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The determination and refinement of the molecular structures of some organic compounds Fawcett, John Keith 1965

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The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES .. PROGRAMME . OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY B.Sc..(Hons»), The University of B r i t i s h Columbia, 1962 TUESDAY, OCTOBER 12, 1965 at 3:00 P.M. IN ROOM 261, CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman: I. McT. Cowan External Examiner: D. W. J . Cruickshank OF . JOHN KEITH FAWCETT N. B a r t l e t t J . P. Kutney C. A. McDowell S. A. Melzak E. Teghtsoonian J. Trotter Chemistry Department University of. Glasgow Glasgow, W. 2, Scotland THE DETERMINATION AND REFINEMENT OF THE MOLECULAR STRUCTURES OF SOME ORGANIC COMPOUNDS ABSTRACT The molecular structures of two polynuclear aromatic hydrocarbons, biphenylene and coronene, have been refined from new three-dimensional data. The p o s i t i o n a l and thermal parameters of the carbon and hydrogen atoms were refined by le a s t squares and the gross features of the structures, previously determined, were confirmed. The anisotropic thermal parameters of the carbon atoms were interpreted i n terms of rigid-body v i b r a t i o n s , and the measured carbon-carbon bond lengths were then corrected for r o t a t i o n a l o s c i l l a t i o n e f f e c t s . The bond lengths for biphenylene r e i n f o r c e the con-c l u s i o n that the molecule must be considered as a cyclobutane d e r i v a t i v e . The bonds jo i n i n g the six-membered rings measure 1.514 "t 0.003 A, and the bonds i n the six-membered rings, s t a r t i n g with the bond i n the four-membered ring, are 1.426 + 0.003 A, 1.372 + 0.002 A, 1.423 + 0.003 A, and 1.385 * 0.004 A. The molecule situated at a centre of symmetry i s planar, the other molecule i s s l i g h t l y non-planar as a result-, of c r y s t a l packing forces. A l l i n t e r -molecular contacts correspond to normal, van der Waals i n t e r a c t i o n s . For coronene, the bond lengths measure 1.425 3 0.004 A in the centre ring, 1.433 t 0.004 A for the "spokes", 1.346 1 0=005 A and 1.415 + 0.003 A for the two types of outer bond. Only the shortest bonds (1,346 A) are s i g n i f i -cantly less than the t h e o r e t i c a l values predicted by valence-bond and molecular-orbital c a l c u l a t i o n s and, since t h i s discrepancy i s observed also f or a l l other polynu-c l e a r aromatic hydrocarbons for which accurate bond dis-tances are av a i l a b l e , an amended order/length c o r r e l a t i o n curve i s suggested which improves the agreement between theory and experiment for these shorter bonds. Small, but s i g n i f i c a n t , deviations from pla n a r i t y , which reduce the molecular symmetry from 6/mmm to 3, may be a r e s u l t of either i n t r a - or inter-molecular forces. A l l intermolecular separations correspond to van der Waals i n t e r a c t i o n s ; the perpendicular distance between the molecular planes i s 3.46 A. The c r y s t a l and molecular structure of the hydroiodide of 1,2-0-aminoisopropylidene- - -glucopyranose has been determined. The iodine p o s i t i o n was located by Patterson methods, and a l l carbon , nitrogen and oxygen atoms were found on successive three-dimensional electron-density d i s t r i b u t i o n s . The p o s i t i o n a l and i s o t r o p i c thermal para-meters of the seventeen I, C, N, 0, atoms i n the asymmetric unit were refined by least squares. The configuration of the asymmetric dioxolane 2-carbon atom was determined and the absolute configuration i s established since the com-pound, i s derived from -glucose. The five-membered ring has an envelope conformation with C(7) displaced 0.34 A from the plane of the other four atoms, and the pyranose ring has a twisted chair conformation. the bond distances and valency angles are normal. The c r y s t a l i s held toge-ther by a system of 0-H...0, N-H...0, and 0-H...I hydro-gen bonds. To investigete the structure of an intermediate i n an attempted removal of the 14 -methyl group of 3-acetoxylanost-8-ene, the structure of the dibromo deriva-t i v e of the intermediate has been determined by X-ray an a l y s i s . The bromine positions were determined by Patter-son methods and a l l carbon and oxygen atoms were located on successive three-dimensional electron-density d i s t r i b u -t i o n s . P o s i t i o n a l and anisotropic temperature parameters were refined by le a s t squares. The absolute configuration was determined by the anomalous dispersion method. The de r i v a t i v e i s 3- -acetoxy-7 ,11 • -dibromolanostane-8 \ , 9 -epoxide. Steriod ring A i s i n the normal chair form and ring D has a h a l f - c h a i r conformation. The epoxide prevents rings B and C from adopting the chair' form. The bond lengths and valency angles are normal, and the i n t e r -molecular separations correspond to van der Waals i n t e r -actions. GRADUATE STUDIES F i e l d of Study: Physical-Organic Chemistry Topics i n Physical Chemistry Topics i n Inorganic Chemistry Topics i n Organic Chemistry Seminar (Organic Section) Crystal Structures (Organic) Steriochemistry Physical Organic Chemistry Organic Reaction Mechanisms Related Studies: D i g i t a l Computer Programming Linear Algebra D i f f e r e n t i a l Equations J. A. R. Coope W. C. L i n H. C„ Clark N„ B a r t l e t t W. R. Culler: J . T. Kwon J. P. Kutney £. I. Scott D. E, McGreer F. McCapra J. P.. Kucney J. T r o t t e r S. A„ Melzak L. D. Hayward R. Stewart R. E. Pincock R. Henderson H. A. Simons R. A. Jennings PUBLICATIONS J. K„ Fawcett and J . Tr o t t e r A Refinement of the Structure of Biphenylene Acta Cryst., i n press, J . K. Fawcett and Tr o t t e r The Crystal and Molecular Structure of Coronene Proc. Roy. S o c , i n press. J . K. Fawcett and J . Trotter The Crystal and Molecular structure of 1, 2-0-Arninoiso-propylidene- - -glucop ranose hydroiodide In preparation. J . K. Fawcett and J . Trotter The C r y s t a l and Molecular Structure of 3- -Acetoxy 7 ,11 -dibromolanostane-8 ,9 -epoxide In preparation. THE DETERMINATION AND REFINEMENT OF THE MOLECULAR STRUCTURES OF SOME ORGANIC COMPOUNDS by JOHN KEITH FAWCETT .Sc. (Hon.), The University of B r i t i s h Columbia, 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of CHEMISTRY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1965 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 a g r e e 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 p u r p o s e s may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s * I t i s u n d e r s t o o d t h a t 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 t h o u t my w r i t t e n p e r m i s s i o n . Department o f CHEMISTfiV The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date i ? T U flcTOTteQ f 1^5. ABSTRACT Supervisor: Professor James Trotter The molecular structures of two polynuclear aromatic hy-drocarbons, biphenylene and coronene, have been refined from new three-dimensional data. The p o s i t i o n a l and thermal para-meters of the carbon and hydrogen atoms were refined by least squares and the gross features of the structures, previously determined, were confirmed. The anisotropic thermal parame-ters of the carbon atoms were interpreted i n terms of r i g i d -body vibrations, and the measured carbon-carbon bond lengths were then corrected for r o t a t i o n a l o s c i l l a t i o n e f f e c t s . The bond lengths f o r biphenylene reinforce the conclusion that the molecule must be considered as a cyclobutane deriva-t i v e . The bonds joining the six-membered rings measure 1.514 ± O.OO3X, and the bonds i n the six-membered rings, s t a r t i n g with the bond i n the four-membered rin g , are 1.426 + O.OO3I, 1.372 ± 0.0021, 1.423 ± 0.0031, and 1.3&*5 ± 0.004.A. The mole-cule situated at a centre of symmetry i s planar, the other mole-cule i s s l i g h t l y non-planar as a res u l t of c r y s t a l packing f o r -ces. A l l intermolecular contacts correspond to normal van der Waals in t e r a c t i o n s . For coronene, the bond lengths measure 1.425 ± O.OO4I i n the centre r i n g , 1.433 ± O.OO4I for the "spokes", I.346 ± O.OO5I and 1.415 + 0,003l f o r the two types of outer bond. Only the shortest bonds (1.346A) are s i g n i f i c a n t l y less than the t h e o r e t i c a l values predicted by valence-bond and molecular-i i i o r b i t a l calculations and, since t h i s discrepancy i s observed also f o r a l l other polynuclear aromatic hydrocarbons f o r which accurate bond distances are avai l a b l e , an amended order/length cor r e l a t i o n curve i s suggested which improves the agreement be-tween theory and experiment f o r these shorter bonds. Small, but s i g n i f i c a n t , deviations from planarity, which reduce the molecular symmetry from 6/mmm to 3, may be a res u l t of either i n t r a - or inter-molecular forces. A l l intermolecular separa-tions correspond to van der Waals interactions; the perpendi-cular distance between the molecular planes i s 3°46A>. The c r y s t a l and molecular structure of the hydroiodide of 1,2-0-aminoisopropylidene-ot-p-glucopyranose has been deter-mined o The iodine position was located by Patterson methods, and a l l carbon, nitrogen and oxygen atoms were found on suc-cessive three-dimensional electron-density d i s t r i b u t i o n s . 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 seventeen I, C, N, 0 , atoms i n the asymmetric unit were refined by least squares. The configuration of the asymmetric dioxolane 2-car-bon atom was determined and the absolute configuration i s esta-blished since the compound i s derived from V-glucose. The five-membered r i n g has an envelope conformation with C ( 7 ) d i s -placed from the plane of the other four atoms, and the pyranose r i n g has a twisted chair conformation. The bond d i s -tances and valency angles are normal. The c r y s t a l i s held to-gether by a system of 0 - H . . . 0 , N-H . . .0, and 0-H...I hydrogen bonds. i v To investigate the structure of an intermediate i n an attempted removal of the 14<*-methyl group of 3-P>-acetoxylanost-8-ene, the structure of the dibromo derivative of the interme-diate has been determined by X-ray analysis. The bromine posi-tions were determined by Patterson methods and a l l carbon and oxygen atoms were located on successive three-dimensional elec-tron-density d i s t r i b u t i o n s . P o s i t i o n a l and anisotropic temper-ature parameters were refined by least squares. The absolute configuration was determined by the anomalous dispersion me-thod. The derivative i s 3-tp>-acetoxy-7o£,lloc-dibromolanostane-8t/,9*-epoxide. Steroid r i n g A i s i n the normal chair form and ring D has a h a l f - c h a i r conformation. The epoxide prevents rings B and C from adopting the chair form. The bond lengths and valency angles are normal, and the intermolecular separa-tions correspond to van der Waals inter a c t i o n s . V A C K N O W L E D G E M E N T S I w i s h t o e x p r e s s my m o s t s i n c e r e t h a n k s a n d a p p r e c i a t i o n t o P r o f e s s o r J a m e s T r o t t e r f o r h i s g u i d a n c e , f r i e n d s h i p a n d c o n -s t a n t e n c o u r a g e m e n t d u r i n g t h e c o u r s e o f t h i s w o r k . I t h a n k D r . L . D . H a l l f o r t h e s a m p l e o f 1 , 2 - 0 - a m i n o i s o -p r o p y l i d e n e - o ^ - p - g l u c o p y r a n o s e h y d r o i o d i d e a n d f o r m u c h v a l u a b l e d i s c u s s i o n , a n d a l s o D r . F . M c C a p r a a n d M r . J . G e r v a y f o r t h e s a m p l e o f 3 - £ > - a c e t o x y - 7 c < , l l ^ - d i b r o m o l a n o s t a n e - S V , 9 o C - e p o x i d e a n d f o r t h e i r h e l p f u l a d v i c e . My t h a n k s a r e d u e t o ( M r s . ) T e s s a Z o b e l f o r h e r h e l p w i t h t h e p r o o f r e a d i n g . I w o u l d l i k e t o t h a n k D r s . F . R . A h m e d , a n d G . A . M a i r f o r m a k i n g a v a i l a b l e t h e i r p r o g r a m s f o r t h e I B M 1 6 2 0 c o m p u t e r . I g r a t e f u l l y a c k n o w l e d g e t h e d o n o r s o f t h e P e t r o l e u m R e s e a r c h F u n d , a d m i n i s t e r e d b y t h e A m e r i c a n C h e m i c a l S o c i e t y , f o r s u p p o r t o f t h i s r e s e a r c h u n d e r G r a n t N o . P R F 1 7 0 4 - A 5 . TABLE OF CONTENTS PAGE TITLE PAGE i ABSTRACT.: i i ACKNOWLEDGEMENTS . . . . . . . v TABLE OF CONTENTS . v i LIST OF FIGURES i x LIST OF TABLES x i GENERAL INTRODUCTION 1 PART I. AN INTRODUCTION TO THE THEORY OF CRYSTAL AND MOLECULAR STRUCTURE DETERMINATION . . . . 3 I. ELEMENTARY CRYSTALLOGRAPHY , 4 I I . DIFFRACTION OF X-RAYS BY CRYSTALS 7 A. Conditions for X-ray D i f f r a c t i o n Maxima . . 7 B. The Reciprocal L a t t i c e 9 C. The Atomic Scattering Factor . . . . . 10 D. The Structure Factor 11 E. I n t e n s i t i e s of Reflected Radiation . . . 12 F. Representation of Electron Density by Fourier Series 13 I I I . STRUCTURE DETERMINATION AND REFINEMENT . . . 15 A. Methods for Establishing Structures . . . 16 B. Refinement of Crystal Structures . . . .'19 C. Assessment of Accuracy . . . . . . . . . 22 v i i PAGE PART I I . REFINEMENTS OF THE STRUCTURES OF BIPHENYLENE AND CORONENE 24 I. A REFINEMENT OF THE STRUCTURE OF BIPHENYLENE . 2 5 Introduction . . . . . 25 Experimental . 2 7 Refinement of the Structure 29 Atomic Parameters and Molecular Dimensions . 30 Discussion 3$ I I . THE CRYSTAL AND MOLECULAR STRUCTURE OF CORONENE . ' 41 Introduction 41 Experimental . 43 Refinement of the Structure 44 Atomic Parameters and Molecular Dimensions . 45 Discussion 50 PART III. THE DETERMINATION OF THE STRUCTURES OF 1,2-O-AMINOISOPROPYLIDENE-ot-T-^GEUCOPYRAN0SE " HYDROIODIDE AND 3-p>-ACETOXY-7<*-,HoC,DIBROMO-LAN0STANE-8c/.,9*-EP0XIBE 56 I. THE CRYSTAL AND MOLECULAR STRUCTURE OF 1,2-0-AMIN0IS0PR0PYLIDENE-tf-:p-GLUC/0PYRAN0SE HYDROIODIDE . . . i . " . . / . . . . 57 Introduction . 57 Experimental 57 Structure Analysis 60 Coordinates and Molecular Dimensions . . . 65 v i i i P A G E PART I I I . (continued) Discussion . > . . . . 68 I I . THE CRYSTAL AND MOLECULAR STRUCTURE OF 3-p*-ACETOXY-7PC, llod-DIBROMOLANOSTANE-8ot,9<*- EPOXIDE . 70 Introduction 70 Experimental . . . . . . . . . . . . 70 Structure Analysis 73 Coordinates and Molecular Dimensions . . 76 Absolute Configuration . . . . . . . 83 Discussion . . . . . . . . . . . 84 APPENDIX I. DESCRIPTION OF SPECIALIZED PROCEDURES . 8 7 A. Corrections to Bond Lengths f o r Thermal Rotational O s c i l l a t i o n . . . . . 88 B. Anomalous Scattering of X-Rays . . . 91 APPENDIX I I . STRUCTURE FACTOR TABLES . . . . . . . 94 REFERENCES . . . . . . . . . . . . . . . 105 i x LIST OF FIGURES FIGURE PAGE 1. Conditions f o r X-ray D i f f r a c t i o n Maxima. . . . 8 Biphenylene 2. Kekule Structures f o r Biphenylene. . . . . . 26 3 . Biphenylene: Atom Numbering. . .• . • . . . . 31 Coronene 4 . The Twenty Kekule Structures f o r Coronene . . ' . 42 5. Bond Lengths and Valency Angles (with Standard Deviations) . . . . .. . . . . . . . 48 6. Comparison of Measured Bond Lengths with Double-bond Character and tr-bond Order .• .. . . . 53 1,2-Q-Aminoisopropylidene-o<-:p-glucopyranose hydro- iodide 7. 1,2-0-Aminoisopropylidene-o(-j>-glucopyranose : Structural formula. . .. . . . . . . . . 58 8. Projected Electron Density . . . . . . . . 61 9. ' Perspective Drawing . . . . . . . . . . 6 2 10. Molecular Packing . . . . . . . . . . . 67 3-(3-Acetoxy-7<* >ll*-dibromolanostane-6V,9*-epoxide 11. Structural Formula. . .. . . . . . . . . . 71 12. Projected Electron Density .. . . . . . 74 13. Perspective Drawing •. . . . . . . • . . • . 75 14. Molecular Packing . . . . . . . . . . . #2 FIGURE PAGE Appendix I. 15. Correction for Thermal O s c i l l a t i o n . . . . . 90 16. Anomalous Scattering 93 x i LIST OF TABLES TABLE .; . PAGE Biphenylene I. F i n a l P o s i t i o n a l Parameters and Standard Deviations, Thermal Parameters, and Deviations from the Mean Molecular Planes .' 32 II . Bond Lengths and Valency Angles (with Standard Deviations) 35 II I . Shortest Intermolecular Contacts . . . . . 37 IV. Mean Measured and Calculated Bond Lengths i n Biphenylene 39 Coronene V. F i n a l P o s i t i o n a l F r a c t i o n a l and Orthogonal Co-ordinates . . . . . . . . . . . . 45 VI. Thermal Parameters and Deviations from the Mean Molecular Plane 46 VII. Shortest Intermolecular Contacts between Carbon Atoms . . . . . . . . . . . . . . 49 VIII. Mean Measured and Calculated Bond Lengths i n Coronene 51 VJ. 1,2-0-Aminoisopropylidene-o<-p-glucopyranose  hydroiodide IX. F i n a l P o s i t i o n a l and Thermal Parameters . . . 63 X. Bond Lengths and Valency Angles (with Standard Deviations) 64 XI. Shorter Intermolecular Distances 66 x i i TABLE PAGE 3-fi-Acetoxy-7AL,lloC-dibromolanostane-8p<:9 9oC- epoxide XII. F i n a l Positional Parameters (with Standard Deviations) . . . . . . . . . . 77 XIII. F i n a l Anisotropic Thermal Parameters . . . 78 XIV. Bond Lengths and Valency Angles (with Standard Deviations . . . . . . . . 79 XV. Shorter Intermolecular Distances . . . . . 81 XVI. Deviations from Mean Planes . . . . . . 83 XVII. Determination of the Absolute Configuration . 85 Measured and Calculated Structure Factors XVIII. Biphenylene (Visual Data) 95 XIX. Biphenylene (Counter Data) . . . . . . . 97 XX0 CoronGMB « <> <> « o » « • • o • © • 99 XXI. 1,2-0-Aminoisopropylidene-o£-p-glucopyranose hydroiodide , 101 XXII. 3-p'-Acetoxy-7t>£,llK-dibromolanostane-8*,9<><-epoxide . . . . . . . 103 GENERAL INTRODUCTION 2 This thesis i s concerned with single c r y s t a l X-ray d i f -f r a c t i o n studies of a number of organic compounds and i s d i v i -ded into three parts. Part I i s a b r i e f description of some aspects of the theory of X-ray d i f f r a c t i o n and i t s application to c r y s t a l and molecular structure analysis. In p a r t i c u l a r i t deals with some of the methods employed to determine the structures i n t h i s thesis and i s intended as an introduction f o r the reader. Part II deals with the detailed refinement of two polynu-clear aromatic hydrocarbons, biphenylene and coronene. .Accu-rate i n t e n s i t y data (collected on a G.'E. spectrogoniometer) and good computing f a c i l i t i e s made possible much more accurate de-terminations of molecular parameters than had previously been attempted. Part III describes the complete s t r u c t u r a l determination of heavy atom derivatives of two organic compounds,, a carbohy-drate, 1,2-0j-aminoi sopropyli dene-rx-p-gluco pyranose hydroiodide, and a steroid, 3-(2-acetoxy-7<*, llM-dibromolanostane-St*, 9*-epoxide. Appendix I contains b r i e f descriptions of two specialized procedures u t i l i z e d during the course of the work, the correc-tions f o r thermal r o t a t i o n a l o s c i l l a t i o n applied to the bond lengths i n biphenylene and coronene and the determination of absolute configuration by anomalous dispersion f o r the steroid. Appendix II l i s t s the observed and calculated structure ampli-tudes f o r a l l compounds i n t h i s t h e s i s . PART I AN INTRODUCTION TO THE THEORY OF CRYSTAL AND MOLECULAR STRUCTURE DETERMINATION I. ELEMENTARY CRYSTALLOGRAPHY A c r y s t a l i s s o l i d homogeneous matter which i s d i s t i n -guished from other condensed states by anisotropy of physical properties. In 1669, Steno recognized that whatever the ex-tern a l appearance, c r y s t a l s of a p a r t i c u l a r substance had constant i n t e r f a c i a l angles, but i t remained f o r Hauy (17&4) to state the fundamental law of crystallography, the law of r a t i o n a l i ndices. If an a r b i t r a r y plane of a c r y s t a l (parametral face) i s chosen having intercepts a, b, and c with respect to a set of three non-coplanar vectors, then any plane of the c r y s t a l can be described completely by i t s M i l l e r indices (hki?) where a/h, b/k, and c/fi are the intercepts of the plane on a, b, and c. The law of r a t i o n a l indices states that the r a t i o s of the i n -dices of any face of a c r y s t a l are r a t i o n a l , and are the r a -t i o s of small integers. This law has an important implication regarding the symmetry of a c r y s t a l , f o r i t l i m i t s the symmetry elements to 1-fold, 2-fold, 3-fold, 4-fold and 6-fold rotation or rota-tory-inversion axes. Hessel (1$30) showed that there are only 32 s e l f - c o n s i s -tent sets, the 32 point groups, involving the 10 symmetry oper-ations l , 2 , 3 , 4 , 6 ,T , 2(=m) , 3 " , 4 ,E. To achieve a condition of lowest pot e n t i a l energy the atoms, molecules or ions making up a c r y s t a l tend to pack 5 p e r i o d i c a l l y with the environment of each unit i d e n t i c a l , f o r -ming a space l a t t i c e . This l a t t i c e i s defined by the repeat distances a, b, and c (known as unit translations) along three non-coplanar axes x, y, and z, and by the angles between these axes. The parallelopiped defined by a, b, and c i s called the unit c e l l . Although there are many choices f o r the axes d e f i -ning the unit c e l l , the most common choice i s that i n which a,, b, and c are as small as possible and the angles between them are as near 90° as possible. The 32 point groups allow only seven d i f f e r e n t shapes for the unit c e l l , the seven c r y s t a l systems, which,, on con-sideration of the p o s s i b i l i t y of centring i n the c e l l , produce only 14 d i f f e r e n t possible types of l a t t i c e s , the 14 Bravais l a t t i c e s . In addition to the 10 symmetry operations already men-tioned there are two types of symmetry operations involving translations possible only i n periodic l a t t i c e s , screw axes, combining rotation with t r a n s l a t i o n , and glide planes which involve r e f l e c t i o n and t r a n s l a t i o n . Self-consistent sets of symmetry elements which may involve screw axes, glide planes and rotation and rotatory-inversion axes are ca l l e d space groups, Federow, S'choenflies, and Barlow, independently de-duced that 230 d i f f e r e n t space groups are possible; they are tabulated i n International Tables f o r X-ray Crystallography, Vol.1 (1). Extinction of certain X-ray spectra due to centring i n the c e l l , and to screw axes and glide planes, i s of primary 6 importance i n determining the space group. Although by Friedel's law, a l l X-ray d i f f r a c t i o n patterns have centres of symmetry, piezo- and pyroelectric effects can often indicate the presence of centrosymmetry i n the space group. I I . DIFFRACTION OF X-RAYS BY CRYSTALS A. Conditions for' X-ray D i f f r a c t i o n Maxima An electron i n the path of an X-ray beam o s c i l l a t e s i n phase with the beam and i s thereby a source of an electromagne-t i c wave of the same frequency, and thus wavelength, as the o r i -ginal X-ray beam. In t h i s way the electron i s said to scatter the X-rays. I f we now consider a row of equally spaced elec-trons, Figure l a shows the condition for additive interference of the wavelets produced by each i n d i v i d u a l electron, that i s , the difference i n path lengths between the two beams must equal an i n t e g r a l number of'wavelengths. Since AB = EF and CD = GH, nA (where n i s an integer) = BC - FG, that i s , a{cos(* - cosa) = nX. In three dimensions we have the Laue equations, a(coso( o - cosrX) = n-jX b(cos(3 o - cos(3) = n£A c(cos2f o - cosi$) = n^X D i f f r a c t i o n i n three dimensions can be represented i n another, more il l u m i n a t i n g , manner (Figure l b ) , as r e f l e c t i o n from p a r a l l e l c r y s t a l planes, p^ and pg, a distance d apart. The condition that the r e f l e c t e d beams reinforce one another i s again that the difference i n path lengths equals an i n t e g r a l number of wavelengths, that i s , nX = 2dsin8. The more usual form of the Bragg equation i s X= 2dsin8 where the order of the r e f l e c t i o n , n, i s absorbed i n the interplanar spacing d. For example, the second-order r e f l e c t i o n from the (100) planes, F i g u r e 1.. (a), (b) (c) D i f f r a c t i o n from a s i n g l e row of e l e c t r o n s * Bragg r e f l e c t i o n c o n d i t i o n . D i f f r a c t i o n i n r e c i p r o c a l space* 9 = 2d-^QQSin82QQ, can be thought of as the f i r s t - o r d e r r e f l e c -t i o n from the (200) planes, "X= 2d 2QQSin0 2QQ where d^ QQ = ^^200° Thus indices of d i f f r a c t i o n , unlike M i l l e r indices, can have a common fact o r , e.g.(462)„ B. The Reciprocal L a t t i c e If we take a point i n the unit c e l l of the dire c t l a t -t i c e as o r i g i n , then each plane can be represented as a point on the normal to that plane through the origin,, The distance-of the point from the o r i g i n i s inversely proportional to the spacing of the plane, d^p = K/d^^(K usually equals "X). The concept of the r e c i p r o c a l l a t t i c e i s of great value in v i s u a l i s i n g d i f f r a c t i o n patterns of a c r y s t a l . The Bragg equation (sin0 =X/2d) implies a maximum value of A/2d = 1. This defines a sphere i n r e c i p r o c a l space, the l i m i t i n g sphere (Figure I c ) . Only r e f l e c t i o n s whose r e c i p r o c a l l a t t i c e points l i e within t h i s sphere are observable (that i s , the shorter the wavelength of the incident radiation used the greater the num-ber of observable r e f l e c t i o n s ) . The smaller c i r c l e i n Figure Ic represents the sphere of r e f l e c t i o n i n three dimensions. It can be e a s i l y shown ('8) that only r e c i p r o c a l l a t t i c e points on the surface of t h i s sphere are able to r e f l e c t r a d i a t i o n incident i n the d i r e c t i o n of i t s diameter. In recording X-ray d i f f r a c -t ion patterns the incident beam i s fixed and the r e c i p r o c a l l a t t i c e i s moved so that each point cuts the sphere of r e f l e c -t i o n . Textbooks by Henry, Lipson, and Wooster (7) and-Buerger u (8) treat thoroughly the geometry of X-ray d i f f r a c t i o n and the recording of r e f l e c t i o n s . Co The Atomic Scattering Factor U n t i l now free electrons have been assumed to be the scat-tering u n i t s . However the actual scattering units are the atoms (or ions) each containing Z( = atomic number) electrons d i s t r i -buted over the volume of the atom according to a r a d i a l d i s t r i -bution function U(r). I f A i s the amplitude scattered by one electron, then fA i s the amplitude scattered by a l l the elec-trons of an atom where f i s the atomic scattering f a c t o r . Since the atom has f i n i t e volume, rays scattered from points (electrons) within t h i s volume w i l l have s l i g h t l y d i f f e r i n g phases. For small d i f f r a c t i o n angles, these phase differences are s l i g h t and f i s very nearly equal to Z, but at larger ang-les interference decreases the amplitude. Atomic scattering factors derived from the expression f - / ° ° T N r O sin (4ttrsin6/"X) , i 0 - / U(r) 4 T r s i n 9 / x ~ d r o have been calculated and are tabulated f o r varying values of sin0/X i n International Tables f o r X-ray Crystallography, V o l . I l l (1). In actual f a c t , the atomic scattering f a c t o r f a l l s o f f even more at large scattering angles because thermal motion tends to make the atom more d i f f u s e . The r e l a t i o n between the scattering f a c t o r of an atom at r e s t , f , and that of a v i b r a t i n g atom,f,is f = f exp(-B(sin8/X) ), the Debye-Waller correction. 1 1 B i s the temperature factor or temperature c o e f f i c i e n t and i s related to the mean square displacement u of the atoms from 2 2 2 th e i r mean positions; B = 8rr u . Since evaluation of u from measurable physical properties i s not easy, B i s usually e s t i -mated empirically at the start of a c r y s t a l structure analysis and adjusted during l a t e r stages of refinement* D o The Structure Factor The structure factor i s the term i n the i n t e n s i t y formula (section HE) which depends upon the atomic arrangement and thus i s of primary importance i n c r y s t a l structure analysis* Suppose we have an atom j with f r a c t i o n a l coordinates x., y., z . , with respect to a, b, and c» The phase difference between the r e f l e c t e d wave from the plane (hkfl) passing through j and from a p a r a l l e l plane passing through the o r i g i n w i l l be 0 . = 2ir(hx . + ky . + 5 z .) . j J J J The scattered wavelet i s described i n amplitude and phase by the expression f.. e x p ( i 0 j ) . The structure factor for (hkfi) i s the sum of these terms over the j atoms and i s given by F(hkfl) = Z f .exp(i$.). F(hki!) can also be written i n i t s j J J component form F(hkfl) = |F(hkJ?)| cos$ + i I F(hkJ? )| sin (j) = E f j c o s ^ : •# i ? f j s i n ^ - j IF(hk5)| , known as the structure amplitude, and a phase con-stant rx(hk8) make up the structure factor and can be evaluated by the expressions: 12 F(hkJ?) = 7 A 2 + B 2 oC(hk$) = arctan(B/A) where A = H f .cos$. and B = ? fisinCh . j J 3 J J These summations are taken over a l l atoms i n the unit c e l l , Eo I n t e n s i t i e s of Reflected Radiation Because most cry s t a l s are not perfect, but are made up of a mosaic of small c r y s t a l l i t e s , they r e f l e c t r a d i a t i o n over a small range around the Bragg angle* I f a c r y s t a l i s turned through the r e f l e c t i n g position with angular v e l o c i t y a), then the integrated i n t e n s i t y I which i s c h a r a c t e r i s t i c of the given c r y s t a l plane, i s given by: I = Eco 2 2 N-^- |F(hkJfc)| mc ^3 f1 + c o s 26 V 2sin29 dV where E = t o t a l r e f l e c t e d energy I 0= i n t e n s i t y of the incident beam N = number of unit c e l l s per unit volume of the c r y s t a l e = electronic charge m = mass of an electron c = v e l o c i t y of l i g h t This equation assumes a small c r y s t a l block, volume dV, i n which absorption of the beam i s small. The geometric factor o consists of two parts. (1 + cos 29)/2 i s the p o l a r i z a t i o n fac-tor which allows f o r the p a r t i a l p o l a r i z a t i o n by r e f l e c t i o n from the c r y s t a l of the unpolarized incident beam. l/sin26 i s the Lorentz factor, and occurs because the r e c i p r o c a l l a t t i c e .points 13 pass through the r e f l e c t i n g sphere at d i f f e r e n t rates depen-ding on t h e i r distance from the o r i g i n . The expression for the Lorentz factor depends on the method used to c o l l e c t the i n t e n s i t y data; l/sin26 being v a l i d f o r Weissenberg and ro-t a t i o n data. Values of the Lorentz and p o l a r i z a t i o n factors are tabulated i n Volume II of the International Tables (1). Absorption of both the incident and r e f l e c t e d X-ray beams by the c r y s t a l i s a d i f f i c u l t f actor to allow f o r , but some corrections f o r c r y s t a l s of varying sizes are also given i n Volume II of International Tables. Primary extinction, the r e f l e c t i n g of the incident X-ray beam by the surface layers of a c r y s t a l which i s too near perfect, and secondary extinction due to the screening of the lower blocks by the upper ones i n mosaic c r y s t a l s , p a r t i c u l a r l y for strong r e f l e c t i o n s , can also be taken into account. F. Representation of Electron Density by Fourier Series We have seen that given the atomic arrangement for a c r y s t a l , the structure factors can be calculated. However, i n practice, we have the structure amplitudes and wish to f i n d the atomic parameters. Bragg proposed the use of Fourier series to represent the d i s t r i b u t i o n of electron density i n a c r y s t a l . Any quantity that i s a periodic function of a single coordinate X can be represented by a Fourier series F(X)r F(X) = A 0 + exp(2niX/a) +...... = S A exp2fri(nX/a) n=o n r 1 4 where a i s the repeat distance* The electron density p(xyz) i n a c r y s t a l i s a periodic function i n three dimensions and can thus be represented as a t r i p l e Fourier series: o(xyz) =2 £ T, A(hkJ? )exp2TTi (hx + ky + Hz) n K J( where x, y, and z are f r a c t i o n a l coordinates referred to a, b, and c* The c o e f f i c i e n t s A ( h k5 ) can be shown to be equal to F ( hkJU/V thus, p(xyz) = 2 2 F(hk#)exp [ -2iri(hx + ky + J?zj] v h k l or p(xyz) = i 2 2 2 |F(.hkfi)| cos('2frhx + 2Trky + 21t|z - o c ( h k i ) ) v h k a where oc(hkJ^) i s the phase angle associated with the amplitude |F ( h k J n l . The l a s t equation i l l u s t r a t e s the fundamental phase pro-blem i n X-ray crystallography. The amplitudes, |F(hkfl)| , are routinely available from the i n t e n s i t i e s of the r e f l e c t i o n s but the phases tf.(hkiO which are also needed to fi n d the elec-tron density d i s t r i b u t i o n cannot be measured. The next sec-t i o n describes b r i e f l y some of the methods of dealing with t h i s problem. I I I . STRUCTURE DETERMINATION AND REFINEMENT In t h i s section the general steps i n solving c r y s t a l structures, that i s , determining the positions of the atoms, w i l l be b r i e f l y outlined. Detailed discussions of the theory of the determination of c r y s t a l structures can be found i n a number of textbooks ("2-6). (-1) After selecting a suitable c r y s t a l , the dimensions of the unit c e l l and the space group, which i n most cases can be found by consideration of the positions of the r e f l e c t i o n s , are de-termined. (2) Accurate integrated i n t e n s i t i e s , are recorded, either on photographic f i l m or by an i o n i z i n g spectrometer, and are redu-ced to structure amplitudes as described i n section HE. (3) The next step i s the most basic, though unfortunately be-cause of the phase problem the most d i f f i c u l t , procedure i n v o l -ved i n structure analysis. It consists of f i n d i n g atomic posi-tions that w i l l give a set of calculated structure amplitudes agreeing as nearly as possible to the observed amplitudes. A b r i e f discussion of methods of determining these positions i s given i n section IIIA. (4) Once the approximate atomic positions have been found they are generally refined, usually by one or more of the methods described i n section IIIB, to give the best possible agreement between the observed and calculated structure amplitudes( IF I Ts and | F C I ' s ) . 16 (5) F i n a l l y , some estimate of the accuracy of the determina-t i o n i s made, and, most important chemically, the bond lengths and valency angles are calculated, A. Methods f o r Establishing Structures (i) T r i a l and Error Methods. An approximate t r i a l structure can sometimes be arrived at by chemical considerations (expected shape of the molecule), c r y s t a l packing (which may l i m i t the orientation of the mole-cules i n the c e l l ) , and certain physical properties such as r e f r a c t i v e index and magnetic methods (which may also indicate the approximate orientation of molecules i n the c e l l ) . The t r i a l structure may then be used to calculate phases which, with the measured amplitudes, w i l l enable a Fourier series to be summed, giving an electron density d i s t r i b u t i o n possibly allowing more accurate p o s i t i o n a l parameters to be found. This procedure i s it e r a t e d u n t i l the gross features of the structure are established. ( i i ) The Patterson Function. Unlike the di r e c t methods of t a c k l i n g the phase problem (part iv) which t r y to obtain some information about the phases themselves, a Fourier series method, developed by Patterson ( 9 ) , derives the most information possible from the structure ampli-tudes. The Patterson function uses as i t s c o e f f i c i e n t s |F(hkJ2)l and thus does not involve the phases. I f the Patter-son and electron density functions are compared: 17 p(xyz) = k I 2 Z F('hkfi)exp-2iri(hx + ky + iz) v h k i A(uvw) = ~2 s s S lF(hkJo)| 2exp-2Ui(hu + kv + 4w) " u v w then i t i s found that whereas p(xyz) has peaks corresponding to atomic positions,A(uvw) has peaks which occur at the ends of vectors between atomic positions. I f the location of these vector peaks can be found then the atomic positions can be de-rived. However, fo r n atoms i n the unit c e l l there are (n^-n)^ independent peaks i n general positions i n the Patterson d i s t r i -bution (the n peaks between each of the n atoms and i t s e l f coa-lesce at the origin) and f o r even moderately complicated struc-tures interpretation of the Patterson function i s extremely d i f f i c u l t , i f not impossible, due to overlap of peaks, ( i i i ) Heavy Atom Method. The method most often used to circumvent t h i s d i f f i c u l t y , p a r t i c u l a r l y f o r organic molecules, i s the heavy atom method. Here use of an atom of large atomic number, (compared to the other atoms i n the structure) causes the peaks due to the vec-tors between the heavy atoms to greatly outweigh the others and the heavy atom position can be found. A Fourier series, using the observed structure amplitudes and phases based on the heavy atom can then be summed, often enabling some of the l i g h t e r atoms to bev.located. By successive Fouriers, a l l the atoms i n the unit c e l l can then be found. One d i f f i c u l t y with the heavy atom method i s that the heavy atom so dominates the structure that the positions of the l i g h t e r atoms cannot be found with 18 great accuracy. I f greater accuracy i s desired the isomorphous replacement method can sometimes be used. It depends on a de-r i v a t i v e •without the heavy atom whose c r y s t a l structure i s i s o -morphous to the heavy atom derivative and therefore whose ato- . mic coordinates are similar, f o r example, potassium and ammo-nium s a l t s , (iv) Direct Methods. These methods depend upon some estimate of the phasps from consideration of the structure amplitudes but are extreme-l y complex mathematically and have not been used extensively as yet. The f i r s t attempt to f i n d the phases was by algebraic n methods solving IF(hkj?)| expio((hkJ) = P f . . e x p M (hx -+ky ) 3—1 <J j J J for x, y, z, and oc(hki). However, these equations are not l i -near, and many equations are required i f the solution i s to be unambiguous. This method has been investigated by Banerjee (10) and extended by Hughes (11). Harker and Kasper (12) have used the Cauchy and Schwartz i n e q u a l i t i e s to place l i m i t a t i o n s due to symmetry elements on some r e l a t i v e amplitudes for centro-symmetric c r y s t a l s . Unfortunately, as the complexity of the structure increases, the usefulness of Harker-Kasper i n e q u a l i -t i e s decreases. Karle and Hauptman (13), using only the fact that the electron density i s everywhere p o s i t i v e , derived ine-q u a l i t i e s between the r e a l and imaginary parts of the structure factors which include the Harker-Kasper i n e q u a l i t i e s as special cases. Sayre (14) and Zachariasen (15) have also developed methods fo r sign determination of the F(hki?) ?s. 19 The p r o b a b i l i t y that the magnitude of a structure factor l i e s between certain l i m i t s , as a function of a l l the amplitudes, i s the basis of a s t a t i s t i c a l method developed by Karle and Haupt-man (16). This method has been used to elucidate the structure of p,p'-dimethoxybenzophenone (17), 36 atoms per asymmetric unit (no heavy atoms), and thus would seem to o f f e r some pro-mise. B. Refinement of Crystal Structures In order to gauge the correctness of a structure, the r e l i a b i l i t y index or r e s i d u a l , R, i s i n common use although i t i s not related to the standard deviations and thus has no r e a l t h e o r e t i c a l s i g n i f i c a n c e . It i s defined by R = S ( l F 0 l -|FCI )/ Z |FQ| . In general a structure i s considered to be worth r e f i n i n g i f R 4 0.45; correct structures usually have R <C 0,25. (i) Refinement by Successive F Q Syntheses. This method has already been mentioned i n the previous section (IIIA). For each successive synthesis more nearly cor-rect phases are introduced and the r e s u l t i s better atomic posi-tions usually with a corresponding decrease of R. The main ob-jection to refinement i n t h i s fashion i s the series termination errors caused by r e s t r i c t i n g the number of terms of the Fourier series. In order to lessen the c a l c u l a t i o n involved at each stage of the refinement,.two-dimensional projections of the structure onto a plane can be found. '.For example', the projection onto a 20 point i n the (001) plane y i e l d s the following expression for the electron density: where the summation now i s over the zone hkO only. This method i s p a r t i c u l a r l y useful for planar molecules, f o r example, the structures of both biphenylene and coronene were o r i g i n a l l y de-termined from two-dimensional projections. ( i i ) D i f f e r e n t i a l Synthesis. Using the fact that at the maxima of p(xyz), that i s , at atomic positions, the f i r s t derivatives of p with respect to x, y, z vanish, Booth (18) has developed a refinement method which finds the deviations of the coordinates from the correct struc-ture by use of these derivatives. Series termination errors can be l a r g e l y obviated by application of backshift corrections (from an F c synthesis) to the coordinates, and the d i f f e r e n t i a l synthesis also has the advantage that the atomic positions are located accurately so that i n t e r p o l a t i o n on a Fourier map i s unnecessary. ( i i i ) Difference or (F - F ) Synthesis. The electron density map produced by difference synthesis using a correct model i s featureless. Small deviations of the proposed model from the correct one can thus be pinpointed by a difference synthesis. A great advantage to t h i s procedure i s that the series termination errors f o r the correct model and a proposed one that i s nearly correct almost cancel by the sub-t r a c t i o n involved. This method can be used to locate hydrogen 2 Z c 21 atoms by using the remaining atoms only to calculate the F ' s, although t h i s can only be done i f the structure i s already very well refined. ' (iv) Least Squares. Since the object i n r e f i n i n g a structure i s to obtain the best possible agreement between the set of F Q's and the set of F ' s, least squares, which minimizes the sum of the squares of c the errors, i s an obvious choice for refinement. The advan-tages of least squares are that i t i s free from series termina-ti o n errors and that d i f f e r i n g weights can be given to various F ' s which are considered to be more or less accurate than o t h e i r fellows. It i s predicted by error theory that, i f the errors i n the F Q T s follow a Gaussian law, the best atomic parameters are those obtained by minimizing the function R-^  = 2 w (hki) (|FQ (hki)| - |F c(hk#)|) 2 where w(hkfi) i s inversely proportional to the pro-bable error i n |F Q(hkfi)| and the summation extends over a l l c r y s t a l l o g r a p h i c a l l y independent planes i n the l i m i t i n g sphere. The parameters occurring" i n the F c(hkJ?)'s are usually the p o s i t i o n a l parameters, i s o t r o p i c or anisotropic thermal para-meters, and a scale factor r e l a t i n g the F ' s to the F 's. To ' ° o c minimize R-^  with respect to these parameters, say u-^ , Ug u n , a l l 3 ^ / 3 u. = 0(j = 1,2 n) or Z w(hk4) A (hkfl ) &(hkQ)/3u. = 0 where A(hkfl) = |F ( h k i l ) l - |F ( h k j l ) l . Note J . that since F does not depend on the u., 3 A(hkJ?)/d u . = - (5 F ( h k C ) / S u . . For a set of u. close to the correct set the c j j least squares normal equations f o r small corrections £ . to the 22 parameters u . are the n simultaneous l i n e a r equations n r 3 F c ( h k i ) 3F_(hkfl)-) 2F.(hk4)' E e .[_£ w ( h k J ) JL_ J =ZwChkJ?)A(hki) a c U t i = l J i J (j = l,2,...,n) where 3 F (hk^)/3 u ., etc. are evaluated for c j the t r i a l u .. J If these equations are written i n matrix form then obvi-ously where n i s large, a f u l l - m a t r i x solution, that i s , i n v o l -ving the complete solution of a l l these equations simultaneously i s extremely laborious even for d i g i t a l c o m p u t e r s T h e greatest s i m p l i f i c a t i o n i s to consider only the diagonal terms neglecting the small ( i f a large number of equations i s used) off-diagonal terms. Since t h i s procedure does not allow for i n t e r a c t i o n or overlap between atoms i t cannot be used for projections and i s not well suited even to three dimensional refinements. A com-promise between the f u l l - m a t r i x and diagonal methods i s the block-diagonal approximation (19) which i s the method used f o r a l l refinements i n t h i s t h e s i s . The procedure involved the use of 3 X 3 and 1X1 block matrices for the coordinates and thermal parameters (is o t r o p i c and anisotropic) and a 2X2 matrix f o r cor-r e l a t i o n of the scale factor and the average temperature factor. C. Assessment of Accuracy The standard deviations of the coordinates and thermal pa-rameters are calculated from the least squares residuals. I f u. i s a parameter then i t s standard deviation o~(u.) i s given by: 23 cr (u.) = a.. ( ) where a., i s an element of the matrix inverse to ( a. .) = Z w4^- * \^ and (m - n) i s the d i f f e r -1 J a U ^ a U j ence between the number of independent observations and the num-ber of parameters determined. The standard deviation o-(J?) of a bond length between two atoms-A and B i s given by cr2(£) = <r2(A) + o-2(B) where o~(A) and o"(B) are the standard deviations of the coordi-nates of A and B along the d i r e c t i o n of the bond. The standard deviation (in radians) of a valency angle between two bonds AB and BC i s o-2(C) BC 2 A difference of less than two or three times the standard devi-ation of equivalent bond distances or valency angles under i n -dependent measurements i s not generally considered s i g n i f i c a n t . 0-2(0) = e±U! + ( r 2 ( B ) / 1 AB' AB' 2cos6 AB * BC + B C PART II REFINEMENTS OF THE STRUCTURES OF BIPHENYLENE AND CORONENE I. A REFINEMENT OF THE STRUCTURE OF BIPHENYLENE Introduction The s t r u c t u r a l formula of biphenylene (Figure 2 ) , f i r s t given by Niementowski (20) i n 1901, was supported by chemical evidence of Lothrop (21) . However, Baker (22) suggested that Lothrop's evidence could apply equally well to benzopentalene. Coulson (23) agreed with Baker and deduced that the s t r a i n en-ergy of benzopentalene was almost zero whereas that of bipheny-lene was about 100 kcal/mole. However, an electron d i f f r a c t i o n study by Waser and Schomaker (24) i n 1943, confirmed by an X-ray d i f f r a c t i o n analysis by Waser and Lu (25) a year l a t e r , established the structure conclusively as i n Figure 2. Lothrop (21) f i r s t synthesized biphenylene by d i s t i l l a -t i o n of 2 , 2 /-diiodobiphenyl with cuprous oxide. A number of other preparations have been reported, the most unusual of which i s the reaction of o-bromofluorobenzene with lithium amalgam i n ether which i t i s believed involves benzyne as a reactive intermediate (26). A consideration of the f i v e Kekule" structures for b i -phenylene (Figure 2) shows that one (I) represents the mole-cule as a cyclobutane derivative, two (II and III) as a cyclo-butene derivative, and two (IV and V) as a cyclobutadiene d e r i -vative. Simple resonance theory, with a l l f i v e structures con-t r i b u t i n g equally, implies more double bond character f o r the 27 1-2 bond (Figure 2) than f o r the 2-3 bond, and therefore an en-tering substituent should be directed into position 1 by an ortho, para-activating group i n position 2. Molecular o r b i t a l calculations (27) predict that position 3 would be preferred by an entering substituent and t h i s prediction i s borne out by bromination of 2-acetamidobiphenylene to give 2-acetamido-3-bromobiphenylene (28). These r e s u l t s imply that the preferred Kekule' structure i s (I) and that biphenylene.must be considered primarily as a derivative of cyclobutane. The same conclusion i s suggested by the molecular dimen-sions determined by X-ray analysis ( 2 5 , 2 9 ) , but the accuracy of bond length measurement was not very high, as f a c i l i t i e s were not available for a three-dimensional refinement. The present work describes an analysis based on new three-dimensional data. Experimental The c r y s t a l s used were obtained by r e c r y s t a l l i z a t i o n from n-propanol and consisted of pale yellow prisms elongated along c. The unit c e l l parameters were remeasured, a and b being de-termined from least-squares treatment of 50 hkO r e f l e c t i o n s measured on a Weissenberg f i l m , (3 from an hOJ? precession f i l m , and c from a number of r o t a t i o n , o s c i l l a t i o n , and precession f i l m s . Crystal data (TUCuK* ) = 1.54-lSA, ^ (CuK* ^  = 1.5405lA\ 'X(CuK0c 2) = 1.54433A, MoKo< ) = 0.7107^) . Biphenylene, C]_2Hg5 M = 152.2; m.p. = 110°C, Monoclinic, a = ' 1 9 . 7 2 g ± 0 . 0 1 0 , b =-10.57g ± 0.006, 28 c = 5.86-L ± O.OllI, £ = 91°10'± 3f (errors are 2<r). U = 1222.8l 3 . D m = 1.24, Z = 6, D = 1.242 gem"3. Ill J\. F(000) = 480. Space group P2^/a(C2^). An i n i t i a l set of i n t e n s i t y data was recorded on hkL Weissenberg films (L = 0 to 4) , estimated v i s u a l l y , and the structure amplitudes were derived as usual, 818 r e f l e c t i o n s being observed. Refinement of the structure with these data gave rather unsatisfactory r e s u l t s , and a more extensive and more accurate set of i n t e n s i t i e s was therefore measured with counter equipment. The i n t e n s i t i e s of a l l r e f l e c t i o n s with 26 (CuK*) - 148°(corresponding to a minimum interplanar spa-cing d = 0.80A) were measured on a General E l e c t r i c XRD-5 Spectrogoniometer with Single Crystal Orienter, s c i n t i l l a t i o n counter, approximately monochromatic CuK* rad i a t i o n (nickel f i l t e r and pulse height analyser), and the moving c r y s t a l -moving counter technique (34). A l l the i n t e n s i t i e s were cor-rected f o r background, Lorentz and p o l a r i z a t i o n factors were applied and the structure amplitudes were derived. The c r y s t a l was mounted with c p a r a l l e l to the (/> axis of the goniostat, and had dimensions 0.18, 0.10, 0.80 mm. p a r a l l e l to a, b, c respectively; absorption was low and no corrections were ap-p l i e d . Of 2463 r e f l e c t i o n s i n the range 0 < 26 ^ 148°, 2316 (94$) had measurable i n t e n s i t i e s . 29 Refinement of the Structure Starting with the parameters of Mak and Trotter (29), the p o s i t i o n a l and thermal parameters and a scale factor were refined, using the v i s u a l data, by six cycles of (block-diago-nal) least squares, anisotropic temperature factors being used in the f i n a l three cycles* Contributions from the hydrogen atoms were included i n the structure factor calculations, by assuming that they lay on the ring diagonals with C-H = l . O s i , but the hydrogen parameters were not refined* The scattering factors of the International Tables (1) f o r carbon and hydrogen were used. The function minimized was 2w('F - F ') , with Jw = |F o l/30 when | F | < 30, and Jw = 30/|Fjwhen |FQ|>30, and during the refinement process R, f o r the 318 observed r e f l e c -tions, was reduced from 0.262 to 0.156. The differences be-tween chemically-equivalent bond lengths and valency angles at the end of t h i s refinement, while much smaller than i n the pre-vious analysis (29), were s t i l l large enough (maximum d i f f e r -ences 0.061 and 9° ), to suggest that the r e s u l t s were of l i m i -ted accuracy. The f i n a l observed and calculated structure fac-tors f o r the v i s u a l data are given i n Table XVIII(Appendix I I ) . A more accurate set of data was collected by counter methods, and the whole refinement was repeated. Since the in t e n s i t y measurements were r e l i a b l e f o r a l l but the very weak r e f l e c -tions, the weighting scheme used was ,)w = JF | /3 whenJFj <C 3, and Jw = 1 when |F | - 3» The i n i t i a l parameters were the f i n a l p o s i t i o n a l parameters of the refinement with v i s u a l data, 30 with an o v e r a l l i s o t r o p i c thermal parameter B = 4.5A* ; the parameters refined were carbon and hydrogen p o s i t i o n a l para-meters, carbon anisotropic and hydrogen i s o t r o p i c thermal para-meters, and an o v e r a l l scale f a c t o r . R, f o r the 2316 observed r e f l e c t i o n s , was reduced from 0.250 to 0.062 i n four cycles, the maximum parameter s h i f t i n the f i n a l cycle being one-half of a standard deviation.- Measured and calculated structure factors f o r the counter data are l i s t e d In Table XIX. Atomic Parameters and Molecular Dimensions The f i n a l p o s i t i o n a l and thermal parameters, those from the least-squares cycle with the counter data, are l i s t e d i n Table I, together with t h e i r standard deviations computed from the least squares residuals, x, y, z are f r a c t i o n a l coordi-nates with respect t o the monoclinic c r y s t a l axes, and IL . are the component's of the mean square v i b r a t i o n tensors with res-pect to orthogonal axes a, b, and c". The equations of the mean molecular planes are: Molecule 1 (C(l) - C(6) and C(l') - C('6')): 0.6245 x' + 0.6340 Y + 0.4560 z'= 0 Molecule 2 (C(7) - C(18)) : 0.5936 x' -ff 0.6922 Y - 0.4105 Z1 = 2.8332 where x', Y , z' are coordinates i n 1 referred to orthogonal axes a, b, and c . The deviations of the atoms from these planes are included i n Table I. 32 TABLE I FINAL POSITIONAL PARAMETERS (FRACTIONAL, x 10*") AND STANDARD DEVIATIONS (£), CARBON ANISOTROPIC THERMAL PARAMETERS ( l 2 x 1 0 2 , MEAN' STANDARD DEVIATION IS 0.0030 X 2 ) , HYDROGEN ISOTROPIC THERMAL PARAMETERS ( I 2 , MEAN <r = 1.9 &2) , AND DEVIATIONS ( A ) FROM THE MEAN MOLECULAR PLANES Atom X y z o-(x) <r(y) <r(z) A ( ! ) | C (1) 0235 0040 -1469 0.0053 0.0060 0.0054 -0.004 C 12) 0730 -0083 -3224 0 .0057 0.0066 0.0057 +0.-006 C (3) 1207 -1073 -2965 0.0061 0.0066 0.0060 -0.003' c ,4) 1233 -1353 -1074 0.0061 0.0065 0.0063 .-0.003 c (5) 0771 -1706 0754 0.0061 0.0065 0.0060 +0.002 c (6) 0303 -0749 0491 0.0055 0.0059 0,0055 +0.005 c 17) 3649 0000 5747 O.OO55 0.0060 0.0053 +0.016 c 13) 4090 -0140 7565 0.0061 0.0067 0,0059 -0.019 c [9) 4603 -1065 7266 0.0061 0.0069 0.0062 -0.023 c [10) 4651 -1781 5307 0.0061 0.0067 0,0064 -0.005 c 11) 4187 -1638 3441 0.0061 0.0065 0.0059 +0.018 c 12) 3693 -0742 3727 0.0055 0.0058 0.0053 +0,025 c 13) 3063 -0099 2761 0.0053 0.0060 0.0053 +0.003 c :H) 2611 -0006 0973 0.0059 0.0068 0.0057 -0,020 c 15) 2096 0910 1259 0.0063 0.0072 0.0063 -0,025 c 16) 2059 1663 3139 0.0063 0.0069 0.0064 +0.006 c •17) 2533 1540 5039 0.0065 0.0066 0.0063 +0.012 c aa) 3026 0656 4766 0.0055 0.0059 0.0053 +0.011 H ,2) 0733 063 2 -4514 O.O7O 0.076 0.069 +0.15 H 3) 1610 -1191 -4141 0.079 0.082 0.076 +0.11 H 4) 1572 -2557 -0984 0.069 0.074 0.067 -0.03 H 5) 0784 -2333 2162 0.066 0.072 O.O65 -0..07 H 3) 4065 0495 9007 0.079 0.082 0.076 +0.06 H 9) 4993 -1245 3552 0.078 0.032 0.075 -0.02 H 10) 5013 -2466 5204 0.079 0.079 0.077 -0.06 H ;n) 4203 -2301 2166 0.072 0.073 0.O71 -0.13 HI 14) 2627 -0693 -0474 0.074 0.077 0.072 -0.15 H 15) 1722 0999 -0008 0.079 0.034 0.077 -0.03 H( 16) 1675 2395 3353 0.074 0.031 0.072 +0.05 H(17) 2523 2222 6331 0.075 0.030 0.073 +0.17 TABLE I (continued) U l l U12 U13 U22 u 2 3 U33 B C(l) 3.63 0 -0.23 3.93 -0.23 3 . 9 3 c ,2) 4„20 - 0 . 1 7 0.15 4o92 -0.23 4*23 c 3) 4»27 - 0 . 0 3 0.24 5.16 -1.05 4.74 c [4) 4.30 0.54 - 0 . 1 6 4.45 -0.63 5.59 c (5) 4 = 54 0 . 2 1 - 0 . 1 6 4o32 , - 0 . 0 9 4 . 3 0 c ,6) 3o73 -0.14 - 0 . 0 8 3.84 -0:13 3 . 9 7 c ,7) 3 ° 3 9 0.03 0.47 4.00 0.07 3o72 c [ 3 ) 4»69 -'0.34 - 0 . 1 6 5»09 0.21 4 . 2 6 c 1 9 ) 4 * 34 -0.23 - 0 . 4 1 5 o 7 0 1 . 1 9 5.03 c n o ) 4o40 0.55 0.63 4.95 0.94 5.65 c I D 4.67 0.43 0 . 8 0 4 « 6 1 0.09 4 . 5 0 c 12) 3 . 3 9 - 0 . 0 6 0.41 3 . 3 9 0.19 3.56 c 13) 3.75 -0.01 0.49 4.00 -0.05 3.72 c 14) 4.34 -0.11 - 0 . 0 6 5.26 -0.22 4.30 c :i5) 4.24 0.25 -0.36 6 . 1 3 0.36 5.04 c 1 6 ) 4-56 0.77 0.62 5*23 0.47 5.50 e [ 1 7 ) 4.93 0.52 0.85 4.75 - 0 . 0 3 4.40 c [ 1 3 ) 4.01 - 0 . 0 8 0.41 4.00 0.21 3»43 H '2) 4«64 H 3) 5.63 H 4) 3.90 H 5) 3.72 H( 3 ) 5.79 H 9) 5.30 H 10) 4.74 H 11) 4.69 H 14) 4.94 H 15) 6.07 H 16) 4.92 H 17) 5.23 The orientation angles of the molecules i n the c r y s t a l are ( s l i g h t l y d i f f e r e n t from previously (29)h * * L = 3 3 . 7 , 3 6 . 3 ° 9 ( M = 9 0 . 9 , 9 4 . 4 ° ^ N = 5 1 . 4 , 1 2 6 . 4 ° y L = 1 1 9 . 3 , 1 1 7 . 4 ° r M = 5 4 . 0 , 5 6 . 2 ° y N = 50.7, 133.3° w = 1 1 2 . 3 , 6 7 o 5 ° 6 J M = 144.0, 3 4 . 1 ° C0 N = 62.9, 6 5 . 3 ° where *X , ^ , and 10 are the angles which the molecular axes L, M (see Figure 3 ) . and the normal N to the molecular plane 34 make with the orthogonal axes a, b, and c . The axes L were taken through the mid-point of bond 3-4 and the molecular centre f o r molecule 1 and through the mid-points of bonds 9-10 and 15-16 for molecule 2; axes M through bond 1-6^ and the mo-lec u l a r centre and through the mid-points of bonds 7-18 and 12-13. L, M, and N are thus not accurately mutually perpendi-cular, the angles being ZLM = 39°9° , ZLN = 9 0 . 0 ° , and ZMN = 90.4° f o r molecule 1 and correspondingly for molecule 2, 9 0 . 2 ° , 90.0°, and 3 9 . 3 ° . The measured bond distances and valency angles, before correction f o r r o t a t i o n a l o s c i l l a t i o n errors, are shown i n Table II, together with the standard deviations computed from the least squares residuals. The anisotropic thermal parameters of the carbon atoms were transformed to U\ . referred to the orthogonal molecular axes L, M, and N, and the thermal motion was then analyzed i n terms of the rigid-body vibrations of the molecules ( 3 0 ) . The T and co tensors are: Molecule 1: T Molecule 2: T 3 TABLE IT BOND LENGTHS (%) ( cr = 0.008 - 0.0091 FOR C - C, O . l l l FOR C - H ) AND VALENCY ANGLES (DEGREES) (er = 0.7° - 0.3° FOR C - C - C, 3? FOR C - C - H) Bond C(3) - C(4) 1.382 C(9) - c(io) 1.380 C(15)- C(16) 1.387 Mean Bond A 1.383 C(2) - C(3) 1.414 C(4) - C(5) 1.429 cm -C(9) 1.421 C(10)~ C ( l l ) 1.420 0 ( 1 4 ) - C(15)' 1.417 C(16)- C(17) 1.423 Mean Bond B. 1.421 C(l) - C(2) 1.373 C(5) - C(6) 1.370 C(7) - C(8) 1.371 C ( l l ) - C(12) 1.372 C(13)- C(14) 1.371 C(17)- C(18) 1.362 Mean Bond C 1.370 Bond C(l) - C(6) C(7) - C(12) C(T3)- C(18) Mean Bond D C(l) - C(6 ;) C(7) - C(18) C(12)- C(13) Mean Bond E C(2) C(3) C(4) C(5) C(8) C(9) C(10) C ( l l ) C(14) C(15) C'(T6) C(17) Mean er ~ H(2) - H(3) - H(4) - H(5) - H(S) - H(9) - H(10) - H ( l l ) - H(14) - H(15) - H(16) - H("17) C - H (C - H) 1.420 1.425 I .425 1.423 1.512 1.513 1.509 1 . 5 H 1.07 1.07 1.00 1.09 1.03 1.03 1.02 1.03 1.12 1.04 1.09 1.07 1.06 0.02 C(6)-C(l)-C(2) 122.6° C(2)-C(3)-C(4) 122.3 C(3)-C(4)-C(5) 121.6 C(5)-C(6)-C(l) 122.4 C(12)-C(7)-C(3) 122.5 C(3)-C(9)-C(10) 122.3 C(9)-C(10)-C(ll) 121.9s C(ll)-C(12)-C(7) 122.6 C(13)-C(13)-C(14) 122.3 C(14)-C(15)-C(16) 122.6 C(15)-C(16)-C(17) 121.6 C(17)-C(13)-C(13) 122.4 Mean 122.4 36 TABLE II (continued) C( l)-C(2)-C(3) 115.1° C 1)- C(2)-H(2) 118° C(4)-C(5)-C(6) 115.5 C , 3 ) - C(2)-H(2) 126 C(7)-C(8)-C(9) 114.9 C k2)- C(3)-H(3) 121 C (10)-C ( l l)-C(12) 115.3 C ,4)- C(3).-H(3) 116 C(13)-C(H)-C(15) 114.9 C 3 ) - C(4)-H(4) 120 C(16)-C(17)-G(18) 115.7 C ,5)- C(4)-H(4) 119 Mean 115.2 C (4)-•C(5)-H(5) 119 C (6)-•C(5)-H(5) ' 125 C (6 /)-C ( l)-C (6) C ( l)-C ( 6)-C ( l ' ) 89.9 C 7 ) -•C(8)-H(8) 120 90»1 C (9)-•C(3)-H(8) 125 C(18)-C(7)-C(12) 90.0 C ,8)- C(9)-H(9) 122 C(7)-C(12)-C(13) 90.0 c (10) -C(9)-H(9) 115 C(12)-C(13)-C(18) 90.2 c (9)-•C(10)-H(10) 120 C(13)-C(18)-C(7) 89.8 c (11) -C(10)-H(10) 118 Mean 90.0 c (10) -G(ll)'-H(ll) 117 c (12) -C ( l l)-H ( l l ) 126 C (6 /)-C ( l)-C ( 2 ) H7.4 c a3) -C(14)-H(14) 120 C (5)-C (6)-C ( l / ) 147.5 c (15) -C(14)-H(14) 124 C(l8)-C(7)-C(8) 147.4 ' c a4) -C(15)-H(15) 119 C( l l)-C(12)-C(13) 147.4 c (16) -C(15)-H(15) 119 C(12)-C(13)-G(1U 147.0 c (15) -C(16)-H(16) 122 C(17)-C(18)-C(7) 147.8 c ,17) -C(16)-H(16) • 116 Mean 147.4 c (16) -C(17)-H(17) 119 c (18) -C(17)-H(17) 125 Mean C-C-H 120 cr(C-G-H) = = 1 The r.m.s. amplitudes of t r a n s l a t i o n a l o s c i l l a t i o n i n the d i r e c t i o n of the molecular axes, L, M, and N, are, f o r mo-lecule 1, 0 . 2 0 , 0 . 2 0 , and 0.181 respectively, and f o r molecule 2, 0 . 2 0 , 0 . 1 9 , and 0.18A*. The t r a n s l a t i o n motion i s thus very nearly i s o t r o p i c , being s l i g h t l y smaller normal to the molecu-l a r planes than i n the planes. The corresponding amplitudes of angular o s c i l l a t i o n - are 3 « 6 & , 1 . 7 ° , and 2.3° f o r molecule 1, and 3 . 8 ° , 2 .1 6 , and 2.8° f o r molecule 2. The largest o s c i l l a -t i o n i s about the long molecular axis L as found also i n anth-racene ( 3 2 ) , and the smallest i s about axis M. 37 TABLE III SHORTEST INTERMOLECULAR CONTACTS (X) A l l C...C, C...H, and H...H contacts - 4. OA" between standard molecules (1) and neighbouring molecules were calculated; only the shortest separations are l i s t e d Atom (Molecules 1) C(3) c(4) C(4) C(3) C(8) C(l') C(8) C(9) C(2) C ( l l ) C(12) C(10) CC7) C(10) C ( l l ) C(12) H(3) H(2) H(2) H(5) H(10) to atom i n molecules C(15). 1 3.66 C(14) 1 3.54 C(15) 1 3.64 C(13) 2 3.69 C(14) 2 3.57 C(2) 2 3.67 C(10) 4 3.65 C(10) 4 3.69 C ( l l ) 6 3.65 C(16) 9 3.66 C(16) 9 3.62 H(2) 7 2.38 H(16) 9 2.33 H(16) 9 2.33 H(16) 9 2.76 H(16) 9 2.72 H(9). 5 2.45 H(10) 6 2.52 H ( l l ) 6 2.59 H(8) 9 2.37 H(5) 10 2.37 Molecules 1 at x y z 2 x y 1 + z 4 1 - x -y 1 - z 5 1 - x -y 2 - z 6 1/2 - x 1/2 + y -z 7 1/2 - x -1/2 + y -z 9 1/2 - x -1/2 + y 1 - z 10 1/2 + x -1/2 - y z-38 Slight corrections were applied to the bond distances to allow f o r the angular o s c i l l a t i o n s , which cause the atoms to appear too close to the centre of the molecule (31,33)« These varied from 0.002 to 0 .003^; the corresponding corrections to the bond angles were negligible(see Appendix I ) . A l l the C...C, C...H, and H...H intermolecular separa-tions less than 4 A* were calculated; a l l these contacts corre-spond to normal van der Waal's interactions, and the more s i g -n i f i c a n t distances are given i n Table I I I . Discussion The deviations of the carbon atoms from the mean mole-cular planes (Table I) are quite small. Molecule 1 i s com-pl e t e l y planar within experimental error, but some of the d i s -placements i n molecule 2 are about three standard deviations, and are therefore s i g n i f i c a n t . Closer examination of the d i s -placements indicates that they follow a regular pattern, which involves a s l i g h t bending of molecule 2. This d i s t o r t i o n i s probably a r e s u l t of c r y s t a l packing forces, as i n other simi-l a r polynuclear hydrocarbons ( 3 5 ) . The differences between chemically equivalent bond lengths and valency angles are very small and i n no cases are the differences s i g n i f i c a n t . For comparison with t h e o r e t i c a l values the measured bond lengths which are chemically equiva-lent were averaged, and the mean values are given i n Table IV, together with t h e i r standard deviations, o~ being calculated from the least squares standard deviations of the i n d i v i d u a l 39 TABLE IV MEAN MEASURED AND CALCULATED BOND LENGTHS {!) IN BIPHENYLENE Bond Measured Calculated (Fig.. 3) , A  tm o V ' V.B. M.O. Uncor- Corrected 5 Kekule I Model rected f o r rota- struc- only d t i o n a l os- tures c i l l a t i o n A 1.3^3 1.385 0.0052 0.0021 1.411 1.337 1.375 1.383 B 1.421 1.423 0.0037 0.0021 1.384 1.477 1.421 1.401 C 1.370 1.372 0.0033 0.0016 1.411 1.337 1.375 1=395 D 1.423 1.426 0.0046 0.0017 1.4H 1.477 1.421 1.416 E 1.511 1.514 0.0046 0.0012 1.442 1.477 1»477 1.497 bond distances (Table II) and o~/ being derived d i r e c t l y from m 0 J the deviations between the i n d i v i d u a l measured values and the means. The s i g n i f i c a n t l y smaller values of suggest that the least squares standard deviations are an overestimate of the errors.. Using the mean of cr and cr^  as a measure of the 0 m m accuracy, the f i n a l bond distances may be given as .1.514 ± O.OO3A f o r the bonds j o i n i n g the six-membered rings, and f o r the bonds i n the six-membered rings, s t a r t i n g with the bond i n the four-membered r i n g , 1.426 ± O.OO3A, 1.372 ± 0.0021, 1.423 + O.OO3A, and 1.335 ± O.OO4A. The mean valency angle i n the four-membered r i n g i s 90.0° + 0.2° (mean cr as for bond 40 lengths), but the angles i n the six-membered rings d i f f e r s i g -n i f i c a n t l y from 120°. The angle adjacent to the four-membered ring i s 122.6° + 0.2°(with the external angle being 147.4° ± 0.2°), and the other angles are 115*26 + 0,2° and 122,2° + 0 . 2 ° . The differences between the various C-H bonds are not s i g n i f i c a n t , and the mean C-H bond length i s 1.06 ± 0,021 (no thermal o s c i l l a t i o n correction). The f i n a l mean molecular dimensions are summarized i n Table IV, The dimensions are very s i m i l a r to (but much more accurate than) the values of the previous two-dimensional study; the largest difference i s fo r bond D, which has increased from 1,381 to 1,426$. The t h e o r e t i c a l bond distances, derived using standard correlations (35) from the molecular-orbital bond-orders and from various valence-bond models (29) , are compared with the measured lengths i n Table IV, As before, the molecular-orbital method gives a much closer estimation of the electron d i s t r i -bution i n the molecule than does simple valence-bond theory; the best valence-bond model i s d ( 2 9 ) , which considers the molecule as predominantly a cyclobutane derivative, with a smaller amount of cyclobutene, but n e g l i g i b l e cyclobutadiene, character (weights of Kekule'structures, I, 4/9, I I , 2:/9, I I I , 2/9, IV, 1/9). The i n d i v i d u a l agreement between measured and calculated bond lengths i s quite good. A l l the intermolecular separations i n the biphenylene c r y s t a l (Table III) correspond to van der Waals interactions, the shortest C,.,C, C.,.H, and H...H contacts being 3»54, 2 .72, and 2,37l respectively. I I . T H E C R Y S T A L AND M O L E C U L A R S T R U C T U R E OF CORONENE I n t r o d u c t i o n T h e h i g h l y - s y m m e t r i c a l a r o m a t i c h y d r o c a r b o n - c o r o n e n e ( F i g u r e 4), ^21+^12' ^ a s a D e a u t i f u l l y s i m p l e c r y s t a l s t r u c t u r e , w h i c h i s v e r y s u i t a b l e f o r d e t a i l e d X - r a y a n a l y s i s . C o r o n e n e w a s f i r s t s y n t h e s i z e d . ( 1 9 3 2 ) , w i t h v e r y , s m a l l o v e r a l l y i e l d , i n t e n s t e p s f r o m t h e c h l o r i d e o f a n t h r a q u i n o n e -1, 5 - d i c a r b o x y l i c a c i d (36). A f t e r t w o o t h e r s y n t h e s e s , b o t h i n l e s s t h a n 5% y i e l d , f r o m 7 - m e t h y l t e t r a l o n e i n 6 s t e p s (37) a n d f r o m 2 , 7 - d i m e t h y l n a p h t h a l e n e i n 4 s t e p s (38), C l a r a n d Z a n d e r i n 1957 (39) p r e p a r e d c o r o n e n e i n 25% y i e l d f r o m c o m -m e r c i a l l y a v a i l a b l e p e r y l e n e . T h e s y n t h e s i s i n v o l v e d t w o s u c -c e s s i v e D i e l s - A l d e r c o n d e n s a t i o n s w i t h m a l e i c a n h y d r i d e , t h e i n t e r m e d i a t e b e i n g 1 , 1 2 - b e n z o p e r y l e n e . T h e c r y s t a l s t r u c t u r e w a s d e t e r m i n e d b y t w o - d i m e n s i o n a l m e t h o d s b y R o b e r t s o n a n d W h i t e (40), a n d i t w a s p o s s i b l e t o o b t a i n f a i r l y a c c u r a t e m e a s u r e m e n t s o f t h e b o n d l e n g t h s a n d o f o t h e r s t r u c t u r a l d e t a i l s . I t w a s f o u n d t h a t t h e c a r b o n - c a r b o n b o n d l e n g t h v a r i e s i n d i f f e r e n t p a r t s o f t h e m o l e c u l e , a n d t h i s d e t e r m i n a t i o n r e p r e s e n t e e ! t h e f i r s t d e f i n i t e m e a s u r e m e n t s o f ' v a r i a b l e c a r b o n - c a r b o n l e n g t h f o r a n y c o n d e n s e d r i n g a r o m a -t i c h y d r o c a r b o n . T h e v a r i a t i o n s w e r e i n a g r e e m e n t w i t h t h o s e p r e d i c t e d b y q u a n t u m - m e c h a n i c a l c a l c u l a t i o n s . T o o b t a i n m o r e a c c u r a t e v a l u e s o f t h e b o n d d i s t a n c e s i t i s n e c e s s a r y t o e m p l o y 42 Figure 4. The Twenty Kekule Structures f o r Coronene (VI) (VII) (VIII) Six Structures Six Structures Four Structures (IX) (X) Three Structures One Structure 43 three-dimensional methods, and the present work describes a de-t a i l e d analysis based on new three-dimensional data* Experimental Crystals of coronene, obtained by slow c r y s t a l l i z a t i o n from xylene, are yellow needles elongated along b. The unit c e l l parameters were determined from various rotation and Weis-senberg f i l m s , and on the G. E. Spectrogoniometer. Crys t a l data ( 7v(CuK0c)= 1 . 5 4 1 8 1 , • MCuK^) = 1 , 5 4 0 5 1 1 , ( C u K o t 2 ) = 1 . 5 4 4 3 3 1 ) . Coronene, C 2 4 H 1 2 ' M= 3 0 0 . 3 ; m.p. = 4 3 4 - 436°C. Monoclinic, a = 1 6 . 1 1 ^ + 0 . 0 0 ^ , b = 4 . 7 0 2 + 0 . 0 0 ^ , c = 1 0 . 1 0 2 ± 0 . 0 0 6 1 , p = 1 1 0 . 9 ° ± 0 . 1 ° (errors are 2 t r ) . U = 715o3A 3. D m = 1 . 3 8 , Z = 2, D x = 1 . 3 9 gem - 3. Absorption c o e f f i c i e n t f or CuK^ X-rays, - 6 cm F ( 0 0 0 ) = 312 Absent spectra: hOJ? when h i s odd, OkO when k i s odd. Space group i s P2-^/a ( 0 2 ^ ) . Molecular symmetry - centre. The i n t e n s i t i e s of a l l r e f l e c t i o n s with 2 0 ( C u K o < ) = 125° (corresponding to a minimum interplanar spacing d = O .87I) were measured on a General E l e c t r i c XRD-5 Spectrogoniometer with Single Crystal Orienter, s c i n t i l l a t i o n counter, approxi-mately monochromatic C u K r x r a d i a t i o n (nickel f i l t e r and pulse height analyser), and the moving crystal-moving counter techni-que. A l l the i n t e n s i t i e s were corrected for background, Lorentz and p o l a r i z a t i o n factors were applied and the structure amplitudes were derived. The c r y s t a l used i n recording the i n -t e n s i t i e s was mounted with b p a r a l l e l to the 0 axis of the go-niostat, and had cross-section 0,1 x 0,05 mm; absorption was-low and no corrections were applied, 936 r e f l e c t i o n s i n the range 0 < 26 - 125° were observed, 82$ of the t o t a l number of r e f l e c t i o n s i n t h i s range. Refinement of the Structure The parameters used as the s t a r t i n g point i n the r e f i n e -ment were the carbon and hydrogen p o s i t i o n a l and thermal para-meters of a two-dimensional refinement of Robertson and White's data (41), with the.scattering factors of the International  Tables (1), The discrepancy f a c t o r , R, was 0.228 f o r the 936 observed r e f l e c t i o n s . A l l the carbon and hydrogen parameters, and an o v e r a l l scale factor, were refined by block-diagonal least squares, minimizing 2w ( F Q - F c ) 2 , with w^ = IF Q\/F', when|F |< F " \ and Jw = F ' V | F q | when | F Q | = F"\ F " ' was taken as 34, to give somewhat heavier weight than i s usual (for v i s u a l data) to the accurately-measured strong r e f l e c t i o n s , and less weight to the rather less accurate very weak i n t e n s i t i e s , . Re-finement was complete i n f i v e cycles, anisotropic thermal para-meters being used f o r the carbon atoms i n the f i n a l two cycles. The f i n a l measured and calculated structure factors are l i s t e d i n Table XX (Appendix I I ) ; the f i n a l R i s 0,157 f o r the 936 ob-served r e f l e c t i o n s . The greater part of the discrepancy factor 45 arises from the small differences between F and F„ f o r the o c very many weak r e f l e c t i o n s , as i s clear from Table XX, so that the o v e r a l l agreement i s quite s a t i s f a c t o r y . Atomic Parameters and Molecular Dimensions The f i n a l p o s i t i o n a l parameters are given i n Table V, x, y, and z being coordinates referred to the monoclinic c r y s t a l axes and expressed as fr a c t i o n s of the unit c e l l edges, and x', Y and Z^  coordinates i n % referred to orthogonal axes a, b, and c*. TABLE V FINAL POSITIONAL FRACTIONAL CO-ORDINATES, x, y, z, AND ORTHOGONAL CO-ORDINATES (!) , l!, Y, Z . atom X y z x' Y z' C 1 -0.1201 -0.4079 0.0381 -2.0737 -1.9179 0.3596 2 -0.1122 -0.4788 0.1782 -2.4506 -2.2513 1.6814 3 -0.0497 -O.36OO 0.2913 -1.8508 -1.6928 2.7492 4 0.0121 -0.1607 0.2786 -0.8090 -0.7554 2.6294 5 0.0799 -0.0339 0.3941 -O.I32I -0.1595 3.7194 .6 0.1364 0.1555 0.3761 0.8434 0.73H 3.5494 7 0.1339 0.2444 0.2410 1.2902 I.I489 2.2746 8 0.1909 0.4490 0.2167 2.2965 2.1111 2.0452 9 0.1843 0.5286 0.0847 2.6657 2.4856 0.7996 10 -0.0606 -0.2029 O.OI83 -1.0433 -0.9542 0.1724 11 O.OO57 -0.0823 O.I38O -0.4047 -0.3869 1.3022 12 0.0666 0.1210 0.1206 0.6386 0.5689 1.1384 H 2 -0.1574 -0.6338 0.1946 -3.2386 -2.9800 I.8364 3 -0.0444 -0.4214 0.3940 -2.1353 -1.9814 3.7181 5 0.0827 -0.0955 0.4955 -0.4534 -0.4489 4.6761 6 0.1876 0.2462 0.4647 1.3497 1.1574 4.3357 8 0.2406 0.5440 0.3084 2.7662 2.5577 2.9104 9 0.2283 O.6848 0.0696 3.4288 3.2198 0.6566 46 TABLE VI THERMAL PARAMETERS bj_ . x lcA AND B ( l 2 ) , AND DEVIATIONS (A ) FROM THE MEAN MOLECULAR PLANE atom b l l b12 b13 b22 b23 b33 A ai C 1 48 54 70 457 51 143 ' 0.0055 2 53 49 94 540 99 185 -0.0112 3 65 62 96 . 591 102 154 -0.0216 4 50 49 60 503 49 133 -0.0055 5 66 59 57 670 65 116 0.0086 6 60 45 34 679 14 128 0.0143 7 50 34 52 507 -2 130 0.0162 8 50 33 49 618 -37 161 -0.0094 9 50 3 89 566 -26 198 -0.0285 10 41 26 51 400 13 123 -0.0051 11 45 65 57 422 77 109 0.0039 .12 43 49 45 407 32 111 0.0078 B: U) ff 2 5*3 -0.0115 3 5.3 -0.0070 5 4.9 -0.0078 6 5.0 0.0392 8 4.7 -0.0245 9 5-. 8 -0.0514 The thermal parameters are l i s t e d i n Table VI, b^j being coef-f i c i e n t s i n the expression exp- [ b 1 ] L h 2 + D i 2 h k + b i 3 h J ^ + b 2 2 k 2 + b23 k j^ + b33^ The hydrogen parameters, although they are probably not p a r t i -c u l a r l y accurate, must be approximately correct since omission of t h e i r contributions from the calculated structure factors increases R by about 0.03. The best plane through the twenty-four carbon atoms i n 47 the molecule has equation 0 . 6 7 7 0 5 X7 - 0 . 7 3 5 9 2 Y - 0 . 0 0 5 2 1 Z = 0 , and the deviations of the carbon and hydrogen atoms from t h i s plane are included i n Table VI. The orientation angles of the molecule i n the c r y s t a l are 84 o 4° = 43.3° ~ 4 7 . 4 ° r L = 85»5° =-47° 7° 137 o 4° 7o2° = 97»3° 90.3°, where "X, 'f', and to are the angles which the molecular axes L, M (see Figure 5) and the plane normal N make with the orthogo-nal axes a, b and c'. Axis L was taken through the molecular centre and the mid-point of bond C(5) - C ( 6 ) , and axis M through the molecular centre and C ( l ' ) . L, M, and N are a l -most exactly mutually perpendicular, the angles between them being ZLM = 39.9% ^LN = 89°8° and £ MN = 3 9 . 9 ° . The orien-t a t i o n angles are very close to those of Robertson and White ( 4 0 ) ; the angle between the plane of the molecule and (010) i s 4 2 . 6 °(Robertson and White, 4 3 ° 7 ° ) . The measured bond distances and valency angles, before correcting f o r r o t a t i o n a l o s c i l l a t i o n e f f e c t s , are shown i n Figure 5 , together with the standard deviations computed from the l e a s t squares residuals. A l l the carbon-carbon intermole-cular separations less than l+k were calculated; a l l these con-tacts correspond to normal van der Waals int e r a c t i o n s , and the more s i g n i f i c a n t distances are given i n Table VII. The perpen-dicular distance between molecular planes i s 3 » 4 6 l . The C...H and H...H contacts also correspond to van der Waals interactions. Figure 5, (a} (b) Measured bond lengths CA) with standard deviations. Measured valency angles (degrees), cr = 0,3" - 0,5° for C-C-C angles, 3° - 5° f o r C-C-H angles. CQ. 49 T A B L E V I I S H O R T E S T I N T E R M O L E C U L A R C O N T A C T S (A) B E T W E E N C A R B O N ATOMS C r y s t a l l o g r a p h i c a l l y i n d e p e n d e n t c o n t a c t s b e t w e e n a s t a n d a r d m o l e c u l e (1) a n d m o l e c u l e 2 ( $ - 3 » 7 A ) a n d m o l e c u l e s 3 a n d 4 ( ^ 4001) a r e l i s t e d : a t o m t o a t o m i n m o l e c u l e a t o m t o a t o m i n m o l e c u l e 3 5 6 7 7 8 8 8 9 9 3 3 4 4 11 12 1 2 M o l e c u l e s 3 3 2 2 2 2 2 2 4 4 a t 2 a t 3 a t 4 a t 3*857 3.905 3 . 6 1 8 3 . 6 8 2 3.516 3 . 6 5 5 3 . 5 6 5 3 . 6 8 2 3.795 3.731 9 9 Q y 9 11 12 12 l ' 2' 10' x X X 11 12 10' 2 1 2 10 8' 10 h + • x y i + y y I - y 2 2 4 2 2 2 2 2 4 2 z 1 + z 3 . 6 1 0 3 . 4 6 2 3.941 3.692 3.519 3.'588 3.658 3.654 4..000 3.504 A s f o r b i p h e n y l e n e , t h e a n i s o t r o p i c t h e r m a l p a r a m e t e r s , b . . , w e r e t r a n s f o r m e d t o U. . r e f e r r e d t o t h e o r t h o g o n a l m o l e c u -l a r a x e s , L , M a n d N , a n d t h e t h e r m a l m o t i o n w a s t h e n a n a l y z e d i n t e r m s o f t h e r i g i d - b o d y v i b r a t i o n s o f t h e m o l e c u l e (30) . T h e T a n d co t e n s o r s a r e T = V 0.050 - 0 . 0 0 6 - 0 . 0 1 8 \ K' 0.065 0 . 0 0 6 0.039, /4.77 0 . 1 5 0 . 3 8 \ d e g ' 7 . 7 0 0 . 0 6 V 7.11 50 The r.m.s. amplitudes of t r a n s l a t i o n a l o s c i l l a t i o n i n the d i -rections of the molecular axes L, M and N are 0 , 2 2 , 0 „ 2 5 and 0 o 2 0 l respectivelyo The t r a n s l a t i o n a l motion i s thus smallest perpendicular to the molecular plane, but i s very nearly i s o -t r o p i c . The corresponding amplitudes of angular o s c i l l a t i o n about the three molecular axes are 2 . 2 ° , 2 . . 8 ° , and 2 . 7 ° , and these too are almost i s o t r o p i c . Slight corrections were applied to the bond distances to allow f o r the angular o s c i l l a t i o n s , which cause the atoms to appear too close to the centre of the molecule (31, 3 3 ) ; the corrections however were only O.OOlg - 0„002g K; the corres-ponding corrections to the valency angles were ne g l i g i b l e (see Appendix I ) . Discussion The deviations of the carbon atoms from the mean molecu-l a r plane (Table VI) are quite small, but several of the d i s -placements, p a r t i c u l a r l y among the outer atoms, are highly s i g n i f i c a n t . A closer study of the deviations reveals that they follow a regular pattern, pairs of outer atoms being alterna-t e l y above and below the mean molecular plane, so that the mol cule has only approximately D ^ (6/mmm) symmetry, and approxi-mates more c l o s e l y to symmetry C^^(S^ , 3 ) . The symmetrical cha racter of the displacements suggests that they may be a r e s u l t of intramolecular forces, although the only close non-bonded a proaches are H...H contacts of about 2 . 4 ^ , which i s about the usual van der Waals distance. The deviation from the higher 51 symmetry may also be due to c r y s t a l packing forces, as with many other s i m i l a r molecules (35). TABLE VIII MEAN MEASURED AND CALCULATED BOND LENGTHS (X) IN CORONENE Bond (Fig.5 m measured J-Uncor- Corrected for rected Rotational O s c i l l a t i o n m calculated ^ R.M,S. V.B. dev. 20 ( cr') Kekule struc-tures M.O, a 1.343 1.346 0.004 0.006 1.371 1.368 b 1.414 1.415 0.003 0.002 1.426 1.423 c 1.430 1.433 0.003 0.004 1.411 1.423 d 1.422 1.425 0.004 0.003 1.426 1.428 The differences between chemically equivalent bond lengths are very small (Figure 5), and only f o r one pair of bonds C(5) - C(6) and C(8) - C(9) i s the difference even i n the p o s s i b l y - s i g n i f i c a n t region. For comparison with t h e o r e t i -cal values therefore the measured bond lengths which are chemi-c a l l y equivalent were averaged according to t h e i r estimated standard deviations, and the mean values are given i n Table VIII together with t h e i r standard deviations, o~m being calculated 52 from the least squares standard deviations of the i n d i v i d u a l bond distances (Figure 5), and cr^ being derived d i r e c t l y from the deviations between the i n d i v i d u a l measured values and the means. The general agreement between the two di f f e r e n t e s t i -mates of standard deviation indicates that the accuracy quoted i s r e a l i s t i c . For comparison with these measured distances, the t h e o r e t i c a l bond lengths were derived from the twenty non-excited valence bond structures (Figure 4) and from the molecu-l a r - o r b i t a l Tf-bond orders (52), using standard c o r r e l a t i o n curves (35), and the values are included i n Table VIII. The bonds i n the central r i n g measure 1.425 ± 0.0041, the "spokes" 1.433 ± 0.0041, and the two types of outer bonds 1.346 + O .OO5I, and 1.415 + O .OO3A. The general agreement between these mea-sured lengths and the corresponding t h e o r e t i c a l distances i s reasonably close, the root mean square difference between mea-sured and calculated values for the four types of bond being 0.0181 f o r the valence-bond method and O.OI3A f o r the molecular-o r b i t a l method. Closer study does indicate however that neither t h e o r e t i c a l method gives a completely s a t i s f a c t o r y account of the measured bond distances. Considering the three longer bonds f i r s t (b, c, d i n Table VIII), i t i s seen that the v a r i a t i o n predicted by valence-bond theory i s i n the wrong d i r e c t i o n , bond c having the longest measured, but shortest calculated length. Molecular o r b i t a l theory gives somewhat better agree-ment, but i s s t i l l not completely s a t i s f a c t o r y f o r bond c. For the short bond (a i n Table VIII), the agreement i s even poorer, 53 d. b. character 7r -bond order Figure 6 . Comparison of measured bond lengths with double-bond character and 1T-bond order. F u l l l i n e s represent the usual c o r r e l a t i o n s , dotted--l i n e s new correlations which improve agreement for the shorter bonds. o naphthalene x chrysene • anthracene 6 pyrene A perylene • coronene • triphenylene 54 each theory predicting a distance about 0.021 longer than the measured bond length. The quite close general agreement be-tween measured and calculated distances i s probably as much as one can expect from the simple quantum-mechanical approxima-tions (more sophisticated t h e o r e t i c a l methods usually tend to give worse agreement with measured distances (42)). It did however- seem useful to examine the other polynu-clear aromatic hydrocarbons f o r which accurate bond distances are a v a i l a b l e , to discover whether the discrepancies between measured and calculated distances followed any trend, which might indicate i n what way the theories might be improved. Figure 6 shows the re l a t i o n s between the measured bond d i s -tances, and valence-bond double-bond character and molecular-o r b i t a l TT-bond order, f o r a l l the bonds i n naphthalene, an-thracene, perylene, triphenylene, chrysene, pyrene and coronene (see (35) for references). The f u l l l i n e s i n t h i s figure re-present the correlations which were used to derive the calcu-lated bond distances i n Table VIII (note that for the molecular-o r b i t a l method t h i s c o r r e l a t i o n i s much steeper than that nor-mally used (35)), and one feature which does emerge c l e a r l y i s that the points f o r the shortest bonds l i e mainly below the cor r e l a t i o n l i n e s . In f a c t , f o r the m.o. TT-bond orders, the shortest bonds i n a l l seven hydrocarbons are represented by points below the correl a t i o n s , and for the v.b. double-bond character, only the shortest bond i n anthracene i s s l i g h t l y above the c o r r e l a t i o n l i n e . The performance of both t h e o r e t i -c a l methods could therefore be improved f o r the shorter bonds by 55 using the correlations represented by the broken l i n e s i n Figure 6. Neither method can however be made.completely s a t i s -factory, as the type of anomaly noted above for bond c i n coro-nene cannot be removed'by any a l t e r a t i o n i n order/length cor-r e l a t i o n . A l l the intermolecular separations i n the coronene cry-s t a l correspond to normal van der Waals in t e r a c t i o n s . The shortest distances are given i n Table VII, and the packing of the molecules i n the unit c e l l i s as described by Robertson and White ( 4 0 ) ; the perpendicular distance between the planes of molecules related by t r a n s l a t i o n b i s 3.461, but the i n d i -vidual atoms do not occur v e r t i c a l l y over each other but are situated as i n Figure 6 of Robertson and White's paper. The shortest l a t e r a l C...C contact i s 3.731. P A R T I I I T H E D E T E R M I N A T I O N OF T H E S T R U C T U R E S OF l , 2 - 0 - A M I N O I S O P R O P Y L I D E N E - c * - P - G L U C O P Y R A N O S E H Y D R O I O D I D E AND 3 - P - A C E T O X Y - 7 t f , H c < - D I B R 0 M 0 L A N 0 S T A N E - 8 o ( , 9 © < - E P O X I D E I. THE CRYSTAL AND MOLECULAR STRUCTURE OF l,2-0-AMIN0IS0PR0PYLIDENE- oc-D-GLUCOPYRANOSE HYDROIODIDE Introduction 1,2-0-aminoisopropylidene- oc -D-glucopyranose (XI) (Figure 7) was synthesized from 2 , 3 , 4 , 6-tetra - 0-acetyl-OC-D-glucopyranosyl bromide (43) but the configuration at the dioxo™ lane 2-carbon (C(7), Figure 9) was unknown. The Proton Mag-netic Resonance (PMR) spectrum of (XI) was l a t e r measured by Coxon and Ha l l (44) during an investigation of the conforma-tions of the rings i n (XI) and si m i l a r compounds. Using mea-sured coupling constants between hydrogens on adjacent carbons around the pyranose ring and applying the Karplus equation, Coxon and Hall deduced the dihedral angles between these hy-drogens and thus concluded that the pyranose r i n g existed i n solution i n the skewed boat form. The present X-ray analysis of the hydroiodide of (XI) establishes the configuration at C(7) as that i n Figures 8 and 9 and determines the shape of the pyranose r i n g as a twisted chair form and-that of the five-membered r i n g as an envelope. Experimental Crystals of 1,2-0-aminoisopropylidene-oC-p-glucopyranose hydroiodide are needles s l i g h t l y elongated along c. The u n i t -c e l l parameters and space group were determined from various 5 9 rotation and Weissenberg photographs and on the G.E. Spectro-goniometer. Crystal Data ( TUCuK*) = 1.54188, XMoK*) = 0.7107 A5) 1,2-0-aminoisopropylidene- <X.-p-glucopyranose hydroiodide, C 9 H 1 8 ° 6 N I ; M = 363.2. Monoclinic, a = 10.09 ± 0.01, b = 7.88 ± 0.01, c= 8.16 ± 0.01 K, P = 100.6% 0.1°. U = 637.3A3 D = 1.38 ( f l o t a t i o n i n CC1,-CHBr 0), Z = 2, D = 1.90 g cm"3, m 4 3 ' x Absorption c o e f f i c i e n t f o r MoKrx, X-rays JX= 26 cm-"1*. F(000) =360 2 Absent Spectra: OkO when k i s odd. Space group P2^(C2)« The i n t e n s i t i e s of a l l r e f l e c t i o n s with 26 (MoK^) = 5 3° (corresponding to a minimum interplanar spacing d = 0 . 8 0 A ) k were measured on a G.E. XRD-5 Spectrogoniometer, with Single Crystal Orienter, using a s c i n t i l l a t i o n counter, MoK<x radia-t i o n (zirconium f i l t e r and pulse height analyser), and the moving crystal-moving counter technique. A l l the i n t e n s i t i e s were corrected for background (approximately a function of 0 only) and the structure amplitudes were derived as usual. The c r y s t a l was mounted with c p a r a l l e l to the (j> axis of the go-niostat, and had cross-section 0.3 x 0.2 mm: absorption was f a i r l y low and no corrections were applied. 1360 r e f l e c t i o n s i n the range 0 <. 26 ^ 53° were observed, 95% of the t o t a l number of r e f l e c t i o n s i n t h i s range. 60 Structure Analysis The position of the iodine atom was determined from the [Old] Patterson projection as (0.170, 0, 0.140), and structure factors were calculated f o r a l l the three-dimensional data f o r the iodine only, the scattering f a c t o r l i s t e d by Sagel (45) for uncharged I being used, with B = 4.5A*2. The discrepancy factor R, at t h i s point was 0.390 fo r the observed r e f l e c t i o n s . A three-dimensional Fourier series was summed with phases based on the iodine atom; since y-r was ( a r b i t r a r i l y ) zero, the r e s u l -t i n g electron-density d i s t r i b u t i o n had a f a l s e mirror plane at y = 0. Despite t h i s i t was possible to pick out a l l carbon, oxygen, and nitrogen atoms. These were introduced into the structure factor calculations with the scattering factors of the International Tables (1), except that the carbon curve was used f o r N , and B = 4.5A* • R was reduced to 0.208 and a second three-dimensional electron-density d i s t r i b u t i o n (Figure 8) gave sharply resolved peaks f o r a l l 17 atoms with no spurious d e t a i l . Further refinement of the p o s i t i o n a l and i s o t r o p i c ther-mal parameters, together with an o v e r a l l scale f a c t o r , pro-ceeded by (block-diagonal) l e a s t squares using a program f o r the IBM 1620 computer. The function minimized was 2w(|FQl - |F cl ) 2 with Jw. = |FQ| /30 when F Q < 30, and Jw = 30/|FQ| when | F Q | - 30. At t h i s stage a more r e a l i s t i c scattering f a c t o r curve f o r I" was obtained from the curve for uncharged I (1) by comparison with the differences . 0 1 2 3 4 A Figure 8\ Superimposed sections of the second three-dimensional electron-density d i s t r i b u t i o n , taken through the atomic centres p a r a l l e l to (001) . Con-tours are at i n t e r v a l s of 2 , 3 , 4 , . : . e A " 3 f o r C, N, 0.; 10, 20, 30,.„„eA~ 3 f o r I. The correct absolute configuration i s shown, the p o s i t i v e direc- op-t i o n of the c-axis being towards the viewer, M b 0 1 2 3 4 A Figure 9. A perspective drawing of the molecule with the atom numbering used. The correct absolute configuration i s shown, the positive d i r e c t i o n of the c-axis being towards the viewer. 63 i n the values of X and X(X = F, CI, Br); i t was then cor-rected for anomalous dispersion, according to the expression f (corrected ) = Jijf-r- + Af^) 2 + (Afj)2H using the values Af', Af"given i n International Tables (1). After two cycles of i s o t r o p i c least squares refinement R was 0.154. A more suitable scattering curve f o r N + , obtain-ed by comparison of the curves f o r 0 and 0 + (1), was introduced and refinement was complete i n three more cycles of i s o t r o p i c least squares, R = 0.138. During the f i v e cycles Zw(iF | - |F |) 3 3 was reduced from 18 x 10 to 8 x 10 . The f i n a l measured and calculated structure amplitudes are given i n Table XXI (Appen-dix II)., TABLE IX FINAL FRACTIONAL POSITIONAL AND THERMAL PARAMETERS Atom X y z B ( l 2 ) C(l) 0.4151 -0.1044 0.5926 1.38 CC2) 0.4059 0.0854 0.6035 1.88 C(3) 0.2809 0.1511 0.6730 1.37 C(4) 0.1684 ' 0.0316 0.6395 1.74 C(5) 0.2140 -0.1464 0.7022 1.43 C(6) 0.0995 -0.2714 0.6720 1.68 C (7) 0.5798 -0.0013 0.8199 1.95 C(8) 0.5418 -0 .0094 0.9904 2.58 C(9) 0.7269 0.0164 0.8346 2.30 N(10) 0.7765 -0.0260 0.6752 2.83 0(11) 0.5288 -0.1433 0.7186 2.49 0(12) 0.5261 0.1436 0.7189 2.35 0(13) 0.2431 0.3166 0.5933 2.09 0(14) 0.0599 0.0832 0.7253 1.80 0(15) 0.3016 -0.2058 0.5909 1.61 0(16) 0.1337 -0 .4328 0.7473 2.41 1(17) 0.8302 - 0 . 5 0 0 0 O .856I 2.88 64 TABLE BOND LENGTHS (X) AND AND VALENCY ANGLES Bond C(l) -C(2) 1. 50 Oo04x C(2) -C(3) 1. 56 0,03 3 C(3) -C(4) 1.46 0.03 6 C(4) -C(5) 1. 53 Oo036 C(5) -C(6) L 50 0.03g C(7) -C(8) 1. 51 0.02 9 C(7) -C(9) 1. 47 0.03 2 Mean Csp^-Csp3 1. 51 0.01^ C(9) -N(IO) 1. 51 0.03Q C(2) -c(D- 0(11) 102.8° C(2) -c(D- 0(15) 120.8 0(11)-C(1) -0(15) 115-7 C(l) -C(2)- C(3) 114.5 C(l) -C(2)- 0(12) 107.3 C(3) -C(2)- 0(12) 106.9 C(2) -CC3)- C(4) 111.6 C(2) -C(3)- 0(13) 107.1 C(4) -C(3)- 0(13) 111.0 C(3) -C(4)- C(5) 110.6 X STANDARD DEVIATIONS (<r = 1.8° -. 2.8° ) Bond C(l)-0(11) 1.43 0 ° ° 3 4 C(l)-0(15) 1.39 0.03Q C(2)-0(12) 1.47 0.03 5 C(3)-0(13) 1.48 0.03 3 C(4)-0(14) 1.47 0.02g C(5)-0(15) 1.46 0.02,-, C(6)-0(16) ;. 1.43 0.03^ C ( 7 ) - 0(ll) 1.43 0.03 3 C(7)-0(12) 1.45 °°° 3 4 Mean O-Csp3 1.45 o . o i 1 C(5)-C(6)- 0(16) 113.3° C(8)-C(7)- C(9) 110.5 C(8)-C(7)- 0(11) 111.9 C(8)-C(7)- 0(12) 115.1 C(9)-C(7)- 0(11) 111.9 C(9)-C(7)- 0(12) 103.7 0(11)-C(7) -0(12) 103.3 C(7)-C(9)- N(10) 113.3 3 Mean Csp^ 110.0 65 TABLE X (continued) C(3) -C(4) -0(14) 110.1° C(l) -0(11)-C(7) 113.9* C(5) -C'(4) -0(14) . 108.3 C(2) -0(12)-C(7) 107.3 C(4) -C(5) -C(6) 111.7 C(l) -0(15)-C(5) 113.6 C(4) -C(5) -0(15) 105.4 . Mean Csp 3-0-Csp 3 111.6 C(6) -C(5) -0(15) 102.9 Coordinates and Molecular Dimensions The f i n a l p o s i t i o n a l and thermal parameters are given i n Table IX; x, y, and z are f r a c t i o n a l coordinates referred to the c r y s t a l axes, and B are i s o t r o p i c temperature f a c t o r s . The bond distances and valency angles, together with t h e i r standard deviations calculated from the least squares r e s i -duals, are l i s t e d i n Table X. Figure 9 shows, i n .a perspec-t i v e drawing of the molecule, the atom numbering used. Various mean planes were calculated to determine the conformations of the rings. The best plane f o r the system 0(11)-C(1)-C(2)-0(12), has equation 0.6831X7 + 0.0348Y - 0.7295Z' = -1.2955 where x', Y, and Z1 are coordinates i n K referred to the ortho-gonal axes a, b, and c . The deviations of the atoms are: 0(11), -0.04A\ C ( l ) , 0.051, C(2), - 0 . 0 3 A , 0(12), 0.02^; the distance of C(7) from t h i s plane i s 0.34A. The intermolecularpacking i s depicted i n Figure 10 and a l l intermolecular distances less than 4«5l were calculated; the most s i g n i f i c a n t of these being given i n Table XI. 66 TABLE XI SHORTER INTERMOLECULAR DISTANCES [K) A l l contacts £ 4.5^ between a standard molecule (1) and neighbouring molecules were calculated, but only the most s i g n i f i c a n t c r y s t a l l o g r a p h i c a l l y Independent separations are l i s t e d ( ^ 3 . 7 & f o r C, N, 0 contacts) Atom to (Molecule 1) Atom i n Molecule 1 4 6 9 10 10 11 14 15 15 16 16 16 16 17 17 17 17 17 17 2 12 6 13 14 13 14 2 6 10 12 3 8 9 13 5 6 9 14 15 16 7 7 6 3 2 7 2 7 6 7 7 3 11 11 3 11 2 3 11 7 2 3.59 3*36 3.70 3.66 3.67 2.49 2.95 3.54 3.53 3.33 3.53 3.70 3.62 3.47 2.68 3.89 3.79 3.95 3.46 3.99 3.38 Molecule 1 2 3 6 7 11 x 1 + x X - X 1 - X 1 - X y y -1 + y s + y -s + y -h + y Z'. z z 1 - z 1 - z 2 - z Projection of the structure, along Coiol.showing the molecular packing. One hydrogen-bond of each type i s shown. 68 Discussion The present analysis has established the configuration at C(7) where the aminomethyl group i s , as expected, i n the equatorial position (Figure 10). The deviations of the atoms i n the five-membered acetal r i n g from the mean plane through the system 0 (11)-C (1)-G (2 )-0(12) suggests an envelope conformation f o r t h i s r i n g , C(7) being 0.34-1 from the plane. The dihedral angle between 0(11) and 0(12) has a value of only £° and, assuming C(l) and C(2) are approximately tetrahedral, t h i s implies that the H atoms on C(l) and C(2) are almost eclipsed. The very small dihedral angle of 8° between the bridgehead hydrogens disagrees with an approximate value of 40° deduced from PMR studies (44) of s i -milar systems (acetal rings cis-fused to pyranose r i n g s ) . The dihedral angles between the hydrogens attached to the other adjacent pairs of carbon atoms around the pyranose ring are a l l approximately 180° (assuming tetrahedral angles). Thus the rin g i s i n a twisted chair conformation, the d i s t o r -t i o n being due to the acetal r i n g . There i s no i n d i c a t i o n of conformational inversion about the C(2)-C(3) bond, proposed by Coxon and Hall (44) f o r 1,2-0-aminoisopropylidene-oc-p-glucopyranose.and si m i l a r compounds, which produces a skew boat form f o r the pyranose r i n g . The bond distances i n the molecule are a l l approximately 2cr or less from the accepted values, the mean distances being C-C, 1 . 5 l l and C-0, 1.45 A*. The mean values of the valency 69 angles are, at C gp3, 110°(almost tetrahedral) and at ring oxy-gen atoms, 112°. The nitrogen atom l i e s almost midway between the iodines at y = - h (Figures 8 and 9 ) , the distances being N-I(y = £), 4.40X and N-I(y = - 53) , 4»02Xo These distances correspond to ionic interactions., In addition the c r y s t a l i s held together by a be a u t i f u l system of 0-H., .0, N-H...0, and 0-H.o.I - i n t e r -molecular hydrogen bonds, i n which every active hydrogen takes part. Details of the hydrogen-bond distances are given i n Table XI, and the bonds are i l l u s t r a t e d i n Figure 10. The hy-drogens of the NH^+ group form one strong N-H...0 bond of 2.49A with 0 (13) , and two weaker bonds, 2.95A* with 0(14) and 3°33l with 0(15). The 0...N...0 angles are 80°, 88°, and 101°, and the C-N...0 angles are 106°, 108°, and 152°. The 0(13) hydro-gen atom forms an 0-H...0 bond of 2.68A with 0(16) of the mole-cule related by tr a n s l a t i o n b, the C-0...0 angle being 1 2 3 ° , and the 0(14) and 0(16) hydrogens form 0-H...I" bonds of 3»46l and 3.381 with C-0...I" angles 106° and 95°° As the compound i s derived from p-glucose the absolute configuration i s established: the parameters of Table IX re-ferred to a right-hand set of axes give the true absolute con-f i g u r a t i o n . Figures 8 and 9 also depict the correct absolute configuration. I I . THE CRYSTAL AND MOLECULAR STRUCTURE OF 3-£-ACETOXY-7oC, 11* -DIBROMOLANOSTANE-&V, 9*-EPOXIDE Introduction In the biosynthesis of cholesterol from lanosterol, the f i r s t step i s the removal of the 14<x-methyl group. Work has been i n progress (46) on a possible i n v i t r o method involving a Corey type reaction (47) of 3-^>-acetoxylanost-8-ene to produce a cy-c l i c ether (bridged through the 14tx-methyl to C ( 9 ) ) which could then be oxidized and decarboxylated removing the 14oc-methyl group from the lanosterol molecule. Oxygen was bubbled through an i r r a d i a t e d solution of 3-ip >-acetoxylanost-8-ene with para-nitrobenzene sulphonyl chlo-ride and haematoporphyrin i n dry pyridine (46). Amongst other products, a s o l i d , which analyzed f o r a c y c l i c ether as £ 3 2 ^ 5 2 ^ 3 ' .was separated by column chromatography. This compound was of interest as a possible intermediate i n the o v e r a l l scheme, and since i t had a double bond (IR) i t was brominated with p y r i -dinium bromide perbromide to provide a suitable derivative, pre-sumably a 1,2-dibromo compound, for X-ray structure analysis. The present work describes the X-ray analysis of t h i s d i -bromide,. and i t s structure has been established as 3-^-acetoxy-7.X, lLx-dibromolanostane-8e<-, 9o<-epoxide (XII) (Figure 11). Experimental Crystals of (XII), r e c r y s t a l l i z e d from petroleum ether ( 3 0 ° - 60*) , are colourless needles elongated along c. The unit c e l l parameters were determined from various r o t a t i o n and Weis-72 senberg f i l m s , and on the G.E. Spectrogoniometer. Crystal Data ( ^ (CuK^) = 1.54181 ). C 3 2 H 5 2 ° 3 B r 2 ; M = 644 06; ra.p.1'980 - 200*0 Orthorhombic, a = 26,03^ ± O.OOg, b = 9.89^ +• 0 . 0 0 2 , c = 12.26g ± O.OOgA (errors are 2 o r ) . U = 3 1 6 0 . 4 l 3 -D„ = 1.33 ( f l o t a t i o n i n aqueous KI), Z = 4 , D v = 1.35gcm~3. Absorption c o e f f i c i e n t for' CuK^ X-rays, JLK = 39°6cm~"'~, F(000) = 1352. Absent Spectra: hOO when h i s odd, OkO when k i s odd, 0 0 / when i . i s odd. Space Group: ?2-[2121 (D^). The i n t e n s i t i e s of a i l r e f l e c t i o n s with 2${CuK^) ^  148 B (corresponding to a minimum interplanar spacing d = 0.80l) were measured on a G.E. XRD-5 Spectrogoniometer with Single Crystal Orienter, s c i n t i l l a t i o n counter, approximately mono-chromatic CuK^ radiation (nickel f i l t e r and pulse height ana-l y z e r ) , and the moving crystal-moving counter technique. A l l the i n t e n s i t i e s were corrected f o r background (approximately a function of 6 only), Lorentz and p o l a r i z a t i o n factors were ap-p l i e d and the structure amplitudes were derived. The c r y s t a l used f o r recording the i n t e n s i t i e s was mounted with c p a r a l l e l to the (fi axis of the goniostat, and had cross-section 0.08 x 0.12 mm; absorption was f a i r l y low and no corrections were applied. 2236 r e f l e c t i o n s i n the range 0 <20- 148°were obser-ved, 94$ of the t o t a l number of r e f l e c t i o n s i n t h i s range. 73 Structure Analysis The two bromine positions were determined from the three-dimensional Patterson function as (0.161, - 0.097, - 0.150) and (0.161, - 0.243, 0.150). Structure factors were calculated for a l l the data with these coordinates, using the scattering factor fo r Br of the International Tables (T), corrected f o r anomalous dispersion and with B = 4• 5-^  ° R was 0.510, and because x-^ = x 2 and z^ = - Z g many F c values were zero. A Fourier series was summed with phases based on the bromine atoms, and, from the re-su l t i n g three-dimensional electron-density d i s t r i b u t i o n , 23 peaks were chosen as light-atom s i t e s without regard f o r chemi-cal considerations. Structure factors were calculated f o r 25 atoms, using International Tables (1) scattering f a c t o r s , and a second electron-density map revealed almost the whole struc-ture, i t being now apparent that we were dealing with a 1,4-di-bromide and not a 1,2 as o r i g i n a l l y suggested. A t h i r d three-dimensional map (Figure 12) showed no spurious d e t a i l s , every atom being well resolved, except C ( l l ) bonded to Br (37), and C(26) and C(27), the outer atoms of the side chain, these three carbon atoms being rather poorly defined. R at t h i s stage was 0.300. Further refinement of the p o s i t i o n a l and i s o t r o p i c ther-mal parameters, together with an o v e r a l l scale f a c t o r , proceed-ed by (block-diagonal) least squares. The function minimised was 2w( lF Q | - |F C |) 2 withjw = |F | /30 when |F | < 30 and w= 1 when|Fj= 30. After four cycles R was 0.229 and 2w(|F j - |F I ) 2 was reduced from 2.63 x 10 5 to 1.00 x 10 5 . 74 i i i 0 1 2 3 4A Figure 12. Superimposed sections of the f i n a l three d i -mensional electron density d i s t r i b u t i o n , through the atomic centres p a r a l l e l to (001); contours f o r carbon and oxygen atoms are at i n t e r v a l s of l e l ~ 3 , s t a r t i n g at 2eX~3 and f o r the bromine atoms at i n t e r v a l s of 5eA~3, s t a r t i n g at 10el""3 s The correct absolute configuration i s shown, the p o s i t i v e d i r e c t i o n of the c axis being to-wards the viewer. 75 0 1 2 3 4 A Figure 13. A perspective drawing of the molecule giv-ing the atom numbering used. The correct absolute configuration i s shown, the posi-t i v e d i r e c t i o n of the c axis being towards the viewer. 76 At t h i s stage anisotropic temperature factors were i n t r o -duced and after six more cycles refinement was complete, the f i n a l R being 0.133 and 2w(|F | - |F | ) 2 - 2.3 x 1 0 4 . The maximum co-ordinate s h i f t i n the f i n a l cycle was one-third a standard deviation and the maximum anisotropic thermal para-meter s h i f t was one-half a standard deviation. The f i n a l mea-sured and calculated structure amplitudes are l i s t e d i n Table XXII (Appendix I I ) . Coordinates and Molecular Dimensions The f i n a l p o s i t i o n a l parameters with t h e i r standard de-viations are given i n Table XII; x, y, and z are f r a c t i o n a l co-ordinates referred to the c r y s t a l axes. The anisotropic ther-mal parameters are l i s t e d i n Table XIII, b^ . being c o e f f i c i e n t s i n the expression exp - £b]_]_h2 + b ] _ 2 b k + b-j^hi.+ D 2 2 k ^ + ^ 2 3 ^ + b-^!2^] • The bond distances and valency angles, together with t h e i r standard deviations, are tabulated i n Table XIV. Figure 13 shows, i n a perspective drawing of the molecule, the atom numbering used. A l l intermolecular contacts less than 4 . 5 ^ were calculated, and the shorter distances are l i s t e d i n Table XV. The intermolecular packing i s depicted i n Figure 14. 77 T A B L E X I I F I N A L P O S I T I O N A L P A R A M E T E R S ( F R A C T I O N A L , x 1 0 % AND S T A N D A R D D E V I A T I O N S (K x 1 0 3 ) A t o m X y z er(x) 0- ( y ) er{z) C ( l ) 2568 -4085 2649 24 2 6 20 C(2) 2960 -5311 2 8 0 1 22 28 25 C(3) 3486 -4668 2843 28 23 24 C(4) 3660 -3711 3747 28 21 19 C(5) 3217 -2627 3727 23 24 21 C ( 6 ) 3255 - 1 6 4 6 4613 25 2 4 1 9 C(7) 2947 -357 4401 22 25 20 C(8) 2484 -497 3 802 23 1 9 17 C (9) 2329 -1843 3452 20 20 1 9 C(10) 2654 -3072 3599 24 24 : 24 C ( l l ) 1 8 1 4 - 2 0 6 0 3210 31 30 17 C(12) 1304 -982 3515 25 2 8 24 C(13) 1549 104 4373 25 21 17 C(14) 2 0 6 0 666 3914 25 2 6 20 C(15) 2181 1829 4713 2 6 2 6 22 C ( 1 6 ) 1 6 2 8 2366 4952 25 29 20 C(17) 1215 1356 4551 25 25 21 C ( 1 8 ) 1679 -617 5423 35 26 18 C(19) 2428 -3809 4697 29 29 20 C(20) 753 1 1 9 7 5305 23 31 1 8 C(21) 362 96 4943 24 2 8 22 C(22) 483 2497 5422 25 30 20 C(23) 311 3194 4381 3 4 30 25 C(24) 25 4484 4500 29 30 23 C(25) -39 5288 3597 29 33 33 C(26) -393 6385 3649 35 45 29 C(27) 454 5864 3092 34 47 33 C ( 2 3 ) 4O83 -6364 1949 29 34 25 C(29) 4498 -7367 2111 28 3 3 27 C(30) 4146 -3071 3554 22 23 22 C(3D 3663 -4478 4820 28 34 22 C(32)- 1989 1370 2778 29 27 18 0(33) 3874 -5734 2341 , 17 19 14 0(34) 3865 -6037 1019 21 22 17 0(35) 2538 - 9 4 4 2652 17 1 8 13 B r ( 3 6 ) 3397 959 3624 3.6 3 . 4 2 B r ( 3 7 ) 1605 -2407 1 6 1 4 3.4 3 . 6 2 TABLE XIII FINAL ANISOTROPIC THERMAL PARAMETERS b i J x 10 4 Atom b l l b12 b22 b23 b33 C(l) 22 16 -11 155 179 63 C(2) 10 -3 -20 196 68 112 C(3) 28 -47 -1 110 -2 115 C(4) 55 -27 7 55 -65 32 C(5) 30 66 13 129 34 69 C(6) 28 -2 -17 118 10 53 C(7) 17 68 -11 169 130 44 C(8) 25 30 20 67 -22 20 C(9) 16 14 • -5 86 5 37 C(1Q) 27 36 • 27 136 -42 68 C ( l l ) 64 -12 -13 283 70 3 C(12) 35 3 -20 182 107 75 C(13) 23 19 -3 123 18 32 C(14) 28 13 17 130 -52 54 C(15) 30 4 -14 155 98 67 C(16) 19 -45 2 215 15 75 C(17) 27 -16 29 139 134 64 C(l8) 58 48 -26 182 37 30 C(19) 42 -4 27 175 -53 33 C(20) 20 -22 13 279 -44 32 C(21) 22 40 -5 180 7 74 C(22) 29 -84 15 185 38 52 C(23) 53 -68 -64 168 -8 79 C(24) 38 -54 -43 192 30 76 C(25) 35 -53 88 279 -228 201 C(26) 55 -203 43 550 -89 84 C(27) 40 108 -24 495 -346 187 C(28) 33 1 5 309 38 95 C(29) 31 -113 -35 309 133 131 C(30) 22 46 -15 151 -48 57 C(3D 39 -55 15 277 -93 51 C(32) 48 -12 5 206 -127 16 0(33) 28 -33 32 195 16 74 0(34) 45 -6 4 212 90 112 0(35) 28 48 -1 175 36 36 Br(36) 35 57 3 232 -18 78 Br(37) 33 30 3 288 124 69 7 9 TABLE XIV BOND LENGTHS {I) AND STANDARD DEVIATIONS, AND VALENCY ANGLES ( cr = 1.4° - 3.0°) Bond :iO)-C(l). -C(2) -C(3) -C(4) -C(5) -C(10) -CC6J -C(7) -C(8) -C(9) -C(10) - C ( l l ) -C(12) -6(13) -C(14) -C(8) -C(15) -C(16) -C(17) -C(13) -C(20) -C(21) -C(22) -C(23) 1 2 3 4 5 5 6 7 8 9 9 11 12 13 14 14 15 16 17 17 20 20 22 1.55 1.60 1.51 1.53 1.58 1.54 1.46 1.53 1.42 1.46 1.49 1.39 1.74 1.63 1.55 1.60 1.54 1.56 1.55 1.53 1.52 1.56 1.47 1.52 0 . 0 3 3 0 . 0 3 5 0 . 0 3 6 0 . 0 3 2 0.03^ 0 . 0 3 3 0.03 0.03-0 . 0 3 ' 0.02g 0 . 0 3 1 0 . 0 3 5 0 . 0 3 9 0 . 0 3 3 0 . 0 3 3 0 . 0 3 o 1 0 0.03 0.03 0.03, 0 .03 ' 0 .03| O . O 3 J 0 . 0 3 ( 0.03 4 Bond 4 C(23)-C(24) 1.49 C(24)-C(25) 1.37 C(25)-C(26) ' 1.43 C(25)-C(27) 1.53 C(4)-C(30)' 1.43 C (4)-C (3D 1.52 C(10)-C(19) 1 . 6 4 C(13)-C( l8) 1.51 C(14)-C(32) 1.57 Mean ^ 3 - ^ 3 1 . 5 2 , 0 . 0 4 3 0 . 0 4 2 0 . 0 5 ! 0.04g 0 . 0 3 3 0 . 0 3 3 ° ° ° 3 4 0 . 0 3 0 0.03 1 0.00, C(28)-C(29) 1.48 0.04 5 C(3)-0(33) 1 .46 0.03] C(28)-0(33) 1 .37 0 .03-C(8)-0(35) 1 .49 0.02' C(9)-0(35) 1.43 0.02' 5 C ( .28)-0(34) 1.31 0.03 4 7 C(7)-Br(36) 1.99 0.02 C(ll)-Br ( 3 7 ) 2.06 0.02-Mean C s p 3~Br 2.03 0.01 3 6 80 TABLE C(10-)-C(l)-C(2) 108.1° C(l)-C ( 2)-C ( 3 ) 105.2 C(2)-C(3)-C(4) 123.7 C(2)-C(3)-0(33) 108.8 CU)-C(3)-0(33) 104.1 C(3)-C(4)-C(5) 101 ..2 C(3)-C(4)-C(30) 114.6 C(3)-C(4)-C(3D 108.7 C(5)-C(4)-C(30) 110.1 C(5)-C(4)-C(3D 110.9 C(30)-C(4)-C(3D 111.0 C(4)-C(5)-C(6) 113.0 C(4)-C(5)-C(10) 120.3 C(6)-C(5)-C(10) IO9.4 C(5)-C(6)-C(7) 113.0 C(6)-C(7)-C(8) 116.9 C(6)-C(7)-Br(36) 108.5 C(8)-C(7)-Br(36) 108.4 C(7)-C(8)-C(9) 118.5 C(7)-C(8)-C(14) 118.1 C(7)-C(8)-0(35) 116.1 C(9)-C(8)-C(14) 119.5 C(14)-C(8)-0(35) 111.1 C(8)-C(9)-C(10) 123.6 C(8)-C(9)-C(ll) 118.1 C ( 1 0)-C ( 9)-C(ll) 116.5 C(10)-C(9)-0(35) 111.9 C(ll)-C(9)-0(35) 108.4 C(l)-C(10)-C(5) 113.5 C(l)-C(10)-C(9) 110.7 C(l)-C(10)-C(19) 106.1 C(5)-C(10)-C(9) 108.6 C(5)-C(10)-C(19) 112.7 C(9)-C(10)-e(19) 104.9 XIV (continued) c (9)-- c ( l l ) --C(12) 126.4° c 9)- - c ( i i ) --Br(37) 118.9 c 12 1 - C ( l l ) -Br(37) 96.0 c 11] -C(12] -C(13) 104.1 c k 12' - 0 ( 1 3 ' -C(14) 109.7 c (12 -C(13 -C(17) 113.8 c i l 2 -C(13, -C(18) 109.1 c I V -0(13^ -C(17) 104.4 c ,14 -C(13 -C(18) 106.7 c (17 -C(13 -C(18) 112.8 c (8)- -C(14)--C(13) 111.4 c (8)- -C(14)--C(15) 116.7 c (3)--C(14)--C(32) 108.9 c ,13 -C(14 -C(15) 102.3 c (13 -C(14 -C(32) 112.5 c (15 -C(14 -C(32) 104.9 c (14 ).-C(15 -C(16) 100.6 c (15 -C(16 -C(17) 111.2 c ,13 -C(17 -C(16) 100.0 c ,13 -C (17 -C(20) 116.8 c (16 -C(17 )-C(20) 114.9 c (17 -C(20 )-C(21) 114.5 c k17 -C(20 -G(22) 11.0.2 c (21 -C(20 -C(22) 109.1 c (20 )-C(22 -C(23) 117.1 c (.22 >-C(23 -C(24) 117.1 c (23 -c (24 -C(25) 118.6 c (24 -C(25 -C(26) 118 .9 c (24 -C(25 )-C(27) 116 .1 c (26 -C(25 )-C(27) 106.0 Mean C 3 sp3 111.6 C(3)--0(33)'--C(28) 127.2 81 TABLE XIV (continued) 0(33)~C(28)-C(29) 0(33)-C(28)-0(34) G(29)-C(28)-0(34) Mean C s p 2 1 1 9 . 1 ° C(9)-C(8)-0(35) 114.2 C ( 8)-C ( 9 ) - 0 ( 3 5 ) 126.8 G(8)-0(35)-C(9) 120.0 58.2° 61.9 59.9 TABLE XV SHORTER INTERMOLECULAR DISTANCES {1) A l l contacts 4.5^ between a standard molecule (l)and neighbouring molecules were calculated, but only the most s i g n i f i c a n t c r y s t a l l o g r a p h i c a l l y independent separations are l i s t e d (*k 4.0A) Atom to (Molecule 1) C(2) C(6) C(12) C(15) C(T5) C ( l 8 ) C(18) C(22) C(22) C(2'4) C(26) C(28) C(29) 0(33) Br(36) B r(37). Atom i n Molecule Br(36) 2 C(32) 3 C(27) 2 0(35) 3 Br(37) 3 0(35) 3 Br(36) 3 0(34) 3 C(30) 3 0(34) 3 C(30) 4 Br(36) 2 Br(36) 2 Br(36) 2 Br(37) 3 C(27) 2 3.99 3-94 3.86 3.78 3.97 3.74 3.95 3.96 4 .00 3.77 4 . 0 0 3.80 3.80 3.63 3.94 3.90 Molecule 1 2 x x y -1 + y z z 32 Figure 14. Projection of the structure onto (001), i l -l u s t r a t i n g the packing of the molecules. The molecules i n f i n e l i n e s are related to the mo-lecules over which they l i e by the two-fold screw axis p a r a l l e l to c. Only two examples of these are shown. 83 Mean molecular planes were calculated, to help determine the conformations of the rings of the steroid skeleton. The equation of the mean molecular plane, through the system C(l)-C(3)-C(4)-C(10) of rin g A (XII) i s 0.2259X + 0.7057Y - 0.6716Z = -3.5369...(A), X, Y, Z being coordinates i n K; the equation of the system C(5)-C(8)-C(9)-C(10) of rin g B i s 0.1405X + 0.1326Y - 0.9812Z = -3.6759.(B), and the best plane through the five-membered ring D i s -0.1709X + 0.3868T - 0.9062Z = -5.2961...(D). The deviations of the atoms i n rings A, B, and D from these planes are given i n Table XVI. Ring C contains no well de-fined planes. TABLE XVI DEVIATIONS FROM MEAN PLANES Atom Plane A Atom Plane B Atom Plane '. 1 0.0141 5 0.0221 13 -O.215X 3 -0.014 8 -0.057 14 0.284 4 0.012 9 0.131 15 -0.214 10 -0.012 10 -0.088 16 -0.028 2 -0.739 6 -0.902 17 0.215 5 O.524 7 -0.590 Absolute Configuration The f i n a l step i n the analysis was the determination of the absolute configuration of the molecule by the anomalous d i s -persion method (48). Structure factors were calculated for a l l the hkj! and Efcl r e f l e c t i o n s , using scattering factors f o r the 84 two bromines of the form f = (f- + A f ' ) + i A f ' ' . Br Br . Br With CuK(/ r a d i a t i o n the differences between |Fc(hk£)l and |F (hkf)l are small, but there are several r e f l e c t i o n s f o r which the differences were large.enough to be measured with the counter equipment. The r e s u l t s are given i n Table XVII. A l l pairs of r e f l e c t i o n s unambiguously indicated that the coordi-nates of Table XII referred to a right-handed set of axes re-present the true absolute configuration. (XII) and Figures 12 and 13 also show the correct absolute configuration. Discussion The present analysis has established the structure, i n -cluding the absolute configuration, as 3 - £ -acetoxy-7 <X , 11* -dibromolanostane -8 << , 9<* -epoxide (XII). Consideration of the deviations from the best plane through the atoms C(1)-C(3)-C(4) -C(10) (Table XVI) shows that r i n g A of the steroid structure i s i n the chair conformation. The 8 , 9-epoxide d i s t o r t s the usual chair forms of rings B? and C to the extent that B i s i n a s l i g h t l y distorted boat form and C i s not i d e n t i f i a b l e i n terms of any of the usual nomenclatures f o r conformations of six-membered rings. The five-membered ring D i s i n the h a l f -chair conformation, and l i k e A does not seem to be affected by the strained epoxide system. The bond distances (Table XIV) involving well-resolved atoms do not d i f f e r s i g n i f i c a n t l y ( < 2 c - ) from normal values. The poorer bond lengths are those i n the side chain and ones involving C.(ll). These l a t t e r seem to r e s u l t from the effect TABLE XVII DETERMINATION OF THE ABSOLUTE CONFIGURATION (CuKpt radiation) h k J? |FcChkfi)| \Fc(hkl)\ I0(hk£) I 0 ( h k 2 ) I0(hk£) I0(hkfl) lFp(hU)| 2 lFc(hB)| 2 14 1 1 3.5.5 37.6 98 110 0.89 0.89 7 1 2 36.8 ' 34.3 263 218 1.21 1.15 3 1 3 32 . 6 27.6 236 161 1.47 1.39 5 1 3 14.6 17.1 148 168 0.88 0.73 10 1 3 55.8 59.0 340 364 0.93 0.89 3 1 4 • 24.3 19.0 132 103 1.28 1.64 5 1 4 71.4 75.0 872 895 0.97 0.91 7 • 2 1 74.5 80 .8 1027 1129 0.91 0.85 4 2 2 27.9 24.3 191 128 1.49 1.32 1 2 6 25.1 21.8 61 40 1.53 1.33 9 3 1- 73.7 69.3 545 492 1.11 1.13 7 3 2 85.8 89.0 811 855 0.95 0.93 1 3 4 91.4 95.9 1184 1203 0.98 0.91 oa 86 of Br(37) on the C ( l l ) position which i s rather poorly resolved (Figure 1 2 ) . The mean.C-C single bond distance i s 1.53 ± O.OlX. The valency angles (Table XIV) are reasonable, the mean tetrahedral value being 111.6*. The C- T - C 3 angles i n v o l -° sp-2 sp-> to ving the £ and 9'carbon atoms, which are part of the epoxide rin g , are somewhat distorted; the angles i n the epoxide ri n g are l e s s than 2<r from 6 0 ° . A l l intermolecular contacts (Table XV) are greater than the sum of the van der Waals r a d i i f o r the atoms involved. The shortest contacts are C-C, 3 .861, C-0, 3 .7 /Jl , C-Br, 3 .801, 0-Br, 3 . 6 3 I , and Br-Br, 3*94A\ In view of the fact that (XII) i s a 1 ,4-dibromide rather than the expected 1 ,2- compound, i t would seem that bromination of the intermediate involves rearrangement and thus the struc-ture of (XII) i s of doubtful value i n determining the course of the reaction. APPENDIX I DESCRIPTION OF SPECIALIZED PROCEDURES 88 A. Corrections to Bond Lengths f o r Thermal Rotational O s c i l l a t i o n For biphenylene and coronene, the bond lengths were cor-rected f o r r o t a t i o n a l o s c i l l a t i o n effects which involved inter-pretation of the anisotropic thermal parameters of the carbon atoms i n terms of rigid-body vibrations of the molecule. A b r i e f discussion of p r i n c i p l e s involved, which are given i n d e t a i l by Cruickshank (30, 31, 3 3 ) , follows. The anisotropic thermal parameters b^j with respect to the monoclinic c r y s t a l axes must f i r s t be referred to an ortho-gonal set of axes (49) and then transformed by orthonormal tensor transformations to a suitable set of orthogonal mole-cular axes. These symmetric tensors,. U\j (referred to the orthogonal molecular axes), f o r each atom, are given by 3 3 i = l j=l 1 3 1 3 where u i s the mean square amplitude of v i b r a t i o n of the atom i n the d i r e c t i o n s p e c i f i e d by the unit vector JL_ = ( ! ? > ^3 ) • To interpret the thermal parameters i n terms of rigid-body v i -brations i t i s assumed that the molecular motion can be given by two symmetric tensors, T^j giving the mean-square amplitude of the t r a n s l a t i o n a l vibrations and cJ^j giving the angular os-c i l l a t i o n s about the centre of the molecule. Each atomic U^j i s expressed by: i= l j = i ! J 1 0 i = i j = i 1 J 1 J i J 1 3 89 where r = (x,y,z), the atomic position referred to the mole-cular axes, and ( l A r ) . i s the i t b - term of the vector product of 1 and r. By expanding the right hand side, remembering T\ .. and 03^ j are symmetric ( i . e . , T\ . = T.^), grouping the c o e f f i -cients of a n ^ equating these c o e f f i c i e n t s with those on the l e f t hand side, the u\ . T s can be expressed i n terms of the 2 2 T. .'s andoj. .'s, f o r example, , = T,, +z c o 0 0 + y c o 0 0 - 2 y z c o 0 0 . i j i j 11 11 "-22 33 23 Least squares i s used to obtain best values for the 12 indepen-dent T. .'s and CO. .'s, since the number of U. . i s , i n general, greater than 12. I f the molecule i s planar, l y i n g on z = 0 , and i f , i n addition, i t i s symmetric about the x and y axes, the case for biphenylene and coronene, the least-squares nor-mal equations reduce to two third-order equations f o r ( T ^ , T 2 2» ^33^ a n c * ^ 3 3 ' ^ 1 1 ' ^ 2 2 *" ' t w o s e c o n d - ° r d e r equations f o r (^23,,Ui23^ a n ( ^ ^13 , C o 13 ^  a n c* t w 0 f i r s t _ o r d e r equations f o r andco^2° r o o t m e a n square amplitudes of t r a n s l a t i o n a l and ro t a t i o n a l o s c i l l a t i o n i n the directions of the molecular axes are the square roots of the diagonal elements of the <T and co tensors. A computer program (in Fortran-II) has been written which, s t a r t i n g with the thermal parameters b^ . referred to the monoclinic c r y s t a l axes, calculates the T andco tensors. Figure 15 shows that angular o s c i l l a t i o n s of an atom about the radius OP = r cause the apparent position B of the electron density maximum to be closer to the centre of rota-t i o n 0 , usually the molecular centre, than the true position P 2 2 by an amount A = BP. A Gaussian function, p(x)ocexp-(x /2q ) , can be used to represent the shape of the atomic peak, where 90 2 x i s the distance from the centre of the atom and q i s a Gaussian breadth parameter for the peak. It i s assumed that the molecule makes harmonic angular o s c i l l a t i o n s and therefore that the atom w i l l move on the surface of a sphere with P i t s middle po s i t i o n . \ Under these conditions the maximum of the time average den-s i t y , which l i e s along the radius OP, i s sought. The distance between t h i s maximum at P and the apparent position B, i s de-rived by Cruickshank (31) and i s given by: where s and t are the mean square amplitudes of o s c i l l a t i o n i n the rotations about the two p r i n c i p a l axes perpendicular to the radius r . As Cruickshank, i n his 1961 paper (33) points out, t h i s formula i s only correct i f a p r i n c i p a l axis of to ^^ coincides with the radius to the atom. In t h i s case, f o r an / Figure 15. Correction f o r Thermal O s c i l l a t i o n 91 atom at ( r , 0 , 0 ) and co-^ = ^13 = 6u223 = ® (these terms are usu-a l l y ignored as they are generally much less than the diagonal 2 2 2 2 terms) s = ^ 2 2 a n c i t = c ° 3 3 r * F o r biphenylene a n d coronene with the atom i n general at positions (x,y ,0) (^^2 = c 0 1 3 = ^23 = 0) the x correction i s - 6 x - 2 1 / ^22xZ_ \ + x / a J 3 3 r 2 x I q 2 + ^ 2 x 2 + c o l i y 2 ) r 2 ( l + c o 3 3 r 2 / q 2 2 2 2 where r = x + y . The y correction i s simi l a r . These correc-tions are calculated for each atom and the bond lengths correc-ted by the appropriate amount. B. Anomalous Scattering of X-rays In deriving the scattering curves for the atoms i t i s generally assumed that the frequency of the incident radiation i s much greater than a natural absorption frequency i n the atom. When any atom i n a c r y s t a l has an absorption edge f r e -quency of the same order of magnitude as the frequency of i n -cident radiation, the above assumption breaks down, and the scattering factor of the atom must be adjusted to account f o r anomalous scattering. It has been noted (50) that anomalous scattering takes place to some extent even i f the frequency of the radia t i o n i s considerably d i f f e r e n t from that of the ab-sorption edge. Under normal conditions, f o r non-centric c r y s t a l s F(hkJ-l) and F(hicf) are given by 92 F(hkA) - |P(hki)| exp(i# ) F(EkT) - lF(hk£)| e x p ( - i 0 ) that i s , (hkfl) has the same i n t e n s i t y as (EO) (Friedel's Law). I f , however, anomalous scattering occurs, the scattering fac-t o r f f o r the normal case must be modified by a r e a l and ima-ginary correction Af 7 and i A f ' ' giving f - f + Af y + i A f " . A p o s i t i v e phase s h i f t of IT/2 i s caused by i and i n general t h i s a f f e c t s the i n t e n s i t i e s from hk4 and EkT d i f f e r e n t l y . We may write the amplitude of the d i f f r a c t e d wave from (hk4) as follows t F(hki) = F (hk!) + F'(hktf) + V ( h k i ) i 3 3 and s i m i l a r l y f o r (EEJ) ,F(EH) - ,F ( E H ) + IF'(EH) + F* ( E H ) r 3 3 where |F'(hk£)| i s the normal amplitude of the anomalous seat-ter e r , |F*'(hki)| i s that part of the amplitude from the anoma-lous scatterer whose phase i s *ft/2 ahead of the normal, and |F r(hki)| i s the amplitude from the remainder of the structure ( s i m i l a r l y f o r (ESI)). Since |F r(hk^)\ - |F r(REl)| and |FQ(hkjl)| - |F0(EH)1 then the difference between |F (hktf)| and 3 3 |F (EH)( i s due only to the difference between JFa'(hkl)\ and |F''(EH)I (see Figure 16). Use of the anomalous dispersion of X-rays as a t o o l f o r determining absolute configuration of molecules owes i t s de-velopment to Bijvoet and co-workers (4#, 51). In order to dis t i n g u i s h between two enantiomers, struc-ture amplitudes f o r (hkj£) and (EH) f o r one enantiomer are c a l -culated and the amplitudes compared to the observed i n t e n s i t i e s 93 from (hkfl) and ( h H ) . I f i t i s found that when |F(hk£)l > lF(hkJ)| , I(hk£) ? I(hk£) also, ( s i m i l a r l y when lF(hH)| < ,F(hk2)|) then we have chosen the correct enantiomer. Figure 16. Anomalous Scattering APPENDIX II STRUCTURE FACTOR TABLES 9 T A B L E X V I I I B I P H E N Y L E N E M E A S U R E D 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 ( V i s u a l D a t a ) ( V a l u e s l i s t e d a r e o n o n e - h a l f t h e a b s o l u t e s c a l e ; u n o b s e r v e d r e f l e c t i o n s , w h i c h a r e l i s t e d a s 0 . 0 , h a v e i l F | < 3 - 5 ) h k I obs calc 0 2 . 6 0 7.7 0 7.9 o i . e 0 5.3 0 55.7 2 L' .o _ 3 . S 3.6 24.2 3.0 0-0 ' a . 7 0.0 2.9 5.0 1.9 0.5 1 0 . 0 - 1 0 . 1 o . a - 3 . 2 3.<• - 2 . 0 0 . 0 - 1.3 2 . 3 - " 1.3 16.2 0.2 O.S 1.0 1.9 1.8 3.6 1.9 9.2 2.6 3.3 3.6 4.2 O.t •6.1 0.3 4.5 3.3 0.3 0.9 4.5 0.0 0.0 0.0 b . o 13.1 4.1 3.0 3.5, 14.9 9.3 2.9 26.e 9.4 • 20.3 10.1 0.0 27.2 6.7 20.2 0.0 2.0 2.2 2,8 2.5 2.5 6.2 - 7.0 0.4 5.2 0.9 14.0 12.2 3.5 5.3 10.5 10.1 11.9 5.6 | 12.6 37.3, • 15.3 21.0 2B.6 33.6 18.2 17.2 • 9.6 2.5 1.4 10.2 0.6 • 7.5 13.4 • 6.2 2.3 3.2 o . e • 9.6 10.5 9.0 10.9 11.6 4.1 25.5 4 7 . 1 "11 . 3 34.2 13.S i a .5 30.3 34.2 18.3 18.!) 9.8 1.8 0.0 10.6 0.0 6.7 13.6 5.9 2.0 2.1 0.0 10.2 0.0 0.0 2.5 2.8 2.2 7.5 5.2 4.1 2.6 1.9 1.8 2.4 4.S 12.1 0.0 4.2 22.3 3.2 47.5 43.2 0.0 1 4 . 0 1.7 4.6 3 . 9 17.0 '29.4 15.5 11.9 2.6 13.3 - 13.3 4.0 - 4.9 0. 0 - 0.5 1. e 3 . 1 3.8 4 . 1 10.6 - 11.4 10.2 - . 9.4 4.3 - 5.3 0.0 2.8 3 .1 - 3.0 0.0 - 1.8 0.0 0.3 3.3 5.8 2.1 3.9 0.0 - 2.7 2.2 - 2.7 0.0 2.8 5.2 - 6.6 010 - 2.7 5.6, - 5.6 3.7 3.4 3.6 2.7 2.4 5.7 - 21.0 • 2.0 42.3 40.2 0.2 \ 14.3 ' 1 . 6 3.2 I B . 5 27.1 16.0 -12 -11 -10 0.0 " 5 . 7 -0.0 4 . B 0.0 17.0 0.0 "0.0 0.0 0.0 2.0 2.9 0.0 0.0 0.0 2.2 5.9 0.0 0.0 19.2 6.7 0.0 0.0 2.2 3 . 1 2.2 2.2 0.0 5.0 0.0 •2.7 1.9 0.0 2.1 7.5 3.6 0.0 6.0 10.1 0.0 2 . 4 0.0 0.0 0.0 3.6 11.0 0.0 3.0 0.0 0.0 3.0 4.9 13.9 5.3 14.8 11.9 2.1 18.1 28.5 4*. 9 15.7 12.6 8.3 6.3 13.4 9.9 22.9 0.7 12.0 11.7 12.7 0.1 •' 5.7 2.4 • 4.7 3.8 15.1 0.0 2.6 0.3 1.7 0.6 0.0 2.9 5.9 4.3 2.8 .20.2 34.7 10.2 14.2 8.0 1.7 6.9 2.8 6.9 3 . T 6.0 9.6 10.5 0.4 10.1 0.9 6.4 11.6 - 11.7 3.3 - 1 3 - 1 2 -a -10 o ; o ' o . o 0.0 4.8 1.8 5.4 3.7 0.0 3.7 0.0 10.0 11.4 2.8 5.5 0 . 6 ' " 6.0 6.0 0.0 5.9 0.0 0.0 0.0 6.8 0.0 0.0 0.0 0.0 2.2 4.0 0.0 2 . 9 2 . 9 0.0 0.0 0.0 0.0 2.5 0 . 0 0 . 0 0.0 0.0 8.5 4.9 « . 7 24.5 12.3 0.0 20.0 '"Oi*" 1 3.8 0.5 5.0 2.3 4.2 2.6 9 . 9 3.5 5.3 0.3 2.3 4.9 4.6 5.7 24.7 4.8 | 0.5 19.2 0.8 5.8 3.2 5.0 0.0 3.4 - 2.6 2.8 - 2.1 O.B 0.2 7.4 5.3 .7 - 1.3 10.2 0.9 16.8 7 . 6 0.0 0.0. 4.5 4.4" 3.8 9.2 5.7 2.5 0.0 0.0 0.0 0.0 2 . 9 2.2 15.7 8.2 3.7 3.9 0.0 6.2 0.0 0.0 0.0 0.0 0.0 0.0 7 . 9 0 . 0 0 . 0 0 . 0 ' 6". o 0.0 1 0 . 9 3.0 I C S 0.0 3.6 0.0 6.3 0.0 0.0 6.2 2.2 3.9 3.7 1.9 3.3 3.3 9.0 1.3 9.3 11.5 3. J O.B 11.1 0.7 3.2 0.7 2.2 0.6 3.8 2.5 9.0 8.3 7 . 6 5.9 1 1 . 7 6.0 0.9 0.2 - 4.9 0.5 0.1 0.5 0.7 2.3 , 6.9 3.7 ' 8.9 4.3 5.6 2.6 11.6 2.0 4.3 1.1 3.2 6.2 10.7 4.5 4.3 2.5 18.8 6.7 0.0 3.6 4.7 , 27.1. 9 .6 ' 4.61 96 TABLE XVIII (continued) continued: h k I 'obs 'calc 0.0 6.7 0.0 _5.0 0.0 0 .0 12.7 0.0 0.0 0.0 4.8 3.6 0.0 0.0 3.5 0.0 0.0 2.9 0.0 0.0 9.2 2.7 0.0 0.0 4.5 2.6 5.3 0.0 3.9 0.0 5.4 ' 0.0 ' 0.0 B . l 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.0 0.0 5.6 0.0 0.0 0.0 2.2 3.6 13.5 5.9 6.9 0.3 1.7 3.0 6.9 5.0 8.0 4 .0 5.6 10.7 2.5 0.2 10.1 0.2 " 2.0 9.6 0.3 0.0 0.9 3.3 7.2 '2.6 • 2.4. 11.3 5 .6 5 .7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.1 0.0 0.0 2.5 0.0 0.0 3.0 3.9 10.2 4.9 2.8 9 .2 0.0 1 .6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.6 0.0 0.0 3.5 2.0 ' 3.9 3.3 3.9 8.7 6.2 3.0 a . a 0.0 2.5 0.0 6.9 0.6 0.9 10.0 - 9.1 1.1 .- 0.2 0.0 0.2 4.7 - 7.0' 2.7 3.4 0.0 - 0.0 0.0 0.7 4.7 5.9 0.0 - 1.2. 0.0 0.9 0.0 2.3 0.0 - 0.4 0.0 - 2.B 0.0 - 3.6 0.0 - 0.3 1.2 o . a 0.0 2.5 0.0 ~ 0.1 3.7 - 5.0 0.0 - 1.4 0.0 - 1.6 0.0 - 0.4 0.0 ' 0.8 0.0 - 1.6 5.2 - 7.6 2.4 5.9 0.0 6.2 3.9. 10. a 1.8 9.8 0.7 9.6. 3.6 3.0- 3.9 3.2 - 4.4 0.0 - 2.3 2.8 4.4 2.5 - 3.2 .0.0 0.0 9.3 0.0 0.0 0.0 ' 7.6 1.9 0.0 0.0 7.7 0.0 0.0 0.0 0.0 2.2 ' 3.8 0.2 9.5 3 .a 7.9 7.7 0.2 10.2 2.9 11.9 0.7 2.0 2.8 3.4 0.8 0.9 0.3 5.5 0.7 6.9 5.9 2.7 - . 1.1 0.0 13.2 5.2 10.0 0 . 5 6.9 0.0 6 .0 0.0 3.7 0.0 3.6 4 .5 0.0 3.8 0.0 2 .5 - 2.0 0.0 - 0 .5 0.0 0.3 4,1 - 6.0 0.0 0.0 0.0 0.0 0.0 . - 2 0.0 0 0.0 - 0 0.0 - 0.4 0.0 - 0.8 0.0 0.7 0.0 - 0.4 0.0 0.0 0.0 1.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 .4 0.0 0.0 0.0 2.9 0.0 0.0 - 2 . 7 0.0 0.0 6.3 0.0 3.1 0.0 o ; o 9.3 0.5 0.8 2.9 12.5 7.2 5.5 2.7 0.9 5.0 0.8 11.5 ' 5.8 0.4 0 .5 10.6 6.0 0.0 0.0 0.0 0.0 3.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.9 0.0 0.0 7.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.2 0.0 0.0 0.0 5.9 5.7 4,5 3.0 6.9 10.0 8.3 2.0 5.9 - 3.5 6.0 I 0.0 0.0 • 6.0 - : 0.0 0.0 0.0 0.0 3.4 0.4 5.0 0.6 2.9 0.3 0.7 3.0 97 TABLE XIX BIPHENYLENE MEASURED AND CALCULATED STRUCTURE FACTORS (Counter Data) (Each group of three columns contains h, 10F , and 10F ; unob-served r e f l e c t i o n s , which are l i s t e d as 0, have /F^<1?0-1.5) 9 134 -122 10 12 13 i 94 «6 -14 -70 -72 -16 -40 - IB 4 50 47 -2 -27 -25 -14' 0 3 -9 -21 -17 ' 2 -15 -16 HKO 10 -18 -13 11 7 * 11 . 2 144 H 5 .-13 -32 -24 -15 0 12 to 0 6 -1 497 4 70 -13 -32 -28 -8 41 44 3 -31 -34 11 - 9 - 7 12 -41 -43 ' 3 411 yio -12 -152 -148 -14 -52 -S2 11 -30 -32 0 -231 -224 -12 -44 -40 -7 - 206 -204 4 -16 -17 K- 0 12 94 92 13 0 -1 4 583 5/4 -11 -34 -34 -13 39 lo -9 -7 1 20 l o -11 -34 -31 -6 -37 -12 14 12 2 96 54 13 9 1 5 334 326 -10 -101 -93 -12 -33 -16 2 -396 -361 -10 -45 -57 -5 60 61 6 0 1 4 62 55 14 I t 9 6 586 2«4 -9 -It -77 -11 10 IZ K-12 3 14 28 -9 131 133 -4 -43 -44 -25 -26 6 -515 - s u a 15 48 61 0 228 733 7 -56 -53 - 8 -36 -16 -10 36 35 -19 -17 4 160 131 - a -102 -41 - 3 -12 -32 a 0 - 0 16 31 34 1 74 76 a 121 105 - 7 228 205 -9 55 55 -31 -28 5 -197 -172 -7 -215 -207 -2 - 134 -139 . 10 54 53 17 15 13 2 14 B • 9 -2f>3 -283 30B 302 -a -36 -28 45 44 6 121 124 - 6 -95 -86 -1 64 61 HK3 12 -296 -2.15 18 -84 -84 3 21 22 .10 -97 -9B - 5 -171 -171 -7 15B 153 -6 - I * -14 7 143 l i e . -5 -119 -117 0 21B -216 14 -28 -79 19 9 4 13 14 i t -23 -14 -4 50 50 -6 136 -1 33 40 40 8 182 168 -4 43 38 1 14 11 K- 0 16 3B 41 20 ti - 3 5 12 17 12 73 70 -3 -142 -143 -5 -50 -54 2B 26 9 - 8 -13 -3 -243 -231 2 -29 -11 -22 0 -2 • 18 -341 -357 21 -75 - lb 6 -31 -34 13 90 U4 -2 59 61 134 132 6 9 10 -21 -21 -2 56 54 3 26 25 -20 -56 -54 20 -87 - )2 22 0 -4 7 -11 -11 14 -240 -244 -1 162 171 - 3 44 43 -2 14 11 11 103 90 -1 -112 -108 4 0 3 - l a 20 20 2? -55 -57 8 -5 -8 15 -190 -103 0 82 92 -2 -59 -55 -I 40 19 12 -107 -107 0 -40 -40 5 -8 -2 -16 115 119 24 124 121 Ka 6 9 -2B -28 16 -111 -109 1 117 120 -1 106 -106 -14 - l l 13 68 64 1 -B4 -82 6 31 33 -14 72 76 0 478 471 10 - S -0 17 47 48 2 -207 -201 0 0 6 1 -27 -26 14 t e a m o 2 136 136 7 -92 -89 -12 22 23 K- t 1 75" 74 lB 7o 73 3 232 2 34 I n Bl 42 38 15 128 128 3 -227 -213 8 159 160 -10 30 29 t -25 -23 2 21 24 K«13 19 -32 -29 4 28 30 2 -76 -72 t>7 16 -20 -22 4 -38 -28 9 0 6 -8 -92 -80 2 19 17 3 26 25 1 6 0 20 14 12 5 -201 -214 3 i o a -105 4 56 02 17 -45 -47 5 -91 -87 10 12 9 -6 0 -0 3 507 509 4 9 17 2 -16 -18 21 96 93 6 22 5 4 12 92 -60 -62 18 40 40 6 29 .27 11 116 107 -4 -376 -362 32 30 5 41 37 3 101 103 22 - B -11 7 121 110 5 -74 -77 7 2~ 19 -4B -4ft 7 74 72 12 4a 42 -2 145 146 5 18 i a 6 - 326 -2^4 23 -2B a 212 210 6 168 L67 7 -4 1 -41 20 -51 -49 8 65 BO 13 - l l -8 0 60 60 -504 -499 7 -74 - 6 ? K» 3 9 " 24 25 7 -25 -27 0 -2 21 -24 -36 9 84 83 14 91 42 2 1 10 111 T -24 -25 a -30 -29 HK1 -23 8 31 10 65 ' (-.4 6 -14 -39 -22 -24 22 16 IB . 10 66 61 15 22 24 4 -281 -269 8 -31 -31 9 -14 -2 -22 40 18 11 - 9 - 7 . 9 49 56 23 5 1 11 400 396 16 34 17 6 -15a -145 9 -64 -57 10 -22 -20 K- G -21 43 i4 12 -193 -146 ID 0 6 K-13 12 151 153 17 -65 -67 10 ao 79 10 -13 -11 u -29 -3l -24 4t 40 -20 23 20 13 -45" -39 I t - J ? -19 «4 ni K- 3 13 16 16 18 56 •il 12 0 7 11 -a -I 12 169 177 -22 -32 -15 -19 72 69 14 -12 - 9 12 11 14 0 -25 -24 -23 -8 -13 14 -54 -61 14 126 145 1? - 9 -10 13 13 20 -20 -5> - i l -18 -45 -48 15 99 1(17 13 -26 -25 1 -7 -I -22 -2 3 -24 15 94 ae K» 9 16 -48 -53 13 9 6 14 21 24 -18 -154 -144 -17 -79 - 19 16 -38 -39 14 -27 -25 -21 36 34 16 -16 -13 -16 31 13 18 0 14 -18 -19 15 20 IB -16 -147 -I 18 -16 52 52 17 17 22 15 -21 -21 -20 58 58 17 -41 -36 - I s -23 -ri 20 -76 -78 15 -18 -20 16 19 23 -14 3B 16 -15 -103 - I i 7 18 25 19 16 -14 -11 HK2 -19 71 63 16 -24 -26 -14 20 17 22 3B 38 16 -37 -39 17 9 12 -12 74 *8 . -14 -53 -12 19 -2d -24 17 i a 4^. - IB 78 73 19 9 20 -13 155 -I-iO 17 -25 -21 18 - 122 -129 -10 . 43 30 -13 -155 -159 20 0 0 16 10 8 K- 0 -17 30 10 20 -37 -16 -12 -46 -47 K« 1 18 tb 134 141 19 - 8 -t -8 10 2 -12 76 62 21 -32 -42 19 a 7 -22 -68 -69 -16 -34 -35 21 25 26 - I t 16 14 -22 18 19 63 64 20 -2B -10 -6 316 305' - n B4 82 22 5 4 11 30 -15 -44 -51 -10 27 73 -21 -22 -21 20 28 26 21 -10 -11 -4 213 m -10 -127 -1 OB K- 9 -18 -35 -32 -14 -9B -46 K« 6 -4 -1* -8 -20 -32 -32 21 -219 -230 -2 -74 -64 - 9 301 ;-99 *• 6 -17 -27 -27 -16 172 166 -13 -224 -236 -20 0 0 -8 67 67 -19 0 -2 22 i a 19 K» 7 0 -378 -310 -109 -107 -21 -19 -17 -16 -6 -4 -90 -87 -12 -7fl -79 -19 -18 -19 -7 165 -163 -18 -15 - l o 23 - IB -22 1 -25 - ? 3 2 5B4 560 -7 336 31B -20 0 3 -15 -39 -39 -12 0 -2 -11 -46 -44 -18 42 4) - 6 12 9 -17 -14 -11 24 -27 -29 2 -20 -17 216 201 - 6 237 214 -19 - a -9 -14 -7 - 6 -563 -635 -10 -66 -64 -17 0 -6 -5 74 . 77 -16 50 45 3 4? 41 6 -433 -420 -5 1H 2 -18 15 17 -13 0 -7 -67 -£,B - 9 51 49 -16 44 43 -4 -42 -45 -15 44 50 K- 2 4 10 3 8 29 29 -4 -396 -402 -17 -9 -12 -12 -41 -44 116 107 -8 -98 -97 -15 41 16 -3 -23 -21 -14 -fl -4 0 9C6 1009 5 9 5 10 58 49 -3 -624 -620 -16 76 77 -11 -37 -38 -4 559 652 - 7 -304 -310 -14 53 48 -2 -28 -31 -13 64 72 1 11 10 6 - u -14 12 59 54 -i 71 72 - 1 5 0 -12 -10 as as 119 108 -6 -311 -311 -13 21 14 -1 L10 115 -12 14 15 2 -107 -96 7 U 3 14 -133 -123 -1 -328 -309 -14 -20 -24 - 9 -8 -1 10 4 -5 100 104 -12 -27 -27 0 51 51 -11 12 7 J 1220 13') 6 a 0 -1 16 -117 -114 0 -257 -250 -13 43 52 - B 53 55 -493 -465 -30 -26 -11 -35 -22 1 137 -136 -10 -<»6 -84 4 35 32 4 -59 -60 i a 290 2<>7 I -167 -15B -12 -29 -a -7 83 B3 4 150 136 - 3 -B5 -B4 -10 -563 -565 2 -21 -23 -9 -27 -21 5 61 56 10 -18 -15 20 -78 - B l 2 -146 -1 37 -11 -33 - i l -6 10 3 77 0 6 -2 74 ft9 -9 -21B -204 3 -25 - 2 2 -8 -163 -T$4" 6 29 14 11 10 12 22 -24 -29 3 293 273 -10 99 90 -5 -22 - / 4 528 510 - I 218 706 -8 91 too 4 -62 -59 -7 -206 -186 7 -10 -2 12 -52 ' -76 24 -7B -HI 4 ilr 211 - 9 109 99 -4 121 129 55 63 0 -18 -17 -7 -14 -26 5 1«5 164 - 6 -104 -101 a -22 -19 13 -20 -22 5 49 2 4 70 - B -9 8 -3 -186 -lrt9 12 45 46 I -245 -235 - 6 -74 -71 6 -18 -17 -5 256 241 9 332 327 14 -25 -25 K- 6 34 15 - 7 -47 -29 -2 12 a -35 -34 2 239 219 -5 - 9 -16 7 39 34 -4 -114 -106 10 44 46 L5 70 70 -24 -11 -9 7 243 ?2B -6 -266 -251 -1 -158 -157 -117 -111 3 -46 -47 -4 153 162 8 19 19 -3 70 66 u 48 4S 16 - 8 -A -23 45 *2 a 263 262 -5 -16 -i 0 10 12 i a -59 -60 4 69 63 -3 -11 -11 9 -9 -3 -2 232 225 12 -129 -119 17 0 -3 -22 117 111 9 -252 -247 -4 -149 -111 I -20 -12 20 -33 -31 5 246 252 -2 -130 - H 6 10 0 -12 -1 I b t IB1 13 25 25 18 28 32 -21 39 19 I c l a b -3 -34 -44 2 -88 -98 22 16 19 126 323 - l 7 4 11 36 37 0 84 80 14 -20 -20 19 17 18 -20 22 is i i -124 -110 -2 -33 -24 3 175 175 7 202 713 0 -60 -07 12 -32 -30 1 -110 -106 15 -30 -29 20 0 14 -19 -123 -121 12 50 15 -1 -83 -74 4 -49 -54 K- 1 a 91 96 1 7 9 13 11 7 2 0 -0 16 18 15 -18 -62 - r , l 13 -101 -105 0 -92 -38 5 84 a* -23 15 14 9 94 96 2 171 160 14 31 IH 3 -114 -134 17 25 21 K« 8 -17 -103 - w o 14 59 70 1 56 52 6 52 49 -22 -26 -27 10 -9 -1 3 79 11 15 -7 -1 4 84 B5 18 -150 -157 0 36 40 -16 -33 —.0 15 297 <*9« 2 -16 -15 7 68 FO -21 39 37 11 142 142 4 -171 - l o 7 16 17 16 5 -266 -261 19 41 42 1 0 -1 -15 73 67 16 10 3 -12 -4 a -79 -81 -20 39 40 12 93 100 5 104 l')4 6 -d8 -79 20 -10 -7 2 - i i -14 -14 43 J9 17 -4L -37 -43 -40 9 0 2 -19 27 23 13 -33 -29 6 -55 -48 K-10 7 19 5 21 - i e s -189 3 81 73 -13 -315 -292 IB -8 - 0 5 -12 -84 10 -45 -45 -18 6 4 14 -107 -111 -3S -41 -14 11 12 a 52 54 22 17 14 4 24 22 -12 252 2J2 14 41 40 6 242 232 11 0 1 -17 -7B -74 15 -40 -45 8 292 2S9 -13 -20 -15 9 17 9 23 -43 -46 5 12 13 -11 -100 -100 20 -66 -63 7 23 13 12 -42 -46 -16 -1 15 -110 16 6 8 139 129 -12 0 to 22 17 24 -38 -38 6 -31 -16 -10 -109 -101 21 -12 -12 a 82 13 -28 -12 -15 -9 I 17 -91 -84 10 153 1W -11 33 33 11 47 48 7 0 3 -9 -223 -230 22 -7 -11 9 -a -4 14 -17 -19 -14 -51 -50 IB -80 -74 11 12 4 -10 -60 -63 12 59 57 K- 3 a 24 31 - B -189 - IS2 23 -27 -29 10 36 13 15 54 53 -13 -60 -50 19 9 14 12 29 : i 15 20 13 - IB -23 1 7 1 9 -1 16 -208 -7 214 196 11 93 95 16 22 24 -12 -0 20 -67 -73 13 24 24 -8 -10 -11 14 23 23 2 -126 -11 1 10 -41 -47 -ft -2L0 -252 R - 4 12 4B 47 17 6 1 -11 - IB -5 21 24 30 14 -119 -117 - 7 38 42 IS 0 -4 3 96 3 1013 11 -51 -56 -5 103 >7 -21 -6 - i 13 - 6 -11 -10 56 52 22 -a -12 15 -6 3 -53 - 6 46 44 16 -45 -51 4 32 11 12 71 H5 -4 -533 -52U -22 -45 —.3 14 35 43 • M 6 --s -72 -63 16 ?6 26 -5 79 76 17 5B 59 5 68 70 13 0 3 -3 -941 -95H -21 19 •W 15 - a -4 -15 0 4 - B -62 - i l K- * 17 -56 -60 -4 -69 -64 IB -35 -40 6 37 3b 14 -JO -21 -2 - i i i -20 32 11 16 55 59 -14 -13 -17 - 7 -191 -1 '3 -22 53 52 IB 30 13 -3 74 71 19 15 16 7 35 11 15 92 96 -1 860 0*4 -19 88 »2 17 - 8 -3 -13 6 10 -6 -136 -123 -21 B -9 19 9 8 -2 -32 -27 20 -a a 64 62 16 10 11 0 -346 -311 - i a 19 •0 18 45 46 -12 -15 -12 - 5 17C 160 -20 17 20 20 -40 -19 -1 e 1 21 22 ii 9 -360 -345 17 16 18 I 437 4 62 -17 24 16 19 1 I 20 - t l 0 -2 -4 208 194 -19 -88 -90 K" 0 -98 -93 22 -6 -4 10 -33 -12 18 -8 -9 2 645 626 -16 -15 -74 20 -35 -38 - t o 0 -8 -3 148 143 - l e i& 35 -19 50 51 t -66 -67 11 -20 -17 19 6 1 3 702 6dS -15 -67 -71 21 -7 -10 -9 14 t l -2 -62 -57 -17 B6 66 -18 -49 -50 2 39 32 K- 2 12 117 l tH 4 393 Ml -14 -126 -1?1 - B 16 21 -1 ?ae 270 -16 .0 -1 -17 . 44 45 3 -85 -84 -22 6 2 13 37 41 K« 9 5 356 340 -13 -102 -110 K. • 7 . -7 28 2B 0 - B -16 -15 -16 -36 -16 -89 -rt9 4 ID 9 -21 0 -4 14 23 23 1 a 14 (, -215 -205 -12 24 19 -20 -14 -13 -6 -57 ">2 1 -49 -46 -14 -15 -14 -15 0 -6 5 -24 -21 -20 0 -4 15 -201 -206 2 -<.i --.I 7 49 41 -11 -55 -55 -19 -20 -15 -5 10 4 2 297 274 -13 -211 -212 -14 67 63 6 10 B -19 a 0 16 -20 -18 3 49 53 8 35 31 -10 -114 -9B - i a -V - 6 -4 115 117 J 260 46 -12 -L IB - I 2 J -13 -B4 -95 7 -10 -14 -18 26 25 17 -55 -59 4 -16 -12 9 232 217 -9 0 3 -17 -7 -2 - 3 -24 -75 4 149 140 -11 -36 - 3 S . -12 -8 -10 8 59 64 -17 -103 -102 IB 20 26 i -10 -16 10 6 0 - B 47 16 -16 -30 -29 -2 -87 -92 5 -255 -231 -10 -246 -254 -11 42 ' 37 4 0 -7 -16 125 127 . 19 . -9 -10 6 -20 -11 11 -153 -16? -7 -432 -412 -15 -64 -66 -1 73 '6 6 212 202 - 9 -119 -116 -10 63 61 10 22 24 -15 15 10 20 0 4 7 a 11 12 267 255 - 6 -691 - c s a -14 0 -6 0 67 f.7 7 25 14 -8 112 109 -9 70 69 11 -24 -33 -14 -149 -I'-fO 21 -61 -68 a 11 9 13 -130 -119 -5 -134 -134 -13 61 68 1 -21 -16 a -2D8 -252 -7 448 441 -8 60 67 12 -11 -4 -13 -21 -15 22 IB 20 - 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75 16 22 19 -5 -54 -•ia -7 -71 -70 0 -12 -7 -14 u -3 74 -2 19 24 -5 80 •10 - 1 1 95 -102 -10? 17 -8 -81 -tr -6 -19 -23 1 -47 -56 -12 76 ra -2 110 120 -1 - 4 -112 -101 -10 61 56 -16 0 0 . -14 67 Ao 18 - 12 -2 - 3 -109 - n o -5 0 a 2 34 17 -10 - 7 -0 -1 - 7 -2 0 0 -5 -3 -100 -19 -9 1 7 9 -14 -127 -117 -13 14 8 -2 0 -2 - 4 12 5 3 -11 -13 - 8 -48 -55 0 -60 -t>2 26 33 - 2 68 62 -tt -90 -87 -12 102 108 -12 -18 -11 K" * 20 19 -I -43 -48 -3 154 156 4 43 44 -6 20 16 1 24 24 2 29 36 -I -156 -146 -7 13 6 - 1 0 27 26 -11 -89 -81 -17 0 -30 - J I -2 121 119 5 13 20 - 4 66 67 2 57 59 3 31 38 99 TABLE XX CORONENE MEASURED AND CALCULATED STRUCTURE FACTORS (Each group of three columns contains h , 5 l F q l , 5 F c ; unobserved r e f l e c t i o n s which are l i s t e d as 0 , have IF I < 1 .4-2 .2) H1L L» 0 1 71 73 2 334 -331 3 312 30 7 4 105 -101 5 29 -28 6 35 36 7 17 15 8 20 -19 9 8 -3 10 8 -1 U 10 3 12 56 58 13 85 87 1* 56 55 15 20 21 16 7 3 17 0 -7 L" 1 -17 7 0 -16 12 -7 -15 17 17 -14 30 -28 -13 28 26 -12 0 3 -11 12 -12 -10 7 7 -9 23 23 -8 30 -31 -7 78 -78 -6 41 39 -5 147 147 -4 348 355 -3 500 538 -2 257 257 -1 46 -45 0 12 15 1 111 -111 2 90 87 3 51 -50 4 46 50 5 10 -7 6 17 -17 7 38 40 a 25 23 9 78 -75 10 53 55 11 21 -15 12 40 35 13 36 35 14 0 1 15 12 -5 16 0 -0 L" 2 -18 10 12 -17 10 -10 -16 8 3 -15 8 -0 -14 8 8 -13 15 -14 -12 0 -0 -11 10 12 -10 0 7 -9 0 1 -8 73 70 -7 182 -180 -6 101 -5 28 -20 -4 25 20 -3 12 7 -2 88 -87 -1 33 -34 0 1? 15 1 107 107 2 28 -25 3 51 -51 4 92 -90 5 34 -31 6 15 12 7 20 -12 8 56 58 9 61 -61 10 24 17 11 17 -12 1? 8 -8 13 8 -3 14 0 -6 1 ?ft ?fr 2 7 -5 3 8 3 4 23 17 5 12 -10 6 12 -3 7 0 -1 8 20 -23 9 28 -34 10 20 -20 11 10 -10 12 0 -3 L- 6 -18 7 8 -17 10 -5 -16 0 -3 -15 0 3 -14 9 -0 -13 0 -3 -12 0 3 -11 25 29 -10 23 -26 -9 20 -12 -8 58 -58 -7 92 -88 .-6 39 -36 -5 12 8 -4 0 -1 -3 17 15 -2 17 -19 -1 7 -1 0 31 -29 1 17 -17 2 0 -0 3 14 -15 4 34 -36 5 73 75 6 70 -68 7 48 43 8 30 -25 9 17 -17 10 7 3 11 0 0 L- 7 -17 0 3 -16 b 0 -15 8 -10 -14 8 -5 -13 15 14 -12 58 -58 -11 96 97 -10 68 -71 -9 25 29 -8 14 -5 -7 12 -10 -6 15 17 - 5 0 8 -4 8 -10 -3 12 -12 -2 7 10 -1 40 45 0 58 58 1 34 30 2 15 7 3 30 23 4 61 -60 5 55 56 6 34 -30 7 10 7 8 12 7 9 8 -1 L- 8 -16 31 30 -15 7 3 -14 0 -I -13 15 14 -12 38 -35 -11 41 35 -10 12 -7 -9 0 -0 -8 0 a -7 8 8 -6 10 -8 -5 10 -17 -4 15 8 -3 26 23 -2 71 70 -1 97 97 0 61 58 1 20 17 2 0 0 3 19 -15 4 0 0 5 0 -5 6 12 8 7 8 -5 L- 9 -15 0 -3 -14 14 3 -13 12 -7 -12 8 8 -11 8 -10 -10 8 3 -9 0 -0 -8 0 -3 -7 8 3 -6 15 15 -5 29 -34 -4 30 30 -3 0 0 -2 20 17 -1 8 12 0 0 -7 1 17 -12 2 0 0 3 10 5 4 7 3 5 0 -1 L-10 -14 0 -0 -13 0 5 -12 10 -7 -11 12 -12 -10 14 -15 -9 12 -3 -8 8 7 -7 10 -7 -6 8 20 -5 25 -25 -4 0 3 -3 15 -7 -2 10 -7 -1 0 -3 0 10 -1 1 10 7 2 0 0 H2L L» 0 0 92 91 1 8 3 2 51 -46 3 25 25 4 15 -14 5 17 19 6 0 -0 7 12 7 8 28 -2? 9 14 15 10 70 71 11 56 56 12 17 12 13 34 30 14 30 -29 15 0 -0 16 8 5 L» 1 -16 8 7 -15 8 3 -14 15 -15 -13 0 7 -12 8 3 - l l 10 6 -10 20 -25 -9 0 -1 -8 35 29 -7 112 110 -6 209 205 -5 229 227 -4 38 -38 - 3 86 90 -2 98 -97 -1 15 -23 0 48 43 1 14 -14 2 20 -19 3 21 21 4 7 1 5 0 0 6 25 -24 7 15 -7 8 40 43 9 71 76 10 71 75 11 86 87 12 28 -24 13 20 20 14 20 -17 15 0 0 L- 2 -17 10 0 -16 0 3 -15 8 1 -14 , 10 3 -13 0 3 -12 0 7 -11 17 -17 -10 20 -23 -9 7 6 -8 106 102 -7 165 157 -6 105 105 -5 137 137 -4 113 -112 - 3 26 31 -2 12 -8 -I 31 28 0 10 7 1 26 -24 2 15 21 3 7 -7 4 38 35 5 12 -12 6 15 -12 7 14 -7 8 14 8 9 21 20 10 15 I 11 8 -1 12 17 -7 13 0 -0 14 0 7 L- 3 -17 0 -3 -16 10 -7 -15 12 -7 -14 0 3 -13 12 12 -12 0 5 -11 0 -3 -10 20 -24 -9 17 -15 -8 15 7 -7 21 -25 -6 17 -17 - 5 46 -48 -4 17 19 -3 17 20 -2 25 24 -1 38 -40 0 96 -92 1 40 -41 2 102 -102 3 86 85 4 if -36 5 17 20 6 8 -3 7 14 -14 8 8 1 9 10 -6 10 12 -0 11 0 -3 12 8 3 13 10 3 L« 4 -17 ?\ -20 -16 35 -34 -15 0 0 -14 29 -31 -13 25 31 -12 0 -8 - l l 0 0 HOL L= 0 2 31? 329 4 160 -160 6 34 30 8 15 -7 10 23 23 12 20 -17 14 75 29 16 66 70 L= 1 -16 91 96 -14 8 1 -12 0 -1 -10 0 10 -8 0 0 -6 65 63 -4 158 -153 -2 260 262 0 284 300 2 172 -167 4 120 116 6 31 -25 8 53 -51 10 31 30 12 17 -12 14 8 -8 16 0 -5 L= 2 -18 24 19 -16 10 3 -14 10 -10 -12 17 17 -10 97 -95 -8 41 -35 -6 107 102 -4 128 -127 -2 160 -153 0 158 -153 2 63 61 4 17 -10 6 265 -250 8 85 -78 10 28 25 12 8 0 14 0 3 16 8 0 L" 3 -18 0 -1 -16 8 -7 -14 15 15 -12 58 -55 -10 182 -180 __^ -8 _48 -43 -6 24 20 -4 73 71 -2 150 143 0 46 46 2 12 -6 4 81 -82 6 87 -81 8 10 7 10 10 0 12 12 -0 14 10 -1 L> 4 -18 7 3 -16 0 0 -14 8 10 -12 28 -17 -10 17 -17 -8 7 0 -6 17 -10 -4 78 -76 -2 95 -91 0 14 -8 2 25 20 4 46 41 6 26 30 8 0 1 10 8 -15 12 39 -41 14 28 -25 -18 7 -12 -16 8 -0 -14 8 7 -12 17 12 -10 17 12 -8 28 28 -6 71 -70 -4 282 -275 -2 76 -71 0 43 38 2 25 -21 4 30 -30 6 24 -25 8 10 3 10 0 -7 12 29 -30 L= 6 -18 0 0 -16 0 -1 -14 15 -15 -12 25 -23 -10 24 -24 -8 35 34 -6 41 -36 -4 58 -45 -2 41 39 0 35 -33 2 12 20 4 53 51 6 12 -8 8 0 3 10 19 1 L- 7 -16 8 3 -14 71 68 -1? 33 38 -10 23 -21 -8 15 17 -6 17 15 -4 24 24 -2 21 -25 0 34 34 2 197 200 4 88 87 6 20 -23 8 8 -0 10 0 0 L" 8 -16 51 46 -14 118 116 -12 34 26 -10 12 -12 -8 8 0 -6 0 -7 -4 0 • 6 -2 10 -10 0 63 56 2 71 71 4 21 -14 6 0 1 8 8 0 L« 9 -16 14 -12 -10 17 _Zfl_ 20 10 15 _L2_ 0 25 2 28 4 0 6 10 17 _L5_ 12 -20 -14 17 -14 -19 -20 0 6 L.10 -14 10 -10 -12 0 3 -10 20 -14 -8 56 -56 -6 25 -17 -4 . 0 6 -2 0 1 0 . 15 10 2 14 7 L' 3 -18 17 16 -15 -14 -13 -12 26 40 41 -11 -10 -9 -8 -7 - 5 -4 -3 -2 -1 0 1 2 3 4 5 0 19 15 51 71 _0_ 25 12 25 0 41 14 58 117 ISO 92 25 6 7 8 9 10 12 13 14 L- 4 -18 0 20 0 17 10 _12--17 -16 -15 -14 -13 -12 0 0 25 34 43 29 -11 -10 -9 -8 -7 -6 0 7 20 7 43 20 -3 3 -0 1 -26 -41 -41 0 20 -10 46 -71 0_ -21 -12 -21 -6 43 15 -56 -118 -143 -87 -24 3 20 -5 12 -0 IP_ 6 -0 5. -1 3 -26 -30 -43 -29 3 -12 20 -5 43 -4 15 -3 19 -2 86 -1 147 0 123 87 15 10 7 14 0 7 8 9 10 11 12 0 0 12 0 0 43 23 46 14 -15 83 -143 122 -85 -12 7 -I 12 3_ -7 -I -12 -3 -7 - 5 -1 -18 17 20 -17 15 -19 -16 15 17 -15 0 - 5 -14 0 -I -13 0 3 -12 10 8 -11 0 - 5 -10 10 12 -9 28 -25 -8 17 -15 -7 70 -70 -6 63 -63 -5 19 -20 -4 25 -26 -3 25 -25 -2 83 78 -1 61 -55 0 43 39 100 TABLE XX (continued) - 1 0 0 0 - 9 0 3 - 8 0 3 - 7 7 7 - 6 0 - 3 - 5 17 15 - 4 0 5 - 3 10 - 8 - 2 33 - 3 3 - 1 92 - 9 3 0 103 ^101 1 21_ 2 87 - 8 2 3 61 61 4 17 - I 5 17 - 7 6 8 10 7 19 12 a 0 - 3 9 8 12 10 10 0 l l 0 3 12 10 - 3 L » 5 - 1 7 17 - 1 4 - 1 6 21 - 2 5 - 1 5 8 10 - 1 4 15 - 1 7 - 1 3 0 3 - 1 2 0 7 - 1 1 0 - 3 - 1 0 8 0 - 9 14 15 - 8 0 - 0 - 7 0 -1 - 6 10 3 - 5 10 10 - 4 19 - 1 5 - 3 7 8 - 2 15 12 - 1 10 - 1 2 0 15 15 1 17 14 2 12 8 3 12 - 1 2 4 10 - 1 5 12 - 7 6 24 - 2 5 7 25 - 2 5 8 15 15 9 48 - 4 6 10 35 34 11 15 - 1 0 L - 6 - 1 6 0 0 - 1 5 0 3 - 1 4 10 7 - 1 3 8 - 3 - 1 2 19 - 1 7 - 1 1 26 - 2 3 - 1 0 30 - 3 4 - 9 88 - 8 8 - 8 63 66 - 6 55 58 - 5 8 - 0 - 4 17 - 1 2 - 3 10 12 - 2 8 1 - 1 10 - 1 0 0 0 0 1 8 - 6 2 0 5 3 0 0 4 17 - 1 7 5 20 - 2 0 6 0 - 1 0 7 66 - 6 1 8 53 46 9 36 - 3 8 in ?n 20 L= 7 - 1 6 0 - 0 - 1 5 0 0 - 1 4 10 7 - 1 3 0 1 - 1 2 30 - 2 8 - 1 1 30 - 2 9 - 1 0 0 3 - 9 70 - 7 1 - 8 76 71 - 7 41 - 3 5 - 6 10 3 - 5 8 - 1 - 4 14 - 1 0 - 3 0 - 5 - 2 0 - 3 -1 0 - 0 0 17 - 1 5 1 0 - 0 2 10 12 3 0 - 0 4 0 - 3 5 8 - 6 6 0 0 7 10 - 5 8 8 6 L - a - 1 5 0 - 1 - 1 4 10 10 - 1 3 8 3 - 1 1 12 10 - 1 0 0 - 0 - 9 12 10 - a 8 - 1 2 - 7 0 3 - 6 0 - 0 - 5 28 24 - 4 61 61 - 3 61 60 - 2 17 8 - 1 31 30 0 23 - 2 0 1 8 - 3 2 0 6 3 8 - 0 4 8 - 3 5 10 7 6 0 - 1 L= 9 - 1 4 10 3 - 1 3 0 - 0 - 1 2 7 - 0 - 1 1 0 3 - 1 0 0 0 - 9 8 - 3 - 8 0 - 6 - 7 15 3 - 6 33 31 - 5 60 51 - 4 38 35 - 3 55 51 - 2 26 - 2 4 - 1 12 10 0 20 - 1 0 1 0 0" 2 12 3 . t 3 0 - 3 4 0 0 L - 1 0 - 1 2 0 0 - 1 1 0 0 - 1 0 7 3 - 9 0 - 0 - 8 0 - 5 - 7 0 0 - 6 0 3 - 5 0 3 - 4 0 - 6 - 3 17 - 6 - 2 7 - 3 - 1 7 0 0 15 7 H31 l L« 0 1 82 - 7 8 ' 2 15 - 1 2 3 38 35 ' 4 8 - 5 5 21 - 2 0 6 12 7 7 17 - 1 7 8 25 20 9 10 - 7 , 10 10 - 0 1 11 15 - 8 12 8 - 6 13 0 3 14 15 15 L= 1 - 1 5 7 - 7 - 1 4 7 0 - 1 3 10 7 - 1 2 0 - 0 - 1 1 a - 1 0 - 1 0 15 12 - 9 33 23 - 8 29 26 - 7 0 3 - 6 15 - 1 5 - 5 0 -1 - 4 0 0 - 3 8 - 7 - 2 70 68 - I 91 - 8 8 0 63 61 1 20 - 1 7 2 14 8 3 7 - 0 4 24 - 2 3 5 17 19 6 35 36 7 90 91 a 58 58 9 36 33 10 14 - I 11 15 - 1 0 12 14 - 0 13 10 - 6 L- 2 - 1 5 7 - 0 - 1 4 0 - 3 - 1 3 0 - 7 - 1 2 0 - 1 - 1 1 43 43 - 1 0 82 80 - 9 113 108 - 8 76 73 - 7 17 19 - 6 17 - 1 5 - 5 0 - 7 - 4 0 - 7 - 3 0 3 - 2 7 3 - 1 0 - 0 0 0 7 1 15 7 2 12 - 7 3 24 - 1 7 4 12 10 5 17 20 6 97 95 . 7 *8 36 8 43 40 9 0 - 3 10 15 - 1 0 11 0 .0 .12 J> 0 13 10 3 L= 3 - 1 5 - 1 4 . , -13 -12 -11 -10 - 9 - 8 0 -12-14 28 19 73 25 1 =1P_ - 1 2 24 15 76 15 - 7 15 - 1 2 - 6 8 . - 3 - 5 17_ 19 - 4 7 0 - 3 0 - 3 - 2 25 - 2 3 - 1 7 0 0 12 6 1 21 17 2 12 - 8 3 24 - 2 3 4 36 30 5 51 - 5 0 6 55 46 7 25 - 2 8 a 10 - 8 9 8 1 10 14 3 11 10 1 12 10 0 L» 4 - 1 5 10 6 - 1 4 0 - 5 - 1 3 17 - 2 0 - 1 2 17 20 i —11 26 - 3 0 - 1 0 0 5 - 9 8 - 1 2 - 8 17 - 1 5 - 7 10 7 - 6 20 20 - 5 25 - 2 1 - 4 30 - 3 0 - 3 71 - 6 6 - 2 33 - 3 5 - I 30 - 2 8 0 14 10 1 12 15 2 15 - 8 3 12 - 0 • 4 21 12 5 17 - 7 6 0 3 7 0 5 8 0 0 9 0 - 0 10 7 0 11 8 0 L- 5 - 1 5 7 5 - 1 4 0 - 0 - 1 3 0 0 - 1 2 10 10 - 1 1 8 6 - 1 0 0 - 1 - 9 10 6 — f l 0 7 - 7 0 0 - 6 35 - 3 0 - 5 25 25 - 4 97 - 1 0 2 - 3 14 17 -7 20 - 2 0 - 1 10 - 7 0 17 15 1 10 1 2 10 - 8 3 8 8 4 15 - 3 5 17 6 6 8 - 0 7 10 - 0 8 0 5 9 10 6 L- 6 - 1 4 7 - 5 - 1 3 10 . - 3 - 1 2 8 - 7 - 1 1 8 - 1 - 1 0 10 0 - 9 8 - 8 - 8 8 6 -T... 25„ - . -29 . - 6 60 - 6 1 - S 87 87 - 4 to - 5 8 - 3 41 34 - 2 0 8 . . - - 1 . . . ao . . - - 6 . 0 8 0 1 8 - 7 2 a - 1 5 3 21 - 2 5 4 • 20 - 1 9 5 12 . - 8 6 10 - 3 7 12 1 8 20 <t L= 7 - 1 4 . 17 . - 1 5 - 1 3 25 - 2 5 - 1 2 25 - 2 0 - 1 1 10_ - 0 - 1 0 0 0 - 9 8 - 5 - 8 10 6 - 7 8 - 0 - 6 10 - 1 2 - 5 0 - 0 - 4 0 - 1 - 3 8 - 1 0 - 2 0 - 0 - 1 10 7 0 0 - 0 1 17 - 1 9 2 10 - 0 3 30 - 2 9 4 0 - 7 5 10 3 6 0 - 0 L» 8 - 1 1 0 7 - 1 0 0 - 0 - 9 8 - 7 - 8 0 6 - 7 0 - 0 - 6 19 15 - 5 0 0 - 4 0 0 - 3 0 - 0 - 2 0 - 1 - 1 10 - 3 0 20 20 1 30 - 2 5 2 17 17 3 14 - 8 L« 9 - 1 0 7 - 3 - 9 17 15 - 8 24 25 - 7 50 46 - 6 30 30 - 5 24 15 - 4 12 - 0 - 3 10 - 5 - 2 7 0 - 1 7 - 6 0 12 7 H4t L» 0 0 17 - 1 2 1 40 35 2 46 - 4 3 3 43 40 4 33 - 2 9 5 12 - I 6 15 0 _ . ^  19 - 1 4 8 0 - 3 9 8 - 3 10 12 6 11 8 0 L« 1 r l 2 . _ 7 -a. - 1 1 10 5 - 1 0 10 - 6 - 9 17 - 1 ? - 8 0 - 0 - 7 10 0 _--6._. —19 .15 - 5 0 - 3 - 4 15 - 1 5 - 3 25 - 2 5 - 2 10 - 7 - 1 8 0 „ 0 „ _ 0., .„_ri I ' 20 12 2 12 - 2 3 3 17 12 .4 20 12 5 23 20 6 17 . 10 7 IS - 3 8 12 - 8 9 12 3 10 8 - 3 11 14 6 L" 2 - 1 2 29 26 - 1 1 7 21 - 1 0 10 7 - 9 10 0 - 8 20 - 1 5 - 7 8 17 - 6 10 - 7 - 5 8 7 - 4 8 - 3 - 3 0 0 - 2 15 ' 10 - 1 12 - 7 0 10 - 0 1 20 - i z 2 29 29 3 51 50 • 4 73 70 5 50 46 6 IS 10 7 15 12 8 40 - 3 4 9 30 25 10 17 - 1 7 L= 3 - 1 2 . 51. 48. - 1 1 25 25 - 1 0 0 - 5 - 9 15 17 - 8 29 - 3 0 - 7 24 24 - 6 12 - 6 - 5 8 - 1 - 4 10 6 - 3 8 10 - 2 15 - 3 - 1 12 1 0 21 - 1 5 1 19 10 2 24 20 3 43 40 4 35 28 5 10 0 6 17 - 7 7 12 7 8 19 - 1 0 9 17 12 L» 4 - 1 2 12 7 - 1 1 10 - 3 - 1 0 12 - 7 - 9 14 12 - 8 10 - 0 - 7 10 - 6 - 6 17 - 8 - 5 21 - 1 5 - 4 8 - 7 - 3 8 1 - 2 21 21 - 1 35 - 3 3 0 17 19 1 17 - 1 0 2 15 - 5 3 12 3 4 1 4 - - 6 » 23 - 1 0 6 12 7 7 8 0 1 - 5 0 40 35 1 14 - 1 • 2 . 10 - 1 3 a 7 4 10 1 5 12 0 6 12 0 L - 6 - 1 1 0 ' 3 - 1 0 7 - 0 - 9 14 - 6 - 8 7 - 7 - 7 15 - 1 0 - 6 15 - 1 0 - 5 10 3 - 4 14 12 - 3 20 - 1 7 - 2 25 19 - 1 19 - 1 2 0 12 - 3 1 10 - 1 2 10 - 0 3 0 - 1 4 10 - 0 L= 7 - 9 0 - 0 - 8 7 7 - 7 7 - 0 - 6 0 - 0 - 5 14 10 - 4 12 - 7 - 3 14 5 - 2 17 - 1 5 - 1 15 - 1 0 0 23 - 1 7 1 20 - 1 5 H5L L- 0 1 15 1 2 17 0 3 14 - 3 4 21 15 5 21 - 1 5 6 19 14 L» 1 - 7 IS - 1 2 - 6 21 - 2 3 - 5 24 - 2 3 - 4 7 - 5 - 3 7 - 6 - 2 12 6 - 1 12 - 3 0 19 - 5 1 15 0 2 12 - 6 3 17 - 0 4 19 - 8 5 14 - I 6 17 - 0 L- 2 - 7 12 - 1 0 - 6 10 6 - 5 20 - 2 1 - 4 24 20 - 3 7 - 1 2 - 2 10 - 0 - 1 12 3 0 19 12 1 30 21 2 30 24 3 19 T 4 12 - 0 5 15 - 5 L» 3 - 7 7 - 3 - 6 IT 12 - 5 12 - 8 • - 4 0 0 - 3 12 - 3 - 2 7 0 - 1 26 20 0 *« 41 1 48 41 2 19 14 3 17 14 L- 4 - 5 14 1 - 4 12 - 5 - 3 8 - 3 - 2 19 6 - I 25 17 0 15 - 7 1 51 41 101 TABLE XXI 1,2-O-AMINOISOPR0PYLIDENE-*-p-GLUCOPYRAN0SE HYDROIODIDE MEASURED AND CALCULATED STRUCTURE AMPLITUDES (Columns are h, 101F 1, 10 |F | ; unobserved r e f l e c t i o n s , f or i - o _ 1 _ 1 3 7 142 ~2 559 580" 3 1078 1190 265 368 250 2 8 2 " 345 295 227 262 239 936 620 157 4 1 5 237 3tiO 520 405 371 270 192 2 2 0 - 5 355 - 4 556 - 3 340 - 2 536 -1 766 0 941 1 1078 2 4 70 3 374 4 4 1 9 5 385 6 112 7 217 8 326 9 235 10 215 11 113 1023 636 169 536 75 501 356 126 376 569 413 5 8 5 ' 1150 816 1533 575 443 531 388 115 262 363 230 227 130 280 6 30 282 323 793 155 237 365 212 320 359 50 416 302 110 225 112 - 1 2 359 320 97 339 718 307 466 1053 2 5 0 " 192 426 240 360 394 25 353 379 141 353 360 207 533 595 3 933 353 100 500 200 8 232 290 330 389 122 326 307 212 415 6 6 ) - 4 « y — 9 IS1 160 7 4 3 0 4 4 9 - 5 250 230 -8 113 73 9 0 48 - 1 1 127 122 - 8 137 1 t l - 3 566 511 1 146 112 10 113 103 8 438 430 - 4 209 182 - 7 317 180 - 1 0 209 245 - 7 275 237 - 2 360 156 9 232 212 - 3 488 411 - 6 312 317 L= 6 - 9 197 217 - 6 0 12 -1 63 48 L * 5 10 267 272 - 2 302 277 - 5 170 ISO - 1 1 195 160 - 8 170 170 - 5 250 202 0 641 583 H5L - 1 2 48 35 11 179 195 -I 165 122 - 4 5 3 0 504 - 1 0 95 78 - 7 295 275 - 4 355 294 1 310 297 - 1 1 " 1 4 0 10B 12 0 35" "485 428 " - 3 763 695 - 9 103 '9 7" " - 6 371 353 - 3 68 "17 2 227 179 L - 0 - 1 0 179 158 1 14 1 292 - 2 315 302 - 8 307 102 - 5 363 329 - 2 340 294 3 359 136 1 389 150 - 9 98 91 L - 1 48 25 -1 1113 946 - 7 107 110 - 4 515 451 -1 235 185 4 320 140 2 509 475 - B 292 280 - 1 2 92 108 3 425 433 0 976 763 - 6 187 160 - 3 596 548 0 82 46 5 136 126 3 142 127 - 7 155 118 - 1 1 2 1 7 222 4 142 165 1 848 653 - 5 4 8 0 410 - 2 4 8 0 393 1 285 260 6 189 224 4 350 340 - 6 242 260 - 1 0 91 68 5 97 167 2 778 711 - 4 359 3 34 - 1 559 559 2 164 160 7 224 230 5 529 506 - 5 320" ' 385 - 9 ' 262 ' 260 "" 6 269" 3 2 4 " 3 325 252 - 3 282 224 0 6 6 8 560 3 0 46 ' B 91 78 6 167 131 - 4 329 344 - 8 195 197 7 46 71 4 443 381 - 2 614 539 1 623 499 4 194 197 9 160 207 7 405 186 - 3 227 279 - 7 106 78 8 116 147 5 292 120 -1 277 255 2 503 445 5 112 l i t 10 92 110 a 180 200 - 2 401 538 - 6 4 2 5 441 9 113 157 6 225 232 0 4 3 5 363 3 656 816 6 65 29 9 62 14 - 1 S40 733 - 5 563 600 7 76 81 1 360 309 4 136 167 I- 4 10 157 200 0 110 81 - 4 290 245 L " 6 6 270 311 2 9 5 97 5 4 4 3 455 L - 8 - 1 1 0 36 V " 2 5 0 " 360 - 3 4 2 0 4 3 5 " - 1 1 0 " "29" 9" 78 " "80 3 270 "257 6 480 4 9 1 " - 8 "255 222 - 1 0 "170 160 L« 1 _ .... _. _ 2 335 404 - 2 1203 1086 - 1 0 225 180 10 92 107 4 225 220 7 165 146 - 7 63 66 - 9 232 235 - 1 0 46 23 3 131 142 - 1 4 2 5 341 - 9 165 143 11 192 195 5 101 97 8 91 126 - 6 232 190 -8 0 51 - 9 128 153 * 264 341 0 83 86 - 8 87 96 6 165 195 9 205 229 - 5 265 162 - 7 205 182 - 8 2 54 267 5 194 235 1 1136 946 - 7 398 365 L " 2 7 137 200 10 86 53 - 4 66 50 - 6 323 307 - 7 106 86 6 0 36 2 290 205 - 6 2 8 0 265 - 1 2 56 19 8 0 25 t l 68 112 - 3 227 195 - 5 56 33 - 6 78 111 7 2 8 2 " " 2 9 7 3 6 1 0 768 " - 5 91 86 - 1 1 170 1 77 - 2 235 175 " -4 385 165 - 5 353 376 8 174 207 4 743 768 - 4 506 463 - t o 2 2 5 242 L " 7 L» 3 -1 128 106 - 3 395 325 - 4 192 155 9 83 21 5 116 142 - 3 4 4 6 390 - 9 6 3 75 - t o 73 61 - 1 2 87 92 0 272 237 - 2 140 103 - 3 401 369 6 518 589 - 2 194 185 - 8 398 435 - 9 217 200 - 1 1 78 60 1 277 242 - 1 491 440 - 2 371 380 L - 6 7 368 395 - 1 425 359 - 7 126 365 — B 146 t i e - t o 118 145 2 65 51 0 54B 523 , - 1 82 65 - 1 1 290 249 S 68 12 0 145 287 - 6 63 33 - 7 92 61 - 9 157 184 3 262 247 1 61 78 410 418 - 1 0 146 " "152 ' 9 158 " 1 5 7 1 t to 68 -5 "6 3 0 ' ~605 - 6 2 9 0 ' " 2 1 7 - a U O 56 ' ' 4 177 ISO 2 333 " 3 3 5 i 525 505 - 9 143 147 10 197 225 2 475 483 - 4 675 6 2 9 ' -5 212 190 - 7 4 4 6 44B 5 0 31 3 525 514 2 195 200 - 8 315 284 11 0 31 3 187 194 - 3 102 265 - 4 235 215 - 6 247 280 4 137 143 3 355 345 - 7 174 187 12 122 131 4 0 12 - 2 9 5 6 833 - 3 315 249 - 5 265 222 L " 9 5 200 222 4 423 415 - 6 237 252 5 325 404 -1 451 375 - 2 177 142 - 4 6B6 64 3 - 6 152 i t o 6 329 325 s 39 58 - S 3 9 a 395 L - 2 6 JOO 195 0 4 7 0 401 - 1 2 7 5 250 - 3 1 10 197 - 5 140 112 7 87 40 6 312 120 - 4 2 4 5 295 - 1 2 L89 190 7 53 61 1 915 aot 0 356 112 - 2 378 117 - 4 195 1 5 1 " 8 174 204 " 7 71 91 - 3 260 290 - 1 1 48 46 a 146 170 2 265 292 1 98 97 -1 750 696 - 3 205 192 9 125 145 35 41 - 2 33B 419 - 1 0 195 180 3 148 108 2 152 141 0 71 101 - 2 68 50 9 180 194 - 1 136 167 - 9 416 395 L - 7 4 773 723 3 290 314 1 355 368 - 1 194 151 L - 5 to 101 116 0 240 232 - 8 245 265 - 1 0 179 128 5 360 369 4 56 66 2 720 629 0 217 142 - 1 0 158 167 1 398 455 - 7 297 297 - 9 50 58 6 92 137 5 65 95 3 142 116 1 36 48 - 9 0 48 L - 2 2 0 7 - 6 648 708 - 8 262 242 7 374 443 6 116 165 4 240 200 2 122 102 - 8 212 199 - 1 0 73 95 3 192 269 - 5 383 386 - 7 250 224 8 237 282 7 50 67 5 443 403 - 7 320 280 - 9 142 170 4 300 353 - 4 393 378 - 6 121 111 9 122 142 6 50 97 - 6 43 34 - 8 179 175 5 0 68 - 3 961 926 - 5 300 275 10 269 272 L» 8 7 155 170 H4L - 5 172 122 - 7 165 160 6 68 11B - 2 350 254 - 4 240 184 11 174 179 - 9 127 115 a 212 275 - 4 521 475 - 6 4 6 5 460 7 197 2 2 0 - 1 529 446 - 3 61 BO - 8 78 76 9 0 63 I • 0 - 3 146 110 - 5 212 136 " 8 76 35 0 1143 l i l t - 2 295 230 I - 3 - 7 267 227 10 110 155 0 74 1 6 6 3 - 2 242 210 - 4 189 370 I 371 297 - 1 365 307 - 1 2 194 172 - 6 192 151 1 536 425 -I 565 494 - 1 4 4 1 434 t « 7 2 666 626 0 ao 51 - 1 1 225 195 -5 143 127 L* 4 2 54 8 495 0 91 100 - 2 260 262 - 1 0 46 to 3 711 713 1 317 265 - 1 0 B6 78 - 4 333 28? - 1 1 182 202 3 5 5 9 530 1 287 2 6 0 - 1 413 166 - 9 2 3 9 205 4 305 272 2 141 340 - 9 264 302 - 3 307 2B5 - 1 0 143 151 4 344 295 2 314 294 0 344 169 -8 113 85 5 390 415 3 0 17 -8 262 2 7 5 - 2 136 91 - 9 58 75 5 312 275 3 80 68 1 2 5 4 210 - 7 56 46 6 302 368 4 210 227 - 7 38 30 - I 4 0 5 14} - 6 344 32 3 6 303 394 4 152 197 2 400 381 - 6 275 2S9 7 82 65 5 125 170 - 6 420 421 0 215 195 - 7 230 210 7 194 189 5 2 2 4 247 3 401 410 - 5 164 169 8 277 295 6 97 107 - 5 344 331 I 140 123 - 6 157 128 6 179 202 6 0 56 4 46 48 - 4 n o 107 9 217 257 7 87 131 - 4 185 142 2 220 199 - 5 5B1 501 9 187 217 7 146 167 5 262 239 - 3 277 345 10 0 51 - 3 45B 454 3 67 B5 - 4 265 217 10 78 75 8 83 135 , 6 458 459 -2 148 165 It 122 147 L« 8 - 2 745 443 4 71 70 - 1 182 146 I 1 122 160 7 l i t 36 - 1 167 219 - 9 t t o 70 - 1 2 2 0 230 5 137 142 - 2 741 665 L» 6 g 180 192 0 548 535 I- 3 - 8 217 175 0 795 6B8 -I 262 212 L« 1 - 1 0 56 66 9 182 215 1 0 53 - 1 2 56 56 - 7 43 68 1 763 653 L» 9 0 165 10B - l l 83 75 - 9 86 55 10 0 24 2 41 82 - 1 1 36 34 - 6 209 172 2 66 63 - 7 152 103 1 705 645 - 1 0 101 151 - 8 280 240 1 307 334 - 1 0 290 295 - 5 290 234 3 536 506 - 6 46 25 2 355 358 - 9 245 265 - 7 121 97 I" 3 4 0 2 9 " - 9 128 122 - 4 60 51 4 320 336 - 5 217 157 3 210 192 - 8 1 70 148 - 6 50 73 - 1 0 151 167 aa 5 86 78 - B 210 170 - 3 30O 229 5 151 121 - 4 177 116 4 540 550 - 7 2 6 0 292 - 5 416 365 - 9 91 6 146 160 - 7 312 324 - 2 395 330 6 217 245 - 3 61 41 5 200 215 - 6 329 340 - 4 43 6 5 -8 127 117 7 0 56 - 6 207 22S -1 56 55 7 267 314 - 2 227 169 6 254 277 - 5 68 30 - 3 210 187 - 7 135 330 -5 330 141 0 195 127 B 66 76 -1 121 B7 7 200 242 - 4 470 455 - 2 391 346 - 6 118 156 L - 8 - 4 524 483 1 344 305 9 160 205 101 7B 8 56 55 - 3 533 486 - 1 197 192 - 5 ©T 38 - 9 136 82 - 3 393 399 2 71 73 10 86 93 1 162 146 9 53 63 - 2 290 272 0 335 385 4 5 3 463 ' -8 43 20 - 2 614 524 3 164 1B7 2 121 107 - 1 6 4 6 633 1 267 297 - 3 232 225 - 7 307 277 - 1 776 634 4 1 70 190 L " 4 224 3 0 17 t - 5 0 620 545 2 195 217 -2 260 267 - 6 136 112 0 375 32B 5 0 15 - 1 2 . 177 - 1 1 148 115 1 648 576 3 329 315 -I 4 1 9 409 - 5 121 102 1 4 1 6 320 -11 0 38 - 1 0 0 7 2 550 515 4 165 217 0 209 197 - 4 314 349 2 6 2 5 618 1 - 9 - 1 0 i a o 170 M 3 l - 9 212 207 3 267 254 5 95 58 1 3 1 4 488 314 - 3 179 189 i 252 245 " - 7 "142 127 - 9 297 ' 304 -8 227 210 4 2 6 7 - 250 b 137 140 2 466 - 2 136 175 4 539 610 - 6 2 ) 9 207 - B 71 48 L» 0 - 7 48 46 5 4 1 0 410 142 162 3 222 215 -1 209 245 5 329 415 - 5 113 82 - 7 317 329 1 4 7 0 450 - 6 506 460 6 53 55 197 185 0 116 136 6 128 135 - 4 102 158 - 6 378 3 75 2 873 74 3 - 5 320 264 7 36 41 L» 7 5 375 374 1 65 51 7 353 404 - 3 217 174 - 5 242 247 3 97 96 - 4 116 102 B 165 174 - 9 164 145 6 68 35 z 185 202 8 127 175 - 2 51 51 - 4 468 401 4 721 6 1 5 - 3 589 5 2 5 9 6 3 6 3 -6 122 100 7 113 122 3 122 " 162 9 I 18 117 - 1 180 126 - 3 '64 5 ' "5 74 5 514 4 7 T - 2 239 209 10 0 58 - 7 172 " 160 6 61 92 4 127 75 10 92 102 0 284 245 - 2 174 147 6 51 73 -1 209 207 11 165 tao - 6 242 212 9 56 31 5 1 ?4 190 11 103 145 1 0 23 - 1 601 510 7 435 420 0 371 110 - 5 177 150 6 165 192 2 151 153 524 475 8 164 170 1 300 267 L " 2 - 4 143 165 l_- 4 L« 4 3 174 192 1 172 210 9 97 87 2 280 280 - 1 1 118 136 - 3 344 285 - t o 148 141 L - 9 - 1 2 0 t 5 4 1 9 403 10 282 287 3 217 189 - 1 0 217 25 7 - 2 227 209 - 9 0 11 - 0 180 151 ' - 1 1 194 "iao" L " 10 1 473 "435 11 118 164 4 242 229 - 9 46 26 -1 262 225 "' - a 170 i a o " - 7 140 107 - 1 0 158 142 - 4 240 167 4 56 68 5 174 158 - 8 260 245 0 257 197 - 7 317 294 - 6 4 6 7 - 9 155 162 - 3 106 91 393 4 0 9 L " 1 6 118 150 - 7 295 287 1 113 92 - 6 112 106 - 5 174 155 - 8 395 363 - 2 177 117 6 285 345 - 1 2 41 45 7 106 190 - 6 71 78 2 1 72 152 - 5 4 75 4 4 1 - 4 140 157 - 7 4 5 8 474 - 1 227 141 7 61 63 - 1 1 128 157 B 82 SB - 5 574 54 3 3 107 105 202 169 - 3 48 12 - 6 345 364 0 122 96 8 2 2 4 28 7 - 1 0 65 90 9 106 165 - 4 257 257 4 82 71 - 3 225 207 - 2 116 t i o - 5 589 564 9 158 192 - 9 95 140 - 3 16 70 5 68 66 - 2 468 445 - 1 185 245 - 4 691 6B5 10 82 68 - 8 348 391 I- 6 - 2 •718 696 6 91 170 - 1 207 207 0 0 145 - 3 604 556 H2L - 7 158 142 - 1 0 157 155 - 1 390 365 0 103 142 1 160 1B4 - 2 6 8 6 625 L - 5 - 6 4 5 0 418 - 9 222 227 0 91 66 L • 8 1 350 340 2 121 112 - 1 413 384 L - 0 - 1 1 160 131 - 5 465 463 - B 0 31 1 765 710 - 7 187 121 2 197 1B5 3 50 96 0 458 404 0 1372 L 161 - 1 0 225 210 -4 170 116 - 7 305 247 2 282 297 - 6 2 2 0 202 3 224 217 t 818 " 7 5 6 1 560 418 - 9 7 6 ' 87 - 1 569 529 - 6 297 280 3 179 153 - 5 97 76 4 232 2 5 0 " L - 1 0 2 257 230 2 428 394 - 8 195 190 •2 506 4 9 0 - 5 179 165 4 559 546 247 209 5 63 58 - 5 137 128 3 242 249 3 1068 915 - 7 254 230 - I 314 257 - 4 260 214 5 187 212 - 3 148 112 6 131 126 - 4 0 41 4 4 4 5 496 4 4 6 0 421 - 6 136 111 0 653 695 - 3 374 328 6 56 45 - 2 76 82 7 240 274 -Z 155 192 5 232 274 5 574 540 - 5 307 2 79 1 559 511 - 2 157 138 7 401 195 -1 282 245 8 65 87 -1 51 125 6 140 151 6 438 475 -4 435 363 2 237 230 - 1 269 219 B 122 165 0 92 125 0 0 " ' 8 2 " " 7 2 0 9 24 7" " " 7" 222 "230 " - 3 83 142 3 721 ' " 6 5 8 " 0 368" 4 1 0 9 65 6 8 " 1 131" 1 4 5 " L» "5 • —— a 125 142 a 195 262 - 2 115 279 4 374 351 1 63 88 10 172 192 2 224 220 - 1 0 53 23 9 91 102 9 307 156 - I 756 653 5 2 8 5 239 2 359 350 1 137 142 170 152 H U 10 195 209 10 146 138 0 146 112 6 559 506 1 335 360 I" 3 4 98 113 195 170 i i 112 121 1 4 0 0 160 7 2 75 315 4 95 87 - 1 1 133 130 _ j 151 115 1 - 0 l_" 5 12 182 177 2 610 568 6 41 51 5 335 353 - 1 0 61 48 I- 9 - 6 329 315 1 93B 766 - i t 2 2 0 180" 3 0 2 6 " 9 2 6 9 317 ' 6 125 153 - 9 275 287 -5 195 157 ' - 5 110 128" 2 9 4 6 810 - 1 0 0 30 t - 1 4 117 320 10 73 130 7 83 107 - 8 250 245 - 4 131 75 _^ 83 43 3 158 102 - 9 287 257 - 1 2 151 142 5 2 1 0 239 11 0 70 8 131 170 - 7 0 28 - 3 82 61 _ 3 405 391 4 4 4 6 * 7 0 -8 325 287 - t l 36 17 6 76 76 - 6 156 350 - 2 262 2 ) 0 _2 160 ao 142 5 625 653 - 7 127 147 - 1 0 179 212 7 151 190 L - 2 L " 7 - 5 331 310 - 1 95 76 _ l 102 6 242 292 - 6 383 374 - 9 2 3 9 262 a 127 167 - 1 2 148 177 - 9 51 46 - 4 169 175 0 t a 76 0 2 6 0 2 8 0 TABLE XXI (continued) 102 2 4 0 194 2 3 / 285 128 192 - 9 164 148 307 2 35 125 285 " 267 146 212 113 ' 194 180 167 272 121 121 142 2 9 0 4 0 0 267 277 295 435 148 285 325 4 5 6 103 IBS 305 300 326 106 376 505 128 2 9 7 2 2 0 265 202 128 2 2 0 185 177 280 254 103 222 325 280 2B0 155 425 282 110 165 112 133 2 6 0 152 295 103 224 185 106 172 146 262 405 136 220 299 222 137 148 307 - 6 230 230 - 5 46 24 - 4 125 137 - 3 386 400 - 2 103 73 - 1 270 292 0 285 312 295 165 151 267 131 133 140 230 192 2 0 7 162 172 152 106 179 102 160 160 247 143 197 177 116 122 164 - 6 116 113 267 1 74 177 237 116 148 125 164 137 172 107 247 230 101 162 145 - 1 133 172 1 158 172 103 TABLE XXII 3-$-ACETOXY-7*.,llec.-DIBROMOLANOSTANE-8*, 9*-EPOXIDE MEASURED AND CALCULATED STRUCTURE AMPLITUDES (Values l i s t e d are h, lOl F |, and 10 IF I. Unobserved r e f l e c t i o n s , which are l i s t e d as 0, have |F |<5-11) 13 384 415 13 465 469 4 145 48 12 267 277 17 87 68 14 2 7 5 305 14 162 103 5 247 2B7 13 6 6 3 688 IB 0 30 15 4 3 0 441 15 395 388 6 153 185 14 280 305 19 132 102 16 237 275 16 175 179 7 2 4 0 252 15 5 t 5 560 20 127 100 n 200 250 IT 142 150 8 235 215 16 204 257 Z l 75 31 IS 103 132 18 150 107 9 2 0 2 156 17 tft 71 ZZ 73 46 14 19 275 282 19 320 277 10 162 135 18 187 194 23 61 20 66 15 20 86 12 11 131 117 19 317 310 21 200 175 21 150 96 12 162 141 20 112 82 L" 7 22 105 60 22 105 83 13 174 202 21 180 197 0 128 98 23 187 190 2.* 78 63 14 112 150 22 76 75 1 257 257 24 97 55 24 107 97 15 i a o 202 23 86 48 2 207 180 25 125 123 25 103 56 16 120 6 5 24 66 8 3 116 123 26 0 15 17 86 107 25 172 113 4 174 152 27 53 63 L - 6 26 50 41 5 •209 222 0 1001 1025 L - l l 6 97 63 L« 2 1 267 240 0 162 120 L» 3 7 145 130 0 360 312 2 1150 1216 1 207 310 0 207 180 B 165 185 1 1116 1126 3 663 718 2 157 152 1 691 70b 9 312 336 2 1287 1307 4 701 685 3 250 252 2 395 438 10 115 151 3 488 553 5 404 408 4 9 5 66 169 160 11 383 375 4 320 277 6 5Z8 4 8 0 5 3 0 9 343 4 73 97 12 167 220 5 1003 1028 7 295 302 6 117 100 5 187 20b 13 240 2 f 4 6 648 608 8 350 280 7 165 195 197 185 14 78 35 7 643 708 9 130 66 8 68 107 7 333 32 3 15 56 56 75 e 606 620 10 325 262 9 230 210 4 0 0 4 1 0 16 78 9 539 565 11 220 175 10 127 122 9 353 33B 17 118 76 10 235 244 12 465 464 11 187 210 10 222 328 IB 66 82 11 611 701 13 167 194 12 103 132 11 490 531 19 120 73 12 335 310 14 151 123 13 107 91 12 87 122 20 75 25 . 13 305 300 15 179 140 14 7B 53 13 165 197 21 22 97 0 97 14 4 6 6 505 16 295 295 14 142 68 90 21 15 317 325 17 107 31 L»12 15 30 16 217 220 IB 167 130 0 2 5 7 304 16 17 95 96 L- 8 17 360 371 19 76 75 1 187 215 202 232 0 146 115 IB 127 28 20 102 136 2 153 205 18 73 5D 1 307 310" 19 B l 105 21 60 21 3 71 73 19 I BD IBO 2 365 414 20 66 34 22 156 148 4 142 172 20 53 50 3 595 708 21 320 328 23 113 65 5 227 225 21 162 122 4 4 10 444 22 56 60 24 97 80 6 177 242 22 53 29 5 Z77 111 270 23 212 202 7 175 244 23 76 10 6 197 24 56 35 L- 7 6 l i t 73 24 0 21 7 ~ 393 396 25 0 40 0 220 179 9 103 133 25 51 35 6 383 394 26 76 60 1 643 676 10 140, 1 JO 26 0 23 9 400 424 27 91 41 2 302 365 10 247 zao 3 671 705 L« 4 11 117 102 L" 3 4 165 101 H3L 0 560 475 12 110 70 0 566 6 0 5 5 715 651 1 9 7 8 94H 13 385 420 1 504 560 6 3 76 374 L - 0 2 4 4 0 431 14 234 240 2 776 745 7 365 360 1 4 40 466 3 865 650 15 2 6 0 272 3 394 297 B 265 267 2 435 386 . 4 220 229 16 112 101 4 651 620 9 300 275 , 3 215 257 5 205 199 17 136 1 32 5 1046 963 10 106 1 IR 4. 97 162 6 242 219 18 1 16 133 6 262 242 11 448 423 5 6 8 6 741 7 678 653 " l 9 " 1 4 7 " 97 7 863 856 12 133 142 6 247 307 8 219 200 20 147 140 a 270 353 13 310 305 7 345 380 9 524 538 9 143 200 14 133 137 8 62 51 10 63 33 L * 9 10 343 374 15 222 217 9 200 194 11 175 1B9 0 355 383 u 4 4 9 523 16 165 131 10 0 20 12 145 135 1 212 207 12 252 225 17 220 IBO 11 131 125 13 207 225 2 97 132 13 292 297 18 53 53 12 240 242 14 136 142 3 93 133 14 Z44 275 19 121 101 13 43 55 15 162 187 4 232 292 IS 229 260 20 53 8 14 78 83 16 103 103 5 360 410 16 138 167 21 145 137 15 81 2 5 17 195 162 6 4 0 0 426 17 336 330 22 0 41 16 167 199 18 98 68 7 476 518 IB 142 123 23 141 113 17 137 83 19 295 310 8 300 314 19 B2 25 18 71 48 20 86 86 9 1B4 157 20 123 125 L " 1 19 190 175 21 13B 86 10 108 126 21 17Z 116 0 310 29 r ZO 53 56 ZZ 53 56 11 242 220 22 120 106 1 269 335 21 0 29 23 76 21 12 117 165 23 88 53 2 172 254 22 0 36 24 0 39 13 125 103 24 68 36 3 510 635 23 53 14 25 117 97 14 0 115 25 0 35 4 117 90 24 0 43 15 130 71 26 75 68 5 6 2 5 620 25 0 23 L" 5 16 177 190 6 117 105 26 6 3 1 0 511 509 17 239 212 L» A 7 491 460 > 1 1271 1322 18 164 130 0 723 656 8 88 45 L - 1 2 633 624 1 903 961 9 305 312 0 4 8 0 446 3 307 302 L»10 2 500 530 10 267 255 I 1256 1307 4 117 153 0 as 76 3 1381 1362 11 330 315 2 325 295 5 6 3 5 658 1 112 117 4 6 0 0 610 12 106 6 3 3 4 4 5 508 6 4 9 9 525 2 0 73 5 8 3 6 BOO 13 227 217 4 209 177 7 581 576 3 63 66 6 184 122 14 53 105 5 1555 1692 8 217 212 4 111 60 7 4 5 5 483 15 167 222 6 118 87 9 267 285 5 112 10S S 117 107 16 76 17 7 1006 1023 10 418 461 6 190 138 9 573 560 17 220 214 8 365 346 I I 903 933 7 73 103 10 199 2 0 2 . ia 53 36 9 713 716 12 394 4 30 8 92 95 11 4 2 0 4 5 3 19 98 80 10 320 333 13 499 495 9 71 73 12 212 194 20 62 46 11 307 366 14 187 219 t o 0 48 13 4 9 9 525 21 91 56 12 110 148 15 275 302 11 12 93 102 14 257 277 13 394 366 16 245 252 76 101 15 329 328 L - 9 14 101 130 17 354 302 13 55 53 56 16 125 126 0 4 3 5 493 15 394 459 18 101 61 14 61 53 17 272 2 8 9 I 182 209 16 97 6 5 19 53 40 15 63 i a 0 41 2 424 478 17 528 544 20 127 141 16 81 43 19 118 111 3 260 267 IB 80 26 21 220 185 20 0 68 4 401 426 19 2 3 0 205 22 92 71 L " U 21 170 1S8 5 97 165 20 98 122 23 189 142 0 202 195 22 0 12 6 380 389 21 175 143 24 71 83 1 177 2S2 23 126 107 7 290 325 22 0 Z l 2 83 45 24 68 17 8 4 0 8 398 23 185 142 L- 6 3 157 209 25 92 97 9 2 3 2 '204 24 66 46 0 598 6 0 3 4 2 5 7 330 26 0 .51 10 2 70 285 25 0 25 1 4 6 3 SOB 5 227 247 11 103 112 26 51 39 2 363 368 6 240 287 L» ) 12 192 197 3 596 671 7 205 209 0 638 67B 13 200 195 L- 2 4 138 155 B 70 76 1 535 543 14 287 260 0 43 - 10 5 4 5 5 435 9 237 Z5Z 2 295 287 15 101 93 1 8 9 0 940 6 152 200 10 .56 31 3 651 635 16 147 126 2 167 165 7 - 4 9 4 491 11 282 314 4 2 6 9 2 1 0 17 83 51 3 1196 1300 8 295 2 6 7 12 121 137 5 755 6 6 6 u 164 125 4 500 438 9 544 -520 13 " •"130 l i e 6 4 7 0 536 19 133 73 5 375 420 10 120 91 7 721 720 6 4 0 0 385 11 141 172 L - 1 2 S 4 3 8 4B0 L M O 7 861 903 12 80 29 0 141 122 9 898 940 0 192 234 a 471 474 13 344 321 1 158 153 10 259 230 1 225 274 9 1093 1178 14 116 70 2 212 320 11 96 50 2 127 152 10 385 375 15 262 217 3 242 242 12 395 3 79 3 2 6 4 305 11 116 as 16 117 48 4 214 307 10 1620 12 1106 14 2 2 2 16 584 IB 465 20 2 7 5 22 41 1 24 315 2 4 0 7 1166 2 0 1 0 118 1725 1151 275 59 5 415 249 396 317 9 5 28 132 103 4 1248 1295 50 1776 716 790 297 556 800 319 563 41 1128 16 304 292 17 0 30 18 373 361 24 2 8 5 219 25 0 41 26 184 122 1078 1156 . 5 5 170 353 478 40 15 4 1193 1061 5 398 458 6 1248 1313 7 431 495 B 122 9B 9 Z54 230 510 137 748 262 505 174 336 197 2 0 0 262 215 112 157 586 170 212 215 280 138 0 1318 1297 135 2 309 3 153 4 791 5 219 6 1036 7 285 6 Z92 58 67 1 586 624 I 18 103 205 470 _ 132_ 310 83 255 2 to 790 254 103 3 2 75" 340 66 671 625 62 3 142 414 1225 753 663" 2 5 0 164 6 3 3 9 8 0 155 564 167 245 3 34 . 511 319 207 136 255 411 1165 _ 7 4 6 S f 6 230 165 599 991 147 " 5 7 6 153 234 325 515 297 142 1 10 167 90 160 8 210 222 9 73 50 10 320 335 t l 190 145 12 187 222 21 187 160 247 157 468 299 147 220 401 Z77 195 123 132 16 157 167 20 175 136 385 165 180 4 1 5 4 8 0 254 369 2 74 4 1 5 162 . 18 127 122 325 381 321 265 326 184 242 147 177 175 128 117 289 287 1 1278 2 733 3 605 4 878 5 6 3 5 6 836 7 1146 6 1048 9 128 0 579 1 716 1482 1051 708 1065 6 9 0 935 1246 1203 232 673 810 325 2 3 4 635 292 349 ^214 "~30T 24 0 520 668 1 1165 1146 2 845 643 3 836 756 4 3 70 545 5 605 598 6 913 1071 7 2 32 345 8 786 933 9 423 4B8 10 760 768 11 9 0 3 B85 12 312 356 13 408 406 14 314 3 74 15 180 167 16 411 43d 17 80 58 18 274 300 19 205 225 20 1 32 101 21 56 6 22 227 219 23 73 35 24 105 96 25 46 17 26 56 41 27 53 46 L- 2 0 9 1 3 990 1 961 876 2 2 3 1 7 2051 3 1101 1060 4 B7B 808 5 53 30 6 4 4 4 451 7 369 356 8 668 686 9 300 31 7 10 393 439 11 277 287 12 270 262 13 172 210 14 167 187 15 105 157 16 290 295 17 148 155 18 177 170 19 68 87 20 195 197 21 65 5B 22 200 195 23 66 107 24 66 56 25 56 34 26 0 - 0 27 0 20 L* 0 207 36 I ate 825 2 1116 953 3 355 319 4 1236 1181 5 245 162 6 1577 1627 7 625 636 8 292 341 9 8 5 6 901 10 575 598 11 39 53 12 638 661 13 331 310 14 195 185 15 290 292 16 394 399 17 117 107 16 295 312 19 212 153 20 132 137 21 13B 101 22 320 Z70 23 110 65 24 113 9Z 25 73 56 26 70 51 27 0 40 L- « 0 157 117 1 100B 930 2 1221 1161 3 267 227 4 1246 1116 5 780 753 6 335 292 7 335 280 8 838 836 9 6 7 5 696 10 4 2 6 4 1 9 11 471 454 12 545 536 13 403 395 14 470 510 15 247 220 16 212 215 . 17 222 209 18 162 131 19 152 131 20 269 260 21 175 207 22 93 107 23 105 86 24 107 112 25 78 56 26 81 76 312 923 391 530 584 643 509 315 534 13? B l l 1 77 858 . 383 267 160 746 220 455 101 147 123 110 107 170 107 175 388 132 42B 102 202 151 160 132 175 386 540 31Z 69B 518 514 790 706 346 465 48B 438 550 324 105 2 1 5 317 217 2 70 Z45 5b 142 195 122 2 4 0 175 4 4 6 323 128 257 384 126 267 143 2 9 9 13 244 255 21 121 116 390 195 2 S 0 ?6 2 8 0 299 297 200 222 135 4 5 0 194 130 217 121 16 113 17 112 97 16 111 122 19 63 61 20 121 113 117 374 267 l ' Z . 4 6 0 353 157 255 365 287 214 187 215 195 242 137 112 102 147 280 143 143 205 113 184 13 147 143 15 135 135 156 133 30 7 214 107 107 102 2 2 5 125 110 141 810 355 2B5 2 8 5 1246 811 960 389 155 4 8 3 816 250 336 215 41 204 991 365 373 364 1332 896 995 426 112 496 896 297 350 247 18 2 7 0 292 0 631 t 1216 2 334 3 1785 4 2 0 2 5 6 3 4 6 611 7 791 8 559 9 500 10 5 3 5 11 2 5 5 12 2 5 0 565 1246 400 1836 , 3 0 4 713 933 795 611 . 570 575 354 292 104 TABLE XXII (continued) 5 97 20 1 553 581 L « 9 199 257 6 535 526 1 194 205 fl 319 330 B 353 331 IT 127 78 8 71 12 L - 4 8 51 51 , 6 78 132 2 295 344 0 7 132 151 2 184 148 9 98 7 3 9 73 56 IS 128 111 9 117 111 0 6 3 1 137 58 .0 113 31 33' 7 187 195 3 100 92 1 120 105 8 136 141 3 167 192 10 170 Bl 10 202 190 19 68 68 10 172 147 1 269 222 10 U 8 214 24Z 4 4 7 6 480 2 262 307 9 317 355 4 132 142 11 87 91 11 140 152 20 6 26 I L 155 137 2 112 36 5 496 540 3 217 254 10 227 242 260 307 12 164 117 12 185 137 21 6 5 19 12 245 242 3 259 227 12 56 a 6 305 349 4 317 361 U 175 197 207 210 13 121 92 13 0 56 13 14 127 105 63 4 15T I B S 13 1* 87 66 55 6 H4L 7 410 4 4 4 5 2 0 7 185 12 360 369 7 147 155 14 250 235 14 91 65 L - 2 103 5 16T 120 a 341 375 6 361 4 2 0 13 158 122 101 127 15 100 132 15 142 101 0 95 15 15 107 75 6 217 217 L - 0 9 2 5 9 265 7 157 92 14 76 28 9 71 103 16 B2 39 16 172 180 I 93 98 7 2 1 9 244 L - 3 0 0 87 110 10 160 151 a 2 3 5 2 6 0 15 169 184 10 2 5 5 2 5 0 17 82 101 17 97 112 2 126 123 L - 8 B 111 58 6 6 3 1 48 20 u 363 355 9 250 215 16 237 229 11 93 41 18 143 91 18 96 112 3 90 aa 0 91 10 9 240 2 2 0 197 138 164 156 117 103 2 214 174 12 192 247 10 170 141 17 0 120 12 121 61 19 92 7 1 19 6 6 3 4 6 6 46 1 137 174 10 0 78 3 3 8 0 205 376 151 13 140 135 175 11 110 87 18 138 152 13 125 174 20 a2 43 5 95 76 2 92 56 11 137 130 3 * 14 81 12 175 180 19 111 86 14 71 82 21 0 6 3 L - 7 6 162 165 3 B7 33 12 92 IT 107 71 82 123 5 103 9b IS 177 204 13 2 0 5 205 20 87 96 15 185 220 22 BB 71 0 76 36 7 68 14 4 71 78 13 192 150 5 6 6 725 6 9 0 748 741 16 17 185 190 230 179 14 15 207 167 21 130 71 16 147 132 23 71 71 1 175 105 8 U T 219 5 101 112 14 91 25 112 165 138 22 138 113 17 127 105 2 2 5 5 244 9 127 125 6 101 90 15 97 102 5fl 71 122 33 43 51 8 461 465 10 142 172 16 157 142 23 0 61 18 0 7 L - 2 3 237 227 10 180 192 7 106 107 16 87 17 9 449 4 8 6 19 97 111 17 6 3 28 24 88 7 3 19 51 14 0 434 393 4 2 6 7 275 11 58 75 8 56 7 9 10 122 189 20 68 25 1 92 39a 78 5 BT 58 12 13 93 97 120 56 107 53 L - 5 10 11 12 56 68 0 26 t o 35 l l 106 51 21 125 121 L - 1 0 L - 3 L - 8 2 383. 6 61 43 85 51 10 0 63 48 12 13 132 267 85 259 22 23 78 132 39 0 0 5 0 4 B 9 514 0 187 125 3 102 92 7 2 2 0 205 14 103 75 11 97 91 1 174 151 110 1 65 137 1 215 182 1 279 272 4 2 2 5 262 B 267 265 15 T3 39 12 66 28 2 BO 66 13 TB 40 14 120 16S 24 0 5 5 2 117 165 2 350 359 2 128 140 5 101 150 9 185 189 16 73 53 3 117 126 15 85 160 86 259 3 56 117 3 373 378 3 239 257 6 93 147 10 147 172 17 0 66 L - 9 4 61 87 L " * 16 I • 5 4 132 190 4 586 626 4 309 309 7 51 58 U 112 127 18 19 56 68 48 185 76 162 35 5 93 4 3 0 63 137 65 14 75 73 IT 63 46 0 4 4 5 453 5 0 15 5 170 222 5 150 153 8 202 217 12 127 165 56 1 6 0 53 i e 19 76 78 101 63 1 2 S06 428 498 390 6 7 0 93 6 250 247 6 277 272 9 100 55 13 102 162 20 76 71 2 147 106 7 0 29 2 9 5 113 7 83 83 7 93 102 10 229 290 14 137 151 3 73 48 a 71 -48 131 61 123 92 58 101 20 87 165 3 766 B33 8 102 158 8 148 212 8 133 127 11 78 76 15 138 160 L - 3 4 68 40 9 92 46 21 0 25 25 * 390 315 3S0 9 93 45 9 2 2 5 2 4 9 9 147 108 12 97 80 16 96 6 6 0 4 0 9 361 5 88 107 10 58 113 5 22 0 5 312 10 79 103 10 280 287 10 217 162 13 82 70 88 17 0 43 1 195 187 97 39 75 i i 71 6 6 88 6 7 82 148 56 126 23 0 48 6 370 371 11 70 61 11 195 220 I L 195 156 14 147 2 249 225 7 100 12 71 24 25 0 0 7 IT 7 4 0 4 4 1 3 12 68 118 12 137 217 12 182 123 15 0 43 L ° e 3 255 257 a 66 71 13 98 108 B 78 56 8 2 2 4 214 13 96 61 13 172 220 13 123 6B 16 0 63 0 182 212 4 103 56 9 53 15 14 7B 80 80 56 117 93 25 63 26 0 1 9 4 6 4 4 6 5 14 67 112 14 331 355 14 71 53 17 92 123 i 212 1B5 5 103 29 15 53 17 10 11 10 11 202 160 177 ZOO 15 50 6 6 15 262 285 15 127 103 18 131 IZO 2 160 190 6 302 2T9 (.- 1 16 3 0 7 294 16 1?7 127 19 82 ra 3 123 92 r 212 222 HflL L * 6 12 53 43 0 2 8 4 319 12 200 195 L - l l 17 101 118 17 9 5 60 20 152 147 4 118 147 a 12T 110 0 102 60 1 2 4 8 8 179 491 92 13 14 297 287 255 321 0 145 118 177 18 102 46 IB B5 29 21 56 70 5 6 3 90 9 182 180 L - 0 1 138 82 L - 5 175 19 68 24 22 68 6 5 . 6 76 76 10 217 229 0 155 82 2 112 63 126 7B 101 136 76 ao 3 851 919 15 265 2 4 0 2 113 162 20 78 48 L" 9 T 132 126 11 132 122 1 1T2 142 3 157 118 1 4 204 219 239 249 16 17 177 87 142 3 192 245 21 55 55 0 232 277 L - 3 8 ' 172 169 12 299 317 2 T6 38 4 76 61 2 5 102 4 86 81 22 76 97 1 131 50 350 0 132 157 9 73 41 13 175 170 3 312 2 3 0 300 2 3 5 5 71 60 3 4 61 60 35 63 6 725 751 10 2 1 2 158 5 126 169 23 0 34 2 335 1 195 174 10 162 146 14 73 17 4 6 143 164 7 ' 686 548 766 545 ' 19 20 277 125 267 157 6 7 101 58 175 L » 4 3 .93 36 2 548 523 11 117 112 15 7 3 26 5 195 146 7 135 142 5 121 164 157 4 2 4 0 229 3 185 162 12 108 112 16 83 174 6 2 0 5 225 B 122 83 * 97 90 48 111 9 429 4 8 8 21 169 156 8 146 202 0 2 9 4 282 5 61 39 * 524 543 13 122 102 IT 117 85 7 118 118 9 107 61 10 11 4 B 4 2 0 4 516 220 22 23 113 51 122 31 9 10 187 212 1 269 295 295 310 6 172 170 5 92 73 14 88 73 18 155 87 8 160 1S6 10 0 60 8 7 120 128 112 164 B2 1?7 207 210 197 210 15 83 29 19 20 78 0 B7 39 2 0 9 102 170 105 11 40 117 0 68 78 12 210 190 11 65 68 3 205 185 8 7 10 12 87 50 10 13 14 4 8 0 192 546 195 t - 6 0 361 390 L - 1 2 5 113 205 101 i e o 9 83 35 a 436 438 L - 9 I I 83 68 13 66 4 3 10 259 300 9 2 4 5 230 0 151 185 L - 4 12 103 43 IS 455 434 I 2 7 0 456 2 2 0 0 269 336 : 6 297 310 11 B2 56 10 400 404 1 92 61 0 96 73 13 140 116 L * T 0 61 92 16 282 317 2 434 1 180 167 7 307 315 12 262 307 11 90 70 . 2 184 210 1 262 295 14 83 83 0 B8 40 107 33 17 10S 98 3 205 237 2 140 185 8 355 395 13 14 97 244 3B 257 12 215 153 189 120 3 97 105 2 3 328 151 299 151 15 16 110 58 53 21 1 217 142 205 2 3 T6 82 56 35 IB 142 120 4 209 212 3 115 98 9 366 390 13 4 177 158 2 91 19 20 202 56 133 82 5 A S 5 0 343 563 326 4 5 2 3 9 125 299 107 10 11 137 2 1 9 165 232 IS 115 68 14 375 320 5 93 103 4 212 2 7 9 165 157 275 200 17 18 80 78 48 107 3 192 7 3 237 212 116 230 4 0 24 21 158 142 7 302 4 1 5 305 431 12 13 365 349 157 L - 1 0 16 202 192 T 58 63 6 5 5 6 110 66 S I 46 22 0 5 8 184 0 219 252 17 T l 75 8 167 167 7 100 48 L - 1 6 81 10 110 46 33 23 24 0 0 51 46 9 10 66 257 282 51 244 L « 0 H5L 14 15 2 3 7 2 1 0 255 212 1 2 146 2 9 0 107 290 18 19 117 122 75 78 9 10 92 157 76 172 B 9 1T4 123 152 175 0 1 78 2 2 9 53 210 7 8 147 56 127 25 8 T8 25 130 101 11 255 209 16 153 111 3 190 220 20 156 132 11 97 105 10 184 182 2 90 90 . 9 157 122 L - 7 12 215 207 1 222 17 137 187 4 177 185 21 68 23 12 141 125 11 103 73 3 112 80 10 102 82 41 26 L - 2 98 13 14 155 215 120 157 2 565 616 18 19 9 5 ?a 1 2 * 43 S 97 58 22 0 40 13 93 97 [2 60 43 4 172 162 11 204 2 0 2 1 83 5 3 6 6 6 . 189 254 13 120 108 5 169 107 z T l 40 1 768 825 15 304 321 4 2 6 0 249 20 87 SO 102 170 113 200 L - 4 L - 1 0 0 14 15 199 135 58 108 148 L * 8 2 324 353 16 103 185 85 5 170 250 21 6 6 4 5 a 0 4 0 0 360 1B0 177 111 7 155 0 B6 12 3 262 237 17 142 6 150 217 ' 22 65 61 9 100 58 1 113 91 1 2 4 5 290 16 102 87 8 117 t o o 1 116 101 HIOL 4 4 2 6 455 18 157 202 7 279 355 23 81 63 10 151 111 2 195 179 2 126 147 17 8T 35 9 5B 58 2 75 53 5 820 B68 19 0 122 100 8 305 336 11 78 58 3 15a 187 3 112 41 18 78 6 6 10 118 3 5 3 62 40 L - 0 6 614 641 20 128 9 58 105 t * 5 160 140 12 151 126 4 361 374 4 86 76 19 6 6 61 11 132 120 4 0 30 0 63 12 7 580 615 21 85 68 10 167 113 0 5 12S 71 5 132 170 12 0 102 5 87 46 I 0 T 8 560 6 6 0 22 63 48 11 333 346 I 2 1 5 245 449 L - l l 6 589 S60 6 155 172 L - 5 13 133 113 6 86 75 2 63 14 9 416 428 12 185 172 2 0 132 127 7 170 128 7 68 56 0 87 76 14 0 51 7 9 3 93 3 aa 68 10 2 4 0 205 L- 7 13 90 162 3 100 111 1 158 125 a 235 225 a 93 120 1 142 137 I S 0 41 4 0 3 11 623 613 0 175 141 136 133 14 170 153 4 356 34S 334 389 2 162 160 9 105 125 9 121 147 2 110 7B 16 71 4 3 5 73 12 12 267 292 15 117 71 5 3 56 63 10 151 133 3 195 1B2 17 88- 108 H9L 6 56 30 13 195 2 0 0 2 122 130 16 97 71 6 132 80 4 106 73 t i 116 123 4 2 3 5 2 4 0 16 b 36 7 66 4 3 14 2 2 5 200 3 2 3 2 87 260 120 17 0 20 7 2 9 5 290 300 317 S 147 195 12 148 155 H7L 5 242 302 L " 0 8 68 35 15 170 103 I B 111 82 8 6 no 132 13 0 14 6 130 137 L - 2 1 80 17 9 46 53 16 81 38 5 210 2 4 5 19 0 29 9 102 6 6 7 128 156 t 4 111 41 L - 0 T 190 20S 0 91 12 2 147 177 17 331 320 6 55 121 20 96 121 10 222 140 B 93 S 7 15 137 132 1 222 187 8 58 33 1 175 160 3 107 133 L * 1 i a 153 1*7 ? 87 87 21 0 36 11 2B2 299 16 21S 202 2 535 515 9 0 110 2 185 162 4 87 61 0 6 3 35 19 123 160 8 105 92 22 0 17 12 2 3 9 255 17 71 71 3 152 122 10 103 6 6 3 96 56 5 19T 120 1 100 71 20 147 118 162 9 10 2 9 5 185 307 165 23 6 6 6 6 13 14 344 3 6 5 343 390 H6L 18 92 7* 4 2 9 0 312 11 103 142 4 162 138 6 93 115 2 63 10 21 81 24 97 70 19 0 14 5 237 192 12 9 5 63 5 82 142 7 1*0 116 3 98 66 22 0 51 11 2S5 275 15 108 61 L * 0 20 0 48 6 106 103 13 140 128 6 110 145 B 115 136 * 58 21 23 151 117 * z. 152 110 L * 1 16 185 147 0 796 SOS 21 55 40 7 122 53 14 73 17 7 108 7? 9 58 29 5 B3 63 24 82 43 13 169 147 0 310 297 17 160 132 1 184 146 s 366 381 15 92 39 8 83 123 10 58 41 6 6B 68 a 25 50 31 14 197 207 1 409 419 IB 118 71 2 3 2 0 334 L - 5 9 158 138 16 0 25 9 83 56 11 128 41 7 35 15 16 111 68 50 6 5 2 393 431 .19 20 122 127 102 78 3 50 14 0 189 167 10 172 14B 17 73 40 10 111 102 12 0 31 8 55 31 L - 3 3 344 355 4 4 6 5 490 I t i l 122 u 2 1 0 207 18 53 39 11 0 66 13 80 0 9 56 6 3 0 262 321 17 68 87 4 4 3 3 511 21 0 10 5 2 0 7 200 2 177 172 12 92 58 12 0 38 14 78 26 1 297 321 18 96 102 5 269 295 22 6 3 S3 6 435 4 4 3 3 90 21 13 73 30 L - 6 13 73 23 15 66 T l L - 2 2 390 409 19 53 6 3 6 320 345 7 71 17 4 200 224 14 2 54 242 0 12T 200 14 0 58 0 90 40 3 460 514 20 S3 40 7 265 2 9 5 L « 6 a 0 23 5 111 101 15 152 143 1 165 130 15 0 50 L - 1 1 140 66 4 326 345 21 81 71 e 388 435 0 7 0 6 142 761 . 1 0 9 123 87 6 229 220 16 85 a 2 210 160 16 0 33 0 0 12 2 6 3 33 5 285 312 9 202 202 1 10 415 443 7 70 6 5 . IT 78 0 3 151 67 17 78 20 1 66 TO 3 76 20 6 353 405 L- 8 10 3 7 0 356 2 408 4 0 3 i i 116 83 6 21Z [92 t a 152 127 4 190 170 18 6 6 46 2 8 0 40 * 82 34 7 421 470 0 411 478 11 2 8 0 312 3 167 ISO 12 376 365 9 187 195 19 80 97 5 2 0 5 187 3 107 117 5 110 73 fl 324 384 1 4 3 6 459 12 312 317 4 4 2 4 443 13 107 200 10 315 351 20 156 152 6 B B 25 L - 3 4 BT 30 6 68 B6 20 9 312 331 2 348 399 13 310 345 5 2 0 0 383 I BO 197 349 242 14 76 108 11 117 100 21 98 122 T 83 33 0 179 127 5 217 22T 7 92 10 202 200 3 137 107 14 4 0 5 4 4 9 6 15 6 3 43 12 222 185 8 200 192 1 209 14B 6 T l 78 a 55 25 11 192 220 4 252 255 15 259 312 16 92 19 13 0 76 L - 1 9 111 122 2 227 210 7 133 138 12 111 98 5 459 480 16 195 227 6 264 270 17 71 61 14 0 28 ' 0 319 295 10 164 122 3 61 3 8 63 61 L - 3 13 180 185 6 2 9 9 300 17 98 70 9 80 307 ' 58 300 IB 71 143 ' 15 0 21 I 148 137 t l 132 67 4 195 174 9 0 4 3 0 76 3 14 156 165 7 2 9 9 277 16 145 157 10 19 20 101 107 126 152 16 17 137 58 112 41 2 1 0 87 190 51 12 13 9 3 92 76 36 131 82 116 61 10 11 10 53 61 0 23 26 15 170 151 a 219 240 19 103 6 3 11 170 385 225 137 330 244 3 6 58 2 16 133 142 9 185 285 190 260 20 117 63 12 13 21 92 108 18 113 91 4 160 136 14 152 131 7 121 82 12 0 20 3 61 5 17 202 170 10 21 68 25 22 182 142 19 0 46 5 121 73 I S 106 92 8 192 172 13 6B 51 4 5B 10 18 150 160 11 12 315 180 270 152 22 0 33 14 15 190 82 1 72 103 23 50 53 20 53 31 6 202 192 16 T8 46 9 102 97 14 55 65 5 70 35 19 147 128 23 92 60 7 175 214 10 162 101 6 66 21 20 0 46 13 15S 152 24 6 3 . 75 16 175 180 L - 1 0 L - 6 0 137 97 169 82 L - 7 0 11 12 162 102 137 86 7 0 2 6 21 78 93 14 95 93 17 92 86 282 265 233 257 9 312 302 0 93 15 22 87 83 IS 16 102 9S 78 97 L - 2 751 776 18 19 199 66 187 61 1 202 212 1 270 289 10 174 177 1 147 137 13 92 71 1 122 122 L - 4 23 53 26 0 2 314 ao 335 2 3 1 5 282 11 123 106 2 160 112 14 82 B l 30 2 1 1 3 86 0 86 35 24 0 I S 17 18 2 4 0 125 210 1 259 320 20 . 2 1 97 61 61 53 3 39 3 132 106 12 244 235 3 165 146 15 6 3 3 229 235 1 120 75 25 70 48 132 2 315 320 4 235 250 4 4 3 9 479 13 102 78 4 0 45 16 105 102 4 107 66 2 0 20 19 102 82 3 4 5 5 4 5 0 . 5 6 41 2 3 7 51 2 1 2 5 6 257 498 272 500 14 15 7 3 6 0 25 S l 102 126 90 105 17 95 73 5 58 71 25 65 116 132 46 101 I - 4 121 106 4 . 4 6 9 516 L - 7 0 341 354 6 6 4 0 . 5 365 4 1 5 7 101 73 7 375 369 16 141 103 T 170 167 T 157 1T0 REFERENCES 106 1. 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