UBC Theses and Dissertations

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UBC Theses and Dissertations

Structure determination of some organic, inorganic and organometallic compounds by X-ray diffraction 1971

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THE STRUCTURE DETERMINATION OF SOME ORGANIC, INORGANIC AND ORGANOMETALLIC COMPOUNDS BY X-RAY DIFFRACTION b ^ CYRIL STEPHEN GIBBONS B.Sc.(Hons.), Memorial University of Newfoundland, 1966 M.Sc, University of B r i t i s h Columbia, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Chemistry . We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Br i t ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of Br i t ish Columbia Vancouver 8, Canada Date ZL k f / v J L 1911 A B S T R A C T S u p e r v i s o r : P r o f e s s o r James T r o t t e r T h e s t r u c t u r e s o f f o u r c o m p o u n d s r e p r e s e n t i n g e a c h o f t h e o r g a n i c ( n a t u r a l p r o d u c t ) , i n o r g a n i c a n d o r g a n o m e t a l l i c c l a s s e s o f c o m p o u n d s h a v e b e e n d e t e r m i n e d b y s i n g l e - c r y s t a l X - r a y d i f f r a c t i o n , a n d t h e m e t h o d s e m p l o y e d i n s o l u t i o n o f t h e s t r u c t u r e s h a v e b e e n d i s c u s s e d b r i e f l y . F o r a l l f o u r s t r u c t u r e s , t h e i n t e n s i t y d a t a w e r e c o l l e c t e d o n a s i n g l e - c r y s t a l d i f f r a c t o m e t e r w i t h Mo-K^ r a d i a t i o n a n d a s c i n t i l l a t i o n c o u n t e r . T h e s t r u c t u r e o f t h e a l k a l o i d , d a p h m a c r i n e m e t h i o d i d e ( a c e t o n e s o l v a t e ) , was d e t e r m i n e d f r o m h e a v y - a t o m P a t t e r s o n a n d F o u r i e r s y n t h e s e s , a n d r e f i n e d b y b l o c k - d i a g o n a l l e a s t - s q u a r e s m e t h o d s t o a f i n a l R v a l u e o f 0 .089 f o r 1834 o b s e r v e d r e f l e c t i o n s . 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 d e t e r m i n e d b y t h e a n o m a l o u s d i s p e r s i o n m e t h o d . T h e m o l e c u l e c o n s i s t s o f t w o c a g e - s t r u c t u r e s w h i c h a r e l i n k e d b y a c h a i n o f t w o c a r b o n atoms., a n d t h e b o n d l e n g t h s a n d v a l e n c y a n g l e s d o n o t d i f f e r f r o m n o r m a l v a l u e s . 2 4-, F o r b o t h e x o - t r i c y c l o [ 3 . 2 . 1 . 0 ' J o c t - 6 - e n e . s i l v e r n i t r a t e a n d s i l v e r n i t r a t e i t s e l f , t h e s i l v e r i o n was d e t e r m i n e d f r o m P a t t e r s o n s y n t h e s e s t o b e l y i n g i n a p s e u d o - s p e c i a l p o s i t i o n , s o t h a t t h e r e s u l t i n g e l e c t r o n - d e n s i t y , m a p s e x h i b i t e d p s e u d o - s y m m e t r y . A t r i a l - a n d - e r r o r m e t h o d b a s e d o n d e t a i l e d s t u d y o f t h e s h a p e o f t h e A g - A g P a t t e r s o n p e a k s was a d o p t e d t o f i n d t h e e x a c t l o c a t i o n o f t h e s i l v e r i o n s , a n d f r o m t h e r e s u l t i n g e l e c t r o n - d e n s i t y m a p s t h e t r u e l i g h t a t o m p e a k s c o u l d b e d i s c e r n e d f r o m t h e i r i m a g e s . T h e r e f i n e m e n t was c a r r i e d o u t b y f u l l - m a t r i x l e a s t - s q u a r e s , a n d t h e f i n a l R f o r t h e c o m p l e x o f s i l v e r n i t r a t e was 0.105 a n d f o r s i l v e r n i t r a t e was 0 . 0 6 7 . T h e s t r u c t u r e o f t h e c o m p l e x c o n s i s t s o f t h i c k l a y e r s p e r p e n d i c u l a r t o t h e a c r y s t a l l o g r a p h i c a x i s , a n d s e p a r a t e d b y % a . T h e s i l v e r i o n i s c o o r d i n a t e d r o u g h l y t e t r a h e d r a l l y t o t h e d o u b l e b o n d o f t h e h y d r o c a r b o n ( i n t h e e x o - p o s i t i o n , A g . . . C = 2.4A*), a n d t o t h r e e n i t r a t e g r o u p s ( A g . . . O = 2.45 - 3 . 0 3 A 1 ) . T h e l a y e r s a r e h e l d t o g e t h e r b y v a n d e r W a a l s f o r c e s . T h e s i l v e r n i t r a t e s t r u c t u r e c o n s i s t s o f l a y e r s o f s i l v e r i o n s p a r a l l e l t o t h e b c r y s t a l l o g r a p h i c a x i s , a n d s e p a r a t e d b y h b , w i t h t h e n i t r a t e g r o u p s b r i d g i n g t h e g a p b e t w e e n l a y e r s . P r e v i o u s l y o b s e r v e d i n e q u a l i t i e s i n t h e N—O d i s t a n c e s h a v e b e e n r e m o v e d , a l l t h r e e b o n d l e n g t h s i n t h e n i t r a t e i o n b e i n g 1.26 (l)i£. T h e a n i s o t r o p i c t h e r m a l m o t i o n h a s b e e n d e s c r i b e d . T h e N , N - d i m e t h y l ( f e r r o c e n y l m e t h y l ) a m m o n i u m t e t r a c h l o r o z i n c a t e h y d r a t e s t r u c t u r e c o n t a i n s s e v e n h e a v y a t o m s , a n d i t w a s n o t p o s s i b l e t o r e s o l v e t h e P a t t e r s o n p e a k s b e c a u s e o f t h e o v e r l a p . A d i r e c t s i g n - d e t e r m i n i n g p r o c e d u r e was e m p l o y e d t o l o c a t e t h e h e a v y a t o m s , a n d t h e l i g h t a t o m s w e r e l o c a t e d f r o m r e s u l t i n g e l e c t r o n - d e n s i t y m a p s . T h e s t r u c t u r e was r e f i n e d t o a f i n a l R v a l u e o f i v 0.068 for 2012 observed r e f l e c t i o n s . The mean bond distances are Fe-C = 2. 04& and C-C (cyclopentadienyl rings) = 1.43.R. Groups of four cations, two anions and two water molecules (two formula u n i t s ) , are linked around centres of symmetry by N-H...C1 (3. N-H...0 (2.76&) and 0-H...C1 (3.05, 3.17&) hydrogen bonds. V T A B L E OF CONTENTS P A G E T I T L E P A G E i A B S T R A C T i i T A B L E OF CONTENTS V L I S T OF T A B L E S v i i L I S T OF F I G U R E S i x ACKNOWLEDGEMENTS x i PART I GENERAL I N T R O D U C T I O N •. 1 H i s t o r i c a l 2 O u t l i n e o f t h e P r i n c i p l e s o f X - R a y D i f f r a c t i o n . 4 S o l u t i o n o f t h e P h a s e P r o b l e m 9 " • R e f i n e m e n t o f t h e S t r u c t u r e 16 PART I I T H E S T R U C T U R E D E T E R M I N A T I O N OF T H E M E T H I O D I D E D E R I V A T I V E OF DAPHMACRINE, AN A L K A L O I D FROM DA P H N I P H Y L L U M MACROPODUM 18 I n t r o d u c t i o n . . . 19 E x p e r i m e n t a l 19 S t r u c t u r e A n a l y s i s 20 C o o r d i n a t e s a n d M o l e c u l a r D i m e n s i o n s 2 9 A b s o l u t e C o n f i g u r a t i o n 2 9 R e s u l t s a n d D i s c u s s i o n . . . . 37 PART I I I T H E S T R U C T U R E D E T E R M I N A T I O N OF E X O - T R I C Y C L O [ 3 . 2 . 1 . 0 2 , 4 ] O C T - 6 - E N E S I L V E R N I T R A T E AND A R E F I N E M E N T OF T H E S I L V E R N I T R A T E S T R U C T U R E . . . . 41 v i P A G E A. T H E S T R U C T U R E OF E X O - T R I C Y C L O [ 3 . 2 . 1 . 0 2 ' 4 ] O C T - 6-ENE S I L V E R N I T R A T E I n t r o d u c t i o n . , 42 E x p e r i m e n t a l 4 3 S t r u c t u r e A n a l y s i s 45 C o o r d i n a t e s a n d M o l e c u l a r D i m e n s i o n s 52 R e s u l t s a n d D i s c u s s i o n 57 B. A R E F I N E M E N T OF T H E S I L V E R N I T R A T E S T R U C T U R E I n t r o d u c t i o n 63 E x p e r i m e n t a l 63 S t r u c t u r e A n a l y s i s . 6 5 C o o r d i n a t e s a n d M o l e c u l a r D i m e n s i o n s . . . . . . 7 0 R e s u l t s a n d D i s c u s s i o n 77 PART I V T H E S T R U C T U R E D E T E R M I N A T I O N OF N , N - D I M E T H Y L - (FERROCENYLMETHYL)AMMONIUM T E T R A C H L O R O Z I N C A T E . . 80 I n t r o d u c t i o n . 81 E x p e r i m e n t a l 81 S t r u c t u r e A n a l y s i s 83 C o o r d i n a t e s a n d M o l e c u l a r D i m e n s i o n s 93 R e s u l t s a n d D i s c u s s i o n . 104 SUMMARY I l l R E F E R E N C E S 113 v i i L I S T OF T A B L E S T A B L E P A G E D a p h m a c r i n e m e t h i o d i d e 1 M e a s u r 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 . . . 2 3 2 F i n a l p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s . . . . 30 3 B o n d l e n g t h s a n d a n g l e s 32 4 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 . . 36 r 2 4 n E x o - t r i c y c l o I 3 . 2 . 1 . 0 ' [ o c t - 6 - e n e — s i l v e r n i t r a t e 5 M e a s u r 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 . . . 48 6 F i n a l p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s . . . . 53 7 B o n d l e n g t h s a n d a n g l e s 54 8 A n g l e s b e t w e e n t h e A g , C=C p l a n e a n d C, C=C, C p l a n e a n d A g . . . C ( o l e f i n ) d i s t a n c e s 62 S i l v e r n i t r a t e 9 M e a s u r 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 . . . 67 10 F i n a l p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s . . . . 71 11 I n t e r a t o m i c d i s t a n c e s a n d a n g l e s 72 12 M a g n i t u d e s a n d d i r e c t i o n s o f t h e p r i n c i p a l a x e s o f t h e v i b r a t i o n e l l i p s o i d s 78 v i i i T A B L E P A G E N , N - d i m e t h y l ( f e r r o c e n y l m e t h y l ) a m m o n i u m t e t r a c h l o r o z i n c a t e h y d r a t e 13 C o m p a r i s o n o f |E| s t a t i s t i c s w i t h t h e o r e t i c a l v a l u e s 84 14 B a s e s e t o f r e f l e c t i o n s f o r s i g n d e t e r m i n a t i o n . 85 15 M e a s u r 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 . . . 88 16 F i n a l p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s . . . . 96 17 B o n d l e n g t h s a n d a n g l e s 97 18 E q u a t i o n s o f t h e m e a n p l a n e s t h r o u g h t h e c y c l o p e n t a d i e n y l r i n g s 99 19 C r y s t a l l o g r a p h i c a l l y i n d e p e n d e n t d i s t a n c e s b e t w e e n a t o m s i n d i f f e r e n t a s y m m e t r i c u n i t s . .107 20 A n g l e s f r o m t h e e c l i p s e d p o s i t i o n f o r t h e c y c l o p e n t a d i e n y l r i n g s 110 i x L I S T OF F I G U R E S F I G U R E P A G E D a p h m a c r i n e m e t h i o d i d e 1 (a) S u p e r i m p o s e d s e c t i o n s o f t h e t h r e e - d i m e n s i o n a l e l e c t r o n - d e n s i t y d i s t r i b u t i o n a n d (b) a d r a w i n g o f t h e s t r u c t u r e 2 7 2 P a c k i n g d i a g r a m v i e w e d a l o n g t h e a a x i s . . . 34 3 D i a g r a m m a t i c r e p r e s e n t a t i o n o f t h e s t r u c t u r e . 39 2 4i E x o - t r i c y c l o [ 3 . 2 . 1 . 0 ' | o c t - 6 - e n e — s i l v e r n i t r a t e 4 (a) S u p e r i m p o s e d s e c t i o n s o f t h e t h r e e - d i m e n s i o n a l e l e c t r o n - d e n s i t y d i s t r i b u t i o n a n d (b) a d r a w i n g o f t h e s t r u c t u r e 5 0 5 P a c k i n g d i a g r a m v i e w e d a l o n g t h e b a x i s . . . 55 6 C o o r d i n a t i o n a r o u n d t h e s i l v e r i o n 59 S i l v e r n i t r a t e 7 P a c k i n g d i a g r a m v i e w e d a l o n g t h e b a x i s . . . .73 8 T h e t h e r m a l v i b r a t i o n e l l i p s o i d s 75 N , N - d i m e t h y l ( f e r r o c e n y l m e t h y l ) a m m o n i u m t e t r a c h l o r o z i n c a t e h y d r a t e 9 A d i a g r a m o f t h e s t r u c t u r e , w h i c h s h o w s t h e n u m b e r i n g s y s t e m u s e d 94 X F I G U R E P A G E 10 V i e w s o f t h e f e r r o c e n y l p o r t i o n s a l o n g t h e n o r m a l s t o t h e r i n g p l a n e s 100 11 P a c k i n g d i a g r a m v i e w e d a l o n g t h e c a x i s . . . 102 -2 12 T h e e n v i r o n m e n t o f a Z n C l ^ g r o u p , w h i c h s h o w s t h e h y d r o g e n b o n d i n g a r o u n d a c e n t r e o f s y m m e t r y 105 ACKNOWLEDGEMENTS I would l i k e to express my appreciation to Professor J. Trotter for his encouragement and guidance during my years at the University of B r i t i s h Columbia. I want to thank Dr. T. Nakano for the samples of daphmacrine methiodide and Dr. J. P. Kutney for h e l p f u l discussion. I am also indebted to Dr. R. E. Pincock for the c r y s t a l s of the s i l v e r n i t r a t e complex and to Dr. E. W. Neuse for the c r y s t a l s of the ferrocene derivative. I am also g r a t e f u l for the encouragement my wife has given me, and my associations with other students and post-doctoral fellows which have made t h i s work an enjoyable and rewarding experience. PART I GENERAL INTRODUCTION 2 H i s t o r i c a l The foundations of the science of c r y s t a l - lography were l a i d i n the seventeenth century by Steno, Hooke, Huygens and other workers of t h a t e r a , who proposed elementary t h e o r i e s of c r y s t a l s t r u c t u r e based on the study of the e x t e r n a l shapes of c r y s t a l s . In 1784, Haiiy discovered the fundamental law of r a t i o n a l i n d i c e s , and even before Dalton's atomic theory, Haiiy considered the c r y s t a l u n i t as 'molecules elementaires' or chemical atoms of d e f i n i t e and constant form. The idea of the c r y s t a l as a l a t t i c e s t r u c t u r e was developed by Bravais who showed g e o m e t r i c a l l y t h a t only fourteen d i s t i n c t types of space l a t t i c e are p o s s i b l e . These important advances were made without t o o l s f o r the examination of c r y s t a l l i n e matter on an atomic s c a l e , and such a t o o l d i d not become a v a i l a b l e u n t i l 1912 when von Laue demonstrated the three-dimensional l a t t i c e nature of c r y s t a l s , and at the same time the wave nature of X-rays, by the f i r s t d i f f r a c t i o n experiment. The e l u c i d a t i o n of the f i r s t c r y s t a l s t r u c t u r e s , KC1, NaCl, KBr and KI by W.L. Bragg followed q u i c k l y , and f o r the f i r s t time the p r e c i s e l o c a t i o n s of atoms i n c r y s t a l s could be determined. This i n i t i a l r e s t r i c t i o n to simple i n o r g a n i c compounds of high symmetry passed w i t h the subsequent refinement of the methods, and soon afterward more complex organic s t r u c t u r e s of low symmetry were a l s o e l u c i d a t e d . 3 The advent of high speed d i g i t a l computers brought about the development of powerful new methods and the c a p a b i l i t y of c o n s i d e r i n g much more d i f f i c u l t problems,' e s p e c i a l l y those of b i o l o g i c a l i n t e r e s t . The p r i n c i p l e s and methods of s t r u c t u r e a n a l y s i s by X-ray d i f f r a c t i o n have been discussed i n 1-4 d e t a i l i n a number of reference books, and are not reproduced here. However, the methods r e l e v a n t to the present s t r u c t u r e s are reviewed b r i e f l y , as a d e f i n i t i o n of terms and a general knowledge of the methods used may be of use to one u n f a m i l i a r w i t h the techniques. 4 O u t l i n e o f t h e P r i n c i p l e s o f X - R a y D i f f r a c t i o n One o f t h e e a r l i e s t o b s e r v a t i o n s m ade o n n a t u r a l c r y s t a l s i s t h a t f o r a g i v e n c r y s t a l l i n e s t r u c t u r e , t h e a n g l e s b e t w e e n c o r r e s p o n d i n g f a c e s a r e c o n s t a n t . H a u y f o l l o w e d u p t h i s w o r k b y d i s c o v e r i n g t h e l a w o f r a t i o n a l i n t e r c e p t r a t i o s . A c r y s t a l f a c e may b e d e s c r i b e d i n t e r m s o f t h e i n t e r c e p t s t h e f a c e m a k e s o n a s e t o f r e f e r e n c e a x e s a , b , c . I f t h e s e i n t e r c e p t s a r e a / h , b / k , c/l, t h e f a c e i s s a i d t o h a v e M i l l e r i n d i c e s ( h k £ ) . T h e f u n d a m e n t a l l a w w h i c h H a u y d i s c o v e r e d s t a t e s t h a t t h e r a t i o s o f t h e i n d i c e s o f a n y f a c e a r e r a t i o n a l , a n d i n g e n e r a l a r e t h e r a t i o s o f s m a l l w h o l e n u m b e r s . T h i s l a w l i m i t s t h e s y m m e t r y a c r y s t a l may e x h i b i t t o 1 , 2 , 3 , 4 , 6 a n d t h e c o r r e s p o n d i n g i n v e r s i o n e l e m e n t s 1 , 2 , 3 , 4 , 6 . O n l y t h i r t y - t w o d i s t i n c t c o m b i n a t i o n s ( c r y s t a l c l a s s e s ) o f t h e s e s y m m e t r y e l e m e n t s a r e p o s s i b l e , a s s h o w n b y H e s s e l i n 1 8 3 0 . B r a v a i s i n v e s t i g a t e d c r y s t a l s t r u c t u r e o n a p u r e l y g e o m e t r i c a l b a s i s w i t h o u t r e g a r d f o r t h e f u n d a m e n t a l p a r t i c l e s , o r t h e p r o p e r t i e s o f c r y s t a l s . He s h o w e d t h a t o n l y f o u r t e e n t y p e s o f s p a c e l a t t i c e a r e p o s s i b l e , a n d t h e e x t e n s i o n o f t h i s i d e a t o c r y s t a l s t r u c t u r e s e x t e n d e d i n d e f i n i t e l y i n a l l d i r e c t i o n s b r o u g h t a b o u t t h e c o n s i d e r a t i o n o f f u r t h e r s y m m e t r y e l e m e n t s i n v o l v i n g t r a n s l a t i o n s ( m i r r o r p l a n e p l u s t r a n s l a t i o n i s a g l i d e p l a n e ; r o t a t i o n a l a x i s p l u s t r a n s l a t i o n i s a s c r e w a x i s ) . T h e s e l f - c o n s i s t e n t 5 s e t s o f a l l s y m m e t r y o p e r a t i o n s c o n s t i t u t e t h e 2 3 0 s p a c e g r o u p s a s s h o w n b y F e d o r o v , S c h o n f l i e s a n d B a r l o w i n t h e l a t e n i n e t e e n t h c e n t u r y . V o n L a u e ' s f a m o u s e x p e r i m e n t s h o w e d a t o n c e t h e w a v e n a t u r e o f X - r a y s , a n d t h e l a t t i c e s t r u c t u r e o f c r y s t a l s , b u t h e w a s u n a b l e t o i n t e r p r e t t h e r e s u l t s i n t e r m s o f a t o m i c p o s i t i o n s . W. L . B r a g g ' s s u c c e s s i n s o l v i n g t h e f i r s t c r y s t a l s t r u c t u r e s w a s b a s e d o n h i s i n t r o d u c t i o n o f t h e c o n c e p t o f r e f l e c t i o n o f X - r a y s f r o m p l a n e s w i t h i n t h e c r y s t a l . B y a s i m p l e g e o m e t r i c p r o o f , i t may b e s h o w n t h a t r e i n f o r c e m e n t o f X - r a y s o f w a v e l e n g t h X, r e f l e c t e d f r o m p a r a l l e l c r y s t a l p l a n e s a t a d i s t a n c e d a p a r t , o c c u r s w h e n t h e i r p a t h d i f f e r e n c e e q u a l s a w h o l e n u m b e r o f w a v e l e n g t h s , o r nX = 2 d S i n 0, w h i c h h a s b e c o m e k n o w n a s t h e B r a g g Law, a n d i s t h e b a s i s f o 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 . T h e p r o b l e m i s n o t t h i s s t r a i g h t f o r w a r d , h o w e v e r , s i n c e t h e s c a t t e r i n g c e n t r e s ( a t o m s ) d o n o t l i e o n t h e c r y s t a l p l a n e s , b u t a r e d i s t r i b u t e d b e t w e e n t h e p l a n e s t h r o u g h o u t t h e u n i t c e l l . T h i s g i v e s r i s e t o a r e d u c t i o n o f some o f t h e i n t e n s i t i e s s i n c e w a v e s s c a t t e r e d b y a t o m s b e t w e e n p l a n e s a r e o u t o f p h a s e t o v a r y i n g d e g r e e s , d e p e n d i n g o n t h e e x a c t p o s i t i o n o f t h e a t o m s b e t w e e n t h e p l a n e s . T h e c r y s t a l l o g r a p h e r ' s t a s k i s t h e d e t e r m i n a t i o n o f t h e d i s t r i b u t i o n o f t h e s c a t t e r i n g m a t t e r w i t h i n t h e u n i t c e l l f r o m t h e r e l a t i v e i n t e n s i t i e s o f t h e X - r a y r e f l e c t i o n s . 6 S i n c e t h e e l e c t r o n s a r e r e s p o n s i b l e f o r t h e s c a t t e r i n g o f X - r a y s , t h e s c a t t e r i n g p o w e r o f a g i v e n a t o m , k n o w n a s i t s s c a t t e r i n g f a c t o r f , i s d e p e n d e n t o n t h e n u m b e r o f e l e c t r o n s i n t h e a t o m ( Z ) . T h e s c a t t e r i n g f a c t o r v a r i e s w i t h d i f f r a c t i o n a n g l e b e c a u s e o f t h e f i n i t e s i z e o f t h e a t o m r e g a r d e d a s a s c a t t e r i n g s o u r c e . T h e r m a l m o t i o n t e n d s t o s p r e a d t h e e l e c t r o n c l o u d o v e r a l a r g e r v o l u m e a n d t h u s c a u s e s t h e s c a t t e r i n g p o w e r t o d e c r e a s e m o r e r a p i d l y t h a n f o r t h e i d e a l s t a t i o n a r y m o d e l . T h i s f a c t o r c a n b e g i v e n b y t h e e x p r e s s i o n e x p { - B S i n 2 6 / A 2 } , w h e r e B i s r e l a t e d t o t h e m e a n - s q u a r e a m p l i t u d e o f a t o m i c v i b r a t i o n (B = 8 T T 2 U 2 ) . ( I f t h e a s s u m p t i o n o f s p h e r i c a l s y m m e t r y f o r t h e v i b r a t i n g e l e c t r o n c l o u d i s a b a n d o n e d , a n i s o t r o p i c t h e r m a l f a c t o r s o f t h e f o r m e x p { - ( b h 2 + b k 2 + b I 2 + b h k + b k i l + b hi) } r 11 2-2 3 3 12 2 3 13 ' may b e u s e d . T h e s e s i x b^.. p a r a m e t e r s d e f i n e t h e s i z e a n d o r i e n t a t i o n o f t h e e l l i p s o i d o f v i b r a t i o n . ) C o n s i d e r a s e r i e s o f a t o m s s c a t t e r i n g X - r a d i a t i o n , t h e w a v e s c a t t e r e d f r o m e a c h a t o m b e i n g c h a r a c t e r i s e d b y a n a m p l i t u d e f ^ , f ^ , f ... ( d e p e n d i n g o n t h e s c a t t e r i n g p o w e r o f t h e a t o m ) , a n d a p h a s e c o n s t a n t . T h e n e t a m p l i t u d e r e s u l t i n g f r o m a c o m b i n a t i o n o f t h e s e w a v e s i s k n o w n a s t h e s t r u c t u r e a m p l i t u d e , s y m b o l i z e d b y |F|. F o r t h e g e n e r a l p l a n e (hkl), t h e r e s u l t a n t i s F ( h k & ) = E f . exp{2-rri ( h x ,+ky , + lz .) } , 7 s u m m i n g o v e r a l l t h e a t o m s i n t h e u n i t c e l l , a n d w h e r e x . , y . a n d z . a r e f r a c t i o n a l c o o r d i n a t e s o f t h e a t o m s 3 *3 3 r e f e r r e d t o u n i t c e l l a x e s a , b , c . T h i s c o m p l e x r e s u l t a n t , k n o w n a s t h e s t r u c t u r e f a c t o r , i s c h a r a c t e r i s e d b y a n a m p l i t u d e |F| a n d a p h a s e c o n s t a n t a, w h i c h may b e e v a l u a t e d b y m e a n s o f t h e e x p r e s s i o n s F ( h k £ ) = / A 2 + B2 a(hkA) = T a n - 1 B/A w h e r e A = E f . C o s 2TT ( h x . + k y .+lz .) 3 I D 3 B = E f . S i n 2TT ( h x .+ky .+ £ z .) . 3 3 3 3 T h i s e x p r e s s i o n may b e s i m p l i f i e d b y t h e p r e s e n c e o f s y m m e t r y . F o r e x a m p l e , i f a c e n t r e o f s y m m e t r y i s c h o s e n a s o r i g i n , t h e p o s s i b l e p h a s e a n g l e s a r e l i m i t e d t o 0 o r TT d e p e n d i n g o n w h e t h e r t h e e x p r e s s i o n f o r A i s p o s i t i v e o r n e g a t i v e . T h e e x p r e s s i o n f o r B m u s t b e z e r o . T h e s i g n i f i c a n c e o f t h e s e e q u a t i o n s i s e v i d e n t w h e n i t i s r e a l i z e d t h a t t h e s q u a r e o f t h e s t r u c t u r e a m p l i t u d e i s p r o p o r t i o n a l t o t h e i n t e n s i t y o f t h e X - r a y r e f l e c t i o n . I f t h e a p p r o p r i a t e c o r r e c t i o n s f o r t h e p a r t i a l p o l a r i z a t i o n b y t h e r e f l e c t i n g o f t h e X - r a y s , a n d f o r t h e g e o m e t r y o f t h e d a t a r e c o r d i n g m e t h o d ( L o r e n t z - p o l a r i z a t i o n f a c t o r ) a r e a p p l i e d t o t h e o b s e r v e d i n t e n s i t y , t h e o b s e r v e d s t r u c t u r e f a c t o r F q may b e c o m p a r e d d i r e c t l y t o t h e v a l u e c a l c u l a t e d f r o m t h e a b o v e e x p r e s s i o n s , F . 8 S i n c e t h e e l e c t r o n - d e n s i t y i n a c r y s t a l i s p e r i o d i c i n t h r e e d i m e n s i o n s , i t c a n b e r e p r e s e n t e d b y a t h r e e - d i m e n s i o n a l F o u r i e r s e r i e s a s p ( x y z ) = 1 ZZE F ( h k £ ) e x p { - 2 T T i ( h x + k y + Hz) } V h k £ w h e r e V i s t h e v o l u m e o f t h e u n i t c e l l . I t w o u l d s e e m t h e r e f o r e , t h a t b y o b s e r v a t i o n o f t h e i n t e n s i t i e s , t h e F ( h k £ ) ' s c o u l d b e c a l c u l a t e d , a n d t h e a b o v e s e r i e s summed t o g i v e a r e p r e s e n t a t i o n o f t h e e n t i r e c r y s t a l s t r u c t u r e . H o w e v e r , t h e s t r u c t u r e f a c t o r i s c o m p l e x , a n d t h e m e a s u r e m e n t o f i n t e n s i t y c a n g i v e i n f o r m a t i o n o n l y a b o u t t h e m o d u l u s , a n d n o t t h e p h a s e . T h i s i s t h e f u n d a m e n t a l d i f f i c u l t y i n X - r a y a n a l y s i s , a n d i s k n o w n a s t h e p h a s e p r o b l e m . I t i s t h e t a s k o f t h e c r y s t a l l - o g r a p h e r t o f i n d m e a n s o f o v e r c o m i n g t h i s d i f f i c u l t y , a n d , h a v i n g d e d u c e d t h e p h a s e s , t o f i n d t h e a t o m i c p o s i t i o n s c o r r e s p o n d i n g t o a c h e m i c a l l y r e a s o n a b l e s t r u c t u r e ; a n d t o t e s t t h e s t r u c t u r e b y c a l c u l a t i n g s t r u c t u r e f a c t o r s b a s e d o n t h e p r o p o s e d p o s i t i o n s a n d c o m p a r i n g t h e m w i t h t h e o b s e r v e d v a l u e s . 9 S o l u t i o n o f t h e P h a s e P r o b l e m I f t h e F o u r i e r s e r i e s i s summed w i t h t h e p h a s e l e s s q u a n t i t i e s | F | 2 a s c o e f f i c i e n t s , t h e r e s u l t i n g map h a s p e a k s w h i c h c o r r e s p o n d t o t h e i n t e r a t o m i c v e c t o r s . T h i s o b s e r v a t i o n w a s made b y A. L . P a t t e r s o n i n 1 9 3 4 , a n d t o d a y p r o v i d e s t h e b a s i s f o r many s t r u c t u r e a n a l y s e s . I f t h e r e a r e N a t o m s i n a c e l l , t h e r e a r e N ( N - l ) / 2 d i s t i n c t P a t t e r s o n v e c t o r s c o n t a i n e d i n a c e l l o f t h e same s i z e , a n d w i t h t h e i n h e r e n t l y g r e a t e r b r e a d t h o f P a t t e r s o n p e a k s c o m p a r e d w i t h F o u r i e r p e a k s , r e s o l u t i o n may b e p o o r . T h u s , a l t h o u g h t h e P a t t e r s o n s y n t h e s i s a p p e a r s t o p r o v i d e a n e a s y s o l u t i o n t o t h e p h a s e p r o b l e m , i t s a p p l i c a t i o n t o s t r u c t u r e s i n v o l v i n g m a n y a t o m s o f t h e same w e i g h t i s d i f f i c u l t . T h e P a t t e r s o n f u n c t i o n may n o t p o s s e s s t h e e x a c t s y m m e t r y o f t h e s p a c e g r o u p o f t h e a t o m i c d i s t r i b u t i o n , r e f l e c t i n g t h e l o s s o f i n f o r m a t i o n i n v o l v e d i n u s i n g t h e p h a s e l e s s | F | 2 q u a n t i t i e s . T o i l l u s t r a t e i n a s i m p l e w ay t h e a l t e r e d P a t t e r s o n s y m m e t r y , c o n s i d e r t w o a t o m s A a n d B w h i c h g i v e r i s e t o t w o v e c t o r s AB a n d BA. T h e s e a r e e q u a l i n m a g n i t u d e , b u t o p p o s i t e i n d i r e c t i o n , s o t h a t t h e P a t t e r s o n map h a s a c e n t r e o f s y m m e t r y r e g a r d l e s s o f w h e t h e r t h e o r i g i n a l s p a c e g r o u p h a s o n e o r n o t . I n a d d i t i o n , a l l e l e m e n t s o f s y m m e t r y i n v o l v i n g t r a n s l a t i o n a r e r e d u c e d t o t h e c o r r e s p o n d i n g n o n - t r a n s l a t i o n a l o n e s 10 ( i e . screw axes become r o t a t i o n a l axes; g l i d e planes become m i r r o r p l a n e s ) . Harker pointed out t h a t u s e f u l i n f o r m a t i o n i s contained i n c e r t a i n planes or l i n e s of the three-dimensional Patterson f u n c t i o n due to the presence of symmetry i n the c r y s t a l . These Harker l i n e s and planes a r i s e because the v e c t o r s between corresponding atoms of molecules r e l a t e d by symmetry elements other than centres have one or two constant coordinates. As an example, the space group Pm has a m i r r o r plane perpendicular to the b a x i s so t h a t f o r every atom at x, y, z there i s another at x, y, z. The v e c t o r s between these atoms a l l have coordinates 0, 2y, 0, so t h a t they are concentrated on the Harker l i n e which i s the y a x i s of the Patterson f u n c t i o n . For a molecule w i t h a l a r g e number of atoms of equal weight, t h i s o f t e n does not s i m p l i f y the a n a l y s i s . However, i f the s t r u c t u r e under c o n s i d e r a t i o n has a 'heavy' atom, the vectors between i t and i t s symmetry- r e l a t e d e q u i v a l e n t s w i l l stand out s t r o n g l y against the poorly r e s o l v e d background of l i g h t atom peaks. In t h i s case the Patterson f u n c t i o n provides i n f o r m a t i o n about p a r t of the s t r u c t u r e , t h a t i s , the p o s i t i o n of the heavy atom. I f t h i s atom comprises the l a r g e r share of the s t r u c t u r e f a c t o r , the component due to the l i g h t e r atoms being s m a l l , a f i r s t approximation to the phases may be obtained. 11 E x p r e s s e d a n a l y t i c a l l y : I f F ( h k £ ) = f u e x p { 2 T r i ( h x t I + k y T , + £ z „ ) } + E f T e x p { 2 - r r i ( h x T + k y T + £ z T ) } n n r l r i Jj l_i Li ±j a n d f „ >> f _ r l i j t h e n F ( h k £ ) - f „ e x p { 2 T r i ( h x „ + k y „ + £ z „ ) } . r l r l r l r l U s i n g t h i s f i r s t a p p r o x i m a t i o n t o t h e p h a s e s , a F o u r i e r s e r i e s c a n b e summed, a n d a l t h o u g h i t i s o n l y a n a p p r o x i m a t e r e p r e s e n t a t i o n o f t h e t r u e e l e c t r o n - d e n s i t y d i s t r i b u t i o n , i t may r e v e a l t h e p o s i t i o n o f some e a s i l y r e c o g n i z a b l e f e a t u r e o f t h e m o l e c u l e . I f t h i s p o r t i o n i s t h e n i n c l u d e d , t o g e t h e r w i t h t h e h e a v y a t o m , i n t h e p h a s i n g m o d e l , m o r e a c c u r a t e p h a s e s a r e o b t a i n e d , a n d t h e r e f o r e a c l o s e r r e p r e s e n t a t i o n o f t h e t r u e e l e c t r o n - d e n s i t y d i s t r i b u t i o n r e s u l t s . I n t h i s w a y , t h e e n t i r e s t r u c t u r e may b e d e d u c e d . T h e f u n d a m e n t a l d i f f i c u l t y o f t h i s m e t h o d i s i n c h o o s i n g a n a p p r o p r i a t e h e a v y a t o m d e r i v a t i v e . On t h e o n e h a n d , t h e h e a v i e r t h e a t o m , t h e e a s i e r i t i s t o f i n d b y t h e P a t t e r s o n m e t h o d , a n d t h e b e t t e r a p h a s i n g ' m o d e l i t i s ; w h i l e o n t h e o t h e r h a n d , t h e m o r e i t d o m i n a t e s t h e s t r u c t u r e , t h e l e s s t h e | F Q | a n d |F | c o m p a r i s o n i s s e n s i t i v e t o t h e p o s i t i o n s o f t h e l i g h t a t o m s . T h u s , t h e l i g h t a t o m p o s i t i o n s a r e i n c r e a s i n g l y u n c e r t a i n , a n d i n t h e e x t r e m e , may n o t b e f o u n d a t a l l . F o r t h i s r e a s o n t h e h y d r o g e n a t o m s i n a h e a v y a t o m d e r i v a t i v e o r o r g a n o m e t a l l i c c o m p o u n d a r e f r e q u e n t l y n o t l o c a t e d . A c o n v e n i e n t r u l e o f 12 t h u m b u s e d i n s e l e c t i n g a h e a v y a t o m i s £ Z 2 / £ Z 2 * 1, r l Li a l t h o u g h f a i r l y l a r g e d e v i a t i o n s f r o m i t c a n b e t o l e r a t e d . I f t h e h e a v y a t o m i s l o c a t e d o n o r v e r y c l o s e t o a s y m m e t r y e l e m e n t , i t may c o n t r i b u t e o n l y t o a c e r t a i n c l a s s o f r e f l e c t i o n ( e . g . h - e v e n ) w h i l e f o r t h e o t h e r s ( h - o d d i n t h i s c a s e ) t h e h e a v y a t o m c o n t r i b u t i o n s a r e o u t o f p h a s e a n d c a n c e l . T h u s o n l y t h e l i g h t a t o m s c o n t r i b u t e t o t h e o d d r e f l e c t i o n s . A F o u r i e r map c o m p u t e d f r o m t h e h e a v y a t o m a l o n e w i l l e x h i b i t a d d i t i o n a l , f a l s e s y m m e t r y , b e c a u s e t h e o m i s s i o n o f t h e o d d h r e f l e c t i o n s i m p o s e s t h e h i g h e r s y m m e t r y o n t h e e n t i r e s t r u c t u r e . T h u s t h e l i g h t a t o m s may b e a c c o m p a n i e d b y t h e i r m i r r o r i m a g e s , a n d t o s o l v e t h e s t r u c t u r e , i t i s n e c e s s a r y t o s e l e c t a s e t o f p e a k s w h i c h c o r r e s p o n d t o a c h e m i c a l l y r e a s o n a b l e m o l e c u l e , a n d w h o s e p o s i t i o n s g i v e g o o d a g r e e m e n t b e t w e e n F q a n d F C f o r t h e h - o d d r e f l e c t i o n s . F o r t h e c a s e w h e r e t h e h e a v y a t o m i s n o t e x a c t l y o n a s y m m e t r y e l e m e n t , b u t s o m e w h e r e n e a r i t , t h e h e a v y a t o m w i l l c o n t r i b u t e t o a s m a l l p a r t o f t h e o d d r e f l e c t i o n s . T h e P a t t e r s o n map may n o t d e t e c t t h i s s l i g h t d i s p l a c e m e n t , b u t i f a m e a n s c a n b e f o u n d t o e s t i m a t e i t , a F o u r i e r s e r i e s c o m p u t e d f r o m t h e h - e v e n r e f l e c t i o n s , a n d t h e h - o d d r e f l e c t i o n s w h i c h a r e a p p r o x i m a t e d b y t h e h e a v y a t o m , may s h o w t h e p e a k s c o r r e s p o n d i n g t o t h e t r u e s t r u c t u r e t o b e o f h i g h e r e l e c t r o n - d e n s i t y t h a n t h e i r u n r e a l i m a g e s . C a r e f u l s e l e c t i o n o f t h e h i g h e r d e n s i t y p e a k s w h i c h f o r m 13 a r e a s o n a b l e m o d e l c a n t h e n r e v e a l t h e t r u e s t r u c t u r e . M e t h o d s n o t e m p l o y i n g t h e P a t t e r s o n f u n c t i o n . , b u t e x a m i n a t i o n o f t h e i n t e n s i t y d a t a a l o n e a r e c a l l e d d i r e c t m e t h o d s , a n d a r e g a i n i n g i m p o r t a n c e w i t h g r e a t e r a v a i l a b i l i t y o f h i g h s p e e d c o m p u t e r s . D i r e c t m e t h o d s a r e b a s e d o n t h e p r o b a b i l i t y r e l a t i o n s h i p s d e d u c e d b y S a y r e w h i c h d e t e r m i n e p h a s e s o f o n e r e f l e c t i o n i n t e r m s o f o t h e r k n o w n p h a s e s . T o e v a l u a t e t h e r e l i a b i l i t y o f t h e p h a s e s s o d e t e r m i n e d , i t i s c o n v e n i e n t m a t h e m a t i c a l l y t o d e f i n e t h e n o r m a l i z e d s t r u c t u r e f a c t o r E ( h k i l ) s u c h t h a t E 2 ( h k £ ) = | F ( h k £ ) | 2 / e £ f ± 2 . T h e s y m b o l e r e p r e s e n t s a n i n t e g e r w h i c h i s g e n e r a l l y 1, b u t v a r i e s f o r c e r t a i n s p e c i a l s e t s o f r e f l e c t i o n s d e p e n d i n g o n t h e s y m m e t r y o f t h e s p a c e g r o u p i n q u e s t i o n . T h e d i s t r i b u t i o n o f |E| v a l u e s i s i n d e p e n d e n t o f t h e s i z e a n d s h a p e o f t h e u n i t c e l l , b u t d e p e n d e n t o n t h e p r e s e n c e o f a c e n t r e o f s y m m e t r y . T h u s t h e s e v a l u e s p r o v i d e a s t a t i s - t i c a l t e s t f o r c e n t r i c a n d a c e n t r i c d i s t r i b u t i o n s o f i n t e n s i t i e s ( c o m p a r e T a b l e 1 3 ) . T h e b a s i s f o r t h e p r o b a b i l i t y r e l a t i o n s h i p s f o r d e t e r m i n i n g p h a s e s m e n t i o n e d a b o v e i s t h e r e l a t i o n s h i p d e d u c e d b y S a y r e , who s h o w e d t h a t f o r t h e c e n t r o s y m m e t r i c c a s e F ( h k £ ) = < M h k £ ) E E E F ( h ' k , £ ' ) • F ( h - h 1 ,k-k ' , £ - £ ' ) h ' k ' i i ' w h e r e $ ( h k £ ) i s a s i m p l e s c a l i n g t e r m . T h i s i m p l i e s t h a t a n y s t r u c t u r e f a c t o r F ( h k £ ) i s d e t e r m i n e d b y t h e p r o d u c t s o f a l l t h e p a i r s o f s t r u c t u r e f a c t o r s w h o s e i n d i c e s a d d 14 t o ( h k £ ) . F o r e x a m p l e , F ( 2 1 3 ) d e p e n d s o n t h e p r o d u c t o f F ( 3 2 2 ) a n d F ( l l l ) , o r F ( 6 1 2 ) a n d F ( 4 0 1 ) . T h i s r e s u l t a p p e a r s t o b e o f l i t t l e v a l u e , s i n c e t h e s i g n s a r e d e t e r m i n e d o n l y i n t e r m s o f o t h e r s , n o n e o f w h i c h a r e k n o w n . H o w e v e r , S a y r e p o i n t e d o u t t h a t f o r l a r g e F ( h k £ ) ' s t h e s e r i e s m u s t t e n d s t r o n g l y i n o n e d i r e c t i o n (+ o r -) a n d t h a t t h i s d i r e c t i o n i s i n d i c a t e d b y a g r e e m e n t i n s i g n among p r o d u c t s o f l a r g e F ' s . T h u s f o r l a r g e r e f l e c t i o n s S ( F ( h k £ ) ) ^ S ( F ( h ' k ' £ ' ) ) • S (F ( h - h ' , k - k ' , £-5, *) ) . S m e a n s ' t h e s i g n o f ' , a n d ^ m e a n s ' i s p r o b a b l y e q u a l t o ' . A s s h o w n b y C o c h r a n a n d W o o l f s o n , t h e p r o b a b i l i t y o f t h e a b o v e r e l a t i o n s b e i n g t r u e i n g e n e r a l i s g i v e n b y P = 35+3sTanh{2J-3 ,2 |E(hk£) E ( h ' k ' £ ' ) E ( h - h ' , k - k ' , £ - £ ' ) I } 0 2 w h e r e a 2 = E n 2 a n d a 3 = E n ? ; n . i s t h e f r a c t i o n o f t h e t h t o t a l s c a t t e r i n g p o w e r r e p r e s e n t e d b y t h e i a t o m ( i e . n . = f . / E f . = 1/N i f t h e a t o m s a r e a l l a l i k e ) , l i ' j ' T h e a p p l i c a t i o n o f S a y r e ' s e q u a t i o n t o t h e d e t e r m i n a t i o n o f p h a s e s h a s r e c e i v e d m u c h a t t e n t i o n r e c e n t l y , a n d t h e u s u a l m e t h o d e m p l o y e d i s c a l l e d t h e s y m b o l i c a d d i t i o n m e t h o d . T h i s i n v o l v e s t h e s e l e c t i o n o f a s m a l l n u m b e r o f p h a s e s w h i c h c a n b e a s s i g n e d a r b i t r a r i l y ( s i n c e t h e y r e p r e s e n t a c h o i c e o f o r i g i n w h i c h i s a r b i t r a r y ) , a n d f r o m t h e s e , a n d t h e s u b s e q u e n t l y d e t e r m i n e d o n e s , t o d e d u c e t h e s i g n s o f t h e o t h e r s . I f a n i m p a s s e i s r e a c h e d , o t h e r 15 phases may be assigned symbols, and the remainder determined i n terms of these symbols, which can then be varied and the consistency of the r e s u l t i n g sets of phases checked mathematically. A consistency index has been defined C = <lE(hk£)EE(h'k'£') E(h-h',k-k',£-£')[> <|E(hk£) I l l E f h ' k ' D l |E(h-h' ,k-k' ,1-1') |> the sums being taken over a l l pairs of (h'k'Ji 1) and (h-h 1 ,k-k1 , l - l 1 ) whose sum i s (hkJl) and where < > means the average over a l l values of (hk£). If for each r e f l e c t i o n a l l of the terms i n the sum i n Sayre's equation have the same sign as a l l other terms i n that p a r t i c u l a r sum, C equals 1, and the solution i s completely consistent. In general the true solution w i l l be the one with the highest consistency index. Having thus determined a set of phases for the E's, a Fourier series can be summed using the E's as c o e f f i c i e n t s , and from t h i s the structure (or a p a r t i a l structure) can be deduced. If the E-map i s i n s u f f i c i e n t l y resolved to give the pos i t i o n of the entire molecule, a p a r t i a l structure may be used as a phasing model for further F Fourier syntheses. 16 R e f i n e m e n t o f t h e S t r u c t u r e O n c e a m o d e l o f t h e s t r u c t u r e h a s b e e n p r o p o s e d o r e l u c i d a t e d f r o m e i t h e r P a t t e r s o n o r d i r e c t m e t h o d s , some c r i t e r i o n f o r j u d g i n g t h e c o r r e c t n e s s o f t h e s t r u c t u r e i s n e c e s s a r y , a s w e l l a s a m e a n s f o r i m p r o v i n g t h e m o d e l a s r e q u i r e d . T h e m o s t o b v i o u s m e t h o d i s d i r e c t c o m p a r i s o n o f t h e s t r u c t u r e f a c t o r s c a l c u l a t e d f r o m t h e p o s t u l a t e d a t o m i c p o s i t i o n s w i t h t h e o b s e r v e d v a l u e s . T h e a g r e e m e n t b e t w e e n t h e s e q u a n t i t i e s i s u s u a l l y d e s c r i b e d i n t e r m s o f a ' r e s i d u a l ' o r ' d i s c r e p a n c y i n d e x ' R, d e f i n e d b y R = ZM F 0I-I F CI l / E l F 0 l - I f a p o s t u l a t e d m o d e l i s c o r r e c t , r e f i n e m e n t w i l l u s u a l l y p r o c e e d t o a n R v a l u e o f 0.10 o r l e s s . S i n c e t h e o b s e r v e d i n t e n s i t i e s a r e s u b j e c t t o e r r o r s o f o b s e r v a t i o n , t h e a g r e e m e n t b e t w e e n t h e F q 1 s a n d F C ' s i s n o t e x p e c t e d t o b e e x a c t . A c c o r d i n g t o L e g e n d r e ' s P r i n c i p l e , t h e m o s t a c c e p t a b l e s o l u t i o n i s t h e o n e w h i c h m a k e s t h e sum o f t h e s q u a r e s o f t h e e r r o r s E, a m i n i m u m , a n d t h i s o c c u r s w h e n t h e p a r t i a l d e r i v a t i v e s o f E£ 2 v a n i s h . A s e t o f ' n o r m a l e q u a t i o n s ' may b e s e t u p (n e q u a t i o n s i n n u n k n o w n s ) a n d f r o m t h e m t h e b e s t s e t o f v a r i a b l e s w h i c h s a t i s f y L e g e n d r e ' s P r i n c i p l e c a n b e d e t e r m i n e d b y m a t r i x , a l g e b r a . T h i s p r o c e d u r e i s c a l l e d t h e ' l e a s t - s q u a r e s m e t h o d ' . 17 I n c r y s t a l s t r u c t u r e a n a l y s i s t h e f u n c t i o n m i n i m i z e d i s R- = E W ( | F O | - | F C | ) 2 w h e r e w i s a w e i g h t i n g f a c t o r e m p l o y e d b e c a u s e some o f t h e r e f l e c t i o n s may b e m e a s u r e d m o r e r e l i a b l y t h a n o t h e r s . I f s u c h w e i g h t s a r e u s e d , t h e w e i g h t e d R f a c t o r may b e d e f i n e d R W = { E w | | F O | - | F c | | 2 A w | F O | 2 } J 5 , a n d i f t h e a s s i g n e d w e i g h t s a r e c o r r e c t , R a n d R^ s h o u l d b e a p p r o x i m a t e l y t h e s a m e . S i n c e e a c h a t o m i n t h e s t r u c t u r e i s f i x e d b y f o u r v a r i a b l e s ( x , y , z , B ) , l a r g e s t r u c t u r e s i n v o l v e l a r g e m a t r i c e s f o r s o l u t i o n o f t h e n o r m a l e q u a t i o n s , a n d a g r e a t d e a l o f c o m p u t a t i o n i s r e q u i r e d . I t h a s b e e n f o u n d t h a t i f a l a r g e n u m b e r o f e q u a t i o n s i s u s e d , t h e o f f - d i a g o n a l t e r m s o f t h e n o r m a l e q u a t i o n s a r e s m a l l , a n d may b e n e g l e c t e d , t o a f i r s t a p p r o x i m a t i o n . A b e t t e r a n s w e r i s o b t a i n e d w i t h t h e b l o c k - d i a g o n a l a p p r o x i m a t i o n a t t h e c o s t o f g r e a t e r c o m p u t i n g t i m e , a n d i f s u f f i c i e n t c o m p u t i n g f a c i l i t i e s a r e a v a i l a b l e , t h e f u l l m a t r i x may b e u s e d . N o n e o f t h e s e p r o c e d u r e s w i l l g i v e t h e c o r r e c t a n s w e r i m m e d i a t e l y , a n d u s u a l l y a n u m b e r o f c y c l e s o f r e f i n e m e n t i s r e q u i r e d t o g i v e t h e m o s t a c c e p t a b l e f i t o f F 1 s t o t h e F ' s . ^ c o P A R T I I T H E S T R U C T U R E D E T E R M I N A T I O N O F T H E M E T H I O D I D E D E R I V A T I V E O F D A P H M A C R I N E , A N A L K A L O I D F R O M D A P H N I P H Y L L U M M A C R O P O D U M 1 9 INTRODUCTION The i s o l a t i o n and properties of daphmacrine 5 ^ 3 2 H 4 9 ^ 4 ^ have been described by Nakano and Saeki. An X-ray c r y s t a l analysis of the methiodide derivative was undertaken to show the d e t a i l s of the molecular structure, including the absolute configuration, and to provide additional evidence for the novel framework of daphniphyllum al k a l o i d s . EXPERIMENTAL Crystals of daphmacrine methiodide (acetone solvate) are colourless plates with ( 0 1 0 ) developed, and smaller { 1 0 1 } forms. Unit c e l l and space group data were determined from various ro t a t i o n , Weissenberg and precession films. Crystal D a t a . — X (Cu-K ) = 1 . 5 4 1 8 ; X (Mo-K ) = 0 . 7 1 0 7 & . — a a Daphmacrine methiodide acetone solvate (from acetone-ether), C 3 3 H 5 2 ° 4 N I * ( M e 2 C 0 ) ' M = 7 1 1 - 8 ' m * P * = 2 7 4 - 2 7 5 ° . Orthorhombic, a = 1 4 . 2 3 ( 2 ) , b = 2 4 . 8 5 ( 2 ) , c = 1 0 . 0 2 ( 1 ) & . U = 3543.R 3, D^ ( f l o t a t i o n i n aqueous KI) = 1 . 3 6 g.cm.3, Z = 4 , D = 1 . 3 3 g.cmT3 c ^ F ( 0 0 0 ) = 1 4 9 6 . Absorption c o e f f i c i e n t s : u(Cu-K a) = 7 6 cm.1; u(Mo-K^) = 9 . 6 cm. Absent r e f l e c t i o n s : hOO, h odd; OkO, k odd; 00&,& odd. Space group P 2 i 2 1 2 i ( D 2 ' ) . 20 T h e i n t e n s i t i e s o f a l l r e f l e c t i o n s w i t h 2 8 ( M o - K a ) < 4 0 ° ( m i n i m u m i n t e r p l a n a r s p a c i n g , d - 1.04&) w e r e m e a s u r e d o n a D a t e x - a u t o m a t e d G e n e r a l E l e c t r i c XRD 6 s p e c t r o g o n i o m e t e r w i t h a s c i n t i l l a t i o n c o u n t e r , a p p r o x i m a t e l y m o n o c h r o m a t i c Mo-K^ r a d i a t i o n ( Z r f i l t e r a n d p u l s e - h e i g h t a n a l y s e r ) , a n d a 6-2 0 s c a n . B a c k g r o u n d c o u n t s w e r e made a t t h e b e g i n n i n g a n d e n d o f e a c h s c a n . T h e c r y s t a l u s e d w a s a p l a t e w i t h d i m e n s i o n s 0.1 mm. p a r a l l e l t o b a n d 0.3 mm. p a r a l l e l t o <101> a n d w a s m o u n t e d w i t h a p a r a l l e l t o t h e (}> a x i s o f t h e g o n i o s t a t . No a b s o r p t i o n c o r r e c t i o n was m a d e . L o r e n t z a n d p o l a r i z a t i o n f a c t o r s w e r e a p p l i e d , a n d t h e s t r u c t u r e a m p l i t u d e s w e r e d e r i v e d . O f 2 0 4 7 r e f l e c t i o n s w i t h 26 < 4 0 ° , 1 8 3 4 ( 9 0 % ) w e r e o b s e r v e d , a n d t h e 213 u n o b s e r v e d r e f l e c t i o n s w e r e i n c l u d e d i n t h e s t r u c t u r e r e f i n e m e n t w i t h F Q = 0.6 F ( m i n ) . S T R U C T U R E A N A L Y S I S T h e i o d i n e p o s i t i o n w a s d e t e r m i n e d f r o m t h e t h r e e - d i m e n s i o n a l P a t t e r s o n f u n c t i o n ( 0 . 0 4 1 , 0.196 , 0 . 1 6 7 ) , a n d t w e n t y - f o u r a t o m s , m a i n l y i n t h e l a r g e r , n i t r o g e n - c o n t a i n i n g c a g e , w e r e l o c a t e d o n a f i r s t t h r e e - d i m e n s i o n a l e l e c t r o n - d e n s i t y map. E l e v e n a d d i t i o n a l a t o m s o f t h e c h a i n a n d t h e s m a l l e r , n i t r o g e n - f r e e c a g e w e r e l o c a t e d o n a s e c o n d t h r e e - d i m e n s i o n a l e l e c t r o n - d e n s i t y map o n t h e b a s i s o f t h e p h a s e s c o m p u t e d f r o m t h e p o s i t i o n s o f t h e f i r s t 21 t w e n t y - f i v e a t o m s . T h e p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s w e r e r e f i n e d b y b l o c k - d i a g o n a l l e a s t - s q u a r e s m e t h o d s , w i t h m i n i m i z a t i o n o f Ew (|Fq | - | F j ) 2 f w i t h A T = 1 w h e n |F | 4 F*, • a n d /w = F * / | F | w h e n |F | > F * . F * w a s i n i t i a l l y t a k e n a s 3 0 . F o r t h e 213 u n o b s e r v e d r e f l e c t i o n s , F w a s t a k e n ' o a s 0.6 F ( m i n ) a n d /w = 1.0. T h e s c a t t e r i n g f a c t o r s o f t h e 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 w e r e u s e d . A f t e r t w o c y c l e s o f i s o t r o p i c r e f i n e m e n t , a t h r e e - d i m e n s i o n a l d i f f e r e n c e map r e v e a l e d f i v e f u r t h e r a t o m s , w h i c h w e r e s u b s e q u e n t l y i n c l u d e d i n t h e r e f i n e m e n t . T h r e e o f t h e a t o m s p r e v i o u s l y a s s i g n e d a s c a r b o n w e r e p r o p e r l y a s s i g n e d a s o x y g e n o n t h e b a s i s o f t h e i r h i g h e r e l e c t r o n d e n s i t i e s ; o n l y t w o p o s i t i o n s a r e p o s s i b l e f o r t h e n i t r o g e n a t o m o f t h e l a r g e r c a g e ( s i n c e i t c a r r i e s a m e t h y l g r o u p ) , a n d o n e o f t h e s e was a s s i g n e d a s n i t r o g e n f r o m c h e m i c a l c o n s i d e r a t i o n s . A f t e r t h r e e f u r t h e r c y c l e s o f r e f i n e m e n t , R was 0.18; /w f o r t h e u n o b s e r v e d r e f l e c t i o n s w a s c h a n g e d t o 0 . 8 , a n d t h e i o d i d e i o n was a l l o w e d 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 . A f t e r f o u r m o r e c y c l e s o f r e f i n e m e n t , a s e c o n d t h r e e - d i m e n s i o n a l d i f f e r e n c e s y n t h e s i s r e v e a l e d t h e l o c a t i o n o f t h e f i n a l t w o a t o m s . T h e s e v e n a t o m s l o c a t e d o n t h e d i f f e r e n c e maps w e r e t h o s e o f t h e a c e t y l s i d e c h a i n a n d o f t h e m o l e c u l e o f s o l v e n t o f c r y s t a l l i z a t i o n ( a c e t o n e ) ; t h e s o l v e n t a t o m s h a v e h i g h t h e r m a l p a r a m e t e r s . A t t h i s p o i n t a l s o , t w o o t h e r a t o m s w e r e r e - a s s i g n e d a s o x y g e n s , a n d a n 2 2 , * a n a l y s i s of w ( F Q - F c ) z suggested t h a t F be changed to 40, and /w f o r the unobserved r e f l e c t i o n s be changed to 0.6. Four f u r t h e r c y c l e s of refinement w i t h a l l the atoms inc l u d e d and pr o p e r l y assigned r e s u l t e d i n an R value of 0.095. Four c y c l e s w i t h a n i s o t r o p i c thermal parameters f o r a l l 4 3 atoms completed the refinement, the maximum s h i f t i n the f i n a l c y c l e being 0.3a, and the f i n a l R was 0.089 f o r 1834 r e f l e c t i o n s . Measured and 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 are l i s t e d i n Table 1. A f i n a l three-dimensional F o u r i e r s e r i e s was summed, and se c t i o n s of the r e s u l t i n g e l e c t r o n - d e n s i t y d i s t r i b u t i o n are shown i n Figure 1, together w i t h a drawing of the molecule. A f i n a l d i f f e r e n c e map showed no spurious d e t a i l , the maximum f l u c t i o n s being ±0.6 e£ I except at the io d i d e p o s i t i o n , where f l u c t u a t i o n s of ±1.3 eR 3 were observed. Table 1 Measured and calculated structure factors for daphmacrine methiodide. Unobserved r e f l e c t i o n s have |F | = 0.6 F(min) and are indicated by a negative sign before F . With respect to the right-handed a x i a l set used to describe the absolute configuration, the F q values are those for r e f l e c t i o n s hk£. 24 Table 1 h k I F0 FC 1 1 6 . 3 100 4 4 . 1 37 1 2 6 . 6 119 4 0 . 5 36 4 8 . 7 45 1 0 8 . T \OT 1 6 5 . 6 I " 8 5 . 0 77 1 ?.6 3 3 4 . 8 32 5 0 . 4 S3 1 6 . 8 l a 5 1 . 5 49 1 * 0 . 0 136 5 0 . ? 2 2 . 2 1 1 . ? 790 .3 298 7 3 . 1 I B . 9 4 7 . 0 1 4 . 5 11.1 5 2 . 1 4 6 . 9 1 1 7 . 5 2 5 . 5 7 9 . 3 - 4 . 7 - 5 . 1 ? 1 . ? 22.1 2 2 . 8 2 e . o 2 C . 6 17.4 1 1 . 2 2 3 .7 1 1 . 6 1 0 . 5 7 5 . 3 1 5 . 1 - 6 . 1 17. 1 4 6 . 2 1 5 . 3 1 1 . 2 - 5 . 8 1 5.0 3 6 . 2 2 3 . 6 2 2 . 0 1 0 . 6 ? 0 . 5 2 9 . 4 1 3 . 9 1 3 . 4 1 2 4 . 7 6 5 . 0 17.1 1 3 . 5 5 3 . 5 7 6 . 6 1 2 7 . 3 2 6 . 5 6 9 . 9 ? 2 . 4 6 5 . 5 7 2 . 8 1 4 . 5 1 0 1 . 5 3 3 . 9 3 8 . 0 3 6 . 8 2 8 . 5 2 4 . 0 3 3 . 2 2 7 . 8 1 0 . 1 6 5 . 2 3 3 . 1 2 1 . 7 1 6 . 4 3 3 . 0 1 0 . 7 3 1 . 0 9 . 8 3 7 . 6 3 0 . 0 2 9 . 0 6 1 . 3 3 3 . ? 7 1 . 8 5 1 . 1 J B . f i 2 J . I 2 0 . 9 2 9 . 0 5 . 6 64 . 4 1 6 . 6 1 0 . 6 2 6 .5 2 2 . 5 1 2.6 7 1 . 5 1 1 . 9 5 . 0 1 2 . 0 3 8 . 8 1 9 . 6 1 0 . f i 2 1 . 8 2 0 . 1 1 3 . 8 2 3 . 0 1 9 .5 6 2 . 7 142.5 154.4 1B.T 44 . 5 3 0 . 5 2 7 . 8 2 8 . 3 6 5 . 0 2 8 . 2 5 8 . 1 5 T . ? 2 3 . I 2 1 .0 5 8 . 5 5 9 . 2 1 3 3 . 5 1 1 0 . 1 2 5 . 7 4 7 . 5 3 0 . 6 2 5 . 5 2 8 . 1 7 . 1 1 3 7 . 6 5 6 . 2 8 0 . 7 5 8 . 3 8 5 . 9 7 8 . 5 3 0 . 6 2 5 . 2 3 1 . 4 5 7 . 3 2 9 . 2 1 4 . 0 1 1 4 . 6 7 1 . 0 5 0 . 0 1 0 2 . 0 111.7 1 0 6 . 5 7 4 . 4 1 3 5 . 0 1 5 . I 110. 7 2 7 . 5 1 2 . 2 1 4 3 . 5 11.1 1 0 9 . 3 2 8 . 2 1 3 . 2 1 5 . 9 5 4 . 1 7 . 4 1 0 . 0 1 2 6 . 9 8 6 . 2 1 7 . 3 3 7 . 4 3 7 . 2 1 7 . 8 - 1 . 0 1 0 2 . 5 5 0 . 1 1 1 2 . 4 7 7 . 5 3 7 . B 1 6 . 2 9 9 . 8 6 8 . 3 1 4 . 5 6 0 . 5 3 3 . 1 4 0 . 6 6 2 . 1 3 5 . I - 5 . 8 I 1 , 5 2 1 . 2 4 . 2 9 7 . 2 4 9 . ? 111.1 8 1 . 9 6 9 . 7 1 9 . 2 1 4 . 1 * 2 . 2 4 2 . 0 1 4 . 9 2 4 . 2 4 3 . 1 1 1 . 5 5 6 . 0 7 0 . 2 1 5 . 7 3 5 . 2 2 2 . 2 21.1 3 8 . 9 2 2 . 6 1 0 . 2 1 6 . 4 2 5 . 1 1 9 . 6 1 2 . 2 4 3 . 4 2 9 . I 10. 7 7 2 . 5 2 0 . 9 1 2 . 0 1 9 . 4 2 6 . 9 1 3 . S 2 1 . 0 1 3 . 9 - 5 . 5 2 0 . 5 9 7 . 9 8 4 . 5 4 5 . 6 1 5 . 9 2 0 . 1 2 7 . 2 4 1 . 9 1 1 . 2 1 1 . 0 1 8 . 7 3 1 . 0 1 9 . 1 2 5 . 6 2 5 . 8 3 3 . 7 2 6 . 6 1 9 . 5 7 . 7 17.7 1 5 . 6 1 7 . 6 2 7 . 5 2 5 . 6 1 8 . 8 3 8 . 4 1 2 . 2 5 . 9 6 . 5 1 1 4 2 . 5 1 2 8 . 8 7 2 . J 1 7 4 .6 1 0 8 . 0 6 7 . 9 2 8 . 4 6 2 . B 2 6 . 5 2 4 . 3 4 6 . 9 9 7 . 0 6 2 , 1 3 2 . 5 4 2 . 2 2 6 . 0 2 2 . 9 9 6 . 1 9 5 . 3 2 9 . 9 5 5 . 4 4 8 . B 4 2 . 8 2 B . 1 8 6 . ? 1 1 9 . 2 7 7 . 5 9 1 . 9 5 3 . 6 6 5 . 2 3 3 . 1 5 8 . 2 2 1 . 5 7 7 . 2 25 T a b l e 1 continued h k 1 F„ Fc 4 4 7 2 2 3 6 2 . 7 e e . o 54.2 8 5 , 9 4 17 17 1 9 . 1 4 1 3 . 0 5 13 7 6 5 5 i ! 16 : 16 . 8 39 0 33 5 6 6 6 6 - 5 . 4 7 2 1 . 1 4 22 1 0 1 6 5 i a b 3 8 7 } e a 1 6 <* i 9 0 5 2 . 5 2 5 . 3 3 2 . 0 1 4 . 0 - 6 . 3 6 1 . 3 4 9 . 1 7 4 . 0 3 0 . 6 1 3 . 0 0 , 7 5 2 . 7 4 4 2 5 2 7 2 8 2 9 4 0 . 1 4 0 . 6 6 2 . 4 1 6 . 8 3 7 . 2 8 2 . 5 3 5 . 8 4 2 . 5 5 5 . 9 1 9 . 9 3 5 . 5 9 6 . ft 4 4 '4 4 4 IT IB 18 18 18 18 6 3 2 . 9 0 - 5 . 0 1 20.a 2 1 4 . 6 3 2 7 . 1 4 - 5 . 7 30 6 21 14 ?B 2 B 1 9 6 6 5 5 5 5 5 5 5 51 6 22 7 27 8 20 0 - 4 3 35 7 52 0 20 7 73 3 IB 3 1 9 9 6 2 3 I t t t 0 T 4 . 2 1 6 5 . 1 2 4 0 . 3 3 2 1 . 4 4 1 8 . 7 80 58 39 25 1 7 3 0 3 1 1 9 2 3 9 J 1 9 4 1 9 5 9 7 6t>. 3 3 2 . 5 3 * . 3 3 5 . 6 - 5 . ? 3 0 . 2 66.1 7 7 . 2 3 7 . 7 3 8 . 7 1 1 . 6 3 0 . 6 4 3 1 3 3 3 5 3 6 1 1 3 . 0 1 0 3 . 3 8 4 . 0 7 1 . 4 17. a 1G0.B 1 0 0 . 3 B 9 . 5 7 4 . 1 6 5 . 5 3 9 . 1 4 4 4 4 18 18 19 19 19 19 5 2 5 . 4 6 . - 6 . 2 0 1 9 . 2 1 - 5 . 3 2 1 0 . 9 3 1 2.4 31 2 20 16 6 6 5 6 7 2 a i 5 5 5 5 5 5 17 1 45 2 43 3 45 4 22 5 23 6 15 1 49 5 45 7 50 1 24 3 72 .1 11 1 6 8 4 8 B 8 6 4 0 . 4 7 1 5 . 1 8 1 7 . 9 0 4 2 . a 1 4 4 . 7 2 4 2 . 1 41 19 35 53 44 6 3 9 1 I 0 0 0 1 C 2 0 1 0 * 0 5 0 6 0 7 6 3 . 5 8 8 . 4 7 6 . 5 21.1 2 7 . 6 * I . 6 2 0 . 1 2 6 . 2 2 2 . 3 6 0 . 3 8 9 . 9 72. J 1 7 . 8 3 2 . 8 4 6 . 4 7 0 . 3 2 7 . 1 4 4 3 8 4 0 4 7 4 1 4 5 3 1 . 7 1 9 . 0 7 5 . 6 2 8 . 9 1 1 4 . 6 5 0 . 3 1 0 4 . 7 3 1 . 1 1 5 . 4 18.1 5 8 . 8 3 1 . 8 1 1 0 . 0 4 0 . 4 9 5 . 1 3 1 . 2 4 4 4 4 19 20 20 20 70 20 21 21 5 1 4 . 6 0 5 5 . 7 1 - 5 . 4 2 1 2 . 7 3 1 4 . 1 4 - 6 . 0 0 1 2.4 1 2 0 . 4 13 50 5 79 12 5 29 15 7 8 1 7 0 B 6 5 5 5 5 5 5 5 5 jj a et 1 - 4 2 26 3 25 5 25 6 53 4 79 6 7 2 27 2 7 3 .0 30 . 3 27 . 7 55 . 1 6 1 3 7 2 3 2 8 e a e B 9 9 9 4 3 2 . 7 5 I B . B 6 - 5 . 5 7 3 9 . 0 8 3 2 . 1 0 7 6 . 0 1 3 2 . 6 2 2 5 . 6 33 .2 19 32 83 35 28 7 0 2 5 2 0 8 t 0 1 1 1 2 1 1 I 5 I T 1 e 2 0 1 8 . 1 3 7 . 5 5 1 . 7 3 6 . 7 3 0 . * 4 1 .1 4 3 . 4 2 3 . 0 - 5 . 7 3 1 . 8 - 4 . 0 15.1 3 0 .0 51 . 3 4 0 . 9 17.0 4 9 . a 5 4 , B 7 4 . 6 3 1 . a 1 0 . 4 4 4 4 4 4 4 6 4 8 4 9 5 0 5 1 5 2 5 3 5 5 7 6 . 4 3 4 . 0 3 1 . 7 - 6 . 7 2 0 . 6 1 0 7 . 5 3 9 . 0 5 0 . 4 6 0 . 4 1 1 . 8 2 5 . a 3 7 . 3 3 5 . 6 4 , 5 7 5 . 6 1 0 5 , 3 6 0 . 5 3 5 , 6 4 3 . 4 5 8 . 4 1 8 . 0 4 4 4 4 5 .5 5 21 21 21 22 22 22 22 23 0 0 0 2 1 3 . 8 3 1 1 . 6 4 1 7 . 6 0 2 0 . 9 1 1C. 7 2 2 1 . 5 3 1 2 . 8 0 - 5 . 8 1 2 4 . 4 2 1 1 8 . 7 3 - 4 . 1 1 1 10 8 70 1 3 17 B 2 20 1 1 3 3 2 1 0 8 1 6 5 6 5 5 5 5 5 5 5 5 5 5 5 |* 0 - 4 1 35 2 8 3 76 4 15 5 18 6 10 0 80 1 23 2 14 6 1 1 5 35 4 9 0 75 9 Ik 0 17 . 6 8 . 2 11 2 79 . 6 76 7 1 3 1 9 4 8 9 0 5 3 0 4 t t t t 9 9 9 9 9 9 0 0 0 0 0 3 1 3 . 2 4 3 2 . 1 5 2 0 . 5 6 7 2 . 1 7 1 7 . 5 8 1 4 . 4 0 - 4 . 2 1 9 1 . 5 2 1 2 . 8 3 9 3 . 9 4 2 1 . 3 1 1 31 19 15 4 87 12 91 70 8 9 8 6 b 2 1 0 2 1 2 2 2 3 2 5 5 9 . 0 6 6 . 8 7 4 . 8 7 0 . 5 7 4 . 8 5 9 . 0 6 5 . 6 2 6 . 0 2 3 . 7 2 9 . 9 4 4 5 7 5 B 5 9 6 0 6 1 4 9 . 5 2 2 . 7 1 1 . 0 - 3 . 1 3 3 . 5 5 0 . 8 2 7 . 8 3 . 0 1 . 4 3 5 . 7 5 5 5 5 5 0 0 0 0 0 4 1 3 4 . 6 5 2 3 . 5 6 1 3 . 3 7 - 5 . 5 8 3 7 . 5 119 19 14 8 36 8 0 0 5 5 5 5 5 5 1 15 4 22 5 17 6 22 0 12 9 70 8 19 1 16 «. 74 7 15 5 2 7 0 t 0 c 0 5 17 .7 6 1 3 . 4 7 2 4 . a 0 8 3 . 1 1 3 4 . 5 9 73 84 36 0 .1 3 5 2 7 ? e 1 0 1 7 . 2 2 5 . 5 ? 0 . 5 6 1 . 6 1 6 . 7 3 1 . 4 77 .1 6 4 . 7 4 4 4 6 2 6 3 6 5 9 2 . 6 4 5 . 0 6 3 . 2 2 2 . 1 8 5 . 1 4 6 . 3 6 2 . 0 2 4 . 7 5 5 5 5 0 9 - 6 . 3 0 7 0 . 5 1 1 0 5 . 5 2 8 9 . 0 1 65 88 78 3 B 3 5 5 5 5 it 1 - s 7 70 3 3B 4 18 0 10 . 4 70 . 9 38 7 16 2 3 3 2 2 7 . 6 3 - 4 . 9 4 - 5 . 1 5 2 8 . 8 27 t l 6 29 3 1 7 1 2 3 3 J 4 1 5 2 5 . 2 4 4 . 6 3 7 . 6 1 7 . 6 I S . 2 3 0 . 4 4 5 . 1 3 9 . 1 11.a 4 0 . 3 4 6 7 6 a 6 9 7 0 1 6 . 6 3 1 . 7 1 a . 2 1 0 3 . 4 4 4 . 9 1 6 . 1 3 1 . 6 1 5 . 2 9 0 . 4 5 5 . 6 5 5 5 5 5 ! 4 T 4 ! l 5 9 0 . 1 6 4 4 . 1 7 4 4 . 0 8 - 5 . 9 62 86 44 15 6 I 5 5 5 5 5 6 - 6 0 25 1 - 5 2 13 3 14 0 9 4 24 1 9 7 12 2 12 3 3 5 t 7 2 1 . 5 0 - 4 . 5 1 7 1 . 8 2 11 . 7 20 0 19 79 10 6 5 2 0 6 3 7 3 a 4 0 7 1 . 1 1 7 . B 3 0 . 9 7 3 . 7 1 5 . 2 3 2 . 3 4 7 2 7 3 7 5 4 8 . 9 3 5 . 5 3 4 . 8 6 1 . 2 4 9 . 5 4 1 . 7 3 3 . 9 5 4 . B 5 5 5 \ 9 1 9 . 9 0 B 5 . 2 1 6 2 . 7 14 77 55 3 B 1 5 5 5 \] 4 1 1 5 10 6 10 . 8 4 . 0 13 . 7 a 8 5 - 5 . 5 6 2 0 . 3 7 21 0 7 4 4 1 4 2 4 3 4 4 4 5 1 1 . 3 2 0 . 5 4 9 . 8 7 4 . 7 1 8 . 5 1 8 . 3 2 0 . 8 5 4 . 1 2 4 . 7 2 3 . 3 4 7 6 7 7 7 8 7 9 2 1 . 2 2 1 . 3 12.1 1 7 . 6 2 2 . 1 7 3 . 6 1 0 . 7 1 3 . 1 5 5 5 5 \ 3 8 6 , 2 4 1 0 1 . 3 5 12.1 6 7 4 . 5 87 90 6 24 1 0 0 5 5 5 5 18 18 18 18 24 2 21 3 - 5 4 23 . a 25 . 6 16 b 2 2 19 i • 0 2 7 ! o 1 4 8 . 1 7 2 9 . 2 3 3 8 . 5 7B 49 29 39 1 2 6 4 7 5 0 5 2 5 1 2 C . 7 - 6 . 0 3 1 . 8 3 7 . 1 1 7 . 2 2 6 . 1 7 3 . 5 2 9 . 0 4 0 . 5 IB.3 S 0 e i e 2 B ) a 4 8 5 9 7 . 3 4 1 . 9 9 9 . 1 9 6 . 6 5 2 . 6 2 9 . 7 5 0 . 1 97 . 7 9 9 . 4 4 8 . 6 7 9 . 9 5 5 5 5 5 5 \ 7 3 7 . 0 B 2 3 . 9 9 3 1 . 4 0 7 7 . 6 1 8 6 . 4 2 7 5 . 7 78 27 76 86 72 3 2 6 4 5 5 5 5 5 5 18 19 19 1? 19 5 16 0 12 1 36 7 1 B 3 - 5 4 9 7 15 . 6 35 . 2 17 8 5 9 6 7 8 7 . 4 1 9.0 5 2 9 . 0 6 7 1 . 4 0 - 4 . 7 1 1 3 . 8 23 78 73 20 10 1 9 5 5 1 1 . 3 2 0 . 1 1 7 . 8 1 7 . 4 1 9 . 0 1 9 , 5 4 8 6 a 7 a a 9 0 3 3 . 0 I 3 .7 2 C . 9 1 3 . 7 1 3 . 6 i a . o 5 5 \ 3 1 8 . 7 4 2 5 . 4 5 5 5 . 9 15 73 49 2 1 5 5 5 19 20 20 5 21 0 - 5 1 21 . 4 16 4 6 9 18 0 7 7 7 4 8 . 4 3 1 6 . 5 4 3 9 . 3 51 13 39 6 8 6 5 7 6 0 6 1 1 3 . 9 1 1 .B 1 8 . 9 1 1 . 4 3 0 . 0 2 6 . 0 4 9 1 9 2 8 5 . 0 3 1 . 5 7 0 . 4 1 6 . 6 I I 7 3 6 . 9 8 2 0 . 1 38 73 3 5 5 20 70 1 27 4 2C 0 77 6 16 1 6 1 5 . 6 0 2 4 . 8 10 27 2 b 2 6 3 3 9 . 0 2 8 . 7 3 8 . 2 2 6 . 7 9 3 9 4 9 5 7 0 . 5 5 0 . 7 7 2 . 4 4 8 . 1 5 \ 9 - 6 . 3 0 7 6 . 6 ;i 7 6 5 21 0 2b 1 19 . 0 75 . 0 71 » 1 3 9 . 6 2 - 5 . 7 19 3 0 6 4 6 5 3 4 . 6 2 0 . 6 1 6 . 7 2 3 . 4 9 b 9 7 5 1 . 7 2 2 . 1 5 5 . 1 2 0 . 5 \ 2 5 8 . 7 55 2 5 ? t . 3 - 6 . 0 3 8 • 5 4 - 5 . 5 2 9 6 7 7 0 7 I 7 I 2 6 . 3 - 4 . 8 1 5 . 7 3 1 . 8 2 6 . 2 6 . 5 7 0 , 8 2 9 . 8 2 7 . 1 4 4 1 4 1 9 a 0 0 0 1 0 2 0 3 - 6 . 0 - 3 . 9 2 7 . 5 6 4 . 0 9 6 . 1 8 . 9 9 . B 2 6 . 4 6 3 . 4 9 7 . 1 \ 4 3 l ! s 5 6 8 . 3 6 7 6 . 6 7 3 3 . 5 8 2 4 . 1 78 66 23 35 71 9 1 2 A 5 5 6 22 22 0 0 0 - 5 2 - 6 0 71 1 63 2 28 . 8 11 . 0 4 . 5 60 . 8 62 . 7 27 4 e 1 5 : 5 6 6 6 6 6 1 5 : 6 0 - 5 . 0 1 16.1 2 2 8 . 3 3 3 0 . 4 1 1 1 16 24 31 4 4 3 4 T 5 e o e i a 2 1 1 . 5 3 0 . a 1 7 . 3 - 4 . 9 1 4 . 6 3 6 . 0 1 7 .B 3 0 . 2 1 7 . 3 1 . 3 2 6 . 0 1 1 . 7 4 1 4 1 0 4 0 5 0 6 0 7 0 e 1 0 2 5 . 1 2 4 . 9 3 1 . 6 2 9 . 5 2 7 . <> 8 5 . 1 7 8 . 0 7 5 . 4 24 . 6 3 1 . 5 2 8 . 3 2 6 . 3 8 3 . 5 71 . 0 \ i 9 3 4 . 9 0 7 0 . 7 1 4 5 . 3 2 4 0 . 6 3 2 1 . 8 4 5 7 . 1 5 1 5 . 0 70 50 50 70 60 IB 5 6 6 6 6 0 0 0 0 0 0 3 157 5 38 6 13 T 25 B 1C 0 93 . 7 149 . 6 3 . 8 10 . 9 27 . 9 9 . 4 101 0 5 0 4 6 6 7 7 7 7 4 2 1 . 1 6 - 6 . 2 0 6 1 . 0 1 3 1 . 7 7 2 2 . 9 3 1 9 . 0 27 10 9 53 15 22 17 0 s 5 6 8 3 * a 5 8 6 7 4 . 0 2 0 . 5 1 8 . 8 2 0 . 7 1 7 . n 1 8 . 4 4 1 1 2 1 3 4 5 5 .0 3 2 . 7 3 4 . 4 4 9 . 0 4 0 , 6 32 . 5 I 1 6 8 6 . 3 7 2 6 . 6 a - 6 . o 5 0 5 6 6 1 1 66 2 95 3 20 7 51 5 90 5 18 a : 7 8 4 1 6 . 7 5 2 0 . 6 0 - 5 . 3 11 21 3 6 9 0 9 1 - 5.1 - 5 . 7 3 . 7 7 2 . 9 4 1 7 2 9 . 5 2 6 . 6 2 9 . 6 7 4 . 6 fl 4 0 . 9 40 J 6 \ 5 31 . 0 33 i S 2 - 5 . 6 3 3 9 2 9 3 1 6.0 - 5 . 6 1 4 . 6 5 . 9 1 a 2 0 - 6 . 1 - 4 . 1 8 . 4 1 . 5 \ 2 81 . 1 1 7 5 . 7 72 71 7 7 6 6 J 7 20 B 15 . 0 18 i 7 : a 8 4 - 5 . 9 5 1 0 . 8 7 a 9 5 7 3 . 9 2 4 . 0 4 1 2 1 7 2 3 2 . 0 1 4 . 2 I 4 6 7 . 5 62 3 2 0 - 3 9 0 2 0 . 1 19 * 0 0 C 1 1 1 . a 2 2 . 4 9 . 5 1 1 . a 4 1 2 3 2 4 . 1 2 9 . 2 ) 2 1 . 5 18 9 6 2 ! 63 8 18 6 56 7 9 2 l a . 5 1 5 7 a 2 0 3 2 1 . 7 1 9 . 0 1 7 . 1 7 1 . 8 * | » 5 2 8 . 7 3 2 . 2 I 1 1 4 . 5 9 B 6 2 4 86 9 80 5 9 4 29 . 2 27 6 a <• 0 5 9 . 1 i a . a 3 . 8 2 2 . 3 4 I ! T 2 8 1 0 . 6 2 0 .9 2 7 . 9 1 6 . 7 \ 1 8 4 . 6 2 2 9 . 5 82 ; 6 2 2 b 15 7 28 1 t o 6 77 I 0 0 I 1 7 11 1 1 1 2 - 5 . 5 1 3 . ? 9 . 9 1 2 . 5 ' ' 4 1 3 0 3 1 1 8 . 7 2 7 . 2 2 1 . 8 3 0 . 2 3 j 3 2 6 . 6 4 2 1 . 9 34 2? 5 6 2 3 8 25 0 94 7 24 4 100 7 a 2 0 1 3 3 5 . 6 0 - 5 . 7 33 9 0 1 3 1 6 . a - 6 . 0 1 5 . 2 1 0 . 6 t \ 3 3 1 2 . 4 B.B 5 6 2 6 . 6 78 7 6 3 I 28 3 31 5 21 2 - 6 . 0 lb 2 2 0 2 1 2 2 1 7 . 3 - 5 . 7 1 2 . 4 9 . 8 1 t . 1 8 . 7 4 1 1 5 1 7 2 7 * 6 - 5 . 7 1 4 . 4 10*1 8 . 0 1 2 . 5 5 5 5 8 8 8 - 6 . 0 0 2 0 .9 1 1 8 . 1 12 1 6 3 3 3 4 24 5 75 6 40 3 27 4 73 B 14 0 22 C C I 7 3 .9 b 80 fl 0 1 3 0 3 2 1 0 . 5 1 0 . 7 1 4 . 4 8^5 4 1 4 1 7 4 3 4 6 . 3 3 1 . 1 1 9 . 9 5 0 . 3 3 3 . 7 17.2 5 5 8 8 B 2 e e . 9 3 1 6 . 7 4 5 7 . 6 82 55 3 I 0 6 6 b 3 3 4 7 17 9 70 0 26 6 39 1 2D 4 20 7 0 c 0 4 76. 9 5 9 . 1 71 6 1 2 3 1 ) 0 - 5 . 9 1 4 . 6 1 7 . 6 1 0 . 3 4 1 4 1 4 4 4 5 3 1 . 4 7 7 . 8 3 3 . 2 2 9 . 8 5 5 8 B 6 1 C . 3 7 2 4 . 2 10 71 7 a 6 6 4 4 2 101 1 44 2 99 9 42 1 5 c 0 7 1 8 . 6 B 5 0 . 1 15 47 8 a • 2 0 1 c 4 4 8 . 9 3 0 . 5 7 4 . 7 4 3 . 0 3 9 , 3 71.1 4 1 4 7 5 0 2 0 . 4 2 1 . 1 2 5 . 8 2 2 . 8 2 0 . 6 7 3 . 0 5 5 5 8 9 B 2 7 . 7 0 7 1 . 8 1 9 2 . 1 29 65 94 2 I 7 6 4 4 61 5 1C b 21 9 61 2 B 1 19 1 7 0 3 6 . 5 1 1 1 9 . 3 2 8 . 8 77 1 14 10 0 2 0 0 5 0 6 0 T 0 ft 6 1 . 2 4 2 . 5 3 5 . 3 19.1 5 1 . 7 3 7 . 0 1 5 , 6 15.ft ' : i 5 2 5 3 • 4 1 1 . 3 - 5 . | 2 5 . 4 4 1 .7 3 0 . 6 3 . 3 2 6 . 1 5 5 5 9 9 9 3 1 4 . 5 4 2 1 . 7 5 5 2 . 4 1 1 71 I 6 6 4 5 5 1 33 0 7 129 9 35 4 7 I 179 1 I 4 2 8 . 6 5 71 . 5 25 64 7 1 1 1 0 9 1 0 • 4 3 . 9 1 3 3 . 7 1 7 5 . 0 a c . o 4 5 .0 1 4 5 . 2 1 0 9 . 6 77 . 1 4 1 5 7 6 0 2 3 . 6 2 6 . a 2 1 . 6 2 4 . 2 7 5 . 6 2 2 . 4 5 5 5 9 9 10 ' 4 3 .0 fl 1 2 . 3 0 5 2 . 5 45 7 55 0 1 1 6 6 6 5 5 5 3 11 4 23 5 79 7 28 2 24 6 73 5 1 1 8 - 6 . 2 0 8 . 3 1 6 5 . 5 5 4 61 7 I * 3 8 . 3 7 3 . 8 3 8 . 7 7 6 . 7 4 1 6 2 4 3 . 8 4 1 , 4 5 10 ! 7 2 . 8 73 1 6 5 7 43 3 45 7 3 4 4 . 2 49 5 1 I 2 3 . 1 7 1 . 8 2 1 . 8 6 6 . 7 ; \ 1 3 . 9 1 0 . 9 5 10 4 5 9 . 7 58 I 6 6 I 15 7 10 6 5 18 2 1 8 2 5 . 7 19.1 7 4 . 8 1 5 . 5 4 I 7 0 1 1 . 9 2 9 . 7 1 5 , 4 28 . 8 5 10 6 - 5 . 5 8 4 6 6 89 6 89 6 7 1 8 . 7 1 7 I 2 0 1 3.4 1 1 0 . 1 1 7 2 . 0 • * 1 7 I 9 . 7 12.1 5 10 B 4 4 . 8 43 1 6 6 4 75 1 73 0 0 7 4 . 8 69 8 Table 1 26 continued •h k I F- Fc 45. 3 3 8 . 0 3 5 . 5 2 8 . 3 4 5 . 8 7 9 . 5 3 0 . 0 3 7 . 9 3 4 . 7 1 0 . 2 9 . 9 1 0 . 8 2 4 . 2 1 3 . 9 - 5 . 8 5 6 . 4 1 7 . 9 4 3 . 0 3 3 . 0 5 5 . 9 2 9 . 1 7 7 . 3 3 5 . 9 ' 2 9 . 9 - 6 . 0 1 9 . 5 1 5 . 3 2 4 . 0 - 5 . - 5 1 9 . 9 1 7 . 0 5 2 . 0 1 5 . 0 2 2 . 5 15. » 1 7 . 9 - 6 . 2 4 2 . 1 3 9 . 2 2 8 . 9 2 9 . 5 1 6 . 9 4 3 . 4 3 7 . 9 2 B . 2 4 5 . H 2 9 . 8 3 2 . 2 2 4 . 3 1 9 . 8 5 7 . 0 2 8 . 5 3 0 . 3 4 9 . 8 2 9 . 2 1 9 . 4 2 9 . 5 1 5 .B 4 8 . 8 3 6 . 9 9 . 5 3 4 . 3 4 6 . B 1 8 . 7 2 7 . 0 1 5 . 5 1 6 . 9 1 5 . 6 2 7 . 2 2 5 . 4 2 5 . 0 2 7 . 5 2 0 . 4 I B . 5 1 6 . 8 5 3 . 1 1 9 . 9 4 0 . 2 1 7 . 4 5 3 . 0 - 5 . 9 4 9 . 1 3 0 . 9 2 6 . 2 3 4 . 3 7 5 . 3 2 3 . 9 4 1 . 9 3 7 .1 2 1 . 9 7 5 . 0 7 2 . 3 4 . 5 5 5 . 1 7 4 . 2 1 0 . 8 I 9 . 0 j e . s 1 1 . 5 1 0 . 5 4 2 . 2 4 6 . 8 5 . 8 3 9 , 0 3 2 . 7 4 2 . 7 31 . 6 3 7 . 5 1 5 . 7 4 2 . 0 14.1 6 . 5 3 2 . 7 3 1 . 9 1 0 . 0 2 8 . 7 1 7 . 9 3 D . 9 - 5 . 3 2 2 . 7 3 5 . 5 - 5 . 9 3 1 . 2 11 .7 2 6 . 0 1 8 . 6 I C O 1 9 , 1 1 3 . ? 2 L . 2 1 6 . 5 31 . 7 2 2 . 0 1 4 . 3 1 9 . 3 2 7 . 0 1 6 . 6 2 2 . 2 4 5 . 3 1 0 . 7 1 7 . 0 2 2 . J 2 4 . 7 17 .7 1 5 . 1 1 2 . 2 1 0 . 2 1 4 . 0 3 5 . 0 2 9 . 2 2 0 . 2 3 2 . 5 1 5 . I 1 6 . 8 6 . 7 11.7 2 . 7 10.11 6 . 0 2 1 . 1 4 2 . 2 3 0 . 5 1 5 . 7 3 6 . 5 ) ? , ? 2 3 . 3 1 4 . 0 1 . 4 2 2 . 7 7 0 , 9 1 5 , 7 1 2 . 0 1 8 . 5 1 5 . 6 Figure 1 (a) Superimposed s e c t i o n s of the three-dimensional e l e c t r o n - d e n s i t y d i s t r i b u t i o n (contours at i n t e r v a l s of 2, 3, 4, ... ei£ 3 f o r carbon, oxygen and n i t r o g e n , and 2, 20, 30, 40, ... eR 3 f o r i o d i n e ) , and (b) a drawing of the molecule. The solvent (acetone) i s omitted f o r c l a r i t y . 28 29 C O ORDINATES AND M O L E C U L A R DIMENSIONS T h e f i n a l p o s i t i o n a l a n d 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 g i v e n i n T a b l e 2. I n a s t r u c t u r e o f t h i s c o m p l e x i t y t h e d e t a i l e d v a l u e s o f 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 a r e p r o b a b l y o f l i t t l e s i g n i f i c a n c e , a n d t h e y a r e n o t l i s t e d . T h e b o n d d i s t a n c e s a n d v a l e n c y a n g l e s a r e g i v e n i n T a b l e 3, a n d F i g u r e 2 s h o w s a p a c k i n g d i a g r a m o f t h e s t r u c t u r e . A B S O L U T E C O N F I G U R A T I O N T o c o m p l e t e t h e a n a l y s i s , t h e a b s o l u t e c o n f i g - 7 u r a t i o n was d e t e r m i n e d b y t h e a n o m a l o u s d i s p e r s i o n m e t h o d . F i f t e e n p a i r s o f r e f l e c t i o n s o f v a r y i n g i n t e n s i t y a n d | F c ( h k £ ) | 2 / | F c ( h k £ ) | 2 r a t i o w e r e c h o s e n , a n d t h e i n t e n s i t i e s w e r e m e a s u r e d w i t h a s c i n t i l l a t i o n c o u n t e r a n d C u - K a r a d i a t i o n . T h e r e s u l t s a r e g i v e n i n T a b l e 4, a n d i n d i c a t e u n a m b i g u o u s l y t h a t t h e p a r a m e t e r s u s e d t o c a l c u l a t e t h e s t r u c t u r e f a c t o r s ( t h o s e o f T a b l e 2 r e f e r r e d t o a r i g h t - h a n d e d a x i a l s e t ) r e p r e s e n t t h e t r u e a b s o l u t e c o n f i g u r a t i o n . A l l d i a g r a m s i n t h i s w o r k s h ow t h e c o r r e c t a b s o l u t e c o n f i g u r a t i o n . T h e m o l e c u l a r s t r u c t u r e p r e v i o u s l y d e p i c t e d 5 8 ( a r b i t r a r i l y ) i n r e p o r t s o f d a p h m a c r i n e ' i s t h e o p t i c a l e n a n t i o m o r p h o f t h e t r u e c o n f i g u r a t i o n d e t e r m i n e d h e r e . 30 Table 2 Fi n a l p o s i t i o n a l ( f r a c t i o n a l x 10 3 ) and i s o t r o p i c (R2) ther: parameters. Mean standard deviations are a(x) = a(y) = a(z) =0.001 R for I, 0.013 R for N , 0.015 R for 0, 0.020 R for C; cr(B) = 0.05, 0.28, 0. 34, 0. 45 for I~, N, 0, C. Atom X y z B N(l) 347 372 180 3.5 C(2) 414 327 219 3.3 C(3) 491 339 326 3.3 C(4) 456 342 472 4.7 C(5) 377 305 501 5.1 C(6) 299 298 391 * 3.0 C(7) .347 281 262 3.0 C(8) 275 280 144 3.0 C(9) 302 252 010 4.9 C(10) 250 286 -090 5.7 C ( l l ) 278 342 -051 4.6 C(12) 265 341 104 3.5 C(13) 169 364 147 4.6 C(14) 149 352 294 5.6 C(15) 245 355 369 4.0 C(16) 306 396 311 4.3 C(17) 563 384 296 4.2 C(18) 633 389 411 5.8 C(19) 613 375 165 6.0 C(20) 389 414 096 4.1 ....'/continued Table 2, continued Atom X y z B C(21) 226 258 451 4.6 C(22) 402 228 268 4.3 C(23) 343 174 272 3.8 C ( l ' ) 405 126 221 3.6 C(2' ) 480 100 310 3.6 C(3' ) 444 080 444 4.6 C(4' ) 360 040 426 5.2 C(5' ) 296 057 311 5.4 C(6' ) 345 075 195 3.8 0(7 1 ) 421 036 163 5.1 C(8') 495 050 232 4.8 0(9' ) 569 024 222 6.5 C(IO') 285 082 066 6.7 C ( l l ' ) 571 133 331 5.0 0(12 ' ) 416 128 523 4.0 C(13') 407 122 661 5.1 0(14') 418 077 706 8.1 C(15' ) 383 171 724 6.1 C(l") 817 039 339 10.5 C(2") 894 018 239 8.1 C(3") 992 039 263 11.4 0(4") 869 -008 145 7.8 I (43) 040.6 196.7 164.0 5.4 32 Table 3 Bond distances (a = 0.03 k) and valency angles (a - 1.6°) Large cage: C-C = 1.45-1.62 (21 bonds), mean = 1.54 & Angles at C: i n 6-membered rings, 107.2- 117.5 (13 angles), mean = 111.1° i n 5-membered rings, 101.9-106.0 (9 angles), mean = 103.2° others (substituent groups and external angles), 105.3- 120.2 (19 angles), mean = 112.6° C-N = 1.48-1.59 (4 bonds), mean = 1.54 & Angles at N: 103.6 i n 5-membered ring 107.2-114.4 (5 angles), mean = 110.6° Small cage: C-C = 1.43-1.57 (9 bonds), mean = 1.53 k Angles at C: 97.5 i n Y ~ l a c t o n e others i n 6-membered ring 111.1-114.5 (5. angles), mean = 113.0 others (substituent groups and external angles), 98.7-121.6 (14 angles), mean = 109.7° Substituent groups Chain C(7)-C(22) = 1.54 C(22)-C(23) = 1.57 C(23)-C(l') = 1.56 C(7)-C(22)-C(23) = 117.7 C(22)-C(23)-C(l') = 109.9 y-lactone C(6')-0(7') = 0(7')-C(8') = C(8')-0(9') = 1.49 1. 30 1.23 C(6')-0(7*)-C(8') = 107.9 0(7')-C(8')-0(9') = 120.8 0(7 ,)-C(8 ,)-C(2 I) = 112.5 0(9')-C(8')-C(2') = 126.5 Acetoxy C(3')-0(12') = 1.49 0(12')-C(13') = 1.39 C(13')-0(14') = 1.22 C(13')-C(15') = 1.40 C(3')-OU2,)-C(13') = 117.9 0(12')-C(13')-0(14') = 116.9 0(12')-C(13')-C(15') = 112.0 0(14')-C(13 ,)-C(15') = 130.9 ./continued Table 3, continued Solvent (acetone): C(l , ,)-C(2") = 1.58 C(2")-C(3") = 1.50 C(2")-0(4") = 1.20 C(l")-C(2")-C(3") = 115 C(l")-C(2 , ,)-0(4") = 117 C(3 M)-C(2")-0(4") = 126 Figure 2 Packing of the molecules i n the unit c e l l (heavy l i n e s indicate molecules i n the upper part of the c e l l ) . 35 36 Table 4 Determination of the absolute configuration (Cu-K^ radiation) h k I 1 2 1 1 4 2 1 4 3 1 5 7 1 6 2 2 1 1 2 2 4 2 4 2 2 10 3 3 1 3 3 4 2 3 6 1 4 8 3 5 1 1 6 7 1 F c(hk£) | 119.7 90.7 11.7 27.4 43.3 34.0 55.1 78.1 53.4 25.3 93.3 103.5 93.4 81.5 53. 8 F (hkii) 105.8 106.8 19.0 37.2 29.2 56.7 64.0 65.1 43.4 36.4 105.8 87.2 103.5 98.8 70.6 c(hk£) | 2 I (hkA) c(hkl") | 2 I Q (hkl) 1.28 1.31 0.72 0.64 0.39 0.54 0.54 0.94 2.20 1.66 0.36 0.42 0.74 0.77 1.44 1.53 1.51 1.33 0.48 0.39 0.78 0.81 1.41 1.51 0.81 0.82 0.68 0.69 0.58 0.53 37 RESULTS AND DISCUSSION The c r y s t a l analysis has established the structure and absolute configuration of daphmacrine methiodide (acetone solvate). The compound consists of two cage structures which are linked by a f l e x i b l e chain of two carbon atoms (Figures 1 and 3). The nitrogen- containing portion consists of two six-membered rings i n the chair form, and one i n the boat form, which are fused together with two five-membered rings, as has been reported 5 9 10 for daphniphyllamine.' ' The smaller, nitrogen-free cage i s formed of one six-membered ring i n the chair form, bridged by carbon and oxygen atoms to form a five-membered lactone (ylactone) , with methyl groups at each bridgehead. The C(6')-C(1')-C(2') angle (97.5°) i s smaller than the other angles i n the six-membered ring (111.1-114.5, mean of 5 angles 112.9°), presumably because of the bridging. Other bond lengths and angles generally appear to be normal, and considering the complex framework involved, are not s i g n i f i c a n t l y d i f f e r e n t from expected values. The p o s i t i o n of the acetoxy group has been determined as shown i n Figure 3, and the chain connecting the two cages contains two unsubstituted carbon atoms. The acetone solvent molecule i s i n the same general region of the unit c e l l as the oxygen-containing cage (Figure 2), but i s involved i n only van der Waals 38 contacts. The shortest distances from acetone are to the acetyl group, the minimum 0...0 and C...0 contacts being 3.54 and 3.21 R respectively. The shortest intermolecular C...C distance i s 3.53 R. Figure 3 Diagrammatic representation of the structure of daphmacrine methiodide. 40 P A R T I I I T H E S T R U C T U R E D E T E R M I N A T I O N OF E X O - T R I C Y C L O [ 3 . 2 . 1 . 0 2 ' 4 ] O C T - 6 - E N E S I L V E R N I T R A T E AND A R E F I N E M E N T OF T H E S I L V E R N I T R A T E S T R U C T U R E 42 A. THE STRUCTURE OF EXO-TRICYCLO [3. 2 .1. 0 ' ] OCT-6-ENE- SILVER NITRATE. INTRODUCTION A study of poten t i a l cyclopropyl •silver ion 11 complex formation had shown that s i l v e r n i t r a t e forms a r 2 4i s o l i d complex with exo - t r i c y c l o [3.2.1.0 ' Joct-6-ene (I), but not with the corresponding endo-isomer (II) . The observed differences i n the equilibrium constants for complex formation could be interpreted i n terms of the inductive electron-withdrawing properties of the cyclopropyl group, and provided no evidence for cyclopropyl s i l v e r ion int e r a c t i o n , although such i n t e r a c t i o n could not be d i s - counted by the data obtained. An X-ray c r y s t a l structure analysis was undertaken to determine whether the s i l v e r ion i s complexed to the cyclopropyl ring or the double bond, or to both, as has been reported for analogous platinum 12 complexes (III) . CI CI I IT III exor-(study compound) endo-isomer 43 EXPERIMENTAL r 5 4i Crystals of exo-tricyclo[3.2.1.0 ' Joct-6-ene s i l v e r n i t r a t e are colourless, but become white on exposure to l i g h t and a i r , and tend to cleave into i r r e g u l a r fragments elongated along the b crystallographic axis. The unit c e l l dimensions and space group were determined from rot a t i o n , Weissenberg and precession photographs. The density was not measured because of the i n s t a b i l i t y of the complex. Crystal Data.— X(Cu-K ) = 1.5418; X(Mo-K ) = 0.7107 ft. — a •• a Exo-tricyclo[3.2.1.0 ' Joct-6-ene s i l v e r n i t r a t e , C gH 1 0AgNO 3, M = 276.0. Orthorhombic, a = 25.54(5), b = 6.28(1), c = 5.60(3) ft. U = 898.2 ft3, Z = 4, D c = 2.04 g.cmT3 F(000) = 544. Absorption c o e f f i c i e n t s : u(Cu-K ) = 182 cm.1; u(Mo-K ) = 22 cm. Absent r e f l e c t i o n s : hOO, h odd; OkO, k odd; 001, I odd. Space group P2 12 12 1 (Dip. The c r y s t a l s , although quite unstable on exposure to l i g h t and. a i r , were found to remain for about a week i n sealed c a p i l l a r y tubes without s i g n i f i c a n t decomposition. Two c r y s t a l s were therefore used i n the analysis; one to determine the c e l l dimensions and space group from fi l m s , and the second to c o l l e c t the int e n s i t y data on a d i f f - ractometer. The i n t e n s i t i e s of a l l r e f l e c t i o n s with 44 28(Mo-Ka) £ 40° (minimum interplanar spacing, d = 1.04 ft) were measured on a General E l e c t r i c XRD 5 spectrogoniometer with a s c i n t i l l a t i o n counter, approximately monochromatic Mo-K^ radiatio n (Zr f i l t e r and pulse-height analyser), and a 6-2 6 scan. Background counts were made at the beginning and end of each scan. Two r e f l e c t i o n s measured p e r i o d i c a l l y as a check showed e s s e n t i a l l y no change i n i n t e n s i t y over the time required to c o l l e c t the data. Some decomposition while mounting the c r y s t a l and sealing o f f the c a p i l l a r y i s not precluded, however, and i t was noted that the cry s t a l s became translucent during manipulation. The c r y s t a l used for i n t e n s i t y measurement was an i r r e g u l a r cleavage fragment with approximate dimensions 0.25 x 0.80 x 0.15 mm., and was mounted with b p a r a l l e l to the <|) axis of the goniostat. No absorption correction was made. Lorentz and p o l a r i z a t i o n factors were applied and the structure amplitudes derived. Of the 554 r e f l e c t i o n s with 28 « 40°, 322 (58%) had i n t e n s i t i e s greater than 3a(I) above background, where a(I) i s defined as : a (I) = {S + B + (0.05S) where S = scan count and B = background count. The remaining 232 r e f l e c t i o n s were c l a s s i f i e d as unobserved and given zero weight i n the refinement; they are included i n the structure factor table with I(unobs) = a (I (unobs)) .. 45 STRUCTURE ANALYSIS Examination of the i n t e n s i t y data indicated that a l l planes (hk£) for which h i s odd were weak, so that the s i l v e r ion was expected to be at or very close to a p o s i t i o n which would confer f a l s e symmetry on the electron-density map based on the heavy atom alone. The three-dimensional Patterson function revealed t h i s p o s i t i o n to a f i r s t approximation to be on a screw axis (0.056r 0.25, 0.0), so that as expected from the observed i n t e n s i t y r e l a t i o n s h i p s , the r e s u l t i n g electron-density map exhibited pseudo- symmetry and could not be interpreted to give a reasonable hydrocarbon or n i t r a t e structure. To compound t h i s d i f f i c u l t y , no p a r t i a l structure would ref i n e by l e a s t - squares methods, the s h i f t s to coordinates being large, and the temperature parameters ill-behaved (this occurred i n spite of the p a r t i a l structures being correct, as v e r i f i e d by the subsequent structure a n a l y s i s ) . A re-examination of the Patterson function, and an accurate p l o t t i n g of the cross-section of the peaks then showed that there was some elongation of the peaks i n the y and z d i r e c t i o n s , so that the s i l v e r ion appeared to be displaced s l i g h t l y from the screw axis. The extent of t h i s elongation was used to estimate new y and z parameters (0.259 and 0.02 respectively) and an electron-density map based on the phases computed from t h i s s i l v e r p o s i t i o n 46 showed c l e a r l y a l l the atoms except C(4) and C(7). These were subsequently located on a three-dimensional difference map as the highest peaks (but quite low electron-density) and included i n the refinement. A least-squares c a l c u l a t i o n with a l l atoms assigned the appropriate scattering curves for C, N, 0 and Ag +, i s o t r o p i c temperature factors equal to 4.0 ft2, and unit weights resulted i n an R value of 0.15. A comparison of the observed structure factors with films indicated that some of the r e f l e c t i o n s had been mis-indexed, probably due to the long a a x i a l length (25.54 ft) , dr inaccurately measured, p a r t i c u l a r l y the weak odd h planes. Eighty-four r e f l e c t i o n s were re-evaluated on the basis of f i l m measurements, sixty-one of these being odd h planes. Two further cycles of fu l l - m a t r i x least-squares refinement with anisotropic thermal parameters for the s i l v e r ion, and a weighting scheme of the form w = 1 / a 2 ( F Q ) where a 2 ( F ) = 59.56 - 2.561F I + 0.037 IF I 2 resulted i n o 1 o 1 1 o 1 a f i n a l R o f .0.105, and a weighted R of 0.127. Calculated and observed structure factors are l i s t e d i n Table 5. The maximum r a t i o of parameter shift/estimated standard deviation (esd) i n the f i n a l cycle was 0.23 and a f i n a l difference map showed maximum fluctuations of ±1.3 eft . A f i n a l Fourier map was computed, and sections of the r e s u l t i n g electron-density d i s t r i b u t i o n are shown i n Figure 4, together with a drawing of the structure. Table 5 Measured and calculated structure factors for exo- t r i c y c l o [3.2.1.0 ' joct-6-ene s i l v e r n i t r a t e . Unobserved r e f l e c t i o n s have I = a(I) and are indicated by a negative sign before F . Table 5 49 h k i F 0 F c 2 t: 6 c A r lt» 0 12 -~ C 136. r.i 1 7 * . T 9 " - 7 . P I 11. lh' " - •>. 1 . ' - 0 ?6 .7 1 r, 11 t . l L l ' 6 . 6 4 K 7 . 7 3 1-7.OH 0 "".31 1 1 J . 1 ' 14 ( 16 c 18 t 70 f 2? t 74 C i -1 J.r.S 1 2 . 1 2 » ^ . ' 6 3 6 . 1 5 * V - . 6 4 1 - l i . ? 2 1 1 . f - 1 l . " f l 2 . 5 T 1 c- 2 P 3 r 5 C 6 0 1 ' IH.rtft ' 4 .7 .05 l'J.1.41 1 H . 1 5 1 ' T . 1 ? 2 7 . n f-4 .r-c 6 ? . 1 ft i r i . ' . n 2T.-/9 1 P4.. ] ft H i . 1 7 ,T C 8 C 9 t 1C r 1 1 c 17 C. • . * 4 . t * 7 1 . 3 4 41 ,•• 3 4 " . 45 1 7 . 9 2 rs .r . 5 -».<?*< u . u ? f t . T* - ? T .57 i i , , 9 0 J5 . C > 13 ( 14 f 11 C 16 P • IT C IB P ~ H . / ° 6 . n 116. -JC I-"" .""? - « . 4 5 ' . 1 4 55. (.ft 5 1 . "7 - I S . - H 9 . 5 3 - 1 1 . i R *>,',? ]9 C 70 C 71 c 22 r 73 C 74 C • - i r . * « 1 9 . t \ ? j ; i 7 7 4 . 5 5 - l j . ^ 3 5 . 1 7 1 1 . 6 1 ? 4 . 9 ( - - 1 2 . r H 4 . : ' 2 7 . 3if V . 3 1 i c 1 c ? r 3 C 4 0 5 f 2 |14 . 4 7 1 4 7 . 5 4 3 ft. 4 9 " O ' S 117.71 1 3 " . 2 a . 5? -1 . 1 1 4 . H J 77.^tt r . " > j 6 '"• 1 C 8 • 0 9 c- 10 r 11 '< /I . ' 7 Ti . 77. 4 4 . (.7 4--,. 3^ 1 -1. t rt 1 7 . 5 B - = 3 . '5 ? l ( . : 4 i 11 i f . . - * ? 12 P 13 r 14 'T- IS i lis t IT 0 i B r 1") 0 20 • c 21 <",• 72 C 23 C 1 5 . M * B . T : < . 4 i .4*. i i. n T i . 7 1 -1 ,14 - K . i ] 1 1 . 1 i .11.77 ' - 4 . 1 3 - 1 ( . ftT ?U . 7 9 n.yi j 7 . u 4>\17 43.-T'.' - 1 ! . ' ? ?".<-7 ? » . J 5 - K ' . ' . B " 1 t. 2 ( 3 : 5 C ft P ??.. '4 , 7 1 '•'..4JI 6 2 . ^4 ? / . "ft ' <•--.. i i . ' ' '5 , < U - o . r T 4 , f l ^ 7 ^7 4l . f .(> 7 f * C 9 I 10 C 11 C 12 r ('.111 1 * t .^4 7 ;<;!.' ^4,s^ -1 . M 12 2 5 . ' ' - - " . 7 3 1 3 14 C 15 r lis r 1T n I e c -1 ' . IH ! . . , . | S*.',r 4 ? . 7? 2 t . 75 , 5 ' -1 2 ."7 - 1 1 - 1 7 . I f . 9 . 1 - 19 c 70 f 0 P 1 T 2 r- i r M . S 1 ^ 1 . 7e - l ^ . i ' t l">.7l 4-,. -7 • 1 J . ' 4 5 C 6 r 7 : * B f - ! 1 . i ' l ft-.1'? 1 7 . 7 2 11'. ' ri 1 5 i i . rtr» T J . " J ' 1. 7 - 1 1 . 7 f 1 3 . 4 f i 10 r 11 C 12 f 4 13 C » 14 i * 15 " 4 A ' . . 7? i ^ . - ' - ' l - . I 2 K . ' - C -1 ,' ft IH . M- 21.7 7 ."•.•.•4 - 1 1 . " " ^ . ' ' f t - 1 ? . ^ 1 7 T . 7 7 16 C « 1 r. 2 r 5 <• - H . f . ' P . 1 1 - 1 7 . 5 f t I f .17 ' - 1 7 . ' P I ? . - 7 - 1 7 . V 4 1 2 . - 5 - 1 1 . « 7 *..f-4 ft C 1 rt r 1 I ( 2 I - 1 7 . 1 4 1f.;7 - I ? . . 1 ' ' 11 2ft."4 \ \ .4? ri 5 . 5 5 H 1 7 -i 1 1 4 i r 5 1 < 6 1 f T i r a ] r 9 I 10 I 11 I 17 I 1 1 t 14 1 75. ; t 1 7 0 . Kft. 1 72 l i f t . 2 2 1 2 f t . I S 1 1 ' . . 2 1 l l f . l . 5 i b T . f l . * 7 . i | « B . 2 ° 7 1 . 7 7 - U . 1 7 I t . ' ? 7 2,:-f . 5 7. M ' J . IT 1 1 1 . ' ? 1 . 4 . en u . 4 7 13.7'. 7 l i . 77. 15 1 1 4 1 \ T 1 1* I 1 V 1 ' i\ 1 ?1 1 7? 1 73 1 24 1 1 1 V . ) 4 1 , 4 - 1 7 . 1 J 1'J . '. 4 - 17 , r 4 :•.•>'. 4 4 . 7 6 , ; . ) = ; -1 » . '•(• l * . 74 1 * ? . " ? 117.1c 7 t ' . M . H 137.4? i l . 72 7 5 . t;? 4 1 4 2 . 7 I 4 2 . ' 4 5 1 ' 2 5 . 4H 71 . 9 7 6 1 3 r , . 4 1 . 4 ' ; 7 1 4 t i . H 3 4 0 . 3ft 1 4 5 , 16 1 " , 44 9 1 - 1T1. 4 8 7" . TP 10 1 H'- ft . ? 9 1 2 t . 4 5 11 1 21 . " 9 2 4 . 1 5 12 ftl . . i n •JI . I P 11 1 - 1 4 . 7 5 14 1 - 9 . 3 4 6 , 7 7 15 1 - 1 ' , . ? T 1 3 5 , . - 1 . ' 4 . " 9 1 7 1 - 1 I • 2 T 15 . r 7 19 1 f . 4 . 14 19 1 -12 .^.4 1 ' J . M 20 ' 4 9 .^5 4 9 . 16 21 1 - 1 2 . 3 3 5 . S T 22 1 -1 .1 . ? B 1 1 . 4 4 23 1 - 1 2 .op 1 , Bft 1 - 1 2 . 5 1 9 . 9 ? 0 2 -B.9C) 7 * . "i T 1 2 ' 5 1 . IL' •^0, ftP 2 2 n 7 .'. ft B 2 . ?S ? 4 11. ») 1 i P . I f 4 ' 2 1 2 P . . 3 " 1 2 7 , 7H 5 ? 7 7 . b? 2 4 6 2 If: 7. "5 16. ' 4 T 2 2 6 . 4 1 2 . : i 3 2 4 1 . 1 1 1 ° . i 7 . 9 2 17. 75 i t 2 - 9 1 7 7 7 . P 1 1 1 7. 1 7.HC 14 , H j 12 2 T ? , 6 4 6 7. 11 13 2 - 1 3 . 4 4 14.BA 14 7 bC. 7? 5". 54 IS 2 1 0 . 2 5 I B . 9? 1 6 2 9 . 5 1 J? . 0 5 17 2 7 1 . ' 4 ' 5 , 4B IB 2 i : . ? p 1 7 . 1 •) 19 ! 13. 34 20 ? - 1 7 . 2 4 14,*.ft 21 2 - 1 2 . 4 7 i 5 . ; : i 22 I 2 r i . I t r.9 C 1 3 3 2 1 . <•<, 0 5 . M 7'1.12 2 3 4 5 . ]A 4 9 , (• H 4 . 1 . 9 ? 4 7.7" 4 3 2 1 . ' 5 • ' 2 . '4 5 4 7 . *• H J ^ . T 3 14.5-' 7 J 1 6 , 4 1 34. r ? A 1 V. ."I 9 1 - i * ; . T H 1 2 . 9 1 ? - i l . ' " - ! t 3 . i 2 1 3 . ' 7 12 1 3 J 3 3 ^ . ' . 2 I? .15,4!: 3 1 . 4 9 ? - - 1 2 . " • l ' . , M 15 ' i 3 1 . 3i* •7.. 2 4 17 3 2 1 ..••) -A 2. t t , ?|J . 1 1 1 i . " ' ' IP ) - 1 ? . 16 ! ,4ft 1 " l<i. . 1 3 - 1 1 . 4 3 U . 6 J 1 45 . 7T • 7 . 5 1 7 2 5 . 7 7 2 " . 14 ? i . : i 4 71 . 1 S 4 4 4 (,, . •; 4 7 . 2 r 5 A I 2 . >:\ l « . t i *• 4 h F ' . r 4 ? . 4 < » £ - 11 . ' ! 7 2 d I f 4 - 1 2 . * 17. ^ 11 4 M . 7 4 ' 11 - 1 7 . 15 11. ft 4 l i . ' 1 7 1 , 4 3 15 4 - ! ? . " - ( 7 . 4 2 16 4 - 1 7 . 7H. 1 2 . 4 7 5 - W . 7 7 ? 1.1 2 I * - 1 1 . : 5 1 5 7 4. .1 7 5 . ' j ) 5 - 1 ! , u 4 5 •J ? 7 . '• 2 ' 1 . 4 1 ft 5 • - 1 ! . •. '' 6. ' 4 a 5 -13 .1 C 16.51 5 - 1 2 . ' t 5, M i r 11. f, P 11 .11 2 " ;̂ 1' ^ 54 . « 1 1.11 4 r , . ' . 7 6 6 2 . "7 7 S ' . . 2 4 5 2 . 1 3 B 1 7 4 . S 4 ? i- 10 r- 1 i , f 7 S h , n ! - 1 3 . 1 U 17 4 7 , ' 1 13 - 1 2 ."ft 1 7 . 1 1 14 ' - ). Pft 6 , 0 | - 1 1 . ^ 1 11. f. 5 16 ? S . 74 4 1 . 7 9 - J.o<; 5 ft • 1 '.- 1 9 1. r 1.3 . 7 1 » , » • - r- 4 7 . ft 5 72 c 2^,. 77 ? j . ' f ! " - 1 2 . : C r I - a . 7 ft ? 1. ° i 7 2B 2 1 1 2 ? . 4 1 l - * f . » l 3 1 H. 5? 71 .7 j I 171. 17 l ' f t . '-"I 5 1 1 3 .7t! • 14 .-:•> 7 1 1 1 1 ">.64 1 t . fc 3 1 2 ? . T 5 • a 1 7 1 . 4 7 77 , *i1 0 1 H. c i" 1 . 10 1 - 1 . " 2 t c . *: •. 1 24 . ' * i 22 1 12 1 3 1 •>-'•. 4 3 1 ? . r> 7 c 1 .11 1 15 1 i 74. 15 1 i r , 7 ? I 7 1 -1 l . " 2 1 '. • 4 9 i n 2 1 -11 . ' . t 1 2 . - ? 19 I -1 1 . 4 7 1 2 , ^ " 70 22 I I 1 1 1 - 1 1 . )<; - i i . " ( , 7 » . ^ « 1 1 . 4 '1 ? 7 . i 7 5 . 1 1 14 3 i - 1 2 . 1 7 1 1 . 6 7 15 1 - 1 2 . 1ft 1 1 . 5 4 16 3 3 - 1 2 . ' 2 lb .9) 0 3 - 1 7 . 2 * 1 3 4 2 5 . 7 ( ? 4 . * c 2 3 4 - 1 7 . 4 ? 14 . >i 3 4 - 1 1 . / I 14. ;>(» 3 3 I . i f 1 5 . 2 7 5 3 4 - 1 2 . 5 6 1 2 . 1 4 6 3 4 - 1 1 . 'I 7 }(, . 2 ' 7 - 1 7 . 5 0 I T . f 5 H 3 4 - 1 ^ . 4 4 1 4 . / . ? 9 3 4 -1 ! . J f c /">.61 10 1 -1 1.<6 7 . 6 I 11 t - 1 J . "-T 7 2 . r-\ 0 54 .1 5 6T . P ? 1 4 5 J . T 51 . T 4 2 4 " - 3 . 4 7 6 5 . ; 5 4 2'. .7^5 1 1 . 5-'! 4 4 c 2 " . * 5 71 . 4 5 5 4 0 2 1 . T 2 1 . 6 7 4 - i 11 ^ 1 7 4 r. - I T . B C 4 . 1 T P. 4 0 44,.M 5 1 . 4 7 "i 4 - 1 5 . "ih l t . \ i i 10 4 0 5 1 . 4 1 5 5 . r 6 11 - 1 4 . 7 5 IP . T 12 c 12, f 1 2 7 . f 2 13 - 1 2 . 4 a t r . * 2 14 4 p -1 I , f .4 l T . i f i 15 -1 1 . 16 fc r - 1 2 . 6 ? 1 B . b 1 1 7 fc -1 1 . 7 8 ? i . l 3 18 4 n ?>J.« I 2ft. BC 0 4 I H. . ?4 ft . 72 1 4 1 - 1 r.. 5 5 1 L . * 7 2 1 3 . . ift 35.5. 7 3 4 1 2 5 . v . l 15 ..14 1 5 " i . J 1 5 4 1 - 1 . ? 7 2 l ' . " B 6 4 I ^7 . *P 4 0 . 7 1 T 4 1 - 1 1 . 4 2 1 5 . 1 5 a 4 1 " - 1 2 .47 4 - 1 . 1 P . l " . 2 1 1C 4 1 2 2 . " 7 7 7 . 5 n l i 4 I - l ? . i 1 12 .2-1 12 1 2 7.71 7 5 . 51 13 4 1 -17 .1" 1 3 . 4 7 14 4 1 37.-.1 .11 . d 4 15 4 t - 1 >. If ? 6 . t i l 16 1 2ft. .4 17 4 1 ft.f 1 IB 1 5 . 5 ' . - P 4 2 1 . •> 5 52 . 1 3 1 2 - 11 . J 1 6 . 6 * 2 4 2 1 6 . 6 0 3 4 ? -1 1 , 2 6 1H..1 7 4 4 ? 1 ? 1 9 , 4 3 5 2 6 4 2 2V. 66 2 J . 1 J T Z 27.17 2 1 .5" n 4 2 4!'. 15 7 - I . • » . . - * 11 . 1 <i 7 i , i . ft e " 5 . 4 5 u ? 1 a . 4 b 12 4 7 7 o . ' l •»2. 61 1 3 7 - l l . f t r t 1 5 . h i 1 4 4 7 - 1 2 . ' ) C I " . 1!'. 1 5 2 - n . i 16 fc 2 - 1 3 . 15 4 - I t .'.7 4.5-". I 4 ? 7 6 . 4 1 2? . 7 2 2 2-r.4ft '.2. 55 3 1 2? 4 4 3 2 5 . SO , ? T . ( U 14 '1 . 76 1 7 . 7 4 T 4 :t 7 5 . 5C ?f . 5G - 1 2 . r t ; 1.5fc 9 4 i -1 2 .' 1 (. 1 5 ... -J IP - 1 2 . 4 ? 1 2 . 7 " 1 1 4 - 1 7 . 7 9 ( 3 . 3 4 1 2 4 3 - 1 2 . 7 8 17.21 0 4 4 - 1 i . 7 C ? C . = 4 1 - i ; . 5 ? 1 7 . 7 3 2 - 1 1 . 4 7 1 6 , - 6 4 - 1 1 . 1 9 -1 >. "7 1 6 . 7 4 1 5 -11 .(.•: 7 . « 2 2 5 1 •2.->r . ' * - . ( - c . ~ l 21 . '7 4 5 2 4 . 7 " " - 1 7 . ^ 7 3 . 1 5 2 5 . ^ K 5 ] » . • . " 7 1 . 5 1 B 5 r -1 1 .77 •>. '»7 5 - 1 1 . 5 * I , 1ft 10 5 r - 1 7 . " 1 7.51 11 5 P - 1 1 . 4 2 12 5 - 1 2 . 7 6 2 2 . 1 1 l i 5 r -1 1 . f 7 1 9 . ?4 1 4 5 p < a • 7 6 ? H , 4 1 0 5 i 35' . H j 1 ^ . - 2 1 l - 1 1 . 1 2 17 .6') 2 i 14 . 9 7 14. 3 5 I -11 . 4 4 1 4 . ; 4 5 5 i i - 1 7 . ' 2 - 1 1 . 1 6 17.7.3 3. f " 6 i -I 1 . 6 3 t 7. ' * 5 i 2 >. 19 2(1. 2 8 5 i 7 >. * ? 2*.<-.:i 9 5 i - 1 2 . - 7 • i B . r 4 10 5 i 2 5 . 5 4 7 1 . J -) 11 5 i - 1 2 . P 5 11 - •>' 1 2 5 i - 1 ? . * 1 1 7 .-5 1 3 5 l 5 . 1 3 0 5 7 - 1 1 . 7 1 9.11 5 2 - 1 7 . 1 5 ' ' " . 1 5 2 5 2 -11 .54 1 ^ . 4 1 ' 3 5 7 -11 1 5 . 7 1 7 ""• IT . ' 2 5 5 2 4 0 . 4 4 76 . 2 5 6 2 S|> T b 2 2 ' . ' 2 1^ .76 fl 5 7 -1 J , * l 11 . 5 4 1 5 2 - 1 7 . 4 0 11 .72 IP 2 - 1 ? .. 'fc r -4C 11 5 2 - 1 : . 4 > 1 3 . 6 2 C 5 3 - 1 2 . 5 4 7 5 j 2 4 . S3 1 6 . 1 7 3 5 » - 1 7 . 7 " 1 2 . H 4 5 J - 1 2 . . . t 7. J7 0 - 1 2 . " ' 1 -1 1 . 71 l l . . 1 ! 2 ft f - 1 1 . l i 1 2 . 6 7 3 6 r. - 1 7 . . 4 7. 1 1 4 6 r- • -11 . 4 7 7 . ' ) 1 - 1 2 . . '2 2 . 1 * 1 * 1 -12.-"5 l r . 1 5 Figure 4 (a) Superimposed sections of the three-dimensional electron- density d i s t r i b u t i o n (contours at 2, 3, 4,... eft 3 for carbon, oxygen and nitrogen, and 2, 10, 20, 3 0,... eft 3 for s i l v e r ) , and (b) a drawing of the structure of the complex.  52 COORDINATES AND MOLECULAR DIMENSIONS The f i n a l p o s i t i o n a l and thermal parameters, together with t h e i r standard deviations, are l i s t e d i n Table 6. Table 7 l i s t s the bond lengths and angles, and Figure 5 shows a view of the structure along the b crystallographic axis. Although some bond lengths appear abnormal, they do not d i f f e r from the expected values by more than 3a, and i t would appear that any differences are due to inaccurate data. 53 Table 6 F i n a l p o s i t i o n a l ( f r a c t i o n a l x lo 1*) and i s o t r o p i c (&2) thermal parameters, with standard deviations i n parentheses. Atom x Y z B C(l) 1207(21) -1799 (076) 0053 (092) 4. 26 (125) C(2) 1823 (19) -2171(111) -0205 (094) 4. 96 (13?) C(3) 2131(35) -3624(131) 1799 (151) 6. 40(209) C(4) 2114 (34) . -0936(116) 1290 (148) 5. 59 (210) C(5) 1654 (19) 0535(077) 2422 (088) 2. 34(100) C(6) 1430(20) 1470 (085) 0175 (100) 3. 69(116) C(7) 1190 (28) 0220(127) -1039 (141) 6. 53 (202) C(8) 1189(21) -1183(100) 2743 (100) 3. 81(129) 0(1) 0208 (19) 5632 (085) 6743 (087) 6. 75(131) 0(2) 0209(17) 5334 (077) 3170 (072) 5. 24 (104) 0(3) 0817(23) 3789 (086) 5413 (100) 8. 21 (136) N 042 0 (14) 4948(063) 5231(074) 3. 34(086) Ag + 0532 (02) 2687 (009) 0316(006) 4. 69(014) The anisotropic thermal factor for Ag + i s exp{ -(19h 2 + 345k2 + 334J12 + 8hk + 17k£ - 15M) X - h 10 }. Table 7 Bond distances (a - 0.09 £ for C-C; 0.05 for others) and valency angles (a - 5°) for CpH, nAgN0-,. C(l)-C(2) = 1.60 C(2) -C(l) -C(7) = 97 C(l)-C(7) = 1.41 C(2) -c(i) -C(8) = 99 C(l)-C(8) = 1.56 C(7) -C(l) -C(8) = 101 C(2) -C(3) 1.65 C(l) -C (2) -C(3) 119 C(2)-C(4) = 1. 36 C(l) -C(2) -C(4) = 113 C(3)-C(4) = 1.71 C(3) -C(2) -C(4) = 69 C(4)-C(5) = 1.62 C(2) -C(3) -C(4) = 48 C(5)-C(8) = 1.61 C(2) -C(4) -C(3) = 64 C(5)-C(6) = 1.50 C(3) -C(4) -C(5) = 121 C(6)=C(7) = .1.21 C(2) -C (4) -C(5) = 100 N-O(l) = 1. 09 C(4) -C(5) -C(8) = 101 N-0(2) = 1. 30 C(4) -C(5) -C(6) 100 N-0(3) = 1. 25 C(6) -C(5) -C (8) = 94 C (5) -C(6) -C (7) 114 C(l) -C(7) -C(6) = 109 Ag-C(6) = 2 .42 C(l) -C(8) -C(5) = 92 Ag-C(7) = 2 .41 0(1) - ' N -0(2) = 114 Ag-0(2) = 2 .45 0(1) - N -0(3) = 124 Ag-0(3) = 3 . 03 0(2) - N -0(3) = 121 Ag-O(l) I= 2 .85 Ag-0(3) z= 2 .92 Ag-Od) 1^ 2 .56 2 .55 I II x, y, -1 + z -x, -h +: Y, h - z Figure 5 A view of the structure along the b crystallographic axis.  57 RESULTS AND DISCUSSION The c r y s t a l analysis has established the structure of the s i l v e r n i t r a t e complex (Figure 4). The s i l v e r ion occupies the exo- p o s i t i o n and i s therefore quite distant from the three-membered r i n g , so that no s i l v e r ion cyclopropyl i n t e r a c t i o n i s possible. This i s i n agreement with the conclusion that such i n t e r a c t i o n i s not required to explain the r e l a t i v e equilibrium constants for complex formation''"]" As i n other complexes of t h i s type (cf. ref 13), the n i t r a t e groups are linked by coordination to the s i l v e r ions to b u i l d up layers, i n t h i s case p a r a l l e l to (100). The layers are centred around 0 and ha (Figure 5 ) , with the hydrocarbon molecules between, and with only van der Waals forces between the hydrocarbon molecules (the closest i n t e r l a y e r contact i s C...C at 3.6 R.) . The s i l v e r ion approaches three n i t r a t e groups i n the layer, so that close contact i s made with two oxygen atoms of one n i t r a t e group (Ag...O = 2.55 and 2.56 k); a second n i t r a t e group i s more distant (Ag...O = 2.85 and 2.92 A)/" a n d t n e t h i r d n i t r a t e group shares i t s oxygen atoms unequally (Ag...0 = 2.45 and 3.03 A") . Thus the s i l v e r ion appears to be coordinated to each n i t r a t e group as a whole rather than to individual oxygen atoms, Similar zo ciner compounds cz 13-15 t h i s type . On t h i s basis the s i l v e r ion coordination can be described as d i s t o r t e d tetrahedral (to three 58 n i t r a t e groups and one double bond), and Figure 6 shows the lengths and angles involved i f the mid-points of the 0...0 vectors and the C=C double bond are taken as apices of the tetrahedron. This type of d i s t o r t e d tetrahedral coord- ination has been reported for germacratriene 1 4 and gei jerene"'"6 s i l v e r n i t r a t e complexes. Within the somewhat lim i t e d accuracy of the refinement, the bond lengths and angles do not d i f f e r 17 s i g n i f i c a n t l y from the expected values (average C ( s p 3 ) - C(sp 3) = 1.59, C(sp 3)-C(sp 2) = 1.46, C (sp 2)-C (sp 2 ) = 1.21 &) . The n i t r a t e group i s planar (average O-N-0 angle i s 120°), and the average N-0 distance of 1.21 A1 i s comparable to values determined for other s i l v e r n i t r a t e complexes,"'"3 "^' 2 0 and for s i l v e r n i t r a t e (see next section). No attempt should be made to correlate N-0 and corresponding Ag...0 distances 21 as has been done for AgCN*2AgN03, since the low accuracy precludes any comparison of i n d i v i d u a l values. In a case where the accuracy i s low, t h i s c o r r e l a t i o n i s not always j u s t i f i e d . For example, the apparent d i s t o r t i o n of the . 22 n i t r a t e group i n s i l v e r n i t r a t e reported previously has . 15 led others to make t h i s c o r r e l a t i o n , but the present refinement of the s i l v e r n i t r a t e structure has shown that there i s i n fact no s i g n i f i c a n t d i s t o r t i o n , so the comparison i s not v a l i d . The s i l v e r ion contacts the two carbon atoms of the double bond at Ag...C distances of 2.41 and 2.42 £ Figure 6 Coordination around the s i l v e r ion i n the compl  61 (Ag—mid-point of C=C = 2.34 R.) , and the i n t e r a c t i o n i s sim i l a r to that i n other s i l v e r - o l e f i n complexes to which reference has been made. The s i l v e r ion i s equidistant from the two carbon atoms, although i n other complexes this i s not always the case (see Table 8). Maximum overlap of the metal o r b i t a l s with the T T - o r b i t a l of the alkene 23 would be expected when the Ag, C(6), C(7) and the C ( l ) , C(5), C(6), C(7) planes are at 90° to each other. This angle was found to be 114°, somewhat larger than the corresponding value for s i m i l a r compounds, but as shown in Table 8, large deviations from 90° have been reported. It appears that trans-double bonds afford the greatest a b i l i t y to meet the requirement for maximum overlap, and cis-double bonds show deviations from i t depending at least p a r t i a l l y on the amount of s t e r i c hindrance involved. It should be noted that the greatest deviation from 90° reported previously, 112°, i s for norbornadiene, which i s closely related to the present compound, so that the angles may be expected to be s i m i l a r . 62 Table 8 Angles between the Ag, C= C plane and the c, C= :C, C plane and Ag-C(olefin) distances for some related compounds. Compound Angle(° ) C=C type Ag-C <&> Reference C 7H 8(AgN0 3) 2 112 c i s 2. 31, 2. 41 19 (Norbornadiene) C 8H gAgN0 3 93 c i s 2.78, 2. 84 (Cyclooctatetraene) 100 c i s 2.46, 2. 51 18 C 9H 1 2(AgN0 3) 3 107 c i s 2. 38, 2. 41 20 (Cyclononatriene) 91 c i s 2.69, 2. 84 (Bullvalene) 92 c i s 2.66, 2. 78 23 103 c i s 2.45, 2. 58 104 c i s 2.48/ 2. 55 C 1 2 H 1 8 ( A g N 0 3 ) 2 105 c i s 2.30, 2. 33 (Geij erene) 84 terminal 2.39, 2. 59 16 82 terminal 2.54 , 2. 54 C 1 5H 2 4AgN0 3 86 trans 2.48, 2. 57 14 (Germacratriene) 90 trans 2.52, 2. 54 C 1 5 H 2 4 ( A g N 0 3 ) 2 85 trans 2.35, 2. 43 (Humulene) 87 trans 2. 33, 2. 42 13 C 8H 1 0AgNO 3 114 c i s 2.41, 2. 42 (Study compound) 63 B. A REFINEMENT OF THE SILVER NITRATE STRUCTURE. INTRODUCTION During the course of refinement of the complex of s i l v e r n i t r a t e (CgH^0AgNO3) described previously, attempts were made to compare the coordination i n the complex with that i n s i l v e r n i t r a t e . A structure analysis had been 22 carried out , and showed s i l v e r n i t r a t e to have a structure unique i n the AXO^ class of compounds, and quite i r r e g u l a r s i l v e r ion coordination. Unfortunately the accuracy of the analysis was no better than for the unstable complex (a,bond distances 0.05-0.08 K), because of the use of v i s u a l photographic data, the l i m i t e d number of r e f l e c t i o n s measured and the use of Cu-K radiation, for which the absorption i s high. It was considered useful to c o l l e c t more extensive data by the s i n g l e - c r y s t a l diffractometer method, with an attempt to minimize the errors due to absorption by using Mo-K^ r a d i a t i o n . EXPERIMENTAL Crystals of s i l v e r n i t r a t e are colourless plates with well-developed {001} faces. The space group was determined from precession photographs and diffractometer data, and accurate unit c e l l parameters were determined by application of the extrapolation method of Farquhar and 24 Lipson to a back-reflection Weissenberg photograph 64 obtained with Cu-K rad i a t i o n . The values obtained agree a 22 2 5 well with those reported previously, ' and the 25 parameters of the U.S. National Bureau of Standards are used throughout. Crystal Data. X(Cu-K , K , K ) = 1.5418, 1.54051, — - a a i a 2 1.54433; X(Mo-K ) = 0.7107 a S i l v e r n i t r a t e , AgNO^, M = 169.9. Orthorhombic, a = 6.995, b = 7.328, c = 10.118 R, U = 518.6 R - 3 .. - 3 D = 4.35 g.cm. , Z = 8, D = 4.35 g.cm. m i t i c ^ F(000) = 624. Absorption c o e f f i c i e n t s : u(Cu-K ) = 617 cm.) u(Mo-K ) = 73 cm a a Absent r e f l e c t i o n s : 0k£, k odd; h0£, I odd; hkO, h odd. Space group Pbca (D*^) • The i n t e n s i t i e s of a l l r e f l e c t i o n s with 2 0(Mo-K ) < a 54° (minimum interplanar spacing, d = 0.83 R) were measured on a Datex-automated General E l e c t r i c XRD 6 spectro- goniometer with a s c i n t i l l a t i o n counter, approximately monochromatic Mo-K^ radiation (Zr f i l t e r and pulse-height analyser), and a 0-20 scan of 2° per minute i n 20. Back- ground counts of 20 seconds were made at the beginning and end of each scan. The c r y s t a l used for data c o l l e c t i o n was cut to a roughly square cross-section of 0.2 mm., and length 0.6 mm., and was mounted with a (needle axis) p a r a l l e l to the <j) axis of the goniostat. No absorption correction was made. Lorentz and p o l a r i z a t i o n factors were applied, 65 and the structure amplitudes derived. On the basis of comparison with the i n t e n s i t i e s of systematically absent r e f l e c t i o n s , 410 (76%) of the 538 independent r e f l e c t i o n s were c l a s s i f i e d as observed. The remaining 128 were assigned t h e i r measured value, but were given zero weight i n the refinement. STRUCTURE ANALYSIS Because r e f l e c t i o n s hk£, k + £ odd are weak, the s i l v e r ion was expected to l i e on or near to a p o s i t i o n which causes the appearance of f a l s e symmetry i n the electron-density map based on the s i l v e r ion alone. The three-dimensional Patterson function showed an apparent s i l v e r ion p o s i t i o n at 0.125, 0.0, 0.125, but s l i g h t elongation of the peaks i n the y d i r e c t i o n indicated that the y parameter could be changed to 0.01. This change resulted i n enhancement of some of the r e s u l t i n g Fourier peaks at the expense of others, so that the true n i t r a t e group could be discerned from i t s f a l s e image. A cycle of fu l l - m a t r i x least-squares refinement with the l i g h t atoms 6 assigned the scattering curve for oxygen, i n i t i a l i s o t r o p i c thermal parameters equal to 4.0 k2, and with unit weights, resulted i n an R value of 0.15. Two further cycles with weights based on the counting s t a t i s t i c s , and with the nitrogen assigned i t s usual scattering curve reduced R to 66 0.13, and two cycles with anisotropic temperature factors further reduced R to 0.082. Examination of the structure factors indicated that the 211, 004, 020, 024, 040 and 102 r e f l e c t i o n s were reduced due to extinction. These were excluded from the refinement, and the two anisotropic cycles were repeated, r e s u l t i n g i n an R value of 0.064, and R of 0.094. Two w further cycles of f u l l - m a t r i x least-squares refinement with a weighting scheme of the form w = 1/a 2(F ) where a 2 ( F ) = 32.66 - 1. 091F | + 0.0088|F q| 2 + 0.00008|F q| 3 gave a f i n a l R of 0.067 and R, of 0.068 for the remaining 404 r e f l e c t i o n s . w J The maximum r a t i o of parameter s h i f t / e s d i n the f i n a l cycle was equal to 1.0. A f i n a l difference map - 3 showed maximum fluctuations of ±2.2 eA , except at the — 3 s i l v e r ion pos i t i o n , where a trough of -4.4 eA was observed. F i n a l measured and calculated structure factors are l i s t e d i n Table 9. Table 9 Measured and calculated structure factors for s i l v e r n i t r a t e . Unobserved r e f l e c t i o n s are assigned t h e i r measured value, but are given zero weight i n the refinement, and are indicated by a negative sign before F . 68 Table 9 h k I 1 7 2 . 7 0 1 1 . 6 6 73.->d 72 . Hd 7 1 . 1 9 7 . 8 2 9 9 . 4 1 1 9 . S 2 2 9 . 35 3 . 9 „ 5 6 . 0 8 1 3 . B 6 1 4 9 . 1H fl6. 10 6 . H 5 7 4 . HO 3 7 . 1 1 6 . 5 9 4 8 . 19 4 7 . 1 4 1 0 7 . 8 6 1 3 . 9 1 . 4 „ 5 . ? 1 *.. * i i * . l i . J7 . 7? 1 0 . 3 5 1 7 . 2 7 5 7 . C I 4 0 , 5 9 1 3 . 16 94 . 0 6 1 1 . 1 3 7 0 . CO - 6 . 1 2 3 . 5 7 9 7 . 0 3 9 , 76 7 . 2 7 19.•> \ 0 . 3 2 10 . 1 9 _4 3 ._4 4_ I . 1 1 " 69 Table 9, continued The following r e f l e c t i o n s were excluded from the refinement for suspected e x t i n c t i o n . F c values were determined from the l a s t cycle i n which they were included. h k I F^ o c 0 0 4 188 320 0 2 0 153 282 0 2 4 208 290 0 4 0 171 230 1 0 2 121 171 2 1 1 165. 238 70 COORDINATES AND MOLECULAR DIMENSIONS The f i n a l p o s i t i o n a l and anisotropic thermal parameters, with t h e i r standard deviations, are l i s t e d i n Table 10. Interatomic distances and angles are l i s t e d 22 i n Table 11, together with those determined previously , for comparison. Figure 7 i s a view of the structure along the b crystallographic axis, and Figure 8 shows the thermal vibrati o n e l l i p s o i d s projected i n the plane of the n i t r a t e group. Table 10 Fi n a l p o s i t i o n a l ( f r a c t i o n a l x 101*) and anisotropic thermal (.R 2 x 10 2) parameters for s i l v e r n i t r a t e , with standard deviations i n parentheses. Atom x y z Ag 3650(1) 4902(1) 1298(1) N 3749(14) 3608 (12) 4074(9) 0(1) 3841 (13) 3164 (11) 5264 (8) 0(2) 4860 (14) 2930 (12) 3243 (8) 0(3) 2580 (12) 4757 (11) 3711 (8) Atom U n U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 mean a (U) Ag 4.59 3.49 3.09 -0.23 -0.81 0.54 0.05 N 2.64 2.29 2.27 -0.38 -0.25 -0.25 0.4 0(1) 4.73 3.47 2.04 -0.97 0.18 0.23 0.4 0(2) 4.04 3,92 3.06 1.10 1.75 0.41 0.4 0(3) 2.87 3.45 4.51 1.01 -0.43 -0.26 0.4 72 Table 11 Interatomic distances (k, a - 0.01 K) and valency angles (degrees, a - 1°) for s i l v e r n i t r a t e , with previously determined values for comparison. ref. 22 N-O(l) = 1.25 1.19±0.06 N-0(2) = 1.25 1.32+0.06 N-0(3) = 1.23 1.23+0.06 0(l)-N-0(2) = 121 0(l)-N-0(3) = 120 0(2)-N-0(3) = 119 ref. 22 11815.6 117+5.6 125+6.0 Ag...0 and Ag...N contacts Ag. Ag. Ag. Ag. Ag. Ag. Ag. Ag. Ag. Ag. Ag. .0(1) .0(1) .0(2) .0(3) .0(2) .0(3) .0(3) .0(2) . N II III IV V .N" .N III 2 2, 2 2, 2. 2. 2. 3, 2, 3, 3. ,48 48 , 50 56 58 75 77 05 97 01 29 2 2, 2, 2, 2. 2, 2, 2, 2, 2. 3. re f . 22 ,51+0.05 ,5410.05 ,4810.05 5310.05 59+0.05 73+0.04 80±0.05 9910.05 98+0.06 99+0.06 3210.06 I h - X 1 - y h + z II X h - y -h + z III l - X h + y h - z IV h + X y h - z V -h + X y h - z Figure 7 The s i l v e r n i t r a t e structure, viewed along the b crystallographic axis. Heavy l i n e s are nearer the viewer; the d i s t o r t e d octahedron of n i t r a t e groups i s indicated.  Figure 8 The thermal v i b r a t i o n e l l i p s o i d s viewed perpendicular to the plane of the n i t r a t e group. 76 77 RESULTS AND DISCUSSION The c r y s t a l analysis has v e r i f i e d the structure 22 of s i l v e r n i t r a t e , as previously determined , and has provided more accurate interatomic distances and angles (Table 11), as well as a detailed analysis of the aniso- t r o p i c thermal motion. The average N-0 distance i n the n i t r a t e group i s 1.24(1) k, and the average O-N-O angle i s 120°. As shown in Table 11, the i n d i v i d u a l values do not d i f f e r s i g n i f i c a n t l y from the averages, so the s l i g h t asymmetry of the n i t r a t e environment does not cause any s i g n i f i c a n t d i s t o r t i o n of the n i t r a t e ion from D ^ symmetry. After correction for 2 6 rot a t i o n a l o s c i l l a t i o n errors , the mean N-0 distance i s 1.26(1) A", s l i g h t l y longer than that reported for sodium n i t r a t e 2 7 1.218(4) R, but comparable to the values reported for several s i l v e r n i t r a t e — o l e f i n complexes discussed 22 previously. The average N-0 length reported e a r l i e r , 1.25 R, i s i n good agreement, but the v a r i a t i o n i n length (1.19-1.32 R), although not s i g n i f i c a n t i n terms of t h e i r estimated standard deviations, suggests a d i s t o r t i o n of the n i t r a t e group which i n f a c t , does not e x i s t , as shown by the present analysis. The thermal v i b r a t i o n e l l i p s o i d s are shown i n Figure 8, and Table 12 l i s t s the lengths and directions of the p r i n c i p a l axes with respect to axis 1 along the N-O(l) bond, axis 5 perpendicular to the NO-, plane, and axis 3* Table 12 P r i n c i p a l components of the thermal v i b r a t i o n e l l i p s o i d s and t h e i r orientations with respect to axis 1 along the N-O(l) bond, axis 1 perpendicular to the NO-, plane and axis 3 equal to 1 x 2. Angle with respect to Atom Component U (& ) Axis 1 Axis 2 -* Axis 3 Ag 1 0.160 17.6 91.3 72.5 2 0.189 85.9 162.1 107.4 3 0.225 72. 9 72.1 154.9 N 1 0.134 65. 0 152.4 101.0 2 0.159 155.0 114.7 93.6 3 0.170 91. 3 78.5 168.4 0(1) 1 0.140 11.4 83.5 99.3 2 0.174 86.0 164.5 104.9 3 • 0.230 100.7 76.0 162.3 0(2) 1 0.130 49.6 80.1 137.9 2 0.183 130.7 112.1 131.1 3 0.245 113.1 24.4 97.6 0(3) 1 0.145 105.8 83.3 162.8 2 0.197 114.0 27.7 77.0 3 0.220 29.3 63.3 101.1 79 equal to 1 x 1. The nitrogen atom has i t s smallest component of motion perpendicular to t h i s plane, and approximately equal components i n the plane. The smallest vibrati o n of a l l three oxygen atoms i s directed along the N-0 bonds, and the largest motion i s roughly i n the plane of the n i t r a t e group. The structure i s composed of s i l v e r ions co- ordinated to n i t r a t e ions to form a three-dimensional network so that the s i l v e r ions, which l i e e s s e n t i a l l y i n layers p a r a l l e l to (010) separated by hh, are linked by coordination to the n i t r a t e groups which bridge the gap between layers. Ag...O and Ag...N distances are l i s t e d i n 22 Table 11 with the values determined previously , for comparison. The eight Ag...0 lengths l i s t e d do not form any ea s i l y recognizable geometric coordination around the s i l v e r ion, and the s i l v e r environment i s best described as ir r e g u l a r . . 22 As noted i n the e a r l i e r report , there are groups of six n i t r a t e ions i n an i r r e g u l a r octahedral arrangement around centres of symmetry. These form a large cavity (Figure 7) which i s occupied by two s i l v e r ions 3.2 38 (2) A5 apart, related by the centre of symmetry. No n i t r a t e group i s uniquely associated with any one s i l v e r ion, but a l l contacts are shared; of the eight nearest oxygen neighbours, three are very close to the s i l v e r layers (0(3)), and the other f i v e (0(1) and (0(2)), l i e between layers to bridge the gap and form the three-dimensional network. PART I V T H E S T R U C T U R E D E T E R M I N A T I O N OF N , N - D I M E T H Y L ( F E R R O C E N Y L M E T H Y L ) A M M O N I U M T E T R A C H L O R O Z I N C A T E 81 INTRODUCTION The i s o l a t i o n of N,N-dimethyl(ferrocenyl- methyl)ammonium tetrachlorozincate, an intermediary complex i n the ZnCl 2-HCl catalysed self-condensation of N,N-di- 2 8 methylaminomethylferrocene, has been reported . Although the ammonium structure was indicated by the strong infrared absorption near 3.7u for the solution, infrared data on KBr p e l l e t s for the c r y s t a l l i n e compound appeared to be inconsistent with N-protonation i n .the s o l i d state, and suggested the p o s s i b i l i t y of coordinate covalent N+Zn 2 8 ' bonding . The c r y s t a l structure analysis was undertaken to resolve t h i s problem, and to obtain information about the orientation of the rings i n the ferrocene portion of the structure. EXPERIMENTAL Crystals of N,N-dimethyl(ferrocenylmethyl)ammonium tetrachlorozincate hydrate, [ c 5H 5FeC 5H 4«CH 2*NHMe 2] 2«ZnCl 4 • H20, are thi n orange-brown plates elongated along c with {100} developed. The unit c e l l parameters and space group were determined from rotation and Weissenberg photographs, the unit c e l l parameters being refined by a least-squares procedure applied to the 29 values of 30 r e f l e c t i o n s measured on a s i n g l e - c r y s t a l diffractometer with Mo-K radiation. 82 Crystal D a t a . — X (Cu-K ) = 1.5418; X (Mo-K ) = 0.7107, ft. N,N-dimethyl(ferrocenylmethyl)ammonium tetrachlorozincate hydrate, [C^H-^NFe] 2ZnCl 4-H^O, M = 713.5. Monoclinic, a = 18.076(6), b = 14.038(5), c = 12.246(5) ft, 3 = 95.70(1)°, U = 3092.1 ft3, D m ( f l o t a t i o n i n bromoform- — 3 — 3 benzene) = 1.522 g.cm. , Z = 4, D = 1.532 g.cm. c F(000) = 1464. Absorption c o e f f i c i e n t s : y(Cu-K a) = 118 cm?1; y(Mo-K^) = 21 cmT Absent r e f l e c t i o n s : h0£, l odd; OkO, k odd. Space group P2 1/c (C^) • The i n t e n s i t i e s of a l l r e f l e c t i o n s with 20 (Mo-K ) a 40° (minimum interplanar spacing, d = 1.04 ft) were measured on a Datex-automated General E l e c t r i c XRD 6 spectrogoniometer with a s c i n t i l l a t i o n counter, approximately monochromatic Mo-K^radiation (Zr f i l t e r and pulse-height analyser), and a 8-2 0 scan of 2° per minute i n 20. Background counts were made at the beginning and end of each scan. The c r y s t a l used was a thi n plate with dimensions 0.1 x 0.4 x 0.6 mm., and was mounted with c p a r a l l e l to the cj> axis of the goniostat. No absorption correction was made. Lorentz and po l a r i z a t i o n factors were applied, and the structure amplitudes derived. Of the 2991 independent r e f l e c t i o n s 2012 (67%) had i n t e n s i t i e s greater than 3a(I) above back- ground, where a(I) i s defined by a(I) = {S + B + (0.05S) 2 where S = scan count and B = background count. The 83 remaining 979 r e f l e c t i o n s were c l a s s i f i e d as unobserved. STRUCTURE ANALYSIS The data were placed on an absolute scale using 29 i i Wilson's method , and values of |E| were calculated with 3 0 the program of Ha l l . The |E| s t a t i s t i c s obtained are 31 compared with the t h e o r e t i c a l values for centrosymmetric and non-centrosymmetric structures i n Table 13. The structure was solved by a d i r e c t sign-determining 32 procedure , which uses a r e i t e r a t i v e application of Sayre 33 relationships . The origin-determining r e f l e c t i o n s and symbols (Table 14) were selected from those r e f l e c t i o n s of highest |E| which enter into the greatest number of Sayre relationships and which were of suitable p a r i t y groups. Permutations of the signs of the symbols 'a', 'b', 'c' and 'd' led to 16 sta r t i n g sets. Planes having |E| values greater than 1.7 were used and twelve passes through the l i s t were performed for each sta r t i n g set, with newly determined signs not used to estimate additional signs u n t i l the next pass. This procedure yielded two possible solutions with consistency index of 0.83 (next highest 0.60), and the E-map computed with the signs of one of these showed the two -2 Fe positions and the ZnCl^ group. Compared with the f u l l y refined structure, 280 of the 296 predicted signs were correct. The E-map computed from the other set with consis- tency index 0.8 3 did not show recognizable s t r u c t u r a l features. 84 Table 13 |E| s t a t i s t i c s for N,N-dimethyl(ferrocenylmethy1)ammonium tetrachlorozincate hydrate. <|E|> <|E2|> <|E 2 - 1|> |E| > 3.0 (%) |E| > 2.0 (%) |E| > l . o (%) Experimental 0. 785 1. 008 0.995 0. 37 4.28 32. 83 Theoretical Centro. Non-centro. 0.798 1.000 0.968 0.30 5.00 32. 00 0. 886 1. 000 0.736 0.01 1.80 37.00 85 Table 14 Base set of r e f l e c t i o n s for sign-determination. determined h k £ E sign/symbol sign 1 2 1 4.64 + ] To 2 1 3.23 + 1 o r i g i n 4 5 9 3.77 + 2 2 1 2.61 a + 1 0 2 3.02 b - . 1 4 4 2.93 c - 5 2 5 2.33 d _ 86 A structure factor c a l c u l a t i o n based on the heavy- atom coordinates from the E-map, with the Wilson scale, scattering factors from the International Tables and i s o t r o p i c thermal parameters B of 3.0 ft2 for a l l seven atoms gave an R value of 0.40. A difference map based on the heavy-atom positions was computed, from which twenty- two l i g h t atoms were located. With these included i n the phasing model, subsequent difference maps revealed the positions of the remaining non-hydrogen atoms. With a l l l i g h t atoms assigned the scattering curve for carbon, and i s o t r o p i c thermal parameters of 4.0 ft2, the R value was 0.35. The nitrogen and oxygen atoms were assigned t h e i r appropriate scattering curves, and three cycles of f u l l - matrix least-squares refinement with the Fe, Zn and CI atoms allowed anisotropic thermal parameters, and unit weights for observed, zero weights for unobserved r e f l e c t i o n s , reduced R to 0.082. Two cycles of block-diagonal l e a s t - squares with a l l atoms assigned anisotropic thermal parameters further reduced R to 0.068, but the anisotropic thermal parameters for the l i g h t atoms are not considered accurate, and are not l i s t e d . In the f i n a l cycles the data were weighted so that /w = 1 when |F | < 45, and /w = 45/|F | when IF I > 45. For the 979 unobserved r e f l e c t i o n s , /w was taken as 0.80. F i n a l measured and calculated structure factors are l i s t e d i n Table 15. 87 A f i n a l difference electron-density map showed spurious fluctuations as high as ±1 eft , and hydrogen atoms could not be located r e l i a b l y . Table 15 Measured and calculated structure factors for N,N-di- methyl(ferrocenylmethyl)ammonium tetrachlorozincate hydrate. Unobserved r e f l e c t i o n s are assigned t h e i r measured value, but weighted as described i n the text, and are indicated by a negative sign before F . 89 Table 15 h k z 3 C 4"44 F F 4 4 C P ? ' 3 . l l C 0 117.33 C C 5C.C7 l ? 5 . t * " 4 4 4 14 * 0 -?<..*< -I—HtH- 4 4 i t * 4 - 4 15 1 4 - 4 o 7 1C • 7 li J 4 4 4 " J 4 4 4 4 B r&S ~m ,44 2 2 . n n . - i c 441—-44 i s ' [ ' . { ) ii i 1* 3 7] r - , . : ^ 15 ' !] I ? r . 7 * !'.<•'• ; : cc 4 4 jj--5-4--S^~ 4 4 . C i 3f . 5 ' (•O.b" ( 5 . T * 5G.C4 i'..47 4:4 .44 4 - 4 V, I 15 S J 5 - f - - T 4 4 > - 4 4 - 4 4 4 4 -44 7C7. 7n - 5 4 4 - 44 •44- - 4 . 4 -—44 -444 -144 >44 4 4 4 4 -'4 4 4 4 4 4 4 4 ? 3 . i i 11 / . j 1 I I . V> 1 I /.Tt'- 44*—44r 4 ~ 4 4 - - 4 ^ - )T. i t -44 I i • -44/ IC S C - > . 9 | i i o " . ' . I 1? •) o n . c 4 . 4 i U S C - 1 1 . 4 5 1 .35 i IS S -ll:tl i44 1C 0 - 7 . 1 7 S. If 51 ,<ti 17.14 4 4 4 I I? ! ! 10 0 2r . ' s . J IE s it:;; C It C 77.21 1 Id 0 7 5 . i s PS.21 4 - ; 14 4 4 - 71. 1 4 4 1 ».4"* " 4 4 ^ 444- -1 2.T-> - 1 * . b ' 44 3 r . '. 4 4 4 4 : 4 M 4 • 7. ••• •44 '4,' ; 4 4 4 4 4 " J 7. * • i 4 4 4 4 - 44f4 4 4 4 4,4 i • <t. i i * 1.12 4 4 4 4 H i e f r " 4 - f 4 4 4 iiiiil 4 4 4 4 4 4 4 4 4 ^ 4 4 it::: -Mr 1 7' . 7:i i?ft 4is 7".4 1 ' 4 W h 4 t ^ ^ <7. *2 l b . 72 4«?«- -4#- ••1 .01 I f " . I- M . H 15. jr. - 1 2 . 5 4 44r 1.0 J I- 4J- 11 4f- 24. 77 4 t s f - i 7 . 4 « !J:i; M4. 75 4 j ^ ^ 1 " .45 4 j ^ l * * . 2r- 4 f : £ - 4i# -4tf- 4?4J 54^ 4S:tr- 4f - : #- - j U 4 i - -41 4i:if- i l l K C . 7? 4 r t 4 4 4 T ~ 21. 5'. 4 4 f i f f - 4 i : - H - -rf«f 4 ^ 4 - l(^. 72 4 7 4 4 -4:4 12. 77 444 4 4 4 - - 4 : 4 4 H . l t 4 - 4 - 2 h . 5 ) 51.05 S S 4 - 4 - 4 5 , 1 5 4 h t t - 4f>.11 4 4 4 "44 414 i i 4 H 4 t l f - -444 4 4 4 - 4 17 :3 11 •I 12 4 4 4 - 4 - 4 - 1 11 f t - 4 - 4 -2 P -4—4 10 0 4 4 4 - 4 4 - 1 4 . n i i . 3 * 1144 - 4 4 4 4 4 4 - -414 4 4 4 4t :^ S-:4 7 H . n i . l h i r . " i 7 , i 4 4 4 24. !J .'J .'.<•• r . r 4 4 4 — 4 4 ;;4i -4 ' - 4 4 — 4 : 4 4 : : ; i - — 4 4 4t:4:— !?:4 - 4 : 4 4 4 « - 4 1. V , 1 . 2 - 4 4 4 - 4 - 4 - - 4 4 - - 4 - J . 4 T T . 4 71 7 . ? .1 M . 1 I -4:4- 1 J4 .71 !t;:" -4W4 - 4 4 = 7 - 11. y- - ^ ? : 4 i . r i. 14L'. 1̂ 7' . .re 4:4 i ' . i . ' , , i f . - . * f 7.17 - 4 4 7 T 4 > 4 v 4 4 ^ 4 4 - 4 3 . 4 3 - I 3 . . i ; i I I . 71 ^fM4 17,4} 2 3 2 . H 2 - 3 . 4 C 7 •!6.<! M:,v, - 4 4 1 4 s 4 1-1.7* 4 4 4 -7 1 7 17A.>-r. -1 1 2 10.9b 29.b-- 0 I 2 77. ' 6 17. i c 1 1 2 8 5 , T f "7,ir- 3 ft 2 126. C* !•«.-!/ 2 7 f . l l 77.."' 1 2 31.57 ; J . I - . 2 1 . C t . » t 7 - n ! n ii.*6<! 9 If 11 2 1 9 . M ;^. h7 2 21. 77 7 2 . » . i 1 2 2 9 , I) :t..!>r . 2 ? . « / 1 2 75.^1 7->.4- i i 4 - 4 ; 5 's:r " 4 , ; ::: i 1 -,':." . ?:U -11 2 ! - l i 2 J - t l . . ' S : > . \ / :\i ; i 4 4 -<5 2 7 71.1', ?. .61 -A 7 7 - f . , 7 • -7 niii - ; : i ' . - 6 7 7 7 7 . n ?<•.!• - 5 2 2 IL7,22 '17.1 l 5 1 U:£ -7 7 7 11.11 >•..!<;• -1 J 2 !)".!•. 1 JiNl 5 ' ; ;:4- 2 7 2 ' . f . l - ; 3 7 2 f . ? * ? J l i t . - " . If. 5 If 7 7 13.-.4 .' '•. M \ \ 7 - i . f ' i . ^ i 2 r , . ' . 11 17 14 11 16 2 7 i f l i l X...72 2 7 3 7 . i t 7 7 -17 .IT I-,3c 2 2 - o . 3" 7? 2 - I . V i • . . i - - 7 7 - 1 * . i i ] ! .h • -17 :i: :i) 1 2 17. iv . V ^ i 2 - I C . d J - . S " •7 - i r . ' H ,..-•] -\\ -8 - 6 -S ii 7 ^ . 5 9 . - .1 . 7 7 7 2 . n . 4 " . l',:'A ;;::: ; - 3. • i1 ".m 7 i r . i i .,..^1 1 5 2 I M . i l 1'.'.-" \ r£i 2 > ; . i i c . . - 7 I f 1 1 12 1 7 - 7 . , , ' 2 -J:;: 7 7 7. = 7 1 . 1 1 2 2 " . 7" i ' . i - '7 -11.11 U . ^ 1> 1* 3 7 7 5 . \ , 2 ^ . . H 2 -r̂ : : ; -\\ -B 2 -1C..1 . . i f 1 2 i 3 * . ' . , : i w . s ' 2 ' ' '• ' -7 -b :) 7 -11.11 I ' . M 2 i i . M * ;.•>'• 7 1 71. f Z 1 ! . 7 ' ' 2 i i . t l ; i 4 2 lbS.11 I M . V , 2 i - ; , * i • ?. 7b 2 71.72 •:.•.-•> 2 64.17 7',.!/_ 2 - .4.7* ..7,sr: 5 ; 2 f l 2 - 1 . * ' , -.77 2 1 1 1 . e l i r . K 2 I4.f-H I ' . i ' l 12 i: -1ft  -7.1-1 7.,-- 2 41.24 -1.1 ' 7 1 1 . h i M .-. ' 2 4 5 . ' 4 * ! . " • 7 -1.7b '•. «7 7 - 1 4 . 1 3 M . U -15 - 1 3 -4 -10 7- -7 .71 '7 . . • 2 27.. CZ 2 19. M . t l -•1 - b 2 1-).61 - ' . H . - 2 61.11 '> ) . 1 1 2 3 2 . 15 'i. -"• 7 44.71 '.7.7. - 2 - " 2 - "'oic" 7 Ifc.bJ ,37 ,4^ 2 I S . - P 4 ' 2 - r . . 4 3 •• . ' . . • 2 .16.53 11. 1 1 j 2 ; e . i b v . . . . 2 15.43 3 * . . T 2 114.40 i : b . c 2 2 2 * . 5 1 'C.7H 7 1 1 . b? I ' . J S 10 12 \l 11 2 30.15 2 - . 1 * 2 19,71 1,1 ;• 2 -1 1. 55 7 . T 2 -8 . 16 r . 7 1 2 31.55 I f . 7 1 1 ?<;. ha if..n<. -15 ft 2 - 7 . 6 5 P . ™ 90 Table 15 continued:- h k I Fo I I • :Jj44- 411- 4-444- £ 2 444-4- 444 19.73 ; ? 1 J M . i i l 3 2 5.1.14 1 -X.il J 3 L 64 14 i i 4;, i'. -vi.9. -ft 2 JL_L H - 3 ! J . ft 1 444~ 3 13.71 - r - ^ H - 4—4:4- 4—sw?- \ '-til - 4 - 4 - 1 \ .24 -16 5 1 2 C . l i ?<. . ! ' -15 5 1 24.44 -14 5 3 lit -B 5 3 4-4—firK—=H:fr 4 4 - 4 4 4 f r •4h 4 - 4 - - 6 B 3 -44 s : ; 4 - 4 — S 4 4 - 4 ^ 11 1 J 2fl ir. 76 1* .54 12.22 ^ : ; — ^ 4 - - 3 4- 3 53. 91 a 9 3 c o -444 - i . r . 6 :ll IS I -444—444 Si I 44 ^4v44—4:4- I IS I iVM 4 K 3 73.ft? 5 1C 3 2 9.3d 2.5B 24. f 4 4 4 -17. fit 4 ^ 4 4 ; 7tl4 4—145 £ t r 4-4r:4- 4-4444 4 - ^ 4 4 4 --1. '^ 4 I 6 . P J 4—4:4- 4 24. 7<> 4 16.0> 4 >rt.77 4^:4 i :<..?i 44 ,4 4t 12. 41 -444 i i . 9 T i ' .Hi 11.07 1 ; i . 4 1 444 V7.7-} >"..!• : i : ft?; B 2 4 1 . 4 6 *%.B7 i! I : IT:-! 'iiil 15 3 4 - 5 . 5 H 1.22 :!S j : jf:;;—feff -13 3 » - 1 1 . 3 9 1J.37 -11 ! 1 6 « . « 7. .53 : : J ; it:;: - 4 J 4 (,2.90 5 * . 36 - 5 — ? — f — S t ^ ^ i I : "H:H -ft* 77. 59 7* . 16 1 4 -1T.12 ' . 7 4 1 : : St:H~ : : : '• 3 . ' 1 444 IS 444 .47 —4i4" « 4 1 K . U 0 5 4 102.42 4-4-4^444- 444 2*-. -1? - i , * 4 4̂:4 ; i .71 44^4-M44 6 4 - 1 7 . S I . » 17. H 1" .*> -444 "^tti~4t4r 7 1 . i J ±rt 91 Table 15 continued .- 4 7 4 1 4 -1 ; — 4 : 4 4 ; ; S); 4 - 4 4 - 4 ^ - ^ 4 4 - 4 4 4 44 - 4 : 4 - 4 4 4 - 4 : f - 4 * 4 4 4 W 4 4r:4- 4 — £ 4 4 5 -11 .16 4 4 f 4 - 4 4 -4 ; :S 4 M 44 -? 2 1 14.17 U . 7 „ -1 7 5 1 ' < • . « » , Ir-V. ' l/ r. 2 b 2 ' . 2 i - ? i . : i 7 4 — 4 4 — 4 4 1 4 4 : i ; - 4 4 - 4 - 4 4 4 4 = z 5 , - r . i i 1, | j : : 4 4444—44 44 44 44 • • ' 4 4 n>.7', 4:44 44 - 4 — 4 4 -1 ] 5 ?>•. i l - J ) 5 n . '2 1 5 ! • • . ' ! 1 I I 4- 4 4 1.17 - 4 : 4 4 4 5 3 1 - 4 4 - 4 - II . 1 5 4ti~ •r - M f - 4 - f — ! t : 4 4 4 - 4 - 4 - r ; ! 4 - 5 V . * * - 4 4 - 4 - 4 4 4 - - 4 4 44 41? :!? I \ • 12 6 1 22. 14 ? ! , 71 •11 6 1 15 .-J 7 If .IT 4 4 4 - 4 - 4 4 4 4 4 -1 J 5 - » 7 5 - 4 - 4 - 4 - 5 7 - 5 17. n 4 4 4 - 4 4 £ 4 4 4 4 — 7 4 4 4 4 1 7 5 71. y 1 7 ' . i 1 7 5, K . ' ^ V . . T - 1 7 5 4.. . l i M .-,7 I I i 4,;—44 11 I i ••-.4 12 " 1 -1 3 . Ob ,4< =454-44 4 S S J7.V(. - 4 4 - 4 — ^ : 4 i ! - 4 41 : ; 4 4 14 c 7. ? i K M -4 4 - 4 4 — 4 : 4 -1 « 5 J1 . I 44444 4;} 4 4 '44444" 4 J ! 44 • 4 - 4 - 4 — 4 4 ^ 1 11.1. 5 7 7 , 1 * - 4 4 'I . 77 : 4 i 14 \ If ! 44-4-44- - 4 4 - 4; ; if 4:1 • <• n i n . - -41! 4 4 4 4 4 - V - 4 S - 4 - 4 4 4 - :i I! I " 17 5 * > . f i 4 4 4 4 — 4 : 4 - H - M - ; ; 4 - 4 4 4 - 4 - :!S f - 4 4 4 4 - 4 4 4 444-T744- 4 4 4 4 4 4 4 — 4 4 — 4 4 4 I - . s s : ".sr. 4 4 [6.14 - 4 4 11 l i iB 11 C b O.r ? . 1 ' i i * c 6 a. 7J :,• . i " - H t h 71. '17 441-44:4!—441 - U 1 t -11 ."2 b 17.47 4 H - 4 : 4 L7.4C (. 111. > •• 1.' I . i ; - 4 - 4 : 4 — - ] ? . t - ' n . v ;t.'".7 !7. . ? . • i . ; ; . ' :-..!7 4 - 4 t ' 4 ^ 4 4 4: \ 1 444 7f i44 -4 I - :4 -11 7 h 3 « . 7 - >7.f* -444-444 4r:4, - 4 4 4 — S 4 — 4 - K -. !—h-?-4f;74 ' •' . ? 7 -44f u ! ? "J-'-' i i '4 II I : 44—44f -jj \ I 44 ,4J 4i4-4- ji:4 -444 -1! 3 * - 1 . > ] . 1 -1C 3 (. | ' . 1 J I . . . , : ! u 4 - 4 1 fc- •4-44-T i f : S — 4 : 4 44r 4 4 — 4 4 ; : - i ; 4 — 4 4 4 4; I I 4444- 7 4 - 4 4 - - 4 4 4 - :;:;; -44 - 4 4 - r i 4 - 4 4 - 4 4 - 4 - 4 41 i I -11 b 6 4 4 4 - 4 -T 4 4 4 - •44 4f -4|s •b.C'' '1 .07 44 1 .? * -4:4 4 — S : 4 4 h ' o . J t ' 44- : 4 44 --\\ b 21. 6<" ; 2 . 1 i J 4 : - " ' 4 4 h 4(-. S ' 4 ? . 7" -14 z 7 3n.44 .';'.]-i -11 7 7 ' r . ; ? 71". 1* - i ? ? 7 - i i - . ' . * : . • . ) - 1 1 ? 7 - 0 . - 1 1 ' . . ' 4 - 1 - i 7 I S . 01 11.14 •i ; - e - i * / 1 . 4 » 71. i r . 6 . sc.7> 6 3 1 . 1 ' T 1 6 -17.71 7 6 4i). 1J H . r l - 0 1 7 - I f .r.7 11.1'. - f 7 7 M . I ' ' l ' ; . i 7 -7 -7 7 2ft ,C t 27. u 2 - 6 7 7 l i f t . 7" 141 , M -4 ? 7 i r i 4 . ' 4 l 7 - 4 : i "I, 1 6 14. Of -1.77 f> 45. 31 4 6 16.10 }' .7.7 6 77.77 »7.(.o 6 77.76 T . M 6 46.71 47.0ft - • 7 7 7 , . . - , 1-..77 -1 2 7 51 47 ." 7 \ i ; S:;̂ • 7 7 7 17H.-.4 I7S.1" 7 1 5 ' 7 6 2 s . \ « ; t . i - • b ' 4 . 7 1 6 frt.P1 12. l o 6 76. 41 24 ,M,i 6 - 4 . 2 3 7 . < , fr O.rt ' . ^ 1 2 7 - 3 . 4 ' : -H. 77 4 7 7 .". .14 Jl .Hfr 4 4 444 44i ; A 2 7 . 27^7? 27.47 e 10 ft s i . i t . vr.tr 9 2 7 27. J4 V : . ^ , 1C 7 7 44.07 W.41 1 1 2 7 76.67 ? * . 2 4 -14 » 7 i 27. ?4 '1 .^ip 4 4 4 4 4 — 4 i 4 >; i f . i l :• 2 1 . ? ? .' i . -• 7 i—445—44 . 2 5 . 3 ? K.". - r l . '1 1.44 - ^ 4 - - - 4 : 4 V<il ":U i44.._..i;E 41 ;:4, 4 - ^ - 4 4 4 (. 1 » . * 6 I 44 4—44 6 18.12 2 ^ , : ' ' . 4 4 4 r 4i! 4;ii - 4 4 4 - 4 f e r - - 7 t - . - n 1 .67 7N 4 4 4 i44 6 14.60 6 7 2.77 T444 - 4 . 4 f . 12 . 4 - 1 4 - 4 - I K . 6 ; if •7 it t i — J i * : S! 7 1C 6 ' 41 144 44 4 4 4 - 4 — 4 4 - 7 17. - 5 ' ; ; ; : : " 4 — 4 s 4 44 2 . ; . 1 ' . 3 l 4:4 2 ' . •• 3 - 4 : 3 IK. (1 4 4 4 - 4 4 - 4 4 - 4 — 4 4 - , ' 4 - 4 4 — - 4 : 4 44; 4 : 4 Table 15 92 continued :- h k I F n 4 ! — - 6 h - 4 4 , — - 4 : 4 7 -11.55. 2.17 :?:;; 7 - 1 . C 1 7.54 2 J . 8 T 1 i. lb -5 -1 - 2 - i " I S . U.oi 29.72 ? * . L C !*..«•? r*.0> 7 ' 22.11 Pf.tr 7 5 7 . 6 * ; t . M 65.17 67.19 i -| s 25.80 3 4 . 4 6 31,77 - 1 0 . J'! » .• . !- 41."1 4?..57 7 22.73 21.17 7 ,5 li - I * 7 0 . 0 f . . ' 2 17.16 I-..-.S 3C. 41 3' . . KP -12.11 12.HO C P t .H9 71.01 72.77 -13 -12 -10 • -ft .8- , b . ' l - 1 4 , 5 5 1 J . M , J4.27 ? i . 6 ? • -8.71, ' . 7 ( 40.C4 *• .»** -7 - 6 -5 - 2 10.03 ' ? i . 4 > 70. 30 . ' 7 . M 27.0[ 2, .77 2 4 . 2 5 45.B1 t : . K ' . 74.31 71 . 7C -1 0 * 54.HI '.ll' 30.P3 - i . t . 4 , . n 5 ft 7 a -0 .55 »:>! 2 6 . 0 4 • 1 -12 -11 4 4 - : - 4 44- - i . e . / . - . i r I - 4 f S — ^ : v i - o.c i . * 1 30.ft! > 5 . J i ":JJ - ^ 4 4 - M . 11:1', - i . f t f t 4t.t 44- - 4 4 - 4 4 57.67 * 1 . 06 57. 24 - 4 4 4 - - 4 : 4 i ; . 7 4 (:,: 4lf i;:i; 4 1 .04 44 - 4 : 4 44 ill 4 4 4 :4 44 - 4 4 4 4 4 4 444 4 4 - 4 44 -444 4 4 4: 4 4 10.71 -T4 4 4ii 44- 2ft.8 > 4 4 4 - 7 24,71 7 _ . - J . l l . f t t - * r •!5 S 4 - 4 - 4 7 e a - 4 4 r 28.1% 8 : . n 4 4 4 - 4 - 4 - ^ 4 4 - 21.11 , - 4 : 4 - 2 4 , . - 4 4 4 4 4 44 4 — ! 4 4 - -4 } • 4 - 4 - -s- i : 4 - 4 - 44 4 : 4 :::;; • s4 - i z . i i ; ; ; - 4 - 4 - 4 - - O . - M - 4 : 4 - 4r 4 4 \l:'l 4144 4 — 4 4 4 4 — 4 4 4 8 4 : 4 I 4 - 4 - 444 B LO.'B i 44 - 4 - 4 4 4 - 2o;fi 1:1; 3 9 . 6 * - 4 4 4 - 44 4 4 4 ?6 .65 4 4 4 - 4 4 4 • 1 . 2 * 1". 7 I ' 5 . C = 1.42 - r44J 4 4 4 4S - 4 4 4 T : 4 4 4 4 Ml 4t4t 41.77 8 . 1 2 •..1', 4 4 4 4 44 - 4 4 2 . i s 21 . I t - 4 4 4^45- 4«r 4-1 .r - 61.19 17.76 44 4 f 22.31 18.74 44 2.1.0 7 7.77 '1:11 - 4 4 - !:SJ 4 - 1 4 : ! ! 1 4 4 4 — 4 4 - 4 4 4 - B 47.16 t - 2 . 4 5 fl - L S I ft -5,HI 4 - 4 4 4 - 4 ^ 4 -44:fi- 4 2 . JM 4 4 4 4; 44 - 4 4 4 44 -44 4 4 4: 44 • -1.2! a 2 ' ) . ^ i 4 - 4 4 4 - 44 4 — ^ : 4 - 4 — ? 4 4 - * 24,74 444 4 : 4 i i , i « !-'.:̂ ;4: 4̂ 4 - 4 4 77,41 - 4 4 4 - 9 - 8 . 7 - i t 4: 44 - 4 4 - - 4 4 4 4 4 4 4 - !4r f ! | : i ; 4 4 4 J : 4 :::i? 74." 7 ; i . ; 7 .11:™ - 4 : 4 5:4- !'•::; 44 4 4 4 - 4^,34 5 - . . " e l , oo 5 ' ) . " " - 4 4 ^ 46. 12 I I J I ? i .30 44 1-..63 5 . 0 6 4 4 4 45. 01 - 4 4 4 20.5 7 O.C -444 4 - 44- - 4 - 4 - 4i j;:;J 29, »? 21 . PS 4 4 4 - - 4 4 4 - SJ:?: "44" llii; l i - 4 4 4 - 1:4 -H44- 4 4 4 4 4 1 4 -'1:51 4 4 - 4 4 4 - h - 4 4 - 1 8 9 :\l I IS -» 0 10 4 - 4 4 4 4 4 - :\V.V, - 5 . S • - S : f 4 is 4;; - 4 4 1 - 4 4 4 - 1' . 1 7 71. 11 4 4 4 - 4 - 4 7 14 4 - 444 -S:5, .21.12 - 4 4 4 1 3 5 49.16 - 1 2 . h 5 4̂ 4 4.fl • 10 ^ 10 4 - 4 - l i 34.6-> - 4 r 4 - : 7 2 , i - . 4 t r 4 4 4 f 4f - 4 4 4 1t;f44a4 - n , * 7 - " i ; * * * 1 . « S "..7.3 34.12 l i - i ' l - i t t i 4 4 44r ; - 4 4 ^ 28.21 4 l 4 l 44 ••ill -ft:;; 4 n : : ; r.c 6.41 r..o . 7 . 8 6 -5 . 7 6 ft,*? 3 . . ' ? . is::; 4 4 4 . •7-72 - T 4 4 4:1 44 17.-11 ,;:•;;• -44V. - 14.78 4 4 17.t = If 44 4 * 4 -4TH 14 .r"7 . . ? . 3 4 - 4 4 f 21. 1' 6 .13 8.76 1,:1I 16. »0 4 4 4 '11:;: 4 4 ? 4t 1 . * i 44 4 4 4 1 11 4 4 4 - 11. n . i i l i 4 4 4 - 4 4 4 -i ; 1 ; 1 ll:V, '1:V- -ir.i-t 4.•>» * 7./f-. U 7. • " 11. M ^ 4 t . H 0 '• - 1 ' 4 102.'.J l I H . - ' l -1 I": -7 12 44 liiii -7 2 - 6 7 14 1 -11 4 - ! 4 }?.71 7-.I4?- 7^.4 7 7 , '-0'- i;:!,' " : " 61.16 V . 1 ? • i t . 6 ' s i . 1 * 8 5 ' -12 7 1C 0 ' - 2 12 -6 8 16. -is 2;>.r6 -1 .17 ^ . - 2 35.11 27.6ft 2 5 . 0 ) 7 » . " -3,7rt - 1 . 6 4 ' . , / • -t 5 ' -1 I 1? 2 - 8 C 1 a 21.81 24.\> l C 4 . b ' l U 2 . 11 - 1 3 . 3 7 1! .66 -14.1,-i | t . B 5 0 . 0 \.rt - I J . 70 8 . " 4 5 2 -3 4 -1 t 28. 34 V . l * 44.;-, • . ^ . i f T 93 COORDINATES AND MOLECULAR DIMENSIONS The numbering system used i s shown i n the diagram of the structure i n Figure 9, and the f i n a l p o s i t i o n a l and thermal parameters are l i s t e d i n Table 16. Bond lengths and valency angles are given i n Table 17, and Table 18 gives the equations of the mean planes through the cyclopenta^ dienyl rings with the angles between the normals of these planes. Figure 10 shows a view of the ferrocenyl groups along the normals of these planes, and Figure 11 i s a packing diagram viewed along the c crystallographic axis. Figure ? A diagram of the structure, which shows the numbering system used.  Table 16 F i n a l p o s i t i o n a l (fractional x lo1*) and thermal parameters (ft2x i o 2 for anisotropic; ft2 for i s o t r o p i c ) , with standard deviations .in. parentheses. Atom X y • z U n u 2 2 U 3 3 U l 2 Ui 3 U.2 3 Fe(l) 3640 (2) . 1096 (2) 4383 (3) . 5 .41(18) 5. 69(19) . 5 .19.(18) -1 .15(33) 1. 78 (31) -1. 56(32) Fe(2) " -3735.(2) •• 1086 (2) •• 0954 (2) 5 .41(18) 4. 69(17) 3 ;61(15) 0 .77(31) 2. 22 (28) 0. 35 (29) Zn 1170 (2) 4360(2) 2753 (2) 6 .39 (16) 5. 49(15) 5 .34 (14) -0 .51(27) 1. 00 (26) 0. 26 (2.6) C l ( l ) 1190 (4) 4281(5) 4631(5) 10 .98^48) 6. 59 (36) 5 .04 (32) -6 .01(72.) 3. 00 (67) -1. 56(61) Cl(2) 0090 (4) 3641 (6) 2099 (6) 7 .21(39) 10. 98 (54) 7 .60 (41) -3 .58(78) -0. 44 (70) -0. 95(81) Cl(3) 2148(4) 3599 (5) 2198{5) 7 .87 (38) 7. 19 (40) 7 .82 (39) 1 .79(68) 5. 88 (63) 1. 91(68) Cl(4) 1188(5) 5901(5) 2185 (6) 11 .64 (54) 5. 69 (37) 7 .97 (42) 0 .77 (77) -3. 33 (82) 2. 95(69) Cation 1 Cation 2 Atom X y z B X y z B C(l) 2547 (11) 0890 (15) 3870(16) 3. 8 (4) -2 92 8 (12) 1194 (16) -0077 (16) 4 .6(4) C(2) 2980(14) 0865 (19) 2965 (19) 5. 5 (5) -3588(12) 16 82 (16) -0528(16) 4 • 4(4) CX3) 3525 (14) 0097 (20) 3177 (21) • 5. 6 (5) -4184 (14) 0982 (18) -0652 (18) 5 • 9(5) C(4) 3407(15) -0322 (16) 4167(22) 7. 4 (7) -3870(13) 0086(18) -0258(19) 4 • 7(5) C(5) 2813(12) 0165 (16) 4627(19) 4. 6 (5) -3099(12) 0218 (15) 0082 (17) 3 .9(4) C(6) 3926(15) 1735 (20) 5866 (22) 6. 3 (6) -3316(14) 1545(21) 2458(18) 6 • 4(6) C(7) 3702(16) 2427 (18) 5035 (24) 7. 3 (7) -3601(16) 0627 (22) 2551(20) 6 .7(6) C(8) 4218(15) 2311 (19) 4184 (25) 7. 4 (7) -4350(14) 0642 (21) 2182(18) 6 • 9(6) C(9) 4732 (16) 1568 (21) 4535 (23) 6. 3 (6) -4562 (14) 1514(22) 1842(18) 7 • 2(6) C(10) 4543(15) 1220 (20) 5550 (22) 5. 8 (5) -3943 (17) 2139 (18) 1999(18) 7 • 0(6) C ( l l ) 1972 (12) 1593 (16) 4080 (18) 4. 2 (4) -2204 (12) 1684 (18) 0224(19) 4 .8(4) C(12) 0630(15) 1756 (23) 4214(24) 7. 5 (7) -1811(14) 1415(19) -1676 (20) 5 .8(5) C(13) 1063(14) 1134 (19) 2472 (20) 5. 7 (5) -0864(15) 1801 (21) -0131(23) 6 •4(6) N 1214(10) 1184 (14) 3723 (15) 4. 7 (4) -1613(10) 1314(13) -0480(16) 4 •5(3) 0 -1110 (13) 4391(17) 0389 (20) 10. 2 (6) Table 17 Bond lengths (R) and valency angles (degrees) with standard deviations i n parentheses. Cyclopentadienyl Rings Cation 1 Cation 2 Fe-C(l) 2.03(2) 2.03 (2) Fe-C(2) 2.03 (2) 2.04(2) Fe-C (3) 2.03(3) 2.06 (2) Fe-C(4) 2.05(2) 2.04 (2) Fe-C(5) 2.03 (2). 2.05 (2) Fe-C(6) 2.05 (3) 2.03(2) Fe-C(7) 2.03 (3) 2.05 (2) Fe-C(8) 2.03(3) 2.05 (3) Fe-C(9) 2.07 (3) 2.03 (3) Fe-C(10) 2.07 (3) 2.02 (2) Mean = C(l)-C(2) 1.42(3) 1.44(3) C(2)-C(3) 1.46(4) 1.46 (3) C(3)-C(4) 1.38 (4) 1.44 (3) C(4)-C(5) 1.44 (4) 1.43(3) C(5)-C(l) 1.43(3) 1.42(3) C(6)-C(7) 1.44 (4) 1.40 (4) C(7)-C(8) 1.48 (4) 1. 3.8 (4) C(8)-C(9) 1.43(4) 1.34 (4) C(9)-C(10) 1.41 (4) 1.42 (4) C(10)-C(6) 1.41 (4) 1.47 (4) Mean = C(5)-C(l)- C(2) 108(2) 109 (2) C(l)-C(2)-•C(3) 107 (2) 107 (2) C(2)-C(3)- C(4) •108(2) 107(2) C(3)-C(4)- C(5) 109(2) 109 (2) C(4)-C(5)- C(l) 108(2) 108 (2) 2.04 1.43 . .../continued Table 17, continued C(10)-C(6)-C(7) 109(2) C(6)-C(7)-C(8) 106(2) C(7)-C(8)-C(9) 108(2) C(8)-C(9)-C(10) 108(3) C(9)-C(10)-C(6) 109(2) Side Chains: C ( l ) - C ( l l ) 1.47(3) N-C(ll) 1.51(3) N-C(12) 1.50(4) N-C(13) 1.53(3) C( 2 ) - C ( l ) - C ( l l ) 127(2) C(5)-C(l)-C(;ll) 124(2) C ( l ) - C ( l l ) - N 109(2) C(X1)-N-C(12) 110(2) C(ll)-N-C(13) 112(2) C(12)-N-C(13) 111(2) Tetrachlorozincate group: Zn-Cl(1) = 2.299 (7) Cl(1) Zn-Cl (2) = 2.270 (8) C l ( l ) Zn-Cl(3) = 2.229(7) C l ( l ) Zn-Cl(4) = 2.274 (7) Cl(2) Cl(2) Cl(3) 106(2) 108 (3) 111 (3) 109 (2) 106 (2) Mean = 108 1.49(3) 1.53(3) 1.48(3) 1.54 (3) 123 (2) 127 (2) 110 (2) 114(2) 110(2) 111(2) Zn--Cl(2) = 105 -2(3) Zn--CK3) = 110 .2 (3) Zn--ci(4) = 110 .6 (3) Zn--Cl(3) = 111 .1(3) Zn--Cl (4) = 110 .7(3) Zn--Cl(4) = 109 .0(3) 99 Table 18 Equations of mean planes, i n the form JIX1 + mY' + nZ 1 where X 1, Y1 and Z' are coordinates i n ft referred to orthogonal axes a, b and c*. = P Atoms i n plane Cation 1: 1 C(l)-C(5) 2 C(6)-C(10) Z m n max. p d i s p l . (ft) 0.6056 0.6440 0.4673 5.5153 0.010 0.5725 0.6704 0.4720 8.6592 0.005 Cation 2: 3 C(l)-C(5) -0.3197 0.2112 0.9237 1.9555 0.006 4 C(6)-C(10) -0.3202 0.2127 0.9232 5.2432 0.006 Angles between plane normals; 1 - 2 2.4° 3 - 4 0.1° Figure 10 Views of the cyclopentadienyl rings normal to t h e i r planes. Heavier l i n e s are nearer the viewer.  Figure 11 Packing diagram viewed along the c crystallographic axis. 103 104 RESULTS AND DISCUSSION The c r y s t a l analysis has confirmed the formulation of the compound as the tetrachlorozincate, and precludes any p o s s i b i l i t y of N->Zn coordination. The lack of absorption i n the NH+ stretching region (3.8-4.2u) for the 2 8 c r y s t a l l i n e compound i s probably related to the strong hydrogen bonding from N-H to 0 and Cl (discussed below). As shown i n the packing diagram (Figure 11), the structure i s composed of 'ionic layers' p a r a l l e l to (100) -2 which contain the ZnCl^ groups; the nitrogen-containing side chains are directed into the layers, with the Fe- hydrocarbon portions between layers. Within the io n i c layers groups of four cations, two anions and two water molecules (two formula units) are linked around centres of symmetry by N-H...C1 (3.11 ft), N-H...0 (2.76 ft), and O-H... Cl (3.05, 3.17 ft) hydrogen bonds as i l l u s t r a t e d i n Figure 12. The layer i s extended i n the (100) plane by weaker C...C1 interactions ranging upwards i n length from 3.56 ft (Table 19). These involve primarily the N-methyl carbon atoms of adjacent side chains. The shortest contact between layers i s C C = 3.65 ft. The two chlorine atoms which are hydrogen bonded to the water molecule subtend an angle of 127° at the oxygen atom so that the hydrogen atoms of the water molecule are most probably.directed not far from the O...C1 vectors. Figure 12 -2 The environment of a ZnCl^ group, which shows the hydrogen bonding around a centre of symmetry.  107 Table 19 A l l c r y s t a l l o g r a p h i c a l l y independent distances < 3.7 ft between atoms i n d i f f e r e n t asymmetric units. Cation 1 Atom 1 to Atom distance (ft) 0 . . . .H - N ( l ) 1 1 1 2.76 0 - H . . . C1(2) T 3.05 0 - H . . . C l ( 4 ) 1 1 3.17 C l ( l ) . . H - N ( 2 ) I I 3 : 3.11 C l ( l ) . . . . ^ ( 1 3 ) ™ 3.56 C l ( l ) . . . . C 2 ( 1 3 ) 1 1 1 3.65 Cl(:3) . . . . C 1 ( l l ) 1 3.67 Cl(4) . . . . c 2 ( i i ) I i : E 3.67 cx{9). . . . C 2 ( 9 ) V 3.65 C 1 (12) . . . C 2 ( 1 3 ) I V 3.53 C 2(12) . . . C 2 ( 1 0 ) V I 3.46 C 2 (2) . . . C 2 ( 6 ) V I 3.57 . 2 Cation 2 I II III IV V VI x - x . - x x 1 + x X y i - y h + y h - y y h - y z - z h - z h + z z •h + z 108 The N...O...C1 angles are 97° and 1 2 1 ° , and the C-N...0 and C-N...C1 angles are very close to the tetrahedral value at 109°, 105° and 1 1 0 ° , and 107°, 117° and 98° respectively. The extent to which the chlorine atoms take part i n hydrogen bonding i s r e f l e c t e d i n the Zn-Cl bond lengths (Table 17). Cl(2) and Cl(4) each in t e r a c t with an oxygen atom at distances of 3.05 and 3.17 X respectively, and have similar Zn-Cl lengths (2.270 and 2.274 ft r e s p e c t i v e l y ) . C l ( l ) i s hydrogen bonded to a nitrogen atom at 3.11 ft, and the corresponding Zn-Cl distance i s somewhat longer (2.299 ft), while Cl(3) has no contacts less than 3.6 ft, and i s involved i n the shortest Zn-Cl distance (2.229 ft). A si m i l a r -2 si t u a t i o n has been reported for the ZnCl^ groups i n the 34 L ^ Z n C l ^ • 2H2O structure .. Two hydrogen bonds to one chlorine atom lengthen the Zn-Cl distance to 2.30 ft, and a single i n t e r a c t i o n for two other chlorine atoms r e s u l t i n lengths of 2.28 ft, while the chlorine atom which i s not involved i n hydrogen bonding has the shortest Zn-Cl distance of 2.25 ft. These values may be compared with the normal 35 distance for covalent tetrahedral zinc-chlorine bonds of 2.30 ft. Comparable Zn-Cl distances have been reported for 3 6 the three modifications of ZnCl 2 , and for several related 37-39 compounds The; iron atoms are sandwiched between two cyclo- pentadienyl rings which are planar within experimental error (Table 18), approximately p a r a l l e l , and separated by 109 3.28 ft (cf. r e f . 40). The rings are nearly eclipsed as shown i n Figure 10, and can be described i n terms of the rotation of one of the rings from the eclipsed p o s i t i o n as determined by the vectors from each carbon atom to the Fe atoms i n the projection shown. The angles l i s t e d i n Table 20 show that both ferrocene groups d i f f e r by only approximately 7° from the f u l l y eclipsed p o s i t i o n (0°) compared with the f u l l y staggered position (36°) , and are best described as approximately eclipsed. Similar small rotations from the eclipsed p o s i t i o n have been reported for other ferrocene derivatives, for example, 5° i n d i f e r r o - 40 o 41 cenyl ketone , 12 i n a-keto-1,1'-trimethyleneferrocene o 42 and 9 i n 1,1 1-tetramethylethyleneferrocene . The bond lengths and angles i n the cyclopenta- dienyl rings and the side chains do not d i f f e r from 17 expected values (Table 17), and the iron atoms appear to be bound equally to a l l the carbon atoms of the rings, the mean values being Fe-C = 2.04 and C-C (rings) = 1.43 ft. 110 Table 20 Angles from the eclipsed p o s i t i o n for the cyclopentadienyl rings of the cations. Cation 1 C(l)-Fe-C(7) = 6.6 C(2)-Fe-C(8) =7.5 C(3)-Fe-C(9) = 4.4 C(4)-Fe-C(10)= 7.3 C(5)-Fe-C(6) =8.0 Mean = 6.8 Cation 2 C(l)-Fe-C(6) = 11.2 C(2)-Fe-C(10)= 5.5 C(3)-Fe-C(9) = 2.1 C(4)-Fe-C(8) = 6.4 C(5)-Fe-C(7) = 9.7 Mean = 7.0 SUMMARY 112 One of the objects of t h i s work has been to show how the various methods of X-ray d i f f r a c t i o n can be used to overcome the phase problem and deduce c r y s t a l and molecular structure. Although i t i s extremely useful and i n t e r e s t i n g to examine a series of related compounds and to correlate the r e s u l t s i n terms of bonding, intermolecular interactions, etc., i t i s also of value to gain f a m i l i a r i t y with the methods of X-ray crystallography by applying them to as d i v e r s i f i e d a set of problems as possible. Examples have been chosen from organic (natural products), inorganic and organometallic compounds, and, while a l l contained heavy atoms, structure elucidation was not always straightforward because of problems peculiar to each compound. These differences are also r e f l e c t e d i n the f i n a l r e s u l t s ; one involved hydrogen bonding interactions between molecules; others i o n i c coordination to b u i l d up the c r y s t a l network (Ag...O and Ag...C). Since i n t h i s case there can be no continuing of a s e r i e s , and since the analyses have provided answers to the immediate problems proposed, an appropriate project to follow might be the investigation of compounds of higher symmetry, as a l l those studied were either monoclinic or orthorhombic. This would l o g i c a l l y involve mineral or metallic c r y s t a l s , and i s not inconsistent with the author's i n t e r e s t s . REFERENCES 114 1. J. M. 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Hogeveen and M. M. P. Gaasbeek, J . Amer. Chem. S o c , 1969, 91, 2137. 115 13. A. T. McPhail and G. A. Sim, J. Chem. S o c , (B) , 1966, 112. 14. F. H. Al l e n and D. Rogers, Chem. Commun-ic , 1967, 588 and J . Chem. S o c , i n press. 15. M. B. Hossain and D. van der Helm, J . Amer. Chem. Soc., 1968, 90, 6607. 16. D. J. Robinson and C. H. L. Kennard, J . Chem. S o c , (B), 1970, 965. 17. L. E. Sutton, ed. 'Tables of Interatomic Distances and Configuration i n Molecules and Ions', Chem S o c Spec. Publ., No. 11, 1958 and No. 18, 1965. 18. F. S. Mathews and W. N. Lipscomb, J. Phys. Chem., 1959, 63, 845. 19. N. C. Baenziger, H. L. Haight, R. Alexander and . J. R. Doyle, Inorg. Chem., 1966, 5, 1399. 20. R. B. Jackson and W. E. Streib, J. Amer. Chem. S o c , 1967, 89, 2539. 21. D. Britt o n and J. D. Dunitz, Acta Cryst., 1965, 19, 815. 22. P. F. Lindley and P. Woodward, J. Chem. S o c , (A), 1966, 123. 23. J. S. McKechnie, M. G. Newton and I. C. Paul, J. Amer.. Chem. 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