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The structure and vibrational spectrum of succinimide Fischer, Peter Hans Herman 1961

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THE STRUCTURE AND VIBRATIONAL SPECTRUM OP SUCCINIMIDE by Peter Hans Herman F i s c h e r B. Sc., U n i v e r s i t y of B r i t i s h Columbia, 1959 A t h e s i s submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of Master of Science i n the Department of Chemistry We accept t h i s t h e s i s as conforming to the r e q u i r e d standard The U n i v e r s i t y of B r i t i s h Columbia A p r i l 1961 In presenting 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 requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree tha 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 reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives. It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 3, Canada. Date /7<£?C<y J? / ' £ ^ y ' Acknowledgement I wish to express my s i n c e r e a p p r e c i a t i o n to P r o f e s s o r C. A. McDowell f o r h i s con t i n u e d i n t e r e s t and he l p d u r i n g the course of t h i s work, and to P r o f e s s o r C. R e i d f o r many h e l p f u l h i n t s and d i s c u s s i o n s . Thanks are due to Mr. Dempster f o r h i s help i n programming of the computer, to Mr. L. Muenster f o r p r e p a r a t i o n of some of the compounds employed, and to Messrs. Muehlchen and Hawkins f o r help i n d e s i g n i n g and b u i l d i n g of apparatus. I am a l s o i n d e b t e d to Mrs. M. Z e l l f o r her pa t i e n c e i n r e c o r d i n g innumerable s p e c t r a and to the N a t i o n a l Research C o u n c i l of Canada f o r a s t u d e n t s h i p . - i i -ABSTRACTo Due to the many c r y s t a l l o g r a p h i c and s p e c t r o s c o p i c anom-a l i e s found i n i n v e s t i g a t i o n s of amides, polyamides, and imides, s u c c i n i m i d e suggested i t s e l f as an i n t e r e s t i n g com-pound f o r s p e c t r a l i n v e s t i g a t i o n s The spectrum of s o l i d s u c c i n i m i d e ( KBr p e l l e t ) was r e -corded i n the range I4.OOO - 2$0 cm"*1, whereas the s p e c t r a of vapour, s i n g l e c r y s t a l , and s o l u t i o n s of s u c c i n i m i d e i n a v a r i e t y of s o l v e n t s and at v a r y i n g c o n c e n t r a t i o n s , were ob-t a i n e d i n the r e g i o n I4.OOO - 250 cm"^ Por the r e c o r d i n g of vapour s p e c t r a , and f o r the growth of t h i n s e c t i o n s of s i n g l e c r y s t a l s , s p e c i a l apparatus and techniques were d e v i s e d and are d e s c r i b e d i n d e t a i l s N - d - s u c c i n i m i d e , N - h - s u c c i n i m i d e - d^, N - d s u c c i n i m i d e - d|^, and v a r i o u s r e l a t e d compounds were a l s o i n v e s t i g a t e d . The a b s o r p t i o n bands of s u c c i n i m i d e have been a s s i g n e d by comparison with s p e c t r a of r e l a t e d compounds and by study-i n g a s s o c i a t i o n phenomena and i s o t o p e s u b s t i t u t i o n e f f e c t s . An PG m a t r i x treatment has been undertaken and agreement bet-ween c a l c u l a t e d and observed f r e q u e n c i e s i s good when o n l y a minimum number of i n t e r a c t i o n constants are employedo The anomalous behaviour of s u c c i n i m i d e i n the Amide I I and Amide I I I r e g i o n s has been e x p l a i n e d by the assumption of a dimer, as has the 3080 cm""l band. S o l u t i o n s t u d i e s i n d i c a t e t h a t the dimer e x i s t evn i n moderately c o n c e n t r a t e d s o l u t i o n . - i i i -CONTENTSc Page Acknowledgement i A b s t r a c t i i L i s t of Tables v L i s t of F i g u r e s and P l a t e s v i i Chapter I. I n t r o d u c t i o n 1 I - l . The Problem 1 I- 2 . Methods of I n v e s t i g a t i o n LL Chapter I I . Experimental Procedure 7 I I - l . Chemicals 7 I I - 2 . Apparatus and Methods 8 I I - 3 . R e s u l t s lk Chapter I I I . S t r u c t u r e of Succinimide 3k Chapter IV. Theory and D i s c u s s i o n 38 I V - l o Symmetry of I n t e r n a l and Normal Coordinates k® I V - 2 . S e l e c t i o n Rules 53 IV - 3 . Isotope E f f e c t and Product Rule 58 IV-ij.. Assignment of Observed Frequencies 60 IV-5« P o t e n t i a l and K i n e t i c Energy i n I n t e r n a l Coordinates 6k IV - 6 . Symmetry Coordinates 70 IV - 7 . F a c t o r e d P o t e n t i a l and K i n e t i c Energy F u n c t i o n s 79 IV-8 . C a l c u l a t i o n of Frequencies 79 - i v -CONTENTS ( c o n t ' d . ) . Page IV - 9 » D i s c u s s i o n and Conclusions 8 5 Appendix I . P r e p a r a t i o n of N-h-succiniraide-di^ 8 9 Appendix I I . F^k i n Symmetry Coordinates 9 0 Appendix I I I . A 2 and B 2 G M a t r i c e s 92 B i b l i o g r a p h y 9 3 LIST OF TABLES. Page Table 1. A b s o r p t i o n Bands of I s o t o p i c a l l y S u b s t i t u t e d Succinimides 16 2. I n t e r m o l e c u l a r Bond Dis t a n c e s of Succinimide 36 3» Symmetry Species of Normal Coordinates l\£ k> " " of In-plane Modes 5 l 5o K " of Out-of-plane Modes 52 6. 11 11 of CH Coordinates 53 7. Character of the P o l a r i z a b i l i t y 55 8. Symmetry Species of B i n a r y Combinations 56 9. Force Constants of S t r e t c h i n g Coordinates 65 10. Force Constants of Bending and I n t e r a c t i o n Coordinates 66 11. f o r In-plane Coordinates 67 12. Force Constants f o r Out-of-plane Coordinates 69 13. G t t ' ^ o r O ^ - o f - p l a n e Coordinates 6 9 l l | o A]_ Symmetry Coordinates 72 15* B X " u 72 I 6 0 A 2 » " 72 17. 3 2 n " 73 18. F Terms of A]_ Symmetry Coordinates 7l± 19. F " of B 1 " ** 75 - v i ~ L I S T OP TABLES ( c o n t ' d . ) a Page 20« F Terms o f A 2 Symmetry C o o r d i n a t e s 75 21. P 11 o f B 2 " ,,; 75 22. G E l e m e n t s o f Aj_ Symmetry C o o r d i n a t e s 76 23 o G " o f B x " 1 5 77 2l+ e G " o f A 2 n n 78 25. G w o f B 2 1 1 " 79 26. F o r c e C o n s t a n t s o f A]_ Symmetry C o o r d i n a t e s 80 27« E i g e n v a l u e s and F r e q u e n c i e s o f A^ V i b r a t i o n s 83 2 8 . F o r c e C o n s t a n t s o f Symmetry C o o r d i n a t e s 81}. 29s E i g e n v a l u e s and F r e q u e n c i e s o f B]_ V i b r a t i o n s 85 - v i i -LIST OP FIGURES AND PLATES<• F i g . 1. 2. 3* k. 5. 6. 7o 8. 9c 10. C o n s t r u c t i o n D e t a i l of Vapour C e l l Heater D e t a i l P o l a r i z o r D e t a i l Succinimide Spectrum (i+OOO-650 cm" 1) ! t " (6^0-250 cm - 1) " "' , Vapour " 11 , i n THF u 11 , i n 1 , 2-diaeth-oxyethane , i n Chloroform , i n THF i n v a r i o u s c o n c e n t r a t i o n s To f o l l o w page 8 8 u IS tt l ie Spectrum of N-d-succinimide 12. it of N-h-succinimide-dj^ 13. ti- of N=d-succinimide-dj^ 11+. re of N - C l - s u c c i n i m i d e 15. tt of N-Br-succ inimide 16. tt of 2 - P y r r o l i d i n o n e 17« tt of P y r r o l i d i n e 18. tt of Hydantoin 19 o ti of G l y c i n e Anhydride 20. tt of S u c c i n i c Anhydride 21. Succinimide Molecule 22. Succinimide C r y s t a l S t r u c t u r e 16 3k 36 - v i i i -LIST OP FIGURES AND PLATES (cont'd.). To follow page Pi g . 23o Symmetry Elements of Succinimide I4.I 2I4.0 Internal Coordinates I4.6 25. In-plane Coordinates I4.9 26. Postulated Succinimide Dimer 86 Plate Io Crystal Growing Apparatus 11 I I . C r y s t a l l i z a t i o n Chamber 11 -1= CHAPTER 1. INTRODUCTION. 1 - 1 . The P r o b l e m . In i n v e s t i g a t i o n s o f a m i d e s , p o l y a m i d e s , and i m i d e s o f v a r i o u s t y p e s , b o t h b y s p e c t r o s c o p i c and by c r y s t a l l o g r a p h i c methods, s e v e r a l i n t e r e s t i n g b u t n o t a l w a y s e x p l i c a b l e phenomena have been o b s e r v e d . I n X - r a y c r y s t a l l o g r a p h i c i n v e s t i g a t i o n s o f v a r i o u s amides ( 1-lj. ) a s h o r t e r C - N bond d i s t a n c e t h a n i s commonly a s s o c i a t e d w i t h a C - N s i n g l e bond h a s been o b s e r v e d . However, a c o r r e s p o n d i n g i n c r e a s e i n t h e C - 0 bond d i s t a n c e makes a s i m p l e r e s o n a n c e e x p l a n a t i o n v e r y a t t r a c t i v e , i . e . ° ^> £>~ R e p r e s e n t a t i v e bond l e n g t h s , as i n a c e t a m i d e ( 5 )> a r e CN 138A ( n o r m a l s i n g l e bond d i s t a n c e , l.]|7A ) and CO 128A ( n o r m a l d o u b l e bond d i s t a n c e , 1.22A ) . In s u c h c a s e s i t seems r e a s o n a b l e t h a t t h e e l o n g a t i o n o f t h e CO bond b y O.OI4. t o 0<.06A and t h e c o n t r a c t i o n o f t h e CN bond by 0.09 t o 0.11A c a n n o t be due t o a h y d r o g e n - b o n d i n g phenomenon a l o n e . Many o t h e r a m i d e s , however, e x h i b i t an a n a l o g o u s o r e v e n l a r g e r c o n t r a c t i o n o f t h e CN bond w i t h o u t the c o r r e s p o n d i n g i n c r e a s e i n t h e CO d i s t a n c e ( 6-12 ) , s u c h t h a t a r e s o n a n c e t y p e p i c t u r e does n o t seem a p p l i c a b l e . To t h i s d a t e no s a t i s -f a c t o r y e x p l a n a t i o n i s a v a i l a b l e . I n t h e s p e c t r o s c o p i c f i e l d t h e knowledge o f t h e amide s y s t e m ' s v i b r a t i o n i s i n an e q u a l l y u n s a t i s f a c t o r y s t a t e . -2-Whereas primary and secondary amides can t h e o r e t i c a l l y e x i s t as e i t h e r a keto or e n o l form, both of which would be s t a b i l i z e d by e l e c t r o n d e r e a l i z a t i o n , i t has been found through chemical evidence and through d i p o l e and i n f r a r e d data, t h a t the k e t o n i c form i s by f a r the predominant one. In consequence, a l l amides are expected to show a c a r b o n y l a b s o r p t i o n band. T h i s band, whose p o s i t i o n i s near 16^0 cm" 1 i n s o l i d s , i s markedly a f f e c t e d by n e i g h b o r i n g groups and by hydrogen - bond formation.. I t i s thus f a i r l y w e l l c h a r a c t e r -i z e d . In a d d i t i o n s e v e r a l o t h e r s t r o n g bands due to the amide group are observed, which however have not been d e f i n i t e l y a s s i g n e d and are the o r i g i n of much c o n t r o v e r s y . Primary and secondary amides show a s t r o n g band i n the 1600 - 1500 cm"*1 r e g i o n , which i s absent i n the s p e c t r a of t e r t i a r y amides, c y c l i c lactams, and many s p e c i a l s t r u c t u r e s i n v o l v i n g the CONH grouping. The band i s commonly r e f e r r e d to as the a m i d e l l bando One commonly accepted e x p l a n a t i o n of t h i s amide I I band i s that i t a r i s e s from the i n - plane NH deformation mode, t h i s view being supported by the band's absence i n t e r t i a r y amides ( 13 ) and by d e u t e r a t i o n s t u d i e s ( 1I+, 15 ) 3 by the d i r e c t i o n s of the frequency s h i f t s accompanied by changes of s t a t e and by p o l a r i z a t i o n s t u d i e s ( 16 )« T h i s e x p l a n a t i o n , however, i s not e n t i r e l y s a t i s f a c t o r y as i t f a i l s , f o r i n s t a n c e , to e x p l a i n the band's absence i n - 3 -c y c l i c lactams. Whereas t h i s o b j e c t i o n c o u l d p o s s i b l y be overcome, other r e l e v a n t o b j e c t i o n s remain. Among these are i n e x p l i c a b l e Raman s p e c t r a and ambiguous d e u t e r a t i o n r e s u l t s . A second e x p l a n a t i o n i s t h a t the band i s due to a CN s t r e t c h i n g motion i n which the CN l i n k a g e possesses c o n s i d e r -able double bond c h a r a c t e r ( 17 ). As b e f o r e , s e v e r a l f a c t s support t h i s theory while others are i n disagreement. Another e x p l a n a t i o n which has r e v i v e d the two molecular-s t a t e t h e o r y i s due to Lenormant ( 1 8 , 19 ) . Here both the amide I and amide I I bands are a t t r i b u t e d to c a r b o n y l v i b r a t i o n s o f the normal keto form and of an a s s o c i a t e d dimer, r e s p e c t i v e l y . A weakening of the theo r y i s p r o v i d e d by G i e r e r ' s observatiom ( 20 ) that the amide I I band p e r s i s t s i n the vapour phase spectrum. These views have been r e c o n c i l e d , at l e a s t p a r t l y , by F r a z e r and P r i c e ( 2 1 , 22 ), who p o i n t out that the motion of any s i n g l e p a i r of atoms i n the CONH system cannot be co n s i d e r e d alone© They s t a t e t h a t a c o u p l i n g of CO and CN motions lea d s to an asymmetric OCN mode ( amide I ) and a symmetric mode which i s i n the frequency r e g i o n o f the i n - plane NH bending mode. Coupling between these two motions takes p l a c e to r e s u l t i n an asymmetric mode ( amide I I ) and a symmetric mode ( amide I I I ) . Th i s view of mixed v i b r a t i o n s has found almost g e n e r a l acceptance, although s m a l l d i s c r e p -a n c i e s s t i l l remain ( 23* 21). ) . Further ambiguities are observed i n the spectra of com-pounds containing specialized structures such as -C0NHC0-, This group i s found i n several c y c l i c compounds, among them hydantoin, succinimide, the purines, and related compounds0 In t h e i r spectra, the carbonyl absorptions appear as two widely separated bands, one usually having much greater i n t e n s i t y than the other ( $ ) a It has been suggested that the two bands are due to a mechanical coupling of the GO motions, but no de f i n i t e assignement and explanation i s available« In addition, many -CONH- group containing compounds show a band near 3080 cm" 1in the inf r a r e d i n addition to the normal NH absorption bands i n t h i s region of the spectrum. The band was at f i r s t t e n t a t i v e l y assigned to an NH absorpt-ion ( 26 ). Later work, however, has shown other factors to be involved and a de f i n i t e assignement i s lacking at t h i s time o The presence of the above ambiguities suggested succin-imide as an in t e r e s t i n g compound for spectral investigation and l e d to the experiments and results which appear i n the present paper. 1 - 2 e Methods of Investigation. In making assignements to the absorption bands of succinimide, f i v e d i f f e r e n t approaches have been u t i l i z e d . The f i r s t of these i s simply a compar-ison of the succinimide spectrum with the spectra of mole-c u l e s c o n t a i n i n g s i m i l a r or p r e f e r a b l y i d e n t i c a l s t r u c t u r a l u n i t s . The compounds which were thus i n v e s t i g a t e d are: 2 - p y r r o l i d i n o n e , NHC0CH 2CH 2CH 2; p y r r o l i d i n e , NHCH2 C H 2 C H 2 C ; s u c c i n i c anhydride, 0G0CH 2CH 2CQ; N - c h l o r o - s u c c i n i m i d e , NG1G0CH 2CH 2G0; N - bromo - s u c c i n i m i d e , NBrC0GH 2CH 2G0; hydantoin, NHC0NHCQCH 2; 2,5 - d i k e t o p i p e r a z i n e , N H C 0 C H 2 N H C 0 C H 2 » The s p e c t r a of some s i m p l e r , but r e l a t e d compounds, were a l s o r e c o r d e d , these compounds being succinamide NH 2C0CH 2CH 2C0NH 2, oxamide NH 2C0C0NH 2, and s e v e r a l s i m p l e r amides. The second method i s the study of d i s s o c i a t i o n phenomena. Here s p e c t r a of v a r i o u s c o n c e n t r a t i o n s of su c c i n i m i d e i n v a r i o u s s o l v e n t s are re c o r d e d and the e f f e c t o f d i l u t i o n ( i . e . breaking of hydrogen bonds ) i s observed. I t i s obvious t h a t the e f f e c t o f both s o l v e n t and c o n c e n t r a t i o n must be taken i n t o c o n s i d e r a t i o n i n e v a l u a t i n g such d a t a . A spectrum of the monomeric species was a l s o o b t a i n e d ( su c c i n i m i d e vapour ) . T h i r d l y , i s o t o p i c s u b s t i t u t i o n on the n i t r o g e n and carbon atoms should y i e l d v a l u a b l e i n f o r m a t i o n about bands i n v o l v i n g X - H modes» N - bromo - su c c i n i m i d e and N - c h l o r o - s u c c i n -imide were not c o n s i d e r e d i n t h i s category, as i t was f e l t t h a t the s i z e o f the c h l o r i n e and bromine atoms would cause d i s t o r t i o n of the c r y s t a l l a t t i c e ( perhaps even the molec-u l a r u n i t ) and thus invoke changes i n the spectrum not due to X - H modes a l o n e s -6-A f o u r t h method was to u t i l i z e p o l a r i z e d i n f r a r e d r a d i a t i o n on a s i n g l e , o r i e n t e d c r y s t a l of s u c c i n i m i d e . Whereas t h i s would not y i e l d bond d i r e c t i o n s , but r a t h e r the d i r e c t i o n s of the t r a n s i t i o n moments of the v i b r a t i o n s i n v o l v e d , i t would n e v e r t h e l e s s c h a r a c t e r i z e c e r t a i n bands. The f i n a l method, a t h e o r e t i c a l c a l c u l a t i o n of the s u c c i n -imide monomer's a b s o r p t i o n bands, i s more of a check f o r p r e -vious assignments, than a method of band c h a r a c t e r i z a t i o n s Here, the w e l l - known PG m a t r i x method of W i l s o n i s used to c a l c u l a t e f r e q u e n c i e s and f o r c e c o n s t a n t s e -7-CHAPTER 2 . EXPERIMENTAL WORK. 2 - 1 . Chemicals. The chemicals which were s p e c t r o s c o p i c a l l y i n v e s t i g a t e d are the f o l l o w i n g : S u c c i n i m i d e : - Eastman Kodak # 1257> reagent grade, r e c r y s t -a l l i z e d twice from 1 0 0 $ e t h a n o l and sublimed under vacuum, m. p» 1 2 5 - 126°C. N - d - s u c c i n i m i d e : - Prepared by exchanging s u c c i n i m i d e with a 1 0 0 mole percent excess of 9 9 * 8 2 $ D 2 0 f i v e times. N - h - s u c c i n i m i d e - d^:- S y n t h e z i z e d from 1 , 2 - dibromo-ethane - d^ ( Merck # 6 O C D 9 9 6 ) v i a n i t r i l e , d i b a s i c a c i d , and ammonium s a l t . P y r r o l i d i n e : - Eastman Kodak # P 1 3 3 2 , p r a c t i c a l grade, p u r i -f i e d by d i s t i l l a t i o n , b. p. 87 - 8 8 . 5 ° C . 2 - P y r r o l i d i n o n e : - Eastman Kodak # P 6 9 6 I , p r a c t i c a l grade, p u r i f i e d by d i s t i l l a t i o n , b. p. 2i+ij_ - 2l4-6°C. N - c h l o r o - s u c c i n i m i d e : - K & K # 1 8 5 3 8 , reagent grade, sublimed under vacuum. N - bromo - s u c c i n i m i d e : - K & K # 8o57# reagent grade, sublimed under vacuum. Hydantoin:- Eastman Kodak # 3131+* reagent grade, sublimed under vacuum. 2 , 5 - D i k e t o p i p e r a z i n e : - H. M. Chemical Co., L o t # J+ . 9 7 . 2 5 * sublimed under vacuumo S u c c i n i c anhydride:- Eastman Kodak # 8 6 8 , reagent grade, sublimed under vacuum. - 8 -A l l other chemicals employed were of reagent grade p u r i t y . S o l v e n t s were p u r i f i e d by f r a c t i o n a l d i s t i l l a t i o n and d r i e d as w e l l as was p r a c t i c a l l y f e a s i b l e * 2 - 2 . Apparatuso ^he s p e c t r a were re c o r d e d on a P e r k i n -Elmer I n f r a r e d Spectrophotometer, Model 2 1 , u s i n g NaCl o p t i c s . The s p e c t r a below 6$0 cm~ x were re c o r d e d on a P e r k i n -Elmer instrument, Model 1 1 2 , u s i n g CsBr o p t i c s . S p e c t r a were o b t a i n e d from KBr pressed d i s c s , N u j o l and hexachlorobuta-diene m u l l s , s o l u t i o n s , vapour, and s i n g l e c r y s t a l . F o r the growth of s i n g l e c r y s t a l s and f o r the r e c o r d i n g of vapour and c r y s t a l s p e c t r a , s p e c i a l p i e c e s of apparatus had to be c o n s t r u c t e d . These are d i s c u s s e d below. Vapour C e l l : The s p e c t r a of s u c c i n i m i d e i n the vapour phase were o b t a i n e d by f i t t i n g a 5 cm g l a s s c e l l w i t h NaCl end windows, and s e a l i n g the c e l l under h i g h vacuum, a f t e r a s m a l l amount of the sample to be i n v e s t i g a t e d had been i n t r o d u c e d ( P i g . 1 )o The c e l l assembly was then p l a c e d i n a h e a t i n g arrangement ( P i g . 2 ), and the whole i n s e r t e d i n the l i g h t - p a t h of the spectrophotometer. R a i s i n g the temp-e r a t u r e to 1 5 0 - 160°C gave a s u f f i c i e n t vapour p r e s s u r e f o r the spectrum to be r e c o r d e d without the use of an o r d i n a t e s c a l e expander. S i n g l e C r y s t a l Growth: The s i n g l e c r y s t a l s of s u c c i n i m i d e were grown i n a s p e c i a l l y designed apparatus, s i n c e the more c o n v e n t i o n a l methods of s u b l i m a t i o n or growth from s o l u t i o n Vacuum Tap TV N a C l Window Set Screw 777771 Al H o l d e r Po ly thene W a s h e r S i l i cone Grease F i g . I Construction Details of Vapour Cell. Lid - T h e r m o m e t e r I) •4 \// /> * // // v g a # . / a t <? z: 117 VAC F i q . 2 H e a t e r D e t a i l Window H o l d e r N a C l Window C e l l H o i de r T o a s t e r E l e m e n t -11-y i e l d e d u n s a t i s f a c t o r i l y bulky c r y s t a l s . Attempts to p o l i s h and c l e a v e these c r y s t a l s to o b t a i n s p e c t r o s c o p i c a l l y t h i n s e c t i o n s were u n s u c c e s s f u l A f t e r the c r y s t a l growing apparatus had been set up as shown i n P l a t e I, and a f t e r the sample c o n t a i n e r had been f i l l e d w i t h powdered s u c c i n i m i d e , the system was p l a c e d under vacuum* A f t e r e v a c u a t i o n of both the l a r g e c a v i t y and the space between the NaCl d i s c s , the upper p o r t i o n of the s t a i n -l e s s s t e e l c r y s t a l l i z a t i o n chamber ( P l a t e I I ) was brought to a temperature of c a . l8°C by means of a c o l d f i n g e r i n -s e r t e d i n an o i l bath i n the Dewar top of the apparatus. The lower p a r t of the chamber was heated to c a . 100°C, while the sample c o n t a i n e r was allowed to r e a c h c a . 150°C. A f t e r e q u i l i b r i u m had been e s t a b l i s h e d , the needle valve was opened s l i g h t l y to allow e n t r y of the s u c c i n i m i d e vapour i n t o the NaCl c a v i t y . C r y s t a l l i z a t i o n s t a r t e d at the c o l d e r p a r t of the c a v i t y and proceeded toward the h o t t e r p a r t , u n t i l a f t e r u s u a l l y 12 to 15 hours the c a v i t y was f i l l e d . O r i e n t a t i o n and q u a l i t y of the c r y s t a l was observed w i t h c r o s s e d p o l a r o i d g l a s s e s . In the above manner, i t was found p o s s i b l e to grow s i n g l e c r y s t a l s up to 0.5 cy 0.5 cm, a f t e r which s i z e had been a t t a i n e d , Imperfections g e n e r a l l y began to appear. The t h i c k n e s s of the c r y s t a l was c o n t r o l l e d by means o f T e f l o n and mica washers r a n g i n g from 0.03 to 0.10 mm0 S i l v e r C h l o r i d e P o l a r i z o r . The p o l a r i z e r which was employed was a s i x AgCl - p l a t e model, P e r k i n - Elmer # 127 - ll6i+. 2 cm -11+-At the o r i e n t a t i o n f a v o u r e d by the instrument the t r a n s -m i s s i o n v a l u e s were: 2.5 microns - 1+0$, 1+ microns - l+3$> 6 microns - 1+6$, t e n microns - 50$, and 15 microns - 1+1$. F i g u r e 3 i s a schematic drawing of the p o l a r i z e r . 2 - 3» R e s u l t s . The s p e c t r a which were o b t a i n e d are shown i n diagrams 1+ to 20. I t w i l l be n o t i c e d t h a t a spectrum employing p o l a r i z e d r a d i a t i o n on a s i n g l e c r y s t a l i s not presented due to the f a c t t h a t the regions o f primary i n t e r e s t , i . e. the NH, CO, and CN r e g i o n s , were completely u n r e s o l v e d . A summary of the p o s i t i o n of a b s o r p t i o n bands f o r s u c c i n i m i d e , N - h - su c c i n i m i d e - dj^, and N - d - s u c c i n -imide ( a l l p o l y c r y s t a l l i n e i n KBr d i s c ) are giv e n i n Table 1. i n the t a b l e , t c s u , "mu, "w", and "vw" i n d i c a t e s a st r o n g , medium, weak, and very weak band, r e s p e c t i v e l y . Fig. 3 Polarizor Detail -16-Table 1« Absorption Bands of the I s o t o p i c a l l y Substituted Succinimides* Succinimide 3162 cm"} 3080 s 2955 w 2800 m 2610 w 251+0 w 1829 m 1783 sh 1771 s 1695 s 11+31+ m 11+20 ra 11+00 w 1376 s 1361 sh 1296 s 121+1 m 1193 s 1001+ s 937 s 852 s 822 s 720 w 639 s 552 s 1+21+ s 370 w 359 w 352 m 337 w 326 m 316 w 30i+ s 290 s 280 s W-d-succinimide 3165 cm~l, w 3080 w 2957 w 2535 w 2392 s 2325 s 2200 m 1771 s 1685 s 11+32 m 11+06 w 1363 s 1300 s 1273 3 1236 m 1195 s 1100 s 1003 s 931+ VVJ 81+8 s 821+ s 751+ m 633 s 1+18 s unresolved N-h-succinimide-d -1 3160 cm 3070 s 2792 m 2610 vw 2538 vw 1825 m 1780 sh 1768 s 1690 s 11+10 m 1363 s 1285 s 1271 s 121+1 s 1192 s 1122 m 1080 m 1010 s several peaks 81+0 s several peaks 626 s 1+11 s unresolved 4 0 0 0 3 0 0 0 2 0 0 0 1 5 0 0 C M - i 1 0 0 0 9 0 0 8 0 0 7 0 0 "— \ n r \ a f / \ f j J \ A f \ / 1 U \ / / \ 1 / V / V / J V -1+ 1— t 1 IN v' 137 3 4 Fig. 4 7 8 9 1 0 11 W A V E L E N G T H ( M I C R O N S ) 1 2 1 3 1 4 1 5 S P E C T R U M N O ^ I A . S A M P L E ORIGIN_£JSJ2£Z P U R I T Y Reagent PHASE SjQlid_ THICKNESS, L E G E N D , 1 2. D A T E . O P E R A T O R . R E M A R K S . K B r P e l l e t 1 . 2 / 2 0 0 mg co co C m IE — i Z o THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 0.0 .10 £ 2 0 < fT £.30 V o \ ^.40 < C.50 .60 .70 1.0 oo lui i , 1,1. i. i i 1 , i i, i i - 1 1 i, i, , M I . i i I ; 1 , ! i 1 1 1 1 ,—1 I J . .. 1 .I_1.J_L. ! i i ,J 1-1,, . i . ,1 f—1—h i I L—1 ,1 r\ / \ A / \ / / • f\ / / 1— __*iiatffitaa Fig. 5 W A V E L E N G T H ( M I C R O N S ) S P E C T R U M N O . _ E 5 ^ A O R I G I N E K I 2 5 7 L E G E N D R E M A R K S S A M P L E 1. C s B r P e l U t S u c c in imide PUR ITY R e a g e n t 7. P r i s m P H A S E S o l i d D A T E T H I C K N E S S O P E R A T O R CO CO C m 12 — i 70 C Z c m THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4000 3000 2000 1500 11 j ' ' I '. • ' ' 1 ' 1 ,1 1 I 1 1 1 ,1 1 1 .1 I u—I i . l i i L C M-1 1000 900 800 1 1 1 1 1 1 1 1 i i ' ' i ' 1 ' .' ' ' 1 ' ' i ' 700 3 4 Fig- 6 7 8 9 10 11 12 13 14 15 WAVELENGTH (MICRONS) SPECTRUM N O . _ 5 D A ^ O R I G I N F K 1 2 5 7 I E G E N D R E M A R K S S A M P L E 1- ! J C • * C s n r r.iMiMifiF P U R I T Y R e g e n t 9 . P H A S E Vapor D A T E T H I C K N E S S 4.0 cm O P E R A T O R CO CO C m z O THE PERKIN-ELMER CORPORATION. NORWALK, CONN. 4000 3000 2000 1500 0.0 CM-i 1000 900 800 700 f h f l l ^ — - ' — • — / ——— A / / V I / / • 1 -" i f V — |N FRACC v? 137 .10 £ 2 0 < £.30 o 2-40 < . 50 .60 .70 1.0 o o 3 4 5 6 7 8 9 Fig. 7 10 11 12 13 14 15 WAVELENGTH (MICRONS) SPECTRUM NO. 643 ORIGIN EK 1257 LFGEND REMARKS SAMPLE 1. 0.5 M in Tetr a -Succinimide PURITY Reaaent 2. hydrofuran PHASE Solution DATE THICKNESS OPERATOR CO C/J >"° TJ LJ z THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4000 3000 2000 1500 CM-i 1000 900 ' ' ' I 1 1 ,' 1 1 1 1 1 ' 1 .' 1 U I L_ I U 1 I 1 , I . I ,1 i i i i I i i i 800 700 WAVELENGTH (MICRONS) SPECTRUM NO. 670 SAMPLE Succinimide ORIGIN EK 1257 PURITY Rpnqpnt PHASE Solution THICKNESS, LEGEND, DATE. OPERATOR. REMARKS. 0.5M in 1,2- Pi-rn ethoxyethone CO > -D I— rn THF PFRKIN-FLMFR CORPORATION. NORWALK. CONN. 4000 3000 2000 1500 CM-i 1000 900 800 700 1 I I I I I I I I I I ) I I I • I | I I I I I I L I I I | WAVELENGTH (MICRONS) SPECTRUM NO. 1006 ORIGIN EK1757 LEGEND REMARKS SAMPLE 1. 0.5 M in Chloroform Su ccinimide PURITY ReaQent 7. PHASE Solution DATE THICKNESS OPERATOR CO CO C m r n TO O THE PERKIN-ELMER CORPORATION, NORWALK, CONN. SPECTRUM NO, SAMPLE O O o CO < LU ~9> CQ E O O Q Z LU o LU ^ C N LU h -< O < CY. LU Q_ O z o o ZD o (/) LU C O < X to to LU Z u CD to 6 Z Z) r— u LU Q_ C O 0> T 3 C y o CO I o o O O O O O O O O 0 C N co u-> O N r-: Q 33'NVoclOSaV' 4 0 0 0 3 0 0 0 0.0 2 0 0 0 1500 C M - i t . l i 1 I i ! i I 1000 9 0 0 8 0 0 7 0 0 S P E C T R U M N Q . 9 1 7 Y O R I G I N L E G E N D R E M A R K S S A M P L E 1. KRr Pellet N - D - succinimide-d/j PURITY ? . P H A S E Solid D A T E T H I C K N E S S O P E R A T O R CO > TJ I— m c o TJ m O —I TO c z o THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4 0 0 0 3 0 0 0 2 0 0 0 1 5 0 0 0.0 C M - i I O O O 9 0 0 8 0 0 /oo /I J 1 , / J / / \ 1/ / 1 1 / / / / / £ IN FRACORDr-fe/ 137-1280 . 10 £ 2 0 < £ . 3 0 o £ • 4 0 < . 5 0 .60 .70 1.0 o o 3 4 5 6 7 8 9 10 11 12 13 14 15 W A V E L E N G T H (MICRONS) Fig. 14 SPECTRUM N O . 791 O R I G I N K&K L E G E N D REMARKS SAMPLE 1. Mulls N- C l - succinimide PURITY Reagent 7. PHASE Solid D A T E THICKNESS O P E R A T O R CO CO C r n z o THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4000 3000 2000 1500 0.0 CM-i 1000 900 800 700 11 1 1 1 1 1 1 1 1 I I I ' 1 I 1 1,1 1 1 1 1 1 1 1 1 1 I 1 1 i I i i 1 1 i i i 1 , i 1 J_L. 1,-1-1— i i i I 1 1 L . I 1 I L _ _ l , h 1 j ' 1 4 / f 1 / • \ V — i ini wroga 5> 137-1280 .10 UJ £ 2 0 < £.30 o £ 4 0 ^ 5 0 .60 .70 1.0 o o 8 9 10 11 12 13 14 15 Fig.15 WAVELENGTH (MICRONS) SPECTRUM NQ.7QI ORIGIN KftK 8057 LEGEND REMARKS SAMPLE 1. Mulls N- Br - su ccinimide PURITY Reagent ? . PHASE Solid DATE THICKNESS OPERATOR CO CO K g z o THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4 0 0 0 3 0 0 0 2 0 0 0 1500 0.0 C M - i 1000 9 0 0 8 0 0 7 0 0 1 1 1 1 1 1 1 LJ_J_1 I L. J _ 1 1. J — I . . 1 i 1 i 1 i ! i 1 i i i 1 i i 111 J | 1 1 1 1 11, ,i i, i , i , i i , 1 < J—1—u I 1 i i r / r /I \ vi. A / \ \ w r \/ \ V / 4 -i — |N .10 LU £ 2 0 < £ . 3 0 o S - 4 0 < . 5 0 .60 .70 1.0 oo 3 4 5 6 7 8 9 Fig. 16 W A V E L E N G T H ( M I C R O N S ) 10 11 12 13 14 15 S P E C T R U M NO._Z8J_ S A M P L E -Z" PyrrQlidinone ORIGIN Fisher P696I PURITY Practical PHASE_Li<uud_ THICKNESS_Fii£TL L E G E N D , D A T E . O P E R A T O R . R E M A R K S . PiSt, (b.p.244-?46°C) CO CO C m I -o THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4 0 0 0 3 0 0 0 0.0 2 0 0 0 I5UU CM-1 IUU0 9 0 0 8 0 0 7 0 0 — 1 \ \ / V 7 / \ A \ f\ J / / — 1 IN FRACORD- 137-1280 . 10 £ 2 0 < £.30 0 £•40 ^ 5 0 .60 .70 1.0 o o 3 4 Fig. 17 7 8 9 10 11 W A V E L E N G T H (MICRONS) 12 13 14 15 SPECTRUM NO.JZJ£2_ SAMPLE Pyrrolidine  O R I G I N EK PI33? PURITY PrnctiCQl PHASE_JLUiiid THICKNESS_FiliTL LEGEND. 1 2. DATE. OPERATOR. REMARKS. Dist.fh p .87-f l8 5°C) C O C O 1> T J C m S 2 Z o THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4 0 0 0 3 0 0 0 0.0 2 0 0 0 1500 C M - i 1000 9 0 0 8 0 0 700 m i l l . 11 i I i i, i i 1 I - ,1 ,1, , , 1 , 1 , 1 1 1 1 1 1 1 1 I , 1 1 1 - U 1 J | 1111 j 111 i,.U i i i i ,i | • i 1 |—1 u r 1 1 > / J /I V J / l /} / \ ( / / \J / \ / "\ / V / / / 1 . FRACORD •-•.<•.' 137-1280 . 1 0 £ 2 0 < £ . 3 0 0 £ . 4 0 < . 5 0 .60 .70 1.0 o o 3 4 Fig. 18 8 10 11 12 13 14 W A V E L E N G T H ( M I C R O N S ) 15 S P E C T R U M NO. 664 ORIGIN F_K 3134 LEGEND REMARKS S AMPl E 1. KBr Pellet Hydantoin PURITY Reagent 7 PHASE Solid DATE THICKNESS OPERATOR CO > i — m CO TJ m O —! ?3 C z o THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4 0 0 0 3 0 0 0 0 .0 2 0 0 0 1 5 0 0 C M - i 1 0 0 0 9 0 0 8 0 0 7 0 0 IIII111 1 1 1 1 1 1 1 i i i, i i 1 i ,1 i 1 1 ., 1 „ In., ! 1 _ ! j i .1 .... J l l l l l i , , , 1 , , M-I.J-, 1 1 1 1 > • i J i ) i—i—J—1—;—i i. / \ i f\ f\ / / 1 1 \ / i - V \ A — • I 1 i — IN F R A C O R D . 1 3 7 - 1 2 8 0 .10 JJ ^ . 2 0 < 3 . 3 0 3 2 - 4 0 < . 5 0 . 6 0 . 7 0 1.0 o o 3 4 F ig . 19 7 8 9 10 11 12 13 14 15 W A V E L E N G T H ( M I C R O N S ) S P E C T R U M N O . 612 S A M P L E O R I G I N _bLM.4^Z25 L E G E N D 1. R E M A R K S . K B r Pellet G l y c i n e Anhydr ide PUR ITY R e a g e n t 7. P H A S E S o l i d D A T E T H I C K N E S S O P E R A T O R CO CO C m l Q : c It Z o m THE PERKIN-ELMER CORPORATION, NORWALK, CONN. 4 0 0 0 3 0 0 0 2 0 0 0 1 5 0 0 0 . 0 C M - i 1 0 0 0 9 0 0 8 0 0 7 0 0 1XU .U, l l l l t i 1 [, i i 1 ! 1 ! . 1 i I , i , 1 1 _ .1. . 1 i L 1 1 JJ-, i , , 1 1 1 r . i . I.,. f — 1 — h i i i i i f \ 1 \ V r k A) / \ V \ / i / j / \ j A / / \ •1/ V \ / / / \ / \ / / 1 / \ / \ / vv \ r / " / - V f— L— - t FRACORD,.^ 137-1280 .10 LU £ 2 0 < £ . 3 0 o £ . 4 0 ^ 5 0 . 6 0 . 7 0 1.0 o o 3 4 5 6 7 8 9 1 0 11 1 2 1 3 1 4 1 5 W A V E L E N G T H ( M I C R O N S ) F i g . 2 0 S P E C T R U M N O . 6 3 1 O R I G I N F K 8 6 8 L E G E N D R E M A R K S S A M P L E 1. K B r P e l l e t S u c c i n i c A n h y d r i d e P U R I T Y R e a g e n t 9 P H A S E S o l i d D A T E T H I C K N E S S O P E R A T O R CO CO C m Z o THE PERKIN-ELMER CORPORATION, NOR WALK. CONN -31+-CHAPTER 3» THE STRUCTURE OF SUCCINIMIDE. The c r y s t a l s t r u c t u r e o f s u c c i n i m i d e has been d e t e r m i n e d b y X - r a y d i f f r a c t i o n methods ( 27)» I t c r y s t a l l i z e s i n s p a c e g r o u p P b c a w i t h e i g h t m o l e c u l e s p e r u n i t c e l l , t h e d i m e n s i o n s o f w h i c h a r e : a = 7.50 t 0.01+ A b = 9.62 t 0 . 0 5 A c = 12.75 * 0 . 0 5 A o r a:b:c = 0 . 7 8 0 : 1 : 1 . 3 2 5 -Measurements o f t h e d i a m a g n e t i c a n i s o t r o p y s u g g e s t t h a t a p l a n e c o n t a i n i n g t h e atom g r o u p OC'NCO i s n o t p a r a l l e l t o any o f t h e a x i a l p l a n e s b u t t h a t i t may be n e a r e s t t o ( 100 ) . A s c h e m a t i c d r a w i n g o f t h e m o l e c u l e p r o j e c t e d o n t o t h e m o l e c u l a r p l a n e i s shown i n F i g u r e 21 , w i t h i n t e r b o n d a n g l e s a n d i n t e r a t o m i c d i s t a n c e s b e i n g I n d i c a t e d . By a ' l e a s t - s q u a r e s ' method t h e d e v i a t i o n o f t h e atoms f r o m a mean a t o m i c p l a n e were c a l c u l a t e d t o be N +O . O I 7 A 01 - 0.01], A C1 t 0.018 A 0 2 +0.013 A ° ° ~ 0 . 0 3 ^ A Cn + 0 . 0 0 ^ A C^ -O.OOg A As c a n be s e e n , t h e s e d e v i a t i o n s a r e e x t r e m e l y s m a l l , so t h a t f o r p u r p o s e s o f t h i s d i s c u s s i o n t h e m o l e c u l e w i l l be assumed p l a n a r ( e x c e p t i n g h y d r o g e n atoms ) . Whereas t h e i n t e r a t o m i c d i s t a n c e s and bond a n g l e s a r e g i v e n i n F i g . 21 , i n t e r m o l e c u l a r bond d i s t a n c e s a p p e a r i n T a b l e 2 . H I I Fig. 2 1 Succinimide Molecule \ -36-Table 2. I n t e r m o l e c u l a r Bond D i s t a n c e s . N - H . 0 o • 90p 2.85 A 0.. o e s 0 ( s h o r t e s t ) 3.75 A 0. . . . .0 ( l o n g e s t ) 1L.23 A Co. • a « G ( s h o r t e s t ) 3.91 A c.. ^ ( 9 0 C ^ \ l o n g e s t ) IL.22 A c. . « e «0 ( s h o r t e s t ) 3.26 A c.. ...0 ( l o n g e s t ) I4..6I A F i g u r e 22 shows the c r y s t a l s t r u c t u r e p r o j e c t e d onto the ( 100 ) p l a n e . The d o t t e d l i n e s show the p o s i t i o n of p o s s i b l e dimer - forming hydrogen bonds, which are to be d i s c u s s e d l a t e r e Fig- 2 2 Succinimide Crystal Structure Projected on ( 1 0 0 ) -38-CHAPTER k* THEORY AMD DISCUSSION. A study of molecular v i b r a t i o n s should r e a l l y be i n t r o -duced by a c o n s i d e r a t i o n of the dynamical p r i n c i p l e s of small v i b r a t i o n s . I f we then wish to d e s c r i b e the motion of p a r t i c l e s i n a polyatomic molecule of N atoms, a s e l e c t i o n of 3N c o o r d i n a t e s i n a c a r t e s i a n system of r e f e r e n c e x j , y^, and z^, w i l l d e s c r i b e the motion completely. Since s i x c o o r d i n a t e s are r e q u i r e d to d e f i n e the t r a n s l a t i o n and r o t a t i o n of the molecule as a whole, 3N - 6 degrees of freedom e x i s t f o r the n o n l i n e a r molecule. In a system as d e s c r i b e d above, the k i n e t i c energy i s r e p r e s e n t e d as * T - % # (i) where q^ are mass - weighted displacement c o o r d i n a t e s ( I.e.<^» f^u ) and q.i i s the f i r s t time d e r i v a t i v e of q^, while the p o t e n t i a l energy i s expressed as Here cub i c and h i g h e r terms have been n e g l e c t e d , V Q has been set equal to zero as has (dV/o^- ) 0, while and may be i d e n t i f i e d as a f o r c e constant between c o o r d i n a t e s i and j . S u b s t i t u t i o n of ( l ) and (2) Into Newton's equations of motion y i e l d s a set o f 3N l i n e a r d i f f e r e n t i a l e q u a t ions, one s o l u t i o n of which i s -39-f . > + e ) (3) A^,A, and e being p r o p e r l y chosen c o n s t a n t s . F u r t h e r m a n i p u l a t i o n y i e l d s the s e c u l a r equation the expansion and s o l u t i o n of which y i e l d s 3N - 6 nonzero r o o t s A^, each one corresponding to a set of amplitudes and consequently to a s o l u t i o n of the o r i g i n a l e q uation of motion. However, these c l a s s i c a l methods have proved to be too i m p r a c t i c a l f o r molecules of even s m a l l s i z e , such that v a r i o u s other types of c o o r d i n a t e s are f r e q u e n t l y used. One type of c o o r d i n a t e s i s r e f e r r e d to as " i n t e r n a l coor-d i n a t e s " , i n which a s u i t a b l e set of valence bond and bond angle changes are c o n s i d e r e d , the t r a n s l a t i o n and r o t a t i o n of the molecule as a whole being d i s r e g a r d e d . Even these methods have proved too i n e f f i c i e n t , so t h a t the more powerful v e c t o r and mat r i x methods, which have been developed, are commonly employed today. A f u r t h e r s i m p l i f i c a t i o n i s the use of molecular symmetry, which not o n l y reduces the degree of the s e c u l a r e q u a t i o n , but a l s o a i d s i n d e t e r m i n a t i o n of fundamental f r e q u e n c i e s and t h e i r degeneracy, s e l e c t i o n r u l e s f o r both Raman and i n f r a r e d s p e c t r a , p o l a r i z a t i o n p r o p e r t i e s of Raman l i n e s , e t c . The method used here i s a combination of symmetry and m a t r i x methods to present a syst e m a t i c treatment of t h e motions and spectrum of the su c c i n i m i d e m o l e c u l e a - I L O -2j- — 1 • Symmetry of Normal and I n t e r n a l C o o r d i n a t e s 6 a ) Concept of Symmetry and Groups - As a f i r s t step i n the u t i l i z a t i o n o f molecular symmetry, a c o n c i s e method of c l a s s i f y i n g symmetry elements and corre s p o n d i n g symmetry op e r a t i o n s i s needed. These elements are ( i ) Plane of symmetry, cr ( i i ) A x i s of symmetry, C n ( i i i ) Center of symmetry, i ( i v ) A l t e r n a t i n g a x i s of symmetry, S n ( v ) I d e n t i t y , E or I» A c c o r d i n g to the nature and number of the above symmetry elements, a l l p o s s i b l e molecules ( n u c l e a r c o n f i g u r a t i o n s ) may be c l a s s i f i e d i n t o a s m a l l number of groups* , the s o - c a l l e d symmetry p o i n t g r o u p s e Simply, a p o i n t group i s d e f i n e d as a combination of symmetry o p e r a t i o n s t h a t leave at l e a s t one p o i n t of the n u c l e a r c o n f i g u r a t i o n unchanged. Thus every molecule may be a s s i g n e d to one of the f o l l o w i n g p o i n t groups: C n , D n , C n h , D n h , C n v , S n , D n d , J , J d , J H , 0 , 0 N , and I f , i n s u c c i n i m i d e , we assume the hydrogen atom a t t a c h e d to the n i t r o g e n to be p o s i t i o n e d as i n d i c a t e d i n P i g . X21 ( d o t t e d l i n e ), the molecule w i l l possess the f o l l o w i n g elements of symmetry: A plane c o n t a i n i n g a l l atoms except the hydrogens a t t a c h e d to carbon, a plane p e r p e n d i c u l a r to the plane of the heavy atoms and p a s s i n g through the NH bond and the midpoint of the G^Cj^ bond, and a two - f o l d r o t a t i o n * The word group i s used i n a mathematical sense. - i l l -axis in the intersection of the above two planes. This is illustrated in Pig* 23» Summarizing, the symmetry elements of the succinimide molecule consist of the identity E, a two - fold rotation axis -.and two symmetry planes c v(yz) and <rv(zx) . The point group of the molecule is by definition C2 V. b ) Representation and Characters - The effect which a symmetry operation has on a distorted molecule may be repre-sented by a linear transformation connecting the old values Ax n, A y n > and A z n of the displacement coordinates with the new values A x n ' , A y n ' , and A Z n ' , Analytically this is repre-sented b y Since the above set of linear transformations possesses a l l the properties of a group, these transformations of coor-dinates, as well as the symmetry operations, constitute a group. This group of transformations is obviously closely connected with the group of symmetry operations. In partic-ular, the group of linear transformations is said to be a representation of the other group. A further definition is required, that of the character of a transformation. If a transformation, i.e. equation (5), is written out in f u l l , x i ' * RliXi <-Ri2X2 ^%,3W X3N x 2 ' = R 2 1 x l * R 2 2 X 2 *R2,3NX3N * (6) X3N'= R3N,l Xl + R3N , 2 X 2 + e o o e o *R3N,3NX3N then the character of the transformation is defined as Fig. 23 Symmetry Elements of the Succinimide Molecule the sum of the d i a g o n a l c o e f f i c i e n t s , namely ( 7 ) As s e l e c t i o n of the X,^  i n equation (5) i s a r b i t r a r y , a second or even more sets c o u l d be chosen. The most e f f i c i e n t choice of the » say rij» would be the one i n which the t r a n s f o r m a t i o n assumes the d i a g o n a l form r l ' " % l r l r 2 ' = R 2 2 r 2 d d ^ (8) r3N* = R3N,3N Such a choice of the which would s i m u l t a n e o u s l y reduce every t r a n a f o r m a t i a n of the group i s not always p o s s i b l e , but i t i s g e n e r a l l y p o s s i b l e to f i n d a s i n g l e change of c o o r d i n a t e s which w i l l g r e a t l y s i m p l i f y the t r a n s f o r m a t i o n s . By such r e d u c t i o n s the t r a n s f o r m a t i o n s of the v a r i a b l e r^_, r 2 > can be separated i n t o i n d i v i d u a l sets which do not mix with one another. Such a c o o r d i n a t e system which cannot be broken down i n t o s m a l l e r non-mixing sets i s s a i d to form a completely reduced r e p r e -s e n t a t i o n . The non-mixing s e t s of c o o r d i n a t e s which make up the completely reduced r e p r e s e n t a t i o n s can be c o n s i d e r e d by themselves as making up t r a n s f o r m a t i o n s which form a r e p r e s e n t a t i o n of the group. They are commonly r e f e r r e d to as 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 or symmetry s p e c i e s . A f u r t h e r d e f i n i t i o n , t h a t needs to be made, i s that of a c l a s s , the l a t t e r being d e f i n e d as a set of symmetry oper a t i o n s having the same c h a r a c t e r X . Thus, i f g j i s the -kh-number of o p e r a t i o n s i n the j ' t h c l a s s and X^ i s the char-a c t e r of t h a t c l a s s ( i.e» the c h a r a c t e r of each o p e r a t i o n i n t h a t c l a s s ), then m(y) 3 the number of times that 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 appears i n the completely reduced r e p r e s e n t a t i o n i s g i v e n by where g i s the number of o p e r a t i o n s i n the group, X^ r e f e r s to the r e d u c i b l e r e p r e s e n t a t i o n , and X ^ ^ to the y ' t h i r r e -d u c i b l e representation*) Once the symmetry of the molecule, here s u c c i n i m i d e , has been determined, the atoms c o n s t i t u t i n g the m o l e c u l a r con-f i g u r a t i o n may be p l a c e d i n t o s y m m e t r i c a l l y e q u i v a l e n t s e t s * Table 3 c o n t a i n s i n a d d i t i o n to the c h a r a c t e r t a b l e f o r the group 02v* k*16 a n a l y s i s of the v a r i o u s c o o r d i n a t e represen-t a t i o n s i n t o i r r e d u c i b l e s p e c i e s , a The columns headed -^oly\ (Y) • A/ •nf -n*-^ 3 fi}^3 -njys and nJ^ give the number i n each s p e c i e s of e x t e r n a l symmetry c o o r d i n a t e s formed from the c a r t e s i a n displacement c o o r d i n a t e s of e q u i v a l e n t atoms, namely oxygen, n i t r o g e n , carbon at t a c h e d to n i t r o g e n , carbon a t t a c h e d to carbon o n l y , hydrogen att a c h e d to nitrogen,, and (y) 0 hydrogen a t t a c h e d to carbons The columns headed -r?^ and g i v e 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 (y\ a whole© -^7^ gives the number of genuine v i b r a t i o n s , namely The normal v i b r a t i o n s of the s u c c i n i m i d e molecule are thus -45-Table 3« Symmetry Species of Normal C o o r d i n a t e s , E G2 o" v(zx) <*v(yz) °# A l 1 1 1 1 2 1 2 2 1 3 1 0 10 4 1 1 -1 - l 1 O i l 0 3 0 1 5 1 -1 1 - l 2 1 2 2 l 3 1 1 9 B 2 1 -1 -1 1 1 1 1 1 1 3 1 1 6 As s t a t e d b e f o r e , the molecule may be c o n s i d e r e d p l a n a r except f o r the hydrogen atoms. I f we d i s r e g a r d the hydrogen atoms att a c h e d to carbon ( i . e . c o n s i d e r the CH2 groups as p o i n t masses ) and assume the hydrogen atom a t t a c h e d to n i t r o g e n to be i n the plane of the heavy atoms ( a not un-tenab l e assumption ), i t might prove f r u i t f u l to d i v i d e Ire/U i n t o i n - plane and out - of - plane modes. There w i l l then be 2N - 3 i n - plane modes 7? and N - 3 out - of - plane 7-7 modes i0 c o n s t i t u t e d as f o l l o w s : 7\° 7/},*68l (11) T0 (12) The i n - plane and out - of - plane modes are d i s t i n -guished by r e f e r r i n g to the c h a r a c t e r of o~ v(zx), which should be 1 i n the f i r s t and -1 i n the l a t t e r c a s e e Using the apprach through c a r t e s i a n c o o r d i n a t e s as above, i t i s seen that zero r o o t s w i l l be i n t r o d u c e d i n t o the s e c u l a r e q u a t i o n through presence of the s i x t r a n s l a t i o n a l and r o t a t i o n a l modes. An a l t e r n a t e approach, w i t h c e r t a i n advantages, employs " i n t e r n a l c o o r d i n a t e s " such as a s u i t a b l e set of valence -1*6-bond length and interbond-angle changes. The reduct ion i n the number of coordinates i s i n th i s case accomplished by-employing an e n t i r e l y new set. of coordinates S t , which are defined by r e l a t i o n s connecting the s t with the car tes ian displacement coordinates q^, namely Pour types of i n t e r n a l coordinates , which w i l l be em-ployed for the molecule at hand, w i l l be discussed below. Since these coordinates are the most p h y s i c a l l y s i g n i f i c a n t i n descr ib ing the p o t e n t i a l energy of a system, while the k i n e t i c energy is more e a s i l y discussed i n cartes ian coor-dinates , a r e l a t i o n between the two i s needed and w i l l also be given. a ) Bond Stre tch ing: This coordinate represents the d i f -ference i n distance between two d i r e c t l y bonded atoms i n a d i s t o r t e d conf igurat ion and the distance at e q u i l i b r i u m . If th is increase i s defined as S^, then the most e f f i c i e n t d i r e c t i o n of displacement i s along the l i n e r ^ 2 but i n oppo-s i t e d i r e c t i o n ( see P i g . 2i|.a ) . The change is not represented by car tes ian displacement coordinates d i r e c t l y , but by vectors sfoi , which i n turn are expressed i n terms of unit vectors ettt along c e r t a i n con-venient interatomic connecting l i n e s . Thus for the bond s tre tch S t : b ) Bond-angle Bending:, This coordinate represents the F i g . 2 4 I n t e r n a l C o o r d i n a t e s -in-d i f f e r e n c e between the angle formed by two adjacent bonds i n a d i s t o r t e d and the corresponding e q u i l i b r i u m c o n f i g u -r a t i o n ( see P i g . 2l\.b ) . I f i s the angle-change4$ i n the angle (6 , then arguments s i m i l a r to those of the b o n d - s t r e t c h i n g case show the d i s -placement v e c t o r s to be SH* ft6*'** (15) *3Z 'j/ S'" t ^SZ J<» + c ) Out-of-plane Bending: The t h i r d c o o r d i n a t e , which can be d e f i n e d at any atom where three or more copl a n a r bonds are c o i n c i d e n t , i s taken as the angle change of the one bond r e l a t i v e to the plane d e f i n e d by the ot h e r two or more bonds ( see P i g . 2JLLC ) . Thus i f i s gi v e n by 46, the s v e c t o r s are g i v e n by ti </« Sin  /ffZSt'*> 4, (16) r¥3 Si Whereas the above formulae (16) apply o n l y to f o u r c o p l a n a r atoms, a c o n d i t i o n found i n s u c c i n i m i d e , g e n e r a l i z a t i o n s to the non-coplanar case are e a s i l y made. -14-9-d ) Bond Torsion:. The l a s t i n t e r n a l c o o r d i n a t e to be used, may be d e f i n e d whenever the atoms at each end of a bond, each are a l s o bonded to a d d i t i o n a l atoms by bonds not colUnear with the bonds connecting the two atoms i n q u e s t i o n . The bond t o r s i o n angle i s thus d e f i n e d as the change i n the d i h e d r a l angle betw.een the two planes which are present ( see F i g . 2'lj.d ) . Since the a n a l y t i c a l d e f i n i t i o n o f r 4s cos r • S>'n fij Sin <f>j ( 17 ) the s v e c t o r s are d e f i n e d as f o l l o w s : **,*,zS.-„+2 s;«4>L -TJJSM^ ^ ^ ( L 8 ) Here the expr e s s i o n s i n b r a c k e t s simply i n d i c a t e a per-mutation of atom s u b s c r i p t 1 and I4., and 2 and 3. A l s o , care must be taken i n a s s i g n i n g the s i g n of - r i n the i n t e r -v a l -ir< T£7T » U s i n g the above p r i n c i p l e s , i n t e r n a l c o o r d i n a t e s f o r the s u c c i n i m i d e molecule were s e l e c t e d , and are represent:ed i n F i g . 25« The out - of - plane c o o r d i n a t e s are not pres e n t e d d i a g r a m a t i c a l l y , but w i l l be d i s c u s s e d at l e n g t h l a t e r . As o n l y 13 i n - plane c o o r d i n a t e s occur i n the s t r u c t u r e Fig. 2 5 I n - p | o n e C o o r d i n a t e s o f S u c c i n i m i d e -51-of 7 T ( equation 11 ), but 16 i n t e r n a l c o o r d i n a t e s were chosen, i t i s obvious t h a t the 16 c o o r d i n a t e s cannot a l l be independent. The set of dependent c o o r d i n a t e s i s s a i d to form a redundant s e t . I t would be p o s s i b l e to modify the i n t e r n a l c o o r d i n a t e s to account f o r t h i s redundancy, but i t was found more convenient to r e t a i n s y m m e t r i c a l l y complete sets of c o o r d i n a t e s and cope with the redundancy at a l a t e r stage. I t i s l e l f - e x p l a n a t o r y t h at the t o t a l number of i n t e r n a l c o o r d i n a t e s w i l l exceed the number of normal c o o r d i n a t e s by the number of redundancy c o n d i -t i o n s . A f t e r the c h a r a c t e r s "Xy f o r the r e d u c i b l e r e p r e s e n t a -t i o n had been obtained, they were s u b s t i t u t e d i n t o equa-t i o n 9 to give the s t r u c t u r e of the r e d u c i b l e represen-t a t i o n of the S t ( see Table 1+ ) . Table i+. Symmetry Species o f In - plane Modes. S t r u c t u r e E c 2 cr v (zx) 2 0 2 0 2 0 2 0 2 0 2 0 1 1 1 1 1 1 1 1 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 s ( C 0 ) t(CG) u(CN) v(NH) t 3 ( C C ) 0 1 2(OGC) (OCN) yiCNH) <*(CCC) A &1 1* °1 A t * B t A l A l A l + B l A t f B t A 1 * B 1 A 1 * B 1 A comparison w i t h 7^  shows that two redundancy c o n d i t i o n s are of type A^, while one i s of type B-j_, S e v e r a l out - of - plane c o o r d i n a t e s w i l l be i n t r o d u c e d , -52-two d e a l i n g w i t h the NH and CO bending out of the plane of the three nearest neighbours. The c o o r d i n a t e s are l a -b e l l e d y (NH) and >^ (CO), r e s p e c t i v e l y . Three sets of coor-d i n a t e s w i l l be chosen as t o r s i o n s . Thus, one set ( <$ ) w i l l d e s c r i b e the change i n the d i h e d r a l angle T between the planes C^C-^N and C-^NCg, and between the planes C^C^N and C2NC^o The second set ( f) d e s c r i b e s the d i h e d r a l angle change between planes C^C^C^ and ^^2^ and between planes G3 Gi| G2 a n ( * G i } . G l ^ e A l s o b e l o n g i n g to the second s e t , if r e f e r s to planes C^C^C^ and C^C.jC2« The symmetry s p e c i e s are g i v e n i n Table 5« Table 5« Symmetry Species of Out-of-plane Coordinates E c 2 o" v(zx) ffv(yz) S t r u c t u r e y ( N H ) 1 -1 -1 1 B2 ? ( C O ) 2 0 -2 0 & ( C N ) 2 0 -2 0 A2 * B2 y(cc) 2 0 -2 0 A P + B p T T ( C C ) 1 1 -1 -1 4 A comparison with equation (12) shows t h a t two redundan-c i e s are of type A 2 while one i s of type B2« For the CH modes, the two s e t s of i n t e r n a l c o o r d i n a t e s which were chosen r e p r e s e n t the changes i n the C - H i n t e r -atomic d i s t a n c e and the angle changes between the CH and CC bonds. They are d e f i n e d as r(CH) a n d ^ ( C C H ) , r e s p e c t i v e l y * In t a b l e 6 the symmetry species of the CH modes are shown* I t w i l l be seen that no redundancies are present i n the s e t . - 5 3 -Table 6. Symmetry Species of CH Co o r d i n a t e s . s t E c 2 o" v(zx) S t r u c t u r e r(CH) k 0 0 0 A , +• B, c A ? t Bp /3(CCH) 8 0 0 0 2A^2BJ+2A|^-2B| IJ. - 2 . S e l e c t i o n R u l e s . a ) Species of the E l e c t r i c Moment and P o l a r i z a b i l i t y . In order to be able to d i s c u s s the i n f r a r e d and Raman s e l e c t i o n r u l e s , i t i s nece s s a r y to determine the symmetry s p e c i e s of the e l e c t r i c moment and p o l a r i z a b i l i t y . The d i p o l e moment of a molecule i s r e p r e s e n t e d i n wave mechanics by a m a t r i x formed from the i n t e g r a l s where M i s a v e c t o r w i t h components ^-IeLXi} ^ r l e i S i ) Mz'Ze.-Z; (20) and ^ and l f m are the time-dependent e i g e n f u n c t i o n s of the system i n s t a t e s n and m. The d i a g o n a l elements of the ma-t r i x r e p r e s e n t the permanent d i p o l e of the s t r u c t u r e , where-as the o f f - d i a g o n a l elements correspond to t r a n s i t i o n s from s t a t e n to s t a t e m. The t r a n s i t i o n p r o b a b i l i t y i s then p r o p o r t i o n a l to the square of the time-dependent f a c t o r I f (/^  and l/^i r e p r e s e n t two v i b r a t i o n a l s t a t e s , then the v i b r a t i o n a l t r a n s i t i o n p r o b a b i l i t y i s p r o p o r t i o n a l to the square of for'* J % n € ° t r ( 2 D -5k-In words, t h i s means t h a t a v i b r a t i o n a l t r a n s i t i o n v -^»v' i s allowed when at l e a s t one of the components of the d i p o l e moment ^ has the same s p e c i e s as the product of ^  and ^ / o C o n s i d e r i n g the e l e c t r i c moment of s u c c i n i m i d e , i t i s obvious that the z component ^Uz i s of s p e c i e s A-^ , s i n c e if i s sent i n t o i t s e l f by a l l the symmetry o p e r a t i o n s o f the group C £ v . The x and y components,^ K and^ y , are of type and Bg r e s p e c t i v e l y , s i n c e they transform as fo l l o w s ? Y A* M/<K Si ^ (~0/<r (22) A (-0/<, A A ^ - (-')/* A -^(-Ofy The reduced r e p r e s e n t a t i o n o f the e l e c t r i c m o m e n t i s thus T L - A, +3, +3Z (23) In Raman spectroscopy, the i n t e n s i t y of s c a t t e r e d l i g h t depends upon the induced d i p o l e moment P, which i s r e p r e -sented by the mat r i x formed from the i n t e g r a l s where P i s a v e c t o r w i t h the components PK c<KK £x * <<Ky *• o<xz Ez. where the <x.'j are components of the p o l a r i z a b i l i t y v e c t o r o C , and E .is t h e e l e c t r i c v e c t o r of the i n c i d e n t r a d i a t i o n . I f P° i s the amplitude of P, then the i n t e n s i t y of a -55-Raman tran s i t i o n s n«—>m i s proportional to the square of f p ° J n m , which has components In the above three equations, the E° are the components of the amplitude of the incident l i g h t , and the integrals are the matrix elements of the s i x components of the polar-i z a b i l i t y tensor. Thus a Raman t r a n s i t i o n i s allowed i f at least one of the s i x <x's i s nonzero. ( For further d e t a i l see reference #28 ). The symmetry species of the p o l a r i z a b i l i t y components are obtained by a reduction of the representation ) (27) with characters f o r succinimide given i n Table 7» ( See reference #2:9 ) » Table 7« Character of the P o l a r i z a b i l i t y of Group C 2 v„ R E c 2 o~v(zx) <*« 0 IT 0 0 ** 6 2 2 2 The following species are obtaineds T^Jfit+Ajt+fy + Si (28) b ) Selection Rules f o r Fundamentals e The fundamentals, that i s the tr a n s i t i o n s from the ground state to leve l s with only one quantum of one vib r a t i o n excited, w i l l be infrared active i f the excited state i s one of the species of 7^  „ -56-In succinimide, /^ a i s of species A^, w h i l e a n d ^ / / x are of species B 2 and B]_ respectively. Therefore the only in f r a r e d active fundamentals are those whose coordihates are of spe-cies A^, B^, or B 2« In an analogous fashion, consideration of the p o l a r i z a t i o n representation 7^  , shows that Raman active fundamentals may be of type A-^ , A 2, B^, or B2,. c ) Selection Rules f o r Binary Combinations. The selec-t i o n rules f o r binary combination frequencies, derived as above, w i l l be given i n Table 8 , where R denotes Raman a c t i -v i t y , while IR denotes in f r a r e d a c t i v i t y . Table 8 . Binary combination Symmetry Species. A l A 2. Bl B 2 A l Ar^H^R) A 2(R) B-j^  (IR,R) B 2(IR,R) 4 AjJIR,!*) B2>(IR,R) B T(IR,R) B i A^IR.R) A 2(R) A-,_(IR,R) d ) Selection Rules for Overtoneso The overtones of degenerate modes, the only type present i n C 2 v symmetry, are ea s i l y described, namely A ] _ N - A^_ f o r n odd and n even, A 2 N = A-j_ f o r n even, A 2 for n odd, B-j_n = A-JL f o r n even, B-j_ for n odd, B 2 n = A]_ f o r n even, B 2 for n odd. Thus a l l overtones are Raman active, while a l l overtones except odd ones of an A 2 fundamental are infrared active. The above considerations, of course, represent arya? i d e a l i z e d case, i n which a single molecule, under no outside influences-. -57-i s c o n s i d e r e d * T h i s c o n d i t i o n i s approached most c l o s e l y i n the gas phase, such that the s e l e c t i o n r u l e s h o l d e x a c t l y f o r the vapour spectrum* In s o l i d form, the c r y s t a l i s of course under the i n f l u -ence of the c r y s t a l f i e l d . The f a c t t h a t the s e l e c t i o n r u l e s might be d i f f e r e n t was r e a l i z e d e a r l y and treatments due to Bhagavantam and Venkatarayudu were proposed i n 1 9 3 9 ( 3 0 , 31 )• They s t a t e that a l l the s p e c t r o s c o p i c a l l y im-portant f r e q u e n c i e s may be d i s c o v e r e d and c l a s s i f i e d by examination of the c r y s t a l l o g r a p h i c u n i t c e l l . The method however i s v e r y cumbersome and t e d i o u s to a p p l y i n most cases, and does not warrant the e f f o r t , as the f r e q u e n c i e s so o b t a i n e d are r e a l l y f i c t i t i o u s * In s u c c i n i m i d e , f o r example, the m o l e c u l a r u n i t s O^H^O^N are c o n t a i n e d e i g h t times i n the u n i t c e l l , so t h a t i t should e x h i b i t 288 d i s -t i n c t modes of motion? d i s t r i b u t e d i n t o 21+0 m o l e c u l a r and I4.8 l a t t i c e modes.. The spectrum of course i s much si m p l e r , the d i s c r e p a n c y b e i n g not the r e s u l t of e x c e e d i n g l y s t r i c t s e l e c t i o n r u l e s , but being the r e s u l t of the circumstance, that the 288 modes can be c o l l e c t e d i n t o s e t s , the theore-t i c a l l y d i s t i n g u i s h a b l e f r e q u e n c i e s of which are i n d i s t i n -g u i s h a b l e i n p r a c t i s e . As a matter of f a c t , these sets have a frequency which i s not a p p r e c i a b l y d i f f e r e n t from the f r e q u e n c i e s of an i s o l a t e d m o l e c u l e 0 A d i f f e r e n t approach, due to H a l f o r d ( 31 )* t r e a t s the motions of one molecule moving i n a p o t e n t i a l f i e l d which - 5 8 -r e f l e c t s the symmetry of the surrounding c r y s t a l , i . e . the space group. The space group i s generated by a s i t e , so t h a t a molecule l y i n g on such a s i t e i s s a i d to have t h i s p o i n t ' s s i t e symmetry. To be a c c e p t a b l e as a s i t e group, the l a t t e r must of course be a sub-group of both the space group and 15 15 the m o l e c u l a r group. For space group Pbca ( ^>zh~ ^h ) t h e r e are two s e t s of s i t e s having p o i n t symmetry wi t h f o u r s i t e s per s e t . i s , however, a sub-group of n e i t h e r 02^ nor C2v* a n ( i the H a l f o r d approach does not seem a p p l i c a b l e . Due to the i n h e r e n t l y weak c o u p l i n g of i n t e r m o l e c u l a r modes, i t i s b e l i e v e d more c o r r e c t to apply C 2 v s e l e c t i o n r u l e s to c r y s t a l l i n e s u c c i n i m i d e , with c e r t a i n r e l a x a t i o n s of these due to the o v e r a l l symmetry of the observed c r y s t a l f i e l d . The main e f f e c t of the f i e l d would be to remove any degeneracy from E or T type modes. These types of v i -b r a t i o n s are not found i n the present case. I4. - 3. Isotope E f f e c t and the Product Rule. Since i s o t o p i c a l l y s u b s t i t u t e d molecules, have the same e l e c t r o n i c s t r u c t u r e , i t i s assumed t h a t the p o t e n t i a l f i e l d i n which the n u c l e i are moving, i s changed by a n e g l i g i b l e amount o n l y . But because of the mass d i f f e r e n -ces, the change i n the v i b r a t i o n a l f r e q u e n c i e s may be a p p r e c i a b l e . T h i s i s e s p e c i a l l y t r u e f o r hydrogen. The above statement of the constancy of p o t e n t i a l energy may be rephrased to g i v e the well-known T e l l e r - R e d l i c h pro-duct r u l e : For two i s o t o p i c molecules, the product of the -59-<Ji/a> values f o r a l l v i b r a t i o n s o f a given symmetry type i s independent of the p o t e n t i a l constants and depends o n l y on the masses of the atoms and the geometric s t r u c t u r e of the molecule. The ge n e r a l formula i s where the u>, and are the v i b r a t i o n a l f r e q u e n c i e s of the normal and i s o t o p i c a l l y s u b s t i t u t e d molecule, m^ and m£ are the masses of the atoms of a r e p r e s e n t a t i v e s e t , while r a t i o s M ' / M and I ' / l enter the eq u a t i o n because i n a l i m i t i n g case, the t r a n s l a t i o n and r o t a t i o n of the molecule as a whole, are t r e a t e d as o s c i l l a t o r y motions of very low frequency. Since i s o t o p i c s u b s t i t u t i o n does not a l t e r the symmetry of the s u c c i n i m i d e molecule, the product r u l e f o r v i b r a t i o n s of the same species may be w r i t t e n out by an i n s p e c t i o n of the c h a r a c t e r t a b l e . Thus (29) 0.70? ( 3 0 ) P-7/f -60-Using the frequency values of a s s i g n e d v i b r a t i o n s ( next s e c t i o n ) i n the a v a i l a b l e r e g i o n of the spectrum, the ex-p e r i m e n t a l values of Tfcoi/iO/\ were c a l c u l a t e d to be A xs 0.72lj. ApS IR i n a c t i v e B-.S 0.751 B 2 J 0.791 These values are seen to agree w e l l w i t h the c a l c u l a t e d ones, showing d e v i a t i o n s of 2.1%, k.°3>%» and 9»1^> r e s p e c t i v e l y . 4 - 4* Assignment of Observed Frequencies« The bands which are observed i n the 4000 - 650cm""1 r e g i o n of the s u c c i n i m i d e spectrum are a s s i g n e d by t a k i n g i n t o con-s i d e r a t i o n the f i v e d i f f e r e n t approaches mentioned i n the i n t r o d u c t i o n . The assignment of somewhat ambiguous bands w i l l be d i s c u s s e d i n d e t a i l i n a l a t e r s e c t i o n p 4 "° 9* A l s o , due to a l a c k of i n f o r m a t i o n , the asignment of bands below 650cm" 1 i s l e s s c e r t a i n o 3162cm- 1; This s t r o n g band i s e a s i l y i d e n t i f i e d with the hydrogen - bonded NH s t r e t c h i n g v i b r a t i o n , a f a c t which i s supported by i t s p e r s i s t e n c e i n c o n c e n t r a t e d s o l u t i o n ( var-ious s o l v e n t s ), i t s s h i f t to h i g h e r f r e q u r n c y upon d i l u t i o n to a l i m i t i n g value of 3420cm" 1 i n the gas phase, and by i t s d e u t e r a t i o n s h i f t to 2392cm~ 1 ,<^' = 1.32. 3080cm"ls T h i s band, which seems to s h i f t to 2325cm"*1 upon d e u t e r a t i o n (co/c?'= 1.33 )» i s present i n s o l u t i o n s p e c t r a but absent i n the vapour spectrum An NH mode i s indicated,. 2955cm"* 1; Due to i t s constancy of p o s i t i o n , t h i s medium i n -t e n s i t y band has been a s s i g n e d to an asymmetric CH s t r e t c h i n g -61-mode. In the vapour spectrum, a weaker band near 2850cm" 1 i s assigne d to the corresponding i n - phase v i b r a t i o n * 2800cm" 1 ; Consecutive weakening of t h i s band upon deutera-t i o n , and absence i n N - Br and N - C l - su c c i n i m i d e s p e c t r a , suggest an NH mode. T h i s band i s consequently a s s i g n e d to the f i r s t overtone of an In - plane bending v i b r a t i o n o c c u r i n g at 1376cm" 1o Upon d e u t e r a t i o n , the band i s s h i f t e d to 2 2 0 0 c m " 1 , the f i r s t overtone o f an i n - plane ND bending v i b r a t i o n at 1100cm*" 1. 2610cm" 1 ; T h i s v e r y weak band seems to disappear upon deu-t e r a t i o n . No assignment has been made. 25U.0cm""1; T h i s band i s r a t h e r constant i n su c c i n i m i d e spec-t r a r e c o r d e d under v a r i o u s c o n d i t i o n s . I t i s assign e d to a combination band of y'(CC) at 1296cm" 1 and v(CC) at 12ltlcm-lo 1829cm" 1 ; Disappearance of t h i s band i n d i c a t e s an NH mode* and the band has been a s s i g n e d to the 1st overtone o f the out - of - plane NH bending v i b r a t i o n at 937cm"" 1. 1783cm" 1 ; In the r e g i o n near 1775cm" 1 an extremely s t r o n g and wide band i s observed, which upon c l o s e r i n s p e c t i o n i s seen to c o n s i s t of two bands, one of them ( 1783cm" 1 ) ap-p e a r i n g as a shoulder o n l y . In v a r i o u s s o l v e n t s t h i s l a r g e band i s s p l i t completely i n t o two w e l l - d e f i n e d bands., the 1783cm" 1 p o r t i o n having s h i f t e d to lower frequency. Upon deu-t e r a t i o n the 1783cm" 1 band disappears completely, g i v i n g r i s e to a new band at 1273cm" 1 , <^/u?' being 1.39« ^he band has been a s s i g n e d to an i n - plane NH deformation mode. -62-1771cm""1; T h i s band, because of i t s p o s i t i o n , i n t e n s i t y , shape, and i n s e n s i t i v i t y to environmental change, has been assign e d to the f r e e GO s t r e t c h i n g motion ( d e t a i l e d e x p l a -n a t i o n i n S e c t i o n 4""9 ) • 1695cm"1; An upward s h i f t i n d i l u t e s o l u t i o n , and complete disappearance i n the vapour phase, where presumably o n l y non-hydrogen bonded species are pre s e n t , has l e d to the a s s i g n i n g of t h i s extremely broad and in t e n s e band to a hydrogen-bonded GO s t r e t c h i n g mode. lij/iUl-cm "*": T h i s band has been a s s i g n e d to a CH deformation frequency, as has the band near 1400cm "*". 1420cm"1; Absence of t h i s band i n the spectrum of N - h -succ i n i m i d e - d.^  suggests a CH mode. 1376cm""1: T h i s band disappears completely upon deutera-t i o n i n the N p o s i t i o n , a new band appearing at 1100cm 1 . An i n - p l a n e bending motion i s i n d i c a t e d , o/u?' being 1.25, the low value b e i n g a s c r i b e d to anharmonicity. 1361cm"1: The shoulder which appears on the low frequency s i d e of the 1376cm™1 band, remains as a w e l l - d e f i n e d band upon d e u t e r a t i o n . A. lo w e r i n g of frequency i s observed i n d i l u t e s o l u t i o n s , a l i m i t i n g value of 1335cm""1 being ob-served i n the vapour phase. The band i s a s c r i b e d to an asymmetric CN v i b r a t i o n . 1296, 1241, 1193cm"""1": These three bands a l l show great constancy of i n t e n s i t y and p o s i t i o n i n va r i o u s s o l v e n t s , and not very l a r g e frequency changes i n the vapour phase. - 6 3 -A l l three are as s i g n e d to C C s t r e t c h i n g v i b r a t i o n s . lOOllcm" 1: T h i s band i s thought to be due to the symmetric C N s t r e t c h i n g mode, an assumption born out by normal coor-d i n a t e c a l c u l a t i o n s o 937cm" 1 ; T h i s band disappears completely upon d e u t e r a t i o n , i n the n i t r o g e n p o s i t i o n , a new band at 751|-cm~1 appearing i n i t s plac e and u>/u?' being 1.2lj.. The band has been a s s i g n e d to an out - o f - p l a n e N H deformation frequency,, 852cm""~*~: T h i s band has been a s s i g n e d to a deformation mode of the five-membered r i n g . 822cm" 1: D e u t e r a t i o n on the n i t r o g e n had no e f f e c t on t h i s band, whereas d e u t e r a t i o n on the carbon atoms caused t h i s band to d i s a p p e a r . I t seems to i n d i c a t e t h a t the o r i g i n of the band i s a C H r o c k i n g mode, g a i n i n g i n t e n s i t y from the adjacent c a r b o n y l groups* 639cm" 1 : T h i s s t r o n g band has been a s s i g n e d to a C O d e f o r -mation frequency. 552cm" 1 : Absence of t h i s band i n the de u t e r a t e d compound and normal c o o r d i n a t e a n a l y s i s , make the assignment of t h i s band to a C N C i n - p l a n e deformation q u i t e f e a s i b l e . 1121+cm"1: T h i s band has been a s s i g n e d to a s k e l e t a l mode of the B2 t y p e e 370, 359* 352, 337. 326, 316cm" 1: T h i s s e r i e s of weak bands has been l e f t unassigned due to a l a c k of f u r t h e r data© 3011cm"1: T h i s a b s o r p t i o n band has been a s s i g n e d to a ske-l e t a l ( mainly C C C ) deformation mode of the BJL type. -614,-290cm"1; Unassigned* 280cm"1: Whereas no d e f i n i t e data i s a v a i l a b l e to charac-t e r i z e t h i s band, normal c o o r d i n a t e treatment i n d i c a t e s a band i n t h i s r e g i o n to be an CGO in- p l a n e s k e l e t a l d e f o r -mation* 4 - 5 * P o t e n t i a l and K i n e t i c Energy i n I n t e r n a l Coordinates* In t h i s s e c t i o n , the most general expressions f o r the p o t e n t i a l and k i n e t i c energy of the su c c i n i m i d e molecule w i l l be d e r i v e d , the f i r s t i n terms o f the i n t e r n a l coor-d i n a t e s , whose symmetry p r o p e r t i e s were d i s c u s s e d i n sec-t i o n 4 - 1 , while the l a t t e r Is d i s c u s s e d as a q u a d r a t i c f u n c t i o n of the momenta conjugate to these i n t e r n a l coor-d i n a t e s * In i n t e r n a l c o o r d i n a t e s , the p o t e n t i a l energy i s e a s i l y v i s u a l i z e d and needs no f u r t h e r comment* I t i s 2V* £ ( 3 D where the S^ . are the two 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 , w h i l e i s t n e f o r c e constant e x p r e s s i n g t h e i r i n t e r -a c t i o n * The p o t e n t i a l f u n c t i o n employed i n the present d i s c u s s i o n i s a s i m p l i f i e d q u a d r a t i c valence f o r c e f i e l d 2 v - £ kco (AS)\ I kCAJ (AU)7- +1 K c c CMf-* K c t KHH (AV)\£ «C« [<+,*U/2 * A j 2 + i > c ^ & W / ; * 4 u > ] % i H c c o (s^f ( 3 2 ) - 6 5 -where o? = <fy-^ , y > c / ^ - * K, H, and P are b o n d - s t r e t c h i n g , angle-bending, and i n t e r a c t i o n c o n s t a n t s , r e s p e c t i v e l y , and i s the change i n the C^ - C 2 nonbonded i n t e r a t o m i c d i s -t a nce. The other symbols are s e l f - e x p l a n a t o r y , as are the s u b s c r i p t s 0 As b e f o r e , the i n - p l a n e and out - o f - p l a n e c o o r d i n a t e s w i l l be t r e a t e d s e p a r a t e l y . Since a treatment o f the 12 CH modes ( c o o r d i n a t e s ) would n e c e s s a r i l y be ve r y complex, the f o u r hydrogen s u b s t i t u e n t s w i l l be co n s i d e r e d as po i n t masses, and t r e a t e d as such. I f f e a s i b l e at a l l , a more d e t a i l e d t r e a t -ment w i l l be undertaken at a l a t e r time. The q u a d r a t i c f o r c e constants f o r the in- p l a n e fcnd) v i b r a -t i o n s are l i s t e d i n t a b l e s 9 and 10. Here i t w i l l be n o t i c e d t h a t o n l y the f i r s t row f o r each s y m m e t r i c a l l y e q u i v a l e n t set of co o r d i n a t e s i s given, the other rows c o n s i s t i n g of i d e n t i c a l f o r c e constants i n a p p r o p r i a t e l y permuted order, as determined by symmetry. I t should a l s o be noted t h a t the f o r c e constants i n a gi v e n row are not a l l d i f f e r e n t . Table 9° Force Constants o f S t r e t c h i n g C o o r d i n a t e s . s l s2 v l u l u2 ^1 "^2 ^3 s l v l t 1 t 1 3 Fs Fj1 Fsv FsJ Fs<?~ Fst Fst Fv Fyu FyiA FJ+ frjr Pd F? Fut F«$ f& Ft FS & Whereas the p o t e n t i a l energy i s e a s i l y v i s u a l i z e d and i l l u s t r a t e d i n what i s r e f e r r e d to the F matrix, the k i n e t i c -66-energy i s d e s c r i b e d i n terras of the s o c a l l e d G matrix, the l a t t e r being not as i n t u i t i v e as the F m a t r i x . Table 1 0 . In-plane Bending and I n t e r a c t i o n Constants. j>, A & <t>< <f, <A <*, #2. <Pr,z Zf,' Fsf Fsf Fs<f>« Fsc/' fat' Fs«* W/ -Fu/ Fvf - Fvf F„c/' ~F,<f' ft,*' -F/*! T«f' Fuf Fu<j>3 Fuf," F«cf' Fucf1 FU*' Fc**.1 -i<p' Ftf Frf F+t" F*f Ffcf* ffvc' FtSt -Ftj$ Ftjf -F^f Ftjtf'-Frf' F^' fy* Q,' F f F$u Ftf' Ftf* Ffi*' F+S nj fy1 F4rf' FW1 fyc' F ^ Ftf' Fc/7- F^' F\f*x F> F>Fuf Fi<p Ft In d e s c r i b i n g the k i n e t i c energy, use i s commonly made of a s e t of q u a n t i t i e s G^, which are d e f i n e d by a set of equations where m^ i s the mass of the i ' t h atom and the B ^ are c o e f f i c i e n t s of the equations r e l a t i n g i n t e r n a l c o o r d i n a t e s S£, and c a r t e s i a n c o o r d i n a t e s q^, namely Thus the G^ t, form a matrix G such that the v i b r a t i o n a l k i n e t i c energy T i s g i v e n by , - 1 where G i s the r e c i p r o c a l of G and P t i s the momentum conjugate to S^. - 6 7 -I n s t e a d of the 3N c o e f f i c i e n t s B t i , i t has proved more convenient to use the v e c t o r s » as d e f i n e d p r e v i o u s l y . Now _ *1 * " ( 3 5 ) w h e r e / / ^ c = / ^ and the dot s i g n i f i e s a s c a l a r p r o d u c t . Using the above p r i n c i p l e s , the G^t 1 assume the same p a t t e r n as the f o r c e constant matrix, w i t h the a d d i -t i o n a l s t i p u l a t i o n that some G ^ t ( those whose c o o r d i n a t e s have no atoms i n common ) w i l l v a n i s h . Using a symbolism p a r a l l e l to t h a t employed f o r the F-tt'* 1* f o l l o w s t h a t <?s* Gsl, 6su, 6 st, 6sl, 6?+, Gut, Gut, 6// <&y* 6S ft Gsttj Cslf,^, a l l v a n i s h . The expre s s i o n s f o r the remaining G^t' a r e l i s -t e d i n t a b l e 1 1 . In the t a b l e , r e f e r s to the r e c i p r o c a l mass of atom i and o (£ to the r e c i p r o c a l i n t e r a t o m i c d i s t a n c e between atoms i and j o Table 1 1 . G^, f o r In-plane C o o r d i n a t e s . <?s= 6J= /re*/*" = 2/tc 6fJs -o.S-91/tc Out * ~ 0. HZ?/fe. Gfy* - o.Vtf f c»//r c - 6 8 -6^ - " (ty* - 0.fff G^U = - O. fgS 0.1 Ot f^/c G^/ = A ^y^2- * A f f«j +0 8 t*t fan)/** 6* / *-(0-1QQ f«« * 7 0 fa) ^c GJ * /Sfcc2 + O.J VS fee {Cl *rZ^)^c 6f ~- pc?f0 --(fee + 0.HH2 pc^ fee * 0S8lfa^ ~0.*23Cc*> <V* p**A" +(PA£ * / - ^ ( ^ ( V ^ f ' ^ A = ^fc* - ^ p^  /AjA^ = ^ ^ - i - r 5 - ^ p ^ ~ ^ . ^ y o ^ 3 A 6 f i - ^ . ^ p<*(A>A <£^* = (2{ct +0./7«(>cc fee. + <?.U92pa>f^Ac 6* R * 0- 383 fafes ) A 6 fi ' 0.3^2 fif/tAt - 6 9 -The GO out - o f - p l a n e bends ^,t% and NH out-of - p l a n e bend y , are unambiguously d e f i n e d i f s u b s c r i p t s 1 and 2 correspond to the GO s t r e t c h e s s^^2 a n < ^ ^ s t r e t c h V]_, r e s p e c t i v e l y . The two t o r s i o n s <S , ( i correspond to the CN s t r e t c h i n g modes u-^  2* the t o r s i o n s YtZ to the CC s t r e t c h e s t ^ g ' a n d t o r -s i o n T to CC s t r e t c h t ^ , r e s p e c t i v e l y . Using t h i s scheme, the P mat r i x f o r the out-of - p l a n e motions assumes the form of t a b l e 12. Table 12• P M a t r i x f o r Out-of-plane. C o o r d i n a t e s . f. f x y, s, Si y< & r, e, y, re F? ^ Fn % Fw As f o r the i n - p l a n e c o o r d i n a t e s , a s u i t a b l e set ofs^j was s e l e c t e d and s u b s t i t u t e d i n t o e q u a t i o n (35) to com-pute the Gr^^-t l i s t e d i n t a b l e 13<> Table 13. G^t* f o r Out-of-plane C o o r d i n a t e s . 6<? * $tl/Ji0 +0.m pc2/^ *l.6QL ft r D.112$ 792 + /. (<?Z f<u> (?W *•(• ?20 <?<LCL fe*,)^c 6^ • $$$f§£ifi+(*.060{h, +0.83ff£ +l.22t>{£ H.S/Dfcfa +/-4ZjpKfi.„)/tfc 6b' - ?.?ff fe^ Toffe rf. M f i .j.pzZ fee ^ c G{r (0.871 fr.fr +o.K8 f« ^O.S^jy -(0 M f ^ f a +,./i72e * JL, $\ : L*-?U {« ^  H. 7Sb tffc ^BfS-^/r^ -70-Gfo - -(l-ou fafa<-#.?f£fa ^ft-ox2^)/fc * 9 H (Sj, * -(4 06O f£.+t-3/D pci P « L ^ C 6^v-(iw?eZ- i-o.9s?p£ ti. pec f/.*3opec fcj/tc -z/eo e^//^ fyf (/./Sy(?<Z i-f.O&Ofct i-O.f/ofc. fee + /./OV pcoftAJ + 0.6>44fafa */. 608^pCfJ)/Uc + f.C6o pcl^ Gfo -  (/UO fapec, -/./77{& -C6?6(>cc />^ c -2iXO p j ^ , 6 f 7 r " -('-Z27fa +O.3I7(?C£CC +0.17? faf^ +/0,Sfafa)^ $SfT * (XJf7 f>cl -0.227 fa fa +0.391 p«f 6jt * -(1.301 fee *0-7lfrfX +2.2S8po.fa - r l - U l f a ^ f a , ) ^ l± - 6o Symmetry Coordinates e In order that the simplifications made possible through group theory be attained f u l l y , a further change of coor-dinates is necessary. What is done, is to form the inter-nal coordinates into linear combinations, called sym-metry coordinates, such that each symmetry coordinate be-longs to one of the symmetry species of the molecular group® In the formation of these symmetry coordinates, several points must be considered. Generally, symmetry coordinates are not chosen to give linearly independent combinations of internal coordinates, but are chosen, so that complete sets - 7 1 -o f e q u i v a l e n t c o o r d i n a t e s a r e u t i l i z e d , t h e r e d u n d a n c y c o n d i -t i o n s t h u s i n t r o d u c e d , y i e l d i n g z e r o r o o t s i n t h e s o l u t i o n o f t h e s e c u l a r equation.) F u r t h e r m o r e , t h e symmetry c o o r d i n a t e s must be o r t h o n o r m a l , Qi as w e l l ^ h a v i n g t o t r a n s f o r m a c c o r d i n g t o t h e c h a r a c t e r s o f t h e v i b r a t i o n t y p e c o n c e r n e d . As an example, t h e GO s t r e t c h e s ( S]_ and s 2 ) w i l l be t r e a t e d i n d e t a i l . I f t h e l i n e a r c o m b i n a t i o n s R l = ( S-L + s 2 )/j2 and f t a r e f o r m e d , t h e y a r e s e e n t o be o f t h e f o r m h'2,w* ( 3 6 ) where R^ i s t h e j ' t h symmetry c o o r d i n a t e , i s t h e c o e f -f i c i e n t o f t h e k ' t h i n t e r n a l c o o r d i n a t e s^., and t h e summa-t i o n i s e x t e n d e d o v e r a l l e q u i v a l e n t i n t e r n a l c o o r d i n a t e s . x2 , ( s 1 + s 2 )/(2 1 ( 3 7 ) The n o r m a l i z a t i o n c o n d i t i o n i s t h a t Thus i t i s s e e n t h a t t h e e q u a t i o n h o l d s f o r R^ and R 2 J f o r t h e o r t h o g o n a l i t y c o n d i t i o n t o be f u l f i l l e d ZfyfM-0 ( 3 8 ) has t o h o l d , w h e r e a n d / ^ r e f e r t o d i f f e r e n t symmetry c o o r d i n a t e s . A g a i n R\ a n d R 2 a r e s e e n t o o b e y t h i s r e l a t i o n , and a l s o do t h e y t r a n s f o r m a c c o r d i n g t o t h e symmetry t y p e s c o n t a i n e d i n t h e g r o u p C 2 V , n a m e l y AQ_ and B-j_ r e s p e c t i v e l y , . A l l s u c c i n i m i d e c o o r d i n a t e s o f t h e s u c c i n i m i d e m o l e c u l e -72-were c h o s e n i n s u c h a f a s h i o n , and a r e l i s t e d i n t a b l e s II4., 15* 16, and 17, belows T a b l e II4.0 A-j_ Symmetry C o o r d i n a t e s . T a b l e 15• B]_ Symmetry C o o r d i n a t e s 0 T a b l e 16« A 2 Symmetry C o o r d i n a t e s 0 ****(*, + hi) Ifc *2H s % - 7 3 -Table 17o B 2 Symmetry C o o r d i n a t e s . fill' (f, + Px)/J* k - 1» F a c t o r e d P o t e n t i a l and K i n e t i c Energy F u n c t i o n s . Since the symmetry c o o r d i n a t e s are l i n e a r l y r e l a t e d to the r e c t a n g u l a r c o o r d i n a t e s , as l o n g as i n f i n i t e s i m a l d i s -placements are c o n s i d e r e d , the p o t e n t i a l energy i s a qua-d r a t i c f u n c t i o n of the symmetry c o o r d i n a t e s as w e l l as the c a r t e s i a n c o o r d i n a t e s , i . e . M'Zc^Rttt (39) and the k i n e t i c energy i s Since the p o t e n t i a l and k i n e t i c energy must be i n v a r i a n t w i t h r e s p e c t to a l l symmetry o p e r a t i o n s , i t f o l l o w s that c i k ~ d i k " 0 w i l 6 n e v e r R i a n d R k D e l o n S t o d i f f e r e n t sym-metry s p e c i e s , and t h a t the T and V f u n c t i o n s may be f a c -t o r e d . Making use of the p r o p e r l y o r i e n t e d and normalized sym-metry c o o r d i n a t e s , the c o e f f i c i e n t s which give the poten-t i a l energy i n terms of symmetry c o o r d i n a t e s can be w r i t t e n out by making use of the e x p r e s s i o n - 7 l r f o r d i a g o n a l terms, and f o r the c r o s s - t e r m s . A d e r i v a t i o n and d e f i n i t i o n of the above F k k are to be found i n appendix 2 . Table 18. P Terms of Symmetry Co o r d i n a t e s . Fvv * F, fuf" Fuj, ~r«<t> Fit - r+'+F^ H= fy-ty f = fl' Fu/c - FJK •* Fu*. Fl/Y: fy'-Fcf Ffj = Ftp ' ftp ft*.-- FX+F+ Ftif- Fttf-F+?j> F$</ - Fx Fs!t • Ft* - F4c + Ff-«c Fsu^ Fsu +Fsu Ffjp- Ft F+3p Fst- Fst +Fs+ Ft^Fi Ft^ Fsi, - Jz Fs+ f »- r~ cr 'p hsj>= Fs$ ~ \rs$ r— r~ i c r-3 r\ ft*L - <lz r+* Fsr Fs'^Fstf fy,s Fp-Fp^ fs±* Fsk + fsl W' Fv*- ftFsL Ffr* Ffjc +FfZ F^ FIFA fyf' F&-F#f Fiy Fz F>/t Fpj0L= F^ + F ^ A %" ^ f"+ ftfic - F^ - Fcfi F/j>y~ FT. F\/p FMJ*- FX F^ Fu-f ' 0. FUL4- I- Feci--75-Table 19. F Terms o f B 1 Symmetry Coordinates Fa ~ Fs' -Z-}2" ru4> ~ Fu.fi r Fu.fi £,« - fc'-Fu.1- FU+3S fU'f. Fu"f FH- = Ft' ^ FJ-*~ FUX- - FuU ~F<-UK ftf-- F/tF^ Fu^-Fuf+Fu<f Fhhs f*J +F'f t F f Fu - FsJ-Fsu F«f* F«f*F>f Fst- Fsi-G FsV Fs'f+Fs} F^-F^'-F^ Fs*\ - Fs\ t Ft} F^'' FW FSK  s Fsk -FsX Ffa* F*yk ~F<tj><. Fscf- Fs^Fslf Ffccf-- FM F«+ Fat - F«S Fc/k F<fic +Fcf* Table 20. P Terms of A 2 Symmetry Coordinates., F(?? - F(' - Ff fpy - +F?} Fhh'- Fs't Ff (I Fprr Fn * Ff'tFy ?iir* F h ' g F™ ~~ fv\ ^ F*T- Fx Fh4 Table 21. P Terms of B 2 Symmetry C o o r d i n a t e s . FW~~ Fz' +F%~ F?y = Fz Fpy Fytr f1 Fjh - F^F{\ FH * H '  f% Fn - JJ Fyl Fnz F i ~ F f F i r - r * F w -76-Using i d e n t i c a l c o e f f i c i e n t s , the G elements of the i n t e r n a l c o o r d i n a t e s are combined i n the same way, such that the k i n e t i c energy terms become those l i s t e d i n t a b l e s 2 2 , 2 3 , 2 1 L , and 2£« Table 2 2 . G Elements of A-j_ Symmetry Coordinates* Gsu: -- -fi-SS'ftt. <*St * -PV^/Sc 6*J - ° ^©l^Ki * -0.X7O fcc/*c = £> 6,cf= ^CJO/*, Gut" -PVlJ/Sc -77-G»cf~ 0.?«£> fa/tv O.IP6«/'C-Gtcf * -0?06 %CK>//c G*L-- 0.frsfye^-ecc)j*c G/3^ ~/.3f3(=>c^c o^4>3 = o Gcficf? (o.reZfcopcv -O-H23 (?cZ*0.393pcofc^.<-(0.6Cc> fit +/.If0 6 fa* (P- yj? fee fa,-0. p*)^*. Table 23. G Elements of B1 Symmetry C o o r d i n a t e s . Gss' fc*/o Gtf: Ccf//,, +2 £ ^ • W f c o p ^ -78-Gtf' faf,.* *?J+{0-6&?J + 2 fa +*-*f* faf**)/'* 6su - 'DSS/^ Gs<j> -0 S7o fcc/<c 6s fa' fa/t^ 6>s«* -0 *7V GUtL-- D.f06 fct/tc 6«uf° '(0. W fci * /• 638fy«)/t*i 6+fa -' ~(D- IK fa +0.8 70f?co)^c Gcfci.-- - 0.1(2 3 fee {(M/U^ Table 21+. G Elements of A 2 Symmetry Coordinates • 6(?P ' ? c o ^ 0 ^co^-kOt pec ±0-m& H.7f2&o fee +/• fcofct+t- 720(?cc &bhs 7-711?^^ ±t2.70</{£ *J.S7fec# ttf.&tofafaj/tc G n - i.zzo ^0ui p£ -j.ooofe H-2Z.t>p& +/• VZJf*^^ ^* (2o * o .iff fcX +1. HJi f^cc /^/JA -(*.of{(cL + (.82* fa +1 2/ffiofcc +/.r?7pco(?c^ +X.S7/(?cc(?CJiJ/tc -3-7<)v?J-f„ 6p!r « '((.I37^d * 0- qfrtf<c p«; * / J SO fee pc^  * /• 436 fee fee )yU^ ' 6 4 Tr = (2 • fee - p . X?5" pecfoo + D.er& fee fesjfic Gfr -z - (/. fS~D pJ: +1. Oil, fit +3-2*0 fecfejL 4. f. it7fcc pew^/c -79-Table 25« G- Elements of B 2 Symmetry C o o r d i n a t e s 6 + /• / ft fee fc*> + /• T2D f>c^ P^J/c 6ft = / 22 o fcZ/s + {6- /ZD (?cZ+ * g3/fc? 4-/ 22D + 2- 62 V fee fee +/• f<c c 6?y? (/.Z3t (>co ( V +/• pec fao +1. M {Jfo ' (/3 ? 8fa fa* + *.3(>8 pc^2)^ <^& = (Q.ZM f>cZ +1 OU frofa -Off? peefc* -2Dg/ (?c*-)^(c " O- fee + I. OtV p^ v-/ /fit/fiefc,/ 6 J/tffa fa +/ 6V8 (pec p c ^ c G n 0 ^ 3«*>&)/c +(?-7Kfafa* ^.g^pj)^ ~«-«fSfe -0.«S1$ +2.Z«Dfa P^//?Y~(W//C [j. - 8. C a l c u l a t i o n of Frequencies© In p r e v i o u s s e c t i o n s i t was shown t h a t the k i n e t i c energy of v i b r a t i o n can be w r i t t e n as whereas the p o t e n t i a l energy i s expressed as T h i s leads to a s e c u l a r equation of the form where >.» HiF~-F~ » I f the above e q u a t i o n i s m u l t i p l i e d by G, a second e q u a t i o n , lGF-e\\'0 w i s o b tained, which i s very convenient f o r machine s o l u t i o n , i f i t e r a t i v e processes are to be f o l l o w e d . In e q u a t i o n E i s the u n i t m a t r i x . -80-Since both F and G are symmetrical, equation (44) can be r e w r i t t e n as I F G - E \ h 0 (45) t h i s e q u a t i o n b e i n g used i n the presen t c a l c u l a t i o n s of f r e -q uencies, s i n c e the i n v e r s e G m a t r i a G" 1 d i d not have to be c o n s t r u c t e d , and s i n c e of course X w i l l o n l y appear on the main d i a g o n a l 0 In symmetry c o o r d i n a t e s , the P mat r i x w i l l have the form the P^j b e i n g the p o t e n t i a l energy terms g i v e n i n t a b l e 18» I n s e r t i o n o f the f o l l o w i n g f o r c e constants ( i n terms of symmetry c o o r d i n a t e s ) gave the numerical P matrix (47)• Table 2 6 e Force Constants f o r Symmetry Coordinates 0 Fss-- F' ,Fsl Fsu- Fs« rFsu -F/y - F' ~ Fu^FJfFJ- *j.FSi? fn--Ff'<FF =H.3t,f fy3- Ftj X-I3H Frf-Ft'-Ff ' o.zi? f^yF^-FSj- 0.21? Fiftf-- Ff'-Fif'- 0.1x0 Ftt-.Ft+fJt'O.no - 8 1 -E q u a t i o n s h.7, 9 . 8 4 1 0 0O000 2 . 4 7 0 0 . 0000 . 0 0 0 0 oOOOO . 0000 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 6.6210 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 2 . 4 7 0 0 aOOOO 3 . 8 5 0 0 . 0 0 0 0 . 0000 . 0000 . 0 0 0 0 . 0 0 0 0 .0000 .0000 . 0 0 0 0 . 0 0 0 0 a.3690 . 0 0 0 0 oOOOO . 0000 .0000 . 0 0 0 0 . 0000 . 0 0 0 0 . 0 0 0 0 . 0000 4 . 1 3 4 0 . 0 0 0 0 oOOOO oOOOO . 0 0 0 0 . 0 0 0 0 . 0000 . 0000 . 0 0 0 0 . 0000 .2330 , 0000 . 0000 .0000 . 0 0 0 0 . 0000 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 2 3 3 0 . 0000 . 0000 .0000 . 0 0 0 0 . 0 0 0 0 .0000 oOOOO . 0 0 0 0 .0000 .7200 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0000 . 0 0 0 0 . 3 7 0 0 The e v a l u a t e d . G m a t r i x ( f r o m t a b l e 22 ) y i e l d s t h e f o l l o w i n g e q u a t i o n s (48) E q u a t i o n s 48* . 1 4 5 8 . 0000 - . 0 4 8 4 - . 0 4 1 0 . 0 0 0 0 - 0 0 4 8 9 - . 0 5 3 6 . 0 5 3 6 - . 0 4 8 9 . 0000 1 . 0 6 3 5 - . 0 5 7 9 - . 0 5 7 9 . 0000 .0000 . 0 0 0 0 . 0 6 5 4 - . 0 6 5 4 . 0 0 0 0 - . 0 4 8 4 . 1 3 0 3 - . 0 3 5 2 . 0 0 0 0 - . 1 0 5 2 . 0 0 1 2 .0530 . 0 5 1 0 - . 0 4 1 0 . 0 0 0 0 - . 0 3 5 2 . 1 6 6 5 - . 0 2 0 5 - . 0 5 7 9 . 1 1 7 5 - . 0 5 9 6 . 0 0 2 2 . 0000 . 0 0 0 0 .0000 - . 0 2 0 5 . 1 6 6 5 - . 0 7 8 4 .0000 . 0 0 0 0 - . 0 7 8 4 - . 0 4 8 9 . 0 0 0 0 - . 1 0 5 2 - . 0 5 7 9 - . 0 7 8 4 . 2 1 3 6 - . 1 2 7 2 . 0 0 8 3 .1112 - . 0 5 3 6 . 0 6 5 4 .0012 . 1 1 7 5 . 0000 - . 1 2 7 2 . 2 3 0 5 . 1 6 5 9 - . 0 0 3 4 *0536 - . 0 6 5 4 .0530 - . 0 5 9 6 ,0000 . 0 0 8 3 . 1 6 5 9 . 1 1 1 9 - . 0 1 8 8 - . 0 4 8 9 oOOOO . 0 5 1 0 .0022 - . 0 7 8 4 . 1 1 1 2 - . 0 0 3 4 - . 0 1 8 8 . 0 7 6 0 whereas m a t r i x m u l t i p l i c a t i o n o f (47) and (48) y i e l d s e q u a t i o n s 49 E q u a t i o n s 4 9 . 1 . 3 1 5 2 . 0000 .1739 - . 1 7 9 1 . 0 0 0 0 - . 0 1 1 4 - . 0 1 2 5 . 0 3 8 6 - . 0 1 8 1 - . 1 4 3 0 -7 . 0 4 1 5 -- . 2 2 2 9 . 0 0 0 0 -. 0000 . 0000 -. 0 1 5 2 - . 0 4 7 1 .0000 . 1 5 4 5 . 3 8 3 4 .3820 . 1 5 3 8 . 0 0 0 0 . 0 2 4 5 . 0 0 0 3 e0382 . 0 1 8 9 • .4905 . 0 0 0 0 • .2368 . 7 2 7 4 • .0848 ' . 0 1 3 5 . 0 2 7 4 . 0 4 2 9 . 0 0 0 8 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 - . 0 8 9 6 . 6 8 8 3 - . 0 1 8 3 . 0 0 0 0 . 0000 - . 0 2 9 0 • .7411 . 0 0 0 0 • .5258 • .2530 • .3241 . 0 4 9 8 . 0 2 9 7 . 0 0 6 0 . 0 4 1 1 • .5245 -4330 • .1278 . 5 1 3 3 . 0 0 0 0 . 0 2 9 7 .0537 . 1 1 9 4 . 0 0 0 3 . 6 5 8 4 - . 4 3 3 0 . 3 3 6 4 - 9 2 6 0 4 . 0 0 0 0 . 0 0 1 9 . 0 3 8 7 o0806 - . 0 0 7 0 - . 3 5 5 2 . 0 0 0 0 . 0 7 5 1 . 0 0 9 6 - . 3 2 4 1 . 0 2 5 9 - . 0 0 0 8 - * 0 1 3 5 . 0 2 8 7 I t s h o u l d be n o t e d t h a t a l l o f t h e i n t e r a c t i o n c o n s t a n t s have been s e t e q u a l t o z e r o e x c e p t i n g F s u > a t e r m r e p r e s e n t i n g 2 CO and CN i n t e r a c t i o n . A. CN - CN i n t e r a c t i o n c o n s t a n t P u i s o f - 8 2 -c o u r s e c o n t a i n e d i n t h e terra F u u « S i n c e many o f t h e i n t e r -a c t i o n terms a r e u n d o u b t e d l y v e r y c l o s e t o z e r o i n t h e un-p e r t u r b e d monomer ( v a p o u r ) m o l e c u l e , t h e l a c k o f o f f d i a -g o n a l t e r m s i s n o t q u i t e as c r u d e an a p p r o x i m a t i o n as w o u l d a t f i r s t a p p e a r . S e c o n d l y , i t s h o u l d be n o t e d t h a t t h e H m a t r i x i s unsym-m e t r i c a l . As t h e Alwac I I I co m p u t e r was o n l y a b l e t o s o l v e symmetrica'l m a t r i c e s , t h e H m a t r i x was m u l t i p l i e d b y i t s t r a n s p o s e a n d t h e p r o d u c t m a t r i x s o l v e d i t e r a t i v e l y t o g i v e t h e s q u a r e o f t h e e i g e n v a l u e s , i . e . X ^ » As a c o n s e q u e n c e , t h e t r a n s f o r m a t i o n c o e f f i c i e n t s ( i . e . e i g e n v e c t o r s ) b e t -ween symmetry and n o r m a l c o o r d i n a t e s a r e n o t g i v e n . The e i g e n v a l u e s , a l o n g w i t h c a l c u l a t e d and o b s e r v e d f r e -q u e n c i e s , a n d t h e i r p e r c e n t a g e d e v i a t i o n , a r e l i s t e d i n t a b l e 27o The r e l a t i o n s h i p b e t w e e n e i g e n v a l u e and f r e q u e n c y A • V * - 4JTV w X - (oofosoJl.f)*- (50) t h e l a s t f o r m o f e q u a t i o n £0 b e i n g c o n s i s t e n t w i t h t h e f o l -l o w i n g u n i t s : masses i n a t o m i c w e i g h t u n i t s , l e n g t h s i n A n g s t r o m u n i t s , s t r e t c h i n g f o r c e c o n s t a n t s i n 10^ dynes cm"' and b e n d i n g f o r c e c o n s t a n t s i n 1 0 " 1 1 dyne cm. I n t a b l e 27, t h e symbol (1) r e f e r s t o bands o c c u r i n g i n t h e v a p o u r s p e c -trum, whereas (2) r e f e r s t o bands i n t h e s p e c t r u m o f s o l i d s u c c i n i m i d e . I t w i l l be n o t i c e d t h a t agreement i s e x c e l l e n t f o r b ands i n t h e v a p o u r s p e c t r u m , whereas h i g h v a l u e s f o r t h e s y m m e t r i c CN s t r e t c h i n g mode and GWC b e n d i n g mode a r e o b t a i n e d . T h i s d i s c r e p a n c y i s i n t h e r i g h t d i r e c t i o n . - 8 3 -Table 27 . Eigenvalues Sc Frequencies of A.-j_ Vibrations. Eigenvalue Frequency(calc.) Frequency(obs.) $Dev, As= I.98I4.O K= 7«0875 0.5815 A,« 0.881+7 /V 0.7756 - 0.0000 H - 0.0374 A ^ ^ 0.1581 A*-0 . 0 0 0 0 1883 cm"1 3468 994 1226 1147 252 518 3460 cm-^ -U) 0.2$ 1001 (2) 0.7 1226 (1) 0 .0 1150 (1) 0 .3 552 (2) 6.1 Furthermore, i t i s noticed that the presence of the two re-dundancy conditions i n the secular equation resulted i n zero roots f o r h$>} and A« , as had been hoped for* The F matrix of B-j_ symmetry coordinates w i l l have the form (5D Fss Fsu Fs+ Fstf, Fsf, FS</ Fs« F«u F*t F<f> Fufij Fucf Fu« F* RH- FM Ffy Fty F+{ Ffc< Ft,*, F4}<f %•< Ffcf Ffa Ft* where the F^. are the terms given i n table 19* If the force constants of table 28 are inserted, the numerical F matrix w i l l be equations 52 . Equations 5 2 . F-9.8410 2.4700 0.0000 0.0000 0.0000 0.0000 0.0000 2.4700 5.1190 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 4.3690 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2330 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0*0000 0.2330 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5200 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500 -6J+-Table 28« Force Constants of Symmetry V i b r a t i o n s . Fss* Fs'-Fsz= f«u: FJ-FS *r.i/9 F«- fr>~FS Ftf- Ff + Ff "  0 2 3 3 Ftf-Ff+Rf* * S * ° The e v a l u a t e d G m a t r i x ( from t a b l e 23 ) i s r e p r e s e n t e d by equations 53* below: Equations 53* .Uj.58 — .014.824. -oOJ+lO -.0I4.89 - o 0 5 3 6 . 0536 -.0I4.89 - o0li.81| . 1 7 9 1 - . 0 3 5 2 - o l 0 5 2 - . 1 0 7 2 - . 1 6 8 8 . 0 5 1 0 -.Olj.10 - . 0 3 5 2 a l 6 6 5 - . 0 5 7 9 - . 1 1 7 5 - « 0 5 9 6 - . I O 8 7 -.Oii.89 - o l 0 5 2 - . 0 5 7 9 . 2136 . 1272 . 0 0 8 3 . 0 9 8 1 - . 0 5 3 6 - . 1 0 7 2 - . 1 1 7 5 o l 2 7 2 .2662 - . 1 3 2 0 .0031]-. 0536 - 0 I 6 8 8 - . 0 5 9 6 . 0 0 8 3 - . 1 3 2 0 2.2914-7 - . 0 1 8 8 -.0l}.89 a 0 5 l 0 - . 1 0 8 7 . 0 9 8 1 .0031}- - . 0 1 8 8 .2J+18 M a t r i x m u l t i p l i c a t i o n of equations 52 and 53 y i e l d s H-Equations $k. 1 . 3 1 5 2 - o 0 3 3 9 -.14-905 - . 7l4.ll - . 7 9 2 3 . 1 1 0 5 - . 3 5 5 2 o l l 2 5 o7972 - . 2 8 1 5 - . 6 5 9 3 - . 6 8 1 1 - . 7 3 1 7 *1203 - . 1 7 9 1 - . 1 5 3 8 • 727k . 2 5 3 0 - . 5 1 3 3 - .26OI4. -.14-714.9 -.0111). - . 02I4.5 - . 0 1 3 5 .OI4.98 . 0 2 9 7 .0019 .0229 - . 0 1 2 5 - . 0 2 5 0 - . 0 2 7 4 . 0 2 9 7 . 0 6 2 1 - . 0 3 0 8 - . 0 0 0 8 . 0 2 8 0 - . 0 8 8 0 - . 0 3 1 1 .001+3 - 0 O 6 8 9 1.1914-7 - . 0 0 9 9 - . 0 1 2 2 . 0 1 2 8 -0O27I4. .0214.5 . 0 0 0 9 - .001+7 . 0 6 0 5 The e i g e n v a l u e s , c a l c u l a t e d and observed f r e q u e n c i e s , and the percentage d e v i a t i o n of the B-^  v i b r a t i o n s are t a b u l a t e d i n t a b l e 29. - 8 5 -Table 29 •> Eigenvalues and Frequencies of B-j_ V i b r a t i o n s . E i g e n v a l u e F r e q u e n c y ( c a l c . ) Frequency(obs.) $Dev» Xr- 1.9040 1798 cm" 1 1770 crrT^-d) 1 .6$ 0.9991 1303 1335 (1) 2 .4 At: 1.0318 1320 1290 (1) 2 .3 / U , 0.0000 A\*0.0265 284 290 (2) 2.0 Atf-. 1.4606 1576 ca . 1550 (1) Ax- 0.6050 321 304 (2) 5.6 Again agreement i s seen to be as good as can be expected without t a k i n g Into account i n t e r a c t i o n c o n s t a n t s . The e v a l u a t e d G- matrices f o r the Ag and Bg v i b r a t i o n s are g i v e n i n appendix 3 . As i t was f e l t t h a t not s u f f i c i e n t low-frequency data was a v a i l a b l e to make d e f i n i t e assignments, no c a l c u l a t i o n of f r e q u e n c i e s f o r B 2 and i n f r a r e d i n a c t i v e A 2 fundamentals was undertaken. 4 - 9 . D i s c u s s i o n and C o n c l u s i o n s . As has been mentioned i n the i n t r o d u c t i o n , the e l u c i d a t i o n of amide, polyamide, and imide s p e c t r a , Is plagued by s e v e r a l d i f f i c u l t i e s . To date, the s p l i t t i n g of the CO a b s o r p t i o n i n t o two w e l l -d e f i n e d bands near 1770 and 1690 cm" 1 i n v a r i o u s compounds, i n c l u d i n g s u c c i n i m i d e , has been e x p l a i n e d by assuming a mecha-n i c a l c o u p l i n g between the two CO o s c i l l a t o r s , thus l e a d i n g to symmetric and asymmetric v i b r a t i o n s . T h i s c o u p l i n g e f f e c t would c e r t a i n l y be present , and p r o b a b l y c o n s i d e r a b l y more pronounced, i n molecules with two adjacent CO f u n c t i o n s , as i s the case i n i s a t i n * However, s p e c t r a l i n v e s t i g a t i o n of -86-o f i s a t i n d i d n o t show two CO b a n d s , but s i n g l e Amide I and Amide I I bands i n n o r m a l p o s i t i o n s n e a r 1725 and 1615 cm" 1. T h i s f a c t does n o t l e n d much s u p p o r t t o t h e c o u p l i n g theory., A r a t h e r d i f f e r e n t e x p l a n a t i o n i s o f f e r e d h e r e . Prom d i a -gram 22 , i t c a n be s e e n t h a t t h e i n d i v i d u a l s u c c i n i m i d e mole-c u l e s a r e f a v o u r a b l y p o s i t i o n e d f o r t h e f o r m a t i o n o f a d i m e r , t h r o u g h an e i g h t - m e m b e r e d r i n g , a s i t u a t i o n i l l u s t r a t e d i n f i g u r e 26. I f t h i s s i t u a t i o n i s p r e s e n t , t h e m o l e c u l e w o u l d c o n t a i n one h y d r o g e n - b o n d e d CO f u n c t i o n and one n o n - h y d r o g e n -b o n d e d CO f u n c t i o n , t h e f o r m e r r e s u l t i n g i n t h e h i g h e r i n t e n -s i t y 1690 c m - 1 band, t h e l a t t e r i n t h e 1770 cm""1 b a n d . S e c o n d l y , t h e a b s e n c e o f t h e Amide I I band has p r e s e n t e d c o n s i d e r a b l e d i f f i c u l t y i n t h e lband a s s i g n m e n t o f v a r i o u s CONH g r o u p c o n t a i n i n g compounds. I n t h e p o s t u l a t e d d i m e r , t h e e q u i l i b r i u m i n t e r h y d r o g e n d i s t a n c e i s 2 .3 A, w i t h an i n t e r h y d r o g e n d i s t a n c e o f 1.65 A a t maximum a p p r o a c h * ( An NH d i s t a n c e o f l.Olj. A has b e en assumed ) . I f t h e u n i t g i v i n g r i s e t o t h e i n f r a r e d s p e c t r u m i s c o n s i d e r e d t o be t h i s d i m e r , and n o t t h e s u c c i n i m i d e monomer, t h e n t h e p o s s i b i l i t y o f an a s y m m e t r i c b e n d i n g f r e q u e n c y ( d i s p l a c e d t o w a r d s h i g h e r cm" 1 ) a n d o f a s y m m e t r i c f r e q u e n c y ( d i s p l a c e d t o w a r d s l o w e r cm" 1 ) e x i s t . The two bands i n t h e s p e c t r u m o f c r y s t a l l i n e s u c c i n -i m i d e , a t I783 and 1376 cm" 1, have been a s s i g n e d t o s u c h modes, s i n c e b o t h bands d i s a p p e a r upon d e u t e r a t i o n , g i v i n g r i s e t o two c o r r e s p o n d i n g new b a n d s , as w e l l as s h o w i n g t h e e x p e c t e d s h i f t upon d i l u t i o n o f v a r i o u s s o l u t i o n s o f s u c c i n i m i d e . -88-I t i s a l s o e x t r e m e l y i n t e r e s t i n g to n o t e t h a t t h e a v e r a g e o f t h e 1783 a n d 1376 c m - 1 bands i s 1579 cm"*1, a f r e q u e n c y r e g i o n i n w h i c h a "normal"' h y d r o g e n - b o n d e d NH i n - p l a n e d e f o r m a t i o n f r e q u e n c y w o u l d be e x p e c t e d , a n d where i n f a c t t h e Amide I I ba n d i n l e s s ambiguous s p e c t r a o c c u r s . To s u b s t a n t i a t e t h e c l a i m o f i n t e r a c t i o n o f h y d r o g e n atoms, p o t e n t i a l e n e r g y d i a g r a m s , u s i n g b o t h a h a r m o n i c o s c i l l a t o r and a Morse t y p ^ p o t e n t i a l f u n c t i o n , were drawn» The p o t e n t i a l e n e r g y was p l o t t e d as a f u n c t i o n o f d i s p l a c e -ment o f f t h e l i n e o f c e n t e r s o f oxy g e n and n i t r o g e n atoms. A l t h o u g h t h e p o t e n t i a l f u n c t i o n s showed no o v e r l a p f o r a s m a l l number o f v i b r a t i o n a l q u a n t a , t h i s o b j e c t i o n may be overcome* S i n c e t h e above p o t e n t i a l c u r v e s a r e f o r a n e u t r a l atom, and s i n c e t h e h y d r o g e n atoms i n t h e c a s e I n q u e s t i o n do u n d o u b t e d l y p o s s e s s a c o n s i d e r a b l e amount o f i o n i c c h a r a c -t e r , w h i c h i s n o t e a s i l y e s t i m a t e d , t h e f a i l u r e o f t h e c u r v e s t o o v e r l a p , i s n o t c r i t i c a l * . The p o s s i b i l i t y t h a t t h e 3160 c m - 1 b a n d r e p r e s e n t s an aymmetric NH s t r e t c h i n g mode o f s u c h a d i m e r , whereas t h e ambiguous 3080 c m - 1 b a n d o r i g i n a t e s i n t h e c o r r e s p o n d i n g exists-s y m m e t r i c a l mode, i s a l o o p o s c i b l o u -89-APPENDIX I . PREPARATION OP N-h-SUCCINIMIDE-d^. 3.2 ml ( 0.0266 moles ) o f ( C D 2 B r ) 2 were b r o u g h t t o b o i l i n a r e a c t i o n f l a s k w i t h 8 ml o f 95$ EtOD. I4..2 gm ( 0.06i|.6 moles ) o f KCN i n 7 ml o f 99.82$ D2O were added o v e r a 12 m i n u t e p e r i o d , and t h e m i x t u r e r e f l u x e d f o r 25 h o u r s . F i l -t r a t i o n a nd w a s h i n g w i t h 100$ EtOQ y i e l d e d c r u d e ( C D 2 C N ) 2 , w h i c h was h y d r o l y z e d t o (CT>2C00Na)2 by r e f l u x i n g f o r 2if. h o u r s w i t h 25 ml o f 6N NaOD i n D 20 o C o n v e r s i o n t o t h e a c i d , (CD 2C00H) 2, was a c c o m p l i s h e d b y p a s s i n g t h e s a l t s o l u t i o n t h r o u g h a n A m b e r l i t e r e s i n c o l u m n , and t h e n pumping t h e e l u a t e t o d r y n e s s . 2.69 gm o f s l i g h t l y y e l l o w i s h , c r u d e (CD 2C00H) 2, h a v i n g a m e l t i n g p o i n t o f 176 - l80°C, was o b t a i n e d . The c r u d e d e u t e r o s u c c i n i c a c i d was p l a c e d i n a 10 ml E r l e n m e y e r f l a s k , i c e - c o o l e d t o g e t h e r w i t h 3 ml o f c o n e . NHjjOH, a n d s i n c e s o l u t i o n o f t h e s u c c i n i c a c i d d i d n o t t a k e p l a c e , h e a t e d t o 100°C. A f t e r c a . 3 ml o f l i q u i d a nd ammonia v a p o u r h a d b e e n g i v e n o f f , h e a t i n g t o c a . 280°C c a u s e d t h e c r u d e d e u t e r o s u c c i n i m d e t o d i s t i l . R e c r y s t a l l i z a t i o n f r o m E tOH y i e l d e d 0).82 gm (30.0$ y i e l d ) o f N - h - s u c c i n i m i d e - d ^ , h a v i n g a m e l t i n g p o i n t o f 117 - 119°C ( c o r r . ) . - 9 0 -APPENDIX I I . P k k IN SYMMETRY COORDINATES. The potential energy in internal coordinates of a system is of the form Since this expression can be divided into parts which run over equivalent coordinate sets only, i t follows that the introduction of symmetry coordinates w i l l not mix additive parts of the potential energy. If the symmetry coordinates of such a diagonal part or block are given by then Insertion in the potential energy equation yields Evidently the coefficients of the potential energy in sym-metry coordinates in terms of internal coordinates are fa' Hence Since the indices k' and t" can be chosen arbitrarily, i t follows that -91-Consequently which i s the r u l e f o r computing d i a g o n a l elements of the F m a t r i x . Por the o f f - d i a g o n a l elements, an analogous proof applies« - 9 2 -APPENDIX I I I . AND B 2 G MATRICES. A 2 M a t r i x . . 14-605 - . 6 2 5 1 •I4.I88 -.2081). 6251 .81+15 -4746 . 1 3 1 9 6= . 1+188 -.1+746 .11+26 - . 2 9 5 0 2081+ . 1 3 1 9 - » 2 9 5 0 . 2 1 8 0 B 2 M a t r i x . .521+8 .oooo - . 1 0 8 2 . 2 5 7 7 f_ . 0 0 0 0 . 6 5 1 4 » 5 5 8 9 - . 3 1 4 8 - . 1 0 8 2 . 5 5 8 9 .0811+ -.1614-9 o2577 - . 3 1 4 8 -.161+9 . 5 2 3 3 - 9 3 -BIBLIOGRAPHYo 1) L a d e l l & Post, A c t a C r y s t . 7*. 559 (1954) 2) Brathoude & L i n g a f e l t e r , A c t a C r y s t . l i s 729 (1958) 3) Leung & Marsh, A c t a C r y s t * 11: 17 (1958) 1+) Vaughan & Donohue, Ac t a C r y s t . 5s 530 (1952) 5) S e n t i & Harker, J . Am. Chem. Soc* 62: 2008 (1940) 6) A y e r s t & Duke, A c t a C r y s t . 1% 588 (1951+) 7) Wright & K i n e , A c t a C r y s t e 7s 283 (1954) 8) Parry, A c t a C r y s t . 7% 313 (1951J-) 9) Pasternak, A c t a C r y s t . 6s 808 (1953) 10) Davies & Blum, A c t a C r y s t . 8: 129 (1955) 11) Wiebanga & Moerman, J . Am. Chem. Soc. 7J4.S 6156 (1952) 12) Corey, J . Am» Chem. Soc. 60s 1598 (1938) 13) Richards & Thompson, J . Chem. So c e 1947s 121+8 11+) Darmon, D i s c . F a r a d . Soc. 9s 325 (1950) 15) P a u l i n g , Corey, & Brenson, P r o c . U.S. Wat. Acad. S c i . 231+s 2057 (1950) 16) E l l i o t , Ambrose, & Temple, J . Chem. Phys. 16: 877 (191+8) 17) Bath & E l l i s , J . Chem. Phys. 1+5: 20l+ (191+1) 18) Lenormant, D i s c . F a r a d . Soc.. 9s 319 (1950) 19) Lenormant, Ann. Chim. 5s 459 (1950) 20) G i e r e r , Z. N a t u r f o r s c h . 8B: 61+1+, 654 (1953) 21) F r a z e r & P r i c e , Nature 170: 1+90 (1952) 22) F r a z e r & P r i c e , Proc* Roy. Soc. 11+1B: 66 (1953) 23) Abbott & Ambrose, Pr o c . Roy. S o c 0 231+A: 21+7 (1956) -9l+-21+) Miyazawa, Shimanouchi, & Mizushima, J. Chem. Phys 0 21+; I4.O8 (1956) 25) Randall, Fowler, Fusan, & Dangl, Infrared Determination of Organic Structures (Van Nostrand, 191+9) 26) Darman & Sutherland, J. Am* Chem. Soc e 69; 2071+ (191+7) 27) Mason, Acta Cryst. 9; l}-05 (1956) 28) Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, 191+5) 29) Wilson, Decius, & Cross, Molecular Vibrations (McGraw-H i l l , 1955) 30) Bhagavantam & Venkatarayudu, Proc. Ind* Acad. S c i . 9A; 22k (1939) 31) Bhagavantam, Proc. Ind, Acad. S c i . 13A; 51+3 (191+1) 32) Halford, J . Chem. Phys. ll+s 8 (191+6) 

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