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The determination and refinement of the molecular structures of some organic compounds by single crystal.. Camerman, Arthur 1964

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THE DETERMINATION AND REFINEMENT OF THE MOLECULAR STRUCTURES OF SOME ORGANIC COMPOUNDS BY SINGLE CRYSTAL X-RAY DIFFRACTION by ARTHUR CAMERMAN B.Sc. (Hon.), University of B r i t i s h Columbia, 1961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the department of CHEMISTRY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1964 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 of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study* I f u r t h e r agree that per m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission* Department of (Jju^^St The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8 f Canada The Uni v e r s i t y 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, The Univ e r s i t y of B r i t i s h Columbia, 1961 WEDNESDAY, AUGUST 26th, 1964, AT 10:00 A.M. IN ROOM 261, CHEMISTRY BUILDING of ARTHUR CAMERMAN COMMITTEE IN CHARGE Chairman: I. McT. Cowan W.R. Cullen C A . McDowell S.A. Melzak G.B. Porter A. Rosenthal J. T r o t t e r R.M. Thompson External Examiner: Professor L. H. Jensen University of Washington THE DETERMINATION AND REFINEMENT OF THE MOLECULAR STRUCTURES OF SOME ORGANIC COMPOUNDS BY SINGLE CRYSTAL X-RAY DIFFRACTION ABSTRACT The c r y s t a l and molecular structure of perylene has been refined from new three-dimensional data, confirm ing the gross features of the structure previously de termined from two projections. The p o s i t i o n a l and thermal parameters of the carbon atoms have been r e f i n  ed by least-squares and d i f f e r e n t i a l syntheses and the hydrogen atoms have been approximately located. There are small but s i g n i f i c a n t deviations from a completely planar arrangement; seemingly a r e s u l t of s l i g h t i n t e r  molecular s t e r i c e f f e c t s . A comparison of the measured bond lengths with those predicted by the valence-bond and molecular-orbital theory shows f a i r l y close agree ment with both sgts of figures; the peri-bond lengths are 1.471-0.005 A. In a s i m i l a r vein the molecular structure of pyrene was refine d by least-squares and d i f f e r e n t i a l synthesis treatment of new three-dimensional data. The thermal motion of the atoms was found to be anisotropic and was interpreted i n terms of r i g i d body v i b r a t i o n s . Small corrections were made to the bond lengths to correct errors due to r o t a t i o n a l o s c i l l a t i o n s . The general v a r i a t i o n of the mean bond distances i s i n agreement with trends predicted by valence-bond and molecular-orbital c a l c u l a t i o n s , but the i n d i v i d u a l agreements are not very good. The molecule i s s l i g h t l y non-planar, probably as a r e s u l t of c r y s t a l packing forces. Hydroformylation of t r i - O - a c e t y l - D - g l u c a l y i e l d s two isomeric products and, to e s t a b l i s h the configur ations, X-ray analysis of the p-bromobenzenesulphonyl deri v a t i v e of one of these has been ca r r i e d out. The bromine and sulphur positions were determined from the three-dimensional Patterson function and the other atoms were located from successive three-dimensional Fourier summations. Refinement was c a r r i e d out by least-squares methods. The d e r i v a t i v e studied i s 1-0-(p-bromobenzenesulphonyl)-4,5,7-tri-0-acetyl-2, 6- anhydro-3-deoxy-U-glucoheptitol, and t h i s establishes the configurations of the t r i a c e t y l derivatives and parent polyols. The sugar r i n g i s i n the chair p o s i t -"ion with a l l substituents equatorial. 10-Chloro-5,10-dihydrophenarsazine c r y s t a l l i z e s from xylene with h a l f a molecule of xylene of c r y s t a l l i z a t i o n i n a monoclinic space group. This material r a p i d l y loses the solvent of c r y s t a l l i z a t i o n , the solvent-free c r y s t a l s being orthorhombic. The complete structure of the orthorhombic c r y s t a l s has been determined using Patterson !methods to determine the arsenic and chlorine positions and a three-dimensional electron-density d i s  t r i b u t i o n map to locate the other atoms. A l l the posit ional and anisotropic thermal parameters were refined by least-squares. The molecule i s s l i g h t l y folded about the As-N axis, the angle between the two o-phenylene groups being 169°, and the chlorine atom being outside th i s angle. The deviation from p l a n a r i t y i s thus not very large and i t i s u n l i k e l y that geometrical isomers could be i s o l a t e d . GRADUATE STUDIES F i e l d of Study: Chemistry Topics i n Physical Chemistry J o A . R , Coope R „ F o Snider A . Bree Topics i n Inorganic Chemistry N„ B a r t l e t t WoR„ Cullen Topics i n Organic Chemistry Chemical Kinetics D 0E, McGreer R.E.I, Pincock J„P„ Kutney E.A. Ogryzlo G„B, Porter D 0G.L 0 James Cr y s t a l Structures Related Studies Calculus and D i f f e r e n t i a l Equations Linear Algebra D i g i t a l Computer Programming Elementary Quantum Mechanics J„ T r o t t e r S.A.M. Melzak W.H. Gage R. Cleveland C„ Froese Wo Opechowski PUBLICATIONS 1. A. Camerman and J . T r o t t e r , "The C r y s t a l and Mol ecular S t r u c t u r e of Perylene", Proc.Roy.Soc., A.279, 129 (1964) 2. A. Camerman and J . T r o t t e r , "The C r y s t a l and Mol ecular S t r u c t u r e of 10-Chloro-5,10-Dihydrophenar- sazine", J.Chem.Soc. (1964). In Press 3. A. Camerman and J . T r o t t e r , "The C r y s t a l and Mol ecular S t r u c t u r e of 1-0-(p-bromobenzenesulphonyl)- 4,5,7-tri-p-acetyl-2,6-anhydro-3-deoxy-D -gluco- h e p t l t o l " , A cta.Cryst. (1964). In Press 4. A. Camerman and J . T r o t t e r , "The C r y s t a l and Molecular S t r u c t u r e of Pyrene", Acta. C r y s t . To be published. 5. A. Camerman and J . T r o t t e r , " C r y s t a l Data f o r Two Sugar A l c o h o l s " , Acta. Cryst. (1964) In Press 6. A. Camerman, H. Koch, A. Rosenthal and J . T r o t t e r , " C o n f i g u r a t i o n of Anhydrodeoxyheptitols! 1, Can. J . Chem. (1964). In Press ABSTRACT The c r y s t a l and molecular structure of perylene has been refined from.^ew three-dimensional data, confirming the gross features of the structure previously determined from two projec tions. The p o s i t i o n a l and thermal parameters of the carbon atoms have been refined by least-squares and d i f f e r e n t i a l syn theses and the hydrogen atoms have been approximately located. There are small but s i g n i f i c a n t deviations from a completely planar arrangement; seemingly a result of s l i g h t intermolecular s t e r i c e f f e c t s . A comparison of the measured bond lengths with those predicted by the valence-bond and molecular-orbital theory shows f a i r l y close agreement with both sets of figures; the , o peri-bond lengths are 1.471*0.005 A. In a s i m i l a r vein the molecular structure of pyrene was refined by least-squares and d i f f e r e n t i a l synthesis treatment of new three-dimensional data. The thermal motion of the atoms was found to be anisotropic and was interpreted i n terms of r i g i d body vibrations. Small corrections were made to the bond lengths to correct errors due to r o t a t i o n a l o s c i l l a t i o n s . The general v a r i a t i o n of the mean bond distances i s i n agreement with trends.predicted by valence-bond and molecular-orbital calcu l a t i o n s , but the i n d i v i d u a l agreements are not very good. The molecule i s s l i g h t l y non-planar, probably as a res u l t of cr y s t a l packing forces. Hydroformylation of tri-O-acetyl-d-glucal yields two isomeric products and, to establi s h the configurations, X-ray i i i analysis of the p-bromobenzenesulphonyl derivative of one of these has been carried out. The bromine and sulphur positions were determined from the three-dimensional Patterson function and the other atoms were located from successive three- dimensional Fourier summations. Refinement was carried out by least-squares methods. The derivative studied i s 1-0-(p- bromobenzenesulphonyl)-4,5,7-tri-0-acetyl-2,6-anhydro-3-deoxy- d-glueoheptitol, arid t h i s establishes the configurations of the t r i a c e t y l derivatives and parent polyols. The sugar r i n g i s i n the chair position with a l l substituents equatorial. 10-Chloro-5,10-dihydrophenarsazine c r y s t a l l i z e s from xylene with half a molecule of xylene of c r y s t a l l i z a t i o n i n a monoclinic space group. This material rapidly loses the solvent of c r y s t a l l i z a t i o n , the solvent-free crystals being orthorhombic. The complete structure of the orthorhombic crystals has been determined using Patterson methods to determine the arsenic and chlorine positions and a three-dimensional electron-density d i s t r i b u t i o n map to locate the other atoms. A l l the p o s i t i o n a l and anisotropic thermal parameters were refined by l e a s t - squares. The molecule i s s l i g h t l y folded about the As-N a x i s , the angle between the two o-phenylene groups being 169°, and the chlorine atom being outside £his angle. The deviation from plan a r i t y i s thus not very large and i t i s u n l i k e l y that geometrical isomers could be i s o l a t e d . To MY MOTHER for her love, devotion and s a c r i f i c e V ACKNOWLEDGEMENTS My warmest thanks are due to Dr. James Trotter whose guidance, advice, and friendship have made my research under his supervision and my entire association with him both in s t r u c t i v e and pleasant. I am indebted to my brother Norman Camerman f o r continual a i d , discussion, and encouragement. His help i n a l l phases of my work i s greatly appreciated. I thank Dr. A. Bree for the sample of pyrene, Dr. A. Rosenthal and Mr. H. Koch f o r the tri-O-acetyl-d-glucal deriv ative and Dr. W. Cullen for the crystals of 10-chloro-5,10- dihydrophenarsazine. I also g r a t e f u l l y acknowledge Drs EAhmed and G. Mair f o r kindly making available t h e i r IBM 1620 computer programs. F i n a l l y I wish to express my appreciation to the National Research Council of Canada for the award of a Bursary for the period 1961-62 and a studentship f o r the period 1962-64. 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 PART I. INTRODUCTION TO THE THEORY OF CRYSTAL STRUCTURE DETERMINATION 1 I. Elementary Crystallography . . . . . . •. 2 A. Introduction 2 B. Crystals as Geometric Figures 3 C. Crystal Symmetry 4 D. Lattice Structure of Crystals, and Space Groups 4 I I . D i f f r a c t i o n of X-Rays by a Crystal 9 A. Scattering'by Electrons 9 B. Conditions f o r D i f f r a c t i o n Maxima . . . . 9 C. The Reciprocal Lattice . 11 D. The Structure Factor 12 E. Intensity of Reflected Radiation . . . . 13 F. Generalized Structure Factor and Fourier Series .' ' 14 I I I . Structure Determination and Refinement . . . 17 A. Methods f o r Establishing the Structure . . 17 B. Refinement of Crystal Structures . . . . 19 v i i PAGE PART I I . THREE-DIMENSIONAL REFINEMENTS OF THE STRUCTURES OF PERYLENE AND PYRENE 24 I. The Crystal and Molecular Structure of Perylene 25 Introduction 25 Experimental . 2 6 Refinement of the Structure . 2 8 Coordinates and Molecular Dimensions . . . 3 0 Discussion 39 I I . The Crystal and Molecular Structure of Pyrene . 50 Introduction . 50 Experimental ! . . . 50 Refinement of the Structure 51 Coordinates and Molecular Dimensions . . . 54 Discussion 58 PART I I I . DETERMINATION OF STRUCTURES OF 1-0-(p-BROMO- BENZENESULPHONYL)-4,5,7-TRI-0-ACETYL-2,6- ANHYDR0-3-DE0XY-d-GLUC0HEPTIT0L AND 10- CHL0R0-5,10-DIHYDROPHENARSAZINE 64 I. Crystal and Molecular Structure of 1-0-(p-Bromo- benzenesulphbnyl)-4,5,7-Tri-0-Acetyl-2,6- Anhydro-3-Deoxy-d-Glucoheptitol . . . . . . 65 Introduction 65 Experimental . . . . . . . , . . . 6 6 Structure Analysis . . . . . . . . . 67 Coordinates and Molecular Dimensions . . . 70 v i i i PAGE PART I I I . (continued) Discussion 72 I I . C r y s t al and Molecular Structure of 10-Chloro- 5,10-Dihydrophenarsazine 75 • Introduction 75 Preliminary X-Ray Study . . . . . . . . 77 Experimental 79 Structure Analysis 80 Discussion 86 APPENDIX X STRUCTURE FACTOR TABLES 89 APPENDIX I I CRYSTALLOGRAPHIC DATA FOR SOME MOLECULAR CRYSTALS , 102 REFERENCES 106 LIST OF FIGURES FIGURE PAGE 1. Standard or Parametral Face 3 2. The 14 Bravais Lattices 6 3. D i f f r a c t i o n and Reflection 10 4. D i f f r a c t i o n i n Reciprocal Space 12 Perylene 5. Measured Bond Lengths 35 6. Measured Valency Angles 36 7. Deviations from Mean Molecular Plane 38 8. Normal Projection of 2 P a r a l l e l Molecules . . . 42 9. Perspective Drawing of 2 P a r a l l e l Molecules . . 43 Pyrene 10. Measured Bond Lengths and Valency Angles . . . 57 11. Kekule Structures 62 1-0-(p-Bromobenzenesulphonyl)-4,5 <7-Tri-0-Acetyl-2, 6-Anhydro-3-Deoxy-d-Glucoheptitol 12. Projected Electron Density . 69 10-Chloro-5,10-Dihydrophenarsazine 13. Projected Electron Density 82 14. Measured Bond Lengths and Valency Angles . . . 84 LIST OF TABLES TABLES PAGE I. Symmetry Operations i n Crystals 4 I I . Symmetry Operations Involving Translation . . 5 Perylene I I I . Progress of Refinement 29 IV. Carbon Atom Electron-Densities and Curvatures , 31 V. Hydrogen Atom Electron-Densities 31 VI. F i n a l Coordinates 32 VII. Standard Deviations 33 V I I I . Orientation of the Molecule 37 IX. Shorter Intermolecular Contacts 39 X. Measured and Calculated Bond Lengths . . . . 44 Pyrene XI. Hydrogen Atom Electron-Densities 52 XII. Carbon Atom Electron-Densities and Curvatures , 53 X I I I . F i n a l P o s i t i o n a l Parameters and Standard Devia t i o n s , and Deviations from Molecular Plane . 54 XIV. Anisotropic Thermal Parameters 55 XV. Orientation of the Molecule . . . . . . . 58 XVI. Shorter Intermolecular Contacts . 59 XVII. Measured and Calculated Bond Lengths . . . . 6 l 1-0- (p-Bromobenzenesulphonyl) .-4.5 ,7-Tri-0-Acetyl- 2,6-Anhydro-3-Debxy-d-Glucoheptitol XVIII. F i n a l Parameters . . . . 70 XIX. Bond Lengths and Valency Angles 71 XX. Shorter Intermolecular Contacts 73 x i TABLES PAGE • / 10-Chloro-5 t10-Dihydrophenarsazine XXI. F i n a l P o s i t i o n a l and Thermal Parameters . #1 XXII. Shorter Intermolecular Contacts 85 XXIII. Deviations from Mean Planes . « 86 Comparison of Measured and Calculated Structure  Factors A l . Perylene 90 A2. Pyrene . . 93 A3. 1-0-(p-Bromobenzenesulphonyl)-4,5,7-Tri-O-Acetyl- 2,6-Anhydro-3-Deoxy-d-Glucoheptitol Structure Amplitudes 96 A4. 10-Chloro-5,10-Dihydrophenarsazine Structure Amplitudes 99 PART I INTRODUCTION TO THE THEORY OF CRYSTAL STRUCTURE DETERMINATION I. ELEMENTARY CRYSTALLOGRAPHY A. Introduction The postulation by Von Laue i n 1912 of the d i f f r a c t i o n of X-rays by c r y s t a l s led to s c i e n t i f i c advancement i n two main dir e c t i o n s . The f i r s t concerned the nature of X-radiation i t  s e l f and led through the work of W.H. Bragg, Moseley, and others to fundamental advances i n the theory of atomic structure. The second aspect entailed the use of X-ray d i f f r a c t i o n as a power f u l t o o l f o r elucidating the atomic arrangement i n various molecules and c r y s t a l s . I t i s t h i s second aspect, generally referred to as X-ray crystallography, with which t h i s thesis i s concerned. Crystals d i f f e r from l i q u i d s or other amorphous materials in that certain of t h e i r properties o p t i c a l , thermal, elec t r i c , and magnetic display marked anisotropy. Since the inte r n a l texture of a c r y s t a l i s obviously homogeneous these d i r e c t i o n a l properties, as well as the well-developed symmetry common to many c r y s t a l s , must be related to some feature of the ultimate structure of the matter of which the c r y s t a l i s composed. To come to an understanding of the relationship of c r y s t a l symmetry and anisotropy to interna l atomic structure we must examine the c r y s t a l both externally (as a geometric figure) and i n t e r n a l l y (as a l a t t i c e of atoms, ions, or molecules). 3 B. Crystals as Geometric Figures Crystals of the same compound, regardless of shape, always have the same angles between corresponding faces (law of constancy of i n t e r f a c i a l angles). I t i s thus the orienta tions and not the sizes of the faces that i s c h a r a c t e r i s t i c of any p a r t i c u l a r c r y s t a l . As a system of describing c r y s t a l faces l e t us choose the intersections of any three non-parallel faces represented by OA, OB, and OC i n figure 1 as axes. We may choose any plane of the c r y s t a l a r b i t r a r i l y to meet these l i n e s at A, B, and C with intercepts a, b, and c. This plane i s c a l l e d the standard or parametral face as i t deter mines the parameters a, b, and c. I f now any other face of the c r y s t a l has intercepts along the axes of |> >^ c i t i s said to have the M i l l e r indices (hk£). The indices (after clearing of fractions) are thus the reciprocals of the intercepts of any face, or plane drawn p a r a l l e l to i t , Figure 1 on the calibrated set of a x i s . The indices of our standard face are then (111) and those of the dotted plane are (142). If a plane i s p a r a l l e l to one of the axes i t s intercept i s at i n f i n i t y and the corresponding M i l l e r index i s zero. This i s an i l l u s t r a t i o n of the fundamental law of r a t i o n a l indices 4 discovered by Ha'uy i n 1784, which says that the ra t i o s of the indices of any face of a c r y s t a l are small integers. C. Crystal Symmetry A symmetry operation i s one which when applied to a geometric figure leaves the figure co-incident with i t s e l f . There are ten symmetry operations possible for c r y s t a l s . These are l i s t e d i n Table I with t h e i r appropriate symbols. TABLE I SYMMETRY OPERATIONS IN CRYSTALS Symbol Operation 1 i d e n t i t y operation = onefold rotation axis 2 two-fold rotation axis 3 'three-fold rotation axis 4 f o u r - f o l d rotation axis 6 s i x - f o l d r o t a t i o n axis JL = i center of symmetry 2 = m mirror plane 3. three-fold rotatory inversion axis 4 four-fold rotatory inversion axis o" s i x - f o l d rotatory inversion axis Hessel showed there are only 32 ways of combining the ten symmetry operations l i s t e d above. These are known as the 32 point groups or c r y s t a l classes. A complete l i s t i n g of these point groups and the common symbols used to designate them may be found i n reference (1). D. Lattice Structure of Crystals, and Space Groups As early as the seventeenth century Hooke and Huygens thought of cry s t a l s as being composed of small i n v i s i b l e equal 5 p a r t i c l e s arranged i n three-dimensional nets or l a t t i c e s . It was i n 16*50 that Bravais demonstrated by r i g i d geometrical proofs that only 14 d i s t i n c t types of space l a t t i c e are possible. Figure 2 i l l u s t r a t e s unit c e l l s of the 14 Bravais l a t t i c e s . Structures which are b u i l t up on regular l a t t i c e s i n d e f i  n i t e l y extended i n every d i r e c t i o n can be brought into s e l f - coincidence in a new way, namely by translations along any of the l a t t i c e d i r e c t i o n s . The l a t t i c e points are by d e f i n i t i o n i d e n t i c a l so such movements over the repeat distance leave the structure unchanged. Hence a new class of symmetry operations i s applicable to l a t t i c e structures, i n addition to those which apply to f i n i t e geometrical figures. These new operations are the screw a x i s , which combines a rotation axis with a trans l a t i o n , and the glide plane, which combines a mirror plane with a t r a n s l a t i o n . Table I I l i s t s these new symmetry operations and t h e i r symbols. Symbol 2 1 3 l 32 4 1 4 2 4 TABLE I I SYMMETRY OPERATIONS INVOLVING TRANSLATION Operation rot a t i o n of HJL with t r a n s l a t i o n -i 2 3 t» T 2 T 3 t t 2JT 4 n " I 3 tt 2 7 1 4 2 4 • I r e f l e c t i o n + t r a n s l a t i o n o r S+£ 6 1. TRICLINIC £7 2 SIMPLE MONOCLINIC I 3. SIDE-CENTERED MONOCLINIC 4=71 4=71 ) 1 -* 1 1 \ ' 4 SIMPLE ORTHORHOMBIC S END-CENTERED ORTHORHOMBIC i FACE-CENTERED ORTHORHOMBIC 7 BODY-CENTERED ORTHORHOMBIC I > =u-' 8 H f c K A & O N A L 9 RHOMBOMEDRAL 10 SIMPLE TETRAGONAL 11 BODY-CENTERED T£ TRAOONAL 4=71 -T- It SIMPLE CUBIC 13 BODY- CENTERED CUBIC 14 FACE- CENTERES CUBIC Figure 2. The lU Bravais L a t t i c e s 7 TABLE II (continued) Symbol Operation 61 rotation of with t r a n s l a t i o n 1 6 6 A - tt it tt it tt 2 2 rj A - « i» " w 11 3 °3 75 A , 11 11 11 it tl 4 A _ »i 11 it it 11 5 ° 5 75 a,b,c r e f l e c t i o n + t r a n s l a t i o n ^, -| d r e f l e c t i o n + ~ diagonal t r a n s l a t i o n 4 By combining these new symmetry operations with those u t i l i z e d i n forming the 32 point groups, Federow, Barlow, and Schoenflies independently derived the 230 space groups that are possible f o r l a t t i c e structures. These space groups are l i s t e d i n Vol, I, the International Tables for X-Ray Crystallography. A knowledge of the space group of a c r y s t a l hence includes a knowledge of a l l the symmetry properties of the c r y s t a l . The space group cannot be determined from external form alone, but must be determined from X-ray d i f f r a c t i o n patterns. The basis f o r t h i s determination i s the extinction of cert a i n X-ray d i f  f r a c t i o n spectra caused by the presence of screw axes, glide planes, and centered l a t t i c e s . Since mirror planes and rota t i o n axes do not cause spectral extinction and because (due to Fri e d e l ' s law) X-ray d i f f r a c t i o n patterns contain a center of symmetry, i t i s not always possible to ascertain the correct space group from the d i f f r a c t i o n pattern alone. S t a t i s t i c a l analysis of the d i s t r i b u t i o n of d i f f r a c t i o n i n t e n s i t i e s ( 2 , 3) may be useful i n t h i s respect as well as measurement of c r y s t a l pyro- and p i e z o e l e c t r i c properties. I I . DIFFRACTION OF X-RAYS BY A CRYSTAL A. Scattering by Electrons Crystals are composed of groups of atoms repeated at regular i n t e r v a l s , with the same orientation, i n three dimen sions. Each atom i s composed of a nucleus and surrounding electrons, and when these electrons are i n c o l l i s i o n with an X-ray beam they are forced into o s c i l l a t i o n by the periodically- varying e l e c t r i c f i e l d and emit radiation of the same wave length as the X-rays. In t h i s manner the electrons scatter or d i f f r a c t the X-ray beam. The waves scattered by the several electrons of each atom combine and the r a t i o of the wave scattered by an atom at rest to that scattered by a single electron i s known as the atomic scattering factor f Q . The atomic scattering factor i s dependent upon the angle of i n c i  dence of the X-ray beam and at a zero angle of incidence i t i s equal to the number of electrons i n the atom. B. Conditions f o r D i f f r a c t i o n Maxima If we consider the X-ray d i f f r a c t i o n effects to be expected from a single row of the c r y s t a l l i n e l a t t i c e of period a (Figure 3), the condition to be f u l f i l l e d f o r reinforcement of waves and production of a d i f f r a c t e d beam i s that the path difference between waves scattered from successive points should equal a whole number of wavelengths, nA. If the incident beam makes an angle cx0 with the row, and the d i f f r a c t e d beam an angle ex, t h i s condition i s a(coscx D - coscx) = nX 10 For a three dimensional l a t t i c e with parameters a, b, c, the d i r e c t i o n of the d i f f r a c t e d beam i s given by the angles ex > p> > V when the three Laue equations a(costx 0 - cos o< ) = n-^ A b(cos@ 0 - cos ^  ) = n 2A c(cos Y 0 - cos 's ) = nj\ are simultaneously s a t i s f i e d . The t r i p l e set of integers n l n2 n3 denotes the order of the.spectrum. Figure 3. D i f f r a c t i o n and r e f l e c t i o n by a single row, and the equivalence of the Laue and Bragg equations A great s i m p l i f i c a t i o n to Laue's equations was made by W.L. Bragg on his introduction of the idea of r e f l e c t i o n of X-rays from c r y s t a l planes. When an X-ray beam i s incident on a c r y s t a l plane at an angle © a reflected beam w i l l be formed by Huygen's p r i n c i p l e . Reinforcement by X-rays reflected from the next p a r a l l e l c r y s t a l plane, at distance d, w i l l occur when the path difference i s equal to a whole number of wavelengths, or when nX = 2dsinG From Figure 3 i t can be shown (using the usual trigonometric 11 relationships) that the Laue and Bragg equations are equivalent. C. The Reciprocal Lattice It i s d i f f i c u l t and laborious to v i s u a l i z e a large number of planes of varying orientation i n a c r y s t a l ; i t i s easier to think of the normals to the planes rather than the planes them selves. Each plane i s then represented by a point on the nor mal to that plane, and the distance S from the o r i g i n to the point i s inversely proportional to the spacing of the respec t i v e planes. S = |[(plane), K i s usually taken as /\ . The reciprocal l a t t i c e axes are l a b e l l e d a*, b*, and c* and i n vector notation are defined as a* - AbXc/V b* = AcXa/V c* = AaXb/V where V i s the volume of the unit c e l l . Reciprocal l a t t i c e theory i s extremely useful in affording a simple geometrical interpretation of d i f f r a c t i o n phenomena. Bragg's law states Sin 8 = A/2d hence the maximum value of A/2d f o r r e f l e c t i o n to occur i s 1. This defines a sphere i n recip r o c a l space (Figure 4). Every point of the r e c i p r o c a l l a t t i c e contained by t h i s sphere can r e f l e c t incident r a d i a t i o n . This i s the l i m i t i n g sphere. Any reciprocal l a t t i c e point on the surface of the smaller sphere (Figure 4), can r e f l e c t r adiation incident i n the d i r e c t i o n of i t s diameter. This smaller sphere i s c alled the sphere of r e f l e c t i o n . As the d i r e c t i o n of i n c i  dence of the r a d i a t i o n changes the sphere of r e f l e c t i o n moves within the l i m i t i n g sphere. 12 Figure 4. D i f f r a c t i o n i n r e c i p r o c a l space (4) The basis of most single c r y s t a l X-ray photographs i s to rotate the c r y s t a l so that i n effect the d i r e c t i o n of incidence of the radiation changes and many reciprocal l a t t i c e points intersect the sphere of r e f l e c t i o n . D. The Structure Factor In general the X-ray wavelets scattered by the various atoms i n any given plane are of d i f f e r e n t amplitude and phase and are compounded v e c t o r i a l l y to give the resultant d i f f r a c t e d wave. This resultant i s c a l l e d the structure f a c t o r , F(nkjZ,)> f o r the plane with M i l l e r indices hkl, and i s a complex quantity characterized by an amplitude |F(hk&)|, and a phase tX(hkjfc) . The structure f a c t o r , being a vector summation of the wavelets d i f f r a c t e d by the N atoms i n the unit c e l l may be therefore written N where x-jy-jz-; are the f r a c t i o n a l coordinates of the j th atom i n 13 the c e l l . It can be evaluated by means of the following expressions where The quantity f j i s the scattering factor of the j t n atom corrected for thermal v i b r a t i o n of the atom. The quantity B i s related to the mean square displacement of _2 the atom at ri g h t angles to the r e f l e c t i n g plane, /JL , by the expression In practice an a r b i t r a r y value i s assigned to B and t h i s value i s refined during the structure refinement. E. Intensity of Reflected Radiation When 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 co, d i f f e r e n t planes are successively brought into the position of maximum r e f l e c t i o n . For a mosaic (non-perfect) c r y s t a l i t can be shown that the t o t a l integrated r e f l e c t i o n which i s cha r a c t e r i s t i c of a given c r y s t a l plane •^o i s proportional to the volume dv" of the c r y s t a l block and inde pendent of the shape. The following r e l a t i o n can be derived: -B s i n 2 6 —JT- B = ctrr 2^ 2. ELO = N2[~V:~|2A3 F2(hk£) 1+ Cos^e dV mc2 2Sin26 14 In t h i s expression I 0 = i n t e n s i t y of the incident beam E = t o t a l r e f l e c t e d energy N = number of unit c e l l s per unit volume of the c r y s t a l e and m = charge and mass of the electron c = v e l o c i t y of l i g h t The quantity l+Cos 228 i s the p o l a r i z a t i o n f a c t o r and provides the averaging necessary due to the incident beam being unpolar- ized, while the r e f l e c t e d beam i s p a r t i a l l y polarized, and w , I ^ i s the Lorentz factor, which arises from the difference Sm26 in speeds at which various r e c i p r o c a l l a t t i c e points pass through the r e f l e c t i n g p o s i t i o n . In experimental procedure the integrated r e f l e c t i o n expression must be modified i n accordance with the method employed fo r measuring the i n t e n s i  t i e s . This stems from the f a c t that the Lorentz factor has d i f f e r e n t forms i n d i f f e r e n t experimental techniques. F. Generalized D e f i n i t i o n of the Structure Factor and the Expression of Electron Density as a Fourier Series In our previous d e f i n i t i o n of the structure factor we assumed that a l l the scattering matter in the unit c e l l i s con centrated into a number of s p h e r i c a l l y symmetrical atoms. We s h a l l now consider a more general d e f i n i t i o n in terms of an electron density function. If p(XYZ) i s the density of scat t e r i n g material at a point X,Y,Z in the unit c e l l , then the number of electrons in the volume element dXdYdZ w i l l be (0(XYZ)-I_dXdYdZ where V i s the volume of the unit c e l l and v abc 15 a,b,c, are the a x i a l lengths. Then i f x,y,z are f r a c t i o n a l co ordinates r 1 f 1 r 1 / v 2TTi(hx+ky+£z) F(hki-) = V\ \ \ p(xyz) e dxdydz Jo Jo do The e s s e n t i a l l y periodic nature of c r y s t a l s , which a r i s e s from t h e i r l a t t i c e structure, suggests expansion i n the form of a Fourier series as the natural representation of any phys i c a l property of the c r y s t a l . The idea of representing t'he electron, density of a c r y s t a l in such a way was f i r s t suggested by W.H. Bragg in 1915. Thus / \ , / ^ 2TTi (px+qy+rz) p(xyz) = ^ > 2 Z A ( p q r ) e - 0 0 where p,q,r are integers and A(pqr) the c o e f f i c i e n t of the general term. By substituting t h i s equation f o r p(xyz) into the gener a l i z e d expression f o r the structure f a c t o r and integrating, i t is e a s i l y shown that A(hkjft) - F(hkU V Thus the structure f a c t o r and electron density are Fourier transforms of one another. (?(xy z\ = l S S Z p f v i k / , ) p -2TTi(hx+ky+^z) ' T h k Jb v ; —oo It can e a s i l y be shown (l) that the above expression can be written in the following convenient form: 4-00 p(xyz) = A Z 2 S |F(hk&)| cos[2TT (hx+ky+^z) -0((hk£)] v h k I 1 1 -oo Where (X(hkj0/) represents the phase angle associated with the 16 amplitude |F(hk£)| . We can calculate |F(hk&)| from the inten s i t i e s of the reflected radiation but we have no immediate way of measuring the values of the phase constants. This d i f f i c u l t y i s the fundamental obstacle to the solution of c r y s t a l struc tures and i s known as the phase problem of X-ray c r y s t a l l o  graphy. The phase problem i s indeed a formidable one, as i t can be seen that an i n f i n i t e number of electron density d i s t r i b u  tions can be obtained by assigning a r b i t r a r y phases to the structure amplitudes. Of some help, however, i n l i m i t i n g the combinations of phases possible, i s the knowledge that the electron density must everywhere be non-negative and composed of more-or-less s p h e r i c a l l y symmetrical atoms, and that the resultant structure must be chemically f e a s i b l e . I I I . STRUCTURE DETERMINATION AND REFINEMENT The sequence of steps employed i n c r y s t a l structure analysis i s usually 1. The determination of unit c e l l parameters and i d e n t i  f i c a t i o n of space group. This information i s obtained from the positions of the r e f l e c t i o n s . 2. Measurement of the i n t e n s i t i e s of the refl e c t e d r a d i  ation from each of the c r y s t a l planes. 3. Establishment of the structure. This usually e n t a i l s the successive location of various atoms i n the unit c e l l and culminates i n the reasonably certain i d e n t i f i c a t i o n of a l l atomic positions. 4. Refinement of the structure. This involves adjust ment of a l l atomic coordinates to ensure closest agreement between observed and calculated structure amplitudes. There are many good textbooks dealing with the many aspects of c r y s t a l structure analysis and some of these are l i s t e d i n references (4-8). A b r i e f discussion of the estab lishment of the structure and some refinement methods i s given in the next two sections. A. Methods f o r Establishing the Structure Methods for attacking the phase problem may be c l a s s i f i e d into the three following categories. i . T r i a l and Error Methods. As the name implies, these methods are based on the combination of a l l chemical, physical, 18 and crystallographic evidence obtainable, to form t r i a l struc tures. When some atoms have been approximately located, phases are calculated based on the located atomic coordinates and a Fourier synthesis i s calculated using the measured ampli tudes and calculated phases. It i s hoped t h i s Fourier synthesis leads to more and better atomic positions which would be used to calculate new structure factors f o r use in a further Fourier synthesis. This i t e r a t i v e process i s repeated u n t i l a l l atoms are located and may be used also to refine the structure i f no better means i s a v a i l a b l e . i i . Patterson and Heavy Atom Methods. A.L. Patterson, in 1934, (9) extended to c r y s t a l s the theory of scattering of X-rays i n l i q u i d s and i n doing so developed one of the most powerful and widely used of modern methods of c r y s t a l analysis. The function which has come to bear Patterson's name i s defined by the equation CO A(uvw) | | | |F(hk£)| 2e- 2 l r t ( hf kf^> -CD and represents vector distances between atoms in the c r y s t a l . Hence a peak on the Patterson map at coordinates u^v^w^ cor responds to an interatomic distance in the c r y s t a l defined by a vector whose components are u]_, vj_, v>]_. The height of a peak on the vector map i s proportional to the product of the atomic numbers of the two atoms involved. Hence Patterson's function i s used most often to f i n d the coordinates of a heavy atom (one containing more electrons than any other atom i n the mole cule) i f one i s present. If the position of the heavy atom can 19 be d e t e r m i n e d p h a s e s c a l c u l a t e d s o l e l y f o r t h a t atom may be s u f f i c i e n t f o r a F o u r i e r s y n t h e s i s t o r e v e a l t h e l i g h t e r a t o m s . S ometimes i t i s p o s s i b l e t o r e p l a c e a h e a v y a t o m b y a n o t h e r a t t h e same p o s i t i o n w i t h o u t a l t e r i n g t h e c r y s t a l s t r u c  t u r e . I n s u c h a c a s e , c a l l e d t h e m e t h o d o f i s o m o r p h o u s r e p l a c e  ment, p h a s e a n g l e s c a n s o m e t i m e s be d e t e r m i n e d f r o m a d i f f e r e n c e e f f e c t . T h i s m e thod i s i l l u s t r a t e d v e r y n i c e l y b y J.M. R o b e r t s o n i n h i s d e t e r m i n a t i o n o f t h e s t r u c t u r e s o f t h e p h t h a l o c y a n i n e s ( 1 0 , 1 1 ) . i i i . D i r e c t M e t h o d s . T h e s e a r e m a t h e m a t i c a l a t t e m p t s t o d e t e r m i n e t h e p h a s e s o f t h e s t r u c t u r e f a c t o r s d i r e c t l y f r o m o b s e r v a b l e d a t a . H a r k e r a n d K a s p e r ( 1 2 , 1 3 ) , m a k i n g u s e o f C a u c h y ' s a n d S c h w a r t z ' s i n e q u a l i t i e s a n d t h e s ymmetry e l e m e n t s p r e s e n t i n c r y s t a l s , d e r i v e d a s e t o f i n e q u a l i t i e s l i m i t i n g t h e v a l u e s o f c e r t a i n F's and | F | 2 ' S . A more g e n e r a l s y s t e m o f e q u a l i t i e s , i n c o r p o r a t i n g t h e f a c t t h a t p ( x y z ) " ^ 0 , has b e e n f u r n i s h e d by K a r l e and Hauptman ( 1 4 , 1 5 ) , who h ave a l s o p r o  p o u n d e d t h e u t i l i z a t i o n o f s t a t i s t i c a l c a l c u l u s and j o i n t - p r o b a b i l i t y t h e o r y a s a means o f d e t e r m i n i n g p h a s e s ( 1 6 ) . O t h e r w o r k e r s i n t h i s f i e l d ( 1 7 , 1 8 , 19) h a v e a l s o e s t a b l i s h e d s i g n r e l a t i o n s b e t w e e n s t r u c t u r e f a c t o r s i n c e n t r o s y m m e t r i c s p a c e g r o u p s , b u t a g e n e r a l l y s a t i s f a c t o r y d i r e c t method a p p l i  c a b l e t o a l l c a s e s i s y e t t o be f o u n d . B. R e f i n e m e n t o f C r y s t a l S t r u c t u r e s The d i s c r e p a n c y f a c t o r , R « ^ l l F o l ~ l F c l i s a m e a s u r e o f t h e c o r r e c t n e s s o f t h e e x p e r i m e n t a l m o l e c u l a r s t r u c t u r e 20 Correct structures usually have R<0.25 and very well refined ones may have R i n the neighborhood of 0.05. The most common methods of refinement of c r y s t a l struc tures are by means of d i f f e r e n t i a l syntheses, least squares analysis, and difference syntheses. The f i r s t two methods were used i n the refinements of perylene and pyrene, as recorded i n the next chapter, so some d e t a i l of t h e i r p r i n c i p l e s w i l l be discussed i n the succeeding paragraphs. The difference syn thesis employs the quantities (F Q-F C) as c o e f f i c i e n t s i n a Fourier synthesis. F i r s t expounded by Booth (20), i t s features were well developed by Cochran (21). a. D i f f e r e n t i a l Synthesis. Booth (22) also concentrated attention on the problem of f i n d i n g the maxima of the electron-density function. At these maxima, one per atom, the f i r s t derivative vanishes. "dx "dy 9 z If we assume that a coordinate of an atom before r e f i n e  ment i s x and the error i s e, so that the correct coordinate i s x 0 = x+e, then expanding d£(x+£) i n a Taylor series we have, dx (considering the f i r s t two terms only): de(x+e) . - d g i x l + £ d 2g(x) m 0 dx dx dx^ In three dimensions p a r t i a l d i f f e r e n t i a l s are used and three equations of the following type are obtained: The electron density function i s known 2 1 (O(xyz) = I ^ ^ ^ F ( h k ^ ) c o s [ 2 T T ( h x + k y + ^ z ) - a ] so the p a r t i a l derivatives can be e a s i l y evaluated. In the con venient notation adopted by Booth, where A h = | | - . ™_22^{hkt) sin[27T(hx+ky+£z) -«] Ahk =23L = - AlL_2S2hk F / h k n cos[2TT(hx+ky+/z) -ex] *d*dy V h kjL ^ n K J W for each atom we obtain a matrix equation Ahh Ahk A h A /ex\ Ah\ Lhk Akk Akg, ;€y \ = -( A k AhJL A k i A U 7 The d i f f e r e n t i a l synthesis i s affected greatly by series termination errors i f enough terms are not included i n the Fourier series. To correct f or t h i s a backshift correction i s applied a synthesis i s computed with the F c's as c o e f f i c i e n t s in the summations and any coordinate s h i f t s output are sub tracted from those s h i f t s output by the F Q synthesis. b. Method of Least Squares. The p r i n c i p l e of least squares proposes that the values of a set of variables which best s a t i s f y a set of some what inconsistent observations are such as to make the sum of the squares of the errors a minimum. If we have a set of m variables q, each a l i n e a r function of x,y,z,...» and each with an error E, then we have a set of m equations of the form 22 According to the method of least squares 2E2. must be made a minimum, hence = 2 2(ajX + bjy + C j Z + . . . - = 0 and s i m i l a r l y f o r TOSE . 2 and d^E 2 j J . .3 J "2>y Rewriting, we may obtain the following matrix equation 6 2 a ^  c ^  ., 2b i c i . * Z a - q A J J : 7 The above are known as the normal equations, and: since there are n equations i n n unknowns, the desired values of x,y,z,... can be determined. This scheme was f i r s t applied to finding the values of the atomic coordinates of a structure which b e s t . f i t the ( observed F's by Hughes (23) and i s done i n the following manner: Each calculated F i s computed by the r e l a t i o n F = 2 f e ^ ' ^ + k y r + ^ z r ) C r r Here the variables are exponentials i n xyz and i n order to be usable must be transformed into l i n e a r functions. This i s done by using the f i r s t two terms i n Taylor's series as was done i n the method of D i f f e r e n t i a l Synthesis. We then have, following the method used i n the previous section: 23 AF - F 0-F c - f(x+ex, y+£y, z+£z) - f(x,y,z) « F ^Fc+e,SFc+€ 3 F c ) - F This summation i s taken over the R atoms of the structure, When the observational error i s added to each equation above the set of equations can be recast into the form from which the normal equations can be derived. Refinement by least squares has a number of advantages. It i s free of the series-termination errors which characterize Fourier methods; i t i s possible to use less than a l l the F*s in the r e f i n i n g process; i t i s possible to use a weighting func t i o n , w, and minimize 2w( | F Qj - |FC j ) 2 ; and i t i s possible to include a scale factor and isotropic and/or anisotropic tempera ture factors i n the refinement process. With the advent of high speed computers, the method of least squares has become a very popular means of structure refinement. PART I I THREE-DIMENSIONAL REFINEMENTS OF THE STRUCTURES OF PERYLENE AND PYRENE I. THE CRYSTAL AND MOLECULAR STRUCTURE OF PERYLENE Introduction Perylene (I) i s one of the simplest examples of a type of polynuclear aromatic hydrocarbon which contains formally single bonds. Nine non-excited valence bond structures can be drawn for the molecule and these simply represent combinations of the three possible Kekule structures f o r each naphthalene nucleus, the central peri-bonds being single i n every case." The c r y s t a l structure has been determined from projections along two axes (24), but neither of the projections was well resolved. As a consequence the accuracy was not very high, but af t e r averaging in accordance with the expected molecular symmetry the bond lengths could be determined to within about - 0.04 The resu l t s showed that the two bonds connecting the two naphtha lene nuclei were unusually long (1.50 X) , and they were thus about the length suggested by Coulson (25) f o r a C(sp )-C(sp ) single bond distance. A more recent estimate of such a single bond length i s 1.48 %. (26), t h i s estimate being based on the lengths i n molecules such as butadiene. 26 A more r e c e n t a n d more d e t a i l e d a n a l y s i s o f t h e a n a l o g o u s m o l e c u l e q u a t e r r y l e n e (27) h a s shown t h a t t h e a v e r a g e l e n g t h o f t h e s i x p e r i - b o n d s i n t h i s m o l e c u l e i s 1.527 - 0.005 X. T h i s . o a p p e a r s t o be s i g n i f i c a n t l y l o n g e r t h a n 1.48 A, and l o n g e n o u g h t o s u g g e s t t h a t t h e p e r i - b o n d s a r e s i n g l e b o n d s and t h a t a r o m a  t i c c h a r a c t e r i s l o c a l i z e d w i t h i n e a c h n a p h t h a l e n e r e s i d u e . D i s c r e p a n c i e s b e t w e e n t h e s e m e a s u r e d d i s t a n c e s a n d t h o s e p r e  d i c t e d b y m o l e c u l a r - o r b i t a l t h e o r y f o r t h e p e r i - b o n d s have l e d t o t h e s u g g e s t i o n t h a t a new bond o r d e r ~ - ~ b o n d l e n g t h ' c o r r e l a  t i o n c u r v e be c o n s i d e r e d f o r t h i s t y p e o f m o l e c u l e ( 2 8 ) , The m e a s u r e d p e r i - b o n d d i s t a n c e s i n q u a t e r r y l e n e a r e c e r t a i n l y l o n g e r t h a n c u r r e n t t h e o r y p r e d i c t s , so t h a t a more a c c u r a t e a n a l y s i s o f p e r y l e n e , t h e f i r s t member o f t h e p e r y l e n e - t e r r y l e n e - q u a t e r r y l e n e s e r i e s , i s o f i n t e r e s t t o d e t e r m i n e w h e t h e r s u c h a n o m a l o u s l y l o n g b o n d s a r e p r e s e n t i n p e r y l e n e a l s o . D o n a l d s o n , R o b e r t s o n a n d W h i t e (24) n o t e d t h a t f o r a c c u  r a t e b o n d - l e n g t h m e a s u r e m e n t s i t w o u l d be n e c e s s a r y t o e m p l o y t h r e e - d i m e n s i o n a l m e t h o d s , a n d t h a t t h e i r t w o - d i m e n s i o n a l s u r v e y was " a n e c e s s a r y p r e l i m i n a r y t o a n y s u c h u n d e r t a k i n g . " The p r e s e n t w o r k i s a d e t a i l e d a n a l y s i s b a s e d on new t h r e e - d i m e n s i o n a l i n t e n s i t y d a t a . E x p e r i m e n t a l The c r y s t a l s o f p e r y l e n e u s e d i n t h e p r e s e n t i n v e s t i g a t i o n w e r e t h i c k y e l l o w p l a t e s w i t h (001) d e v e l o p e d , a n d s m a l l e r { 1 1 0 } f o r m s . The u n i t c e l l p a r a m e t e r s w e r e d e t e r m i n e d f r o m t h e B r a g g a n g l e s o f h i g h - o r d e r . r e f l e x i o n s m e a s u r e d on t h e G.E, S p e c t r o -27 g o n i o m e t e r w i t h CuKtt r a d i a t i o n . C r y s t a l d a t a (AcuKo^ = 1.54051 X,ACUK^2 = 1.54433 £ ) . P e r y l e n e , C 2 oHi2; m o l . w t . = 252.3; m.p. - 268°C. M o n o c l i n i c , a - 1 1 . 2 7 ^ 0 . 0 1 , b = 1 0 . 8 2 ^ 0 . 0 1 , c » 1 0 . 2 6 3 * 0 . 0 1 X, (3- 1 0 0 . 5 5 O ± 0 o 0 2 ° . Volume o f t h e u n i t c e l l » 1231.78 t . D x ( w i t h Z = 4) - 1.360 gem" 3. D m ( D o n a l d s o n , R o b e r t s o n & W h i t e ) = 1.322 gem . A b s o r p t i o n c o e f f i c i e n t s f o r X - r a y s , A= 1.5418 A y^U.** 7cm 1 . A= 0.7107 0.9 cm" 1. T o t a l number o f e l e c t r o n s p e r u n i t c e l l = F(000) = 528. A b s e n t s p e c t r a : h0i> when h i s o d d , OkO when k i s o d d . S p a c e g r o u p i s P2 1/a(c| h). P r e l i m i n a r y W e i s s e n b e r g f i l m s i n d i c a t e d a r a p i d f a l l o f f i n i n t e n s i t y w i t h i n c r e a s i n g B r a g g a n g l e . The i n t e n s i t i e s o f a l l r e f l e x i o n s w i t h 2 e M o K a 4 4 0 0 ( c o r r e s p o n d i n g t o a minimum i n t e r p l a n a r s p a c i n g d = 1.04 X) w e r e m e a s u r e d on a G e n e r a l E l e c t r i c XRD -5 S p e c t r o g o n i o m e t e r w i t h S i n g l e C r y s t a l O r i e n t e r , u s i n g a s c i n t i l l a t i o n c o u n t e r a n d MoKcx r a d i a t i o n , a n a p p r o x i  m a t e l y m o n o c h r o m a t i c beam b e i n g o b t a i n e d by u s e o f a z i r c o n i u m f i l t e r a n d p u l s e h e i g h t a n a l y s e r . The m o v i n g c r y s t a l - m o v i n g c o u n t e r t e c h n i q u e (29) was u s e d . A l l t h e i n t e n s i t i e s w e r e 28 corrected f o r background, which was found to be a function of 6 only, Lorentz and po l a r i z a t i o n factors were applied and the structure amplitudes 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 O axis of the goniostat, and had dimensions 0.5 mm. p a r a l l e l to [110] and 0.2 mm. p a r a l l e l to c*; absorption was low and no corrections were applied. Six hundred and seventy-nine reflexions i n the range 0<26^40° were observed, representing 60% of the t o t a l number of reflexions in t h i s range. The range of i n t e n s i t i e s recorded was 2 - 9090 on a r e l a t i v e scale; however since the background count was never less than 6, i n t e n s i t i e s less than about 9 were considered to be rather unreliable, and only those 436 reflexions with intensity 9 or greater were used in the refinement process. Refinement of the Structure The parameters used as the s t a r t i n g point in the r e f i n e  ment were the carbon p o s i t i o n a l coordinates O f Donaldson, Robertson and White, together with the scattering factor f o r carbon of the International Tables, Vol. I l l (1), corrected f o r thermal v i b r a t i o n as usual, with B = 5.5 The discrepancy fact o r , R, was 15.8% f o r the 436 reflexions used. The carbon atom p o s i t i o n a l and iso t r o p i c thermal parameters, together with an o v e r a l l scale factor, were refined by le a s t squares, using a program f o r the IBM 1620 computer (30). The function minimized was 2w(F 0 - F c ) 2 , with(w~ = F Q/20 when Fo<20, and J*w = 20/F Q when FQ>20. The f i r s t cycle decreased R to 12.5% (Table I I I ) , but 29 TABLE I I I PROGRESS OF REFINEMENT Parameters R % Donaldson, Robertson and White (24) 15.8 1st Least Squares 12.5 2nd Least Squares 16.0 1/2-shifts oh 1st Least Squares 11.4 1st D i f f e r e n t i a l Syntheses (C atoms) 10.8 2nd D i f f e r e n t i a l Syntheses (C atoms) 10.6 2nd D i f f e r e n t i a l Syntheses + id e a l H positions 8.3 3rd D i f f e r e n t i a l Syntheses (C + H atoms) 8.1 4th D i f f e r e n t i a l Syntheses (C + H atoms) 8.1 the second cycle resulted i n an increase to 16.0% and exami nation of the s h i f t s in the f i r s t and second cycles indicated c l e a r l y that.the coordinates were o s c i l l a t i n g , and that a f r a c t i o n a l s h i f t would be.required to ensure convergence. Application of one-half the indicated s h i f t s of the f i r s t least squares cycle reduced R to 11,4%. Further refinement proceeded by the d i f f e r e n t i a l synthesis method using calculated syntheses to apply "backshift" corrections to the atomic coordinates (31, 32), and corrections to the thermal parameters. Two cycles reduced R successively to 10.8% and 10,6% (Table I I I ) . At t h i s stage contributions from the hydrogen atoms were introduced; p o s i t i o n a l parameters were obtained by assuming that the atoms lay on the r i n g diagonals with C-H distances 1.08 2, and the International Tables Vol. I l l scattering curve was used, with B = 7.0 i 2 for a l l the hydrogen atoms. R was reduced to 8.3%. A t h i r d cycle of observed and calculated d i f f e r e n t i a l syntheses was carried out, i n which the p o s i t i o n a l and isotro p i c thermal parameters of the carbon atoms, and the po s i t i o n a l parameters of the hydrogen atoms were refined. The 30 hydrogen atom peak electron densities were in the range 0,47 - 0.89 eS 3 and the s h i f t s in the hydrogen positions were reasonably small, but the curvatures were u n r e a l i s t i c in some cases, a few having posi t i v e values. R was reduced by these changes to 8.1%. A fourth and f i n a l cycle suggested n e g l i g i b l e changes i n carbon atom p o s i t i o n a l and thermal parameters, the maximum coordinate s h i f t s being 0.0034, 0.0032, and 0.0031 X along x,y, and z respectively, and the mean s h i f t s 0.0012, 0.0015, and 0.0014 X. Further small changes in hydrogen posi tions were indicated. Application of these various s h i f t s l e f t R unchanged at 8.1% (Table I I I ) . The f i n a l observed and calculated structure factors are l i s t e d i n Table A l ; the R factor f o r the 436 observed r e f l e x  ions which were included i n the refinement i s 8.1%. Also included i n Table A l are measured and calculated structure factors f o r the 243 weak reflexions which were omitted from the refinement process and f o r the 456 unobserved reflexions i n the range 0 < 2 6 < 4 0 ° . The f i n a l observed and calculated electron densities and curvatures at the carbon positions are l i s t e d i n Table IV; the excellent agreement between the observed and calculated curvatures i n each of the x,y, and z directions indicates that there i s no s i g n i f i c a n t thermal anisotropy for any of the atoms. The observed and calculated electron densi t i e s of the hydrogen atoms are given i n Table V. Coordinates 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 VI, 31 TABLE IV CARBON ATOM PEAK ELECTRON. DENSITIES (e.S~3) AND CURVATURES (e.S'5) FROM FINAL CYCLE <? --tfp/ax.1 -^p/dy1 -dxp/az* Atom Obs Calc Obs Calc Obs Calc Obs Calc C 1 4.36 4.35 21.8 20.7 19.4 19.4 20.9 20.7 2 4.07 4.19 19.7 19.6 17,5 17.9 17.6 17.8 3 4.86 4.89 27.2 26.2 25.5 24.5 23.9 23.6 4 4.72 4.81 23.9 23.5 24.4 24.2 25.8 25.4 5 4.32 4.42 21.0 21.1 21.3 21.0 22.1 22.2 6 4.53 4.59 22.9 22.4 20.1 20.7 25.1 24.7 7 5.03 5.09 26.0 25.3 26.2 25.6 29.1 28.5 8 5.65 5.71 32.2 31.2 31.1 30.2 34.6 33.5 9 5.40 5.40 30.2 28.9 29.7 28.4 31.9 31.0 10 5.33 5.40 29.3 28.4 29.6 28.8 31.8 31.2 11 4.32 4.38 23.0 22.6 19.2 19.0 21.8 21.5 12 4.22 4.40 20.1 20.6 19.3 19.6 20.9 21.5 13 4.42 4.54 20.9 20.7 21.0 21.0 23.2 23.0 14 4.56 4.68 22.7 22.7 23.2 22.9 26.5 25.8 15 4.33 4.40 18.8 18.9 21.0 20.6 22.7 22.0 16 4.53 4.44 23.1 21.8 21.2 20.2 24.2 23.0 17 4.87 4.98 25.9 25.1 24.4 24.0 27.1 26.5 18 5.69 5.75 • 32.5 31.1 32.1 31.2 34.2 33.3 19 5.52 5.60 ' 32.8 31.6 29.8 28.8 33.7 32.5 20 5.40 5.44 30.0 28.9 30.1 28.7 35.1 34.2 TABLE V HYDROGEN ATOM PEAK ELECTRON DENSITIES (e.£~3) FROM FINAL CYCLE Atom Obs Calc Atom Obs Calc H 1 0.67 0.73 H 11 0.68 0.82 2 0.50 0.45 12 0.52 0.59 3 0.68 0.75 13 0.78 0.78 4 0.78 0.78 14 0.57 0.61 5 0.47 0.59 15 0.89 0.81 6 0.55 0.61 16 0.68 0.68 32 TABLE VI FINAL POSITIONAL FRACTIONAL COORDINATES, x,y,z, AND ORTHOGONAL COORDINATES(X), X',Y,Z' Atom X y z X' Y Z' C 1 0.2624 -0.0474 0.3816 2.2383 -0.5138 3.8525 2 0.3005 0.0432 0.3070 2.8083 0.4683 3.0994 3 0.2636 0.0447 0.1683 2.6537 0.4845 1.6991 4 0.1796 0.0428 -0.1185 2.2473 0.4640 -1.1963 5 0.1417 0.0386 -0.2582 2.0834 0.4184 -2.6067 6 0.0668 -0.0530 -0.3175 1.3510 -0.5745 -3.2054 7 0.0266 -0.1456 -0.2398 0.7515 -1.5783 -2.4210 8 0.0651 -0,1452 -0.0996 0.9213 -1.5740 -1.0055 9 0.1446 -0.0493 -0.0386 1.7024 -0.5344 -0.3897 10 0.1857 -O.O466 0.1050 1.8950 -0/5051 1.0601 11 -0.0517 -0.2387 -0.2959 -0.0252 -2.5875 -2.9873 12 -0.0923 -0.3274 -0.2198 -0.6261 -3.5490 -2.2190 13 -0.0547 -0.3285 -0.0798 -0.4661 -3.5609 -0.8056 14 0.0260 -0.3232 0.2057 -0.0945 -3.5035 2.0767 15 0.0664 -0.3217 0.3450 0.0984 -3.4872 3.4830 16 0.1451 -0.2319 0.4021 0.8777 -2.5138 4.0595 17 0.1841 -0.1419 0.3239 I.4646 -1.5382 3 .2700 18 0.1452 -0.1404 0.1842 1.2894 -1.5219 1.8596 19 0.0652 -0.2353 0.1251 0.4991 -2.5507 1.2630 20 0.0254 -0.2366 -0.0204 0.3247 -2.5647 -0,2060 H 1 0.290 -0.046 0.493 2.3386 -0.4986 4.9762 2 • 0.358 0.114 0.367 3.3384 1.2379 3.7011 3 0.297 0.120 0.108 3.1477 1.3008 1.0934 4 0.243 0.114 -0.070 2.8686 1.2401 -0.7087 5 0.173 0.111 -0.325 2.5560 1.2043 -3.2791 6 0.038 -0.063 -0.423 1.2248 -0.6829 -4.2745 11 -0.078 -0.236 -0.402 -0.1238 -2.5626 -4.0534 12 -0.153 -0.400 -0.266 -1.2217 -4.3382 -2.6814 13 -0.086 -0.400 -0.016 -0.9415 -4.3317 -0,1605 14 -0.037 -0.393 0.161 -0.7205 -4.2590 1.6264 15 0.033 -0.399 0.412 -0.4030 -4.3262 4.1584 16 0.179 -0.232 0.512 1.0501 -2.5181 5.1710 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', o Y, Z' coordinates i n A referred to orthogonal axes a. b. and c*. The parameters for carbon and hydrogen are those of the fourth 33 d i f f e r e n t i a l cycle. The hydrogen coordinates are not considered to be p a r t i c u l a r l y accurate, since a structure factor calcula t i o n with hydrogens positioned on the rin g diagonals with C - H = 1.08 X gave the same discrepancy factor (8.1%) as the observed hydrogen atom positions; however the positions must be at least approximately correct, since omission of hydrogen con t r i b u t i o n s increases R by about 2%, and the electron densities at the hydrogen positions are reasonable (0.47 - 0.89 e.X 3 , Table V; the standard deviation of the electron density being o-3, 0.08 e.A ). Table VII l i s t s the standard deviations of the atomic p o s i t i o n a l coordinates calculated from Cruickshank's (33) formulae, with the reflexions used i n the refinement pro cess only, and the thermal parameters. The increase i n B values with distance from the molecular center must be a result of i n t e r n a l v i b r a t i o n rather than rigid-body v i b r a t i o n s , since thermal anisotropy i s small. TABLE VII STANDARD DEVIATIONS OF FINAL COORDINATES (X) , THERMAL PARAMETER (X2), AND DEVIATIONS ( A ) FROM THE MEAN MOLECULAR PLANE Atom cT(x) <f(y) C(z) B 0, ^(A) C 1 0.0065 0.0073 0.0058 5.98 -0.0112 2 0.0071 0.0080 0.0068 5.72 0.0061 3 0.0052 0.0055 0.0051 5.39 0.0039 4 0.0059 0.0058 0.0047 5.58 0.0394 5 0.0067 0.0068 0.0055 5.95 0.0088 6 0.0061 0.0070 0.0048 5.63 -0.0149 7 0.0054 0.0054 0.0041 4.91 -0.0173 8 0.0044 • 0.0045 0.0035 4.13 -0.0144 9 0.0046 0.0048 0.0038 4.33 -0.0023 10 0.0048 0.0048 0.0038 4.25 -0.0005 34 TABLE VII (continued) Atom 6(x) 6-(y) 6(z) B A(X) C 11 0.0061 0.0073 0.0055 5.47 -0.0109 12 0.0070 0.0073 0.0058 5.56 0.0103 13 0.0067 0.0067 0.0052 5.28 0.0119 14 0.0062 0.0060 0.0046 5.26 0.0244 15 0.0075 0.0067 0.0053 5.23 0.0143 16 0.0061 . 0.0067 0.0050 5.91 -0.0136 17 0.0054 0.0058 0.0045 4.65 -0.0174 18 0.0043 0.0044 • 0.0035 3.98 -0.0037 19 0.0043 0.0047 0.0036 4.10 -0.0003 20 0.0047 0.0047 0.0035 4.22 -0.0102 H 1 0.026 2 0.069 3 0.004 4 0.020 5 0.002 6 -0.078 11 > 0.05 0.05 0.05 7.00 < -0.021 12 0.004 13 0.027 14 0.063 15 0.014 16 -0.048 J The bond distances i n the molecule, and t h e i r standard deviations estimated from the equation of Ahmed and Cruickshank (32) are shown in Figure 5. The valency angles, and standard deviations estimated from the expression i n the International Tables, Vol. I I , are given i n Figure 6. Since thermal anisot- .ropy was n e g l i g i b l e , no corrections f o r errors due to rota- t i o n a l o s c i l l a t i o n s were required (34). The best plane through the 20 carbon atoms of the mole cules whose coordinates are l i s t e d i n Table VI, has equation -0.81746 X' + 0.56751 Y + 0.09841 Z' + 1.73098 - 0 The deviations of the atoms from t h i s plane are l i s t e d i n the H H 35 1.13 16./ 1.13 H 1.420 ( . 0 0 7 ) 1.421 ( . 0 0 6 ) H 1 . 4 0 9 ( . 0 0 9 ) H 1.479 ( . 0 0 5 ) L 4 6 3 ( . 0 0 5 ) 7^4 1.423 ( . 0 0 8 ) H 1 . 4 2 6 ( . 0 0 5 ) 1.421 ( . 0 0 7 ) Figure 5- Measured bond lengths (2), with standard deviations (A*) in parentheses. I 2 0 J U 2 I . 0 119.0 1 2 2 . 5 H H Figure 6. Measured valency angles (degrees). 6"= 0.k° to .0-7 f o r G-C-C .angles. 37 l a s t column of Table VII. The orientation of the molecule in the unit c e l l i s given i n Table V I I I i n terms of the angles which the molecular axes L, M (see Figure 7) and the plane normal, N, make with the orthogonal system. The axis L was taken through atoms C7 and C17, and axis M through the midpoints of bonds 9-10 and 19-20. L, M, and N are almost exactly mutually perpendicular, the angles between them being ZLM » 90.1°, ZMN » 89.9°, and <£LN = 90.0°. Previous values of the orientation angles (24) are included i n Table V I I I f or comparison. TABLE VIII ORIENTATION OF THE MOLECULE IN THE CRYSTAL Donaldson, Robertson Present and White (24) analysis X L 83.3° 82.9° ^L 89.2 89.6 U)L 6.8 7.2 XM 55.4 55.9 35.0 34.5 >^M 94.5 94.5 XN 144.5 144.8 YN 55.0 55.4 u>N 84.9 84.4 The carbon-carbon intermolecular separations less than 4 X are given i n Table IX; a l l these contacts correspond to normal van der Waals interactions. The perpendicular distance between the planes of molecules related by a center of sym metry i s 3.46 2. 39 TABLE IX SHORTEST INTERMOLECULAR CONTACTS (2) BETWEEN CARBON ATOMS A l l c r y s t a l l o g r a p h i c a l l y independent C....C contacts 4 4.0 A between a standard molecule (1) and neighbouring molecules are l i s t e d . Molecule 1 x, y, z 2 x, y, 1+z 3 -x, -y, -z 5 1/2-x, 1/2+y, -z 6 1/2-x, 1/2+y, 1-z 12 1/2+x, -1/2-y, z Dm to Atom in Molecule d Atom to Atom i n Molecule d 1 6 3 3 .806 4 19 3 3.450 1 7 3 3.920 4 19 5 3.760 1 11 3 3.907 4 20 3 3.605 1 15 6 3.950 5 12 12 3.735 1 15 12 3.790 5 14 3 3.709 2 7 3 3.790 5 14 5 3.977 2 11 3 3.500 5 15 3 3.866 2 11 5 3.706 5 15 5 3.871 2 12 3 3.877 5 16 3 3.908 2 12 5 3.829 5 16 5 3.931 2 14 12 3.768 5 17 3 3.779 2 15 6 3.899 5 18 3 3.626 2 15 12 3.804 5 19 3 3.609 2 16 6 3.817 6 16 3 3.903 3 7 3 3.649 6 17 3 3.521 3 8 3 3.801 6 18 3 3.630 3 11 3 3.604 7 10 3 3.633 3 12 3 3.711 7 17 3 3.917 3 12 5 3.899 7 18 3 3.754 3 13 3 3.879 8 9 3 3.644 3 13 5 3.817 8 10 3 3.501 3 14 12 3.774 8 18 3 3.899 3 20 3 3.928 9 9 3 3.653 3 20 5 3.861 9 10 3 3.804 4 12 12 3.758 9 13 12 3.734 4 13 12' 3.753 9 18 3 3.917 4 14 3 3.827 9 19 3 3.889 4 14 5 3.874 9 20 3 3.751 4 18 3 3.751 10 20 3 3.883 16 6 2 3.710 Discussion The deviations of the carbon atoms from the best molecular plane (Table V I I ) , although they are small, are highly s i g n i f i  cant, since X 2 = 145 and for i) = 17, P«0.001 (for "t> =17 and 2 P = 0,001, X = 40.79 only). Furthermore closer examination of the displacements (Figure 7) reveals that they follow a regular pattern, those atoms furthest from the molecular L-axis being displaced in a positive d i r e c t i o n (towards the o r i g i n of the c e l l ) and those closer to the L-axis being displaced i n a negative d i r e c t i o n from the mean plane. The molecule i s thus very s l i g h t l y , but s i g n i f i c a n t l y , bow-shaped, the d i s t o r t i o n involving a bending about the L-axis. To explain t h i s bending of the molecule i t i s necessary to decide whether i t i s a resul t of i n t r a - or intermolecular s t e r i c effects (or both). There may be some intramolecular overcrowding i n a planar model f o r the perylene molecule due to close approaches between atoms H3 and H4, and H13 and H14 (the 1,12 and 6,7 positions i n the usual chemical numbering), and these s t e r i c repulsions could be relieved by displacements of these atoms, and smaller displacements of the carbon atoms, from a s t r i c t l y planar arrangement. It i s quite evident from Figure 7 however that the observed displacements are not due to any such intramole cular e f f e c t s , as the deviations of C3, C4, C13, and C14 are a l l i n the same dire c t i o n and hence would not relie v e i n t r a  molecular s t e r i c s t r a i n . The hydrogen displacements have been measured less p r e c i s e l y , but suggest the same conclusions. Any intramolecular s t e r i c repulsions between hydrogen atoms could indeed be more re a d i l y relieved by in-plane displacements, as observed i n biphenyl (35, 36, 37). The H3-H4 and H13-H14 41 separations are 1.80 and 1.82 X respectively; again the hydro gen positions are not s u f f i c i e n t l y precisely determined to draw de f i n i t e conclusions, but i t does appear that in-plane hydrogen displacements from a regular model are also small. The four perylene molecules in the unit c e l l are grouped in pairs about centers of symmetry, so that the mean planes of the molecules i n each pair are p a r a l l e l , and the perpendicular distance between the planes i s 3.46 X, Examination of the intermolecular distances (Table IX) reveals that a l l the shortest contacts are between molecules related by a center of symmetry (molecules 1 and 3 i n Table IX). When the centro- symmetrically related molecules are projected on t h e i r own plane i t i s found that the carbon atoms do not l i e d i r e c t l y over one another but are staggered as shown i n Figure 8, there being 8 contacts of 3.52 2 or le s s . The s l i g h t bending of the molecules allows the pair of perylene molecules to pack toget her more compactly (this i s i l l u s t r a t e d schematically i n Figure 9), and there seems l i t t l e doubt that the observed molecular d i s t o r t i o n i s a re s u l t of intermolecular forces. The largest displacement from the mean molecular plane i s for atom C4, and t h i s atom i s involved i n the shortest intermolecular sepa ration i n the c r y s t a l (3.45 X) . A l l the l a t e r a l contacts are larger, the shortest being 3.71 X. The differences between chemically equivalent bond lengths are small (Figure 5), but one or two are i n the possibly- s i g n i f i c a n t region, and may be r e a l , and a consequence of the s l i g h t molecular d i s t o r t i o n described above. However, for com-42 Figure.8. Normal p r o j e c t i o n of two p a r a l l e l molecules. Figiire 9- Perspective drawing of two p a r a l l e l molecules. The tending of the molecules i s g r o s s l y exaggerated f o r c l a r i t y . 44 parison with th e o r e t i c a l values the measured bond lengths which are chemically equivalent were averaged according to t h e i r estimated standard deviations assuming (or ^.y) symmetry, and the mean values are given i n Table X. Also l i s t e d i n TABLE X MEAN MEASURED AND CALCULATED BOND LENGTHS (£) IN PERYLENE, AND MEASURED LENGTHS IN QUATERRYLENE Perylene Measured Perylene Calculated _ A Bond . (Fig.7) A. m 6"m (1) (2) (3) (4) (5) Quater rylene Measured (6) >m a . 1.370 0.005 0.002 1.375 1.375 1.387 1.376 1.366 1.374 b 1.418 0.004 0.003 1.421 1.421 1.401 1.398 1.419 1.425 c 1.397 0.004 0.004 1.375 1.375 1.398 1.393 1.373 1.384 d 1.425 0.003 0.006 1.421 1.421 1.423 1.430 1.442 1.403 e 1.424 0.004 0.002 1.421 1.421 1.422 1.432 1.413 1.431 f 1.400 0.004 0.005 1.421 1.421 1.416 1.422 1.436 1.392 g 1.471 0.004 0.006 1.500 1.477 1.444 1.473 1.485 1.527 A = Measured r calculated . A a b c d e f g R.M.S. A over whole molecule -0.005 -0.005 -0,017 -0.006 -0.003 -0.003 0.017 0,020 0.022 0.022 -0.001 0,004 0.004 0.004 0.002 -0.005 0.003 0.003 0.002 -0.008 -0.021 -0.021 -0.016 -0.022 -0.029 -0.006 0.027 -0.002 0.004 •0.001 0.026 -0.017 0.011 -0.036 -0.014 0.015 0.013 0.014 0.013 0.020 (1) .(2) (3) (4) (5) (6) Valence-bond method, With single-bond = 1.50 X. Valence-bond method, with single-bond = 1.477 A . M.O. (Baldock, Berthier and Pullman 1949). M.O. (Goodwin I960 - f i r s t i t e r a t i o n ) . M.O. (Goodwin I960 - t h i r d i t e r a t i o n ) . Shrivastava and Speakman I960. -0.004 -0.007 0.013 0.022 -0.007 0.008 •0.056 Table X are the standard deviations of the mean values, c m / 4 5 / b e i n g c a l c u l a t e d f r o m t h e s t a n d a r d d e v i a t i o n s o f t h e p o s i t i o n a l p a r a m e t e r s ( T a b l e VII and F i g u r e 5), a n d 6"^  b e i n g d e r i v e d d i r e c t l y f r o m t h e d e v i a t i o n s b e t w e e n t h e i n d i v i d u a l m e a s u r e d v a l u e s a nd t h e means. The g e n e r a l a g r e e m e n t b e t w e e n t h e t w o d i f f e r e n t e s t i m a t e s o f t h e s t a n d a r d d e v i a t i o n s i s a n i n d i c a t i o n t h a t t h e a c c u r a c y q u o t e d i s r e a l i s t i c ; f o r b o n d s o f t y p e s d a n d g, t h e s l i g h t l y h i g h e r v a l u e s o f r5"m t h a n g a r e a c o n s e  q u e n c e o f t h e p o s s i b l y - s i g n i f i c a n t d i f f e r e n c e s i n m e a s u r e d d i s t a n c e s . F o r c o m p a r i s o n w i t h t h e s e m e a s u r e d d i s t a n c e s , t h e t h e o r e t i c a l b o n d l e n g t h s were d e r i v e d f r o m t h e n i n e n o n - e x c i t e d v a l e n c e b o nd s t r u c t u r e s ; l e n g t h s c a l c u l a t e d b y t h e m o l e c u l a r o r b i t a l m ethod a r e a l s o a v a i l a b l e ( T a b l e X ) , Two d i f f e r e n t d o u b l e - b o n d c h a r a c t e r b o nd l e n g t h c o r r e l a t i o n s w e r e u s e d f o r t h e v a l e n c e - b o n d m e t h o d , t h e f i r s t c u r v e p a s s i n g t h r o u g h t h e p o i n t s f o r e t h y l e n e , b e n z e n e a n d g r a p h i t e , a nd u s i n g 1.50 £ a s t h e s i n g l e - b o n d d i s t a n c e (25), a n d t h e s e c o n d t h e c o r r e l a t i o n u s e d b y C r u i c k s h a n k a n d S p a r k s (38) , w h i c h t a k e s 1.477 X a s t h e s i n g l e - b o n d d i s t a n c e . T h r e e s e t s o f m o l e c u l a r o r b i t a l d i s t a n c e s a r e a v a i l a b l e ; t h e f i r s t two were c a l c u l a t e d b y t h e s i m p l e H u c k e l m e t h o d , b u t t h e f i r s t s e t was d e r i v e d f r o m a o s m o o t h c o r r e l a t i o n c u r v e , w i t h 1.54 A a s t h e s i n g l e b o n d d i s  t a n c e (39) a n d t h e s e c o n d s e t (28) f r o m a d i f f e r e n t c u r v e (40). The t h i r d M.O. b o n d l e n g t h s w e r e c a l c u l a t e d w i t h a l l o w a n c e f o r v a r i a t i o n o f r e s o n a n c e i n t e g r a l w i t h b o n d d i s t a n c e ( 2 8 ) . The g e n e r a l v a r i a t i o n o f t h e m e a s u r e d d i s t a n c e s i s f a i r l y w e l l r e  p r o d u c e d i n a l l t h e s e t s o f c a l c u l a t e d v a l u e s , b u t t h e r e a r e some i n d i v i d u a l d i s a g r e e m e n t s , p a r t i c u l a r l y f o r b o n d f , f o r 46 which the measured distance i s less than any of the theoreti c a l values. The measured distance of the peri-bond (g) agrees best with Dewar and Schmeising's (26) single-bond length, or with the M.O. distance derived from Goodwin and Vand's (40) correlation curve. In an o v e r a l l comparison the most s o p h i s t i  cated calculated lengths (method (5) i n Table X) show the poorest agreement with the measured distances, while the simple valence-bond method gives quite reasonable agreement. Table X shows also a comparison between the measured bond lengths i n perylene, and average values f or s i m i l a r types of bonds i n quaterrylene (27). The agreement between the values in the two molecules i s on the whole extremely close; bond f, which i n perylene (1.400 - 0.00.5 X) i s shorter than any of the calculated values f o r that bond (1.416 - 1.436 X), i s also short i n quaterrylene (1.393 - 0.009 X) . The largest d i f f e r  ence i s for the peri-bonds, 1.471 - 0.005 X i n perylene and 1.527 - 0.005 X in quaterrylene so that the difference i s 86" and highly s i g n i f i c a n t , and these are just the bonds whose lengths are most important i n t h i s type of molecule. The in d i v i d u a l measured bond distances i n quaterrylene are probably not p a r t i c u l a r l y accurate, since i n the p r i n c i p a l projection 120 p o s i t i o n a l and thermal parameters have been determined from 127 observed reflexions (27) but the value of 1.527 X f o r the peri-bonds i s an average of s i x independent measurements, and i s therefore more r e l i a b l e . Shrivastava and Speakman have sug gested, on the basis of the length of the peri-bonds i n quater- o rylene, f i r s t that the single-bond distance of 1.479 A suggested 47 by Dewar and Schmeising (26) i s not a proper one to use i n discussing p o l y c y c l i c aromatic molecules, and secondly that the peri-bonds in quaterrylene are single-bonds, perhaps leng thened somewhat by intramolecular s t e r i c repulsions, with aro matic character being confined to the naphthalene residues. The peri-bonds in perylene, 1.471 ± 0.005 X, are consi derably shorter than 1.50 X, and s l i g h t l y , although only possibly s i g n i f i c a n t l y , shorter than Dewar and Schmeising's ... o (26) single bond value of 1.479 A. This, while not proving that 1.479 S i s the value to use f o r the single bond length i n th i s type of molecule, does suggest that Dewar and Schmeising's estimate i s not unreasonable. In addition the measured p e r i - bond distances suggest that benzenoid character i n perylene i s probably not completely l o c a l i z e d in the naphthalene residues but tends to be spread over the whole molecule. Further sup port f o r t h i s conclusion i s obtained from a comparison of other bond distances in perylene with those which might be predicted from non-interacting naphthalene residues; bond c(1.398 ± 0.004 t) i s considerably longer than bond a(1.370 ± 0.005 A5), suggesting that the electron d i s t r i b u t i o n i n the naphthalene residues i s being disturbed by in t e r a c t i o n . Goodwin (28) has attempted to account f o r the long p e r i - distances in quaterrylene by deriving a new order-length cor r e l a t i o n curve; t h i s curve however leads to a length of 1.56 X f o r the peri-bonds in perylene, and i s therefore untenable. There seems l i t t l e reason that the peri-bonds in perylene and quaterrylene should be so d i f f e r e n t in length, and further 48 investigation of other molecules with s i m i l a r types of bonds is apparently necessary to obtain more data before conclusions about single-bond distances in t h i s type of molecule can be drawn. It might be noted that the peri-bonds in quaterrylene are about the same length as the bonds joining the six-membered rings in biphenylene (1 .52 - 0.018 X) (41), these bonds being part of a four-membered r i n g and therefore under considerable s t r a i n . The hydrogen atom positions i n perylene have been deter mined rather imprecisely, so that the variations i n the C-H bond distances are not s i g n i f i c a n t . The mean value f o r the C-H length i s 1.11 X. A small dipole moment of 0.45 D has been reported f o r perylene (42), and i t i s tempting to interpret t h i s in terms of the small molecular d i s t o r t i o n described above. However th i s interpretation i s not j u s t i f i a b l e , since the observed d i s t o r t i o n i s almost c e r t a i n l y a resu l t of intermolecular con tacts while the dipole moment measurement was in d i l u t e benzene solution, where a si m i l a r d i s t o r t i o n i s un l i k e l y to be present. In addition the observed displacements are extremely small, and unl i k e l y to give a dipole moment as large as that reported. Examination of the dipole moment measurements indicates that the t o t a l molar pol a r i z a t i o n of perylene in benzene at i n f i n i t e d i l u t i o n i s 104 ccs; the electron p o l a r i z a t i o n estimated from the atomic r e f r a c t i v i t i e s i s 85.8ccs f and from the measured r e f r a c t i v e index 99.5 ccs. Bergmann, Fischer and Pullman take the orientation p o l a r i z a t i o n as (104 - 99.5) ccs, corresponding 49 to a dipole moment of 0.45 D, No correction was made f o r atom po l a r i z a t i o n , since t h i s decreases as the number of polar groups i n the molecule decreases. However since the atom polar i z a t i o n i s usually 5-10% of the electron p o l a r i z a t i o n , omission of such a correction could account for the whole of the difference between t o t a l and electron p o l a r i z a t i o n . I t i s f e l t therefore that i t has not been conclusively established that perylene possesses a permanent dipole moment. II. THE CRYSTAL AND MOLECULAR STRUCTURE OF PYRENE Introduction The c r y s t a l structure of pyrene (II) was determined by Robertson and White (43) from two projections, but resolution of the i n d i v i d u a l atoms was poor in both projections. As a re s u l t the accuracy was not very high, and the present work i s a more detailed analysis based on new three-dimensional data. Experimental Crystals of pyrene are thick colourless plates with (001) developed, and smaller [ l i o } forms. The unit c e l l para- meters were determined by least-squares treatment of the s i n 6 values of the cx-p c* 2-doublets of a number of high-angle r e f l e x  ions, f o r which the Bragg angles were measured on a G.E. Spec trogoniometer with CuKcx radia t i o n . C r y s t a l data (X(CuK(X 1) = 1.54051 £, XtCuKOg) = 1.54433 X) Pyrene, C l 6 H 1 0 ; M = 202.2; m.p. - 150°C. Monoclinic, a - 13.64 q ± 0.01, b = 9.25A - 0.01, c = 8.47n -0.01 X, ^ - 100.28° i 0.04°. U - 1052.9 X3 D m = 1.27, Z = 4, D x = 1.275 gem"3. Absorption c o e f f i c i e n t s f o r X-rays, X= 1.5418 X, 5.6 cm \ X= 0.7107 X, 0.8 cm"1. F (000) - 424 Absent spectra: h0j£ when h i s odd, OkO when k i s odd. Space group i s P2 1/a(c| n). Weissenberg films indicated a rapid f a l l off i n i n t e n s i t y with increasing Bragg angle. The i n t e n s i t i e s were measured on a G.E. Spectrogoniometer with a s c i n t i l l a t i o n counter and MoKoc rad i a t i o n , exactly as for perylene. Nine hundred and s i x t y - f i v e reflexions i n the range 0 <26(MoKoO < 50.2° (corresponding to a minimum interplanar spacing d = 0.84 &) were observed, 59% of the t o t a l number of reflexions i n t h i s range, but since the weak i n t e n s i t i e s were not considered to be very r e l i a b l e , the structure refinement was based only on those 550 reflexions with i n t e n s i t y greater than twice the background. Refinement of the Structure The carbon p o s i t i o n a l parameters of Robertson and White (43) were used as the s t a r t i n g point i n the refinement, with the scattering factor f o r carbon of the International Tables Vol. I l l , with B = 4.0 X2. The discrepancy fact o r , R, was 0.20 f o r the 550 reflexions included i n the refinement. The po s i t i o n a l and isotropic thermal parameters of the carbon atoms were refined as for pery l e n e , f i r s t by d i f f e r e n t i a l 52 syntheses. Contributions from hydrogen atoms were included a f t e r three cycles, assuming ideal positions on the r i n g diagonals with C-H «= 1.08 i\ and B = 8.0 X. The hydrogen atom pos i t i o n a l parameters were refined in the fourth cycle; the peak electron densities were reasonable (Table XI), but some TABLE X I HYDROGEN ATOM PEAK ELECTRON DENSITIES ( e . i T 3 ) IN FOURTH DIFFERENTIAL CYCLE Atom Obs Calc Atom Obs Calc H(l) 0.59 0.73 H( 8) 0.48 0.67 H(2) 0.86 1.01 H( 9) 0.48 0.56 H(4) 0.43 0.57 H(l l ) 0.45 0.50 H(5) 0.40 0.56 H(12) 0.56 0.49 H(7) 0.47 0.45 H(14) 0.68 0.62 of the curvatures were p o s i t i v e , so that the s h i f t s were not considered to be very r e l i a b l e , and in subsequent cycles the H atoms were kept in ideal positions. Refinement was com plete a f t e r seven cycles, and R was 0,12. The observed and calculated electron densities and curva tures at the carbon positions are l i s t e d i n Table XII. The values suggested that the atomic vibrations are s l i g h t l y aniso tropic , and anisotropic thermal parameters were obtained appro ximately from the differences between the observed and calcu lated second derivatives (44). At t h i s stage f a c i l i t i e s f or carrying out anisotropic (block-diagonal) least squares r e f i n e  ment became available to us, and the carbon atom p o s i t i o n a l and anisotropic thermal parameters were further refined. The 53 TABLE X I I CARBON PEAK ELECTRON DE N S I T I E S (e.X~3) AND CURVATURES (e.X" 5) FROM SEVENTH D I F F E R E N T I A L CYCLE e - C J V / W -sxe/3^ -v-p/dz1 ————\ • \ / Atom Obs C a l c Obs C a l c Obs C a l c Obs C a l c C ( 1) 4.16 4.31 24.2 24.5 21.0 21.2 18.3 20.8 C ( 2) 4.45 4.67 29.1 28.6 23.9 24.0 20.9 24.6 C ( 3) 5.45 5.56 38.5 37.1 34.2 32.0 29.9 32.4 C ( 4) 4.72 4.81 31.1 29.9 30.0 27.6 21.8 24.1 C ( 5) 4.70 4.81 27.9 27.7 25.0 24.1 26.1 27.5 C ( 6) 5.32 5.38 36.9 34.8 32,2 30.3 30.8 31.7 C ( 7) 4.37 4,46 25.1 24,7 21.4 21.6 25.1 25.8 c ( 8) 4.16 4.26 25.2 24.6 20.2 20.2 17.9 19.5 c ( 9) 4.39 4.50 28.2 26.5 23.1 22.7 19.4 22.9 c (10) 5.52 5.56 37.8 35.8 36.3 33.5 29.8 31.8 c (11) 4.62 4.65 30.4 28.0 27.9 25.8 21.4 23.5 c (12) 4.78 4.80 29.0 27.9 26.2 24.5 25.6 26.8 c (13) 5.09 5.15 33.4 31.9 27.8 27.0 27.7 29.3 c. (14) 4.47 4.54 25.4 25.9 22.6 21.8 25.1 26.3 c.: (15) 6.06 6.28 43.7 42.7 38.2 36.7 37.3 39.6 c (16) 6.09 6.07 44.2 41.6 40.0 36.1 36.0 37.5 f u n c t i o n m i n i m i z e d was 2 w ( F Q - F C ) , with v[w~= |F 0|/34 when | F 0 | <34, a n d £vF*- 34/|F q| when |F Q|>34. T h r e e c y c l e s w e r e c a r r i e d o u t ; t h e p o s i t i o n a l p a r a m e t e r s h i f t s w e r e n o t s i g n i f i  c a n t , a n d t h e c o o r d i n a t e s o f t h e s e v e n t h d i f f e r e n t i a l c y c l e w e r e r e t a i n e d ; 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 r e q u i r e d a f u d g e f a c t o r o f 0.2 t o e n s u r e c o n v e r g e n c e . R d e c r e a s e d b y 1% i n t h e a n i s o t r o p i c r e f i n e m e n t . The o b s e r v e d a n d c a l c u l a t e d s t r u c t u r e f a c t o r s a f t e r t h e d i f f e r e n t i a l s y n t h e s e s r e f i n e m e n t a r e l i s t e d i n T a b l e A2; t h e R f a c t o r f o r t h e 550 o b s e r v e d r e f l e x i o n s w h i c h w e r e i n c l u d e d i n t h e r e f i n e m e n t i s 0.12 ( r e d u c e d t o 0.11 by u s i n g a n i s o t r o p i c t h e r m a l p a r a m e t e r s ) . A l s o i n c l u d e d i n T a b l e A2 a r e F Q a n d F C v a l u e s f o r a l l t h e weak r e f l e x i o n s a n d f o r some o f t h e 54 unobserved ref l e x i o n s , which were omitted from the refinement process. Coordinates and Molecular Dimensions The f i n a l p o s i t i o n a l and isotropic thermal parameters are given in Table XIII. The coordinates and temperature TABLE XIII FINAL POSITIONAL PARAMETERS (FRACTIONAL), STANDARD DEVIATIONS (X), ISOTROPIC THERMAL PARAMETERS (A 2), AND DISPLACEMENTS (X) FROM THE MEAN MOLECULAR PLANE Atom X y z . Six) < f ( y ) 61*) B(f) All) C ( 1) 0.2817 -0.0402 0.4119 0.007 0.008 0.010 7.05 0.007 C ' 2) 0.2947 0.0246 0.2717 0.006 0.007 0.008 5.95 0.003 c ' 3) 0.2296 -0.0077 0.1274 0.005 0.005 0.006 4.88 0.004 c ( 4) 0.2389 0.0567 -0.0238 0.006 0.006 0.008 5.82 0.003 c ( 5) 0.1783 0„0237 -0.1578 0.006 0.007 0.007 6,06 -0.015 c ( 6) 0.0990 -0.0738 -0.1606 0.005 0.005 0.006 5.39 0.001 c ' 7) 0.0316 -0.1103 -0.3020 0.007 0.008 0.007 7.15 0.000 c ( 8) -0.0449 -0.2090 -0.2966 0.007 0.009 0,010 7.26 0.003 c ( 9) -0.0566 -0.2746 -0.1594 0.006 0.008 0.009 6.62 -0.016 c (10) 0.0071 -0.2396 -0.0131 0.005 0.005 0.006 5.34 0.018 c (11) -0.0030 -0.3070 0.1356 0.006 0.006 0.008 6.53 0.000 c il2) 0.0575 -0.2772 0.2706 0.006 0.007 0.007 6.07 -0.001 c (13) 0.1389 -0.1735 0.2723 0.005 0.006 0.006 5.19 0.004 c f14) 0.2066 -0.1412 0.4161 0.007 0.008 0.007 7.06 -0.020 c (15) 0.1514 -0.1091 0.1303 0.004 0.005 0.005 4.01 -0.002 c (16) 0.0854 -0.1409 -0.0136 0.004 0.004 0.005 4.62 0.011 H : i ) 0.33 -0.03 0.52 H ( 2) 0.36 0.10 0.27 H i 4) 0.30 0.13 -0.03 H 5) 0.19 0.08 -0.27 H 7) 0.04 -0.06 -0.41 > 0.07 0.07 0.10 8.0 H ( 8) -0.10 -0.24 -0.41 H ( 9) -0.12 -0.35 -0.16 H (11) -0.06 -0.38 0.14 H '12) 0.05 -0.33 0.38 H r14) 0.20 -0.19 0.53 factors f o r carbon are those of the seventh d i f f e r e n t i a l cycle, 55 and the hydrogen atoms have been placed on the rin g diagonals with C-H about 1.08 X. The standard deviations calculated from Cruickshank's (33) formulae, with the reflexions used i n the refinement process only, are also given i n Table X I I I . Since a large number of weak and unobserved reflexions have been omitted from the analysis, these values of the standard devia tions are almost certainly over-optimistic (45), and i n d i s  cussing the accuracy of the molecular dimensions these 6"values have been a r b i t r a r i l y increased by a factor of two. The anisotropic thermal parameters are l i s t e d i n Table XIV, being the c o e f f i c i e n t s in the expression: exp-[B 1 : Lh 2 + B 2 2 k 2 + B^l2 + B2^l + B^hl + B 1 2 h k ] . TABLE XIV ANISOTROPIC THERMAL PARAMETERS FOR THE CARBON ATOMS (xlO 4) Atom B l l B22 B33 B23 B13 B12 C( 1) 98 204 277 -29 48 9 C( 2) 88 162 249 5 52 4 C( 3) 64 138 197 -15 45 1 C( 4) 85 150 235 6 57 -10 C( 5) 81 169 243 13 52 8 C( 6) 72 158 234 - 5 54 21 C( 7) 96 214 284 - 5 63 37 C( 8) 103 196 298 -23 54 13 C( 9) 89 185 271 -22 43 9 C(10) 77 148 209 - 7 50 10 C ( l l ) 91 174 264 - 8 48 3 C(12) 88 164 240 0 64 16 C(13) 67 147 210 - 7 40 15 C(14) 100 207 281 32 65 33 C(15) 54 118 171 4 46 17 C(16) 59 137 188 - 6 45 14 56 The bond distances and valency angles in the molecule and t h e i r standard deviations, calculated using twice the p o s i t i o n a l standard deviations of Table XIII as a more r e a l i s t i c estimate of the accuracy, are given i n Figure 10. The standard devia tions of the bond distances and valency angles were also com puted from the l e a s t squares residuals, and the values were i n good agreement with those given in Figure 10. Before averaging for comparison with t h e o r e t i c a l predictions, the bond distances were corrected f o r small errors due to r o t a t i o n a l o s c i l l a t i o n s , as described l a t e r . The best plane through the carbon atoms has equation: -0.64213 X' + 0.74683 Y + 0.17291 Z' + 1.76738 - 0, where X', Y, Z ? are coordinates in X, referred to orthogonal axes a, b, and c*. The deviations of the atoms from t h i s plane are l i s t e d in the l a s t column of Table XIII. The orientation of the molecule in the unit c e l l i s given in Table XV i n terms of the angles which the molecular axes L, M (see Figure 10), and the plane normal, N, make with the orthogonal c r y s t a l axes. L was taken through atoms 1 and 8, and M through the midpoints of bonds 4-5 and 11-12. L, M, and N are almost exactly mutually perpendicular, the angles between them being Z LM = 89.5°, ZMN = 90.0°, and ZLN = 90.0°. Pre vious values of the orientation angles (Robertson and White) are included i n Table XV f o r comparison. A l l the carbon-carbon intermolecular separations less than 4 $ were calculated; a l l these contacts correspond to I t ~ 1.423 0.018 0.018 1.409 12 0 > I 315 0.020 0.014 1.411 0.020 1.315 4 ^ ° ^ 6 ^ 1.418 0.0/8 0.018 1.415 Figure 10. (a) Measured "bond lengths (&), before-application of the small r o t a t i o n a l o s c i l l a t i o n corrections, and standard deviations. (b) Measured valency angles (degrees). 6" = 1.0° - 1.4°. ^) 58 TABLE XV ORIENTATION OF THE MOLECULE IN THE CRYSTAL R o b e r t s o n a n d W h i t e ( 43 ) P r e s e n t a n a l y s i s %l 6 1 . 1 ° 7 7 . 7 3 1 . 9 6 0 . 9 ° 7 7 . 1 3 2 . 5 X M U J M 5 2 . 2 5 2 . 4 1 2 0 . 1 5 3 . 3 5 1 . 1 1 2 0 . 0 X N *JJ N 1 2 8 . 7 4 0 . 2 8 0 . 5 1 3 0 . 0 4 1 . 7 8 0 . 0 n o r m a l v a n d e r W a a l s i n t e r a c t i o n s . The s h o r t e s t d i s t a n c e s a r e b e t w e e n m o l e c u l e s r e l a t e d b y a c e n t e r o f symm e t r y ; t h e p l a n e s o f t h e s e m o l e c u l e s a r e p a r a l l e l a n d s e p a r a t e d by 3 . 5 3 $, a n d t h e r e a r e 59 c o n t a c t s l e s s t h a n 4 X, t h o s e l e s s t h a n 3 . 6 X b e i n g l i s t e d i n T a b l e X V I . The s h o r t e s t l a t e r a l c o n t a c t s a r e a l s o g i v e n i n T a b l e X V I . A l l t h e c a r b o n - h y d r o g e n a n d h y d r o g e n - h y d r o g e n i n t e r  m o l e c u l a r s e p a r a t i o n s l e s s t h a n 3 . 5 °> were a l s o c a l c u l a t e d . The s h o r t e s t d i s t a n c e s ( l e s s t h a n 3 X) a r e l i s t e d i n T a b l e X V I . D i s c u s s i o n The d e v i a t i o n s o f t h e c a r b o n atoms f r o m t h e mean m o l e  c u l a r p l a n e ( T a b l e X I I I ) a r e s m a l l e r t h a n t h e d i s p l a c e m e n t s i n p e r y l e n e , a n d on t h e b a s i s o f t h e s t a n d a r d d e v i a t i o n s a r e n o t s i g n i f i c a n t . The d i s p l a c e m e n t s a r e s u g g e s t i v e o f a s m a l l b e n d i n g o f t h e m o l e c u l e , s i m i l a r t o t h a t i n p e r y l e n e , a n d t h i s , i f r e a l , i s p r o b a b l y a r e s u l t o f c r y s t a l p a c k i n g f o r c e s . 59 TABLE XVI SHORTEST INTERMOLECULAR CONTACTS A) BETWEEN ATOMS A l l C..,C contacts < 4.0 1 and a l l C...H and H...H contacts 4 3.5 A between a standard molecule (1) and neigh bouring molecules were calculated, but only the most s i g n i  f i c a n t separations are l i s t e d . Atom to Atom in Molecule d (molecule l ) 3 9 3 3.55 5 11 3 3.58 6 10 3 3.67 7 13 3 3.56 8 15 3 3.67 16 16 3 3.53 2 11 12 3.78 4 15 5 3.64 4 16 5 3.68 14 7 2 3.67 2 H 11 12 2.79 10 H 4 13 2.86 13 H 4 13 2.97 15 H 4 13 2.68 16 H 4 13 2.62 1 ; H 12 6 2.52 2 H 11 12 2.64 2 H 14 6 • 2.80 Molecule 1 x y z 2 x y 1+z 3 -x -y -z 5 1/2-x 1/2+y -z 6 1/2-x 1/2+y 1-z 12 1/2+x -1/2-y z 13 1/2-x -1/2+y -z The anisotropic thermal parameters, B^^, were transformed to U^j referred to the orthogonal c r y s t a l axes a, b, and c* (46), and then to U tensors referred to the molecular axes L, M and N. The thermal motion was analysed i n terms of the r i g i d - body vibrations of the molecule (47). The T and cd tensors are: 60 x 2 deg T = 0.0589 -0.0067 0.0076 0.0501 0,0025 0.0500 O) - 14.56 0.55 -0.42 10.67 -1.37 17.18 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 direc- t i v e l y , and the corresponding amplitudes of angular o s c i l l a t i o n tude as those found f o r anthracene (48) and i l l u s t r a t e that the molecule seems to move most ea s i l y in the directions offering least resistance, i . e . greatest t r a n s l a t i o n a l motion i n the d i r e c t i o n of the long axis and greatest r o t a t i o n a l o s c i l l a t i o n s about axes N and L. Slight corrections i n bond distances are necessary 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 center of the molecule (34). The bond . o length corrections, which vary from 0.004 to 0,006 A, were applied to the distances of Figure 10a before the f i n a l mean values of Table XVII were derived. Differences between chemically-equivalent bond lengths are generally small (Figure 10a), but one or two differences are f a i r l y large: e.g. bond 5-6 i s shorter and bond 12-13 i s longer than (with t h e i r mean about equal to) chemically, equiva- lent bonds; bond 8-9 i s very short, but i t s chemically equiva lent bonds are also f a i r l y short. These variations are only possibly s i g n i f i c a n t and, although the differences may be r e a l , the chemically equivalent bond distances were averaged f o r comparison with t h e o r e t i c a l values. The mean bond distances tions of the molecular axes are 0.24, 0.22, and 0.22 $ respec- are 3.8°, 3.3°, and 4.1°. These values are of the same magni-61 TABLE XVII MEAN MEASURED AND CALCULATED BOND LENGTHS •(£) IN PYRENE Bond Measured Calculated / : ; ^ Uncorrected Corrected for r o t a t i o n a l o s c i l l a t i o n a 1.376 1.380 0.011 0.012 1.397 1.388 b 1.416 1.420 0.009 0.003 1.397 1.408 c 1.411 1.417 0.007 0.012 1.421,: 1.427 d 1.437 1.442 0.009 0.012 1.448 1.433 e 1.411 1.417 0.014 - 1.421 1.424 f 1.315 1.320 0,014 - 1.355 1.360 are given i n Table XVII, together with t h e i r standard deviations, (S~m being calculated from the standard deviations of the i n d i  vidual distances (Figure 10a), and ^  being derived 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 d i f f e r e n t estimates of the standard deviations suggests 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  cal bond lengths were derived from the s i x non-excited valence bond structures (Figure 11), and from the LCA0 TT-bond orders (49). The correlation curve of Cruickshank and Sparks (38) was used for the valence bond method, and f o r the molecular o r b i t a l method a l i n e a r c o r r e l a t i o n between (0.40, 1.46 X) and (0.85, 1.34 h ( 38). The general v a r i a t i o n of the measured distances i s w e l l reproduced in both sets of calculated values, but some of the in d i v i d u a l agreements are not p a r t i c u l a r l y good. Bond f i s the shortest i n the molecule, but the measured distance 63 (1.320 + 0.014 A) i s shorter than either of the calculated distances, and apparently shorter than the C=C distance i n ethylene (1.337 * 0.003 X) ( 5 0 ) . This i s s i m i l a r to the s i t u  ation i n p-benzoquinone (51) where a similar bond has length 1.322 ± 0.008 X, and suggests that the value in ethylene i s perhaps not the normal double bond distance i n t h i s type of molecule (52). Bond a i s the next shortest bond in the mole cule (measured length 1.376 °J and bond d the longest bond (measured 1.437 °J, with bonds b, c, and e of intermediate length. These features are reasonably well reproduced i n the calculated distances, with the molecular o r b i t a l method giving somewhat better i n d i v i d u a l agreement, p a r t i c u l a r l y f o r bonds a and b. PART I I I THE DETERMINATION OF THE STRUCTURES OF 1-0-(p-BROMOBENZENESULPHONYL)-4,5,7-TRI-O- ACETYL-2,6-ANHYDRO-3-DEOXY-d-GLUCOHEPTITOL AND 10-CHL0R0-5,10-DIHYDROPHENARSAZINE I. THE CRYSTAL AND MOLECULAR STRUCTURE OF 1-0-(p-BROMOBENZENESULPHONYL)-4,5,7-TRI-O- ACETYL-2,6-ANHYDRO-3-DEOXY-d-GLUCOHEPTITOL Introduction Hydroformylation of tri-O-acetyl-d-glucal y i e l d s two isomeric products, which can be deacetylated, and the parent polyols then separated by paper chromatography. The fast running f r a c t i o n has m.p. 132°C, and the other isomer m.p. 156°C. Rotation rules and proton magnetic resonance spectra suggest the tentative structures I I I (Rj_ = R2 - H) f o r the lower-melting isomer, and IV for the higher-melting isomer, that i s the compounds are isomeric anhydrodeoxyheptitols which d i f f e r only i n the configuration of the hydroxymethyl group at C 2 (53). ( I l l ) (IV) To es t a b l i s h the structures conclusively an X-ray analy s i s of the p-bromobenzenesulphonyl, t r i a c e t y l derivative of the lower-melting polyol was undertaken. This derivative was pre pared by treatment of the mixture of triacetylanhydrodeoxy- heptitols with p-bromobenzenesulphonyl chloride, and the 6 6 required compound p r e f e r e n t i a l l y c r y s t a l l i z e d out of the re action mixture. It was subsequently deacetylated and de- brosylated to y i e l d a pure sample of the lower-melting p o l y o l . The analysis described i n t h i s work shows that the derivative has structure I I I (R]_ = CH3.CO-, R 2 - Br.C^H^.S02-) , so that the tentative s t r u c t u r a l assignment was correct. The systema t i c name of the derivative examined i s 1-0-(p-bromobenzene sulphonyl) -4 ,5,7-tri-0-acetyl-2 ,6-anhydro -3~deoxy-d-gluco- h e p t i t o l . Experimental Crystals of the p-bromobenzenesulphonyl, t r i a c e t y l derivative from methanol-water are needles elongated along c with (100) and (010) developed. The unit c e l l dimensions and space group were determined from r o t a t i o n , Weissenberg and precession f i l m s , and the density was measured by f l o t a t i o n i n aqueous caesium bromide. Crystal data (X(CuKcx) = 1.5418 A, X(MoKCX) - 0.7107 A) C 1 9 H 2 3 0 1 0 SBr, M - 523.4, m.p. - 104°C. Orthorhombic, a - 13.71 * 0.03, b = 29.37 ± 0.08, c = 5.79 - 0.01 i\ U =• 2331 °- . D m ^ l , 5 , Z = 4, D x = 1.49 g cm""3. o -1 Absorption c o e f f i c i e n t s f o r X-rays, A= 1.5418 A,yU,= 39 cm , X= 0.7107 £, yu-= 20 cm"1. F (000) = 1072 6? A b s e n t s p e c t r a : hOO when h i s o d d , OkO when k i s o d d . S p ace g r o u p P2-]_222. The i n t e n s i t i e s o f a l l r e f l e x i o n s w i t h 2 e C u K x ^ ^ ° ^ c o r"* r e s p o n d i n g t o a minimum i n t e r p l a n a r s p a c i n g d = 1.09 X) were m e a s u r e d on a G.E. XRD-5 S p e c t r o g o n i o m e t e r , w i t h S i n g l e C r y s t a l O r i e n t e r , u s i n g a s c i n t i l l a t i o n c o u n t e r , CuKoc r a d i a t i o n ( n i c  k e l f i l t e r a n d p u l s e h e i g h t a n a l y s e r ) , a n d t h e m o v i n g c r y s t a l - m o v i n g c o u n t e r t e c h n i q u e (29). A l l t h e i n t e n s i t i e s w e r e c o r  r e c t e d f o r b a c k g r o u n d , L o r e n t z a n d p o l a r i z a t i o n f a c t o r s w e r e a p p l i e d , a n d t h e s t r u c t u r e a m p l i t u d e s were d e r i v e d . The c r y s t a l u s e d was mounted w i t h c p a r a l l e l t o t h e c j > a x i s o f t h e g o n i o s t a t , a n d had a s m a l l u n i f o r m c r o s s - s e c t i o n , so t h a t a b s o r p t i o n c o r r e c t i o n s w e r e n o t c o n s i d e r e d n e c e s s a r y . E i g h t h u n d r e d a n d f i f t y - o n e r e f l e x i o n s w e r e o b s e r v e d , 74% o f t h e t o t a l number i n t h e r a n g e 0 <20QUKO( ^90°. S t r u c t u r e A n a l y s i s The b r o m i n e a n d s u l p h u r a t o m p o s i t i o n s w e r e d e t e r m i n e d f r o m t h e t h r e e - d i m e n s i o n a l P a t t e r s o n f u n c t i o n , a n d a t h r e e - d i m e n s i o n a l F o u r i e r s e r i e s was summed w i t h p h a s e s b a s e d on t h e B r a n d S a t o m s . On t h e r e s u l t i n g e l e c t r o n - d e n s i t y d i s t r i b u t i o n f o u r t e e n p e a k s , i n a d d i t i o n t o t h e b r o m i n e a n d s u l p h u r p e a k s , w e r e c h o s e n a s a t o m i c s i t e s w i t h o u t a n y r e g a r d f o r c h e m i c a l c o n s i d e r a t i o n s . A s e c o n d F o u r i e r , p h a s e d on t h e s e s i x t e e n a t o m s , r e v e a l e d p o s i t i o n s f o r 24 a toms i n a l l , t h e g e n e r a l s t r u c t u r e o f t h e m o l e c u l e now b e i n g c l e a r , a n d a t h i r d F o u r i e r showed a l l 31 a toms i n t h e m o l e c u l e , a l t h o u g h t h e a c e t y l g r o u p s 68 were rather poorly resolved at thi s stage. Throughout th i s structure determination, the scattering factors of the Inter- atoms, and oxygen atoms were distinguished at the f i n a l stage; R, the usual discrepancy f a c t o r , decreased flbrrxO.46 f o r Br and S only to 0.26 for a l l 31 atoms. Refinement of the p o s i t i o n a l and is o t r o p i c thermal para meters then proceeded by computing successive observed and calculated d i f f e r e n t i a l syntheses, and a f t e r seven cycles R was reduced to 0.183. At t h i s stage a three-dimensional Fourier series was summed, and superimposed sections of the re s u l t i n g electron-density d i s t r i b u t i o n taken through the atomic centers are shown i n Figure 12. There was no spurious d e t a i l so that the structure appeared to be e s s e n t i a l l y correct. Refinement of the atomic parameters, and an o v e r a l l scale factor, was completed by (block-diagonal) least squares. The complete in f i v e cycles, during which R was reduced from 0.183 to 0.090, and Sw.AF 2 from 26 x 10 3 to 6 x 10 3. In the f i n a l cycles anisotropic thermal parameters were introduced for the bromine atom and f o r the outer atoms of the ace t y l groups (our 40K IBM 1620 could not accommodate a l l the atoms anisotropic- a l l y , and the atoms treated were those whose thermal vibrat i o n seemed most a n i s o t r o p i c ) . The measured structure amplitudes are compared i n Table A3 with the values calculated from the f i n a l parameters, those national Tables Vol. H I were use d, with B = 4.5 °- f o r a l l Figure 12. Superimposed sections of the 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 t o ( O O l ) . Contours s t a r t .at 2eA*~3 and are at i n t e r v a l s of leS"3, except f o r B r ( l ) and S(2) which s t a r t - a t zero and are at i n t e r v a l s of 2. 5 eS~3.. A perspective drawing of the molecule is,-also shown. ON 70 f r o m t h e f i f t h l e a s t s q u a r e s c y c l e (R = 0 . 0 9 0 f o r t h e 851 o b s e r v e d r e f l e x i o n s ) . A t o m i c P a r a m e t e r s a n d M o l e c u l a r D i m e n s i o n s The f i n a l p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s a r e g i v e n i n T a b l e X V I I I ; x , y, and z a r e f r a c t i o n a l c o o r d i n a t e s r e f e r r e d t o t h e c r y s t a l a x e s , B a r e i s o t r o p i c t e m p e r a t u r e f a c t o r s a n d TABLE X V I I I F I N A L POSITIONAL (FRACTIONAL) AND THERMAL PARAMETERS Atom X y z B (A B r (1) 0 . 1 6 8 0 0 . 7 3 9 8 0 . 3 8 4 1 _ ' S (2) 0 . 4 0 2 7 0 . 5 6 3 3 0 . 0 7 2 8 2 . 8 9 0 (3 ) 0 . 4 0 3 2 0 . 5 6 2 4 -O .1658 4 . 6 3 0 (4 ) 0 . 4 9 3 5 0 . 5 6 2 0 0 . 1 8 9 4 4 . 2 6 0 (5) 0 . 3 3 7 8 0 . 5 2 3 1 0 . 1 5 5 6 3 . 2 2 0 (6) 0 . 1 9 8 1 0 . 4 6 3 5 0 . 4 2 3 2 3 . 1 3 0 (7 ) 0 . 0 0 9 3 0 . 4 4 5 3 0 . 5 9 6 0 3 . 3 3 0 (8) 0 . 1 4 6 4 0 . 3 4 9 0 0 . 6 3 8 7 4 . 2 2 0 (9) 0 . 3 1 6 5 0 . 3 7 2 9 0 . 8 7 9 7 3 . 9 3 0 (10) 0 . 4 5 1 3 0 . 3 4 0 6 0 . 7 3 0 8 - 0 (11) 0 . 0 5 7 3 0 . 3 6 0 4 0 . 9 4 8 9 - 0 (12) - 0 . 1 3 7 3 0 . 4 1 6 1 0 . 5 3 3 5 -C (13) 0 . 2 4 2 4 0 . 6 8 4 4 0 . 3 0 0 9 4 . 4 0 C (14) 0 . 3 1 3 5 0 . 6 7 1 4 0 . 4 4 6 5 4 . 5 5 C (15) 0 . 3 6 6 4 0 . 6 3 2 1 0 . 3 9 3 1 3 . 2 8 C (16) 0 . 3 3 6 3 0 . 6 1 2 1 0 . 1 6 3 9 2 . 5 7 C (17) 0 . 2 6 7 6 0 . 6 2 8 5 0 . 0 0 8 5 4 . 1 3 C (18) 0 . 2 1 5 0 0 . 6 6 9 1 0 . 0 8 2 8 5 . 3 6 C (19) 0 . 3 3 9 3 0 . 5 0 9 9 0 . 3 9 4 2 2 . 9 9 C (20) 0 . 3 0 4 2 0 . 4 6 0 4 0 . 4 0 3 5 2 . 2 1 C (21) 0 . 3 3 5 6 0 . 4 3 9 7 0 . 6 4 2 9 3 . 7 3 C (22) 0 . 2 9 5 2 0 . 3 9 2 0 0 . 6 5 8 8 1 . 8 8 C (23) 0 . 1 8 0 8 0 . 3 9 6 7 0 . 6 4 7 0 2 . 9 6 C (24) 0 . 1 5 6 3 0 . 4 1 8 4 0 . 4 2 4 0 3 . 0 6 C (25) 0 . 0 4 8 0 0 . 4 2 3 0 0 . 3 8 5 2 4 . 0 8 C (26) - 0 . 0 8 6 5 0 . 4 4 1 7 0 . 6 5 6 4 4 . 0 3 C (27) - 0 . 1 1 6 6 0 . 4 6 4 6 0 . 8 5 7 6 -C (28) 0 . 0 9 1 5 0 . 3 3 6 0 0 . 8 1 4 1 4 . 9 3 c (29) 0 . 0 5 9 5 0 . 2 8 4 4 0 . 7 7 5 4 - c (30) 0 . 4 0 0 9 0 . 3 4 5 7 0 . 8 8 5 7 3 . 3 0 c ( 3 D 0 . 4 0 8 0 0 . 3 2 4 3 1 . 1 2 7 9 -71 TABLE XVIII (continued) Anisotropic thermal parameters (x 10M Atom B l l B22 B33 B23 B13 B12 Br (1) 136 20.0 861 2 240 44 0 (10) 57 16.9 353 47 80 13 0 (11) 128 25.3 420 -45 178 -18 0 (12) 84 27.2 453 15 - 1 9 - 1 4 C (27) 4 1 21.3 398 -48 43 18 C (29 102 9.4 604 13 -51 - 1 7 C ( 3 D 77 10.4 258 - 1 9 -62 9 B i j are the anisotropic thermal parameters in the expression: exp- j ^ n n 2 + B 2 2 k 2 + B^jl} + B2jklb + B^ht + B 1 2hk|. A perspective drawing of the molecule, with the atom numbering used, i s shown i n Figure 12, and the bond distances and valency angles are given i n Table XIX, together with t h e i r standard deviations calculated from the least squares residuals. A l l the intermolecular distances less than 4.0 £ were calcu lated, and the shorter contacts are l i s t e d i n Table XX. TABLE XIX BOND LENGTHS (£) AND STANDARD DEVIATIONS, AND VALENCY ANGLES ( 6"VARIES FROM 0 . 9 ° FOR O-S-0 ANGLES TO 2.6° FOR ANGLES IN THE ACETYL GROUPS) Bond I <r Bond I <r B r ( l ) - C ( l 3 ) 1.980 0.027 0(5 ) - C(l9) 1.44 0.029 0(6 ) -C(20) 1.46 0.026 S ( 2)-C ( 1 6 ) 1.777 0.021 0(6 ) -C(24) 1.44 0.024 0(7 ) -C(25) 1.48 0.033 S(2)~0(3) 1.381 0.019 0(8 ) -C(23) 1.48 0.025 S(2)-0(4) 1.416 0.018 0(9 ) -C(22) 1.43 0.028 Mean S O 1.399 0 . 0 1 3 Mean 0-C 3 1.45 0.01-L 72 TABLE XIX (continued) Bond S(2)-0(5) C(13)-C(14) C(14)-C(15) C(15)-C(16) C(l6)-C(17) • C(17)-C(18) C(18)-C(13) Mean C a r-C a r C(19)-C(20) C(20)-C(21) C(21)-C(22) C(22)-C(23) C(23)-C(24) C(24)-C(25) Mean C s 3-Cs ; B£~car""car s-c a r-c a r Car-C a r _ u a r 0(3)- 0(3)- 0(3)- 0(4)- 0(4)- 0(5)- Mean •S(2)- S(2)- •S(2)- •S(2)- •S(2)- S(2)- at S 1.553 00015 1.34 1.40 1.51 1.39 1.46 1.39 1.41 1,53 1.57 1.51 1.58 1.48 1.51 1.53 0.039 0.033 0.036 0.034 0.037 0,044 o . o i 5 0,027 0.036 0.030 0.030 0.034 0.033 O . O l o 0(4) 0(5) •C(16) •0(5) •C(16) •C(16) Range 110.0 - 132.4 (10 angles) Mean 117.8 118.2 107.3 108.3 109.6 109.3 103 .2 109.3 S(2)-0(5)-C(l9) 119.6 C(20)-0(6)-C(24) 109.9 ) Range 103.1 - 0" csp3- csp3 C 113.1 (15 angles) C U - C . J - C J \ Mean 107.2 sp^ sp- s p - Bond I 6~ 0(7)-C(26) 1.36 0.030 0(8)-C(28) 1.32 0.036 0(9)-C(30) 1.41 0.026 Mean 0-C__2 bp 1.36 O.Olg 0(10)-C(30) 1.14 0.032 0(11)-C(28) 1.16 0.038 0(12)-C(26) 1.25 0.034 Mean C-0 1.18 0 . 0 2 0 C(26)--C(27) 1.41 0,042 C(28)-C(29) 1.59 0.038 C(30)-C(31) 1.54 0.040 Mean C s p2-C 3 p3 1.51 O.O23 C(25)-0(7)-C(26) 121.5 C(23)-0(8)-C(28) .115.6 C(22)-0(9)-C(30) 114.4 Mean C s p3-0-C s p2 117.2 0(7)-C(26)-0(12) 116.0 0(8)-C(28)-0(ll) 124.7 0(9)-C(30)-0(10) 123.6 Mean 0-C=0 121,4 0(7)-C(26)-C(27) 117.3 0(8)-C(28)-C(29) 108.9 0(9)-C(30)-C(3l) 107.8 Mean O-C-CH3 111.3 0(12)-C(26)-C(27) 126.6 0(11)-C(28)-C(29) 124.9 0(10)-C(30)-C(31) 128,6 Mean 0=C-CH3 126.7 Discussion The analysis has established that the derivative i n v e s t i  gated , i s 1-0-(p-bromobenzenesulphonyl)-4,5,7~trl~0-acetyl~2,6-73 TABLE XX SHORTER INTERMOLECULAR DISTANCES (X) A l l contacts < 4;.0 X 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 . Atom to Atom in Molecule d (Molecule 1) B r ( l ) 0(10) 6 3.45 B r ( l ) C(30) 6 3.61 0(4) 0(5) 11 3.41 0(4) C(19) 11 3.34 0(4) C(20) 11 3.H 0(4) C(21) 11 3.52 0(10) C(15) 11 3.27 0(11) C(24) 7 3.51 0(11) C(25) 7 3.13 C(15) 0(3) 7 3.31 C(19) 0(3) 7 3.10 C(31) 0(10) 7 • 3.57 . C(14) C(17) 7 3.55 Molecule 1 x y z 6 1 / 2 - x 1/2+y 1 - z 7 x y 1 + z 11 1 - x 1 - y z anhydro-3-deoxy-d-glucoheptitol. The tentative assignment of structures to the two anhydrodeoxyheptitols i s therefore cor rect; the lower-melting isomer i s 2,6-anhydro-3-deoxy-d- glucoheptitol ( I I I , R^ = Rg =H), and the higher-melting isomer i s 2,6-anhydro-3-deoxy-d-mannoheptitol (IV). The sugar r i n g i s in the chair conformation with a l l substituent groups i n equatorial positions, as i s clear from 74 Figure 12. Since the compound i s derived from d-glucose the absolute configuration i s established: the parameters of Table XVIII referred to a right-hand set of axes give the true absolute configuration. Figure 12 also depicts the correct absolute configuration. The bond distances and valency angles in the molecule (Table XIX) are a l l quite normal, and require no spe c i a l comment. A l l the intermolecular separations (Table XX) correspond to normal van der Waals interactions. The shortest distances are three C...0 contacts of 3.1 X, equal to the sum of the van der Waals r a d i i of carbon and oxygen (54). The shortest Br-0 and Br-C contacts are 3.45 8 and 3.61 $ respectively (sum of van der Waals r a d i i 3.35 A and 3.65 X r e s p e c t i v e l y ) . The shortest 0-0 contact i s 3.41 S, and the shortest C-C separa t i o n i s 3.55 X. I I . THE CRYSTAL AND MOLECULAR STRUCTURE OF 10-CHLORO-5,10-DIHYDROPHENARSAZINE (PHENARSAZINE CHLORIDE) Introduction If arsenic retains i t s usual valency angle (of about 98°) in a 5,10-disubstituted 5,10-dihydroarsanthren (V; R = a l k y l or a r y l ) , such a molecule must be folded about the As-As a x i s , the two o-phenylene groups subtending at t h i s axis a (calcu lated) angle of 121° (55). Three geometrical isomers should then e x i s t : two c i s forms, one having both substituents outside the 121° angle ( s t e r i c factors permitting), and the other having both groups within t h i s angle; and one trans form. Two forms of the 5,10-di-p-tolyl derivative (V; R = C^H^Me) have been :' isolated (56), the t h i r d form being too s t e r i c a l l y hindered to e x i s t . I t has recently been asserted however, on the basis of theo r e t i c a l considerations, that systems such as (V) are un l i k e l y to be "stably folded" and that the existence of geometri cal isomers i s due to the s t a b i l i t y of the arsenic pyramidal configuration (57). The only d i r e c t s t r u c t u r a l information which appears to be available i s that f o r 5,10-dimethyl-5,10- dihydroarsanthren dibromide and diiodide (VI, X = Br or I ) , where the angle subtended by the o-phenylene groups was found to be, within rather wide l i m i t s of error, 157° (58). V VI Recently i t has been found that there appear to be two modifications of 10-chloro-5,10-dihydrophenarsazine (phenar- sazine chloride, Adamsite, V I I ) ; yellow crystals are obtained from a var i e t y of solvents, and when these are heated to 200° _3 at 10 mm yellowish-green crystals are formed (59). I f the molecule i s folded as i n the dihydroarsanthren system two geometrical isomers might e x i s t , one with the chlorine within and the other with the chlorine outside the angle formed by the two o-phenylene groups, the configuration at the nitrogen probably being r e a d i l y inverted. ^ I have undertaken an X-ray investigation of the. two c r y s t a l l i n e modifications to es t a b l i s h whether they are geomet r i c a l isomers, and to obtain d e t a i l s of the c r y s t a l and 77 molecular structures. The resul t s show that the yellow crys t a l s are solvated, those from xylene containing one-half molecule of xylene per molecule of phenarsazine chloride. The yellowish-green c r y s t a l s are solvent f r e e , and a complete anal y s i s shows that the o-phenylene groups subtend an angle of 169°, with the chlorine atom outside t h i s angle; the deviation from complete planarity of the t r i c y c l i c r i n g system i s thus quite small, and i t i s u n l i k e l y that geometrical isomers could be i s o l a t e d . Preliminary X-ray Study 10-chloro-5,10-dihydrophenarsazine (phenarsazine chloride) i s obtained, by reaction of diphenylamine and AsCl^ (60) and c r y s t a l l i z a t i o n from any of a number of solvents (xylene, carbon t e t r a c h l o r i d e , g l a c i a l acetic a c i d , e t c . ) , as yellow single crystals which ra p i d l y change to a yellow powder when removed from the mother l i q u o r . When either the single c r y s t a l sample or the powder i s heated at 200 and 10 mm, yellowish- green rectangular needles are formed, which are quite stable. Chemical analyses, infrared (solution and KBr discs) and u l t r a  v i o l e t spectra, and X-ray powder photographs of powdered yellow c r y s t a l s , the yellow powder, and the green crystals (which are yellow when f i n e l y powdered) indicated that the three specimens are i d e n t i c a l , so that the most reasonable explanation of the existence of two types of single c r y s t a l s i s that the yellow metastable modification contains solvent of c r y s t a l l i z a t i o n , which i s r e a d i l y l o s t , and the stable green form i s solvent 78 free. This conclusion was v e r i f i e d by determining the unit c e l l dimensions and space groups of the metastable yellow crystals (from xylene) and the stable green c r y s t a l s , from various rota t i o n , Weissenberg and precession photographs. The yellow crys t a l s were sealed i n thin-walled Lindemann-glass c a p i l l a r i e s , together with some mother l i q u o r , to preserve them during the X-ray exposures. The densities were measured by f l o t a t i o n i n a carbon tetrachloride-methylcyclohexane mixture f o r the yellow c r y s t a l s , and i n bromoform-chloroform f o r the green c r y s t a l s . Crystal data ( X(CuKcx) = 1.5418 X; X (MoKoc) = 0.7107 A), metastable yellow c r y s t a l s C-^HgNAsCl.l/2CgH-Lo Monoclinic, a = 14.50 ± 0.02, b =16.76 - 0.02, c = 13.02 - 0.03 X, p = 113.7° ± 0.1°. U = 2898 ft3 -3 D m = 1.544 g cm . D x (Z = 8) = 1 .272 g cm"3. _3 D x (Z = 8 + 4 molecules of xylene) = 1.515 g cm Absent spectra: hk&when h + k +t i s odd, hO^when h o r t i s odd. Space group i s Ia or 12/a. The density measurement indicates that the yellow crys t a l s are solvated with half a molecule of xylene per molecule of phenarsazine chloride. Crystals from other solvents are no doubt also .solvates ( 6 l ) . Stable yellowish-green c r y s t a l s . Phenarsazine chloride, C-^H^NAsCl, M » 277.5. 79 Orthorhombic, a = 5.47 ± 0.01, b = 13.91 ± 0.02, c = 14.30 ± 0.02 X. U = 1088 X3. -3 D m = 1.693, Z = 4, D x = 1.694 g cm . Absorption c o e f f i c i e n t f o r X-rays, X = 1.5418 X, JJ. = 66 cm - 1, X = 0.7107 X, JX = 35 cm"1. F (000) = 552. Absent spectra: hOO when h i s odd, OkO when k i s odd, 00.£» when fL i s odd. Space group i s ?2^2^2^. The excellent agreement between measured and calculated densities indicates that the stable c r y s t a l s are solvent-free. Structure Determination of Stable Crystals Experimental Crystals of solvent-free phenarsazine chloride are stable yellowish-green needles elongated along a, with {011} developed. The i n t e n s i t i e s of a l l reflexions with 28,-^^ ^  148° (corres ponding to a minimum interplanar spacing d = 0.80 8.) were measured on a G.E. XRD-5 Spectrogoniometerwith Single Crystal Orienter, using a s c i n t i l l a t i o n counter, CuKoc, radiation (nickel f i l t e r and pulse height analyser), and the moving c r y s t a l - moving counter technique (29). The c r y s t a l was mounted with a p a r a l l e l to the <£> axis of the goniostat, and had cross-section about 0.3 x 0.3 mm., so that absorption corrections were not considered necessary. The structure amplitudes were derived as usual. One thousand and th i r t y - t h r e e reflexions were 80 observed, 79% of the t o t a l number i n the range 0 < 2e C u K o c<148°. Structure Analysis The y- and z-coordinates of the arsenic and chlorine atoms were determined from the Ok/. Patterson function and an Okt Fourier series was summed with phases based on the As and CI atoms. On the re s u l t i n g electron-density d i s t r i b u t i o n a l l the atoms (except hydrogens) were re a d i l y d i s c e r n i b l e . Struc ture factors were calculated from the positions obtained from the Fourier map and R f o r the zone was 0.135, The x-coordinates of the arsenic and chlorine atoms were then determined from the h0£ Patterson function and an hOJL, Fourier series was summed with phases based on the As and CI atoms. There was much overlap i n the r e s u l t i n g electron- density d i s t r i b u t i o n so that the x-coordinates of the rest of the atoms could not be obtained with certainty. A three- dimensional Fourier series was then summed based on the phases of the As and CI atoms only and from the r e s u l t i n g electron- density d i s t r i b u t i o n the x-coordinates of a l l the atoms could be obtained. Structure amplitudes, calculated with the positions obtained from the electron-density map, gave R = 0.133 f o r a l l the observed hkt r e f l e x i o n s . Throughout t h i s structure deter mination the scattering factors of the International Tables Vol. I l l (1) were used, with i n i t i a l l y B = 4.5 A*2, for a l l the atoms except arsenic, f or which B = 3.0 A was used. Refinement of the p o s i t i o n a l and anisotropic thermal para-81 meters f o r a l l atoms except hydrogens then proceeded by (block diagonal) least-squares. The function minimized was 2 W ( | F 0 | " | F c | ) 2> w i t h | F Q |/35 when | K Q |< 3 5 ; and - 35/|Fo|when|Fo| ^ -35. Refinement was complete i n f i v e cycles during which R was reduced from 0.133 to O.O56, and 2wAF2 from 6.2 x 10 3 to 1.7 x 10 3. The measured structure amplitudes are compared in Table A4 with the values calculated from the f i n a l parameters, those from the f i f t h least squares cycle (R » O.O56 f o r the 1033 observed r e f l e x i o n s ) . Atomic parameters and molecular dimensions. - The f i n a l posi t i o n a l and thermal parameters are given i n Table XXI (the numbering of the atoms used i n Table XXI and throughout the remainder of t h i s paper i s f o r convenience i n the c r y s t a l l o - graphic analysis, and i s i l l u s t r a t e d i n Figure 13); x, y, and TABLE XXI FINAL POSITIONAL PARAMETERS (FRACTIONAL) Atom X y z As(l) 0.1305 0.4818 0.1659 Cl(2) -0.1196 0.5858 0.2465 N( 3) -0.2282 0.4773 -0.0164 C( 4) -0.1678 0.3165 0.1912 C( 5) -0.3629 0.2545 0.1754 C( 6) -0.5215 0.2698 0.1003 C( 7) -0.4750 0.3461 0.0372 C( 8) -0.2700 0.4079 0.0499 C( 9) -0.1248 0.3935 0.1312 C(10) 0.3277 0.6197 0.0395 C ( l l ) 0.3495 0.6747 -0.0411 C(12) 0.1799 0.6622 -0.1132 C(13) -0.0110 0.5969 -0.1030 C(14) -0.0374 0.5409 -0.0213 C(15) 0.1366 0.5526 0.0516 y 3b_ 4 0 I 2 3 4 A 1 I I I I I I I I Figure 1 3 - Superimposed sections of the 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 (lOO). Contours s t a r t at 1 e and are at .intervals of 1 e A*~3 except f o r the A s ( l ) and C l ( 2 ) which s t a r t at zero and are at i n t e r v a l s of 5 e A~3 and 2 - 5 e X~3 r e s p e c t i v e l y . A perspective drawing of the molecule i s also shown. co. 83 TABLE XXI (continued) F i n a l anisotropic thermal parameters (xioM Atom b l l b22 b33 b23 b13 b12 As 1 Cl(2) N( 3) C( 4) C( 5) C( 6) C( 7) C( 8) C( 9) C(10) C ( l l ) C(12) C(13) C(14) C(15) 241 46 32 - 4 -33 491 49 44 -35 94 307 54 25 -10 -46 335 42 42 -13 - 7 341 47 51 - 5 19 344 41 45 -12 -23 245 54 42 -24 -67 178 36 40 -31 0 149 39 34 -11 -66 200 46 53 +3 -37 335 46 56 - 9 59 286 65 43 - 0 61 328 57 31 - 1 2 177 33 52 -10 27 261 46 35 - 2 -65 -20 -59 -40 22 -12 - 2 25 - 1 -10 -20 - 7 22 -28 -20 7 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^-t are the anisotropic thermal parameters i n the expression: A perspective drawing of the molecule, and superimposed sections of the three dimensional electron-density d i s t r i b u t i o n taken through the atomic centers, are shown i n Figure 13. The bond distances and valency angles, with t h e i r standard devia tions calculated from the least squares residuals, are shown in Figure 14. A l l the intermolecular contacts less than 4.0 X were calculated and are l i s t e d in Table XXII. The mean plane through the twelve carbon atoms was calcu lated and the displacements from the plane suggested some deviation from planarity. Accordingly the mean plane through each of the phenyl rings was calculated. The plane through carbon atoms numbered 4 to 9 (Figure 13) has equation: exp - £ b n h 2 + b 2 2 k 84 Figure ik. Bond'lengths (2) ,and valency, angles (degrees) i n phenarsazine c h l o r i d e . Standard deviations are given i n parentheses. 85 TABLE XXII SHORTER INTERMOLECULAR DISTANCES (X) p A l l crystallographically-independent contacts^, 4.0 A between a standard molecule (1) and neigh bouring molecules are l i s t e d . Atom to Atom i n Molecule d (molecule 1) As(l) C(12) 8 3.88 Cl(2) N(3) 15 3.60 Cl(2) C(4) 4 3.68 Cl(2) C(5) 4 3.70 Cl(2) C(13) 15 3.90 N(3) C(6) 3 3.81 C(4) C(12) 8 3.88 C(4) C(12) 15 3.97 C(4) C(13) 15 3.63 C(5) C(7) 3 3.96 C(5) C(12) 15 3.67 C(5) C(13) 15 3.85 C(6) C(7) 3 3.92 C(6) C(7) 7 3.55 C(6) C(8) 7 3.55 C(7) C(7) 3 3.97 Molecule 1 x y z 3 1/2 + x 1/2 - y - z 4 - x 1/2 + y 1/2 - z 7 - 1/2 + x 1/2 - y - z 8 1 / 2 - x 1 - y 1/2 + z 15 - 1/2 - x 1 - y 1/2 + z 0.58171 X - 0.59819 Y - 0.55115 Z = -4.67686 and the plane through carbon atoms numbered 10 to 15 has equation 0.57104 X - 0.71348 Y - 0.40600 Z = -5.35895 o where X, Y and Z are coordinates i n A referred to the c r y s t a l axes. The angle between the normals to these two planes i s 10°40'. The deviations of the atoms from each of the planes are given i n Table XXIII. 86 TABLE XXIII DEVIATIONS OF THE ATOMS FROM THE MEAN PLANES THROUGH THE PHENYL RINGS Atom Deviation (X) from plane through carbon atoms numbered 4 to 9 10 to 15 As(l) -0.224 0.022 Cl(2) -2.521 -2.260 N (3) 0.108 0.004 C (4) 0.002 0.584 C (5) 0.022 0.681 C (6) -0.018 0.470 G (7) -0.007 0.224 C (8) 0.030 0.178 C (9) -0.029 0.302 C(10) 0.252 0.003 C ( l l ) 0.499 -0.007 C(12) 0.631 0.006 C(13) 0.487 -0.001 C(14) 0.224 -0.002 C(15) 0.107 0.002 Discussion Three c r y s t a l l i n e forms of phenarsazine chloride, a stable green form and two metastable yellow phases, have been reported previously (62). The present investigation suggests the existence of only one form of (unsolvated) phenarsazine chloride, which i s bright yellow when powdered and yellowish green as single c r y s t a l s , although the green colour may be due to traces of impurity formed i n the severe heating necessary f o r c r y s t a l l i z a t i o n . The metastable crystals from a variety of solvents contain solvent of c r y s t a l l i z a t i o n (in the case of xylene half a molecule per molecule of phenarsazine chloride), which i s rapi d l y l o s t when the crystals are removed from the mother l i q u o r . 87 The detailed analysis of the structure of the solvent- free crystals has established that the phenarsazine chloride molecule i s s l i g h t l y folded about the As...N a x i s , the angle between the two o-phenylene groups being 169°20', and the chlorine atom being outside t h i s angle. Each ri n g i s thus d i s  placed by only about 5° from a completely planar arrangement, and these deviations are probably not large enough to permit i s o l a t i o n of stable geometrical isomers. The deviations of the atoms (Table XXIII) from the o-phenylene planes indicate that the As and N atoms are situated accurately on the plane through C(10) - C(15), but are s i g n i f i c a n t l y displaced, i n opposite d i r e c t i o n s , from the C(4) - C(9) plane. These displacements indicate a s l i g h t twisting of the group C(4) - C(9), i n addi t i o n to the f o l d i n g of the molecule about the As...N Axis. This t w i s t i n g i s probably a r e s u l t of c r y s t a l packing forces; Table XXII shows that, of the sixteen shortest intermolecular contacts, thirteen involve atoms of the twisted r i n g . The As-Cl bond (2.30 ± 0.004 A) i s s i g n i f i c a n t l y longer than the distances reported (63) f o r A s C l ^ ^ . ^ X) and Me 2AsCl (2.18 % ), but i s about the same length as the corresponding bond i n chlorodiphenylarsine (2.26 ± 0.02 X) (64). I t i s d i f f i c u l t to account f o r these differences, although the s t e r i c effects of the large phenyl groups might be involved. The As-C bonds (mean length 1.917 ± 0.007 $) are s i g n i f i c a n t l y shorter than the normal single-bond distance (for example, 1.990 ± 0.019 X i n cacodyl disulphide) (65). The C-N distances (mean 1.371 ± 0.009 2) are also s i g n i f i c a n t l y less than the single- bond length (1.48 X) (63), and are about the same length as the C-N bond i n aromatic amines (1.371 X i n p-n i t r o a n i l i n e ( 6 6 ) f o r example). The As-C and C-N lengths suggest an extended aroma t i c system i n phenarsazine chloride, involving interaction of the arsenic and nitrogen lone pair electrons with the o- phenylene T T-electrons, with i n addition possibly dfr- ^ p^ bonding between the -fj--electrons and vacant 4d o r b i t a l s of the arsenic atom. The mean aromatic C-C distance i s 1.406 ± 0 . 0 0 5 X, and although there are some variations none of the ind i v i d u a l lengths d i f f e r s s i g n i f i c a n t l y from the mean value. The Cl-As-C angle (mean value 96.1° + 0.2°) i s normal f o r t r i v a l e n t arsenic, and i s si m i l a r to the corresponding . angle in chlorodiphenylarsine (96° ± 1°) ( 6 4 ) . The C-As-C angle (97.0° ± 0.4°) i s s i g n i f i c a n t l y smaller than the values of 105° - 106° i n other arsenic-phenyl compounds ( 6 4 , 67), probably as a re s u l t of s t r a i n due to the c y c l i c nature of the molecule and to i t s near-planarity. The C-N-C angle (128° + 0.9°) i s s i g n i f i c a n t l y larger than normal, again indicating some s t r a i n i n the central r i n g . The intermolecular distances (Table XXII) a l l correspond to van der Waals interactions, and do not require special comment. APPENDIX I STRUCTURE FACTOR TABLES TABLE A l . PERYLENE OBSERVED AND CALCULATED STRUCTURE FACTORS Planes with intensity 9 or greater. Used in the structure refinement. rt «. L F 0 0 - f CALC 2 0 0 32.2 34.0 4 0 0 6.11 2.5 6 0 0 5.7 4*6 « 0 0 22.6 - 23.2 10 0 0 19.5 - 16.0 10 0 1 12.' - 11.1 0 1 JO.8 34.6 0 1 59.1 67.6 0 1 62.9 73.7 0 1 26.3 - 26.8 0 1 8.8 9.0 0 1 13.0 - 10.7 0 2 7.9 tl.O 0 2 10.9 8.5 0 2 17.0 - 17.0 0 2 72.9 - 82.1 0 2 5.9 - 5.7 0 2 7.6 - 7.6 0 2 9.6 7.5 0 3 21.5 17.6 0 3 29.4 28 .7 0 3 11.0 - 9.5 0 4 10.7 12.6 0 4 34.5 34.7 0 4 29.7 - 30.2 0 4 53.1 53.0 0 4 18.9 19,3 0 5 23.5 22.0 0 5 9.9 9,7 0 5 16.4 - 16.5' 0 5 18.7 - 16.1 0 5 19.5 19,2 0 5 37.6 33.3 0 6 7*4 - 6.8 0 6 6.8 6.8 0 6 16.7 - 14.5 0 7 7.4 - 7.5 0 8 6*8 - 6.9 0 9 8.5 10.2 0 9 15.5 17.2 1 0 49.8 54.4 1 0 39.1 68.0 1 0 43.8 - 46.9 1 0 16.7 17,4 1 0 20.9 19.2 1 0 18.9 16.7 1 0 18.7 - 15.3 1 6.8 - 5.7 1 9.9 9.9 1 5.7 5.6 I 28.3 - 30.5 I 105.7 -118.9 1 28.3 - 31.9 1 43.3 45.8 I 10.7 10.5 1 3.1 - 3,7 I 31.7 - 32.9 1 33.6 34.5 1 16.7 17.5 I 26.3 26.0 1 7.9 8.7 2 9.9 - 9.7 2 14.7 14.4 1 7.9 7.7 2 4.5 - 4.1 ! 5.7 - 3.7 2 27.1 - 28.5 2 26.9 - 27.6 2 14,4 12.3 2 12.4 12.0 2 13.0 - 13.6 2 8.8 9.0 ! 5.1 - 5.7 3 5.9 5.4 3 12.7 - 13.0 3 17,0 16.6 3 20.4 20.0 J 13.0 13.7 3 11,3 - 10.7 i 7.9 - 6.9 4 8.5 - 9,7 4 18*7 16.0 4 11.0 - 11.» » 13.0 - 11.» 4 7.9 7.0 4 7 .4 - 7.5 4 14.1 - 13.7 4 35.6 - 34.7 4 13.9 ' 14.6 4 48.1 - 49.3 4 23.5 22.5 4 7,1 - 8.0 5 8.2 - 8.5 5 6.5 - 6.8 5 10.5 • 10,6 5 13.6 12.0 5 6.5 6.6 5 26.0 - 26.0 5 44.4 - 46.7 5 41.6 - 42.1 5 13.0 12.9 5 13.0 - 13.2 5 9.3 7.2 5 ld.V 17.4 6 11.0 - 11.6 6 7.4 - 6 . 4 6 13,5 9.6 6 7.6 - 7.2 7 13.6 12.8 8 11.9 - 1!,4 H K, L F Oai F CALC - 5 1 tl 22.1. 2C.9 - 4 1 6 - 2 i . l - b 1 9 24*6 - ?^,9 - 5 1 9 If.7 17.5 - 4 1 9 10.2 - 9.1 2 0 ft.9 - 6.1 1 2 0 ' i l .D 47,2 2 2 3 102.6 -123.7 2 c M . J 46. 1 6 • 2 0 8.2 9.3 7 I 3 9.3 8.0 2 0 6.a 7.0 - 4 2 I 43.0 - 47.1 - 3 2 1 1 11.4 - ! <!<>.> - 2 I i 1 17.6 -13 5.3 - 1 2 1 10. 9 - i 1 . 1 1 2 1 4.2 - 3.6 2 2 \ 4C.3 3 2 1 30.« - 32.7 4 2 1 13.6 - 13.9 ft I \ T.V H.5 6 I 1 20.3 29, i 7 I 1 10.2 10.3 - 7 2 2 7.9 - «,e - 5 2 2 8.5 - 11.5 - '* 2 2 9.9 - 11.0 - 1 2 i 2f*.6 so.: - 1 2 2 10.3 1 1.0 2 2 H.2 - 7.? 1 I 2 2>.6 21.3 3 2 2 6.8 - 6.5 6 2 2 6.5 - a,« - 5 2 i 13.3 14,4 - 4 2 3 12.7 - 13,5 - 3 2 3 40.4 41,7 1 2 3 7.6 8.6 4 2 3 13.9 - 13.1 5 2 3 17.0 17.0 6 2 3 9.6 - 8.1 - 6 2 4 11.0 - 11.3 - 5 2 4 25.4 27.3 - 4 2 4 39.7 - 37,7 2 4 9*0 - ti.8 J 2 4 If. 2 - a.3 2 2 4 20.9 19. tt 3 2 4 7.6 6.a 4 2 4 17,2 - 17,3 ft • 2 4 19.2 17.9 - 4 2 5 17,0 16,4 - 3 2 5 16.1 16.4 - 2" 2 ft ft.7 6.2 - l 2 9 * 7.4 - 7.1 2 5 17.0 - 17.4 ft 2 3 20.6 - 23.2 6 2 ft 26.6 - 26.0 7 2 5 14,4 - 12.2 - t. 2 6 11.6 10.7 - J 2 b 13.0 12.0 1 2 6 ft. 0 - 5.4 4 2 6 7,9 - 5,9 5 2 6 25.7 - 25.4 6 2 6 14.1 - 14.3 - l 2 7 7.9 8*0 1 2 7 7.6 - 7.0 - 6 2 8. 11. i 8.9 - 5 it ft 13.0 ' - VI.9 - 4 2 fl 9.0 8.6 - 3 2 tl 12.4 1 I .6 - 2 2 8 12.4 - 11.0 - i 2 0 7.6 6.2 - 5 I 9 7.9 - 7.0 1 ? 0 25.7 27.4 2 3 0 11.0 12.6 3 a ltJ.9 - ie.i 6 3 0 9.3 9.4 - £ 3 i 20.6 28.4 _ 5 3 1 57,7 6 1.6 - 4 3 l 18.7 21.6 - 3 3 1 17.3 - 10.3 - 2 3 l 22.6 - 22.9 - l 3 l 14,7 14.1 3 l 4.2 - 3.4 2 3 i 4.5 - 5.7 3 3 1 31.7 - 34.6 4 3 l 20. 8 - 31.4 ft 3 1 ?ft.7 - 26.0 -10 3 2 7.4 6.8 - 7 3 2 9.9 10.2 - 6 J 2 41. J 41.2 - ft 3 2 33.1 3 3.8 4 3 2 6.5 - 6.6 - 2 3 2 5.7 5.1' I 3 2 11.6 - 11.0 3 2 16.4 - 17.1 3 3 2 26.-t - 27.4 4 3 2 2ft.2 - 25.7 -10 3 3 17,0 16.0 - 5 3 3 15. 0 - 14.5 _ 4 3 i 22.1 22.0 - 2 3 3 31.4 - 31.0 - 1 s j 14. 1 13.4 j 3 7.4 - 5.a 4 3 3 25.7 23.7 5 3 3 24, j - it;-' 3 3 9.3 7.9 - s 3 4 15.3 - 15.C - 4 3 <• 11.6 a.7 - 2 3 4 5.4 - 6.1 3 4 5.7 5.4 2 3 4 6.8 5.0 3 3 4 13.C - 13.6 4 3 4 13.1 1 J.4 5 i 4 V.C - 9.1 - 4 3 5 8.9 3.7 & L F Odd F CALC - J 1 5 18.7 i d . * - 2 ) i .6 21.7 0 3 ; f-.v 3,4 3 5 17.3 - 17,3 7 3 5 11.6 - 10,3 . 6 3 6 " . 0 5, ? - 3 3 6 7.6 7.4 - 4 j 6 20.4 20.0 - 3 3 6 25.2 27.3 2 3 6 13.2 12.3 } i 6 *.9 10.2 5 j t 16.. - 15.7 4 J 6 12.2 - 12..' - i j 7 14.4 - 12.0 _ i J • 7 17.1- 20.4 - 1 3 7 1ft. 1 - 18.1 j 7 9. V *.fr - 4 J 6 t>.8 7.7 - 3 3 8 32. B - 33.4 - j J 9 26.6 26.8 - i' 3 * 11.0 - 9.6 4 0 19.4 4 0 cl.2 - 21.0 2 4 2 17.0 - 11.1 2 4 C 9,9 - 11.1 > o 6.5 6.9 - 6 It 1 17,0 16.0 - ; 4 1 52.6 55.0 - 4 4 1 35.9 37.0 - i 4 1 7. 1 9.1  2 4 1 d.5 - 9,3 - i 4 1 21.5 21.2 2 4 1 l l . i 11.5 3 4 1 U . 6 - 13.2 4 1 17.3 - 19.* 4 1 7.V - ES.4 -IC 4 2 ' 6,5 - 5,9 - b 4 2 J1.9 30,6 - 5 4 2 3V.1 41,& - 4 4 2 8.8 9.0 - 2 4 2 7.1 6.0 - i 4 2 28.6 - 28.4 4 2 22.9 22.6 1 4 I * 7 . l 27,8 2 4 2 7,9 8.0 3 4 2 22*1 - 22.3 7 4 2 7.4 - '6.2 4 2 12.7 11.3 . 3 4 3 14. 1 - 15.2 _ 3 4 3 23.2 - 23,6 . 2 4 3 39.V 40.1 - 1 4 3 33.9 - 33.7 Q 4 3 17.2 16.4 4 3 6.5 6.4 3 4 3 7.1 6.6 4 3 10.2 9.7 7 4 i 15.3 - 14.4 d 4 3 10.3 a.2 - 7 4 4 6.t) - b.2 - /, 4 4 6.2 7.2 • 3 4 4 13.6 - 12.7 - 2 4 4 5.9 4.9 4 4 5.4 - 4.3 1 4 4 5.9 - 5.4 2 4 4 7,9 6.5 3 4 4 8.2 - 8.5 4 4 4 6.5 - 7.3 - j 4 5 11. b 10.D - \ 4 5 5.7 • 6.a 4 4 5 10.2 9.2 5 4 5 9.0 5.2 - 6 4 6 14.7 - 14.5 - 5 * 6 9.9 - 9.0 2 4 6 17,) 21.7 3 4 6 35. 1 37.4 4 4 6 22.1 22.6 - 6 4 7 8.2 - 7.1 - 3 4 7 7, 1 5.2 - 2 4 7 7.9 - 6.4 4 7 20,1 19.5 1 4 7 10.7 - 10.4 3 4 7 13.0 13.2 - 4 4 8 9.6 - 5.3 - 3 4 8 13.0 13.2 - 1 4 8 7.9 - 6.7 4 8 10.2 8.3 1 5 0 8.8 - 9.4 3 5 0 6.8 - 7,3 7 5 0 7.9 6.3 8 5 0 7.4 - 7.0 - 6 5 1 9.3 - 9.7 - 4 5 1 9.3 - 11.2 - i 5 1 9. t - H.e - 1 5 1 7.1 - 5.0 2 5 1 14.4 14,9 '3 5 1 11.6 11.5 6 5 1 9.3 7.6 - 8 5 2 54.8 - 52.6 - 5 5 2 7.6 6.4 - 1 5 2 •13.2 9.1 5 2 30. b 33.2 1 5 2 16.1 17.2 2 5 2 44.4 44,0 A 5 2 9.9 - 8,3 - d 5 i 33.0 - 26.6 - 4 5 J 8,2 7.B - i 5 3 8.5 0.2 - i 5 3 17.3 - 16.7 - 1 5 3 9.9 9.5 5 3 31.4 30.8 5 j 9.9 - 8.1 7 5 3 9.3 7.6 - A 5 4 (1.8 9.8 ~ * 5 4 9.-* 6.5 H K L F Odi F CALC 0 5 4 14.1 - 12.7 0 3 5 10.2 11.2 - & 5 6 14.4 - 13.9 - 5 5 6 9.3 - 7,5 5 6 6.8 - 9.0 2 ft 6 7.1 - 5.6 3 3 6 12.7 13.? 4 3 6 10.7 10,9 - 6 5 f 10.7 - 9.9 - 1 5 7 12.4 -*•« 5 7 45*e - 4 ? . l 1 3 J 14.7 U . 7 0 5 d 13.0 • 12.1 , 0 0 9.0 7.8 1 6 0 d.i> - 9,0 6 0 B.3 9.2 - 7 6 1 10.7 - a.c - 3 6 1 * « * 11.0 - J 6 1 10,2 - 11.3 - 2 6 1 9.3 9.2 - i 6 1 7.1 5.6 2 6 1 5.9 - 6.6 - 7 6 2 27.1 - 25.4 - 6 6 2 14,4 • - 14.2 - 5 6. 2 11.6 11.7 - 2 6 2 7.1 - 6.5 - 1 6 2 11.9 - H . 3 6 i 22.6 - 21.9 1 6 2 41.6 41.5 2 6 2 9.8 - 6.5 7 6 2 7.V - 7.9 3 6 2 9.9 - 9.3 - 2 6 3 20.1 - 17.7 & 3 14.1 - 13.0 1 6 3 14.1 13*1 7 6 3 7.9 - a.7 1 6 4 9.0 - 8.9 j 6 5 7,9 9.0 - ' 6 6 7.9 - 9.8 1 6 6 10.9 - 16.8 2 6 6 20.9 - 18.6 3 6 6 16.4 16.3 4 6 6 16,1 - 13*7 - 1 6 7 16,4 - 13.9 6 7 17.8 - 17.8 1 6 7 19.9 - 20.1 2 6 7 19.0 - 20.3 - i 6 9 9.6 - 9.2 - 6 7 1 15.9 17.2 - 5 7 1 19.9 - 21.1 - 4 7 1 1ft.ft 19.2 - 2 7 I 6.2 5.3 4 7 1 15.3 - 12.7 5 7 1 y.o 7.1 - 7 ? 2 11.9 - 10.8 - 6 7 2 32.5 33.5 - ft 7 2 10.7 - 20.2 - 2 7 2 ' 9.5 - 7.3 - i 7 2 11.3 - 9.7 7 2 7.1 - 7.0 1 7 2 7,4 - 7,2 2 7 2 9.2 - 7.3 J 7 2 11,6 11.2 4 7 2 13.0 - 11.5 - 3 7 3 7.6 - 6*8 - 2 7 3 26.3 - *5.3 - 1 7 3 13.9 - 14.9 7 3 7.9 - 2.0 4 7 3 9.3 9,9 7 4 7.9 1.9 - 3 7 6 9.0 - 7.3 1 7 6 7.4 - 4.ft 2 7 6 14.4 12.5 3 7 6 16.4 - 14.7 - 2 7 7 16.1 14.0 9.6 - 9.9 2 8 0 9.0 8.3 - 6 8 1 - d.2 - 7.7 - 5 a i 11.9 10.0 - J 8 1 21.5 - 22.1 - 2 8 1 14.1 14.7 3 8 1 10.2 - 9.0 4 8 1 15.0 13.3 - 6 8 2 10.5 - 10.8 2 8 2 9.0 0.2 3 8 2 11.3 - 11.0 - 4 8 3 9.5 6.4 - 3 8 3 12.7 11*3 - 1 8 3 7.1 - 6.3 5 8 3 9 .0 10.0 - 5 8 4 10.ft 9.4 - 4 8 4 9.0 0.7 1 V 0 7.4 O.O 2 V 0 12,4 11.0 3 9 0 11.6 9.9 0 10 o 36.5 - 33.6 0 10 1 12.7 - 9.1 1 11 0 20.9 - 20.f 91 TABLE A l . (Continued). Planes with intensity less than 9. Omitted from the structure refinement. K L F Obd F CALC a 0 1 0.0 - 0.4 6 3 I 4.9 4,9 I 9 1 2. J 2.1 0 1 C O 3.1 c 0.0 0,4 0 2 0.0 - 1.5 0 2 0.0 - 0.1 0 2 0.0 - 1.3 0 3 C O - 1.6 0 3 0.0 - 4.5 0 2.ft .3.0 c 3 3. 1 - 3.ft 3 3 3.4 3.3 3 3 0.0 2.3 0 3 2.9 - 0.5 0 4 0.0 - 0.6 0 4 0.0 1.4 0 4 0.0 3.9 0 4 0.0 - 2.5 0 4 3.1 - 3.1 c 5 5.9 - 4.2 0 5 2.5 1.0 3 5 4,0 3.4 0 5 0.0 2.4 0 6 3,4 - 3.6 0 6 0.0 - 1.1 0 6 0.0 0.5 0 6 3.7 5.6 0 6.2 2.2 0 7 3.7 3.2 0 7 4,6 4.0 0 7 0.0 0.4 0 7 3.1 - 3.9 0 7 4.9 - 5.6 0 7 0.0 0.1 0 7 0.0 3.2 0 B 4.2 - 5.0 0 8 6.5 4.9 0 a 0.0 - 0.4 0 a 6.2 9.3 0 B 0.0 - 0.2 0 9 5.7 1.1 0 9 6.8 5.1 0 9 0.0 0.2 1 0 0.0 0.5 1 0 0.0 0.6 1 0 0.0 1.8 1 1 6.8 - 5.9 1 1 0.0 - 2.0 1 1 4.0 - 3.1 1 1 0.0 0.9 1 1 5.9 5.0 1 1 0.0 - 0.9 1 1 0.0 1.4 1 2 0.0 2.0 1 2 0.0 4.1 1 2 • 0.0 2.2 1 I 2.0 0.1 1 I 4.0 3.4 1 2 3.4 - 2.0 1 2 0.0 - 0.0 1 2 0.0 - 1.7 1 2 0.0 2.9 1 3 0.0 4.1 1 3 0.0 5.2 1 3 0.0 2.0. 1 3 2.9 - 2.5 1 3 0.0 - 3.4 1 3 2.8 2.4 1 3 0.0 - 0.9 1 3 4.0 - 2.9 1 3 0.0 - 2.5 1 3 0.0 4.6 1 3 0.0 - 2.7 1 3 0.0 - 1.6 1 4 0.0 - 1.0 1 4 4.2 - 3.9 1 4 0.0 0.9 1 4 3.4 0.0 1 4 0.0 - 0.5 1 4 0.0 0.0 1 4 6.8 5.7 1 5 0.0 1.1 1 3 2.9 0.1 1 5 0.0 - 2.6 0.0 0.9 1 5 2.9 1.0 1 3 0.0 - 6.3 1 ft 0.0 0.2 1 6 0.0 - 0.1 1 t 0.0 1.5 1 6 0.0 - 4.4 1 6 5.4 - 4.5 1 6 2.9 - 3.9 1 6 0.0 0.9 1 6 2.8 0*1 1 6 4,9 1.0 1 6 4.0 - 2.5 1 6 5.7 5.8 1 6 0.0 3.1 1 6 0.0 3.1 1 6 4.5 4.8 1 7 0.0 1.6 1 7 0.0 i.e 1 7 0.0 2.3 1 7 6.2 - 5.3 1 7 o.o - 1.1 1 7 0.0 1.1 1 7 4.2 2.7 i 7 3.7 - 1.1 1.0 3.2 0.2 3.0 0.4 0.1 3.4 2.1 1.3 0.3 0.1 r 0U5 f C»LC 7 * 0 2.6 - 3.7 4 4 3 4.0 4.7 8 i 0 3.0 - 3.3 5 4 3 5.9 6.6 9 3 0 0.0 - 4.0 - 9 4 4 0.0 - 0.1 10 i 0 3.0 - 3.1 - a 4 4 0.0 - 1.3 -10 i 1 0.0 - 0.8 - 6 4 4 3.7 - 0.9 - 9 i 1 3.4 - 1.7 - 5 4 4 4.5 2.6 - 9 i 1 0.0 1.9 - 1 4 4 0.0 1*3 - 7 i 1 5.1 3.6 ft 4 4 0.0 - 3.7 1 i 1 3.1 - 1.8 6 4 4 0.0 3.3 6 1 1 4.5 - 2.9 7 4 4 0.0 0*6 7 t l 3.7 3.3 6 4 4 0.0 0.9 9 i l 0.0 0.3 - 9 4 ft 0.0 0.1 9 t l 0.0 0.8 - 8 4 ft 0.0 3.1 - 9 2 4.2 - 4,6 - 7 4 ft 0.0 - 0.3 - 8 0.0 - 2.0 - 6 4 5 3.1 2.5 - 3 2 0.0 0.4 - 5 4 5 4.2 - 1.3 - 1 2 2.9 - 1.7 - 4 4 ft 4.3 - 3.6 0 2 3.1 0.6 - 2 4 ft 4.9 - 4.3 ft 3.4 2.2 0 4 5 4.2 - J .T 6 2 3.4 1.4 1 4 f t 0.0 0.9 7 2 0.0 - 2.7 2 4 f t 9. 1 - 1.2 9 0.0 - 3.3 3 4 5 0.0 1.6 9 2 0.0 0.2 6 4 f t 0.0 - 2.6 - 9 3 6.5 - 6.4 7 4 ft 5.9 6.S - 9 3 0.0 - 0.9 • - 8 4 6 0.0 - 3.4 - 7 3 0.0 0.4 - 7 4 6 9.4 - 2.9 - 6 3 4.8 - 3.1 - 4 4 6 0.0 - 0.2 - 3 3 3.7 6.4 - 3 4 6 0.0 - 0.2 1 3 0.0 - 1.3 - 2 4 6 9.4 5.1 2 3 0.0 0.2 - 1 4 6 0.0 - 1.6 3 3 0.0 2.6 0 4 6 2.6 1.6 7 3 0.0 • 0.6 1 4 6 3.1 - 3.9 3 0.0 - 2.0 ft 4 6 0.0 3.4 9 3 0.0 - 0.7 6 4 6 - 0.0 - 2.1 -10 4 0.0 2.2 - 7 4 7 o.o - 3.3 - 9 4 0.0 0.9 - ft 4 7 0.0 - 0.1 - 9 4 0.0 1.3 - 4 4' 7 0.0 8'* - 7 4 5.9 4.6 - 1 4 7 0.0 5.2 - 6 4 5.7 4.9 4 4 7 0.0 2.0 - 3 4 4.0 - 2.9 - 6 4 8 0.0 1.9 - i 4 0.0 - 0.7 - ft 4 8 0.0 - 2.5 1 4 3.1 2.6 - 2 4 8 9.4 - 2.9 6 4 0.0 2.2 1 4 8 0.0 - 0.7 7 4 0.0 - 0.7 2 4 9 C O - 2.5 9 4 0.0 - 0.1 3 4 8 5.1 - ft.7 - 9 5 0.0 - 0.3, - 3 4 9 0.0 2.4 - $ 3 0.0 - 0.4 - 2 4 9 0.0 0.3 - 7 3 5.1 3.3 • 1 4 9 6.2 3.1 - 6 3 4.9 3.0 2 ft 0 3.1 2.T . ft 5 4.0 1.0 4 ft 0 0.0 1.0 - 1 5 0.0 1.4 ft ft 0 0.0 1.6 1 3 2.5 4.1 6 9 0 0.0 - O.ft 2 5 3.4 - 0.6 9 ft 0 0.0 0.0 3 3 0.0 - 0.0 - 9 9 1 0.0 - 0.3 4 3 0.0 1.9 - 6 5 1 4.0 0.1 3 3 0.0 - 4.9 - 7 ft 1 4.5 - 4.0 _ 9 0.0 - 0.4 - ft 5 1 4.0 2.9 - 8 0.0 0.7 - 2 9 1 4.5 - 4.6 - 7 6 0.0 • 1.6 0 ft 1 2.9 - 2.5 - 2 4.8 - 3.6 1 9 1 4.2 4.9 - i 6 4.5 2.6 4 ft 1 9.4 - 2.9 6 4.5 - 0.6 9 ft 1 4.9 2.6 I & 5.1 - 2.7 7 ft 1 C O - 1.1 4 A 0.0 - 0.8 6 5 1 0.0 2.6 - g 7 0.0 3.0 9 5 1 0.0 0.9 - 7 7 0.0 1.4 - 9 ft 2 9.T - 2.9 _ j 7 0.0 - 1.0 - 7 9 2 ft.7 - 2.0 - 3 7 0.0 2.3 - 6 9 2 4.0 - 4 . 9 - 4 7 0.0 0.5 - 4 9 2 4.2 - 4*6 7 5.7 - 3.0 - 3 ft 2 C O 0.0 1 7 0.0 - 4.1 - 2 ft 2 4.2 - 2.6 3 7 0.0 0.9 3 ft • 2 0.0 3.3 4 7 0.0 - 0.5 4 ft 2 0.0 - 1.2 3 7 0.0 1.5 5 9 2 2.0 - O.ft - 7 8 0.0 - 0.6 6 9 2 0.0 - 2.9 - 4 8 0.0 0.5 7 5 2 9.4 2.6 - 5 9 0.0 - 0.9 - 9 5 3 0.0 9.7 8 0.0 - 1.3 - 7 .9 3 0.0 3.9 j 9 0.0 2.0 - 6 5 3 0.0 0.2 2 8 0.0 - 0.6 - 5 9 3 4.ft - 3.2 9 0.0 - 0.5 1 5 3 2.5 - 1.7 - 4 9 0.0 6.3 2 ft 3 C O - 0.3 - 3 9 0.0 - 3.7 3 5 3 0.0 0,2 _ ^ 9 0.0 - 1.1 4 3 3 2.8 2.4 _ t 9 0.0 0.4 9 9 3 0.0 4.0 9 0.0 0.5 8 ft 3 0,0 - 9.6 9 0.0 3.3 - 9 9 4 0.0 - 0.4 3 0 0.0 - 0.4 - 7 9 4 0.0 - 1.5 4 0 0.0 3.6 - 6 ft 4 0.0 - 0.2 0 4.0 . o .9 - ft ft 4 0.0 - 0.7 •j t 0 0.0 - 0.8 - 3 5 4 2.0 1.0 9 * 0 0 0.0 0.0 0.8 1.3 - 1 5 4 0.0 0.0 - 1.9 - 0.2 _ 9 0.0 - 1.3 1 5 4 0.0 0.0 _ 8 I 0.0 0.1 2 ft 4 4.0 - 3.9 _ j 1 3.1 - 0.9 1 ft 4 0.0 1.6 1 4.2 - 2.4 4 5 4 0.0 0.9 2.5 4.1 ft 9 4 0.0 0.6 I 2,8 - 0.9 6 ft 4 0.0 • 1.0 ft.7 3.2 7 9 4 0.0 0.0 a J_ 0.0 - 3.0 - 6 5 9 0.0 - 2.9 9 , 1 0.0 1.0 - T 5 ft' 0.0 0.0 _ 9 , 2 0.0 0.9 - 6 5 J C O 1.1 - 9 » 2 6.2 - 3.2 - ft 9 ft 4.0 - 1.0 _ T • 2 ft.9 6.1 - 4 9 ft 4.8 - 2.6 2 0.0 1.0 - 3 6 9 2.6 - 2.5 2' 4.6 - 6.2 - 2 ft ft 2.6 - 0.9 • 2 2,6 - 1.9 - 1 5 ft 9.4 - 2.6 » 2 3.1 1.2 1 5 9 0.0 - 1.5 t 2 0.0 2.2 2 ft 9 4.2 3.9 _ 9 , 3 0.0 - 1.9 3 9 9 0.0 0.2 - a 4 3 0.0 3.5 4 ft 5 ft.l 2.1 _ j 4 3 0.0 1.2 9 9 9 0.0 1.6 - 6 4 3 4.0 - 3.9 6 5 9 4.5 - 6.4 _ 4 h 3 ft.l - 5.8 - T 9 6 4.5 - 4.0 2 4 3 0.0 - O.ft - 4 ft * 0.0 - 1.9 TABLE A l . (Continued). 92 H K L F 085 F CALC - 2 6 • 4 2 .8 _ 1.1 - 1 6 4 2 8 - 0.) 6 4 4 2 3.0 2 6 4 0 *0 - 3.3 9 ft 4 0 .0 - 1.9 * 6 4 0 • 0 0.0 3 ft 4 0 • 0 1.3 6 ft 4 0 .0 - 1.7 - 7 ft 9 0 0 - 0.7 - 6 6 3 0 .0 • 2.0 - 3 6 9 0 0 - 0.8 - * 6 3 0 0 9.3 - 3 ft 3 5 4 3.2 - 2 ft 3 3 1 3.3 - 1 ft 3 0 0 - 2.1 0 ft 3 3 7 2.2 2 ft 5 0 0 3.7 3 6 3 0 0 - 0.0 * ft 5 0 0 - 3.ft 3 6 3 0 0 - 2.9 - 7 ft 6 0 0 - 1.2 - 6 ft 6 7 1 9.9 - * 6 ft 0 0 3.8 - 3 6 ft 0 0 0.6 - 2 6 ft 0 0 0.9 - 1 ft ft 0 0 0.1 0 ft ft 0 0 - 4.9 » 7 2.4 - 4 ft 7 0 0 0.4 - 3 ft 7 0 0 1.6 - 2 ft 7 0 0 - 1.6 • 2 ft 6 9 T - 4.9 7 0 9 4 4.1 2 7 0 2 8 - 1.6 3 7 0 3 7 2.8 4 7 0 0 0 - 1.2 9 7 0 0 0 9.4 6 7 0 0 0 7.3 7 7 0 0 0 0.2 • 8 7 1 0 0 0.4 - 7 7 1 0 0 - 0.4 - 3 7 1 2 8 - 1.3 - x 7 1 4 0 1.5 7 1 3 4 1.1 1 7 1 0 0 - 0.7 2 7 1 0 0 0.0 3 7 1 9 7 3.8 ft 7 1 0 0 - O.ft 7 7 1 0 0 0.1 - 8 7 2 0 0 1.0 — 4 7 2 4 5 ft.4 • 3 7 2 3 1 - 0.4 9 7 2 5 9 2.9 6 7 2 0 0 0.4 7 7 2 0 0 - 2.9 - 7 7 3 A 2 - 3.8 - ft 7 3 0 0 - O.T - 3 7 3 0 0 4.« - * 7 3 0 0 - 0.3 1 7 3 0 0 1.1 H K L F OBS _ F CALC H K L F OBS F CALC T j 0.0 0.0 ' 0 0 O.O - 1.2 7 3 0.0 - 0.7 8 3 0.0 • 0*1 3 y 1 0.0 4.2 6 9 0*0 - 0.0 j j 0.0 0.3 0 3 0.0 9.4 _ •» 7 4 0.0 1.9 8 9 4.9 7.0 - 6 4.2 _ 4.1 - 0 4 0.0 2.9 - 3 7 4.8 1.8 0 4 0.0 - 2.0 _ i 7 0.0 _ 0.1 - 0 4 0*0 0.3 _ j j 3.1 - 2.5 - 0 4 0.0 2.9 _ 2 7 4.8 1.9 0 4 0.0 2.6 . x 7 4 9.9 3.3 0 4 0.0 1.0 j 7 4 0*0 1.4 | 4 0.0 2.6 2 7 4 0.0 - 0.7 0 4 0.0 3.2 3 7 4 0.0 2.3 0 4 6.6 7.0 4 7 4 0.0 - 1.0 - 0 3 0.0 - 0.2 3 7 4 0.0 1.9 * 9 9 6.6 • 9.2 - 6 7 3 0.0 2.2 - 0 9 6.3 9.0 . 3 7 3 0.0 0.4 • 0 5 0.0 - 4.6 . 4 7 3 0.0 1.8 • 0 3 0.0 1.9 . i 7 3 0.0 - 2.2 9 5 0.0 0.7 - 2 7 3 3.1 5.4 0 9 0.0 1.4 _ | 7 3 0.0 - 0.2 0 3 0.0 0.1 7 9 0*0 - 1.1 0 3 0.0 1.1 7 3 0.0 1.3 0 4 6.2 7.3 2 7 3 0.0 - 4.1 0 ft 0.0 - 4.7 3 7 3 0.0 1.6 - 0 0 0.0 0.0 4 7 3 ft.2 4.6 0 0 3.7 0.9 - 3 7 0 0.0 2.2 0 ft 0.0 - O.O * 4 7 0 9.9 6.1 9 0.0 - 1.0 - 2 7 ft o.o - 3.0 9 0.0 - 0.9 . 1 7 0 0.0 - 0.1 - 9 1 0.0 2.9 o 7 ft 0.0 - 0.3 9 1 4.0 1.1 - 3 7 7 0.0 6.0 9 ] 0.0 - 0.9 _ j 7 7 6.2 4.8 9 1 0.0 - 3.9 7 7 6.8 - 3.6 9 1 0.0 - 6.1 1 0 g 0.0 3.0 9 1 0.0 - 2.1 3 0 0 0.0 6.3 9 1 0*0 - 6.1 4 ft 0 0.0 - 1.0 - 9 2 0.0 0.2 3 0 0.0 2.3 9 2 0*0 1.8 0 Q 0 0.0 4.4 9 2 0.0 - 2.3 _ 4 4.8 - 3.1 9 2 0.0 2.2 - 1 g I 3.4 2*7 9 2 0.0 2.4 0 j 0.0 - 0.7 V 2 0.0 1.6 I 5 1 0.0 2.3 - 9 3' 0.0 - 0.0 2 § 0.0 1.2 9 3 6.9 3.5 3 0 0.0 - 1.3 9 3 0.0 - 0.9 ( 0 * i 0.0 - 4.3 9 3 0.0 - 1.9 . 3 0 2 3.4 4.4 9 3 0.0 - 2.5 - 4 0 2 4.8 3.2 - 9 4 0.0 1.1 . 3 2 3.1 - 2.3 9 4 0.0 - 4.9 _ 2 0 2 0.0 O.ft 9 4 0.0 - 2.1 0.0 1.9 0.0 6.9 8 2 4.3 3.2 - 9 9 6.2 9.2 1 6 2 0.0 3.6 10 0 0.0 1.8 4 6 2 5.1 4.3 10 0 0*0 2.1 3 8 2 0.0 - 0.2 10 0 0.0 3.1 6 6 2 0.0 2.0 10 1 0*0 2.4 - ft 8 3 0.0 0.8 10 1 0.0 2.8 3 8 3 3.7 3.0 0 10 2 6*8 4.9 - 2 8 3 0.0 - 1.1 1 10 2 0.0 - 0.2 93 TABLE-A2. PYRENE OBSERVED AND CALCULATED STRUCTURE FACTORS (The r e f l e c t i o n s used i n the refinement are l i s t e d • f i r s t . Unobserved r e f l e c t i o n s , f o r which F Q i s l i s t e d as 0.0. have threshold values i n the range 1.5-3-0). plones included < 1 F OflS ft" f*LC e 0 7.4 6,9 0 0 44.4 44.1 0 0 4,1 - " 1.0 0 0 *.4 4.7 0 1 74,1 40,9 0 1 - *.7 fl 1 '4.4 14.• 0 4A.2 40.2 n 1 77,1 TA.2 0 1 T.A 6.A 0 t 70, 4 - 71,4 0 1 25.1 74,7 0 1 4,1 7,5 0 7 14.0 19,9 0 7 14,1 1ft,A 0 7 4.4 - 7.4 0 7 14.1 14.1 0 7 47,4 - 4ft. 1 0 7 11.* - 14,1 0 9 11.9 - 19.5 0 9 74.0 77.5 0 9 14.7 - 14,3 0 9 ft.* ft.l 0 9 4.1 7,1 0 7 IT,*, 16,7 0 1 4.4 - 7,9 0 4.1 - 1.7 0 11.0 1 y. A 0 •.0 7.* 0 ?o . i 70,» 0 1A,4 19,0 0 9 10.1 - 10,3 0 4.T 9.0 0 * 4.0 - 7.5 0 4 14.0 - 15.4 0 4 1*6 7.0 0 4 19. A 19.A 0 4 6.4 7.4 0 4 1,7 1.4 0 4, 4.0 - 7.7 0 9 17.2 11.3 0 4 1.7 A.A 0 4 14.0 - 17.9 0 5 T.6 7.9 0 4 4.9 - 4.9 0 4 9. A - T.5 0 9 6.4 6.4 0 A 4.6 - 4.9 0 ft 17.4 14,0 0 A 7.9 11.4 0 A 1«.4 71.4 0 T ft.l - 7.A 0 T 77.4 14,9 0 J T.A ft.4 0 A 6.7 9.1 0 9 5.0 4.6 0 40.A 45.6 0 44,2 51.4 0 74.0 - 26.9 0 11.9 - 9,5 0 9.4 - A . ? 0 9.0 - 7.A 0 1.7 2,0 0 4.7 4.0 0 4.9 - 4.A 1 10.9 10.4 1 10.) 9.0 1 15.4 - 16.4 1 7T.0 711.2 1 2.9 - 7.0 1 17.7 - 16.2 1 73.0 - 79.0' t 11.9 - 10.7 ] 47.6 91.2 1 17.9 14.4 1 1*.7 - 1 ? . A 1 20.0 - 10.1 1 4.1 1.9 1 4.7 4.4 1 1.6 7.8 1 7.3 - 7.1 1 6.8 6.9 1 9.6 1.2 t 10.9 11.7 1 fl.T 7.9 t A.ft - 5.A 7 4.2 - 4,? f 1.7 1.4 7 19,| 14.4 7 14.A 11.A 7 12.6 - 11.7 7 11.3 9.4 2 6.0 5.2 J 4.4 1.7 9 17.2 17.1 } U . I - 17.4 9 9.1 - 0.1 7 17.4 1«.7 9 ft.7 7.A 7 4.ft - 5.7 9 14.4 14,1 9 21*6 74.4 9 12.2 - 17.7 J 4.7 1.A 9 6.7 - 7.A 9 9.1 - 4,7 7 7.1 5.1 K F Li J J 1 F yn.- . 17 1 > 4, ti 4,4 10 y 4,7 - 1,7 • 1 1 1 4,4 4.1 - 9 4 7.A R.A - 7 1 4 l.A 7,4 • 7 4 4,1 4.4 - 4 1 1 77,1 71,7 - 4 4 4.1 - 4 . A - 7 1 * 74,1 - M . 4 - • 1 4 1 A . A - 1*,* - 1 1 11,2 17. 0 - 1 4 4.A A . ' 1 ft. 7 9,7 4 I - 1«,4 •1 1 1 4,4 - 4,1 1 4 14.4 - 7},t 7.4 7.3 4.7 - 4.1 5 1 1 15,0 46.1 4 4 1.9 4.^ * 1 1 77,9 70. A 4 4 7.1 - A . l 4 1 1 9, 1 - 9.1 -17 4 4.1 4.0 * 1 1 11.4 17.4 -10 9 11.0 - 11.1 4 1 1 4,7 - 7,4 - 9 9 17.4 10.4 * 7 1 4 1.* 4*9 - 4 4 7.A - R.R - A 1 4 11.4 - 14.A - 1 A 4.4 - 4.1 - 4 1 4 ?fl,4 - 71.4 4 4 6.4 - 7,7 - 4 1 4 10,1 - 10,7 4, 4 4,6 6,4 • 4 1 4 10,4 14.0 ' — 14 A T.4 - 5,1 - 7 1 4' 15.T - 17,2 -TO 0 4.«» - 4.4 • 1 1 4 4.0 - I,} - 9 A A. 7 4*4 1 4 7.9 - 7,2 7 A "•1 - 0,R 7 1 4 ft.l 9,1 1 A 1ft.1 70.7 1 1 4 4.7 4,4 4 ' A 10,4 - 10.4 4 1 4 9.4 1,7 5 6 4.7 4.7 -11 1 4 11,8 17,1 - 7 7 11.1 - 15.5 -10 1 4 4,4 - 1,» - 1 7 19.0 - 11.9 • 9 1 4 4.7 - 6.1 2 7 ••7 - It.A • A 1 1 n.4 - 14. 9 1 7 4.A ».7 - 1 1 4 10,4 - 4,4 - A A A, 7 6.4 - * 4 T. A - 9,5 - 1 A A, A - T.4 - 4 1 9 4.1 1,4 - 7 A O.O - 17.A 1 5 4.7 4.0 | 0 17.4 - 17.9 1 1 5 4.1 - 1,4 7 0 10, A 14,7 1 1 5 1.7 - 4,4 1 0 27.ft 74.4 A 1 5 5.1 - 6,4 4 0 14,4 19.2 -14 1 A 4.4 - 0.9 % 0 4.2 7.0 -17 1 • A 7.A - 7.0 m 7 J 10.9 - 11.7 -11 1 A 6,7 4.A - A 1 11.ft 14.3 1 A 6,7 - 7.1 a 4. 1 44.1 46.1 1 1 A 14,1 1ft.ft _ 4 1 4.4 - *.A 1 1 A 6,A - 9.7 * 1 1 75.4 - 77.9 4 1 6 5.4 4,4 - | I 11.A - *«,() 6 1 A 4.A - 6,7 - 1 1 4.1 9,9 - 1 1 7 4,5 - 2,5 1 7.A - 0.9 * 2 1 7 12.6 - 13.a I 1 11.4 17.7 - 1 I 7 5.1 - 6,1 7 1 9.7 - 4.9 ] 7 11.0 - 17.4 4 f 5.1 5.0 1 1 7 14,9 17,9 9 I 9,4 7.9 1 1 7 4,4 - 6,1 8 1 6*7 - 9.9 — 1 1 0 T.4 - 7.7 9 1 11.5 10.7 - 7 1 A 7.4 - 0,1 10 1 10.7 - 9,5 1 7 0 41.1 47,7 11 1 A.9 - 0,0 2 2 0 170,4 -177.9 - H 7 4.7 - 4,7 9 7 0 17,4 14.9 -11 7 ft,l - 7.1 4 2 0 2,11 1.0 -10 7 4.1 - 4.4 9 2 0 6.7 - 8.3 _ y 7 4,7 1.4 A 2 0 19.0 - 17.7 - A 2 1ft.ft 1ft.4 15 2 0 A.0 5.4 _ 9 2 17.4 17.0 -10 2 1 5.1 • 4.4 _ 4 2 1,1 - 1.3 - A 7 \ 4.7 - 4.A . 4 2 1,9 - 6.3 - 7 9 1 11,4 17.4 _ j 7 6 , 0 6.4 - A 7 1 17.0 - «,A 7 2.ft - 4.4 — 1 9 1 10.7 11.1 j 10.2 9.4 - 4 9 1 75.6 - 74,ft I y 4.1 - 4.1 - 1 2 1 91,fl -105,0 2 4.7 - 4.1 — 7 2 1 109.1 -106,7 7 2 11.7 14,0 - 1 2 1 T.I - 10.T . N . 2 7.4 - 4,4 1 2 1 14.6 - 11,7 10 7 14.1 - 15.9 2 2 1 1ft.1 16.A • j 7 4.4 - 5.9 1 2 1 4 , 7 - 5.5 -12 1 5.6 - 5.1 5 2 1 9.1 - 4,1 -11 4 5.6 - 4.7 A 2 1 7,4 7,7 _ j 1 1.4 - 2.7 • 7 1 4.A - 4,4 _ ^ 4 4.8' - 4.9 1© 2 1 4.0 - O.O „ 4 4 9.0 - 7.9 11 7 1 7.A - 7.4 „ A 4 4.A 9.1 11 2 1 9.0 4,7 _ j 4. 74.1 - 10.1 14 2 1 4,ft - 7,0 4 74.0 1«.A 19 2 1 5.0 4.0 I 1 76,11 - 74.0 — 17 2 7 7.4 - 4.1 2 4 19.4 - 19.4 -11 2 7 4.7 - 7.9 4 4 5.4 - 5.4 -10 2 7 6.2 - 9,4 4 1 5.0 - 4,ft - A 2 7 5.4 *• A.9 4 4. 9.6 1.A - 6 2 7 5.1 - 4.7 y 4 ft.l 10.1 - 5 2 7 • 1.1 - 1.7 9 1 7.9 - 6.5 - 4 7 7 4.0 - 10.A -10 4 6.7 4.0 - 1 7 ? 4.« - 4,1 — 9 4 10.9 - 11.1 — 7 7 7 7.A 4.A _ 0 4 10.4 17.7 2 7 A,A 0.9 _ y 4 4.7 5.1 1 2 7. ft.l 7.1 „ 4 4- 4.4 - 6.0 4 7 9 4.4 A . l - 7 4 17.4 14.7 4 2 2 9.4 4.3 _ 1 4 17.A - 14.7 6 2 2 22.A - 72.9 4 R.N - R.O T 2 2 5.7 6.8 y 4 1>4.4 - ?0,o 9 2 7 17,5 - 70,1 4 6.0 - 7.3 10 7 7 19.7 - 71 .7 4 4 5.7 - 4.9 IT 7 9 A.? - 4.6 -10 9 17.1 12.9 -17 7 1 4,9 - 4.1 - 9 4 10.1 - 11.7 -11 7 1 4,f< - 4,7 _ H % 14.1 11.ft - 1! 7 1 4.4 4.1 » 7 4 11.• 17.4 - 7 7 1 "a 7' - 7.4 _ 4 1.4 l.ft - 4 2 1 " A.7 4.9 • 4 4 A.7 4.0 - 4 2 1 11.4 14.0 4 9.0 - 4.A - 1 7 1 4.7 - 7,0 4 4.7 4,1 - 2 2 1 10.7 11.7 2 f, 0,0 ft.l - 1 2 1 14,4 15.3 f, 11.ft - 14.4 2 * 77.0 - 71.9 4 4 10.7 14,1 ) 9. 1 0.1 - 11.4 . *, ft A . R 11.ft 7 7 1 1A.4 - » A , * * 1 7 6 . 4 4.4 1 7 * 4.7 4,1 - 1 y 4.4 - 4,0 1 7 1 4.1 4.1 7 7 5.0 4.R A 9 1 4,1 - 4,4 _ A 4 4,1 4.4 ft 7 4.4 - 1 , A - 4 4 7. ^  7.A 9 2 1 6,4 - 6.4 _ 4 4 6.R n u f aai. t- CALL A - 1*.4 4 •> 14.0 . I*,7 7 4 3 4,7 - *,7 4 4 0 17.1 17,7 4 ' 4 r) 70,1 «0,7 4 4 10.9 ft.9 - R 4 | 4,7 4,4 - A 4 1 4*4 17,ft . q 4 • 14,7 11.ft . 4 4 * 44,4 AO a0 . 1 4 y 4,0 4,7 . 7 4 1 7,4 - 7.7 _ 1 4 1A*A 1A*ft 4 1 7.7 9,1 * 4 | A*4 - 5.5 4 4 11.4 1*.4 4 4 | 9*6 - 10*0 0 4 5.1 7*8 9 4 | 4.4 - 5*t -14 4 7 **• 6*A • 9 4 2 4*4 4.4 . 7 4 7 4.7 4,7 _ 4 4 7 74, ft 77.• - 4 4 7 47,7 111,4 - 4 4 7 4,ft 4*4 _ 2 4 7 4.7 4.A 4 7 11,4 - 9.0 7 4 7 ft.l ft.7 1 4 7 14.1 - 17,4 4 4 7 6.8 4,9 7 4 7 4.0 ft.G 0 4 2 74. ft 25.A 9 4 7 4.4 1.0 * l i 4 4 9.1 4.A _ 4 4 4 A.4 - 4.4 - 4 4 4.P - 4.1 - 7 4 4.4 . «.« . | 4 4, 11.2 11.0 4 4 7.0 - 7.9 1 4 4 9.5 - 9.3 2 4 1 ft.l S.7 0 4 1 9.ft 11.4 7 4 1 14.7 71.6 ft 4 1 ft.2 10*7 - 9 4 4 5,9 4*7 - ft 4 4 1.9 4*2 - 7 4 4 17.7 - 70.3 - A 4 4 11.ft 16,4 - 7 4 4 10,2 4.4 — 1 4 4 14.4 77,0 1 4 4 6,0 - 6.2 1 4 4 4.7 4*5 - 0 4 9 11.4 11*6 - 7 4 % 6,0 - 4.7 — 6 4 9 7.6 4.4 - 3 4 A 4.5 5,7 - 7 4 9 9.0 .0.0 5 4 4 9,9 - 10.1 A 4 9 11,6 11.4 - 1 A 6 4.0 - 4.4 7 4 6 4.2 - 1.1 4 4 6 6,8 7.2 - 5 A 0 3,0 4.0 — 4 4 0 11.2 12.11 t 5 0 19 ,0 - 19.4 7 5 0 15.1 - 17.0 1 5 0 7,4 - 6.1 4 5 0 9.5 ft.7 A 5 0 6.5 - 5.5 -11 5 1 4.7 4.6 —10 4 1 6.0 - 6.4 - 9 4 1 4,0 1.7 - 7 9 1 9 , 0 - 9.7 - 6 5 1 4.0 - 1.9 - 5 5 1 16.4 16.8 - 4 5 1 13.2 12.9 - 4 5 1 5.4 - 4.1 5 1 9,3 - 10.2 1 5 I 19,3 - 14.5 7 5 1 4.1 - 4.6 5 1 5,4 1.4 - 9 5 7 4.4 - 7.5 - ft 4 7 1A.1 - 14.ft 7 4 7 16.7 - 14.3 - A 4 7 9 , 0 4,4 - 4 4 7 11.9 10.7 1 5 9 9.1 9.9 7 4 7 lft.3 - 17.0 1 5 7 14.7 14.6 7 4 2 7.1 1.4 ft 4 ? 9.1 9.A - ft 4 1 7.ft - 5.0 7 4 1 A.0 1.1 • A 1 1 ft.4 - 7.0 - 7 4 1 4,1 - 6.0 — 1 4 1 1*9 4.1 4 1 1.4 4.0 1 5 1 11.0 19 .0 7 9 1 11.1 - 11.ft 1 9 1 7.6 7.1 4 4 1 R.2 - 10.1 y 4 1 10.4 11 .0 ft 5 1 6.4 6.7 - ft 4 4 6.0 - 4.6 - 7 4 4 17.4 19.1 - A 4 4 14.0 - 14,4 - 4 4 4 7 4.0 - 7 4 4 4.0 4.1 - 1 5 4 12.7 11.3 4 4 4 4.4 - 4.4 - ft 4 4 . A.7 - 4.4 - 7 4 1 ft.7 9,7 - 9 4 5 4.0 - 1.1 4 4 7.9 ft,4 9k TABLE A2. (Continued). <• L F 0»1 • C 4 L C ti * L ' f ft)l>» LAi,<. ft ft ft.7 l.ft -17 0 1 7,2 l . n 9 * ».l T.O - i n o 1 1.4 >«7 ft 0 1ft.0 - 11." ft 0 1 l.A 0,1 ft 0 1«.It - ift.o a o. 1 l.A 0,4 ft 0 ft.l - l.T 10 o I 1,7 0,0 ft 0 ft. ft - 4.7 -17 0 » W » 0,4 ft 1 ft.l - 1.1 -17 0 4 1,9 0,7 ft 1 a.T - 6.1 -10 o 4 1,7 1.0 ft 1 10.} - a . i - a 0 i o.o - 1,4 ft 1 T.l - ft.T 1 n 0 * 7 ,4 - 1.1 ft 1 T . l - 6.0 -17 o 4 0," - 0,1 ft i n.» - 1 1 . 1 - a o * 7,4 % T ft 1 9.9 - ft.n n o 4 l . o - n,4 ft 7 17.7 - Ift.l ft 0 4 o.o 0,7 ft 7 79.0 - 71.1 a n 4 l . t l.» ft > 0.0 - T.a 0 * 2,0 l.T ft 7 l.ft - i ,a - a 0 . 4 1.4 6.A ft 7 ft.l - ft.ft ft 0 4 0,0 - 0,1 ft 7 4.1 a . l 6 0 4 7,4 at l.T * > l.T - J . 1 a 0 4 2*1 - L A ft 7 ft.l - l.ft -10 n 0 1.0 - 0.1 ft 7 «.ft ft.ft - a 0 A 0,0 1,4 ft 7 a.ft - 6 .1 - ft 0 4 7,4 0.4 ft 1 T.4 - 1 . 1 * n A 7,6 7.7 ft i in.) - 4.7 - 7 0 4 7,A 4.1 » l ?.» - ft.ft ft 0 4 7.7 t.4 ft i ft.* ft.ft ft 0 A 7.A - 1.4 ft i I i . • - 11.T -1? 0 7 1.7 l.T ft 1 10.T 17.9 - a 0 7 2.1 O.A * 1 ft.4 - l.ft • 6 0 7 1.2 7.A » 9 10.T - 11.9 - ft 0 T 2.9 4.9 » 1 lT.a - ia.< ft 0 T 2.4 4,4 ft 1 10.1 - lO.ft - f ft 4 7.4 - 7.2 ft ft ft. 5 - «.t i 1 0 1.9 - 0,0 ft ft lft.ft 1 1 .a ft i 0 7.7 • «.9 » ft 1S.» - i«.a 10 i 0 l.T 1.A » • ft.l ».ft 11 i 1 7.7 ft. 1.0 ft ft 1.0 - ft.T 17 \ 0 1.4 • 0,0 t ft 10 T - in.« 1ft i P 4,7 7.9 ft ft T.ft - ft.i -17 i 1 1.2 0.4 ft ft ft.T - ft.n — 11 i 1 l.T - 1.1 « » ft.ft - ».a -10 1 1 2*6 0.8 T o a.ft ft.T ft l 1 1*4 1.6 » o 1.6 - ft.ft ft 1 1 2.8 1.8 T 0 1 .* - l.ft j 1 2.2 • 7.9 T 1 ft.T - 1 . 1 11 i 1 9.4 - 1*4 T 1 ft.ft l.ft -17 i 7 2.6 - 1.1 T i «.a - ft.l — 1 7 O.A 1.4 9 1 T . l T.n ft i 7 2.1 l.A 9 1 11.ft 11.1 - 1 1 l 1 !•* - 1.* y i ».» T.l — 11 l 4 2.8 — 1.6 » i %.» - ft.l - ft i 9 2.9 7.9 9 1 ».» ft.T — ft 7 4 0.0 — 1*9 T l 7.a - ft.l - ft i 4 0,0 - 7,1 7 1 ft.l 1 . 8 - ft i 1 1.7 7.A 7 J ft.8 l.ft — ft i 9 O.A 0.9 T 7 ft.T 1 . 1 T t ^ 1.6 fl.T 7 7 ft.9 - ft.* a i 4 l.T *>* T 7 ft.a l.ft 10 l 9 1.9 1.7 9 7 9 .9 l.ft -17 l 4 0.0 O.A 9 7 ft.a - ft.T — 11 i 4 2.6 O.A T 7 in.» 9*7 -10 l 4 l.T - 2.9 9 7 9.9 - T.T — 9 i 4 9.1 — 1.2 T 1 9 .9 l.ft — a i 4 2.4 — 0.4 9 i a.l ft.T i i 4 l.T 1*0 » 9 |0.1 - ft.l ft l 4 1.1 7.4 9 9 1 l.T lft.ft a l 4 7.4 - 1.5 T 9 ft.O - ft.ft 9 t 4 0,0 O.A T 9 ft.l - 1.9 a i 4 0,0 0.4 T 1 10.1 - i i . n 4 i 4 7.4 4.A T 9 1.1 - t.ft -1* i 4 9.9 - 7.1 T » 10.1 - 17.0 — a i 4 l.T - O.T T « a.ft ft.ft — T i 4 7.9 — 0.4 T 4 l.ft l.ft - 7 i 4 0.0 - 0.1 T ft 1 .1 - 9.1 - 1 i 4 7.4 9.7 T ft A.a 7 .4 7 i 4 1.9 - 1.4 T ft 1.0 ft.ft * i 4 0,0 - 0.1 ft 0 1.1 4.11 1 i 4 l.T 7 , r a i ft.o 7.ft ft i 4 9.1 — 4.A a i 1 2 . 7 11.7 T i 4 9,A - 6.4 ft 1 *.a 1.9 -10 i 4 1,4 - 0.1 a t l.ft - 4.0 - 4 i A 1.1 - 0.4 a 7 a . l l.ft - a i A 1.7 — 1.4 a > 9 . 1 «.9 - T t A 7.4 - 1.4 a 7 in.? 4 .1 - ft i A l.T - O.T « 7 ft.T - ft.ft - 1 i 6 0.0 0,1 a » i i . 7 T . l — ft i & 2.6 1,4 a i ».« - 1 i A 0,0 0.1 a i a, 7 - ft.l — 7 i 6 0.0 O.A a i l i . i 11.1 - 1 t A l,o - 4,4 a i IO.I - a.ft 7 i A 1,1 • 4,7 a i 4 . 1 ft.n ft A 0,0 1 . A • ft ft.T - l.ft — • i T n.o O.A a * i.» ft.ft - T i T 0,0 7,« « i ».» - 4.1 - ft l T 0.0 7.0 « l i . i ft.ft - ft i T 1.1 - 4,1 ft 7 «.« T.T - ft i T 0,0 1,4 ft •• t»,« - ».l 7 i T 2,4 0,4 » ' .A.7 ft.l ft i T 2.0 - 0.1 10 7 ft.ft - ft.n - ft i 4 1.1 7.A 10 1 ft.7 - 4 . 4 i A 1.7 «.l n 7 O.A 0.9 T 7 ^ 3.4 - 7.4 • 7 " 7.7 ! . C dories omitted in I 7.o ? 1.A % 4 4.1 11 7 1.4 17 7 0 7.1 - 0.1 K L t OftS t rn\.c -I? \ " 4,7 1 0,0 m 9.1 0 n fl.n - 7.1 \ 1 . 1.7 1 " , o 0.4 0,1 0 » ».n - ».7 1 m o.A 0 1,1 n i i.n n.ft *,n * 1 1,4 1 *.1 o,7 4,4 rt K I f Ob* F CALC 1 I f Ubh ¥ CAlC I, 7 1 1.4 O.T • T 1 A 7.9 I." 1 7 7 1 4 , 4 - 0.4 - A 1 A 7.7 •>  1.1 - 9 7 7 7.A 7.4 - A 1 A 1*7 «.4 •» 7 2 9 1.1 m 0.1 • A 1 A 7.7 - 1.0 - 1 2 » 0.0 1.1 - 1 4 A o.O o . l 7 2 7 2.4 4.7 - 7 4 A n.o - 4.4 1 2 7 o.o - O.T - 1 9 A 0.0 - 0,4 8 7 7 7.4 7.0 1 A 7.2 7,4 - t o 7 i 0,0 - 0.4 - 6 1 7 7.4 O.A - 9 7 i 1.1 1.7 - 5 1 7 2.6 - l.T - A 7 1 o.o o . l - A 1 T 7.4 4.1 4 7 *, 7.0 1.4 * 2 1 7 4.0 - 4.4 7 7 * l.T 0.0 1 7 1.4 0*9 -1 1 7 4 1.4 0,0 1 T 7.1 • 0.7 -10 7 ' 4 7.7 _ 1.1 * 1 1 A 1.4 1.1 •> A 7 4 7.1 _ 9.4 - 7 9 A A.ft - 4.4 - A 7 4 1.4 1.4 - A 9 9 1.4 4.9 - 4 7 4 1.4 0.4 4 0 7.7 - •1.0 - 7 2 4 l.A l.T A 0 1.1 1.7 1 2 4 1.1 l.A 4 0 l.T - 9.0 6 7 4 0,0 O.A 4 0 1.7 - 0.1 7 7 4 l.T 1.4 4 0 1.2 0.4 A > 4 7.1 1.4 4 0 0.0 1.1 9 7 4 1.4 1.4 -11 4 1 1.4 - 0.7 -11 ? 4 7.9 4* 1.1 *10 6 1 2.4 l.T - A 7 4 7.9 7.1 - 0 4 1 7.0 - 1.9 - T 7 4 4.6 9.0 - T 4 1 o.O - 1.0 - 4 7< 4 0,0 1.4 4 1 1*4 1*4 - 1 7 4 0.0 • 0,8 4 1 1*1 ft.4 - 7 7 4 0.0 - 0.1 A 1 1.4 - 1.1 9> 1 7 », 0,0 ft* 1.1 4 \ 1.1 — 7.0 7 4 7.4 l.T 4 1 7.1 0.9 | 7 4 4.1 1.1 A t 7,4 7.4 7 7 4 0.0 0.7 • 4»1 J 4 7 1.9 - 2.4 1 7 4 0,0 1.7 -10 A 7 1.6 l.A A 7 i 1.7 0.4 •> A 4 2 7.4 - 1.7 9 7 A 7.4 - 1.7 m % 4 7 0.4 ft.l A 7 4 7.• - 4.0 *• 1 A 7 1.9 7.T -19 7 A 4.7 ft. 4.4 4 2 7.2 l.A - A 2 A 7 . 6 1.4 A 7 !•« 0.4 - 7 7 6 1.4 1.0 4 2 2.4 7.4 - A 2 6 1.2 0.7 A 2 1.1 - 1*7 *» 9 2 6 2.9 l . o -14 4 i 1.9 7.4 - 4 2 6 2.4 ft. 7.4 -11 4 % 7.9 ft.9 - 9 7 A 0,0 0.7 • 10 4 1 0.0 O.T - 7 7 A 7.0 0.4' _ 9 4 i 7.7 1.4 - j 7 A 1.1 7 a A - A A 9 7.0 0.4 7 A l.T ft* 0.4 • 7 4 4 7.A — 0,1 * 7 A 7.0 l.T • A A 4 7.7 7 .A A 7 A 7.4 — 1.0 •» A 4 1 l.T — 7.0 — j 2 T 7.4 O.O 4 4 7.4 7.4 > A 7 T 2.4 • 1.1 A 4 7.A 1.2 •> 9 7 T 2.4 4.4 4 i l.T 0,0 - A 2 7 1.9 ft.4 4 43 2.0 0.9 * 9 2 7 7.6 7.A -10 4 4 7.1 - 0.7 ft 7 T 7.A - ft.l *» 9 4 4 2.7 - 9,4 2 7 4.4 1.7 a A 4 4 o.o •> 0.1 4- A 7 A 4.1 ft. T.7 • 1 4 4 7.4 - 9,5 A 4 0 1.4 - 1.7 4 4 o.o 1.4 T 1 0 7." l.A 4 4 l.A * O.A A 9 0 7.9 7.4 4 4 l.T ft.4 9 9 0 2,9 •> O.A 4 4 1.1 7.0 10 9 0 7.A - 0.4 4 4 1.4 4.4 11 1 0 7.9 ?.A 4 4 2.9 1.9 17 4 0 0.0 1.0 4 4 7.0 0.0 — 19 9 1 4.9 ft. l.T - — 4 4 A 7.6 l.A -17 9 1 7.1 1.0 - 9 4 9 1.7 0.9 — 11 9 1 7.4 - 7.T — 4 4 A 0.0 1.4 -10 4 1 7.A - 7.1 - 1 4 4 7.0 7.4 — tt 4 1 7.1 7.T 4 4 1.1 • 1.1 — A 9 1 l.A 0.7 4 4 O.O 0.2 1 4 1 1.7 • O.A 4 A 4.A 4.1 A 4 1 7.A » 4.1 4 4 1.9 O.A T 1 1 7.A - 4.0 4 A 7.7 0.0 -17 9 7 1.4 7.1 - A 4 A 7.A 7.4 - 9 1 7 7.A 7.0 - T 4 6 1.9 7.1 - A 9 7 4.4 - 7.1 - A 4 A 1.4 O.A 2 4 2 7.9 - 2.4 - 9 4 A 1.4 O.T 9 9 7 7.6 - 7.A - 4 4 A 2.6 - l.A A 1 7 7.9 1.1 — 7 4 A 0.0 7.4 A 4 7 1.4 - 0.9 - | 4 A O.ft » l.A 9 1 7 4.4 4» 0.1 A A 7.7 1,1 -14 1 « 4.9 4.7 4 A 7.7 4* 4.7 -10 4 1 0,0 •> 0.4 4 6 1.4 O.A - 9 1 1 ".0 7.4 — 4 4 T l.A A. A - A 1 1 4.4 • 9.4 - 1 4 T 7.4 •> 1.4 - 1 4 1 7.4 l . o - 7 4 T 9.4 4.4 - 7 . 1 1 1*6 - 7.7 - 1 A T 0.0 0.4 A 4 9 2.4 7.4 4 f 1.4 7.9 A 3 1 4.1 0.1 4 4 A 1.1 7.1 10 9 1 7.A » 1.4 — 9 4 9 4.A 4.4 -11 1 4 0,0 «»0 4 0 O.O 0.4 - A 1 4 0.0 — 4.4 4 0 1.1 1.4 - 4 9 4 1.1 7.4 4 ^ 0,0 1.0 - 9 1 4 o.O - 0.1 4 0 7.A O.A 1 1 4 t.4 1.4 4 f 1.4 0,4 A 1 A 0,0 - 7." - A 4 1 7.4 - l.T A 1 A 7.7 - 0.4 - 7 A 1 1.4 O.A 7 1 4 7.7 m 7.7 o 1 4 1 0,0 ft* 0.1 A 9 4 7.6 7.1 4 1 l.A 0.4 9 1 A 7.0 1.1 4 1 l.A 0.2 -11. 1 4 9.7 - 7*4 9 ) l.A O.A - A 1 A l.T 4.1 4 t 7.1 1,4 - 4 4 4 4.1 - 4.'- A 1 7.7 - 0,A a 4 4 4 1,4 1.4 A 1 0,0 ft* 1.4 — 7 9 4 ' 0,0 O.A 4 i 0,0 •* o.o - 1 1 4 0,0 t.4 4 ? 1*4 - T.l 0 1 4 7.4 4.1 A 7 7.7 0,1 * 4 7.C o . l 4 7 0.0 - o.A 7 9 4 l.T - 1*1 4 1 9.1 - 4.4 1 1 4 l.A • 4.4 9 7 0.0 1.1 4 9 4 7.2 1.4 4 7 7.9 — 1.7 T 1 4 1.9 1*7 4 7 l.A 1.1 — 9 1 A 1.1 1*A, A 7 7.A 7.1 - A 4 A I.** 4.7 4 7 1.4 9.7 95 TABLE; A2. (Continued). L F OBS F CALC H K L F OBS F CALC 7 1.T 1.4 A A 0 7.9 0.8 " * 1.6 7.4 8 6 0 0.0 - 0.9 o.o 1.1 9 6 0 1.9 0.7 *" 1 1 1.9 - 1.1 -11 6 1 9.4 _ 2.9 o.o 7.9 -10 6 1 4.0 4.6 " 1 1 7.4 4,7 • 9 A 1 2.6 0.0 4 1.9 O.A - 1 6 1 9,9 _ 0.9 1.1 9,0 " 4 6 1 2.0 - 0.2 1.4 1.9 - 7 6 1 1.9 1.2 * 7.6 1 ,6 - 1 A 1 2.1 1.9 * 2.1 0,2 9 6 1 2.0 - 1.2 * 1.2 4.4 4 6 1 0,0 _ 0.4 * o.o 4,0 5 6 1 9.6 4,4 4 0.0 1.9 6 A 1 7. 7 0.9 4 7.4 7.A 7 6 1 2.9 1.9 4 0,0 - 0,0 8 6 1 0,0 0.2 " 4 4 1.4 1.0 9 6 1 0.0 0.9 - 9 4 1.1 0,A -11 6 2 4.0 4.1 - 4 4 1.1 4.9 - 9 6 2 9.6 2.0 - 1 1 7.7 •» ] , i " 4 6 7 2.1 0.9 4 1.9 - 4.0 - '2 6 2 1.9 1.6 9 7.4 9.0 - 1 6 7 0.0 0.7 4 1.T 2.8 6 7 1.4 _ 1.1 - 8 4 0.0 - 2*1 1 A ? 7.0 0.1 - 6 4 1.2 1.1 7 6 7 2.A - 1.4 - 9 4 0.0 1.1 8 A 7 7.9 1.2 - 4 4 7.1 1 .2 - 6 6 1 1.7 7.4 - 9 1.4 0.1 - 2 6 3 1.2 m 0.8 0,0 - 0,2 - 1 6 1 2.9 2.7 4 1.9 1,4 6 '1 2.9 m 1.4 A 7.1 1,1 2 6 9 2.8 4.0 4 7.A 1,9 1 6 1 2.9 1.1 - A 6 0,0 1.7 7 6 1 2.9 0.9 - 7 7.6 4.9 - A 6 4 1.6 7.7 " 6 A 1.9 0.6 A 6 4 7.4 - 1.0 - 1 A 2.9 - 9.9 - 9 A 4 1.7 2.4 8 1.4 1.6 - 7 A 4 0,0 0.1 0 0.0 1.1 6 4 2.A _ 1.1 0 1.4 - 4.0' 1 6 4 2.2 _ 1.1 0 7.A - 0.1 7 4 1.9 0.4 F OUS F CALC 9.6 9.7 0.0 0.0 4.1 2.6 1.9 1.6 2.1 2.8 2.1 2.2 2.6 2.6 0.0 9.6 2.6 0.0 2.6 - 0.1 0.0 0.4 6.0 - 4.7 0.0 0.7 1.1 2.1 3.9 - 1.1 1.6 1.2 1.4 o.o - n.7 1.2 2.1 0.6 0.7 O.S 0.6 0.9 9.9 1.7 1.1 2.9 n.a 1.7 7.9 2>.9 7.1 96 TABLE. A3• l-0,r.(p-BROMOBENZEKESULPHONYL)-k,5,7-TRI-O-ACETYL-2,6- ANHYDRO-3-DEOXY-d^GLUCOHEPTITOL MEASURED AND CALCULATED STRUCTURE• AMPLITUDES..{Unobserved r e f l e c t i o n s , . which" are. • l i s t e d as •.0.0,.have threshold values, i n the range :5-17)- H. ft L F 06* F CALC 0 2 0 76,8 62.0 0 * 0 53.6 51.8 0 6 0 97.2 103.7 0 • 6 0 40.4 35.7 0 10 0 210.9 226.7 0 ii 0 92.0 5*. 3 0 1ft 0 20.2 12.9 0 1ft 0 61.V 64.2 0 la 0 27.9 31.0 0 20 0 0.0 6.6 0 22 0 39.5 37.9 0 2* 0 17.6 21.* 0 26 0 16.7 17.5 1 0 ft!.7 39.* 2 0 ft.3 1.3 ) 0 21.5 20.6 ft 0 1ft.7 11.* 3 0 17.9 16.7 6 0 90.6 92.1 7 0 57.1 *9.7 tt 0 ftO.ft 46.2 V 0 75.4 70.* 10 0 19.2 13.5 11 0 31.7 32.* 12 0 24.4 31.* 1» 0 31.7 29.* Ift 0 28.2 30.0 1J 0 62.2 59.9 1ft 0 25.6 23.9 17 0 35.9 35.7 1ft 0 107,2 107.3 IV 0 27.6 27.* 20 0 16.1 8.7 21 0 43.6 44.1 22 0 36.9 37.5 23 0 16.0 18.9 2ft 0 0.0 5.3 2ft 0 29.8 30.2 2« 0 21.1 15.1 0 0 109.7 96.2 1 0 ft*.9 «3.9 2 0 62.9 ft*.9 ) 0 169.5 161.* ft 0 32.1 34.1 3 0 50.* 96.1 ft 0 8.3 1.6 7 0 65.3 81.7 B 0 1*2.3 1*2.9 9 0 46.5 *8.8 10 0 3*.ft 37.1 11 0 43.0 40.7 12 0 0.0 5.6 13 0 58.1 66.4 1ft 0 119.6 115.1 15 0 37.8 37.* 1ft 0 0.0 0 . * 17 0 13.1 13.0 18 0 *6.2 45.1 19 0 33.9 38.8 20 0 0.0 7.8 21 0 20.8 22.7 22 0 0.0 9.2 23 0 0.0 9.9 2ft 0 21.5 22.1 25 0 0.0 8.5 2ft 0 0.0 13.2 1 0 78.9 66.9 2 0 38.2 31.0 3 0 *3.3 39.8 ft 0 239.2 233.6 5 0 23.7 26.8 6 0 80.6 66.3 7 0 75.7 7*.8 8 0 54. 9 55.* 9 0 0.0 3.1 10 0 31.1 31.7 11 0 0.0 5.8 12 0 18.3 22.7 13 0 91.6 91.* 1ft 0 59.7 61.9 15 0 69.9 91.0 16 0 15.* 9.6 17 0 0.0 6.1 18 0 23.7 21.7 IV 0 31.* 32.3 20 0 18.3 13.3 21 0 * 6 . t *7.9 22 0 18.9 26.2 2) 0 30.3 26.9 2« 0 0.0 5.8 25 0 40.1 36.7 26 0 21.1 20.5 0 0 168.9 155.9 1 0 102.7 99.0 2 0 16.0 11.7 3 0 30.0 49.1 ft 0 22.* 19.8 3 0 130.3 126.6 ft 0 41.4 43.6 7 0 95.6 101.4 8 0 2*.* 24.1 0 19.2 15.2 10 0 36.6 39.5 11 0 87.3 67.9 12 0 *8.8 4 6 . * 13 0 48.1 48.1 1« 0 28.9 27.9 15 0 54.9 55.2 16 0 0.0 9.3 17 0 * 8 . * 45.6 18 0 0.0 1.2 19 0 0.0 5.2 20 0 0.0 11.3 21 0 0.0 14.2 M ft L F OSS F CALC 4 22 0 0.0 14.2 4 23 0 0.0 1.6 4 24 0 22.4 22.5 4 25 0 0.0 4.9 5 1 0 9.9 6.0 5 2 0 30.3 32.8 5 J 0 0.0 11.1 5 4 0 25.0 19.4 6 5 0 0.0 7.9 5 6 0 36.6 33.6 3 7 0 59.* 60.0 5 8 0 17.9 20.2 5 9 0 32.3 52.9 5 10 0 62.9 67.2 5 11 0 11.3 9.9 3 12 0 16.3 17.7 5 13 0 32.* 32.0 5 1* 0 70.3 72.2 5 15 0 0.0 3.6 5 16 0 16.0 21.3 3 17 0 29.8 28.8 3 16 0 24.0 28.8 3 19 0 0.0 1.3 3 20 0 0.0 13.1 3 21 0 17.6 15.6 5 22 ' 0 0.0 10.7 5 23 0 29.5 26.0 5 2* 0 19.3 17.0 6 0 0 112.0 99.0 6 1 0 18.3 19.3 6 2 0 ii.a 2.9 6 3 0 0.0 1.3 6 * 0 60.9 67.0 6 3 0 36.6 33.1 6 6 0 69.6 71.0 6 7 0 12.3 6.9 6 a 0 92.4 99.2 6 9 0 24.0 20.8 6 10 0 18.3 14.0 6 11 0 31.1 29.9 6 12 0 0.0 12.3 6 13 0 0.0 6.9 6 1* 0 *7.2 46.5 6 13 0 18.9 21.8 6 16 0 0.0 0.4 6 17 0 16.6 16.2 6 18 0 23.3 25.0 6 19 0 0.0 6.3 6 20 0 0.0 13.2 6 21 0 28.5 33.4 6 22 0 0.0 2.* 6 23 0 0.0 7.9 7 1 0 15.0 11.9 7 2 0 100.1 86.2 7 3 0 22.6 27.8 7 * 0 99.2 92.* 7 5 0 24.0 21.8 7 6 0 16.0 1*.8 7 7 0 33.3 32.1 7 8 0 0.0 6.8 7 9 0 0.0 3.2 7 10 0 26.6 27.* 7 11 0 19.2 16.3 7 12 0 27.6 29.9 7 13 0 31.1 31.9 7 1* 0 69.6 71.0 7 13 0 22.1 21.2 7 16 0 18.9 20.5 7 17 0 0.0 17.3 7 18 0 0.0 10.8 7 19 0 0.0 3.3 7 20 0 17.6 17.3 7 21 0 19.9 19.0 7 22 0 18.3 12.4 6 0 0 48.1 *6.9 8 1 0 10.9 13.8 8 2 0 23.3 28.6 6 3 0 32.4 30.* 8 * 0 19.4 13.6 8 5 0 . 54.5 58.1 8 6 0 10.9 *.3 8 7 0 22.8 25.8 8 8 0 48.4 46.2 8 9 0 0.0 2.0 8 10 0 13.4 6.2 6 11 0 47.6 53.* 6 12 0 16.7 13.7 8 13 0 28.9 31.9 8 1* 0 40.4 *1.9 8 13 0 20.8 21.1 8 16 0 0.0 9.7 a 17 0 0.0 11.* 6 18 0 0.0 6.3 8 19 0 0.0 13.0 6 20 0 0.0 6.2 9 1 0 0.0 4.7 9 2 0 20.2 18.6 9 3 0 18.3 20.1 9 * 0 17.0 16.6 9 5 0 31.4 30.9 9 6 0 16.7 14.5 9 7 0 45.9 49.4 9 9 0 0.0 0.4 9 9 0 13.4 8.0 9 10 0 50.0 51.9 V 11 0 17.9 22.9 9 12 0 38.6 38.7 9 13 0 42.7 41.3 9 14 0 13.8 10.5 9 15 0 17.0 12.9 9 16 0 0.0 16.8 9 17 0 0.0 17.3 9 18 0 0.0 8.2 0 0 0 27.9 23.0 rt ft L F 085 F C A L C 10 1 0 0.0 13.1 10 2 0 44.6 41.8 10 3 0 16.0 20.8 10 4 0 0.0 0.2 10 3 0 16.7 14.7 10 6 0 16.7 16.6 10 7 0 23.1 23.1 10 a 0 4 8 . * 48.5 10 9 0 22.1 26.0 10 10 0 37.2 34.3 10 11 0 26.0 26.7 10 12 0 24.4 18.5 10 13 0 22.4 21.0 10 14 0 16.6 15.2 10 13 0 27.2 21.* 10 16 0 22.8 22.8 11 1 0 32.7 12.0 11 2 0 0.0 1.1 11 3 0 0.0 0.3 11 * 0 0.0 3 . * 11 3 0 0.0 6.1 11 ft 0 0.0 3.3 11 7 0 26.0 23.6 11 . 8 0 0.0 0.1 11 » 0 25.6 23.* 11 10 0 39.8 39.3 11 11 0 0.0 2.3 11 12 0 22.1 21.8 11 13 0 19.2 13.9 12 0 0 38.8 16.3 12 1 0 0.0 2.6 12 2 0 l « . l 9.3 12 3 0 13.7 12.0 12 * 0 13.7 13.1 12 3 0 10.8 23.3 12 ft 0 20.6 19.6 12 7 0 19.2 16.* 12 8 0 0.0 8.3 0 0 1 112.7 103.7 0 1 X 0.0 5.7 0 2 1 29.8 31.1 0 3 1 73.5 71.3 0 * 1 111.0 119.0 0 3 1 67.1 66.2 0 6 1 121.0 118.* a 7 1 50.0 33.2 0 8 1 3ft.3 3*.ft 0 9 1 *1.7 *1.2 0 10 1 12.8 13.2 0 11 1 22.1 20.1 0 12 1 62.6 63.6 0 13 1 0.0 1.3 0 1* 1 61.9 38.6 0 19 1 17.6 23.7 0 16 1 17.9 22.7 0 17 1 *2.3 * 0 . * 0 18 1 29.9 29.2 0 19 1 79.0 81.1 0 20 1 29.5 31.6 0 21 1 0.0 0 22 1 18.3 '25.7 0 23 1 0.0 8.9 0 2* 1 20.8 21.6 0 23 1 0.0 11.8 0 26 1 22.* 22.2 1 0 1 76.7 65.2 1 1 1 218.3 210.0 1 2 1 88.3 88.9 1 3 1 33.9 41.1 1 * 1 139.3 129.2 1 5 1 71.9 61.6 1 6 1 93.3 44.6 1 7 1 137.* 136.6 1 8 1 65.1 66.8 1 9 1 90.2 82.7 1 10 1 22.* 20.1 1 11 1 27.9 28.0 1 12 1 *7.6 32.3 1 13 1 96.8 60.0 1 1* 1 46.5 45.5 1 15 1 17.9 20.5 1 16 1 15.0 12.6 1 17 1 *5.2 43.5 1 18 1 45.9 47.2 1 19 1 15.0 19.6 1 20 1 33.0 32.1 1 21 1 32.1 13.1 1 22 1 13.4 15.4 1 23 1 32.4 34.8 1 2* 1 0.0 14.0 1 25 1 0.0 8.1 1 26 1 33.0 36.7 2 0 1 108.2 106.8 2 1 1 34.2 62.1 2 2 1 46.2 33.3 2 i 1 30.3 30.3 2 * 1 137.1 119.7 2 5 1 164.3 178.6 2 6 1 33.6 34.3 2 7 1 72.8 63.1 2 8 1 48.8 4*. 3 2 9 1 19.9 20.2 2 10 1 41.7 39.9 2 11 1 66.7 63.5 2 12 1 52.3 * 9 . 2 2 13 1 2 2 . 4 19.6 2 1* 1 46.2 *5.7 2 13 1 47.8 50.9 2 16 1 40.7 40.2 2 . 17 1 26.6 2 2 . * 2 18 1 14.7 11.2 2 19 1 2 2 . 6 20.7 2 20 1 34.6 35.2 2 21 1 32.7 14.3 rt ft L f 08S F CALC 22 1 21.5 16.3 23 1 0.0 11.2 2* 1 0.0 7.3 23 1 20.5 21.* 26 1 0.0 10.8 0 1 44.3 44.0 1 1 28.2 33.2 2 1 71.9 73.* 3 1 31.7 30.3 * 1 9ft.0 92.0 3 i ia.a 39.0 ft 1 129.* 12ft.B 7 i is.a 13.6 6 1 31.1 27.6 9 1 81.1 79.7 10 1 80.6 79.3 11 1 42.1 39.* 12 1 10.3 26.8 13 1 1ft.1 • 3.ft 1* 1 21.8 22.3 13 1 49.7 33.1 16 1 99.3 34.6 17 1 24.4 24.6 18 1 27.2 29.9 19 1 45.6 46.1 20 1 21.1 26.0 21 1 18.9 16.0 22 1 17.6 IB.3 23 1 28.2 26.9 2* 1 0.0 ft.2 23 1 18.9 19.9 0 1 0.0 9.0 1 1 22.ft 21.9 2 1 56.a 97.1 3 1 90.6 96.6 " « 1 27.2 29.ft 3 1 72.2 70.0 6 1 1ft.0 16.9 7 1 69.9 67.1 9 1 67.7 6ft.0 V 1 82.3 74.6 10 1 39.0 35.7 11 1 11.8 13.6 12 1 93.3 92.2 13 1 52.0- 49.1 1* 1 12.7 3ft. 9 15 1 26.9 27.9 It 1 22.ft 21.7 17 1 20.2 20.1 ia 1 20.2 21.4 19 1 31.7 30.2 20 1 IB.3 21.4 21 1 0.0 ft.8 22 1 3ft.O 3*.3 23 1 0.0 10.2 2* 1 26.9 2».0 29 1 0.0 5.B 0 1 47.2 ft*.ft 1 1 36.2 37.a 2 1 39.8 »2.0 3 1 0.0 B.7 * 1 0.0 3.7 9 1 45.9 • 7.1 6 1 0.0 B.9 7 1 65.1 60.6 6 1 49.7 45.2 9 1 82.5 78.3 10 1 19.2 22.9 11 1 41.4 39.7 12 1 29.9 29.9 13 1 91.1 .96.* 1* 1 29.2 26.9 13 1 24.7 22.9 16 1 23.7 23.1 17 1 2«. 0 27.3 18 1 36.6 41.3 19 1 26.9 28.ft 20 1 0.0 lft.ft 21 1 21.1 2 3 . * 22 1 0.0 ft.ft 23 1 0.0 11.2 2ft 1 0.0 10.7 0 1 1*9.9 1*7.3 1 1 36.2 31.3 2 1 17.3 18.7 3 1 38.2 39.1 ft 1 17.1 27.0 3 1 *5.6 46.5 6 1 43.6 46.9 7 1 23.6 24.8 8 1 17.6 11.3 9 1 51.3 49.1 10 1 71.9 67.1 11 1 2*.7 27.* 12 1 *1.4 40.3 13 1 28.5 28.7 14 1 19.9 18.9 13 1 30.1 30.6 16 1 23.1 24.4 17 1 15.7 11.0 IB 1 0.0 10.* IV 1 31.7 29.9 20 1 0.0 10.6 21 1 0.0 5.1 22 1 0.0 5.1 23 1 17.0 15.3 0 1 37.8 33.0 1 1 30.7 3 0 . * 2 1 42.0 *2.2 3 1 23.7 2*.7 4 1 35.9 39.6 5 1 17.9 2*.* 0 1 27.2 27.2 7 1 28.2 28.6 97 TABLE A3- (Continued). » IC I F Or*S F C»LC rt a 1 16.3 14.1 0 24 9 1 64.3 37.8 1 0 10 1 14.7 12.7 1 1 11 1 0.0 1.0 1 2 12 1 42.3 41.2 1 i 13 1 27.2 27.3 i 4 1* 1 0.0 6.4 5 .15 1 35.3 36.3 j 6 16 1 0.0 4.7 7 IT 1 0.0 5.4 6 16 1 43.0 42.2 9 I* 1 0.0 4.1 1 10 20 1 0.0 8.3 1 11 21 r 24.4 21.6 1 12 0 1 30.5 29.4 1 13 1 1 0.0 7.9 1 14 2 1 14.4 10.9 1 15 3 i 69.a 66.2 1 16 4 1 29.5 36.6 1 17 3 1 18.3 14.0 1 18 6 1 19.6 22.3 1 19 7 1 0.0 7.6 1 20 a 1 18.6 20.0 1 21 9 1 27.9 27.3 1 22 10 1 25.6 28.0 1 23 11 1 19.9 16.8 1 24 12 1 33.0 32.7 2 0 13 1 39.1 37.4 2 1 1* 1 31.1 30.7 2 2 19 1 18.3 15.1 2 3 It 1 14.4 16.2 2 4 17 1 19.9 20.9 2 3 ia 1 0.0 3.6 2 6 19 1 17.0 14.7 2 7 20 1 17.0 14.8 2 8 0 1 27.2 23.6 2 » 1 1 21.1 17.3 2 10 2 1 0.0 9.3 2 11 3 1 15.0 12.8 2 12 4 1 37.9 35.1 2 13 3 1 13.4 11.1 2 14 t 1 32.1 39.2 2 13 7 1 24.0 27.0 2 16 a 1 21.8 19.6 2 17 V 1 61.1 42.1 2 18 10 1 43.0 42.3 2 19 11 1 0.0 4.2 2 20 12 1 0.0 14.7 2 21 13 1 0.0 11.6 2 22 14 1 0.0 8.9 2 23 15 1 37.5 38.5 2 24 It 1 27.6 23.2 3 0 17 1 16.0 9.7 3 1 10 1 0.0 3.2 3 2 0' 1 27.9 30.7 3 3 1 1 15.4 16.1 3 4 2 1 0.0 3.9 3 3 3 1 0.0 11.8 3 6 4 1 16.0 12.1 3 7 3 1 21.1 27.9 3 8 t 1 17.9 13.6 3 9 7 1 0.0 2.9 3 10 a 1 27.2 25.1 3 11 9 1 37.3 36.4 3 12 10 1 0.0 9.8 3 13 l i 1 18.6 19.8 3 14 12 1 30.1 26.6 3 15 13 1 0.0 2.1 3 16 14 1 44.9 36.7 3 17 15 1 0.0 14.8 3 18 0 1 16.3 17.6 3 19 1 1 28.9 28.3 3 20 2 1 15.0 14.4 3 21 3 1 o.o • 11.6 3 22 4 1 15.7 12.9 3 23 3 1 19.2 19.6 3 24 t 1 24.0 25.6 4 0 7 1 0.0 15.1 4 1 a 1 29.6 27.4 2 V 1 24.0 24.9 4 3 10 1 14.7 8.4 4 4 i i 1 25.3 20.6 4 5 12 1 0.0 12.3 4 6 0 1 0.0 8.2 4 7 1 1 0.0 9.3 4 . 6 2 1 16.7 14.7 4 9 3 1 0.0 4.9 4 10 4 1 0.0 19.6 4 11 3 1 16.7 20.5 4 12 6 1 0.0 3.8 4 13 0 0 2 28.9 28.5 14 0 1 2 13.4 20.2 4 15 0 2 2 20.8 28.5 4 16 0 3 2 10.6 26.9 4 17 0 4 2 0.0 10.6 4 18 0 9 2 66.4 61.8 4 19 0 6 2 28.2 30.8 4 20 0 7 2 35.6 32.2 4 21 0 a 2 17.9 8.9 4 22 0 9 2 76.4 70.4 4 23 0 10 2 22.1 22.7 3 0 0 11 2 35.6 36.0 3 1 0 12 2 0.0 0.8 5 2 0 13 2 24.0 29.7 5 3 0 16 2 12.8 10.5 5 4 0 13 2 34.0 35.3 5 6 0 16 2 17.3 17.5 5 6 0 17 2 12.8 16.6 5 7 0 10 2 23.4 23.7 5 8 0 19 2 68.7 76.0 5 9 0 20 2 0.0 9.7 5 10 0 21 2 32.7 33.5 5 11 0 22 2 0.0 13.9 5 12 0 23 2 27.9 33.2 5 13 F Odb 0.0 62.2 78.3 45.2 109.5 53.9 33.7 54.2 60.0 23.1 31.1 21.3 41.1 36.2 38.8 21.8 29.6 13.4 0.0 0.0 0.0 25.0 23.7 0.0 19.9 0.0 50.7 34.6 13.4 63.3 13.1 33.0 11.8 50.4 0.0 36.2 83.8 43.6 32. 1 18.6 28.5 0.0 23.6 32.7 16.3 18.9 16.0 16.3 33.7 0.0 39.8 43.6 18.3 18.6 33.3 83.8 13.4 91.8 30.8 0.0 52.6 43.0 31.1 14.4 0.0 56.8 15.0 13.7 17.3 0.0 14.7 0.0 35.3 15.4 0.0 0.0 11.5 24.7 41.4 11.5 24.4 12.8 24.4 21.1 39.6 29.2 49. 1 37.8 20.5 22.4 31.4 19.2 17.9 19.9 19.9 0.0 22.4 20.2 0.0 0.0 0.0 66.7 18.9 39.5 25.6 27.2 37.8 43.6 42.0 45.6 23.4 58. 7 0.0 17.3 104 52 119 14 14 15 20 21 22 0 12 13 14 13 16 17 16 IV 20 21 9 10 12 13 13.1 0.0 15.0 34.6 27.2 19.5 39.1 22.4 20.5 18.3 26.3 13.8 18.6 20.8 26.3 28.2 0.0 16.3 35.0 0.0 36.9 0.0 0.0 0.0 38.2 15.0 32.4 43.9 27.2 27.2 42.0 0.0 17.0 0.0 58.1 0.0 0.0 21.3 0.0 .0 12.2 0.5 3.0 20.3 27.2 8.2 21.0 16.2 28.4 27.3 17.3 40.0 16.3 21.4 16.4 24.5 7.6 16.2 16.5 24.7 26.2 10.7 17.0 33.8 7.0 36.3 9.8 14.1 3.3 34.5 12.7 34.8 23.4 42.1 4.0 9.4 2.1 57.6 4.2 11.9 20.6 21.3 11.4 6.9 3.8 6.4 < 8 1 2 26.7 19.1 2 12 8 2 2 0.0 13.8 2 13 8 3 2 29.2 23.7 2 14 6 4 2 33.7 31.9 2 IS 8 5 2 0.0 14.8 2 16 8 6 2 0.0 3.9 2 17 8 7 2 0.0 10.3 2 18 8 8 2 0.0 1.3 2 19 8 9 2 20.8 19.9 2 20 8 10 2 33.3 33.4 2 21 8 11 2 22.4 24.3 3 0 8 12 2 0.0 7.3 3 1 8 13 2 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40.4 40.6 12 13 17 18 19 20 21 22 0 9 10 13 16 17 18 19 20 25.3 30.3 31.7 19.2 17.9 0.0 0.0 32.7 0.0 .22.6 18.3 19.3 0.0 20.8 23.6 0.0 0.0 41.1 74.5 54.2 12.5 . 53.3 13.1 24.4 38.9 27.6 36.6 16.6 17.0 24.4 0.0 13.7 0.0 0.0 27.6 21.8 22.1 27.6 0.0 28.2 29.5 55.8 37.2 74.5 65.8 21.1 0.0 0.0 0.0 24.4 27.6 0.0 16. 7 25.6 28.2 20.2 0.0 17.6 17.3 30.1 23.4 27.9 12.2 40.4 30. 34. 0.0 30. 1 i/.O 29.3 25.6 14.7 24.4 13.0 32.4 0.0 0.0 16.7 46. 1 36.5 22.8 16.3 0.0 0.0 31.1 0.0 F C*LC 26.3 32.1 12.4 10.5 19.2 4.1 8.5 31.6 1.0 27.3 17.1 21.2 0.2 22.2 23.2 12.9 8.2 17.2 63.3 43.4 21.0 51.1 9.2 22.5 41.1 28.8 37.1 23.8 38.6 25.3 11.6 16.0 14.0 16.1 2 9 . J 31.1 24.7 22.0 29.2 7.0 29.8 26.0 43.7 33.7 62.6 99.2 20.6 2.6 3.6 11.0 23.1 28.0 7.3 14.3 27.1 30.6 32.6 6.0 16.4 17.4 26.4 21.5 31.6 8.9 38.6 46.4 22.3 30.5 28.9 32.8 24.9 29.7 35.7 6.7 5.6 37.2 2 l . i 30.2 20.4 8.5 6.6 10.3 11.6 10.2 10.4 23.1 O . l 34. 7 11.9 31.3 2 3 . 3 19.9 2 3 . 5 10.2 34.3 6.4 7.4 12.1 50.9 17.6 23.0 23.0 15.8 1.9 3V.0 4.2 13.1 TABLE A3- (Continued). K I r OBS f CALC H K L P OBS F CALC H K L F OBS F CALC 9 J 20.5 22.1 9 0 J 26.3 22.0 2 s 4 29.0 27.1 10 3 26.6 27.0 9 1 3 17.6 17*8 2 9 4 0*0 19*9 11 9 0.0 7.7 9 2 0.0 4*4 2 10 4 23.4 24.2 12 3 18.6 29.1 9 9 3 14.4 6*6 2 11 4 0.0 13*7 19 9 0.0 9.8 9 4 3 1ft.7 . 14*9 2 12 4 34*6 35.0 14 3 0*0 7.7 9 ft 3 0.0 9*ft 2 19 4 0.0 8.0 19 3 0*0 3.3 9 6 3 40.7 41 .ft 2 14 4 29.2 26.9 16 3 30.1 32.3 9 7 9 22.4 20*9 2 19 4 *23.7 24.8 17 3 0.0 3.1 9 8 9 24.0 20.2 2 16 4 0.0 15.4 IS 3 0.0 13*0 9 9 9 31.1 28*9 2 17 4 0*0 7.9 19 3 0.0 10.7 9 10 9 17.6 16*0 9 4 O.O' 1.7 0 3 0.0 1.4 9 11 3 24.4 24. 7 3 1 4 39*3 39*7 1 3 23.4 17.5 10 ] 19.9 19,5 9 2 4 17*3 17.4 2 3 55.6 36.3 10 I j 0.0 11.4 3 3 4- 20*6 19*8 9 9 14.1 11.0 10 2 3 W.9 16*6 9 4 4 0*0 18*3 * 3 24.4 21.3 10 3 3 0.0 9.2 3 ft 4 14*4 23*7 ft 3 24.4 90.2 10 4 3 16.7 6*8 3 6 4 19.9 29*4 * 3 16.0 0.6 10 5 3 0.0 10.6 3 7 4 0.0 10*1 7 3 23.4 23.3 o 4 3 0 4 22.8 22.0 • 3 0.0 14.6 o I 4 3 9 4 0.0 10.5 9 3 34.6 96.9 o 2 4 26.0 22.9 3 10 4 19.9 27.2 10 3 20.2 20.9 o 3 4 0.0 4.1 3 11 4 27.9 31.3 11 9 0.0 9.3 o 4 4 0.0 11.3 3 12 4 0*0 7.4 12 9 90.1 29.9 ft 4 0.0 2.2 3 13 4 23*4 21.2 19 3 0.0 9.4 o A 4 22.1 22.6 9 14 4 21.0 20.2 14 9 0.0 6*6 o 7 4 33.7 92*1 9 19 4 27.2 22.2 1ft 9 33.3 33.4 o 8 4 0.0 6.0 9 16 4 0*0 7.2 16 9 0.0 6.4 o 9 4 32.4 27.2 4 0 4 49.1 44.5 17 9 19.5 17.6 o 10 4 32.4 92.9 4 1 4 23.4 21*0 10 9 0.0 4.3 n 4 0.0 6*2 4 4 29*2 29.4 0 9 0.0 7.4 o 12 4 0.0 • 0*6 4 9 4 0*0 14*3 1 9 14.4 17.7 o 13 4 0.0 19.9 4 4 4 16*3 16.6 2 9 27.9 31.7 14 4 0.0 13.3 .4 ft 4 20*0 20.5 9 3 39.9 99.6 1ft 4 28.2 26*7 4 6 4 16*6 22.9 4 3 0.0 0.6 o 16 4 19*7 16*2 • 4 7 4 19*9 29.0 ft 3 16.7 • •9 o 17 4 21*1 17*1 4 6 4 17*3 18.6 6 3 17.9 12.3 1 0 4 12.6 1*9 4 9 4 0*0 17.4 7 3 26.0 26.2 1 1 4 22.4 17.2 4 10 4 2ft.0 26.9 a. 3 20.2 13.6 1 2 4 23.7 26*0 4 11 4 14.7 23.4 9 3 22.1 24.4 1 3 4 26*9 99* ft 4 12 4 0.0 3.1 10 3 0.0 10.1 1 4 • 4 0.0 4.9 4 19 4 0.0 12.7 11 3 10.6 10.0 1 ft 4 16.6 16*0 4 14 4 0.0 3.7 12 3 0.0 9*2 1 6 4 32*1 31.0 4 1ft • 4 20.2 20.7 19 3 27.2 26.9 1 7 4 14.7 17.1 ft 0 4 36*9 31*9 14 J 0.0 ft.ft 1 6 4 17*9 10*2 ft 1 4 14*7 9.6 1ft 3 2ft.6 24.1 1 9 4 0.0 19.6 9 2 4 34*0 33.3 16 3 15.0 10*9 1 10 4 16*0 14*9 9 9 4 0.0 13.8 0 3 0.0 a . i 1 11 4 14.1 13.7 ft 4 4 0*0 10*3 1 3 24.0 29.9 1 12 4 0*0 6.2 ft 9 4 0.0 16.3 2 3 24.0 29.4 1 13 4 16.6 19.1 9 6 4 0.0 16.9 9 3 16*7 17.8 1 14 4 21.6 22.4 ft 7 4 0.0 9.7 4 3 0.0 7.1 1 13 4 16.3 19.4 ft 6 4 26.6 39.ft ft 3 2ft.6 29.* 1 14 4 17.4 19.6 ft 9 4 17.3 19.0 6 9 22.4 22.9 1 17 4 0*0 9.0 ft- 10 4 24.4 23.2 7 3 0.0 16.9 2 ' 4 30.9 24,i 3 11 4 0*0 11.2 • 9 16.9 10.6 j 1 4 90*6 27*9 3 12 4 19*0 6*9 9 3 26.0 26.2 j 2 4 0*0 9.4 3 13 4 0.0 19.7 10 3 0.0 2.0 2 j 4 40*4 96.7 3 14 4 17*6 17*9 11 3 0.0 4.7 j 4 4 21* 1 19*2 4 o 4 96.2 99.9 12 3 36.6 95.9 2 9 4 0.0 9*9 4 1 4 40.4 41*8 19 3 0.0 9.9 2 4 4 16.9 21*9- 4 2 4 0.0 6.9 14 3 0.0 7.4 2 7 4 16*6 19*0 6 * 13.7 9.0 F OBS f CALC 10*3 9.7 0.0 6*7 0*0 12*9 18*3 20*1 27*9 94*9 IS. 0 13*0 16*3 17*2 0.0 6.4 0.0 9*7 21.1 29.0 16*0 12.7 24* 7 29.9 20.3 9.1 30.1 31.6 21.8 19.6 18.6 19.9 16.7 11.2 0.0 6*4 0.0 6.9 16.0 12*9 29.9 29.2 92.1 29.ft 21.8 20.6 29*9 27.4 24.4 29*2 28.2 25.6 19*0 12*6 0.0 3*9 19*9 17.7 19.9 16.9 0.0 11.6 29*4 16.9 o.o 12.2 17.3 9.8 0.0 13.0 0.6 2.5 0.0 19*6 0.0 14*9 0.0 0*4 91.4 29*7 19.9 19*1 14.7 10*1 0.0 9*6 19.3 16.6 0.0 10*1 20.0 20*1 0*0 7*7 28*2 29*1 16*9 9.9 0.0 7*9 0*0 9.0 0*0 10*8 16*0 10*2 29.0 29*2 16.9 16.6 0.0 17*4 0.0 10.9 0.0 7.9 16.7 19*9 19.9 16*1 99 TABLE kk< 10-CHL0R0-5,10-DIHYDROPHENARSAZINE (PHENARSAZINE CHLORIDE) MEASURED AND CALCULATED STRUCTURE- AMPLITUDES. (Unobserved r e f l e c t i o n s , which a r e - l i s t e d as 0.0, have threshold values i n the range 2-9). fl ft. L F Odo F CALC n L F Ubo f CALC 0 0 .: a. a 0 . i J 7 > 4 I,-, 40.3 0 0 4 0.6 ),0 0 7 >. 44 • 0 4 J.3 0 0 b oO. 1 O 1.3 J I -j 39.3 >a. j 0 0 U 11 .6 0.9 0 7 0 0 . 0 1 . 7 0 0 10 54.7 > l t » 0 7 7 14 .0 12.3 0 0 1 2 4 3.1 44.3 0 7 0 3 5 .4 34.0 0 u 14 44 . 7 46.3 0 7 9 22.2 < 0 . 7 0 0 lb 0 . 0 7 . 0 0 7 10 25.4 2 4 . 0 u I 1 13. 1 I 3 . 4 0 7 1 1 17.2 1 7.4 0 1 2 10'.4 l . O . 4 0 7 u 0 . 0 2.9 0 1 1 3 4 . » 3 3.4 o 7 1 1 17 .0 17 .3 0 1 4 Ob. 1 6 6 . 4 0 7 14 10. 1 17 .3 0 1 2 3 . 2 2 2 . 3 0 7 13 19. J 2 0 . 9 0 1 b 19.9 20.0 0 7 16 7. ' 9 . 3 0 I 7 0.0 7 . 5 0 0 0 32.0 3 2 .2 0 1 0 b 0 . 5 bo .0 0 6 1 6 3 . 1 bl.9 0 1 V 10. 1 16.9 0 8 2 0 . 0 10.2 0 1 10 3 4 . 0 53.7 0 6 3 37.9 33 .1 0 1 11 12. 1 13.7 0 0 4 4 0 . 2 3 8 .6 0 1 12 23.b 2 4 . 0 0 6 5 13.6 14 .0 0 1 13 0.0 0.2 0 0 6 4 4 . 7 44.2 0 1 14 l b . 6 17.2 0 0 7 24.0 24.7 0 1 15 0.0 1.6 0 0 0 12.2 11.1 0 1 16 27.9 2 9 . 4 0 6 9 2 0 . b 19.6 0 I 17 0.0 O.b 0 0 10 0.0 4.7 0 2 0 121.7 146.9 0 6 11 34.0 33.4 0 i 1 33.2 33.9 0 8. 12 15.2 17.1 0 2 2 21.3 24.6 0 0 15 27.2 27.4 0 2 3 93.3 100.0 0 8 14 0.0 1.1 0 i ' 4 12.7 13.0 0 8 15 0.0 6.0 0 2 5 6 3 . 0 01.7 0 9 1 29.9 26.4 0 2 b 74.7 73,5 0 9 2 43.3 41.3 0 2 7 36.6 37.2 0 9 3 49.2 49.0 0 I 6 0.0 3.9 0 9 4 17.0 18.4 0 2 9 16.6 17.3 0 V 5 22.2 21.0 0 2 10 49.6 46.8 0 9 6 0.0 4.5 0 2 11 17.7 20.0 0 9 7 22.7 22.3 0 2 12 4 6 . 3 48.9 0 9 8 17.0 16.6 0 2 13 0.0 3.4 0 V 9 27.7 24.7 0 2 14 11.4 13.7 0 9 10 0.0 2.4 0 2 15 0.0 2.2 0 9 11 l b . 5 l b . 4 0 2 16 9.3 9.7 0 9 12 0.0 5 . 5 0 2 17 10.b 12.0 0 V 13 15.2 15.5 0 3 1 20.6 16.3 0 9 14 12.2 13.4 0 3 2 71.3 75.7 0 9 13 21.3 22.2 0 3 3 13.4 l b . 6 0 10 0 30.6 29.3 0 3 4 71.3 71.1 0 10 1 50.4 30.8 0 3 5 17.4 15.0 0 10 2 30.6 2 6 . 9 0 3 b 32.2 32.4 0 10 i 21.3 20.0 0 3 7 30.6 30.1 0 10 4 0.0 0.2 0 3 d 41.3 41.1 0 10 3 32.7 32.5 0 3 9 27.9 26.1 0 10 6 0.0 1.3 0 3 10 3 1 .3 52.b 0 10 7 0.0 3.2 0 3 11 0.0 1.2 0 10 6 0.0 4.8 0 12 11.3 10.1 0 10 9 10.6 6.5 0 3 13 10.2 o . l 0 10 10 13.6 12.7 0 3 14 21.1 20.7 0 10 11 3 4 .3 35.6 0 3 15 0.0 2.6 0 10 12 13 .6 13.3 0 3 lb 24.7 25.4 0 10 13 23.6 2 3 . 6 0 3 17 0.0 0.4 0 ' 10 14 0.0 3.0 0 4 0 43.1 43.2 0 11 1 23. 1 21.9 0 4 1 32.9 27.7 0 11 2 0.0 7.0 0 2 34.5 34.1 0 11 3 37.9 38.0 0 4 3 24.3 23.b 0 11 4 20.2 22.2 0 4 4 47.6 48.8 0 11 5 12.2 10.9 0 4 5 64.7 76.7 0 11 b 0.0 5.5 0 b 104.2 103.2 0 11 7 21.3 22.7 0 . 7 3 2 .2 33.3 0 11 8 0.0 9.3 0 0 6 9 61.3 16 .3 40.2 l b . 5 0 0 }} V 10 24.3 0.0 24.3 2.4 0 4 10 0.0 2.1 0 11 11 9.9 11.0 0 11 0.0 7.0 0 11 12 0.0 0.2 0 4 12 44.9 45.5 0 11 13 6.1 9.1 0 4 13 0.0 2.1 0 12 0 29.3 26.b 0 4 14 0.0 3.3 0 12 1 33.6 33.4 0 4 15 14.7 13.1 0 12 2 23.3 22.7 0 4 l b 14.3 l b . 5 0 12 3 0.0 4.1 0 4 17 11.3 13.2 0 12 4 0.0 2.8 0 1 37.9 3b. 7 0 12 3 31.3 31.3 0 9 2 31.7 53.3 0 12 6 0.0 8.3 0 $ 3 b b . i b3.9 0 12 7 25. b 2 b . 1 0 9 4 6b.0 85.3 0 12 8 0.0 5.9 0 5 5 6.b 11.3 0 12 9 0.0 3.0 0 9 b 26. 1 24.4 0 12 10 11. i 12.0 0 3 7 20.8 22.5 0 12 11 17.7 20.2 0 9 6 2 3 .1 21.6 0 12 12 9.0 9.7 0 3 9 19.3 19.4 0 13 1 24.3 23.6 0 3 10 5 5 . b 55.7 0 13 2 0.0 1.3 0 5 11 19.0 10.2 0 13 3 26.b 27.3 0 3 12 0 . 0 9.0 0 13 4 0.0 4.1 0 5 13 11.3 9.9 0 13 5 17.4 16.1 0 3 14 22.2 21.5 0 13 b 0.0 1.3 0 9 15 17.4 16.7 0 13 7 15.2 l b . 3 0 5 lb 12.0 14.1 0 13 0 0.0 5.3 0 3 17 7.2 7.2 0 l i 9 29.9 31.4 0 6 0 22.7 2 2 . 5 0 13 10 0.0 0.3 0 6 1 51.7 49.6 0 1 3 11 7.2 9.2 0 6 2 l b . 3 14.7 0 14 0 13.1 14.4 0 b 3 13.b 13.1 0 14 1 18.1 16.4 0 6 4 33.2 36.0 0 14 2 0.0 6.0 0 b 5 3b. 1 3 4 . 3 0 14 i 23. 1 23.5 0 b b 69.4 69.2 0 14 4 0.0 3 . 4 0 b 7 40.4 37 .2 0 14 5 23.1 23.7 0 b 6 36.0 30.4 0 14 b 0.0 6.6 0 b 9 0.0 4.6 0 14 7 23.b 2 6 . 3 0 b 10 0 . 0 0 . 1 0 14 0 0.0 4.7 0 b 11 2 3 . 3 2 0 . 7 0 14 9 0.0 3 . 7 0 b 12 14.9 11.3 0 14 10 0 . 0 i . b 0 b 13 24.9 2 2 . 5 0 1 3 1 16.6 20.9 0 b 14 0.0 1 .2 0 1 5 2 0 . 0 5.5 a b 15 0.0 1.3 0 13 3 0 . 0 5 . 0 0 b 16 10.5 17.2 0 13 4 0.0 6 . 4 0 7 1 6 . 1 6 . 5 0 1 5 3 10 .2 10.9 0 7 2 3 2 .2 3 0 . 3 0 15 6 0.0 0 . 2 li JL L F Obi F CALC 0 15 7 7 . 2 o.b 0 19 a 0 . 0 2«o 0 lo 0 14.V 11.7 0 lb , 0 . 0 4.4 0 10 c 0 . 0 1.1 0 lb 1 0 . 0 1.0 0 10 4 0 . 0 2.6 0 lo 5 14.9 10.7 0 lo 6 0 . 0 i . 1 0 17 1 7.4 10.1 0 17 2 0.0 .1.0 0 17 1 12.9 13.1 0 1 84.7 0 7 . 9 0 2 23.4 24.b 0 1 0 4 . 7 77.9 0 4 26.3 30. 3 0 5 13.0 37.0 0 b 0.0 4.3 0 7 25.6 25.3 0 0 55. b 57.0 0 9 16.1 15.6 0 10 29.7 31.3 0 11 53.6 56.0 0 12 0.0 2.5 0 11 13.6 13.0 0 14 27.9 29.6 0 15 9.3 8.7 0 lb 0.0 o.9 0 17 0.0 1.9 1 0 25.6 29.7 1 1 66 .1 71.b 1 2 12.2 13.8 1 3 88.5 83.2 1 4 80.1 79.2 1 5 26.5 24.9 1 b 65.4 64.9 1 7 45.1 42.4 1 8 46.9 47.2 1 9 30.2 32.3 1 10 16.1 17.3 1 11 19.0 18.6 1 12 19.7 19.5 1 13 16.9 16.1 1 14 9.5 7.0 1 15 19.3 19.2 1 lb l b . 5 17.2 1 17 7.2 9.6 2 44.9 44.8 4 1 108.1 121.4 2 2 98. 1 97.6 2 3 33.6 31.1 4 b6.3 64.9 2 5 49.2 4b.b 2 b 52.2 50.5 2 7 24.9 24.3 2 8 04.0 62.2 2 9 0.0 3.6 10 29.0 29.4 2 11 39.9, 41.0 2 12 10.6 9.2 2 13 29.7 30.6 2 14 23.1 24.9 2 15 10. b 11.0 2 16 13.1 12.5 17 13.4 13.0 i 0 43.1 47.9 3 1 88.5 89. 1 3 2 94.7 98.6 3 3 69.2 66.5 3 4 47.6 45.9 3 5 44.7 44.0 3 6 53.8 53.7 3 7 26.1 24.6 i 6 3 b . i 34.9 i 9 47.b 48.4 3 10 24.5 24.2 i 11 22.7 22.1 3 12 31.9 31.8 3 13 2b.3 27.1 3 14 0.0 10.1 3 13 21.1 22.1 3 16 6.1 6.5 3 17 0.0 4.2 4 0 22.7 17.1 4 1 21. 1 24.7 4 2 71.1 72.0 4 1 59.2 67.4 4 4 59.2 39.1 4 5 41.5 42.9 4 6 40.b 37.4 4 7 49.5 49.0 4 8 39.7 39.4 4 9 14.9 12.7 4 10 13.6 12.1 11 . l . o 20.4 4 12 0.0 3.2 4 11 0.0 12.3 4 14 i 7.9 20.6 4 13 11. 1 12.0 4 16 12.4 14.1 4 17 13.9 17.3 3 0 77.2 60.5 5 I 32.9 32.6 3 2 4 7 .2 47.1 5 3 36.8 41.7 5 4 2 6 . 3 26.5 5 5 4b. 3 4 3 . 2 b 19.3 17.2 3 7 23.4 i 4 . b 5 6 27.9 27.3 3 9 19 .3 19.9 " 9 iO JO.7 10.2 5 11 23.1 21.7 5 12 2 b . 3 23.0 A L r OBS F CALC 3 11 < i . i 19. b 9 14 17.7 17.4 9 15 11.1 11.0 9 1L 0.0 5.7 6 0 17. 1 17.p 6 1 2 b . l 29.2 b 2 4b. i 47.b 6 i 44 .7 49.3 b 4 19 .2 41.1 b 3 59.1 55. b b 6 25.4 24. b b 7 44.9 44.6 b 6 34.2 34.2 b 9 14.7 34.b b 10 19.0 18.1 6 11 0.0 d . l b 12 17 .9 l d . 1 b l i 9.3 13.4 b 14 20.2 20.8 b 15 10.9 11.5 6 l b d.4 9.9 7 0 58.1 59.5 7 1 30.6 31.7 7 2 41.3 43.1 7 3 53.6 35.5 7 4 43.e 45.1 7 5 33.1 33.5 7 6 13.1 14.0 7 7 41.5 40.3 7 d l b . 9 14.3 7 9 19.3 17.3 7 10 29.0 28.9 7 11 15.9 13.7 7 12 19.3 19.0 7 13 14.3 14.5 7 14 21.1 20.6 7 13 9.6 10.0 7 lb 6.5 8.3 8 0 43.6 46.6 tt 1 12.7 12.3 8 2 46.3 48.3 d 3 36.3 38.1 0 4 l a . 4 18.0 8 3 33. b 34.4 8 b 9.5 8.2 8 7 22.7 21.3 8 8 20.2 20.3 6 9 34.7 34.0 8 10 16.5 14.0 tt 11 10.9 10.6 8 12 28.6 29.0 6 13 0.0 6.8 6 14 14.9 l b . l 8 13 9.7 9.9 9 0 0 . 0 3.4 V 1 18.6 16.b 9 2 22.0 21. b 9 3 28. 1 28.7 9 4 22.7 23.3 9 5 37.7 37.6 9 b 23.3 22.0 9 7 34.2 34.9 9 8 24.7 24.0 9 9 13.8 11.7 9 10 13.1 13.5 9 11 0.0 4.b 9 12 12.7 13.tt 9 13 0.0 9.3 9 14 11.9 11.7 9 15 9.3 10.1 10 0 35.6 35.7 10 1 30.b 31.3 10 2 27.2 27.2 10 3 15.2 3b.4 10 4 13.8 14.8 10 5 13.6 12.4 10 b 17.9 16.5 10 7 12.2 11.2 10 6 12.2 10.9 10 9 27.4 26.1 10 10 22.4 22.9 10 11 10.4 9.6 10 12 l b . 4 16.7 10 13 lO.b 10.0 10 14 10.9 11.7 11 0 15.4 11.9 11 1 20.2 20.2 11 2 31.1 32.2 11 3 2 1 .1 21.0 11 4 20.b 21.3 11 3 2 9 . 3 24.9 11 b 20.4 16.1 11 7 28.3 27.5 11 d 25. b 24.4 11 9 0.0 2.9 11 10 14.3 14.0 11 11 14.0 13.1 11 12 0.0 4.6 11 l i 11.3 l l . l 12 0 14.3 33.4 12 1 12.c 12.4 12 2 11.3 9.1 12 3 2tt.b 2 9 . 6 12 4 17.9 16.1 12 5 12.7 12.5 12 b 2 5 .6 24.3 12 7 0.0 7.4 12 d 9 . 3 10.6 12 9 17.4 10.4 12 10 9 . 7 9.9 12 11 /.4 d . 2 1. 12 7 . 9 d.O l i 0 10. o J . . 11 1 . 1 . 0 2 1 . 4 TABLE" AU. (Continued). 100 K L F OBS F CALC l l ^ < 1 . 1 1 J 1 0 . 0 l . o 1 J 4 19. f 1 7.o i J 3 0 . 0 0.4 n 6 10 . 4 9,d i i 7 11. i 10.3 l i o 11.3 11.1 i i 9 7.9 9.9 i i 10 i 1.0 14.9 i i 1 1 12.2 11.1 1* 0 0.0 4 .6 !<• 1 10.2 6 .2 14 2 0.0 3 . 9 14 i I d . i 20.d 14 4 10.4 10.8 14 5 6 . 6 8 . 9 14 6 21.6 23.3 14 7 0.0 4.3 14 d 12.. 12.3 14 9 11.d 12.2 14 10 0.0 3.0 12 0 9.1 3.5 13 i 21.0 .1 .7 13 2 U . 9 10.9 13 3 0.0 4 .8 13 4 12.0 13.1 13 9 0.0 8 . 6 13 6 0.0 2.9 13 7 7.2 8 . 5 19 6 d . i 7.7 lo 0 11.3 10.0 10 1 11.3 9.7 10 2 0.0 1.3 16 3 19.6 13.6 l o 4 11.9 12.3 16 9 0.0 3.7 16 6 11.1 12.2 17 0 7.0 4 . 8 17 1 8 . 4 0.9 17 2 7.4 6.3 0 0 8.6 13.7 0 1 27.2 28.4 0 2 0.0 1.5 0 3 96.9 94.3 0 4 7.2 10.3 0 5 26.6 29.7 0 6 21.1 20.6 0 7 29.9 31.8 0 6 11.> 10.3 0 9 69.1 66.0 0 10 10.4 11.1 0 11 24.9 27.3 0 12 0.0 2.7 0 13 16.8 18.8 0 14 0.0 6.3 0 19 22.7 24.8 0 16 0.0 1.4 0 17 10.4 11.3 1 0 34.9 35.0 1 1 35.2 39.7 1 2 20.6 20.3 1 3 43.1 40.1 1 4 36.1 33.7 1 5 72.6 70.4 1 6 0 . 0 4 . 6 1 7 93.3 91.3 1 6 0 . 0 2.7 1 V 11.1 12.3 1 10 21.1 19.9 1 11 27.7 26.2 1 12 16.1 19.4 1 13 19.7 21.0 1 14 0.0 10.3 1 19 10.6 10.7 1 16 0.0 6.3 1 17 22.0 25.2 2 0 19.3 15.2 2 1 43 .8 44.0 2 2 20.2 18.9 2 3 71.7 74.7 2 4 10.4 12.4 2 9 32.0 32.2 2 6 0.0 5.7 2 7 19.3 20.9 2 6 0.0 6.6 2 9 S d . l 58.1 2 10 0.0 6.1 2 11 19.7 16.3 2 12 0.0 2.0 2 11 17.4 16.4 2 14 1..4 t i.O . 1 3 . O . o . 2.3 2 16 9.1 10.1 1 0 93.1 32.1 i 1 94.9 96.4 3 2 42.2 42.0 J 3 9.7 10.8 3 4 33.6 31.7 i 5 o6.1 65.1 1 6 11.3 9.9 1 7 47.6 66 . 4 1 d 10.9 12.4 3 9 0.0 4 .2 3 10 19.9 16.9 1 11 . 0 . 6 29.9 1 12 26.1 . 3 . 6 1 13 27.0 24.d 1 14 13.2 15.d 3 11 0.0 2.0 3 16 0.0 4 .4 6 0 5.6 0.0 4 1 52.4 49.1 4 2 21.3 23.9 4 1 79.4 62.7 K L F OBS F CALC 4 4 19 7 3 0 . 0 4 5 17 4 17.1 4 0 1 7 4 1 0 . 7 4 7 <7 4 . 0 . 4 0 20 2 19 .7 4 9 49 9 4 8 . 6 4 10 19 9 19.0 4 11 17 7 15.2 4 12 0 0 4*d 4 l l 17 2 17.7 4 14 12 0 13 .7 4 15 20 .6 2 3 . 0 4 16 6 , 0 7 . 0 3 0 32 6 32 .6 3 1 83 O d 7 . 9 2 39 ,7 59.0 3 22 ,9 24.0 5 4 34 ,0 33.5 3 5 25 ,6 23.7 5 6 32 ,2 32.0 9 7 26 • 3 27.9 5 6 0 0 3.6 5 V 30 ,4 30.0 5 10 11 .3 11.9 3 11 37 . 7 36.7 9 12 29 .9 20.9 9 13 26 6 27.3 5 14 10 2 11.1 5 15 0 .0 4.3 5 16 0 ,0 5.1 6 0 17 .0 16.2 6 1 23 .8 23.1 6 2 28 6 29.1 6 3 54 7 54.3 6 4 46 1 47.3 6 5 11 ,3 8.5 6 6 <1 .6 21.9 6 7 24 .9 26.1 0 20 3 27.3 6 9 19 5 17.0 6 10 27 7 26.2 6 11 0 .0 8.0 6 12 0 .0 6.8 6 13 16 .1 16.0 14 12 .9 13.5 6 13 16 3 17.7 7 0 16 6 18.6 7 1 53 6 33.2 7 2 0 .0 6.3 7 3 23 »0 23.7 7 4 36 • 9 35.9 7 5 24 .3 23.4 7 6 44 7 43.4 7 7 16 6 15.0 7 e 14 .3 12.6 7 9 17 .2 12.8 7 ' 10 12 .9 i i . : 7 11 29 7 26.t 7 12 12 4 13.4 7 13 25 6 24.6 7 14 0 0 0.2 7 19 0 0 1.6 6 0 0 0 1.6 6 1 14 3 14.6 8 2 39 2 40.4 8 3 39 9 39.5 6 4 33 8 35.8 8 5 28 6 2 9 . 9 8 6 17 9 17 .9 8 7 23 3 23.3 6 6 26 1 26.1 6 V 27 2 27.5 d 10 21 3 21.0 8 11 16 8 17.4 9 12 0 0 5.5 8 13 0 0 7.1 d 16 10 4 11.5 9 0 30 4 30.2 9 1 16 1 16.3 9 2 10 2 9.6 9 3 e 6 9.1 9 4 37 0 36.7 9 3 33 1 33.6 9 6 56 3 55.8 9 7 14 3 16.4 9 8 30 4 30.3 9 9 11 1 •' 9 . 9 9 10 0 0 0.2 V 11 10 9 13.1 9 12 12 4 13.1 9 13 15 4 15.2 9 14 0. 0 3.8 10 0 d. 4 10.1 10 1 0. 0 6.0 10 2 34 2 36.3 10 3 9. 7 9 . 4 10 4 31. 7 3 0 . 9 10 3 14, 3 12.6 10 6 13. 4 11.7 10 7 12. 7 11.2 10 8 30 4 29.4 10 V 10 9 13.6 10 10 22 2 2 1 .9 10 . 11 13 6 12.6 10 12 0. 0 4.0 10 13 6, 6 0 . 6 11 0 27, 9 20. 7 11 1 14 7 14.3 11 2 10, 9 10.6 11 3 15. 2 14.4 11 4 19, 0 19.2 11' 3 21. 3 17.9 11 6 29. 3 28. 1 11 7 15. 9 13.3 It L F OBS F CALC H K. L F OBS F CALC 11 0 17.2 10 . 4 3 3 19 16.d i d . 5 11 9 0 . 0 7 . 0 3 4 0 0 . 0 5. 1 11 10 7.9 7.o 1 4 1 29.7 30.6 11 11 0 . 0 0 . 2 3 4 2 30.4 1 2 .3 11 1 £ 12.9 1 1 . 9 3 4 1 14.0 14.9 12 0 0 . 0 1 . 7 3 4 4 42.2 41.0 1 2 1 . 0 . 0 7.5 1 4 9 3 6 .1 36.7 12 2 2 2 . 7 2 1 . 1 1 4 6 3 0 .2 28.6 1 2 1 9.9 d . 3 1 4 7 3 3 . 6 31.1 12 4 21 .1 20.2 1 4 d 22.0 19.2 12 5 0 . 0 3 . 2 3 4 9 14 .3 12.1 12 6 0.0 5.8 3 4 10 14.7 13.5 1 2 7 8 . 8 8 . 6 3 4 11 18. 1 18.1 12 6 l d . l 17.1 3 4 12 9.3 10.6 12 9 0.0 4.5 3 4 13 9.9 10.5 12 1 0 13.6 14 .3 3 4 14 10.6 9.6 12 11 0.0 4.6 3 4 13 7.2 6 . 2 11 0 35.4 36.1 3 5 0 51.7 52.3 13 1 0.0 8.3 3 5 1 38.3 37.9 13 2 15.4 16.4 3 5 2 29.7 2 9 . 6 1 3 3 0.0 6.9 3 5 3 34.9 36.0 13 4 0.0 5.1 1 5 4 2 4 . 3 24.3 13 5 12.2 11.6 3 5 3 13.4 14.3 13 6 16.3 16.0 3 5 6 23.4 23.9 11 7 11.3 10.5 3 5 7 11.6 13.0 0 10.2 10.0 3 5 8 10.9 8.2 1 3 9 0.0 4.5 3 5 9 28.6 25.7 13 10 16 .3 16.5 3 5 10 20.6 21.3 14 0 6.4 9.0 3 5 11 19.7 20.0 14 1 0.0 6.0 3 5 12 23.6 22.7 14 2 22.9 22.8 3 5 13 8. 1 9.3 14 3 0.0 1.3 3 9 14 13.6 19.6 14 4 17.7 19.2 3 5 13 12.4 14.1 14 5 0.0 2.4 3 6 0 29.3 28.2 14 6 0.0 3 . 4 3 6 1 24.7 26.0 14 7 0.0 4.0 3 6 2 27.9 27.8 14 6 13.4 14.8 3 6 1 17.0 15.8 14 9 0.0 4.9 3 6 4 39.4 36.3 13 » 0 25.6 25.9 3 6 5 31.5 29.9 13 1 0.0 1.6 3 6 6 27.9 25.9 15 2 16.3 16.4 3 6 7 35.1 9 3 . 9 15 3 0.0 1.9 3 6 6 12.0 12.3 15 4 0.0 3.9 3 6 9 0.0 8.0 15 5 0.0 0.8 3 6 10 18.4 16.5 15 6 7.7 9.0 3 6 11 18.4 18.0 15 7 7.7 8.0 3 6 12 19.0 16.1 16 0 0.0 1.2 3 6 13 0.0 5.2 16 1 6.3 3.0 3 6 14 9.3 8.6 16 2 13.6 16.4 3 7 0 30.8 30.0 16 3 0.0 2 . 9 1 7 1 19.7 19.7 16 4 9.0 9.6 3 7 2 36.1 36.6 0 1 79.2 77.6 3 7 3 24.7 26.2 0 2 40.6 39.7 3 7 4 37.9 39.0 0 3 0.0 3.1 3 7 5 37.2 36.0 0 4 26.1 24.1 3 7 6 17.7 14.8 0 5 2 1 .9 22.1 3 7 7 26.9 21.8 0 6 0.0 9.4 3 7 6 12.0 6.0 0 7 25.4 24.5 3 7 9 19.7 19.0 0 8 18.1 16.8 3 7 10 21.6 22.4 0 » 11.5 12.9 3 7 11 9.3 9.4 0 10 28.1 29.3 3 7 12 19.3 19.8 0 11 27.4 26.3 3 7 13 0.0 6.1 0 12 0.0 2.0 3 7 14 12.9 13.5 0 13 16.6 21.2 3 6 0 35.6 36.8 0 14 0.0 9.7 3 6 1 12.9 13.3 0 15 0.0 1.4 3 6 2 16.6 18.7 0 16 13.6 16.4 3 0 1 20.6 21.0 1 0 34.9 34.6 .3 6 4 22.9 20.2 1 1 27.7 29.4 3 6 5 30.8 31.1 1 2 18.8 17.0 3 6 6 27.9 26.3 1 3 69.7 65.3 3 a 7 18.1 16.9 1 4 24.0 23.1 3 8 8 11.6 11.8 1 5 2 9 .2 25.6 3 8 9 0.0 7.9 1 6 51.5 30.5 3 6 10 27.2 24.6 1 7 23.0 < 2 . 4 3 d 11 16.3 14.2 1 6 34.2 34.3 3 8 12 16.8 17.7 1 9 31.7 31.9 3 8 13 7.0 7.2 1 10 10.4 5 . 0 3 9 0 16.3 16.0 1 11 0.0 9.4 3 9 1 0.0 5.1 1 12 18.6 15.5 3 9 2 23.0 23.9 1 13 17.0 16.4 3 9 3 16.1 16.9 1 14 0 . 0 3 . 7 3 9 4 13.4 12.3 1 15 13 .2 16.7 3 9 - 3 32.4 31.8 2 0 31.1 31.0 3 9 6 13.1 12.6 2 1 5 3 . 6 34.4 3 9 7 18.6 17.3 2 2 43 .6 4 3 .1 3 9 d 13.6 14.7 2 3 0.0 4.9 3 9 9 13. 1 13.7 2 4 33.6 13.1 3 9 10 0.0 9.0 2 3 41.7 41.o 3 9 11 0.0 9.5 2 6 2 9 .1 , 8 . 4 3 9 1 2 9.3 10.1 2 7 26. i 27.0 3 9 1 1 9.1 1 1 . 0 2 d 32.9 32 .1 1 1 0 0 33.4 3 0 . 2 2 9 1 2 . 9 1 1 . 6 3 1 0 1 22.7 24.9 2 10 2 4 .0 2 5 . 5 3 1 0 2 12.2 12.1 2 11 29.7 31.2 3 10 3 15.2 16.1 2 12 0 . 0 4 . 5 3 10 4 14.0 12.3 2 11 l O . D 10 .3 3 1 0 3 23. 1 21.3 2 14 9 . 1 10.1 3 10 6 14.9 13.7 2 15 0.0 9.0 3 10 7 9.0 1 0 .0 1 0 50.0 3 1 .2 3 10 6 9.7 9.0 1 1 34.9 3 3 . 2 5 10 9 10..' 10.4 3 2 14.9 16.4 3 1 0 1 0 l o . i 19.0 1 1 40.4 3 9 . 3 1 10 11 1 0 . 4 10.6 3 4 30.6 2 9 .1 1 10 1 2 19. £ 14.9 1 3 2 2 . 2 2 0 . 5 J 11 0 0 . 0 3 .6 3 6 3 6 . 3 3 5 . 9 1 11 1 14.7 11.0 1 7 2 1 . 0 18.7 3 11 2 22.4 2 2 . 3 1 d 26.3 .= 7.2 1 11 1 1 1 . 1 12 .0 > 9 41.7 39.9 1 11 4 2 0 . 2 2 1 .2 1 1 0 1 6 . 1 16.2 1 11 9 19.9 19 .3 j 11 ld.O ' 2 2 . 0 1 11 6 19.4 19.5 1 12 17 .0 l r . 4 1 1 1 7 17.. 17.0 t 1 1 16.0 17.9 3 11 0 2 2 . 0 . 2 . 1 > 14 7.9 0 . 5 1 1 1 * 7.4 6 . 0 101 TABLE. -Ah. (Continued). 12 12 1 2 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1 1 3 1 4 1 * u 1 * 1 * 1 * 1 * 1 4 1 3 1 3 1 3 1 9 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 F OBS F CALC H It L F UBS F CALC 13.11 1 4 . 1 4 4 5 3 5 . 2 3 4 . 3 rj.d 9.3 4 4 6 4 1 . 5 3 9 . 5 2 3 . d . 6 . 3 4 4 7 1 6 . 3 1 5 . 6 1 2 . 4 1 3 . 9 4 4 8 33.6 3 2 . 1 0 . 0 8 . 5 - 4 4 9 9.9 9 . 4 1 1 . 9 1 1 . 1 4 4 1 0 1 2 . 7 1 2 . 9 1 1 . d 1 3 . 4 4 4 11 0 . 0 5 . 8 1 0 . 3 1 3 . 9 4 4 1 2 1 6 . 1 Id.3 2 2 . * 2 2 . 6 4 4 13 0 . 0 5 . 9 7 . 2 . 6 . 0 4 0 . 0 1 . 9 1 2 . 2 1 3 , 2 4 5 1 1 3 . 6 1 2 . 6 7 . 2 7 . 6 4 5 2 2 4 . 3 2 4 . 5 0 . 0 0 . 3 4 5 3 2 3 . 1 2 3 . 0 1 4 . 3 1 5 . d 4 5 4 33 .3 33 .4 1 0 . 9 1 9 . 1 4 5 5 2 0 . 4 1 6 . 3 0 . 0 6 . 0 4 3 6 0 . 0 6 . 4 1 4 . 9 1 6 . 9 4 5 7 1 1 . 3 1 2 . 2 0 . 0 3 . 7 4 5 8 3 2 . 4 3 0 . 0 B.B 9 . 0 4 5 9 1 9 . 3 1 8 . 7 9 . 0 9 . 9 4 •3 1 0 2 3 . 6 2 5 . 2 1 2 . 0 1 3 . 2 4 5 11 0 . 0 6 . 5 1 2 . 7 1 1 . 3 4 5 1 2 0 . 0 2 . 5 9 . 9 1 0 . 4 4 5 1 3 0 . 0 J . ) 0 . 0 3 . 1 4 6 2 0 . 8 1 9 . 8 9 . 7 1 0 . 6 4 6 2 4 . 0 2 2 . 9 1 2 . 9 11.4 4 6 2 0 . 0 3 . 6 0 . 0 5.5 6 6 1 1 0 . 9 8 . 2 1 2 . 9 1 3 . 7 4 6 4 3 0 . 2 2 9 . 2 0 . 0 1.0 4 6 3 1 8 . 1 1 6 . 3 0 . 0 0 . 0 4 6 6 3 0 . 2 2 9 . 0 1 3 . 0 1 5 . 4 4 6 7 1 8 . 8 2 0 . 6 1 0 . 9 1 1 . 0 4 6 8 2 1 . 3 2 1 . 8 6 . 1 6 . 9 4 6 9 0 . 0 4 . 1 6 . ) 6.5 4 6 1 0 0 . 0 1 . 1 6 7 . 6 6 3 . 9 4 6 11 1 1 . 1 1 1 . 8 0 . 0 4 . 9 4 6 12 7 . 9 9 . 4 SB.3 5 5 . 4 4 6 11 1 4 . 0 1 6 . 0 1 6 . 7 1 0 . 6 4 7 1 2 . 7 1 2 . 9 2 1 . 1 1 9 . 0 4 7 1 0 . 0 7 . 1 1 9 . 6 1 4 . 0 4 7 2 2 2 . 0 2 3 . 0 3 9 . 9 16.7, 4 7 3 2 3 . 1 2 2 . 9 1 2 . 7 1 0 . 5 4 7 4 24 .3 2 2 . 1 13.6 12 .1 4 7 3 1 7 . 2 1 6 . 9 0.0 0.1 4 7 6 9.1 2.6 11.7 11.4 4 7 7 0 . 0 4 . 4 0.0 1.6 4 7 B 1 5 . 9 1 7 . 0 26.3 2 8 . 0 4 7 9 1 7 . 9 16.3 0 . 0 1.9 4 7 1 0 16 .1 19.2 11 .3 12.6 4 7 1 1 0 . 0 a . 4 0.0 1.9 4 7 1 2 0 . 0 6 . B 9.3 7.2 4 B 1 S . 1 15.2 39.6 5 4 . 2 4 B ' X 11.1 . 3 1 . 6 2 1 . 1 21 .9 4 8 2 1 9 . 9 1 1 . 1 62 .2 4 0 . 6 4 a 3 1 0 . 4 1 0 . 0 0.0 5.1 4 B 4 1 9 . 0 17.2 0.0 2.1 4 a 9 9 . 7 9.1 1 1 . s a.7 4 a 6 2 4 . 7 23.8 31.6 3 2 . 4 4 a 7 a.s 9.1 0 . 0 5.4 4 a B 12.2 9.6 1 9 . 3 19.8 4 B 9 0.0 3 . 0 1 6 . 9 11.6 4 B 1 0 0 . 0 6 . 0 0 . 0 1.2 4 B 11 16.B 1 6 . 7 0 . 0 2.6 4 9 0 . 0 1.1 19 .1 21 .1 4 9 1 11.3 11.8 67.2 47 .1 4 9 2 18.6 20 .9 9 . 3 7 . 9 4 9 3 2 4 . 9 2 5 . 6 33.6 3 4 . 9 4 y 4 14 .1 1 6 . 0 0 . 0 2.8 4 9 3 1 4 . 7 1 5 . 7 2 6 . 3 2 9 . 9 4 9 £ 0 . 0 3.1 3 6 . 1 13.4 4 9 7 0 . 0 8.0 2 6 . 1 21.8 4 9 a 1 1 . B 1 2 . 7 1 9 . 6 11.4 4 9 9 22.4 2 2 . 1 11.8 13.6 4 9 1 0 0 . 0 2 . a 11.3 1 1 . 5 4 9 11 o . o 5.1 2 6 . 3 2 3 . 9 4 1 0 1 9 . 6 1 5 . 1 0 . 0 3 . 7 4 1 0 1 2 9 . 4 2 7 . 0 2 2 . 7 2 4 . 9 4 1 0 2 1 1 . 9 1 3 . 6 0 . 0 3 . 3 4 1 0 3 0 . 0 6 . 6 9 . 9 i o . a 4 1 0 4 0 . 0 1 .1 0 . 0 2.8 4 1 0 3 1 7 . 9 1 4 . 9 11.6 1 3 . 4 4 1 0 6 B.6 8 . 9 4 2 . 2 4 3 . 0 4 1 0 7 1 2 . 7 1 2 . 6 2 2 . 9 2 3 . 4 4 1 0 6 1 0 . 9 1 0 . 3 2 4 . 7 2 3 . 4 4. 1 0 9 6.B 6 . 6 1 1 . 3 a . 9 4* 1 0 1 0 6 . 1 6 . 4 l l . a 9 . 3 4 11 9 . 5 6 . 4 1 6 . 1 1 4 . 9 * 11 1 13.8 1 5 . 2 18.6 3 8 . 4 4 ' 1 1 2 9 . 7 8 . 4 0 . 0 9 . 4 4 11 3 2 0 . B 2 1 . 7 i a . i 2 0 . 2 4 11 4 1 0 . 4 1 1 . 9 9 . 7 9 . 7 4 11 3 0 . 0 8.1 0 . 0 2 . 9 * 11 6 8 . 1 7 . 3 0 . 0 2.8 4 11 7 9 . 7 1 0 . 6 1 9 . 4 1 7 . 0 4 11 a 0 . 0 2 . 6 i o . a 9 0 . 9 4 1 2 1 0 . 9 9 . 6 9 . 0 9 . 1 4 . 1 2 I 1 7 . 7 1 9 . 1 i a . 6 1 8 . 6 4 1 2 2 9 . 0 1 0 . 9 0.0 9 . 0 4 12 3 0 . 0 4 . 3 2 6 . 6 27 .2 4 1 2 4 0 . 0 4 . 4 H K L F O B S F C A L C M K L F O B S F C A L 4 12 5 16.3 1 7 . 0 9 7 5 1 8 . 6 1 9 . 7 4 12 6 7 . 9 2 . 4 9 7 6 1 2 . 4 1 3 . 0 4 12 7 1 4 . 7 1 6 . 2 5 7 7 1 5 . 6 1 5 . 1 4 13 0 . 0 3.2 5 7 8 0 . 0 7 . 5 4 1 3 1 8 . 4 8 . 8 5 7 9 1 0 . 9 1 0 . 8 4 1 3 2 0 . 0 3 . 9 5 6 0 1 0 . 6 1 0 . 8 13 3 2 1 . 1 22.2 5 6 1 1 1 . 9 1 0 . 6 13 4 0 . 0 5 . 0 5 6 2 1 4 . 3 1 3 . 8 1 3 5 5 . 6 6 . 0 5 6 3 1 7 . 9 1 9 . 3 1 4 5 . 4 2.6 5 6 4 1 0 . 6 8 . 2 1 4 1 8 . 8 7 . 8 5 8 5 9 . 7 1 0 . 1 0 1 3 2 . 9 3 4 . 1 5 8 6 0 . 0 7 . 4 0 2 2 1 . 3 1 7 . 1 9 8 7 1 9 . 2 1 5 . 8 0 3 1 1 . 6 1 0 . 4 5 8 8 8.8 8 . 3 0 4 1 3 . 4 1 2 . 6 9 9 0 . 0 0 . 0 0 3 1 3 . 4 0 . 9 5 V 1 1 2 . 4 1 2 . 7 0 6 0 . 0 3 . 0 9 9 2 1 1 . 1 1 0 . 2 0 7 1 0 . 4 8 . 8 9 9 3 8 . 1 9 . 6 0 8 2 4 . 3 2 5 . 2 5 9 4 9 . 3 1 0 . 1 0 9 8 . 6 9 . 4 5 9 5 1 8 . 1 1 8 . 4 0 1 0 1 8 . 1 2 0 . 4 5 9 6 8 . 6 7 . 7 0 11 7 . 0 7 . 4 5 9 7 1 0 . 9 1 2 . 1 0 1 2 7 . 7 6 . 7 9 1 0 1 2 . 2 1 3 . 1 1 6 1 . 9 4 2 . 5 9 1 0 i 1 0 . 2 1 0 . 6 1 1 1 3 . 4 1 1 . 6 » 1 0 2 1 0 . 9 1 2 . 2 1 2 0 . 0 7 . 9 5 1 0 1 1 4 . 1 1 5 . 5 1 3 2 1 . 3 1 9 . 9 9 1 0 4 0 . 0 6 . 0 1 4 0 . 0 6 . 1 3 1 0 3 8.8 8 . 1 1 5 1 2 . 4 1 0 . 4 9 1 0 6 0 . 0 5 . 0 1 6 2 9 . 5 3 0 . 4 5 11 0 . 0 0 . 6 1 7 0 . 0 3 . 7 5 11 1 1 0 . 6 1 1 . 1 1 1 3 . 1 1 3 . 3 9 11 2 9 . 9 9.3 1 9 2 1 . 5 2 2 . 3 9 11 3 0 . 0 3 . 6 1 1 0 1 2 . 7 1 2 . 3 9 11 6 1 0 . 2 1 1 . 2 1 1 1 0 . 0 2 . 7 6 0 1 6 . 7 1 9 . 7 1 1 2 d . 6 1 0 . 4 6 0 X 1 1 . S 1 1 . 7 2 0 . 0 7 . 1 6 0 2 0 . 0 1 . 1 2 1 2 3 . 6 2 4 . 1 6 0 3 1 6 . 6 2 0 . 9 2 2 3 1 . 7 3 1 . 6 6 0 4 1 0 . 6 7 . 1 2 3 0 . 0 t . O 6 0 9 1 1 . 1 1 6 . 1 2 4 2 6 . 7 2 6 . 8 6 0 6 0 . 0 4 . 6 2 9 10.2 1 1 . 3 6 0 7 1 0 . 2 9.3 2 6 0 . 0 5 . B 6 0 N 0 . 0 2 . 2 2 7 1 B . B 1 7 . B 6 1 0 0 . 0 2.5 2 a 1 9 . 0 1 9 . 3 6 1 J 1 1 . 6 1 9 . 2 2 9 0 . 0 6 . 1 6 1 2 0 . 0 8 . 2 2 1 0 1 9 . 9 2 0 . 7 6 1 1 0 . 0 4 . 7 2 11 a . l 1 0 . B 6 1 4 0 . 0 4 . 6 1 0 2 9 . 0 3 0 . 0 6 1 3 1 9 . 5 2 1 . 1 J \ 1 7 . 0 1 6 . 5 6 1 6 0 . 0 2 . 5 1 2 1 6 . 1 1 6 . 0 6 1 7 1 5 . 2 1 8 . 0 1 1 2 6 . 1 2 6 . 0 4 I a 0 . 0 7 . 5 1 4 1 6 . 9 1 9 . 1 6 2 0 . 0 1 . 9 ] 9 9 . 1 7.3 6 2 i 1 6 . 0 1 7 . 3 1 6 2 6 . 1 2 6 . 4 6 2 2 0 . 0 2 . 6 1 7 0 . 0 6 . 2 6 2 1 1 2 . 9 1 4 . 8 3 a 9 . 1 9 . 6 6 2 4 6 . 6 1 0 . 9 1 9 1 0 . 4 1 1 . 1 6 2 9 1 2 . 2 1 4 . ] 1 1 0 B . l 7 . 7 6 2 6 0 . 0 4 . 1 1 11 1 1 . 8 1 1 . 1 6 2 7 1 0 . 6 1 1 . 1 4 0 . 0 l . B 6 2 a 0 . 0 1 . 6 4 X 1 0 . 9 9 . 6 6 3 0 . 0 1 . 0 4 2 2 2 . 0 1 9 . 7 6 3 i 1 6 . a 2 0 . 9 4 ) 1 9 . 4 1 7 . 4 6 3 2 9.3 1 1 . 7 4 4 23.a 2 6 . 1 6 3 1 0 . 0 1 . 6 4 3 16.3 1 7 . 9 6 3 4 0 . 0 1 . 0 4 6 1 1 . 1 1 6 . 5 6 - 3 5 1 5 . 2 1 8 . 4 4 7 1 9 . 4 1 5 . 7 6 3 6 0 . 0 6 . 2 4 6 1 2 . 9 1 1 . 2 6 3 7 1 2 . 9 1 5 . 5 4 9 8 . 6 9 . 4 6 6 0 . 0 0 . 2 4 1 0 1 0 . 6 1 1 . 7 6 4 1 1 6 . 5 1 9 . 9 4 I X 6 . 1 7 . 7 6 4 2 0 . 0 8 . 0 9 2 6 . 7 2 6 . 8 6 4 3 1 4 . 7 1 9 . 9 9 X 1 2 . 0 1 0 . 9 6 4 4 1 0 . 4 9 . 9 5 2 1 9 . 9 1 6 . 0 6 4 9 1 1 . 1 1 1 . 9 5 3 1 6 . 1 1 8 . 2 6 4 6 0 . 0 2 . 6 3 4 1 0 . 9 1 0 . a 6 4 7 8 . 4 1 1 . 6 3 3 1 4 . 0 1 2 . 5 6 5 1 0 . 4 1 2 . 3 9 6 1 7 . 9 1 8 . 0 6 3 1 1 9 . 9 2 3 . 2 5 7 0 . 0 8.6 6 9 2 9 . 1 1 1 . 6 5 8 0 . 0 4 . 0 6 9 1 0 . 0 3 . 6 5 9 8 . 6 9 . 7 6 9 4 0 . 0 5 . 7 5 1 0 1 1 . 3 1 2 . 1 6 5 3 1 1 . 8 1 3 . 4 6 0 0 . 0 3 . 2 6 5 6 9 . 5 1 0 . 1 6 1 0 . 0 5 . 8 6 6 0 . 0 6 . 2 6 2 1 3 . 6 1 6 . 7 6 6 1 7 . 7 6 . 1 6 3 1 4 . 9 1 8 . 3 6 6 2 1 1 . 8 1 4 . 2 6 4 1 9 . 6 2 0 ' . 2 6 6 3 1 3 . 4 1 5 . 5 6 3 1 4 . 9 1 6 . 2 6 6 4 8 . 6 9 . 1 6 6 1 0 . 2 1 1 . 0 6 6 3 6 . 1 7 . 2 6 7 2 1 . 8 2 1 . 3 6 7 9 . 3 1 2 . 2 6 B 8 . 6 1 0 . 0 6 7 I 1 1 . 8 1 6 . 0 6 9 7 . 6 1 0 . 0 6 7 2 0 . 0 4 . 7 6 1 0 6 . 3 6 . 0 6 7 3 5 . 9 5.2 7 0 1 9 . 0 2 0 . 1 6 7 4 9.3 1 1 . 7 7 1 1 2 . 9 1 3 . 2 6 8 0 . 0 2.0 7 2 0 . 0 1 0 . 3 6 8 1 5 . 4 5 . 2 7 3 1 2 . 9 1 3 . 3 6 8 2 9 . 9 1 1 . 2 7 4 1 0 . 6 1 0 . 2 APPENDIX I I CRYSTALLOGRAPHIC DATA FOR SOME MOLECULAR CRYSTALS 1,5-ANHYDRO-4-DEOXY-d-ARABO-HEXITOL AND 1-0-(p-TOLUENESULPHONYL)-2,5-ANHYDR0-3-DEOXY-d-GLUCO-HEPTITOL The two compounds were investigated to determine the configurations of hexitols and he p t i t o l s obtained by hydro- formylation of glucals and arabinals (68). The c r y s t a l data were determined from various r o t a t i o n , Weissenberg, and pre cession photographs. Crystal data ( \ (CuKa) = 1.5418 ft;\(MoKoO = 0.7107 ft). l,5-Anhydro-4-deoxy-d-arabo-hexitol ( I ) , C^H^O^, M.W. = 148.2. Orthorhombic, a = 11.47 ± 0.01, b = 8.14 ± 0.01, c = 7.52 + 0.01 ft U = 702 ft3. D m = 1.4, Z = 4, D x = 1.40 g cm"3. Absent spectra: hOO when h i s odd, OkO when k i s odd, OO^when H i s odd. Space group i s P2-j_2-j_2 ^ . CHjOH CHiOH OH O H H O II 1-0-(p-toluenesulphonyl)-2,6-anhydro-3-deoxy-d-gluco-heptitol ( I I ) , C 1 4H 2 00 7S, M.W. = 332.3. 104 Monoclinic, a - 8.52 + 0.01, b = 33.81 ± 0 . 0 5 , c = 6 .25 ± 0.01 ft, p= 116.3° ± 0.1°. U - 1614 ft3. Dm = 1.33, Z = 4, D x = 1.37 g cm"3. Absent spectra: OkO when k i s odd. Space group i s P2j. A more suitable derivative was obtained (69), and no further detailed analysis i s planned. Polymer of (CH^AsS) (CH-jAsS)n was investigated i n order to determine the value of n and the structure of the molecule. Crystal data: (CH 3AsS) n M.W. = n(l26.2) T r i c l i n i c , a = 12.90 + 0.02, b = 10.22 ± 0.02, c = 8.82 ± 0.01 ft; <X = 90.0°, p= 110.0°, X= 104.6°. U = 1053 ft3. 2.28 < D m < 2.55, D x(n - 12) - 2.308. No absent spectra: Space group PI or PI. Because of i t s ready r e a c t i v i t y with, or solution in most solvents the density could be determined only approxi mately . Molecular weight measurements on s i m i l a r molecules (70) have shown that trimers and tetramers are common for As-S and As-0 compounds. In the absence of a molecular weight deter mination f o r (CH-jAsS) , i t i s impossible to specify the number of molecules i n the assymetric unit. Because of the above d i f f i c u l t i e s , and because a l l r y s t a l s were twinned, no further work i s planned. REFERENCES 107 1. International Tables f or X-ray Crystallography. Vol. I, 1952; Vol. I I , 1959; Vol. I l l , 1962. Kynoch Press, Birmingham. 2. E.R, Howells, D.C. Phi l l i p s - a n d D. Rogers', Acta. Cryst. 3, 210 (1950). 3. A.J.C. Wilson, Acta. Cryst. 2, 318 (1949). 4. J.M. Robertson, "Organic Crystals and Molecules." Cornell University Press, Ithaca, 1953. 5. M.J. Buerger, "X-Ray Crystallography." Wiley, New York, 1942. 6. M.J. Buerger, "Crystal Structure Analysis." Wiley, New York, I960. 7. M.J. Buerger, "Vector Space and i t s Application in, Crystal Structure Investigation." Wiley, New York, 1959. 8. H. Lipson and W. Cochran, "The Determination of Crystal Structures." B e l l , London, 1957. 9. A.L. Patterson, Phys. Rev. 4_6_, 372 (1934) . 10. J.M. Robertson, J. Chem. Soc., 615 (1935); 1195 (1936). 11. J.M. Robertson and I. Woodward, J. Chem. Soc., 219 (1937); 36 (1940). 12. David Harker and J.S. Kasper, J. Chem. Phys. 15, 882 (1947). ~ 13. D. Harker and J.S. Kasper, Acta. Cryst. 1, 70 (1948). 14. J . Karle and H Hauptman, Acta. Cryst. 3_> 181 (1950). 15. H. Hauptman and J. Karle, Phys. Rev. 80, 244 (1950). 16. H. Hauptman and J. Karle, "Solution of the Phase Problem. I. The Centrosymmetric C r y s t a l . " Am. Cryst. Assoc. Monograph No. 3, Edwards, Ann Arbor, 1953; J. Karle and H. Hauptman, Acta. Cryst. 9, 635 (1956); 12, 404 (1959). ~ ~" 17. D. Sayre, Acta. Cryst. 5, 60 (1952. 18. W. Cochran, Acta. Cryst. 5_, 65 (1952). 19. W.H. Zachariasen, Acta. Cryst. 5, 68 (1952). 20. A.D. Booth, Nature l 6 l , 765 (1948). 108 21. W. Cochran, Acta. Cryst. 4, 81, 408 (1951). 22. A.D. Booth, Trans. Faraday Soc. 42., 444, 617 (1946). 23. E.W. Hughes, J. Amer. Chem. Soc. 6 1 , 1737 (1941). 24. D.M. Donaldson, J.M. Robertson and J.G. White, Proc. Roy. Soc. A220, 311 (1953). 2 5 . C.A. Coulson, "Victor Henri Memorial Volume; Contribution a 1'Etude de l a Structure Moleculaire," p. 15. 2 6 . M.J.S. Dewar and H.N. Schmeising, Tetrahedron 5, 166 (1959). 27. H.N. Shrivastava and J. Speakman, Proc. Roy. Soc. A257, 477 (I960). 28. T.H. Goodwin, J. Chem. Soc., 4851 (i960). 29. T.C. Furnas, "Single Crystal Orienter Instruction Manual." General E l e c t r i c Company, Milwaukee, 1957. 30. N. Camerman and J. Trotter, Acta. Cryst. l6_, 922 (1963). 31. A.D. Booth, Proc. Roy. Soc. A188, 77 (1946). 32. F.R. Ahmed and D.W.J. Cruickshank, Acta. Cryst. 6, 385 (1953). ~~ 33. D.W.J. Cruickshank, Acta. Cryst. 2, 65 (1949). 34. D.W.J. Cruickshank, Acta. Cryst. 9, 757 (195o). 35. J. Trotter, Acta. Cryst. 14, 1135 (196l). 36. A. Hargreaves and S.H. R i z v i , Acta. Cryst. 15, 365 (1962). 37. G.B. Robertson, Nature 191, 593 (1961). 38. D.W.J. Cruickshank and R.A. Sparks, Proc. Roy. Soc. A258, 270 (I960). 39. G. Baldock, G. Berthier and A. Pullman, C.R. Acad. S c i . , P a r i s , 228, 931 (1949). 40. T.H. Goodwin and V. Vand, J. Chem. S o c , 1683 (1955). 41. T.C.W. Mak and J. Trotter, J. Chem. S o c , 1 (1962). 42. E.D. Bergmann, E. Fischer and B. Pullman, J. Chim. Phys. 48, 356 (1951). 43. J.M. Robertson and J.G. White, J. Chem. S o c , 358 (1947). 109 44. D.W.J. Cruickshank, Acta. Cryst. 9, 747 (1956). 45. R.A. Sparks, Ph.D. Thesis, University of C a l i f o r n i a , Los Angeles, 1958. 46. J.S. R o l l e t t and D.R. Davies, Acta. Cryst. 8, 125 (1955) 47. D.W.J. Cruickshank, Acta. Cryst. 9, 754 (1956). 48. D.W.J. Cruickshank, Acta. Cryst. 9, 915 (1956). 49. Dictionary of Values of Molecular Constants, Vol. I I . Centre National de l a Recherche Sc i e n t i f i q u e , and I.C.I. Ltd., 1955. 50. H.C. A l l e n and E.K. P l y l e r , J. Amer. Chem. Soc. 80, 2673 (1958). ~ 51. J. Trotter, Acta. Cryst. 12, 86 (I960). 52. D.W.J. Cruickshank, Tetrahedron 17, 155 (1962). 53. A. Rosenthal and H.J. Koch', (1964) . In preparation. 54. L. Pauling, "The Nature of the Chemical Bond," 3rd edition.,.Cornell University Press, Ithaca, I960. 55. F.G. Mann, J. Chem. Soc., 4266 t(1963). • -. 56. J. Chatt and F.G. Mann, J. Chem. S o c , 1184 (1940). 57. K. Mislow, A. Zimmerman and J.T. M e l l i l o , J . Amer. Chem. Soc. 85, 594 (1963). 58. D.J. Sutor and F.R. Harper, Acta. Cryst. 12, 585 (1959). 59. W.R. Cullen, private communication. 60. H. Burton and C.S. Gibson, J. Chem. Soc., 451 (1926). 61. K.E. Jackson, Chem. Rev. 17, 251 (1935). 62. R. Fischer, Mikrochemie 12, 257, 1932. 63. L.E. Sutton et a l . , "Table of Interatomic Distances and Configuration i n Molecules and Ions." Chem. Soc. Special Publ. No. 11, 1958. 64. J. Trotter, Canad. J. Chem. 40, 1590 (1962). 65. N. Camerman and J. Trotter, J. Chem. Soc, 219 (1963). 66. K.N. Trueblood, E. Goldish and J. Donohue, Acta. Cryst. Ik, '1009* (1961) . 67. J. Trotter, J. Chem. Soc., 2567 (1962). 68. A. Rosenthal and D. Read, Methods of Carbohyd. Chem. 2:, 457 (1963). 69. A. Camerman and J. Trotter, Acta. Cryst. 17.(1964). In press. 70. F.F. Blicke and F.D. Smith, J. Am. Chem. Soc. 52, 2946 (1930). ~ 

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