naphtha-lene-dg. A l s o l i s t e d i n Tables 24 and 25 are the r e s u l t s of c a l c u l a t i o n s c a r r i e d out with f o r c e constant s e t s I-A, II-A and I I I - A from Table 23; a l l other s e t s of f o r c e constants from Table 23 produced i m p o s s i b l e r e s u l t s ( i . e . f r e q u e n c i e s t h a t have imaginary values) when t r a n s f e r r e d to naphthalene. The i n t e r n a l c o o r d i n a t e s used f o r the c a l c u l a t i o n are shown i n F i g u r e 24. The f o r c e constant matrix can be d e f i n e d , as 34 i n the manner of Freeman and Ross, by the f o l l o w i n g l i s t . Force constants f o r naphthalene: The f o r c e constants are those l i s t e d i n Table 23 and they are to be understood as e n t r i e s i n a matrix o f f o r c e constants r e f e r r e d t o the i n t e r -n a l c o o r d i n a t e s of F i g u r e 24. T h e i r p o s i t i o n i n the m a t r i x i s determined by the i n t e r n a l c o o r d i n a t e number a s s o c i a t e d with them; symmetry permits omission of many e n t r i e s from the l i s t . Diagonal elements: 1,1 = 2,2 = 9,9 = P; 11,11 = 12,12 = 14,14 = 21,21 = Q; O f f - d i a g o n a l elements: 1,2 = 2,3 = 1,9 = 9,10 = P o ; 1,3 = 1,10 = p m ; 1,4 = 2,10 = p p ; 11,12 = 13,14 = 14,21 = q Q ; 11,13 = 12,14 = 11,21 = q m ; 11,14 = 12,21 = q ; 1,11 = -2,11 = 2,12 = 9,20 = -1,20 = P t Q ; 2,20 = -1,12 = -2,13 = 1,21 = tm. 144 8 17 18 16 5 13 12 Figure 24. Non-planar i n t e r n a l valence coordinates f o r naphthalene. Numbers l o c a t e d at atom p o s i t i o n s represent out-of-plane wags and numbers centered i n bonds represent t o r s i o n s ; both types of coordinates are i d e n t i c a l to those defined by S c u l l y and W h i f f e n . 3 6 Comparison of the average e r r o r s i n Tables 24 and 25 i n d i c a t e s t h a t although a l l sets of force constants have reproduced the known frequencies of naphthalene w e l l , s e t II-A and p a r t i c u l a r l y set I I I - A give somewhat b e t t e r f i t s to the observed values. The most n o t i c e a b l e d i f f e r e n c e s between force constants II-A and I I I - A , and set I-A (which 35 i s the set chosen by S c u l l y and Whiffen ) i s t h a t set I-A has a smaller diagonal entry f o r the t o r s i o n force constant and a l a r g e r i n t e r a c t i o n constant between para-hydrogen-wags. I t i s perhaps worthy of note t h a t i n general the o f f - d i a g o n a l fo r c e constants are smaller f o r sets I I and I I I than f o r set I (except where the set I constants were f i x e d at z e r o ) . 145 Table 24. Observed and c a l c u l a t e d non-planar frequencies of Naphthalene-h„ Observed Symmetry Freq. S c u l l y and Whiffen35 C a l c u l a t e d I-A II-A I I I - A A u 212 1022 807 594 207 980 864 613 161 978 863 632 198 978 863 638 206 i g 933 725 390 920 704 365 933 724 363 937 732 381 938 734 386 B o 2g 980 878 786 467 971 881 770 485 989 900 754 471 983 889 752 474 982 885 750 474 3u 957 782 475 181 962 759 445 177 972 777 439 182 961 770 445 177 958 768 445 175 Average e r r o r 14.3 cm 1 15.8 cm 1 11.4 cm 1 10.6 cm 1 146 Table 25. Observed and c a l c u l a t e d non-planar frequencies of Naphthalene-d R Observed C a l c u l a t e d Symmetry Freq. S c u l l y and Whiffen35 I-A II-A I I I - A — 829 814 813 813 A u — 648 685 677 675 — 511 520 538 543 193 185 144 178 187 761 751 756 756 757 i g 547 528 543 548 549 348 316 318 335 340 — 812 825 826 827 2g — 754 739 742 742 649 665 668 653 649 410 429 424 425 425 791 798 797 792 790 3u 628 594 607 604 602 402 382 382 384 384 166 163 168 164 162 Average e r r o r 16.8 cm 1 17.1 cm 1 9.6 -1 cm 8.5 cm 1 147 3. A n t h r a c e n e The f i r s t t r a n s f e r o f t h e b e n z e n e o u t - o f - p l a n e f o r c e c o n s t a n t s t o a n t h r a c e n e was c a r r i e d o u t by E v a n s and 40 S c u l l y . T h e i r r e s u l t s a r e l i s t e d i n T a b l e s 26 and 27, a l o n g w i t h t h e most r e c e n t d a t a on a n t h r a c e n e and a n t h r a c e n e -d^g. A l s o l i s t e d i n T a b l e s 26 and 27 a r e t h e r e s u l t s o f c a l c u l a t i o n s c a r r i e d o u t w i t h f o r c e c o n s t a n t s e t s I-A, I I - A , and I I I - A f r o m T a b l e 23. The i n t e r n a l c o o r d i n a t e s u s e d f o r t h e c a l c u l a t i o n a r e i l l u s t r a t e d i n F i g u r e 25. The f o r c e 23 3 0 29 16 F i g u r e 25. N o n - p l a n a r i n t e r n a l v a l e n c e c o o r d i n a t e s f o r a n t h r a c e n e ; d e f i n i t i o n s as i n F i g u r e 24. c o n s t a n t m a t r i x can be w r i t t e n , w i t h r e s p e c t t o F i g u r e 25, i n t h e a b b r e v i a t e d f o r m u s e d f o r n a p h t h a l e n e a s : D i a g o n a l 148 T a b l e 26. O b s e r v e d and c a l c u l a t e d n o n - p l a n a r f r e q u e n c i e s o f A n t h r a c e n e - h , n O b s e r v e d Symmetry F r e q . E v a n s and S c u l l y 4 0 I-A C a l c u l a t e d I I - A I I I - A — 966 982 980 980 — 876 881 874 872 A u • — 826 696 706 708 — 552 500 504 505 137 137 104 131 138 915 936 952 949 948 B i i g — 739 755 751 750 — 466 419 437 440 243 235 243 237 234 978 960 984 981 980 904 909 935 915 909 B o 2a — 871 868 866 866 765 754 753 750 747 — 617 571 598 606 290 321 245 290 299 954 952 972 958 954 883 892 894 896 896 3u 730 732 736 743 745 469 504 437 444 444 166? 383 350 373 378 110 96 96 94 93 A v e r a g e A v e r a g e e r r o r * ( a ) e r r o r * ( b ) 28 13 . 7 cm . 0 cm" 1 1 33 20 .0 .2 -1 cm cm"-'-27.1 cm" 12.1 cm" 1 1 27.6 cm 12.2 .cm" 1 1 A v e r a g e e r r o r (a) was c a l c u l a t e d i n c l u d i n g t h e o b s e r v e d f r e q u e n c y a t 166 c m ~ l ; a v e r a g e e r r o r (b) was c a l c u l a t e d b y o m i t t i n g t h a t f r e q u e n c y . 149 Table 27. Observed and c a l c u l a t e d non^planar frequencies of Anthracene-d.^ Observed Symmetry Freq, Evans and S c u l l y 4 0 C a l c u l a t e d I-A II-A I I I - A A u B i g — 859 818 818 818 — 787 710 708 708 — 656 627 628 620 — 481 455 459 460 109 124 94 120 126 — 774 775 773 772 — 578 584 580 579 — 403 370 387 390 228 220 228 222 220 B 2g — 910 821 822 823 — 801 782 782 781 — 682 691 681 678 — 602 679 657 649 — 510 491 514 522 261 287 219 263 273 784 819 798 791 788 722 729 727 727 726 3u 560 556 557 562 564 397 416 380 382 381 153? 337 307 330 336 102 90 91 89 88 Average e r r o r * ( a ) 28 . 7 cm" 1 29. 0 cm - x 26 . 4 cm" 1 29 . 1 cm" 1 Average erro r * ( b ) 13 .0 cm" 1 13. 4 cm~l 7 . 6 cm -1 9 . 9 crn-1 Average e r r o r (a) was c a l c u l a t e d i n c l u d i n g the observed frequency at 153 cm~x; average e r r o r (b) was c a l c u l a t e d by o m i t t i n g t h a t frequency. 150 elements: 1,1 = 2,2 = 9,9 = 11,11 = P; 15,15 = 16,16 = 18,18 = 19,19 = 29,29 = Q; O f f - d i a g o n a l elements: 1,2 = 1,11 = 2,3 = 9,11 = 11,12 = p Q ; 1,3 = 1,12 = 2,11 = 9,12 = 12,13 = p m ; 1,4 = 2,12 = 9,10 = 11,13 = p p ; 1,15 = -2,15 = 2,16 = -1,28 = 11,28 = -11,27 = 9,27 = t ; 2,28 = -1,16 = 1,29 = 9,30 = -2,17 = t m . 4. D i s c u s s i o n of Results This study of the out-of-plane fo r c e f i e l d of benzene, naphthalene and anthracene was undertaken i n an e f f o r t to f i n d a set of force constants which would reproduce, w i t h i n reason-able l i m i t s , the observed frequencies of the three molecules, i n c l u d i n g the second lowest frequency of anthracene. This e f f o r t was not s u c c e s s f u l ; i n Tables 26 and 27 i t can be seen th a t none of the sets of fo r c e constants used could account f o r the low energy of t h a t anthracene v i b r a t i o n . There are three p o s s i b l e explanations f o r t h i s discrepancy: (1) the observed assignment may be i n c o r r e c t ; (2) a simple force f i e l d which w i l l f i t a l l non-planar frequencies of the three molecules e x i s t s but was not found; (3) the force f i e l d of anthracene i s s u f f i c i e n t l y d i f f e r e n t so t h a t t r a n s f e r of fo r c e constants from benzene and naphthalene cannot be s u c c e s s f u l . The second p o s s i b i l i t y i s l e a s t l i k e l y , s ince many force f i e l d s were t r i e d without success, and although other force f i e l d s based on d i f f e r e n t r e l a t i o n s h i p s between benzene's 151 i n t e r n a l f o r c e constants do e x i s t , i t i s f e l t t h a t the most p h y s i c a l l y reasonable p o s s i b i l i t i e s were considered. In a d d i t i o n to the d i r e c t t r a n s f e r of force constants, a p e r t u r -8 2 b a t i o n program which adjusts the force constants to f i t a l l the observed frequencies was used on some of the b e t t e r f i e l d s . In each case, however, i t was found to be impossible to f i t the 166-153 cm 1 p a i r i n anthracene and anthracene-d.^ w i t h a f o r c e f i e l d t h a t would reproduce the observed frequencies of the other molecules. The f i r s t e x p l a n a t i o n r e q u i r e s t h a t the 166-153 cm 1 p a i r a r i s e from combinations i n v o l v i n g l a t t i c e modes and a l s o r e q u i r e s t h a t an a c c i d e n t a l l y i n a c t i v e B^ u fundamental be l o c a t e d some 200 cm 1 higher i n energy than the assigned values. Since a l l other B.j u f u n d a m e n t a l s — i n other molecules as w e l l as a n t h r a c e n e — a r e marked by strong i n f r a r e d absorp-t i o n bands, the occurrence of one w i t h l i t t l e or no i n t e n s i t y seems somewhat u n l i k e l y , and i n the absence of any f i r m experimental evidence t o the contrary the assignment as given must be accepted as c o r r e c t . Thus i t appears t h a t the force f i e l d f o r anthracene m u s t . d i f f e r s u f f i c i e n t l y from t h a t f o r benzene and naphthalene so t h a t no s i n g l e valence force f i e l d can reproduce a l l the observed frequencies. Since only set A of the four p o s s i b l e sets of sym-metry force constants f o r benzene produced i n t e r n a l constants which would t r a n s f e r to naphthalene, i t i s c l e a r t h a t Whiffen's 30 . choice of symmetry constants i s c o r r e c t . I t appears, 152 however, t h a t a force f i e l d (e.g. II-A or III-A) i n v o l v i n g s maller p a r a - i n t e r a c t i o n terms leads to somewhat more accur-ate r e s u l t s than the i n t e r n a l f i e l d chosen by Whiffen. C. Planar Force F i e l d f o r Aromatic Molecules The planar force f i e l d of aromatic molecules has been the subject of much d i s c u s s i o n i n recent years. The f i r s t s i g n i f i c a n t c a l c u l a t i o n s were c a r r i e d out using a modi-f i e d valence fo r c e f i e l d ; 2 ^ ' ' ^ 4 ' ^ 5 emphasis then s h i f t e d to 3 7 _ 3 9 33 modified Urey-Bradley f i e l d s , ' r e t u r n i n g to valence 31 f i e l d s when Scherer showed th a t such a f i e l d was s i g n i f i -c a n t l y more s u c c e s s f u l than a Urey-Bradley f i e l d i n f i t t i n g the frequencies of some c h l o r i n a t e d benzenes. Since then, 41 Neto, Scrocco and C a l i f a n o have developed a modified . valence f o r c e f i e l d designed to f i t simultaneously the planar frequencies of benzene, naphthalene and anthracene and t h e i r deuterated analogues. In t h i s chapter the p r e d i c t i o n s of the Neto, Scrocco 41 and C a l i f a n o (NSC) f i e l d w i l l be compared w i t h the e x p e r i -mental assignments i n Chapters I I I and IV f o r naphthalene 32 and anthracene. In a d d i t i o n , a f i e l d r e c e n t l y developed f o r benzene w i l l be extended to naphthalene and anthracene and a comparison of the p r e d i c t i o n s of the two f i e l d s w i l l be made. 153 1. The Neto, Scrocco and C a l i f a n o F i e l d The NSC f i e l d f o r aromatic molecules was developed i n the f o l l o w i n g manner. F i r s t , a s i m p l i f i e d f o r c e f i e l d was found f o r benzene alone, using the minimum number of force constants compatible w i t h a reasonable f i t to the 3 observed frequencies. Although the source of the i n i t i a l benzene force constants was not s p e c i f i e d , the very c l o s e agreement wi t h the constants found by S c l i e r e r 3 1 i n d i c a t e s t h a t the s t a r t i n g p o i n t was a Urey-Bradley f i e l d . This benzene f i e l d was then extended to naphthalene and to anthra-cene s e p a r a t e l y , r e f i n i n g the force constants to f i t observed frequencies which the authors considered to be secure. I t should be pointed out, however, t h a t the experimental f r e -quencies accepted by Neto, Scrocco and C a l i f a n o f o r naphtha-lene and anthracene were taken, i n g e n e r a l , from assignments 34 35 83 based on previous c a l c u l a t i o n s . ' ' When the refinement f o r each molecule was completed, a l l frequencies which had p r e v i o u s l y been omitted as u n c e r t a i n were reconsidered; i f the c a l c u l a t i o n s i n d i c a t e d a choice could be made between the c o n f l i c t i n g experimental assignments, t h a t value assumed to be c o r r e c t was entered i n the l i s t of secure frequencies f o r the f i n a l step of the refinement. This f i n a l step was to r e f i n e a s i n g l e force f i e l d f o r a l l the molecules simultaneously. Force constants which r e f e r r e d to i n t e r n a l coordinates of the same type i n 154 each of the three molecules were c o l l e c t e d together i n t o one term, provided the three separate refinements i n d i c a t e d they were of n e a r l y the same magnitude. This produced a f i e l d c o n t a i n i n g only 34 independent force constants, which was r e f i n e d to f i t a l l the frequencies assigned i n the previous step. One unusual feature of t h i s force f i e l d i s t h a t an i n t e r n a l coordinate which has a seemingly i d e n t i c a l e n v i r o n -ment i n two of the molecules not uncommonly has a q u i t e d i f f e r e n t force constant i n each molecule. This i s , of course, a r e s u l t of the i n i t i a l refinement of each force 4 f i e l d s e p a r a t e l y . Another p o i n t worthy of mention i s t h a t e i g h t of the 34 force constants r e f e r to only one molecule. One consequence of t h i s i s t h a t these constants may be adjusted by the•refinement procedure to values f a r removed from p h y s i c a l r e a l i t y i n order to compensate f o r other de-f i c i e n c i e s i n the force f i e l d . The r e s u l t s of the Neto, Scrocco and C a l i f a n o c a l -c u l a t i o n are t a b u l a t e d i n Section.C-3 of t h i s chapter, where they are compared w i t h the frequencies p r e d i c t e d by a s i m i l a r c a l c u l a t i o n (described i n the next s e c t i o n ) , and f u r t h e r d i s c u s s i o n w i l l be postponed u n t i l then. 2. The D u i n k e r - M i l l s F i e l d S h o r t l y a f t e r Neto, Scrocco and C a l i f a n o developed 32 t h e i r general force f i e l d , Duinker and M i l l s presented a new planar valence f i e l d f o r benzene. They had found t h a t 155 31 39 84 the p r e v i o u s l y published force f i e l d s f o r t h a t molecule ' ' 33 d i d not give accurate values of the r e c e n t l y observed C o r i o l i s c oupling constants. Although the C o r i o l i s constants do not provide s u f f i c i e n t i n f o r m a t i o n to determine a unique f i e l d f o r benzene, a modified valence f i e l d was developed, i n v o l v i n g the f o l l o w i n g i n t e r a c t i o n constants: (1) a l l i n t e r -85 a c t i o n constants p r e d i c t e d by the M i l l s ' h y b r i d o r b i t a l model to be s i g n i f i c a n t (stretch-bend i n t e r a c t i o n s ) were i n c l u d e d ; * 37 39 (2) a "Kekule" type i n t e r a c t i o n constant ' between CC st r e t c h e s was i n c l u d e d ; (3) i n t e r a c t i o n s between CH in-plane wags and between CCC angle bending coordinates were i n c l u d e d ; these are p r e d i c t e d on the b a s i s of Lin n e t ' s o r b i t a l - f o l l o w i n g 86 arguments to be s i g n i f i c a n t ; (4) i t was a l s o found necessary to i n c l u d e i n t e r a c t i o n constants between meta and para CH bending coordinates. A thirteen-parameter f i e l d i n c l u d i n g the above i n t e r a c t i o n constants was r e f i n e d by Duinker and M i l l s , and they found i t p o s s i b l e to o b t a i n simultaneously a good f i t 5 both to the observed frequencies of benzene and to the 33 C o r i o l i s c oupling constants. I t was t h i s success t h a t prompted us to attempt to extend t h i s f i e l d to naphthalene and anthracene. 3. Refinement of the D u i n k e r - M i l l s F i e l d The f o r c e constants of the D u i n k e r - M i l l s benzene f i e l d were t r a n s f e r r e d to naphthalene and anthracene w i t h as 156 f e w c h a n g e s a s p o s s i b l e . The CC s t r e t c h i n g f o r c e c o n s t a n t was m u l t i p l i e d b y a f a c t o r r e l a t e d t o t h e b o n d l e n g t h s o t h a t t h e f o r c e c o n s t a n t s w o u l d f i t a c u r v e o f t h e f o r m f = Ae w h e r e f a n d r a r e t h e f o r c e c o n s t a n t and b o n d l e n g t h r e s p e c -t i v e l y a n d A a n d x w e r e g i v e n t h e v a l u e s 1170 and 3.65 r e s ~ 8 7 p e c t i v e l y as s u g g e s t e d by S t e e l e . T h i s f o r m f o r t h e c u r v e was c h o s e n s i n c e t h e f o r c e c o n s t a n t s f o r s i n g l e , d o u b l e a n d t r i p l e CC b o n d s o f a l i p h a t i c s y s t e m s f i t s u c h a c u r v e q u i t e w e l l when x = 3.65 and A = 1 2 3 9 . To r e p r o d u c e t h e D u i n k e r -M i l l s v a l u e f o r t h e s t r e t c h i n g c o n s t a n t o f b e n z e n e i t was 87 f o u n d t o be n e c e s s a r y t o s e t A = 1170. I n t e r a c t i o n c o n s t a n t s b e t w e e n CC s t r e t c h e s when one o f t h e i n t e r n a l c o o r d i n a t e s i n v o l v e d i s a r i n g - j u n c t i o n b o n d , o r when t h e two c o o r d i n a t e s a r e i n d i f f e r e n t r i n g s w e r e s e t e q u a l t o f o r c e c o n s t a n t number 21 m u l t i p l i e d b y a w e i g h t i n g f a c t o r whose v a l u e i s d e t e r m i n e d 37 i n t h e manner s u g g e s t e d by S c h e r e r . The i n t e r n a l c o o r d i n a t e s u s e d f o r b e n z e n e , n a p h t h a -l e n e and a n t h r a c e n e a r e i l l u s t r a t e d i n F i g u r e s 2 6 - 2 8 , i n w h i c h CC b o n d s t r e t c h e s a r e d e s i g n a t e d by R, CH b o n d s t r e t c h e s b y r , CCC a n g l e b e n d s by a and i n - p l a n e h y d r o g e n wags by T h e s e i n t e r n a l c o o r d i n a t e s c a n be d e f i n e d w i t h r e f e r e n c e t o 30 b e n z e n e i n t h e manner o f W h i f f e n b y s e t t i n g up a l o c a l t h C a r t e s i a n a x i s s e t a t e a c h atom. The m o t i o n o f t h e j c a r b o n atom f r o m i t s e q u i l i b r i u m p o s i t i o n i n t h e r a d i a l , t h e x ( o u t - o f - p l a n e ) , and t h e m u t u a l l y p e r p e n d i c u l a r d i r e c t i o n t h i s g i v e n b y R j , X.. and IK . The j h y d r o g e n atom i s a t t a c h e d 157 th to the j carbon atom and i t s motion i s described i n a simi-l a r manner by r . , x. and u.. 3 3 3 The i n t e r n a l coordinates in.these C a r t e s i a n a x i s sets are given by: R. = - (R. + R.,,) - ^1 (u. - U..,) -3 2 3 3 + 1 2 3 3+1 r . = r . - R. -3 3 3 /T, - 1 6. = - (u. - U.) + ^ - (R. - - R. , ) - — (U. + 2U. +U ~ 3 r o 3 J 4R Q + 1 11 1 4R Q 3 1 3 ^ / T i a. = (R. -2R. + R._,_,) + -=— (U. , - U.^,) "3 2R 3-1 3 3 + 1 2 R o . 3-1 3 + 1, o where R Q i s the CC bond length and r Q the CH bond length . The l i s t which f o l l o w s each diagram gives the force constants (unrelated by molecular symmetry) used to c a l c u l a t e the fundamentals. The abbreviated nomenclature i s s i m i l a r to 34 tha t of Freeman and Ross and to th a t used e a r l i e r i n t h i s chapter f o r the out-of-plane force f i e l d , except t h a t where p r e v i o u s l y the l i s t contained the value of the force constant, i n t h i s case i t contains only the force constant number. The i n i t i a l and f i n a l values of the for c e constants are l i s t e d a f t e r Figures 26-28 i n Table 28. 158 0, F i g u r e 26. The p l a n a r i n t e r n a l c o o r d i n a t e s o f b e n z e n e E n t r i e s i n t h e b e n z e n e f o r c e c o n s t a n t m a t r i x D i a g o n a l e l e m e n t s : R j R i = 1* r i r i = 2* = ^1^1 = ^' O f f - d i a g o n a l e l e m e n t s : R j R 2 = 7 ; R i R 3 = 8 ; R i R 4 = 9 ; r l r 3 = 10; a ]_« 2 = 1 1 ; & ±& 2 = 1 2 ; 3 ]_3 3 = - 1 3 ; 3]_B4 = -14; a1r± = 15; R l a l = R l a 2 = 1 6 ' ^ l a 2 = ~ ^ l a 6 = 1 8 ' R l ^ l = _ R 1 ^ 2 = 1 9 ' R l 3 6 = - R 1 B 3 = 2 0 -1 5 9 1 r ^7 7 • . R " Q s R \ ~ . R a ' ~ R . r c i a r a a R 7 6 6^ a 5 J ! a . R - i 4 ^ R . „ R : 4 Figure 27. The planar i n t e r n a l coordinates of naphthalene. E n t r i e s i n the naphthalene fo r c e constant matrix Diagonal elements: 0.870 RJRJ, = 1.083 R 2 R 2 = 1 * 0 9 6 R 4 R 4 = 1.040 R l l R l l = 1; r ^ = r 2 r 2 = 2; = a 2 a 2 = 3; a 9 a 9 = 4; a ] _ 1 a 1 1 = 5; 3]_31 = 3 28 2 = 6. Off - d i a g o n a l elements: R 1 R 2 = R i R i o = 7 ; R 1 R 3 = 8 ; R 1 R 4 = 9 ; r 1 r 3 = 10; = a 2 a 3 = 0 ^ 0 ^ = a 1 0 a 1 3 = 11; 8 16 2 = ~3 23 3 = 1 2 ; B l 3 3 = 1 3 ; 31 64 = 1 4 a l r l = a 2 r 2 = 1 5 ; R l a l = R 2 a 2 = R l a 2 = R 1 0 a f R 1 0 a l 0 = R l l a 1 0 = 1 6 ? R 1 0 a 9 = 1 7 ; 3 l a 2 = _ p l a 1 0 = e 2 a 3 = _ 3 2 a l = 18; R 18 1 = -Rlfl8-, = -R-,3, = R 98 9 = 19; R-, 3 4 =-R i n3 A = R 48, = \ L 0 M 1 1 M2 2 M 2 v l P 4 " 1 0 P 4 ~ " 4 P 2 160 ~ R 1 1 3 2 " 2 0 ; " R 1 R 1 1 " R 2 R 1 1 " R 4 R 1 1 ~ " R 1 R 5 " R 1 R 6 ~ " R 1 R 7 " R-jRg = " R j R g = R- 2 R5 = ~ R 2 R 6 = R 2 R 7 = 0 , 3 3 3 * 2 1 • /38 £s £' " i r r > R.e »Sa A ^ < —I - J L -F i g u r e 28. The p l a n a r i n t e r n a l c o o r d i n a t e s o f a n t h r a c e n e E n t r i e s i n t h e a n t h r a c e n e f o r c e c o n s t a n t m a t r i x D i a g o n a l e l e m e n t s : 0.885 ~ ! ' 1 2 9 R 2 R 2 = 1 « 1 2 9 R 4 R 4 = R 5 R 5 = 1.139 R 1 5 R 1 5 = 1 '* r i r i = r2*2 ~ r 9 r 9 = 2 ; a i a i = a2®2 = 3 ;  a l l a l l = a 1 2 a 1 2 = 4 ; a 1 3 a 1 3 = 5 ; 3 1 3 1 = B 2 6 2 = B 9 6 9 = 6 ' O f f - d i a g o n a l e l e m e n t s : R i R 2 = R 1 R 1 4 = R 1 2 R 1 3 = 7 ; R l R 3 = =  R 2 R 4 = R 6 R 1 2 = 8 ; R 1 R 4 = R 5 R 1 2 = 9 ; r l r 3 = 1 0 ; a l a 2 8 8 a 2 a 3 = a l a 1 2 = a 1 2 a 1 5 = a 9 a l l = a l l a 1 4 = 1 1 ; B l 3 2 = " 3 2 B 3 = 1 2 ; • e 1B 3 = 1 3 ; 8 ^ 4 = - e 98 1 0 = 14; = = a 1 ( J r 1 0 = 1 5 ; R l a l = R l a 2 = R 2 a 2 = R 4 a 1 5 = R l 5 a 1 2 = R 1 5 a l l = Vl4 = 161 V l O = 1 6 ; R 1 4 a l l = R 1 3 a 1 2 = 1 7 ' * 3 l a 2 = " 6 2 a l = B 3 a 2 = V l l = " 3 9 a 2 0 = 1 8 ; B l R l " = ~ 3 1 R 1 4 = 3 9 R 1 3 = " 6 9 R 1 2 = 1 9 ;  6 1 R 3 = ~ 3 1 R 4 = 3 2 R 4 = - B 2 R 1 5 = B 9 R 5 = - * 9 R 6 = 2 0 ? ~ R 1 R 5 = R 1 R 6 = R 1 R 1 2 = " R 1 R 1 3 = R 2 R 5 = ~ R 2 R 6 = R 4 R 5 = " R 4 R 6 = " R 4 R 1 2 = R 4 R 1 3 0.50 x 2 1 . The o b s e r v e d f r e q u e n c i e s t o w h i c h t h e i n i t i a l f o r c e c o n s t a n t s h a v e b e e n r e f i n e d ( t h e s e a r e - t h e o n e s n o t e n c l o s e d i n p a r e n t h e s e s i n T a b l e 2 9 , w h i c h f o l l o w s l a t e r ) w e r e c h o s e n i n t h e f o l l o w i n g m a nner: (1) f o r b e n z e n e , a l l a s s i g n m e n t s 5 made by B r o d e r s e n a nd L a n g s e t h w e r e u s e d ; (2) t h e more c e r -t a i n a s s i g n m e n t s l i s t e d i n T a b l e 8 f o r n a p h t h a l e n e - d g a nd t h o s e f r e q u e n c i e s f o r n a p h t h a l e n e - h g f o r w h i c h t h e r e i s g e n -6-9 14 e r a l a g r e e m e n t ' w e r e u s e d . The p r o p o s e d a s s i g n m e n t o f a B 2 U r i n g mode n e a r 1700 cm 1 i n n a p h t h a l e n e - h g h a s n o t b e e n 3 6 a c c e p t e d , s i n c e i t h a s b e e n s u g g e s t e d t h a t t h e s t r o n g b a n d s i n t h i s r e g i o n a r e due t o c o m b i n a t i o n s a nd s i n c e t h e p r e v i o u s 34 35 37 41 70 c a l c u l a t i o n s ' ' ' ' h a v e u n a n i m o u s l y p l a c e d t h i s f u n d a m e n t a l some 150 cm 1 l o w e r i n e n e r g y ; (3) t h e l e s s c o n t r o v e r s i a l f r e q u e n c i e s f r o m T a b l e s 1 5 , 18 a n d 20 w e r e u s e d f o r a n t h r a c e n e . A r g u m e n t s s i m i l a r t o t h o s e i n v o l v e d f o r t h e B 2 u b l o c k o f n a p h t h a l e n e r e s u l t e d i n t h e h i g h e s t r i n g modes o f t h i s s y m metry b e i n g p l a c e d a t 1533 and 1493 cm 1 f o r t h e p r o t o n a t e d a n d d e u t e r a t e d a n t h r a c e n e s r e s p e c t i v e l y . 162 T a b l e 28. I n i t i a l a n d f o r c e - f i e l d * f i n a l f o r c e c o n s t a n t s f o r p l a n a r + Type Number I n i t i a l V a l u e F i n a l V a l u e RR 1 7.015 7.040 r r 2 5.125 5.061 oca 3 1.097 1.103 a a 4 0.731 0.711 a a 5 0.731 0.814 B B 6 1.034 1.020 RR o 7 0.531 0.650 R R m 8 -0.531 -0.609 RRp 9 0.531 0.295 r r m 10 0.000 0.034 aa o 11 -0.097 -0.097 12 0.028 0.028 6 Bm 13 0.022 0.015 a . r . a .R. 3 3 a . R j B . R . J 3 3 D+2 R R I . R . 14 15 16 17 18 19 20 21 0.032 -0.014 0.441 0.000 -0.063 -0.364 0.000 0.531 0.032 -0.014 0.602 -0.323 -0.063 -0.315 -0.027 0.090 * o Units are mdyn/A f o r s t r e t c h i n g congtants, mdyn/radian f o r stretch-bend i n t e r a c t i o n s and mdyn A/radian f o r bending con-s t a n t s . o,m,p i m p l y i n t e r a c t i o n s b e t w e e n c o o r d i n a t e s o r t h o , m e t a a nd p a r a t o one a n o t h e r ; t h e s u b s c r i p t ' j ' s p e c i f i e s t h e c a r b o n atom w h i c h i d e n t i f i e s t h e c o o r d i n a t e ( s e e t e x t ) . 163 The a d j u s t m e n t o f t h e f o r c e c o n s t a n t s was c a r r i e d 82' 88 o u t w i t h a p r o g r a m (FPERT) w r i t t e n by S c h a c h t s c h n e i d e r ' a n d m o d i f i e d t o meet t h e r e q u i r e m e n t s o f t h e a v a i l a b l e com-p u t i n g s y s t e m ( i n i t i a l l y an IBM 7044 c o m p u t e r a n d s u b s e -q u e n t l y an IBM m o d e l 3 6 0 / 6 7 ) • The p r o g r a m i s d e s i g n e d t o s e l e c t t h o s e i n t e r a c t i o n c o n s t a n t s t o w h i c h t h e f r e q u e n c i e s a r e m o s t s e n s i t i v e a nd t o r e f i n e t h e s e a n d t h e d i a g o n a l c o n s t a n t s t o g i v e a w e i g h t e d l e a s t s q u a r e s f i t b e t w e e n t h e 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 . U n c e r t a i n f r e q u e n c i e s w e r e g i v e n z e r o w e i g h t a n d t h e known f r e q u e n c i e s w e r e g i v e n a w e i g h t of V\ , , . 3 o b s e r v e d The t h i r t e e n n o n - z e r o f o r c e c o n s t a n t s u s e d b y 32 D u i n k e r a n d M i l l s f o r b e n z e n e g a v e r i s e t o e i g h t e e n c o n -s t a n t s when t h e f i e l d was t r a n s f e r r e d t o n a p h t h a l e n e a n d a n t h r a c e n e . Two o f t h e e x t r a c o n s t a n t s (numbers 4 and 5) a r o s e b e c a u s e t h r e e a n g l e b e n d s w e r e d e f i n e d a t e a c h r i n g 87 j u n c t i o n i n t h e manner d e s c r i b e d b y S t e e l e . Two more f o r c e c o n s t a n t s w e r e n e e d e d when t h e s i n g l e K e k u l e c o n s t a n t u s e d by D u i n k e r and M i l l s was s p l i t i n t o t h r e e s e p a r a t e t e r m s ( f o r c e c o n s t a n t s 7, 8 a n d 9 ) , one f o r e a c h o f t h e o r t h o , m e t a and p a r a CC s t r e t c h i n t e r a c t i o n s . The f i n a l n o n - z e r o f o r c e c o n s t a n t e n t e r e d i n t o t h e r e f i n e m e n t ( f o r c e c o n s t a n t 21) was t h e i n t e r - r i n g CC s t r e t c h i n g c o n s t a n t p r e v i o u s l y m e n t i o n e d . 164 In a d d i t i o n to the non-zero fo r c e constants, s e v e r a l other i n t e r a c t i o n s which were thought to be p o s s i b l y important were defined but given i n i t i a l f o r c e constants of zero. Three of these fo r c e constants (numbers 10, 17 and 20) were found to a f f e c t the frequencies a p p r e c i a b l y and were entered i n t o the refinement. I t i s , of course, very dangerous t o form conclusions about the p h y s i c a l meaning of the force constants i n such a modified f o r c e f i e l d , where so many i n t e r a c t i o n constants have been neglected. Thus, w h i l e the f a c t t h a t force con-stants 9 and 21 decrease considerably during the refinement may imply t h a t long range i n t e r a c t i o n s between CC s t r e t c h e s 32 37 are l e s s important than p r e v i o u s l y thought, ' i t may e q u a l l y imply t h a t some d e f i c i e n c y e x i s t s elsewhere i n the force f i e l d and force constants 9 and 21 are being adjusted to compensate f o r i t . The value of t h i s c a l c u l a t i o n l i e s not i n i t s p h y s i c a l s i g n i f i c a n c e , but r a t h e r i n the f a c t that i t permits an estimate of the accuracy of the previous work t o be made. Since the s t a r t i n g p o i n t i n t h i s c a l c u l a t i o n was q u i t e d i f f e r e n t from t h a t f o r the NSC f i e l d , the a s s i g n -ments which were made i n t h a t work can be checked against the p r e d i c t i o n s of t h i s . f i e l d . I t i s , however, i n t e r e s t i n g to compare the i n i t i a l and f i n a l f orce constants l i s t e d i n Table 28. The f i r s t s i x constants appear on the diagonal of the F-matrix and f i v e of 165 these remain w i t h i n three percent of t h e i r i n i t i a l v a l u e s ; the o ther, number 5, increased by only eleven percent. F i v e of the f i f t e e n i n t e r a c t i o n constants remained unchanged, and only four of them (numbers 9, 1 6 , 17 and 21) were adjusted to values very f a r removed from t h e i r i n i t i a l v a lues. E v i d e n t l y the D u i n k e r - M i l l s f i e l d f o r benzene i s q u i t e w e l l s u i t e d f o r t r a n s f e r r i n g t o naphthalene and anthracene. During the p r e l i m i n a r y stages of t h i s work two sets 34 35 of force, constants published f o r naphthalene ' were t r a n s -f e r r e d t o anthracene and s e v e r a l attempts were made to c a r r y out a refinement s i m i l a r to t h a t described above f o r the D u i n k e r - M i l l s benzene f i e l d . For both f i e l d s many of the f i n a l f o r c e constants were found to be q u i t e d i f f e r e n t from the i n i t i a l ones; sometimes, i n f a c t , the f i n a l f o r c e f i e l d was unrecognizable. I t was, t h e r e f o r e , encouraging to f i n d t h a t the Duinker and M i l l s benzene f i e l d needed so l i t t l e refinement to f i t the naphthalene and anthracene frequencies. 4. Results of the Refinement The observed frequencies to which the refinement was made and the r e s u l t s of the c a l c u l a t i o n are l i s t e d i n Table 29. A l s o i n c l u d e d i n Table 29 are the observed and 41 c a l c u l a t e d frequencies from the NSC c a l c u l a t i o n . The average e r r o r w i t h the newly-developed f i e l d i n the f i t to the 119 observed frequencies was 1.50 percent or 14.8 cm 1 . 166 T a b l e 29. The o b s e r v e d a n d c a l c u l a t e d p l a n a r f r e q u e n c i e s o f b e n z e n e , n a p h t h a l e n e a nd a n t h r a c e n e * 41 T h i s work Neto,, S c r o c c o & C a l i f a n o O b s e r v e d C a l c u l a t e d C a l c u l a t e d O b s e r v e d C 6 H 6 A ^2g : 2 g B B E l u 2u l u C 6 D 6 E '2g 2g B l u B 2u 3073 993 1350 3056 1599 1178 606 3057 1010 1309 1146 3064 1482 1037 2303 945 1059 2274 1558 869 579 2285 970 1282 824 3075 979 1356 3040 1581 1167 611 3074 1015 1290 1149 3041 1476 1028 2287 931 1054 2257 1551 840 583 2288 965 1269 826 3063 993 1346 3046 1602 1165 601 3043 1007 1316 1173 3056 1482 1026 2279 946 1058 2268 1159 836 580 2266 957 1287 848 3073 993 1350 3056 1599 1178 606 3057 1010 1309 1152 3064 1482 1037 2303 945 1059 2274 1558 869 579 2285 970 1282 824 167 T a b l e 29 ( C o n t i n u e d ) T h i s w o r k O b s e r v e d C a l c u l a t e d N e t o , S c r o c c o & C a l i f a n o C a l c u l a t e d O b s e r v e d 41 J l u C 1 0 H 8 B l u B 2u 2288 1333 814 3058 1579 1465 1380 1148 1021 765 514 1596 1390 1125 359 1509 1008 622 2259 1307 812 3065 3040 1610 1464 1418 1160 1018 716 482 3063 3042 1608 1388 1297 1129 800 359 3064 3039 1521 1382 1241 1174 1020 637 2272 1339 793 3085 3038 1577 1445 1368 1173 1013 767 504 3064 3020 1597 1379 1258 1125 795 369 3084 3037 1529 1357 1186 1136 1007 628 2288 1333 814 3055 3025 1579 1460 1379 1144 1025 763 512 3065 3029 1595 1389 1265 1125 810 362 3056 3029 1509 1361 1209 1144 1008 618 168 T a b l e 29. ( C o n t i n u e d ) T h i s w o r k O b s e r v e d C a l c u l a t e d N e t o , S c r o c c o & C a l i f a n o C a l c u l a t e d O b s e r v e d 41 B 3g D 10 8 A, B l u B 2u 2980 1636 1446 1240 1168 953 509 1552 1386 1294 862 838 697 494 (1562) 1257 (1045) 879 738 328 (1439) (1341) 3062 3042 1644 1445 1236 1150 950 518 2281 2256 1586 1443 1251 856 824 660 463 2279 2266 1570 1260 1058 863 741 326 2280 2254 1466 1346 3062 3019 1625 1442 1253 1117 938 488 2295 2260 1542 .1370 1288 852 830 695 484 2282 2249 1543 1245 1045 840 749 336 2293 2256 1466 1273 3055 2980 1624 1436 1240 1099 936 506 2272 2257 1553 1381 1293 866 835 698 493 2278 2232 1545 1260 1050 885 734 328 2299 2258 1290 169 Table 29. (Continued) This work Observed C a l c u l a t e d Neto,Scrocco & C a l i f a n o C a l c u l a t e d Observed 41 B 3g C14 H10 B l u 1082 1102 1086 1082 (880?) 840 837 828 828 834 803 T 590 610 606 593 (2276?) 2276 2275 2302 (2261) 2263 2246 2257 1605 1620 1598 1574 — 1334 1338 1330 (967?) 1029 1023 1030 884 877 860 881 831 825 821 828 494 501 472 490 3064 3085 3088 3056 3052 3053 — 3027 3039 3037 — 1557 1563 1584 1561 1481 1494 1476 1481 1402 1390 1398 1403 1261 1308 12 40 1261 1163 1167 1169 1165 1007 999 1007 1007 754 713 : 735 745 (622?) 643 658 652 395 362 369 — 3108 3063 3063 3100 3050 3053 3053 3049 3024 3042 3019 3022 1616 1612 1616 1620 170 T a b l e 29. ( C o n t i n u e d ) 41 T h i s w o r k N e t o , S c r o c c o & C a l i f a n o O b s e r v e d C a l c u l a t e d C a l c u l a t e d O b s e r v e d 1447 1436 1446 1448 1314 1318 1341 1316 1270 1282 1277 1274 1145 1145 1123 1150 903 925 921 907 (650?) 657 647 651 235 227 214 244 (3093?) 3064 3085 3079 3050 3039 3037 3048 1533 1559 1532 1533 (1495) 1510 1441 1462 (1392) 1397 1394 1398 (1345) 1344 1377 1346 (1163) 1207 1169 1169 (1068) 1147 1127 1125 998 992 1007 999 (808?) 745 812 — 600 597 609 615 3066 3063 3063 — 3045 3042 3019 3006 1630 1632 1612 1631 — 1558 1563 1596 — 1387 1389 — 1291 1273 — 1187 1184 1206 1188 — 1106 1093 956 912 912 — 522 531 517 522 — 398 388 400 171 Table 29. (Continued) 41 This work Neto,Scrocco & Calxfano Observed C a l c u l a t e d C a l c u l a t e d Observed (2288) 2280 2294 — (2266) 2269 2275 — (2258) 2254 2255 — 1534 1542 1553 — — 1438 1407 1388 1366 1347 — 1156 1158 1149 — — 841 848 — (842) 832 819 — 709 672 690 — — 617 634 — 382 349 356 — 2283 2278 2280 2288 2264 2270 2271 2262 2248 2263 2246 2247 1584 1585 1582 1583 (1406?) 1354 1380 1389 1258 1268 1275 1264 — 1050 1041 — (879) 879 861 881 825 825 822 (565?) 626 617 592 220 211 199 2267 2280 2294 2275 2238 2254 2257 2238 1493 1542 1487 1500 (1401) 1466 1392 1384 (1335) 1316 1315 1325 172 T a b l e 29. ( C o n t i n u e d ) T h i s w o r k N e t o , S c r o c c o & C a l i f a n o O b s e r v e d C a l c u l a t e d C a l c u l a t e d O b s e r v e d 1175?) 1199 1267 — (982) 948 943 920 (879?) 835 840 831 824 830 811 --703 662 701 706 575 574 588 580 2276) 2277 2278 — — 2264 2247 — 1615 1615 1588 — — 1526 1522 1233 1238 1244 1043 1027 943 931 960 816 868 846 777 804 810 502 506 . 494 (415) 370 361 The o b s e r v e d f r e q u e n c i e s e n c l o s e d i n p a r e n t h e s e s w e r e g i v e n z e r o w e i g h t i n t h e f o r c e c o n s t a n t r e f i n e m e n t . 173 In the e a r l i e r w o r k 4 1 the for c e constants were r e f i n e d t o d i f f e r e n t frequencies and, as i n d i c a t e d i n Chapters I I I and IV, a few of them are almost c e r t a i n l y i n c o r r e c t and some others are d o u b t f u l . Thus comparison of the average e r r o r s i s d i f f i c u l t to i n t e r p r e t ; however, the average d i f f e r e n c e between the observed and c a l c u l a t e d frequencies of Neto e t a l . i s 13.1 cm The r e s u l t s of the two c a l c u l a t i o n s are, i n g e n e r a l , q u i t e s i m i l a r ; there are some d i f f e r e n c e s , however, and these w i l l now be considered and a comparison w i t h the experimental assignments from Chapters I I I and IV f o r naphthalene-dg, anthracene-h.^ and anthracene-d^^ w i l l be made. a) Naphthalene-dg. There i s l i t t l e cause f o r comment i n the Ag and B 3 g blocks s i n c e the t o t a l l y symmetric modes are experim e n t a l l y secure and both c a l c u l a t i o n s are i n f a i r l y good agreement about the B 3 a frequencies. The NSC f i e l d was, however, somewhat more s u c c e s s f u l i n f i t t i n g the r i n g modes i n the Ag block. In the B^ u block the c a l c u l a t e d value of 1570 cm 1 supports the experimental assignment i n which the 1562 cm 1 l i n e replaces the .1545 cm 1 l i n e pre-7 41 v i o u s l y assigned. ' This c a l c u l a t i o n a l s o p r e d i c t s a funda-mental i n t h i s block i n the region of very weak absorption near 1050 cm and thus gives added weight to the co n c l u s i o n p r e v i o u s l y made1**'41 t h a t t h i s mode i s i n t r i n s i c a l l y weak i n the i n f r a r e d . In the B^^ block the assignment of a funda-174 m e n t a l n e a r 1450 cm 1 i s s u p p o r t e d , a nd b o t h c a l c u l a t i o n s i n d i c a t e t h a t t h e 1452 cm 1 l i n e m e n t i o n e d as a p o s s i b l e f u n d a m e n t a l i n C h a p t e r I I I s h o u l d r e p l a c e t h e r a t h e r t e n t a -t i v e l y a s s i g n e d l i n e a t 1439 cm S i n c e t h e two o b s e r v e d l i n e s a r e o n l y 13 cm 1 a p a r t , h o w e v e r , t h i s c o n c l u s i o n i s n o t p a r t i c u l a r l y c o m p e l l i n g a n d i n any e v e n t an i n c o r r e c t c h o i c e w i l l r e s u l t i n o n l y a s m a l l e r r o r . I t i s v e r y i n t e r e s t i n g t o n o t e t h a t t h e a s s i g n m e n t o f t h e n e x t mode a t 1341 cm 1 i n p l a c e o f t h e 1290 cm 1 l i n e 41 p r e v i o u s l y s u g g e s t e d h a s b e e n s t r o n g l y s u p p o r t e d b y t h e c a l c u l a t i o n ( c a l c u l a t e d f r e q u e n c y 1346 cm ^) e v e n t h o u g h t h i s f r e q u e n c y was g i v e n z e r o w e i g h t i n t h e r e f i n e m e n t p r o c e d u r e . The o n l y o t h e r p o i n t o f i n t e r e s t i n t h e b l o c k i s t h a t t h e o b s e r v e d l i n e a t 828 cm 1 may be a s s o c i a t e d w i t h t h e s e c o n d l o w e s t f u n d a m e n t a l i n t h i s b l o c k r a t h e r t h a n t h e t h i r d l o w e s t as p r e v i o u s l y s u g g e s t e d . b) A n t h r a c e n e - h . ^ . Once a g a i n t h e r e i s l i t t l e t o d i s c u s s a b o u t t h e Ag a n d b l o c k s ; b o t h f i e l d s p r e d i c t t h e known f r e q u e n c i e s q u i t e w e l l , a n d b o t h a g r e e o n t h e a p p r o x i -mate l o c a t i o n o f t h e unknown f u n d a m e n t a l s . The same s o r t o f a g r e e m e n t i s f o u n d f o r t h e B ^ u modes. The B 2 u symmetry s p e c i e s i s i n t e r e s t i n g i n s e v e r a l r e s p e c t s . F i r s t , t h e new e x p e r i m e n t a l a s s i g n m e n t o f a f u n d a m e n t a l a t 1495 cm 1 i s s u p p o r t e d , a l t h o u g h o n c e a g a i n t h i s f r e q u e n c y was g i v e n z e r o 175 weight i n the refinement. The danger of making assignments from c a l c u l a t e d frequencies i s a l s o c l e a r l y i l l u s t r a t e d i n t h i s b l ock. Complete r e l i a n c e on the c a l c u l a t i o n s would r e s u l t i n the replacement of the experimentally assigned l i n e at 1068 cm 1 w i t h the l i n e p r e v i o u s l y mentioned (see' Chapter IV) at 1219 cm \ sin c e then the f i t w i t h the high-energy c a l c u l a t e d frequencies i s e x c e l l e n t . However, the 41 e a r l i e r c a l c u l a t i o n s have suggested yet another assignment of the B 2 u b l o c k , and by choosing the experimental values p r o p e r l y a good f i t was obtained (see Table 29). Since the two f i e l d s support d i f f e r e n t assignments the choice of the proper set of fundamentals from the c a l c u l a t i o n s cannot be made, and, i n g e n e r a l , great care must be taken i n comparing observed and c a l c u l a t e d fundamentals when s e v e r a l c l o s e - • l y i n g frequencies are p r e d i c t e d and there are many observed l i n e s which can be f i t t e d to them. Another p o i n t worthy of 41 note i s tha t the previous c a l c u l a t i o n was r e f i n e d to a fundamental at 146 2 cm 1 where i n f a c t only a very weak band 16 i s seen at t h a t energy i n s o l u t i o n and no l i n e at a l l i s 16 — 18 found there i n the c r y s t a l ; as p r e v i o u s l y mentioned, t h i s l i n e has been replaced i n the assignment by the strong c-p o l a r i z e d l i n e at 1495 cm 1 . c) Anthracene-d.^. Very l i t t l e new inf o r m a t i o n can be gained from the c a l c u l a t e d frequencies i n the Ag, B^g or B^ u b l o c k s . Both f i e l d s agree f a i r l y w e l l i n t h e i r pre-176 d i c t i o n s o f t h e s e f u n d a m e n t a l s , a n d t h e o n l y p o i n t o f i n t e r e s t i s t h a t t h e c a l c u l a t i o n s c a r r i e d o u t i n t h e c o u r s e o f t h i s 41 -1 wo r k f a v o r t h e p r e v i o u s a s s i g n m e n t o f 1380 cm f o r t h e s e c o n d B ^ u r i n g mode r a t h e r t h a n t h e 1406 cm 1 l i n e t e n t a -t i v e l y s u g g e s t e d i n C h a p t e r I V . T h r e e p o i n t s f o r c o n s i d e r a -4 t i o n a r i s e i n t h e B 2 u b l o c k . F i r s t , t h e i n c o r r e c t a s s i g n m e n t o f a f u n d a m e n t a l a t 1384 cm 1 ( t h i s l i n e i s i n f a c t o f B_ 3u symmetry) c a n c o n v e n i e n t l y be c o r r e c t e d b y t h e a s s i g n m e n t o f a l i n e a t 1401 cm S e c o n d l y , t h e s e c a l c u l a t i o n s i n d i c a t e t h a t t h e 1175 cm 1 a s s i g n m e n t o f t h e f o u r t h r i n g mode s u g -g e s t e d i n C h a p t e r I V may be c o r r e c t , r a t h e r t h a n t h e a l t e r -n a t i v e a s s i g n m e n t a t 1298 cm 1 as s u g g e s t e d b y t h e NSC f i e l d . T h i r d l y , t h e f a c t t h a t t h e p e r t u r b a t i o n p r o g r a m was u n a b l e t o move t h e h i g h e s t r i n g mode i n a n t h r a c e n e - d ^ g more t h a n 17 cm 1 f r o m i t s v a l u e i n a n t h r a c e n e - h ^ , w h i l e t h e e x p e r i -m e n t a l f r e q u e n c i e s d i f f e r b y 94 cm 1 i s p r o b a b l y due t o some d e f i c i e n c y i n t h e f o r c e f i e l d . T h a t s u c h a d e f i c i e n c y d o e s e x i s t i s n o t s u r p r i s i n g , o f c o u r s e , s i n c e s o many i n t e r a c t i o n c o n s t a n t s h a v e b e e n n e g l e c t e d . 5. C o n c l u s i o n s i ) V e r y l i t t l e r e f i n e m e n t o f t h e b a s i c f i e l d d e r i v e d by D u i n k e r a n d M i l l s f o r b e n z e n e i s n e c e s s a r y t o a c h i e v e a g o o d f i t t o m o s t o f t h e p l a n a r o b s e r v e d f r e q u e n c i e s o f n a p h -t h a l e n e a n d a n t h r a c e n e . The a v e r a g e e r r o r i n t h e f i t t o t h e 177 frequencies t o which the refinement was made was 14.8 cm - 1. However, some evidence of inadequacies i n the r e s u l t i n g f i e l d does e x i s t ; t h i s i s not s u r p r i s i n g since only 21 f o r c e constants were r e f i n e d i n the attempt to f i t the 184 planar frequencies of the s i x molecules s t u d i e d . i i ) Although, as shown i n Chapters I I I and IV, the 41 NSC f i e l d was r e f i n e d t o some i n c o r r e c t assigned frequen-c i e s , i t s p r e d i c t i o n s are i n general q u i t e accurate. Compari-41 son of t h e i r observed and c a l c u l a t e d frequencies gives an average e r r o r of 13.1 cm "*"; however, because of the i n c o r r e c t assignments, t h i s i s somewhat misleading as the average e r r o r i n the f i t t o the c o r r e c t e d observed frequencies i s somewhat greater (about 14 cm 1 ) . I t i s i n t e r e s t i n g t o compare the agreement of the NSC 41 c a l c u l a t e d frequencies w i t h experimental assignments to which the f o r c e constants were not r e f i n e d . In p a r t i c u l a r , Neto e t a l . d i d not r e f i n e to any data i n the Ag and B^g v i b r a t i o n a l species of anthracene-d^g, and the agreement of t h e i r c a l c u l a t i o n s w i t h the c e r t a i n experimental frequencies f o r those blocks (see Table 20) i s not as good (average e r r o r = 21.5 cm "*") as f o r the frequencies to which they d i d r e f i n e . This i s not s u r p r i s i n g , p r i n c i p a l l y because i t would be expected t h a t the refinement procedure would mask any defects i n the n e c e s s a r i l y approximate force f i e l d ; t h i s c r i t i c i s m i s e q u a l l y t r u e , of course, f o r the f o r c e f i e l d r e f i n e d i n t h i s work. 178 i i i ) The c a l c u l a t i o n s performed i n t h i s work are valuable i n t h a t they give some i n d i c a t i o n of the r e l i a b i l i t y of the p r e d i c t i o n s of the previous work. In g e n e r a l , the frequencies generated by the two force f i e l d s were very s i m i l a r and t h i s r e s u l t gives added weight to many of the assignments made by Neto, Scrocco and C a l i f a n o from t h e i r c a l c u l a t i o n s . However, i n regions where s e v e r a l fundamentals of the same symmetry are expected to f a l l c l o s e together and where the experimental s i t u a t i o n i s un c l e a r , the danger of using the c a l c u l a t i o n s t o support a p a r t i c u l a r assignment was pointed out. The best example of t h i s i s i n the anthra-cene-h^Q and - d ^ Q B 2 u symmetry species where each fo r c e f i e l d suggests a d i f f e r e n t assignment. CHAPTER VI THE VIBRATIONS OF PYRENE A. I n t r o d u c t i o n 1. C r i t i c a l Review Two v i b r a t i o n a l assignments of pyrene have been 89 reported r e c e n t l y . Mecke and Klee measured the i n f r a r e d spectrum of the ab face and, by comparison w i t h the s o l u t i o n and vapor phase s p e c t r a , attempted to deduce the appearance of the sp e c t r a along a l l c r y s t a l axes. The s o l u t i o n Raman spectrum was a l s o recorded and some assignments were made from the d e p o l a r i z a t i o n r a t i o measurements. C a l i f a n o and 90 Abbondanza have proposed a f a i r l y complete assignment of the i n f r a r e d - a c t i v e ungerade v i b r a t i o n s of both pyrene-h^Q and -d^Q from t h e i r p o l a r i z e d measurements of the ab and ac c r y s t a l faces. However, t h e i r s p e c t r a extended only down to 400 cm 1 and one aim of t h i s work has been to continue the p o l a r i z e d measurements to about 50 cm 1 to l o c a t e a l l the low energy molecular fundamentals. Knowledge of these low-energy modes i s important since i t enables the existence of combinations at higher energies to be recognized. A new assignment of the fundamental v i b r a t i o n s has been proposed, based on the new low frequency i n f r a r e d i n f o r m a t i o n and the 179 180 91 r e s u l t s of a study c a r r i e d out i n t h i s l a b o r a t o r y of the l a s e r - e x c i t e d Raman sp e c t r a from s i n g l e c r y s t a l s of pyrene. Another aim of the present work was to c a l c u l a t e the fundamental frequencies of pyrene. The in-plane f o r c e constants were t r a n s f e r r e d from the s i m p l i f i e d force f i e l d developed f o r benzene, naphthalene and anthracene as des-c r i b e d i n Chapter V; the out-of-plane fo r c e constants were a l s o taken from Chapter V. The c r y s t a l s t r u c t u r e of pyrene does not permit a c l e a r d i s t i n c t i o n to be made between and B 3 u modes and i n the region below 1000 cm 1 where funda-mentals of both species are expected the c a l c u l a t e d frequen-c i e s are va l u a b l e as a guide to d i f f e r e n t i a t e between them. A normal coordinate a n a l y s i s of pyrene has a l s o been c a r r i e d 91 out i n t h i s l a b o r a t o r y using force constants t r a n s f e r r e d 41 from the planar f i e l d described by Neto e t a l . and the out-36 of-plane f i e l d used f o r naphthalene, and a comparison of the two sets of c a l c u l a t e d frequencies was made. 2. S e l e c t i o n Rules The pyrene molecular axes have been chosen t o con-64 . form to the i n t e r n a t i o n a l convention and are shown i n Figure 5. Since the pyrene molecule does not s i t at a s p e c i a l p o s i t i o n i n the u n i t c e l l , a l l free-molecule s t a t e s can mix i n the c r y s t a l . Each molecular s t a t e gives r i s e to four c r y s t a l s t a t e s w i t h k = 0 and the s e l e c t i o n r u l e s f o r the 181 fr e e molecule and the c r y s t a l are summarized i n Table 30. In the i n f r a r e d spectrum of the f r e e molecule, three and two B 2 u CH s t r e t c h e s are expected so t h a t below 2000 cm "nine B, , ten B_ and seven B_ fundamentals l u ' 2u 3u should appear. In the c r y s t a l the spectrum may be more com-plex due to the presence of molecule-forbidden bands appear-ing because of the absence of s i t e symmetry. In the usual oriented-gas approximation the r e l a t i v e i n t e n s i t y of absorption along v a r i o u s c r y s t a l axes can be determined from the d i r e c t i o n cosines r e l a t i n g molecular and c r y s t a l axes; a summary of the r e s u l t s i s given i n Table 31. Table 30, C o r r e l a t i o n t a b l e f o r Pyrene* Molecular group S i t e group Factor group D 2 h C l C 2 h N Bases Bases n 13 xx, y_y_, zz A g aa, bb, cc, ac 5 A u a g 6 4 ^ B l g a u b 5 12 * B l u 7 ™ B 2 g b g ab, be 6 12 TL B2u 12 ^ B 3 g a, b 4 7 £ B 3 u * N i s the number of molecular fundamentals and n i s the number of l a t t i c e f r equencies, assuming k=0. Factor group symmetry species are d i s t i n g u i s h e d by lower case l e t t e r s . 182 Table 31 t The o r i e n t e d -gas p r e d i c t i o n s of the r e l a t i v e i n t e n s i t i e s of the i n f r a r e d a c t i v e l i n e s of pyrene along v a r i o u s c r y s t a l axes * l u 3u a* 0.010 0.562 0.433 a 0.237 0.357 0.413 b 0 .050 0.394 0.557 g' 0.711 0.250 0.030 c* 0.937 0.046 0.011 * The axes a*, c* and c 1 are defined i n Chapter I I . 183 B. Results The low frequency i n f r a r e d s p e c t r a of pyrene-h^g are shown i n Figure 29 f o r the ab and ac se c t i o n s and f o r a s o l u t i o n i n benzene. In Figure 30 are shown the spect r a of an ab s e c t i o n of pyrene-d^g and of a s o l u t i o n of pyrene-d^g i n benzene. Because the supply of pyrene-d^g was l i m i t e d , s i n g l e c r y s t a l s l a r g e enough to prepare a£ se c t i o n s could not be grown and some symmetry assignments f o r t h i s molecule ( p a r t i c u l a r l y i n the B^ u species) were made by analogy w i t h pyrene-h^Q. The s o l u t i o n s p e c t r a were e s p e c i a l l y v a l u a b l e since i n a d d i t i o n to d i f f e r e n t i a t i n g between molecular and l a t t i c e modes they aided i n the i d e n t i f i c a t i o n of molecular modes appearing only through c r y s t a l f o r c e s . The spect r a were recorded at higher frequencies but are not presented since good agreement was found w i t h the r e s u l t s already pub-90 l i s h e d by C a l i f a n o and Abbondanza. Only two s i g n i f i c a n t d i f f e r e n c e s were noted; i n the ac spectrum of pyrene-h^g, both the l i n e at 1002 cm 1 and an intense shoulder at 1585 cm 1 were found to be c* p o l a r i z e d . C a l i f a n o and Abbondanza reported t h a t the 1002 cm 1 l i n e was d e p o l a r i z e d and d i d not f i n d the 1585 cm 1 shoulder. The l i n e s which appear i n the low-energy i n f r a r e d s p e c t r a of pyrene-h-^g and pyrene-d^g are summarized, along wi t h t h e i r assignment, i n Table 32. The f o l l o w i n g d i s c u s s i o n i s based on pyrene-h^g; the assignments of the corresponding l i n e s of pyrene-d^g are r e a d i l y deduced from Table 32. 184 Figure on f o l l o w i n g page. ure 29. The low-frequency i n f r a r e d s p e c t r a of pyrene-h^Q. Upper, 0.30 mm t h i c k ab s e c t i o n ; f u l l l i n e // b, broken l i n e // a. Middle, 0 30 mm t h i c k ac s e c t i o n ; f u l l l i n e // c*, broken l i n e // a*. Lower, s o l u t i o n i n benzene. 185 L O S S I U U S U D J i . % T I I I I 1 1 - , , . . 100 2 0 0 3 0 0 4 0 0 5 0 0 Wavenumber (cm."1) Figure 30. Low-frequency i n f r a r e d s p e c t r a of p y r e n e - d 1 Q . Upper, 0.40 mm t h i c k ab s e c t i o n ; f u l l l i n e // b, broken l i n e // a. Lower) s o l u t i o n i n benzene. 187 Table 32. The low-frequency i n f r a r e d spectra of pyrene-h and pyrene-d, n Pyrene S o l u t i o n //b _ h10 //a //a* //£* Pyrene-d^o S o l u t i o n //b //a Symmetry 71? 89 70? 89 V a ? u b u 102 99 a u 105 105 105 105 b u 124 123 129 129 114 115 122 B 3 u 158 158 147? 219 220 217 217 201 203 200 3u 258 258 240 319 320 A u? 350 349 349 349 349 323 324 324 B 2 u 392 392 392 355 351 B, l u 406 396 452 453 453 484 482 485 485 432 430 431 3u 449 448 495 494 493 493 461 462 460 B l u 500 497 509 472 505 520 525 524 538 536 537 537 537 520 518 520 B 2 u 570 573 571 572 565 566 570 B. 3u 3u 585 585 586 586 596 600 188 The intense l i n e s i n the pyrene-h^g s o l u t i o n spectrum a t 124, 219, 350, 484, 495 and 538 cm - 1 were taken as molecular fundamentals. The strong c* p o l a r i z e d l i n e at 495 cm 1 marks a fundamental and the two lowest energy l i n e s at 124 and 219 cm 1 must a r i s e from out-of-plane B 3 u modes. As observed f o r naphthalene and anthracene, these B^ u l i n e s are e s p e c i a l l y intense and show a factor-group s p l i t t i n g i n the c r y s t a l . A t h i r d l i n e which has these char-o -1 a c t e r i s t i c s appears i n s o l u t i o n at 484 cm and i s a c c o r d i n g l y assigned B^ symmetry. The strong a and b p o l a r i z e d l i n e s at 349 and 537 cm - 1 t h a t show no s p l i t t i n g i n the c r y s t a l are taken as B 2 u fundamentals. These assignments are i n agreement 90 w i t h C a l i f a n o ' s c r i t e r i o n , deduced from o l d e r c r y s t a l 92 s t r u c t u r e data, t h a t f o r an ab s e c t i o n B ^ modes are some-what stronger along b w i t h B 2 u modes nea r l y d e p o l a r i z e d but s l i g h t l y stronger along a. 6 8 The more recent c r y s t a l s t r u c t u r e determination shows th a t the p o l a r i z a t i o n r a t i o s ( Rk/ a) c a l c u l a t e d i n the usual manner, should be 1.35 f o r B ^ and 1.10 f o r B 2 u modes, both g r e a t e r than u n i t y . There i s thus a discrepancy between the observation t h a t B 2 u modes are s l i g h t l y stronger along a i n ab and the p r e d i c t i o n s of the oriented-gas model, using the l a t e s t c r y s t a l data. The above values, however, are simply the r a t i o s of the squared d i r e c t i o n cosines taken with respect to a and b. For l i g h t passing down c 1 i n c i d e n t on an 189 ab s e c t i o n , the b p o l a r i z e d beam (the o r d i n a r y ray) continues on through the sample along c' w h i l e the a p o l a r i z e d beam (the e x t r a o r d i n a r y ray) may d e v i a t e from c 1 i n the ac plane by an angle £. (The s i t u a t i o n i s shown i n F i g u r e 3, Chapter I.) For t h i s case the p o l a r i z a t i o n r a t i o should be e v a l u a t e d f o r the a x i s frame r o t a t e d about b through £. T h i s c o r r e c t i o n has been noted by Rohleder and L u t y 5 ^ who have a l s o suggested a method f o r measuring £. Using v i s i b l e l i g h t , £ was found to be 8.6 1 0.5° f o r pyrene and the d e v i a t i o n i s from c' towards c; indeed, the e x t r a o r d i n a r y ray i s w i t h i n 2° of c. R e f r a c t i v e i n d i c e s (y) were measured by immersion methods i n y e l l o w l i g h t and found to be 1.76 and 1.66 with the e l e c t r i c v e c t o r along a and b r e s p e c t i v e l y . The i n s e r t i o n of t h i s i n f o r m a t i o n i n t o equation (10) of r e f e r e n c e 56 y i e l d e d new p o l a r i z a t i o n r a t i o s of 1.59 f o r B_ modes and 1.57 f o r B n * 3u 2u modes. These c o r r e c t i o n s move the r a t i o s s t i l l f u r t h e r from the experimental v a l u e s . The cause f o r t h i s d i s c r e p a n c y must be the use of data taken i n v i s i b l e l i g h t t o i n t e r p r e t i n f r a -r e d r e s u l t s . The s t r o n g u l t r a v i o l e t a b s o r p t i o n systems are 93 l o n g - a x i s p o l a r i z e d and so the e f f e c t of anomalous d i s p e r -s i o n i s to make y c * the l a r g e s t . On the other hand, the i n d i c a t r i x should be very d i f f e r e n t i n the i n f r a r e d where B 3 u fundamentals are the most i n t e n s e , and the e x t r a o r d i n a r y ray would be expected to bend from c 1 i n a d i r e c t i o n away from c. A s m a l l s h i f t i n t h i s d i r e c t i o n (7 or 8°) would be s u f f i c i e n t to make the p o l a r i z a t i o n r a t i o f o r B_ modes change from 190 greater than u n i t y to l e s s than u n i t y i n agreement w i t h the experimental r e s u l t s . The l e s s intense bands i n the i n f r a r e d s p e c t r a are given the f o l l o w i n g i n t e r p r e t a t i o n . The bands at 585, 500, 453, 406, 258 and 158 cm 1 which appear only i n the c r y s t a l 91 spect r a mark A g, B 3 g / A g / B 2 g a n d A u molecular fundamentals r e s p e c t i v e l y , which i n the low s i t e symmetry can appear through c r y s t a l f o r c e s . A u and g modes, forbidden i n the free-molecule spectrum, give r i s e to four components (k=0), t r a n s i t i o n s to two of which are f o r m a l l y i n f r a r e d a c t i v e i n the c r y s t a l (see Table 30). The i n t e n s i t y of these induced bands i s d e r i v e d from other strong bands nearby. In p a r t i -c u l a r , the bands at 158 and 258 cm 1 probably appear by mixing wi t h l a t t i c e modes, much as the low-energy Raman-active mole-c u l a r modes of anthracene-d^Q were shown to gai n i n t e n s i t y from the l a t t i c e (see Chapter I V ) . While some of these weak bands a t t r i b u t e d above to g fundamentals have a l t e r n a t i v e explanations as combinations, t h i s i s not true f o r the bands at 406 and 500 cm 1 and, f u r t h e r , i t should be pointed out (see a l s o Table 32) th a t the molecule-forbidden l i n e s induced i n the i n f r a r e d spectrum of pyrene-d^^ c r y s t a l correspond e x a c t l y to those observed i n pyrene-h^^. Among the remaining weak low-energy l i n e s i n the -1 pyrene-h^g i n f r a r e d spectrum the combination at 39,2 cm 191 i s most important, s i n c e the energy f i t shows t h a t the fun-damentals at 126 cm 1 (mean of observed components) and -1 91 263 cm (seen i n the Raman spectrum ) are i n v o l v e d . Thus the 26 3 cm 1 i n t e r v a l i s shown to be of symmetry, a f a c t which i s not c l e a r from the Raman evidence alone. The weak l i n e s at 525 and 572 cm 1 probably mark the combinations 126 (B_ ) + 406 (A„) and 228 (B.. ) + 349 (B„ ) 3u g l g 2u r e s p e c t i v e l y . No energy match can be found to account f o r the l i n e a t 320 cm 1 and so i t i s t e n t a t i v e l y assigned as an A u fundamental. Lines i n the spectrum of pyrene-d^^ which have not been i n d i r e c t l y considered i n the above d i s c u s s i o n appear at 448, 497 and 505 cm 1 and are assumed to be caused by the presence of i s o t o p i c i m p u r i t y molecules which do not have f u l l D„, symmetry. C. C a l c u l a t i o n of Fundamentals A normal coordinate a n a l y s i s was c a r r i e d out f o r pyrene using planar force constants t r a n s f e r r e d from the f i e l d 32 developed i n Chapter V from the D u i n k e r - M i l l s benzene f i e l d to f i t simultaneously benzene, naphthalene and anthracene. The CC s t r e t c h i n g constants were made p r o p o r t i o n a l to the bond length by f i t t i n g them to the curve f = Ae described 192 i n Chapter V. Two sets of out-of-plane force constants were t r i e d ; they were taken from the benzene force f i e l d s d e s i g -nated II-A and I I I - A i n Chapter V. The i n t e r n a l coordinates are defined i n Figure 31 where CC bond s t r e t c h e s (designated as R ) , CH bond s t r e t c h e s ( r ) , CCC angle bends ( a ) , and in-plane hydrogen wags (8) are shown. The CC bond t o r s i o n s (<f>) and the out-of-plane wags (y) are numbered i n the same way as the R and the a r e s -p e c t i v e l y and are not shown on the diagram. The l i s t f o l l o w i n g Figure 31 gives the for c e con-s t a n t s u n r e l a t e d by molecular symmetry i n an abbreviated nomenclature s i m i l a r to t h a t used e a r l i e r . The constants are named w i t h reference to the i n t e r n a l coordinates and the u n i t s are mdyn/A f o r s t r e t c h i n g constants, mdyn/radian f o r o 2 s t r e t c h bend i n t e r a c t i o n s and mdyn A/radian f o r bending constants. In-plane force constants: Diagonal terms: 0.934 R^R-^ = 1.081 R 2 R 2 = 1.161 R3R3 = 0.680 R 4 R 4 = 1.068 R 1 5 R i 5 = 1.068 R 1 9 R 1 9 = 7.040; r ^ = r ^ = = 5.061; Yl = °2°2 = 1.103; a_a_ = a . a . = 0.712; a c a c = 0.814; a~-.a~-. = a 0 . a 0 . 3 3 4 4 5 5 23 23 24 24 i ( a 3 a 3 + a 4 a 4 + = 0.746; 3 ^ - B 2 B 2 = 6363 = 1.020. Off - d i a g o n a l terms: R ^ = R 1 R 1 4 = R 3 R 4 = 0-650; R 1R. 1 3 = R 3 R 5 = -0.609; R 2 R 1 3 = 0.295; r 2 r 1 Q = 0.034; = a 2 a 3 = 193 Figure 31. The i n t e r n a l coordinates of pyrene. 194 a 4 a 6 = a 6 a 7 = a 3 a 2 3 = a 4 a 2 4 = - ° - 0 9 7 ' ^ 2 = _ 6 i e i O = - 6 3 3 4 = 0.028; 3 2 3 1 0 = -0.015; = a 2 r 2 = a g r 3 = -0.014; R , a , = R ,a~ = R~a 0 = R „ a 0 = R 0 a . = R 0 a , = R . a , = R, ,-ou = 1 1 1 2 2 2 2. 3 3 % 3 b 4 6 15 3 R 1 5 a 4 = R15 a23 = R15 a24 = R19 a24 = ° ' 6 0 2 ; R 3 a 3 = R 2 a 4 = -0.323; 3 2 a 3 = -&2al = ®la2 = ~ 3 l a 2 2 = _ 3 3 a 4 = 3 4 a 6 = _^*063; B 1 R 1 = " e i R 1 4 = 6 2 R 2 = " B 2 R 1 = e3 R4 = " e 3 R 3 = - ° - 3 1 5 ; B1 R15 = - 31 R18 = 62 R18 = " 6 2 R 1 3 = B3 R16 = " 6 3 R 1 9 = - 0 ' 0 2 7 -A long-range Kekule-type i n t e r a c t i o n constant between RR st r e t c h e s was a l s o i n c l u d e d and i s best described thus: any i n t e r a c t i o n between CC s t r e t c h i n g coordinates when one or both bonds were not on the perimeter or when the two bonds were i n d i f f e r e n t r i n g s was given a for c e constant of 0.090, m u l t i -p l i e d by a weighting f a c t o r found i n a manner already des-37 c r i b e d . Out-of-plane force constants: Diagonal terms: Y^Y^ = Y 2 Y 2 = Y 3 Y 3 = Y 4 Y 4 = Y15 Y15 = ° ' 2 9 3 ; *1*1 =*2*2 = *3*3' = *4*4 = ^ l S ^ l S = *19*19 = °- 0 8 7-Off-d i a g o n a l terms: y±y2 = Y 2 Y 1 7 = Y3Y4 = Y 4 Y 5 = Y 1 5 Y 1 6 =Y J 7Y 2 5= 0.006; Y L Y 3 = Y 2 Y 1 5 = Y 2 Y 4 = Y 1 ? Y 2 6 = Y 1 ? Y 5 = Y 4 Y 1 5 = Y 3 Y 1 3 = -0.006; <J>1<|,2 = ( f r ^ = $ 2* 1 5 = 4> 2<f» 3 = <f>3<f>4 = <t>3*15 = 4 > 1 5 * 1 8 = * 1 5 * i 9 = 0.00.2; ^ ^ 1 5 = <()1<|)13 = c ^ c j , ^ = ( f r ^ g = 4 > 3 * ; L 9 = *3*5 = *4*15 = ^ 1 6 = ° - 0 0 7 ; *1 Y2 = - ( ) ) 1 Y 1 = *2 Y3 = _ c f ,2 Y2 = CJ>3Y4 = -<r>3Y3 = <f>4Y5 = _ (t> 4Y 4 = -0.016. 195 The c a l c u l a t i o n s were c a r r i e d out on an IBM 360/67 computer using a somewhat modified v e r s i o n of a program 8 8 (VSEC) w r i t t e n by Schachtschneider • and the r e s u l t s are summarized i n Tables 33 and 34. A l s o i n c l u d e d i n Tables 33 and 34 are the r e s u l t s of a s i m i l a r c a l c u l a t i o n c a r r i e d 91 out i n t h i s l a b o r a t o r y using force constants from d i f f e r e n t 35 41 sources. ' The two sets of c a l c u l a t e d frequencies are compared w i t h the new assignment of the fundamentals to be described i n the next s e c t i o n . D. Assignment The assignment of the Raman-active molecular fundamentals given i n Table 34 was taken from the recent 91 laser-Raman study of pyrene c r y s t a l s and s o l u t i o n s . The i n f r a r e d - a c t i v e molecular fundamentals were assigned at low energy from the spec t r a presented i n t h i s chapter and at higher energy from the spec t r a published by C a l i f a n o and 90 Abbondanza, although even at higher energy the assignment proposed here does not agree completely with the one given 90 i n t h a t paper. The two c o r r e c t i o n s noted e a r l i e r i n the ac s p e c t r a were taken i n t o account i n making t h i s assignment. Table 33. Observed and c a l c u l a t e d u-fundamentals of pyrene Pyrene-h-LQ P y r e n e - d 1 Q Observed C a l c u l a t e d Observed C a l c u l a t e d Ref. 90 This work This work Ref. 91 Ref. 90 This work This work Ref. 91 965 942 803 789 906 897 731 736 648 660 582 592 320? 410 391 367 344 188 163 179 161 151 165 3098 3098 3064 3081 2294 2294 2279 2292 3080 3080 3052 3029 2278 2278 2270 2247 3040 3040 3051 3020 2256 2256 2265 2241 1517 1585 1569 1613 1523 1570? 1549 1588 1468 1468 1487 1432 1427 1427 1442 1392 1449 1449 1393 1418 1366 1366 1248 1314 1417 1242 1238 1255 1302 1188? 1047 1026 1242 1095 1089 1074 1188 841 983 954 1094 1064 1020 982 841 821? 829 814 1064 820? 810 767 821 755 753 711 683 651 659 626 495 493 502 503 462 461 465 468 T a b l e 33. ( C o n t i n u e d ) P y r e n e - h O b s e r v e d R e f . 90 T h i s w ork 10 C a l c u l a t e d T h i s w o r k R e f . 91 P y r e n e - d ^ Q O b s e r v e d R e f . 90 T h i s w ork C a l c u l a t e d T h i s w o r k R e f . 91 B 2u 3028 2989 1599 1432 1310 1272 1204 1184 1002 962 820 540 3028 2989? 1599 1487? 1432 1310 1272 1184 1085? 963 537 349 3057 3040 1692 1608 1489 1370 1190 1179 1127 982 567 344 3073 3049 1607 1472 1397 1384 1172 1169 1145 954 506 355 2242 2211 1561 1338 1276 1037 996 973 945 789 762 521 2242 2211 1561 1461? 1338 1276 1037 945 903 762 519 324 2288 2257 1668 1576 1454 1209 1039 954 842 815 545 320 2289 2264 1564 1425 1382 1271 1016 H 911 ^ 833 828 489 330 B 3u 963 845 748 710 487 447 963 845 748 710 484 219 126 988 825 767 703 484 206 112 957 816 753 717 483 195 113 804 745 603 571 432 804 745 598 568 431 202 119 817 704 620 576 436 189 105 798 703 638 568 428 178 105 198 Table 34. Observed and c a l c u l a t e d g-fundamentals of pyrene Pyrene-hio Pyrene-dio Observed C a l c u l a t e d Observed C a l c u l a t e d Ref.91 This work Ref. 91 Ref. 91 This work Ref. 91 3101 3064 3081 2302 2289 2294 3060 3057 3073 2292 2278 2287 3029 3052 3021 2273 2270 2242 1628 1669 1656 1619 1641 1644 1554 1614 1567 1504 1597 1517 1407 1500 1407 1388 1462 1358 1354 1337 1300 1275 1270 1263 1242 1220 1232 1164 1146 1162 1143 1152 1142 875 860 841 1066 1069 1058 833 830 820 807 805 737 752 752 703 592 5.74 607 564 550 579 406 402 393 399 392 383 907 899 744 739 819 811 650 653 507 512 458 463 228 262 251 205 237 224 988 963 820 808 966 947 796 768 788 764 752 754 765 755 600 600 583 579 506 489 475 469 424 414 263 267 272 235 251 254 199 Table 34. (Continued) Pyrene-hio Observed C a l c u l a t e d Ref.91 This work Ref. 91 Pyrene-dio Observed C a l c u l a t e d Ref. 91 This work Ref. 91 B 3g 3048? 3051 3049 2273? 2268 2265 3016? 3040 3028 2252 2258 2245 1593 1603 1601 1582 1586 1590 1568? 1509 1509 1433? 1477 1451 1411 1383 1373? 1319 1313 1382 1357 1239 1212 1198 1230 1220 1064 1036 1163 1160 939 904 1110 1135 1077 833 839 835 739 741 694 690 695 647 503 492 496 466 449 455 457 442 425 437 427 411 200 For the B^ u s p e c i e s , the frequency 820 cm 1 has been i n c l u d e d i n the pyrene-h^Q set and 755 cm 1 i n the pyrene-d^Q s e t . The 820 cm 1 l i n e , which appears i n the ac spectrum as a shoulder to the very strong l i n e at 845 cm \ has g r e a t e r s t r e n g t h i n c* than i n a* p o l a r i z a t i o n and i s a c c o r d i n g l y assigned as a B^ u and not a B 2 u fundamental, i n 89 -1 agreement w i t h Mecke and Klee. The l i n e at 755 cm i s . not a component of the stronger 762 cm 1 l i n e s ince no f a c t o r -group s p l i t t i n g should appear i n the ac spectrum. The other a d d i t i o n to the B^ u species i s the l i n e at 1585 cm 1 i n the protonated molecule which replaces the l i n e assigned by 90 -1 C a l i f a n o at 1517 cm The most obvious change i n the modes of B 2 u sym-metry f o l l o w s from the r e c o g n i t i o n of a fundamental near 350 cm The ten fundamentals below 2000 cm 1 may be c l a s s i -f i e d r a t h e r crudely as f i v e r i n g modes, three CH in-plane wags and two s k e l e t a l deformations. Although some mixing w i t h the CH in-plane wags must occur, at l e a s t four of. the f i v e r i n g modes should show a r e l a t i v e l y small drop i n f r e -quency upon de u t e r a t i o n and so the band at 1487 cm 1 has been taken to mark a fundamental i n pyrene-h^g, and 1461 cm 1 i n place of 996 cm 1 i n pyrene-d^g. The other changes are minor, i n v o l v i n g , f o r the deuterated molecule, the choice of the f a i r l y intense l i n e at 903 cm 1 i n s t e a d of the weak 973 cm 1 l i n e and the prominent l i n e at 762 cm 1 i n place of a band at 789 cm 1 not observed i n t h i s work. The t h e o r e t i c a l 201 value of 5.52 f o r the product r u l e r a t i o now places the r e -maining B 2 u fundamental of pyrene-h^g near 1100 cm ^ so t h a t i t may be t e n t a t i v e l y i d e n t i f i e d w i t h the weak l i n e at 10 85 cm - 1. With the new low-energy inform a t i o n the assignment of the B 3 u fundamentals i s now complete. The experimental value of 2.74 f o r the product r u l e r a t i o i s very c l o s e to the expected 2.76. E. Conclusion 1. Out-of-Plane Assignment The c a l c u l a t i o n of the out-of-plane fundamentals has now been c a r r i e d out w i t h three s l i g h t l y d i f f e r e n t f o r c e f i e l d s . In the course of t h i s work, two sets of force con-st a n t s were t r a n s f e r r e d from benzene (sets II-A and I I I - A of Chapter V). The r e s u l t s were very good f o r both f i e l d s and only the frequencies c a l c u l a t e d w i t h set I I I - A constants are presented i n Tables 33 and 34. Since the out-of-plane f i e l d used i n reference 91 was made up w i t h force constants d e r i v e d f o r b e n z e n e ^ ' ^ i n a s i m i l a r manner i t i s not s u r p r i s i n g that the frequencies c a l c u l a t e d (see Tables 33 and 34) are a l s o very c l o s e to the observed v a l u e s , and, i n f a c t , there 202 was l i t t l e to choose between the three sets of c a l c u l a t e d r e s u l t s . The average e r r o r i n the f i t to the c e r t a i n funda-mentals was i n each case about 15 cm 1 . 2. In-plane Assignment While agreement between the observed fundamentals and e i t h e r s et of c a l c u l a t e d frequencies was q u i t e good, i n s p e c t i o n of Tables 33 and 34 shows th a t the f i e l d d e r i v e d 32 from the Duinker and M i l l s benzene f i e l d (see Chapter V) was n o t i c e a b l y b e t t e r f o r the fundamentals below about 1100 -1 41 91 cm and the Neto, Scrocco and C a l i f a n o f i e l d ' was appreciably b e t t e r above th a t energy. As f o r anthracene, the former f i e l d was l e a s t s u c c e s s f u l i n f i t t i n g the highest-energy B 0 r i n g modes and a l s o p r e d i c t e d A modes considerably higher than the experimental values. Both f i e l d s were unable to f i t the CH in-plane bending frequencies of the B^ u species of pyrene-d^g and t h i s may be due to the presence i n t h i s region of a fundamental i n t r i n s i c a l l y weak i n the i n f r a r e d . As pointed out i n Chapters I I I and IV an analogous s i t u a t i o n e x i s t s i n the B, species of naphthalene-d„ and anthracene-d, n CHAPTER V I I THE VIBRATIONS OF ACENAPHTHENE I n t r o d u c t i o n 1. C r i t i c a l Review P o l a r i z e d i n f r a r e d s p e c t r a of acenaphthene s i n g l e -1 94 95 c r y s t a l s at energies above 400 cm have been reported ' 96 97 and a comparison w i t h o l d e r Raman data ' has l e d to a 94 f a i r l y complete assignment of the fundamental v i b r a t i o n s . Some d i f f i c u l t i e s s t i l l e x i s t , however; f o r example, the i n t e r p r e t a t i o n of the fluorescence and phosphorescence 98 99 spectra ' has re q u i r e d molecular fundamentals to be loc a t e d -1 -1 98 99 near 220 cm and near 416 cm ' and these have not been 94 recognized i n the l a t e s t assignment. One aim of the pre-sent work has been to extend the i n f r a r e d s o l u t i o n and s i n g l e c r y s t a l measurements to low energy to assign more f i r m l y the low frequency fundamentals. Laser Raman st u d i e s on s i n g l e c r y s t a l s of acenaphthene were being c a r r i e d out i n t h i s l a b o r a t o r y simultaneously w i t h t h i s work"*^ and a comparison of the i n f r a r e d spectra w i t h the more complete Raman data permitted a more secure assignment of the molecular funda-mentals to be made. 203 In a d d i t i o n , the frequencies of the normal modes of acenaphthene were c a l c u l a t e d w i t h f o r c e constants t r a n s -f e r r e d from other molecules. The c a l c u l a t e d and assigned frequencies were compared i n an attempt to assess the t r a n s -f e r a b i l i t y of the force f i e l d s . 2. S e l e c t i o n Rules The acenaphthene molecular axes have been chosen 64 to conform w i t h the i n t e r n a t i o n a l convention and are de-f i n e d i n Figure 4. Since the acenaphthene molecule does not con t a i n a center of symmetry, Raman and i n f r a r e d s p e c t r a supplement each other; the s e l e c t i o n r u l e s f o r the fre e molecule and f o r the c r y s t a l are summarized i n Table 35. Because there are four molecules i n the u n i t c e l l , each l i n e i n the spectrum of the fre e molecule i s expected t o s p l i t i n t o four components i n the c r y s t a l although comparison w i t h the s p e c t r a of naphthalene, anthracene and pyrene suggests th a t only f o r the out-of-plane modes w i l l the s p l i t t i n g be appr e c i a b l e . The A 2 s t a t e s are i n f r a r e d i n a c t i v e i n the f r e e molecule but can appear i n the Raman spectrum and a l s o , by mixing w i t h B 2 s t a t e s , i n the i n f r a r e d spectrum of the c r y s t a l . Four CH s t r e t c h i n g v i b r a t i o n s are expected i n each of the A-, and B~ molecular symmetry b l o c k s , and one CH s t r e t c h i n \ each of the A 2 and B^ b l o c k s . 205 Table 35. C o r r e l a t i o n t a b l e f o r acenaphthene* N Molecular group S i t e group '2v Bases Factor group C, '2v Bases n 20 xx, yy, zz ; z_ A-|_ 11 xz ; x 10 xy_ 19 y_z_ ; y B. A' a l £' fL3.' bb/ £ £ 5 b^ a; ac 5 a 2 ab b 2 b; be N i s the number of fundamentals i n the free molecule and n i s the number of l a t t i c e f requencies, assuming k = 0. Factor group symmetry species are d i s t i n g u i s h e d here and elsewhere i n the t e x t by lower case l e t t e r s . 206 The r e l a t i v e i n t e n s i t i e s of i n f r a r e d - a c t i v e funda-mentals i n the various c r y s t a l d i r e c t i o n s may be c a l c u l a t e d , i n the usual o r i e n t e d gas approximation, from the d i r e c t i o n cosines r e l a t i n g molecular and c r y s t a l axes, and are sum-marized i n Table 36. Table 36. The oriented-gas p r e d i c t i o n s of the r e l a t i v e i n t e n s i t i e s of the i n f r a r e d - a c t i v e l i n e s of acenaphthene along various c r y s t a l axes B 2(y) I 1.00 0.63 0.00 a I. b 0.00 0.00 1.00 I 0.63 1.00 0.00 c 207 B. Results The p o l a r i z e d i n f r a r e d s p e c t r a of an ac s e c t i o n of acenaphthene are presented i n Figure 32 and the observed frequencies at low energy are l i s t e d w i t h t h e i r assignments i n Table 37. The assignments were based, as u s u a l , on the assumption t h a t c r y s t a l f orces would not mix the molecular s t a t e s s u f f i c i e n t l y to reverse p o l a r i z a t i o n r a t i o s . The spectr a at higher energies agreed w e l l w i t h both previous 94 95 r e s u l t s ' and so the assignments i n Table 37 were not c a r r i e d past 650 cm \ At energies l e s s than 200 cm \ however, where the spect r a overlap w i t h those of Wyncke e t a l . , ^ there i s disagreement i n th a t the c r y s t a l axes a and c appear to have been reversed i n t h a t work. This a s s e r t i o n i s based not only on the e x c e l l e n t agreement of our r e s u l t s 94 95 with those of Colombo and of Nefedov and Fialkovskaya where they o v e r l a p , but a l s o on t h e i r consistency w i t h the r e s u l t s of the laser-Raman s t u d i e s . A l s o i n c l u d e d i n Table 37 are the l i n e s observed i n the i n f r a r e d spectrum of acenaphthene i n benzene at low energy. The spectrum i s presented as Figure 33. The measurements extend only up to about 580 cm ^ where the s o l -vent began to absorb s t r o n g l y . This spectrum was e s p e c i a l l y u s e f u l i n th a t i t (a) demonstrates that a l l l i n e s above 150 cm represented molecular and not l a t t i c e modes and (b) d i s -t i n g u i s h e s factor-group components from n e a r l y degenerate molecular v i b r a t i o n s . 208 Figure on f o l l o w i n g page. Figure 32. The i n f r a r e d spectra of an ac s e c t i o n of acenaphthene about 45 microns t h i c k . The spect r a near 1000 cm 1 are a l s o shown f o r a 0.25 mm t h i c k c r y s t a l . F u l l l i n e //a, dotted l i n e / / c . 209 UOISSIUUSUDJ^  % UOISSIUUSUDJ|_ % A i ( i n • i ^ — lk lUkJ i 2 0 0 3 0 0 4 0 0 5 0 0 w a v e n u m b e r ( c m - 1 ) Figure 33. The low-frequency i n f r a r e d spectrum of acenaphthene i n benzene s o l u t i o n . The peak at 225 cm -* was remeasured using a d i l u t e s o l u t i o n . 211 Table 37. The low-energy i n f r a r e d spectrum of a s o l u t i o n of acenaphthene i n benzene and of an ac s e c t i o n of an acenaphthene c r y s t a l S o l u t i o n //a Assignment 54 b l 70 b l 71 a l 88 a l 99 b l 102 a l 167 174 m 190 B l 19 8 225 225 vs 234 B l 252 414 ms 414 415 A l 442 m 471 vw 460 460 B l 460 w 467 A l 500 w B 2 a 540 m 540 538 B l 546 m 553 549 A l 632 A l pi See, f o r example, reference 94 and the Raman spectra i n reference 100. 212 The s o l u t i o n spectrum c l e a r l y shows th a t the lowest-energy molecular v i b r a t i o n s are at 174 and 225 cm ^. These are as s o c i a t e d w i t h the c r y s t a l , l e v e l s at 167, 190 and 19 8 cm 1 and at 225, 234 and 252 cm - 1 r e s p e c t i v e l y . The p o l a r i z a t i o n r a t i o , found by summing the c o n t r i b u t i o n s i n each p o l a r i z a t i o n , favors a assignment i n both cases. The observation t h a t the means of the energies of the c r y s t a l l e v e l s are gr e a t e r than the s o l u t i o n values may be a t t r i b u t e d to mixing of c r y s t a l and l a t t i c e s t a t e s , a phenomenon which has already been observed i n the Raman spectrum of anthra-cene-d^Q (see Chapter I V ) . The next two l i n e s i n the i n f r a r e d spectrum appear at 414 and 442 cm ^ i n s o l u t i o n , and are assigned as A^ and B 2 molecular fundamentals r e s p e c t i v e l y . The l a t t e r a s s i g n -94 -1 ment was made by Colombo; the l i n e at 415 cm was not inc l u d e d i n h i s l i s t of fundamentals although i t s symmetry assignment i s c l e a r from the ac spectrum; i t i s obv i o u s l y n e i t h e r an overtone nor a combination of two lower energy fundamentals. The i n t e r p r e t a t i o n of the various s p e c t r a near 460 cm i s complicated. The i n f r a r e d s o l u t i o n spectrum demonstrates the presence of two molecular l e v e l s and the 94 absence of any b - p o l a r i z e d absorption shows th a t these l e v e l s can only have A^ or B^ symmetry. Using the i n f r a r e d and Raman"^^ s o l u t i o n .data f o r the lower-energy fundamentals 213 a s i g n i f i c a n t energy mis-match f o r a l l p o s s i b l e combinations i s found so t h a t the presence of two fundamentals i s i n d i -cated. The o v e r a l l i n t e n s i t y r a t i o i n the i n f r a r e d c r y s t a l spectrum c l e a r l y demonstrates the presence of an funda-mental. On the other hand, the Raman s p e c t r a 1 ^ i n d i c a t e the presence of a molecular mode whose b^ c r y s t a l component was seen i n t h a t work at 469 cm ^. The a^ c r y s t a l component of t h i s B^ mode must be ass o c i a t e d w i t h the l i n e observed i n the i n f r a r e d at 460 cm These observations are c o n s i s t e n t w i t h the p r e d i c t i o n s of the oriented-gas model th a t a B^ mode of the f r e e molecule should have i t s a^ c r y s t a l compon-ent most intense i n the i n f r a r e d spectrum and i t s b^ compon-ent most intense i n the Raman spectrum. The b^ component of t h i s B^ molecular mode can a l s o be a c t i v e i n the i n f r a r e d and may be adding to the a - p o l a r i z e d i n t e n s i t y at 46 7 cm 1 already a s s o c i a t e d w i t h an A^ fundamental. That the "in-plane" A^ fundamental does not e x h i b i t factor-group s p l i t t i n g w h i l e the "out-of-plane" B^ fundamental does i s c o n s i s t e n t w i t h the r e s u l t s observed e a r l i e r f o r naphthalene, anthracene and pyrene. 9 4 95 The two e a r l i e r s t u d i e s ' have d i f f e r e d i n the assignment of the strong but ne a r l y d e p o l a r i z e d band at 1369 -1 94 cm . Colombo ;: assigned i t as a B^ fundamental and Nefedov and F i a l k o v s k a y a ^ as an A^ fundamental. The Raman s p e c t r a 1 ^ have shown tha t t h i s l i n e i s c l e a r l y a s s o c i a t e d w i t h an A^ 214 f u n d a m e n t a l a n d t h i s a s s i g n m e n t i s i n c l u d e d i n t h e l a t e r summary o f m o l e c u l a r f u n d a m e n t a l s . O t h e r r e v e r s a l s o f 94 C o l o m b o ' s a s s i g n m e n t s w h i c h w e r e c l e a r f r o m t h e Raman s p e c t r a " * " 0 0 a n d w h i c h a r e o f i m p o r t a n c e h e r e a r e ( i ) t h e 746 cm l i n e m a r k s t h e p r e s e n c e o f a n A 2 mode, ( i i ) t h e 765 an d 1358 cm ^ i n t e r v a l s a r e a s s o c i a t e d w i t h B 2 modes and ( i i i ) t h e l i n e s a t 806 a n d 842 cm 1 a r e n o t f a c t o r - g r o u p 94 c o m p o n e n t s o f t h e same m o l e c u l a r f u n d a m e n t a l b u t a r e due t o two d i s t i n c t m o l e c u l a r l e v e l s . A new a s s i g n m e n t o f t h e m o l e c u l a r f u n d a m e n t a l s i n c o r p o r a t i n g t h e a b o v e i n f o r m a t i o n w i l l be made f o l l o w i n g a d i s c u s s i o n o f t h e c a l c u l a t i o n o f t h e n o r m a l v i b r a t i o n s . C. C a l c u l a t i o n o f F u n d a m e n t a l s S i n c e t h e f o r c e f i e l d o f a c e n a p h t h e n e i s , o f c o u r s e , n o t known, i n o r d e r t o c a r r y o u t a n o r m a l c o o r d i n a t e a n a l y s i s f o r c e c o n s t a n t s m u s t be t r a n s f e r r e d f r o m o t h e r m o l e c u l e s . A l t h o u g h t h e a c e n a p h t h e n e m o l e c u l e i s n o t p l a n a r , t h e A^ and B 2 symmetry s p e c i e s i n v o l v e p l a n a r i n t e r n a l c o o r d i n a t e s a l m o s t e x c l u s i v e l y . Two. c a l c u l a t i o n s o f t h e f u n d a m e n t a l f r e q u e n c i e s i n t h e s e s ymmetry b l o c k s w e r e c a r r i e d o u t , u s i n g two d i f f e r e n t s e t s o f f o r c e c o n s t a n t s f o r t h e n a p h t h a l e n e 215 s e c t i o n of the acenaphthene molecule. C a l c u l a t i o n 1 used the f o r c e constants r e f i n e d from the D u i n k e r - M i l l s benzene 32 f i e l d i n Chapter V; c a l c u l a t i o n 2 used constants t r a n s -41 f e r r e d from the Neto, Scrocco and C a l i f a n o f i e l d . For the e s s e n t i a l l y a l i p h a t i c — C H 2 — C H 2 — fragment of acenaphthene the force constants f o r the A 2 and as w e l l as f o r the A-^  and B 2 symmetry species were deri v e d from a f i e l d used to describe the normal modes of c y c l o p e n t a n e . O n l y one c a l -c u l a t i o n of the e s s e n t i a l l y out-of-plane A 2 and B-^  frequencies was c a r r i e d out. The source of the f o r c e constants f o r the naphthalene s e c t i o n of the acenaphthene molecule was the 35 out-of-plane f i e l d of S c u l l y and Whiffen. The i n t e r n a l coordinates were defined as i n Figure 34. In t h i s f i g u r e CC bond s t r e t c h e s (designated by R) , CH bond s t r e t c h e s (r) and angle bends ( a ) are shown. The CC bond t o r s i o n s (<}>) and out-of-plane bends ( y ) are not shown i n Figure 34 but were numbered i n the same way as the R and a r e s p e c t i v e l y . The l i s t which f o l l o w s defines the force constant matrix by g i v i n g the number of the force constant a s s o c i a t e d w i t h each matrix element. The numerical values of the con-st a n t s are given i n Table 38. The CC s t r e t c h i n g force con-st a n t s used f o r the c a l c u l a t i o n c a r r i e d out w i t h the planar constants taken from Chapter V (Calc. 1) were made to f i t —xr the curve f = Ae where r i s the bond length and x and A 216 Figure 34. The i n t e r n a l coordinates of acenaphthene 217 were defined e a r l i e r (Chapter V). For the c a l c u l a t i o n 41 c a r r i e d out w i t h the Neto, Scrocco and C a l i f a n o f i e l d (Calc. 2) the CC s t r e t c h i n g constants' were i n t e r p o l a t e d from a p l o t of the CC force constants quoted there against the corresponding bond lengths. To reduce the order of the matrices to be handled, the angle bending coordinates out-41 side the naphthalene r i n g and re - d e f i n e d as in-plane wags of the CH bonds. Diagonal elements: R i R i = 1/ R 2 R 2 = 2 ; R 3 R 3 = 3 ? R 4 R 4 = 4 ; R10 R10 = 5 ; R 1 1 R 1 1 = 6 ; R12 R12 = 7 ; R13 R13 = 8 ; r l r l = r 2 r 2 =  r 2 r 3 = 9; r ^ r ^ = 10; a^a^ = 11; o^o^ = ^2a3 = a 4 a 4 = 1 2 ?  a10 a10 = a13 a13 = 1 3 ; a l l a l l = a14 a14 = a16 a16 = 1 4 ; a17 a17 = a 1 9 a 1 9 = 15; a 2 ] a 2 1 = a 2 5 a 2 5 = 16; 0 ^ = ^ = 17; 6363 = IP. Y-Y _ Y Y _ Y Y _ Y Y. _ Y Y _ Y Y _ i q . ' 1 1 2 2 3 3 4 4 11 11 14 14 x*' Ml = *2*2 = *3*3 = *4*4 = ^lO^lO = *11*11 = 2 0 ; *12*12 = MM = 21' O f f - d i a g o n a l elements: R^ R2 = R 2 R 3 = R 3 R 4 = R 1 R 1 0 = 2 2 ' R 4 R 5 = R 9 R 1 0 = R 4 R 1 1 = R 1 0 R 1 1 = 23'* R 1 R 3 = R 2 R 4 = R 2 R 1 0 = R 4 R 1 0 = 2 4 ; R 1 R 9 = R 3 R 5 = R 1 R 1 1 = R 3 R 1 1 = 25"' R 4 R 9 = 26; R XR 4 = R 3R 1 ( ) = 27; R ^ = R 3R g = 28; R^g = R 3R g = R 2R 9 = R 2R 5 = R 2R 1 X = 29; R^g = - R 2 R g = R 2 R 7 " R x R 7=30; R 9R 1 2= R12 R13 = 3 1 ; a l R 1 0 = a 4 R 4 = a10 R10 = a 1 3 R 4 = a 1 0 R l l = 218 a 1 3 R l l = 3 2 ; a l l R 1 0 = 3 3 ; a 1 4 R 4 = 3 4 ; a l R l = a 4 R 3 = a 2 R l = a 3 R 3 = a 2 R 2 = a 3 R 2 = 3 5 ; a 1 6 R l = a18 R10 = 3 6 ; 3 1 R 1 = 3 2 R 3 = 6 3 R 4 = " B 1 R 2 = " 6 2 R 2 = " 3 3 R 3 = 3 7 ' a17 R12 = a19 R12 = a 1 9 R 1 3 = 38; a ^ R ^ = a 2 5 R 1 2 = 39; = a 2 a 3 =a 3a 4 = a 4 a 1 3 = a i a 1 ( J = a 1 ( J a 1 3 = 40; = a 4 a 1 4 = a 1 0 a 1 2 = 41; a21 a22 = a25 a26 = ~ a21 a25 = 4 2 ; a 1 9 a 2 1 = a19 a25 = 4 3 ; r l r 2 = r 2 r 3 = 44; r ? r 8 = 45; Y l Y 2 = Y 2Y 3 = Y 3 Y 4 = Y 4 Y 1 4 = Y 1 1 Y 1 4 = y l Y l l = 46; Y l Y 3 = Y l Y 1 4 = Y 2 Y 4 = Y 2 Y n =-Y 3Y 1 4 = Y 4 T U = 47; Y 1 Y 4 = Y 2 Y 1 4 = Y 3 Y 1 1 = 4 8 ; *1*2 = M 3 = *3*4 = -Ms ^ V l O : 49; <J,lYl = <f>2Y2 = * 3 Y 3 = * 4 Y 4 = * 1 0 Y n = -*iY2 = -* 2 :Y 3 = -cf 3Y 4 = - * l o Y l = " * 4 Y 1 4 = 50; B 23 3 = -0^2 = 51; 6 ^ = 52;. a 2 r l = a 3 r 2 = a 4 r 3 = 5 3 ; a 9 R 1 0 = a l 2 R 4 = 5 4 ; a 2 3 2 = a 3 e i = ~ a l 3 l = a 3 6 3 = " a 1 3 e 3 = 5 5 ; B 1 R 4 = 32 R10 = B 3 R 1 = - B 1 R 1 1 = - B 2 R 1 1 = - 63 R10 = 5 6 ' 219 Table 38. Force constants f o r acenaphthene c a l c u l a t i o n Number Value* Number Value* Ca l c . 1 Ca l c . 2 Calc. 1 Calc. 2 1 7.814 6.85 24 -0.609 -0.316 2 6.266 5.86 25 -0.030 -0.176 3 8.518 7.20 26 0.030 0.158 4 6 .477 6.00 27 0.295 0.342 5 7.000 6.25 28 -0.030 -0.160 6 7.040 6.43 29 0.030 0.156 7 4.560 4.66 30 0.030 0.000 8 4.239 4.43 31 0. 064 9 5.061 5.05 32 0.602 0.397 10 4 .56 33 0.351 0.397 11 0.711 0.934 34 0.000 0.397 12 1.103 0.934 35 0.602 0.279 13 0.711 0.619 36 0.000 0.174 14 0.814 0.920 37 0.315 0.174 15 0 .833 38 0. 351 16 0 .666 39 0. 263 17 1.020 1.00 40 -0.097 -0.045 18 1.020 1.02 41 0.000 0.111 19 0 .317 42 -0. 016 20 0 .057 43 -0. 124 21 0 .029 44 0.020 0.068 22 0.650 0.750 45 0. 016 23 0.030 0.457 46 0. 013 220 Table 38. (Continued) Number Value* C a l c . 1 C a l c . 2 Number Value* Cal c . 1 C a l c . 2 47 -0.024 52 0.015 0.000 48 -0.019 53 -0.014 0.000 49 -0.019 54 -0.323 0.000 50 -0.021 55 -0.063 0.000 51 0.028 0.000 56 -0.027 0.000 The sources from which the two sets of force constants were derived are described i n the t e x t . The u n i t s throughout are mdyn/A f o r s t r e t c h i n g c o n s t a n t s 6 mdyn/radian f o r s t r e t c h bend i n t e r a c t i o n s and mdyn A / r a d i a n 2 f o r bending constants. 221 D. Assignment 1. A j Species In the i n f r a r e d spectrum the strong l i n e s appearing at 415, 467, 551, 632, 1170, 1251, 1418, 1446, 1500 and 1602 cm 1 were assigned as fundamentals. Strong i n f r a r e d 94 -1 l i n e s have been reported at 2838, 2925 and 3055 cm , the l a t t e r having the appearance of a near degeneracy. The Raman e x p e r i m e n t s 1 0 0 have added 806, 1001, 1042, 1172, 1221 and 1369 cm 1 i n t e r v a l s to t h i s l i s t of t o t a l l y symmetric 94 modes and the remaining A^ fundamental has been l o c a t e d at 1593 cm \ an assignment which i s i n agreement w i t h the r e s u l t s of the c a l c u l a t i o n s , both of which p r e d i c t two high energy r i n g modes. 2. B i Species The s t r o n g l i n e s at 186, 234, 463, 539, 743, 775, 835 and 890 cm 1 i n the i n f r a r e d spectrum must correspond to B^ fundamentals. The values quoted here are the means of factor-group components; f o r example, 463 cm 1 i s the mean of the a^ and b^ components observed i n the i n f r a r e d spectrum at 460 cm 1 and a second b^ component seen at 469 cm 1 i n the Raman s p e c t r u m . 1 0 0 The four intense l i n e s between 700 and 900 cm 1 are not factor-group components since they a l l 94 appear i n the s o l u t i o n spectrum. The two remaining funda-222 mentals may be represented by the weaker c - p o l a r i z e d l i n e s at 903 and 935 era \ I f these l a t t e r assignments are c o r r e c t then the force f i e l d on which the c a l c u l a t i o n of these e s s e n t i a l l y out-of-plane fundamentals was based must be d e f i c i e n t , since the c a l c u l a t e d values are nea r l y 200 cm 1 higher. 3. B 2 Species 94 95 The b - p o l a r i z e d i n f r a r e d spectrum ' i n d i c a t e s t h a t the l i n e s at 446, 500, 647, 1015, 1093, 1209, 1275, 1429, 1500, 1618, 2920, 3038 and 3068 cm"1 have B 2 symmetry c h a r a c t e r i s t i c s . A d d i t i o n a l B 2 fundamentals i d e n t i f i e d 1 ^ from the Raman spectrum occur at 765, 1097, 1153, 1358 and 1474 cm The one remaining, fundamental i s p r e d i c t e d by C a l c u l a t i o n 1 to l i e j u s t above 500 cm 1 and by C a l c u l a t i o n 2 to l i e j u s t below 500 cm 1 (see Table 39) but cannot be lo c a t e d i n e i t h e r the i n f r a r e d or Raman 1^ spectrum. The assignments are summarized i n Tables 39 and 40 along w i t h the r e s u l t s of the force constant c a l c u l a t i o n s . In the column headed ' C a l c . l 1 are the frequencies c a l c u l a t e d by using f o r the naphthalene s e c t i o n of the acenaphthene molecule those force constants r e f i n e d from the Duinker and 32 M i l l s benzene f i e l d (see Table 28). In the column headed 'Calc. 2' the force constants f o r tha t p a r t of the molecule 41 were taken from the Neto, Scrocco and C a l i f a n o f i e l d . Table 39. The A, and B„ fundamentals of acenaphthene A, symmetry B 2 symmetry 94 Calc. 1 C a l c . 2 Experiment Colombo Calc . 1 Cal c . 2 Experiment Colombo 430 439 415 459 436 432 446 446 513 496 467 465 501 479 500 500 586 592 551 552 521 498 631 643 632 630 680 646 647 b 647 818 762 806 851 796 765 1003 1000 1001 1000 1046 1047 1015 1015 1014 1019 1042 1042 1178 1114 1093 1093 1092 1083 1170 1145 1217 1189 1153 1150 1210 1209 1221 1176 1293 1234 1209 b 1209 1266 1237 1251 1254 1330 1288 1275 b 1275 1364 1349 1369 1310 1390 1360 1358 1442 1466 1420 1426 a 1416 1473 1441 1429 c 1500 1506 1449 1450 a 1435 1529 1533 1474 1595 1543 1533 1500 1502 1625 1600 1500 b 1770 1656 1649 1593 1598 1705 1673 1618 c 1792 1690 1659 1605 1605 2903 2900 2920 b 2840 2911 2909 2838 2838 3040 3019 3018 2920 3041 3020 2926 2925 3054 3048 3038 3038 3054 3049 3055 3015 3064 3079 3068 b 3068 3065 3080 3061 3050 a T h i s value i s the mean of the observed factor-group components. bTaken from Colombo. cTaken from Nefedov and Fialkovskaya.95 224 Table 40. The A 2 and fundamentals of acenaphthene A 2 C a l c u l a t e d symmetry Experiment 94 Colombo B l C a l c u l a t e d symmetry Experiment 94 Colombo 176 173 179 186 a 271 252 229 234 a 460 478 463 a 635 . 617 615 536 539 a 819 746 760 731 743 745 999 872 816 775 784 1048 910 835 835 1055 1352 1018 890 940 1226 1938? 1087 1365 2877 1159 2870 2943 1445 2940 a T h i s value i s the mean of the observed factor-group components. 225 4. A_2 Species The A 2 fundamentals are i n a c t i v e i n the i n f r a r e d spectrum of the f r e e molecule and the assignments given i n Table 40 are c a r r i e d over d i r e c t l y from the Raman r e s u l t s . E. D i s c u s s i o n Comparison of the observed and c a l c u l a t e d frequen-c i e s i n Tables 39 and 40 i n d i c a t e s t h a t the synthesis of a force f i e l d f o r acenaphthene from the force constants of naphthalene and of cyclopentane has been reasonably success-f u l . I t should not be f o r g o t t e n , however, t h a t some r e l i a n c e was placed on the r e s u l t s of the c a l c u l a t i o n s i n making the assignment of 1593 as the second r i n g mode and, perhaps more important, the assignment of a f i n a l B 2 mode near 500 cm 1. The two c a l c u l a t i o n s c a r r i e d out f o r the A^ and B 2 species show tha t w h i l e the f i e l d r e f i n e d f o r benzene, naphthalene and anthracene i n Chapter V was s l i g h t l y more s u c c e s s f u l f o r the low frequencies, the Neto, Scrocco and 41 C a l i f a n o f i e l d was b e t t e r able to f i t the r i n g modes. For the B^ and A 2 v i b r a t i o n s a comparison w i t h the observed frequencies i s l e s s h e l p f u l , since the experimental a s s i g n -226 ments are not complete. I t appears, however, that the c a l -c u l a t i o n has placed the higher-energy modes too hi g h , perhaps i n d i c a t i n g t h a t the out-of-plane bending force constants used were too l a r g e . In g e n e r a l , however, the r e s u l t s of the force con-st a n t c a l c u l a t i o n s were reasonably encouraging. The t r a n s f e r of force constants between s i m i l a r molecules or even s i m i l a r s e c t i o n s of molecules seems to be j u s t i f i e d , at l e a s t f o r the purposes of using the c a l c u l a t e d frequencies as a guide to l o c a t e the molecular fundamentals. CHAPTER V I I I CONCLUSION The spectroscopy of aromatic molecules and the study of the forc e f i e l d s of these molecules are areas of r a p i d l y growing i n t e r e s t . With the a i d of new spectro-meters and w i t h techniques designed to produce the maximum amount of p o l a r i z a t i o n i n f o r m a t i o n from the Raman and i n f r a -red s p e c t r a of molecular c r y s t a l s i t has been p o s s i b l e t o re-evaluate e x i s t i n g assignments of the fundamental v i b r a -t i o n s of the two simples t polyacenes, naphthalene and anthracene. While the e x t r a p o l a r i z a t i o n i n f o r m a t i o n obtained from s i n g l e c r y s t a l faces which are l e s s e a s i l y obtained and there f o r e not normally s t u d i e d confirmed the l o c a t i o n of many higher-frequency fundamentals, s e v e r a l misassignments were a l s o noted. In a d d i t i o n , many low-frequency fundamentals were l o c a t e d as p o l a r i z e d f a r - i n f r a r e d s p e c t r a of naphthalene-dg, anthracene-h.^ and anthracene-d^Q were obtained f o r the f i r s t time. A l s o s t u d i e d f o r the f i r s t time were the l a s e r -e x c i t e d p o l a r i z e d Raman sp e c t r a of naphthalene-dg and anthracene-d.^. When the experimental assignments were as complete as p o s s i b l e , a t t e n t i o n was d i r e c t e d to the force f i e l d s . The 227 228 out-of-plane f i e l d of benzene was completely reconsidered, and w h i l e t r a n s f e r of force constants to naphthalene showed 30 that the b a s i c assumption made by Whiffen t h a t a l l i n t e r -a c t i o n constants should be as small as p o s s i b l e was com-p l e t e l y supported, i t was a l s o found t h a t minor changes i n the benzene f i e l d could s l i g h t l y improve the f i t to the observed frequencies of naphthalene. Whether these changes are meaningful or not cannot be determined s o l e l y from the observed frequencies, since the improvement i s s m a l l ; a more s e n s i t i v e t e s t might be the form of the normal modes p r e d i c t e d by each benzene f i e l d , but u n t i l some way of r e l a -t i n g the motion of the atoms to some p h y s i c a l observable i s developed (e.g. a r e l i a b l e method of c a l c u l a t i n g i n t e n s i t i e s f o r each normal mode), any r e a l d i s t i n c t i o n between the out-of-plane f i e l d s remains impossible. Such a r e l i a b l e method of c a l c u l a t i n g i n t e n s i t i e s would a l s o be very h e l p f u l i n l o c a t i n g the out-of-plane fundamentals of anthracene, where one la r g e discrepancy e x i s t s ( f o r the second-lowest B^ u v i b r a t i o n ) between the observed and c a l c u l a t e d frequencies; the p o s s i b i l i t y t h a t the 166 cm 1 l i n e (anthracene-h^^ value) a r i s e s from l a t t i c e e f f e c t s and tha t the second lowest B^ u fundamental i s weak and absent from the i n f r a r e d spectrum could be t e s t e d more f u l l y . An in-plane force f i e l d developed by Duinker and 32 M i l l s f o r benzene was t r a n s f e r r e d to naphthalene and 229 anthracene and r e f i n e d to f i t simultaneously the observed frequencies of a l l three molecules and t h e i r three perdeuter-ated analogues. The r e s u l t s were compared w i t h those of a s i m i l a r c a l c u l a t i o n c a r r i e d out by Neto, Scrocco and C a l i f a n o 41 (NSC). Although the l a t t e r f i e l d gave a s l i g h t l y b e t t e r f i t to the observed frequencies (the average e r r o r i n t h i s work was about 14.8 cm 1 ; the NSC r e s u l t s were about 1 cm 1 b e t t e r ) t h i s i s perhaps not s u r p r i s i n g i n view of the l a r g e r number of for c e constants r e f i n e d i n the NSC c a l c u l a t i o n (34 constants compared w i t h 21 constants f o r the f i e l d des-c r i b e d i n t h i s t h e s i s ) . The planar f o r c e f i e l d presented i n t h i s t h e s i s has at l e a s t two p o i n t s to recommend i t . F i r s t , the force con-st a n t s r e f i n e d to f i t a l l s i x molecules are remarkably c l o s e to the o r i g i n a l benzene constants proposed by Duinker and M i l l s . In p a r t i c u l a r , the carbon-carbon s t r e t c h i n g constant o was r e f i n e d to 7.040-mdyn/A, a value very near the o r i g i n a l o D u i n k e r - M i l l s value and a l s o much c l o s e r to the 7.43 mdyn/A 87 expected f o r a normal aromatic bond length than the value o 41 of 6.43 mdyn/A found by Neto et a l . A second advantage of the general f i e l d described here i s that i t contains no for c e constants which are unique 41 to one molecule.. The NSC for c e f i e l d contains e i g h t such constants and we f e e l t h i s i s dangerous because of the p o s s i -b i l i t y t h a t such constants w i l l be r e f i n e d to values f a r removed from p h y s i c a l r e a l i t y i n order to compensate f o r 230 other d e f i c i e n c i e s i n the f i e l d . The r e s u l t s of the normal coordinate a n a l y s i s c a r r i e d out i n the course of t h i s work gave a d d i t i o n a l sup-port to many assignments which were made i n the e a r l i e r work 41 (NSC ) on the b a s i s of c a l c u l a t i o n s , but which we f e l t were not experimentally c e r t a i n . However, s e v e r a l assignments made i n tha t work, p a r t i c u l a r l y i n the in-plane B 2 u species of anthracene, were not supported ( i n f a c t a new assignment was suggested by our c a l c u l a t i o n s ) and we f e e l t h a t at t h i s time no f i r m conclusions about such assignments should be made. As f o r the out-of-plane frequencies, a r e l i a b l e method of c a l c u l a t i n g the i n t e n s i t y of v i b r a t i o n s would be extremely v a l u a b l e . In order to f i n d out how w e l l force f i e l d s developed f o r benzene, naphthalene and anthracene would t r a n s f e r to r e l a t e d but l e s s s i m i l a r molecules, the v i b r a t i o n s of pyrene and acenaphthene were considered. The i n f r a r e d s p e c t r a of these molecules were measured (with emphasis on the p r e v i o u s l y unstudied low-energy region) and, by using Raman data obtained by others i n t h i s l a b o r a t o r y 9 1 ' 1 0 0 f a i r l y complete assignments of the normal v i b r a t i o n s were p o s s i b l e . C a l c u l a t i o n of the molecular fundamentals w i t h planar force constants from the two f i e l d s mentioned e a r l i e r and out-of-plane constants o r i -g i n a t i n g i n the benzene f i e l d (Chapter V and reference 30) showed th a t i t was indeed p o s s i b l e to t r a n s f e r the force con-231 s t a n t s q u i t e s u c c e s s f u l l y t o t h e s e r e l a t i v e l y d i s s i m i l a r m o l e c u l e s . A l t h o u g h t h e p l a n a r f i e l d d e r i v e d f r o m t h e D u i n k e r -32 M i l l s b e n z e n e f i e l d was s l i g h t l y more s u c c e s s f u l i n f i t t i n g t h e l o w e r - e n e r g y f u n d a m e n t a l s (below a b o u t 1000 cm o f 41 p y r e n e and a c e n a p h t h e n e , t h e NSC f i e l d was s i g n i f i c a n t l y b e t t e r a t f i t t i n g t h e h i g h e r - e n e r g y r i n g modes, p a r t i c u l a r l y t h o s e o f symmetry. 34 Freeman and Ross have r e p o r t e d i n t h e i r c a l c u l a -t i o n o f t h e p l a n a r f u n d a m e n t a l s o f n a p h t h a l e n e a p r o b l e m s i m i l a r t o t h a t e n c o u n t e r e d by us i n t h e c a l c u l a t i o n s w i t h t h e D u i n k e r - M i l l s t y p e f i e l d . They have a t t r i b u t e d t h e d i f f i c u l t y t o t h e a b s e n c e , i n t h e i r f i e l d , o f a f o r c e c o n -s t a n t c o n t r o l l i n g t h e d e f o r m a t i o n s w h i c h s e n d t h e m o l e c u l e t o w a r d one o f i t s K e k u l e s t r u c t u r e s . A l t h o u g h t h e i r d e t a i l e d argument w i l l n o t be p r e s e n t e d h e r e , i t i s b a s i c a l l y t h a t when n a p h t h a l e n e d i s t o r t s t o w a r d s two o f i t s t h r e e K e k u l e s t r u c t u r e s , i t i s u n d e r g o i n g a B 2 u r i n g v i b r a t i o n ; s i n c e t h e Kekule' s t r u c t u r e s a r e p a r t i c u l a r l y c o m p a t i b l e w i t h t h e r e -q u i r e m e n t s o f o r d i n a r y v a l e n c e , t h e r e s i s t a n c e t o t h i s t y p e o f d e f o r m a t i o n m i g h t be e x p e c t e d t o be a b n o r m a l l y low. A s i m i l a r argument shows t h a t s u c h a f o r c e c o n s t a n t s h o u l d a l s o be i m p o r t a n t f o r t h e B 2 U v i b r a t i o n s o f a n t h r a c e n e and a c e n a p h t h e n e , w h i l e f o r p y r e n e t h e K e k u l e s t r u c t u r e s c a n n o t 232 f be r e a d i l y i d e n t i f i e d w i t h one p a r t i c u l a r planar symmetry c l a s s . Although a fo r c e constant c o n t r o l l i n g t h i s type of motion was introduced f o r benzene i n the D u i n k e r - M i l l s f i e l d , and was extended by us t o the other molecules i n the manner 37 o u t l i n e d by Scherer, the d i f f i c u l t i e s encountered i n c a l -c u l a t i n g the B 2 u r i n g frequencies suggest t h a t f u r t h e r study of t h i s type of i n t e r a c t i o n i s r e q u i r e d . R E F E R E N C E S i 234 1. C.K. Ingold et a l . , J . Chem. Soc. 1936, 912 e t seq., 1210. 2. C.K. Ingold e t a l . , J . Chem. Soc. 19 46, 222 et seq. 3. R.D. 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Schachtschneider, S h e l l Development Company. (E m e r y v i l l e , C a l i f o r n i a ) , T e c h n i c a l Report No. 57-65. 89. R. Mecke and W.E. Klee, Z. Elektrochem. 65, 327 (1961). 90. S. C a l i f a n o and G. Abbondanza, J . Chem. Phys. 39, 1016 (1963) . 91. A. Bree, R.A. Kydd, T.N. Mi s r a and V.V.B. V i l k o s , to be published. 92. J.M. Robertson and J.G. White, J . Chem. Soc. 358 (1947), 93. G.J. H o i j t i n k , N.H. V e l t h o r s t and P.J. Zandstra, Mol. Phys. 3_, 533 (1960); H. Zimmerman and N. Joop, Z. Elektrochem. 65_, 138 (1961); A. Bree and V.V.B. V i l k o s , J . Chem. Phys. 40, 3125 (1964). 239 94. L. Colombo, J . Chem. Phys. 3_9, 1942 (1963). 95. O.V. Nefedov and O.V. F i a l k o v s k a y a , Opt. Spektrosk. 20, 1016 (1966) [Opt. Spectrosc. 20, 445 (1966)]. 96. H. Luther and C. R e i c h e l , Z. Physik. Chem. 195, 103 (1960) 97. J.P. Mathieu, M. E c o l l a n and J.F. E c o l l a n , J . Chim. Phys. 5_0, 250 (1954) . 98. L. P e s t e i l , J . Chim. Phys. 58, 204 (1961). 99. V.I. Mikhailenko and P.A. Teplyakov, Opt. Spektrosk. 22, 48 (1967) [Opt. Spectrosc. 22, 24 (1967)]. 100. A. Bree, R.A. Kydd and T.N. M i s r a , to be published. 101. F.H. Kruse and D.W. S c o t t , J . Mol. Spectry. 20, 276 (1966) A P P E N D I X 241 A. D e f i n i t i o n of Out-of-Plane I n t e r n a l Coordinates 1. Out-of-plane wag (Y) at atom 1 a Figure 25. The arrangement of atoms used to define an out-of-plane wag. The p o s i t i v e d i r e c t i o n of the x - a x i s i s up out of the plane of the paper. The out-of-plane deformation at atom 1 i s defined as y± = (X 2 - X±)/a + (X 3 - X±)/b + (X 4 - X-^/c where a, b and c are the bond lengths and the X's are the per-p e n d i c u l a r displacements of the atoms. Figure 36. The arrangement of atoms used to define a t o r s i o n . The t w i s t i n g of the bond between atoms 1 and 2 i s described by the coordinate <J> which i s defined as <f> l r 2 = k { ( x i - x 4 ) / a ~ < xi ~ x 3 ) / b - < x 2 " x 5 ) / d + ( X2 ~ x 6 ) / e } 7 3 B. C a l c u l a t i o n of the Out-of-Plane Force Constants of Benzene 1. Out-of-plane I n t e r n a l Coordinates of Benzene 11 8 4 Figure 37. The out-of-plane i n t e r n a l coordinates of benzene The out-of-plane i n t e r n a l coordinates of benzene are shown i n Figure 37. The numbers at the.atom p o s i t i o n s repre-sent out-of-plane wags and the numbers centered i n the carbon-carbon bonds represent t o r s i o n s about those bonds. 2. Method of C a l c u l a t i n g the Elements of F from G and the  Frequencies From equations 13 and 17 of Chapter V, t h a t i s 2 V = Rfc F R V.13 243 and 2 T = Rfc c f 1 R V.17 and from the transformation from i n t e r n a l coordinates to normal c o o r d i n a t e s , R = A Q 1 we get 2 v = Q t ^ Z A . Q 2 and 2 T = Qfc A 1 G _ 1 A Q 3 From the above two equations and from equations 11 and 12 of Chapter V, 2 T = Q t Q V . l l 2 V = Qfc A Q V.12 t -1 i t i s e a s i l y seen t h a t A G A = E 4 and Afc F A = A . 5 where A i s the diagonal matrix of the eigenvalues of the GF sec u l a r equation. Using the p r o p e r t i e s of matrices t h a t Tr(B C) = Tr(C B) and t h a t Det(B C)= Det (C B), where Tr(B) means the t r a c e of the matrix B, and Det(B) means the determinant of B, we get, from equations 4 and 5, T r ( A - 1 G F A) = Tr(G F) = Tr(A) 6 and a l s o , D e t ( A - 1 G F A) = Det(G F) = Det(A) 244 which are the equations used i n t h i s t h e s i s to f i n d the elements of the out-of-plane force constant m a t r i x , F, f o r benzene. The elements of G are r e a d i l y c a l c u l a t e d from the molecular geometry, by the method o u t l i n e d i n r e f . 29, and the r e l a t i o n s h i p between the fundamental frequencies, v , i n wave numbers, and the elements, A, of the diagonal matrix A i s : \ = 4TT2 V 2 C 2 3. Out-of-plane Symmetry Coordinates and Fundamental  Frequencies of Benzene . Symmetry coordinates are l i n e a r combinations of the i n t e r n a l coordinates chosen so as to transform l i k e 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 of the p o i n t group of the molecule. The symmetry coordinates are defined i n Table 41, which a l s o 5 contains the frequencies a s s o c i a t e d w i t h each out-of-plane symmetry species of benzene. Table 41. The out-of-plane symmetry coordinates of benzene Symmetry coordinate I n t e r n a l , coordinates -1 a Symmetry Frequencies (cm ) Values of A type C 6 H 6 C 6 D 6 C 6 H 6 C 6 D 6 1 1+2+3+4+5+6 A-2u 2 1-2+3-4+5-6 S 3 7-8+9-10+11-12 \ ^ £ ' -2 (D+2+3-2 (4)+5+6 5 7-9+10-12 L E 2 u 6 -2+3-5+6 > 7 -7+2(8)-9-10+2(11)-12 J 8 1-3-4+6 > 9 -1-2(2)-3+4+2(5)+6 > 5 10 7+8-10-11 11 7-8-2 (9)-10+11+2(12) J 673 990 707 967 398 846 496 829 599 787 345 600 0.2668 0.5774 0.2944 0.5509 0.0933 0.4216 0.1449 0.4048 0.2114 0.3648 0.0701 0 .2566 to cn A i s defined i n the t e x t the l i n e a r combinations are to be m u l t i p l i e d by a norm a l i z i n g f a c t o r . 246 and F- Matrices f o r the Out-of-plane Benzene Problem a) block. —2u C 6 H 6 C6°6 G F 0.9150 a 0.4933 b) B, block, - i g C 6 H 6 2.0381 1.5786 1.5786 4.6173 C 6 D 6 1.6164 0.6407 0.6407 2.3680 c) E_ block, —2u D 'x y 0 °1 G y z 0 0 0 0 X y ,o 0 y z . f o r CgHg x = 1. 6293 , y = - l . 7940, 6 x = 1.2075, y = -0. 9505, z = 1 fo- 0 °1 F e 0 0 0 0 a 0 247 d) E n block. — l q 'x 0 z o v G = 0 X 0 z z 0 y 0 0 z 0 where, f o r C gH 6 x = 1.0678, 6 = 1.4237, z = 1.2329 and f o r C rD, x = 0.6460, y = 0.8613 z = 0.7459. The symmetry co-ordinates S R and Sg form a degenerate p a i r , as do symmetry coordinates S-^Q and S ^ , and the two coordinates i n each p a i r have been chosen to be orthogonal. In a d d i t i o n , the p a i r s of symmetry coordinates S R , and S P , S^g have been chosen so th a t the sum of the F-matrix elements, f^^•, connecting them i s zero. I t can be shown th a t fg g = f^ Q , f10,10 = f l l , l l ' f8,10 = f 9 , l l * T h u S t h e F ~ m a t r i x i s F = 8,8 0 f 8,10 0 0 8,8 0 :8,10 8,10 0 f :10,10 0 f 0 8,10 0 10,10j The redundancy r e l a t i o n s i n t h i s block are: S10 ~ k S 8 = 0 a n d S l l kSg = 0 where k = J3 The F-matrix can then be s i m p l i f i e d by making the s u b s t i t u -t i o n s S 1 Q = kSg and S.^ = k S q 248 to give • F = / 2 f8,8 + 2 k f 8 , 1 0 + k f10,10 0 2 f8,8 + 2 k f 8 , 1 0 + k f10,10 The rows corresponding to symmetry coordinates S ^ Q and S^^ can then be omitted from the G-matrix, i n the manner 29 described by Wilson, Decius and Cross (page 140 e t seq.) to give G = v. 0 where the values of x are given above. For convenience the 2 sum f g g + 2kfg io + k f10 10 l s c a H e ^ $i so we have F = 0 0 The u n i t s f o r the out-of-plane f o r c e constants are mdyn A/radian' 1 

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