Cristal Structure Dimer Rh Cl COD

8/12/2019 Cristal Structure Dimer Rh Cl COD

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Acta Cryst . (1962) . 15, 923r y s ta l S t r u c t u r e o f t h e D i m e r o f R h o d i u m h l o r i d e 1 5-cyclooctadien e

BY JA MES A. IBER S AND I~OBERT G. SNYD ERS h e l l D e v e lo p m e n t C o m p a n y , E m e r y v il le , C a l i fo r n i a , U . S . A .

Received 11 December 1961)R h o d i u m ( I ) c h l o r i d e 1,5-cyclooctadiene, R hC l ( C sH 12) , c r ys t a l l i ze s i n t he space g r oup C~h-P21/n,w i t h f o u r d i m e r i c m o l e c u l e s in t h e u n i t c e l l o f d i m e n s i o n s

a = 9 . 0 5 , b=25.4 , c = 7 . 2 8 / ~ ; f l = 9 1 . 7 .T h e c r y s t a l s t r u c t u re h a s b e e n d e t e r m i n e d f r o m t h r e e - d im e n s i o n a l P a t t e r s o n a n d d i ff e r en c e F o u r i e rf u n c t io n s a n d h a s b e e n r e f in e d b y l e a s t- s q u a re s t e c h n i q u e s . T h e c o n f o r m a t i o n o f t h e d i m e r i cm o l e c u le s su g g e s te d b y C h a r t & V e n a n z i is c o n fi r m e d . E a c h r h o d i u m a t o m i s b o n d e d t o t h e d o u b l e -b o n d c e n t e r s o f a cyclooctadiene r i n g ( b o a t c o n f i g u r a t io n ) a n d t o t w o c h l o r i n e a t o m s i n s u c h a w a ya s to g i v e i t a s q u a r e - p l a n a r c o n f i g u r a t i o n . T h e b o n d i n g i n th i s c o m p o u n d i s t h u s v e r y d i f f e r e n tf r o m t h a t i n ( R hC I( CO )2 ) 2, i n w h i c h t h e r h o d i u m a t o m s a r e d e s c r i b e d b y D a h l , M a r t e l l & W a m p l e ra s o c t a h e d r a l l y c o o r d i n a t e d . T h e g e o m e t r y o f t h e cyclooctadiene r i n g s i s n o t t o o w e l l d e f i n e d i n t h ep r e s e n t s t u d y . N e v e r t h e l e s s t h e l e n g t h e n i n g o f t h e d o u b l e b o n d s f r o m a ' n o r m a l ' v a l u e o f 1 .3 4 At o 1 . 4 4 _ 0 . 07 / ~ i s s i g n i f i c a n t , a n d i s c o n s i s t e n t w i t h e v i d e n c e b a s e d o n t h e i n f r a r e d s p e c t r a o f t h ec o m p o u n d a n d o f 1,5-cyclooctadiene.

I n t r o d u c t i o nT h e p r e s e n t d e t a i l e d i n v e s t i g a t i o n o f t h e m o l e c u l a ra n d c r y s t a l s t r u c t u r e o f r h o d i u m ( I ) c h l o r i d e 1 ,5 -cyc looc tad iene w a s u n d e r t a k e n f o r t w o m a i n r e a so n s .F i r s t , D a h l , M a r t e l l & W a m p l e r ( 19 61 ) r e p o r t e d a nu n e x p e c t e d s t r u c t u r e f o r ( R hC I (C O )2 )~ , i n w h i c h e a c hr h o d i u m i s d e s c r i b e d a s o c t a h e d r a l l y c o o r d i n a t e d .T h e c lo s e p a r a l l e l is m b e t w e e n t h e p h y s i c a l p r o p e r t ie so f o l ef i n c o m p l e x e s a n d c a r b o n y l h a l i d e s o f t r a n s i t i o nm e t a l s h a s f r e q u e n t l y b e e n n o t e d , a n d , i n f a c t, C h a t t& V e n a n z i ( 19 5 7) r e m a r k o n t h i s p a r a l l e l i s m i n t h ec a s e o f ( R h C l ( C O ) 2 ) e a n d r h o d i u m c h l o r i d e 1,5-cyclo.o c t a d ie n e . W e t h u s t h o u g h t i t o f i n t e r e s t to i n v e s t i g a t et h e s t r u c t u r e o f r h o d i u m c h l o ri d e 1,5-cyclooctadiene,e s p e c i a l l y s i n c e w e w e r e u n a b l e t o v i s u a l i z e a s t r u c t u r ei n w h i c h t h e r h o d i u m a t o m s w e r e o c t a h e d r a l l y c o -o r d i n a t e d . A s e c o n d r e a s o n f o r t h e p r e s e n t i n v e s t i g a -t i o n w a s to a t t e m p t t o a n s w e r t h e q u e s t i o n : H o ww e l l c a n c a r b o n r i n g g e o m e t r y b e d e f i n e d i n th ep r e s e n c e o f s e co n d - r ow t r a n s i t i o n m e t a l s , i f i n t e n s i t yd a t a c o l le c t ed a t ro o m t e m p e r a t u r e a n d e s t i m a t e dv i s u a l l y a r e u s e d ? P r e v i o u s s t u d i e s ( e. g. , B a e n z i g e r ,D o y l e , R i c h a r d s & C a r p e n t e r , 1 96 1) h a v e r e v e a l e dt h a t u n d e r t h e s e c o n d i t io n s t h e r i n g g e o m e t r ie s a r ed i f f i c u l t t o d e f i n e a c c u r a t e l y , b u t s i n c e s u c h s t u d i e si n g e n e r a l d i d n o t t a k e a c c o u n t o f a n i s o t r o p y i n t h et h e r m a l v i b r a t i o n s o f t h e h e a v y a t o m s i t w a s n o t c l ea rt o u s w h e t h e r s u c h p o o r d e f i n i t i o n r e s u lt s f r o mi n a d e q u a c i e s i n t h e d a t a o r in t h e t h e o r e t i c a l m o d e l .I n a p r e l i m i n a r y c o m m u n i c a t i o n ( I b e r s & S n y d e r ,1 96 2) w e i n d i c a t e d t h a t t h e c o n f o r m a t i o n o f t h e

Presen t address : De par tme nt o f Chemist ry, BrookhavenNat ional Laboratory , Upton , L .I . , New York .

r h o d i u m c h l o r i d e 1 , 5 -c y c l o o c ta d i e n e d i m e r i c m o l e c u ls u g g e s t e d b y C h a t t & V e n a n z i ( 19 5 7) is c o r r e c t : e a c hr h o d i u m a t o m i s i n a s q u a r e - p l a n a r c o n f i g u r a t i o nI n t h e p r e s e n t p a p e r w e p r e s e n t t h e d e t a i l s o f o u rs t u d y , d e f i n e m o r e t h o r o u g h l y t h e s tr u c t u r e , a n di n d i c a t e t h a t t h e r i n g g e o m e t r y i s d i f f ic u l t t o d e f i n ee v e n w h e n a n i s o t r o p i c t h e r m a l m o t i o n s o f t h e h e a v ya t o m s a r e i n c o r p o r a t e d i n t o t h e t h e o r e t i c a l m o d e l .

U n i t c e l l a n d p r o b a b l e s p a c e g r o u pT h e c r y s t a l s of r h o d i u m c h J o r id e 1,5-cyclooctadieneu s e d i n t h e p r e s e n t s t u d y w e r e k i n d l y p r e p a r e d b yD . W . B a r n u m o f th e s e l a b o r a t o r ie s b y t h e r e a c t i o no f r h o d i u m c h l o ri d e t r i h y d r a t e w i t h t h e d i e ne , a sd e s c r i b e d b y C h a r t & V e n a n z i ( 19 5 7) . T h e d e e py e l l o w c ry s t a l s e x h i b i t a t a b u l a r h a b i t . O n t h e b a s i so f c a li b r a t e d p r ec e s s io n p h o t o g r a p h s t a k e n w i t h M o K ar a d i a t i o n R h C I ( C s H l e ) c r y s t a l l iz e s i n a m o n o c l i n i c c e lo f d i m e n s i o n s

a = 9 -0 5 _ + 0 0 5 , b = 2 5 . 4 _ 0 . 1 , c = 7 . 28 + _ 0 . 0 5 A ;fl = 91 .7 +__0.2 .

T h e o n l y s y s t e m a t i c a b s e n c e s o b s e r v e d o n o v e r -e x p o s e d p r e c e s s io n p h o t o g r a p h s o f t h e hkO a n d hOz o n e s a n d o n W e i s s e n b e r g p h o t o g r a p h s o f t h e h k lt h r o u g h h k 6 z o n e s w e r e : 0 k 0 , k o d d ; h O 1, h + l o d d .T h u s t h e s p a c e g r o u p i s p r o b a b l y C~I~-P21/n, a n d ar e a s o n a b l e s t r u c t u r e h a s b e e n f o u n d o n t h i s a s s u m p -t i o n .A d e n s i t y o f 1 . 9 3 _ + 0 .0 2 g . c m . - 3 w a s m e a s u r e dp y c n o m e t r i c a l l y . W a t e r , w i t h a s m a l l a m o u n t o fA e r o s o l O T 7 5 % w e t t i n g a g e n t a d d e d , w a s u s e d a s

A C 15-- 60


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924 S T R U C T U I ~ E O F T H E D I M E R O F R H O D I U M C H L O I ~ I D E 1 5 - CY CL O O CT AD I ENEt h e p y c n o m e t r i c f lu i d . T h e c a l c u l a t e d d e n s i t y f o r e ig h tm o n o m e r m o l e c u le s o f m o l e c u l a r w e i g h t 2 4 7 i n t h eu n i t c e l l i s 1 . 9 5 g . c m . - ~ .H e n c e t h e s o l u t i o n o f t h e s t r u c t u r e i n v o l v e s t h el o c a t io n o f t w o r h o d i u m , t w o c h l o ri n e , a n d s i x t e e nc a r b o n a t o m s ( a n d , o f c o u r se , i d e a l l y t h e t w e n t y - f o u rh y d r o g e n a t o m s ) .

o l l e c t io n a n d r e d u c t i o n o f i n t e n s i t y d a t aA c r y s t a l o f a p p r o x i m a t e d i m e n s i o n s 0 -0 6 0. 0 2 0 .0 0 3c m . w a s c h o s e n f o r t h e i n t e n s i t y w o r k . T h e u s e o f ac r y s t a l o f t h i s s i ze i s a r e a s o n a b l e c o m p r o m i s e b e t w e e np o s s ib l e a b s o r p t i o n e r r or s a n d c o n v e n i e n t e x p o s u r et i m e s ( M o K c~ r a d i a t i o n ) . W i t h a p r i s m a t i c c r y s t a lt h e p o s s i b i l i ty e x is t s t h a t t h e a b s o r p t i o n c o r re c t io n st o p a r t i c u l a r i n t e n s i t i e s m a y b e l ar g e , e v e n t h o u g ht h e a v e r a g e v a l u e o f /~ R i s s m a l l ( a b o u t 0 .3 h e r e )a n d t h e a n g u l a r r a n g e o f t h e d a t a l i m i t e d ( 0 _< 2 3 h e re ) . T h e r e a s o n a b l e n e s s o f t h e a n i s o t r o p i c t h e r m a lp a r a m e t e r s o f t h e h e a v y a t o m s ( se e be lo w ) is ta k e na s a n i n d i c a t i o n t h a t a b s o r p t i o n e r r o r s w e re n o ts e r i o u s .S i n c e l ~ h C l( C s H 1 2) i s s t a b l e , t h e s e l e c t e d c r y s t a l w a ss i m p l y a t t a c h e d t o a q u a r t z r o d w i t h s i l ic o n e g r e as ea n d m o u n t e d i n a ir . D a t a f o r t h e hkO t h r o u g h hk6z o n es w e re c o l l e ct e d a t ro o m t e m p e r a t u r e b y t h ee q u i - i n c l i n a t io n W e i s s e n b e r g te c h n i q u e w i t h t h e u s eo f M o K a r a d i a t i o n f i l t e r e d t h r o u g h Z r f o il . E x -p o s u r e s o f t h e o r d e r o f 10 0 0 m A - h r , w e r e t a k e n .F o r e a c h e x p o s u r e t h e c a m e r a w a s l o a d e d w i t h t h r e es h e e t s of I lf o r d G I n d u s t r i a l X - r a y f i lm i n t e r l e a v e dw i t h c o p p e r s h e e ts . T h e d a t a w e r e a r b i t r a r i l y l i m i t e dt o t h e r e f l e c t i n g s p h e r e 2 - 1 s i n 0 _< 0 . 5 5 A - 1. T h er a t io o f t e m p e r a t u r e - m o d i f i e d a t o m i c s c a t t e r i n g f a c-t o r s o f R h : C 1 : C i s a b o u t 3 0 : 6 : 1 o n t h i s s p h e r e ;w e f e lt t h a t d a t a b e y o n d t h i s p o i n t w o u l d c o n t r i b u t eo n l y t o t h e b e t t e r r e s o l u t i o n o f t h e h e a v y a t o m s ,p o s s i b l y a t t h e e x p e n s e o f t h e r e s o l u t i o n o f t h e l i g h ta t o m s .T h e i n t e n s i t i e s w er e e s t i m a t e d v i s u a l l y b y c o m p a r -i s o n w i t h a n i n t e n s i t y s t r ip . T h i s s t r i p , w h i c h c o n s i s t e do f t i m e d e x p o s u r e s o f t h e ( 27 0 ) r e f l e c ti o n , h a d a s c a lef r o m 1 t o 8 0 , w i t h 1 b a r e l y v i s i b l e . I n i t i a l l y t h ei n t e n s i t i e s o f o n l y t h o s e r e f l e c t i o n s w i t h i n t h e s p h e r e2 -1 s i n 0


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J A M E S A . ] [ B E R S A N D ~ O B E I ~ T G . S N Y D E ~ 9 2t u r e i s t h a t p r o p o s e d b y C h a r t & V e n a n z i ( 1 9 57 ),a n d d e s c r i b e d b e l o w ( F i g . 1 ) .

e f i n e m e n t o f t h e s t r u c t u r eR e f i n e m e n t o f t h e s t r u c t u r e w a s c a rr i e d o u t a l m o s te n t i r e l y b y l e a s t - s q u a r e s t e c h n i q u e s . S i n c e n o r e fl e c-t i o n s w e r e o b s e r v e d i n d e p e n d e n t l y m o r e t h a n o n c et h e w e i g h t i n g s c h e m e s u g g e s t e d p r e v i o u s l y ( I be r s,1 9 5 6) c o u l d n o t b e e m p l o y e d ; r a t h e r , a s c h e m ed e s i g n e d to b e a s m o o t h e d a p p r o x i m a t i o n t o w e i g h t ( F )i n v e r s e ly p r o p o r t i o n a l t o t h e v a r i a n c e ( F ) w a s a d o p t e d .T h e s c h e m e a l l o t t e d c o n s t a n t w e i g h t f o r F _ 3 5 Fm l n,a n d w e i g h t p r o p o r t i o n a l t o F - 2 f o r F > 3 5 F m in . T h i si s e s s e n t i a l l y t h e s c h e m e d e v i s e d b y H u g h e s ( 19 4 1 ).A l t h o u g h d i f fe r e n t, ' r e as o n a b l e ' w e i g h t i n g s c h e m e sm a y r e s u l t i n d i f f e r e n t b o n d d i s t a n c e s , s u c h d i f f e r e n c e sw i l l p r o b a b l y n o t b e s i g n i f i c a n t ( c f. e. g. I b e r s &C r o m e r , 1 9 5 8 ; B a e n z i g e r , D o y l e , R i c h a r d s & C a r p e n -t e r , 1 9 6 1 ). R e f i n e m e n t s w e r e b a s e d o n F , n o t F 2 a n do n o b s e r v e d r e f le c t i o n s o n l y . T h e B u s i n g - L e v y ( 1 95 9 a )l e a s t- s q u a r e s p r o g r a m f o r t h e I B M 7 0 4, w i t h s p e c i a lp a t c h e s a s n e c e s s ar y , w a s u s e d w i t h t h e ' C o m p a t i b i l i t yP a c k a g e ' o n t h e I B M 7 0 90 . I n th i s w a y a b o u t at h r e e f o l d a d v a n t a g e i n s p e e d is r e a l i z e d o v e r c a l c u l a -t i o n s o n t h e 7 0 4 . I n t h e p r e s e n t c a s e o n e c y c l e o ff u l l - m a t r i x l e a s t - s q u a r e s ( 8 0 0 d a t a , 8 7 p a r a m e t e r s ,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 ) r e q u i r e s a b o u t 8 r a in .o f m a c h i n e t i m e .

F o r t h e c a l c u l a t i o n o f s t r u c t u r e f a c t o r s t h e a t o m i cs c a t t e r i n g f a c t o r s f o r R h , C 1, a n d C of T h o m a s &U m e d ~ ( 19 5 7 ), D a w s o n ( 19 6 0 ), a n d H o e r n i & I b e r s( 1 95 4 ) w e r e u se d . A c o r r e c t i o n f o r a n o m a l o u s d i s p e rs i on w a s a p p l ie d t o t h e r h o d i u m a t o m s c a t t e r i n g f a c to( T e m p l e t o n , 1 9 6 2 ) .

T h e i n i t i a l r e f i n e m e n t w a s b a s e d o n a l l o f t h eo b s e r v e d r e f le c t i o n s , o n s e p a r a t e s c a le f a c to r s f o r t hi n d i v i d u a l z o n e s, a n d o n i n d i v i d u a l i s o tr o p i c t h e r m ap a r a m e t e r s f o r a l l a t o m s . T h u s t h e r e w e r e 8 7 p a r a m -e t e r s to b e d e t e r m i n e d f r o m t h e 7 7 9 n o n - z e r o r e fl e ct i o n s . ( T h e p r es e n c e o f h y d r o g e n a t o m s i n t h e s t r u c t u r ew a s i g n o r e d i n t h i s a n d i n s u b s e q u e n t r e f i n e m e n t s .T h i s r e f i n e m e n t c o n v e r g e d a f t e r s e v e r a l c y c l es t o s t r u c t u r e i n w h i c h t h e C - C s i n g le b o n d s r a n g e d f r o m1 .2 t o 1 . 8 J~ i n l e n g t h . A d i f f e r e n c e F o u r i e r , i n w h i c ht h e F c o f t h e h e a v y a t o m s w e r e s u b t r a c t e d f r o m F ow a s t h e n c a l c u l a te d . T h e c a r b o n a t o m p o s i t io n s ot h i s d i f fe r e n c e F o u r i e r w e r e fa r b e t t e r r e s o l v e d t h a nt h e y w e r e o n t h e i n i t i a l d i f f e re n c e F o u r i e r . T h e g e n e r aa g r e e m e n t b e t w e e n t h e s e p o s i t i o n s a n d t h o s e o f t hl e a s t - s q u a r e s w a s n o t t o o g o o d ; s o m e p o s i t i o n s d ev i a t e d b y a s m u c h a s 0 3 ~ f r o m t h e l e a s t - s q u a r ep o s i t io n s . * C o n t r a r y t o t h e e x p e r i e n c e o f o t h e r

* T h e p e a k c e n t e r s w e r e c a l c u l a t e d w i t h t h e u s e o f aI B M 7 0 9 0 p r o g r a m b a s e d o n t h e 27 p o i n t l e a s t - s q u a r e s m e t h oo f S h o e m a k e r et al ( 1 95 0 ). S i n c e t h e g r i d s p a c i n g w a s a b o u0 2 /it a n d s i n c e t h e p e a k s o v e r l a p s l i g h t l y , t h e u n c e r t a i n t y it h e p o s i t i o n s o f t h e p e a k c e n t e r s is p r o b a b l y a b o u t 0 . 1 A

T a b l e 1 . A t o m i c p a r a m e t e r s f o r ( R h C I ( C s H l e ) ) 2 *A t o m x a x ) y a y ) z a z ) B a B )

R h 0.3894 0.0004 0.3248 0.0002 0.4347 0.0005 2.21 0.10R h ' 0.6419 0.0004 0.4137 0.0001 0.6342 0.0005 2-39 0.10C1 0.4242 0-0015 0.3677 0.0006 0.7225 0.0018 3-71 0.30CI ' 0.6241 0.0014 0.3605 0.0006 0.3645 0.0020 3.81 0.301 0.394 0-006 0.265 0.002 0.236 0-008 4.8 1.42 0.318 0.004 0.314 0.002 0.164 0.006 2-0 0.93 0.154 0.008 0.327 0.003 0-119 0.010 7.3 1.84 0.080 0.007 0.317 0.003 0-286 0-010 6-5 1.75 0.155 0.006 0-317 0-002 0-487 0.008 4.4 1.26 0.238 0.005 0.272 0.002 0.544 0.007 3-1 1.07 0.236 0-005 0.215 0.002 0.440 0-007 3.4 1.18 0.299 0.005 0.219 0.002 0.270 0.007 3.3 1.11' 0.870 0.005 0.431 0.002 0.597 0.008 3-6 1.22' 0.787 0.006 0.468 0.002 0.510 0.009 4.7 1.33 0.773 0.007 0.526 0.002 0.600 0.009 5.5 1.54' 0.649 0.010 0.529 0.004 0.753 0.015 10.8 2.85' 0.595 0.005 0.474 0-002 0.831 0.007 2.8 1-06' 0.695 0-005 0.436 0.002 0.912 0.007 3.4 1.27' 0.858 0.006 0.439 0.002 0.954 0-009 4.9 1.48 0.925 0.006 0.438 0.002 0.790 0.009 5.2 1-5

A t o m #11 U( #ll ) #22 (7( #2 2) #33 (~( #3 3) #12 (Y(#12) #13 (Y(#13) #23 (Y(~23R h 0 0 0 5 6 0 0 0 0 4 0 0 0 1 0 0 0 0 0 1 0 0 1 0 5 0 0 0 0 8 - - 0 0 0 0 1 0 0 0 0 2 - - 0 0 0 0 3 0 - 0 0 0 5 - - 0 . 0 0 0 1 0 0 0 0 2l~h ' 0.0077 0.0005 0.0009 0-000 t 0-0113 0.0009 --0.00 04 0.0002 --0.00 03 0.0005 -- 0.0001 0.0002CI 0.0146 0.0021 0.0016 0.0003 0.0121 0.0032 --0.0 024 0.0006 0-0018 0.0019 --0.00 12 0-0007CI ' 0.0124 0.0020 0.0014 0 0003 0.0201 0 003 8 -- 0.0010 0.0006 0.0031 0.0020 -- 0.0010 0.0008

* T he po s i t i ona l pa r a m e t e r s o f aU t he a t om s a nd t h e a n i s o t r op i c t he r m a l pa r a m e t e r s o f the he a vy a t om s a r e ba s e d on t ha n i s o t r op i c r e f i ne m e n t i n w h i c h t he i s o tr op i c t he r m a l pa r a m e t e r s o f t he c a r bon a t om s g i ve n he r e w e re he l d c ons t a n t . T he i s o t ropt he r m a l pa r a m e t e r s o f t he he a vy a t om s g i ve n he r e a r e t hos e de r i ve d f r om t he i s o t r op i c r e f i ne m e n t .


4/8

9 2 6 S T R U C T U R E O F T H E D I M E R O F R H O D I U M C H L O R I D E 1 5 - C YC L O O C T A D I E N Ee.g. l~ossmann e t a l . , 1959) the thermal parametersof the misplaced carbon atoms were not significantlylarger than the average. A final refinement withisotropie thermal parameters and the carbon atomsrelocated in accordance with the positions of thedifference Fourier converged rapidly to a structurewith more reasonable bond distances. The value ofthe R factor, ~ l F o - f F o [ J / ~ F o ) , was 0-101 for the

779 non-zero reflections; the error of fit functionX W F o - - J F c J )~ / m - n ) ) had the value 7.15.The difference Fourier provided evidence that theheavy atoms, particularly the chlorine atoms, werevibrating anisotropically. On the assumption that

proper account of such motion would lead to impr ovedpositions for the carbon atoms, a refinement based onanisotropic thermal parameters of the heavy atomswas attempted. The first attempt, in which thepositional parameters of all the atoms, the six in-dependent thermal parameters of each of the heavyatoms, and the scale ~aetors were varied, was un-successful: physica lly unreasonable shifts in the scalefactors were obtained. We had failed to realize thatsince the scale ~actors and the ~s of the heavy atomsdepend only upon l, and since the heavy atoms arethe principal contributors to the structure amplitudes,the least squares matrix of normal equations is nearly

Table 2. Obs e r ve d a nd c a l c u l a t e d s t r uc t u r e f ac t o r sK o 5 5 C At . I ~ X 0 8 S C ~ t . ~ < 0 8 S C At . ~ K O ~ S C ~ t . ~ ~ 0 8 S C a ' , ~ ~ O ~ S C ~ " 0 ~ C ' t .

e e e e e l - l O e l e e e e O o I I L I e l I I e l ~ o l 0 5 1 o a .~ 0 0 6 1 0 1 0 8 0 6 1 0 0 5 9 - 0 6 2 5 2 1 0 6 0 ~ 0 7 5 1 1 0 1 1 2 - 1 1 00 o o A 8 T I , 2 I O 0 B - O , Z O l O S l 0 6 , 1 0 6 0 , , 0 . 1 6 I 1 1 2 , 0 2 3 1 I 2 2 0 5 6 - 0 5 , ~ z n 0 6 8 0 6 542 . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . 2 . . . . . . . . ~ ....... . 2 . . . . . . . . . . . . . . . . . .o o 2 9 9 - 2 9 9 o o 0 , 8 - 0 , 7 5 0 l 0 , 8 0 2 9 . 1 0 6 0 ~ .5 0 , ~ 1 1 1 5 0 - 1 5 1 . 2 k 0 5 9 0 5 1 I 1 1 0 8 0 - 0 8 98 o o 1 0 , 0 9 , 7 o o 1 0 3 0 9 8 6 0 l 0 5 1 . - 0 , 8 q 0 6 1 5 8 - 1 3 3 7 1 1 0 6 6 - 0 7 1 ~ . I I O z . ( , 0 ~ * .1

Ol 100 -116 01 B 073 80l OT, 077 07 ~4~ 188 ~ 12 05~ -058 I O0LR 3 08 12 05, 0,6

o 6 : i : i i . . . . . . . .o 1 0 6 2 7 6 0 l 0 ~ 5 0 5 5 o ~ o 6 5 - 0 ? 20 2 - 0 5 6 0 0 2 - 0 7 0 0 3 1 6 " 1 6 3 6 0 7 0 6 2 - 0 8 6 0 9 5 - 1 0 8 O 1 1 0 8 1 0 2 0 7 9 0 8 1O Z 0 5 9 - 0 4 7 0 2 8 - 0 7 1 6 o i 0 5 ~ 0 5 9 0 7 0 6 7 - 0 5 7 1 0 Z - 1 0 ~ * . 1 0 1 0 4 6 0 " 8 5 0 6 1 - 0 6 32 0 2 0 2 6 - 0 1 6 0 2 0 7 6 0 7 6 7 0 1 0 , 9 0 5 8 9 0 7 0 3 9 0 2 5 ~ 1 5 0 7 2 0 7 2 z ,. 0 1 0 6 8 0 8 1 6 ~ . , 0 5 3 - 0 5 31 0 2 o , 1 0 5 6 5 0 Z 0 5 6 0 6 7 I 0 z ~ 0 7 - 0 8 0 O 0 8 1 2 6 - 1 1 6 1 6 0 5 5 - 0 ~ ' 6 0 1 O S T - 0 6 7 2 5 0 6 9 0 6 90 2 0 , 9 0 5 2 0 2 0 = 7 0 - 0 5 6 1 , 6 1 2 , 08 i ~ I i i , 1 8 0 6 0 0 5 ~ 1 0 . 1 0 7 7 ~ 1 6 0 4 9 - 0 * 57 0 2 0 ' 5 - 0 4 5 0 0 1 - 1 7 7 Z . 0 ( , 1 8 ~ - 1 7 2 3 0 8 0 7 9 - 0 8 6 4 1 9 0 7 6 0 7 9 0 3 1 0 5 - 1 0 ( , 3 1 7 1 0 8 - 1 1 1

. . . . ~ . . . . ~ 03 98 . . . . . 00~ . . . . . . z . . . . . . . . . 23 . . . . . . . . . . . . . . . . . . . 0 . . . . . . . .I o ~ - 1 7 6 o .1 o . 1 - o m s 6 IO O .116 5 0 8 0 8 0 - 0 8 2 2 0 0 5 2 0 6 0 5 0 ~ 0 7 8 - O B ? 1 8 0 ( , 8 - 0 4 905 088 08.1 k 03 102 12~ 1 5 030 -025 0 09 133 120 21 079 076 151 -178 1 20 061 -06,. . . . . . . . . ~ . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . o ~ . . . . . . ~ . . . . . . . .

6 ~ 0 3 1 0 7 1 1 6 o , 0 6 5 - o 5 9 " * o 5 o 6 9 0 7 0 o 9 1 1 , - 1 0 3 8 o 8 8 0 5 9 2 1 o 6 8 - o 5 ( ,o , 0 7 9 0 0 ~ 0 0 4 1 9 , - 2 5 5 6 0 5 0 4 5 - 0 4 5 5 0 9 0 7 7 0 7 1 ~ e e e e L l S e e e e 1 0 5 1 3 2 1 1 1 2 1 0 6 4 - 0 6 69 o, o 6 6 - o 5 9 z o, 1 6 , . - 1 , 5 T os o 9 2 o e ~ , , 0 9 1 2 5 - 1 ~ o ~ o o e - 2 o 9 . 1 o~ o 5 , - o 7 60 o , 8 - 1 , 7 o , 1 9 5 - 1 6 9 1 0 7 0 " *1 0 , 9 5 0 9 0 7 9 0 7 5 o o 0 2 0 6 1 , o s 0 6 2 - 0 7 0 * * * * * c . - - ~ * * * *00: 98 . . . . . . . . . . . . . . . . . . . . . 6 . . . . . . . . o o l B . . . . . . . . . . . . . . . . . . . . . . .0 o - 0 7 0 " ' 1 0 3 1 1 6 3 0 7 2 5 8 2 0 3 1 0 0 5 9 - 0 6 1 O l 1 8 2 I 0 6 0 9 9 0 8 9 z . O 0 1 , 5 1 5 ~ .5 0 ~ . . . . . . . . . . . . . . . . . . . . . . . . 32 . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . 6 . . . . . . . . . 1 5 2 1 5 1 1 5 0 3 6 - o , o 1 o 8 2 5 2 - 1 9 5 1 o 1 1 8 - 1 2 3 O l 0 ( , 6 o , ~ . o 7 o ~ 6 - 0 5 0 o o 1 1 2 - 0 9 2 '

o ~ 0 6 ~ 0 6 7 5 0 5 0 5 8 0 6 2 t 0 8 0 7 1 - 0 6 2 1 0 0 9 3 0 8 5 9 O 1 0 7 5 0 6 8 5 0 9 8 0 9 1 2 0 1 0 6 ~ 0 6 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . ~ o ? o ~ . . . . . . . . . . . . . . . . . .0 5 0 7 9 - 0 7 7 & 0 5 0 6 6 0 5 3 5 0 8 0 9 6 0 9 8 1 1 0 , 6 - 0 5 1 * I 0 2 - 0 5 1 0 8 O & 3 - 0 , 6 ~ * O 1 0 7 1 0 7 .1. .. . . .. . 10 . .. . . .. . 16 . . . . . .. . . 36 . . . .. . . . . ~ . . . . . . . . . . . . . . . . . . . .. . . .. . . .0 5 0 * 6 - 0 , 7 0 6 1 0 3 1 0 1 0 9 0 ' 0 - 0 1 9 1 1 0 5 1 0 3 8 0 2 0 8 2 0 7 9 " * o e 0 9 2 1 1 2 2 0 2 0 5 6 - 0 6 1o 0 7 2 ~ . . . . . . . . ; . . . . . . . .

OO6 O57 O6 125 -12~. ~ 09 O69 O68 12 O37 O35 O2 I 8 -12 9 08 O5O 0 ~, O3 0~2 -O570 6 0 3 6 0 3 .1 6 0 6 0 4 5 - 0 4 3 ~ * 0 9 0 5 6 0 ~ 9 2 1 2 1 6 6 - 1 ~ 5 0 3 0 3 0 7 0 8 0 7 5 0 6 ~ * 2 0 . 1 1 ' 1 1 5 02 0 6 0 8 0 6 1 9 0 6 1 0 9 0 9 2 6 0 9 0 ~ . 8 0 " T 3 1 2 0 8 ~ * 0 8 " * 32 0 3 1 6 0 1 37 8 0 8 0 8 2 - 0 7 8 , o : 1 , 2 - 1 2 . 13 0 6 0 , 1 0 2 9 I 0 7 2 2 0 1 9 6 1 1 0 0 8 2 0 7 8 , 1 2 0 , 5 - 0 , 2 0 .1 0 7 5 0 8 1 . I 0 9 1 . 1 1 - 1 1 6 6 0(,5 - 0 6 1, 06 0,, -022 2 07 1,I 11, 2 11 169 165 6 12 051 0 5 9 " * 02 O,T 05.1 6 09 057 -060 70 ~ 068 0695 06 05" - 0 5 8 .1 07 055 0 6 2 ' I I 156 -123 42 I~ 153 126 5 0 0~ 0 6 9 - 0 7 6 0 9 0 6 0 0~5 I 0* 128 1 2 81 3 0 ' 6 0 ~ 5 6 O ' 9 - 0 5 . 1 2 1 0 0 5 9 - 0 6 e 2 0 ~ 0 8 0 - 0 6 5o ? 0 6 6 0 5 1 0 7 0 8 7 - 0 6 9 I ~ 1 8 8 1 9 6 1 .1 0 9 0 6 a 0 - 1 9 7 l o 0 6 .9 0 4 8 6 ~ * 0 9 0 - 0 ? 70 7 2 0 2 1 7 , 0 0 8 1 8 6 1 6 5 2 1 2 0 5 0 5 ~ 1 3 0 7 Z . - 0 8 4 1 1 I 1 3 5 1 1 1 3 8 1 , ' * ' ' l z . 3 - 1 2 20 7 0 0 9 - 0 " 1 0 0 0 6 2 0 7 , t . 1 0 , 8 0 2 8 ' 0 ( , ~ 0 ' 2 ~ * 1 1 6 1 0 9 6 l l 1 , 7 - 1 2 , 1 5 l l . 1 0 9 8

06 . . . . . . . . . 3 . . . . . . . . . 143 . . . . . . . ' . . . . . . . . i O0 . . . . . . . . . . . . . . . . . . . . . . . . .o e 1 9 0 - 1 7 , 0 8 0 0 8 - 0 9 S Z O 7 O - O 6 7 4 1 , O 6 7 O 7 O 2 1 8 8 1 7 2 . 1 1 2 1 2 1 l O S ~ . 0 5 0 8 .1 - 0 ~ 71 0 8 196 1 6 0 5 0 8 0 , 4 0 3 8 1 , 0 5 1 - 0 5 1 0 1 5 1 0 ' - l O ~ * 0 5 1 6 8 - 1 3 9 5 1 2 O 9 2 - 0 8 0 5 0 5 O 5 7 - 0 5 73 O 8 O 9 4 O 8 6 8 O 8 O 5 5 O ~ * S ~ 1 5 0 ~ . 1 - 0 , 1 . 1 1 5 O S 6 O 6 2 23 O 5 O 3 2 - 0 , 1 7 1 2 o 8 9 - o 7 9 6 o 5 o ~ .5 - o z . ,, * 0 8 1 2 9 1 0 9 l O O 9 0 5 2 - 0 7 3 1 5 O 6 7 - O T , , l S O 5 9 O 7 , O5 O 5 6 0 ~ 1 Z 1 . 1 0 ' . 0 O 3 6 I O 6 O 6 O -0 5 ~, 08 090 -086 09 038 00 3 15 172 -1,8 I 16 063 -098 z. 05 139 -13,. I/* 079 -089 2 O6 I16 111. . . . . . . . . . . . . . . . . . . 76 . .. .. .. . . .. .. .. .. 85 . .. .. .. . ~ ~ . .. .. . ~ . .. .. .. .z . 0 9 0 , 9 - 0 8 8 , 0 9 0 7 0 0 7 5 1 5 0 6 9 0 7 1 0 1 8 0 5 8 0 5 6 0 5 0 6 9 0 7 6 0 6 ~ 0 5 7 0 " 7 0 6 9 - 0 6 6O 9 o ~ . . . . . . . . . . . . ~ . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I 0 0 1 5 I I 0 0 , 8 - 0 5 7 1 6 o 9 3 - 1 0 5 l e 0 6 8 - 0 6 7 . 1 0 6 1 . 1 9 - 1 2 ~ 2 i s o 5 6 - o s ? 6 o 7 0 5 6 o 6 0

1 0 0 4 8 0 5 7 1 0 0 6 0 - 0 6 0 6 1 6 0 6 6 0 7 0 1 9 0 , 9 0 5 2 0 6 o 7 5 o 9 2 1 5 o 6 8 0 7 1 . o 8 0 " * l - 0 ' *1 1 1 0 8 1 0 7 9 4 l O 0 6 6 - 0 6 7 2 1 8 0 5 1 o 8 o 2 2 1 0 5 2 - 0 5 0 0 0 7 0 ~ 5 0 3 2 ~ , 1 6 1 0 6 - 0 9 5 5 0 8 0 9 1 0 8 63 1 1 1 1 7 - 1 2 1 ~ 1 0 0 5 5 O aO 3 19 0 9 3 093 2 2 2 0 6 6 - 0 5 7 ~ O 7 0 8 2 0 7 3 1 1 9 O 7 2 - 0 7 1 2 0 9 0 . 1. 1 - O 3 8z . 1 1 0 , 9 - 0 1 . 4 6 1 0 0 9 1 . 0 8 8 ~ * 1 9 O 6 5 0 7 , ~ 2 . 1 0 7 0 - O 6 " 0 7 O 6 O - 0 5 9 ~ 1 9 O 5 2 - 0 , ~ i 1 1 o 6 8 o 7 o5 1 1 0 2 .2 - 0 2 . 2 8 l O 0 6 9 0 7 3 ~ 2 0 0 7 8 - 0 7 8 2 7 0 7 ~ * - 0 8 1 " * 7 0 7 8 - 0 9 0 1 9 0 8 2 0 7 8 7 l l 0 6 5 - 0 6 91 1 0 6 0 o 6 2 0 l l 1 , 6 1 , 5 2 0 O , 9 0 5 6 5 0 7 0 ~ 6 - 0 6 2 . 1 2 2 0 2 7 0 7 I I 1 2 0 . 18 - O ' 212 1 5 6 1 ' 5 3 2 1 1 l Z * . 1 - I k 7 ~ 20 0 6 7 0 6 9 e * * * e L e - 2 * e * e 0 0 8 1 , 5 1 5 8 2 2~ 0 9 1 0 8 5 2 1 2 0 3 8 O z . '12 0 9 8 0 8 6 11 0 5 8 - 0 2 6 2 2 0 6 3 0 7 8 2 O 0 B 0 8 0 I 0 8 0 5 6 0 6 . 1 ~ * 12 0 5 4 0 6 73 12 O39 051 , Ii 120 -112 8 22 071 -072 a oo 05, -0,6 ~ 08 050 -0~ 8 e**etL-+~*eeee l ~ 05, -0634 1 2 1 5 7 - 1 4 5 ~ I I 0 5 9 0 6 0 2 .1 0 9 1 - 0 9 1 ~ O 0 1 1 0 - I 1 5 0 8 0 7 2 0 5 9 : 0 O 0 B - 0 9 1 ~ 0 5 0 - 0 6 .18 1 2 0 6 6 O 6 5 1 2 0 , 8 0 5 5 1 2 ~ 0 5 5 0 5 6 O 0 O 6 6 0 6 7 ~ . O 8 0 " *3 -O 6 5 2 O 0 O 6 8 -0 7 . 1 1 5 0 8 0 O 8 8. . . . . . . . . . . . . . . . . . . 3~ ol 86 0 5 6 0 . . . . . . . . . . . . . ~ . . . . . . . . . . . . ., 1 5 0 , 8 - O 5 , 1 2 O S " O , 6 * * * * * L = + 2 * * * ~ - 0 1 0 6 O 6 5 O 9 0 6 8 - 0 6 ~ 0 0 Z 1 1 8 6 1 5 O 5 , - 0 5 60 ~ 4 . . . . 7 6 . . . . . . . . . 26 oo 9~ . . . . " ... .... . 23 . . . . . . . . . . . B . . . . . . . . . . . . .0 6 - 0 , 8 1 2 0 7 6 O 7 O O 0 0 7 O 9 2 5 0 1 0 7 0 - O 9 O O 9 o e e - 0 6 9 2 0 1 0 z . 0 9 1 ~ 1 6 O 8 O - 0 8 0. . . . . . . . . . . . . . . . . . o o l ~ o i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 5 0 . 1 9 - O , 2 2 1 5 O , 9 - O , 7 O l - I 0~ , , O 3 i ' 0 - I ' 0 ~ O 9 O 5 7 O 6 3 ' * 0 1 I 0 2 - 0 8 8 ~ 1 8 0 ' , 5 - 0 5 1

. . . . . . . . . o . . . . . . . . . i o . . . . .8 1 ~ O 6 9 O 6 6 1 o c - 0 1 6 O 2 1 9 0 * ' * ' * L ' . 5 * * ' *. . . . . . : . . . . . . . . 6 0 1 l~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 8 0 9 8 0 9 7 5 a 0 6 2 O 6 5 0 2 - 0 , ~ 3 0 ' * 2 0 5 - 1 5 8 2 1 0 1 0 8 - 0 9 9 ( , 0 2 0 . 15 0 4 1 ~ oo 0 3 1 0 2 8

o o . o . o o I . . . . . . . . . . . . . . .1 6 I 0 -1 , ~ . 1 0 1 8 0 9 2 -0 T 6 O 2 0 5 0 ST 7 0 0 ~, 0 5 1 -0 S '~ 1 1 0 5 g -0 6 t 0 6 -0 ~ *S 0 1 B 0 6 81 6 0 4 1 O ' 5 1 5 1 ' 7 - 1 ' 1 " 0 2 0 5 2 0 7 O " * 0 9 .1 1 0 9 1 1 i I I - 0 9 6 0 7 8 O 1 0 , 8 - 0 5 ~1 6 1 0 6 - 1 0 1 2 1 5 1 1 3 1 0 9 5 0 2 O 7 2 - 0 B 8 2 O 5 0 2 8 - 0 3 0 5 1 1 0 ~ 7 O ' 2 2 0 ~ 11 4 1 0 ~ . 5 0 l O 5 2 - O 5 7~ 1 6 O 8 9 O 8 7 3 1 5 O 4 - 0 3 8 7 O 2 O 8 O - O 7 , & 0 5 1 1 - 1 2 2 6 1 1 0 5 2 O S 6 3 0 1 0 ~ 5 O 6 O 0 O 2 0 O T 8; ~ o o:73 1 7 0 5 , 0 ~ 0 0 1 5 0 9 3 0 9 6 0 2 0 8 5 8 0 6 0 0 6 0 5 2 - 0 ~ . 8 1 ~ 0 8 8 - 0 9 0 " 3 0 5 7 0 5 8 3 0 2 0 6 .1 0 5 117 08 - O , 9 16 O 9 5 -O 9 0 0 0 . 1 -li t .1 O 6 0 4 9 O 5 2 5 1 2 O 5 0 0 5 9 6 0 " * 0 , 8 - 0 3 ~ * " * O 2 O 7 8 - 0 6 60 . . . . .. . . . ~ . . . . .. . . . ~ . . . . . . . 21 . . . . .. . . . 0 . . . . .. . . . 0 0 5 c . . . . ~ . . . . .. . . .1 8 o 8 6 0 8 7 1 6 0 , 8 o , 6 0 3 0 2 8 0 2 1 o 7 o 9 o 0 8 ~. 1 .1 0 5 7 o 6 0 o 5 1 2 - 1 1 7 o ~ R O 6 53 1 8 0 5 5 0 6 2 6 1 6 0 7 7 0 7 9 . 1 0 3 1 5 6 12 1 3 0 7 0 9 , - 1 0 3 1 .1 0 8 2 0 7 6 7 0 5 0 8 7 08 . 1 O ~ 0 5 8 06 ~ .I 19 O 9 0 - 0 8 9 1 17 0 , 5 - 0 , 7 4 0 3 0 5 Z 0 5 S , 0 7 1 6 16/* ' 11 O 5 O - 0 6 8 0 0 6 0 7. 1 6 ~ O 5 9 - O S ?

19 0 5 8 0 5 8 1 8 O , B 0 6 5 0 1 0 ~ ,6 - 0 ' 2 ? 0 6 7 - 0 9 5 3 0 8 0 0 7 , 0 6 0 , 4 - 0 , . 1 5 1 2 1 - 1 1 71 9 0 6 2 0 6 1 1 8 0 5 " - 0 / * 9 7 0 , 0 6 2 - 0 5 , 0 8 1 , 2 - 1 ~ 0 1 8 0 , 6 o ~ * o 0 6 6 O 5 O 8 5 0 9 0. . . . . . . . . . . . . . . . . . . 0043 . . . . . . . . . . . . . . . . o . . . . . . . . ~ . . . . . . . . . . . . . . . . .o 2 0 1 3 8 - 1 1 8 0 1 19 1"3 1 3 2 ~ 1 9 7 - 2 1 . 1 , 0 8 2 0 6 1 6 6 1 6 0 6 5 -071 0 7 " 0 7 7 . 1 0 6 0 8 2 - 0 7 3, 2 0 0 7 1 0 6 7 2 ~ 0 8 5 0 9 1 O z . 0 ~ 6 0 5 8 , 0 8 0 / * 9 0 ' 2 1 6 0 5 9 - 0 6 ( , 2 O 7 0 6 8 - 0 6 9 , 0 6 0 8 5 0 8 7

o 22 129 If 5 O" 156 12~. 06 io i 1o9 17 O~T -0" , 07 0~9 -O,5 07 051 05.1a 2 2 0 6 2 - 0 7 5 * * * * * L = - I * * * * 6 O , 0 ~ 6 - 0 , , 7 O 8 1 0 "* - 1 0 6 4 1 7 0 8 5 - 0 9 4 0 0 8 O 4 8 O , 6 I O 8 O 7 O 5 61 2 8 O 8 6 O89 1 o o 0 , 0 7 0 0 5 1 2 1 - 1 1 6 1 o 9 1 0 5 - 1 0 2 0 1 8 o 6 2 0 6 1 0 8 0 . 18 - 0 , 8 1 o 9 0 . 8 , - 0 9 12 3 0 5 4 - O 6 , O 0 1 8 1 - 2 " 2 O 5 0 ~ .6 - 0 5 ~ ~ O 9 0 ~ .2 O ' 5 1 0 O 6 3 - 0 6 ~ * O 9 O 7 2 - O 6 3 ~ ) 9 O 8 O 0 7 7

o 2 6 ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . i . . . . . . . .. . . . . . . . o o o ~ . . . . . . . . . . . . ~ . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . .01 06, 9505 lO, -122 I0 108 115 2o o68 06o , o9 09.1 o85 10 12, -1290 2 0 7 ~ O 66 3 I 0 O 4 ' 9 - O 5 5 2 1 0 6 6 - 0 7~ , ,

H K o o q C At .4 lO 1 18 1 o 7s z o 0 , . 9 - 0 4 ,0 1 1 0 6 9 - 0 6 00 l Z 0 7 9 0 8 . 14 1 2 o s e - 0 2 91 1 . 1 0 7 8 0 7 21 .1 0 7 9 - 0 8 85 1 : . . . . . . .0 0 8 0 0 8 51 1 : . . . . . .4 0 8 6 - 0 8 82 17 0 9 2 - 0 9 4' ' ' ' L * - S ' ' ' '

. 1 o o 0 9 , 0 8 90 0 0 6 ~ , 0 ' *7o o lo l - o 8 91 0 1 - o r * 6. 1 o z 0 2 5 0 5 80 1 0 6 . 1 0 6 7

3 o;t 06.1 -061& 0 ; ' 0 7 3 o ~ s2 o ~ 0 7 6 - o 7 7"~ 0"~ zo,, , 097, . 0 " ~ 0 ~ , 7 -0 , 9

~ 092 0966 0,. o66 -or62 05 089 089. 1 0 5 0 3 ~ . 0 3 ?i 0 6 0 8 0 0 7 . 1

s o s 0 6 ~ - 0 " * 90 7 0 8 0 - 0 8 00 7 0 o ~ 16 o 7 0 " *9 -o ' *~8 o ~ - 0 3 90 8 0 * 7 - 0 5 ~

6 0 8 0 6 9 0 7 21 o 9 0 6 ~ 0 6 ' .2 0 9 0 5 1 - 0 ' , ?. 1 O 9 0 ' . 7 -O ' . 8: 1 0 0 5 1 - O 5 8l o 0 6 2 - O S 85 10 0 " *7 O ' *8"* 11 094 08'~l 1 2 0 5 6 - 0 6 9. 1 1 2 0 6 2 0 5 95 1 2 0 ' *9 0 6 2

I I~ 0 9 2 - 0 9 95 0 ' *7 0 5 1

2 1 6 0 6 6 0 7 52 1 7 0 T 8 0 6 9

o ol a o56o l 0 6 8 - 0 7 7' . 0 1 0 7 4 - o 6 8o o 2 ~ o .0 2 0 0 5 2.1 02 1 1 o - 1 o 61 o . 1 o 0 7 ~a o ~ 0 ~ 2 - 0 , 65 0.1 077 -071

0 5 0 7 8 - 0 9 ?os 0 8 5 0 8 20 0 6 0 , . 9 - 0 2 , .2 0 6 0 9 ~ - 0 9 9z . 0 6 0 7 1 0 5 86 0 6 0 7 0 0 ? 30 7 0 6 t - 0 7 ,0 7 0 5 7 0 5 ' .o 0 9 0 9 6 - 1 1 1i 0 9 0 6 5 o ? , .* 0 9 0 7 0 0 6 0. 1 1 0 o 8 o r eo 1 2 C - o 1 ~0 1 ~ 0 8 6 0 8 2

4 l ~ 0 . ~ 9 - 0 6 61 1 7 0 7 T - 0 7 8* . . . . L . - 6 . . . .2 o o 6 1 - 0 6 2i o : . o - 0 7 02 o z 0 5 3 - 0 3 8 o , 0 *6 - 0 5 0, 0 '* 0 6 7 0 6 5' t 0 5 1 0 2 0 9 22 0 6 0 8 2 0 7 52 0 7 0 ' , 2 - 0 ( , 708 0 5 4 - 0 5 ~,, 08 0 5 0 - 0 5 50 9 0 6 . 1 - 0 5 00 9 0 6 7 - 0 7 91 1 0 0 8 8 0 8 5lO 0 *6 -o , . . 1

1o 0 6 7 - 0 6 65 1 1 0 7 7 0 7 0i 12 0 5 6 - 0 6 0,. 12 056 o~z2 1.1 o5~ -o~91 o7, -o7.1

I'* 0 " 9 - 0 " 7

A - F ( C A L I A R E I N E L E C T R O N S . H Y O R OO E N A T O N C O N T R I B U T I O N S AR E N O T I N C L U D E D .B - R E F L E C T I O N H I D D E N O Y T H E B E A M S T O P .C - R E F L E C T I O N O B S C U RE D B Y R A D I A T I O N S T R E A K O R O Y F I L M I H R E R F E C T I O N t


5/8

J A M E S A . I B E R S A S ID I ~ O B E R T G . S N Y D E R 9

A t o mR hR h 'C1CI'

T a b l e 3 . Root-mean -square thermal displacements in J~)*Root -mean-square di splacement

Max. Int . Min. J_ to Rh , C1 plan e In Rh , C1 plan e0.18 0.17 0.15 isotro pic0.19 0.18 0.16 isotropic0.29 0 18 0 16 0.28 0.17, isotro pic0.27 0.20 0.19 0.27 0-20, isotro pic

* Est im ated s tanda rd d evia t ions : Rh, 0 .01 /~ ; C1, 0 .02 /~.s i n g u l a r , t I n t h e s u c c e e d i n g r e f i n e m e n t t h e s c a l ef a c t o rs f r o m t h e i s o tr o p i c r e f i n e m e n t w e r e u s e d a n dw e r e n o t v a r ie d . T h e t h e r m a l p a r a m e t e r s o f t h e c a r b o na t o m s f r o m t h e i s o tr o p i c r e f i n e m e n t w e r e h e l d c o n -s t a n t i n th i s r e fi n e m e n t , f o r a t t e m p t s t o v a r y t h e s ew h i l e v a r y i n g t h e t h e r m a l p a r a m e t e r s o f th e h e a v ya t o m s a n i s o t r o p i c a l l y l e d to p h y s i c a l l y u n r e a s o n a b l et h e r m a l p a r a m e t e r s f o r t h e c a r b o n a t o m s . T h ea n i s o t r o p i c r e f i n e m e n t ( 8 4 p a r a m e t e r s ) c o n v e r g e d t oa r e l i a b i l i t y f a c t o r o f 0 .0 9 6 a n d t o a v a l u e o f 6 .8 8 f o rt h e e r ro r o f f it f u n c t io n . T h e f i n a l p a r a m e t e r s f r o m t h i sr e f i n e m e n t ( w i t h c a r b o n a t o m t h e r m a l p a r a m e t e r sf r o m t h e i s o t r o p i c r e f i n e m e n t ) a r e l i s t e d i n T a b l e 1 .T h e v a l u e s o f F c b a s e d o n t h e s e d a t a , t o g e t h e r w i t ht h e v a l u e s o f Fo f o r o b s e r v e d a n d o b s c u r e d r e f l e c t i o n s ,a r e l i s te d i n T a b l e 2 . T h e F c v a l u e s a c c o r d i n g l y d o n o ti n c l u d e t h e c o n t r i b u t i o n s fr o m h y d r o g e n a t o m s . T h eFo v a l u e s h a v e b e e n s c a l e d a b s o l u t e ly w i t h t h e u s eo f t h e s c a l e f a c to r s f r o m t h e i s o t r o p i c r e f i n e m e n t .A c h e c k o f t h e s t r u c t u r e a m p l i t u d e s o f t h e a p p r o x -i m a t e l y 1 4 0 0 u n o b s e r v e d r e f le c t io n s w i t h i n t h e s p h e r e~ -1 s i n 0 < 0 . 55 j ~ - i r e v e a l e d n o n e w h i c h w e d e e m t oe x c e e d s i g n i f i c a n t l y ( 1 0 % l e v e l ) o u r e s t i m a t e s o fF m i n . T h e r e f o r e t h e s e d a t a a r e n o t l i s t e d i n T a b l e 2 .N o n e o f t h e p o s i t i o n a l p a r a m e t e r s f r o m t h e a n is o -t r o p i c r e f i n e m e n t d i f f e r s s i g n i f i c a n t l y (1 5 % l e v e l )f r o m t h e p a r a m e t e r s o b t a i n e d f r o m t h e i s o tr o p i cr e f i n e m e n t . S i m i l a r ly , t h e i m p r o v e m e n t i n t h e r e l i-a b i l i t y f a c t o r i s n o t s i g n i f i c a n t ( H a m i l t o n , 1 9 6 1) .T h e r e a s o n f o r t h i s l a c k o f i m p r o v e m e n t , w h i c h i sc o n t r a r y t o g e n e r a l e x p e r ie n c e , is a p p a r e n t f r o m t h ee l l i p s o id s o f v i b r a t i o n o f t h e h e a v y a t o m s ( T a b l e 3 ).I n a g r e e m e n t w i t h e x p e c t a t i o n s , t h e c h l o ri n e a t o m sa r e v i b r a t i n g w i t h c o n s i d e r a b l y g r e a t e r a m p l i t u d e sn o r m a l to t h e r h o d i u m - c h l o r i n e p l a n a r r i n g t h a n i n i t.H o w e v e r , t h e v i b r a t i o n s o f t h e r h o d i u m a t o m s a r ee s s e n t i a l l y i s o tr o p i c . T h i s w e b e l i e v e i s r e a s o n a b l e o nt h e b a s i s o f t h e m o l e c u l a r s t ru c t u r e . S i n c e t h e r h o d i u ma t o m s a r e v i b r a t i n g i s o t r o p i c a l l y , l i t t l e i m p r o v e m e n ti n a g r e e m e n t b e t w e e n o b s e r v e d a n d c a l c u l a te d s t ru c -t u r e a m p l i t u d e s s h o u l d r e s u l t w h e n t h e h e a v y a t o m sa r e a l l o w e d to v i b r a t e a n i s o t ro p i c a l ly . I n c i d e n t a l l y ,t h e v a l u e s o f t h e r e l i a b i l i t y f a c t o r a n d e r r o r o f fi tf u n c t i o n f o r F c c a l c u l a t e d w i t h o m i s s i o n o f t h e c a r b o n -a t o m c o n t r i b u t i o n s a n d w i t h ( a ) i s o tr o p ic t h e r m a lp a r a m e t e r s a n d (b) a n i s o t ro p i c t h e r m a l p a r a m e t e r s

t We are indebted to Prof . D. H. T empleton for a discuss ionin which he pointed thi s fac t out to us .

o n t h e h e a v y a t o m s a r e ( a ) 0 . 1 62 a n d 1 2 .0 9 , a n d 0 . 1 5 7 a n d 1 1 . 8 8 .S i n c e t h e a n i s o t ro p i c t h e r m a l p a r a m e t e r s a r e s es i t i v e t o s y s t e m a t i c e r r o r s i n t h e d a t a , t h e r e s u l t s T a b l e 3 w o u l d s e e m t o i n d i c a t e , i n s o f a r a s t h e y a g rw i t h o u r e x p e c t a t i o n s c o n c e r n i n g th e n a t u r e o f tv i b r a t i o n s o f a to m s i n t h e m o l e c u le , t h a t s y s t e m ae r r o r s in th e d a t a a r e n o t s e r io u s . O n t h e o t h e r h a ns y s t e m a t i c e r ro r s i n th e d a t a m i g h t p o s s i b l y b e te x p l a n a t i o n fo r t h e t h e r m a l p a r a m e t e r o f a to m ( T a b l e 1 ) . (S e e F i g . 1 f o r t h e d e s i g n a t i o n o f a t o mT h e i s o t r o p i c t h e r m a l p a r a m e t e r o f a t o m 4 ' i s sn i f i c a n t l y h i g h e r ( a t t h e 1 % l e v e l) t h a n t h e m ev a l u e o f 4 .3 _+ 1 .4 A e d e r i v e d f r o m t h e i n d i v i d ut h e r m a l p a r a m e t e r s o f t h e o t h e r f i f t e e n c a r b o n a t o m( N o n e o f t h e s e d i f f e r s s i g n i f i c a n t l y f r o m a n o t h eT h e r e i s n o s t r u c t u r a l e x p l a n a t i o n f o r th i s . O f c o u rt h e h i g h t h e r m a l p a r a m e t e r m i g h t i n d i c a te t ha t o m 4 ' is m i s p l a c e d s li g h t l y f r o m m i n i m u m p o s i t i( R o s s m a n n et al., 1 9 59 ). B e c a u s e o f t h i s , a n d b e c a ut h e d a t a o f T a b l e 1 l e a d t o r i n g s w i t h o b v i o u s d i s tot io n s , f u r t h e r r e f i n e m e n t s w e re a t t e m p t e d i n w hp a r t i c u l a r c a r b o n a t o m s , s u c h a s 4 ', o r p a r t i c ug r o u p s o f c a r b o n a t o m s , w e r e d e l i b e r a t e l y d i s p l a cf r o m t h e p o s i t i o n s o f T a b l e 1 t o ' m o r e r e a s o n a bp o s i t i o n s . I n a l l ca s e s a f te r a f e w c y c l e s t h e a t o mp o s i t i o n s w e r e t h o s e o f T a b l e 1 . T h i s r e s u l t , w h i l ep r o v i d e s n o e x p l a n a t i o n f o r t h e h i g h t h e r m a l p a r ae t e r v a l u e f o r 4 ' , i s c o m f o r t i n g , f o r i t m a k e s i t s el i k e l y t h a t t h e r e f i n e m e n t h a s c o n v e r g e d t o a t rm i n i m u m i n m u l t i - d i m e n s i o n a l s p a c e. A c h e c k o f tc o r r e l a t i o n m a t r i x r e v e a l s n o u n u s u a l c o r r e l a t i ob e t w e e n B o f a t o m 4 ' a n d o t h e r v a r i a b l e s. A s m et i o n e d a b o v e s y s t e m a t i c e rr o rs i n t h e d a t a m i g h t t h e e x p l a n a t i o n fo r t h e h i g h t h e r m a l p a r a m e t e r a t o m 4 ' . H o w e v e r , o n th e F o u r i e r m a p , w h i c hb a s e d o n a w e i g h t i n g s c h e m e v e r y d i f f e r e n t f r o m t hu s e d i n t h e l e a s t - s q u a r es c a l c u la t i o n , th e p e a k h e i go f a t o m 4 ' is o n l y a b o u t 7 5 % o f t h e a v e r a g e p eh e i g h t o f t h e c a r b o n a t o m s . T h u s , w e o ff e r n o p o s i tr e a s o n f or t h e h i g h v a l u e o f t h e t h e r m a l p a r a m eo f a t o m 4 ' .

A s i n d i c a t e d i n th e n e x t s e c ti o n , t h e d a t a o f T a b ll e a d t o r i n g s w h i c h a r e d i s t o r t e d , a l t h o u g h t h e dt o r t io n s a r e n o t s i g n i f i c a n t w h e n a c c o u n t i s t a k e nt h e u n c e r t a i n t i e s i n t h e p o s i t i o n s o f i n d i v i d u a l c a r ba t o m s . A l t h o u g h i t w o u l d b e o f g r e a t i n t e r e s t t o c op a r e t h e p r e s e n t r e s u l t s w i t h t h o s e b a s e d o n a m o di n w h i c h t h e r i n g s w e r e c o n s t r a i n e d t o h a v e c e r t


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928 STRUCTURE OF THE DIMER OF RHODIUM CHLORIDE 1 , 5 - C Y C L O O C T A D I E N Edimensions, the present case was not deemed to bea favorable one for a refinement with constraints.Such a refinement would be sensible (although itwould involve much labor) for a problem in whichthe data were more reliable than here and in whichthe contributions of the atoms in the rings to thestructure amplitudes were greater than they are here.

e s c r i p t i o n o f t h e s t r u c t u r eThe structure defined by the parameters of Table 1and by the equivalent positions of the space groupis one in which individual molecules of (RhCl(CsH12))2of conformation depicted in Fig. 1 pack togethertightly, with a given cyclooctadiene ring in contactwith rings from three or four adjacent molecules.The cyclooctadiene rings have the boat configuration.Each rhodium atom is in an approximately square-planar configuration, being bonded to two chlorineatoms and to the double-bond centers of a cyclo-octadiene ring (Fig. 2). The closest approaches ofcarbon atoms from other molecules to a given rhodiumato m are 3.79, 4.03, and 4.07 A_ in directions notnormal to the plane of the double-bond centers,chlorine atoms, and rhodium atoms. Thus there isno evidence for a configuration other than d s p 2 forthe rhodium atoms. This configuration is markedlydifferent from that found by Dahl et al. (1961) forthe rhodium a toms i n (RhCl(CO)2)2. The proper tiesand reactions of these two compounds are similar,and thus one is reminded that it is often difficult tocorrelate molecular structure with physical properties.

7

3

6Rh C I~ 1 , ~ ~ 8 , 7

2 , ~ 4 '3'

F i g . 1 . S k e t c h o f t h e R h C l - l , 5 - c y c l o o c t a d i e n e ) 2 m o l e c u l e .T h e r h o d i u m s , c h l or in e s , a n d d o u b l e - b o n d c e n t e r s a r e n e a r l yc o p l a n a r .There are two imperfections in the square-planararrangement of the rhodium atoms. First, a givenrhodium atom is closer to the double-bond centers(2.00 /~) th an to the chlorine atoms (2.38 /~), but thebond angles are only slightly different from 90 (Fig. 2). Second, the double-bond centers, chlorineatoms and rhodium atoms do not lie exactly in aplane. In Table 4 the equation of the formal (unitweight) least-squares plane is given, together with the

deviations of the individual atoms and double-bondcenters from this plane. Only the deviations of thecMorine atoms are significant (at the 1% level);the two rhodium atoms and four double-bond centersdo not deviate significantly from the plane. Thedouble bonds are normal to this plane, within theaccuracy with which their directions are determinedin this study.

C1

90o _ .

c1F i g . 2 . P r i n c i p a l b o n d d i s t a n c e s ( A ) a n d a n g l e s b e t w e e n t h eR h , C 1, a n d d o u b l e - b o n d c e n t e r s ( s y m b o l i z e d b y O ) .

The packing of the molecules is tight. There is oneC-C intermolecular contact (between symmetry re-lated 5' atoms) which is 3.3 A; all other C-C inter-molecular contacts are 3-7/~ or longer. There are someC1-C intermolecular contacts as short as 3-65 A. Suchclose packing may be the explanation for the devia-tions of the chlorine atoms from the least-squaresplane.Table 4. Dev ia t ions i n A) o f a toms and double-bondcenters f ro m least-squares plane

A t o m o r A t o m o rc e n t e r D e v i a t i o n c e n t e r D e v i a t i o nR h - - 0 . 0 1 0 1 - 2 0 - 12Rh' -- 0.003 5-6 0.04C] -- 0.16 1 -2 0.08Cl' --0.19 5--6 0.I1

Equation of unit normal to the formal (unit weight)least-squares plane ism ---- - - 4 .5 89 b~ - t- 19.381 b 2 - - 2-8 05 b3

~vV " ~h e r ~ t h e b i s a re t h e r e c i p r o c a l l a t r i n e v e c t o r s . T h e o r i g i nt o p l a n e d i s t a n c e i s 3 .3 5 5 A . L e a s t - s q u a r e s p l a n e w a s b a s e do n e q u a t i o n ( 11 ) o f S c h o m a k e r e t a l . ( 1959) .

Table 5 lists selected intramolecular bond distancesand angles. These have been computed with the helpo~ the Busi ng- Levy (1959b) error function programfrom the final least-squares output tape. The standarddeviations attached to individual distances and anglesare those derived in this way from the completeinverse error matrix and so include the effects ofcorrelation between variables. In Table 5 there arealso given for a given set of distances or angles,mean bond distances or mean b o n d an g l e s t o g e t h e rwith the standard deviation of an individual memberof the set on the assumption of equivalence. Thereare no significant deviations (5% level) of membersof a given set from the mean of the set, and so theensuing discussion is limited to mean distances andangles. Similarly, the distances and angles depictedin Fig. 2 are mean values.

The Rh-C1 distance of 2.38 + 0.01 A is within t herange of 2-32 to 2.41 /~ tabulat-ed by Baenziger et al.(1961) for Pt-C1 and Pd-C1 distances. The distancealso compares well with the Rh-C1 distances of 2.33


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J A M E S A . I B E R S A N DT a b l e 5 . Selected in tramoIecular bond d is tancesin t~) and angles

D i s t a nc e A - BA - B d A - B ) a d A - B ))

R h- R h ' 3 .498 0 -005Rh -C1 2.37 0.01Rh -C I ' 2 .38 0 .01Rh' -C 1 2 .39 0 .01Rh ' -C I ' 2 .39 0 .01

2.38 0.01R h- 1 2 . 10 0 . 06R h- 2 2 . 07 0 . 04R h- 5 2 . 18 0 - 05R h- 6 2 . 10 0 . 05R h ' - l ' 2 .1 3 0 .0 5R h ' - 2 ' 2 . 13 0 . 06R h ' - 5 ' 2 . 14 0 . 05R h ' - 6 ' 2 . 14 0 . 05

A- B d A-B) a d A-B) )Cl-CI 3.22 0.02Rh-3 3 .09 0-06R h- 4 2 . 98 0 . 06Rh-7 3 .12 0 .05R h- 8 3 . 04 0 . 05R h ' - 3 ' 3 . 10 0 . 06R h ' - 4 ' 3 .05 0 . 10R h ' - 7 ' 3 .07 0 -06R h ' - 8 ' 2 . 84 0 . 06

3.04 0.091-2 1.52 0.075-6 1-42 0.071 ' -2 ' 1 .36 0 .075 ' -6 ' 1 .44 0 .06

2-12 0.03 1.44 0.072-3 1 .54 0 .04 1-6 2 .69 0 .083-4 1.43 0-09 2-5 2.81 0.074-5 1 .59 0 .09 1 ' -6 ' 2 .82 0-076-7 1.63 0.07 2' -5 ' 2.95 0.087-8 1-39 0.07 2-82 0.108-1 1.46 0.072 ' -3 ' 1 .61 0 .08 3-8 3 .21 0 .083 -4' 1.61 0.12 4-7 3.14 0.084 ' -5 ' 1 .58 0 .10 3 ' -8 ' 2 .95 0 .096' - 7' 1.50 0.07 4 ' -7 ' 3.27 0.117 ' -8 ' 1 .36 0 .088--1 ' 1-48 0.08 3.14 0.14

1-52 0.09A ng l e s A - B - C

A - B - C /_ A - B - C ) a / A - B - C ) )1-2-3 132 44 - 5 - 6 118 55-6- 7 125 48-1 -2 117 41 ' - 2 ' - 3 ' 119 54 ' - 5 ' - 6 ' 123 55- -6 ' -7 ' 130 58 ' - 1 ' - 2 ' 122 5

123 62-3 -4 105 53-4-5 125 56-7 -8 110 47-8-1 118 52 -3' -4 113 53 ' - 4 ' - 5 ' 116 76 ' - 7 ' - 8 ' 106 57 ' - 8 ' - 1 ' 133 5

116 10CI ' -R h-C 1 85 3 0- 4CI ' -Rh ' -C1 84.7 0 .4R h - C 1 - R h ' 94 .4 0 .5R h - C I ' - R h ' 9 4. 5 0 .5

a n d 2 . 38 f o u n d b y D a M et al. ( 1961 ) i n ( l Z hC l ( C O ) e ) 9 .T h e l ~ h - R h d i s t a n c e o f 3 . 4 98 + _ 0 0 0 5 /~ m a y b ec o m p a r e d w i t h t h a t o f 3 -3 1 /~ i n th e c a r b o n y l a n d

R O B E R T G . S N Y D E R 9 2w i t h a P d - P d d i s t a n c e o f 3 . 4 6 A i n ( s t y r e n e - P d C l 2 ) 2( g o l d e n B a e n z i g e r , 1 9 5 5 ) a n d i n ( E t P d C l e ) 2 ( D e m p -s e y B a e n z i g e r , 1 9 5 5 ) . T h e d o u b l e - b o n d c e n t e r tr h o d i u m d i s t a n c e o f 2 . 0 0 i 0 . 0 4 / ~ c o m p a r e s w e l l w i t ht h e d o u b l e - b o n d c e n t e r t o p a l l a d i u m d i s t a n c e o2 . 0 4 ~ i n n o r b o r n a d i e n e d i c h l o r o p a l l a d i u m ( I I ) ( B a e nz i g e r e t a l . 1 9 6 1 ) .E v e n t h o u g h a c c o u n t h a s b e e n t a k e n o f t h e a n i s ot r o p i c n a t u r e o f t h e h e a v y a t o m v i b r a t i o n s t h e r i ng e o m e t r y i s n o t w e l l d e f i n e d . T h e s i n g l e b o n d s c a n n ob e d i s t i n g u i s h e d f r o m t h e ' d o u b l e ' b o n d s o n t h e b a s io f l e n g t h . O n t h e b a s i s o f t h e i r p o s i t i o n s r e l a t i v e tt h e r h o d i u m a t o m s t h e y c a n b e . T h e t w e l v e s i n gb o n d s a v e r a g e 1 . 5 2 0 - 0 9 ~ , w i t h n o i n d i v i d u as i g n i f i c a n t v a r i a t i o n s ( 5 % l e v el ) f r o m t h i s m e a n . T hf o u r d o u b l e b o n d s a v e r a g e 1 . 4 4 __ 0 . 0 7 - ~ w i t h ns i g n i f ic a n t v a r i a t io n s . T h i s v a l u e m a y b e c o m p a r ew i t h 1 .4 6 +_ 0 - 0 4 / ~ i n n o r b o r n a d i e n e d i c h l o r o - p a l l a d i u( I I ) a n d w i t h 1 . 4 3 _ +0 1 5 / ~ i n ( s t y r e n e - P d C 1 2 )( B a e n z i g e r et al. , 1 9 6 1) . T h e 9 5 % f i d u c i a l li m i t s ft h i s m e a n a n d s t a n d a r d d e v i a t i o n a r e 1 -3 5 a n d 1 . 5 3 /a n d s o t h e r e is a b o u t a 2 % c h a n c e t h a t t h e m e a n 1 . 44 ~ w i t h a s t a n d a r d d e v i a t i o n o f 0 . 0 7 J~, b a s eo n a s a m p l e s iz e o f f o u r , c a n b e f r o m a n o r m a l p o p u l at i o n w h o s e m e a n i s 1 . 34 J~ , t h e n o r m a l d o u b l e - b o nl e n g t h . I t i s t h u s l i k e l y t h a t t h e d o u b l e b o n d s 1 ,5 . cyc looc tad iene h a v e l e n g t h e n e d u p o n b e i ng b o n d et o th e r h o d i u m a t o m .A c o m p a r i s o n o f t h e i n f r a r e d s p e c t r u m ( R hC l (C s H 19 . )) 2 w i t h t h a t o f 1 , 5 - c y c l o o c t a d i e n e p r o v i dc o r r o b o r a t iv e e v i d e n c e fo r a w e a k e r d o u b l e - b o n d t h e c o m p l e x . A b a n d a t 1 6 57 c m . - 1, w h i c h o c c u r s t h e s p e c t r u m o f 1,5-cycIooctadiene a n d w h i c h a s s o c i a t e d w i t h C = C s t r e t c h i n g , d o e s n o t o c c u r i n ts p e c t r u m o f t h e c o m p l e x a t a f r e q u e n c y h i g h e r t h a1 47 5 c m . -1 , w h e r e t h e m e t h y l e n e d e f o r m a t i o n b a no c c u r s. W e w e r e u n a b l e t o i d e n t i f y t h e C = C s t r e t c h ib a n d i n th e s p e c t r u m o f t h e c o m p l e x , a n d i t i s p o s s ibt h a t i t oc c u rs a t a f r e q u e n c y c o n s i d e r a b l y l o w e r th1 4 7 5 cm . - 1 . * N o t a b l e a m o n g o t h e r d i f f e re n c e s b e t w et h e s p e c t r a i s a s h i f t in t h e f r e q u e n c y o f t h e o l e f ih y d r o g e n o u t - o f- p l a n e b e n d i n g m o d e . I n t h e s p e co f 1 , 5 cyc looc tad iene a n d o f m o s t o t h e r cis-o left h i s m o d e a p p e a r s a s a s t r o n g i n f r a re d b a n d n e6 7 5 c m . - 1. I n t h e c o m p l e x t h i s b a n d i s d i s p l a c e d h i g h e r f r e q u e n c ie s ( > 7 7 5 c m . -1 ) t o w a r d t h e r e g io f h y d r o g e n b e n d i n g f r e q u e n c i e s i n s a t u r a t e d m oc u l e s ( > 1 0 0 0 c m . - 1 ) .

U n f o r t u n a t e l y i t i s n o t p o s s i b l e , o n t h e b a s i s o f i n f r a r e d d a t a , t o e s t i m a t e w i t h c o n f id e n c e t h e e x t eo f t h e l e n g t h e n i n g o f th e d o u b l e b o n d s i n t h e c o m p lT h e r e is a b o u t a 9 5 % c h a n c e th a t t h e d o u b l e b om e a n i s l es s t h a n t h e s i n g l e b o n d m e a n , t h a t i s, t ht h e d o u b l e b o n d s a n d s i ng l e b o n d s a r e fr o m d i f f erp o p u l a t i o n s . M o r e o v e r , t h e r e is a b o u t a 9 5 % c h a nt h a t t h e C - C - C a n g l e i s g r e a t e r t h a n t h e C - C

* Fo r c om pa r i s on a C - C s i ng l e bond s t r e t c h i ng f r e quei s i n the r egion 1100-1000 cm. -1 .


8/8

930 S T R U C T U R E O F T H E D I M E R O F R H O D I U M C H L O R I D E 1 , 5 - C Y C L O O C T A D I E N Ea n g l e . I t s e e m s l i k e l y t h e n t h a t t h e ' d o u b l e ' b o n d si n t h e c o m p l e x a r e i n t e r m e d i a t e i n le n g t h t o a n o r m a ls i n g le a n d a n o r m a l d o u b l e b o n d .W e f e e l t h a t w e h a v e o b t a i n e d a l l o f t h e i n f o r m a t i o no n t h e r i n g g e o m e t r y w h i c h i s p o s s ib l e w i t h t h e p r e s e n tv i s u a l i n t e n s i t y d a t a . W e a g r e e w i t h B a e n z i g e r et al.( 19 6 1) t h a t i n t h is t y p e o f p r o b l e m b e t t e r d a t a a r ep r o b a b l y r e q u i r e d i f s ig n i f i c a n t i n f o r m a t i o n o n r i n gg e o m e t r y i s t o b e o b t a i n e d .

R e f e r e n c e sBAENZIGER, N. C. , DO YLE , J . R. , RICHARD S, G. F .CARPENTER, C. L . (1961) . Advances in the Chemistryof Coordination Compounds, p . 1 3 1 . . N e w Y o r k : M a c -m i l l a n .B u s r ~ G , W . R . L E V Y , H . A . ( 1 95 9 a ). O a k R i d g e: N a t io n a l L a b o r a t o r y R e p o r t 5 9 -4 -3 7 .B us I N G , W. R . LEVY, H . A . ( 1959b). O ak R i dg e: N a ti o n a l L a b o r a t o r y R e p o r t 5 9 -1 2 -3 .Cm~TT, J . VENANZI, L . M. (1957) . J. Chem. Soc.p. 4735.

DAHL, L. F . , MARTELL, C . WAr~-PT.ER, D. L. (196 1).J. Amer. Chem. Soc. 83, 1761.DAWSON, B. (1960). Acta Cryst. 13, 403.DEMPSEY, J. :N. BAENZIQER, N. C. (1955). J. Amer.Chem. Soc. 77, 4984.H A MIL TO N , W. C . (1961). Pa pe r H - 5 , A m er . C r ys t . A ssn .M e e t i n g , B o u l d e r , C o l o r a d o , J u l y 3 1 - A u g u s t 4 .HOERNI, J . A. IBERS, J . A. (1954) . Acta Cryst. 7, 744.HOT,DEN, J . R . BAEN ZmER , N. C. (1955) . J. Amer.Chem. Soc. 77 , 4987 .HUGHES, E . W . (1941) . J. Amer. Chem. Soc. 63, 1737.IBERS, J . A. (1956) . Acta Cryst. 9, 652.IBE~S, J . A. CRO~ER, D. T . (1958) . Acta Cryst. 1 1 , 7 9 4 .IBERS, J. A. S~-YDER, R. G. (1962). J. Amer. Chem. Soc.84, 495.ROSSMANN, M. G. , JACOBSON, R. A. , Hn~SHFELD, F. L .LIPSCOMB, W . N . (1959). Acta Cryst. 12, 530.SCHOMAKER, V., W ASER, J . , MA RSH, R . E . BERGM_AN, G.(1959). Acta Cryst. 12, 600.SHOEMAKER, D. P. DONOHUE J . , SCHOMAKER, V.COREY, R. B. (1950). J. Amer. Chem. Soc. 72 , 2328 .TEMPLETON, D . H. (1962). International Tables for X rayCrystallography. Vol . 3 , Sect ion 3.3 .2 .THOMAS, L . H. UMEDA, K. (1957) . J. Chem. Phys. 2 6 ,293.

Acts Cryst. (1962) . 15, 930T h e r y s t a l S t r u c t u r e o f I r o n P e n t a c a r b o n y l

B Y A . W . HANSONDivision of Pure Physics, National Research Council, Ottawa, Canada

Received 4 December 1961)I r o n p e n t a c a r b o n y l a t - 8 0 C . i s m o n o c l in i c , p r o b a b l y Cc, w i t h

a = 1 1 . 7 1, b = 6 . 8 0 , c = 9 . 2 8 A ; f l= 1 0 7 .6 ; Z = 4 .I n t e n s i t i e s w e r e c o l l e c te d f o r t h e t h r e e z o n e s [ 0 10 ], [ 0 0 1] , a n d [ 11 0 ] a t t e m p e r a t u r e s r a n g i n g f r o m- - 7 0 to - - 1 1 0 C . T h e c r y s t a l s tr u c t u r e w a s d e t e r m i n e d b y h e a v y - a t o m m e t h o d s , a n d r e f i n e d w i t ht h e a i d o f tw o - d i m e n s i o n a l F o u r i e r s y n t h e s e s . T h e m o l e c u l e h a s t h e e x p e c t e d f o r m o f a t r i g o n a lb i p y r a m i d , b u t i s s l i g h t l y d i s t o r t e d i n s u c h a w a y a s t o a l l o w c l o se r p a c k i n g .

I n t r o d u c t i o nE w e n s L i s t e r ( 19 3 9) h a v e s h o w n b y e l e c t ro n -d i f f r a c t i o n s t u d i e s o f t h e g a s t h a t t h e m o l e c u l e o f i r o npentacarb0ny l Fe C0)s) has the f0 rm 0f a tr ig0nalb i p y r a m i d . H o w e v e r , r e c e n t i n v e s t i g a t io n s i n t h eD i v i s i o n o f P u r e C h e m i s t r y h a v e m a d e i t d e s i ra b l et o c o n f i r m t h i s i m p o r t a n t r e s u l t b y c r y s t a l - s t ru c t u r ea n a l y s i s .

E x p e r i m e n t a l d e t a i l sI r o n p e n t a c a r b o n y l i s a s t ra w - c o l o u r e d l i q u i d w h i c hf re e z es a t - 2 0 C. T h e X - r a y d a t a w e r e o b t a i n e df r o m p r e c e ss i o n a n d W e i s s e n b e r g p h o t o g r a p h s t a k e n

a t t e m p e r a t u r e s r a n g i n g fr o m - - 7 0 to - - 1 1 0 C.D i s t i l l e d m a t e r i a l w a s s e a l e d i n a th i n - w a l l e d g l a s sc a p i l l a r y o f a b o u t 0 . 4 r a m . d i a m e t e r , a n d s i n g l e c r y s t a l sw e r e g r o w n b y a l t e r n a t e s lo w f re e z i n g a n d p a r t i u lm e l t i n g o f t h e s a m p l e . S u i t a b l e c r y s t a l s w e r e e a s yt o g ro w , b u t w h e n c o o le d to t h e w o r k i n g t e m p e r a t u r et h e y i n v a r i a b l y s p l it in t o t w o o r m o r e f r a g m e n t s .S o m e t i m e s t h e d a m a g e t o t h e c r y s t a l w as c o m p a r a -t i v e l y s li g h t, a n d t h e p h o t o g r a p h s w e r e u s a b le . A l lt h e X - r a y d a t a h a v e b e e n o b t a i n e d f r o m s u c h p h ot o -g r a p h s . M o K ~ r a d i a t i o n w a s u s e d t h r o u g h o u t .

T h e c r y s t a l d a t a a t - 8 0 C. ( o b t a i n e d fr o m p r e c es -s i o n p h o t o g r a p h s ) a r e

Cristal Structure Dimer Rh Cl COD

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