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X-ray crystallographic studies of racemic and optically active 4, 4’-dimethyl-1, 1’-binaphthyl 1978

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X - R A Y C R y S T A L I O G R A P H I C S T U D I E S OF R A C E M I C AND . O P T I C A L L Y A C T I V E 4 , 4 ' - D I M E T H Y L - 1 , 1 • - B I N A P H T M Y L b y RICHARD A - P A U P T I T E . S c , U n i v e r s i t y o f C a p e T o w n , 1975 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 FOR THE DEGREE OF MASTER OF S C I E N C E IN THE FACULTY OF GRADUATE STUDIES i n t h e d e p a r t m e n t o f C H E M I S T R Y He a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d z The U n i v e r s i t y o f B r i t i s h C o l u m b i a N o v e m b e r 1978 © R i c h a r d A . P a u p t i t , 1978 In presenting th i s thes i s in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I further agree that permission for extensive copying of th is thes is for scholar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thesis for f inanc ia l gain sha l l not be allowed without my written permission. Department of The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date i i A B S T B A C T I n c o n t r a s t t o 1, 1 ' - b i n a p h t h y l , r a c e m i c 4 , 4 * - d i r a e t h y l - 1 , 1 ' ^ b i n a p h t h y l d o e s n o t u n d e r g o s p o n t a n e o u s r e s o l u t i o n u p o n h e a t i n g f r o m room t e m p e r a t u r e t o j u s t b e l o w t h e m e l t i n g p o i n t . O p t i c a l l y a c t i v e d i m e t h y l b i n a p h t h y l may be o b t a i n e d by s e e d i n g t h e r a c e m i c m e l t s i t e o p t i c a l l y a c t i v e n a p h t h i d i n e . T h e c r y s t a l s t r u c t u r e s o f b o t h t h e r a c e m i c a n d o p t i c a l l y a c t i v e d i m e t h y l b i n a p h t h y l s w e r e s o l v e d i n t h e h o p e o f u n d e r s t a n d i n g t h e a h o v e o b s e r v a t i o n s . f h e r a c e m a t e c r y s t a l l i z e s i n t h e m o n o c l i n i c s p a c e g r o u p C 2 / c w i t h c e l l p a r a m e t e r s a = 1 3 - 2 2 5 , b = 1 Q . 7 6 8 , c = 1-1.572 A a n d 114.04 0 . T h e r e a r e f o u r m o l e c u l e s p e r u a i t - c e l l ; two h a v e t h e B a n d two h a v e t h e S c o n f i g u r a t i o n . The s t r u c t u r e was s o l v e d u s i n g d i r e c t m e t h o d s a n d r e f i n e d t o a = 0 . 0 7 4 . T h e r e i s a 3 ° h e a d i n t h e p l a n e o f t h e n a p h t h a l e n e r e s i d u e s , w h i c h a r e c i s - o r i e n t e d w i t h a n a n g l e o f 6 8 ° b e t w e e n t h e m . The o p t i c a l l y a c t i v e f o r m b e l o n g s t o one o f t h e t e t r a g o n a l s p a c e g r o u p s P 4 t 2 \ 2 o r P 4 j 2 i 2 w i t h c e l l p a r a m e t e r s a = b = 8 . 3 0 3 1 a n d c = 2 3 . 7 0 6 X . D i r e c t m e t h o d s s e r e u s e d t o s o l v e t h e s t r u c t u r e and t h e f i n a l fi was 0 . 0 6 0 . T h e r e a r e f o u r m o l e c u l e s p e r u n i t - c e l l o f i d e n t i c a l c o n f i g u r a t i o n , h u t i t c o u l d n o t be d e t e r m i n e d w h e t h e r t h i s was R o r S . T h e n a p h t h a l e n e r e s i d u e s show a 2 - 7 0 b e n d a a d a r e a l s o c i s - o r i e n t e - d , h u t " K i t h a n a n g l e o f 8 0 » b e t w e e n t h e m . B o n d l e n g t h s and a n g l e s a r e c o n s i s t e n t » i t h v a l u e s i i i p r e v i o u s l y r e p o r t e d f o r 1,1 " - h i n a p h t h y l and n a p h t h a l e n e - The r a c e m a t e p a c k s somewha t more e f f i c i e n t l y a n d p e r h a p s f o r t h i s r e a s o n i t i s s l i g h t l y more s t a b l e t h a a t h e o p t i c a l l y a c t i v e f o r m - I t i s d i f f i c u l t h o w e v e r t o e x p l a i n t h e d i f f e r e n c e i n b e h a v i o u r b e t w e e n t h e m e t h y l a t e d a n d u n m e t h y l a t e d b i n a p h t h y l s on t h e b a s i s o f t h e s e r e s u l t s a l o n e . F u r t h e r s t u d i e s w o u l d i n c l u d e t h e c r y s t a l s t r u c t u r e s o f o p t i c a l l y a c t i v e 1 , 1 * - b i n a p h t h y l a n d v a r i o u s n a p h t h i d i n e s . XV T A B L E OF CONTENTS T i t l e P a g e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i A b s t r a c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . r - . » - - - , - . . - - - i i T a b l e o f C o n t e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i v L i s t o f T a b l e s . . . . . . . . . . . . . . . . . . . . . . . . . . v i L i s t o f F i g u r e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v i i A c k n o w l e d g e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v i i i PART O N E : INTRODUCTION . . . . . . . . . 1. . P r e p a r a t i o n o f C r y s t a l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 PART TWO: C R Y S T A L STRUCTURE OF RACEMIC 4 , 4 ' - D I M E T H Y L - 1, 1 * - B I N A P H T H Y L . . . . . 7 E x p e r i m e n t a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 S t r u c t u r e A n a l y s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 11 PAST T H R E E : C R Y S T A L STRUCTURE OF O P T I C A L L Y A C T I V E 4 , 4 » - D I M E T H Y L - 1 , 1 » - B I N A ? H T H Y L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 E x p e r i m e n t a l . . . . . . . . . . . . . . . . . . . . . . « . . . . . . . . . . . . . . . . . . . 20 S t r u c t u r e A n a l y s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 P A R T F O U R : CONCLUSION 31 B o n d L e n g t h a n d A n g l e C o m p a r i s o n . . . . . . . . . . . . . . . . . . . . . . 32 I n t r a m o l e c u l a r D i f f e r e n c e s 32 C e l l P a r a m e t e r C o m p a r i s o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 P a c k i n g C o m p a r i s o n . . . . . . . . . . . . . . . . . . . . . . 35 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 V R E F E R E N C E S . . . . . . . . . . . . . 4 0 A P P E N D I X I i S t r u c t u r e F a c t o r s f o r t h e R a c e m a t e . . . . . . . . . . . 42 A P P E N D I X I I : S t r u c t u r e F a c t o r s f o r t h e O p t i c a l l y A c t i v e F o r m 5 1 v i L I S T OF T A B L E S . PART TWO; C R Y S T A L STRUCTURE OF R A C E M I C 4 , 4 « - D I M E T H Y L - 1 , 1 B I N A P H T H Y L . . . . . . . . . . . . 7 T A B L E I : C r y s t a l D a t a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 T A B L E I I s E S t a t i s t i c s 10 T A B L E I I I : F r a c t i o n a l A t o m i c P a r a m e t e r s . . . . . . . . . . . . . . 12 T A B L E I V : T h e r m a l P a r a m e t e r s . . . . . . . . . . . . . . . . . . . . . . . . . 13 T A B L E V : Mean P l a n e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 T A B L E V I : B o n d L e n g t h s 17 T A B L E V I I : B o n d A n g l e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 PART T H R E E ; C R Y S T A L STRUCTURE OF O P T I C A L L Y A C T I V E 4 , 4 ' - D I M E T H Y L - 1 , 1 ' - B I N A P H T H Y L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 : C r y s t a l D a t a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 £ S 1 3 1 1 s t i c s 21 ? r a c t i o , n a l A t o m i c P a r a m e t e r s . , . « , . , . . . - . , . , - - 24 T A B L E X I : T h e r m a l P a r a m e t e r s . . . . . . . . . . . . . . . . . . . . . . . . . 25 Sean P l a n e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 C X O S € COXl fc CI C t S » » « m •» m m m »•*•<» * «» « o • •* «• 2 "7 Bond L e n g t h s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 PART F O U R : CONCLUSION . . . . . . . . . . . . . . . , . , - . . - - - . - - . 3 1 T A B L E X V I : A v e r a g e B o n d L e n g t h C o m p a r i s o n 34 T A B L E V I I I T A B L E I X : T A B L E X :  I : T A B L E X I I T A B L E X I I I T A B L E X I V T A B L E XV : v i i L I S T OF F I G U R E S F i g u r e 1. E n a n t i o m e r i c C o n v e r s i o n o f 1,1 ' - B i n a p h t h y l . . . . . 2 F i g u r e 2 . P h a s e D i a g r a m f o r 1 , 1 * - B i n a p h t h y l . 4 F i g u r e 3 . P r e p a r a t i o n o f S a c e m i c 4 r 4 » - D i m e t h y l - 1 , 1 * - c i n a p h t h y l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 F i g u r e 4 . M o l e c u l a r D r a w i n g o f S a c e m i c 4 , 4 * — D i m e t h y l - 1 , 1 F i g u r e 5 . flolecular D r a w i n g o f O p t i c a l l y A c t i v e 4 , 4 J - D i m e t h y l - 1 , l « - h i n a p h t h y l . . , . . , . , . . . , . . . , . „ , . , . . , . . , . . - 30 F i g u r e 6 . B o n d L e n g t h C o m p a r i s o n . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 F i g u r e 7 . P a c k i n g D i a g r a m f o r t h e B a c e o a t e . . . . . . . . . . . . . . . . . . , 36 F i g u r e 8 . * Wedge N e s t i n g * i n t h e B a c e m a t e U n i t C e l l . . . . . . 37 F i g u r e 9 - P a c k i n g D i a g r a m f o r t h e O p t i c a l l y A c t i v e F o r m - . 38 v i i i ACKNOWLEDGEMENTS I am v e r y g r a t e f u l t o P r o f . J a m e s T r o t t e r f o r h i s v a l u a b l e a s s i s t a n c e a n d a d v i c e d u r i n g t h e l a s t two : y e a r s , a n d a l s o D r . S t e v e H e t t i g a n d t h e p o s t d o c t o r a l f e l l o w s i n o u r g r o u p f o r t h e i r a d v i c e a n d h e l p w i t h t h e e x p e r i m e n t a l w o r k - I w o u l d l i k e t o t h a n k D r . H i c h a r d P i n c o c k f o r s u p p l y i n g t h e c r y s t a l s and b a c k g r o u n d m a t e r i a l . F i n a l l y I s o u l d l i k e t o t h a n k P r o f . C . A . M c D o w e l l f o r i n t e r e s t i n g me i n t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . 1 PART ONE INTRODUCTION 2 T h i s t h e s i s d e s c r i b e s t h e X - r a y c r y s t a l s t r u c t u r e a n a l y s e s o f r a c e m i c a n d o p t i c a l l y a c t i v e k,4'-dimethyl-1,1'-binaphthyl. T h e b a c k g r o u n d t h e o r y i n v o l v e d i n x - r a y t e c h n i g u e s i s c o v e r e d i n s e v e r a l s t a n d a r d t e x t s , * - — s and a l l n o m e n c l a t u r e , c o n v e n t i o n s a n d c r y s t a l l o g r a p h i c s y m b o l s u s e d a r e c o n s i s t e n t v i t h t h o s e d e s c r i b e d i n I n t e r n a t i o n a l T a b l e s f o r X - r a y C r y s t a l l o g r a p h y - 6 T h e r e h a s b e e n c o n s i d e r a b l e i n t e r e s t i n b i n a p h t h y l s i n r e l a t i o n t o t h e s p o n t a n e o u s r e s o l u t i o n o f r a c e m i c m i x t u r e s i n t o o p t i c a l l y p u r e s a m p l e s . 0 1 , 1 ' - B i n a p h t h y l i s c o n v e r t e d i n t o i t s e n a n t i o m e r by a s i m p l e r o t a t i o n a b o u t t h e 1 ,1* b o n d ( s e e F i g . 1 ) , Two c r y s t a l l i n e f o r m s o f 1,1 * - b i n a p h t h y l a r e k n o w n ; " R - 1 , 1 * - B i n a p h t h y l S - 1 , 1 f - B i n a p h t h y l F i g u r e 1. E n a n t i o m e r i c C o n v e r s i o n o f 1 , 1 ' - B i n a p h t h y l t h e l o w m e l t i n g f o r m ( m - p . = 1 4 5 ° C ) h a s h e e n s h o w n by X - r a y s t r u c t u r e a n a l y s i s 4 2 t o be t h e r a c e m a t e w i t h t w o B a n d t w o S m o l e c u l e s p e r u n i t - c e l l , a n d t h e h i g h m e l t i n g f o r m ( m . p . 1 5 8 ° C ) t o be t h e o p t i c a l l y a c t i v e f o r m ( i . e . o n l y m o l e c u l e s o f o n e e n a n t i o m e r p e r u n i t - c e l l ) . 3 I t h a s b e e n f o u n d t h a t i n a c e r t a i n t e m p e r a t u r e r a n g e , t h e o p t i c a l l y a c t i v e f o r m i s t h e more s t a b l e t h e r m o d y n a m i c a l l y a n d s o upon h e a t i n g a r a c e m i c s a m p l e i n t o t h i s t e m p e r a t u r e r a n g e s p o n t a n e o u s r e s o l u t i o n c o u l d o c c u r - ' T h e p h a s e d i a g r a m c o r r e s p o n d i n g t o t h i s i s s h o w n i n F i g - 2 w h e r e t h e d o t t e d l i n e s h o w s t h e b e h a v i o u r c f t h e r a c e m a t e upon h e a t i n g - I t » a s f o u n d t h a t o n e c o u l d c o n t r o l t h e c h o i c e o f e n a n t i o m e r t o « h i c h t h e r a c e m a t e w o u l d r e s o l v e b y p i c k i n g a n o r i g i n a l c o m p o s i t i o n e g u i v a l e n t t o a p o i n t ( e . g . P) j u s t t o t h e r i g h t ( o r l e f t ) o f t h e v e r t i c a l d o t t e d l i n e a n d h e a t i n g i t - A t a l l t i m e s t h e m i x t u r e w o u l d c o n s i s t o f t h e r a c e m a t e p l u s S ( o r B) i m p u r i t y , a n d c r y s t a l s o f t h e R f o r S) f o r m w o u l d n o t n u c l e a t e . T h e s e o b s e r v a t i o n s o f t h e b e h a v i o u r o f 1 , 1 ' - b i n a p h t h y l w e r e n o t n o t i c e d i n 4 , 4 * - d i m e t h y l - 1 , 1 ' . b i n a p h t h y l : 1 3 i n t h e d i m e t h y l c o m p o u n d t h e r a c e m i c f o r m s e e m s t o b e a t a l l t i m e s t h e more s t a b l e , a n d no o p t i c a l a c t i v i t y d e v e l o p s u p o n h e a t i n g ( e x p e r i m e n t a l l y t h e a - f o r m o f t h e d i m e t h y l c o m p o u n d h a s been o b t a i n e d by s e e d i n g t h e a s - m e l t w i t h B - n a p h t h i d i n e . ) . I t i s h o p e d t h a t t h i s m i g h t be b e t t e r u n d e r s t o o d by c o m p a r i n g c r y s t a l s t r u c t u r e s o f t h e r a c e m i c a n d o p t i c a l l y a c t i v e f o r m s . P r e p a r a t i o n o f C r y s t a l s ( B . E - P i n c o c k ) T h e p r e p a r a t i o n o f t h e r a c e m a t e * * i s i l l u s t r a t e d i n F i g . 3 . , 4 - B r o m o - 1 - m e t h y l n a p h t h a l e n e (3) was p r e p a r e d f r o m 1- m e t h y l n a p h t h a l e n e Q ) b y t h e s u l f o n a t i o n - b r o m o d e s u l f o n a t i o n p r o c e d u r e ( d e v e l o p e d by F i e s e r 1 5 ) v i a (2) i n 35% y i e l d . B a c e m i c 4 , 4 » - d i m e t h y l - 1 , 1 * - b i n a p h t h y l (4) was f o r m e d (26 - 4 1 $ y i e l d ) 158 145 C b 1 L U I - 0 RS 50 %-S-enantiom<2r R + S r i I i i RS+R RS+S P • 100 F i g u r e 2 - P h a s e D i a g r a m f o r 1,1 * - B i n a p h t h y l 5 6 b y t h e c o u p l i n g o f t h e G r i g n a r d r e a g e n t d e r i v e d f r o m ( 3 ) , a n d was c r y s t a l l i z e d f r o m a c e t o n e t o g i v e c o l o r l e s s r o d s . O p t i c a l l y a c t i v e 4 , 4 f - d i m e t h y l - 1 , 1 • - . b i n a p a t h y ! was p r e p a r e d 1 * b y t h e i n d u c e d r e s o l u t i o n o f t h e r a c e m i c c o m p o u n d u s i n g o p t i c a l l y a c t i v e n a p h t h i d i a e a s a s e e d . B e s t r e s u l t s s e r e o b t a i n e d by w e i g h i n g o u t 50mg s a m p l e s o f r a c e m a t e c o n t a i n i n g 1% n a p h t h i d i a e i n t o a m p u l e s w h i c h w e r e s e a l e d i n a i r . T h e s e s a m p l e s were h e l d i n a b a t h a t 1 5 0 ° C f o r 4 m i n u t e s a l l o w i n g t h e d i m e t h y l b i n a p h t h y l t o m e l t w h i l e t h e n a p h t h i d i n e ( m . p . 206 - 2 0 7 ° C ) r e m a i n e d s o l i d a n d w o u l d s e e d t h e s u b s e q u e n t c r y s t a l l i z a t i o n . N o r m a l l y c r y s t a l s f o r m e d o v e r n i g h t . 7 PART TWO; C R Y S T A L STRUCTURE OP RACEMIC 4 . 4 ' — D I B E T H Y L — 1 , 1 ' - B I N A P H T H Y L 8 E x p e r i m e n t a l - P r e l i m i n a r y x—ray p h o t o g r a p h y s h o w s t h e w e l l - r f o r m e d c o l o r l e s s c r y s t a l s t o be m o n o c l i n i c ; s y s t e m a t i c a b s e n c e s { f o r g e n e r a l h k l , h+k=2n+1 ; f o r t h e h O l z o n e , l = 2 n + 1 ) i n d i c a t e t h a t t h e s p a c e g r o u p i s e i t h e r C 2 / c o r C c - U n i t - c e l l a n d i n t e n s i t y d a t a were m e a s u r e d on a D a t e x - a u t o m a t e d GE XfiD 6 d i f f r a c t o m e t e r w i t h Cu K x r a d i a t i o n u t i l i z i n g t h e € - 2 9 s c a n t e c h n i q u e . U n i t - c e l l p a r a m e t e r s w e r e r e f i n e d by l e a s t - s g u a r e s m e t h o d s f r o m m a n u a l l y o b t a i n e d 2% v a l u e s o f t h i r t y r e f l e c t i o n s , a n d t h e f i n a l p a r a m e t e r s a r e l i s t e d i n T a b l e I . T h e d a t a w e r e T A B L E I C r y s t a l D a t a C ? 2 H l 8 f - w . ,= 2 8 2 . 4 amu M o n o c l i n i c Z = 4 S p a c e G r o u p = C 2 / c a = 1 3 . 2 2 5 (8) 1 b = 1 0 . 7 6 8 ( 4 ) A F ( 0 0 0 ) = 6 0 0 c = 1 1 . 5 7 2 ( 7 ) A 1 - 5 4 1 8 A 13 = 1 1 4 . 0 4 ( 2 ) o Dc = 1 . 2 4 6 ( 1 ) g / c c V = 1 5 0 5 ( 1 ) A3 c o l l e c t e d a t a 20 s c a n r a t e o f 4 0 m i n _ * o v e r a r a n g e o f ( 1 . 8 0 + 0 . 8 6 t a n € ) o w i t h 10 s e c o n d b a c k g r o u n d c o u n t s a t e a c h e n d o f t h e s c a n - The 14 s t r o n g e s t r e f l e c t i o n s w e r e r e m e a s u r e d w i t h aja a t t e n u a t i o n o f 2 8 . 5 . The 7 1 3 r e f l e c t i o n was u s e d a s a s t a n d a r d a n d c h e c k e d e v e r y 50 r e f l e c t i o n s . T h e r e w e r e s e v e r a l l a r g e d e v i a t i o n s i n t h e s c a n c o u n t s o f t h e s t a n d a r d r e f l e c t i o n due t o e l e c t r o n i c d i f f i c u l t i e s w i t h t h e d i f f r a c t o m e t e r . The s t r u c t u r e was s o l v e d w i t h t h i s s e t o f d a t a , b u t a new s e t was c o l l e c t e d f o r r e f i n e m e n t . In t h e s e c o n d s e t t h e s t a n d a r d v a r i e d more s m o o t h l y a n d was u s e d t o s c a l e t h e d a t a . 611 o f t h e 1497 9 u n i g u e r e f l e c t i o n s i n t h e 0 0 < 2 8 < 1 2 0 ° r a n g e had i n t e n s i t i e s l e s s t h a n 3-0q-(I) , w h e r e <r 2 (I) =S*B* ( 0 . 06S) 2 , S i s t h e s c a n c o u n t a n d B i s t h e b a c k g r o u n d c o u n t . L o r e n t z and p o l a r i z a t i o n c o r r e c t i o n s w e r e a p p l i e d t o g i v e t h e s t r u c t u r e a m p l i t u d e s . No a b s o r p t i o n c o r r e c t i o n was a p p l i e d . S t r u c t u r e A n a l y s i s . A l i l s o n p l o t was u s e d t o d e t e r m i n e o v e r a l l t e m p e r a t u r e I B = 3 . 5 9 ft2) and s c a l e f a c t o r s . £ s t a t i s t i c s ( s e e T a b l e I I ) i n d i c a t e a c e n t r o s y m m e t r i c s p a c e g r o u p ( i . e . C 2 / c ) a n d 204 E * s > 1.4 w e r e o b t a i n e d . 334 ^ ^ - r e l a t i o n s h i p s w e r e f o u n d f r o m t h e l a r g e s t 50 E * s a n d u s e d t o s e l e c t o r i g i n and s y m b o l r e f l e c t i o n s . F o r t h e s p a c e g r o u p C 2 / c two o r i g i n d e t e r m i n i n g p h a s e s a r e n e e d e d o f s u g g e s t e d p a r i t i e s uug a n d g g u 6 ( c e n t e r e d c e l l i n d i c e s ) . T h e l a r g e s t two E * s (9 5 2 a n d 2 6 7) s e r e c h o s e n and t h r e e i n d e p e n d e n t s y m b o l s s e l e c t e d p r o v i d i n g 8 (=2 3 ) s t a r t i n g s e t s t o be u s e d i n a s y m b o l i c a d d i t i o n a n d t a n g e n t r e f i n e m e n t p r o c e d u r e . An E-map was c a l c u l a t e d f r o m t h e b e s t s e t o f p h a s e d E ' s ( t h a t w i t h t h e l o w e s t R - K a r l e o f 0 . 2 1 ) and a l l 11 c a r b o n s i n t h e a s y m m e t r i c u n i t c o u l d be l o c a t e d . 3 i s o t r o p i c a n d 2 a n i s o t r o p i c l e a s t - s g u a r e s r e f i n e m e n t c y c l e s w e r e c a r r i e d o u t b e f o r e a n e l e c t r o n - d e n s i t y d i f f e r e n c e map showed a l l b u t o n e (a m e t h y l H) o f t h e h y d r o g e n s . The m e t h y l h y d r o g e n p o s i t i o n s were c a l c u l a t e d g e o m e t r i c a l l y , a n d t h r e e more l e a s t - s g u a r e s r e f i n e m e n t c y c l e s ( a l l r e f l e c t i o n s u n i t w e i g h t , 11 C ' s a n i s o t r o p i c , 9 H ' s i s o t r o p i c ) l o w e r e d t h e R v a l u e t o 0 . 0 8 9 . T A B L E I I E S t a t i s t i c s OBSERVED Mean | E] Mean 1 E | Z Mean | E 2 - 1| 0 . 6 7 3 2 1 . 0 4 8 9 1 . 2 4 8 6 SI R e f l e c t i o n s w i t h : E > 3 . 0 1 .74 E > 2 . 0 5 . 8 1 I > 1-0 2 5 . 2 5 C e n t r o . 0 . 7 9 8 0 1. 0 0 0 0 0 . 9 6 8 0 T H E O R E T I C A L K o n - c e n t r o . 0 . 8 8 6 0 1 .0000 0 . 7360 0 . 3 0 5 . 0 0 3 2 . 0 0 0 . 0 1 1-80 3 7 . 0 0 ************************* 11 A n o t h e r f o u r r e f i n e m e n t c y c l e s w i t h p o l y n o m i a l w e i g h t i n g s c h e m e s * 6 (w= V { A + B j F o J + C | F o j 2 + D | F o | , w h e r e A , B , C a n d D a r e r e c a l c u l a t e d a f t e r e a c h c y c l e , f i n a l v a l u e s b e i n g - 0 - 0 1 1 5 3 , 0 - 0 8 3 0 8 , - 0 . 0 1 8 0 6 a n d 0 - 0 0 1 3 9 6 r e s p e c t i v e l y ) r e d u c e d B t o 0 - 0 7 8 a n d Rw t o 0 - 0 74 - T h e a n i s o t r o p i c t h e r m a l p a r a m e t e r s u s e d i n t h e r e f i n e m e n t a r e t h e B i j i n f = f o e x p { - { B w h 2 * B 2 i k 2 + B ^ 1 2 + 2 B r i h k + 2 B » - i h l * 2 B a ^ f c l ) ) , w h e r e f 0 i s t h e t a b u l a t e d s t r u c t u r e f a c t o r a n d f i s t h a t c o r r e c t e d f o r t h e r m a l m o t i o n . T h e i s o t r o p i c t h e r m a l p a r a m e t e r s a r e t h e B » s i n f = f 0 e x p ( - B s i n 2 e / < \ 2 ) . F i n a l p a r a m e t e r s a n d t e m p e r a t u r e f a c t o r s a r e shown i n T a b l e s I I I a n d I V , a n d a c o m p a r i s o n o f o b s e r v e d a n d c a l c u l a t e d s t r u c t u r e f a c t o r s a p p e a r s i n A p p e n d i x I . R e s u l t s a n d D i s c u s s i o n . The n u m b e r i n g scheme ( s e e F i g . 4) i s t h a t g e n e r a l l y u s e d f o r n a p h t h a l e n e a n d h y d r o g e n s a r e g i v e n t h e same number a s t h e c a r b o n t o w h i c h t h e y a r e a t t a c h e d ( H ( 1 1 1 ) , H ( 1 1 2 ) and H1113) b e i n g t h e m e t h y l h y d r o g e n s ) - T h e a s y m m e t r i c u n i t i s o n l y o n e h a l f o f t h e d i m e t h y l - b i n a p h t h y l m o l e c u l e ; t h e o t h e r h a l f i s g e n e r a t e d by r o t a t i o n a b o u t a t w o - f o l d a x i s . E q u a t i o n s o f a n d d e v i a t i o n s f r o m v a r i o u s p l a n e s t h r o u g h t h e a s y m m e t r i c u n i t a r e s h o w n i n T a b l e V - T h e r e i s a s l i g h t b e n d i n t h e u n i t , t h e r i n g s l y i n g a t a n a n g l e o f t h r e e d e g r e e s t o e a c h o t h e r . F o r a s i m i l a r d i s t o r t i o n i n 1, 1 » - b i n a p h t h y l t h e c l o s e c o n t a c t s b e t w e e n t h e t w o h a l v e s ( e . g . C (8) . , _ C (8* ) ) h a v e b e e n s u g g e s t e d * 2 a s p o s s i b l e r e a s o n s - T h e d i m e t h y l - b i n a p h t h y l s h o w s c l o s e c o n t a c t s a t C (2) . . . C ( 2 ' ) 43 . 11.6 (5) &) a n d C ( 9 ) . . . C ( 9 * ) ( 3 . 3 4 3 ( 4 ) 5 ) b u t t h e C (8) . . . C ( 8 ' ) d i s t a n c e i s T A B L E I I I F r a c t i o n a l A t o m i c P a r a m e t e r s ( C s l 0 4 . H x l Q 3 ) 8 i t h T h e i r S t a n d a r d D e v i a t i o n s f | Atom . , _ T J x / a 1 i y/b - f .. i 1 i j T 1 1 C{3) J 4 3 8 6 ( 2 ) 1 2 9 7 8 (2) 1 2 2 9 6 ( 2 ) | C ( 2 ) | 3 8 9 8 (2) 1 2 0 3 9 (2) } 2 6 8 6 ( 2 ) i C{3) | 2 7 4 5 ( 2 ) 1 1996 (2) 1 2 3 4 3 ( 2 ) i cm | 20 56 (2) i 2 8 8 6 (2) J 1 5 8 6 ( 2 ) 1 C (5) i 1 8 3 4 ( 2 ) 4 7 4 7 (2) i 2 2 9 ( 2 ) J C ( 6 ) ) 2 2 7 7 ( 2 ) ! 5637 (3) 1- 2 6 9 ( 2 ) I C ( 7 ) | 3 4 2 8 ( 2 ) 5 6 8 S (3) 1 8 3 ( 2 ) i c { 8 ) J 4 1 1 2 ( 2 ) ! 4 8 3 8 ( 2 ) i 9 2 1 ( 2 ) 1 C | 9 ) J 3 6 8 1 ( 2 ) 3 8 9 2 (2) \ 1 4 9 2 ( 2 ) j C ( 1 0 ) | 2 5 1 3 ( 2 ) ! 3844 (2) 1 1 0 8 7 ( 2 ) I C ( 1 1 ) | 8 3 3 ( 2 ) j 2 8 4 3 (3) | 1 2 7 8 ( 3 ) 1 H (2) J 4 3 4 ( 2 ) ! 136(2 ) | 3 2 2 ( 3 ) 1 H (3) 1 2 4 3 ( 2 ) ! 1 3 3 ( 3 ) I 2 7 0 ( 3 ) 3 H(5) i 9 8 ( 3 ) 1 4 7 0 ( 3 ) I - 4 3 ( 3 ) I H(6) I 176(2) ! 6 2 6 (3) | - 8 8 ( 3 ) J H(7) i 3 7 5 ( 3 ) i 6 3 2 ( 3 ) | - 2 6 ( 3 ) 1 H(8) i 4 9 4 ( 3 ) ! 4 9 2 ( 2 ) 1 1 1 4 ( 3 ) 1 H{111) 1 37 (3) ! 266 (3) 1 3 4 ( 3 ) 1 H ( 1 1 2 ) | 5 2 ( 2 ) I 3 6 7 ( 3 ) ] 1 4 4 ( 3 ) I H ( 1 1 3 ) 1 6313) ! 223 (3) 1 178(4 ) _ - . i _ ._.— j — _ _ j ******************** ( 6 ) 0 * L ( E t t ) e (Ll t *9 ( 2 U ) H ( 8 H "9 ( U l ) H ( 9 ) 8 T (8 J H <8>9"9 ( £ ) H ( 9 * 6 * E f 9 ) H (L) 0 - 9 (9>h (9>t7"t7 ( r ) H (5) I "£ (2>H ******************** g mo}? * * * * * * * * * * * * * * * * * * * * ******************************************************* ( r ) 9 (2) t r2 ( 2 ) 6 1 - CE) 16 (£)911 (2) 19 ( U > 3 (2) o i - ( t ) f t t ( 1 ) 6 - C2) E9 (2) 09 (2) ftft (0E) D ( 2 k - (6) E l C U s - (2) 99 f 2 ) L 9 it) 2t? ( 6 ) D ( 3 ) 9 ( 2 ) 6 1 ( 2 ) £ - (2) LL (2) £L (2) £tr (8) D (3) 61 ( 2 ) 9 2 (2*8 - (2) E8 (2) trX (2) E 9 ( £ ) D (27 E l (2) E l ( 2 ) 9 (2) 8£ (2) 0£. (2) 69 (9) D ( 2 U - ( 1 ) 6 ( 2 ) 2 - (2) 99 ( 2 ) 9 t (2) 2ft ( 9 ) D (2 J 6 - ( t ) 9 t ( t ) 9 t - (2) 69 (2) 08 (2) ftii (ft?3 ( 2 ) 9 (2) L2 ( 2 ) E 2 - f2) 69 f2) EX ( 2 ) E 9 ( E ) D (2 )8 (2) f t ( 2 ) 9 - (2) tr9 (2) fe9 (2) 69 (2) D ( 2 ) 9 - U ) ll ( 1 ) 2 - (2) LS (2) 09 (2) Etr ( 1 ) 3 ******************************************************* £ T g t t g t \ g t C g XXg n g mo}? ******************************************************* AT 3 T l ? I 14 F i g u r e 4 . flolecular D r a w i n g o f R a c e m i c 4 # 4 » - D i i B e t h y l - 1 , 1 fcinapbthyl. T A B L E V Mean P l a n e s E q u a t i o n s o f P l a n e s : P l a n e 1 1 2 3 0 . 2 3 8 0 0 - 2 3 1 1 0- 2250 ( lX»mY»nZ=p> m - 0 - 5 6 1 5 - 0 - 6 0 5 0 - 0 . 5 8 6 6 n - 0 . 7 9 2 5 - 0 . 7 6 1 9 - 0 . 7 7 8 0 - 2 - 5 7 7 9 - 2 - 7 3 1 4 - 2 . 6 7 4 1 D e v i a t i o n s f r o m P l a n e s : Atom P l a n e J . P l a n e Z . P l a n e 3 . c n ) - 0 . 023 (2) * 0 . 0 3 5 (2) - 0 . 0 3 4 (2) * C ( 2 ) 0 . 0 2 1 (2) * 0 . 1 4 1 (2) 0 . 0 5 2 (2) * C ( 3 ) 0 . 0 1 0 (3) * 0 . 131 (3) 0 . 0 5 5 ( 3 ) * C<4) - 0 . 0 2 6 ( 2 ) * 0 . 0 3 3 ( 2 ) - 0 . 0 0 9 (2) * C ( 5 ) 0 . 0 6 8 ( 3 ) - 0 . 0 0 7 (3) * 0 . 0 0 9 (3) * C ( 6 ) 0 . 143 (3) 0 . 0 0 4 ( 3 ) * 0 . 0 4 1 ( 3 ) * C ( 7 ) 0 . 141 (3) 0 . 0 0 2 ( 3 ) * 0 . 0 2 6 ( 3 ) * C ( 8 ) 0 . 0 7 3 ( 3 ) - 0 . 0 0 3 ( 3 ) * - 0 - 0 1 3 (3) * C ( 9 ) 0 . 0 0 8 (2) * - 0 . 0 0 7 ( 2 ) * - 0 . 0 3 4 (2) * C ( 1 Q ) 0 . 0 1 3 ( 2 ) * 0 . 0 0 4 ( 2 ) * - 0 . 0 1 5 ( 2 ) * C ( 1 1 ) - 0 . 0 9 3 (3) - 0 . 0 3 2 ( 3 ) - 0 . 0 6 1 (3) * H(2) 0 . 0 6 (3) 0 . 2 2 (3) 0 . 1 1 (3) H ( 3 ) - 0 - 0 2 (3) 0 . 14 (3 ) 0 . 0 5 ( 3 ) H ( 5 ) 0 - 0 9 ( 3 ) 0 - 0 1 (3) 0 . 0 4 ( 3 ) H(6) 0 . 1 8 ( 3 ) 0 . 0 0 ( 3 ) 0 . 0 6 ( 3 ) H<7) 0 - 1 9 ( 3 ) 0 . 0 0 ( 3 ) 0 . 0 4 ( 3 ) H{8) 0 . 0 7 (3) - 0 . 0 1 (3) - 0 . 0 2 ( 3 ) * A t o m s i n c l u d e d i n mean p l a n e c a l c u l a t i o n s . A n g l e s B e t w e e n N o r m a l s t o t h e P l a n e s ; ( d e g r e e s ) P l a n e s (1) and (2) 3 . 1 P l a n e s (1) and (3) 1.8 P l a n e s (2) a n d (3) 1.4 *********************** 16 s l i g h t l y t o o l a r g e ( 3 - 4 4 7 ( 5 ) 1 ) t o be u s e d f o r s u c h a n a r g u m e n t . H o w e v e r t h e c l o s e a p p r o a c h e s a t C ( 2 ) a n d C ( 9 ) m i g h t s t i l l be t h e r e a s o n f o r d i s t o r t i o n . T h e r e a r e no i n t e r m o l e c u l a r s t e r i c r e p u l s i o n s o f i m p o r t a n c e . The two m e t h y l - n a p h t h a l e n e r e s i d u e s a r e c i s - o r i e n t e d w i t h a n a n g l e o f 6 8 . 4 ( 2 ) ° b e t w e e n t h e m . T h i s i s i n a g r e e m e n t w i t h t h e r e p o r t e d v a l u e o f 6 8 ° f o r 1 , 1 ' - b i n a p h t h y l ( w h i c h a l s o c r y s t a l l i z e s i n s p a c e g r o u p C 2 / c ) . B o n d l e n g t h s a n d b o n d a n g l e s a r e l i s t e d i n T a b l e s V I a n d V I I , w i t h s t a n d a r d d e v i a t i o n s c a l c u l a t e d f r o m e r r o r s i n p o s i t i o n a l p a r a m e t e r s . T h e y a r e n o t s i g n i f i c a n t l y d i f f e r e n t f r o m t h o s e i n 1,1 a - b i n a p h t h y l o r n a p h t h a l e n e . T h e C ( 1 ) - C ( 1 » ) b o n d c o n n e c t i n g t h e two a s y m m e t r i c u n i t s h a s a l e n g t h o f 1 . 4 9 5 ( 4 ) a a n d i s b i s e c t e d by t h e t w o - f o l d a x i s . T A B L E V I B o n d L e n g t h s J & l C a r b o n - C a r b o n B o n d s cm - C ( 2 ) 1 .371 (3 C (1) - C { 9 ) 1. 433 (3 C ( 1 ) -co *) 1 . 4 9 5 ( 4 C (2) - C ( 3 ) 1 . 4 1 1 ( 3 C (3) - c (4) 1 . 3 6 7 ( 3 C (4} - C ( 1 0 ) 1 . 4 3 2 (3 C ( 4 ) - C ( 3 1 ) 1 . 5 0 9 ( 3 C 15) - C (6) 1 . 3 6 7 (4 C ( 5 ) - C ( 1 0 ) 1.4181(3 C (6) - C ( 7 ) 1 . 4 0 8 (4 C ( 7 ) - C ( 8 ) 1 . 369 (4 C (8) - C ( 9 ) 1.4 22 (3 C (9) - C ( 1 0 ) 3 - 4 2 6 ( 3 C a r b o n - H y d r o g e n B o n d s C (2) -H(2) 0 . 9 8 ( 3 ) C ( 3 ) - a (3) 1. 0 0 ( 3 ) C ( 5 | - H ( 5 ) 1. 0 5 ( 3 ) C ( 6 ) - H(6) 1. 0 2 ( 3 ) C (7) - H(7) 0 . 9 7 ( 3 ) C (8) " H(8 ) 1. 0 2 ( 3 ) C (11) - H ( l 11) 1. 02 (3) C (11) - H ( 1 1 2 ) 1- 0 3 ( 3 ) C { 1 1 ) - H ( 1 1 3 ) 0 . 9 5 ( 4 ) ********* MM-M vxi B o n d A n g l e s j°) I n v o l v i n g C a r l s o n s O n l y I n v o l v i n g H y d r o g e n s C (9) - C ( 1 ) - C ( 2 ) 1 1 8 . 0 (2 ) C ( l ) - C ( 2 ) - H ( 2 ) 321 41 C {1 •« ) - c ( 1 | - C ( 2 ) 1 1 9 . 5 ( 2 ) C ( 3 ) - C ( 2 ) - H { 2 ) 11741 C (1 • ) - C ( 1 ) - C ( 9 ) 1 2 2 . <H2) C ( 2 ) - C ( 3 ) - H ( 3 ) 319 42 C ( 1 ) - C ( 2 ) - C ( 3 ) 1 2 2 . 1 (2 ) C ( 4 ) - C ( 3 ) - H ( 3 ) 119 (2 C{2) - C ( 3 ) - C ( 4 ) 1 2 1 . 3 ( 2 ) C ( 1 0 ) - C ( 5 ) - H (5) 118 42 C ( 6 ) - C | 5 i - H 4 5 ) 120 (2 C ( 3 ) - C ( 4 ) - C ( 1 1 ) 1 2 0 . 0 ( 2 ) C | 3 ) - C ( 4 ) - C ( 1 0 ) 1 1 8 . 9 ( 2 ) C ( 5 ) - C ( 6 ) - H ( 6 ) 118 (2 C ( 1 0 ) - C (4) - C 411) 1 2 1 . 0 (2 ) C ( 7 ) - C ( 6 ) - H ( 6 ) 122 (2 C ( 1 0 ) - C ( 5 ) - C (6) 1 2 1 . 2 ( 2 ) C ( 6 ) - C ( 7 ) - H ( 7 ) . 119 (2 C ( 8 ) - C ( 7 ) - H ( 7 ) 121 (2 C { 5 ) - C ( 6 ) - C ( 7 ) 120- 1 (2) C 4 7 ) - C | 8 ) - H ( 8 ) 1 1 7 ( 2 C (6) - C ( 7 ) - C ( 8 ) 1 2 0 . 4 (2) C ( 9 ) - C 4 8 ) - H ( 8 ) 122 (2 CO) - C ( 8 ) - C ( 9 ) 3 2 1 . H 2 ) C 4 4 ) - C ( 1 1 ) - H (111) 112 (2 C ( 4 ) - C ( 1 1 ) - B (112) 113 42 C ( 8 ) ~ C ( 9 ) - C ( 1 0 ) 1 1 8 . 3 <2) C ( 4 ) - C | 1 1 ) - H (113) 110 (2 C<8) - C { 9 ) - C { 1 ) 1 2 1 . 5 ( 2 ) H ( 1 3 3 ) - C ( 1 1 ) - H ( 1 1 2 ) 105 (3 C ( 1 ) - C ( 9 ) - 1 2 0 . 1 (2) H f 3 11) .-C ( 1 1 ) - H (113) 110 (3 H ( 1 1 2 - C ( 1 1 ) - H ( 1 1 3 ) 107 (3 C (9) - C (10) - c m 1 1 9 . 5 42) C ( 9 ) - C (10) - C (5) 1 1 8 . 9 ( 2 ) C ( 4 ) - C ( 1 0 ) - C (5) 1 2 1 . 7*2) *************************** 19 PART T H R E E ; THE C R Y S T A L STRUCTPRE OF O P T I C A L L Y A C T I V E 4 ,4* — D I M E T H Y L - 1 . 1 * - B I N A P H T H Y L 20 E x p e r i m e n t a l . F r o m x - r a y p h o t o g r a p h y t h e c r y s t a l was f o u n d t o be t e t r a g o n a l a n d o f one o f t h e e n a n t i o m e r i c s p a c e g r o u p s B1\2\2 o r P 4 j 2 i 2 ( s y s t e m a t i c a b s c e s s e s : 0 0 1 f o r l # 4 n , hOO f o r h # 2 n ) . U n i t - c e l l p a r a m e t e r s were r e f i n e d by l e a s t - s g u a r e s m e t h o d s f r o m t h e o b s e r v e d 2B v a l u e s o f 2 8 p l a n e s ( s e e T a i s l e V I I I f o r f i n a l c e l l p a r a m e t e r s ) . T A B L E V I I I C r y s t a l D a t a C * ^ H i 6 f . w. = 2 8 2 . 4 amu T e t r a g o n a l Z = 4 S p a c e G r o u p = ? 4 ( . 2 \ 2 o r P 4 s 2 i 2 a = b = 8 , 3 0 3 1 (8) A c = 2 3 . 706 47) A F ( 0 0 0 ) = 6 0 0 Dc = 1. 1 4 7 8 ( 4 ) g / c c \ = 1 . 5 4 1 8 A V = 1 6 3 4 . 3 (5) A3 I n t e n s i t y d a t a were c o l l e c t e d a s b e f o r e f o r 0 - ° < 2 9 < 1 6 0 . ° # t h e c r y s t a l m o u n t e d w i t h ( 0 , 2 , 3 ) p e r p e n d i c u l a r t o t h e g o n i o s t a t a x i s a n d u s i n g 4 2 2 a s t h e c h e c k r e f l e c t i o n . T h e c h e c k r e f l e c t i o n s c a n c o u n t showed o n l y s l i g h t r andom v a r i a t i o n s a n d no d a t a s c a l i n g was u s e d . 3 9 5 o u t o f 1117 u n i q u e r e f l e c t i o n s h a d i n t e n s i t i e s l e s s t h a n 3 . 0 c r ( I ) » a n d s t r u c t u r e a m p l i t u d e s w e r e c a l c u l a t e d a s b e f o r e . S t r u c t u r e A n a l y s i s . A W i l s o n p l o t y i e l d e d a n o v e r a l l t e m p e r a t u r e f a c t o r o f 6 . 1 1 A 2 a n d a n o v e r a l l s c a l e f a c t o r . E s t a t i s t i c s ( w h i c h a r e n o t c o n c l u s i v e f c r e i t h e r a c e n t r o s y m m e t r i c o r a n o n - c e n t r o s y m m e t r i c s t r u c t u r e ) a r e s h o w n i n T a b l e I X a n d 17 2 E * s a r e g r e a t e r t h a n 1.4 . F r o m t h e l a r g e s t 50 E * s 5 5 9 21 .TABLE I X E S t a t i s t i c s Mean | E j Mean J E J * Mean | E 2 - 1 J OBSERVED 0 . 8 1 9 3 0 . 9 8 7 3 0 . 9 0 3 1 T H E O R E T I C A L C e n t r o . 0 . 7 9 8 0 1 . 0 0 0 0 0 . 9 6 8 0 N p n - c e n t r o . 0 . 8 8 6 0 1 .0000 0 . 7 3 6 0 SI R e f l e c t i o n s a i t h : E > 3 . 0 0 . 1 8 E > 2 . 0 3 . 3 8 E > 1-0 3 1 - 5 8 0 . 3 0 5 . 0 0 3 2 - 0 0 0 . 0 1 1-80 3 7 . 0 0 t********* *************** 22 r e l a t i o n s w e r e o b t a i n e d a n d u s e d t o a i d i n o r i g i n a n d s y m b o l c h o i c e . The s p a c e g r o u p s P 4 ( 2 ( 2 a n d P 4 3 2 \ 2 b e l o n g t o t y p e 2 P 2 2 f o r w h i c h s u g g e s t e d o r i g i n s 6 a r e 0(OOu)=O o r TT a n d $ (hkO)=0 o r (h+.k=odd) o r o t h e r s e t s o f i n d i c e s f o r w h i c h t h e s t r u c t u r e f a c t o r a m p l i t u d e e x p r e s s i o n s r e s u l t i n a c h o i c e o f t w o p h a s e s d i f f e r i n g by f t . T h e (OOu) r e f l e c t i o n s a r e s y s t e m a t i c a l l y a b s e n t i n t h e s e s p a c e g r o u p s a n d c o u l d n o t be u s e d . The 6 7 0 r e f l e c t i o n was a s s i g n e d p h a s e 0 ( t h e a m p l i t u d e e x p r e s s i o n s s i m p l i f y t o B = 0 , i . e . o n l y p h a s e s 0 a n d Tf a l l o w e d ) , t h e 5 5 10 r e f l e c t i o n (a s t r u c t u r e i n v a r i a n t h e n c e n o t o r i g i n d e t e r m i n i n g , b u t mus t h a v e p h a s e 0 o r tt ) was a s s i g n e d p h a s e 0 , a n d t h e 3 3 17 r e f l e c t i o n ( f o r w h i c h a m p l i t u d e e x p r e s s i o n s r e s u l t i n A=G a n d h e n c e o n l y ± TT/2 a r e a l l o w e d ) was g i v e n p h a s e + f V 2 - W i t h t w o s y m b o l s , e x p r e s s i o n s may b e d e r i v e d f o r t h e p h a s e s o f t h e 50 l a r g e s t E * s , s o o n l y t w o s y m b o l s , (0 7 7) a n d {2 4 1 5 ) , w i t h e i g h t s t a r t i n g v a l u e s e a c h , w e r e u s e d t o g i v e 64 s t a r t i n g s e t s i n a s y m b o l i c a d d i t i o n a n d t a n g e n t r e f i n e m e n t p r o c e d u r e . T h e b e s t s t a r t i n g s e t (3 rT/2 ,3YT/2) r e f i n e d t o an R— K a r l e o f 0 . 1 7 1 a n d d e t e r m i n e d 169 o u t o f t h e 172 p h a s e s . U s i n g t h e s e 169 p h a s e d E ' s an E -map was c a l c u l a t e d i n w h i c h a l l 11 c a r b o n s i n t h e a s y m m e t r i c u n i t c o u l d b e l o c a t e d . A f t e r 3 i s o t r o p i c a n d 3 a n i s o t r o p i c l e a s t - s g u a r e s r e f i n e m e n t c y c l e s , when t h e R v a l u e had d r o p p e d t o 0 . 1 2 , a d i f f e r e n c e map was c a l c u l a t e d t o l o c a t e one m e t h y l h y d r o g e n e n a b l i n g a l l o t h e r h y d r o g e n p o s i t i o n s t o b e d e t e r m i n e d g e o m e t r i c a l l y . 3 more l e a s t - s g u a r e s c y c l e s i n c l u d i n g t h e h y d r o g e n s r e d u c e d R t o 0 . 0 6 3 . A w e i g h t i n g scheme w h e r e w= 1/ {1+J. {| F o J - F * ) / G * j 2 j was 23 i n t r o d u c e d ( f i r s t w i t h F*=5 a n d G*=20 a n d t h e n a f u r t h e r c y c l e w i t h F*=6 a n d G*=15) and l o w e r e d fi t o i t s f i n a l v a l u e o f 0 , 0 6 0 . S t r u c t u r e f a c t o r t a b l e s a p p e a r i n A p p e n d i x I I , a n d f i n a l a t o m i c p a r a m e t e r s a n d t e m p e r a t u r e f a c t o r s a r e l i s t e d i n T a b l e s X a n d X I - D e t e r m i n a t i o n o f t h e a b s o l u t e c o n f i g u r a t i o n was a t t e m p t e d u s i n g a n o m a l o u s d i s p e r s i o n t e c h n i g u e s , b u t d i f f e r e n c e s i n B v a l u e s b e t w e e n t h e two e n a n t i o m e r s were i n s i g n i f i c a n t l y s m a l l ( p e r h a p s u n d e r s t a n d a b l y s o a s we a r e d e a l i n g w i t h a h y d r o c a r b o n ) y e t a l l d i f f e r e n c e s l e a n i n t h e same d i r e c t i o n ; t h e s l i g h t l y s m a l l e r r e s i d u a l f a c t o r s s u g g e s t P 4 | 2<2 ( i n w h i c h t h e s t r u c t u r e was s o l v e d ) . R e s u l t s a n d D i s c u s s i o n . T a b l e X I I s h o w s t h e r e s u l t s o f mean p l a n e c a l c u l a t i o n s . T h e m o l e c u l e e x h i b i t s t h e same b e n d i n g f o u n d i n t h e r a c e m i c c o m p o u n d , t h e a n g l e b e t w e e n t h e r i n g s now b e i n g 2 . 7 ° . T h e t w o m e t h y l - n a p h t h a l e n e r e s i d u e s a r e l i n k e d by b o n d C ( 1 ) - C ( 1 * ) o f l e n g t h 1 .510 (8)& a n d t h e a n g l e b e t w e e n them i s now 8 0 . 6 ( 3 ) ° - T'he s l i g h t l y l e s s e r b e n d i n g m i g h t a g r e e w i t h t h e s l i g h t l y g r e a t e r d i h e d r a l a n g l e t h a n i n t h e r a c e m i c d i m e t h y l — b i n a p h t h y l , b u t i t i s h a r d t o s e e why t h i s b e n d i n g s h o u l d be t h r e e t i m e s t h a t i n b i n a p h t h y l . C o m p a r i n g c l o s e c o n t a c t s f o r t h e two s t r u c t u r e s u n d e r s t u d y a n d b i n a p h t h y l 1 2 ( s e e T a b l e X I I I ) , we s e e no o b v i o u s t r e n d . I t w o u l d s e e m t h a t t h e C ( 8 ) . . . C ( 8 « ) c l o s e a p p r o a c h s h o u l d p l a y a g r e a t e r r o l e i n t h i s b e n d i n g t h a n t h e o t h e r c l o s e a p p r o a c h e s , b u t t h i s i s n o t e v i d e n t f r o m t h e r e s u l t s . M o r e T A B L E X F r a c t i o n a l A t o m i c P a r a m e t e r s ( C x l O » . H x l 0 3 ) W i t h T h e i r S t a n d a r d D e y i a t i o n s * • — '• - ] Atom - i — - I x / a 1 y / b ~ 1— 1 z / c i I H I C ( 1 ) 1 9 5 1 ( 5 ) J 271 (5) ( 2 4 0 1 ( 2 ) i C{2) ) 2 4 8 9 ( 6 ) J 2 7 6 ( 7 ) J 2 6 1 8 ( 2 ) I C ( 3 ) | 3641 (6) | 1444 (9) i 2 4 3 1 ( 2 ) 1 C ( 4 ) | 3 2 6 9 ( 6 ) 1 2 5 6 3 ( 7 ) } 2 0 3 5 ( 2 ) 1 C ( 5 ) i 1 2 5 0 ( 8 ) i 3 6 9 6 ( 7 ) 1 1 3 7 1 ( 2 ) 1 C ( 6 ) j - 2 4 3 ( 8 ) I 3 6 3 6 ( 9 ) 1 1 1 3 0 ( 3 ) 1 C ( 7 ) 1 - 1 3 7 7 ( 7 ) | 2 5 7 7 ( 8 ) 1 1 3 2 5 ( 2 ) 1 C{8) 1-1014 (6) 1 1493 (6) I 1 7 4 2 ( 2 ) ] C ( 9 ) J 5 2 5 ( 5 ) J 1450 (6) I 1 9 8 8 ( 2 ) 1 C ( 1 0 ) j 1690 (5) | 2 6 0 4 ( 6 ) 1 1 7 9 5 ( 2 ) i C ( 1 1 ) I 454 (1) 1 3 7 4 ( 1 } | 1 8 3 6 ( 4 ) I H<2) I 2 7 1 ( 5 ) J - 5 7 ( 5 ) I 2 9 1 ( 2 ) 1 H<3) i 4 8 5 ( 6 ) 3 1 1 8 ( 5 ) J 2 6 2 ( 2 ) J B ( 5 ) I 206 (7) 1 4 3 4 ( 7 ) I 121 (2) i H(6) J - 42 (7) I 4 3 5 ( 7 ) } 8 1 ( 2 ) i H(7) 1 -254(8 ) I 2 5 9 ( 7 ) I 121 (2) 1 H(8 ) 1 -177(7 ) i 8 6 ( 6 ) 1 185 J2) J H (111) I 4 8 2 ( 8 ) J 3 3 9 ( 8 ) | 139 (3 ) 1 H ( 1 1 2 ) 1 5 6 2 ( 8 ) | 3 4 1 ( 8 ) j 2 0 1 ( 3 ) j H ( 1 1 3 ) I 4 0 8 ( 9 ) | 4 7 0 ( 7 ) | 192 (3 ) i _ j .. .... - J L _ _ a - . j T A B L E XI A n i s o t r o p i c T h e r m a l P a r a m e t e r s Of The C a r b o n A t o m s J i t h T h e i r S t a n d a r d D e v i a t i o n s fx 10 4 ) ******************************************** A t o m Bt i B2.2. B33 B v i Biz B r * ******************************************************* C ( l ) 190 (8) 2 2 9 (8) 21 m 2 5 ( 6 ) 3 42) - 9 ( 2 ) C ( 2 ) 216 (9) 3 3 3 ( 1 2 ) 21 (1) 49 49) -10<2) - 6 43) C J 3 ) 173 (8 ) 4 2 5 ( 1 5 ) 24 (1J - 1 6 (10) 2 ( 3 ) - 2 2 43) C ( 4 ) 2 1 3 | 9 ) 3 2 0 ( 1 2 ) 2 5 (1) - 3 6 ( 8 ) 14 43) - 2 1 ( 3 ) C ( 5 ) 264 (11) 2 7 3 ( 1 1 ) 35 (1) - 8 ( 1 0 ) 3 0 ( 3 ) 2 4 ( 3 ) C<6) 260 (12) 385 (16) 43 (2) 3 4 ( 1 2 ) 15 44) 65 (5) C (7 ) 2 0 5 (10) 3 7 2 ( 1 4 ) 3 5 (D 6 7 ( 1 0 ) - 143) 35 44) C ( 8 ) 172 (8) 239 (9) 28 (1) 1 5 ( 8 ) - 2 42) 12 43) C ( 9 ) 175 47) 230 (8) 22 03 15 46) 5 42) - 4 42) C ( 1 Q ) 172 (8) 2 4 7 (9) 26 (D - 6 47) 22 42) - 8 43) C (11) 2 3 8 ( 1 4 ) 513 425) 47 (2) - 1 2 2 ( 1 6 ) 3145) - 1 6 46) ******************************************************* H y d r o g e n I s o t r o p i c T h e r m a l P a r a m e t e r s jkx) ******************** A t o m B * * * * * * * * * * * * * * * * * * * * H (2) 5 | 1 ) H43) 8(1 ) H (5) 9 42) H ( 6 ) 11(2) H ( 7 ) 11(2) H48) 8 (1) H(11 1) 12(2) H (112) 12(2) H ( 1 1 3 ) 12 42) ******************** T A B L E X I I Mean P l a n e s E q u a t i o n s o f P l a n e s : P l a n e 1 1 2 3 0- 29 33 0 . 3 1 0 5 0 . 3001 (lX+mY>nZ=p) m - 0 . 6 2 6 7 - 0 . 6 5 5 6 - 0 . 6 4 12 n - 0 . 7 2 2 0 - 0 . 6 8 8 3 - 0 . 7 0 6 3 - 4 . 0 2 1 3 - 3 . 9 0 9 8 - 3 - 9 4 0 1 D e v i a t i o n s f r o m P l a n e s : Atom P l a n e 1. P l a n e 2 . P l a n e 3 . C ( 1 ) 0 . 0 0 0 (5) * 0 . 0 3 7 ( 5 ) 0 . 0 1 3 * 4 ) * C i l 2 ) - 0 . 0 0 5 ( 6 ) * 0 . 0 9 6 ( 6 ) 0 . 0 3 0 | 5 ) * C<3) 0 . 0 0 3 (5) * 0 . 1 3 0 ( 5 ) 0 . 0 0 8 ( 6 ) * C ( 4 ) 0 . 003 (4) * 0 . 0 9 0 ( 4 ) - 0 . 0 1 8 (6) * CC5) 0 . 0 1 6 ( 5 ) - 0 . 0 0 7 45) * - 0 . 0 1 2 ( 6 ) * C { 6 ) 0 . 0 7 7 (6) - 0 . 0 1 1 ( 6 ) * 0 . 0 5 1 (7) * C ( 7 ) 0 . 135 (7) 0 . 0 2 3 { 7 ) * 0 . 0 0 6 (6) * C ( 8 ) 0 . 0 5 6 j6) - 0 . 0 1 7 ( 6 ) * - 0 . 0 2 4 (5) * C ( 9 ) 0 . 0 0 6 (4) * - 0 . 0 0 1 (4) * - 0 . 0 2 9 ( 4 ) * C { 1 0 ) - 0 . 007 (4) * 0 . 0 1 3 ( 4 ) * - 0 . 0 3 0 (4) * C<11) 0 . 0 4 (1) 0 . 0 5 ( 1 ) - 0 . 0 0 ( 1 ) * H ( 2 ) 0 . 1 1 (4) 0 . 2 4 (4) 0 . 0 4 ( 4 ) H (3) - 0 . 0 1 (4) 0 . 1 7 (4) 0 . 13(4) H(5) - 0 . 0 3 ( 5 ) - 0 . 0 4 ( 5 ) 0 . 12 (5 ) H{6) - 0 . 0 1 (6) - 0 . 1 3 ( 6 ) 0 . 1 6 | 6 ) H ( 7 ) 0 . 2 7 ( 6 ) 0 . 1 1 (6) - 0 . 0 9 ( 6 ) H<8) 0 . 2 0 45) 0 . 1 1 ( 5 ) - 0 . 0 6 (5) * A t o m s i n c l u d e d i n mean p l a n e c a l c u l a t i o n s . A n g l e s B e t w e e n N o r m a l s t o t h e P l a n e s : ( d e g r e e s ) P l a n e s (1) a n d (2) 2 . 7 P l a n e s (1) a n d (3) — 1.3 P l a n e s (2) a n d 43) — 1.5 *********************** 27 T A B L E X I I I C l o s e C o n t a c t s E a c e m i c d i m e t h y l - b i n a p h t h y l O p t i c a l l y a c t i v e d i m e t h y l - b i n a p h t h y l 1, 1 • - B i n a p h t h y l C ( 2 ) . . . C ( 2 » ) C (9) C 19*) C (8) C (8*) 3 . 1 1 A 3 . 3 4 A 3 . 4 5 A 3 . 3 1 A 3 . 3 6 A 3 . 6 3 A 3 . 1 0 7 A 3 . 2 7 7 A 3 . 3 2 1 A B e n d i n g a n g l e ; A n g l e b e t w e e n a s y m m e t r i c u n i t s ; 3 o 6 8 . 4 o 2 . 7 0 80 o 68 o 1 o r e s u l t s f r o m o t h e r s t r u c t u r e s M o u l d b e n e c e s s a r y f o r a more c o n c l u s i v e a r g u m e n t . B o n d d i s t a n c e s a n d a n g l e s a r e l i s t e d i n T a b l e s X I V a n d X V . The n u m b e r i n g s c h e m e i s t h e same a s b e f o r e ( s e e m o l e c u l a r d r a w i n g F i g . 5) , a n d s t a n d a r d d e v i a t i o n s were o b t a i n e d f r o m e r r o r s i n p o s i t i o n a l p a r a m e t e r s o n l y a s u n i t - c e l l e r r o r s w e r e n e g l i g i b l e . T h e b o n d l e n g t h s a n d a n g l e s h a v e n o r m a l v a l u e s . T A B L E X I V B o n d L e n g t h s (&) C a r b o n - C a r b o n B o n d s C (1) - C ( 2 ) 1. 3 7 7 ( 6 ) C (1) - C ( 9 ) 1. 4 2 9 ( 5 ) C (1) - C ( l ' ) 1. 510 (8) C (2) - C ( 3 ) 1. 4 3 2 (8) C ( 3 ) - C ( 4 ) 1. 3 5 7 ( 7 ) C(4 ) - C ( 1 0 ) 1. 429 (6) C ( 4 ) - C ( 1 1 ) 1. 512 (8) C ( 5 ] - C ( 6 ) 1. 366 (8) C ( 5 ) - C < 1 0 ) 1. 4 0 2 ( 7 ) C (6] - C ( 7 ) 1. 369 (8) C ( 7 j -C<8) 1. 371 (7) C ( 8 ] - C (9) 1. 405 (6) C (9] -C{10) 1. 4 3 6 (6) C a r b o n - H y d r o g e n B o n d s C ( 2 ) - H ( 2 ) 1- 01 (4) C ( 3 ) - H ( 3 ) 1. 11 (4 ) C ( 5 ) - H ( 5 ) 0- 9 4 ( 6 ) C ( 6 ) - H ( 6 ) 0 . 9 8 ( 6 ) C ( 7 ) - H ( 7 ) 1- 0 2 ( 6 ) C ( 8 ) - H ( 8 ) 0 . 86 (6) C ( 1 1 ) - H ( 1 1 1 ) 1. 1 2 ( 7 ) C ( 3 1 ) - H ( 1 1 2 ) 1- 0 2 ( 6 ) C (1 1 ) - H ( 1 1 3 ) 0 - 91 (6) ********* T A B L E XV B o n d A n g l e s J ° l I n v o l v i n g C a r b o n s C n l y I n v o l v i n g H y d r o g e n s C ( 9 ) - C { 1 ) - C ( 2 ) 1 38 . 9 ( 4 ) C ( 1 ) - C ( 2 ) - H ( 2 ) 1 1 5 ( 2 C ( 1 » ) - C { 1 ) - C (2) 1 2 0 . 6 (4) C ( 3 ) - C ( 2 ) - H ( 2 ) 1 2 5 ( 2 C ( 1 f ) - C < 1 ) - C ( 9 ) 1 2 0 . 5 ( 3 ) C ( 2 ) - C ( 3 ) - H ( 3 ) 110 (2 C ( 1 ) - C ( 2 ) - C ( 3 ) 1 2 0 , 4 (5) C ( 4 ) - C ( 3 ) - H (3) 128 (2 C 12) -C { 3 ) - C ( 4 ) 1 2 1 - 8(5 ) C ( 1 0 ) - C ( 5 ) - f l ( 5 ) 1 1 9 ( 3 C ( 6 ) - C ( 5 ) - H ( 5 ) 119 (3 C ( 3 ) - C ( 4 ) - C ( 1 1 ) 1 2 0 . 0 ( 6 ) C (3) - C ( 4 ) - C J 1 0 ) 1 2 0 . 0 (5) C ( 5 ) - C ( 6 ) - f l { 6 ) 116 (4 C ( 1 0 ) - C ( 4 ) - C ( 1 1 ) 1 2 0 . P (6) C ( 7 ) - C ( 6 ) - B (6) 1 2 3 ( 4 C ( 1 Q ) - C ( 5 ) - C ( 6 ) 1 2 0 . 8 ( 5 ) C ( 6 ) - C ( 7 ) - H ( 7 ) 124 (3 C ( 8 ) - C ( 7 ) - H ( 7 ) 115 (3 C ( 5 ) - C ( 6 ) - C { 7 ) 1 2 0 . 5 ( 6 ) C ( 7 ) - C ( 8 ) - H ( 8 ) 117 (3 C ( 6 ) - C ( 7 ) - C ( 8 ) 1 2 0 . 9 ( 5 ) C ( 9 ) - C ( 8 ) - H (8) 122 (3 C ( 7 ) - C ( 8 ) ~ C ( 9 ) 1 2 1 . ? (5) C ( 4 ) - C ( 1 1 ) - H (11 1) 106 (4 C ( 4 ) - C ( 1 1 ) - H (112) 109 (4 C ( 8 ) - C ( 9 ) ~ C {1-0) 117- 7 ( 4 ) C ( 4 ) - C ( 1 1 ) - i I (113) 102 (5 C ( 8 ) - •C ( 9 ) - C { 1 ) 1 2 1 . 6 ( 3 ) H ( 1 1 1 ) - C ( 1 1 ) - H ( 1 1 2 ) 9 7 ( 5 C ( 1 ) - C { 9 ) - C ( 1 0 ) 1 2 0 - 6 (4) H ( 1 1 1 ) - C ( 1 l ) - H ( 1 1 3 ) 120 (6 H ( 1 1 2 ) — C ( 1 1 ) - H (113) 122 (6 C ( 9 ) - C ( 1 0 ) - C (4) 118- 4 ( 4 ) C ( 9 ) - C ( 1 0 ) -C<5) 1 1 9 . 0 (4) C ( 4 ) -•c ( 1 0) - C ( 5 ) 1 2 2 . 6 (5) *************************** 30 F i g u r e 5 - M o l e c u l a r D r a w i n g o f O p t i c a l l y A c t i v e 4 , H ' - D i m e t h y l - 1 , 1 • - b i n a p h t h y l . PART F O U R : C O N C L U S I O N 32 B o n d L e n g t h a n d A n g l e C o m p a r i s o n A s s h o w n i n F i g - 6 , t h e n a p h t h a l e n e r e s i d u e c o n s i s t s o f f o u r t y p e s o f b o n d s , h e r e c a l l e d t y p e s a , b, c a n d d . T h i s f i g u r e a l s o s c h e m a t i c a l l y s h o w s t h e b o n d l e n g t h s a n d b o n d a n g l e s o f h o t h t h e r a c e m i c a n d o p t i c a l l y a c t i v e 4 , 4 * - d i m e t h y l - 1 , l * - b i n a p h t h y l t o f a c i l i t a t e v i s u a l c o m p a r i s o n . F o r e a c h c o m p o u n d , t h e b o n d l e n g t h s h a v e b e e n a v e r a g e d w i t h i n e a c h t y p e , a n d t h e r e s u l t s c o m p a r e d t o t h o s e o f 1, 1 0 - b i n a p h t h y l a n d n a p h t h a l e n e i n T a b l e X V I . T h e s e a v e r a g e b o n d l e n g t h s a r e v e r y s i m i l a r i n a l l c a s e s , a n d one may s a y t h a t t h e s t r u c t u r e o f t h e n a p h t h a l e n e r e s i d u e i s r e a s o n a b l y i n v a r i a n t i n t h e s e f o u r c o m p o u n d s . R e a s o n s f o r d i f f e r e n c e s o f s t a b i l i t y w i l l h a v e t o b e s o u g h t i n o v e r a l l m o l e c u l a r g e o m e t r y and i n t e r m o l e c u l a r i n t e r a c t i o n s , i - e . p a c k i n g d i f f e r e n c e s . I n t r a m o l e c u l a r D i f f e r e n c e s . T h e s e new r e d u c e t o d i f f e r e n c e s i n t h e a n g l e b e t w e e n t h e r e s i d u e s a n d t h e d i f f e r e n c e s i n b e n d i n g o f t h e n a p h t h a l e n e u n i t . A s m e n t i o n e d b e f o r e , i t s e e m s t h e r e i s no c o r r e l a t i o n b e t w e e n t h e a m o u n t o f b e n d i n g a n d t h e d i h e d r a l a n g l e ( o r t h e c l o s e c o n t a c t s i n v o l v e d ) . T h e d i h e d r a l a n g l e i n e a c h c a s e i s p r o b a b l y t h a t w i t h w h i c h t h e m o l e c u l e p a c k s mos t e a s i l y i n t o i t s s p a c e g r o u p . C e l l P a r a m e t e r C o m p a r i s o n . The t o t a l mass c o n t e n t o f t h e u n i t c e l l s o f t h e r a c e m i c a n d o p t i c a l l y a c t i v e f o r m s i s t h e s a m e , b u t t h e c e l l v o l u m e o f t h e r a c e m a t e i s s m a l l e r {1505 & 3 a s c o m p a r e d t o 1634 A 3 ) a n d F i g u r e 6 . Bond L e n g t h C o m p a r i s o n . 34 TABJLE X V I A v e r a g e B o n d L e n g t h C o m p a r i s o n B o n d L e n g t h s {%) Compound a b c d B a c e m i c 4 , 4 * - d i m e t h y l - 1,1 ' - b i n a p h t h y l ; 1 . 4 1 0 ( 3 ) 1 -369 (2) 1 . 4 2 6 ( 3 ) 1 . 4 2 6 (3) O p t i c a l l y a c t i v e 4 , 4 * - d i - m e t h y l - l , 1 » - b i n a p h t h y l : 1 .401 (22) 1 . 3 6 8 ( 4 ) 1 . 4 1 6 ( 6 ) 1 . 4 3 6 ( 6 ) A v e r a g e 4 , 4 , - d i m e t h y l - 1 , 1 « - f c i n a p h t h y l : 1 . 4 0 5 ( 1 2 ) 1 . 3 6 8 ( 2 ) 1 - 4 2 1 ( 4 ) 1-431 (4) 1 , l ' - E i n a p b t h y l ; 1 . 4 0 4 ( 3 ) 1 . 3 5 7 ( 4 ) 1 . 4 1 8 ( 4 ) 1 . 4 1 6 ( 3 ) N a p h t h a l e n e : ' 1 1 - 4 1 6 ( 6 ) 1 . 3 5 7 ( 4 ) 1 - 4 2 0 ( 3 ) 1 . 4 0 5 ( 6 ) ( e r r o r s a r e t h e maximum o f t h e rms d e v i a t i o n f r o m t h e mean a n d t h e r m s s t a n d a r d d e v i a t i o n o f t h e b o n d l e n g t h s ) 35 h e n c e t h e d e n s i t y i s g r e a t e r ( 1 . 2 4 6 g / c m 3 a s c o m p a r e d t o 1 . 1 1 8 g / c m 3 ) . I n o t h e r w o r d s , t h e r a c e m a t e i s p a c k e d s l i g h t l y • t i g h t e r ' a n d f o r t h i s r e a s o n i t s l a t t i c e w i l l b e o f s l i g h t l y h i g h e r l a t t i c e e n e r g y , h e n c e s o m e w h a t more s t a b l e t h a n t h a t o f t h e o p t i c a l l y a c t i v e f o r m . P a c k i n g C o m p a r i s o n . The mode o f p a c k i n g i s q u i t e d i f f e r e n t f o r t h e t w o s t r u c t u r e s s o l v e d . By i n s p e c t i o n o f t h e p a c k i n g d i a g r a m f o r t h e r a c e m a t e ( F i g . 7 ) , we s e e t h a t t h e s t r u c t u r e e s s e n t i a l l y c o n s i s t s o f l a y e r s p a r a l l e l t o t h e (001) p l a n e s , e a c h l a y e r c o n t a i n i n g m o l e c u l e s o f one e n a n t i o m e r i c f o r m , a n d s o we h a v e a l t e r n a t i n g l a y e r s o f H a n d S m o l e c u l e s . The u n i t c e l l i s a c r o s s - s e c t i o n o f two s u c h l a y e r s , a s i s n e c e s s a r y f o r i t t o c o n t a i n t h e e n t i r e r e p e a t i n g u n i t . F u r t h e r m o r e , w i t h i n e a c h l a y e r a l l m o l e c u l e s h a v e t h e same o r i e n t a t i o n w i t h r e s p e c t t o t h e c r y s t a l a x e s , s o t h e r e a r e o n l y two o r i e n t a t i o n s w i t h w h i c h a m o l e c u l e may a d d t o t h e l a t t i c e d u r i n g c r y s t a l l i z a t i o n , a n d t h e s e t w o o r i e n t a t o n s a r e e n a n t i o m e r i c . I f we p i c t u r e t h e m o l e c u l e a s t w o p l a n e s f o r m i n g a w e d g e , t h e m o l e c u l e s a r e o r i e n t e d s u c h t h a t t h e wedges a r e ' n e s t e d * a l o n g t h e s h o r t e s t a x i s (c=10.8%), an a x i a l l e n g t h a p a r t ( s e e F i g . 8 ) - I n o p t i c a l l y a c t i v e 4 , 4 » - d i m e t h y l - 1 , 1 * - b i n a p h t h y l ( F i g - 9) t h e m o l e c u l e s s p i r a l a r o u n d a 4 - f o l d s c r e w a x i s s o t h e r e a r e f o u r u n i q u e o r i e n t a t i o n s - The s h a p e o f t h e u n i t - c e l l i s ( u n l i k e t h e r a c e m a t e ) q u i t e a n e l o n g a t e d s q u a r e p r i s m . T h e s q u a r e e d g e i s o n l y 8 -3 S l o n g , w h i c h means t h a t f o u r i d e n t i c a l l y o r i e n t e d m o l e c u l e s s u r r o u n d e a c h m o l e c u l e a t t h i s d i s t a n c e - T h i s a t F i g u r e 7- P a c k i n g D i a g r a m f o r t h e S a c e m a t e . F i g u r e 8 . ' H e d g e N e s t i n g ' i n t h e R a c e m a t e U n i t C e l l F i g u r e 9 . P a c k i n g D i a g r a m f o r t h e O p t i c a l l y A c t i v e F o r m . 39 f i r s t m i g h t seem t o be v e r y d e n s e p a c k i n g , b u t i n f a c t t h e 1 - 1 ' b o n d i s o r i e n t e d c l o s e r t o t h e s g u a r e d i a g o n a l t h a n t o t h e a x e s , w h i c h means t h a t t h e d i r e c t i o n o f • w e d g e - n e s t i n g * i s a l o n g t h e d i a g o n a l , a n d t h e r e p e a t d i s t a n c e h e r e i s a p p r o x i m a t e l y 1 1 . 7 A*, i . e . , n o t a s c l o s e a s f o r t h e r a c e m a t e . P e r h a p s t h e c o m p l i c a t i o n s o f p a c k i n g f o u r m o l e c u l a r o r i e n t a t i o n s a c c o u n t f o r t h e l o n g c - a x i s and t h e s l i g h t l y l o w e r d e n s i t y o f t h e o p t i c a l l y a c t i v e f o r m . S u m m a r y . Any d i f f e r e n c e i n s t a b i l i t y i n c r y s t a l l i n e r a c e m i c a n d o p t i c a l l y a c t i v e 4 , 4 * - d i m e t h y l - 1 , 1 • - b i n a p h t h y l i s r e f l e c t e d i n t h e l a t t i c e e n e r g i e s o f t h e t w o s t r u c t u r e s - a h i g h e r l a t t i c e e n e r g y i s a s s o c i a t e d » i t h g r e a t e r s t a b i l i t y o f t h e l a t t i c e . T h e r a c e m a t e i s l i k e l y t o h a v e t h e g r e a t e r l a t t i c e e n e r g y , a s i t i s p a c k e d s l i g h t l y t i g h t e r and w i t h a l i t t l e more s t r a i n i n t h e m o l e c u l e s ( l o w e r d i h e d r a l a n g l e b e t w e e n n a p h t h a l e n e r e s i d u e s ) . T h i s w o u l d a g r e e w i t h t h e o b s e r v a t i o n t h a t t h e d i m e t h y l - b i n a p h t h y l d e e s n o t r e s o l v e s p o n t a n e o u s l y upon h e a t i n g t o t h e o p t i c a l l y a c t i v e l a t t i c e ( a s i t i s l e s s s t a b l e ) i n c o n t r a s t t o 1 , 1 • - b i n a p h t h y l , b u t t h i s d o e s n o t e x p l a i n t h e d i f f e r e n c e i n b e h a v i o u r b e t w e e n t h e s e two s p e c i e s . I t w o u l d be o f i n t e r e s t t o s t u d y t h e c r y s t a l s t r u c t u r e s o f o p t i c a l l y a c t i v e 1 , T ' - b i n a p h t h y l a n d o t h e r r e l a t e d c o m p o u n d s f o r c o m p a r i s o n , b u t e v e n t h e n t h e e f f e c t o f i n c r e a s e d t e m p e r a t u r e on t h e l a t t i c e i s n o t a l w a y s p r e d i c t a b l e . 40 B E F E B E N C E S G . H . S t c u t a n d L . H . J e n s e n . X - r a y S t r u c t u r e D e t e r m i n a t i o n ! A P r a c t i c a l G u i d e . The M a c M i l l a n C o m p a n y , L o n d o n - 1 9 6 8 . H . L i p s o n a n d W . C o c h r a n . The C r y s t a l l i n e S t a t e , V o l . I l l : The D e t e r m i n a t i o n o f C r y s t a l S t r u c t u r e s , 3 r d e d n . G . B e l l a n d S o n s , L t d , L o n d o n . 1 9 6 0 . H . J . B u e r g e r . C r y s t a l S t r u c t u r e A n a l y s i s . J . H i l e y a n d S o n s , I n c . , New Y o r k . 1 9 5 9 . M . J . B u e r g e r . V e c t o r S p a c e . J . H i l e y a n d S o n s , I n c . , New Y o r k . 1 9 5 9 . M . M . W o c l f s o n . X - r a y C r y s t a l l o g r a p h y - C a m b r i d g e U n i v e r s i t y P r e s s . 1 9 7 0 . I n t e r n a t i o n a l T a b l e s f o r X - r a y C r y s t a l l o g r a p h y , V o l s - I - I V . K y n o c h P r e s s , B i r m i n g h a m . V o l . I , 1 9 5 2 ; V o l . I I , 1 9 5 9 ; V o l . I l l , 1 9 6 2 ; V o l . I V ; 1 9 7 4 . B . E . P i n c o c k a n d K . B . H i l s o n . , J . C h e m . E d . 5 0 , 455 ( 1 9 7 3 ) . 41 8- R . E . P i n c o c k , R . P . B r a d s h a w , a n d R . R . P e r k i n s . J . M o l . E v o l . 4 , 6 7 ( 1 9 7 4 ) . 9 . R . E . P i n c o c k and K . R . W i l s o n . J . A m . C h e m . S o c . 9 7 , 1474 (1975) - 1 0 . R . E . P i n c o c k a n d K . R - W i l s o n . C a n . J . C h e r a . 5 5 , 889 ( 1 9 7 7 ) . 1 1 . Y . B a d a r , C . C . K . L i n g , A . S . C o o k e a n d M . M . H a r r i s - J . C h e m - S o c . , 1543 ( 1 9 6 5 ) . 1.2. K . A . K e r r a n d J . H . R o b e r t s o n . J . C b e m . S o c . (B) , 1146 ( 1 9 6 9 ) . 1 3 - J . S a n d e r s , B . S c . T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1 9 7 1 . 1 4 . F . H . F u n g a n d R . E . P i n c o c k , u n p u b l i s h e d w o r k , 1 9 7 5 . 1 5 - L - F - F i e s e r . J . A m . C h e m . S o c . 6 J , 136 ( 1 9 3 9 ) . 1 6 . D . K - J . C r u i c k s h a n k i n J . S . R o l l e t t , e d . C o m p u t i n g M e t h o d s i n C r y s t a l l o g r a p h y , p . 1 4 . P e r g a m o n P r e s s . ( 1 9 6 5 ) . 1 7 . D . H . J . C r u i c k s h a n k . A c t a C r y s t . J O , 504 ( 1 9 5 7 ) . A P P E N D I X I . STRUCTURE FACTOR T A B L E S FOR HACEHIC 1 . 1 « - D I M E I H Y L - a , 4 ' - B I N A P H T H Y L fa k 1 F o F c - 6 0 12 4 - 6 1 4 . 5 6 - 8 0 12 2- 12 2 . 4 4 - 5 - 1 12 2 - 1 4 2 . 2 5 - 2 - 2 12 5 -4 0 5 . 3 4 - 4 - 2 12 9 - 5 0 8 - 8 4 - 6 - 2 12 4-31 4 - 7 9 - 3 - 3 12 1 1 - 5 9 11.52 - 5 - 3 12 4 - 7 1 5 . 0 1 - 7 - 3 12 4 - 2 6 4 . 4 8 - 9 - 3 12 6 - 5 3 6 . 6 4 - 6 - 4 12 3 - 26 3 . 2 0 - 8 - 4 12 2 - 5 8 2 - 7 1 - 1 - 1 11 6 . 9 6 6 . 9 5 - 7 - 1 11 4 - 2 4 4 - 2 4 - 1 1 - 1 11 5 . 0 3 4 - 9 6 - 2 - 2 11 9 - 9 8 9 - 5 4 - 4 - 2 11 6 - 9 0 6 . 4 9 - 1 0 - 2 11 3 - 2 5 3 - 1 9 - 3 - 3 11 3 - 8 6 3 - 6 7 - 5 - 3 11 5 - 3 5 5 - 2 2 - 9 - 3 11 4 - 8 2 4 . 6 3 - 2 - 4 11 4 - 3 1 4 - 3 3 - 4 - 4 11 1 2 - 7 6 1 1 . 9 0 - 8 - 4 1 1 2 . 9 3 3 . 1 7 - 3 - 5 11 2 . 4 6 2 - 6 5 - 4 - 6 11 5 - 5 9 5 - 7 0 - 2 0 10 2 . 2 7 2 - 2 7 - 4 0 10 6 - 2 2 5 . 9 6 - 6 0 10 1 1-78 1 0 . 5 9 - 1 0 0 10 1 2 . 11 1 1 - 7 0 - 1 2 0 10 2 4 . 2 3 2 2 . 6 8 - 3 - 1 10 4 . 17 3 . 8 1 - 5 - 1 10 5 . 3 7 5 . 3 1 - 7 - 1 10 9 . 1 9 8 . 4 0 - 1 1 - 1 10 6 - 0 9 5 . 7 7 - 4 - 2 10 4 . 6 1 4 . 4 4 - 6 - 2 10 5 - 6 2 5 . 3 8 - 8 - 2 10 2 . 19 2 . 2 5 - 1 - 3 10 3 - 6 6 3 . 2 3 - 3 - 3 10 1 0 - 8 4 1 0 . 4 0 - 7 - 3 10 3 . 7 3 3 . 5 2 - 1 1 - 3 10 2 . 6 6 2 . 9 6 - 2 - 4 10 1 2 . 0 5 1 1 . 4 6 - 4 - 4 10 1 0 . 4 6 9 - 3 8 - 1 - 5 10 5- 10 5 - 19 - 3 - 5 10 1 4 . 7 1 1 3 . 7 6 - 5 - 5 10 2 . 86 2 - 8 5 - 7 - 5 10 4 . 2 1 4 . 3 1 - 9 - 5 10 1 1 . 6 7 1 1 . 6 5 - 2 - 6 10 5 , 4 8 5 . 6 5 - 4 . - 6 10 5 . 8 2 5 . 7 3 - 1 0 - 6 10 2 . 13 2 . 4 0 -1 - 7 10 3 - 12 3 . 2 1 - 3 - 7 10 1 7 . 55 1 7 . 4 1 - 5 - 7 10 6 . 0 6 5 . 9 9 - 5 - 1 9 1 0 . 5 3 1 0 . 2 5 - 9 -1 9 3 . 1 5 3 . 3 9 - 1 1 - 1 9 1 5 . 6 0 1 4 . 8 5 b k 1 F o F c - 4 - 2 9 2 - 3 9 2 . 3 3 - 6 - 2 9 2 . 4 1 2 . 29 - 8 - 2 9 3 . 2 9 3 . 2 6 - 3 - 3 9 5 . 2 1 5 . 0 1 - 1 1 - 3 9 4 . 81 5 . 0 4 - 2 - 4 9 1 6 . 12 1 5 . 85 - 4 - 4 9 3 . 8 0 3 . 9 3 - 8 - 4 9 2 . 17 2 . 59 - 1 2 - 4 9 3 - 6 5 3 . 7 8 - 1 - 5 9 8 . 5 1 8 . 2 7 - 3 - 5 9 10 . 48 1 0 . 09 - 9 - 5 9 4 . 58 4 . 68 - 4 - 6 9 1 0 . 18 9 . 5 7 - 8 - 6 9 9 . 3 5 9 . 7 4 - 1 - 7 9 3 - 0 3 3 . 3 9 - 3 - 7 9 7 . 4 5 7 . 5 1 - 9 - 7 9 2 - 03 2 - 6 7 - 2 - 8 9 6 . 0 6 6 . 36 - 4 - 8 9 3 . 3 8 3 . 5 9 - 4 0 8 2 . 7 8 2 . 30 - 6 0 8 1 3 . 10 1 2 . 8 9 - 8 0 8 3 . 16 3 . 4 2 - 1 0 0 8 15- 51 1 5 . 59 - 1 2 0 8 6 . 8 5 6 - 7 2 - 1 - 1 8 2 - 5 1 2 . 4 9 - 5 - 1 8 1 6 . 50 1 5 . 42 - 7 - 1 8 6 . 3 4 5 . 9 3 - 9 - 1 8 3 . 5 9 3 - 4 2 - 1 1 - 1 8 6 . 83 6 . 8 8 - 1 3 - 1 8 5 . 6 1 5 . 6 7 - 2 - 2 8 3 . 25 3 . 2 7 - 4 - 2 8 5 . 8 1 5 . 20 - 1 0 - 2 8 9 . 15 9 . 4 9 - 1 2 - 2 8 9 . 95 9 . 7 4 - 1 - 3 8 4 - 0 7 4 . 08 - 3 - 3 8 2 . 5 9 2 - 6 8 - 7 - 3 8 5 . 12 4 . 7 9 - 1 1 - 3 8 4 . 2 4 4 - 4 6 - 2 - 4 8 1 6 . 5 0 1 6 - 1 6 - 4 - 4 8 5 . 0 9 5 . 12 - 6 - 4 8 2 - 15 2 - 15 - 8 - 4 8 9 . 3 4 8 . 9 8 - 1 0 - 4 8 3 . 2 8 3- 12 - 1 - 5 8 9 . 8 6 1 0 . 35 - 3 - 5 8 3 2 . 4 4 3 1 . 4 2 - 5 - 5 8 3 . 0 8 3 . 6 1 - 7 - 5 8 2 . 9 1 3 . 0 3 - 9 - 5 8 3 . 4 7 3 . 18 - 2 - 6 8 9 . 9 9 9 . 7 8 - 8 - 6 8 4 . 5 2 4 . 8 9 - 1 0 - 6 8 2 . 25 2 . 5 4 - 1 2 - 6 8 3 . 84 3 . 4 2 - 3 - 7 8 2 . 9 1 2 - 8 6 - 5 - 7 8 2 . 6 5 3 . 0 2 - 6 - 8 8 2 - 2 4 2 . 05 - 1 - 9 8 2 - 5 5 2 . 70 - 3 - 9 8 4 . 7 6 4 . 4 3 - 5 - 9 8 2 - 5 4 2 . 8 0 h k 1 Fo F c - 3 - 1 7 1 9 . 0 3 1 4 . 5 1 - 5 - 1 7 1 8 . 6 2 1 5 . 5 4 - 7 - 1 7 2 . 6 8 2 . 6 9 - 9 - 1 7 9 . 2 7 9 . 15 - 1 1 - 1 7 1 4 . 0 4 1 3 . 37 - 2 - 2 7 1 1.58 1 1 . 6 3 - 4 - 2 7 5 . 39 5 . 2 7 - 1 0 - 2 7 1 8 . 2 1 1 8 . 2 7 - 1 2 - 2 7 1 0 . 3 3 1 0 . 09 - 1 - 3 7 2 . 6 9 3 . 12 - 3 - 3 7 2 . 2 3 2 . 6 4 - 9 - 3 7 7 . 4 0 7 . 7 0 - 1 1 - 3 7 3 . 7 8 4 . 0 3 - 1 3 - 3 7 7 . 5 7 7 . 2 6 - 2 - 4 7 9 . 2 9 9 . 5 9 - 4 - 4 7 1 1. 11 1 1 . 4 8 - 8 - 4 7 1 2 - 7 4 1 3 . 13 - 1 - 5 7 8 . 3 1 8 . 16 - 3 - 5 7 5- 18 5 - 4 3 - 5 - 5 7 3 . 0 8 2 . 9 3 - 7 - 5 7 4 . 0 3 4 . 3 1 - 9 - 5 7 5 . 64 5 . 8 5 - 1 1 - 5 7 4 . 8 5 4 - 6 9 - 2 - 6 7 4 2 . 2 7 3 4 . 9 8 - 4 - 6 7 6 . 9 0 6 . 8 3 - 8 - 6 7 6 . 6 1 7 . 6 4 - 1 0 - 6 7 3 . 99 3 . 8 7 - 1 - 7 7 9 . 8 3 9 . 6 9 - 7 - 7 7 7 . 6 1 8 - 1 6 - 9 - 7 7 4 . 6 7 5 . 16 - 6 - 8 7 4- 38 4 - 6 6 - 8 - 8 7 5 . 0 5 5 - 1 6 - 1 0 - 8 7 4 - 4 3 5 - 0 0 - 1 - 9 7 ii. 63 5 - 0 2 - 3 - 9 7 4 - 7 2 4 . 7 4 - 4 - 1 0 7 3 - 3 5 3 . 7 6 - 2 0 6 1 1 . 6 4 9 . 7 3 - 4 0 6 1 2 - 3 9 1 3 . 3 4 - 6 0 6 9 - 4 0 8 . 8 3 - 8 0 6 3 . 5 1 3 - 5 8 - 1 2 0 6 3 . 18 3 . 3 9 - 1 - 1 6 5 . 89 5 - 8 5 - 3 - 1 6 1 1 . 2 6 1 2 - 0 5 - 5 - 1 6 1 0 . 2 8 1 1 - 10 - 9 - 1 6 5 -44 5 - 5 3 - 1 1 - 1 6 8 . 2 7 8-63 - 2 - 2 6 5 . 3 3 5 - 0 1 - 6 - 2 6 1 2 . 6 9 13 -51 - 1 0 - 2 6 1 8 . 0 4 1 7 . 2 0 - 9 - 3 6 9 . 5 4 9 . 2 4 - 2 - 4 6 1 5 . 7 2 1 5 . 2 0 - 4 - 4 6 8 . 7 8 9 . 2 4 - 6 - 4 6 8 . 0 6 8 -44 - 1 0 - 4 6 3 . 15 3 . 1 2 - 1 2 - 4 6 4 . 7 5 5 . 0 4 - 1 - 5 6 1 5 . 9 6 1 7 . 5 9 - 3 - 5 6 4 . 9 5 5 . 7 0 - 7 - 5 6 4 . 2 6 4 . 1 6 h k 1 Fo F c - 1 1 - 5 6 2 . 6 5 3 - 10 - 2 - 6 6 3 . 04 3 . 3 8 - 4 - 6 6 2 . 27 2 - 53 - 6 - 6 6 3 . 4 7 3 - 7 0 - 8 - 6 6 3 . 5 6 3 . 9 3 - 1 - 7 6 6 . 01 5 - 9 2 - 3 - 7 6 1 2 - 4 6 1 2 . 14 - 7 - 7 6 4 . 7 7 5 - 2 0 - 9 - 7 6 2 - 5 5 2 . 8 3 - 1 1 - 7 6 3 . 6 6 3 . 8 5 - 2 - 8 6 10 . 92 1 0 . 9 0 - 4 - 8 6 4 . 3 0 4 . 6 3 - 6 - 8 6 3 . 7 4 3 . 8 9 - 9 - 9 6 4 . 6 0 5 . 0 1 - 1 - 1 5 8 - 7 6 8 . 9 1 - 3 - 1 5 7 . 7 2 8 - 3 1 - 7 - 1 5 1 0 . 4 7 1 0 . 3 1 - 1 1 - 1 5 4 . 71 4 - 9 8 - 2 - 2 5 3 - 4 1 2 - 9 2 - 4 - 2 5 2 7 . 45 2 5 . 20 - 6 - 2 5 4 . 0 5 4 - 3 8 - 8 - 2 5 1 7 . 9 9 1 6 . 53 - 1 - 3 5 5 5 . 32 4 2 . 9 3 - 3 - 3 5 4 2 . 7 6 3 5 . 3 9 - 5 - 3 5 1 2 . 9 3 1 2 . 3 9 - 7 - 3 5 1 3 . 3 2 1 3 . 7 1 - 9 - 3 5 1 7 . 7 7 1 7 - 4 5 - 1 1 - 3 5 1 3 . 7 3 1 3 . 39 - 2 - 4 5 4 9 . 2 0 3 9 . 6 9 - 8 - 4 5 4 . 11 4 - 6 9 - 1 0 - 4 5 2 2 - 6 7 2 2 . 10 - 1 2 - 4 5 2 . 8 5 3 . 0 0 - 3 - 5 5 3 . 7 8 3 . 9 8 - 5 - 5 5 4 . 19 4 . 35 - 9 - 5 5 3 - 1 5 2 . 9 1 - 2 - 6 5 3 . 6 0 3 . 6 4 - 4 - 6 5 9 . 18 8 . 5 9 - 1 0 - 6 5 7 . 2 5 7 . 0 6 - 1 - 7 5 1 3 . 8 0 1 4 . 18 - 3 - 7 5 1 0 . 4 7 1 0 . 7 8 - 9 - 7 5 4 . 8 0 5 - 2 1 - 1 1 - 7 5 6 . 7 6 6 - 3 8 - 2 - 8 5 1 5 . 5 6 1 4 - 9 7 - 4 - 8 5 9 . 75 9 . 15 - 8 - 8 5 5 . 3 2 5 - 8 9 - 1 0 - 8 5 7 . 8 2 8 - 3 9 - 1 - 9 5 3 . 9 8 4 . 15 - 5 - 9 5 8 . 5 1 8 . 7 5 - 7 - 9 5 8 . 9 6 9 - 2 0 - 1 - 1 1 5 5 . 7 5 5 . 3 7 - 2 0 4 3 0 . 7 0 2 8 - 6 7 - 6 0 4 1 1 . 2 6 10 . 64 - 8 0 4 6 . 8 4 7 . 15 - 1 0 0 4 5 . 54 5 . 2 8 12 0 - 4 5 . 9 7 5 - 8 8 14 0 - 4 6 . 5 4 6 . 44 - 1 - 1 4 1 4 . 5 7 1 2 . 7 9 - 3 - 1 4 8 - 5 5 9 . 0 0 l l k 1 Fo F c - 7 -1 4 5 - 7 7 5 . 4 5 - 9 - 1 4 8 - 5 2 7 . 5 8 13 1 - 4 4 . 3 0 4 . 5 8 - 2 - 2 4 2 0 . 8 2 1 9 . 7 7 - 4 - 2 4 2 0 - 7 9 1 6 - 7 4 - 6 - 2 4 1 5 . 5 6 1 5 - 8 0 - 8 - 2 4 7 . 8 1 8- 14 - 1 0 - 2 4 3 . 3 2 3 . 4 9 12 2 - 4 8 . 19 8 -34 14 2 - 4 3 . 3 8 4 . 2 4 - 1 - 3 4 3 4 - 8 8 3 0 . 2 5 - 3 - 3 4 3 0 - 9 4 2 4 - 5 6 - 5 - 3 4 1-83 1.94 - 7 - 3 4 1 4 . 4 1 1 3 . 9 0 - 9 - 3 4 2 3 . 2 6 1 8 . 8 5 - 1 1 - 3 4 1 2 - 6 6 1 1 - 9 2 - 6 - 4 4 9 - 3 8 8 . 9 5 - 8 - 4 4 1 4 . 5 2 1 5 . 0 1 - 1 0 - 4 4 1 3 . 0 9 1 3 . 6 0 12 4 - 4 2 . 9 0 2 . 9 2 - 3 - 5 4 4 . 55 5 . 2 1 - 9 - 5 4 4 . 7 0 4 . 9 6 - 1 1 - 5 4 5 . 6 2 5 - 5 0 - 2 - 6 4 2 . 5 3 2 . 5 8 - 4 - 6 4 7 . 6 3 7 - 7 2 - 6 - 6 4 3 - 9 3 3 . 6 7 - 1 0 - 6 4 2 - 6 9 2 - 6 8 12 6 - 4 4 . 9 8 4 . 8 8 - 1 - 7 4 1 8 . 0 7 1 8 - 3 4 - 7 - 7 4 4 - 3 8 4 . 5 3 -11 - 7 4 8 . 2 7 7 . 7 1 - 2 - 8 4 8 . 5 8 8 . 1 3 - 4 - 8 4 4 . 5 7 4 . 7 2 - 6 - 8 4 5 . 2 1 5 . 9 6 - 8 - 8 4 6 . 4 5 6 . 3 7 - 1 0 - 8 4 7 . 7 4 7 . 5 6 - 3 - 9 4 8 - 7 2 8 . 5 9 - 7 - 9 4 6 . 2 3 6 . 6 8 - 2 - 1 0 4 2 . 9 5 3 . 4 1 - 1 - 1 1 4 4 , 4 5 4 . 4 7 - 3 - 1 3 9 . 8 3 1 0 . 7 9 - 5 - 1 3 5 . 2 2 4 . 7 7 11 1 - 3 3 . 5 1 3 - 1 8 - 4 — 2 3 8 . 7 3 8 . 6 1 - 6 - 2 3 4 . 13 4 . 13 - 1 - 3 3 9 . 9 4 1 0 . 2 9 - 3 - 3 3 2 - 3 2 2 - 3 2 - 5 - 3 3 4 . 3 2 4 . 13 9 3 - 3 1 6 - 7 4 1 4 - 5 8 11 3 - 3 3 - 0 7 3 . 4 4 - 2 - 4 3 1 2 . 3 8 1 3 - 3 6 - 4 - 4 3 2 4 - 8 2 2 2 . 2 0 - 8 - 4 3 1 0 . 2 6 1 0 . 3 6 - 1 - 5 3 9 . 3 4 S . 3 4 - 3 - 5 3 9 . 6 6 8 - 7 3 - 5 - 5 3 7 . 7 7 7 . 2 3 11 5 - 3 4 . 5 0 4 . 6 6 - 4 - 6 3 1 0 . 19 9 . 5 7 h k 1 Fo F c - 8 - 6 3 9 . 8 0 9 - 8 3 12 6 - 3 3 . 7 0 3 - 4 6 - 1 - 7 3 3 . 20 3<• 25 - 3 - 7 3 7 . 2 7 7 - 1 4 - 5 - 7 3 1 0 . 04 9 - 8 3 11 7 - 3 4 . 82 5 . 0 0 - 2 - 8 3 4 . 02 4 . 0 3 - 4 - 8 3 3 . 5 4 3 - 7 8 - 6 - 8 3 4 . 5 1 4 . 6 2 10 8 - 3 3 . 0 4 3 . 17 - 1 - 9 3 1 8 - 6 0 1 8 . 62 - 3 - 9 3 4 . 5 2 4 . 3 2 - 5 - 9 3 4 . 68 4 - 7 4 - 2 - 1 0 3 2 . 8 8 3 - 19 - 6 - 1 0 3 3 . 35 3 . 8 7 - 1 - 1 1 3 2 . 3 7 2 . 9 7 - 5 - 1 1 3 3 . 7 2 3 - 9 5 - 4 0 2 3 . 65 3 . 6 3 8 0 - 2 8 . 3 1 8- 16 10 0 - 2 9 . 0 8 8 . 92 12 0 - 2 1 3 . 2 6 1 5 . 3 8 14 0 - 2 4 . 67 5 . 42 - 3 - 1 2 2 2 . 37 1 9 . 6 8 - 5 - 1 2 2 7 . 2 6 2 1 . 8 8 7 1 - 2 2 5 . 8 4 2 0 . 3 7 - 4 - 2 2 15 . 91 1 7 . 21 6 2 - 2 1 6 . 18 1 2 . 7 5 8 2 - 2 1 0 . 47 9 . 7 7 10 2 - 2 4 . 65 4 . 14 14 2 - 2 3 . 3 0 3 . 4 6 - 1 - 3 2 1 7 . 4 4 1 7 . 08 - 3 - 3 2 2 3 . 03 1 9 . 3 7 - 5 - 3 2 6 . 86 6 . 8 5 7 3 - 2 1 .74 1. 60 9 3 - 2 6 . 3 6 6 . 7 7 - 2 - 4 2 1 4 . 90 1 6 . 3 9 - 4 - 4 2 2 2 . 0 1 1 8 . 2 5 6 4 - 2 3 . 84 4 . 16 8 4 - 2 4 . 28 3 . 9 5 10 4 - 2 8 . 2 6 8 . 25 - 1 - 5 2 4 . 3 6 4 . 6 0 - 3 - 5 2 2 6 . 60 2 2 . 5 0 - 5 - 5 2 7 . 42 7 . 3 4 7 5 - 2 9 . 03 9 . 0 8 9 5 - 2 4 7 . 7 9 3 8 . 7 0 11 5 - 2 7 . 0 7 7 . 06 - 2 - 6 2 5 - 19 5 . 0 3 - 4 - 6 2 1 1 . 0 3 1 1 . 89 8 6 - 2 3 - 6 8 4 . 0 4 10 6 - 2 6 . 92 6 . 90 - 3 - 7 2 1 7 . 15 1 7 . 2 9 - 5 - 7 2 5 . 74 5 . 49 9 7 - 2 7 . 5 1 7 - 7 0 10 8 - 2 3 . 13 3 . 5 0 - 1 - 9 2 17 . 52 1 5 . 51 9 9 - 2 6- 05 6 . 0 6 6 10 - 2 7 . 12 7 . 7 5 - 3 - 1 1 2 2 - 5 9 2 . 6 9 h k 1 F o F c 3 1 - t 3 - 7 4 3 . 7 0 7 1 - 1 1-63 1.76 11 1 - 1 7 . 5 2 8 . 4 9 - 2 - 2 1 6 . 12 6 . 3 2 4 2 - 1 4 . 19 4 . 0 7 6 2 - 1 5 - 7 7 5 - 3 7 8 2 - 1 7 . 7 4 7 . 3 3 - 1 - 3 1 1 2 . 0 2 1 3 . 2 1 3 3 -1 4 . 2 1 4 . 19 5 3 - 1 3 . 9 8 4 - 4 4 7 3 -1 2 . 8 8 2 - 6 0 9 3 - 1 4 . 4 2 4 - 7 4 11 3 - 1 3 - 0 1 3 - 2 8 - 2 - 4 1 2 1 . 13 1 8 - 2 3 4 4 - 1 5 . 2 9 5 . 5 3 6 4 - 1 4 . 6 5 4 - 9 6 10 4 - 1 8 . 5 2 7 . 9 8 12 4 - 1 3 . 4 7 3 - 2 5 - 1 - 5 1 9 - 5 5 1 0 - 0 0 3 5 - l 2 4 . 0 5 19- 15 5 5 - 1 3 . 6 0 3 . 1 4 7 5 - 1 6 - 2 7 6 . 7 1 9 5 - 1 1 3 - 8 2 1 3 - 6 8 11 5 - 1 5 . 13 4 . 7 7 4 6 - 1 1 5 . 5 9 1 3 . 3 3 8 6 - 1 2 7 . 4 0 2 2 . 7 2 10 - 1 5 - 7 5 5 - 4 2 3 7 - 1 8 . 8 5 8 . 2 2 5 7 - 1 4 - 3 9 4 . 14 9 7 - 1 9 . 0 0 8 . 9 1 31 7 - 1 2 - 9 6 2 - 6 6 4 8 - 1 3 . 4 0 3 - 5 5 - 1 - 9 3 - 2 4 3 - 4 3 6 10 - 1 8 . 2 8 8 - 0 2 8 10 -1 2 - 3 5 2 . 4 5 - 1 - 1 1 1 2 5 . 5 1 2 1 . 0 2 3 11 - 1 3 . 9 5 3 -71 5 11 - 1 4 - 5 2 4 . 3 7 4 <Q 0 9- 10 9 . 2 4 12 0 0 3 . 9 1 4 . 0 8 1 1 0 2 4 - 2 6 2 1 - 19 3 1 0 7 . 8 5 7 . 1 2 5 1 0 3 9 - 4 8 3 0 - 11 9 1 0 5 . 0 0 4 . 9 9 13 1 0 3 . 2 0 3 - 8 0 0 2 0 1 6 . 8 6 1 5 . 0 3 2 2 0 2 0 . 2 4 1 7 . 3 7 4 2 0 6 . 7 2 6 . 7 2 6 2 0 2 6 . 9 6 2 1 . 18 8 2 0 3 . 4 1 3 , 3 0 12 2 0 5 . 9 4 7 . 0 7 1 3 0 2 1 . 3 4 1 8 - 3 7 3 3 0 2 - 9 4 2 - 5 1 5 3 0 9 . 2 8 9 , 4 0 7 3 0 9 - 0 6 9 - 4 2 9 3 0 1 1 . 7 5 1 1 . 5 2 11 3 0 4 . 3 2 4 . 6 3 13 3 0 2 . 8 4 2 . 9 2 h k 1 F o F c 2 4 0 1 5 . 8 7 1 5 . 6 7 4 4 0 6 . 7 7 6 . 4 1 6 4 0 5 . 7 9 5 - 3 9 8 4 0 1 7 . 5 1 1 7 - 2 4 10 4 0 1 4 . 4 8 1 4 - 2 9 1 5 0 1 3 . 49 1 1 - 9 0 3 5 0 4 5 . 6 0 3 5 - 1 7 5 5 0 7 . 7 3 7 . 25 7 5 0 3 . 89 4 . 10 9 5 0 9 . 5 4 9 . 3 0 0 6 0 4 . 42 4 . 2 7 2 6 0 1 1 . 98 1 1 . 34 4 6 0 2 . 24 2 . 2 0 6 6 0 2 . 19 2 . 15 8 6 0 9 . 2 8 8 . 7 9 10 6 0 8 . 13 7 . 54 1 7 0 6 . 9 1 6 . 5 5 3 7 0 7 . 3 6 6 . 16 7 7 0 1 1 . 11 1 1 - 8 6 9 7 0 1 5 - 9 2 1 8 . 35 0 8 0 7 . 2 7 7 . 2 5 2 8 0 3 . 04 3 . 7 5 8 8 0 5 - 00 5 . 8 2 3 9 0 2 . 02 2 . 32 5 9 0 2 . 00 2 . 5 1 0 10 0 1 6 . 4 5 1 7 - 3 7 4 10 0 2 . 4 0 2 . 4 5 6 10 0 6 . 3 7 7 . 45 1 11 0 3 . 0 3 3 - 3 4 0 12 0 1 1 - 5 0 1 1 . 9 6 1 1 1 1. 11 1. 15 3 1 1 9 . 50 1 0 . 5 7 7 1 1 6 . 3 2 6 . 4 3 9 1 1 5 . 7 3 6 . 0 8 2 2 1 5 - 0 1 5 . 6 4 4 2 1 6 . 3 7 6 . 7 9 8 2 1 3 - 6 3 3 - 9 0 10 2 1 11- 11 1 2 - 4 5 12 2 1 2 - 62 3 . 5 1 1 3 1 1 5 - 6 6 1 7 . 3 9 3 3 1 7 - 0 0 7 . 9 4 7 3 1 6 . 8 6 7 . 0 2 0 4 1 8 . 0 7 9 . 16 2 4 1 1 5 - 2 7 1 3 . 9 1 4 4 1 8 . 66 9 . 0 1 6 4 1 8 . 23 9 - 0 6 8 4 1 2 5 . 6 2 2 7 - 8 4 10 4 1 3 . 5 2 3 . 9 3 1 5 1 3 - 4 1 3 - 3 0 3 5 1 8 . 13 7 . 11 9 5 1 7 - 9 1 8 . 01 0 6 1 2 - 4 4 2 . 5 8 2 6 1 2 9 - 2 1 2 4 . 5 0 4 6 1 8- 08 7 . 0 7 8 6 1 1 4 . 87 1 3 - 9 7 1 7 6 . 6 1 6 . 7 2 7 7 1 . 1 5 . 28 1 5 . 0 5 9 7 1 1 0 . 72 1 0 . 59 h k 1 Fo F c 0 8 ! 5 - 3 8 4 - 8 6 4 8 1 6 - 2 7 6 . 2 2 8 8 1 9 . 6 2 8-31 1 9 1 1 3 - 0 5 1 2 - 2 4 5 9 1 2 . 5 7 3 - 0 3 0 10 1 9 . 6 0 8 - 5 2 2 10 1 3 . 6 2 3 - 8 0 4 10 1 2 . 9 4 3 . 5 6 6 10 1 2 . 6 5 3 - 16 1 11 1 7 . 0 5 6 - 6 6 5 11 1 5 . 94 6 . 17 0 12 1 2 . 4 2 2 . 3 4 2 0 2 2 0 - 15 1 9 . 2 1 6 0 2 5 . 8 1 5 . 6 7 10 0 2 3 . 6 5 4 . 0 0 3 1 2 1 8 - 3 8 1 7 . 6 5 5 1 2 9 - 0 0 8 . 7 4 2 2 2 7 - 9 8 8 . 2 4 4 2 2 7 . 2 5 7 . 3 4 6 2 2 8 - 4 5 7 . 4 3 8 2 2 1 7 . 3 5 1 7 . 8 3 1 3 2 1 9 . 6 2 1 8 . 1 0 3 3 2 2 9 . 6 5 2 4 . 7 6 5 3 2 1 9 . 6 8 1 8 . 0 6 7 3 2 7 . 3 7 7 . 0 8 9 3 2 1 2 . 9 7 1 2 . 8 4 2 4 2 1 0 . 18 1 0 - 3 2 4 4 2 7 . 0 1 6 . 7 6 6 4 2 7 . 4 7 7 . 8 2 8 4 2 4 . 2 4 4 . 3 1 3 5 2 6 . 3 5 6 - 3 1 0 6 2 9 -91 1 0 . 1 3 2 6 2 7 . 0 7 7 . 3 2 4 6 2 2 . 7 3 2 . 8 0 6 6 2 3 . 15 3 . 2 2 8 6 2 7 . 6 6 7 - 4 5 1 7 2 2 - 0 5 2 . 3 1 3 7 2 1 1 . 5 5 1 0 . 4 6 7 7 2 1 0 . 15 9 . 6 0 0 8 2 5 . 0 6 5 . 0 6 2 8 2 1 1. 01 1 0 . 6 9 6 8 2 9 . 2 5 S - 3 6 8 8 2 4 . 3 8 4 . 3 2 1 9 2 1 2 . 9 1 1 2 . 8 2 5 9 2 3 . 5 3 4 . 2 9 7 9 2 1 1 . 0 8 1 0 . 6 6 0 10 2 1 5 . 0 4 1 3 - 9 3 2 10 2 4 . 6 2 4 . 6 4 1 1 3 9 . 2 6 8 - 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4 . 4 * — B I N A P H T H Y L h k 1 Fo F c 1 1 0 4 2 - 9 4 8 0 . 4 7 0 2 0 1 7 - 6 5 2 9 . 0 9 3 2 0 3 7 . 15 6 5 . 4 6 2 2 0 6 . 5 2 1 0 . 8 9 1 3 0 3 5 . 11 2 4 . 18 2 3 0 8 . 6 9 1 4 . 11 3 3 0 2 9 - 6 8 5 0 - 5 6 0 4 0 3 3 . 0 8 5 7 - 0 9 1 4 G 6 - 2 6 8 -99 2 4 0 1 3 . 9 9 2 3 . 2 0 3 4 0 4 . 13 7 . 5 6 4 4 0 3 . 6 5 5- 84 1 5 0 6 . 2 5 8 - 8 2 2 5 0 1 0 . 2 8 1 6 . 8 3 3 5 0 3 - 9 9 6 - 3 1 4 5 0 2 . 79 3 . 03 0 6 0 3 . 6 6 5 - 7 2 1 6 G 9 . 2 1 1 5 . 6 6 2 6 0 9 . 3 9 1 6 . 3 7 4 6 0 4 - 85 8 . 3 9 1 7 0 5 . 9 2 8 -96 2 7 0 5 . 3 3 7 . 9 5 3 7 0 6 . 6 0 3 1 - 1 9 0 8 G 9 -81 1 7 . 2 9 2 8 0 3 - 2 4 5 - 1 7 0 1 1 1 1 . 6 4 11 -51 0 2 1 3 , 5 8 2 . 5 8 1 2 1 1 7 . 0 6 2 7 - 4 0 1 3 1 2 5 . 8 7 4 0 . 2 2 2 3 1 1 2 . 4 9 1 3 . 3 7 0 4 1 5 -84 6- 34 1 4 1 2 6 . 8 0 4 . 8 8 2 4 1 1 9 . 0 6 1 5 - 85 3 4 1 9 . 0 2 7 . 7 1 1 5 1 1 5 . 5 7 2 . 19 2 5 1 1 6 . 4 5 1 0 - 7 7 3 5 1 1 0 . 7 4 1 0 . 7 5 1 6 1 1 2 . 0 2 1 7 . 9 5 2 6 3 8 - 0 3 1 3 . 11 3 6 1 1 3 . 3 5 2 1 . 8 7 4 6 1 4 . 3 5 4 . 17 5 6 1 3 . 0 4 4 . 4 1 0 7 1 5 . 36 5 . 8 2 1 7 1 4 . 2 2 5 . 0 8 2 7 3 3 1 .34 1 5 - 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