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The crystal structure of hexamethylcyclotriphosphazene - iodine (1:1 adduct) and the structural redetermination.. 1974

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\ \ \ THE CRYSTAL STRUCTURE OF HEXAMETHYLCYCLOTRIPHOSPHAZENE - IODINE (1:1 ADDUCT) AMD THE STRUCTURAL REDETERMINATION OF SODIUM FORMATE by PETER I. MARKILA B.Sc. (Hon.), U n i v e r s i t y of B r i t i s h Columbia, 1972 A THESIS SUBMITTED IS PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of CHEMISTRY We accept t h i s t h e s i s as conforming to the tfeg^ited standard THE UNIVERSITY OF BRITISH COLUMBIA MAY 1974 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requ i rement s f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Co lumb ia , I ag ree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department: or by h i s r e p r e s e n t a t i v e s . It i s unde r s t ood that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i thout my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada i i 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 i s t h e s i s c o n s i s t s of the s t r u c t u r e s of two compounds as determined by s i n g l e c r y s t a l x-ray d i f f r a c t i o n . The f i r s t s t r u c t u r e i s t h a t of a phosphazene - i o d i n e complex: hexamethylcyclotriphosphazene - i o d i n e (1:1 adduct) and the second s t r u c t u r e i s the r e d e t e r m i n a t i o n of sodium formate. C r y s t a l s of hexamethylcyclotriphosphazene - i o d i n e (1:1 adduct) are t r i c l i n i c , a = 10.707(13), b = 8.873 (5), c = 8.871(6)1, «* = 96. 65 (6), /3 = 103.91 (12), y = 97.81(12)°, Z = 2, space-group PI. The s t r u c t u r e was determined with Mo-K« d i f f r a c t o m e t e r data by P a t t e r s o n and F o u r i e r s y n t h e s i s , and was r e f i n e d by f u l l - m a t r i x l e a s t - squares c a l c u l a t i o n s to R = 0.053 f o r 1934 observed r e f l e x i o n s . The i o d i n e molecule i s weakly bonded to a ni t r o g e n atom on the phosphazene r i n g , N - I = 2.417(7), I - I = 2. 823 (1) 1, N - I - I = 177.8(2)°. The six-membered phosphazene r i n g i s s l i g h t l y , but s i g n i f i c a n t l y , ncn-planar, the conformation being t h a t of a c h a i r . The molecule has pseudo-m symmetry. Two d i s t i n c t P - N bonds are pre s e n t ; the o longer ones, mean P - N = 1.64A, i n v o l v e the n i t r o g e n that i s weakly bonded to the i o d i n e molecule, while the other f o u r 0 P - N bonds are e q u i v a l e n t , mean P - N = 1.598A. A l l the o P - C bonds are e q u i v a l e n t , mean P - C = 1.789A. The mean e n d o c y c l i c N - P - N and P - N - P angles are 114.7 and 124.0° r e s p e c t i v e l y , while the mean e x o c y c l i c C - P - C angle i s 104°. i i i C r y s t a l s of sodium formate are mc n o c l i n i c , a = 6.2590 (6), b = 6.7573 (16) , c = 6. 17 1 6 (5) A, yS = 116.140(6)°, Z = 4, space-grcup C2/c. The s t r u c t u r e was determined by d i r e c t methods, and was r e f i n e d by e l e c t r o n d e n s i t y and f u l l - m a t r i x l e a s t - s q u a r e s procedures t o E = 0.022 f o r 250 r e f l e x i o n s . Sodium formate i s planar and has C2V symmetry. P a r t i a l charges were r e f i n e d on the formate i o n . The p a r t i a l charges found on each atom are as f o l l o w s : 0 -0.23(1)e, C +0.16(3)e, H -0.49(10)e, and Sa +0.79(14)e. The sodium ion has s i x oxygen neighbours a t an average e d i s t a n c e of 2.45A and there are weak Na. ..0 i n t e r a c t i o n s . There i s a C - H...Na hydrogen bond which forms continuous rows of sodium formate i o n s . The C - 0 bond d i s t a n c e i s 1 . 2 4 6(1) A and the 0 - C - 0 angle i s 126.3(2)°. i v TABLE OF CONTENTS Page TITLE PAGE , i ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v i LIST OF FIGURES ......................................... v i i ACKNOWLEDGEMENTS . . v i i i GENERAL INTRODUCTION 1 PART 1. CRYSTAL STRUCTURE OF HEXAMETHYLCYCLOTRIPHOSPHAZENE- IODINE (1:1 ADDUCT) 3 I n t r o d u c t i o n 4 Experimental 5 S t r u c t u r e a n a l y s i s 7 R e s u l t s and d i s c u s s i o n 12 PART 2. CRYSTAL AND MOLECULAR STRUCTURE OF SODIUM FORMATE 22 I n t r o d u c t i o n 23 Experimental 24 S t r u c t u r e a n a l y s i s 26 R e s u l t s and d i s c u s s i o n 38 APPENDIX 1 49 APPENDIX 2 67 V REFERENCES 70 v i IIST OF TABLES T a b l e Page Hexamethylcyclotriphosphazene - Iodine (1:1 adduct) 1 |E| - s t a t i s t i c s 8 2 F i n a l atomic c o o r d i n a t e s 10 3 F i n a l thermal parameters 11 4 Bond l e n g t h s 14 5 Bond angles 15 6 Mean plane 16 Sodium Formate 7 |E| - s t a t i s t i c s ................................ 27 8 S t a r t i n g s e t of r e f l e x i o n s 29 9 R e s u l t s of the phase de t e r m i n a t i o n procedure: Koncentrosymmetric case 31 10 R e s u l t s of the phase de t e r m i n a t i o n procedure: Centrosymmetric case 32 11 R e f l e x i o n s given zero weight 34 12 F i n a l atomic c o o r d i n a t e s 36 13 F i n a l thermal parameters 37 14 Bond l e n g t h s and angles 39 15 Formate i o n geometries i n d i f f e r e n t s a l t s 40 16 Sodium - oxygen c o n t a c t d i s t a n c e s ............... 43 17 Average sodium - oxygen d i s t a n c e s ............... 44 18 Refined atomic charges .......................... 45 v i i LIST OF FIGURES Fig u r e Page Hexamethylcyclotriphosphazene - Iodine (1:1 adduct) 1 A gen e r a l view of the adduct 13 2 The s t r u c t u r e viewed down b 21 Sodium Formate 3 Resonance s t r u c t u r e s of the molecule ............ 23 4 The s t r u c t u r e viewed down b 42 5 F i n a l d i f f e r e n c e map ............................ 47 v i i i Acknowledgements I wish to thank P r o f e s s o r James T r o t t e r f o r h i s a s s i s t a n c e and guidance throughout my r e s e a r c h . I am a l s o indebted to my f e l l o w graduate students and p o s t d o c t o r a l f e l l o w s f o r the a s s i s t a n c e they have given me. I would a l s o l i k e to thank Prof, U. L. Paddock and T. W. J. Mah f o r the c r y s t a l s of the phosphazene d e r i v a t i v e and P r o f . C. A. McDowell, J . M. Park and fl. S. D a l a i f o r the c r y s t a l s of sodium formate. 1 GENERAL INTRODUCTION 2 The h i s t o r i c a l background and e s t a b l i s h e d p r i n c i p l e s of x-ray c r y s t a l l o g r a p h y are d e a l t with i n a number of standard t e x t s ( 1 - 5 ) . The c r y s t a l l o g r a p h i c symbols and nomenclature appearing throughout t h i s t h e s i s have t h e i r c o n v e n t i o n a l meanings d e s c r i b e d i n the " I n t e r n a t i o n a l Tables f o r X-ray C r y s t a l l o g r a p h y " (6). T h i s t h e s i s c o n s i s t s of two p a r t s . Both p a r t s c o n s i s t of the c r y s t a l l o g r a p h i c study of a compound and i n c l u d e i n t r o d u c t o r y m a t e r i a l r e l e v a n t to t h a t compound as w e l l as d e t a i l s of the s t r u c t u r e d e t e r m i n a t i o n and a d i s c u s s i o n of the r e s u l t s . For each c r y s t a l s t r u c t u r e the l e a s t - s q u a r e s refinement was based on the minimization of Iw (F 0 - F c ) 2 where F 0 and F c are the observed 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 and w i s the assigned weighting f a c t o r . The a n i s o t r o p i c thermal parameters employed i n the refinement are Uij i n the e x p r e s s i o n : f = f°exp[-2i7 2 (D„ h 2 a * 2 + U t 2.k 2b* 2 + U 3 3 A 2 c * 2 + U u hka*b* + U,3 h J U * c * + 0 2 3 k i b * c * ) ] where f° i s the t a b u l a t e d s c a t t e r i n g f a c t o r and f i s t h a t c o r r e c t e d f o r thermal motion. The i s o t r o p i c thermal parameters have the form: f = f°exp[-B (sine/A) 2 ] where B i s r e l a t e d to the mean-square displacement, U 2, of the atom from i t s mean p o s i t i o n by the e x p r e s s i o n : B = 8ir 2U 2. 3 P A R T 1 C R Y S T A L S T R U C T U R E O F H E X A M E T H Y L C Y C L O T R I P H O S P H A Z E N E - I O C I N E ( 1 : 1 A D D U C T ) 4 INTRODUCTION In r e c e n t years the cyclophosphazenes have been e x t e n s i v e l y s t u d i e d , the primary concern being the bonding. The bonding systems i n these r i n g s are now w e l l e s t a b l i s h e d (7-9). D e t a i l e d s t r u c t u r a l i n f o r m a t i o n i s a v a i l a b l e f o r s e v e r a l cyclophosphazene d e r i v a t i v e s i n which the bonding i n the r i n g has been d i s t u r b e d by p r o t c n a t i o n (10-12), or by complexing with a t r a n s i t i o n metal (13-15). The s t r u c t u r e of hexamethylcyclotriphosphazene - i o d i n e i s the f i r s t s t r u c t u r a l study done i n which the cyclophosphazene r i n g has been perturbed by the formation of a charge t r a n s f e r complex. The c r y s t a l s t r u c t u r e of the parent compound has not been determined because of badly developed c r y s t a l s . 5 EXPERIMENTAL C r y s t a l s of N 3P 3Me f e.I 2 c r y s t a l l i z e d as purple fragments, g e n e r a l l y elongated along b. U n i t - c e l l and space-group data were taken from v a r i o u s r o t a t i o n , Weissenberg and p r e c e s s i o n photographs; accurate l a t t i c e parameters were determined by a l e a s t - s g u a r e s procedure a p p l i e d to 2© values f o r t w e n t y - f i v e g e n e r a l r e f l e x i o n s measured on a spectrogoniometer. C r y s t a l Data: C 6 H , 8 I j N 3 P 3 f.w. = 478.96 T r i c l i n i c , a = 10.707 (13), b = 8.873 (5), c = 8.871(6)1, c< = 96.65 (6) , / 3 = 103.91 (12), * = 97. 81 (1 2) °, U = 800. 8A 3 , Z = 2, Dc = 1.99, F(000) = 452, )v (Mo-K<0 0.71069A, yu. (Mo- KoO 42.6cm-*. Space-group PI (Cj) or P1 (C*, ). I n t e n s i t i e s were measured on a Datex-automated General E l e c t r i c XRD 6 d i f f r a c t o m e t e r , with a s c i n t i l l a t i o n counter, Mo-K« r a d i a t i o n (zirconium f i l t e r and pulse height a n a l y s e r ) , and a 6-26 scan at 2° m i n - 1 over a range of (1.80 + 0.86tan9) degrees i n 26, with 20s background counts being measured at each end of the scan. Data were measured to 29 = 45° (minimum o i n t e r p l a n a r spacing 0.93 A). R e f l e x i o n s which had a net count of l e s s than 3cr above background, where cr(I) i s d e f i n e d by ffz (I) = S + B • (0.05)S 2, where S and E are the scan and background counts r e s p e c t i v e l y , were taken as unobserved. Of 2259 r e f l e x i o n s with 2% < 45°, 325 (14.4?) were c l a s s i f i e d as 6 unobserved. A check r e f l e x i o n was monitored every 50 reflexions and a l l the reflexions were appropriately scaled. Lorentz and polarization corrections were applied, and the structure amplitudes were derived. The c r y s t a l used had length ca. 0.45mm and cross-section of ca. 0.3 x 0.2mm. No absorption correction was made. 7 STRUCTURE ANALYSIS The data were s c a l e d by Wilson's method (16), and the |E| - s t a t i s t i c s (17) (Table 1 ) suggested the c e n t r i c space- group PI. T h i s space-group was subsequently shown c o r r e c t during s t r u c t u r e a n a l y s i s . The two i o d i n e atom p o s i t i o n s were determined from a thr e e - dimensional P a t t e r s o n f u n c t i o n . I n i t i a l i s o t r o p i c o thermal parameters were s e t at 4.25A 2. The p o s i t i o n a l and i s o t r o p i c thermal parameters and an o v e r a l l s c a l e f a c t o r were r e f i n e d by f u l l - m a t r i x l e a s t - s g u a r e s methods. The weights w i n the mi n i m i z a t i o n were such t h a t w = 0 f o r the unobserved r e f l e x i o n s and w = [A + B J F 0 | + C | F 0 | 2 + E13?0 1 3 ]~1 t o r t h e observed r e f l e x i o n s . The c o e f f i c i e n t s A, B, C, and D were adjust e d to achieve best constancy of l o c a l averages of lw (F 6 - F t) 2 over the f u l l range of | F e | , the f i n a l values being -0.553, 0.391, -0.017, and 0.0002 r e s p e c t i v e l y . S c a t t e r i n g f a c t o r s were taken from r e f e r e n c e 18. I s o t r o p i c refinement of the two i o d i n e atoms converged at R = 0.35. A t h r e e dimensional d i f f e r e n c e s y n t h e s i s c l e a r l y r e v e a l e d a l l the other 12 non-hydrogen atoms. S t r u c t u r e f a c t o r s were c a l c u l a t e d with the i o d i n e atoms being c o r r e c t e d f o r anomalous s c a t t e r i n g and the R f a c t o r was 0.135. A f t e r s e v e r a l c y c l e s of a n i s o t r o p i c refinement R was reduced to 0.056. A d i f f e r e n c e s y n t h e s i s at t h i s p o i n t f a i l e d to r e v e a l the hydrogen atoms and c a l c u l a t e d hydrogens were used f o r the s t r u c t u r e f a c t o r c a l c u l a t i o n s , but these were not r e f i n e d . These hydrogen atoms were arranged i n staggered t e t r a h e d r a l T a b l e 1 j E | - STATISTICS FOB N 3P 3Me 6.l£ THEORETICAL OBSERVED CENT RO NON-CENT RO Mean|E| Mean|E| 2 Mean|E2-1| I E| > 3 {%) IE | > 2 (*) |E| > 1 (%) 0.8145 0.9948 0.9193 0.04 3.98 33.29 0.7980 1.0000 0.9680 0.30 5.00 32.00 0.8860 1.0000 0.7360 0. 01 1. 80 37.00 9 c o n f i g u r a t i o n s , 1.00A away from the carbon atoms to which they were bonded. The hydrogen atoms were a l l given i s o t r o p i c o thermal parameters of 5.OA2. T h i s produced a f i n a l R cf 0.053. 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 g i v e n i n Appendix 1 . The f i n a l p o s i t i o n a l parameters and t h e i r standard d e v i a t i o n s f o r the non-hydrogen atoms, as w e l l as the p o s i t i o n s of the c a l c u l a t e d hydrogens, are g i v e n i n Table 2. The hydrogen atoms are numbered according to the carbon atoms to which they are bonded. The f i n a l a n i s o t r o p i c temperature f a c t o r s f o r the heavy atoms are given i n Table 3. Table 2 FINAL POSITIONAL PARAMETERS (FRACTIONAL X 10* ) WITH ESTIMATED STANDARD DEVIATIONS IN PARENTHESES A torn X y 2 I (1) 5665(1) -2030 (1) 7128 (1) I (2) 3567 (1) -4508 (1) 6515 (1) P ;i) 7575(2) 1576 (2) 8881 (2) P [2) 991 1 (2) 2785 (2) 8182 (2) P (3) 8502 (2) -0098 (2) 6508 (2) N (1) 7515 (7) 0023 (8) 7630 (8) N (2) 8907(7) 2773 (8) 9251 (8) N (3) 9746 (7) 1248 (8) 6966 (8) C (1) 7390(10) 0960 (11) 10672 (10) c (2) 6184 (11) 2476 (13) 8146 (15) C (3) 11532(8) 3145 (12) 9441 (1 1) c CO 9864 (10) 4395 (11) 7147 (11) C (5) 9045 (8) -1908 (9) 6567 (10) c (6) 7605(9) -0202 (13) 4507 (10) H (1) • 8110 0387 11088 H (1) ' ' 7426 1876 11461 H (1) 1 ' 1 6528 0266 10470 H (2) • 6211 2774 7102 H (2) ' • 5362 1734 8033 H (2) 1 • » 6208 3414 8903 H (3) • 11658 2285 10067 H (3) ' • 12175 3220 8791 H (3) " » 11666 4137 10170 H (4) • 8987 4289 6390 H (4) « • 10026 5367 7914 H 10554 4437 6560 H (5) • 9531 -1968 7666 H (5) » • 8273 -2759 6213 H (5) " ' 9634 -2017 5854 H (6) • 7229 0761 4376 H (6) • • 8201 -0317 3805 H (6) " • 6882 - 1111 4221 11 Table 3 FINAL THERMAL PARAMETERS AND THEIR ESTIMATED STANDARD DEVIATIONS ANISOTROPIC THERMAL PARAMETERS (b\; X 100 A 2) Atom U n 0 XX "33 U 1 X "13 1(1) 3. 55 (4) 4. 41 (4) 4. 53 (4) -0. 16(3) 0.58 (2) 0.27 (3) 1(2) 5. 19 (5) 5. 99 (5) 10. 04 (6) -1. 90(4) 1.98 (4) -1.40 (4) P(1) 3. 6 (1) 3. 4(1) 3. 7(1) 0. 3 (1) 0.9(1) -0.4 (1) P(2) 3. 3 (1) 2. 5 (1) 3. 9 (1) 0. 0 (1) 0.5(1) 0.1 (1) P (3) 3. 6(1) 2. 8 (1) 3. 1(1) 0. 3(1) 0.7 (1) 0.0 (1) NO) 4. 1 (4) 2. 9 (4) 4. 6 (4) -1. 0(3) 1.8(3) -1.1 (3) N(2) 5. 0 (4) 3. 4(4) 4. 7(4) -0. 1 (3) 1.9(3) -1.4 (3) N(3) 4. 3 (4) 3. 8 (4) 4. 9 (4) -0. 1 (3) 2.5 (3) -0.6 (3) C(1) 6. 5(6) 5. 5(6) 4. 3(5) -0. 1(5) 2.2 (4) -0.4 (4) C(2) 5. 7 (7) 6. 2 (7) 10. 1 (9) 1. 8(6) 0. 3 (6) 0.2 (6) C(3) 3. 6(5) 6. 5(6) 4. 8 (5) -0. 1 (5) -0.3 (4) 0.4 (5) C(4) 6. 1 (6) 4. 7(6) 5. 6 (6) 0. 7(5) 0.5 (5) 1.9 (5) C(5) 4. 0(5) 2. 5 (4) 6. 0 (5) 0. 0 (4) 1.0 (4) 0.1 (4) C(6) 5. 5(6) 7. 6(7) 3. 2(4) 0. 8(5) -0. 1 (4) 0.8 (5) 12 RESULTS AND DISCUSSION The i o d i n e molecule i s weakly bonded to a n i t r o g e n atom on the phosphazene r i n g i n a l i n e a r arrangement. A g e n e r a l view of the adduct i s shown i n Figure 1. I n d i v i d u a l bond len g t h s along with standard d e v i a t i o n s are given i n Table 4 and the valency angles with standard d e v i a t i o n s are given i n T a b l e 5. A weighted l e a s t - s g u a r e s plane was c a l c u l a t e d f o r the phosphazene r i n g . T h i s was done by the use of the o r t h o g o n a l c o o r d i n a t e s , X, Y, Z, which were d e r i v e d as f o l l o w s : X a bcosX ccos^fl x Y = 0 bsinV c (cos<<-cosyS. coslO/sintf y Z 0 0 V/absintf z where V i s the c e l l volume as d e f i n e d i n r e f e r e n c e 6. The equation of the plane and d i s t a n c e s of the atoms from the plane are given i n Table 6. The phosphazene r i n g i s s l i g h t l y , but s i g n i f i c a n t l y , o non-planar, a l l atoms l y i n g between -0.141 and 0.005A away from the weighted mean plane. The standard d e v i a t i o n s of the phosphorus atoms are l e s s than those of the n i t r o g e n atoms and consequently they are given more weight than the n i t r o g e n atoms. That i s why the phosphorus atoms are c l o s e r to the mean plane (see Table 6). A l l the nitrogen atoms are below the plane while a l l the phosphorus atoms are above. T h i s produces a c h a i r conformation because the phosphorus and n i t r o g e n atoms a l t e r n a t e around the r i n g . Of (NPX^Jj molecules whose s t r u c t u r e s have been r e p o r t e d , the f l u o r i d e 13 F i g u r e 1 A g e n e r a l v i e w o f t h e a d d u c t . 14 Table 4 INDIVIDUAL BOND LENGTHS (A) WITH STANDARD DEVIATIONS IN PARENTHESES. o o Atoms Bond Length (A) Atoms Bond Length (A) I (1) - K 2 ) 2 .823 (1) N (3) - P(3) 1.600 (7) I (1) - N (1) 2 .417 (7) P (1) - C (1) 1.785 (9) N (1) - P ( D 1 .650 (7) P(1) - C(2) 1.805 (1 1) N (1) - P(3) 1 .623 (7) P (2) " C(3) 1.787 (8) N (2) - P(1) 1 .597 (7) P (2) - C (4) 1.786 (9) N(2) - P(2) 1 .596 (7) P (3) - C(5) 1.783 (8) N (3) " P(2) 1 .599 (7) P(3) - C(6) 1.789 (8) Table 5 VALENCY ANGLES (DEG.) WITH STANDARD DEVIATIONS IN PARENTHESES Atoms Angle Atoms Angle 1(2) -- I (1) - N(1) 177 .8 (2) C (2) - P (1) - N d ) 111. 1 (5) 1(1) • - N (D - P(D 1 18 .5(3) C (2) - P (1) - N (2) 108. 8 (5) 1(1) -- N d ) - P {3 ) 1 17 .3 (3) C (3) - P (2 ) - N (2 ) 108. 4 (<*) c (3) - P (2) - N (3 ) 108. 5 (») N(D -- P (D - » ( 2 ) 113 .9(3) c <«0 - P (2) - N (2 ) 110. 7 (<0 N(2) -- P (2) - N(3) 115 .7 (3 ) c <«») - P (2) - N (3) 109. 3 N(3) -- P (3) - N(1) in . 6 ( 3 ) c (5) - P (3) - N (3) 109. 1 (*) c (5) - P (3) - N (D 108. 4 < « » > P(1) • - N (2) - P ( 2 ) 123 .4(4) c (6) - P (3) - N (3) 111. 0 <«0 P(2) -- N (3) - P ( 3 ) 124 • 2 (4) c (6) - P (3) - N (D 109. 1 (<») P{3) • - N (D ~ P(1) 124 .5(4) c (D - P (D - c (2) 106. 5 (5) C(1) • - P (D - N(1) 107 .5(4) c (3) - P (2) - C (<») 103. 5 (5) C(1) -- P (D " N(2) 108 .7 (4) c (5) - P (3) - C (6) 104. 0 (5) Table 6 WEIGHTED LEAST-SQUA RES PLANE FOB THE PHOSPHAZENE RING (X, Y AND Z IN A) AND DEVIATIONS, D, OF THE ATOMS IN THE RING FROM THE PLANE. -0.4377X + 0.5764Y - 0.6901Z = -7.7582 Atom D D/cr N(1) -0. 103 3.50 N(2) -0.141 4.57 N(3) -0.084 2.82 P(1) 0.024 1.92 P(2) 0.005 0.80 P(3) 0.007 0.84 17 (19) has a planar r i n g , the dimethylamino d e r i v a t i v e (20) i s s l i g h t l y non-planar i n the boat conformation while the c h l o r o - (21-23), bromo- (24), and the phenyl (25) d e r i v a t i v e s are s l i g h t l y non-planar i n the c h a i r conformation. Of the two perturbed c y c l o t r i p h o s p h a z e n e r i n g s , N-jPg Cl2. (NHPrL )^ H + (11) i s s l i g h t l y boat-shaped and N 3Pj (NMe z) 6H + (12) has teen shown to have two n e a r l y planar s t r u c t u r e s , one i n a d i s t o r t e d boat and the other i n a c h a i r conformation. These s m a l l d e v i a t i o n s from n o n - p l a n a r i t y have been a s s o c i a t e d with i n t e r - and i n t r a - m o l e c u l a r s t e r i c e f f e c t s (21,24,25). Two d i s t i n c t P - N bond lengths are present. The longer ones are a s s o c i a t e d with N(1), the n i t r o g e n bonded to the i o d i n e molecule. These two bond lengths are 1.650(7) and o 1. 623 (7) with an average length of 1.64 (2) A. The number i n parentheses a f t e r average l e n g t h s i s the root-mean-square d e v i a t i o n . The f o u r other P - N bond le n g t h s are e q u i v a l e n t o with an average value of 1.598 (2)A. T h i s value agrees very w e l l with the P - N bond le n g t h i n N^P^Meg, P - N = 1. 596 (5)A (26). The n i t r o g e n atom, N(1), donates e l e c t r o n s i n t o an ant i - b o n d i n g o r b i t a l of the i o d i n e molecule (27). T h i s decreases the amount of e l e c t r o n charge that c o u l d be used f o r IT - bonding i n the r i n g and consequently the two P - N bonds, P(1) - S(1) and P (3) - N(1), are longer than the other P - K bonds, which have normal 7f - bonding present i n unperturbed c y c l o t r i p h c s p h a z e n e s (8). The perturbed n i t r o g e n w i l l be c a l l e d N p. In one s t r u c t u r e of NgP^ (NMe^)^ H + , the c P - Np bond d i s t a n c e i s 1.668 (2)A, while i n the other o s t r u c t u r e i t i s 1.69(1)A (12). The mean P - N bond length i n 18 N 3 P 3 ( N M e £ ) G i s 1.588 (3) A (20). The P - N bond d i s t a n c e i s o i n c r e a s e d by 0.08 and 0.11 A r e s p e c t i v e l y upon p e r t u r b a t i o n f o r the two s t r u c t u r e s of N 3 P 3 (NMe 2) f c H+. In our case the o P - Np d i s t a n c e i n c r e a s e s by 0.04A upon p e r t u r b a t i o n . T h i s i s compatible with the f a c t t h a t H + i s a stronger a c c e p t o r than The N(1) - 1 (1 ) bond l e n g t h i s 2.417(7) A. The sum of the o c o v a l e n t r a d i i f o r n i t r o g e n and i o d i n e i s 2.03A (28). T h i s shows t h a t a weak bond i s present. Values f o r N - I bond lengths i n other charge t r a n s f e r complexes are: 2.26 f o r p y r i d i n e . I C l (29), 2.31 f o r y - p i c o l i n e . I j . (30), 2. 30 f o r o trxmethylamine.ICl (31) and 2.27A f o r trimethylamine.I2 (32). It i s more d i f f i c u l t f o r a n i t r o g e n atom i n the cy c l o t r i p h o s p h a z e n e to donate e l e c t r o n s to the i o d i n e molecule than i t i s i n the other compounds above because of the use of the n i t r o g e n e l e c t r o n s i n IT - bending i n the phosphazene r i n g and consequently the N - I bond distance i s g r e a t e r i n the phosphazene. o The i o d i n e - i o d i n e bond l e n g t h i s 2.823 (1)A. T h i s compares f a v o u r a b l y with I - I bond lenghts of 2.83 o i n cf - p i c o l i n e . I ^ (30) and 2.84A i n tr i m e t h y l a m i n e . 1% (32). o The I - I d i s t a n c e i n the f r e e halogen i s 2.67A (28). T h i s agrees with the molecular o r b i t a l theory that the n i t r o g e n atom donates some e l e c t r o n i c charge i n t o an anti - b o n d i n g o r b i t a l on the i o d i n e molecule (27) and coseguently i n c r e a s e s the I - I bond le n g t h . M(1), 1 ( 1 ) , and 1(2) are almost l i n e a r , the valence angle being 177.8(2)°. T h i s agrees with 19 other halogen - n i t r o g e n complexes (29-32). The P - C bonds are a l l e g u i v a l e n t and have an average o value of 1.789(8)A. T h i s i s i n good agreement with the value of 1.805(8)1 f o r Ni,P HMe 8 (26). The mean e n d o c y c l i c phosphorus angle i s 114.7(8)°. The i n d i v i d u a l v a l u e s vary from 113.9(3) to 115.7(3)°. The mean value i s a l i t t l e l e s s than t h a t given f o r ( N P X 2 J 3 molecules (19-25). These values range from 116.6(20) f o r the bromo d e r i v a t i v e (24) to 120.0(4)° f o r the c h l c r o d e r i v a t i v e (21). However, the mean N - P - H angle i s not as s m a l l as i t i s i n N 3 P 3 (NMe2)k H+ (12). The mean angles f o r the two s t r u c t u r e s are 110.0(2) and 112.0(2)° r e s p e c t i v e l y f o r the c h a i r and d i s t o r t e d boat conformations. T h i s shows that the amount of if - bonding i n the phosphazene r i n g decreases with i n c r e a s i n g p e r t u r b a t i o n and consequently the angle at the phosphorus atom decreases and aproaches t h a t c f a tetr a h e d r o n (109.5°) (8) . The mean e n d o c y c l i c n i t r o g e n angle i s 124.0(8)°. The angles at H(2) and N(3) are the same but the angle at N(1) i s a l i t t l e s m a l l e r . T h i s would be expected because of the i n c r e a s e d N - P bond d i s t a n c e s a s s o c i a t e d with t h i s angle. Values f o r P - S - P angles f o r (NPX^)^ molecules vary from 119.7(10)° f o r the c h l o r o d e r i v a t i v e (21) to 123.0(4)° f o r the dimethylamino d e r i v a t i v e (20). The mean e n d o c y c l i c n i t r o g e n angle i s somewhat g r e a t e r than f o r the (NPX^)^ molecules. This i s c o n s i s t e n t with the smal l e r phosphorus angle i n that the lower the ft - bonding, the g r e a t e r the 20 n i t r o g e n angle (8) . The mean e x o c y c l i c C - P - C angle i s 104(2)°. T h i s i s c o n s i s t e n t with an angle of 104.1(2)° f c r N^P^Meg (26). The u n i t - c e l l viewed down b i s shown i n Fig u r e 2. A l l the i n t e r - m o l e c u l a r d i s t a n c e s correspond to normal van der Waals i n t e r a c t i o n s ; the s h o r t e s t d i s t a n c e s being 3.58 and 3.67A f o r N(3)...C(6) and N(2)...C(4) r e s p e c t i v e l y . Figure 2 The u n i t - c e l l as viewed down b. Hydrogen atoms have been removed for c l a r i t y . 22 P A R T 2 C R Y S T A L A N D M O L E C U L A R S T R U C T U R E O P S O D I U M F O R M A T E ( A R E D E T E R M I N A T I O N ) 23 INTRODUCTION The s t r u c t u r e of sodium formate was o r i g i n a l l y determined i n 1940 by W. H. Zachariasen (33). Be found t h a t c r y s t a l s of sodium formate were m o n c c l i n i c , space-group C2/c, with an a x i a l system of a = 6.19, b = 6.72, c = 6.49A and /8 = 121°42'. There was nothing unusual reported about the s t r u c t u r e and complete resonance between the two s t r u c t u r e s (Figure 3) was r e p o r t e d . No i n t e r - m o l e c u l a r i n t e r a c t i o n s were given and the hydrogen atom was net found but r a t h e r a c a l c u l a t e d hydrogen p o s i t i o n was used. The agreement between the observed 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 was not very s a t i s f a c t o r y . Accurate hydrogen p o s i t i o n s were r e q u i r e d as a b a s i s f o r an E.S.R. and Endor study because hydrogen bonding was thought to e x i s t i n sodium formate (34). The s t r u c t u r e of sodium formate was t h e r e f o r e redetermined. H - C ^ Na + *• N 0 " 0 * H - C ^ Na + ^ 0 F i g u r e 3 The two c o n v e n t i o n a l resonance s t r u c t u r e s of sodium formate. 24 EXPERIMENTAL Zachariasen had r e p o r t e d that c r y s t a l s of sodium formate were elongated along c. A c r y s t a l of sodium formate was mounted on a goniometer, using t h i s c a x i s as a guide, and the s e t of axes used by Z a c h a r i a s e n was found. The systematic absences found by p r e c e s s i o n and Weissenberg photographs co u l d not be made to f i t the space-grcup C2/c. Upon f u r t h e r i n v e s t i g a t i o n a d i f f e r e n t set of axes was l o c a t e d t h a t d i d meet the r e q u i r e d symmetry c o n d i t i o n s f o r C2/c and Cc. I t was found t h a t the c a x i s used by Zachariasen was not the c a x i s at a l l , but the 1 0 1 d i r e c t i o n . Accurate l a t t i c e parameters were obtained by a l e a s t - s q u a r e s refinement of s i x t e e n 2% values measured on a spectrogoniometer. C r y s t a l Data: CHNa0 2 f.w. = 68.01 M o n o c l i n i c , a = 6.2590(6), b = 6.7573(16), c = 6. 1716 (5) A, = 116.140(6)°, U = 234. 32 ( 6 ) A 3 , Z = 4 Dc = 1.9278 (6), F(000) = 136, * (Cu-K«) 1.54178A, yi (Cu-K*) 30. 85cm-*. Absent s p e c t r a : h k i , h+k=2n, hOi,X =2n d e f i n e the space-group as C2/c (Cfh , No. 15) or Cc (C*, No. 9). S i n c e Z = 4, the c o r r e c t space-group cannot be determined by photographic means as the compound can possess the r e q u i r e d symmetry f o r C2/c; a t w o - f o l d r o t a t i o n a x i s . I n t e n s i t i e s were measured on a Datex-automated General 25 E l e c t r i c XRD 6 d i f f T a c t o m e t e r , with a s c i n t i l l a t i o n c ounter, Cu-K* r a d i a t i o n ( n i c k e l f i l t e r and pulse height a n a l y s e r ) , and a ©-29 scan at 2° min- 1 over a range of (1.80 + 0.86tan9) degrees i n 26, with 20s background counts being measured a t each end of the scan. Data were measured to 26 = 145° o (minimum i n t e r p l a n a r spacing 0.81 A). A check r e f l e x i o n was monitored every 20 r e f l e x i o n s and a l l the r e f l e x i o n s were a p p r o p r i a t e l y s c a l e d . Two s e t s of data were c o l l e c t e d and averaged. The averaged data s e t contained 253 r e f l e x i o n s of which 2 had i n t e n s i t i e s l e s s than 3<r above background, where o-(I) i s d e f i n e d by<r 2(I) = S + B + (0.05) S 2, where S and B are the scan and background counts r e s p e c t i v e l y , and only 1 r e f l e x i o n had an i n t e n s i t y l e s s than 2cr. A l l the data were used i n the s t r u c t u r e a n a l y s i s . L orentz and p o l a r i z a t i o n c o r r e c t i o n s were a p p l i e d and the s t r u c t u r e amplitudes were d e r i v e d . The c r y s t a l used had dimensions 0.32 x 0.34 x 0.28mm3. No a b s o r p t i o n c o r r e c t i o n was a p p l i e d . 26 STRUCTURE ANALYSIS The |E| - s t a t i s t i c s are compared with t h e o r e t i c a l values (17) f o r centrosymmetric and noncentrcsymmetric s t r u c t u r e s i n Table 7. As can be seen, the |E| - s t a t i s t i c s are ambiguous and give no i n d i c a t i o n about the symmetry of the space-group and t h e r e f o r e i t was decided to assume no molecular symmetry. T h e r e f o r e the s t r u c t u r e was solved i n the space-group Cc. The s t r u c t u r e was s o l v e d using the symbolic a d d i t i o n procedure f o r non-centrcsymmetric c r y s t a l s (35), with 90 r e f l e x i o n s with |E| > 1.00. The c h o i c e of the o r i g i n determining p a i r of r e f l e x i o n s i n space-group Cc (type 2P00) (36) i s r e s t r i c t i v e , r e q u i r i n g t h a t : = ±1 0) H, + K, L| + L 2 where H n,K r i,L r >, are r e f e r r e d to a p r i m i t i v e c e l l ; i f h n r k n , l n r e f e r t o the centred c e l l then: 0.5 0.5 0 h„ 0.5 -0.5 0 K (D 0 0 -1 L« or Th = H S u b s t i t u t i o n of r e l a t i o n (2) i n t o (1) g i v e s h, 1, h, = ±1 ( 3 ) and o r i g i n s p e c i f i c a t i o n and the phase-determining procedure can then proceed by use of the c o n v e n t i o n a l i n d i c e s f o r the cen t r e d c e l l . O r i g i n determining r e f l e x i o n s were chosen by use of equation (3) and t h e i r phases were a r b i t r a r i l y f i x e d T a b l e 7 |E| - STATISTICS FOR SODIUM FORMAT E THEORETICAL OBSERVED CENT RO NON-CENTRO Mean|E| Mean|E| 2 Mean|E 2-11 |E| > 3 (%) IE | > 2 {%) |E| > 1 {%) 0. 8902 1. 1467 0.9823 0.0 4.72 38.63 0.7980 1 .0000 0.9680 0.30 5.00 32.00 0.8860 1.0000 0.7360 0.01 1.80 37.00 28 at si - 0 m i l l i c y c l e s . Three r e f l e x i o n s were assigned symbol phases, a, b, e and the value f o r the phase of a was c o n s t r a i n e d to l i e between 0 and T 7 " ; although both enantiomorphs are present i n the space-group Cc, t h i s r e s t r i c t i o n , i n t h i s case, d e f i n e s a x i a l d i r e c t i o n . The three symbol phases along with the o r i g i n determining phases comprise the b a s i c s t a r t i n g group given i n Table 8. E i g h t s t a r t i n g s e t s were generated by a l l o w i n g symbol a to have i n i t i a l v alues o f 125 and 375mc and symbols b and c to have i n i t i a l values of ±250mc. These s e t s were used as i n p u t to a computer program which determines phases using the tangent formula (37,38) tan[*J(h)] ^ I j j E (k). E (h-k) | . s i n [ j* (k) + ^ f ( h - k ) ] £ K|E(k).E(h-k) |.cos[*f(k) + /J(h-k) ] - B/A where h and k are the M i l l e r i n d i c e s and A and B are the two c o n v e n t i o n a l p a r t s of the s t r u c t u r e f a c t o r . For each s t a r t i n g se t f i f t e e n c y c l e s of tangent refinement were performed as f o l l o w s : the l a r g e s t 30 E values were i n c l u d e d i n the f i r s t f i v e c y c l e s , between c y c l e s 5 and 10 the l a r g e s t 60 values were i n c l u d e d and a l l 90 r e f l e x i o n s were i n c l u d e d f o r the f i n a l 5 c y c l e s . A phase assignment was r e j e c t e d i n any c y c l e i f (1) the c o n s i s t e n c y index, t = /A2 + B V l K | E ( k ) 1. )E (h-k) | (0 < t < 1) was < 0.25, (2) the parameter (35,39) o( = | E (h) |</A2 + B 2 was < 1,0 and (3) there was a phase change Ajtf(b) > 250mc from the previous c y c l e . A f t e r each c y c l e o v e r a l l values were Table 8 BASIC STARTING SET OF REFLEXIONS FOR CHOtNa h k 1 |E| phase(mc) 4 2 - 1 1 .70 0 1 7 3 - 2 1 .62 o J 3 7 - 2 2.08 a 1 7 -4 2.08 b 4 2 1 1 .96 c o r i g i n determining 30 computed f o r t, c< , and the agreement f a c t o r s , Q and 8k, where Q i s d e f i n e d by: (38) Q = i h I E ( h ) - t(h) E(h) |/£ K|E (h) | and Rk by: (35) Rk = | E (h) | cbs - |E (h) | c a l c | / l w | E (h) |obs the method of o b t a i n i n g | E ( h ) | c a l c i s given i n r e f e r e n c e 35. The v a l u e s of o v e r a l l t , <* , Q, Rk, and N, the number of phases determined, on the f i n a l c y c l e f o r each of the non- centrosymmetric s e t s are given i n Table 9. For a c o n s i s t e n t s e t of phases one would expect and t to be high and Q and Rk to be low. As can be seen from Table 9, there i s no c l e a r s o l u t i o n , and from experience, r e s u l t s l i k e t h i s , ones i n which there i s no s e p a r a t i o n between the s e t s , are regarded q u i t e dubiously. T h e r e f o r e , another e i g h t s e t s were generated with i n i t i a l values f o r a l l symbols of 0 and 500mc, corresponding to the centrosymmetric case. The r e s u l t s from these s e t s are shown i n Table 10. These r e s u l t s are much b e t t e r than those of the non-centrcsymmetric case and set 6 appears to be the c o r r e c t s o l u t i o n . An |E| - map based on the 90 phased r e f l e x i o n s of set 6 gave p o s i t i o n s f o r a l l f i v e atoms, i n c l u d i n g the hydrogen. The s t r u c t u r e was then r e f i n e d i n the centrosymmetric space-group C2/c. Three c y c l e s of f u l l - m a t r i x l e a s t - s q u a r e s refinement of the p o s i t i o n a l and i s o t r o p i c thermal parameters of the atoms gave R = 0.080, T h i s was f o l l o w e d by two c y c l e s of a n i s o t r o p i c refinement of the non-hydrogen atoms which reduced R to 0.07-1. At t h i s stage three r e f l e x i o n s were g i v e n Table 9 RESULTS FOR THE EIGHT NON-CENTRCSYMMETRIC STARTING SETS IN THE PHASE DETERMINATION PROCEDURE Set a (mc) b(mc) c(mc) t «* Q Rk N 1 125 250 2 125 250 3 125 -250 4 125 -250 5 375 250 6 375 250 7 375 -250 8 375 -250 250 86 101 -250 83 99 250 87 102 -250 84 99 250 84 99 -250 95 111 250 86 101 -250 86 101 0. 13 0. 19 90 0. 16 0.17 90 0. 12 0.18 90 0. 15 0. 17 90 0. 15 0.19 90 0. 05 0. 19 90 0. 13 0.19 90 0. 13 0.18 90 T a b l e 10 RESULTS FOR THE EIGHT CENTROSYMMETRIC STARTING SETS IN THE PHASE DETERMINATION PROCEDURE Set a (mc) b (mc) c (mc) t °< Q Rk N 1 0 0 2 0 0 3 0 500 4 0 500 5 500 0 6 500 0 7 500 500 8 500 500 0 79 80 500 65 56 0 75 81 500 84 97 0 79 80 500 98 114 0 75 74 500 68 62 0, 22 0.38 80 0. 33 0.44 73 0. 22 0.34 82 0. 14 0.27 87 0. 19 0. 34 82 0. 02 0.20 90 0. 25 0.39 79 0. 30 0.42 77 33 z e r o weight i n f u r t h e r refinement due to suspected e x t i n c t i o n or counter e r r o r s (Table 11). Three c y c l e s of a n i s o t r o p i c refinement brought R to 0.028. The p a r t i a l atomic charges were estimated by the method giv e n i n r e f e r e n c e UO. A "double atom" was placed at the p o s i t i o n of each atom, with t o t a l s c a t t e r i n g power given by ( f e + p f v ) where f c and f v are the core and valence s c a t t e r i n g f a c t o r s r e s p e c t i v e l y . The occupancy of the valence s h e l l was found by v a r y i n g the m u l t i p l i e r p. The core and valence e l e c t r o n s were c o n s t r a i n e d to l i e at the same p o s i t i o n with one o v e r a l l temperature f a c t o r f o r each "double atom". The core s c a t t e r i n g f o r the hydrogen atom i s zero. The m u l t i p l i e r s p, along with a l l other v a r i a b l e s , were r e f i n e d f o r the HCOz part of the compound f o r three c y c l e s . T h i s reduced R to 0.023. The t o t a l net charge on the HCOj part was -0.79e. The charge on the sodium was t h e r e f o r e s e t at +0.79e and the s c a t t e r i n g f a c t o r f o r Na was modified s l i g h t l y to g i v e the s c a t t e r i n g f a c t o r f o r N a + 0 - 7 ? . Two f i n a l c y c l e s of a n i s o t r o p i c refinement brought R to 0.022. The s t r u c t u r e was then r e f i n e d i n the non- centrosymmetric space-group Cc. In t h i s case R went to 0.024. With a higher R f a c t o r i n the non-centrosymmetric case as compared to the centrosymmetric one, i t i s c l e a r that the centrosymmetric space-group (C2/c) i s the c o r r e c t one. The s c a t t e r i n g f a c t o r s f o r H, C, and 0 were taken from r e f e r e n c e 41 and those f o r Na were modified from r e f e r e n c e 18. The f i n a l weights used were w = (0.0313 + 0.0137|F o| - T a b l e 11 REFLEXIONS GIVEN ZERO WEIGHT IN REFINEMENT R e f l e x i o n |Fobs| | F c a l c | ( F c - F c ) /<r (F 0 ) 1 1 0 2 2 . 7 2 3 2 . 1 6 7 . 0 6 0 2 0 4 8 . 9 1 6 0 . 8 8 1 1 . 9 6 0 0 2 6 3 . 3 1 7 8 . 4 9 1 5 . 1 8 35 0.0027|F 0| 2 + 0 . 0 0 0 1 | F 0 | 3 ) - i which gave constant average values of £w (F e - F c ) 2 over ranges of |F 0|. On the f i n a l c y c l e of refinement no parameter s h i f t was g r e a t e r than 0.05<r and a f i n a l d i f f e r e n c e map gave peaks no g r e a t e r than 0.20e/A 3. The f i n a l p o s i t i o n a l and thermal parameters appear i n Tables 12 and 13 r e s p e c t i v e l y . Observed 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 given i n Appendix 2. T a b l e 12 FINAL POSITIONAL PARAMETERS (FRACTIONAL X 10* ) WITH ESTIMATED STANDARD DEVIATIONS IN PARENTHESES Atom x y z Na(1) 5000 6380(1) 2500 0 (1) 3643 (2) 3034 (2) 3204 (2) C(1) 5000 2201 (2) 2500 H(1) 5000 0732 (30) 2500 Table 13 FINAL THERMAL PARAMETERS AND THEIR ESTIMATED STANDARD DEVIATIONS (A) ANISOTROPIC THERMAL PARAMETERS (Ucj X 100 A 2) Atom U M U t t D33 U ti 0)3 UL3 Na{1) 1.74(3) 2.38(4) 1.79 (3) 0.00 0.76 (2) 0.00 0(1) 1.84(5) 3.16(6) 2.18(5) -0.21(3) 1.01(4) -0.41(3) C(1) 2. 67(7) 2.08(7) 2. 13 (7) 0.00 0.90 (5) 0.00 (b) ISOTROPIC THERMAL PARAMETER (A 2) Atom B H(1) 6.1(8) 38 RESULTS AND DISCUSSION T h i s x-ray a n a l y s i s has confirmed the b a s i c s t r u c t u r e of sodium formate as found by Zachariasen (33). The molecule i s p l a n a r and possesses a two-fold r o t a t i o n a x i s through the middle, g i v i n g i t C a v symmetry. The bond d i s t a n c e s and angles appear i n Table 14. The C - 0 d i s t a n c e of 1.246 (1 )A and the 0 - C - 0 angle of 126.29(16)° are somewhat d i f f e r e n t from those given by Zachariasen, 1.27A and 124° r e s p e c t i v e l y . Table 15 g i v e s a l i s t of some formate i o n geometries f o r d i f f e r e n t s a l t s . The agreement between the present s t r u c t u r e and those of the more recent ones, notably r e f e r e n c e s 43 and 46, i s very good. The d i f f e r e n c e s i n symmetry, i e . l o s s of the two-fold r o t a t i o n a x i s , are due to d i f f e r e n t packing arrangements, and i n the NH+ case i s due to the presence of hydrogen bonding. The e n t i r e i o n i s planar and the equation of the plane i s : -0.3510X + 0.0Y - 0.9364Z = -2.1568 where X, Y, and Z are the orthogonal c o o r d i n a t e s d e r i v e d as f o l l o w s : X a 0 ccosytf X Y = O b 0 y Z 0 0 csinyt? z The sodium atom has s i x oxygen neighbours at an average d i s t a n c e of 2.45A. T h i s i s g r e a t e r than the sum of the o c o v a l e n t r a d i u s of oxygen (0.66A) and the i o n i c r a d i u s of o o sodium (0.95A), 1.61A, but i s l e s s than the sura of the van Table 14 o BOND LENGTHS (A) WITH STANDARD DEVIATIONS IN PARENTHESES o Atoms Bond Length (A) C - 0 1. 246 (1) C - H 0.993 (20) VALENCY ANGLES (DEG.) WITH STANDARD DEVIATIONS IN PARENTHESES Atoms Angle (cleg.) 0 - C - H 0 - C - 0 116.85(8) 126.29 (16) Table 15 FORMATE ION GEOMETRIES IN DIFFERENT SALTS Cat i o n C - 0 Distance(A) 0 - C - 0 Angle (deg.) Ref. Ca++ 1.25(avg.) 125, 124 42 Sr++ 1.243 (avg.) 126. 4, 127.5 43 Ba++ 1.25(avg.) 127, 128 44 Pb++ 1.26 (avg.) 127 (avg.) 44 Gd + + + 1.27, 1 .33 121 (avg.) 45 NH+ 1. 237, 1.246 126.3 46 41 o der Waals r a d i o s f o r oxygen (1.40A) and the m e t a l l i c r a d i u s a o of sodium (1.572A), 2.972A. Therefore there i s a weak i n t e r a c t i o n between the sodium and i t s s i x oxygen neighbours. A l l r a d i i were taken from r e f e r e n c e 28. See F i g u r e 4 f o r a view of the packing i n the u n i t - c e l l . I n d i v i d u a l Na...O d i s t a n c e s are giv e n i n Table 16. The average Na...O d i s t a n c e compares w e l l with Ma...0 d i s t a n c e s i n s i m i l a r type s t r u c t u r e s . See Table 17 f o r some average Na...0 d i s t a n c e s . The charges of a l l the atoms were r e f i n e d . These charges appear i n Table 18. I f the s t r u c t u r e c f sodium formate c o u l d be e n t i r e l y d e s c r i b e d by the two resonance forms i n Figure 3, one would expect the charges on the oxygens to be -0.5e. The r e f i n e d charge i s -0.23(1)e. There i s some i n t e r a c t i o n between the sodium and the oxygens which would account f o r a sm a l l decrease i n the oxygen negative charge, but t h i s i n t e r a c t i o n i s s m a l l and would not be expected to reduce the charge by 0.27e, T h e r e f o r e , there appear to be other resonance forms i n v o l v e d . The charge on the hydrogen atom i s -0.49 (10)e. T h i s i n d i c a t e s a major resonance form of the type: Na + 42 • Na Figure 4 The u n i t - c e l l as viewed down b. Dotted l i n e s show weak sodium - oxygen bonds. T a b l e 16 SODIUM - OXYGEN CONTACT DISTANCES Atoms D i s t a n c e (A) Sa...O(x,y,z) 2.4008(9) Na...O(-x,y,0.5-z) 2.4008 (9) Na.. ,O(0.5-x,0.5-y,-z) 2.43 37 (9) Na...0(0.5+x,0.5-y,0.5+z) 2.4337 (9) Na.. .0 (0.5 + x,0.5 + y, z) 2.5194 (11) Na...O(0.5-x,0.5+y,0.5-z) 2.5194 (11) T a b l e 17 AVERAGE H a . ..0 D ISTANCES FOR SOME SODIUM COMPOUNDS o Compound A v g . N a . . . C d i s t a n c e ( A ) R e f . S o d i u m 2 - 0 x o v a l e r a t e 2 . 4 6 47 S o d i u m <X - K e t o b u t y r a t e 2 . 5 48 S o d i u m P y r u v a t e 2 . 5 0 49 S o d i u m O x a l a t e 2 . 4 8 50 T a b l e 18 REFINED ATOMIC CHARGES Atom Charge (e) Na(1) 0 (1) C(1) H (1) + 0.79 (14) -0. 23 (1) + 0.16 (3) -0.49 (10) 146 The p o s i t i v e charge on the carbon (0.16e) i s probably the r e s u l t of some minor resonance forms of the f o l l o w i n g type: 0" H" (£ Na + •• • H C+ Na + 0 . The d i s t a n c e between a sodium atom of one molecule and the hydrogen atom of the next molecule along the y - a x i s i s 2.94 (2)A. The sum of the i o n i c r a d i u s of sodium and the van o o der Waals r a d i u s of hydrogen (1.2A) i s 2.15A. The hydrogen atom has almost h a l f an e l e c t r o n charge on i t and t h e r e f o r e i t i s not very a p p r o p r i a t e to use the van der Waals r a d i u s . The t r u e r a d i u s to be used would be somewhere between the van der Waals r a d i u s and the i o n i c r a d i u s (2.08A). The i o n i c o r a d i u s would give a d i s t a n c e of 3.03A f o r Na...H i n t e r a c t i o n . Although t h i s d i s t a n c e i s not much more than the measured d i s t a n c e , i t might be p o s s i b l e that there i s some Na...H i n t e r a c t i o n . T h i s i n t e r a c t i o n was found to e x i s t and can be seen i n the f i n a l d i f f e r e n c e map (Figure 5 ) . T h i s d i f f e r e n c e map i s viewed p e r p e n d i c u l a r to the formate plane along the y- a x i s . There i s much e l e c t r o n d e n s i t y between the scdium and the hydrogen atoms. E l e c t r o n d e n s i t y between the oxygens and Figure 5 F i n a l difference map. Dotted lines indicate regions of electron density. Contours are drawn at 0.05e/A3. 48 the sodium can a l s o be seen as well as the lone p a i r e l e c t r o n s on the oxygens. The standard d e v i a t i o n of the e l e c t r o n d e n s i t y was c a l c u l a t e d by the method given i n o r e f e r e n c e 51 and was found to be 0.021e/fl 3. T h e r e f o r e a l l the peaks found on the d i f f e r e n c e map are s i g n i f i c a n t l y present. The d i f f e r e n c e map shows that the c r y s t a l s t r u c t u r e of sodium formate c o n s i s t s of sodium formate ions hydrogen bonded together i n t o rows. There i s much d e l c c a l i z a t i o n of e l e c t r o n s throughout the c r y s t a l , and the rows i n t e r a c t with each other through weak Na - 0 bonds. A P P E N D I X 1 S T R U C T U R E F A C T O R S F O R H E X A M E T H Y L C Y C I O T R I P H O S P H A Z E N E - I O C I M E (1:1 A E D U C T ) 50 h k 1 Fo Fc 0 0 1 59. 28 50.03 0 0 2 162.84 139.08 0 0 3 134.97 119.37 0 0 5 63 .39 63.85 0 0 6 20. 13 21.30 0 1 0 5.36 3.77 0 1 1 28. 33 26. 12 0 1 2 137.47 1 13.08 0 1 3 25.98 27. 35 0 1 4 32 .68 31.80 0 1 5 34.56 32.89 0 1 6 10.53 12.51 0 2 0 14.70 14.08 0 2 1 99.48 82.36 0 2 2 17. 19 18.26 0 2 3 92.94 86.36 0 2 4 65.68 62.88 0 2 6 36 .45 35.29 0 3 0 100.36 88. 17 0 3 1 16.35 1 1.97 0 3 2 60.08 58.71 0 3 3 120.16 110.04 0 3 4 18.53 18.70 0 3 5 97.25 92.64 0 3 6 44. 16 44.51 0 4 0 85.28 76.43 0 4 1 90.40 79.92 0 4 2 128.45 117.64 0 4 4 48. 51 47.96 0 4 5 8.80 7.27 0 5 0 63. 11 59.32 0 5 1 83.35 78.22 0 5 3 23.95 24. 10 0 5 4 19.48 19.50 0 6 0 15.72 15.98 0 6 1 37.01 37.61 0 6 2 26. 17 24.82 0 6 3 41 .73 42. 17 0 7 0 23.25 21.94 0 7 1 42.00 38.98 0 1 22.61 23.11 0 2 15.08 13.53 0 3 24.76 31. 15 0 4 29.75 28.03 0 5 31.18 29.97 0 6 36.70 35.30 1 0 60.55 58.27 1 2 66.24 65.46 1 3 27.79 29.06 1 4 73 .74 70.08 1 5 67.45 66.68 1 6 18.05 17.15 2 0 22.47 24.62 2 1 143.81 114.89 2 2 44.93 40.78 2 3 47.77 46.99 2 4 92. 26 86.44 h k 1 Fo Fc 1 2 5 28.37 26.20 1 2 6 76. 15 75.55 1 3 0 192.29 164.97 1 3 2 72.85 64.65 1 3 3 124.59 112.00 1 3 4 11.08 10. 92 1 3 5 35.85 34.63 1 4 0 52.73 52. 48 1 4 1 55.82 51.25 1 4 2 87.08 76. 51 1 4 3 6.63 5. 86 1 4 4 27.72 27. 35 1 4 5 8.88 7.55 1 5 0 28.96 29. 08 1 5 1 34.38 31.79 1 5 2 25. 12 24.44 1 5 3 34.90 34.58 1 5 4 50.44 49. 15 1 6 0 63.46 59.85 1 6 1 17.01 16. 86 1 6 2 41.99 37.33 1 7 0 50.91 47. 63 2 0 0 26.41 27.52 2 0 1 53.49 46. 43 2 0 2 12.94 9.78 2 0 3 49.72 46. 56 2 0 4 36.91 34.50 2 0 5 45.72 44. 90 2 0 6 38.34 34.98 2 1 1 13. 22 12. 68 2 1 2 101.44 90.09 2 1 3 56.03 53.73 2 1 4 21.12 21.20 2 1 5 73.57 67.96 2 1 6 27.65 25.55 2 2 0 18.39 19.26 2 2 1 193.67 166.59 2 2 2 116.63 104.43 2 2 3 53.79 50.08 2 2 4 87. 34 81.37 2 2 5 17.65 17.30 2 3 0 137.36 120.04 2 3 1 97.44 85.99 2 3 2 27.95 25. 82 2 3 3 77.74 73. 14 2 3 4 8. 29 6. 68 2 3 5 27.52 26.42 2 4 0 31.74 32. 02 2 4 1 34.31 31.79 2 4 2 43.99 42. 28 2 4 3 36.61 35. 83 2 4 4 37. 10 36. 86 2 5 0 36.01 35.07 2 5 1 79.52 73.36 2 5 2 6.18 7.93 2 5 3 23.28 20. 84 2 6 0 43.70 41.01 h k 1 Fo Fc 2 6 1 80. 87 76.32 2 6 2 16.81 16.02 3 0 0 55.91 53.44 3 0 1 103.46 85.36 3 0 3 53.60 55.60 3 0 4 59 .28 58.08 3 0 6 48.81 48.80 3 1 0 198.49 175.05 3 1 1 49. 4 3 46.53 3 1 2 167.30 144.22 3 1 3 129.82 119.79 3 1 4 18.91 20.97 3 1 5 60.03 59. 14 3 2 0 38.25 34.88 3 2 1 1 16.18 100.75 3 2 2 63 .24 62.26 3 2 3 16.6 3 17. 11 3 2 4 67.47 65.67 3 3 0 12.71 14.36 3 3 1 36.41 35.68 3 3 2 36.55 33.84 3 3 3 50.22 48.26 3 3 4 52.85 50. 19 3 4 0 47.60 46.62 3 4 1 25.28 20.27 3 4 2 76.05 68.85 3 4 3 9. 86 8.95 3 5 1 53.85 49.63 3 5 2 105. 13 97.79 3 5 3 11 .98 10.50 3 6 0 94.92 90.25 3 6 1 59.77 55.83 4 0 0 44. 15 42. 15 4 0 1 159.90 142.58 4 0 2 51.82 47.52 4 0 3 117.25 107.02 4 0 4 78. 32 73.82 4 1 0 185.30 158.59 4 1 1 18.99 18.73 4 1 2 63.02 59.35 4 1 3 47.46 45.45 4 1 4 16.71 16.19 4 1 5 46.74 48.35 4 2 0 31 .97 31.20 4 2 1 12.42 13.02 4 2 2 19.59 18.20 4 2 3 31.55 30.71 4 2 4 45.75 44.49 4 3 1 57.33 55.47 4 3 2 21 .80 21.22 4 3 3 48.89 46.09 4 3 4 22.38 21.68 4 4 0 97.96 91.58 4 4 1 19.55 20.19 4 4 2 54.63 52. 18 4 4 3 99.06 93.96 4 5 0 15.95 14.91 4 5 1 80.24 74.82 h k 1 Fo Fc 4 5 2 61.32 57. 93 5 0 0 73.66 67.97 5 0 1 127.99 117.22 5 0 2 7.78 5.77 5 0 3 35.73 34.22 5 0 4 37. 42 37. 11 5 1 0 56.98 54.51 5 1 1 61. 37 61.73 5 1 2 15.05 14.05 5 1 3 6.70 5.61 5 1 4 29.13 28.45 5 2 2 50.51 50. 17 5 2 3 7.43 9.04 5 2 4 32.09 30. 61 5 3 0 28.83 29.37 5 3 1 106.03 98.46 5 3 2 50.99 49.96 5 3 3 36.42 35.37 5 4 - 0 105.88 99.60 5 4 1 26.63 24.92 5 4 2 59.82 56.58 5 5 0 39.07 39.63 6 0 1 40.26 39.23 6 0 2 41.56 41. 64 6 0 4 6.50 5.38 6 1 0 6.59 0.80 6 1 1 20.71 21.97 6 1 2 14.92 15. 38 6 1 3 41.63 40.23 6 2 0 63. 12 61. 60 6 2 1 17.49 14.81 6 2 2 96.05 90. 74 6 2 3 54.09 52.85 6 3 0 47.58 44.43 6 3 1 84.51 81.06 6 3 2 32. 13 32.20 6 4 0 44.61 44.81 6 4 1 41.94 41. 76 7 0 0 29.24 28.35 7 0 2 19. 18 18.84 7 1 0 41.43 42.75 7 1 1 66.76 64.88 7 2 0 84. 10 82.65 7 2 1 33. 39 34.00 7 3 0 15.28 16.58 8 0 0 15. 35 14. 63 8 0 1 27.52 28.08 8 1 0 36.50 35.27 0 0 -1 56.94 50.03 0 0 -2 158.54 139.08 0 0 -3 134.16 119.37 0 0 -4 26.57 25. 86 0 0 -5 62.76 63. 85 0 0 -6 20.69 21. 30 0 1 -1 102.32 86.16 0 1 -2 140. 10 120.24 0 1 -3 104.31 92.47 0 1 -4 103. 17 97. 09 h k 1 Fo Fc 0 1 -5 8.50 9.45 0 1 -6 52.39 51.22 0 1 -7 15.96 14.29 0 2 -1 69.71 63.68 0 2 -2 58.53 52.34 0 2 -4 38.23 38. 84 0 2 -5 70.36 66.31 0 2 - 6 6. 86 7. 38 0 2 -7 33.25 31.56 0 3 -1 41.96 39.77 0 3 -2 78.23 63.13 0 3 -4 21.63 20.90 0 3 -5 15.83 16.54 0 3 - 6 53.58 52.87 0 3 -7 19.09 18.76 0 4 -1 158.28 135.90 0 4 -2 27.96 29.22 0 4 -3 60. 19 55.69 0 4 -4 43.09 41.67 0 4 -5 11.38 9.67 0 4 - 6 28.56 27.55 0 5 -2 99.62 93. 30 0 5 -3 69.93 65.81 0 5 -4 53.99 51.57 0 5 -5 59.26 58.37 0 6 -1 38. 31 36.91 0 6 -2 13 .34 12.05 0 6 -3 28.07 26.29 0 6 -4 15.30 13.26 0 7 -1 47.48 45. 12 0 7 -2 26 .87 25.30 0 7 -3 24. 19 23.93 1 0 -1 90.95 93.31 1 0 -2 123.88 118.00 1 0 -3 123.49 113.25 1 0 -4 12.86 13.22 1 0 -5 62.54 60.56 1 0 -6 24.39 24.60 1 0 -7 42 .86 43.41 1 1 -1 34.76 40.40 1 1 -2 18.24 18.06 1 1 -3 63. 12 71.95 1 1 -4 97.86 91.03 1 1 -5 40.49 38.06 1 1 - 6 65.89 64.68 1 1 -7 54 . 01 52.67 1 2 -1 25.73 31.28 1 2 -2 22.08 24. 10 1 2 -3 6.68 8.66 1 2 -5 65.27 61.27 1 2 -6 17.37 17.05 1 2 -7 34.56 32.80 1 3 -1 22.36 20.93 1 3 -2 82.97 87.51 1 3 -3 63.49 64.65 1 3 -4 10.84 8.47 1 3 -5 41 .79 42.30 1 3 - 6 30.60 30.01 52 h k 1 Fo Fc 1 3 -7 21.31 20.58 1 4 -1 108.00 116.75 1 4 -2 58.96 58. 66 1 4 -3 92.47 89.79 1 4 -4 91. 32 85. 33 1 4 -5 20.74 21.39 1 4 -6 27.41 25. 77 1 5 -1 20.89 22.29 1 5 -2 35.65 36. 98 1 5 -3 7.06 6. 14 1 5 -4 18.88 17. 18 1 5 -5 44.72 42. 87 1 5 -6 7.72 7. 65 1 6 -1 36.05 40.82 1 6 -2 22.20 23.39 1 6 -3 11.26 13.36 1 6 -5 19. 52 19. 12 1 7 -1 28.21 30.18 1 7 -3 29.88 28.26 2 0 -1 16.19 20.37 2 0 -2 163.51 158.71 2 0 -3 95.60 93.93 2 0 -4 64.98 63. 42 2 0 -5 86.84 89.04 2 0 -6 63.76 61.50 2 0 -7 39. 14 40.02 2 1 -1 46. 11 48. 52 2 1 -2 15.67 18.72 2 1 -3 28. 34 30. 41 2 1 -4 57.08 58.49 2 1 -5 12. 14 12.33 2 1 -6 45.04 44.35 2 1 -7 18.96 18. 84 2 2 -1 171.69 166.50 2 2 -2 71.64 76. 73 2 2 -4 48.76 50.41 2 2 -5 46.50 45.54 2 2 -6 30.93 32.74 2 2 -7 7.27 4.35 2 3 -1 39.47 46.33 2 3 -2 117.95 125.35 2 3 -3 113.32 114.43 2 3 -4 61. 83 60. 60 2 3 -5 48.53 49. 14 2 3 -6 8. 48 8. 43 2 3 -7 11.82 13.68 2 4 -1 30.69 34. 14 2 4 -2 22.82 23.93 2 4 -3 39.37 42.39 2 4 -4 55.75 58.44 2 4 -5 11. 33 10. 15 2 4 -6 58.67 57. 13 2 5 -1 25.68 28. 69 2 5 -2 10.45 10.44 2 5 -3 12.30 15. 14 2 5 -4 25.42 26.67 2 5 -5 35.81 36.70 2 6 -2 44.87 48.63 h k 1 Fo Fc 2 6 -3 28.86 30.28 2 6 -4 20.17 20.45 2 7 -1 74.72 80. 15 2 7 -2 9.79 10.30 3 0 -1 36. 10 33.62 3 0 -2 56.95 59.89 3 0 -3 34.76 42.68 3 0 -4 9.19 9.06 3 0 -5 56.98 59.05 3 0 -6 10.53 9.41 3 1 -1 77.75 75.34 3 1 -2 23 .23 22.74 3 1 -3 50.89 60.51 3 1 -4 58.21 61.58 3 1 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46.65 45.38 -7 1 6 49.79 48.43 -7 1 7 9.71 7. 39 -7 1 8 13.42 11.58 -7 2 7 18.47 17.50 -7 3 7 41.40 40.43 -7 4 5 20.62 20. 08 -7 4 6 29.54 29.70 -7 5 3 46.55 47.33 -7 5 4 29.28 29.02 -7 5 5 35. 20 36.20 -7 5 6 7.79 4.02 -7 6 0 15.21 15.79 -7 6 1 66.10 68.61 -7 6 3 33.95 35. 42 -7 6 4 20.44 21.23 -7 7 2 6.90 2. 53 -7 7 3 9. 10 8.45 -7 7 4 18.53 18. 23 -7 8 2 15.79 13.45 -8 0 6 19.63 18. 20 -8 0 7 23.48 21. 84 -8 1 5 18. 38 16. 24 -8 1 6 48.72 50.45 -8 1 8 30. 25 26. 78 -8 2 5 50.99 51.22 -8 2 6 16.78 15.38 h k 1 Fo Fc -8 2 7 20.21 17.51 -8 3 6 18.73 18.04 -8 4 3 9.50 7.84 -8 4 4 13.77 15.92 -8 4 5 7.68 6.81 -8 4 6 39.42 37.18 -8 5 0 19.50 18.44 -8 5 1 8. 34 8.50 -8 5 2 19.89 19. 19 -8 5 4 26.05 24.33 - 8 5 5 27.61 26.72 -8 5 6 10.03 10.94 -8 6 1 27.28 24.82 -8 6 2 29.63 30.05 -8 6 3 25.33 24.68 -8 6 4 29. 23 28.76 -8 7 0 47.91 47.34 -8 7 1 10. 13 8.43 -8 7 2 34 .14 33.59 -8 7 3 14.04 13.60 - 9 0 0 41 .41 43.89 -9 0 1 27.88 29.93 -9 0 3 20.25 19.42 -9 0 4 18.75 17.51 -9 0 5 18.94 19.14 -9 0 7 11.75 9.92 -9 1 0 41 .50 41.75 -9 1 3 16.70 14.79 -9 1 5 24.10 23.83 -9 1 6 20.99 19.08 -9 2 0 36 .90 37.47 -9 2 1 20.26 20.44 -9 2 2 30.29 30.42 -9 2 4 12.72 11.44 -9 2 5 42.30 42.34 -9 2 6 10.43 8.01 -9 2 7 29.98 27.28 -9 3 0 28.63 29.61 -9 3 1 50.67 50.83 -9 3 2 25. 98 27.70 -9 3 3 60.13 61.75 -9 3 4 43.23 43.24 -9 3 5 19.25 18.44 -9 3 6 15.48 13.89 -9 4 0 44.23 45.86 -9 4 1 12.41 12.32 - 9 4 2 33.61 36. 16 -9 4 3 10. 13 10.31 -9 4 5 22 .40 20.69 -9 4 6 9.28 7. 27 -9 5 1 7.17 7.18 -9 5 3 14.50 14,90 -9 5 4 8.16 6.63 -9 5 5 29.64 28.07 -9 6 1 17.19 14.66 -9 6 3 20. 15 20.00 -9 6 4 16 .92 15.29 -10 0 0 43.25 42.71 64 h k 1 Fo Fc -10 0 1 57. 20 57. 42 -10 0 3 52. 18 51.58 -10 0 4 4 1.66 40. 13 -10 0 5 21.61 20.61 -10 0 6 22.91 20.90 -10 1 0 15.78 16.22 -10 1 2 22.80 23.28 -10 1 3 10.21 9.55 -10 1 4 15.38 15.73 -10 1 6 7.74 5. 96 -10 2 0 7.99 7. 87 - 10 2 1 14.27 14.61 -10 2 2 9.99 9. 40 -10 2 4 24.85 24.97 -10 2 5 18.00 16. 47 -10 2 6 9.74 7.88 -10 3 0 8.69 7.74 -10 3 1 20.29 18.44 -10 3 3 15.90 14. 12 -10 3 4 26.87 26.44 -10 3 5 12. 11 11. 52 - 10 4 0 28.69 28.43 -10 4 1 16.45 16.32 -10 4 2 43.08 42.95 -10 4 3 31.53 30.20 -10 4 4 19.86 19.84 -10 4 5 14,99 12. 65 -10 5 0 13.35 13.10 -10 5 1 31.96 32.95 -10 5 4 15.88 14. 87 -11 0 0 16.04 17. 32 -11 0 1 26.86 25.53 -11 0 2 7.59 5.82 -11 0 3 28.97 28.52 -11 0 4 22.08 21. 97 -11 1 0 40.59 41.68 -11 1 1 11.89 10.41 -11 1 2 47.48 46.81 -11 1 3 29.04 28. 16 -11 1 4 28.35 26.48 -11 2 0 11.27 10.97 -11 2 1 24.55 23.35 -11 2 3 17.83 17.25 -11 3 0 11.86 12.67 -11 3 1 13.31 13. 16 -11 3 3 19.87 18.68 -11 3 4 15.36 13.75 -1 0 -7 16.25 14. 80 -1 0 -8 8.21 8. 28 -1 1 -8 11.50 12.36 -1 2 -8 8.60 10. 53 -1 2 -9 12.02 13.02 -1 3 -7 9.73 5.47 -1 3 -8 18.64 19.30 -1 4 -7 35.79 35.46 - 1 4 -8 17.18 17.23 -1 5 -7 20.63 20. 35 -1 5 -8 11.46 12.67 h k 1 Fo Fc 1 6 -6 34.98 36.31 1 7 -4 14.36 15.34 1 7 -5 13.04 13.60 1 7 -7 18.02 18.01 1 8 -1 18.77 17.69 1 8 -2 32 .92 30.20 1 8 -3 10. 32 10.22 1 8 -4 17.84 17.46 1 8 -5 11.99 11.41 1 9 -1 17.80 16.39 1 9 -2 19. 14 19. 17 1 9 -4 8.95 7.23 2 0 -7 20.51 22. 15 2 0 -8 15.19 16.52 2 1 -7 33. 60 33.44 2 1 -8 15.80 16.83 2 2 -7 26.25 27.93 2 2 -8 11 .70 14.01 2 3 -7 8. 87 7.22 2 3 -8 11 .77 12.95 2 4 -7 25.73 26.36 2 5 -6 22 .53 22.46 2 5 -7 9.15 7.31 2 5 -8 20.49 21.08 2 6 -5 31.42 30.54 2 6 -6 16 .32 17.50 2 7 -4 37.40 35.67 2 7 -5 35.58 33.67 2 7 -6 13.52 13. 17 2 8 - 1 20.76 19.48 2 8 -2 8.93 7.83 2 8 -3 23.56 22.92 2 9 -1 24. 67 23. 17 2 9 -2 9.01 10.75 2 9 -3 21.92 20.73 3 0 -7 23.42 22.30 3 0 -8 25.51 26.82 3 1 -7 19.38 19.51 3 1 -8 16.60 15. 16 3 2 -7 17.80 19.10 3 2 -8 19. 50 19.50 3 3 -7 14 .62 12.54 3 3 -8 16.96 19.07 3 4 -7 24 .11 26.38 3 4 -8 9. 14 7.06 3 5 -6 14.85 12.36 3 6 -5 12.82 14.45 3 6 -7 12.65 13.58 3 7 -4 26. 21 25.44 3 7 -5 9.21 10.61 3 7 -6 11.50 10.71 3 8 -1 18.39 15.97 3 8 -2 10.83 10.73 3 8 -3 36.83 35.83 3 8 -4 12.04 10.68 3 8 -5 20.94 20.94 3 9 -2 16.75 16.41 4 0 -6 41 .88 43.81 65 h k 1 Fo Fc -4 0 -7 14.12 16.03 -4 1 -7 24.78 27.54 -4 2 -6 29.49 28.93 -4 3 -6 19.58 22. 13 -4 3 -7 20.58 20.92 -4 4 -6 14.72 15.44 -4 4 -7 18.43 20.65 -4 5 -5 13.64 15.05 -4 5 -6 43.47 43.35 -4 6 -4 20.08 18. 47 -4 7 -2 18.22 17.90 -4 7 -3 19.34 19. 94 -4 7 -4 18.97 17. 94 -4 8 -1 30. 11 29.93 -4 8 -2 25.68 24.33 -4 8 -3 20.92 20. 21 -4 9 -1 11.95 11.51 -4 9 -2 13.01 12. 78 -5 0 -6 30.41 31.88 -5 0 -7 15.87 16.07 -5 1 -7 23.04 26.44 -5 2 -6 35. 18 35.64 -5 2 -7 12.49 10.07 -5 3 -5 10.79 12. 43 -5 3 -6 8.33 8.46 -5 3 -7 17. 17 16.99 -5 4 -7 9.04 9.30 -5 5 -5 39.37 40.70 -5 5 -6 9.27 9.72 -5 6 -3 11. 20 12. 61 -5 6 -4 21.11 21.52 -5 6 -5 29.28 29. 93 -5 6 -6 13.13 1 1.56 -5 7 -1 13. 29 11. 61 -5 7 -2 29.59 29.54 -5 7 -3 19.63 18. 86 -5 7 -4 13.10 12. 19 -5 8 -1 17.58 15. 08 -5 8 -3 14.48 11.71 -5 8 -4 13.45 15. 16 -5 9 -1 14.61 13.57 -6 0 -5 26. 40 26. 14 -6 0 -6 15.33 15. 14 -6 1 -5 18. 30 22. 82 -6 1 -6 8.19 7. 32 -6 2 -5 36.92 39. 92 -6 2 -6 26.23 28.90 -6 3 -5 31.37 32.29 -6 4 -4 14.31 15.25 -6 4 -6 13. 15 13. 52 -6 5 -3 21.44 22.79 -6 5 -5 7.93 7. 98 -6 6 -2 28.87 29.73 -6 6 -4 30.55 31. 57 -6 7 -1 13.95 13.52 -6 7 -2 18.61 18. 80 -6 7 -3 25.32 25.37 -6 8 -1 12.20 10.69 h k 1 Fo Fc h k 1 Fo Fc 6 8 -2 15.23 14.48 -8 5 -3 11.69 10.81 •6 8 -3 21.49 21.88 -8 5 -4 16.18 16.61 7 0 -4 27.54 28.37 -8 6 -1 14.42 14. 02 •7 0 -5 20.46 20.71 -8 6 -2 26.65 25.59 7 1 -4 9.66 8.21 -8 6 -3 9.81 8. 62 7 2 -5 9.27 8.54 -8 7 -1 14.45 13.97 7 3 -4 50.84 53.48 -8 7 -2 14.99 14.51 7 3 -5 25. 30 27.71 -9 0 -1 14.84 17. 19 7 4 -3 26.39 27.60 -9 0 -2 53.69 55. 80 7 4 -5 10.42 10. 14 -9 1 -2 14.68 15. 16 7 5 -2 16 .54 16.13 -9 1 -3 34. 55 36. 73 7 5 -3 27. 81 31.22 -9 2 -2 23.72 24.03 7 5 -4 10.27 8.39 -9 2 -4 16.36 15. 46 7 5 -5 13. 16 12.69 -9 3 -1 22.51 23.11 7 6 -1 34.27 35. 19 -9 3 -2 37. 17 39.03 7 6 -2 24.77 25.10 -9 4 -1 28.79 29.73 7 6 -4 17.58 18.27 -9 4 -2 10. 10 9.99 7 7 -1 15.51 16.98 -9 4 -3 27.61 29. 13 7 7 -2 16.16 13.57 -9 5 -1 14.64 13. 09 7 7 -3 16. 34 15.98 -9 5 -2 9.36 9.33 7 8 -1 10.56 8.90 -9 6 -1 14.66 14.26 8 0 -2 50.91 53.60 -10 0 -1 20.73 22.09 8 0 -3 12.99 1 1.33 -10 0 -2 19.92 22. 13 8 0 -4 35.25 37.45 -10 1 -1 34.85 36. 14 8 1 -2 7.06 5.40 -10 2 -1 27. 44 27. 81 8 1 -3 19.07 17.46 -10 2 -2 7.97 7.45 8 1 -4 17.03 16.06 -10 3 -1 28. 21 28. 63 8 1 -5 12.33 13.40 -10 4 -1 20.34 20.96 8 2 -3 15.84 17.33 -10 4 -2 10.92 9. 83 8 2 -4 9.95 11.27 -10 5 -1 26.21 25. 86 8 2 -5 9.92 12.32 8 0 -3 22.96 24. 11 8 3 -2 39.11 40.22 -3 3 2 91.85 94.55 8 3 -4 21 .48 23.19 -7 0 2 59.92 61.91 8 4 -1 9.25 8.73 0 1 7 13.90 13.98 8 4 -2 12 .89 13.63 7 0 3 19.57 18.44 8 4 -3 27.60 28.53 8 1 1 71.76 72.94 8 4 -4 13.95 15.28 -8 3 4 14. 37 15. 40 8 5 -1 14.37 14. 17 -7 0 -3 18.45 18.44 8 5 -2 23.14 23.09 -7 3 -3 8.33 7.53 67 APPENDIX 2 STRUCTURE FACTORS FOR SODIUM FORMATE h k 1 Fo Fc - 1 -1 7 8.42 8.58 -3 -1 7 4. 16 4. 10 -5 -1 7 1 .02 1.04 -2 -2 7 9.43 9.78 -4 -2 7 4.28 4.36 -3 -3 7 10.94 10.99 -2 0 6 13.78 13.36 -4 0 6 30.09 30.04 -6 0 6 14 .20 14.38 -1 -1 6 3.11 3.02 -3 -1 6 9.17 9.18 -5 - 1 6 9.57 9.46 -2 -2 6 3.18 3.08 -4 -2 6 15.40 14.98 -6 -2 6 5.12 5.24 -1 -3 6 1.44 1.50 -3 -3 6 11.21 11.09 -5 -3 6 13. 18 12.76 - 2 -4 6 6.03 5.93 -4 -4 6 3.78 3.51 - 3 -5 6 1 .83 1.84 - 1 -1 5 22.46 22.68 -3 -1 5 5.97 5.91 -5 -1 5 8.06 7.95 -7 - 1 5 6.32 6.31 -2 -2 5 25.06 25.56 -4 -2 5 9.12 9.04 - 6 -2 5 8.44 8.23 - 1 -3 5 3.85 3.74 -3 -3 5 12.23 12. 17 -5 -3 5 15 .36 15.47 -2 -4 5 15.44 15. 1 1 -4 -4 5 2.31 2.16 - 6 -4 5 1.01 0. 65 -1 -5 5 12 .07 12.04 -3 -5 5 12.31 12.06 -5 -5 5 8.60 8.69 -2 - 6 5 0.93 0.96 -2 0 4 7.03 6.82 -4 0 4 34.41 35.96 - 6 0 4 27.20 29.00 - 1 - 1 4 5. 36 5.36 -3 -1 4 8.37 8.63 -5 -1 4 13.80 14.26 -7 -1 4 5.50 5.88 -2 -2 4 6.76 7. 11 -4 -2 4 14.71 14.95 -6 -2 4 13.65 13.98 - 1 -3 4 1 .23 1.30 -3 -3 4 5. 19 5.56 -5 -3 4 19.40 19.59 -7 -3 4 5.76 6.07 -2 -4 4 13.55 13.38 -4 -4 4 7.26 6.99 -6 -4 4 4.38 4.09 - 1 -5 4 18.22 18.03 -3 -5 4 12,36 12.07 -5 -5 4 2.59 2.50 68 h k 1 Fc Fc -2 -6 4 1.35 1,25 -4 -6 4 3.74 3.45 -1 -7 4 14.89 14.83 -1 -1 3 28.04 29.52 -3 -1 3 30.35 31.04 -5 -1 3 6.42 6.56 -7 -1 3 1.93 1.79 -2 -2 3 40.71 47.53 -4 -2 3 22.50 22. 14 -6 -2 3 5.80 5.87 -1 -3 3 9.35 9. 01 -3 -3 3 6. 87 7.18 -5 -3 3 16.94 17. 53 -7 -3 3 9.99 9. 96 -2 -4 3 27. 49 27. 73 -4 -4 3 7.80 7.64 -6 -4 3 3.82 3. 96 -1 -5 3 17.10 17.06 -3 -5 3 16.88 16. 79 -5 -5 3 10.78 10.88 -2 -6 3 3.60 3. 81 -4 -6 3 4.81 4.83 -1 -7 3 1.76 1. 97 -3 -7 3 3.21 3.23 -2 0 2 9.65 10.01 -4 0 2 21.26 21.12 -6 0 2 30.95 32.48 -1 -1 2 14.40 14.47 -3 -1 2 3.02 3.79 -5 -1 2 12.26 12.67 -7 -1 2 8. 33 8.37 -2 -2 2 11.18 10.91 -4 -2 2 2. 19 2. 17 -6 -2 2 16.44 16.02 -1 -3 2 13.88 13.37 -3 -3 2 5.18 5.07 -5 -3 2 15. 11 15.05 -7 -3 2 11.86 11.51 -2 -4 2 19.02 18. 74 -4 -4 2 11.88 11.98 -6 -4 2 4.20 4.00 -1 -5 2 13.41 13.57 -3 -5 2 22.65 23. 01 -5 -5 2 2.80 2.76 -2 -6 2 0.92 0.66 -4 -6 2 1.12 1.04 -1 -7 2 14.41 14. 69 -3 -7 2 17.53 17.35 -1 -1 1 4.93 5.07 -3 -1 1 39.42 44.22 -5 -1 1 7. 17 7. 13 -7 -1 1 6.00 5.97 -2 -2 1 39. 18 49.89 -4 -2 1 34. 10 34.00 -6 -2 1 7.38 7.31 -1 -3 1 26.62 27. 11 -3 -3 1 3.89 3. 91 -5 -3 1 11.03 10. 93 h k 1 Fo Fc 2 -4 1 22.68 23.54 4 -4 1 20.09 19.49 6 -4 1 1.40 1.51 1 -5 1 19 .90 20. 18 3 -5 1 18.31 18.49 2 -6 1 0.96 0.72 4 -6 1 1.59 1.66 1 -7 1 3 .00 2.81 3 -7 1 4.56 4.67 2 -8 1 0.86 0.88 2 0 0 38.52 44.17 4 0 0 6.17 6.09 6 0 0 20. 3 3 20.25 3 1 0 5.28 5.32 5 1 0 6.37 6. 46 2 2 0 10.75 10.44 4 2 0 6.37 6.66 6 2 0 8.68 8.57 1 3 0 35.02 38.74 3 3 0 2 .22 2.20 5 3 0 3.72 3.77 0 4 0 10.31 10.64 2 4 0 14.98 14.92 4 4 0 12.97 12.71 6 4 0 4.74 4.72 1 5 0 0.62 0.51 3 5 0 20.75 20.47 5 5 0 10.19 10. 14 0 6 0 8.89 9.59 2 6 0 2 .49 2.52 4 6 0 1.63 1.00 1 7 0 9.41 9.83 3 7 0 16. 55 16.10 0 8 0 0.91 0.33 2 8 0 6.50 6.55 1 1 1 29.57 31.44 3 1 1 23.60 22. 19 5 1 1 15.02 14.84 0 2 1 15. 16 14.36 2 2 1 26 .15 25.09 4 2 1 29.46 28.60 6 2 1 9.89 9.94 1 3 1 35. 10 36.29 3 3 1 9.88 9.53 5 3 1 4. 14 4.20 0 4 1 10.70 10.69 2 4 1 4.62 4.40 4 4 1 19.25 18.45 1 5 1 18.32 18.26 3 5 1 15.96 15.72 5 5 1 9.47 9.51 0 6 1 16 .97 17.70 2 6 1 9.09 9.05 4 6 1 3 .06 3.05 1 7 1 6. 25 6.37 3 7 1 2.20 2. 18 0 8 1 3.12 3.34 h k 1 Fo Fc 2 0 2 50.79 53.54 4 0 2 7.70 7.71 1 1 2 27.77 27. 12 3 1 2 9.95 9.59 5 1 2 2.58 2.55 0 2 2 33. 19 32.41 2 2 2 25.31 2 3.31 4 2 2 1.73 1. 84 1 3 2 35.53 36.65 3 3 2 8.67 8.49 5 3 2 1.65 1.72 0 4 2 11.88 11.91 2 4 2 7.83 7. 94 4 4 2 8. 17 8.06 1 5 2 4.50 4. 64 3 5 2 8.40 8.25 0 6 2 7.39 6. 98 2 6 2 5.03 4. 92 1 7 2 6.54 6.67 1 1 3 12,47 11. 97 3 1 3 1.24 1.19 0 2 3 24. 52 22.90 2 2 3 9.59 9.45 4 2 3 15.01 15. 17 1 3 3 23.80 23.05 3 3 3 12.69 12. 65 0 4 3 5.01 4.99 2 4 3 3.70 3.99 4 4 3 8.77 8.90 1 5 3 12.95 12. 94 3 5 3 10.56 10.69 0 6 3 7.30 7. 24 2 6 3 10.85 10.69 1 7 3 5.20 5. 11 0 0 4 25. 13 23.68 2 0 4 34.00 33. 83 4 0 4 10.98 11.44 1 1 4 13. 58 13.45 3 1 4 8.41 8.53 0 2 4 5.51 5.20 2 2 4 16.67 16.50 1 3 4 16.68 16.79 3 3 4 10.79 11.04 0 4 4 10.62 10.78 2 4 4 4.60 4.32 1 5 4 1. 16 1.31 0 6 4 2.54 2.40 1 1 5 2.83 2.57 0 2 5 20.06 20.16 2 2 5 5.48 5.60 1 3 5 9.04 9.37 0 4 5 11.85 11.81 0 0 6 5.32 5.57 1 1 6 4.55 4.64 0 2 6 1.84 1.73 0 4 6 6.71 6. 82 -5 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