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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.), U n i v e r s i t y 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 i n the department of CHEMISTRY We accept t h i s t h e s i s as conforming t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September 1964  In the  presenting  r e q u i r e m e n t s f o r an a d v a n c e d  British  Columbia, I agree  available mission  f o r reference  f o r extensive  representatives.  cation  Department o f  the L i b r a r y  and s t u d y *  shall  I further  make i t f r e e l y  agree  that  f o r f i n a n c i a l gain  permission*  (Jju^^St Columbia,  that  per-  f o r scholarly  by the Head o f my Department  The U n i v e r s i t y o f B r i t i s h Vancouver 8 Canada f  fulfilment of  degree a t the U n i v e r s i t y o f  I t i s understood  of t h i s thesis  w i t h o u t my w r i t t e n  that  i n partial  copying of t h i s thesis  p u r p o s e s may be g r a n t e d his  this thesis  o r by  copying or p u b l i -  s h a l l n o t be a l l o w e d  The U n i v e r s i t y o f 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  of  ARTHUR CAMERMAN  B.Sc,  The U n i v e r s i t y  o f B r i t i s h Columbia, 1961  WEDNESDAY, AUGUST 26th, 1964, AT 10:00 A.M. IN ROOM 261, CHEMISTRY BUILDING  COMMITTEE IN CHARGE Chairman: I . McT. Cowan W.R. C u l l e n C A . McDowell S.A. Melzak  External  G.B. P o r t e r A. R o s e n t h a l J. Trotter R.M. Thompson  Examiner:  P r o f e s s o r L. H.  U n i v e r s i t y o f Washington  Jensen  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 m o l e c u l a r s t r u c t u r e o f p e r y l e n e has been r e f i n e d from new t h r e e - d i m e n s i o n a l data, c o n f i r m i n g the gross f e a t u r e s of the s t r u c t u r e p r e v i o u s l y determined from two p r o j e c t i o n s . 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 l e a s t - s q u a r e s and d i f f e r e n t i a l syntheses and the hydrogen atoms have been a p p r o x i m a t e l y l o c a t e d . There are s m a l l but s i g n i f i c a n t d e v i a t i o n s from a c o m p l e t e l y p l a n a r 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 o f the measured bond l e n g t h s w i t h those p r e d i c t e d by the valence-bond and m o l e c u l a r - o r b i t a l t h e o r y shows f a i r l y c l o s e agreement w i t h both sgts o f f i g u r e s ; the p e r i - b o n d l e n g t h s are 1.471-0.005 A. In a s i m i l a r v e i n the m o l e c u l a r s t r u c t u r e o f pyrene was r e f i n e d by l e a s t - s q u a r e s and d i f f e r e n t i a l s y n t h e s i s treatment of new t h r e e - d i m e n s i o n a l data. The thermal motion o f the atoms was found t o be a n i s o t r o p i c and was i n t e r p r e t e d i n terms of r i g i d body v i b r a t i o n s . Small c o r r e c t i o n s were made to the bond l e n g t h s t o c o r r e c t e r r o r s due t o r o t a t i o n a l o s c i l l a t i o n s . The g e n e r a l v a r i a t i o n o f the mean bond d i s t a n c e s i s i n agreement w i t h trends p r e d i c t e d by valence-bond and m o l e c u l a r - o r b i t a l 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 v e r y good. The molecule i s s l i g h t l y non-planar, p r o b a b l y as a r e s u l t of c r y s t a l p a c k i n g 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 i s o m e r i c products and, to e s t a b l i s h the c o n f i g u r a t i o n s , X-ray a n a l y s i s o f the p-bromobenzenesulphonyl d e r i v a t i v e of one o f these has been c a r r i e d out. The bromine and s u l p h u r p o s i t i o n s were determined from the 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 and the o t h e r atoms were l o c a t e d from s u c c e s s i v e t h r e e - d i m e n s i o n a l F o u r i e r summations. Refinement was c a r r i e d out by l e a s t - s q u a r e s methods. The d e r i v a t i v e s t u d i e d i s 1-0-(p-bromobenzenesulphonyl)-4,5,7-tri-0-acetyl-2, 6a n h y d r o - 3 - d e o x y - U - g l u c o h e p t i t o l , and t h i s e s t a b l i s h e s the c o n f i g u r a t i o n s of the t r i a c e t y l d e r i v a t i v e s and parent p o l y o l s . The sugar r i n g i s i n the c h a i r p o s i t -  "ion w i t h a l l s u b s t i t u e n t s  equatorial.  10-Chloro-5,10-dihydrophenarsazine c r y s t a l l i z e s from xylene w i t h h a l f a molecule o f xylene o f c r y s t a l l i z a t i o n i n a m o n o c l i n i c space group. This material rapidly l o s e s the s o l v e n t o f c r y s t a l l i z a t i o n , the s o l v e n t - f r e e c r y s t a l s b e i n g orthorhombic. The complete s t r u c t u r e o f the orthorhombic c r y s t a l s has been determined u s i n g P a t t e r s o n m e t h o d s to determine the a r s e n i c and c h l o r i n e p o s i t i o n s and a t h r e e - d i m e n s i o n a l e l e c t r o n - d e n s i t y d i s t r i b u t i o n map to l o c a t e the other atoms. A l l the p o s i t i o n a l and a n i s o t r o p i c thermal parameters were r e f i n e d by l e a s t - s q u a r e s . The molecule i s s l i g h t l y f o l d e d about the As-N a x i s , the angle between the two o-phenylene groups being 169°, and the c h l o r i n e atom b e i n g o u t s i d e t h i s angle. The d e v i a t i o n from p l a n a r i t y i s thus not v e r y l a r g e and i t i s u n l i k e l y that g e o m e t r i c a l isomers c o u l d be i s o l a t e d . !  GRADUATE STUDIES Field  o f Study:  Chemistry  Topics i n Physical  Chemistry  R„Fo  T o p i c s i n I n o r g a n i c Chemistry  T o p i c s i n Organic Chemistry  Chemical  Kinetics  N„ B a r t l e t t WoR„ C u l l e n D E, McGreer R.E.I, P i n c o c k J„P„ Kutney 0  E.A. O g r y z l o G„B, P o r t e r D G.L James 0  Crystal  Coope Snider A . Bree  JoA.R,  Structures  0  J„ T r o t t e r S.A.M. Melzak  Related Studies C a l c u l u s and D i f f e r e n t i a l E q u a t i o n s Linear Algebra Digital  R. C l e v e l a n d  Computer Programming  Elementary Quantum  W.H. Gage  Mechanics  C„ F r o e s e Wo Opechowski  PUBLICATIONS 1.  A. Camerman and J . T r o t t e r , "The C r y s t a l and Mole c u l a r S t r u c t u r e o f P e r y l e n e " , 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 Mole c u l a r S t r u c t u r e o f 10-Chloro-5,10-Dihydrophenars a z i n e " , J.Chem.Soc. (1964). I n P r e s s  3.  A. Camerman and J . T r o t t e r , "The C r y s t a l and Mole c u l a r S t r u c t u r e o f 1-0-(p-bromobenzenesulphonyl)4,5,7-tri-p-acetyl-2,6-anhydro-3-deoxy-D -glucoh e p t l t o l " , A c t a . C r y s t . (1964). I n P r e s s  4.  A. Camerman and J . T r o t t e r , "The C r y s t a l and M o l e c u l a r S t r u c t u r e o f Pyrene", A c t a . C r y s t . To be p u b l i s h e d .  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 " , A c t a . C r y s t . (1964) I n Press  6.  A. Camerman, H. Koch, A. R o s e n t h a l and J . T r o t t e r , " C o n f i g u r a t i o n o f A n h y d r o d e o x y h e p t i t o l s ! , Can. J . Chem. (1964). I n P r e s s 1  ABSTRACT  The  c r y s t a l and molecular s t r u c t u r e of perylene has been  r e f i n e d from.^ew three-dimensional data, confirming the gross features of the s t r u c t u r e p r e v i o u s l y determined 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 e d 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 l o c a t e d . 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 steric effects.  intermolecular  A comparison of the measured bond lengths  with  those predicted by the valence-bond and m o l e c u l a r - o r b i t a l theory shows f a i r l y close agreement with both sets of f i g u r e s ; the , o peri-bond lengths are 1.471*0.005 A. In a s i m i l a r vein the molecular s t r u c t u r e of pyrene was r e f i n e 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 a n i s o t r o p i c and was i n t e r p r e t e d i n terms of r i g i d body v i b r a t i o n s .  Small c o r r e c t i o n s were made to the bond  lengths to c o r r e c t e r r o r s due t o 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 m o l e c u l a r - o r b i t a l  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 f o r c e s . 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 c o n f i g u r a t i o n s , X-ray  iii a n a l y s i s of the p-bromobenzenesulphonyl d e r i v a t i v e of one these has been c a r r i e d out.  The bromine and sulphur p o s i t i o n s  were determined from the three-dimensional Patterson and the other atoms were located from successive dimensional F o u r i e r summations. least-squares  methods.  of  Refinement was  function  threec a r r i e d out  by  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-deoxyd - g l u e o h e p t i t o l , arid t h i s e s t a b l i s h e s the configurations of the t r i a c e t y l d e r i v a t i v e s and parent p o l y o l s .  The  sugar r i n g i s  i n the c h a i r p o s i t i o n 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 m a t e r i a l 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 s t r u c t u r e of the orthorhombic c r y s t a l s has been  determined using Patterson methods to determine the arsenic c h l o r i n e p o s i t i o n s and a three-dimensional d i s t r i b u t i o n map  to locate the other atoms.  and  electron-density A l l the p o s i t i o n a l  and a n i s o t r o p i c thermal parameters were r e f i n e d by l e a s t squares.  The molecule i s s l i g h t l y folded about the As-N  the angle between the two o-phenylene groups being 169°, the c h l o r i n e atom being outside £his angle. p l a n a r i t y i s thus not very large and  and  The d e v i a t i o n from  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 .  axis,  To MY MOTHER f o r her l o v e , devotion and s a c r i f i c e  V  ACKNOWLEDGEMENTS  My warmest thanks are due to Dr. James T r o t t e r whose guidance, advice, and f r i e n d s h i p have made my research under h i s s u p e r v i s i o n and my e n t i r e a s s o c i a t i o n with him both i n s t r u c t i v e and pleasant. I am indebted t o my brother Norman Camerman f o r c o n t i n u a l a i d , d i s c u s s i o n , and encouragement.  His help i n a l l phases of  my work i s g r e a t l y appreciated. I thank Dr. A. Bree f o r the sample of pyrene, Dr. A. Rosenthal and Mr. H. Koch f o r the t r i - O - a c e t y l - d - g l u c a l d e r i v a t i v e and Dr. W. C u l l e n f o r the c r y s t a l s of 10-chloro-5,10dihydrophenarsazine. I a l s o g r a t e f u l l y acknowledge Drs EAhmed and G. Mair f o r k i n d l y making a v a i l a b l e t h e i r IBM 1620 computer programs. F i n a l l y I wish t o express my a p p r e c i a t i o n to the National Research Council of Canada f o r the award of a Bursary f o r 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  vi  LIST OF FIGURES  ix  LIST OF TABLES  x  PART I . INTRODUCTION TO THE THEORY OF CRYSTAL STRUCTURE DETERMINATION I.  Elementary Crystallography  1 .  .  .  .  .  . •.  A.  Introduction  2  B.  C r y s t a l s as Geometric Figures  3  C.  C r y s t a l Symmetry  4  D.  L a t t i c e Structure of C r y s t a l s , and Space Groups  II.  4  D i f f r a c t i o n of X-Rays by a C r y s t a l  9  A.  Scattering'by Electrons  9  B.  Conditions f o r D i f f r a c t i o n Maxima .  C.  The R e c i p r o c a l L a t t i c e  D.  The Structure Factor  E.  I n t e n s i t y of Reflected Radiation  F.  Generalized Structure Factor and F o u r i e r Series  III.  2  . . .  . 11 12 . . . .  .' '  Structure Determination and Refinement  9  13  14 . . .  A.  Methods f o r E s t a b l i s h i n g the Structure  B.  Refinement of C r y s t a l Structures  .  . . . .  17 . 17 19  vii PAGE PART I I . THREE-DIMENSIONAL REFINEMENTS OF THE STRUCTURES OF PERYLENE AND PYRENE I.  24  The C r y s t a l and Molecular Structure of Perylene  25  Introduction  25  Experimental  .26  Refinement of the Structure  .28  Coordinates and Molecular Dimensions  .  .  .30  Discussion II.  39  The C r y s t a l and Molecular Structure of Pyrene . 50 Introduction Experimental  .  50 .  !  .  . 50  Refinement of the Structure  51  Coordinates and Molecular Dimensions  . . .  54  Discussion PART I I I .  58  DETERMINATION OF STRUCTURES OF 1-0-(p-BROMOBENZENESULPHONYL)-4,5,7-TRI-0-ACETYL-2,6ANHYDR0-3-DE0XY-d-GLUC0HEPTIT0L AND 10CHL0R0-5,10-DIHYDROPHENARSAZINE  I.  64  C r y s t a l and Molecular S t r u c t u r e of 1-0-(p-Bromobenzenesulphbnyl)-4,5,7-Tri-0-Acetyl-2,6Anhydro-3-Deoxy-d-Glucoheptitol . . . . . .  65  Introduction  65  Experimental  .  .  Structure A n a l y s i s  .  .  .  .  .  ,  .  .  . . . . . . . . .  Coordinates and Molecular Dimensions  . . .  .66 67 70  viii PAGE PART I I I .  (continued) Discussion  II.  72  C r y s t a l and Molecular Structure of 10-Chloro5,10-Dihydrophenarsazine  75  • Introduction  75  P r e l i m i n a r y X-Ray Study  APPENDIX  X  . . . . . . . .  77  Experimental  79  Structure A n a l y s i s  80  Discussion  86  STRUCTURE FACTOR TABLES  89  APPENDIX I I CRYSTALLOGRAPHIC DATA FOR SOME MOLECULAR CRYSTALS REFERENCES  ,  102 106  LIST OF FIGURES FIGURE  PAGE  1.  Standard or Parametral Face  3  2.  The 14 Bravais L a t t i c e s  6  3.  D i f f r a c t i o n and R e f l e c t i o n  10  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  12  Perylene 5.  Measured Bond Lengths  35  6.  Measured Valency Angles  36  7.  Deviations from Mean Molecular Plane  38  8.  Normal P r o j e c t i o n of 2 P a r a l l e l Molecules  9.  Perspective Drawing of 2 P a r a l l e l Molecules  . . . .  42 .  43  Pyrene 10.  Measured Bond Lengths and Valency Angles  11.  Kekule S t r u c t u r e s  . . .  57 62  1-0-(p-Bromobenzenesulphonyl)-4,5 <7-Tri-0-Acetyl-2, 6-Anhydro-3-Deoxy-d-Glucoheptitol 12.  Projected E l e c t r o n Density  .  69  10-Chloro-5,10-Dihydrophenarsazine 13.  Projected E l e c t r o n Density  14.  Measured Bond Lengths and Valency Angles  82 . . .  84  LIST OF TABLES TABLES I. II.  PAGE Symmetry Operations i n C r y s t a l s  4  Symmetry Operations I n v o l v i n g T r a n s l a t i o n  .  .  5  Perylene III. IV. V. VI. VII. VIII. IX. X.  Progress of Refinement  29  Carbon Atom E l e c t r o n - D e n s i t i e s and Curvatures  ,  31  Hydrogen Atom E l e c t r o n - D e n s i t i e s  31  F i n a l Coordinates  32  Standard Deviations  33  O r i e n t a t i o n of the Molecule  37  Shorter Intermolecular  39  Contacts  Measured and Calculated Bond Lengths  . . . .  44  Pyrene XI. XII. XIII.  Hydrogen Atom E l e c t r o n - D e n s i t i e s  52  Carbon Atom E l e c t r o n - D e n s i t i e s and Curvatures  XV. XVI. XVII.  53  .  54  F i n a l P o s i t i o n a l Parameters and Standard Deviat i o n s , and Deviations from Molecular Plane  XIV.  ,  A n i s o t r o p i c Thermal Parameters O r i e n t a t i o n of the Molecule  .  55 .  . . .  .  .  Shorter Intermolecular Contacts . Measured and Calculated Bond Lengths  58 59  . . . .  6l  1-0- (p-Bromobenzenesulphonyl) .-4.5 , 7 - T r i - 0 - A c e t y l 2,6-Anhydro-3-Debxy-d-Glucoheptitol XVIII. XIX. XX.  F i n a l Parameters . . . .  70  Bond Lengths and Valency Angles  71  Shorter Intermolecular Contacts  73  xi  TABLES  PAGE •  /  10-Chloro-5 10-Dihydrophenarsazine t  XXI. XXII. XXIII.  F i n a l P o s i t i o n a l and Thermal Parameters  . #1  Shorter Intermolecular Contacts Deviations from Mean Planes .  85 «  86  Comparison of Measured and Calculated Structure Factors Al.  Perylene  A2.  Pyrene  A3.  90 .  . 93  1-0-(p-Bromobenzenesulphonyl)-4,5,7-Tri-O-Acetyl2,6-Anhydro-3-Deoxy-d-Glucoheptitol Structure Amplitudes  A4.  96  10-Chloro-5,10-Dihydrophenarsazine Structure Amplitudes  99  PART I INTRODUCTION TO THE THEORY OF CRYSTAL STRUCTURE DETERMINATION  I.  ELEMENTARY CRYSTALLOGRAPHY  A.  Introduction  The p o s t u l a t i o n 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 l e d to s c i e n t i f i c advancement i n two main directions.  The f i r s t concerned the nature of X - r a d i a t i o n i t -  s e l f and l e d through the work of W.H. Bragg, Moseley, and others to fundamental advances i n the theory of atomic s t r u c t u r e .  The  second aspect e n t a i l e d the use of X-ray d i f f r a c t i o n as a powerf u l t o o l f o r e l u c i d a t i n g 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, g e n e r a l l y  r e f e r r e d to as X-ray c r y s t a l l o g r a p h y , w i t h which t h i s t h e s i s i s concerned. C r y s t a l s d i f f e r from l i q u i d s or other amorphous materials in that c e r t a i n of t h e i r p r o p e r t i e s t r i c , and magnetic  o p t i c a l , thermal, e l e c -  d i s p l a y marked anisotropy.  Since the  i n t e 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 p r o p e r t i e s , as w e l l as the well-developed symmetry common to many c r y s t a l s , must be r e l a t e d to some feature of the  ultimate s t r u c t u r e of the matter of which the c r y s t a l i s  composed.  To come t o an understanding of the r e l a t i o n s h i p of  c r y s t a l symmetry and anisotropy to i n t e r n a l atomic s t r u c t u r e we must examine the c r y s t a l both e x t e r n a l l y (as a geometric f i g u r e ) and i n t e r n a l l y (as a l a t t i c e of atoms, i o n s , or molecules).  3 B.  C r y s t a l s as Geometric Figures  C r y s t a l s 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 o r i e n t a -  t i o n s and not the s i z e s 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 d e s c r i b i n g c r y s t a l  faces l e t us choose the i n t e r s e c t i o n s of any three n o n - p a r a l l e l faces represented by OA, OB, and OC i n f i g u r e 1 as axes. may  We  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 w i t h i n t e r c e p t s a, b, and c.  This plane  i s c a l l e d the standard or parametral face as i t determines 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 s a i d to have the M i l l e r i n d i c e s (hk£).  The  indices  ( a f t e r c l e a r i n g of f r a c t i o n s ) are thus the r e c i p r o c a l s of Figure 1 on the c a l i b r a t e d set of a x i s . are then (111)  the i n t e r c e p t s of any  face,  or plane drawn p a r a l l e l to i t , The i n d i c e s of our standard face  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 i n t e r c e p t 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 i n d i c e s  4 discovered  by Ha'uy i n 1784,  which says that the r a t i o s of the  i n d i c e s of any face of a c r y s t a l are small  C.  integers.  C r y s t a l Symmetry  A symmetry operation  i s one which when applied t o a  geometric f i g u r e leaves the f i g u r e co-incident with  itself.  There are ten symmetry operations possible f o r c r y s t a l s . are l i s t e d i n Table I with t h e i r appropriate  These  symbols.  TABLE I SYMMETRY OPERATIONS IN CRYSTALS Symbol 1 2 3 4 6 JL = i 2 = m 3. 4 o"  Operation i d e n t i t y operation = onefold r o t a t i o n a x i s two-fold r o t a t i o n a x i s 'three-fold r o t a t i o n a x i s four-fold rotation axis s i x - f o l d rotation axis center of symmetry mirror plane three-fold rotatory inversion axis four-fold rotatory inversion axis 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. 32 point groups or c r y s t a l c l a s s e s .  These are known as the  A complete l i s t i n g of  these point groups and the common symbols used t o designate them may be found i n reference (1).  D.  L a t t i c e Structure of Crystals, and Space Groups  As e a r l y as the seventeenth century Hooke and Huygens thought of c r y 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 p o s s i b l e . Figure 2 i l l u s t r a t e s u n i t 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 r e g u l a r l a t t i c e s  indefi-  n i t e l y extended i n every d i r e c t i o n can be brought i n t o s e l f coincidence i n a new way, namely by t r a n s l a t i o n s along any of the l a t t i c e d i r e c t i o n s . identical  The l a t t i c e points are by d e f i n i t i o n  so such movements over the repeat distance leave the  s t r u c t u r e unchanged.  Hence a new c l a s s of symmetry operations  i s a p p l i c a b l e to l a t t i c e s t r u c t u r e s , i n a d d i t i o n to those which apply to f i n i t e geometrical f i g u r e s .  These new operations are  the screw a x i s , which combines a r o t a t i o n a x i s w i t h a t r a n s l a t i o n , and the g l i d e plane, which combines a m i r r o r plane with a translation.  Table I I l i s t s these new symmetry operations  and t h e i r symbols.  TABLE I I SYMMETRY OPERATIONS INVOLVING TRANSLATION Symbol 2  1  3l 32 1 4  4  Operation r o t a t i o n of THJL w i t h t r a n s l a t i o n -i 2I 2T " 3 3 tt  t»  tt  2JT 4  2  43 n  reflection + translation  •  2  7  1 4 2 4  I  o r  S+£  6  I  £7  1. TRICLINIC  3. SIDE-CENTERED MONOCLINIC  2 SIMPLE 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  9 RHOMBOMEDRAL  10 SIMPLE TETRAGONAL  HfcKA&ONAL  4=71  It  F i g u r e 2.  SIMPLE CUBIC  11 BODY-CENTERED T£ TRAOONAL  -T-  13 BODYCENTERED CUBIC  The l U B r a v a i s  Lattices  14 F A C E CENTERES CUBIC  7 TABLE I I (continued) Symbol 61  Operation r o t a t i o n of  with t r a n s l a t i o n 1 6  A-  tt  it  tt  6 it  tt  2 rj  2  3 75  «  i»  "  w  11  A,  11  11  11  it  tl  4  A_  »i  11  it  it  11  5  A-  °3  °5  75  a,b,c d  reflection + translation ^ , -| r e f l e c t i o n + ~ diagonal translation 4  By combining these new utilized  symmetry o p e r a t i o n s w i t h those  i n forming the 32 p o i n t groups, Federow, Barlow, and  S c h o e n f l i e s independently d e r i v e d 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 V o l , I, the I n t e r n a t i o n a l T a b l e s f o r X-Ray C r y s t a l l o g r a p h y . A knowledge of the space group of a c r y s t a l hence i n c l u d e s a knowledge of a l l the symmetry p r o p e r t i e s of the c r y s t a l .  The  space group cannot be determined from e x t e r n a l form a l o n e , but must be determined from X-ray d i f f r a c t i o n p a t t e r n s .  The  basis  f o r t h i s d e t e r m i n a t i o n i s the e x t i n c t i o n of c e r t a i n X-ray  dif-  f r a c t i o n s p e c t r a caused by the presence of screw axes, g l i d e p l a n e s , and centered l a t t i c e s .  Since m i r r o r planes and  t i o n axes do not cause s p e c t r a l e x t i n c t i o n and because  rota(due t o  F r i e d e l ' s law) X-ray d i f f r a c t i o n p a t t e r n s c o n t a i n a c e n t e r of symmetry, i t i s not always p o s s i b l e to a s c e r t a i n the c o r r e c t space group from the d i f f r a c t i o n p a t t e r n a l o n e .  Statistical  a n a l y s i s 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 u s e f u l i n t h i s respect as w e l l 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 p r o p e r t i e s .  II.  DIFFRACTION OF X-RAYS BY A CRYSTAL  A.  S c a t t e r i n g by Electrons  C r y s t a l s are composed of groups of atoms repeated at regular i n t e r v a l s , w i t h the same o r i e n t a t i o n , i n three dimensions.  Each atom i s composed of a nucleus and  surrounding  e l e c t r o n s , and when these electrons are i n c o l l i s i o n w i t h an X-ray beam they are forced i n t o o s c i l l a t i o n by the p e r i o d i c a l l y varying e l e c t r i c f i e l d and emit r a d i a t i o n of the same wavelength as the X-rays.  In t h i s manner the electrons s c a t t e r or  d i f f r a c t the X-ray beam.  The waves scattered by the s e v e r a l  e l e c t r o n s of each atom combine and the r a t i o of the wave scattered by an atom a t r e s t t o that scattered by a s i n g l e e l e c t r o n i s known as the atomic s c a t t e r i n g f a c t o r f . The Q  atomic s c a t t e r i n g f a c t o r 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 e f f e c t s to be expected from a s i n g l e 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 c o n d i t i o n 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 d i f f e r e n c e between waves scattered from successive points equal a whole number of wavelengths, nA.  I f the i n c i d e n t beam  makes an angle cx w i t h the row, and the d i f f r a c t e d beam an 0  angle ex, t h i s c o n d i t i o n i s a(coscx  D  - coscx) = nX  should  10 For a three dimensional l a t t i c e w i t h 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 A  c(cos Y  0  2  - cos's ) = nj\  are simultaneously s a t i s f i e d . n  The t r i p l e set of i n t e g e r s  l 2 3 denotes the order of the.spectrum. n  n  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 s i n g l e 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 h i s i n t r o d u c t i o n 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 i n c i d e n t on  a c r y s t a l plane a t an angle © a r e f l e c t e d beam w i l l be formed by Huygen's p r i n c i p l e .  Reinforcement by X-rays r e f l e c t e d  from  the next p a r a l l e l c r y s t a l plane, a t distance d, w i l l occur when the path d i f f e r e n c e i s equal t o a whole number of wavelengths, or when nX = 2dsinG From Figure 3 i t can be shown (using the usual t r i g o n o m e t r i c  11 r e l a t i o n s h i p s ) that the Laue and Bragg equations are equivalent.  C.  The R e c i p r o c a l L a t t i c e  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 o r i e n t a t i o n i n a c r y s t a l ; i t i s e a s i e r to think of the normals to the planes rather than the planes themselves.  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 i n v e r s e l y p r o p o r t i o n a l to the spacing of the  respec-  t i v e planes. S = |[(plane),  K i s u s u a l l y taken as /\ .  The r e c i p r o c a l l a t t i c e axes are l a b e l l e d a*, b*, and c* and i n v e c t o r notation are defined as a* - AbXc/V b* = AcXa/V c* = AaXb/V where V i s the volume of the u n i t c e l l . R e c i p r o c a l l a t t i c e theory i s extremely u s e f u l i n a f f o r d i n g a simple geometrical i n t e r p r e t a t i o n of d i f f r a c t i o n phenomena. Bragg's law s t a t e s Sin 8 = A/2d f o r r e f l e c t i o n to occur i s 1. r o c a l space (Figure 4 ) .  hence the maximum value of A/2d This defines a sphere i n r e c i p -  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 i n c i d e n t r a d i a t i o n . i s the l i m i t i n g sphere.  This  Any r e c i p r o c a l 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 a d i a t i o n i n c i d e n t i n the d i r e c t i o n of i t s diameter. i s c a l l e d the sphere of r e f l e c t i o n .  This smaller sphere  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 w i t h i n 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 s i n g l e 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 e f f e c t the d i r e c t i o n of incidence of the r a d i a t i o n changes and many r e c i p r o c a l l a t t i c e points i n t e r s e c t 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 r e s u l t a n t d i f f r a c t e d wave.  This r e s u l t a n t i s c a l l e d the structure f a c t o r , F( kjZ,)> n  f o r the plane w i t h M i l l e r indices hkl, quantity  characterized  tX(hkjfc) . The  and  i s a complex  by an amplitude |F(hk&)|, and a phase  structure f a c t o r , being a vector summation of  wavelets d i f f r a c t e d by the N atoms i n the u n i t c e l l may  the  be  therefore w r i t t e n 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 .  I t can be evaluated by means of the f o l l o w i n g  expressions  where  The quantity f j i s the s c a t t e r i n g f a c t o r of the j  t  n  atom  corrected f o r thermal v i b r a t i o n of the atom. -B s i n 6 2  —JT-  The quantity B i s r e l a t e d t o the mean square displacement of _2 the atom a t r i g h t angles to the r e f l e c t i n g plane, /JL , by the expression  B = ctrr ^ . 2  2  In p r a c t i c e an a r b i t r a r y value i s assigned t o B and t h i s value i s r e f i n e d during the s t r u c t u r e refinement.  E.  I n t e n s i t y of R e f l e c t e d R a d i a t i o n  When a c r y s t a l i s turned through the r e f l e c t i n g p o s i t i o n w i t h angular v e l o c i t y co, d i f f e r e n t planes are s u c c e s s i v e l y brought i n t o the p o s i t i o n 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 i n t e g r a t e d reflection  •^o  which i s c h a r a c t e r i s t i c of a given c r y s t a l plane  i s p r o p o r t i o n a l t o the volume dv" of the c r y s t a l block and independent of the shape. The f o l l o w i n g r e l a t i o n can be derived: ELO = N [~V:~| A F (hk£) 1+ Cos^e dV mc 2Sin26 2  2  2  3  2  14 In t h i s e x p r e s s i o n I  = i n t e n s i t y of the  0  E  = t o t a l r e f l e c t e d energy  N  = number of u n i t volume of the  e  and  m  = charge and  c  = v e l o c i t y of  The  q u a n t i t y l+Cos 28 i  the  a v e r a g i n g necessary due  2  i z e d , while the , I ^ i s the Sm26 w  s  i n c i d e n t beam  the  c e l l s per crystal  mass of the  electron  light  p o l a r i z a t i o n f a c t o r and to the  unit  incident  provides  beam being unpolar-  r e f l e c t e d beam i s p a r t i a l l y p o l a r i z e d ,  Lorentz f a c t o r , which a r i s e s from the  and  difference  i n speeds at which v a r i o u s r e c i p r o c a l l a t t i c e p o i n t s pass through the the  reflecting position.  integrated  In experimental procedure  r e f l e c t i o n e x p r e s s i o n must be m o d i f i e d  in  accordance w i t h the method employed f o r measuring the ties.  This stems from the f a c t t h a t the  intensi-  Lorentz f a c t o r  has  d i f f e r e n t forms i n d i f f e r e n t experimental t e c h n i q u e s .  F.  G e n e r a l i z e d D e f i n i t i o n of the E x p r e s s i o n of E l e c t r o n In our  S t r u c t u r e F a c t o r and  D e n s i t y as a F o u r i e r  p r e v i o u s d e f i n i t i o n of the  assumed t h a t a l l the  structure  s c a t t e r i n g matter i n the  the  Series factor  unit c e l l  we i s con-  c e n t r a t e d i n t o a number of s p h e r i c a l l y symmetrical atoms. s h a l l now electron  c o n s i d e r a more g e n e r a l d e f i n i t i o n i n terms of density  tering material  function. at a point  number of e l e c t r o n s  I f p(XYZ) i s the X,Y,Z  of  volume of the u n i t c e l l  an scat-  i n the u n i t c e l l , then  i n the volume element dXdYdZ w i l l  (0(XYZ)-I_dXdYdZ where V i s the abc v  density  We  the  be and  15 a,b,c, are the a x i a l l e n g t h s .  Then i f x,y,z are f r a c t i o n a l co-  ordinates r f r / v 2TTi(hx+ky+£z) F(hki-) = V\ \ \ p(xyz) e dxdydz Jo Jo do 1  1  1  The e s s e n t i a l l y p e r i o d i c 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  s t r u c t u r e , suggests expansion i n the form  of a F o u r i e r s e r i e s as the n a t u r a l r e p r e s e n t a t i o n i c a l property  of the c r y s t a l .  o f any phys-  The idea of r e p r e s e n t i n g t'he  e l e c t r o n , d e n s i t y o f a c r y s t a l i n such a way was f i r s t by W.H.  Bragg i n 1915. Thus / \ ,/ p(xyz) = ^ > 2 Z  ^  A ( p q r )  suggested  2TTi (px+qy+rz) e  -00  where p,q,r are i n t e g e r s and A(pqr) the c o e f f i c i e n t of the general  term.  By s u b s t i t u t i n g t h i s equation f o r p(xyz) i n t o the genera l i z e d expression  f o r the s t r u c t u r e f a c t o r and i n t e g r a t i n g , i t  i s e a s i l y shown that A(hkjft) - F ( h k U V Thus the s t r u c t u r e f a c t o r and e l e c t r o n d e n s i t y a r e F o u r i e r transforms o f one another. (?(xy z \  '  = lSSZpfvik/,) T h k Jb v  p  -2TTi(hx+ky+^z)  ;  —oo  It can e a s i l y be shown ( l ) t h a t the above e x p r e s s i o n can be w r i t t e n  i n the f o l l o w i n g convenient form: 4-00  p(xyz)  =AZ2S v  h  k I -oo  Where (X(hkj0/) represents  |F(hk&)| cos[2TT (hx+ky+^z) -0((hk£)] 1  1  the phase angle a s s o c i a t e d with the  16 amplitude |F(hk£)| . We can c a l c u l a t e |F(hk&)| from the i n t e n s i t i e s of the r e f l e c t e d r a d i a t i o n 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 s o l u t i o n of c r y s t a l s t r u c 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 e l e c t r o n density d i s t r i b u t i o n s can be obtained by assigning a r b i t r a r y phases to the s t r u c t u r e amplitudes. Of some help, however, i n l i m i t i n g the combinations of phases p o s s i b l e , i s the knowledge that the e l e c t r o n 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 r e s u l t a n t s t r u c t u r e must be chemically f e a s i b l e .  III.  STRUCTURE DETERMINATION AND REFINEMENT  The sequence of steps employed i n c r y s t a l s t r u c t u r e analysis i s usually 1.  The determination of u n i t 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  p o s i t i o n s 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 r e f l e c t e d r a d i -  a t i o n from each of the c r y s t a l planes. 3.  Establishment of the s t r u c t u r e .  the successive  This u s u a l l y e n t a i l s  l o c a t i o n of various atoms i n the u n i t c e l l and  culminates i n the reasonably c e r t a i n i d e n t i f i c a t i o n of a l l atomic p o s i t i o n s . 4.  Refinement of the s t r u c t u r e .  This involves  adjust-  ment of a l l atomic coordinates to ensure c l o s e s t agreement between observed and c a l c u l a t e d s t r u c t u r e amplitudes. There are many good textbooks dealing w i t h the many aspects of c r y s t a l s t r u c t u r e a n a l y s i s and some of these are l i s t e d i n references (4-8).  A b r i e f d i s c u s s i o n of the estab-  lishment of the s t r u c t u r e and some refinement methods i s given i n the next two s e c t i o n s .  A.  Methods f o r E s t a b l i s h i n g the Structure  Methods f o r a t t a c k i n g the phase problem may be c l a s s i f i e d i n t o the three f o l l o w i n g i.  categories.  T r i a l and E r r o r Methods.  As the name i m p l i e s , these  methods are based on the combination of a l l chemical, p h y s i c a l ,  18 and c r y s t a l l o g r a p h i c evidence obtainable, to form t r i a l s t r u c tures.  When some atoms have been approximately l o c a t e d ,  phases are c a l c u l a t e d based on the located atomic  coordinates  and a F o u r i e r synthesis i s c a l c u l a t e d using the measured amplitudes and c a l c u l a t e d phases.  I t i s hoped t h i s F o u r i e r synthesis  leads to more and b e t t e r atomic p o s i t i o n s which would be used to c a l c u l a t e new s t r u c t u r e f a c t o r s f o r use i n a f u r t h e r F o u r i e r 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 a l s o to r e f i n e the s t r u c t u r e i f no b e t t e r means i s a v a i l a b l e . ii. i n 1934,  Patterson and Heavy Atom Methods.  A.L.  Patterson,  (9) extended to c r y s t a l s the theory of s c a t t e r i n g 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 a n a l y s i s . The f u n c t i o n which has come to bear Patterson's name i s defined by the equation CO  A(uvw)  | | |  |F(hk£)| e2  2lrt(h  f f^> k  -CD  and represents vector distances between atoms i n the c r y s t a l . Hence a peak on the Patterson map at coordinates u^v^w^ corresponds to an interatomic distance i n 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 p r o p o r t i o n a l to the product of the atomic  numbers of the two atoms i n v o l v e d .  Hence Patterson's f u n c t i o n  i s used most often to f i n d the coordinates of a heavy atom (one c o n t a i n i n g more e l e c t r o n s than any other atom i n the molecule) i f one i s present.  I f the p o s i t i o n of the heavy atom can  19 be  determined  sufficient  phases  for a  Sometimes another at ture.  In  the  Fourier  Robertson  case,  phthalocyanines  determine  Direct the  observable  values  furnished  Schwartz's  pounded  the  probability  Karle  and  theory  as  in this  r e l a t i o n s between  space  groups, but  cable  to  a l l cases  B. The the  a  by  isomorphous from  structures  a  replace-  difference  J.M.  of  the  Kasper  a 2  the  factors  (12,  of  of  who  determining  field  18,  19)  factors  and  in  of  been pro-  joint-  phases  have a l s o  the  (16). established  centrosymmetric  s a t i s f a c t o r y d i r e c t method a p p l i be  of  factor, R the  elements  have a l s o  calculus  a means o f  to  of  system  p(xyz)"^0, has  15),  statistical  structure  symmetry  to  from  making use  A more g e n e r a l  (14,  (17,  directly  13), the  attempts  inequalities limiting  fact that  Hauptman  i s yet  of  set  |F| 'S.  generally  discrepancy  mathematical  structure  Refinement  correctness  the  atoms.  crystal struc-  n i c e l y by  i n e q u a l i t i e s and  and  utilization  Other workers  of  the  incorporating  by  lighter  heavy atom  of  very  These are  H a r k e r and  c e r t a i n F's  equalities,  sign  Methods.  i n c r y s t a l s , derived of  a  be  11).  phases of  data.  Cauchy's and present  (10,  of  the  determined  is illustrated  a t o m may  a l t e r i n g the  method  s o m e t i m e s be  determination  reveal  replace  c a l l e d the  can  method  in his  i i i .  to  to  same p o s i t i o n w i t h o u t  such a  This  s o l e l y for that  synthesis  i t is possible  ment, phase a n g l e s effect.  calculated  found.  Crystal «  Structures  ^ l l o l ~ l cl F  F  experimental molecular  is  a  measure  structure  20 Correct structures u s u a l l y have R<0.25 and very w e l l r e f i n e d 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 s t r u c tures are by means of d i f f e r e n t i a l syntheses, l e a s t squares a n a l y s i s , and d i f f e r e n c e 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 d i f f e r e n c e syn-  t h e s i s employs the q u a n t i t i e s ( F - F ) as c o e f f i c i e n t s i n a Q  F o u r i e r synthesis.  C  F i r s t expounded by Booth (20), i t s features  were w e l l developed by Cochran (21). a.  D i f f e r e n t i a l Synthesis. Booth (22) a l s o concentrated a t t e n t i o n on the problem  of f i n d i n g the maxima of the e l e c t r o n - d e n s i t y f u n c t i o n .  At  these maxima, one per atom, the f i r s t d e r i v a t i v e 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 e r r o r i s e, so that the correct coordinate i s x  = x+e, then expanding d£(x+£) i n a Taylor s e r i e s we have, dx (considering the f i r s t two terms o n l y ) : 0  de(x+e) . - d g i x l dx dx  d g(x) dx^ 2  +  £  m  0  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 f o l l o w i n g type are obtained:  The e l e c t r o n density f u n c t i o n i s known  21  (O(xyz) = I ^ ^ ^ F  ( h k  ^ cos[2TT(hx+ky+^z) - a ] )  so the p a r t i a l d e r i v a t i v e s can be e a s i l y evaluated.  In the con-  venient n o t a t i o n adopted by Booth, where A  A  h  = || - .  ™_22^  sin[27T(hx ky £z) -«]  {hkt)  +  =23L = - AlL_2S2hk F /  hk  *d*dy  V h kjL  ^  h k n n K J W  +  cos[2TT(hx+ky+/z)  -ex]  f o r each atom we obtain a matrix equation A  hh  A  hk  A  L  A  hJL  A  hk  A  /e \  hA  x  k k kg, A  k i U A  Ah\  ;€ \ = -( k A  y  7  The d i f f e r e n t i a l synthesis i s a f f e c t e d g r e a t l y by s e r i e s termination e r r o r s i f enough terms are not included i n the Fourier series. applied  To c o r r e c t f o r t h i s a b a c k s h i f t c o r r e c t i o n i s  a synthesis i s computed w i t h the F ' s as c o e f f i c i e n t s c  i n the summations and any coordinate  s h i f t s output are sub-  t r a c t e d from those s h i f t s output by the F b.  Q  synthesis.  Method of Least Squares. The p r i n c i p l e of l e a s t squares proposes that the  values of a set of v a r i a b l e s which best s a t i s f y a set of somewhat i n c o n s i s t e n t observations  are such as to make the sum of  the squares of the e r r o r s a minimum. I f we have a set of m v a r i a b l e s q, each a l i n e a r f u n c t i o n of x,y,z,...» and each w i t h an e r r o r E, then we have a set of m equations of the form  22 According to the method of l e a s t squares 2E . must be made a 2  minimum, hence = 2 2(ajX + bjy + C j Z + ...  and s i m i l a r l y f o r TOSE . and 2  j  J  d^E .3  .  "2>y  -  = 0  2  J  R e w r i t i n g , we may obtain the f o l l o w i n g matrix equation  6  2 a ^ c ^ ., 2b  Za-qA J  J  ici .*  :  7  The above are known as the normal equations, and: s i n c e there are n equations i n n unknowns, the d e s i r e d values of x,y,z,... can be determined. This scheme was f i r s t a p p l i e d to f i n d i n g the values of the atomic coordinates of a s t r u c t u r e which b e s t . f i t the  (  observed F's by Hughes (23) and i s done i n the f o l l o w i n g manner: Each c a l c u l a t e d F i s computed by the r e l a t i o n F  C  = 2f e^'^+kyr+^zr) r r  Here the v a r i a b l e s are exponentials i n xyz and i n order to be usable must be transformed i n t o l i n e a r f u n c t i o n s .  This  i s done by using the f i r s t two terms i n Taylor's s e r i e s as was done i n the method of D i f f e r e n t i a l Synthesis.  We then have,  f o l l o w i n g the method used i n the previous s e c t i o n :  23  AF - F - F 0  « F  - f(x+e , y £y, z+£ ) - f ( x , y , z ) +  c  x  z  ^ +e, +€ Fc  SFc  3 F c  ) - F  This summation i s taken over the R atoms of the s t r u c t u r e , When the observational e r r o r i s added to each equation above the set of equations can be recast i n t o the form from which the normal equations can be derived. Refinement by l e a s t squares has a number of advantages. I t i s free of the s e r i e s - t e r m i n a t i o n errors which characterize F o u r i e r methods; i t i s possible to use l e s s than a l l the F*s i n the r e f i n i n g process; i t i s p o s s i b l e to use a weighting funct i o n , w, and minimize 2w( | F j - |F j ) ; and i t i s possible t o 2  Q  C  include a scale f a c t o r and i s o t r o p i c and/or a n i s o t r o p i c temperature f a c t o r s i n the refinement process. With the advent of high speed computers, the method of l e a s t squares has become a very popular means of s t r u c t u r e 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 s i n g l e bonds.  Nine non-excited valence bond s t r u c t u r e s can be drawn  f o r the molecule and these simply represent combinations of the three p o s s i b l e Kekule s t r u c t u r e s f o r each naphthalene nucleus, the c e n t r a l peri-bonds being s i n g l e i n every case." The c r y s t a l s t r u c t u r e has been determined from p r o j e c t i o n s along two axes (24), but n e i t h e r of the p r o j e c t i o n s was w e l l resolved.  As a  consequence the accuracy was not very high, but a f t e r averaging i n accordance w i t h the expected molecular symmetry the bond lengths could be determined to w i t h i n about - 0.04  The  r e s u l t s showed that the two bonds connecting the two naphthalene n u c l e i 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 ) s i n g l e bond d i s t a n c e .  A more recent estimate of such a s i n g l e  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 molecule  and more d e t a i l e d  quaterrylene  of the s i x peri-bonds  (27)  a n a l y s i s of the analogous  has shown t h a t t h e a v e r a g e  in this  molecule  length  - 0 . 0 0 5 X.  i s 1.527  This  . o appears to  t o be  suggest  tic  significantly  longer than  that the peri-bonds  character  i s localized  to  curve  be  t h a t a new  considered  bond  for this  The m e a s u r e d p e r i - b o n d certainly accurate  longer than  whether also. rate  such  "a n e c e s s a r y  present  work  dimensional  type  of molecule  predicts,  the f i r s t  and White  (24)  i t w o u l d be  p r e l i m i n a r y t o any such  intensity  (28),  a n a l y s i s based  are  so t h a t a  member o f t h e  i s of interest  pre-  have l e d  i n quaterrylene  methods, and t h a t t h e i r  i s a detailed  residue.  length' correla-  to  l o n g bonds a r e p r e s e n t  measurements  three-dimensional was  series,  Donaldson, Robertson bond-length  aroma-  order~-~bond  current theory  anomalously  bonds and t h a t  f o r the peri-bonds  distances  analysis of perylene,  terrylene-quaterrylene  enough  measured d i s t a n c e s and those  by m o l e c u l a r - o r b i t a l theory  the suggestion  tion  are single  A, a n d l o n g  w i t h i n each naphthalene  D i s c r e p a n c i e s between these dicted  1.48  more  perylene-  determine i n perylene  noted  that f o r accu-  necessary  t o employ  two-dimensional undertaking." o n new  survey The  three-  data. Experimental  The were  crystals  thick  forms. angles  The  of perylene  yellow plates with unit  cell  used  i n the present  (001) d e v e l o p e d ,  parameters were  and  determined  investigation smaller  from  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 o n t h e G.E,  {110}  the Bragg Spectro-  27 goniometer with  Crystal  data  CuKtt  ( A c u K o ^ = 1.54051 X,A  C oHi2;  Perylene,  radiation.  2  252.3;  mol. wt. =  Monoclinic, a - 11.27^0.01,  (3-  ^  1.54433 £ ) .  =  2  - 268°C.  m.p.  b = 10.82^0.01,  c » 10.263*0.01  100.55 0 02°. O ±  o  Volume o f t h e u n i t c e l l - 1.360  »  1231.78  D  x  ( w i t h Z = 4)  D  m  (Donaldson, Robertson & White)  Absorption  CUK  t.  gem" . 3  coefficients  = 1.322  gem  .  A= 1.5418 A^yU.** 7cm  f o r X-rays,  A= 0.7107 Total  number o f e l e c t r o n s p e r u n i t  Absent  spectra:  h0i> w h e n  all  interplanar Electric using  2 e  spacing  films  h  indicated a rapid f a l l o f f  X)  technique  counter  (29)  Single  obtained  analyser.  on a  was u s e d .  General  Crystal Orienter, an  by use o f a  The m o v i n g  of  t o a minimum  a n d MoKcx r a d i a t i o n ,  beam b e i n g  height  The i n t e n s i t i e s  were measured  XRD-5 S p e c t r o g o n i o m e t e r w i t h  and pulse  1  F(000) = 528.  (corresponding  0  a  d = 1.04  mately monochromatic  counter  M K 440 o  a scintillation  filter  1  i n c r e a s i n g Bragg angle.  reflexions with  0.9 c m " .  P2 /a(c| ).  i s  Preliminary Weissenberg intensity with  =  .  h i s o d d , OkO w h e n k i s o d d .  Space group  in  cell  1  approxizirconium  crystal-moving  A l l the intensities  were  X,  28 c o r r e c t e d f o r background, which was found t o be a f u n c t i o n of 6 o n l y , Lorentz and p o l a r i z a t i o n f a c t o r s were a p p l i e d and the s t r u c t u r e amplitudes d e r i v e d .  The c r y s t a l used i n r e c o r d i n g  the i n t e n s i t i e s was mounted w i t h b p a r a l l e l t o the O a x i s of the g o n i o s t a t , and had dimensions 0.5 mm. 0.2 mm.  p a r a l l e l to [110] and  p a r a l l e l t o c*; a b s o r p t i o n was low and no c o r r e c t i o n s  were a p p l i e d .  S i x hundred  and seventy-nine r e f l e x i o n s i n the  range 0<26^40° were observed, r e p r e s e n t i n g 60% of the t o t a l number of r e f l e x i o n s i n 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 s c a l e ; however s i n c e the background  count was never l e s s than 6, i n t e n s i t i e s l e s s than  about 9 were c o n s i d e r e d t o be r a t h e r u n r e l i a b l e , and only those 436 r e f l e x i o n s w i t h i n t e n s i t y 9 o r g r e a t e r were used i n the refinement p r o c e s s .  Refinement  of the S t r u c t u r e  The parameters used as the s t a r t i n g p o i n t i n the r e f i n e ment were the carbon p o s i t i o n a l c o o r d i n a t e s O f Donaldson, Robertson and White, t o g e t h e r w i t h the s c a t t e r i n g f a c t o r f o r carbon of the I n t e r n a t i o n a l T a b l e s , V o l . I l l ( 1 ) , c o r r e c t e d f o r thermal v i b r a t i o n as u s u a l , w i t h B = 5.5  The d i s c r e p a n c y  f a c t o r , R, was 15.8% f o r the 436 r e f l e x i o n s used.  The carbon  atom p o s i t i o n a l and i s o t r o p i c thermal parameters, t o g e t h e r w i t h an o v e r a l l s c a l e f a c t o r , were r e f i n e d by l e a s t squares, u s i n g a program f o r the IBM 1620 computer (30). The f u n c t i o n minimized was  2w(F  F >20. Q  - F ) , with(w~ = F / 2 0 when F <20, and J*w = 2 0 / F when 2  0  c  The f i r s t  Q  o  Q  c y c l e decreased R t o 12.5% (Table I I I ) , but  29 TABLE I I I PROGRESS OF REFINEMENT Parameters  R %  Donaldson, Robertson and White (24) 1st Least Squares 2nd Least Squares 1/2-shifts oh 1st Least Squares 1st D i f f e r e n t i a l Syntheses (C atoms) 2nd D i f f e r e n t i a l Syntheses (C atoms) 2nd D i f f e r e n t i a l Syntheses + i d e a l H p o s i t i o n s 3rd D i f f e r e n t i a l Syntheses (C + H atoms) 4th D i f f e r e n t i a l Syntheses (C + H atoms)  the  15.8 12.5 16.0 11.4 10.8 10.6 8.3 8.1 8.1  second cycle r e s u l t e d i n an increase to 16.0% and exami-  nation of the s h i f t s i n the f i r s t and second c y c l e s indicated c l e a r l y that.the coordinates were o s c i l l a t i n g , and t h a t a f r a c t i o n a l s h i f t would be.required to ensure convergence. A p p l i c a t i o n of one-half the i n d i c a t e d s h i f t s of the f i r s t l e a s t 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 c a l c u l a t e d syntheses to apply " b a c k s h i f t " c o r r e c t i o n s t o the atomic coordinates (31, 32),  and c o r r e c t i o n s to the thermal parameters.  Two cycles  reduced R s u c c e s s i v e l y to 10.8% and 10,6% (Table I I I ) . At t h i s stage c o n t r i b u t i o n s from the hydrogen atoms were introduced; p o s i t i o n a l parameters were obtained by assuming that the atoms l a y on the r i n g diagonals with C-H distances 1.08 2, and the I n t e r n a t i o n a l Tables V o l . I l l s c a t t e r i n g curve was used, w i t h B = 7.0 i  2  f o r a l l the hydrogen atoms.  R was  reduced t o 8.3%. A t h i r d cycle of observed and c a l c u l a t e d d i f f e r e n t i a l syntheses was c a r r i e d out, i n which the p o s i t i o n a l and i s o t r o p i c thermal parameters of the carbon atoms, and the p o s i t i o n a l parameters of the hydrogen atoms were r e f i n e d .  The  30 hydrogen atom peak e l e c t r o n d e n s i t i e s were i n the range 0,47 0.89  eS  and  3  the  s h i f t s i n the hydrogen p o s i t i o n s were  reasonably s m a l l , but cases, a few  the  curvatures were u n r e a l i s t i c  having p o s i t i v e v a l u e s .  changes to 8.1%.  A f o u r t h and  R was  reduced by  0.0015, and  z r e s p e c t i v e l y , and  0.0014 X.  R unchanged at 8.1% The listed  calculated structure  i n Table A l ; the R f a c t o r f o r the 436  included  range 0 < 2 6 < 4 0 ° .  f i n a l observed and  The  Table IV;  e x c e l l e n t agreement between the  carbon p o s i t i o n s are  c a l c u l a t e d c u r v a t u r e s i n each of the x,y, i n d i c a t e s t h a t there i s no The  observed and  the  and  electron listed  observed  z directions  calculated electron  hydrogen atoms are given i n Table  in  and  s i g n i f i c a n t thermal a n i s o t r o p y  Coordinates and The  structure  calculated  c u r v a t u r e s at the  t i e s of the  Also  unobserved r e f l e x i o n s i n the  d e n s i t i e s and  of the atoms.  are  weak r e f l e x i o n s which were omitted from f o r the 456  any  left  observed r e f l e x -  calculated  refinement process and  the  factors  i n the refinement i s 8.1%.  i n Table A l are measured and  f a c t o r s f o r the 243  shifts  III).  f i n a l observed and  ions which were i n c l u d e d  0.0031 X  changes i n hydrogen p o s i -  A p p l i c a t i o n of these v a r i o u s  (Table  the  the mean s h i f t s 0.0012,  F u r t h e r small  t i o n s were i n d i c a t e d .  these  thermal parameters,  maximum coordinate s h i f t s b e i n g 0.0034, 0.0032, and and  i n some  f i n a l c y c l e 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  a l o n g x,y,  -  for densi-  V.  M o l e c u l a r Dimensions  f i n a l p o s i t i o n a l parameters are g i v e n i n Table  VI,  31 TABLE IV CARBON ATOM PEAK ELECTRON. DENSITIES (e.S~ ) 3  AND CURVATURES (e.S' ) FROM FINAL CYCLE 5  <?  --tfp/ax.  1  -^p/dy  -d p/az*  1  x  Atom  Obs  Calc  Obs  Calc  Obs  Calc  Obs  Calc  C  4.36 4.07 4.86 4.72 4.32 4.53 5.03 5.65 5.40 5.33 4.32 4.22 4.42 4.56 4.33 4.53 4.87 5.69 5.52 5.40  4.35 4.19 4.89 4.81 4.42 4.59 5.09 5.71 5.40 5.40 4.38 4.40 4.54 4.68 4.40 4.44 4.98 5.75 • 5.60 ' 5.44  21.8 19.7 27.2 23.9 21.0 22.9 26.0 32.2 30.2 29.3 23.0 20.1 20.9 22.7 18.8 23.1 25.9 32.5 32.8 30.0  20.7 19.6 26.2 23.5 21.1 22.4 25.3 31.2 28.9 28.4 22.6 20.6 20.7 22.7 18.9 21.8 25.1 31.1 31.6 28.9  19.4 17,5 25.5 24.4 21.3 20.1 26.2 31.1 29.7 29.6 19.2 19.3 21.0 23.2 21.0 21.2 24.4 32.1 29.8 30.1  19.4 17.9 24.5 24.2 21.0 20.7 25.6 30.2 28.4 28.8 19.0 19.6 21.0 22.9 20.6 20.2 24.0 31.2 28.8 28.7  20.9 17.6 23.9 25.8 22.1 25.1 29.1 34.6 31.9 31.8 21.8 20.9 23.2 26.5 22.7 24.2 27.1 34.2 33.7 35.1  20.7 17.8 23.6 25.4 22.2 24.7 28.5 33.5 31.0 31.2 21.5 21.5 23.0 25.8 22.0 23.0 26.5 33.3 32.5 34.2  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  TABLE V HYDROGEN ATOM PEAK ELECTRON DENSITIES (e.£~ ) 3  FROM FINAL CYCLE Atom  Obs  Calc  Atom  Obs  Calc  H  0.67 0.50 0.68 0.78 0.47 0.55  0.73 0.45 0.75 0.78 0.59 0.61  H 11 12 13 14 15 16  0.68 0.52 0.78 0.57 0.89 0.68  0.82 0.59 0.78 0.61 0.81 0.68  1 2 3 4 5 6  32 TABLE VI FINAL POSITIONAL FRACTIONAL COORDINATES, x,y,z, AND ORTHOGONAL COORDINATES(X), X',Y,Z' Atom  X  y  z  X'  Y  Z'  0.2624 0.3005 0.2636 0.1796 0.1417 0.0668 0.0266 0.0651 0.1446 0.1857 -0.0517 -0.0923 -0.0547 0.0260 0.0664 0.1451 0.1841 0.1452 0.0652 0.0254  -0.0474 0.0432 0.0447 0.0428 0.0386 -0.0530 -0.1456 -0,1452 -0.0493 -O.O466 -0.2387 -0.3274 -0.3285 -0.3232 -0.3217 -0.2319 -0.1419 -0.1404 -0.2353 -0.2366  0.3816 0.3070 0.1683 -0.1185 -0.2582 -0.3175 -0.2398 -0.0996 -0.0386 0.1050 -0.2959 -0.2198 -0.0798 0.2057 0.3450 0.4021 0.3239 0.1842 0.1251 -0.0204  2.2383 2.8083 2.6537 2.2473 2.0834 1.3510 0.7515 0.9213 1.7024 1.8950 -0.0252 -0.6261 -0.4661 -0.0945 0.0984 0.8777 I.4646 1.2894 0.4991 0.3247  -0.5138 0.4683 0.4845 0.4640 0.4184 -0.5745 -1.5783 -1.5740 -0.5344 -0/5051 -2.5875 -3.5490 -3.5609 -3.5035 -3.4872 -2.5138 -1.5382 -1.5219 -2.5507 -2.5647  3.8525 3.0994 1.6991 -1.1963 -2.6067 -3.2054 -2.4210 -1.0055 -0.3897 1.0601 -2.9873 -2.2190 -0.8056 2.0767 3.4830 4.0595 3 .2700 1.8596 1.2630 -0,2060  -0.046 0.114 0.120 0.114 0.111 -0.063 -0.236 -0.400 -0.400 -0.393 -0.399 -0.232  0.493 0.367 0.108 -0.070 -0.325 -0.423 -0.402 -0.266 -0.016 0.161 0.412 0.512  2.3386 3.3384 3.1477 2.8686 2.5560 1.2248 -0.1238 -1.2217 -0.9415 -0.7205 -0.4030 1.0501  -0.4986 1.2379 1.3008 1.2401 1.2043 -0.6829 -2.5626 -4.3382 -4.3317 -4.2590 -4.3262 -2.5181  4.9762 3.7011 1.0934 -0.7087 -3.2791 -4.2745 -4.0534 -2.6814 -0,1605 1.6264 4.1584 5.1710  C  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  H  1 0.290 2 • 0.358 3 0.297 4 0.243 5 0.173 6 0.038 11 -0.078 12 -0.153 -0.086 13 14 -0.037 15 0.033 16 0.179  x,y, and z being coordinates r e f e r r e d t o the monoclinic c r y s t a l axes and expressed as f r a c t i o n s of the u n i t c e l l edges, and X', o Y, Z' coordinates i n A r e f e r r e d to orthogonal axes a. b. and c*. The parameters f o r carbon and hydrogen are those of the f o u r t h  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 s t r u c t u r e f a c t o r c a l c u l a t i o n with hydrogens p o s i t i o n e d on the r i n g diagonals with C - H = 1.08 X gave the same discrepancy f a c t o r (8.1%) as the observed hydrogen atom p o s i t i o n s ; however the p o s i t i o n s must be at l e a s t approximately c o r r e c t , since omission of hydrogen cont r i b u t i o n s increases R by about 2%, and the e l e c t r o n d e n s i t i e s at the hydrogen p o s i t i o n s are reasonable  (0.47 - 0.89 e.X  3  ,  Table V; the standard d e v i a t i o n of the e l e c t r o n d e n s i t y being o-3, 0.08 e.A  ). Table V I I l i s t s the standard d e v i a t i o n s of the  atomic p o s i t i o n a l coordinates c a l c u l a t e d from Cruickshank's (33) formulae, w i t h the r e f l e x i o n s used i n the refinement process only, and the thermal parameters.  The increase i n B  values with distance from the molecular center must be a r e s u l t of i n t e r n a l v i b r a t i o n r a t h e r than r i g i d - b o d y v i b r a t i o n s , since thermal anisotropy i s s m a l l . TABLE V I I STANDARD DEVIATIONS OF FINAL COORDINATES (X) , THERMAL PARAMETER (X ), AND DEVIATIONS ( A ) 2  FROM THE MEAN MOLECULAR PLANE Atom C  1 2 3 4 5 6 7 8 9 10  cT(x) 0.0065 0.0071 0.0052 0.0059 0.0067 0.0061 0.0054 0.0044 • 0.0046 0.0048  0,  <f(y)  C(z)  B  ^(A)  0.0073 0.0080 0.0055 0.0058 0.0068 0.0070 0.0054 0.0045 0.0048 0.0048  0.0058 0.0068 0.0051 0.0047 0.0055 0.0048 0.0041 0.0035 0.0038 0.0038  5.98 5.72 5.39 5.58 5.95 5.63 4.91 4.13 4.33 4.25  -0.0112 0.0061 0.0039 0.0394 0.0088 -0.0149 -0.0173 -0.0144 -0.0023 -0.0005  34 TABLE V I I (continued) Atom  6(x)  C 11 12 13 14 15 16 17 18 19 20 H  1 2 3 4 5 6 11 12 13 14 15 16  0.0061 0.0070 0.0067 0.0062 0.0075 0.0061 . 0.0054 0.0043 0.0043 0.0047  >  0.05  6-(y)  6(z)  0.0073 0.0073 0.0067 0.0060 0.0067 0.0067 0.0058 0.0044 • 0.0047 0.0047  0.05  0.0055 0.0058 0.0052 0.0046 0.0053 0.0050 0.0045 0.0035 0.0036 0.0035  0.05  J  B  A(X)  5.47 5.56 5.28 5.26 5.23 5.91 4.65 3.98 4.10 4.22  -0.0109 0.0103 0.0119 0.0244 0.0143 -0.0136 -0.0174 -0.0037 -0.0003 -0.0102  7.00 <  0.026 0.069 0.004 0.020 0.002 -0.078 -0.021 0.004 0.027 0.063 0.014 -0.048  The bond distances i n themolecule, and t h e i r standard d e v i a t i o n s estimated from the equation of Ahmed and Cruickshank (32) are shown i n Figure 5.  The valency angles, and standard  d e v i a t i o n s estimated from the expression i n the I n t e r n a t i o n a l Tables, V o l . I I , are given i n Figure 6.  Since thermal a n i s o t -  .ropy was n e g l i g i b l e , no c o r r e c t i o n s f o r e r r o r s due t o r o t a 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 molecules whose coordinates are l i s t e d i n Table V I , has equation -0.81746 X' + 0.56751 Y + 0.09841 Z' + 1.73098 - 0 The d e v i a t i o n s of the atoms from t h i s plane are l i s t e d i n the  H  35  H  1.13  1.13  16./  1.420 (.007)  H 1.409 (.009)  1.421 (.006)  H  H 1.479 (.005)  L463 (.005)  7^4 1.423 (.008)  1.426 (.005)  1.421 (.007)  H  Figure 5-  Measured bond lengths (2), with standard deviations (A*) i n parentheses.  I20JU2I.0  119.0  H  F i g u r e 6.  122.5  H  Measured v a l e n c y angles ( d e g r e e s ) . t o .0-7 f o r G-C-C .angles.  6"=  0.k°  37 l a s t column of Table V I I . The o r i e n t a t i o n of the molecule i n the u n i t 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 w i t h the orthogonal system.  The a x i s L was taken through atoms C7 and  C17, and a x i s M through the midpoints of bonds 9-10 and 19-20. L, M, and N are almost e x a c t l y mutually perpendicular, the angles between them being ZLM » 90.1°, ZMN 90.0°.  » 89.9°, and <£LN =  Previous values of the o r i e n t a t i o n angles (24) are  included i n Table V I I I f o r comparison.  TABLE V I I I ORIENTATION OF THE MOLECULE IN THE CRYSTAL Donaldson, Robertson and White (24)  Present analysis  XL ^L U)L  83.3° 89.2 6.8  82.9° 89.6 7.2  XM  55.4 35.0 94.5  55.9 34.5 94.5  144.5 55.0 84.9  144.8 55.4 84.4  ^>M XN YN  u>N  The carbon-carbon intermolecular separations l e s s than 4 X are given i n Table IX; a l l these contacts correspond to normal van der Waals i n t e r a c t i o n s .  The perpendicular distance  between the planes of molecules r e l a t e d by a center of symmetry 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  Dm  1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4  1 2 3 5 6 12  t o Atom i n Molecule 6 7 11 15 15 7 11 11 12 12 14 15 15 16 7 8 11 12 12 13 13 14 20 20 12 13 14 14 18  3 3 3 6 12 3 3 5 3 5 12 6 12 6 3 3 3 3 5 3 5 12 3 5 12 12' 3 5 3  x, x, -x, 1/2-x, 1/2-x, 1/2+x, d  y, y, -y, 1/2+y, 1/2+y, -1/2-y,  z 1+z -z -z 1-z z  Atom to Atom i nMolecule  3 .806 3.920 3.907 3.950 3.790 3.790 3.500 3.706 3.877 3.829 3.768 3.899 3.804 3.817 3.649 3.801 3.604 3.711 3.899 3.879 3.817 3.774 3.928 3.861 3.758 3.753 3.827 3.874 3.751  4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 9 9 9 10 16  19 19 20 12 14 14 15 15 16 16 17 18 19 16 17 18 10 17 18 9 10 18 9 10 13 18 19 20 20 6  3 5 3 12 3 5 3 5 3 5 3 3 3 3 3 3 3 3 3 3 3 3 3 3 12 3 3 3 3 2  d 3.450 3.760 3.605 3.735 3.709 3.977 3.866 3.871 3.908 3.931 3.779 3.626 3.609 3.903 3.521 3.630 3.633 3.917 3.754 3.644 3.501 3.899 3.653 3.804 3.734 3.917 3.889 3.751 3.883 3.710  Discussion The d e v i a t i o n s of the carbon atoms from the best molecular  plane (Table V I I ) , although they are s m a l l , are h i g h l y s i g n i f i cant, since X = 145 and f o r i) = 17, P«0.001 ( f o r "t> =17 and 2 2  P = 0,001, X  = 40.79 o n l y ) .  Furthermore c l o s e r examination  of the displacements (Figure 7) r e v e a l s that they f o l l o w a r e g u l a r p a t t e r n , those atoms f u r t h e s t from the molecular L-axis being d i s p l a c e d i n a p o s i t i v e 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 c l o s e r t o 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 i n v o l v i n g a bending about the L-axis.  To e x p l a i n t h i s bending  of the molecule i t i s necessary to decide whether i t i s a r e s u l t of i n t r a - or i n t e r m o l e c u l a r s t e r i c e f f e c t s (or both). There may be some i n t r a m o l e c u l a r 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 p o s i t i o n s i n the u s u a l chemical numbering), and these s t e r i c r e p u l s i o n s could be r e l i e v e d by displacements of these atoms, and smaller displacements of the carbon atoms, from a s t r i c t l y planar arrangement.  I t i s quite evident from Figure 7 however that  the observed displacements are not due to any such intramolec u l a r e f f e c t s , as the d e v i a t i o n s of C3, C4, C13, and C14 are a l l i n the same d i r e c t i o n and hence would not r e l i e 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 l e s s p r e c i s e l y , but suggest the same conclusions. Any i n t r a m o l e c u l a r s t e r i c r e p u l s i o n s between hydrogen atoms could indeed be more r e a d i l y r e l i e v e d 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 r e s p e c t i v e l y ; again the hydrogen p o s i t i o n s are not s u f f i c i e n t l y p r e c i s e l y determined to draw d e f i n i t e conclusions, but i t does appear that in-plane hydrogen displacements from a regular model are a l s o s m a l l . The f o u r perylene molecules i n the u n i t c e l l are grouped i n p a i r s about centers of symmetry, so that the mean planes of the molecules i n each p a i r 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 r e l a t e d by a center of symmetry (molecules  1 and 3 i n Table IX).  When the centro-  symmetrically r e l a t e d 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 being 8 contacts of 3.52 2 or l e s s .  as shown i n Figure 8, there The s l i g h t bending of the  molecules allows the p a i r of perylene molecules t o pack together more compactly ( t h i s 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 d i s t o r t i o n i s a r e s u l t of intermolecular f o r c e s .  molecular The l a r g e s t  displacement from the mean molecular plane i s f o r atom C4, and t h i s atom i s involved i n the shortest intermolecular separ a t i o n 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 l a r g e r , the shortest being 3.71 X. The d i f f e r e n c e s between chemically equivalent bond lengths are small (Figure 5), but one or two are i n the p o s s i b l y s i g n i f i c a n t r e g i o n , 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, f o r com-  42  Figure.8.  Normal p r o j e c t i o n o f two p a r a l l e l m o l e c u l e s .  F i g i i r e 9-  P e r s p e c t i v e drawing o f two p a r a l l e l m o l e c u l e s . i s g r o s s l y exaggerated f o r c l a r i t y .  The t e n d i n g o f the m o l e c u l e s  44 parison w i t h t h 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 d e v i a t i o n s 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 Bond . (Fig.7) A.m a. b c d e f g  6"m  1.370 0.005 1.418 0.004 1.397 0.004 1.425 0.003 1.424 0.004 1.400 0.004 1.471 0.004  Perylene Calculated _A  >m 0.002 0.003 0.004 0.006 0.002 0.005 0.006  (1)  (2)  (3)  (4)  1.375 1.421 1.375 1.421 1.421 1.421 1.500  1.375 1.421 1.375 1.421 1.421 1.421 1.477  1.387 1.401 1.398 1.423 1.422 1.416 1.444  1.376 1.398 1.393 1.430 1.432 1.422 1.473  Quaterrylene Measured (6) (5) 1.366 1.419 1.373 1.442 1.413 1.436 1.485  1.374 1.425 1.384 1.403 1.431 1.392 1.527  A = Measured r c a l c u l a t e d a b c d e f g R.M.S. over (1) .(2) (3) (4) (5) (6)  .  -0.005 -0.003 0.022 0.004 0.003 -0.021 -0.029  A  -0.005 -0,017 -0.006 0.004 -0.004 -0.003 0.017 0,020 •0.001 -0.007 0.022 -0.001 0,004 0.026 0.013 0.004 0.002 -0.005 -0.017 0.022 0.003 0.002 -0.008 0.011 -0.007 -0.021 -0.016 -0.022 -0.036 0.008 -0.006 0.027 -0.002 -0.014 •0.056  A 0.015 0.013 0.014 0.013 0.020 whole molecule Valence-bond method, With single-bond = 1.50 X. Valence-bond method, with single-bond = 1.477 A . M.O. (Baldock, B e r t h i e r 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.  Table X are the standard d e v i a t i o n s of the mean values, c m  /  45  /  being  c a l c u l a t e d from  parameters directly values  from  and  VII  and F i g u r e  estimates  the accuracy  The  general  quoted  higher  values  theoretical  bond  valence  bond  orbital  method  double-bond  f o r ethylene,  single-bond  single-bond  bond  smooth  correlation  The  third  variation general produced  m  and  method,  and M.O.  X),  Two  passing  (38) , w h i c h sets  the f i r s t  with  1.54  molecular different  two were s e t was o  o f the measured  1.50  1.477  £  X  as  as  orbital  c a l c u l a t e d by the derived  from  a  A as the s i n g l e  bond  dis-  calculated with  particularly  (40).  allowance  distance  distances  curve  (28).  i s fairly  for The  well re-  of calculated values, but there  disagreements,  the  correlation  of molecular  i n t e g r a l w i t h bond  i n a l l the sets  the  takes  used f o r  through  s e t (28) f r o m a d i f f e r e n t were  conse-  non-excited  c o r r e l a t i o n s were  and t h e second  Three  lengths  of resonance  some i n d i v i d u a l  are a  d  measured d i s t a n c e s , t h e  curve  but the f i r s t  the second  variation  g  c a l c u l a t e d by t h e  length  Sparks  curve,  bond  than  of types  derived from the nine  (25),  distance.  Huckel  (39)  r5"  two  indication  benzene and g r a p h i t e , and u s i n g  distance  simple  measured  d i f f e r e n c e s i n measured  the f i r s t  distances are available;  tance  of  f o r bonds  are a l s o a v a i l a b l e (Table  character  derived  d e v i a t i o n s i s an  these  structures; lengths  used by Cruickshank the  were  valence-bond method,  points the  lengths  being  positional  agreement between t h e  of the p o s s i b l y - s i g n i f i c a n t For comparison w i t h  6"^  the i n d i v i d u a l  i s realistic;  distances.  the  5), a n d  of the standard  g, t h e s l i g h t l y  quence  deviations of the  the d e v i a t i o n s between  and t h e means.  different that  (Table  the standard  are  f o r bond f , f o r  46 which the measured distance i s l e s s than any of the t h e o r e t i c a l values.  The measured distance of the peri-bond  (g) agrees  best w i t h Dewar and Schmeising's (26) single-bond l e n g t h , or w i t h the M.O. distance derived from Goodwin and Vand's (40) c o r r e l a t i o n curve.  In an o v e r a l l comparison the most s o p h i s t i -  cated c a l c u l a t e d lengths (method (5) i n Table X) show the poorest agreement w i t h the measured d i s t a n c e s , while the simple valence-bond method gives quite reasonable agreement. Table X shows a l s o a comparison between the measured bond lengths i n perylene, and average values f o r s i m i l a r types of bonds i n quaterrylene (27). The agreement between the values i n the two molecules which i n perylene  i s on the whole extremely c l o s e ; bond f ,  (1.400 - 0.00.5 X)  i s shorter than any of the  c a l c u l a t e d values f o r that bond (1.416 - 1.436 X),  i s also  short i n quaterrylene (1.393 - 0.009 X) . The l a r g e s t d i f f e r ence i s f o r the peri-bonds, 1.471 - 0.005 X i n perylene and 1.527 - 0.005 X i n quaterrylene so that the d i f f e r e n c e i s 86" and h i g h l y s i g n i f i c a n t , and these are j u s t the bonds whose lengths are most important i n t h i s type of molecule.  The  i n 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 p r o j e c t i o n 120 p o s i t i o n a l and thermal parameters have been determined from 127 observed r e f l e x i o n s (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 b a s i s of the length of the peri-bonds  i n quatero r y l e n e , 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 t o use i n  d i s c u s s i n g p o l y c y c l i c aromatic molecules, and secondly that the peri-bonds i n q u a t e r r y l e n e are s i n g l e - b o n d s , perhaps l e n g thened somewhat by i n t r a m o l e c u l a r s t e r i c  repulsions, with aro-  matic c h a r a c t e r being c o n f i n e d to the naphthalene r e s i d u e s . The peri-bonds i n p e r y l e n e , 1.471 ± 0.005 d e r a b l y s h o r t e r than 1.50 X,  X, a r e c o n s i -  and s l i g h t l y , although only  p o s s i b l y s i g n i f i c a n t l y , s h o r t e r than Dewar and Schmeising's ... o (26) s i n g l e bond value of 1.479 A.  T h i s , w h i l e not p r o v i n g  t h a t 1.479 S i s the value to use f o r the s i n g l e bond l e n g t h i n t h i s type o f molecule, does suggest that Dewar and Schmeising's estimate i s not unreasonable.  In a d d i t i o n the measured p e r i -  bond d i s t a n c e s suggest t h a t benzenoid c h a r a c t e r i n p e r y l e n e i s probably not completely l o c a l i z e d i n the naphthalene r e s i d u e s but tends t o be spread over the whole molecule.  F u r t h e r sup-  port f o r t h i s c o n c l u s i o n i s obtained from a comparison  o f other  bond d i s t a n c e s i n perylene w i t h those which might be p r e d i c t e d from n o n - i n t e r a c t i n g naphthalene  r e s i d u e s ; bond c(1.398 ±  0.004 t) i s c o n s i d e r a b l y longer than bond a(1.370 ± 0.005 A ), 5  s u g g e s t i n g t h a t the e l e c t r o n d i s t r i b u t i o n i n the naphthalene r e s i d u e s i s being d i s t u r b e d by i n t e r a c t i o n . Goodwin (28) has attempted  t o account f o r the l o n g p e r i -  d i s t a n c e s i n q u a t e r r y l e n e by d e r i v i n g a new o r d e r - l e n g t h c o r r e l a t i o n curve; t h i s curve however l e a d s t o a l e n g t h o f 1.56 X f o r the peri-bonds i n p e r y l e n e , and i s t h e r e f o r e u n t e n a b l e . There seems l i t t l e  reason t h a t the peri-bonds i n perylene and  q u a t e r r y l e n e should be so d i f f e r e n t  i n l e n g t h , and f u r t h e r  48 i n v e s t i g a t i o n of other molecules with s i m i l a r types of bonds i s a p p a r e n t l y necessary t o o b t a i n more data b e f o r e c o n c l u s i o n s about  s i n g l e - b o n d d i s t a n c e s i n t h i s type o f molecule  drawn.  I t might be noted t h a t the peri-bonds  can be  i n quaterrylene  are about the same l e n g t h as the bonds j o i n i n g the six-membered r i n g s i n biphenylene  ( 1 . 5 2 - 0.018 X)  (41), these bonds b e i n g  part of a four-membered r i n g and t h e r e f o r e under c o n s i d e r a b l e strain. The hydrogen atom p o s i t i o n s i n perylene have been d e t e r mined r a t h e r i m p r e c i s e l y , so t h a t the v a r i a t i o n s i n the C-H bond d i s t a n c e s a r e not s i g n i f i c a n t .  The mean value f o r the C-H  l e n g t h i s 1.11 X. A s m a l l d i p o l e moment of 0.45 D has been r e p o r t e d f o r perylene  (42), and i t i s tempting t o i n t e r p r e t t h i s i n terms  of the s m a l l molecular d i s t o r t i o n d e s c r i b e d above.  However  t h i s i n t e r p r e t a t i o n i s not j u s t i f i a b l e , s i n c e 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 r e s u l t of i n t e r m o l e c u l a r con-  t a c t s w h i l e the d i p o l e moment measurement was i n d i l u t e benzene s o l u t i o n , where a s i m i l a r d i s t o r t i o n i s u n l i k e l y t o be p r e s e n t . In a d d i t i o n the observed displacements are extremely  s m a l l , and  u n l i k e l y to g i v e a d i p o l e moment as l a r g e as t h a t r e p o r t e d . Examination  of the d i p o l e moment measurements i n d i c a t e s t h a t  the t o t a l molar p o l a r i z a t i o n of perylene i n benzene a t i n f i n i t e d i l u t i o n i s 104 c c s ; the e l e c t r o n p o l a r i z a t i o n estimated the atomic r e f r a c t i v i t i e s r e f r a c t i v e index 99.5 c c s .  i s 85.8ccs  f  from  and from the measured  Bergmann, F i s c h e r and Pullman  take  the o r i e n t a t i o n p o l a r i z a t i o n as (104 - 99.5) c c s , corresponding  49 to a dipole moment of 0.45 D,  No c o r r e c t i o n was made f o r atom  p o 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  p o l a r i z a t i o n i s u s u a l l y 5-10% of the e l e c t r o n p o l a r i z a t i o n , omission of such a c o r r e c t i o n could account f o r the whole of the d i f f e r e n c e between t o t a l and e l e c t r o n p o l a r i z a t i o n .  It  i s f e l t therefore that i t has not been c o n c l u s i v e l y e s t a b l i s h e d that perylene possesses a permanent dipole moment.  II.  THE CRYSTAL AND MOLECULAR STRUCTURE OF PYRENE  Introduction The Robertson  c r y s t a l s t r u c t u r e of pyrene and White  (II) was determined  by  (43) from two p r o j e c t i o n s , but r e s o l u t i o n  of the i n d i v i d u a l atoms was poor i n both p r o j e c t i o n s .  As a  r e s u l t the accuracy was not very h i g h , and the present work i s a more d e t a i l e d a n a l y s i s based  on new t h r e e - d i m e n s i o n a l d a t a .  Experimental C r y s t a l s of pyrene are t h i c k c o l o u r l e s s p l a t e s w i t h (001) developed,  and s m a l l e r [ l i o } forms.  meters were determined  The u n i t c e l l  by l e a s t - s q u a r e s treatment  of the s i n 6  v a l u e s of the cx-p c* -doublets of a number of high-angle 2  para-  reflex-  i o n s , f o r which the Bragg angles were measured on a G.E. Spectrogoniometer w i t h CuKcx r a d i a t i o n . (X(CuK(X ) = 1.54051 £, XtCuKOg) = 1.54433 X)  C r y s t a l data Pyrene,  C  l 6  H  1  1 0  ; M = 202.2; m.p. - 150°C.  M o n o c l i n i c , a - 13.64  q  ± 0.01, b = 9.25  A  - 0.01, c = 8.47  n  -  0.01 X, ^ - 100.28° i 0.04°. U - 1052.9 X  3  D  m  = 1.27, Z = 4, D  = 1.275 gem" . 3  x  Absorption c o e f f i c i e n t s f o r X-rays, X = 1.5418 X, X= 0.7107 X,  5.6 cm  \  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 /a(c| ). 1  n  Weissenberg 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 Bragg angle. The i n t e n s i t i e s were measured on a G.E. Spectrogoniometer w i t h a s c i n t i l l a t i o n counter and MoKoc r a d i a t i o n , e x a c t l y as f o r perylene.  Nine hundred and s i x t y -  f i v e r e f l e x i o n s i n the range 0 <26(MoKoO < 50.2° (corresponding to a minimum i n t e r p l a n a r spacing d = 0.84 &) were observed, 59% of the t o t a l number of r e f l e x i o n s 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 s t r u c t u r e refinement was based only on those 550 r e f l e x i o n s w i t h 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, w i t h the s c a t t e r i n g f a c t o r f o r carbon of the I n t e r n a t i o n a l Tables V o l . I l l , w i t h B = 4.0 X . 2  The discrepancy f a c t o r , R, was  0.20 f o r the 550 r e f l e x i o n s included i n the refinement. The p o s i t i o n a l and i s o t r o p i c thermal parameters of the carbon atoms were r e f i n e d as f o r p e r y 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 c y c l e s , assuming i d e a l p o s i t i o n s on the r i n g d i a g o n a l s w i t h C-H «= 1.08 i\  and B = 8.0 X.  The hydrogen atom  p o s i t i o n a l parameters were r e f i n e d i n the f o u r t h c y c l e ; the peak e l e c t r o n d e n s i t i e s were reasonable  (Table  X I ) , but some  TABLE X I HYDROGEN ATOM PEAK ELECTRON DENSITIES  (e.iT ) 3  IN FOURTH DIFFERENTIAL CYCLE Atom  Obs  Calc  Atom  Obs  Calc  H(l) H(2) H(4) H(5) H(7)  0.59 0.86 0.43 0.40 0.47  0.73 1.01 0.57 0.56 0.45  H( 8) H( 9) H(ll) H(12) H(14)  0.48 0.48 0.45 0.56 0.68  0.67 0.56 0.50 0.49 0.62  of the c u r v a t u r e s were p o s i t i v e , so t h a t the s h i f t s were not  considered to be very r e l i a b l e , and i n subsequent  the  H atoms were kept i n i d e a l p o s i t i o n s .  p l e t e a f t e r seven c y c l e s , and R was The  cycles  Refinement was com-  0,12.  observed and c a l c u l a t e d e l e c t r o n d e n s i t i e s and curva-  tures a t the carbon p o s i t i o n s are l i s t e d  i n Table X I I .  values suggested t h a t the atomic v i b r a t i o n s are s l i g h t l y t r o p i c , and a n i s o t r o p i c  The aniso-  thermal parameters were obtained appro-  x i m a t e l y from the d i f f e r e n c e s between the observed and c a l c u l a t e d second d e r i v a t i v e s  (44). At t h i s stage f a c i l i t i e s f o r  c a r r y i n g out a n i s o t r o p i c  ( b l o c k - d i a g o n a l ) l e a s t squares r e f i n e -  ment became a v a i l a b l e to us, and the carbon atom p o s i t i o n a l and  anisotropic  thermal parameters were f u r t h e r r e f i n e d .  The  53 TABLE X I I  (e.X~ )  CARBON P E A K E L E C T R O N D E N S I T I E S CURVATURES  e Atom  Obs  ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) c ( 8) c ( 9) c (10) c (11) c (12)  4.16 4.45 5.45 4.72 4.70  C C C C C C C  |F | 0  <34,  carried  24.2  x  \  /  28.6 37.1 29.9 27.7 34.8  31.1  27.9 36.9 25.1 25.2 28.2 37.8 30.4 29.0 33.4 25.4 43.7 44.2  5.15 4.54 6.28 6.07  Calc  24,7 24.6  26.5 35.8 28.0 27.9 31.9 25.9  42.7 41.6  Obs  Calc  21.0 23.9 34.2 30.0 25.0 32,2 21.4 20.2 23.1 36.3 27.9 26.2 27.8 22.6 38.2  21.2  18.3 20.9 29.9 21.8 26.1 30.8 25.1  20.8  q  in  factor  the anisotropic  o f 0.2  the anisotropic The  observed  differential  t o ensure  29.8 21.4 25.6 27.7 25.1 37.3 36.0  24.5  27.0 21.8 36.7 36.1  shifts  32.4  24.1 27.5  31.7  25.8  19.5  22.9  31.8  23.5 26.8 29.3 26.3 39.6 37.5  |F |/34 w h e n 0  Three  cycles  were n o t  were signifi-  differential  convergence.  refinement  observed  i s 0.12  thermal parameters). values  17.9 19.4  thermal parameters  and c a l c u l a t e d  syntheses  the refinement  30.3 21.6 20.2 22.7 33.5 25.8  24.6  cycle  required  R decreased  a  b y 1%  refinement.  R f a c t o r f o r t h e 550 in  24.1  Q  cant, and t h e coordinates o f t h e seventh  fudge  32.0 27.6  v  o u t ; the p o s i t i o n a l parameter  were r e t a i n e d ;  24.0  34/|F | when |F |>34.  a n d £vF*-  1  Calc  , with [w~=  C  -v-p/dz  Obs  40.0  was 2 w ( F - F ) Q  CYCLE  -s e/3^  24.5  29.1 38.5  4.80  minimized  •  Obs  5.38 4,46 4.26 4.50 5.56 4.65  6.09  function  ————\ Calc  4.81 4.81  6.06  :  - C J V / W  4.67 5.56  5.32  FROM S E V E N T H D I F F E R E N T I A L  5  4.31  4.37 4.16 4.39 5.52 4.62 4.78 5.09 4.47  c (13) c. (14) c. (15) c (16)  (e.X" )  AND  3  Also  structure  factors  are l i s t e d  i n Table  reflexions which  (reduced included  t o 0.11  were  by u s i n g  i n Table  a f t e r the  A2  A2; t h e included  anisotropic  are F  Q  f o r a l l t h e w e a k r e f l e x i o n s a n d f o r some o f t h e  and F  C  54 unobserved r e f l e x i o n s , which were omitted from the refinement process.  Coordinates and M o l e c u l a r Dimensions The  f i n a l p o s i t i o n a l and i s o t r o p i c thermal parameters  are g i v e n i n Table X I I I .  The c o o r d i n a t e s and temperature  TABLE X I I I FINAL POSITIONAL PARAMETERS (FRACTIONAL), STANDARD DEVIATIONS (X), DISPLACEMENTS Atom  X  y  ISOTROPIC THERMAL PARAMETERS ( A ) , AND 2  (X)  FROM THE MEAN MOLECULAR PLANE z.  C ( 1) 0.2817 C ' 2) 0.2947 ' 3) 0.2296 ( 4) 0.2389 ( 5) 0.1783 ( 6) 0.0990 ' 7) 0.0316 ( 8) -0.0449 ( 9) -0.0566 (10) 0.0071 (11) -0.0030 i l 2 ) 0.0575 (13) 0.1389 0.2066 14) 0.1514 (15) (16) 0.0854  0.0567 0„0237 -0.0738 -0.1103 -0.2090 -0.2746 -0.2396 -0.3070 -0.2772 -0.1735 -0.1412 -0.1091 -0.1409  0.4119 0.2717 0.1274 -0.0238 -0.1578 -0.1606 -0.3020 -0.2966 -0.1594 -0.0131 0.1356 0.2706 0.2723 0.4161 0.1303 -0.0136  H: i) H ( 2) H i 4) H 5) H 7) H ( 8) H ( 9) H (11) H '12) H 14)  -0.03 0.10 0.13 0.08 -0.06 -0.24 -0.35 -0.38 -0.33 -0.19  0.52 0.27 -0.03 -0.27 -0.41 -0.41 -0.16 0.14 0.38 0.53  c c c c c c c c c c c c c c  f  r  0.33 0.36 0.30 0.19 0.04 -0.10 -0.12 -0.06 0.05 0.20  -0.0402 0.0246  -0.0077  61*)  B(f)  All)  0.010 0.008 0.006 0.008 0.007 0.006 0.007 0,010 0.009 0.006 0.008 0.007 0.006 0.007 0.005  7.05 5.95 4.88 5.82 6,06 5.39 7.15 7.26 6.62 5.34 6.53 6.07 5.19 7.06 4.01  0.007 0.003 0.004  0.004  0.008 0.007 0.005 0.006 0.007 0.005 0.008 0.009 0.008 0.005 0.006 0.007 0.006 0.008 0.005 0.004  0.07  0.07  0.10  8.0  Six)  >  0.007 0.006 0.005 0.006 0.006 0.005 0.007 0.007 0.006 0.005 0.006 0.006 0.005 0.007  0.004  < f ( y )  0.005  4.62  f a c t o r s f o r carbon a r e those o f the seventh d i f f e r e n t i a l  0.003  -0.015 0.001 0.000 0.003 -0.016 0.018 0.000 -0.001  0.004  -0.020 -0.002 0.011  cycle,  55 and the hydrogen atoms have been placed on the r i n g diagonals w i t h C-H about 1.08 X.  The standard d e v i a t i o n s c a l c u l a t e d from  Cruickshank's (33) formulae, w i t h the r e f l e x i o n s used i n the refinement process only, are a l s o given i n Table X I I I . a large number of weak and unobserved  Since  r e f l e x i o n s have been  omitted from the a n a l y s i s , these values of the standard d e v i a t i o n s are almost c e r t a i n l y o v e r - o p t i m i s t i c (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 f a c t o r of two. The a n i s o t r o p i c 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 i n the expression: exp-[B h  2  1:L  +B  2 2  k  2  + B^l  + B ^l  2  + B^hl + B h k ] .  2  1 2  TABLE XIV ANISOTROPIC THERMAL PARAMETERS FOR THE CARBON ATOMS ( x l O ) 4  Atom  B  C( 1) C( 2) C( 3) C( 4) C( 5) C( 6) C( 7) C( 8) C( 9) C(10) C(ll) C(12) C(13) C(14) C(15) C(16)  98 88 64 85 81 72 96 103 89 77 91 88 67 100 54 59  ll  B  22  204 162 138 150 169 158 214 196 185 148 174 164 147 207 118 137  B  33  277 249 197 235 243 234 284 298 271 209 264 240 210 281 171 188  B  23  -29 5 -15 6 13 - 5 - 5 -23 -22 - 7 - 8 0 - 7 32 4 - 6  B  13 48 52 45 57 52 54 63 54 43 50 48 64 40 65 46 45  B  12  9 4 1 -10 8 21 37 13 9 10 3 16 15 33 17 14  56 The bond d i s t a n c e s and v a l e n c y angles i n the molecule  and  t h e i r standard d e v i a t i o n s , c a l c u l a t e d u s i n g twice the  positional  standard d e v i a t i o n s of Table X I I I as a more r e a l i s t i c  estimate  of the accuracy, are given i n F i g u r e 10.  The  standard d e v i a -  t i o n s of the bond d i s t a n c e s and v a l e n c y angles were a l s o computed from the l e a s t squares r e s i d u a l s , and the v a l u e s were i n good agreement w i t h those given i n F i g u r e 10.  Before averaging  f o r comparison w i t h t h e o r e t i c a l p r e d i c t i o n s , the bond d i s t a n c e s were c o r r e c t e d f o r s m a l l e r r o r s due  to r o t a t i o n a l  oscillations,  as d e s c r i b e d l a t e r . The best plane through the carbon atoms has e q u a t i o n : -0.64213 X' where X',  Y, Z  ?  are c o o r d i n a t e s i n X,  axes a, b, and c*. are l i s t e d The  + 0.74683 Y + 0.17291 Z' + 1.76738 - 0, r e f e r r e d to orthogonal  The d e v i a t i o n s of the atoms from t h i s  plane  i n the l a s t column of Table X I I I . o r i e n t a t i o n of the molecule  i n Table XV  i n the u n i t c e l l  i s given  i n terms of the angles which the m o l e c u l a r axes L,  M (see F i g u r e 10), and the plane normal, N, make w i t h the o r t h o g o n a l c r y s t a l axes.  L was  taken through atoms 1 and  and M through the midpoints of bonds 4-5  and 11-12.  8,  L, M,  and  N are almost e x a c t l y mutually p e r p e n d i c u l a r , the angles between them b e i n g Z LM = 89.5°,  ZMN  = 90.0°, and  v i o u s values of the o r i e n t a t i o n angles are i n c l u d e d i n Table XV f o r A l l the carbon-carbon  ZLN  = 90.0°.  Pre-  (Robertson and White)  comparison. intermolecular separations less  than 4 $ were c a l c u l a t e d ; a l l these c o n t a c t s correspond t o  It  ~  1.423 0.018  12  0  0.018 1.409  >  0.014 1.411  I 315 0.020  4 ^  ° ^ 6 ^  1.418 0.0/8  Figure  10.  0.020 1.315  0.018 1.415  (a) Measured "bond l e n g t h s (&), b e f o r e - a p p l i c a t i o n of the small r o t a t i o n a l o s c i l l a t i o n c o r r e c t i o n s , and standard d e v i a t i o n s . (b)  Measured v a l e n c y a n g l e s (degrees).  6" = 1.0° - 1.4°.  ^)  58 T A B L E XV O R I E N T A T I O N OF THE M O L E C U L E  I N THE  Robertson and White (43)  M  X  N  *JJ  N  normal van d e r Waals between molecules of these molecules  32.5  52.2 52.4 120.1  53.3 51.1 120.0  128.7 40.2 80.5  130.0 41.7 80.0  interactions.  related  are parallel  a r e 59 c o n t a c t s l e s s  being  listed  i n Table  The s h o r t e s t d i s t a n c e s a r e  b y a c e n t e r o f symmetry; t h e p l a n e s  there  than  XVI.  a n d s e p a r a t e d by 3.53 4 X,  those  less  $, a n d 3.6  than  The s h o r t e s t l a t e r a l  X  contacts are  given i n Table XVI. All  molecular The  60.9° 77.1  77.7 31.9  UJM  also  Present analysis  61.1°  %l X  CRYSTAL  the carbon-hydrogen and hydrogen-hydrogen separations less  than  shortest distances (less  3.5  °> w e r e a l s o  3 X)  than  are l i s t e d  inter-  calculated. i n Table X V I .  Discussion The cular  deviations  plane  of t h e carbon  (Table X I I I )  atoms from  t h e mean  are smaller than the displacements i n  p e r y l e n e , and 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 significant. bending if  real,  The d i s p l a c e m e n t s  of the molecule,  mole-  similar  i s probably a result  are not  are suggestive of a small t o t h a t i n p e r y l e n e , and t h i s ,  of crystal  packing  forces.  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 neighbouring molecules were c a l c u l a t e d , 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 (molecule l )  in  Molecule  d  3 5 6 7 8 16 2 4 4 14  9 11 10 13 15 16 11 15 16 7  3 3 3 3 3 3 12 5 5 2  3.55 3.58 3.67 3.56 3.67 3.53 3.78 3.64 3.68 3.67  2 10 13 15 16  H 11 H 4 H 4 H 4 H 4  12 13 13 13 13  2.79 2.86 2.97 2.68 2.62  H 12 H 11 H 14  6 12 6  2.52 2.64 • 2.80  1 2 2 Molecule  Atom  1 2 3 5 6 12 13  ;  x x -x 1/2-x 1/2-x 1/2+x 1/2-x  y y -y 1/2+y 1/2+y -1/2-y -1/2+y  z 1+z -z -z 1-z z -z  The a n i s o t r o p i c thermal parameters, B^^, were transformed to U^j r e f e r r e d to the orthogonal c r y s t a l axes a, b, and c* (46), and then to U tensors r e f e r r e d to the molecular axes L, M and N.  The thermal motion was analysed i n terms of the r i g i d -  body v i b r a t i o n s of the molecule  (47). The T and cd tensors a r e :  60  T =  0.0589  -0.0067 0.0501  0.0076 0,0025 0.0500  x  2  O) -  14.56  0.55 10.67  -0.42 -1.37 17.18  deg  The r.m.s. amplitudes of t r a n s l a t i o n a l o s c i l l a t i o n i n the d i r e c t i o n s of the molecular axes are 0.24, 0.22, and 0.22 $ respect i v e l y , and the corresponding are 3.8°, 3.3°, and 4.1°.  amplitudes of angular  oscillation  These values are of the same magni-  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 e a s i l y i n the d i r e c t i o n s o f f e r i n g l e a s t r e s i s t a n c e , 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 a x i s 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. S l i g h t c o r r e c t i o n s i n bond distances are necessary to a l l o w 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 c o r r e c t i o n s , which vary from 0.004 to 0,006 A, were a p p l i e d 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 g e n e r a l l y small (Figure 10a), but one or two d i f f e r e n c e s are f a i r l y l a r g e : 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, equival e n t bonds; bond 8-9 i s very short, but i t s chemically l e n t bonds are a l s o f a i r l y s h o r t .  equiva-  These v a r i a t i o n s are only  p o s s i b l y s i g n i f i c a n t and, although the d i f f e r e n c e s 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  61 TABLE XVII MEAN MEASURED AND CALCULATED BOND LENGTHS •(£) IN PYRENE Bond  Measured /  :  ;  ^  Uncorrected  Corrected for rotational oscillation  1.376 1.416 1.411 1.437 1.411 1.315  1.380 1.420 1.417 1.442 1.417 1.320  a b c d e f  Calculated  0.011 0.009 0.007 0.009 0.014 0,014  0.012 0.003 0.012 0.012  -  1.397 1.397 1.421,: 1.448 1.421 1.355  1.388 1.408 1.427 1.433 1.424 1.360  are given i n Table XVII, together w i t h t h e i r standard d e v i a t i o n s , (S~ being c a l c u l a t e d from the standard d e v i a t i o n s of the i n d i m  v i d u a l 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 d e v i a t i o n s suggests that the accuracy quoted i s realistic. For comparison w i t h these measured distances the t h e o r e t i c a l bond lengths were derived from the s i x non-excited valence bond s t r u c t u r e s (Figure 11), and from the LCA0 TT-bond orders (49).  The c o r r e l a t i o n curve of Cruickshank and Sparks  (38) was  used f o r 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  i n both sets of c a l c u l a t e d values, but some  of the i n 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 s h o r t e r than e i t h e r of the c a l c u l a t e d  d i s t a n c e s , and a p p a r e n t l y ethylene  s h o r t e r than the C=C d i s t a n c e i n  (1.337 * 0.003 X) ( 5 0 ) .  T h i s i s s i m i l a r t o the s i t u -  a t i o n i n p-benzoquinone (51) where a s i m i l a r bond has l e n g t h 1.322  ± 0.008 X,  and suggests t h a t the value  i n ethylene i s  perhaps not the normal double bond d i s t a n c e i n t h i s type of molecule cule  (52). Bond a i s the next s h o r t e s t bond i n the mole-  (measured l e n g t h 1.376  (measured 1.437 length.  °J and bond d the longest bond  °J, w i t h bonds b, c, and e of  These f e a t u r e s are reasonably  intermediate  w e l l reproduced i n the  c a l c u l a t e d d i s t a n c e s , w i t h the molecular  o r b i t a l method g i v i n g  somewhat b e t t e r 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 D E T E R M I N A T I O N OF THE S T R U C T U R E S OF 1-0-(p-BROMOBENZENESULPHONYL)-4,5,7-TRI-OACETYL-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-OACETYL-2,6-ANHYDRO-3-DEOXY-d-GLUCOHEPTITOL  Introduction 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, which can be deacetylated, and the parent p o l y o l s then separated by paper chromatography.  The f a s t  running f r a c t i o n has m.p. 132°C, and the other isomer m.p. 156°C.  Rotation r u l e s and proton magnetic resonance spectra  suggest the t e n t a t i v e s t r u c t u r e s I I I (Rj_ = R2 - H) f o r the lower-melting isomer, and IV f o r the higher-melting  isomer,  that i s the compounds are isomeric anhydrodeoxyheptitols  which  d i f f e r only i n the c o n f i g u r a t i o n of the hydroxymethyl group at C (53). 2  (Ill)  (IV)  To e s t a b l i s h the s t r u c t u r e s c o n c l u s i v e l y an X-ray analys i s of the p-bromobenzenesulphonyl, t r i a c e t y l d e r i v a t i v e of the lower-melting p o l y o l was undertaken.  This d e r i v a t i v e was pre-  pared by treatment of the mixture of triacetylanhydrodeoxyh e p t i t o l s w i t h p-bromobenzenesulphonyl c h l o r i d e , and the  66  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 r e a c t i o n mixture.  I t 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 a n a l y s i s described i n t h i s work has s t r u c t u r e I I I (R]_ = CH3.CO-, R  2  shows that the d e r i v a t i v e - Br.C^H^.S0 -) , so that 2  the t e n t a t i v e s t r u c t u r a l assignment was c o r r e c t .  The systema-  t i c name of the d e r i v a t i v e examined i s 1-0-(p-bromobenzenesulphonyl) -4 ,5,7-tri-0-acetyl-2,6-anhydro-3~deoxy-d-glucoheptitol.  Experimental C r y s t a l s of the p-bromobenzenesulphonyl, t r i a c e t y l d e r i v a t i v e from methanol-water are needles elongated along c w i t h (100) and (010) developed.  The u n i t 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 d e n s i t y was measured by f l o t a t i o n i n aqueous caesium bromide. C r y s t a l 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 0.01  i\  ±  0.08, c = 5.79 -  U =• 2331 °- . D ^ l , 5 , Z = 4, D m  = 1.49 g cm"" . 3  x  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= F (000) = 1072  0.7107 £, yu-=  20  ,  cm" . 1  6? Absent Space  spectra:  intensities  responding measured  to  on  Orienter, kel  when h  of  a minimum  a  G.E.  using  filter  and  a  pulse  f o r background, and  interplanar spacing  height  rected  technique  the  u s e d was  (29).  c o r r e c t i o n s were not  and  small  i n the  range  b r o m i n e and  0  Br  and  were  Fourier  S atoms.  fourteen  On  peaks,  chosen as  s h o w e d a l l 31  the  atomic  atoms, revealed of  s e r i e s was  the  moving  to  the  the  A  sites  atom  i n the  (nic-  crystal-  were  corwere  The  cj>axis so  of  74%  the  that  necessary.  p o s i t i o n s were  Eight  of  the  determined  f u n c t i o n , and  summed w i t h  the  p o s i t i o n s f o r 24  atoms  Crystal  Analysis  bromine  w i t h o u t any  now  "*  ^90°.  UKO(  second F o u r i e r ,  molecule  c o r  were  Single  atoms  being  molecule,  and  regard  phased  a  three-  phases based  resulting electron-density to  ^  X)  = 1.09  cross-section,  Patterson  in addition  considerations.  structure  d  CuKx^^°  intensities  considered  <20Q  sulphur  three-dimensional  dimensional  e  f i f t y - o n e r e f l e x i o n s were o b s e r v e d ,  number  the  2  polarization factors  uniform  Structure  from  and  c parallel  absorption  The  odd.  a m p l i t u d e s were d e r i v e d .  mounted w i t h a  and  and  total  is  CuKoc r a d i a t i o n  A l l the  Lorentz  structure  had  counter,  analyser),  goniostat,  hundred  when k  a l l reflexions with  scintillation  counter  crystal  OkO  XRD-5 S p e c t r o g o n i o m e t e r , w i t h  moving  applied,  i s odd,  P2-]_222.  group  The  hOO  on  these  in all,  the  c l e a r , and  a  although  the  the  distribution  sulphur for  on  peaks,  chemical sixteen general  third  Fourier  acetyl  groups  68 were r a t h e r p o o r l y r e s o l v e d a t t h i s stage.  Throughout  this  s t r u c t u r e d e t e r m i n a t i o n , the s c a t t e r i n g f a c t o r s of the I n t e r n a t i o n a l Tables V o l . H I were use d, w i t h B = 4.5 °-  for a l l  atoms, and oxygen atoms were d i s t i n g u i s h e d a t t h e f i n a l R, the u s u a l d i s c r e p a n c y f a c t o r , decreased  stage;  flbrrxO.46 f o r Br and  S only t o 0.26 f o r a l l 31 atoms. Refinement of the p o s i t i o n a l and i s o t r o p i c thermal meters then proceeded  para-  by computing s u c c e s s i v e observed and  c a l c u l a t e d d i f f e r e n t i a l syntheses, and a f t e r seven c y c l e s R was reduced  t o 0.183.  At t h i s stage 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, and superimposed s e c t i o n s of the r e s u l t i n g e l e c t r o n - d e n s i t y d i s t r i b u t i o n taken through the atomic  c e n t e r s a r e shown i n F i g u r e 12.  There was no s p u r i o u s  d e t a i l so t h a t the s t r u c t u r e appeared to be e s s e n t i a l l y Refinement of the atomic f a c t o r , was completed  parameters,  and an o v e r a l l  by ( b l o c k - d i a g o n a l ) l e a s t squares.  complete i n f i v e c y c l e s , d u r i n g which R was reduced to 0.090, and S w . A F  2  from 26 x 1 0  3  correct.  to 6 x 1 0 . 3  scale The  from 0.183  In the f i n a l  c y c l e s a n i s o t r o p i c thermal parameters were i n t r o d u c e d f o r the bromine atom and f o r the outer atoms o f the a c e t y l groups (our 40K IBM 1620 c o u l d not accommodate a l l the atoms a n i s o t r o p i c ally,  and the atoms t r e a t e d were those whose thermal  vibration  seemed most a n i s o t r o p i c ) . The measured s t r u c t u r e amplitudes  a r e compared i n Table  A3 w i t h the values c a l c u l a t e d from the f i n a l parameters,  those  F i g u r e 12.  Superimposed s e c t i o n s o f the t h r e e - d i m e n s i o n a l e l e c t r o n - d e n s i t y d i s t r i b u t i o n , t a k e n through the atomic c e n t r e s p a r a l l e l t o ( O O l ) . C o n t o u r s s t a r t .at 2eA*~3 and are a t i n t e r v a l s o f 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 o f 2. 5 eS~3.. A p e r s p e c t i v e drawing o f the molecule is,-also shown.  ON  70 from  the fifth  observed  least  squares  cycle  (R = 0 . 0 9 0 f o r t h e 851  reflexions).  Atomic The f i n a l  Parameters positional  and M o l e c u l a r Dimensions and thermal parameters  in  Table  X V I I I ; x, y, and z a r e f r a c t i o n a l  to  the c r y s t a l axes, B are isotropic  are given  coordinates  temperature  referred  factors  and  TABLE X V I I I FINAL POSITIONAL Atom B r (1) S (2) 0 (3) 0 (4) 0 (5)  0 0 0 0 0 0 0  C C C C C C C C C C C C C C C C c c c  (6)  (7)  (8) (9)  (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25)  (26) (27)  (28) (29)  (30) (3D  X  0.1680 0.4027 0.4032 0.4935 0.3378 0.1981 0.0093 0.1464 0.3165 0.4513 0.0573 -0.1373 0.2424 0.3135 0.3664 0.3363 0.2676 0.2150 0.3393 0.3042 0.3356 0.2952 0.1808 0.1563 0.0480 -0.0865 -0.1166 0.0915  0.0595  0.4009 0.4080  ( F R A C T I O N A L ) AND THERMAL y  0.7398 0.5633 0.5624 0.5620 0.5231 0.4635 0.4453 0.3490 0.3729 0.3406 0.3604 0.4161 0.6844 0.6714 0.6321 0.6121 0.6285 0.6691 0.5099 0.4604 0.4397 0.3920 0.3967 0.4184 0.4230 0.4417 0.4646 0.3360 0.2844 0.3457 0.3243  z  0.3841 0.0728 -O.1658 0.1894 0.1556 0.4232 0.5960 0.6387 0.8797 0.7308 0.9489 0.5335 0.3009 0.4465 0.3931 0.1639 0.0085 0.0828 0.3942 0.4035 0.6429 0.6588 0.6470 0.4240 0.3852 0.6564 0.8576 0.8141 0.7754 0.8857 1.1279  PARAMETERS B (A _ '  2.89 4.63 4.26 3.22 3.13 3.33  4.22 3.93  4 .-4 0 4.55 3.28 2.57 4.13 5.36  2.99 2.21 3.73 1.88 2.96 3.06 4.08 4.03  3.30 4.93  71 TABLE XVIII  (continued)  A n i s o t r o p i c thermal parameters Atom Br  B  136 57  (1)  0 (10) 0 (11) 0 (12) C (27) C (29 C  B  l l  84  41  102 77  10M  33 861 353 420 453 398 604 258  B  B  20.0 16.9 25.3 27.2 21.3 9.4 10.4  128  (3D  22  (x  23  13 240 80 178  B  B  2 47 -45 15 -48 13  44 13 -18  -14  -19  18  43 -51 -62  -19  12  -17  9  B j are the a n i s o t r o p i c thermal parameters i n the e x p r e s s i o n : i  exp- j ^ n n  2  + B  2 2  k  2  + B^jl} + B2jklb  + B^ht  + B hk|. 12  A p e r s p e c t i v e drawing of the molecule, w i t h the atom numbering used,  i s shown i n F i g u r e 12, and  and v a l e n c y angles are g i v e n i n Table XIX,  the bond d i s t a n c e s together with  standard d e v i a t i o n s c a l c u l a t e d from the l e a s t A l l the i n t e r m o l e c u l a r d i s t a n c e s l e s s than 4.0 l a t e d , and the s h o r t e r c o n t a c t s are l i s t e d  squares  their  residuals.  £ were c a l c u -  i n Table  XX.  TABLE XIX BOND LENGTHS (£) AND  STANDARD DEVIATIONS, AND  ( 6"VARIES FROM 0 . 9 ° FOR Bond  I  <r  1.980  0.027  S(2)-C(16)  1.777  0.021  S(2)~0(3) S(2)-0(4)  1.381 1.416 1.399  0.019 0.018  SO  O-S-0  ANGLES TO  2.6°  ANGLES IN THE ACETYL GROUPS)  Br(l)-C(l3)  Mean  FOR  VALENCY ANGLES  0.013  I  Bond  0(5)-C(l9) 0(6)-C(20) 0(6)-C(24) 0(7)-C(25) 0(8)-C(23) 0(9)-C(22) Mean 0-C  3  1.44 1.46 1.44 1.48 1.48 1.43 1.45  <r 0.029 0.026 0.024 0.033 0.025 0.028 0.01-L  7  2  TABLE XIX (continued) Bond S(2)-0(5)  1.553  0 015  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 - C  1.34 1.40 1.51 1.39 1.46  0.039 0.033 0.036 0.034 0.037 0,044 o.oi  a r  s  s  £~ ar"" ar c  c  s-c C -Ca-c r ar  ar  ar  _ u  1.39  1.41  0  5  0(7)-C(26) 0(8)-C(28) 0(9)-C(30) Mean 0-C__2 bp 0(10)-C(30) 0(11)-C(28) 0(12)-C(26) Mean C-0  1.36 1.32 1.41 1.36  0.030 0.036 0.026 O.Olg  1.14 1.16 1.25 1.18  0.032 0.038 0.034  ar  1,53  1.57 1.51 1.58 1.48 1.51 1.53  0,027 0.036 0.030 0.030 0.034 0.033  C(26)--C(27)  C(28)-C(29) C(30)-C(31) Mean C 2 - C 3  1.41 1.59 1.54 1.51  0,042 0.038 0.040  C(25)-0(7)-C(26) C(23)-0(8)-C(28) C(22)-0(9)-C(30) Mean C 3 - 0 - C 2  121.5 .115.6 114.4 117.2  0(7)-C(26)-0(12) 0(8)-C(28)-0(ll) 0(9)-C(30)-0(10) Mean 0-C=0  116.0 124.7 123.6 121,4  0(7)-C(26)-C(27) 0(8)-C(28)-C(29) 0(9)-C(30)-C(3l) Mean O-C-CH3  117.3 108.9 107.8 111.3  0(12)-C(26)-C(27) 0(11)-C(28)-C(29) 0(10)-C(30)-C(31) Mean 0=C-CH  126.6 124.9 128,6 126.7  sp  3p  Range 110.0 132.4 (10 angles) Mean 117.8  0(3)- •S(2)- 0(4) 0(3)- S(2)- 0(5) 0(3)- •S(2)0(4)- •S(2)- •C(16) 0(4)- •S(2)- •0(5) 0(5)- S(2)- •C(16) Mean at S •C(16)  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 " sp3- sp3 C 113.1 (15 angles) C U - C . J - Cs pJ- \ Mean 107.2 sp^ spc  c  0.02  0  O.O23  O.Olo  sp  0  6~  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 3-C ;  B  I  Bond  sp  3  Discussion The a n a l y s i s has e s t a b l i s h e d that the d e r i v a t i v e 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 (X)  SHORTER INTERMOLECULAR DISTANCES  A l l contacts < 4.0 X between a standard molecule (1) and neighbouring molecules were c a l c u l a t e d , 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 (Molecule 1)  to  Atom  in  Molecule  d  Br(l) Br(l)  0(10) C(30)  6 6  3.45 3.61  0(4)  0(5)  11  3.41  0(4) 0(4) 0(4) 0(10) 0(11) 0(11) C(15) C(19) C(31)  C(19) C(20) C(21) C(15) C(24) C(25) 0(3) 0(3) 0(10)  11 11 11 11 7 7 7 7 7  3.34 3.H 3.52 3.27 3.51 3.13 3.31 3.10 3.57  . C(14)  C(17)  7  Molecule 1 6  x 1/2-x  7 11  y  1 - z y  1-x  1 + z  1-y  anhydro-3-deoxy-d-glucoheptitol.  3.55  z  1/2+y x  •  z  The t e n t a t i v e assignment of  s t r u c t u r e s to the two anhydrodeoxyheptitols i s t h e r e f o r e corr e c t ; the lower-melting isomer i s 2,6-anhydro-3-deoxy-dg l u c o h e p t i t o l ( 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 i n the c h a i r conformation w i t h a l l s u b s t i t u e n t groups i n e q u a t o r i a l p o s i t i o n s , as i s c l e a r from  74 Figure 12.  Since the compound i s derived from d-glucose the  absolute c o n f i g u r a t i o n i s e s t a b l i s h e d : the parameters of Table X V I I I r e f e r r e d t o a right-hand set of axes give the true absolute c o n f i g u r a t i o n . Figure 12 a l s o depicts the c o r r e c t absolute c o n f i g u r a t i o n . The bond distances and valency angles i n the molecule (Table XIX) are a l l q u i t e normal, and require no s p e c i a l comment. A l l the intermolecular separations (Table XX) correspond to normal van der Waals i n t e r a c t i o n s .  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 s h o r t e s t Br-0  and Br-C contacts are 3.45 8 and 3.61 $ r e s p e c t i v e l y (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 separat i o n i s 3.55 X.  II.  THE CRYSTAL AND MOLECULAR STRUCTURE OF 10-CHLORO-5,10-DIHYDROPHENARSAZINE (PHENARSAZINE CHLORIDE)  Introduction I f arsenic r e t a i n s i t s usual valency angle (of about 98°) i n 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 a t t h i s a x i s a (calculated) angle of 121° (55).  Three geometrical  isomers should  then e x i s t : two c i s forms, one having both s u b s t i t u e n t s outside the 121° angle ( s t e r i c f a c t o r s p e r m i t t i n g ) , and the other having both groups w i t h i n t h i s angle; and one trans form.  Two forms  of the 5 , 1 0 - d i - p - t o l y l d e r i v a t i v e (V; R = C^H^Me) have been :' i s o l a t e d (56), the t h i r d form being too s t e r i c a l l y hindered to exist.  I t has r e c e n t l y been asserted however, on the b a s i s of  t h e o r e t i c a l c o n s i d e r a t i o n s , that systems such as (V) are unl i k e l y t o be " s t a b l y f o l d e d " and that the existence of geometric a l isomers i s due to the s t a b i l i t y of the arsenic pyramidal c o n f i g u r a t i o n (57).  The only d i r e c t s t r u c t u r a l information  which appears to be a v a i l a b l e i s that f o r 5,10-dimethyl-5,10dihydroarsanthren  dibromide and d i i o d i d e (VI, X = Br or I ) ,  where the angle subtended by the o-phenylene groups was found to be, w i t h i n r a t h e r wide l i m i t s of e r r o r , 157° (58).  V  VI  Recently i t has been found that there appear to be two m o d i f i c a t i o n s of 10-chloro-5,10-dihydrophenarsazine  (phenar-  sazine c h l o r i d e , Adamsite, V I I ) ; yellow c r y s t a l s are obtained from a v a r i e t y of s o l v e n t s , and when these are heated t o  200°  _3  at 10  mm yellowish-green c r y s t a l s are formed ( 5 9 ) .  I f the  molecule i s f o l d e d as i n the dihydroarsanthren system two geometrical isomers might e x i s t , one w i t h the c h l o r i n e w i t h i n and the other w i t h the c h l o r i n e outside the angle formed by the two o-phenylene groups, the c o n f i g u r a t i o n at the n i t r o g e n probably being r e a d i l y i n v e r t e d .  ^  I have undertaken an X-ray i n v e s t i g a t i o n of the. two c r y s t a l l i n e m o d i f i c a t i o n s to e s t a b l i s h whether they are geometr 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 s t r u c t u r e s .  The r e s u l t s show that the yellow c r y s -  t a l s are s o l v a t e d , those from xylene c o n t a i n i n g 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 a n a l y s i s shows that the o-phenylene groups subtend an angle of 169°, w i t h the c h l o r i n e atom outside t h i s angle; the d e v i a t i o n from complete p l a n a r i t y of the t r i c y c l i c r i n g system i s thus q u i t e s m a l l , 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 .  P r e l i m i n a r y X-ray Study 10-chloro-5,10-dihydrophenarsazine  (phenarsazine  chloride)  i s obtained, by r e a c t i o n 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 a c e t i c a c i d , e t c . ) , as yellow s i n g l e c r y s t a l s which r a p i d l y change to a yellow powder when removed from the mother l i q u o r .  When e i t h e r the s i n g l e c r y s t a l  sample or the powder i s heated at 200  and 10  mm, y e l l o w i s h -  green rectangular needles are formed, which are quite s t a b l e . Chemical analyses, i n f r a r e d ( s o l u t i o n and KBr d i s c s ) and  ultra-  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 c r y s t a l s (which are yellow when f i n e l y powdered) i n d i c a t e d 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 s i n g l e c r y s t a l s i s that the yellow metastable m o d i f i c a t i o n 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 s t a b l e green form i s solvent  78  free. This conclusion was v e r i f i e d by determining the u n i t c e l l dimensions and space groups of the metastable yellow c r y s t a l s (from xylene) and the s t a b l e green c r y s t a l s , from various r o t a t i o n , Weissenberg and precession photographs.  The yellow c r y s -  t a l s were sealed i n t h i n - w a l l e d Lindemann-glass c a p i l l a r i e s , together w i t h some mother l i q u o r , to preserve them during the X-ray exposures.  The d e n s i t i e s 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 . C r y s t a l data ( X(CuKcx) = 1.5418 X; metastable yellow c r y s t a l s  X (MoKoc) = 0.7107 A ) ,  C-^HgNAsCl.l/2CgH-Lo  M o n o c l i n i c , a = 14.50 ± 0.02, b =16.76 - 0.02, c = 13.02 0.03 X, p = 113.7° ± 0.1°. U = 2898 ft D D  m  3  -3 = 1.544 g cm . (Z = 8) = 1.272 g cm" . 3  x  _3 D  x  (Z = 8 + 4 molecules  of xylene) = 1.515 g cm  Absent s p e c t r a : 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 d e n s i t y measurement i n d i c a t e s t h a t the yellow c r y s t a l s are solvated w i t h h a l f a molecule of xylene per molecule of phenarsazine  c h l o r i d e . C r y s t a l s from other solvents are  no doubt a l s o .solvates ( 6 l ) . Stable yellowish-green c r y s t a l s . Phenarsazine  c h l o r i d e , 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 D  m  X. 3  -3  = 1.693, Z = 4, D  Absorption  x  = 1.694 g cm  .  c o e f f i c i e n t f o r X-rays, X = 1.5418 X, JJ. = 66  cm ,  X = 0.7107 X, JX = 35  cm" .  -1  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 e x c e l l e n t agreement between measured and c a l c u l a t e d d e n s i t i e s i n d i c a t e s that the stable c r y s t a l s are s o l v e n t - f r e e . Structure Determination of Stable C r y s t a l s Experimental C r y s t a l s of s o l v e n t - f r e e phenarsazine c h l o r i d e are s t a b l e yellowish-green  needles elongated along a, w i t h {011} developed.  The i n t e n s i t i e s of a l l r e f l e x i o n s w i t h 28,-^^ ^ 148° (corresponding t o a minimum i n t e r p l a n a r spacing d = 0.80 8.) were measured 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 Single C r y s t a l O r i e n t e r , using a s c i n t i l l a t i o n counter, CuKoc, r a d i a t i o n ( n i c k e l f i l t e r and pulse height a n a l y s e r ) , and 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 <£> a x i s of the g o n i o s t a t , and had c r o s s - s e c t i o n about 0.3 x 0.3 mm.,  so that absorption  c o r r e c t i o n s were not  considered  necessary.  The s t r u c t u r e amplitudes were derived  as u s u a l .  One thousand and t h i r t y - t h r e e r e f l e x i o n s were  80 observed, 79% of the t o t a l number i n the range 0 < 2 e  Structure  CuKoc  <148°.  Analysis  The y- and z-coordinates of the arsenic and c h l o r i n e atoms were determined from the Ok/. Patterson f u n c t i o n and an Okt Fourier s e r i e s was summed w i t h phases based on the As and CI atoms.  On the r e s u l t i n g e l e c t r o n - d e n s i t y d i s t r i b u t i o n a l l  the atoms (except hydrogens) were r e a d i l y d i s c e r n i b l e .  Struc-  ture f a c t o r s were c a l c u l a t e d from the p o s i t i o n s obtained from the F o u r i e r map and R f o r the zone was 0.135, The x-coordinates of the arsenic and c h l o r i n e atoms were then determined from the h0£ Patterson f u n c t i o n and an  hOJL,  Fourier s e r i e s was summed w i t h phases based on the As and CI atoms.  There was much overlap i n the r e s u l t i n g e l e c t r o n -  density d i s t r i b u t i o n so that the x-coordinates of the r e s t of the atoms could not be obtained with c e r t a i n t y . dimensional F o u r i e r s e r i e s was then  A three-  summed based on the phases  of the As and CI atoms only and from the r e s u l t i n g e l e c t r o n 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, c a l c u l a t e d with the p o s i t i o n s obtained from the e l e c t r o n - d e n s i t y 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 s t r u c t u r e  deter-  mination the s c a t t e r i n g f a c t o r s of the I n t e r n a t i o n a l Tables V o l . I l l (1) were used, with i n i t i a l l y B = 4.5 A* , f o r a l l the 2  atoms except a r s e n i c , f o r which B = 3.0 A  was used.  Refinement of the p o s i t i o n a l and a n i s o t r o p i c thermal para-  81 meters f o r a l l atoms except hydrogens then proceeded by (block diagonal) least-squares.  2 (| W  F  | " |  | >  F  0  )2  c  w  i  t  |F  h  35/|F |when|F | ^-35. o  The f u n c t i o n minimized was Q  |/35 when | K |< 3 5 ; and Q  -  Refinement was complete i n f i v e cycles  o  during which R was reduced from 0.133 to O.O56, and 2wAF 2 from 6.2 x 1 0 t o 1.7 x 1 0 . 3  3  The measured s t r u c t u r e amplitudes are compared i n Table A4 w i t h the values c a l c u l a t e d from the f i n a l parameters, those from the f i f t h l e a s t 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 p o s i -  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 a n a l y s i s , 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 As(l) Cl(2) N( 3) C( 4) C( 5) C( 6) C( 7) C( 8) C( 9) C(10) C(ll) C(12) C(13) C(14) C(15)  X  0.1305 -0.1196 -0.2282 -0.1678 -0.3629 -0.5215 -0.4750 -0.2700 -0.1248 0.3277 0.3495 0.1799 -0.0110 -0.0374 0.1366  y  0.4818 0.5858 0.4773 0.3165 0.2545 0.2698 0.3461 0.4079 0.3935 0.6197 0.6747 0.6622 0.5969 0.5409 0.5526  z  0.1659 0.2465 -0.0164 0.1912 0.1754 0.1003 0.0372 0.0499 0.1312 0.0395 -0.0411 -0.1132 -0.1030 -0.0213 0.0516  y  3b_ 4  I  0  1I  Figure 1 3 -  I I I  I  2  3  I  I  4 A I  Superimposed s e c t i o n s o f the t h r e e - d i m e n s i o n a l e l e c t r o n - d e n s i t y d i s t r i b u t i o n , taken through the atomic c e n t r e s p a r a l l e l t o (lOO). Contours s t a r t a t 1 e and are a t . i n t e r v a l s o f 1 e A*~3 except f o r the A s ( l ) and C l ( 2 ) which s t a r t a t zero and a r e a t i n t e r v a l s o f 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 o f the molecule i s a l s o shown.  co.  83 TABLE XXI (continued) (xioM  F i n a l a n i s o t r o p i c thermal parameters Atom  b  As 1 Cl(2) N( 3) C( 4) C( 5) C( 6) C( 7) C( 8) C( 9) C(10) C(ll) C(12) C(13) C(14) C(15)  241 491 307 335 341 344 245 178 149 200 335 286 328 177 261  ll  b  22  b  46 49 54 42 47 41 54 36 39 46 46 65 57 33 46  33 32 44 25 42 51 45 42 40 34 53 56 43 31 52 35  b  23  b  13  - 4 -35 -10 -13 - 5 -12 -24 -31 -11 +3 - 9 - 0 - 1 -10 - 2  -33 94 -46 - 7 19 -23 -67 0 -66 -37 59 61 2 27 -65  b  12  -20 -59 -40 7 22 -12 - 2 25 - 1 -10 -20 - 7 22 -28 -20  z are f r a c t i o n a l coordinates r e f e r r e d t o the c r y s t a l axes, and b^-t are the a n i s o t r o p i c thermal parameters i n the expression: exp - £ b n h  2  +  b  2 2  k  A perspective drawing of the molecule, and superimposed sections of the three dimensional e l e c t r o n - d e n s i t y d i s t r i b u t i o n taken through the atomic centers, are shown i n Figure 13.  The  bond distances and valency angles, w i t h t h e i r standard deviat i o n s c a l c u l a t e d from the l e a s t squares r e s i d u a l s , are shown i n Figure 14.  A l l the intermolecular contacts l e s s than 4.0 X  were c a l c u l a t e d and are l i s t e d i n Table XXII. The mean plane through the twelve carbon atoms was c a l c u l a t e d and the displacements from the plane suggested some d e v i a t i o n from p l a n a r i t y .  Accordingly the mean plane through  each of the phenyl r i n g s was c a l c u l a t e d .  The plane through  carbon atoms numbered 4 t o 9 (Figure 13) has equation:  84  F i g u r e ik.  Bond'lengths (2) ,and valency, a n g l e s (degrees) i n phenarsazine c h l o r i d e . Standard d e v i a t i o n s are given i n parentheses.  85 TABLE XXII SHORTER INTERMOLECULAR DISTANCES  (X)  p A l l c r y s t a l l o g r a p h i c a l l y - i n d e p e n d e n t contacts^, 4.0 A between a standard molecule (1) and neighbouring molecules are l i s t e d . Atom to (molecule 1)  Atom  As(l) Cl(2) Cl(2) Cl(2) Cl(2) N(3) C(4) C(4) C(4) C(5) C(5) C(5) C(6) C(6) C(6) C(7)  C(12) N(3) C(4) C(5) C(13) C(6) C(12) C(12) C(13) C(7) C(12) C(13) C(7) C(7) C(8) C(7) Molecule  1 3 4 7 8 15  i n Molecule 8 15 4 4 15 3 8 15 15 3 15 15 3 7 7 3 x y 1/2 + x 1/2 - y - x 1/2 + y - 1/2 + x 1/2 - y 1/2-x 1 - y - 1/2 - x 1 - y  d 3.88 3.60 3.68 3.70 3.90 3.81 3.88 3.97 3.63 3.96 3.67 3.85 3.92 3.55 3.55 3.97 1/2 1/2 + 1/2 +  z z z z z 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 r e f e r r e d to the c r y s t a l axes. 10°40'.  The angle between the normals t o these two planes i s The d e v i a t i o n s of the atoms from each of the planes  are given i n Table X X I I I .  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 t o 15  As(l) Cl(2) N (3) C (4) C (5)  -0.224 -2.521 0.108 0.002 0.022  0.022 -2.260 0.004 0.584 0.681  G (7) C (8) C (9) C(10)  -0.007 0.030 -0.029 0.252  0.224 0.178 0.302 0.003  C (6)  -0.018  C(ll)  0.499  C(12) C(13) C(14) C(15)  0.631 0.487 0.224 0.107  0.470  -0.007  0.006 -0.001 -0.002 0.002  Discussion Three c r y s t a l l i n e forms of phenarsazine c h l o r i d e , a stable green form and two metastable yellow phases, have been reported p r e v i o u s l y (62).  The present i n v e s t i g a t i o n suggests  the existence of only one form of (unsolvated) phenarsazine c h l o r i d e , which i s b r i g h t yellow when powdered and y e l l o w i s h green as s i n g l e 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 for crystallization.  The metastable c r y s t a l s from a v a r i e t y  of solvents contain solvent of c r y s t a l l i z a t i o n ( i n the case of xylene h a l f a molecule per molecule of phenarsazine c h l o r i d e ) , which i s r a p i d l y l o s t when the c r y s t a l s are removed from the mother l i q u o r .  87 The d e t a i l e d a n a l y s i s of the s t r u c t u r e of the solventf r e e c r y s t a l s has e s t a b l i s h e d that the phenarsazine c h l o r i d e molecule i s s l i g h t l y f o l d e d about the As...N a x i s , the angle between the two o-phenylene groups being 169°20', and c h l o r i n e atom being outside t h i s angle. placed by only about 5° from a completely  the  Each r i n g i s thus d i s planar arrangement,  and these d e v i a t i o n s are probably not large enough to permit i s o l a t i o n of s t a b l e geometrical isomers.  The d e v i a t i o n s of the  atoms (Table XXIII) from the o-phenylene planes i n d i c a t e that the As and N atoms are s i t u a t e d a c c u r a t e l y on the plane through C(10)  - C(15), but are s i g n i f i c a n t l y d i s p l a c e d , i n opposite  d i r e c t i o n s , from the C(4) - C(9) plane.  These displacements  i n d i c a t e a s l i g h t t w i s t i n g of the group C(4) - C(9), i n addit i o n to the f o l d i n g of the molecule about the As...N A x i s . 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 f o r c e s ; Table XXII shows t h a t , of the s i x t e e n shortest intermolecular contacts, t h i r t e e n involve atoms of the t w i s t e d 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 AsCl 2  (2.18 % ), but i s about the same length as the bond i n chlorodiphenylarsine (2.26 ± 0.02  X)  corresponding (64).  It is  d i f f i c u l t to account f o r these d i f f e r e n c e s , although the s t e r i c e f f e c t s of the large phenyl groups might be i n v o l v e d . bonds (mean length 1.917  The  As-C  ± 0.007 $) are s i g n i f i c a n t l y shorter  than the normal single-bond distance ( f o r example, 1.990 0.019  X i n cacodyl d i s u l p h i d e ) (65).  1.371  ± 0.009 2)  The C-N  ±  distances (mean  are a l s o s i g n i f i c a n t l y l e s s than the s i n g l e -  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 c h l o r i d e , i n v o l v i n g i n t e r a c t i o n of the a r s e n i c and n i t r o g e n lone p a i r e l e c t r o n s w i t h the ophenylene  TT-electrons, w i t h i n a d d i t i o n p o s s i b l y dfr- ^p^  bonding between the -fj--electrons and vacant 4d o r b i t a l s of the arsenic atom. 0.005  The mean aromatic C-C distance i s 1.406 ±  X, and although  there are some v a r i a t i o n s none of the  i n d 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 a r s e n i c , and i s s i m i l a r to the corresponding . angle i n c h l o r o d i p h e n y l a r s i n e (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 s m a l l e r than the values of 105° - 106° i n other arsenic-phenyl compounds  ( 6 4 , 67),  probably as a r e s u l t of s t r a i n due t o the c y c l i c nature of the molecule and t o i t s n e a r - p l a n a r i t y .  The C-N-C angle (128° +  0.9°) i s s i g n i f i c a n t l y l a r g e r than normal, again i n d i c a t i n g some s t r a i n i n the c e n t r a l r i n g . The i n t e r m o l e c u l a r distances (Table XXII) a l l correspond to van der Waals i n t e r a c t i o n s , and do not r e q u i r e s p e c i a l 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  2 4 6 « 10 10  «.  L  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1  F 00-  0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 5 5 5 5 5 5 6 6 6 7 8 9 9 0 0 0 0 0 0 0 1 1 1 I I 1 1 I 1 I 1 1 I 1 2 2  1 2 ! 2 2 2 2 2 2 ! 3 3 3 3 J 3 i  4 4 4 » 4 4 4 4  4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 7 8  32.2 6.11 5.7 22.6 19.5 12.' JO.8 59.1 62.9 26.3 8.8 13.0 7.9 10.9 17.0 72.9 5.9 7.6 9.6 21.5 29.4 11.0 10.7 34.5 29.7 53.1 18.9 23.5 9.9 16.4 18.7 19.5 37.6 7*4 6.8 16.7 7.4 6*8 8.5 15.5 49.8 39.1 43.8 16.7 20.9 18.9 18.7 6.8 9.9 5.7 28.3 105.7 28.3 43.3 10.7 3.1 31.7 33.6 16.7 26.3 7.9 9.9 14.7 7.9 4.5 5.7 27.1 26.9 14,4 12.4 13.0 8.8 5.1 5.9 12.7 17,0 20.4 13.0 11,3 7.9 8.5 18*7 11.0 13.0 7.9  f  CALC  -  -  -  -  34.0 2.5 4*6 23.2 16.0 11.1 34.6 67.6 73.7 26.8 9.0 10.7 tl.O 8.5 17.0 82.1 5.7 7.6 7.5 17.6 28.7 9.5 12.6 34.7 30.2 53.0 19,3 22.0 9,7 16.5' 16.1 19,2 33.3 6.8 6.8  14.5 7.5 6.9 10.2 17.2 54.4 68.0 - 46.9 17,4 19.2 16.7 - 15.3 5.7 9.9 5.6 - 30.5 -118.9 - 31.9 45.8 10.5 3,7 - 32.9 34.5 17.5 26.0 8.7 9.7 14.4 7.7 4.1 3.7 - 28.5 - 27.6 12.3 12.0 - 13.6 9.0 5.7 5.4 - 13.0 16.6 20.0 13.7 - 10.7 6.9 9,7 16.0 - 11.» - 11.» 7.0 7.4 7.5 14.1 - 13.7 35.6 - 34.7 13.9 ' 14.6 48.1 - 49.3 23.5 22.5 7,1 - 8.0 8.2 8.5 6.5 6.8 10.5 • 10,6 13.6 12.0 6.5 6.6 26.0 - 26.0 44.4 - 46.7 41.6 - 42.1 13.0 12.9 13.0 - 13.2 9.3 7.2 ld.V 17.4 11.0 - 11.6 7.4 6.4 13,5 9.6 7.6 7.2 13.6 12.8 11.9 - 1!,4  H  K,  L  - 5 - 4 -  1 1 1 1 1 2  b  - 5 - 4  1 2 6 7 -  2 2 2 2  •  I  2 2 2  4 3 2 1 1 2 3 4  I  2 2 2 2  2  ft  I I I  6 7 - 7 - 5 -  '*  - 1 - 1  4  5 6 - 6 - 5  - 4 J 2 3  4  ft •  -  4 3 2" l  ft 6 7  - t.  - J 1 4 5 6 -  l  -  1 6 5 4 3 2  -  i  - 5 1  2  _ -  6 £ 5 4 3 2 l 2 3 4  ft  -10 - 7 - 6  -- 4ft - 2  I  3 4 -10 - 5 _ 4  -2 - 1  4 5 - s  - 4 - 2  2  3 4 5 - 4  9 99 0 0  3  c 0  3  0 I 1  i 1 1 \ 1 1  \  1 1  2 2 2 2 2  2 2 2  I  2 2 2  2  1 3 6 - 5 - 4 - 3 1  F Oai tl 6  2 2 2  2 2  2 2  2  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  2  2 2 2 2 2 2 2 2 2 2 2 it 2 2 2 2 I  ? 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 J 3 3 3 3 3 3 3 3 3 3 3 s  j 3 3 3 3 3 3 3 3 3 3 i  3  i  2 2  i  3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 ft 9 5 3 ft 5 6 b 6 6 6 6 7 7 8. ft fl tl 8 0 9 0 0  a  0  i 1 l 1 l l l  i  1 l 1 2 2 2 2 2 2 2  2  2 2 3 3 i  3 j 3 3 3 3 4 <• 4 4 4 4 4 4 5  22.1. 24*6 If.7 10.2 ft.9 'il.D 102.6 M.J 8.2 9.3 6.a 43.0 1 11.4 1 17.6 10. 9 4.2 30.« 13.6 T.V 20.3 10.2 7.9 8.5 9.9 2f*.6 10.3 H.2 2>.6 6.8  6.5  13.3 12.7 40.4 7.6 13.9 17.0 9.6 11.0 25.4 39.7 9*0 If. 2 20.9 7.6 17,2 19.2 17,0 16.1 ft.7 * 7.4 17.0 20.6 26.6 14,4 11.6 13.0  7,9 ft. 25.7  14.1 7.9 7.6 11. i 13.0 ' 9.0 12.4 12.4 7.6 7.9 25.7 11.0 ltJ.9 9.3 20.6 57,7 18.7 17.3 22.6 14,7 4.2 4.5 31.7 20. 8 ?ft.7 7.4 9.9 41. J 33.1  6.5  5.7 11.6 16.4 26.-t 2ft.2 17,0 15. 0 22.1 31.4 14. 1 7.4 25.7 24, j 9.3 15.3 11.6 5.4 5.7 6.8 13.C 13.1 V.C 8.9  &  F CALC 2C.9 - 2i.l - ?^,9 17.5 9.1 6.1 47,2 -123.7 46. 1 9.3 -  47.1  -13 5.3 - i 1 . 1 3.6 4C.3 - 32.7 - 13.9 H.5 29, i 10.3 «,e - 11.5 - 11.0  -  0-  -  -  -  0 7  . 6 - 3  - 4 - 3 2 }  5 4 - i _ i  - 1  - 4 - 3 - j  - i' 2 2  so.:  - 6  1  -4  1.0  7.? 21.3 6.5 a,« 14,4 13,5 41,7 8.6 13.1 17.0 8.1 11.3 27.3 37,7 ti.8 a.3 19. tt 6.a 17,3 17.9 16,4 16.4 6.2 7.1 17.4 23.2 26.0 12.2 10.7 12.0 5.4 5,9 25.4 14.3 8*0 7.0 8.9 VI.9 8.6 1 I .6 11.0 6.2 7.0 27.4 12.6  - ie.i  -  -2  8 .0 7.0  - ! <!<>..>  -  - J  9.4 28.4 6 1.6 21.6 10.3 22.9 14.1 3.4 5.7 34.6 31.4 26.0 6.8 10.2 41.2 3 3.8 6.6 5.1' 11.0 17.1 27.4 25.7 16.0 14.5 22.0 31.0 13.4 5.a 23.7 it;-'  7.9 15.C a.7 6.1 5.4  - ;  -i  - 2 -  i  2 3  -IC - b - 5 - 4 - 2 - i 1 2 3 7 . 3 _ 3 . 2  -1 Q  3 7 d - 7  -• /,3 - 2  -  -  1 2 3 4 j  \  )  i  3 3 3 3 3 j 3 3 i  j J j J • 3 j J 3 J 3  It  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  4 4 4  4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5  i  6  - 8 - 5 - 1 1  2 A  - d - 4 -  i i  - 1 7  - A ~ *  6 t  6  7 7 7 7 6 8 9 *  o  4  1 3 - 4 - 3 - 1  - 1 2 '3  6  6  >  * 4 4 4 4 4 4  -  5 6 6 6  0 0 2  - 5 2 3 4 - 6 - 3 - 2  1 3 7 8 - 6 - 4  ; 5  4 4 4  4  - 6  F Odd 5  4 5  5.0  13.6 1 J.4 9.1 3.7  L  1  4  4  4  5  5 5 5 5 5 5 5 5 5 5 5 5 5  5  5 5 5  C  1  1 11  1 1 1 1 1 2 2 2 2 2 2 2 I  2 2 2 2 3 3 3 3 3 3 3 3 i  3 4 4 4 4 4  4  4 4 4  5 5 5 5  6  6 6 6 6 7 7 7 7 7 7 8 8 8 8 0 0 0 0 1 1 1 1 1 1 1 2  2  2 2 2 2 2 i  J 3 3 3 3  j  3 4 4  id.* 21.7  .6  f-.v 17.3 11.6 ".0  -  7.6  20.4 25.2 13.2  *.9 16..  12.2 14.4 17.11ft. 1 V t>.8 32. B 26.6 11.0 19.4 cl.2 17.0 9,9 6.5 17,0 52.6 35.9 7. 1  9.  d.5  -  -  -  U.6 17.3 7.V ' 6,5 J1.9 3V.1 8.8 7.1 28.6 22.9 *7.l 7,9 22*1 7.4 12.7 14. 1 23.2 39.V 33.9 17.2  -  -  -  -  6.5  7.1 10.2 15.3 10.3 6.t) 6.2 13.6 5.9 5.4 5.9 7,9 8.2 6.5 11. b 5.7 10.2 9.0 14.7 9.9 17,) 35. 1 22.1 8.2 7, 1 7.9 20,1 10.7 13.0 9.6 13.0 7.9 10.2 8.8 6.8 7.9 7.4 9.3 9.3 9. t 7.1 14.4 11.6 9.3 54.8 7.6 •13.2 30. b 16.1 44.4 9.9 33.0 8,2  8.5  17.3 9.9 31.4 9.9  9.3  (1.8 9.-*  • -  -  -  -  -  K 0 0  3,4  -&  5, ?  2 3 4 - 6 - 1  17,3 10,3  - 5  7.4 20.0 27.3 12.3 10.2 15.7 12..' 12.0 20.4 18.1  *.fr  7.7 33.4 26.8  - 9.6  21.5  ll.i  H  F CALC  18.7  21.0 11.1 11.1 6.9 16.0 55.0 37.0 9.1 9,3 21.2 11.5 13.2 19.* ES.4 5,9 30,6 41,& 9.0 6.0 28.4 22.6 27,8 8.0 22.3 '6.2 11.3 15.2 23,6 40.1 33.7 16.4 6.4 6.6 9.7 14.4 a.2 b.2 7.2 12.7 4.9 4.3 5.4  6.5  8.5 7.3 10.D 6.a 9.2 5.2 14.5 9.0 21.7 37.4 22.6 7.1 5.2 6.4 19.5 10.4 13.2 5.3 13.2 6.7 8.3 9.4 7,3 6.3 7.0 9.7 11.2 H.e  5.0 14,9 11.5 7.6 52.6 6.4 9.1 33.2 17.2 44,0 8,3 26.6 7.B 0.2 16.7 9.5 30.8 8.1 7.6 9.8  6.5  1 0 1 -  7 3 J 2 i  -  7 6 5 2 1  2  1 2 7 3 - 2 1 7 1 j  -' 1  2  3 4 - 1 1  2 - i - 6 - 5 - 4  -2  4 5 - 7 - 6  --- i2ft 1 2 J 4 - 3 - 2 - 1 4 - 3 1 2 3 - 2 -  2 6 5 J 2 3 4 6 2 3 4 3 1 5 5 4 1 2 3 0 0 1  ,  5 3 5 5 5 ft 3 3 5 5 5 3 5 0 6 6 6 6 6 6 6 6 6 6 6. 6 6 6 6 6 6 6 6 & 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 ? 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 a 8 8 8 8 8 8 8 8 8 8 8 8 8 V V 9 10 10 11  L  F Odi 4 5 6 6 6 6 6 6 f 7 7 J  d 0  00 1 1 1 1 1 1 2 2 2 2 2 i  2 2 2 2 3 3 3 3 4  5  6 6 6 6 6 7 7 7 7  9  1 1 1 I 1 1 2 2 2 2 ' 2 2 2 2 2 2 3 3 3 3 3 4 6 6 6 6 7 0 1  i  1 1 1 1 2 2 2 3 3 3 3  4 4  0 0 0  o  1 0  14.1 10.2 14.4 9.3 6.8 7.1 12.7 10.7 10.7 12.4 45*e 14.7 13.0 9.0 d.i> B.3 10.7 *«* 10,2 9.3 7.1 5.9 27.1 14,4 • 11.6 7.1 11.9 22.6 41.6 9.8 7.V 9.9 20.1 14.1 14.1 7.9 9.0 7,9 7.9 10.9 20.9 16.4 16,1 16,4 17.8 19.9 19.0 9.6 15.9 19.9 1ft.ft 6.2 15.3  y.o  11.9 32.5 10.7 9.5 11.3 7.1  7,4  9.2 11,6 13.0 7.6 26.3 13.9 7.9 9.3 7.9 9.0 7.4 14.4 16.4 16.1 9.6 9.0 - d.2 11.9 21.5 14.1 10.2 15.0 10.5 9.0 11.3 9.5 12.7 7.1 9.0 10.ft 9.0  7.4  12,4 11.6 36.5 12.7 20.9  F CALC -  12.7 11.2 13.9 7,5 9.0 5.6 13.? 10,9 9.9 -*•«  - 4?.l U.7 • 12.1 7.8 9,0 9.2 - a.c 11.0 - 11.3 9.2 5.6 6.6 - 25.4 - 14.2 11.7 6.5 - H.3 - 21.9 41.5 6.5 7.9 9.3 - 17.7 - 13.0 13*1 a.7 8.9 9.0 9.8 - 16.8 - 18.6 16.3 - 13*7 - 13.9 - 17.8 - 20.1 - 20.3 9.2 17.2 - 21.1 19.2 5.3 - 12.7 7.1 - 10.8 33.5 - 20.2 7.3 9.7 7.0 7,2 7.3 11.2 - 11.5 6*8 - *5.3 - 14.9 2.0  9,9  -  1.9 7.3 4.ft 12.5 14.7 14.0  - 9.9 -  8.3 7.7 10.0 22.1 14.7  9.0  13.3 10.8 0.2 11.0  6.4  11*3 6.3 10.0  9.4  0.7 O.O 11.0 9.9 - 33.6 9.1 - 20.f  91 TABLE A l .  (Continued).  Planes with intensity less than 9. Omitted from the structure refinement. L  K  a 6  F  1  0 3 9 0  I  I  1 1  c  0 0 0 0 0 0  2 2 2 3 3  3 3 3 3 4 4  c  3 3 0 0 0 0 0 0  c  0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i  4 4 4  5 5 5 5 6 6 6 6 7 7 7 7 7 7 7 B 8 a  a  B 9 9 9 0 0 0 1 1 1 1 1 1 1 2 2 2 I I 2 2  2  2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 3 5 5 3  ft  6 t  6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7  Obd 0.0 4.9  J  2. CO 0.0 0.0 0.0 0.0 CO 0.0 2.ft 3. 1 3.4 0.0 2.9 0.0 0.0 0.0 0.0 3.1 5.9 2.5 4,0 0.0 3,4 0.0 0.0 3.7 6.2 3.7 4,6 0.0 3.1 4.9 0.0 0.0 4.2 6.5 0.0 6.2 0.0 5.7 6.8 0.0 0.0 0.0 0.0 6.8 0.0 4.0 0.0 5.9 0.0 0.0 0.0 0.0 • 0.0 2.0 4.0 3.4 0.0 0.0 0.0 0.0 0.0 0.0 2.9 0.0 2.8 0.0 4.0 0.0 0.0 0.0 0.0 0.0 4.2 0.0 3.4 0.0 0.0 6.8 0.0 2.9 0.0 0.0 2.9 0.0 0.0 0.0 0.0 0.0 5.4 2.9 0.0 2.8 4,9 4.0 5.7 0.0 0.0 4.5 0.0 0.0 0.0 6.2  o.o  0.0 4.2 3.7  F CALC 0.4 4,9 2.1 3.1 0,4 1.5 0.1 1.3 1.6 4.5 .3.0 3.ft 3.3 2.3 0.5 0.6 1.4 3.9 2.5 3.1 4.2 1.0 3.4 2.4 3.6 1.1 0.5 5.6 2.2 3.2 4.0 0.4 3.9 5.6 0.1 3.2 5.0 4.9 0.4 9.3 0.2 1.1 5.1 0.2 0.5 0.6 1.8 - 5.9 2.0 3.1 0.9 5.0 0.9 1.4 2.0 4.1 2.2 0.1 3.4 2.0 - 0.0 1.7 2.9 4.1 5.2 2.0. 2.5 3.4 2.4 0.9 2.9 2.5 4.6 2.7 1.6 1.0 3.9 0.9 0.0 0.5 0.0 5.7 1.1 0.1 2.6 0.9 1.0 6.3 0.2 0.1 1.5 4.4 4.5 3.9 0.9 0*1 1.0 2.5 5.8 3.1 3.1 4.8 1.6  r 0U5  1.0 3.2  7 8 9 10 -10 - 9 - 9 - 7 1 6 7 9 9 - 9 - 8 - 3 - 1 0  -  2.3 5.3 1.1 1.1 2.7 1.1  i  3 i  i  i i i i  1 t i t  ft  -  0.2 3.0 0.4 0.1  2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 3 3 3 5 5 3 5 3 3 3  9 -10 - 9 - 9 - 7 - 6 - 3 -  i  -  1 6 7 9 9 $ 7 6  . ft  - 1 1 2 3 4 3 _ 9 - 8 - 7 - 2 -  i  _ -  4 g 7 j 3 4  6  I  1 3 4 3 - 7 - 4 - 5 j 2 - 4 - 3 _ ^ _ t  3.4 2.1 1.3  3 4 •j  t  9  *  _ 9  0 0 0 0 1 1 1 1 1 1 l l l 2 2 2 2  6 7 9 9 9 9 7 6 3 1 2 3 7  _ _ j  6 6 & A 7 7 7 7 7 7 7 7 7 7 8 8 9 8 9 8 9 9 9 9 9 9 9 0 0 0 0 0 0 I  8  1 1 I  0.3 0.1  a 9 _ 9 - 9  _  T  , , » • • »  i.e  -  *  t  _ 9 - a _ j  - 6 _ 4 2  , 4 4 4 h 4  J_ 1 2 2 2  2  2' 2 2 2 3 3 3 3 3 3  2.6 3.0 0.0 3.0 0.0 3.4 0.0 5.1 3.1 4.5 3.7 0.0 0.0 4.2 0.0 0.0 2.9 3.1 3.4 3.4 0.0 0.0 0.0 6.5 0.0 0.0 4.8 3.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.9 5.7 4.0 0.0 3.1 0.0 0.0 0.0 0.0 0.0 5.1 4.9 4.0 0.0 2.5 3.4 0.0 0.0 0.0 0.0 0.0 0.0 4.8 4.5 4.5 5.1 0.0 0.0 0.0 0.0 0.0 0.0 5.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.0 0.0 0.0 0.0 0.0 0.0 3.1 4.2 2.5 2,8 ft.7 0.0 0.0 0.0 6.2 ft.9 0.0 4.6 2,6 3.1 0.0 0.0 0.0 0.0 4.0 ft.l 0.0  -  -  • -  -  • -  -  . -  -  3.7 3.3 4.0 3.1 0.8 1.7 1.9 3.6 1.8 2.9 3.3 0.3 0.8 4,6 2.0 0.4 1.7 0.6 2.2 1.4 2.7 3.3 0.2 6.4 0.9 0.4 3.1 6.4 1.3 0.2 2.6 0.6 2.0 0.7 2.2 0.9 1.3 4.6 4.9 2.9 0.7 2.6 2.2 0.7 0.1 0.3, 0.4 3.3 3.0 1.0 1.4 4.1 0.6 0.0 1.9 4.9 0.4 0.7 1.6 3.6 2.6 0.6 2.7 0.8 3.0 1.4 1.0 2.3 0.5 3.0 4.1 0.9 0.5 1.5 0.6 0.5 0.9 1.3 2.0 0.6 0.5 6.3 3.7 1.1 0.4 0.5 3.3 0.4 3.6 o.9 0.8 0.8 1.3 1.3 0.1 0.9 2.4 4.1 0.9 3.2 3.0 1.0 0.9 3.2 6.1 1.0 6.2 1.9 1.2 2.2 1.9 3.5 1.2 3.9 5.8 O.ft  4 5 - 9 - a - 6 - 5 - 1 ft 6 7 6 - 9 - 8 - 7 - 6 - 5 - 4 - 2 0 1 4 2 3 6 7 • - 8 - 7 - 4 - 3 - 2 - 1 0 1 4 ft 6 - 7 ft - 4 - 1 4 - 6 ft - 2 1 4 2 3 - 3 - 2 • 1 2 4 ft 6 9 - 9 - 6 - 7 ft - 2 0 1 9 4 9 7 6 9 - 9 - 7 - 6 - 4 - 3 - 2 3 ft 4 5 6 7 - 9 - 7 - 6 - 5 1 5 2 3 4 9 8 - 9 - 7 - 6 ft - 3 -  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 f  3 3 4 4 4 4 4 4 4 4 4 ft ft ft 5 5 ft ft 5  t 4 f t 5 4 f t 4 ft 4 6 4 6 4 6 4 6 4 6 4 6 4 6 6 4 6 4 6 4 7 4 7 4' 7 4 7 4 7 4 8 4 8 4 8 8 4 9 4 8 4 9 4 9 4 9 ft 0 ft 0 ft 0 9 0 ft 0 9 1 5 1 ft 1 5 1 9 1 ft 1 1 ft 1 ft 1 ft 1 5 1 5 1 ft 2 9 2 9 2 9 2 ft 2 ft 2 • 2 ft 2 9 2 9 2 5 2 5 3 .9 3 5 3 9 3 3 ft 3 5 3 3 3 9 3 ft 3 9 4 9 4 ft 4 ft 4 5 4 4  1 5 1 5 2 ft 1 ft 4 5 ft 9 6 ft 7 9 - 6 5 - T 5 - 6 5 ft 9 - 4 9 - 3 6 - 2 ft -1 5 1 5 2 ft 3 9 4 ft 9 9 6 5 - T 9 - 4 ft  4 4 4 4 4 4 4 4 9 ft' J ft ft 9 ft ft 9 9 9 5 9 9 6 *  4.0 5.9 0.0 0.0 3.7 4.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.1 4.2 4.3 4.9 4.2 0.0 9. 1 0.0 0.0 5.9 0.0 9.4 0.0 0.0 9.4 0.0 2.6 3.1 0.0 - 0.0  o.o  0.0 0.0 0.0 0.0 0.0 0.0 9.4 0.0 CO 5.1 0.0 0.0 6.2 3.1 0.0 0.0 0.0 0.0 0.0 4.0 4.5 4.0 4.5 2.9 4.2 9.4 4.9 CO 0.0 0.0 9.T ft.7 4.0  4.2 CO 4.2 0.0 0.0 2.0 0.0 9.4 0.0 0.0 0.0 4.ft 2.5 CO 0.0 2.8 0.0 0,0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 4.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 CO 4.0 4.8 2.6  2.6 9.4 0.0 4.2 0.0 ft.l 0.0 4.5 4.5 0.0  f C»LC 4.7 6.6 0.1 1.3  -  - 0.9 2.6  1*3 3.7 3.3 0*6 0.9 0.1 3.1 0.3 2.5 1.3 3.6 4.3 J.T 0.9 1.2 1.6 2.6 6.S 3.4 2.9 0.2 0.2 5.1 1.6 1.6 3.9 3.4 2.1 3.3 0.1  -  -  8'* 5.2  2.0 1.9 2.5 2.9 0.7 2.5 ft.7 2.4 0.3 3.1 2.T 1.0 1.6 O.ft 0.0 - 0.3 0.1 4.0 2.9 4.6 2.5 4.9 2.9 2.6 1.1 2.6 0.9 2.9 2.0 4.9 4*6 0.0 2.6 3.3 1.2 O.ft 2.9 2.6 9.7 3.9 0.2 3.2 1.7 - 0.3 0,2 2.4 4.0 9.6 0.4 1.5 0.2 0.7 1.0 1.9 0.2 0.0 - 3.9  -  1.6  • -  -  0.9 0.6 1.0 0.0 2.9 0.0 1.1 1.0 2.6 2.5 0.9 2.6 1.5 3.9 0.2 2.1 1.6 6.4 4.0 1.9  92 TABLE A l .  H  K  L  - 2 - 1  6 6 6 6  •4 4 4 4 4 4 4 4 9 3 9 3 3 3 3 3 5 3 5 3 6 6  2 9  *  3 6 - 7 - 6 - 3  -*  - 3 - 2 - 1 0 2 3  *  3 - 7 - 6  - * - 3 - 2 - 1 0 •  4 3 2 2  2 3 4 9 6 7 • 8 - 7 - 3  - x 1 2 3  ft  7 - 8 — 4 • 3 9 6 7 - 7  -- *ft - 3 1  ft ft ft ft 6  6 6 6  ft ft ft ft ft 6 ft 6 ft ft 6 ft 6 ft 6 ft ft ft ft ft 7 ft 7 ft 7 ft ft 60 7  7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3  F 085 2 .8 2 8 4 2 0 *0 0 .0 0• 0 0• 0 0 .0 0 0 0 .0 0 0 0 0 5 4 3 1 0 0 3 7 0 0 0 0 0 0 0 0 0 0 7 1 0 0 0 0 0 0 0 0 0 0 »0 07 0 0 0 0 9 T 9 4 2 8 3 7 0 0 0 0 0 0 0 0 0 0 0 0 2 8 4 0 3 4 0 0 0 0 9 7 0 0 0 0 0 0 4 5 3 1 5 9 0 0 0 0 A 2 0 0 0 0 0 0 0 0  (Continued).  F CALC _  •  -  --  ---  ---  -  --  -  1.1 0.) 3.0 3.3 1.9 0.0 1.3 1.7 0.7 2.0 0.8 9.3 3.2 3.3 2.1 2.2 3.7 0.0 3.ft 2.9 1.2 9.9 3.8 0.6 0.9 0.1 4.9 2.4 0.4 1.6 1.6 4.9 4.1 1.6 2.8 1.2 9.4 7.3 0.2 0.4 0.4 1.3 1.5 1.1 0.7 0.0 3.8 O.ft 0.1 1.0 ft.4 0.4 2.9 0.4 2.9 3.8 O.T 4.« 0.3 1.1  H  K  j 3 1 j 4  T  3 _ •» - 6 - 3  _ i  _ j _ 2  . x  j 2 3 4 3 - 6 . 3 . 4  . i  - 2 _ |  2 3 4 - 3 * 4 - 2  . 1 o - 3 _ j  1 3 4 3 0 _ 4 - 1 I  2 3  (  . 3 - 4 . 3  _ 2 1 4 3 6  - ft  - 3 - 2  F OBS _ F CALC  L  7 y j  7 7 7 j  7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0  4 4 4 4 4 4 3 3 3 3 3 3 9 3 3 3 3 0 0  ft ft 7  0  ft Q  g 0 5 §  0 0 0 0  7 7 g 0 0 0 0 I  j 1  0  * i 2 2 2 2  8 6 6 8 6 8 8 8  2 2 2 2 2 3 3 3  0.0 0.0 0.0 0.0 0.0 4.2 4.8 0.0 3.1 4.8 9.9 0*0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.1 0.0 0*0 0.0 0.0 0.0 ft.2 0.0 9.9  o.o  0.0 0.0 0.0 6.2 6.8 0.0 0.0 0.0 0.0 0.0 4.8 3.4 0.0 0.0 0.0 0.0 0.0 3.4 4.8 3.1 0.0 0.0 4.3 0.0 5.1 0.0 0.0 0.0 3.7 0.0  _ _  --  ---  0.0 ' 0.7 4.2 0.3 1.9 4.1 1.8 0.1 2.5 1.9 3.3 1.4 0.7 2.3 1.0 1.9 2.2 0.4 1.8 2.2 5.4 0.2 1.1 1.3 4.1 1.6 4.6 2.2 6.1 3.0 0.1 0.3 6.0 4.8 3.6 3.0 6.3 1.0 2.3 4.4 3.1 2*7 0.7 2.3 1.2 1.3 4.3 4.4 3.2 2.3 O.ft 1.9 3.2 3.6 4.3 0.2 2.0 0.8 3.0 1.1  H  K  0  0 8 6 0 8 0 0 0 0 0 0 | 0 0 0 9 0 0 0 9 0 0 0 0 0 0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 V 9 9 9 9 9 9 9 9  -*  -  • •  0 1  9 10 10 10 10 10 10 10  L 3 9 3 9 4 4 4 4 4 4 4 4 4 3 9 9 5 3 5 9 3 3 4  ft 0 0  ft 1 1 ]  1 1 1 1 2 2 2 2 2 2 3' 3 3 3 3 4 4 4 9 0 0 0 1 1 2 2  F CALC  F OBS O.O 0.0 0*0 0.0 4.9 0.0 0.0 0*0 0.0 0.0 0.0 0.0 0.0 6.6 0.0 6.6 6.3 0.0 0.0 0.0 0.0 0.0 0.0 6.2 0.0 0.0 3.7 0.0 0.0 0.0 0.0 4.0 0.0 0.0 0.0 0.0 0*0 0.0 0*0 0.0 0.0 0.0 0.0 0.0 6.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.2 0.0 0*0 0.0 0*0 0.0 6*8 0.0  -•  -•  -  --  -----  -  1.2 0*1 0.0 9.4 7.0 2.9 2.0 0.3 2.9 2.6 1.0 2.6 3.2 7.0 0.2 9.2 9.0 4.6 1.9 0.7 1.4 0.1 1.1 7.3 4.7 0.0 0.9 O.O 1.0 0.9 2.9 1.1 0.9 3.9 6.1 2.1 6.1 0.2 1.8 2.3 2.2 2.4 1.6 0.0 3.5 0.9 1.9 2.5 1.1 4.9 2.1 6.9 9.2 1.8 2.1 3.1 2.4 2.8 4.9 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 r e f i n e m e n t a r e l i s t e d •first. Unobserved r e f l e c t i o n s , f o r which F i s l i s t e d as 0.0. have t h r e s h o l d v a l u e s i n the range Q  1.5-3-0). K  plones included <  e 0 0 0 0 0 fl 0 n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  F OflS  1 0 0 0 0 1  1  1  1 1 t 1 1 7  7 7 7 7 7 9 9 9 9 9 7  1  9  *  4 4 4 4 4 4, 9  4 4 5  4 4 9  A  ft" f*LC  7.4 6,9 44.4 44.1 4,1 - " 1.0 *.4 4.7 74,1 40,9 - *.7 '4.4 14.• 4A.2 40.2 77,1 TA.2 T.A 6.A 70, 4 - 71,4 74,7 25.1 4,1 7,5 19,9 14.0 14,1 1ft,A 4.4 - 7.4 14.1 14.1 47,4 - 4ft. 1 11.* - 14,1 11.9 - 19.5 74.0 77.5 14.7 - 14,3 ft.l 7,1 4.1 IT,*, 16,7 4.4 - 7,9 4.1 - 1.7 1 y. A 11.0 7.* •.0 70,» ?o.i 1A,4 19,0 10.1 - 10,3 4.T 9.0 4.0 - 7.5 14.0 - 15.4 1*6 7.0 19.A 19. A 6.4 7.4 1.4 1,7 4.0 - 7.7 17.2 11.3 1.7 A.A 14.0 - 17.9 7.9 T.6 4.9 - 4.9 9. A - T.5 6.4 6.4 4.6 - 4.9 14,0 17.4 11.4 7.9 1«.4 71.4 ft.l - 7.A 14,9 77.4 T.A 6.7 9.1 5.0 4.6 40.A 45.6 44,2 51.4 74.0 - 26.9 11.9 - 9,5 9.4 A.? 9.0 - 7.A 1.7 2,0 4.7 4.0 4.9 - 4.A 10.9 10.4 10.) 9.0 15.4 - 16.4 7T.0 711.2 2.9 - 7.0 17.7 - 16.2 73.0 - 79.0' 11.9 - 10.7 47.6 91.2 14.4 17.9 1*.7 - 1?.A 20.0 - 10.1 4.1 1.9 4.7 4.4 1.6 7.8 7.3 - 7.1 6.8 6.9 9.6 1.2 10.9 11.7 7.9 fl.T- 5.A A.ft - 4,? 4.2 1.4 1.7 19,| 14.4 14.A 11.A 12.6 - 11.7 9.4 11.3 6.0 5.2 4.4 1.7 17.1 17.2 U.I - 17.4 0.1 9.1 17.4 1«.7 7.A 5.7 4.ft - 14,1 14.4 74.4 21*6 12.2 - 17.7 4.7 1.A 6.7 - 7.A 9.1 - 4,7 7.1 5.1  ft.*  ft  A A T T J A  9 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1  1 t  ]  1 1 1 1 1 1 1 1 1 t 1 t  7 f 7 7 7 7  2 J 9 } 9 7 9 7 9 9 9 J 9 9 7  ft.4  ft.7  17 •1 - 7 - 4 - 7 - 1  1  5  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  *  -  4 7 A 4 4 4 7  • 1 7 1 4 -11 -10 • 9 • A  - 1  -- 4* 1 1  A  -14 -17 -11 1 1 4 6 - 1 * 2 - 1 1 1 — 1 - 7 1 2 9 4 9 A  15 -10 - A  — -  7 A 1 4 1  — 7  - 1 1 2 1 5 A  •  1© 11 11 14 19 — 17 -11 -10 - A  - 6 -  1  1 1 1 1  •1  * 4 * •  F  1  5  - 4 - 1 — 7  1 4 4 6 T 9 10 IT -17 -11 - 1! - 7 - 4 - 4 - 1 - 2 - 1  )  1 1 1 1 1 1 1 • 1 1 1 1 1 1 1 1 I ]  1 1 1 1  7  2 7 2 2 2 2 2 7 9 7 9 9  2 2 2 2 2 2 2 2 7 2 7 2 2 2 2 2 2 2 2 2 7 7  7 2 2 7 2 2 2 2 7  7 7 7 7 7 2 2 7 2 2 2  A  9. 7 7 7 9  ft  7 2  7  1 1  9  > 1 4 1 *  Li J J 4, ti 4,4  4,4 4.1 l.A 7,4 77,1 71,7 - M.4 74,1 11,2 17. 0 ft. 7 9,7 1 4,4 - 4,1 7.4 7.3 1 15,0 46.1 1 77,9 70. A 1 - 9.1 9, 1 1 11.4 17.4 1 4,7 - 7,4 4 4*9 1.* 4 11.4 - 14.A 4 ?fl,4 - 71.4 4 10,1 - 10,7 4 10,4 14.0 4' 15.T - 17,2 4 4.0 I,} 4 7.9 - 7,2 4 ft.l 9,1 4.7 4,4 4 4 9.4 1,7 4 17,1 11,8 4 4,4 - 1,» 4 4.7 - 6.1 1 - 14. 9 n.4 - 4,4 4 10,4 4 T. A - 9,5 9 4.1 1,4 5 4.7 4.0 5 - 1,4 4.1 5 1.7 - 4,4 5 5.1 - 6,4 A 4.4 - 0.9 A 7.A - 7.0 A 4.A 6,7 A 6,7 - 7.1 A 14,1 1ft.ft A 6,A - 9.7 6 5.4 4,4 4.A - 6,7 A 4,5 - 2,5 7 7 12.6 - 13.a 7 - 6,1 5.1 11.0 - 17.4 7 7 14,9 17,9 7 4,4 - 6,1 0 T.4 - 7.7 A - 0,1 7.4 0 41.1 47,7 0 170,4 -177.9 17,4 14.9 0 0 2,11 1.0 0 6.7 - 8.3 0 - 17.7 19.0 5.4 0 A.0 1 • 4.4 5.1 \ - 4.A 4.7 1 17.4 11,4 1 17.0 - «,A 1 10.7 11.1 1 75.6 - 74,ft 91,fl 1 -105,0 1 109.1 -106,7 T.I 1 - 10.T . 14.6 - 11,7 1 1 1ft.1 16.A 1 4,7 - 5.5 1 9.1 - 4,1 7,4 7,7 1 1 4.A - 4,4 O.O 1 4.0 7.A - 7.4 1 1 4,7 9.0 1 4,ft - 7,0 5.0 4.0 1 7 7.4 - 4.1 7 4.7 - 7.9 7 6.2 - 9,4 7 5.4 *• A.9 7 - 4.7 5.1 7 • - 1.7 1.1 4.0 - 10.A 7 4.« - 4,1 ? 7 7.A 4.A 7 A,A 0.9 7. 7.1 ft.l 9 4.4 A.l 2 9.4 4.3 2 22.A - 72.9 2 5.7 6.8 7 17,5 - 70,1 7 19.7 - 71 .7 9 4.6 A.? 1 4,9 - 4.1 1 4,f< - 4,7 1 4.4 4.1 1 "a 7' - 7.4 1 " A.7 4.9 1 11.4 14.0 1 - 7,0 4.7 1 11.7 10.7 1 15.3 14,4 77.0 - 71.9 * 1 0.1 - 11.4 . - »A,* 1 1A.4 * 4.7 4,1 1 4.1 4.1 1 4,1 - 4,4 4.4 - 1,A 1 6,4 6.4  1 4 4 -17 -10 - 9 -  9  0  A A  7  1 4 5 - 7 - 1 2 1 A  -  7 | 7  A ' A  6 7 7 7 7 A A A  - 1  1 4 %  m 7  - A a 4.  _ 4 * 1  - | - 1 I 7  4 9  8 9 10 11 -H -11 -10 _ y  - A _ 9 _ 4  . 4 _ j I 7 .  N  10 •j -12 -11 _ j _ ^  „ 4 „  A  _ j I  2  4 4 4 y  9 -10 — 9 _ 0 _ y  „ 4 - 7  _ 1 y  -104 - 9 _ H » 7 _ •  4  2  4  *,  * 1 - 1 _  7  A  - 4 _  4  4 4 4 4 4 4 4  4 A 4 4 A  4  -  y  4 4 4 9  - 1 4 4, ' — 14 -TO - 9  n  F yn.- .  1  10 - 9 • 7 - 4 -•1 - 1  0 0 0 0 0 J 1 1 1 1 I 1 1 1 1 f I 1 1 1 1 7  7 7 7 2 2 2 2 7 7 j y 2 2 2 7  7 1 4 1 4 4 4 4. 4 1 4 4 1 4. 4 1 4 4 4 4 44 4 4 4 4 4 9  4 % 4 4 4 4 4 f, f, 4 ft  7  y  7 4 4 4  4,7 7.A 4,1 4.1  1 A. A 4.A I 14.4 4.7 1.9 7.1 4.1 11.0 17.4 7.A 4.4 6.4 4,6 T.4 4.«» A. 7 "•1 1ft.1 10,4 4.7 11.1 19.0 ••7 4.A A, 7 A, A  1,7 R.A 4.4 - 4 .A - 1*,* A.'  1  - 1«,4 -  7},t 4.1  4.^ - A.l 4.0 - 11.1 10.4 - R.R - 4.1 - 7,7 6,4 - 5,1 - 4.4 4*4 - 0,R 70.7 - 10.4 4.7 - 15.5 - 11.9 - It.A ».7 6.4 - T.4 O.O - 17.A - 17.9 17.4 10, A 14,7 74.4 27.ft 14,4 19.2 7.0 4.2 - 11.7 10.9 14.3 11.ft 46.1 44.1 - *.A 4.4 - 77.9 75.4 11.A - *«,() 9,9 4.1 - 0.9 7.A 17.7 11.4 9.7 - 4.9 5.0 5.1 7.9 9,4 6*7 - 9.9 11.5 10.7 - 9,5 10.7 - 0,0 A.9 4.7 - 4,7 ft,l - 7.1 - 4.4 4.1 4,7 1.4 1ft.4 1ft.ft 17.4 17.0 1.3 1,1 - 6.3 1,9 6.4 6,0 - 4.4 2.ft 9.4 10.2 4.1 - 4.1 4.7 - 4.1 14,0 11.7 - 4,4 7.4 14.1 - 15.9 5.9 4.4 - 5.1 5.6 - 4.7 5.6 - 2.7 1.4 4.8' - 4.9 - 7.9 9.0 9.1 4.A - 10.1 74.1 1«.A 74.0 76,11 - 74.0 19.4 - 19.4 - 5.4 5.4 5.0 - 4,ft 1.A 9.6 10.1 ft.l 7.9 - 6.5 6.7 4.0 - 11.1 10.9 17.7 10.4 4.7 5.1 4.4 - 6.0 14.7 17.4 14.7 17.A - R.O R.N - ?0,o 1>4.4 - 7.3 6.0 - 4.9 5.7 12.9 17.1 - 11.7 10.1 11.ft 14.1 17.4 11.• 1.4 l.ft 4.0 A.7 - 4.A 9.0 4,1 4.7 0,0 ft.l 11.ft - 14.4 14,1 10.7 A.R 11.ft 4.4 6.4 - 4,0 4.4 4.R 5.0 4.4 4,1 7. ^ 7.A 6.R  7 4  4 ' 4  . . . .  R A q 4 1 7  _ 1 *  4 4 0  9 -14 • 9 . 7 _ 4 - 4 - 4 _ 2  7  1 4 7 0  9 *li _ 4 - 4 - 7 . | 1 2  0  7  ft  - 9  - A7ft — -  7 1 1 1 0 7  — 6 -  3 7  5 A - 1 7 4 - 5 — 4 t 7 1 4 A -11 —10 - 9 - 7 - 6 - 5 - 4 - 4 1 7 - 9  - ft - 7 - A - 4 1 7 1 7  ft - A7ft  • —  7 1  1 7 1 4 y  ft  - Aft -  -  f  u  A  -  7  4 7 1 4  - ft - 7 - 9  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 A  4 4 A  4 5 5 5 5 5 5 4 4 9 5 5 5 5 5 5 5 5 5 4 4 4 4 5 4 5 4 4 4 4 1 4 4 4 5 9 9 4 4 5 4 4 4 4 4 5 4 4 4 4 4  -  •>  3 0  r)  | • * y  1  1 | | |  7 2 7 7 7 7 7 7 7 7 7 7 2 7  4 4  4, 4 4 1 1 1 1 4 4 4 4 4 4 4 4 9 % 9 A  9 4 9 6 6 6 0 0  0 0 0 0 0 1 1 1 1 1 1 1 1 1 I 1 1 7 7 7 7  7 9  7 7 2  ?  1 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 . 1 5 4  aai. 1*.4 14.0 4,7 17.1 70,1 10.9 4,7 1 4*4 14,7 44,4 4,0 7,4 1A*A 7.7 A*4 11.4 9*6 5.1 4.4  t- CALL  . I*,7 - *,7 17,7 «0,7 ft.9 4,4 17,ft 11.ft AO 0 4,7 - 7.7 1A*ft 9,1 - 5.5 1*.4 - 10*0 7*8 - 5*t 6*A **• 4.4 4*4 4.7 4,7 77.• 74, ft 111,4 47,7 4*4 4,ft 4.A 4.7 - 9.0 11,4 ft.7 ft.l - 17,4 14.1 4,9 6.8 4.0 ft.G 25.A 74. ft 4.4 1.0 4.A 9.1 - 4.4 A.4 - 4.1 4.P 4.4 . «.« 11.0 11.2 7.0 - 7.9 - 9.3 9.5 S.7 ft.l 9.ft 11.4 14.7 71.6 10*7 ft.2 5,9 4*7 1.9 4*2 17.7 - 70.3 16,4 11.ft 4.4 10,2 14.4 77,0 6,0 - 6.2 4.7 4*5 11.4 11*6 6,0 - 4.7 7.6 4.4 5,7 4.5 9.0 .0.0 9,9 - 10.1 11.4 11,6 4.0 - 4.4 4.2 - 1.1 6,8 7.2 3,0 4.0 12.11 11.2 19,0 - 19.4 15.1 - 17.0 7,4 - 6.1 9.5 ft.7 6.5 - 5.5 4.7 4.6 6.0 - 6.4 4,0 1.7 9,0 - 9.7 4.0 - 1.9 16.4 16.8 13.2 12.9 5.4 - 4.1 9,3 - 10.2 19,3 - 14.5 4.1 - 4.6 5,4 1.4 4.4 - 7.5 1A.1 - 14.ft 16.7 - 14.3 9,0 4,4 11.9 10.7 9.1 9.9 lft.3 - 17.0 14.7 14.6 7.1 1.4 9.1 9.A 7.ft - 5.0 A.0 1.1 ft.4 - 7.0 4,1 - 6.0 1*9 4.1 1.4 4.0 11.0 19.0 11.1 - 11.ft 7.6 7.1 R.2 - 10.1 10.4 11.0 6.4 6.7 6.0 - 4.6 17.4 19.1 14.0 - 14,4 7 4.0 4.0 4.1 12.7 11.3 4.4 - 4.4 A.7 - 4.4 ft.7 9,7 4.0 - 1.1 7.9 ft,4 a  9k TABLE A2.  <•  L  9  ft ft ft  F 0»1  ft* ft ft.7 ».l  ft ft ft ft  0 0 0 0 1 1 1 1 1  ft ft  1 i  ft  7 7  17.7 79.0  > 7 7 7 > 7 7 7  l .0.0 ft ft.l 4.1 l.T ft.l «.ft a.ft T.4  ft ft  ft ft ft  ft ft * ft ft ft ft  1ft.0 1«.It ft.l  ft. ft.l ft  a.T 10.} T.l T.l  9.9 n.»  1  •  C4LC  -  l.ft T.O 11." ift.o l.T 4.7 1.1 6.1 a.i ft.T 6.0  -  11.1  ft.n - Ift.l - 71.1 T.a i ,a  - ft.ft  a.l J.1 - l.ft -  ft.ft 6.1 1.1  ft i ft.ft - ft.ft ft ii ft.* ft »  ft * » »  ft ft ft » »  l  ?.» in.)  -  - 11.T 10.T 17.9 I i . • ft.4 - l.ft 10.T - 11.9 lT.a - ia.< - lO.ft ft1 ft.10.1 5 - «.t ft lft.ft 11.a ft 1S.» - i«.a • ft.l - ft.T 1.0 ft 10.T - in.« - ft.i ft T.ft - ft.n ft ft ft.T » ft.ft - ».a a.ft ft.T 1 1 9 1  ».ft  ft ft  ft ft  « T  »  o 0 o  T T T T 9 9  1  1 i 1 1 i i 1 l 1 J  y »  9 T 7 7 T 7 T 9 9 T 9 T 9 » 9 T T T T T T T T T T ft a a ft a a a a « a a a a a a • a « «  ft  4.7  7  7 7 7 7 7 7 1  i 9 9 9 9 1  9 » « 4  ft ft ft 0 i i 1 t 7  1.* 1.6 ft.T ft.ft «.a T.l 11.ft ».» %.» ».» 7.a ft.l ft.8 ft.T ft.9 ft.a  9.9  ft.a in.» 9.9 9.9  a.l |0.1 1 l.T ft.O ft.l 10.1 1.1 10.1 a.ft l.ft 1.1  A.a 1.0  7 •• ' 7 1  -  *.a l.ft a.l  «.« t»,« .A.7 ft.ft ft.7  1.1  l.ft - ft.l T.n 11.1 T.l - ft.l ft.T - ft.l 1.8  l.ft 1.1  - ft.* l.ft  l.ft - ft.T 9*7 T.T l.ft ft.T - ft.l lft.ft  - ft.ft 1.9 -  - ii.n - t.ft - 17.0 -  ft.ft  l.ft 9.1  ft.ft 4.11 7.4  1.1  ft.o 12.7  > 9.1 7 in.? 7 ft.T » ii.7 i ».« i a, 7 i l i . i i IO.I i 4.1 ft ft.T * i.» i ».» l i . i  ft » 10 10  -- lft.ft .ft  7.ft 11.7 1.9 4.0 l.ft «.9 4.1  - ft.ft T.l  - ft.l 11.1 - a.ft ft.n - l.ft -  -  ft.ft  L 0 0 0 n  t OftS n »  fl.n ».n 1,1  i  i.n  ft a  10 -17 -17 -10 - a 1n -17 - a n  ft a  - a  ft  6 a -10 - a  - ft ft -1?ft - * - 7  - a • 6  - ft ft  -iftf 10 11 17 1ft -17 — 11 -10  ft ft  11 -17 —  1  ft  -11  — 11  - ft — ft  - ft  - ft — ft  T a 10 -17 — 11 -10 — 9 — a i  ft  a 9 a 4 -1* — a — T - 7 - 1 7 * 1  ft T  -10 - 4 - a - T  - ft 1 — ft 1  — 7 - 1 7  —  ft •  - T  ft.ft -- ft T.T ».l - 7ft ft  4.1  -  ft.l ft.n  -  4.4  ft  - ft n T  •  dories omitted K  *  ti -17 -in  in 11 17  t rn\.c -  7.1 ».7 n.ft *,n  -I?  *  L 0 o 0 o. o 0 0 o 0 0 o o o 0 n 0 0 0 0 0 n 0 0 n 0 0 0 0 0 0 0 0  ft 1 i i i  \  i i i 1 l 1 j i i i l l i 7 i i i t i l l i l i i i l l t i i i i i i i i i i i i i i i t i i i i i t i i i l i i i i i i 7 7 7  I 7 7  \ \  1 1 1 1 I » 4 4  i * 4 * 4 4 4 * . 4 4 4 4 0 A 4 A 4 4 A 7 7 7 T T 4 0 0 0 1 0 P 1 1 1 1 1 1 1 7 7 7 1 4 9 4 4 1 9 ^ 4 9 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 A A A A 6 & A 6 A A A T T T T T T T 4 A ^ " ? 0 " 1 1 . 1 1 1 1  ' f ft)l>»  LAi,<.  7,2 1.4 l.A l.A 1,7 W» 1,9 1,7 o.o  l. >«7 0,1 0,4 0,0 0,4 0,7 1.0 1,4 1.1 0,1  7,4  0," 7,4 l.o o.o l.t 2,0 1.4 0,0 7,4 2*1 1.0 0,0 7,4 7,6 7,A 7.7 7.A 1.7 2.1 1.2 2.9 2.4 7.4 1.9 7.7 l.T 7.7 1.4 4,7 1.2 l.T 2*6 1*4 2.8 2.2 9.4 2.6 O.A 2.1 !•* 2.8 2.9 0.0 0,0 1.7 O.A 1.6 l.T 1.9 0.0 2.6 l.T 9.1 2.4 l.T 1.1 7.4 0,0 0,0 7.4 9.9 l.T 7.9 0.0 7.4 1.9 0,0 l.T 9.1 9,A 1,4 1.1 1.7 7.4 l.T 0.0 2.6 0,0 0.0 l,o 1,1 0,0 n.o 0,0 0.0 1.1 0,0 2,4 2.0 1.1 1.7 O.A 3.4 7.7 7.o 1.A 7.1 4,7 0,0 1.7 ",o 1,4 *.1  n  -  -  -  at  -  -  -• -  % T  ,4 0,7 l.» l.T 6.A 0,1 l.T LA 0.1 1,4 0.4 7.7 4.1 t.4 1.4 l.T O.A 7.A 4.9 4,4 7.2 0,0 «.9 1.A 1.0 0,0 7.9 0.4 1.1 0.8 1.6 1.8 7.9 1*4 1.1 1.4 l.A 1.* 1.6 7.9 1*9 7,1 7.A 0.9 fl.T *>* 1.7 O.A O.A 2.9 1.2 0.4 1*0 7.4 1.5 O.A 0.4 4.A 7.1 O.T 0.4 0.1 9.7 1.4 0.1 7,r 4.A 6.4 0.1 0.4 1.4 1.4 O.T 0,1 1,4 0.1 O.A 4,4 4,7 1 .A O.A 7,« 7.0 4,1 1,4 0,4 0.1 7.A «.l 0.9 7.4 !.C %4 4.1 1.4 0.1 9.1 n  ft. • -  • —  —  -  — —  -  —  -  —  —  -  •  -  -  m  m  0.4 0,1 o.A o,7 4,4  (Continued).  rt I, 17 - 9 •» 7 - 1 7 1 8 -to - 9 -  A 4  7 -1 1 -10 •> A -  A 4  - 7 1 6 7 A 9 -11 - A - T - 4 - 1 - 7 9> 1  |  7 1 A 9 A -19 - A - 7 - A *» 9  - 4 - 9 - 7 -  j  — > •> -  A j A 9 A  *  *  9  ft  A A T A 9 10 11 17 — 19 -17 — 11 -10 — tt — A 1 A T -17 - 9 - A 2 9 A A 9 -14 -10 - 9 - A - 1 - 7 A A 10 -11 - A - 4 - 9 1 A A 7 A 9 -11. - A - 4 a 4 — 7 - 1 0 4-  7 1 4 T — 9 - A  I  K 7 7 7 2 2 2 2 7 7 7 7 7 7 7 7 7 7 7 2 2 7 7 > 7  1 1 7 9 » 7 7 7 i i 1 *, * 4 '4  7 7 7< 7 7 7 7 7 7 7 7 7 7 7 2 7 2 2 2 7 7 7 7 7 7 2 7 7 2 2 7 2 7 4 1 9 9 9 1 4  4  ?  9  9 9 4 4  9 4 4 1  9 1 9 4 9 1 4 1 1 4  1 1 4  . 1 4 3 9 1 1 9 1 1 1 1 1 9 1 1 1 4 4  9 1 1 * 9 1 9 1 1 4  4 4  4 4 4  4 4  4 4 4  4 4 4 4 », 4  4 4 4 i A 4 A A 6 6 6 6 A A A A A A T T T 7 7 T 7 A 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 7 7 7 2 7 7 7 7 « 1 1 1 1 1 9 1 1 4 4 4 4 4  A A 4  4 A 4  A 4 4  4 '  4 4  4 4 4 4 4 A  A  f Ob*  F CALC  1.4  O.T 0.4 7.4 0.1 1.1 4.7 O.T  4,4  7.A 1.1 0.0 2.4 o.o 7.4 0,0 1.1 o.o 7.0 l.T 1.4 7.7 7.1 1.4 1.4 l.A 1.1 0,0 l.T 7.1 1.4 7.9 7.9 4.6 0,0 0.0 0.0 0,0 7.4 4.1 0.0 0,0 1.7 7.4 7.• 4.7 7.6  1.4 1.2 2.9 2.4 0,0 7.0 1.1 l.T 7.0 7.4 7.4 2.4 2.4 1.9 7.6 7.A 4.4 4.1 1.4 7." 7.9 2,9 7.A 7.9 0.0 4.9 7.1 7.4 7.A 7.1 l.A 1.7 7.A 7.A 1.4 7.A 4.4 7.9 7.6 7.9 1.4 4.4 4.9 0,0 ".0 4.4 7.4 1*6 2.4 4.1 7.A 0,0 0.0 1.1 o.O t.4 0,0 7.7 7.7 7.6 7.0 9.7 l.T 4.1 1,4 0,0 0,0 7.4 7.C l.T l.A 7.2 1.9 1.1 I.**  -  m  - 7.0 - 0.4 1.7 _ _  4*  •  -  ft*  o.l 1.4 0.0 0,0 1.1 9.4 1.4 0.4 l.T l.A O.A 1.4 1.4 1.4 1.1 7.1 9.0 1.4 0,8 0.1 1.1 l.T 1.1 0.7 • 1.7 0.4 1.7 4.0 4.4 1.4 1.0 0.7 l.o 7.4 0.7 0.4' 7aA 0.4 l.T 1.0 O.O 1.1 4.4  -ft.  ft. ft*  — •  -  ft.4  7.A ft.l 1.7 T.7 1.7 l.A 7.4 O.A 0.4 ?.A 1.0 l.T 1.0 7.T 7.1 7.T 0.7 O.A 4.1 4.0 7.1 7.0 7.1 2.4 7.A 1.1 0.9 0.1 4.7 0.4 7.4 9.4 l.o 7.7 7.4 0.1 1.4 «»0 4.4 7.4 0.1 1.4 7." 0.4 7.7 7.1 1.1 7*4 4.1 4.'1.4  ft. •>  -  ft. -  • »  --  -  4» •>  •  » —  -  -m -  O.A  -  •  t.4 4.1 o.l 1*1 4.4 1.4 1*7 1*A, 4.7  1 • • -  T A A A 1 7 1  *  6 5 A 2  * 1 - 7 - A  -11 *10 -  0  - T  4»1 J -10 •> A  m *• 1 % -14 -11 • 10 _ 9 - A • 7 • A •» A  -10 *» 9 a A •  — — -  1  4 9 4 1  - A - T - A -  9  - 4 — 7  - |  — -  4 1 7 1  4 — 9  I 1 1 1 1 4 4  9 1 1 1 1 1 1 1 1 9 9 4 A 4 4 4 4 4 6  4 4 4 4 A 4 4 A 4 A 4 4 A 4 A 4 A 4 4 4 4 A 4 A 4 4 A 4 4 4 4  4 4 4  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  4 4 A 4 4 4 4 4 A 4 4 4 4 4 4 4 4  - A - 7 o 1  4 A 4 4 4 9  4 A A 4 4 A 4 4 9 4  4 A 4  f Ubh A A A A A A A A 7 7 T 7 7 T A A 9 0 0 0 0 0 0 1 1 1 1 1 1 1 \ 1 t 7 7 2 7 7 2 7 2 2 i % 1 i 9 4 4 1 4 4 i 43 4 4  4 4 4 4  4 4 4  4 4 A 9 A 4 4 4 A 4 A A 6 A A A A A A A 6 T T T T f A 9 0  0^ 0 f 1 1 1 1 1 )  t 1 1 i ? 7 7 1 7 7 7 7 7  CAlC  ¥  7.9 •>> 7.7 1*7 7.7 o.O n.o 0.0 7.2 7.4 2.6 7.4 4.0 1.4 • 7.1 1.4  -  -  -  A. ft 1.4 7.7  1.1 l.T 1.7 1.2 0.0 1.4 2.4 7.0 o.O 1*4 1*1 1.4 1.1 7.1 7,4 1.9 1.6 7.4 0.4 1.9 7.2  -  -  I." 1.1 «.4 1.0 o.l 4.4 0,4 7,4 O.A l.T 4.1 4.4 0*9 0.7 1.1 4.4 4.9 •1.0 1.7 9.0 0.1 0.4 1.1 0.7 l.T 1.9 1.0 1*4  - ft.4 1.1 — - 7.0 0.9 -  !•«  7.4 2.4 l.A 1.7 ft.l 7.T l.A 0.4 7.4 1*7 7.4  2.4 1.1 1.9 7.9 O.T 0.0 1.4 7.7 7.0 0.4 — 0,1 7.A 7 .A 7.7 — 7.0 l.T 7.4 7.4 7.A 1.2 0,0 l.T 2.0 0.9 0.7 7.1 2.7 9,4 •> 0.1 o.o 7.4 9,5 1.4 o.o O.A l.A * l.T 7.0 1.1 1.4 4.4 1.9 2.9 7.0 0.0 7.6 l.A 0.9 1.7 0.0 1.4 7.0 7.4 • 1.1 1.1 O.O 0.2 4.A 4.1 1.9 O.A 0.0 7.7 7.A 7.4 1.9 7.1 1.4 O.A 1.4 O.T 2.6 l.A 0.0 7.4 » O.ft l.A 7.7 1,1 4* 7.7 4.7 1.4 O.A l.A A. A •> 7.4 1.4 9.4 4.4 0.0 0.4 1.4 7.9 1.1 7.1 4.A 4.4 O.O 0.4 1.4 1.1 0,0 1.0 7.A O.A 0,4 1.4 l.T 7.4 1.4 O.A ft* 0.1 0,0 0.4 l.A 0.2 l.A l.A O.A 7.1 1,4 0,A 7.7 ft* 0,0 1.4 •* 0,0 o.o 1*4 T.l 7.7 0,1 0.0 o.A 4.4 9.1 0.0 1.1 — 7.9 1.7 l.A 1.1 7.1 7.A 9.7 1.4  -  ft.9  -  -  -  -  -  ft.4  95 TABLE; A2.  L 7 1 1 4  * * * *  4 4 4 4 4 4 1 4 9 4 4 4 4 4  4 A 4 6 A A 8 0 0 0  F OBS  F CALC  1.T 1.6 o.o 1.9 o.o 7.4 1.9 1.1 1.4 7.6 2.1 1.2 o.o 0.0 7.4 0,0 1.4 1.1 1.1 7.7 1.9 7.4 1.T 0.0 1.2 0.0 7.1 1.4 0,0 1.9 7.1 7.A 0,0 7.6 1.9 2.9 1.4 0.0 1.4 7.A  1.4 7.4 1.1 1.1 7.9 4,7 O.A 9,0 1.9 1 ,6 0,2 4.4 4,0 1.9 7.A 0,0 1.0 0,A 4.9 ],i 4.0 9.0 2.8 2*1 1.1 1.1 1 .2 0.1 0,2 1,4 1,1 1,9 1.7 4.9 0.6 9.9 1.6 1.1 4.0' 0.1  -  -  •» -  -  -  H A 8 9 -11 -10 • 9 - 1 " 4 - 7 - 1 9 4 5 6 7 8 9 -11 - 9 " 4 - '2 - 1 1 7 8 - 6 - 2 - 1 2 1 7 - A A - 9 - 7 1 7  (Continued).  K  L  F OBS  F CALC  A 6 6 6 6 A 6 6 6 A 6 6 6 A 6 6 6 6 6 6 6 6 6 A 6 A 6 6 6 6 6 6 6 6 6 A A 6 6  0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 7 2 7 7 ? 7 7 1 3 1 '1 9 1 1 4 4 4 4 4 4 4  7.9 0.0 1.9 9.4 4.0 2.6 9,9 2.0 1.9 2.1 2.0 0,0 9.6 7. 7 2.9 0,0 0.0 4.0 9.6 2.1 1.9 0.0 1.4 7.0 2.A 7.9 1.7 1.2 2.9 2.9 2.8 2.9 2.9 1.6 7.4 1.7 0,0 2.A 2.2 1.9  0.8 0.9 0.7 2.9 4.6 0.0 0.9 0.2 1.2 1.9 1.2 0.4 4,4 0.9 1.9 0.2 0.9 4.1 2.0 0.9 1.6 0.7 1.1 0.1 1.4 1.2 7.4 0.8 2.7 1.4 4.0 1.1 0.9 7.7 1.0 2.4 0.1 1.1 1.1 0.4  _  _  _  _  m m  _ _  " * *" 1 " 1  F OUS  F CALC  9.6 9.7 0.0 0.0  0.0  2.6 0.0 6.0 0.0 1.1 3.9 " -  4 9 4 1  -  8 6 9 4 9  " -  A 7 6 1  2.6  -  0.1  0.4  4.7 0.7 2.1 1.1 1.6 1.2 1.4  o.o 4.1 2.6 1.9 1.6 2.1 2.8 2.1 2.2  2.6 2.6 0.0 9.6  -  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-2,6ANHYDRO-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 t h r e s h o l d values, i n t h e range :5-17)-  H.  ft  L  0 0 0 0 0 0 0  2  0 0 0 0 0 0  0  0 0 0 0 0  •  * 6 6  10 ii  1ft 1ft la 20 22 2* 26 1 2  )  ft 3 6 7  tt  V 10 11 12 1» Ift 1J 1ft 17 1ft IV 20 21 22 23 2ft 2ft 2« 0 1 2 )  ft ft 7 3  B 9 10 11 12 13 1ft 15 1ft 17 18 19 20 21 22 23 2ft 25 2ft 1 2 3  ft  5 6 7 8 9 10 11 12 13 1ft 15 16 17 18 IV 20 21 22 2) 2« 25 26 0 1 2 3  ft ft 7 3  8  10 11 12 13 1« 15 16 17 18 19 20 21  0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  F 06* 76,8 53.6 97.2 40.4 210.9 92.0 20.2 61.V 27.9 0.0 39.5 17.6 16.7 ft!.7 ft.3 21.5 1ft.7 17.9 90.6 57.1 ftO.ft 75.4 19.2 31.7 24.4 31.7 28.2 62.2 25.6 35.9 107,2 27.6 16.1 43.6 36.9 16.0 0.0 29.8 21.1 109.7 ft*.9 62.9 169.5 32.1 50.* 8.3 65.3 1*2.3 46.5 3*.ft 43.0 0.0 58.1 119.6 37.8 0.0 13.1 *6.2 33.9 0.0 20.8 0.0 0.0 21.5 0.0 0.0 78.9 38.2 *3.3 239.2 23.7 80.6 75.7 54. 9 0.0 31.1 0.0 18.3 91.6 59.7 69.9 15.* 0.0 23.7 31.* 18.3 *6.t 18.9 30.3 0.0 40.1 21.1 168.9 102.7 16.0 30.0 22.* 130.3 41.4 95.6 2*.* 19.2 36.6 87.3 *8.8 48.1 28.9 54.9 0.0 *8.* 0.0 0.0 0.0 0.0  F CALC  M  62.0 51.8 103.7 35.7 226.7 5*. 3 12.9 64.2 31.0 6.6 37.9 21.* 17.5 39.* 1.3 20.6 11.* 16.7 92.1 *9.7 46.2 70.* 13.5 32.* 31.* 29.* 30.0 59.9 23.9 35.7 107.3 27.* 8.7 44.1 37.5 18.9 5.3 30.2 15.1 96.2 «3.9 ft*.9 161.* 34.1 96.1 1.6 81.7 1*2.9 *8.8 37.1 40.7 5.6 66.4 115.1 37.* 0.* 13.0 45.1 38.8 7.8 22.7 9.2 9.9 22.1 8.5 13.2 66.9 31.0 39.8 233.6 26.8 66.3 7*.8 55.* 3.1 31.7 5.8 22.7 91.* 61.9 91.0 9.6 6.1 21.7 32.3 13.3 *7.9 26.2 26.9 5.8 36.7 20.5 155.9 99.0 11.7 49.1 19.8 126.6 43.6 101.4 24.1 15.2 39.5 67.9 46.* 48.1 27.9 55.2 9.3 45.6 1.2 5.2 11.3 14.2  4 4 4 4 5 5 5 5 6 5 3 5 5 5 5 3 5 5 5 5 3 3 3 3 3 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 8 8 6 8 8 8 8 8 8 8 6 6 8 8 8 8  a 6  8 6 9 9 9 9 9 9 9 9 9 9 V 9 9 9 9 9 9 9 0  ft 22 23 24 25 1 2 J 4 5 6 7 8 9 10 11 12 13 1* 15 16 17 16 19 20 21 22 ' 23 2* 0 1 2 3  *3 6 7  a  9 10 11 12 13 1* 13 16 17 18 19 20 21 22 23 1 2 3  *  5 6 7 8 9 10 11 12 13 1* 13 16 17 18 19 20 21 22 0 1 2 3  *  5 6 7 8 9 10 11 12 13 1* 13 16 17 18 19 20 1 2 3  *  5 6 7 9 9 10 11 12 13 14 15 16 17 18 0  L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  F OSS 0.0 0.0 22.4 0.0 9.9 30.3 0.0 25.0 0.0 36.6 59.* 17.9 32.3 62.9 11.3 16.3 32.* 70.3 0.0 16.0 29.8 24.0 0.0 0.0 17.6 0.0 29.5 19.3 112.0 18.3  ii.a  0.0 60.9 36.6 69.6 12.3 92.4 24.0 18.3 31.1 0.0 0.0 *7.2 18.9 0.0 16.6 23.3 0.0 0.0 28.5 0.0 0.0 15.0 100.1 22.6 99.2 24.0 16.0 33.3 0.0 0.0 26.6 19.2 27.6 31.1 69.6 22.1 18.9 0.0 0.0 0.0 17.6 19.9 18.3 48.1 10.9 23.3 32.4 19.4 54.5 10.9 22.8 48.4 0.0 13.4 47.6 16.7 28.9 40.4 20.8 0.0 0.0 0.0 0.0 0.0 0.0 20.2 18.3 17.0 31.4 16.7 45.9 0.0 13.4 50.0 17.9 38.6 42.7 13.8 17.0 0.0 0.0 0.0 27.9  F CALC 14.2 1.6 22.5 4.9 6.0 32.8 11.1 19.4 7.9 33.6 60.0 20.2 52.9 67.2 9.9 17.7 32.0 72.2 3.6 21.3 28.8 28.8 1.3 13.1 15.6 10.7 26.0 17.0 99.0 19.3 2.9 1.3 67.0 33.1 71.0 6.9 99.2 20.8 14.0 29.9 12.3 6.9 46.5 21.8 0.4 16.2 25.0 6.3 13.2 33.4 2.* 7.9 11.9 86.2 27.8 92.* 21.8 1*.8 32.1 6.8 3.2 27.* 16.3 29.9 31.9 71.0 21.2 20.5 17.3 10.8 3.3 17.3 19.0 12.4 *6.9 13.8 28.6 30.* 13.6 58.1 *.3 25.8 46.2 2.0 6.2 53.* 13.7 31.9 *1.9 21.1 9.7 11.* 6.3 13.0 6.2 4.7 18.6 20.1 16.6 30.9 14.5 49.4 0.4 8.0 51.9 22.9 38.7 41.3 10.5 12.9 16.8 17.3 8.2 23.0  rt ft 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2  2 2 2  2 2 2 2 2  2 2 2 2  2 2 2 2 2 .  2 2 2 2  1 2 3  4 3 6 7  a  9 10 11 12 13 14 13 16 1 2 3  * 3  ft 7  . 8 » 10 11 12 13 0 1 2 3  * 3  ft 7  8 0 1 2 3  *  3 6 7 8 9 10 11 12 13 1* 19 16 17 18 19 20 21 22 23 2* 23 26 0 1 2 3  *  5 6 7 8 9 10 11 12 13 1* 15 16 17 18 19 20 21 22 23 2* 25 26 0 1 2 i  *  5 6 7 8 9 10 11 12 13 1* 13 16 17 18 19 20 21  L  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  F  085  0.0 44.6 16.0 0.0 16.7 16.7 23.1 48.* 22.1 37.2 26.0 24.4 22.4 16.6 27.2 22.8 32.7 0.0 0.0 0.0 0.0 0.0 26.0 0.0 25.6 39.8 0.0 22.1 19.2 38.8 0.0 l«.l 13.7 13.7 10.8 20.6 19.2 0.0 112.7 0.0 29.8 73.5 111.0 67.1 121.0 50.0 3ft.3 *1.7 12.8 22.1 62.6 0.0 61.9 17.6 17.9 *2.3 29.9 79.0 29.5 0.0 18.3 0.0 20.8 0.0 22.* 76.7 218.3 88.3 33.9 139.3 71.9 93.3 137.* 65.1 90.2 22.* 27.9 *7.6 96.8 46.5 17.9 15.0 *5.2 45.9 15.0 33.0 32.1 13.4 32.4 0.0 0.0 33.0 108.2 34.2 46.2 30.3 137.1 164.3 33.6 72.8 48.8 19.9 41.7 66.7 52.3 22.4 46.2 47.8 40.7 26.6 14.7 22.6  34.6 32.7  F  CALC  13.1 41.8 20.8 0.2 14.7 16.6 23.1 48.5 26.0 34.3 26.7 18.5 21.0 15.2 21.* 22.8 12.0 1.1 0.3 3.* 6.1 3.3 23.6 0.1 23.* 39.3 2.3 21.8 13.9 16.3 2.6 9.3 12.0 13.1 23.3 19.6 16.* 8.3 103.7 5.7 31.1 71.3 119.0 66.2 118.* 33.2 3*.ft *1.2 13.2 20.1 63.6 1.3 38.6 23.7 22.7 *0.* 29.2 81.1 31.6 '25.7 8.9 21.6 11.8 22.2 65.2 210.0 88.9 41.1 129.2 61.6 44.6 136.6 66.8 82.7 20.1 28.0 32.3 60.0 45.5 20.5 12.6 43.5 47.2 19.6 32.1 13.1 15.4 34.8 14.0 8.1 36.7 106.8 62.1 33.3 30.3 119.7 178.6 34.3 63.1 4*. 3 20.2 39.9 63.5 *9.2 19.6 *5.7 50.9 40.2 22.*  11.2 20.7 35.2 14.3  rt  ft  L  22 23 2* 23 26 0 1 2 3  1 1 1 1 1 1 1 1 1 1  * 3  ft 7  6 9 10 11 12 13 1* 13 16 17 18 19 20 21 22 23 2* 23 0 1 2 3 " « 3 6 7 9 V 10 11 12 13 1* 15 It 17  ia  19 20 21 22 23 2* 29 0 1 2 3  *  9 6 7 6 9 10 11 12 13 1* 13 16 17 18 19 20 21 22 23 2ft 0 1 2 3  ft 3  6 7 8 9 10 11 12 13 14 13 16 17 IB IV 20 21 22 23 0 1 2 3 4 5 0 7  i  1  i  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  f 08S 21.5 0.0 0.0 20.5 0.0 44.3 28.2 71.9 31.7 9ft.0 ia.a 129.*  is.a  31.1 81.1 80.6 42.1 10.3 1ft.1 21.8 49.7 99.3 24.4 27.2 45.6 21.1 18.9 17.6 28.2 0.0 18.9 0.0 22.ft 56.a 90.6 27.2 72.2 1ft.0 69.9 67.7 82.3 39.0 11.8 93.3 52.012.7 26.9 22.ft 20.2 20.2 31.7 IB.3 0.0 3ft.O 0.0 26.9 0.0 47.2 36.2 39.8 0.0 0.0 45.9 0.0 65.1 49.7 82.5 19.2 41.4 29.9 91.1 29.2 24.7 23.7 2«. 0 36.6 26.9 0.0 21.1 0.0 0.0 0.0 1*9.9 36.2 17.3 38.2 17.1 *5.6 43.6 23.6 17.6 51.3 71.9 2*.7 *1.4 28.5 19.9 30.1 23.1 15.7 0.0 31.7 0.0 0.0 0.0 17.0 37.8 30.7 42.0 23.7 35.9 17.9 27.2 28.2  F CALC 16.3 11.2 7.3 21.* 10.8 44.0 33.2 73.* 30.3 92.0 39.0 12ft.B 13.6 27.6 79.7 79.3 39.* 26.8 • 3.ft 22.3 33.1 34.6 24.6 29.9 46.1 26.0 16.0 IB.3 26.9 ft.2 19.9 9.0 21.9 97.1 96.6 29.ft 70.0 16.9 67.1 6ft.0 74.6 35.7 13.6 92.2 49.1 3ft. 9 27.9 21.7 20.1 21.4 30.2 21.4 ft.8 3*.3 10.2 2».0 5.B  ft*.ft 37.a »2.0 B.7 3.7 • 7.1 B.9 60.6 45.2 78.3 22.9 39.7 29.9  .96.* 26.9 22.9 23.1 27.3 41.3 28.ft lft.ft 23.*  ft.ft  11.2 10.7 1*7.3 31.3 18.7 39.1 27.0 46.5 46.9 24.8 11.3 49.1 67.1 27.* 40.3 28.7 18.9 30.6 24.4 11.0 10.* 29.9 10.6 5.1 5.1 15.3 33.0 30.* *2.2 2*.7 39.6 2*.* 27.2 28.6  97 TABLE A3-  »  IC  I  F Or*S  F C»LC  a  1 1 1 1 1 1 1 1 1 1 1 1 1 r 1 1 1  16.3 64.3 14.7 0.0 42.3 27.2 0.0 35.3 0.0 0.0 43.0 0.0 0.0 24.4 30.5 0.0 14.4 69.a 29.5 18.3 19.6 0.0 18.6 27.9 25.6 19.9  14.1 37.8 12.7 1.0 41.2 27.3 6.4 36.3 4.7 5.4 42.2 4.1 8.3 21.6 29.4 7.9 10.9 66.2 36.6 14.0 22.3 7.6 20.0 27.3 28.0 16.8 32.7 37.4 30.7 15.1 16.2 20.9 3.6 14.7 14.8 23.6 17.3 9.3 12.8 35.1 11.1 39.2 27.0 19.6 42.1 42.3 4.2 14.7 11.6 8.9 38.5 23.2 9.7 3.2 30.7 16.1 3.9 11.8 12.1 27.9 13.6 2.9 25.1 36.4 9.8 19.8 26.6 2.1 36.7 14.8 17.6 28.3 14.4 11.6 12.9 19.6 25.6 15.1 27.4 24.9 8.4 20.6 12.3 8.2 9.3 14.7 4.9 19.6 20.5 3.8 28.5 20.2 28.5 26.9 10.6 61.8 30.8 32.2 8.9 70.4 22.7 36.0 0.8 29.7 10.5 35.3 17.5 16.6 23.7 76.0 9.7 33.5 13.9 33.2  9 10 11 12 13 1* .15 16 IT 16 I* 20 21 0 1 2 3 4  3  6 7  a  9 10 11 12 13 1* 19 It 17  ia  19 20  0 1 2  3  4  3  t  7  a  V 10 11 12 13 14 15 It 17 10 0' 1 2 3 4  3  t  7  a  9 10  li  12 13 14 15 0 1 2  3  4  3 t  7  a  V 10  ii  12 0 1 2 3 4  3  0 0 0 0 0 0  0 0  0 0 0 0 0 0 0 0  0  0 0 0 0 0 0 0  6 0 1 2 3 4 9 6 7  a  9 10 11 12 13 16 13 16 17 10 19 20 21 22 23  i  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  33.0  39.1 31.1 18.3 14.4 19.9  0.0  17.0 17.0 27.2 21.1 0.0 15.0 37.9 13.4 32.1 24.0 21.8 61.1 43.0 0.0 0.0 0.0 0.0 37.5 27.6 16.0 0.0 27.9 15.4 0.0 0.0 16.0 21.1 17.9 0.0 27.2 37.3 0.0 18.6 30.1 0.0 44.9 0.0 16.3 28.9 15.0  o.o •  15.7 19.2 24.0 0.0 29.6 24.0 14.7 25.3 0.0 0.0 0.0 16.7 0.0 0.0 16.7 0.0 28.9 13.4 20.8 10.6 0.0 66.4 28.2 35.6 17.9 76.4 22.1 35.6 0.0 24.0 12.8 34.0 17.3 12.8 23.4 68.7 0.0 32.7 0.0 27.9  rt 0 1 1 1 1 i j  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3  3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3  3 5 5 5 5 5 5 5 5 5 5 5 5  (Continued).  F C*LC  F Odb 24 0 1 2 i 4 5 6 7 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 3 6 7 8 » 10 11 12 13 14 13 16 17 18 19 20 21 22 23 24 0 1 2 3 4 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 . 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 6 6 7 8 9 10 11 12 13  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  14 15 104 52  20 21 22 0  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  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  12 13 14 13 16 17 16 IV 20 21  9 10 12 13  119 14  8 8 8 6 8 8 8 8 8 8 8 8 8 6 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9  V 9  10 10 10 10 10 10 10 10 10 10 10 10 10 11  a  u n n n n u u  1 2 3 4 5 6 7 8 9  10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9  10 11 12 1i 14 15 1 2 3 4 5 6 7 6 V 10 i 1 12 1 2 3 4 5 6  7  0 0 0 0 0 0  1 i 4 5  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  2 2 2 2 2 2 2 t 2 2 3 i 3 i 3 3  0.0 .0 26.7 0.0 29.2 33.7 0.0 0.0 0.0 0.0 20.8 33.3 22.4 0.0 17.6 26.0 0.0 40.7 0.0 0.0 26.9 20.8 22.1 16.3 16.4 13.8 23.0 29.8 16.0 23.1 21.5 0.0 19.2 36.2 17.6 0.0 16.6 0.0 0.0 0.0 15.0 15.7 22.1 34.6 17.0 14.4 29.2 17.6 0.0 0.0 19.3 0.0 0.0 14.7 17.9 0.0 0.0 14.7 16.0 50.0 41.4 17.3 14.1 40.4  12.2 0.5 3.0 20.3 27.2 8.2 21.0  12 13  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  17 18 19 20 21 22 0  9 10  13 16 17 18 19 20  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 < 19.1 13.8 23.7 31.9 14.8 3.9  10.3 1.3 19.9 33.4 24.3 7.3 17.5 23.5 10.1 39.3 6.3 8.9  25.5 19.2 22.6 19.2 19.1 6.1 23.3 30.9 16.7 23.1 22.9 9.6 13.0 33.4 7.1 2.0 2.0.8 11.6 9.2 6.0 13.7 11.9 20.2 38.4 16.3 12.4 26.6 12.0 6.4 5.9 14.5 9.0 14.5 9.7  9.8  6.1 8.5 3.1 IV.6 44,9 40.0 10.2 1.5 40.6  2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3  12 13 14 IS 16 17 18 19 20 21 0 1 2 3 4 5 6 7 6  3 3 3 3 3 3 3 i 3 3 3 3 4 4 4 4 4 4 4 4 4  10 11 12 li 14 15 16 17 16 19 20 21 0 1 2 i 4 5 6 7 6  4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 3 5  ' • 10 11 12 13 14 13 lb 17 18 19 20 0 1 2 i 4 3  5  3  9  9  O  7  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.  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 29.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 2l.i 30.2 20.4 8.5 6.6 10.3 11.6 10.2 10.4  23.1 O.l 34. 7 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  11.9 31.3 2 3.3 19.9 23.5 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-  K  9 10 11 12 19 14 19 16 17 IS 19 0 1 2 9 *  ft * 7  • 9 10 11 12 19 14 1ft 16 17 10 0 1 2 9 4  ft 6 7 a. 9 10 11 12 19 14 1ft 16 0 1 2 9 4 ft 6 7  • 9 10 11 12 19 14  I J 3  9 3 9 3 3 3 3 3 3 3  3 3 9 3 3 3 3 3 3 3 9 9 3 9 9 9 9 9 9 9 9 3 3 3 3  3 3 3  3 3 3 3 J 3 3 3  3 3 3 3  3 9 3 9  3 3  3 3 3 3  r OBS  f CALC  H  K  20.5 26.6 0.0 18.6 0.0 0*0 0*0 30.1 0.0 0.0 0.0 0.0 23.4 55.6 14.1 24.4 24.4 16.0 23.4 0.0 34.6 20.2 0.0 90.1 0.0 0.0 33.3 0.0 19.5 0.0 0.0 14.4 27.9 39.9 0.0  22.1 27.0 7.7 29.1 9.8 7.7 3.3 32.3 3.1 13*0 10.7 1.4 17.5 36.3 11.0 21.3 90.2 0.6 23.3 14.6 96.9 20.9 9.3 29.9 9.4  9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10  0 1 2 9 4  33.4 6.4 17.6 4.3 7.4 17.7 31.7 99.6 0.6 • •9 12.3 26.2 13.6 24.4 10.1 10.0 9*2 26.9  o  16.7  17.9 26.0 20.2 22.1 0.0 10.6 0.0 27.2 0.0 2ft.6 15.0 0.0 24.0 24.0 16*7 0.0 2ft.6 22.4 0.0 16.9 26.0 0.0 0.0 36.6 0.0 0.0  6*6  ft.ft  24.1 10*9 a.i  29.9 29.4 17.8 7.1 29.* 22.9 16.9 10.6  26.2 2.0 4.7 95.9 9.9 7.4  o  o o o  o o o  o o  o  o  o o  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 j j 2 j 2 2 2  ft 6  7 8 9 10 11  I 2 3 4 5  L J 3 3 3 3 3  9 9 9 9 3 ]  j 3 3 3 3 4 4 I 2 4 3 4 4 4 4 ft 4 A 7 4 8 4 9 4 10 4 n 4 12 4 13 4 14 4 1ft 4 16 4 17 4 0 4 1 4 2 4 3 4 4 •4 4 ft 6 4 7 4 6 4 9 4 10 4 11 4 12 4 13 4 14 4 13 4 14 4 17 4 ' 4 1 4 2 4 j 4 4 4 9 4 4 4 7 4  (Continued).  P OBS  F CALC  H  K  L  F OBS  F CALC  F OBS  22.0 17*8 4*4 6*6 . 14*9 9*ft 41 .ft 20*9 20.2 28*9 16*0 24. 7 19,5 11.4  s 9 10 11 12 19 14 19 16 17  0.0 16.7 0.0  9.2 6*8 10.6  2 2 2 2 2 2 2 2 2 2 9 3 9 3 9 3 3 3 3 3 3 3 3 3 9 9 9 4 4 4 4 4 .4 4 •4 4 4 4 4 4 4 4 4  f CALC  26.3 17.6 0.0 14.4 1ft.7 0.0 40.7 22.4 24.0 31.1 17.6 24.4 19.9 0.0  4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 *  29.0 0*0 23.4 0.0 34*6 0.0 29.2 *23.7 0.0 0*0 O.O' 39*3 17*3 20*6 0*0 14*4 19.9 0.0 22.8 0.0 19.9 27.9 0*0 23*4 21.0 27.2 0*0 49.1 23.4 29*2 0*0 16*3 20*0 16*6 19*9 17*3 0*0 2ft.0 14.7 0.0 0.0 0.0 20.2 36*9 14*7 34*0 0.0 0*0 0.0 0.0 0.0 26.6 17.3 24.4 0*0 19*0 0.0  27.1 19*9 24.2 13*7 35.0 8.0 26.9 24.8 15.4 7.9 1.7 39*7 17.4 19*8 18*3 23*7 29*4 10*1 22.0 10.5 27.2 31.3 7.4 21.2 20.2 22.2 7.2 44.5 21*0 29.4 14*3 16.6 20.5 22.9 29.0 18.6 17.4 26.9 23.4 3.1 12.7 3.7 20.7 31*9 9.6 33.3 13.8 10*3 16.3 16.9 9.7 39.ft 19.0 23.2 11.2  10*3 0.0 0*0 18*3 27*9 IS. 0 16*3 0.0 0.0 21.1 16*0 24* 7 20.3 30.1 21.8 18.6 16.7 0.0 0.0 16.0 29.9 92.1 21.8 29*9 24.4 28.2 19*0 0.0 19*9 19.9 0.0 29*4 o.o 17.3 0.0 0.6 0.0 0.0 0.0 91.4 19.9 14.7 0.0 19.3 0.0 20.0 0*0 28*2 16*9 0.0 0*0 0*0 16*0 29.0 16.9 0.0 0.0 0.0 16.7 19.9  9.7 6*7 12*9 20*1 94*9 13*0 17*2 6.4 9*7 29.0 12.7 29.9 9.1 31.6 19.6 19.9 11.2 6*4 6.9 12*9 29.2 29.ft 20.6 27.4 29*2 25.6 12*6 3*9 17.7 16.9 11.6 16.9 12.2 9.8 13.0  W.9  26.0 0.0 0.0 0.0 22.1 33.7 0.0 32.4 32.4 0.0 0.0 0.0 0.0 28.2 19*7 21*1 12.6  22.4 23.7 26*9 0.0 16.6 32*1 14.7 17*9 0.0 16*0 14.1 0*0 16.6 21.6  16.3 17.4 0*0 30.9  90*6  0*0 40*4 21* 1 0.0 16.9 16*6  16*6  22.9 4.1 11.3 2.2  22.6  92*1 6.0  27.2 92.9 6*2  • 0*6 19.9 13.3 26*7 16*2 17*1 1*9 17.2 26*0 99* ft 4.9 16*0 31.0 17.1 10*2 19.6 14*9 13.7 6.2  19.1 22.4 19.4 19.6 9.0 24,i 27*9 9.4 96.7 19*2 9*9 21*919*0  1 2 3 4  ft 6 7 0 9 10 11 12 13 14 19 16 0 1 9 4  ft 6 7 6 9 10 11 12 19 14 1ft • ft 01 ft 9 2 9 9 ft 4 9 ft 9 6 ft 7 ft 69 ft ft10 3 3 3 3 4 4 4 6  11 12 13 14 o 1 2  17*6  96.2 40.4 0.0 13.7  6*9  19.7 17*9 99.9 41*8 6.9  9.0  2.5  19*6 14*9 0*4 29*7 19*1 10*1 9*6 16.6 10*1 20*1 7*7 29*1 9.9 7*9 9.0 10*8 10*2 29*2 16.6 17*4 10.9 7.9 19*9 16*1  99 TABLE kk<  fl  ft.  0 0 0 0 0  0 0 0 0 0  0 0 0  0  u 0 0 0 0  0 0 0 0 0  0 0 0 0 0 0 0 0  0 0 0  0 0 0  0 0 0 0 0 0  0 0 0  0 0  0 0  0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0  a 0 0 0  u 0  I  1  1 1 1  1 I 1 1 1 1 1 1 1 1  1 I 2 i 2 2 i 2 2 2 I 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3  3 3 3 3 3 4 4 4 4 4  4 4 4 4 4 4 4 9 $ 9  5 9 3 9 3 3  5 3  5 3 9 5  3 6 6 6 b 6 b b b b b b b b b b b b 7 7  L  .  :  4  b U  10 12  14 lb 1 2  1  4  b 7 0 V 10 11 12 13 14 15 16 17 0 1  2 3 ' 4 5 b 7 6 9 10 11  12 13 14 15 16 17 1 2 3 4 5  b 7 d 9 10 11 12 13 14 15 lb 17 0  1 2 3 4 5 b 7 6 9 10 11 12 13 14 15 lb 17 1 2 3 4  5 b 7  6  9 10 11 12 13 14 15 lb 17 0 1  2 3 4 5 b 7 6 9 10 11 12 13 14 15 16 1 2  F Odo a. a 0.6 oO. 1 11.6 54.7 43.1 44.7 0.0 13. 1 10'.4 34.»  Ob. 1 23.2 19.9 0.0 b0.5 10. 1 34.0 12. 1 23.b 0.0 lb. 6 0.0 27.9 0.0 121.7 33.2 21.3 93.3 12.7 63.0 74.7 36.6 0.0 16.6 49.6 17.7 46.3 0.0 11.4 0.0 9.3 10.b 20.6 71.3 13.4 71.3 17.4 32.2 30.6 41.3 27.9 31.3 0.0 11.3 10.2 21.1 0.0 24.7 0.0 43.1 32.9 34.5 24.3 47.6 64.7 104.2 32.2 61.3 16.3 0.0 0.0 44.9 0.0 0.0 14.7 14.3 11.3 37.9 31.7 bb.i 6b.0 6.b 26. 1 20.8 23.1 19.3 55. b 19.0 0.0  11.3 22.2 17.4 12.0 7.2 22.7 51.7 lb.3 13.b 33.2 3b. 1 69.4 40.4 36.0 0.0 0.0  23.3 14.9 24.9 0.0 0.0 10.5 6.1  32.2  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 t h r e s h o l d v a l u e s i n the range 2-9).  F CALC 0.  i  ),0  1.3 0.9 >lt» 44.3 46.3  O  7.0  3.4 l.O.4  I  33.4 66.4 22.3  20.0 7.5  bo .0 16.9 53.7 13.7 24.0 0.2 17.2 1.6 29.4 O.b 146.9 33.9 24.6 100.0 13.0 01.7 73,5 37.2 3.9 17.3 46.8 20.0 48.9 3.4 13.7 2.2 9.7 12.0 16.3 75.7 lb.6 71.1 15.0 32.4 30.1 41.1 26.1 52.b 1.2 10.1 o.l 20.7 2.6 25.4 0.4 43.2 27.7 34.1 23.b 48.8 76.7 103.2 33.3 40.2 lb.5 2.1 7.0 45.5 2.1 3.3 13.1 lb.5 13.2 3b. 7 53.3 b3.9 85.3 11.3 24.4 22.5 21.6 19.4 55.7 10.2 9.0 9.9 21.5 16.7 14.1 7.2 22.5 49.6 14.7 13.1 36.0 34.3 69.2 37.2 30.4 4.6 0.1 20.7 11.3 22.5  1.2  1.3 17.2 6.5  30.3  n  L  J  7  >  7  J  I 7  >.  0  0 0 0 0 0 0 0  o 0 0 0  0 0 0  0  0 0 0  0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0  7 7 7  7 7 7 7 7 7 7 0 6 8 6  0 6  0 0 0 6 0 6  8. 0 8 8 9 9 9 9 V 9 9 9 V 9 9 9 V 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11  }}  11 11 11 12 12 12 12 12 12 12 12 12 12 12  12 12 13 13 13 13 13 13 13 13 li 13 1 3  14 14 14 14 14 14 14 14 14 14 14 1 3 15 13 13 15 15  -j 0 7  0 9 10 1 1  u  1 1  14 13 16 0  1  2 3 4  5 6 7 0 9 10 11 12 15 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 13 0 1 2 i 4 3 6 7 6 9 10 11 12 13 14 1 2 3 4 5 b 7 8 V 10 11 12 13 0 1 2 3 4 3 6 7 8 9 10 11 12 1 2 3 4 5 b 7 0 9 10 11 0 1 2 i 4 5  b 7 0 9 10 1 2 3 4 3  6  F Ubo 4 I,-, 44 • 0 39.3 0.0  14.0 35.4 22.2 25.4 17.2 0.0  17.0 10. 1 19. J 7. ' 32.0 63.1 0.0  37.9 40.2 13.6 44. 7 24.0 12.2 20.b  0.0 34.0 15.2 27.2 0.0 0.0 29.9 43.3 49.2 17.0 22.2 0.0 22.7 17.0 27.7 0.0 lb.5 0.0 15.2 12.2 21.3 30.6 50.4 30.6 21.3 0.0 32.7 0.0 0.0 0.0 10.6 13.6 34.3 13.6 23.6 0.0 23. 1 0.0 37.9 20.2 12.2 0.0 21.3 0.0 24.3 0.0 9.9 0.0 6.1 29.3 33.6 23.3 0.0 0.0 31.3 0.0 25. b 0.0 0.0 11. i 17.7 9.0 24.3 0.0 26.b 0.0 17.4 0.0 15.2 0.0 29.9 0.0 7.2 13.1 18.1 0.0 23. 1 0.0 23.1 0.0 23.b 0.0 0.0 0.0 16.6 0.0  0.0  0.0 10.2 0.0  f CALC  li  JL  L  F Obi  F CALC  A  L  r OBS  F CALC  40.3 4 J.3 >a. j 1.7 12.3 34.0  0 0 0 0 0 0 0 0 0  15 19 lo lb 10 lb 10 lo lo 17 17 17  7  7.2 0.0  o.b 2«o 11.7 4.4 1.1  3  11 14 15 1L 0 1  <i.i 17.7 11.1 0.0 17. 1 2b.l 4b. i 44.7 19.2 59.1 25.4 44.9 34.2 14.7 19.0 0.0 17.9 9.3 20.2 10.9 d.4 58.1 30.6 41.3 53.6 43.e 33.1 13.1 41.5 lb.9 19.3 29.0 15.9 19.3 14.3 21.1 9.6 6.5 43.6 12.7 46.3 36.3 la.4 33. b 9.5 22.7 20.2 34.7 16.5 10.9 28.6 0.0 14.9 9.7 0.0 18.6 22.0 28. 1 22.7 37.7 23.3 34.2 24.7 13.8 13.1 0.0 12.7 0.0 11.9 9.3 35.6 30.b 27.2 15.2 13.8 13.6 17.9 12.2 12.2 27.4 22.4 10.4 lb.4 lO.b 10.9 15.4 20.2 31.1 21.1 20.b 29.3 20.4 28.3 25. b 0.0 14.3 14.0 0.0 11.3 14.3 12.c 11.3 2tt.b 17.9 12.7 25.6 0.0 9.3 17.4  19. b 17.4 11.0 5.7 17.p 29.2 47.b 49.3 41.1 55. b 24. b 44.6 34.2 34.b 18.1 d.l ld.1 13.4 20.8 11.5 9.9 59.5 31.7 43.1 35.5 45.1 33.5 14.0 40.3 14.3 17.3 28.9 13.7 19.0 14.5 20.6 10.0 8.3 46.6 12.3 48.3 38.1 18.0 34.4 8.2 21.3 20.3 34.0 14.0 10.6 29.0 6.8 lb.l 9.9 3.4 16.b 21. b 28.7 23.3 37.6 22.0 34.9 24.0 11.7 13.5 4.b 13.tt 9.3 11.7 10.1 35.7 31.3 27.2 3b.4 14.8 12.4 16.5 11.2 10.9 26.1 22.9 9.6 16.7 10.0 11.7 11.9 20.2 32.2 21.0 21.3 24.9 16.1 27.5 24.4 2.9 14.0 13.1 4.6 ll.l 33.4 12.4 9.1 29.6 16.1 12.5 24.3 7.4 10.6 10.4 9.9  <0.7  24.0 1 7.4 2.9 17.3 17.3 20.9 9.3  32.2 bl.9 10.2 33.1 38.6 14.0 44.2 24.7 11.1 19.6 4.7 33.4 17.1 27.4 1.1 6.0 26.4 41.3 49.0 18.4 21.0 4.5 22.3 16.6 24.7 2.4 lb.4 5.5  15.5 13.4 22.2 29.3 30.8 26.9 20.0 0.2 32.5 1.3 3.2 4.8 6.5 12.7 35.6 13.3 23.6  3.0 21.9 7.0 38.0 22.2 10.9 5.5 22.7 9.3 24.3 2.4 11.0 0.2 9.1 26.b 33.4 22.7 4.1 2.8 31.3 8.3 2b.1 5.9 3.0 12.0 20.2 9.7 23.6 1.3 27.3 4.1 16.1 1.3 lb.3 5.3 31.4 0.3 9.2 14.4 16.4 6.0 23.5 3.4  23.7 6.6 26.3 4.7 3.7 i.b 20.9 5.5 5.0  6.4  10.9 0.2  0 0 0  0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 2 2 2 2 2 2 2 2  2 2 2 2 2 i 3 3 3 3 3 3 3 i i 3 i 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 5 3 5 5 5 3 5 3 " 9 5 5  a 0  , c  1 4 5 6 1 2 1 1 2 1 4 5 b 7 0  9 10 11 12 11 14 15 lb 17 0 1 2 3 4 5 b 7 8 9 10 11 12 13 14 15 lb 17 1 2 3 4 5 b 7 8 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 6 9 10 11 12 13 14 13 16 17 0 1 2 1 4 5 6 7 8 9 10 11 12 11 14 13 16 17 0  I 2 3 4 5 b 7 6 9 iO 11 12  14.V 0.0 0.0 0.0  0.0 14.9 0.0 7.4 0.0 12.9 84.7 23.4 04.7 26.3 13.0 0.0 25.6 55. b 16.1 29.7 53.6 0.0 13.6 27.9 9.3 0.0 0.0 25.6 66 .1 12.2 88.5 80.1 26.5 65.4 45.1 46.9 30.2 16.1 19.0 19.7 16.9 9.5 19.3 lb.5 7.2 44.9 108.1 98. 1 33.6 b6.3 49.2 52.2 24.9 04.0 0.0 29.0 39.9, 10.6 29.7 23.1 10. b 13.1 13.4 43.1 88.5 94.7 69.2 47.6 44.7 53.8 26.1 3b.i 47.b 24.5 22.7 31.9 2b.3 0.0 21.1 6.1 0.0 22.7 21. 1 71.1 59.2 59.2 41.5 40.b 49.5 39.7 14.9 13.6 .l.o 0.0 0.0 i 7.9 11. 1 12.4 13.9 77.2 32.9 47.2 36.8 26.3 4b. 3 19.3 23.4 27.9 19.3 JO.7 23.1 2b.3  1.0  2.6 10.7 i. 1 10.1 .1.0 13.1 07.9 24.b 77.9 30. 3 37.0 4.3 25.3 57.0 15.6 31.3 56.0 2.5 13.0 29.6 8.7 o.9 1.9 29.7 71.b 13.8 83.2 79.2 24.9 64.9 42.4 47.2 32.3 17.3 18.6 19.5 16.1 7.0 19.2 17.2 9.6 44.8 121.4 97.6 31.1 64.9 4b.b 50.5 24.3 62.2 3.6 29.4 41.0 9.2 30.6 24.9 11.0 12.5 13.0 47.9 89. 1 98.6 66.5 45.9 44.0 53.7 24.6 34.9 48.4 24.2 22.1 31.8 27.1 10.1 22.1 6.5 4.2 17.1 24.7 72.0 67.4 39.1 42.9 37.4 49.0 39.4 12.7 12.1 20.4 3.2 12.3 20.6 12.0 14.1 17.3 60.5 32.6 47.1 41.7 26.5 43.2 17.2 i4.b 27.3 19.9 10.2 21.7 23.0  9 9 9 6 6  b 6  b b b b b b b 6 b b b b 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8  tt 8  d 0 8 8 8 8 6 8  tt  8 6 6 8 9 V 9 9 9 9 9 9 9  9 9  9 9  9 9  9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 1. li 11  2  i 4 3  6 7 6 9  10 11  12 li 14 15 lb 0 1 2 3 4 5 6 7 d 9 10 11 12 13 14 13 lb 0 1 2 3 4 3 b 7 8 9 10 11 12 13 14 13 0 1 2 3 4 5 b 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 b 7 6 9 10 11 12 13 14 0 1 2 3 4 3 b 7 d 9 10 11 12 li 0 1 2 3 4 5 b 7 d 9 10 11 12 0 1  9.7  /.4  d.2  7.9  d.O  .1.0  21.4  10. o  J..  100 TABLE" AU. K  L  F OBS  ll 1 J  ^ 1  1  4  < 1 . 1 0.0  n  3 6  J iJ  ii li ii ii ii 1* !<• 14 14 14 14 14 14 14 14 14 12 13 13 13 13 13 13 13 19 lo 10 10 16 lo 16 16 17 17 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2  2  2 2 2 2  . 2 1 i 3 J 3  i  1 1 1 3 3 1 1 1 1 3 3 6 4 4 4  7 o 9 10 1 1 0 1 2 i 4 5 6 7 d 9 10 0 i 2 3 4 9 6 7 6  0 1 2 3 4 9 6 0 1 2 0 1 2 3 4 5 6 7 6 9 10 11 12 13 14 19 16 17 0 1 2 3 4 5 6 7 6 V  10 11 12 13 14 19 16 17 0 1 2 3 4 9 6 7 6  9 10 11 12 11 14 13 16 0 1 2 3 4 5 6 7 d 9 10 11 12 13 14 11 16 0 1 2 1  19. f 0.0 10.4 11. i 11.3 7.9 i 1.0 12.2 0.0 10.2 0.0 Id.i 10.4 6.6  21.6 0.0 12.. 11.d 0.0 9.1 21.0 U.9 0.0 12.0 0.0 0.0 7.2 d.i 11.3 11.3 0.0 19.6 11.9 0.0 11.1 7.0 8.4 7.4 8.6 27.2 0.0 96.9 7.2 26.6 21.1 29.9 11.> 69.1 10.4 24.9 0.0 16.8 0.0 22.7 0.0 10.4 34.9 35.2 20.6 43.1 36.1 72.6 0.0 93.3 0.0 11.1 21.1 27.7 16.1 19.7 0.0 10.6 0.0 22.0 19.3 43.8 20.2 71.7 10.4 32.0 0.0 19.3 0.0 Sd.l 0.0 19.7 0.0 17.4 1..4 .O.o 9.1 93.1 94.9 42.2 9.7 33.6 o6.1 11.3 47.6 10.9 0.0 19.9 .0.6 26.1 27.0 13.2 0.0 0.0 5.6 52.4 21.3 79.4  F CALC l.o  1 7.o 0.4 9,d 10.3 11.1 9.9 14.9 11.1 4.6  6.2 3.9 20.d 10.8 8.9 23.3 4.3 12.3 12.2 3.0 3.5 .1.7 10.9 4.8  13.1 8.6  2.9 8.5 7.7 10.0 9.7 1.3 13.6 12.3 3.7 12.2 4.8  0.9 6.3 13.7 28.4 1.5 94.3 10.3 29.7 20.6 31.8 10.3 66.0 11.1 27.3 2.7 18.8 6.3 24.8 1.4 11.3 35.0 39.7 20.3 40.1 33.7 70.4 4.6 91.3 2.7 12.3 19.9 26.2 19.4 21.0 10.3 10.7 6.3 25.2 15.2 44.0 18.9 74.7 12.4 32.2 5.7 20.9 6.6 58.1 6.1 16.3 2.0 16.4 ti.O .2.3 10.1 32.1 96.4 42.0 10.8 31.7 65.1 9.9 66.4 12.4 4.2 16.9 29.9 .3.6 24.d 15.d 2.0 4.4 0.0 49.1 23.9 62.7  K  L  F OBS  4 4 4 4  4 5 0 7 0 9  7 17 4 17 4 <7 4 20 2 49 9 19 9  4 4 4 4 4 4 4 4 3  3 5 3 5 9 5 5 5 3 9 9 5 5 5 6 6 6 6 6  6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7  7  7 6 6 8 8 6 8 8 8 6 6 d 8 9  8 d 9 9  9 9 9  9 9 9  9 9 9 V 9 9 9  10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11' 11 11  10 11 12 ll 14 15 16 0 1 2 3 4  5 6  7 6 V  10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 0  9 10 11 12 13 14 13 0 1 2 3 4 5 6  7 e 9  ' 10 11 12 13 14 19 0 1 2 3 4 5 6 7 6 V  10 11 12 13 16 0 1 2 3 4 3 6 7 8 9 10 11 12 13 14 0 1 2 3 4 3 6 7 8 V  10 . 11 12 13 0 1 2 3 4 3 6 7  19  17 7 0 0 17 2 12 0 20 . 6 6 ,0 6 O 3 9 ,7  32 83  22 ,9 34 ,0 25 , 6 32 ,2 26 • 3 0 0 30 ,4 11 .3 37 . 7 29 .9 26 6 10 2 0 .0 0 ,0 17 .0 23 .8 28 6 54 7 46 1 11 ,3 <1 .6 24 .9 20 3 19 5 27 7 0 .0 0 .0 16 .1 12 .9 16 3 16 6 53 6 0 .0 23 »0 36 • 9 24 .3 44 7 16 6 14 .3 17 .2 12 .9 29 7 12 4 25 6 0 0 0 0 0 0 14 3 39 2 39 9 33 8 28 6 17 9 23 3 26 1 27 2 21 3 16 8 0 0 0 0 10 4 30 4 16 1 10 2 e 6 37 0 33 1 56 3 14 3 30 4 11 1 0 0 10 9 12 4 15 4 0. 0 d. 4 0. 0 34 2 9. 7 31. 7 14, 3 13. 4 12. 7 30 4 10 9 22 2 13 6 0. 0 6, 6 27, 9 14 7 10, 9 15. 2 19, 0 21. 3 29. 3 15. 9  (Continued). F CALC 30.0  17.1  10.7 .0.4  19.7  48.6  19.0 15.2 4*d 17.7 13.7 23.0 7.0  32.6 d7.9 59.0 24.0 33.5 23.7 32.0 27.9 3.6 30.0 11.9 36.7 20.9 27.3 11.1 4.3 5.1 16.2 23.1 29.1 54.3 47.3 8.5 21.9 26.1 27.3 17.0 26.2 8.0 6.8 16.0 13.5 17.7 18.6 33.2 6.3 23.7 35.9 23.4 43.4 15.0 12.6 12.8 ii.: 26.t 13.4 24.6 0.2 1.6 1.6 14.6 40.4 39.5 35.8 29.9 17.9 23.3 26.1 27.5 21.0 17.4 5.5 7.1 11.5 30.2 16.3 9.6 9.1 36.7 33.6 55.8 16.4 30.3 •' 9 . 9 0.2 13.1 13.1 15.2 3.8 10.1 6.0 36.3 9.4 30.9 12.6 11.7 11.2 29.4 13.6 21.9 12.6 4.0 0.6  20. 7 14.3 10.6 14.4 19.2 17.9 28. 1 13.3  It  L  F OBS  11  0  17.2  9  0.0  11  11  11 11 12 12  12  12  12 12 12  12  12 12 12 12 11 13 13 13 13 13 13 11 13 13 14 14 14 14 14 14 14 14 14 14 13 » 13 15 15 15 15 15 15 16 16 16 16 16 0 0 0  0  0 0 0 0 0  0  0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2  2 2  2 2 2 2 2 2  2 2 1 1 3  1 3  1 3  1 1 > 1 j 1  t >  10 11 1£ 0 1. 2  1 4 5 6  7 6  9 10  11 0 1 2 3 4 5  6 7 0  9 10 0 1 2 3 4 5 6 7 6 9 0 1 2  3  4 5 6 7 0 1  2 3  4 1 2 3 4 5 6 7 8  »  10 11 12 13 14 15 16 0 1  2  3 4 5 6 7 6 9 10 11 12 13 14 15 0 1 2  3 4 3  6  7 d 9 10  11 12 11 14 15 0 1 2  1 4 3 6  F CALC  H  K.  L  10.4  3  3  19  7.0  7.9  7.o  0.0  0.2  11.9 1.7  12.9  0.0 0.0  7.5  22.7 9.9 21.1  21.1  d.3  20.2  0.0  3.2  0.0  5.8  8.8  8.6  ld.l 0.0 13.6 0.0 35.4 0.0 15.4 0.0 0.0 12.2 16.3 11.3 10.2 0.0 16.3 6.4 0.0 22.9 0.0 17.7 0.0 0.0 0.0 13.4 0.0 25.6 0.0 16.3 0.0 0.0 0.0 7.7 7.7  17.1 4.5 14.3 4.6 36.1 8.3 16.4 6.9 5.1 11.6 16.0 10.5 10.0 4.5 16.5 9.0 6.0 22.8 1.3 19.2 2.4 3.4 4.0 14.8 4.9 25.9 1.6  16.4 1.9 3.9 0.8 9.0 8.0 1.2 3.0 16.4  0.0  6.3  13.6 0.0 9.0 79.2 40.6 0.0 26.1 21.9  2.9  9.6 77.6 39.7 3.1 24.1 22.1 9.4 24.5 16.8 12.9 29.3 26.3 2.0 21.2 9.7 1.4 16.4 34.6 29.4 17.0 65.3 23.1 25.6 30.5 <2.4 34.3 31.9 5.0 9.4 15.5 16.4 3.7 16.7 31.0 34.4 43.1 4.9 13.1 41.o ,8.4 27.0 32.1 1 1.6  0.0  25.4 18.1 11.5 28.1 27.4 0.0 16.6 0.0 0.0 13.6 34.9 27.7 18.8 69.7 24.0 29.2 51.5 23.0 34.2 31.7 10.4 0.0 18.6 17.0 0.0  13.2 31.1 53.6  43.6 0.0 33.6 41.7 29.1 26. i 32.9 12.9 24.0 29.7  25.5  31.2  4.5  0.0 lO. D  10.3 10.1 9.0 31.2  9.1  0.0 50.0 34.9 14.9 40.4 30.6  33.2  16.4 39.3 29.1  22.2  20.5  36.3  7 d 9  21.0  10 11 12 11  16.1  14  7.9  26.3 41.7  ld.O 17.0 16.0  '  35.9 18.7 .= 7.2 39.9 16.2 2 2.0 lr.4 17.9 0.5  3  1 3  3 3  1 1 1 1 3  3 3 3  3 3 3 3 3 3  3 1 3 3 3 3 3 3 3  3 3 3 3 3 3  3 3 3 3 3 3 3  3 3 3  3 3  3  3 1  3 3 3 3 3 3 3 3 3 3 3  3 3  3  3 3 3 .3 3  3 3 3 3 3 3  3  3 3 3 3 3 3 3 3 3 3  3 3 3 3 3  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5  5 5 5  5  5 5 5 5 5 5 5 5 5 9 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 6 6 0  6 6 6 a  8 8 6  d 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9  1  10 10 10  3 3 3 3 3  10 10  3 3  3 5 3  1 1 J 1  3  1 1  1 1 1 3  1  10  10 10 10  10 10  10 10 11 11 11 11 11 11 11 11  0 1 2  1 4 9  6  7 d 9 10 11 12 13 14 13 0 1 2 3 4  3  6 7 8 9 10 11 12 13 14 13 0 1 2 1 4 5 6 7 6 9 10 11 12 13 14  0 1  2 3  4 5 6 7 6 9 10 11 12 13 14 0 1 2 1 4 5  6 7 8 9 10 11 12 13 0 1 2 3  4  -3  6 7 d 9 10 11  12 1 1  0 1  2 3  4 3 6 7 6  9 10  11  12  0 1 2  1 4 9  6  7  11  0  11  *  F OBS 16.d  0.0  F CALC id. 5 5. 1  29.7 30.4 14.0 42.2 36.1 30.2 33.6 22.0 14.3 14.7 18. 1 9.3 9.9 10.6 7.2 51.7 38.3 29.7 34.9 24.3 13.4 23.4 11.6 10.9 28.6 20.6 19.7 23.6 8. 1 13.6 12.4 29.3 24.7 27.9 17.0 39.4 31.5 27.9 35.1 12.0 0.0 18.4 18.4 19.0  30.6 12.3 14.9 41.0 36.7 28.6 31.1 19.2 12.1 13.5 18.1 10.6 10.5 9.6 6.2 52.3 37.9 29.6 36.0 24.3 14.3 23.9 13.0  9.3 30.8 19.7 36.1 24.7 37.9 37.2 17.7 26.9 12.0 19.7 21.6  8.6 30.0 19.7 36.6 26.2 39.0 36.0 14.8 21.8  0.0  9.3  19.3 0.0 12.9 35.6 12.9 16.6 20.6 22.9 30.8 27.9 18.1 11.6 0.0 27.2 16.3 16.8 7.0 16.3 0.0 23.0 16.1 13.4 32.4 13.1 18.6 13.6 13. 1 0.0 0.0 9.3 9.1 33.4 22.7 12.2 15.2 14.0 23. 1 14.9 9.0 9.7 10..' lo.i 10.4 19. £ 0.0  14.7 22.4 11.1 20.2  19.9 19.4 17.. 22.0 7.4  8.2  25.7 21.3 20.0 22.7 9.3 19.6 14.1 28.2 26.0 27.8 15.8 36.3 29.9 25.9 93.9 12.3 8.0 16.5 18.0 16.1  5.2  6.0  19.0 22.4 9.4 19.8 6.1 13.5 36.8 13.3 18.7 21.0 20.2 31.1 26.3 16.9 11.8 7.9 24.6 14.2 17.7 7.2 16.0 5.1 23.9 16.9 12.3 31.8 12.6 17.3 14.7 13.7 9.0 9.5 10.1 11.0  30.2 24.9 12.1 16.1 12.3 21.3 13.7 10.0 9.0 10.4 19.0 10.6 14.9 3.6  11.0  22.3  12.0 21.2 19.3 19.5 17.0  . 2 . 1 6.0  101 TABLE. -Ah.  F  12 12  12 13 13 13 13 13 13 13 11 13 14 1*  u  1* 1* 1* 1* 14 13 13 13 19 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  OBS  F CALC  13.11 rj.d 23. d  14.1  12. 4 0.0 11.9 11.d 10.3 22. * 7.2 12.2  13.9 8.511.1 13.4 13.9 22.6 . 6.0 13,2 7.6 0.3 15. d 19.1  7.2 0.0 14.3 10.9 0.0 14.9 0.0  B.B 9.0 12.0 12.7 9.9 0.0 9.7 12.9 0.0 12.9 0.0 0.0 13.0 10.9 6.1 6.) 67.6 0.0  SB.3  16.7 21.1 19.6 39.9 12.7 13.6  0.0 11.7 0.0  26.3 0.0 11.3 0.0  9.3 39.6  21.1 62.2  0.0 0.0 11.s 31.6 0.0 19.3 16.9 0.0 0.0 19.1  67.2 9.3 33.6 0.0 26.3 36.1 26.1 19.6  11.8 11.3 26.3 0.0 22.7 0.0 9.9 0.0 11.6 42.2 22.9 24.7 11.3 l l . a 16.1 18.6 0.0 i a . i 9.7 0.0 0.0 19.4  io.a 9.0 ia.6  0.0 26.6  9.3 .6.3  6.0 16.9 3.7 9.0 9.9 13.2 11.3 10.4 3.1 10.6 11.4 5.5 13.7 1.0 0.0 15.4 11.0 6.9 6.5 63.9 4.9 55.4 10.6 19.0 14.0  16.7,  10.5 12.1  0.1 11.4 1.6 28.0 1.9 12.6 1.9 7.2 54.2 21.9 40.6  5.1 2.1 a.7 32.4 5.4 19.8  11.6 1.2  2.6 21.1 47.1 7.9 34.9 2.8 29.9 13.4 21.8 11.4 13.6 11.5 23.9 3.7 24.9 3.3 io.a 2.8 13.4 43.0 23.4 23.4 a.9 9.3 14.9 38.4 9.4 20.2 9.7 2.9 2.8 17.0 90.9 9.1 18.6 9.0 27.2  H  It  L  F UBS  4 4 4 4 4 4 4 4 4 4  4 4 4 4  5 6 7 8  35.2 41.5 16.3  4  9  4  5 5 5 5 5  4 4 4 4 4 4  4  4 4 4  3  5 5 5  4 4 4 4 4  •53  4  5 5  4 4 4  6 6 6  6 4  6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 B B ' 8 a B a a a a  4 4 4 4 4 4 4  4 4 4  4 4 4 4 4 4 4 4 4 4 4 4 4  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  4  4 4  4  4 4 4 4 4 4 4. 4* 4  *  4' 4 4 4  * 4 4  4 4.  4  4  4  B  B B  9  10 11 12 13 1 2  3  4 5 6 7  8  9  10 11 12 13  2  1  4 3 6 7 8  9  10 11 12  11 1 2 3  4  3 6 7 B  9  10 11 12  X  2 3  4 9 6 7 B  9  10 11  0.0 0.0 11.1 7.9 14.0 12.7 0.0 22.0 23.1 24.3 17.2 9.1 0.0 15.9 17.9 16.1 0.0 0.0 1S.1 11.1 19.9 10.4 19.0 9.7 24.7  a.s  12.2 0.0 0.0  16.B  4 3 6 7 6  12.7 10.9  1 2  9 y  3  10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 12 12 12 12 12  12.7 0.0 16.1 0.0 0.0 13.6 24.3 23.1 33.3 20.4 0.0 11.3 32.4 19.3 23.6 0.0 0.0 0.0 20.8 24.0 0.0 10.9 30.2 18.1 30.2 18.8 21.3  0.0 11.3 18.6 24.9 14.1 14.7 0.0 0.0 11.B 22.4 0.0 o.o 19.6 29.4 11.9 0.0 0.0 17.9  9 9  9 9 9 9 9 9 9  33.6 9.9  4  3 £ 7  a 9  10 11  1 2 3  9  10  1 2 3 4  3 6 7 a  I  2 3 4  B.6  6.B  6.1 9.5 13.8 9.7 20.B 10.4 0.0 8.1 9.7 0.0 10.9 17.7 9.0 0.0 0.0  F CALC 34.3 39.5 15.6 32.1 9.4 12.9 5.8  Id.3 5.9 1.9 12.6 24.5 23.0 33.4 16.3 6.4 12.2 30.0 18.7 25.2 6.5 2.5  J.) 19.8 22.9 3.6 8.2 29.2 16.3 29.0 20.6 21.8 4.1 1.1 11.8 9.4 16.0 12.9 7.1 23.0 22.9 22.1 16.9 2.6 4.4 17.0 16.3 19.2 a.4 6.B 15.2 .31.6 11.1 10.0 17.2 9.1 23.8 9.1 9.6 3.0 6.0 16.7  1.1 11.8 20.9 25.6 16.0 15.7 3.1 8.0 12.7 22.1 2.a 5.1 15.1 27.0 13.6 6.6 1.1 14.9 8.9 12.6 10.3 6.6 6.4 6.4 15.2 8.4 21.7 11.9 8.1 7.3 10.6 2.6 9.6 19.1 10.9 4.3 4.4  (Continued).  H 4 4 4 4 4 4  K 12 12 12 13 13 13 13 13 13 14 14 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2  2 2 2 2  2 2 2 2 1 J 1 1 1  ] 1 1 3 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 9 9 5 5  3 3  9 5 5 5 5 6 6 6 6 6  6 6 6 6  6 6 7 7 7 7 7  L  F  5  16.3 7.9 14.7 0.0 8.4  6 7  1  2 3 4 5 1 1  2 3 4 3  6 7 8 9 10 11 12 1 2 3 4 5 6 7 9 10 11 12 1 2  3  4 9 6 7  a 9  10 11 0 \  2  1 4 9 6 7 a  9  10 11  X 2 ) 4  3  6 7 6 9 10 IX  X 2  3  4 3 6 7 8  9 10 0 1  2  3 4 3 6 7 B 9 10 0 1 2 3 4  OBS  0.0 21.1 0.0  5.6 5.4 8.8 32.9 21.3 11.6 13.4 13.4 0.0 10.4 24.3 8.6 18.1 7.0 7.7 61.9 13.4 0.0 21.3 0.0 12.4 29.5 0.0 13.1 21.5 12.7 0.0 d.6 0.0 23.6 31.7 0.0 26.7  10.2  0.0 1B.B 19.0 0.0 19.9  a.l  29.0 17.0 16.1 26.1 16.9 9.1 26.1 0.0 9.1 10.4 B.l 11. 8 0.0 10.9 22.0 19.4  23.a  16.3  11.1 19.4 12.9 8.6 10.6 6.1 26.7 12.0 19.9 16.1 10.9 14.0 17.9 0.0 0.0  8.6  11.3 0.0 0.0 13.6 14.9 19.6 14.9 10.2 21.8 8.6 7.6  6.3 19.0 12.9 0.0 12.9 10.6  F  CALC 17.0 2.4 16.2  3.2 8.8  3.9  22.2 5.0 6.0  2.6  7.8 34.1 17.1 10.4 12.6  0.9 3.0 8.8 25.2 9.4 20.4 7.4 6.7 42.5 11.6  7.9 19.9 6.1 10.4 30.4 3.7 13.3 22.3 12.3 2.7 10.4 7.1 24.1 31.6 t.O 26.8 11.3 5.B 17.B 19.3 6.1 20.7 10.B 30.0 16.5 16.0 26.0 19.1  7.3  26.4 6.2 9.6 11.1 7.7 11.1 l.B 9.6 19.7 17.4 26.1 17.9 16.5 15.7 11.2 9.4 11.7 7.7 26.8 10.9 16.0 18.2 10. a 12.5 18.0 8.6 4.0 9.7 12.1 3.2 5.8 16.7 18.3 20'. 2 16.2 11.0 21.3 10.0 10.0 6.0 20.1 13.2 10.3 13.3 10.2  M  K  L  F  9  7  9 5 5 5 5 5 5 5 5 5 5 9 5 9 5 9 9 5 5 5 5 9 9 » 5 9  5  7 7 7 7  6  18.6 12.4 15.6 0.0 10.9 10.6 11.9 14.3 17.9 10.6 9.7 0.0 19.2  6 6 6 6 6 8 8 8 8  9  V  6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 6 6 6  6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6  6  6 6 6 6 6 6 6 6 6 6  6 6 6  6  9 10 10 10 10 10  7  2 2 2  22  6 6 6 6 6 6 6 6 6  9  2  6 6 6 6  3 3 3  33 -  3 4 5 6 7 8  9  10 10 11 11 11 11 11 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 I 2 2 2  9 5 5 9 9 9 6 6  2  1 2 3 4 5  9 9 9  3  7 8 9 0 1  3 3  36 4 4 4 4 4 4 4 5 3 9 9 9 5 5 6 6 6  i 2 1 4  3  6  1 2 3 6 X 2  3  4 9 6 7 N 0 J  2 1 4 3 6 7 a  i 2 1 4 9 6 7 a i 2 1 4 5 6 7 1 2 3 4 9 6 7 1 2 1 4 3 6  6  1 2 3 4  6  3  7 7 7 7 7  2 3 4  6  8 8 8  I  1 2  OBS  8.8 0.0 12.4 11.1 8.1 9.3 18.1 8.6 10.9 12.2 10.2 10.9 14.1 0.0 8.8 0.0 0.0 10.6 9.9 0.0 10.2 16.7 11.S 0.0 16.6 10.6 11.1 0.0 10.2 0.0 0.0 11.6 0.0 0.0 0.0 19.5 0.0 15.2 0.0 0.0 16.0 0.0 12.9 6.6 12.2 0.0 10.6 0.0 0.0 16.a  9.3  0.0 0.0 15.2 0.0 12.9 0.0 16.5 0.0 14.7 10.4 11.1 0.0 8.4 10.4 19.9 9.1 0.0 0.0 11.8 9.5 0.0 7.7 11.8 13.4  8.6 6.1 9.3 11.8 0.0 5.9  9.3 0.0 5.4 9.9  F  CAL 19.7 13.0 15.1 7.5 10.8 10.8 10.6 13.8 19.3 8.2 10.1 7.4 15.8 8.3 0.0 12.7 10.2 9.6 10.1 18.4 7.7 12.1 13.1 10.6 12.2 15.5 6.0 8.1 5.0 0.6 11.1  9.3  3.6 11.2 19.7 11.7 1.1 20.9 7.1 16.1 4.6  9.3  2.2  2.5  19.2 8.2 4.7 4.6 21.1 2.5 18.0 7.5 1.9 17.3  2.6  14.8  10.9 14.] 4.1 11.1 1.6 1.0 20.9 11.7 1.6 1.0 18.4 6.2 15.5 0.2 19.9 8.0 19.9 9.9 11.9 2.6 11.6 12.3 23.2 11.6 3.6 5.7 13.4 10.1 6.2 6.1 14.2 15.5 9.1 7.2 12.2 16.0 4.7  5.2  11.7  2.0  5.2 11.2  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 i n v e s t i g a t e d t o determine the configurations of h e x i t o l s and h e p t i t o l s obtained by hydrof o r m y l a t i o n of g l u c a l s and a r a b i n a l s (68). The c r y s t a l data were determined from various r o t a t i o n , Weissenberg, and precession photographs. C r y s t a l 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 ft . 3  D  m  = 1.4, Z = 4, D  = 1.40 g cm" . 3  x  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  OH  HO  II  1-0-(p-toluenesulphonyl)-2,6-anhydro-3-deoxy-d-gluco-heptitol ( I I ) , C H 0 S , M.W. 1 4  2 0  7  = 332.3.  104 M o n o c l i n i c , a - 8.52 + 0.01, b = 33.81 ± 0 . 0 5 , c = 6.25 ± 0.01 ft, p= 116.3° ± 0.1°. U - 1614 ft . 3  D  m  = 1.33, Z = 4, D  = 1.37 g cm" . 3  x  Absent s p e c t r a : OkO when k i s odd.  Space group i s P 2 j .  A more s u i t a b l e d e r i v a t i v e was obtained  (69), and no  f u r t h e r d e t a i l e d a n a l y s i s i s planned.  Polymer of (CH^AsS) (CH-jAsS) was i n v e s t i g a t e d i n order to determine the n  value of n and the s t r u c t u r e of the molecule. C r y s t a l data:  (CH AsS) 3  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 ft . 3  2.28 < D  m  < 2.55,  D ( n - 12) - 2.308. x  No absent spectra:  Space group  PI or P I .  Because of i t s ready r e a c t i v i t y w i t h , or s o l u t i o n i n most solvents the density could be determined only approximately . Molecular weight measurements on s i m i l a r molecules (70) have shown that trimers and tetramers are common f o r As-S and As-0 compounds.  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