UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The crystal and molecular structures of some organic compounds. Mak, Thomas Chung Wai 1963

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1963_A1 M23 C7.pdf [ 10.89MB ]
Metadata
JSON: 831-1.0062271.json
JSON-LD: 831-1.0062271-ld.json
RDF/XML (Pretty): 831-1.0062271-rdf.xml
RDF/JSON: 831-1.0062271-rdf.json
Turtle: 831-1.0062271-turtle.txt
N-Triples: 831-1.0062271-rdf-ntriples.txt
Original Record: 831-1.0062271-source.json
Full Text
831-1.0062271-fulltext.txt
Citation
831-1.0062271.ris

Full Text

THE CRYSTAL AND MOLECULAR STRUCTURES OF SOME ORGANIC COMPOUNDS by THOMAS CHUNG-WAI MAK Sc.(Hon.); U n i v e r s i t y o f B r i t i s h Columbia, i960  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT 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, 1963  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the requirements f o r an advanced degree at the U n i v e r s i t y  of  B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and mission for extensive purposes may  study.  I f u r t h e r agree that per-  copying of t h i s t h e s i s f o r s c h o l a r l y  be granted by the Head of my Department or  his representatives.  I t i s understood that copying, or  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be without my w r i t t e n p e r m i s s i o n .  Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8 , Canada.  by publi-  allowed  line . U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of PUBLICATIONS A.R. Osborn, T.C.W.Mak and E. Whalley; Pressure E f f e c t and Mechanism i n Acid C a t a l y s i s . V I I I . Hydrolysis of Acetamide and Benzamide. Can. J . Chem. , 39, 1,1.01 (1961). T.C.W. Mak and J . T r o t t e r : The Structure of B i ~ phenylene. P r o c Chem. Soc,, 163 (1.961). T.C.W. Mak and J . T r o t t e r ; The C r y s t a l and Molecular Structure of Biphenylene. J . Chem. S o c , 1(1962). T.C.W. Mak and J . T r o t t e r : The C r y s t a l and Molecular Structure of ". Methoxycarbonylmercuric C h l o r i d e . J . Chem. S o c , 3243 (1.962). T.C.W. Mak and J . T r o t t e r ; The C r y s t a l Structure of £-Chloronitrobenzene. Acta Cryst., _15, 1078 (1962). T.C.W. Mak and J . T r o t t e r : C r y s t a l l o g r a p h i c Data for Some Acenaphthene Derivatives. Acta Cryst., 16, 324 (1963).  THOMAS CHUNG=WAI MAK B.Sc.(Hon.), The U n i v e r s i t y of B r i t i s h Columbia THURSDAY, JULY 18, 196.3, at 9;30 A.M. IN ROOM 261, CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman:^ F.H. Soward W.A. Bryce H.C. Clark J.P. Kutney  W. Opechowski S.A. Sutherland RiMi Thompson J. Trotter  External. Examiner; E.C. L i n g a f e l t e r University  CHtS/^tS-r^t  ~tf^G/*fe-  o f Washington  THE CRYSTAL AND MOLECULAR STRUCTURES OF SOME ORGANIC COMPOUNDS ABSTRACT . The c r y s t a l and molecular structure of biphenylene has been r e f i n e d from normal and generalized p r o j e c t i o n s along the c - a x i s . 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 have been confirmed. A comparison of the measured bond lengths and those c a l c u l a t e d by simple resonance theory and by molecular o r b i t a l theory i n d i c a t e s that the l a t t e r gives a better d e s c r i p t i o n of the e l e c t r o n d i s t r i b u t i o n i n the molecule. I n terms of the Kekule s t r u c t u r e s the preferred formulation i s that which describes the molecule as a cyqlobutane d e r i v a t i v e . These conclusions are i n agreement with the chemical behaviour of biphenylene and i t s d e r i v a t i v e s . An adduct formed by passing carbon monoxide i n t o a s o l u t i o n of mercuric c h l o r i d e i n methanol has been shown by X-ray a n a l y s i s to be methoxycarbonylmercuric" c h l o r i d e . The c o o r d i n a t i o n around the mercury atom i s e x a c t l y l i n e a r , and the molecule i s planar, except f o r the methyl group, whose carbon atom i s displaced by 0.39A from the plane of the other atoms.  The acenaphthenequinone molecule i s planar, and the short peri-bonds (average value 1.48i0.OI4A) are i n d i c a t i v e of conjugation between the aromatic rings and the carbonyl groups. The C^=C2 bond distance of 1.53*0.02A agrees w e l l w i t h the value reported for acenaphthene„ In cis-1,2-acenaphthenediol the peri-bonds are s i g n i f i c a n t l y shortened (mean length 1.48-OToio-A) while the 1.60i0,0l4A C^-C2 bond distance shows the e f f e c t of r i n g s t r a i n and s t e r i c r e p u l s i o n of the non-bonded oxygen atoms. The c r y s t a l s t r u c t u r e c o n s i s t s of zigzag chains of i n t e r m o l e c u l a r hydrogen bonds formed between molecules r e l a t e d by a screw a x i s , the intermolecular 0.... 0 distances being 2.72 and 2.70A.  The C]_-C2 bond i n cis-1,2-acenaphthenediol d i n i t r a t e has a length almost i d e n t i c a l to that i n the d i o l . There i s no bonding between the n i t r o x y groups, which .< are planar and i n c l i n e d at angles of +62.1° and +71.2° to the plane of carbon atoms. GRADUATE STUDIES  A re-examination of the c r y s t a l structure of p_-chloro- F i e l d of Study: . Chemistry nitrobenzene has e s t a b l i s h e d that the space group i s not Crystal Structures K.B. Harvey Pa as p r e v i o u s l y assigned, but*P2^/a which implies a J. Trotter molecular centre of symmetry. Projections along the aTopics i n P h y s i c a l Chemistry J.A.R. Coope and b-axes i n d i c a t e that t h i s i s achieved by a disordered R.F. Snider arrangement o f molecules i n v o l v i n g random interchange o f Topics i n Inorganic Chemistry Staff the p o s i t i o n s of the c h l o r i n e atom and n i t r o group. Topics i n Organic Chemistry Staff Spectroscopy and Molecular S t r u c t u r e Staff A s e r i e s o f acenaphthene d e r i v a t i v e s has been examined Quantum Chemistry J.A.R. Coope by X-rays, and the c r y s t a l and molecular s t r u c t u r e s of S t a t i s t i c a l Mechanics R.F. Snider acenaphthenequinone, cis-1,2-acenaphthenediol and c i s - 1 , T h e o r e t i c a l Chemistry R.F. Snider 2-acenaphthenediol d l n i t r a t e determined w i t h p r e c i s i o n . In a l l three compounds the carbon skeleton i s planar, and Related Studies: the s t r a i n i n the p e r i - r i n g i s almost e n t i r e l y taken up C l a s s i c a l Mechanics W..Opechowski by valency-angle- d i s t o r t i o n s , both i n the p e r i - r i n g and Quantum Mechanics W. Opechowski i n the naphthalene r i n g s . The v a r i a t i o n of bond lengths Abstract Algebra N.Ji Divinsky i n the aromatic nucleus i s s i m i l a r to that i n naphthalene. Computer Programming Miss Charlotte Froese  - 11  -  ABSTRACT The c r y s t a l and molecular structure of biphenylene has "been r e f i n e d from normal and generalized p r o j e c t i o n s along the c-axis.  The gross features  of the structure p r e v i o u s l y determined have "been.confirmed. • A comparison ,of the'measured,bond, lengths ,and those calculated  by simple resonance theory  and by molecular o r b i t a l theory i n d i c a t e s that the l a t t e r gives a b e t t e r d e s c r i p t i o n .of the e l e c t r o n d i s t r i b u t i o n i n the molecule.  In terms of the  Kekule s t r u c t u r e s the p r e f e r r e d formulation i s that which describes the molecule as a cyclobutane d e r i v a t i v e .  These conclusions are i n agreement with the  chemicalibehaviour of biphenylene and i t s d e r i v a t i v e s . An adduct formed by passing carbon monoxide i n t o a s o l u t i o n of mercuric c h l o r i d e i n methanol has been shown by X-ray a n a l y s i s t o be mercuric c h l o r i d e .  methoxycarbonyl-  The c o o r d i n a t i o n around the mercury atom i s e x a c t l y " l i n e a r ,  and the molecule i s planar, except f o r the methyl group, whose carbon atom i s o displaced by 0.39 A from the plane of the other atoms. A re-examination of the c r y s t a l structure of p-chloronitrobenzene has e s t a b l i s h e d that the space group, i s not Pa as p r e v i o u s l y assigned, but which i m p l i e s a molecular centre of symmetry.  ^^./a  P r o j e c t i o n s along the a- and  b-axes i n d i c a t e that t h i s i s achieved by a disordered arrangement of molecules i n v o l v i n g random interchange of the p o s i t i o n s of the c h l o r i n e atom and n i t r o group. A s e r i e s of acenaphthene d e r i v a t i v e s has been examined by. X-rays, and the c r y s t a l and molecular s t r u c t u r e s of acenaphthenequinone, c_is_»l,2-acenaphthenediol and c i s - l , 2 - a c e n a p h t h e n e d i o l d i n i t r a t e determined with p r e c i s i o n .  In a l l three  compounds the carbon s k e l e t o n , i s planar, and the s t r a i n i n the p e r i - r i n g i s almost e n t i r e l y taken up by valency-angle d i s t o r t i o n s , both i n the p e r i - r i n g and i n the naphthalene r i n g s .  The v a r i a t i o n of bond lengths i n the aromatic  - iii nucleus i s s i m i l a r to that i n naphthalene. The acenaphthenequinone molecule i s planar, and the short peri-bonds (average value l.kQ  + 0.01^%) are i n d i c a t i v e of conjugation between the  aromatic r i n g s and the carbonyl groups. The C-^-^ bond distance of o 1.53+0-02A agrees w e l l with the value reported f o r acenaphthene. In c i s -1,2 -acenaphthenediol the peri-bonds are s i g n i f i c a n t l y shortened (mean length 1.1+8+0.01 A) .while the 1.60+0.Ol^A Q  bond distance shows the  e f f e c t of r i n g s t r a i n and s t e r i c r e p u l s i o n of the non-bonded  oxygen,atoms.  The c r y s t a l structure c o n s i s t s of zigzag chains of intermolecular hydrogen bonds formed between molecules r e l a t e d by a screw a x i s , the intermolecular 0  0 distances being 2-72  and 2-70  A.  The C-^-C^ "bond i n c _ i s - l , 2-acenaphenediol d i n i t r a t e has a length almost i d e n t i c a l to that i n the d i o l .  There i s no'bonding between the n i t r o x y  groups, which are planar and i n c l i n e d at angles of +62.1° and +71-2° to the plane of carbon atoms.  - V -  ACKNOWLEDGEMENTS I g r a t e f u l l y , acknowledge the i n s p i r a t i o n and.guidance of Dr. James T r o t t e r throughout my graduate study.  His u n f a i l i n g encouragement and warm p e r s o n a l i t y  have made my. a s s o c i a t i o n with him a most memorable one. My thanks.are due t o Professor J.M. Robertson f o r the sample of biphenylene, t o Dr. J . Halpern and Mr. A.L-W. Kemp f o r t h e , c r y s t a l sample of methoxycarbonylmercuric c h l o r i d e , , t o Dr. M.P. Cava f o r c r y s t a l s of several d e r i v a t i v e s of benzocyclobutene, and t o Drs. L.D. Hayward and I.G. • Csizmadia for, the series of acenaphthene d e r i v a t i v e s . Dr. Hayward f o r h i s continuing  I am e s p e c i a l l y g r a t e f u l t o  i n t e r e s t i n the problem, f o r much h e l p f u l  discussion and advice,,and f o r b r i n g i n g t o my.attention important new data i n advance of p u b l i c a t i o n . I am also indebted t o Dr. F.R. Ahmed f o r k i n d l y making a v a i l a b l e h i s IBM 1620 Fourier and structure f a c t o r programs,.to Mr. N. Camerman f o r various a u x i \ l i a r y programs,, and t o the s t a f f of the UBC Computing Centre f o r assistance w i t h the operation of the computer.  For some of the i l l u s t r a t i o n s  i n t h i s t h e s i s I wish to thank Mr. W. Griba. F i n a l l y I wish t o record my.appreciation t o the National Research Council of Canada f o r the award of a bursary f o r the period I96O-61,. and a studentship f o r the period  I96I-63.  To MY PARENTS f o r t h e i r a f f e c t i o n , s a c r i f i c e and encouragement  - vi-  TABLE OF CONTENTS Page TITLE PAGE  (i)  ABSTRACT  (ii)  ACKNOWLEDGMENTS TABLE OF CONTENTS  '  (v)  ......  (vi)  LIST OF FIGURES  . . (viii)  LIST OF TABLES  (x)  GENERAL INTRODUCTION  1  PART I . THEORY AND PRACTICE OF CRYSTAL-STRUCTURE ANALYSIS  3  I.  II.  III.  Elementary Crystallography A. C r y s t a l Geometry B. Symmetry of C r y s t a l s and Point Groups C. Space L a t t i c e s D. Space Groups D i f f r a c t i o n of X-Rays by C r y s t a l s A. . S c a t t e r i n g e f X-Rays by C r y s t a l s B. Conditions f o r X-Ray 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. The I n t e n s i t i e s of- X-Ray Reflexions F. Representation of the C r y s t a l as, a F o u r i e r Series . . . . G. The Phase Problem ' The A. B. C. D. E.  Determination of C r y s t a l Structures Two-Dimensional P r o j e c t i o n s The I n t e r p r e t a t i o n o f D i f f r a c t i o n Patterns Methods f o r Obtaining an Approximate Structure Refinement Procedures Assessment of Accuracy . . .  PART I I . THE CRYSTAL AND MOLECULAR STRUCTURES OF BIPHENYLENE, .METHOXYCARBONYLMERCURIC CHLORIDE AND p-CHLORONITROBENZENE . . I.  9 9 9 11 12 13 15 16 17 17 17 17 19 22 2k 25  Biphenylene •A. Introduction •B. Experimental C. Structure Analysis D. Discussion  k k k 7 7  •  25 29 30 1+0  - Vll-  II.  'III.  Methoxycarbonylmercuric  Chloride  II.  III.  IV.  U3 kk U5 51  p_-Chloronitrobenzene A. Introduction B; Experimental C. Structure Analysis D. Discussion  52 52 52 53 58 60  Acenaphthene and D e r i v a t i v e s A. Introduction B. • The Structure of Acenaphthene C. Survey of Known" Analyses of Acenaphthene D e r i v a t i v e s .  61 6l 62 63  Acenaphthenequinone  66  A. Introduction B. Experimental C. Structure Analysis D. Discussion  66 66 68 77  cis-1,2-Acenaphthenediol A. Introduction B. Experimental C. Structure Analysis D. D i s c u s s i o n  80 80 82 83 91  c i s-1,2-Acenaphthenediol D i n i t r a t e  95  1  A. B. C D. V.  ^3  A. Introduction B. Experimental C. Structure A n a l y s i s D. Discussion  PART' I I I . X-RAY STUDIES ON SOME DERIVATIVES OF ACENAPHTHENE . . . . I.  Page  Introduction Experimental Structure Analysis Discussion  General Conclusions  APPENDIX I . STRUCTURE FACTOR TABLES  95 96 97 106 112 Ilk  APPENDIX I I . CRYSTALLOGRAPHIC DATA FOR SEVERAL ORGANIC COMPOUNDS. .  13O  REFERENCES  135  -viii  -  LIST OF FIGURES Page 1.  The Ik Bravais l a t t i c e s  2.  S c a t t e r i n g from a row of atoms i n a l a t t i c e d i r e c t i o n  10  3-  Modulus and d i r e c t i o n of the d i f f r a c t i o n ,vector S  10  1+.  R e l a t i o n s h i p .between S and,the plane (h-jj^h^)  10  5-  D i f f r a c t i o n i n r e c i p r o c a l space  13  6.  E f f e c t of a small e r r o r i n atom l o c a t i o n on D  20  1  6  /Biphenylene  7.  E l e c t r o n - d e n s i t y p r o j e c t i o n along [oOl]  • .•  8.  Measured bond distances and valency angles  9-  Mean bond distances and valency angles  10.  P r o j e c t i o n of the s t r u c t u r e -along [00l]  32 35 36  '.  38  Methoxycarbonylmercuric Chloride 11.  Patterson p r o j e c t i o n s along [00l]  12.  Electron-density p r o j e c t i o n along [00l]  13-  E l e c t r o n - d e n s i t y p r o j e c t i o n along [l00]  lk.  Dimensions of the molecule  15.  P r o j e c t i o n of the structure along [001~J  1+6  and[l06]  1+8 '.  . . '  1+9 50 50  p-Chloronitrobenzene 16.  Patterson projections along [lOO*] and .[oio]  5)4  17-  Electron-density p r o j e c t i o n along [lOO]  56  l8.  Electron-density p r o j e c t i o n along [Old]  57  19-  Mean-bond lengths and valency angles i n naphthalene -and i n some compounds containing the acenaphthene nucleus  61+  Ac enaphthenequinone 20.  R e l a t i o n , o f the o r i g i n of space group P 2 2 2 , of i t s p r i n c i p a l p r o j e c t i o n s 1  1  1  to the o r i g i n s 67  - ix Page 21.  Patterson p r o j e c t i o n along [ o o i ]  ' . 69  22.  E l e c t r o n - d e n s i t y p r o j e c t i o n along [ o o i ]  23.  E l e c t r o n - d e n s i t y p r o j e c t i o n along [ l O o ]  72  24.  Numbering and average dimensions of the molecule  76  25-  P r o j e c t i o n of the structure along [OOI]  '  1  71  78  cis-1,2-Acenaphthenediol 26.  Patterson p r o j e c t i o n along J010J  84  27-  Electron-density p r o j e c t i o n along [ o i o ' |  86  28.  Numbering and average dimensions of the molecule  90  29-  P r o j e c t i o n of the structure along [010J  92  30.  Perspective diagram showing the hydrogen bonding  93  cis-1,2-Acenaphthenediol  Dinitrate  31.  Patterson p r o j e c t i o n along [0l6]  32.  Electron-density p r o j e c t i o n along [010]  33-  Numbering and average dimensions of the  '  98 100  104  cis-1,2-acenaphthenediol p o r t i o n of the molecule 34.  P r o j e c t i o n of the structure along [oiO^J  35*  Perspective diagram of the molecular structure • • •  108  36.  CENCO Petersen molecular model  109  37-  Dimensions of the n i t r o x y group  110  38.  Average dimensions of the naphthalene moiety of the acenaphthene system  113  1  107  - X "  LIST OF TABLES Page 5  •I.'  Symmetry Elements of C r y s t a l s  II.  The 32 Point Groups or C r y s t a l Symmetry Classes  5  Biphenylene III. IV. V.  P o s i t i o n a l Parameters  •• . . .  3I4.  O r i e n t a t i o n of Molecules i n the U n i t C e l l  37  Measured and C a l c u l a t e d Bond Lengths  1+0  Methoxycarbonylmercuric Chloride VI.  1+7  P o s i t i o n a l Parameters p-Chloronitrobenzene  VII.  P o s i t i o n a l Parameters  1  58  -.  Acenaphthenequinone VIII. IX. X. XI.  Transformations between Space Group and P r o j e c t i o n Coordinates  67  F i n a l Parameters  7I+  Bond Lengths and Valency Angles  •.  75 77  Molecular O r i e n t a t i o n i n the C r y s t a l cis-1,2-Acenaphthenediol  XII. XIII.  F i n a l Parameters  "  88  Bond Lengths, Valency Angles and Some Intramolecular Approach Distances  XIV. -Molecular O r i e n t a t i o n i n the C r y s t a l  89 91  . . . :  cis-1,2-Acenaphthenediol D i n i t r a t e XV. XVI. XVII.  F i n a l Parameters  102  Bond Lengths and Valency Angles  IO3  Molecular Orientation' i n the C r y s t a l  ,  105  - xi Page Comparison of Measured and Calculated Structure Factors A - l . Biphenylene hkO A-2.  115  •  Biphenylene h k l  Il6  A-3. Methoxycarbonylmercuric Chloride hkO and Ok>fc . . .,  118  A-h.  p-Chloronitrobenzene 0k£  119  A-5<  Acenaphthenequinone hkO and O k Z  120  A-6.  cis-1,2-Acenaphthenediol hOJL  122  A-7.  cis-1,2-Acenaphthenediol hlb  123  A-8.  cis-1,2-Acenaphthenediol D i n i t r a t e hoJl  A-9-  cis-1,2-Acenaphthenediol D i n i t r a t e hlJL  and hO-i  .'  ,  ;  125 127  GENERAL INTRODUCTION  -  2  -  This t h e s i s i s concerned with the'X-ray i n v e s t i g a t i o n of several compounds .of s t r u c t u r a l i n t e r e s t .  I t i s d i v i d e d i n t o three p a r t s .  In Part  I are presented some aspects of c r y s t a l symmetry and d i f f r a c t i o n theory, and an o u t l i n e of present p r a c t i c e of s t r u c t u r e determination "by X-ray,methods. The e x p o s i t i o n i s n e c e s s a r i l y b r i e f , and i s intended to serve as an i n t r o d u c t i o n f o r the general reader. Part I I describes the refinement of the c r y s t a l and molecular s t r u c t u r e of biphenylene, and the determination of the s t r u c t u r e of methoxycarbonylmercuric c h l o r i d e and p-chloronitrobenzene.  Adequate computing f a c i l i t i e s  were not a v a i l a b l e during the analyses of these compounds;,the s t r u c t u r e f a c t o r c a l c u l a t i o n s were performed on,a desk c a l c u l a t o r , and  Beevers-Lipson  s t r i p s were used f o r Fourier summations. In the f a l l of 1961,  an IBM 1620 computer was acquired by the UBC Computing  Centre and s h o r t l y afterwards Dr. Ahmed's s t r u c t u r e - f a c t o r and F o u r i e r programs became a v a i l a b l e . complexity.  I t was now p o s s i b l e to t a c k l e s t r u c t u r e s of f a r greater  A s e r i e s of acenaphthene d e r i v a t i v e s was examined, and the  analyses of acenaphthenequinone, cis-1,2-acenaphthenediol, and c i s - 1 , 2 acenaphthenediol  d i n i t r a t e are described i n Part I I I .  Structure f a c t o r t a b l e s f o r the various compounds are c o l l e c t e d together i n Appendix I.  Appendix I I i s a summary of the c r y s t a l l o g r a p h i c data f o r  trans-1,2-acenaphthenediol, other organic compounds.  trans-1,2-acenaphthenediol  d i n i t r a t e , and several  PART I THEORY AND PRACTICE OF CRYSTAL-STRUCTURE ANALYSIS  - h I.  ELEMENTARY CRYSTALLOGRAPHY A.  C r y s t a l Geometry  Geometrical c r y s t a l l o g r a p h y began when the r e l a t i o n s between the plane faces of c r y s t a l s became a subject f o r i n v e s t i g a t i o n .  I t was discovered by  S t e n o i n 1669 that the angle between corresponding faces on c r y s t a l s of a pure substance i s always constant.  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 are c h a r a c t e r i s t i c of the c r y s t a l . The faces of a c r y s t a l , and a l s o planes w i t h i n the c r y s t a l , can be described by reference to a set of c r y s t a l l o g r a p h i c axes which may be  any  three non-coplanar edges of the c r y s t a l , or d i r e c t i o n s i n the c r y s t a l .  Once 1  the choice of axes i s made, some face i n t e r s e c t i n g a l l three axes may  be  chosen as the parametral plane. I f a, b and c are i t s i n t e r c e p t s on.the c r y s t a l " axes, then i t i s found experimentally that the i n t e r c e p t s of any other face may be expressed as ma, nb, and pc where m, n.and p.are small integers or i n f i n i t y . This f a c t , known as the law of r a t i o n a l i n t e r c e p t s , was f i r s t by Hauy i n  enunciated  1784.  A given c r y s t a l plane i s commonly denoted by i t s M i l l e r i n d i c e s (hk£), which are obtained by expressing the r e c i p r o c a l s of m, n and p as integers without a common d i v i s o r .  The M i l l e r i n d i c e s are always small whole numbers  f o r the well-developed faces of a c r y s t a l . According to the set of axes used to describe t h e i r faces, c r y s t a l s are c l a s s i f i e d i n t o seven systems. B.  These are summarised i n Table I I . Symmetry of C r y s t a l s  A geometrical f i g u r e i s s a i d to possess symmetry i f , by performing on i t some movement or symmetry operation such as r o t a t i o n about an a x i s , repeatedly i f necessary, i t can be brought i n t o s e l f - c o i n c i d e n c e . The symmetry elements possessed by c r y s t a l s are l i s t e d i n Table I with the i n t e r n a t i o n a l symbols devised bv Hermann and Mauquin.  - 5 -  Table  1 2  Identity  element rotation  Four-fold Six-fold  Hassel  in  elements  classes,  also  consistent  rotation  of  axis  showed  known  set  axis axis  that  exactly  possible.  as  the  32  symmetry  These  point  elements  of  Crystals  1  Centre  of  2=m  Mirror  plane  7  Three-fold  IT  Four-fold  5"  Six-fold  distinctive  32  constitute  groups which  symmetry  the  since leaves  at  rotatory  crystal  are  least  made one  inversion inversion  inversion  combinations 32  they  rotatory rotatory  of  axis  these  symmetry  up  of  point  a of  is  elements  symmetry  classes  may  be  possession  characterised  by  the  and  to  a  arrangement  referable is  shown  i n  set  Table  divided  of  II  into  seven  of  minimum number  a  crystal  selfthe  crystallographic  with  both  the  axes.  systems,'each of  The  Schoenflies  of  symmetry general  and Hermann-Mauguin  notations.  Table  II.  System  The  Lattice  T r i c l i n i c  Point  32  Groups  a/b^c  2 m=2 C2 C $  2/m C  a/b/c 0  h  222 mm2 mmm 2 2v 2h  £  k/m  1+22  C  D  1+mm 52m  l+/mmm  o  a=b=c  (Rhombohedral)  ^=(3=^/90°  C  Hexagonal  a=b/c  6  <*=p=90°, V=120° a=b=c  *=p=Y=90°  32 3m  3 3  Trigonal  (  2  D  k  a=b^c  Cubic  Classes  Ci  o<=p=-tf=90) o<=p=V=90  Classes  1 1  o<=y=90°//3 '  Tetragonal  Symmetry  Crystal  Cl  Grthorhombic  Crystal  Constants  a/b^c  Monoclinic  or  C  3  C  3 i  6  6 c  6/m 3 h  23 m3 T  ^  c  6 h  D3  C  622  6mm  »6  C6  Im  3  v  D ^  d  %ra2 V  D  3  D  h  1+32 F3m m3m 0 T 0 a  6/mmm  h  6  h  axis axis  invariant.  The which  rotation  are  Elements  axis  rotation  183O  symmetry  crystal  Symmetry  Two-fold  Three-fold  k 6  I.  - 6 -  1 TMCUNIC 2 SIMPLE MONOCLINIC  Vzy  3. SIDE-CENTERED MOMOCLINIC  Mz^  Yuy  4 SIMPLE 0RTHORH0MBIC  S END-CENTERED ORTHO RHOMBIC  6 FACE-CENTERED ORTHORHOMBIC  7 BODY-CENTERED ORTHORHOMB'C  10 SIMPLE TETRAGONAL  11 BODY-CENTERED TETRAGONAL  y-  9  RHOMBOHEDRAL  8 H6XAGOMAL  1/  -A-  £ Z 7 13. BODYCENTERED CUBIC  12. SIMPLE CUBIC  Figure 1.  Tlie  14 FACECENTERED CUBIC  14 Bravais l a t t i c e s .  C  Space L a t t i c e s  The c h a r a c t e r i s t i c geometrical form and e x t e r n a l symmetry of a c r y s t a l •point to a regular i n t e r n a l arrangement i n which a c e r t a i n u n i t of structure i s repeated i n f i n i t e l y i n space "by regular t r a n s l a t i o n s .  The arrangement of the  c r y s t a l u n i t s may he represented by an o r d e r l y three-dimensional p o i n t s known as a space l a t t i c e .  array of  The l a t t i c e p o i n t s represent the p o s i t i o n s  occupied by the repeating u n i t of the c r y s t a l p a t t e r n , composed of atoms or groups of atoms.  Connecting the l a t t i c e p o i n t s by a regular network of l i n e  r e s u l t s i n a number of i d e n t i c a l p a r a l l e l - s i d e d u n i t c e l l s .  The choice of a  u n i t c e l l f o r a given space l a t t i c e i s d i c t a t e d by considerations of convenience i n v i s u a l i z i n g the symmetry and c a r r y i n g out mathematical c a l c u l a t i o n s . Obviously the space l a t t i c e i s completely defined by the three non-coplanar vectors representing the u n i t c e l l edges.  These three b a s i s v e c t o r s , • u s u a l l y  denoted by a, b, and c", are also r e f e r r e d to as the p r i m i t i v e t r a n s l a t i o n s of the l a t t i c e . In lQk& Bravais showed that there are Ik d i s t i n c t space l a t t i c e s . c e l l s of the lh space l a t t i c e s are i l l u s t r a t e d i n Figure D.  Unit  1.  Space Groups  Since the atomic or molecular arrangement of a c r y s t a l i s based on an i n f i n i t e r e p e t i t i v e p a t t e r n , the symmetry operations may e n t a i l t r a n s l a t i o n s . Combination of r o t a t i o n axes and r e f l e c t i o n planes w i t h t r a n s l a t i o n s produce two new types of symmetry elements termed screw axes and g l i d e planes -respectively. The p o s s i b l e groups of symmetry operations of i n f i n i t e f i g u r e s are c a l l e d space groups, and t h e i r t o t a l number was shown to be 230 independently Fedorov, Schoenflies, and Barlow i n the l a t t e r part of the l a s t century.  by A  d e t a i l e d account on space-group notation and nomenclature i s presented i n V o l . I of the I n t e r n a t i o n a l Tables f o r X-Ray Crystallography ( l ) , where diagrammatic  - 8 -  and a n a l y t i c representation of the space groups are also given. The space group expresses the sum t o t a l of the symmetry p r o p e r t i e s of a c r y s t a l , and therefore cannot he e s t a b l i s h e d uniquely by a study of e x t e r n a l form alone.  The b a s i s f o r space-group determination  by X-rays i s  that the t r a n s l a t i o n s of g l i d e planes and screw axes, and the l a t t i c e centering present i n non-primitive l a t t i c e s , lead to the e x t i n c t i o n of c h a r a c t e r i s t i c types of X-ray spectra.  Unfortunately  t h i s determination i s  not always unique as, due to F r i e d e l ' s law, a centre of symmetry i s added to the structure i n taking the d i f f r a c t i o n p a t t e r n .  I t i s p o s s i b l e , however,  to i d e n t i f y the c o r r e c t space group among several p o s s i b i l i t i e s from a s t a t i s t i c a l a n a l y s i s of the i n t e n s i t y d i s t r i b u t i o n (2), and from other p h y s i c a l t e s t s such as pyro- and p i e z o e l e c t r i c measurements.  II. •A.  DIFFRACTION OF X-RAYS BY CRYSTALS  S c a t t e r i n g o f X-Rays by Electrons and Atoms  ,An e l e c t r o n i n the path of an X-ray beam i s 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 varying e l e c t r i c f i e l d , and i t s e l f becomes a source of e l e c t r o magnetic r a d i a t i o n o f the same frequency and wave length.  By t h i s process  the e l e c t r o n i s s a i d to scatter- the o r i g i n a l beam. In an atom the scattered waves from the several electrons combine, and the r a t i o of the amplitude scattered by an atom at 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 c a l l e d the atomic form f a c t o r , designated f . Q  Because of  the f i n i t e s i z e of the atom, interference can occur among waves scattered by d i f f e r e n t parts of the e l e c t r o n cloud, and f angle 6.  Mathematically,  f  Q  Q  decreases with i n c r e a s i n g Bragg  i s r e l a t e d to the e l e c t r o n d i s t r i b u t i o n i n the  atom by the formula o =  f  where k = l+7Tsin6/;\. and ^  \fj  Z  sinkr  kTr r d r ,  (l)  2  i s the atomic wave function.  Tables of f  Q  data  have been computed f o r most common atoms and ions through t h e o r e t i c a l c a l c u l a t i o n s , and are conveniently tabulated as a f u n c t i o n of sine/A. i n V o l . I l l of the I n t e r n a t i o n a l T a b l e s ( l ) . B.  Conditions f o r X-Ray D i f f r a c t i o n Maxima  Consider a p a r a l l e l beam of X-rays impringing on,a space l a t t i c e by the b a s i s vectors j "aj_ j  (i=l,2,3)>  The d i r e c t i o n s of the i n c i d e n t and  d i f f r a c t e d beams may be represented by u n i t vectors u je<ij  and|"|3^j with the l a t t i c e d i r e c t i o n s .  Q  and u which make angles  From Figure 2, i t i s c l e a r that  the c o n d i t i o n f o r constructive i n t e r f e r e n c e - i s  a  ±  defined  (cos Pi-cos 0<i) = hiA.  ,  (2)  10 -  where the h^'s are integers.  This set of three equations, known as Lane's  equations, can be w r i t t e n i n vector form: a  i  j-  u - u  '  o  —  a  = 1,  or  i j -  ° •  -  (1)  = 1.  v^v-fictitious reflect^ p|-a.ne  Figure 2.  S c a t t e r i n g from a row of atoms i n a l a t t i c e d i r e c t i o n .  Figure 3-  Modulus and d i r e c t i o n of the _ d i f f r a c t i o n vector S.  The vector S = u-u i s known as the d i f f r a c t i o n vector.  I t i s i n the  Q  d i r e c t i o n of the b i s e c t o r of the i n c i d e n t and d i f f r a c t e d beams and has magnitude 2 sin© (Figure 3 ) .  Figure h.  R e l a t i o n s h i p between S and the plane  (h-ihpho)  •  - 11  -  From equation 3. we deduce that  _ i i  .  £  , i/ j  = o  (h)  ,  .which shows that S i s normal t o the plane of d i f f r a c t i o n i n d i c e s ( h i ^ h j ) (Figure k).  The spacing cL^t^h^  2 3  1  or  o f  Places (hnhgh^), i s given by  t h e  _ "ai/hi* S* |s |  2dh-j_h2h2 sin© = A  _  A 2sin6  ,  which i s Bragg's equation with the order n absorbed i n the integers h-^hgh^  C.  The Reciprocal L a t t i c e  For each d i r e c t l a t t i c e we can define a r e c i p r o c a l l a t t i c e with b a s i s vectors j~a"j_"*^  such that H  •  = i j S  .  (6)  From t h i s fundamental r e l a t i o n i t i s a simple matter t o deduce the f o l l o w i n g formulae: =  a,. i  a  :i k = V x  a  a  a,.* x a^.*  =  -j  ^  V*  W*  i  vector  /^h-^hgh^  k (i,j,k i n cyclic a,- . a^xa  x  a  ^7^"aj_*^  permutation),  L  _  a^* x a *  _ J  k  k  M  'tf.tf^*  «  it  ) (8)  = 1 ,  S = Yl I f we take  .j  (9)  ( i'S) i* a  a  = A Y  h  i  A *  "  ( ) 10  as b a s i s vectors i n the r e c i p r o c a l l a t t i c e , each  represents a d i f f r a c t i o n vector, which i n t u r n represents  a set of planes ( h ^ l ^ h ^ . i n the d i r e c t l a t t i c e .  The r e c i p r o c a l l a t t i c e provides a simple geometrical picture of d i f f r a c t i o n on the basis of the Bragg law,,as was  f i r s t shown by Bernal.  The  5 i n the form  i n t e r p r e t a t i o n of equation  |5|  sin0  Ph-jhgh-  2d h-j^h^ i s obvious from Figure 5.  A r e c i p r o c a l l a t t i c e point P which happens to  l i e on the surface of the sphere of r e f l e c t i o n w i l l give r i s e to a r e f l e c t i o n . The basis of most.single-crystal techniques  i s to rotate or o s c i l l a t e the  c r y s t a l so that many r e c i p r o c a l l a t t i c e points w i l l be caused to intersect (3)>  the sphere of r e f l e c t i o n  D.  The Structure Factor  In general,,the waves scattered i n any order hkil by the atoms i n a u n i t c e l l d i f f e r i n phase and must be compounded v e c t o r i a l l y .  The resultant  F ( h k f L ) i s known as the structure factor and can be expressed as an e x p l i c i t function of the f r a c t i o n a l coordinates of the N atoms i n the u n i t c e l l : ,  0  v  F(hke) =  22  f  -  27Ti(hx.+ky.+ e  ez.)  (11)  3  The complex quantity F(hk£),is characterised by an amplitude JF(hk&)| and a phase set  of  o<(hk€) •  The  structure-factor formula 11  i s equivalent to t h e  equations  •+ B  |F(hk€) cX  tan  ( h k t )  •A=  N —'  -1  B ,(12)  f , cos 2 Tr (hx.+ky ,+/z.) 0  J  J  J  j = l  N  B =  f j sin>2 7T . J=l  (hJCj+ky^+^Zj )  J  - 13 -  In ci dent  X - ray bea.m  Figure 5-  B i f f r a c t i o n . i n r e c i p r o c a l space.  In equations 11 and 12 the e f f e c t o f thermal v i b r a t i o n s o f the atoms i s taken i n t o account through the r e l a t i o n -Bsin 9/?£ f = fo e 2  .where the constant B i s equal t o 8TT  (13)  times the mean; square displacement o f  the atom i n a d i r e c t i o n perpendicular t o the r e f l e c t i n g plane.  In p r a c t i c e  B ,is treated as an e m p i r i c a l parameter and r e f i n e d i n the course o f a n a l y s i s . E.  The I n t e n s i t i e s o f X-Ray R e f l e c t i o n s  A c r y s t a l r e f l e c t s X-rays over a certain,angular range i n the neighbourhood of the Bragg angle, and when i t 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 an,angular v e l o c i t y to , • d i f f e r e n t p o r t i o n s of the c r y s t a l are successively 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 .  The r a t i o  E ^ / l , where E i s the t o t a l energy r e f l e c t e d during a sweep,and I Q  0  the  i n t e n s i t y o f the primary beam, i s found t o give-a correct measure of the  - 14  r e f l e c t i n g power of the c r y s t a l and  -  i s termed the integrated r e f l e c t i o n .  The majority of r e a l c r y s t a l s appear to have a mosaic block i n which t i n y c r y s t a l fragments of l i n e a r dimension ~ 10"^ but not quite aligned.  For such a c r y s t a l block of volume  cm.  structure,  are nearly  oVDarwin  and  others have derived the following r e l a t i o n :  ECO  =  / Ne  , I o  V \  V2  2  ~3  , l+cos 26 2  / /  m c  2 sin26  I „ I 2B  l»l «v .  (ay  In equation lU the term e /mc arises from the c l a s s i c a l formula for 2  scattering by an electron, of the c r y s t a l .  The  2  and N i s the number of unit c e l l s per unit volume  trigonometric term takes two  The p o l a r i z a t i o n factor ( l + c o s  26)/2  2  factors into account.  allows for the p a r t i a l p o l a r i z a t i o n  of the r e f l e c t e d beam, while the Lorentz factor l/sin2© occurs because the r e c i p r o c a l points pass through the surface of the r e f l e c t i n g sphere at d i f f e r e n t speeds.  For application  to c r y s t a l specimens expression 14 must  be modified according to the' experimental conditions, which may a d i f f e r e n t form for the Lorentz factor.  For example, the  introduce  intensity  formula for the e q u i - i n c l i n a t i o n Weissenberg method i s  ECO  nWge  I  A ( h k e ) [ F /  2  (  ^cos6  }  —*~  where ~% i s the c y l i n d r i c a l coordinate of the reciprocal l a t t i c e point. The  transmission factor A ( h k t ) i s introduced to allow for absorption i n ;  the c r y s t a l , and has A =  |  e"^ J  the form dV  (16)  ,  V  where t i s the t o t a l path length of the X-rays r e f l e c t e d from an element dV,  and jm and V are respectively  volume of the c r y s t a l .  the l i n e a r absorption c o e f f i c i e n t  and  Evaluation of t h i s i n t e g r a l i s i n general d i f f i c u l t ,  -  15  -  and values f o r specimens of simple shapes are tabulated as a function -of © in,the I n t e r n a t i o n a l T a b l e s ( l ) . Two other f a c t o r s a r i s e when the c r y s t a l does not conform t o the i d e a l l y imperfect  structure.  The p e r f e c t block o f the mosaic may be so  large that the upper l a y e r s screen,the lower ones i n the same block an e f f e c t known as primary e x t i n c t i o n ,  Secondary e x t i n c t i o n r e f e r s t o  the screening of the lower blocks by the upper blocks.  Both types o f  e x t i n c t i o n cause a s i g n i f i c a n t diminution of i n t e n s i t y of the strongest reflections.  E x t i n c t i o n c o r r e c t i o n s are u s u a l l y neglected  i n crystal-  structure a n a l y s i s , and are included only when t h e i r magnitudes are suspected of being large. F.  Representation of the C r y s t a l as a Fourier Series  The p e r i o d i c d i s t r i b u t i o n of e l e c t r o n density i n a c r y s t a l may be represented by a t r i p l e Fourier s e r i e s oo  ).=  oo  oo  Y Y Y C(hk£)e h=-<*> k=-«° <£=-«>  -27Ti(hx+ky+^z)  The Fourier, c o e f f i c i e n t s C(hk£) can be r e a d i l y shown to be equal t o F(hk£)/V'.  Thus  jP(xyz) =  i  OO  Y_.  h=  oo  Y  k=  oo  Y  FChkXJe-^^+ky+tz)  '  £=  For convenience i n c a l c u l a t i o n the structure f a c t o r i s replaced "by i t s amplitude and phase.  In, accordance with F r i e d e l ' s law, | F(hk€.) | = JF(hk£.)| ,  so that equation 17 becomes oo  9 (xyz) =  f  o*»  Y  Y  Y  h=  k=  -£=  |F(hk£)| cos r27r(hx+ky+£z)-os(hke) . (18)  In a centrosymmetric c r y s t a l the value of the phase angle i s r e s t r i c t e d to  -  16  -  0 or IT ,. and so.the electron-density expression  OO  5>(xyz)  =  |  oo  oo  Y Y Y h=  k=  G.  e=  l ( F  h k e  )|  i s s i m p l i f i e d to cos 2 7T(hx+ky+e ) Z  .  (l£)  The Phase Problem  Equations 18 and 1 £ i l l u s t r a t e the 'phase problem' of X-ray crystallography.  The structure amplitudes can be determined  experimentally,  but the r e l a t i v e phases are l o s t i n taking the X-ray pattern and must" be recovered by i n d i r e c t means. An i n f i n i t e number of electron-density d i s t r i b u t i o n s may be obtained by assigning a r b i t r a r y phases to the structure amplitudes. However, the number of p o s s i b l e phase combinations i s g r e a t l y reduced by the requirement that  f (xyz) must be everywhere non-negative and composed of s p h e r i c a l l y  symmetric atomic functions, and that the structure postulated i s chemically reasonable.  In f a c t , a set of phases which s a t i s f i e s the above c r i t e r i a i s  almost c e r t a i n l y the c o r r e c t one.  Some of the more important methods of  s o l v i n g the phase problem are o u t l i n e d i n section I I I - C .  - 17  III.  THE DETERMINATION.OF CRYSTAL STRUCTURES A.  The  -  Two-Dimensional P r o j e c t i o n s  summation of the t r i p l e Fourier s e r i e s 18 i s extremely laborious.  Furthermore the c o l l e c t i o n and c a l c u l a t i o n of a l l F(hkC) s involve a great 1  deal o f work.  I t i s usual therefore t o p r o j e c t the structure onto two or  more a x i a l planes using a double s e r i e s , which can be computed from zonal data o f the type F(hkO).  Except f o r very complex s t r u c t u r e s , two-dimensional  p r o j e c t i o n s are s u f f i c i e n t t o y i e l d a f a i r l y accurate set of atomic e x p e c i a l l y when s p e c i a l precautions  coordinates,  t o eliminate e r r o r s are taken ( s e c t i o n  III-D). B.  The 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 Patterns  The determination proceeds i n f i v e  of the s p a t i a l r e l a t i o n s h i p s of the-atoms i n a c r y s t a l  stages:  (a)  Determination of Unit C e l l Parameters and the Space Group.  (b)  C o l l e c t i o n of I n t e n s i t y Data.  (c)  Determination of the Structure.  (d)  Refinement of Atomic Parameters.  (e)  Assessment of Accuracy.  1  Stages (a),and (b) c o n s t i t u t e the routine part o f a c r y s t a l - s t r u c t u r e i n v e s t i g a t i o n , and are described i n d e t a i l i n a number o f t r e a t i s e s ( 3 ) •  In  the paragraphs that f o l l o w , stages ( c ) , (d) and ( e ) a r e given a b r i e f discussion. C.  Methods f o r Obtaining an Approximate Structure  The various methods f o r s o l v i n g the phase problem are conveniently c l a s s i f i e d i n t o three categories; i n general no one method i s c e r t a i n t o lead to the c o r r e c t structure. (a)  T r i a l and E r r o r Methods.  In these methods c r y s t a l l o g r a p h i c , p h y s i c a l  and chemical knowledge are combined t o a r r i v e at a t r i a l structure which gives 1  - 18  -  reasonable agreement between the observed and c a l c u l a t e d structure amplitudes. A good i n d i c a t i o n of the correctness of the postulated structure i s that the discrepancy f a c t o r , defined as R -5J|F | 0  I Fc|| / X j F o |  > should be  about 0.5. and 0.4 f o r centrosymmetric and non-centrosymmetric space groups respectlvely(4).  Leaving out terms f o r which agreement i s poor, the c a l c u l a t e d  phases and the measured amplitudes are used i n a Fourier synthesis, which leads to a r e v i s e d set of atomic coordinates.  This i t e r a t i v e process i s  repeated u n t i l a l l observed r e f l e x i o n s can be included i n the s e r i e s summation. (b)  Heavy-Atom and Patterson Methods.  I f the c r y s t a l contains an atom  of high s c a t t e r i n g power s i t u a t e d at a known p o s i t i o n , i t may determine a s u f f i c i e n t number of phases f o r a Fourier synthesis to r e v e a l the l i g h t e r atoms.  Sometimes i t i s p o s s i b l e to replace such a heavy atom by another at  the same p o s i t i o n without d i s t u r b i n g the e s s e n t i a l nature of the structure, so that the phase r e l a t i o n s h i p s can be determined from a d i f f e r e n c e e f f e c t . The heavy-atom and isomorphous replacement methods are b e a u t i f u l l y exemplified by Robertson's determinations of the structures of the phthalocyanines(5). In an organic structure the p o s i t i o n of the heavy, atom i s r a r e l y f i x e d by symmetry,. and a general method i s needed f o r i t s l o c a t i o n . • In 193^+ Patterson(6) showed that the f u n c t i o n (20)  which can be computed d i r e c t l y from observed data, represents a density d i s t r i b u t i o n such that the vectors from the o r i g i n to the maxima correspond to vectors between a l l p o s s i b l e p a i r s of atoms i n the c r y s t a l .  Systematic  procedures have been developed to derive the atomic p o s i t i o n s from t h i s vector d i s t r i b u t i o n ( 7 ) .  The weight of a Patterson peak i s the product of  the atomic numbers of the two atoms involved, so that the method can be  -  19  -  a p p l i e d most s u c c e s s f u l l y to structures containing heavy atoms. (c)  D i r e c t Mathematical Methods.  These methods seek to determine the  phases d i r e c t l y from the structure amplitudes alone. • The  Harker-Kasper  i n e q u a l i t i e s ( 8 ) , derived by a p p l i c a t i o n of Schwarz and Cauchy i n e q u a l i t i e s to modified  structure amplitudes, impose c e r t a i n r e s t r i c t i o n s on the phases  due to c r y s t a l symmetry. conditions that  Further developments (9)> based upon the l i m i t i n g  j?(xyz) ^ 0 and i s a superposition of d i s c r e t e atomic  f u n c t i o n s , f u r n i s h completely general systems of i n e q u a l i t i e s as v e i l as equalities.  Sign relations- between structure f a c t o r s i n centrosymmetric  space groups have been derived by Sayre(lO), C o c h r a n ( l l ) , and Z a c h a r i a s e n ( l 2 ) . The l a t e s t development - i s the s t a t i s t i c a l approach of Hauptmann and  Karle(l3),  which provides expressions f o r the p r o b a b i l i t y of a .structure f a c t o r being p o s i t i v e or  negative. D.  Refinement Procedures  The' p r i n c i p a l methods f o r c r y s t a l - s t r u c t u r e refinement are o u t l i n e d i n the f o l l o w i n g sections. (a)  F  Q  Synthesis.  Atomic parameters obtained from successive  Fourier  synthesis are a f f e c t e d by ( i ) e r r o r s i n c e l l dimensions; , ( i i ) , i n a c c u r a t e F  D  values; ( i i i ) round-off e r r o r s i n computation; ( i v ) . t e r m i n a t i o n of the Fourier series, while the remaining c o e f f i c i e n t s are s t i l l appreciable; and (v) thermal motion of the atoms.  The d i f f e r e n t i a l synthesis of Booth(lU), which locates  the atoms e x a c t l y at the e l e c t r o n - d e n s i t y maxima, i s subject to the same sources of e r r o r .  The e f f e c t due to s e r i e s - t e r m i n a t i o n i s serious; i t may  be allowed f o r by computing,a F  c  synthesis separately and applying b a c k - s h i f t  c o r r e c t i o n s to the-atomic coordinates (b)  Method of Least Squares.  (15).  This procedure was  f i r s t used by Hughes(l6)  to f i n d the atomic parameters which give the best f i t to the set of  F's.  The f u n c t i o n minimized i s ^ w ( | F | Q  | F | ) , where w i s a weighting f a c t o r . c  To each observed r e f l e c t i o n there corresponds an observational equation,, and the set of equations can be normalised and solved f o r the coordinate  shifts.  Refinement b y ' l e a s t squares i s free from s e r i e s - t e r m i n a t i o n e r r o r s ; i t i s also •possible t o include i n d i v i d u a l i s o t r o p i c or a n i s o t r o p i c temperature f a c t o r s and a scale f a c t o r i n the refinement process, (c)  Difference Synthesis. 1  5b"-Pc = V  B=  oo  Yl E E , h= -OO  The f u n c t i o n  OO  (  ' °I F  "  )  l cl F  c o s  [ ^( 2 7  h x + k  y ^)-o<(hke)J  (21)  +  k= 1 =  — oo —  oo  was f i r s t suggested b y B o o t h ( l 7 ) as a device f o r refinement .and i t s p r o p e r t i e s were f u l l y e x p l o i t e d by Cbchran(l8).  An, atom of the proposed  structure which deviates s l i g h t l y from i t s tree'position l i e s on a steep From Figure 6 i t i s c l e a r that the.atom should  slope of the d i f f e r e n c e map. be s h i f t e d up-the gradient. Ar  /hi 'Ar  where  The displacement i s given by c>D'/*r  (22)  2  i s a constant i n the approximation jp = £  0  -fur' f o r the e l e c t r o n  Q, ' "  density at a distance r from the centre of an atom.  Refinement by ( F - F )  synthesis automatically eliminates s e r i e s - t e r m i n a t i o n e r r o r s ; , i t  0  c  furnishes  valuable information about the thermal motion of the-atoms, and can be used 1  to locate hydrogen atoms  Figure 6.  i  E f f e c t of a email error- i n atom l o c a t i o n on D.  - 21 -  (d) Generalised P r o j e c t i o n s .  Frequently  s t r u c t u r e , say, on (010), can be obtained.  only one c l e a r p r o j e c t i o n of a  Without u t i l i z i n g the complete  (hk€)"data, approximate y-coordinates can be deduced from the Kth l a y e r data by the method of generalised p r o j e c t i o n s due to Cochran,and The expression  f o r a structure f a c t o r belonging to the Kth l a y e r i s  X{ j(  p(hKfc) =  others(l9)<  f  ^  h K  e 2 1 r i K y j  }  e  2 l  r ( 1  h x  J  + g z  j) .  j When the zero and'Kth l a y e r s are close together,  f . ( h K o ) ^ f.(hO&) so that the 3  3  generalised p r o j e c t i o n  5K  ( x z )  =  i  E£ ( F  h K e  ) " e  2 7 r i ( h x + e z )  h= 1= — oo  =  —  OO  ,(23)  C (xz) + i S (xz) K  K  represents a p r o j e c t i o n of the structure on (010), with the e l e c t r o n density at ,the j t h atom modified by a f a c t o r e^TTiKy^ _ Thus yj can be deduced from 277"Kyj = t a n  Q Q s  27rKyj.'+ i s i n 2 ^ K y j .  Sj^/Cj^ .  - 1  E l i m i n a t i o n of s e r i e s termination e r r o r s can a l s o be achieved by the use of ( F - F ) Fourier c o e f f i c i e n t s . 0  c  D  D  generalised p r o j e c t i o n s ,  and S^-  parameters simultaneously ?K,o  A  r  sin  =  ^  c  s  i  s£ .cos27?-Ky  /  n  2  G  - c£ s i n 2 ^ K y  c  ^  + c  t?YL,o cos277-K(y -y )- f ,c 0  , are used to r e f i n e the x, y, z and B  i n the f o l l o w i n g expressions (20):  277"K(y -y ) = 0  The r e s u l t i n g d i f f e r e n c e cosine and sine  K  C  K  C 0 s 2  ^  K y  cV ^?K,o 2  (2J+)  ,  c  (25_)  ,  = K sin27TKy . + C^ cos27^Ky S  c  c  .  (26)  - 22 -  E.  Assessment of Accuracy  Crui'ckshank,. among others,,has i n v e s t i g a t e d the standard d e v i a t i o n i n the e l e c t r o n density and i n atomic p o s i t i o n s ( 2 l ) .  and  <r(*o).-  i { Emi-I*!) }*  C7j(x)  2 7Ts  =  H i s r e s u l t s are  (21)  2  h ( [F |- i F j ) J i / a V C 2  (28)  2  0  c  J:  with s i m i l a r expressions f o r the y and z coordinates.  Here s has values 1 and  2 f o r centrosymmetric and non-centrosymmetric structures r e s p e c t i v e l y , and -\  2  C ji vx = =  .  p  °S'^I ^  x  i s  t l i e  c u r v a  ture  at the centre of t h e j t h atom  The standard d e v i a t i o n of the bond distance between two atoms i s given by the r e l a t i o n o.  o  o  0 " ( d ) = o\  +  2  i 2  where  (29)  and CTg are the standard deviations of the p o s i t i o n s o f the atoms  i n the d i r e c t i o n o f the bond. Two bond lengths measured as d^ and dg d i f f e r i n g by an amount h w i l l have a probability ;rf (-  P =  ^  yir  C?AB  •J  2 . 0"  i  AB  —  2  ,  2  0~ +• CT* A B  of being observed d i f f e r e n t l y because o f experimental e r r o r s .  (30)  Cruickshank(2l)  has suggested the f o l l o w i n g s u b d i v i s i o n of s i g n i f i c a n c e : Comparison of  5$ ,or greater  S £1.645 C A B 1.645^642.327 0 ^ 2.3270*^^3.090 3.090 (7-^ > 6  S i g n i f i c a n c e of observed bond length d i f f e r e n c e  P  S and CT*^g  cr  m  5$ ,1$ -  not s i g n i f i c a n t  1*  possibly significant  o.vf,  significant  .0.1<f> o r l e s s  highly s i g n i f i c a n t  -•23  -  The standard deviation of an angle ©, .between two bonds d-j_ and d 2  given.by  2  *J  » ^3  / 2  V\  2 3  is  \ 2 d  ^ 2 3  +  d  2  ^  •  ^  PART I I  THE CRYSTAL AND MOLECULAR STRUCTURES OF • BIPHENYLENE, METHOXYCARBONYLMERCURIC, CHLORIDE,, AND p-CHLDRONITR0BENZENE  - 25 -  I. . A.  BIPHENYLENE Introduction  The s t r u c t u r a l formula ( l ) , o f t h i s hydrocarbon was f i r s t given by Niementowski(22), who used the name biphenylene.  in,1901  This name i s now-adopted  by most American chemists, although European workers .generally p r e f e r the name diphenylene.  The carbon atoms are numbered as shown i n formula"(I).  Biphenylene'is of i n t e r e s t t o ' b o t h . t h e o r e t i c a l and organic  chemists  since - i t i s the only stable d e r i v a t i v e of the e l u s i v e cyclobutadiene.  The  s y n t h e s i s , chemistry and s t r u c t u r e o f t h i s unusual compound have been the subjects of many s t u d i e s , and several reviews have been published (23)< Synthesis.  Genuine biphenylene was f i r s t synthesised by Lothrop(24) i n 19^1  by the d i s t i l l a t i o n o f 2,2'-diiodobiphenyl ( l l ) or iodide ( i l l ) with cuprous oxide.  biphenylene-2,2'-iodonium  This synthesis has since been improved  (25),and several other methods of preparation,are now a v a i l a b l e (26), the most i n t e r e s t i n g i s that due t o W i t t i g and Pohmer.  of"which  They showed that  o-bromofluorobenzene reacted with l i t h i u m almalgam i n ether t o give biphenylene and t r i p h e n y l e n e ( l V ) w i t h y e i l d s of 2U$ and 3$ r e s p e c t i v e l y .  The r e a c t i o n i s  -  26 -  thought t o proceed v i a the reactive•intermediate benzyne (V). The Structure of Biphenylene.  As evidence f o r the s t r u c t u r e • ( i ) , Lothrop  c i t e d a n a l y t i c a l data f o r the hydrocarbon and i t s p i c r a t e , molecular weight determinations i n benzene and i n camphor, o x i d a t i o n . t o p h t h a l i c a c i d by chromic a c i d , reduction t o biphenyl by hydrogenation over red-hot copper, and formation of the same compound, namely 2,7-dimethylbiphenylene (VT), by the p y r o l y s i s of both 5,5"-dimethyl. (VIl).and 4 , 4 ' - d i m e t h y l (VIII)-biphenylene -2,2'-iodonium iodides.  However, i t was soon pointed out by Baker (27) that  such evidence d i d not exclude -the p o s s i b i l i t y that ,the hydrocarbon was a c t u a l l y benzopentalene ( l X ) , . t h e formation of which could be explained by  (VII)  (VI)  (VIII)  assuming a f r e e - r a d i c a l mechanism. • This view was supported by Coulson(28) who deduced that the s t r a i n energy of biphenylene was much higher "than'that, of benzopentalene  (~ 100 versus a few kcal./mole), while the resonance energies  were about the same (90 and 86 kcal./mole, r e s p e c t i v e l y ) .  The structure was  f i n a l l y s e t t l e d i n 19^ 3 by the e l e c t r o n d i f f r a c t i o n studies of Waser and Schomaker(29)> which e s t a b l i s h e d the dibenzocyclobutadiene formulation conclusively.  Further c o n f i r m a t i o n of the structure was provided by an X-ray  c r y s t a l l o g r a p h i c a n a l y s i s by Waser and Lu(30).  These s t r u c t u r a l determinations  - 27  -  i n d i c a t e d that the C-C bonds in,the six-membered r i n g s had an average length o of 1.39 A, and that the bonds j o i n i n g these r i n g s were s i g n i f i c a n t l y "longer measurements were n o t • s u f f i c i e n t l y accurate to detect the f i n e r d e t a i l s of bond-length v a r i a t i o n i n the molecule. Cyclobutadienoid Character.  Despite the very considerable angular s t r a i n ,  the four-membered r i n g i n biphenylene • i s remarkably i n e r t towards a v a r i e t y of reagents, and can be cleaved only by c a t a l y t i c reduction. • Biphenylene undergoes many of the t y p i c a l aromatic s u b s t i t u t i o n r e a c t i o n s , i n c l u d i n g n i t r a t i o n , sulphonation, halogenation, mercuration, a c e t o x y l a t i o n , and the Friedel-Crafts, reaction ( 3 l ) -  Monosubstitution occurs e x c l u s i v e l y at  p o s i t i o n 2, i n agreement w i t h the t h e o r e t i c a l p r e d i c t i o n s o f Brown(32).and of Fernandez Alonso and Domingo(33)biphenylene  Experiments on d i s u b s t i t u t i o n of  (31) have shown that a meta-directing substituent such as the  a c e t y l group ( x ) at p o s i t i o n 2 d i r e c t s the second substituent i n t o p o s i t i o n 6 by a resonance e f f e c t i n v o l v i n g both six-membered r i n g s , and i t appears therefore that there i s some cyclobutadienoid character about the c e n t r a l four-membered r i n g .  P o s i t i o n s l,3>5>7,are deactivated; p o s i t i o n 6 i s (3 , and hence more r e a c t i v e than p o s i t i o n 8 which i s oi . 5  4-  (X)  I n t e r a c t i o n between the outer r i n g s i s a l s o indicated'by " t h e - u l t r a v i o l e t spectrum (3*0> which shows two main regions of absorption:  a high-intensity  band at 235-260 mu. corresponding t o the lone intense band of biphenyl at 250 mi  - 28 -  and a second band of lower i n t e n s i t y i n the region 330-370 mu a t t r i b u t a b l e to some conjugation between the r i n g s .  Molecular centre of symmetry shown by X-ray c r y s t a l data.  On the other hand, recent attempts t o prepare biphenylene  7"r-complexes of  (35) have succeeded only i n g e t t i n g the benzene type such as  p-biphenylenebis(tricabonylmolybdenum);(Xi).  The a b i l i t y o f biphenylene t o  form .coordination.compounds using each six-membered r i n g independently, but not the four-numbered r i n g system, i s consistent w i t h the preferred' bond structure ( X l l a ) i n which there i s l i t t l e or no.cyclobutadienoid character i n the c e n t r a l r i n g . The foregoing evidence provides d i f f e r e n t answers to'the question regarding the extent of i n t e r a c t i o n between the benzene r i n g s .  A d i r e c t and  more q u a n t i t a t i v e measure of cyclobutadienoid character i n biphenylene would be the mean' length of the c e n t r a l bond 9-10, but u n f o r t u n a t e l y the u n c e r t a i n t y in,the value 1.46+0.05^ determined by e l e c t r o n d i f f r a c t i o n (29) makes i t • d i f f i c u l t - t o • d r a w d e f i n i t e conclusions. Bond Structure.  For biphenylene f i v e Kekule structures may be drawn, one of  which ( X l l a ) r e p r e s e n t s i t as a d e r i v a t i v e of cyclobutane, t w o ( X I I b as a cyclobutene, and t w o • ( X l l d and XIIe),as a cyclobutadiene.  and X I I c )  Simple  resonance theory,-with the f i v e canonical forms c o n t r i b u t i n g e q u a l l y to the  - 29 -  8  5  00  (a)  .(c)  (e)  (XII)  h y b r i d molecule, shows that the 1-2 bond has more double-bond character than the 2-3 bond, and hence an o r t h o , p a r a - a c t i v a t i n g group'in p o s i t i o n 2 should d i r e c t . a n entering substituent i n t o p o s i t i o n 1.  This p r e d i c t i o n i s at  variance w i t h that drawn from 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 which i n d i c a t e that the second substituent should be d i r e c t e d i n t o p o s i t i o n 3 (3^)i t has been shown that bromination  Recently  of 2-acetamidobiphenylene gives 2-acetamido-  3-bromobiphenylene (37)* and that 2-aminobiphenylene couples w i t h benzenediazonium c h l o r i d e at the 3 - p o s i t i o n (38)-  In valence-bond  terminology  these r e s u l t s imply that the p r e f e r r e d Kekule- structure of biphenylene i s (Xlla). Since the two t h e o r i e s also p r e d i c t d i f f e r e n t bond-length v a r i a t i o n s f o r biphenylene,  i t should be p o s s i b l e t o decide between them by an accurate  measure of the bond distances.  The present research i s concerned with the  determination of these distances by a d e t a i l e d X-ray examination of the crystalline material. B.  Exp erimental  A l l the c r y s t a l s i n the o r i g i n a l sample of biphenylene were twinned on (lOO), but well-formed  s i n g l e c r y s t a l s were obtained by r e c r y s t a l l i z a t i o n  from propan-l-ol ( c f . r e f . 3 0 ) . elongated along the c-axis. aqueous potassium i o d i d e .  These consisted of pale yellow prisms The density was determined by f l o t a t i o n i n  The u n i t - c e l l dimensions and space group were  determined from rotation.and o s c i l l a t i o n photographs of c r y s t a l s r o t a t i n g about the b- and c-axes, hC"6 , hkO, h k l , and hk2 Weissenberg f i l m s .  No  - 30 -  precautions were taken to prevent the c r y s t a l v o l a t i l i z i n g , so that they disappeared i n a few days. C r y s t a l Data.  Biphenylene, • C^Hg; M=152.2; m.p.llO°C.  Monoclinic,  a = 19.66+O.O6, b=10.57+0.04, c=5.85+0.01A, j5 =91.0+0.5 . 0  D ( w i t h Z=6) = 1 . 2 4 0 , D =l.24g.cm73 x  m  7v =1.54l8A, jj =6.46 cmT OkO when k i s odd.  1  F(000)=480.  U=1215-5A .  Absorption c o e f f i c i e n t f o r X-rays, Absent s p e c t r a : hOE when h i s odd,  Space group i s "22^/ a-C^  .  The i n t e n s i t i e s of the hkO and h k l r e f l e x i o n s were recorded on Weissenberg photographs f o r a c r y s t a l r o t a t i n g about the c - a x i s , the equii n c l i n a t i o n method being used f o r the-upper l e v e l .  CuK^  r a d i a t i o n was  used, w i t h m u l t i p l e - f i l m technique (39) to c o r r e l a t e strong and weak reflexions.  The i n t e n s i t i e s were estimated v i s u a l l y , the range being about  5000 to 1.  The values of the s t r u c t u r e amplitudes were derived by the usual  formulae f o r a mosaic c r y s t a l , the absolute scale being e s t a b l i s h e d l a t e r by c o r r e l a t i o n with the c a l c u l a t e d s t r u c t u r e f a c t o r s . were applied.  No-absorption c o r r e c t i o n s  65 independent hkO r e f l e x i o n s with h=3n were observed (see  below f o r d i s c u s s i o n of "h=3n rule"'), representing 71$ of the t o t a l number of these r e f l e x i o n s t h e o r e t i c a l l y observable with CuK^  r a d i a t i o n , but only  36 very weak r e f l e x i o n s w i t h h / 3 were observed (about 20$ of the p o s s i b l e n  number).  206 h k l r e f l e x i o n s were recorded, representing about 40$ of the  p o s s i b l e number observable. C.  Structure A n a l y s i s  [OQl] P r o j e c t i o n Since there are s i x molecules i n the u n i t c e l l , two of them must be s i t u a t e d at centres of symmetry at 000 and ^-g-0, and the other four i n general p o s i t i o n s .  As pointed out by Waser and Lu ( 3 0 ) , the hkO  r e f l e x i o n s e x h i b i t a d i s t i n c t i v e feature, being very weak unless h=3n, and  - 31  -  t h i s "h=3n r u l e " requires that to a f i r s t approximation the atoms are grouped i n threes with coordinates  ( x , y , z ) , ( i + x,y, r+z'), ( i - x , y , r-z')> where z'=  + z, and r i s the z coordinate general p o s i t i o n .  of the centre of a molecule which i s i n a  Waser and Lu obtained values f o r a l l the parameters from a  c o n s i d e r a t i o n of the molecular Fourier transform,  and from various  trials.  Structure f a c t o r s were c a l c u l a t e d f o r the hkO r e f l e c t i o n s with h=3n (those with h^3n necessarily, have zero c a l c u l a t e d v a l u e ) , by using the x and y parameters given by Waser and Lu, with the s c a t t e r i n g f a c t o r f o r carbon of Berghuis e_t _al(l+0), with B=U.8^ . 2  r e f l e x i o n s was R=0.20U.  The discrepancy f a c t o r f o r the observed  Refinement proceeded by computing F o u r i e r and  d i f f e r e n c e syntheses, and a d j u s t i n g the positional'parameters.  A f t e r one  c y c l e R had been reduced t o ' ' 0 . 1 8 2 . Further refinement then required consideration of planes f o r which h^3n. The*"h=3n r u l e " had been very u s e f u l i n e s t a b l i s h i n g the corrfect t r i a l structure i n the f i r s t instance,,but  at t h i s stage o f the a n a l y s i s i t proved  troublesome, since i t was very d i f f i c u l t to decide-just what the small deviations of atomic p o s i t i o n s were which gave r i s e - t o ' t h e observation of hkO r e f l e x i o n s with h/3nimpossible  These r e f l e c t i o n s were a l l so weak that i t was  to deduce from the.magnitudes of these structure f a c t o r s what small  displacements were involved.  Refinement o f the hkO data was therefore  terminated at "this p o i n t , and a t t e n t i o n was turned to the h k l zone i n which there are no s y s t e m a t i c a l l y weak r e f l e x i o n s . The p o s i t i o n a l parameters at t h i s stage of the a n a l y s i s are l i s t e d i n the second and t h i r d columns of Table I I I , and,the measured structure f a c t o r s , F are compared w i t h the c a l c u l a t e d values, F ( l ) , i n Table A - l ( R = 0 . l 8 2 ) . c  0  ,  An  e l e c t r o n - d e n s i t y p r o j e c t i o n along the c - a x i s , computed with measured structure amplitudes and c a l c u l a t e d signs f o r h=3n r e f l e x i o n s only, i s shown i n Figure 7-  - 32 -  W y -1  i  H  J  & ro  •HJ  CM  (c\T) O  (CM  F i g u r e 7.  (a) E l e c t r o n - d e n s i t y p r o j e c t i o n a l o n g [ o o i ] , computed w i t h h=3n p l a n e s o n l y . C o n t o u r s a t i n t e r v a l s of 1 e . i " , with, the one e l e c t r o n l i n e b r o k e n . 2  ("b) Numbering of the c a r b o n  atoms.  - 33 -  h k l Refinement Since no r e s o l u t i o n of the i n d i v i d u a l atoms could be expected i n p r o j e c t i o n s down,the a- and b - c r y s t a l axes, the problem of f i n d i n g the z coordinates and o f r e f i n i n g the y. and x parameters f u r t h e r was approached by considering the h k l structure f a c t o r s .  Structure f a c t o r s were c a l c u l a t e d f o r  these r e f l e x i o n s by using the x,y and B parameters from the hkO refinement and the z coordinates given,by Waser and Lu. 0.2U8.  The discrepancy f a c t o r was  Refinement proceeded by computing cosine and sine'difference  generalised p r o j e c t i o n s , r e f i n i n g a l l three p o s i t i o n a l parameters x, y, z, and the - i s o t r o p i c temperature-parameters,<B, simultaneously.  The f i r s t set of  difference maps i n d i c a t e d small s h i f t s i n x and y parameters, the new coordinates v i o l a t i n g the'"h=3n r u l e " ; , a reduction o f B t o K. 5A^ f o r a l l atoms; and s l i g h t l y l a r g e r z-coordinaibe s h i f t s (maximum 0.09A).  Structure  f a c t o r s were r e c a l c u l a t e d , and the R value had been reduced t o 0.200. A second.set of difference generalised p r o j e c t i o n s were computed,. but no f u r t h e r s i g n i f i c a n t changes i n parameters were indicated.  Measured and  c a l c u l a t e d h k l structure f a c t o r s are l i s t e d i n Table A-2. Structure f a c t o r s were then c a l c u l a t e d f o r a l l the hkO r e f l e x i o n s with the parameters determined from the, h k l refinement, and these c a l c u l a t e d values, F (2), are compared with F ( l ) , a n d F c  c  Q  i n Table A - l .  For the r e f l e x i o n s with  h=3n, the R value had been reduced from 0.182 t o 0.1U5, a s i g n i f i c a n t improvement.  For the hj^3n r e f l e x i o n s the F (2) values d i f f e r from zero, and c  hence compare b e t t e r w i t h F  Q  than do the F ( l ) structure f a c t o r s , , but there  i s no r e a l q u a n t i t a t i v e agreement.  c  In general the c a l c u l a t e d values are too  low, i n d i c a t i n g t h a t • f u r t h e r deviations from the i d e a l i s e d h=3n p o s i t i o n s are probably necessary.  In addition,. i n c l u s i o n o f other f a c t o r s which have not  been considered, such as thermal anisotropy, would probably,help to improve  -  3^ -  the agreement. Any further refinement would have to u t i l i z e ' t h e complete data, and since-adequate refinement was  three-dimensional  computing f a c i l i t i e s were not y e t , a v a i l a b l e ,  not c a r r i e d any further,,the f i n a l parameters being taken,as  those determined from the h k l generalised projections.  Table I I I . hkO, Atom  X  Positional'Parameters Final,,from h k l  h=3n y  X  y  z  A(X)  1  0.0300  0.0072  0.0291+  0.001+7  -0.11+6  -0.011  2  O.O765  0.0000  0.071+3  -0.0007  -0.318  +0.026  3  0.1236  -0.1001  0.1237  -0.1006  -0.302  -0.008-  1+  0.1275  -0.1750  0.1250  -0.1782  -0.117  -0.022  •5  0.0810  -0.1695  0.0821  ,-0.1696  0.062  +0.015  .6  O.O31I+  -0.0677  0.0313  -0.0690  0.01+5  -+0.035  7  0.3633  0.0072  0.3637  0.0050  0.587  -0.025  8  O.I+O98  0.0000  ' 0.1+081  0.0008  0.753  +0.027  9  0.1+569  -0.1001  0.1+585  -0.1013  0.729  -0.021  10  O.I+605  -0.1750  0.1+619  -0.1731  0.51+1  "+0.024  11  0.1+11+0  -0.1695  0.1+11+2  -0.1675  0.361+  -0.028  12  0.361+7  -0.0677  ,0.3665  -0.0700  0.393  • +0.006  13  0.3033  -0.0072  0.301+8  -0.0035  0.282  +0.031+  Ik  0.2568  0.0000  0.2599  0.0012  0.113  -0.012  15'  0.2097  0.1001  0.2092  0.0999  0.137  +0.009  16  0.2058  0.1750  0.2058  0.171+8  0.326  -0". 017  17  ,0.2523  0.1695  0.2529  0.1681+  ,0.511  +0.001  18  0.3019  0.0677  0.301+2  0.0682  0.1+78  +0.001  - 36 -  Coordinates, Molecular Dimensions, and Orientation The f i n a l p o s i t i o n a l parameters of the carbon atoms are l i s t e d i n Table I I I , x,y,z being coordinates referred to 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.  The coordinates of the atoms in,each molecule can be f i t t e d t o an equation of the form  + mY + nZ' +.p=0, where X',>Y, Z  1  are coordinates  o expressed i n A and referred to orthogonal axes a, b , and c'.  The equations  of these mean molecular planes are: Molecule I (atoms C^-Cg and c]_-Cg): 0.6109X'  + 0.6353Y + 0.4718Z'  = 0 .  Molecule II (atoms C y - C ^ ) ' 1  0.6035X'  + 0.6582Y - 0.1+500Z  1  - 2.8008 = 0 .  The deviations of the atoms from these planes are l i s t e d i n the l a s t column of Table I I I . The bond lengths and valency angles, calculated .from the f i n a l coordinates of Table I I I , are shown i n Figure 8.  x,y,z  The mean values of the  distances and angles, with symmetry mmm assumed ( t h i s assumption i s discussed below), are shown i n Figure 9-  M  Figure 9-  Mean bond d i s t a n c e s and valency angles.  - 37 The orientations of the molecules i n the c r y s t a l are given i n Table IV, "here  %  L  >  f,  ^  L  <*>.  and ^  M  ^  ^  are-the angles  which the molecular axes L, M (see Figure 9) and the-plane normals N make-with the orthogonal axes a,,b,, and c'.  The axes L were taken through the molecular  centre and the mid-point of bond 3-1+ f o r molecule ( i ) , and through the mid-,' pointsof bonds 9-10  and 15-16  f o r molecule ( l l ) ; and axes M through the  molecular centre and the mid-point of 1-6', bonds 12-13  and 18-7.  and through the mid-points of  L, M, and N, are thus not accurately mutually ^ ^ = 9 1 . 9 ° , and LN=93.2° f o r  perpendicular, the angles being ^04=90.6°, molecule ( i ) , and 88.6°, 88.6°, SO.6° molecule ( l l ) .  f o r the corresponding angles f o r  The orientation angles d i f f e r from those given by Waser and  Lu by a maximum of 5-3°> and a mean of Table IV.  L  y  L  (A . L  1+0.9  37.2  i22»i+°  117.90  112.1°  67-6°  0  — ...  2.1 . 0  Orientation of Molecules i n the Unit C e l l  Molecule Molecule (I) (ID ' 9o  A  0  Molecule Molecule (I) (ID 9^  90.9°  M  55. o  —  x  . . .  H+5-l°  Molecule Molecule (I) '(H)  92.0° ? £ 5 5 < 8  o y ,  3^-2°  523°  N  N  —  cO  r  50  ...  .go  127.1° i  3 1  61.8°  .2° 63.3°  Standard Deviations The standard deviations of the atomic positions were calculated from Cruickshank's formulae.  The mean values f o r a l l the atoms are <J(x) =  C(y),=  (7-(z).= 0.022A\ so that the standard deviations of the -individual bond distances are-0.031A.  This value may be compared with the root mean square  deviation of the i n d i v i d u a l bond lengths from the mean distances, which i s 0.0l+3°v.  F i g u r e 10.  P r o j e c t i o n o f the s t r u c t u r e a l o n g [001^] , showing the s h o r t e r i n t e r m o l e c u l a r c o n t a c t s .  - 39 Intermolecular Distances A l l the intermolecular separations correspond to normal van der Waals interactions.  The shorter contacts are i l l u s t r a t e d i n Figure 10.  General Structure Both of the c r y s t a l l o g r a p h i c a l l y independent biphenylene molecules i n the-asymmetric c r y s t a l unit are completely planar within the l i m i t s of o experimental error, the maximum deviation.from the mean planes being 0.035A and the root mean square deviation - 0.02%, in,comparison  with a standard  o deviation i n atomic coordinates of 0.02A. On the basis of the standard deviations of the measured bond distances ( 0 . 0 3 A ) , some of the differences between chemically i d e n t i c a l but crystallographi c a l l y •distinct bonds are s i g n i f i c a n t , p a r t i c u l a r l y the large discrepancy between bonds 7-8 and 17-18.  However, detailed examination  of a l l the bond  distances (Figure 8) indicates that i n general bonds p a r a l l e l ' t o 7-8 a l l have rather short measured distances, while those p a r a l l e l to 17-18 are much longer.  This suggests that there are systematic errors i n molecular orientation.  Since i t was considered that these differences between chemically similar bonds could scarcely be r e a l , mean values were obtained .by assuming symmetry mmm-D2h f ° the molecule. r  The root mean square difference between the  individual-bond distances and the-corresponding mean values i s  O.O^X, a  little  greater than the estimated standard deviation of bond length. - Fortunately there are s i x independent  estimates f o r bonds of type B and C, and three  independent measurements f o r bond A, D, and E, so that the mean distances are considerably more accurate than the - i n d i v i d u a l measurements.  The~ standard  deviations of the mean bond distances, estimated from the root mean square deviations of the i n d i v i d u a l lengths from the corresponding mean values, a r e : Q  O  O  0.01A f o r bonds A, D, and E; 0.02A f o r bond B; and 0.03A f o r bond C.  - 1+0 -  The mean values of the bond angles indicate that there are deviations from 120° i n the six-membered rings, but that the angles i n the four-mambered -  r i n g do not d i f f e r s i g n i f i c a n t l y . f r o m 90°.  '  Table V.. Measured and Calculated Bond",Lengths (X)  Measured:  A  B  c  1-35  1.1+2  1.38  i<38  •1.52  l.i+l  1.38  1.1+1  • 1.1+1  1.1+5  D  E  Valence-!Bond Theory Weights of Kekule structures(XIl) (a)  .-(b)  (c)  •(d)  a  1  1  1  1  1  b  1  • 1  1  1  0  •1-39  1-39  1.39  1.39  •1-53  c  1+  2  2  1  1  1.38  l.i+l  1.38  1.U3  1.1+8  d  1+  2  2  •1  0  1.37  1.1+2  1.37  1.1+2  1-53  e  2  1  1  0  0  1.36  1.1+1+  1.36  1.1+1+  f  1  .0  0  0  0  1.3^  1-53  1.3^  1.53  1.53  g  1.38  1.1+0  1.38  l.l+l  1.1+7  h  1-39  1.1+1  1.39  l.l+l  1.1+7  i  1-39  1.1+0  1-39  l.l+l  1.53  .(e)  '1-53  Molecular-Orbital Theory  D. Discussion Bond lengths calculated from simple resonance theory, with the f i v e Kekule structures given equal weight, are those l i s t e d f o r model a (Table V). In deriving these distances,. the double-bond character was correlated with o bond length by using a curve based on the points ( 0 , I . 5 2 7 A ) , (0.'33> (0.50, I.392A),  and ( 1 . 0 0 , 1.33c;A).  o 1.U2TA),  This i s similar to the o r i g i n a l c o r r e l a t i o n  .curve given by Pauling(l+l) except f o r a small,change  i n the value used f o r the  - 41  single-bond distance.  -  Coulson(42) ,has suggested that the usual 1.54A s i n g l e -  bond length observed i n diamond and i n a l i p h a t i c molecules  (sp^ hybrid  O  s  o r b i t a l s ) , s h o u l d be reduced t o I.5OA i n aromatic molecules t o allow f o r the change t o s p - h y b r i d i z a t i o n . Recent accurate measurements (43) of the 2  -lengths of f o r m a l l y s i n g l e bonds in.quaterrylene suggest, however, that the pure single-bond distance i n polynuclear aromatic hydrocarbons i s greater o than I.5OA , and the mean value f o r the s i x s i n g l e bonds i n quaterrylene was therefor© ."uaad-inrderving 'the ' c o r r e l a t i o n curve- • There are marked discrepancies between these bond lengths p r e d i c t e d by the simplest resonance theory and those observed.  The p r e d i c t e d lengths  of bonds A, B, C vary i n the order long-short-long, and t h i s i s j u s t the opposite of the measured order. 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 f o r biphenylene were f i r s t c a r r i e d out twenty years ago ( 2 9 ) , and the c a l c u l a t e d bond distances (model g) do not d i f f e r s i g n i f i c a n t l y from those (model h) of a more recent c a l c u l a t i o n ( 4 4 ) . Model i_ has been derived from the c a l c u l a t e d bond orders (44),by using a c o r r e l a t i o n curve passing through the usual p o i n t s (O.525* 1.392ft)  821(1  (l  , 0 0 0  >  1.339ft)*  extra  P°l ' a  te<  1.42-^5.)* (0.667*  l to-lower bond orders.  The  agreement between measured and c a l c u l a t e d distances i s much more s a t i s f a c t o r y than f o r the simple valence-bond method, the v a r i a t i o n of the p r e d i c t e d bond distances A, B, C being i n the same order as the observed v a r i a t i o n . The measured bond lengths then.are i n agreement with the' chemical r e a c t i v i t y i n suggesting that the m o l e c u l a r - o r b i t a l method gives a b e t t e r estimation of the e l e c t r o n d i s t r i b u t i o n i n the molecule than does simple resonance theory.  In terms of the Kekule s t r u c t u r e s , i t appears that a l l  f i v e do not c o n t r i b u t e e q u a l l y t o the h y b r i d molecule, but that the p r e f e r r e d structure i s ( X l l a ) .  The bond distances f o r ( X l l a ) (model f ) obviously  - k2 represent too severe a f i x a t i o n of double and single bonds, and by varying the weights (Table V),best agreement i s obtained f o r model <d, that is" with maximum •weight given to the cyclobutane cyclobutene  formulation (XIIa),,less weight to'the  structures (Xllb and-XIIc),.and only a - l i t t l e weight to the  cyclobutadiene structures. I t . i s apparent that i n a l l the models bond D has calculated values which are considerably greater than the measured distance.  Now  i n a l l the bond-  length c a l c u l a t i o n s , no account has been taken of the s t r a i n introduced i n forming the four-membered r i n g ; , i t might be r e c a l l e d that the correct molecular structure was previously discounted (27, for t h i s s t r a i n energy.  28) .because of the-high value expected  The d i s t o r t i o n involved i n decreasing two-valency  angles at ortho-positions i n .each benzene ring from 120°  to 90° would obviously  r e s u l t i n a considerable compressive force on bond D,.and a shortening below the distances predicted by neglecting the e f f e c t of strain,, i n agfceement with the short measured length.  Best agreement with measured bond distances i s  obtained by using model d or e_ and applying a correction,to bond D f o r compression due to the formation of the four-membered ring; the other bonds .in the six-membered rings are, of course, also affected by t h i s s t r a i n , but probably to a smaller extent.  - 4  II.  3  -  METHOXYCARBONYLMERCURIC CHLORIDE  A.  Introduction  A series of compounds of the general formula XHgC0 R where X=C&, Br,I, 2  OAc,  NO3 and-R=H, CH3,  Essers f i f t y years ago  C2H5 was (45)•  f i r s t prepared by, Schoeller, Schrauth and  Their method of preparation  i s quite  general.  Methoxycarbonylmercuric chloride, f o r example, can be obtained i n the form of colourless needles by passing carbon monoxide slowly into a solution of mercuric chloride i n methanol: HgCe +CH OH+CO — > 2  The  3  C£.H C0 CH +HC£ g  2  3  structure of these compounds was  Schoeller(45)  i n doubt f o r many years,  although  apparently proposed the correct s t r u c t u r a l formulation  at an early date.  The  structure was  (XIIl)  not widely accepted because compounds of  t h i s type had been shown to y i e l d carbon monoxide q u a n t i t a t i v e l y by the action of methyl iodide or a d i l u t e solution of hydrochloric acid.  The  carbon  monoxide molecule thus appeared to be somewhat loosely bonded to the mercury atom, and t h i s l e d to the suggestion of a structure (XIV") involving a coordinate  link  (46).  Cl—H£—C (XIII)  \  0  a — • CH  3  Further work ( 4 7 ) , h a s f a i l e d to decide between,the formulations,  and structure (XIV)  Wi (xiv)  \ x  o»CH^  two•alternative  seems to have gained general acceptance  Recent i n f r a r e d and proton magnetic resonance measurements ( 4 9 ) ,  (48).  however,  furnished r e s u l t s which correlated w e l l with structure (XIIl),,and i t was  felt  - 44 -  that an X-ray i n v e s t i g a t i o n of the c r y s t a l s would e s t a b l i s h the structure conclusively.  The present X-ray a n a l y s i s i n d i c a t e s that the true structure  is (XIII). B.  Experimental  C r y s t a l s of methoxycarbonylmercuric c h l o r i d e are c o l o u r l e s s needles elongated along the c-axis with the (100) face developed. measured by displacement o f carbon t e t r a c h l o r i d e .  The density was  The u n i t - c e l l dimensions  and space group -were determined from r o t a t i o n and o s c i l l a t i o n photographs of a c r y s t a l r o t a t i n g about the c - a x i s , hkO .and h k l Weissenberg f i l m s , and 0k&, lk&,,h0t and hit precession f i l m s . C r y s t a l Data.  Methoxycarbonylmercuric c h l o r i d e , CC.H C0 CH3; M=295.1; m.p.l07°C g  Orthorhombic, a=8.30+0.02, b=17.20+0.03, c=7.52+0.02A. =3.64, £^=3. 58g.cm"3. A=0.7107&,  2  U=107i|X . 3  D ( v i t h Z=8) x  Absorption c o e f f i c i e n t f o r X-rays, ?c =1.54l8&, u=6l0 cm7  0=336 cmT1  F(000)=1024.  Absent spectra: 0k£. when t i s odd,  h0£when € i s odd,, hkO when (h+k),is odd. Space group i s Pccn — D ^ The i n t e n s i t i e s of the•hkO r e f l e x i o n s were recorded on Weissenberg photographs, using CuK<^ r a d i a t i o n and m u l t i p l e - f i l m s t o c o r r e l a t e strong and weak r e f l e x i o n s .  The 0k£, r e f l e x i o n s were recorded on precession f i l m s with  r e l a t e d time exposures, using MoK^ r a d i a t i o n .  A l l t h e • i n t e n s i t i e s were  estimated v i s u a l l y , the range being about 4 0 0 0 . t e l .  The c r y s t a l used was  approximately c y l i n d r i c a l , 2 mm. i n , l e n g t h and 0.09 mm. i n diameter, and absorption c o r r e c t i o n s were applied f o r a c y l i n d r i c a l c r y s t a l .  The structure  -amplitudes were derived by the usual formulae,,the absolute scale being e s t a b l i s h e d l a t e r by c o r r e l a t i o n with the c a l c u l a t e d structure f a c t o r s .  69 hkO  and 76 0 k ^ r e f l e x i o n s were observed, representing 68$ ,and 64$ -respectively of the p o s s i b l e numbers observable under the - experimental conditions.  - 45  C.  -  Structure Analysis  Inspection of the hkO photographs shows that r e f l e x i o n s with h=0,l+,8 are p a r t i c u l a r l y strong while those with h=2,6,10 are e i t h e r very weak or absent.  Since the structure factor expression f o r these r e f l e x i o n s involves  a term cos 2 7rhx, the mercury atom must have x coordinate approximately g . The 0k& i n t e n s i t i e s with k odd are also weak and few i n number.  Consideration  of the term sin27r£. z i n the structure factor expression leads to-the possible values z=0 or ^ f o r the mercury, atom. Patterson projections along the c- and a-axes (Figure l l ) confirmed the above conclusions and provided i n addition coordinates f o r the-chlorine atom. The contribution of these atoms to the hkO and 0k& structure factors were calculated, the atomic scattering factors of neutral mercury and chlorine (50) being used.  The signs of the majority of the structure amplitudes were c o r r e c t l y  determined, except a few with small or no contribution from the mercury atom; for  instance a l l 0k6 terms with k odd had to be omitted u n t i l the f i n a l  stage of refinement. The f i r s t hkO Fourier synthesis was  computed with 67 terms.  The mercury  atom .was well-resolved and had e s s e n t i a l l y the same-coordinates as provided by the Patterson p r o j e c t i o n on (OOl).  The chlorine atom, however, moved  appreciably and the electron-density d i s t r i b u t i o n showed a l i n e a r concentration ,0  of peaks approximately b-axis.  I t was  Q  6A long, c l e a r l y separated- and l y i n g at about 17  to the  obvious that the structure (XIV),must be rejected and the  i n d i v i d u a l peaks corresponded  to the carbonyl and methyl groups of structure (XIIl)  The f i r s t Fourier synthesis f o r the a-axis p r o j e c t i o n was computed with 53 terms.  This p r o j e c t i o n provided another view of the molecule arid confirmed  the correctness of structure ( X I I l ) .  With the help of a b a l l - a n d - s t i c k model,  parameters f o r a l l the atoms were obtained by c o r r e l a t i n g both the a- and c-axes  - he -  Hg-a  vector peak  0 1 i . . . . i.... i  Figure 11.  2 I  3 |  4 I  5 |  k  (a) Patterson p r o j e c t i o n along [ 0 0 l ] . drawn at a r b i t r a r y i n t e r v a l s .  Contours are  (b) Patterson p r o j e c t i o n along [lOO]. drawn at a r b i t r a r y i n t e r v a l s .  Contours are  - U7 -  projections.  A second structure f a c t o r c a l c u l a t i o n was now c a r r i e d out f o r the  hkO and Oko r e f l e x i o n s .  The temperature factor,< B=k.6A"^ f o r both zones, was / | F | j , against s i n 9 .  m |"|F |  obtained by p l o t t i n g  2  C  Q  The discrepancy  f a c t o r R f o r the observed hkO r e f l e x i o n s was 0.195 f o r mercury and c h l o r i n e only, dropping to O.153 when the l i g h t e r atoms were included;, the observed i n t e n s i t y o f the 020 r e f l e x i o n was considerably lower than,the c a l c u l a t e d value, probably because of extenction, and was omitted i n the evaluation of R. For 0k6 r e f l e x i o n s R was 0 . 1 6 9 , f o r a l l atoms and 0.221 f o r mercury and c h l o r i n e only. Second F o u r i e r syntheses f o r both p r o j e c t i o n s were now computed, u t i l i z i n g a l l the observed structure amplitudes and t h e i r c a l c u l a t e d signs. The e l e c t r o n density maps (Figure 12 and Figure 1 3 ) , i n d i c a t e d e s s e n t i a l l y no change i n the mercury and c h l o r i n e p o s i t i o n s , and only s l i g h t s h i f t s of the l i g h t e r atoms.  A t h i r d structure f a c t o r c a l c u l a t i o n was not c a r r i e d out.as  s i g n i f i c a n t improvements were not expected by merely changing s l i g h t l y the p o s i t i o n s o f the carbon and oxygen atoms.  The observed and c a l c u l a t e d  structure f a c t o r s are compared i n T a b l e A - 3 Molecular  Dimensions  The f i n a l atomic coordinates, deduced from Figure 12 and Figure 13 and expressed as f r a c t i o n s o f the u n i t - c e l l , e d g e s , . a r e l i s t e d i n Table VT.  The  bond lengths and valency angles c a l c u l a t e d from these coordinates are shown i n Figure.lh. Table VI. P o s i t i o n a l P a r a m e t e r s 1  Atom  x  y  z  0.0203 -O.O785  0.2500 O.OU25  Hg ce  0.1256 0.1820  C"!  O.O75  0.101  O.i+26  O.O76 0.069 -0.013  O.O95 0.169 ,0.237  O.588 0.373  0-L o 2  -C  2  0,kk2  -  48  -  v  (t>) The structure viewed along [001].  -p-  lliiillinl  Figure 13.  (a) Electron-density p r o j e c t i o n along [lOO]. Contours of the mercury atom are drawn at approximately 10,20,50,100,150 e.°T , and other atoms a t 2  8,10,15 e . X  .  (b) The structure viewed along [lOOJ.  - 51 -  Standard Deviations. The standard deviations of the atomic p o s i t i o n s , c a l c u l a t e d from formulae, are Cr(x)= 0 (y)= Cr(z)=0.007$. , o c h l o r i n e , and 0.054A f o r carbon and oxygen.  Cruickshank's  r  D.  f o r mercury, 0.0U4^ f o r  Discussion  The r e s o l u t i o n o f the l i g h t e r atoms, e s p e c i a l l y the carbonyl group, i s not very good, p a r t l y because of overlap i n the p r o j e c t i o n s , but c h i e f l y due to the dominating e f f e c t on the s c a t t e r i n g of the heavy mercury atom.  Both  p r o j e c t i o n s however i n d i c a t e unambiguously that the -true s t r u c t u r e i s ( X I I l ) . The coordination around the mercury atom i s e x a c t l y l i n e a r , and i n a d d i t i o n a l l the-atoms i n the molecule, except the methyl group, l i e i n one plane, w i t h equation 0.9824X + 0.1671+Y + 0.0830Z - 1.2392 = 0 ,  where X, Y,-Z are coordinates expressed i n %. o displaced from t h i s plane by O.39A.  The methyl carbon atom i s  The Hg—Cl bond length ( 2 . 3 5 A , O-=0.0UA) and the Hg—C distance (1.96%, o. (7" =0.05A) do not d i f f e r s i g n i f i c a n t l y from the values reported f o r corresponding distances i n r e l a t e d structues ( 5 l ) - The other bond lengths and valency  angles  have been determined only r a t h e r imprecisely, but do not d i f f e r s i g n i f i c a n t l y from  the normal values. The packing o f the molecules i s i l l u s t r a t e d i n Figure 15• There are two  short intermolecular distances, a Hg....C£. separation o f 3'21A", and a Hg.... 0.(carbonyl) contact o f 3-01^-  These distances are however very s i m i l a r  to corresponding contacts i n c r y s t a l l i n e mercuric c h l o r i d e ( 5 2 ) , i n which the mercury atoms are surrounded by two c h l o r i n e atoms a t distances o f 2.25A" (bonded d i s t a n c e s ) , two a t , 3 . 3 ^ , and a f u r t h e r two a t 3-63^i n methoxycarbonylmercuric c h l o r i d e are quite s i m i l a r .  The distances  A l l the other contacts  are considerably longer, the shortest Hg.'. ..Hg distance being 4.29A\  -  III.  52 -  p-CHLORONITROBENZENE  A.  Introduction  A preliminary, investigation of the c r y s t a l structure of p-chloronitrobenzene by Toussaint(53).indicated that the absent reflexions corresponded to space group P2]_y  c  (interchanging his"a~and c-axes),,and the measured density  to two molecules i n the unit c e l l , necessitating a molecular centre of symmetry. arrangement  Two types of structures were considered p o s s i b l e :  ( i ) , a disordered  of molecules i n space group P2]_/ , giving a s t a t i s t i c a l l y  centrosymmetric  c  structure, or ( i i ) an ordered.arrangement  i n space group P,c  which gives weak reflexions when k i s odd. Arrangement ( i i ) was considered more l i k e l y , and a structure based on space group Pc. was deduced from consideration of a few structure factors (which were not l i s t e d ) . The present i n v e s t i g a t i o n was made to e s t a b l i s h the correct structure, and the-analysis described .below suggests that the true space group' i s and that a disordered arrangement  P2-jy  c  of molecules e x i s t s i n the c r y s t a l .  B.  Experimental  Crystals of p-chloronitrobenzene (Eastman Kodak), obtained by c r y s t a l l i z a t i o n from ethanol, are colourless needles elongated along the a-axis with the (OlO) face developed.  The density was measured by f l o t a t i o n i n  aqueous potassium iodide solution.  The u n i t - c e l l dimensions and space group  -were determined from rotation and o s c i l l a t i o n photographs of a c r y s t a l rotating about the-a«axis, Q k t C r y s t a l Data.  and lk& Weissenberg f i l m s , and hkO and h O t precession films.  p-Chloronitrobenzene, CgH^N0 CL ;M=157.6; m.p. 8 3 . 5 ° C 2  Monoclinic,.a=3.84+0.01, b=6.80+0.01, c=13-35+O.02A, Dx(with Z=2)=l.514, X=1.5^l8ft, jx=kh.l  Dm=1.52 g.cm r  |3 = 9 7 ° 3 1 ' + 5 ' .  U=3^5.6A . 3  Absorption c o e f f i c i e n t f o r X-rays,  cm"} ; A . = 0 . 7 l 0 7 i , u=5.1 cm"}  F(000)=l60.  Absent 5 h0€ when £, i s odd, OkO when k i s odd. Space group ,is P 2 - ] / - C 2 h • c  spectra:  -  53  -  C r y s t a l s of p-chloronitrobenzene are highly v o l a t i l e at room temperature so that a c r y s t a l v o l a t i l i z e d completely i n a few hours. i n t e n s i t y measurement was a needle about 3 rm  cross-section.  i-  n  The c r y s t a l used f o r  length and 0.15X0.08 mm. i n  I t was sealed i n a t h i n - w a l l e d Lindemann-glass c a p i l l a r y .  The  i n t e n s i t i e s of the 0k£ r e f l e x i o n s were recorded on Weissenberg exposures f o r a c r y s t a l r o t a t i n g about the a-axis, using CuK„< . r a d i a t i o n , and m u l t i p l e - f i l m s to c o r r e l a t e strong and weak r e f l e x i o n s . precession  f i l m s with MoK^  correlation.  The h06 r e f l e x i o n s were recorded on  r a d i a t i o n , - u s i n g m u l t i p l e exposures f o r i n t e n s i t y  The ranges of O k t and h0£ i n t e n s i t i e s -were about 36OO t o l and  1800 t o l r e s p e c t i v e l y , the estimates being made v i s u a l l y .  The, structure  amplitudes were derived from the usual formulae, the absolute scale being e s t a b l i s h e d l a t e r by c o r r e l a t i o n with the c a l c u l a t e d structure factors."' 57 independent 0k£. reflexions-and 35 h0& r e f l e x i o n s were observed,, representing. •* hQ% and hhi> r e s p e c t i v e l y of the p o s s i b l e numbers observable under the experimental conditions. C  Structure  Analysis  [lOO] -Projection The Patterson map (Figure l 6 a ) could be i n t e r p r e t e d on the b a s i s of both ordered and disordered  structures, although the Ct-Cl i n t e r a c t i o n s were much  weaker than expected, suggesting that the ordered structure was l e s s l i k e l y . Nevertheless a few structure f a c t o r s were c a l c u l a t e d using an ordered model, with atomic s c a t t e r i n g f a c t o r s from Tabellen  zur Rontgenstrukturanalyse  (50).  The agreement-between.measured and c a l c u l a t e d structure f a c t o r s was rather poor, and the c a l c u l a t e d values f o r OkO r e f l e x i o n s with k odd- were s i g n i f i c a n t l y l a r g e r than the maximum p o s s i b l e observed values. A disordered model was then set up, c o n s i s t i n g of two h a l f molecules, superimposed so that the carbon atoms coincided, but with the p o s i t i o n s o f  -  54  -  CM  r4  O  (j  F i g u r e 16.  (a) P a t t e r s o n p r o j e c t i o n a l o n g [ l O O ] . Contours are drawn a t a r b i t r a r y i n t e r v a l s . Diagram of one m o l e c u l e i s superimposed. P a t t e r s o n p r o j e c t i o n a l o n g [oicQ. Contours are drawn a t a r b i t r a r y i n t e r v a l s . Diagram of one m o l e c u l e i s superimposed.  the c h l o r i n e and n i t r o groups interchanged.  Approximate c o r r e l a t i o n between  measured and c a l c u l a t e d structure f a c t o r s was obtained, the temperature f a c t o r being apparently quite high, and the electron-density p r o j e c t i o n showed good r e s o l u t i o n of the six-membered.ring and a.peak o f the expected shape and height at the p o s i t i o n of the overlapping c h l o r i n g atom and n i t r o group (Figure 17)-  New coordinates were obtained and the 0k6 structure f a c t o r s  recalculated,. a temperature f a c t o r B=8.5^ being obtained by p l o t t i n g In  | |F |y/ |F | ^ c  high F  against  0  sin ©.  The strongest  2  values, and these discrepancies  c  r e f l e x i o n s had c o n s i s t e n t l y  were a t t r i b u t e d t o secondary e x t i n c t i o n .  An e m p i r i c a l correction,(5^),was applied .using the r e l a t i o n I_ I  =  u+gl  1 + JL I  -  Q  where I = i n t e n s i t y that would be observed i n the absence of secondary e x t i n c t i o n , I  =  observed i n t e n s i t y ,  u  =  l i n e a r absorption c o e f f i c i e n t ,  g  =  constant.  Q  I was taken,to be equal to i t s c a l c u l a t e d value I , and a p l o t of I c / l c  I  c  gave a value of 0.00173^  f o r  t h e  0  against  r a t i o g/u. This procedure appeared t o  have some j u s t i f i c a t i o n since the corrected values of the 00& structure f a c t o r s agreed with those obtained from the h o t MoK^ data.  Measured and  c a l c u l a t e d structure f a c t o r s are l i s t e d i n Table A - k (R=0.23)> both corrected ( i n parentheses)  and uncorrected F  Q  values being given f o r the stronger  reflexions. [OlOJ  Projection  The x coordinates of the atoms were deduced from the o r i e n t a t i o n , o f the molecule i n the (010),Patterson p r o j e c t i o n (Figure l6b) and the h O t structure factors calculated.  A Fourier s e r i e s was summed and the r e s u l t i n g map-  i n d i c a t e d small s h i f t s i n atomic p o s i t i o n s . • Structure f a c t o r s were r e c a l c u l a t e d  0  Figure 17.  1  '  2  i  3  i  A-  i  5  A  1  (a) Electron-density p r o j e c t i o n along | 1 0 0 ) . Contours are drawn at i n t e r v a l s o_2 o_2 of approximately 1 e.A , with the lowest contour at 3 e.A (b) The structure viewed along [lOO].  0  1  2  l  i  18.  3  1  4 L  5  A  1  (a) E l e c t r o n - d e n s i t y p r o j e c t i o n a l o n g [ d o ] . C o n t o u r s are drawn, a t o f a p p r o x i m a t e l y 1 e.ft." , w i t h the l o w e s t c o n t o u r a t k e . A . 2  (b) The s t r u c t u r e viewed a l o n g  [do].  intervals  - 58 -  (and  are  again  included  being  in  omitted Figure  the  in  the  observed  f i n a l  unit  F ,  probably  evaluating  R.  A  positional  parameters  c e l l - edges,  are  final  l i s t e d  Table  VII.  agreement  particularly one,  of  B=8.5A  of  reflexion  extinction,  was  and  projection  factor, as  movements.  It  since  small  errors  sin  produce elegant  is  this is  plane  shown  0.142  0.343  0.312  0.130  o.4o4  0.277  0.097  0.425  0.444  0.097  0.167  0.153  0.064  z  c  3  -0.065  0.017  -0.102  and  calculated  structure  because  the  model  used  is  necessarily  rings  of  the  approximately  so  is  that  the  six-membered  high  value  result quite  not  Discussion  measured  the  was  Parameters  -0.038  the  fractions  VII.  0.169  significant model  as  0.340  is  in  Table  expressed  O.376  this  also  atoms,  y  That  a  the  0.110  probably  exactly.  of  2  assumes  electron-density  more  because  102  C  between  good,  and  temperature  0  the  factor  X  D.  coincide  for  Positional  Cl  crude  temperature  electron-density  in  Atom  The  value  than  c  a  18.  The of  smaller  o2  A - 4 , R=0.26),  Table  indicated;  considerably was  in  of  only  probably  the  disorder,  difficult  steep  slopes  changes tried,  resulting  in and  rather  factors  two  than  a to  determine  the  scale  of  the  of  i n  scale. the  In  view  correlation  of  not  rather  orientations by  the  smearing  out  of  large•thermal  to  plots  a  indicated  from  is  factor  ( I F l /1  these  between  c  precisely,  F  ol}  against  difficulties measured  and  a  - 59  -  c a l c u l a t e d structure f a c t o r s was considered s u f f i c i e n t l y s a t i s f a c t o r y to i n d i c a t e that the disordered arrangement i s the.correct one. The absence of d i f f u s e s c a t t e r i n g on the f i l m s i n d i c a t e s that the two o r i e n t a t i o n s must occur randomly throughout the c r y s t a l .  In, p_-bromochloro-  benzene (55),and 1-bromo-U-chlorocyclohexane•(56),similar disordered arrangements have been observed.  In these structures the.interchangeable  -atoms, chlorine-and bromine, are-of course very s i m i l a r i n s i z e and chemical behaviour.  Although at f i r s t glance the c h l o r i n e atom and n i t r o group.in  p-chloronitrobenzene appear to be r a t h e r d i f f e r e n t i n nature, c l o s e r study suggests that t h e i r s i z e s are not very d i f f e r e n t and that t h e i r e l e c t r o n e g a t i v i t i e s are s i m i l a r , so that i t i s not s u r p r i s i n g that the s t r u c t u r e - i s disordered.  A d i r e c t t e s t of the approximate equivalence of the two  o r i e n t a t i o n s i s provided by an examination of the packing of the molecules i n the c r y s t a l .  Allowing every molecule to have e i t h e r arrangement, i t i s found  that there are several intermolecular distances below-  the smallest being  a C . . . . 0 contact of 3-35A; the approaches thus correspond to normal van der Waals i n t e r a c t i o n s , so that both o r i e n t a t i o n s apparently e x i s t i n t h e . c r y s t a l w i t h no undue s t r a i n . The d i s o r d e r prevents accurate determination of the molecular dimensions, but the bond distances and val'ency angles appear to be normal.  The molecule  i s at l e a s t approximately p l a n a r , but a t w i s t i n g of the n i t r o group, out,of the plane of the aromatic r i n g , of the order of 1 0 ° - 2 0 ° would probably not be detectable.  PART I I I X-RAY STUDIES ON SOME DERIVATIVES OF ACENAPHTHENE  -  I.  61  ACENAPHTHENE AND DERIVATIVES A.  Introduction  In I867, B e r t h e l o t ( 5 7 ) , i s o l a t e d a hydrocarbon of molecular formula ^12%0 f  r o m  c o a l t a r and named i t acenaphthene.  S t r u c t u r a l l y • i t may be  regarded as a d e r i v a t i v e of naphthalene obtained by f u s i o n of a f i v e membered r i n g i n t o i t s angular p o s i t i o n .  The enumeration of the acenaphthene  nucleus, which i s used f o r a l l the d e r i v a t i v e s , follows the I.U.P.A.C. 1957 Rules (58).  The s t r u c t u r a l formula (XV) assigned to•acenaphthene by B e r t h e l o t was based upon i t s synthesis from acetylene and naphthalene (59) and from 1-ethylnaphthalene (6o),by p y r o l y s i s .  The most .convincing evidence was the  o x i d a t i o n of the hydrocarbon to give acenaphthenequinone by chromic oxide and a c e t i c a c i d , naphthalic a c i d .by potassium permaganate, and naphthalic anhydride-by chromic a c i d ( 6 l ) . ' As a consequence of the pioneering work of B e r t h e l o t , and p a r t i c u l a r l y of Graebe(62), the r e a c t i o n s of acenaphthene and i t s d e r i v a t i v e s have been studied i n d e t a i l .  For work p r i o r to 1921 the comprehensive review by Hahn  and Holmes(63) should be consulted. Csizmadia and Hayward(6U).  Recent developments have been reviewed by  - 62 -  B.  The Structure of Acenaphthene  Formula (XV), which shows a-CB^-CR^ bond'length o f 2.k% (width of a •benzene r i n g ) and i n t e r i o r angles of 120°.and 90° i n the five-membered r i n g , i s obviously not an accurate representation o f the molecular acenaphthene.  structure of  Considerable m o d i f i c a t i o n o f the geometry o f t h e - p e r i - r i n g i s  expected, but i t i s uncertain whether the-carbon skeleton would remain planar.  Of p a r t i c u l a r i n t e r e s t i s the length o f the a l i p h a t i c s i n g l e bond  which i s under considerable s t r a i n , as are also the bond-length v a r i a t i o n and .angular d i s t o r t i o n i n the naphthalene nucleus.  "Accordingly, several  attempts have been made to determine the molecular  structure of acenaphthene  by an X-ray a n a l y s i s o f the c r y s t a l l i n e m a t e r i a l . Acenaphthene c r y s t a l l i s e s i n the orthorhombic system; i t s u n i t - c e l l dimensions were f i r s t determined by Bragg(65)-in  1921.  On the b a s i s of the  systematic e x t i n c t i o n s (0k£, absent w i t h & o d d ) , H e r t e l and Kleu(66)  decided  5  that the space group was Pcmm-I^ > i g n o r i n g completely the other two k 2 p o s s i b i l i t i e s , v i z . Pc2"m-C2v and Pcm2Q_-C v • 2  Strangely enough the same  conclusion was reached seven years l a t e r by'Banerjee and Sinha(67), who then proceeded t o solve the c r y s t a l s t r u c t u r e using both X-ray and magnetic data. Their a n a l y s i s revealed a planar molecule with" the unusual length 1  for the CH -CH2 .bond. 2  o f 2.01%  Subsequently i t was pointed-out by K i t a i g o r o d s k i i ( 6 8 )  that the true space group .was Pcm2-[_, on the ground that the other two space groups, v i z . Pcmm and Pc2m, are forbidden to hydrocarbons (69).  He a r r i v e d  at the c o r r e c t structure from .packing considerations and by c o n s t r u c t i n g the centrosymmetric e l e c t r o n - d e n s i t y p r o j e c t i o n on (OOl). The s t r u c t u r e i s i n t e r e s t i n g c r y s t a l l o g r a p h i c a l l y .  The four molecules  i n the u n i t c e l l f a l l i n t o two independent sets and occupy s p e c i a l p o s i t i o n s : the inherent symmetry plane normal t o the molecular plane coincides w i t h the  symmetry p l a n e - i n the c r y s t a l .  The CH -CH bond length therefore depends only 2  2  on the y coordinate of one - a l i p h a t i c carbon atom.  From consideration,of the o  OkO s t r u c t u r e f a c t o r s alone, Kitaigorodskii(68),deduced  a value of 1.8A f o r  t h i s distance. L a t e r , using p a r t i a l hkO CuK x, data c o l l e c t e d by means of an i o n i z a t i o n chamber,, he computed the e l e c t r o n - d e n s i t y p r o j e c t i o n along [OOl] and o r  obtained a CH -CH bond length o f 1.64+0.04A (70). 2  2  Further refinement o f the s t r u c t u r e has been c a r r i e d out by'Ehrlich(7l) using two-dimensional ( F - F ) syntheses. 0  c  The a n a l y s i s reveals a planar  molecule with dimensions as shown i n Figure 19a. Contrary, t o previous claims, the a l i p h a t i c CH -CH bond i s not s i g n i f i c a n t l y . s t r e t c h e d , i t s length'being 2  .  2  o  1.5^+0•01^A.  The bond distances i n the aromatic part o f the molecule are  s t i l l very s i m i l a r t o those-in naphthalene -(Figure•19b),(72).and the s t r a i n i n the p e r i - r i n g i s r e l i e v e d by d i s t r i b u t i n g the angular s t r e s s over the entire  molecule. C  Survey of Known Analyses o f Acenaphthene D e r i v a t i v e s  Several d e r i v a t i v e s of acenaphthene have been axamined by X-rays; the r e s u l t s show that the acenaphthene skeleton i s e s s e n t i a l l y planar,.with large deviations from 120° i n the valency angles. Of the simple acenaphthene d e r i v a t i v e s , only 5*6"-dichloroacenaphthene (Figure 19c) has been i n v e s t i g a t e d (73)- The molecule i s s l i g h t l y non-planar as a r e s u l t of severe s t e r i c hindrance between the  chlorine-atoms.  In pyracene (Figure 19d) a value-of 1-59+0.03A has been reported f o r the CH -CH bond distance (74). 2  2  The bond-lengthening i s p o s s i b l y s i g n i f i c a n t ,  although the authors d i d not consider t h i s t o be so. The s t r a i n i n 2,13-benzfluoranthene (Figure 19e) i s even greater than that i n acenaphthene.  I t has been shown,(75) that the molecule-has the  expected symmetry, and that the longest- bond i s that on the open side of the  - 6k 1-54  F i g u r e 19.  Mean "bond l e n g t h s and v a l e n c y a n g l e s m (a) acenaphthene, (b) n a p h t h a l e n e , ( c ) 5 , 6 - d i c h l o r o acenaphthene, (d) p y r a c e n e , (e) 2 . 1 3 - b e n z i l u o r a n t h e n e , and ( f ) 2 0 - m e t h y l c l i o l a n t h r e n e .  five-membered r i n g . The structure of 20-methylcholanthrene ( X V l ) , which contains the acenaphthene system, has been subjected to r e f i n e d three-dimensional a n a l y s i s (76).  The acenaphthene skeleton has almost  symmetry, and i t s average  dimensions are shown i n Figure 19f•  (XVI)  (XVII)  The structure of an acenaphthylene-dimer (XVTl) has been e s t a b l i s h e d by a c l e a r l y resolved p r o j e c t i o n (77)-  D e t a i l s of the molecular dimensions  f o r t h i s compound are not a v a i l a b l e . F i n a l l y , c r y s t a l l o g r a p h i c data have been -published f o r the f o l l o w i n g compounds ( 7 8 ) :  5-acetylacenaphthene, 3-acetylacenaphthene, 5>6-dibromoacen-  aphthene, and oC -(5-acenaphthyl)ethylamine.  I 1  - 66 -  II.  ACENAPHTHENEQUINONE A.  Introduction  Study of the c r y s t a l structure of acenaphthenequinone-was as part o f an i n v e s t i g a t i o n o f a s e r i e s of acenaphthene  undertaken  derivatives.  B. Experimental C r y s t a l s o f acenaphthenequinone  are orange-yellow needles elongated  along the c - a x i s , w i t h the (010) face w e l l developed.  The c e l l dimensions  and apace group were determined from Weissenberg and precession photographs of a c r y s t a l mounted about the-c-axis.  The density was measured by f l o t a t i o n  i n aqueous potassium iodide. C r y s t a l Data.  Acenaphthenequinone, - C Hg(C0) ; M=l82.2; m.p. 273-274°C. 10  2  03 U=8l2A . D ( w i t h Z=4)  o Orthorhombic, a=7.8l+0.01, b=27.0+0.05, c=3.851+0.005A. =1.49, 1^=1.48 gm.cm 7  i  x  Absorption c o e f f i c i e n t s f o r X-rays, ?v. =1 • 54l8°\., 0  1  u=9-83 c m t ; 7v=0.7107A, u=1.24 cm 7  F(000)=376".'~ Absent s p e c t r a :  hOO-when 4  h i s odd, OkO when ,k i s odd, 001 when t i s odd.  Space group i s P2-]_2-]_2-L-D2 .  For i n t e n s i t y purposes the hkO r e f l e x i o n s were recorded on m u l t i p l e - f i l m Weissenberg photographs, using u n f i l t e r e d CuK^ r a d i a t i o n .  The 0k£, data were  c o l l e c t e d on precession f i l m s w i t h r e l a t e d time exposures, MoK^ r a d i a t i o n being used.  The - i n t e n s i t i e s were estimated v i s u a l l y .  The r e l a t i v e values o f the  s t r u c t u r e amplitudes were-derived by applying the usual Lorentz and p o l a r i z a t i o n f a c t o r s , the absolute scale being e s t a b l i s h e d l a t e r by c o r r e l a t i o n - w i t h the c a l c u l a t e d structure f a c t o r s .  Absorption c o r r e c t i o n s were considered  unnecessary since the c r y s t a l used had a mean diameter o f 0.06 mm. 152 independent hkO r e f l e x i o n s were observed (excluding the 020 r e f l e x i o n , which was cut o f f by the beam t r a p ) , representing 54$ o f the t o t a l number t h e o r e t i c a l l y observable w i t h CuKc* r a d i a t i o n .  Only 33 £ r e f l e x i o n s were 0 k  - 67 -  _  .  W  ///»  Figure 20. R e l a t i o n of the o r i g i n of space group P2]_2]_2]_ t o the o r i g i n s of i t s p r o j e c t i o n s on the pmacoids (100), (010), and (001). The several o r i g i n s are i n d i c a t e d by dots. A f t e r Buerger, Barney and Hahn(79)»  Table V I I I .  Space Group Coordinates  Transformations between Space Group and P r o j e c t i o n Coordinates.  (OOl)  P r o j e c t i o n Coordinates (100) (OlO)  x  x'=x-£  x"=x  y  y'=y  y"=y-<:  x'"=x  y"'=y  - 68 recorded, representing about 20$ of the t o t a l number observable. C  Structure A n a l y s i s  Space group • P2]_2l2]_ • i s non-centrosymmetric,  but i t has  centrosymmetric  p r o j e c t i o n s (plane group pgg) i n a l l three p r i n c i p a l p r o j e c t i o n s (Figure 20). The r e l a t i o n s between space group and p r o j e c t i o n coordinates are-those formulated i n Table V I I I . [00l] P r o j e c t i o n The shortness of the c - a x i s promised good r e s o l u t i o n of a l l the atoms in this projection.  Packing and symmetry considerations suggested that the  four molecules i n the u n i t c e l l must b e • l i n e d up approximately i n the d i r e c t i o n of the b - a x i s .  The search f o r a t r i a l s t r u c t u r e was guided by the observation  that the OkO r e f l e x i o n s e x h i b i t a d i s t i n c t i v e feature," being r e l a t i v e l y weak f o r k=4n+2 and strong f o r k=4n.  The very strong 0 , 2 4 , 0 r e f l e x i o n corresponds  to a planar spacing of 1.13ft, which i s s l i g h t l y l e s s than h a l f the-width of a benzene r i n g .  This i n d i c a t e d that i n the c-axis p r o j e c t i o n the aromatic carbon  atoms must l i e very close to the ( 0 , 2 4 , 0 ) planes.  The angle between the  molecular plane and the (OOl) plane was estimated to be about 2 4 ° by comparing the lengths of the molecule and the a-axis. 29°)•  (The f i n a l r e s u l t s show i t to be  The o r i e n t a t i o n of the aromatic nucleus was a l s o i n complete agreement  with that deduced from the "benzene" r e f l e c t i o n s .  The x and y parameters  r e f e r r e d to the molecular o r i g i n (defined as centre of the Cc; -C8b hond) a  were obtained from the p r o j e c t i o n of a CENCO Petersen molecular model held i n the deduced o r i e n t a t i o n . Examination of the Patterson p r o j e c t i o n along [OOl] the above deductions.  (Figure 21) confirmed  From the m u l t i p l e vector peak between naphthalene  rings  r e l a t e d by symmetry, the coordinates of the molecular o r i g i n were estimated as y =0.125, x =0.190 or O.3IO. o  o  The former value f o r x  Q  was taken since i t gave  - 69 -  Figure 21.  Patterson p r o j e c t i o n along [c-Ol]. Contours are drawn at a r b i t r a r y i n t e r v a l s . Diagram of one molecule i s superimposed.  - 70 -  b e t t e r agreement between the observed and c a l c u l a t e d structure amplitudes f o r some low-order r e f l e x i o n s .  (The f i n a l coordinates of the molecular o r i g i n  are x =0.1762, y = 0 . 1 2 U 9 ) .  S t r u c t u r e f a c t o r s were now c a l c u l a t e d  o  Q  f o r a l l hkO  r e f l e x i o n s using the carbon and oxygen s c a t t e r i n g f a c t o r s from Tabellen,zur Rontgenstrukturanalyse ( 5 0 ) , with an o v e r a l l i s o t r o p i c temperature f a c t o r 1  °  . o  2  B=4.5A . The discrepancy f a c t o r R f o r the observed r e f l e x i o n s was 0.408, but there-appeared t o be no serious discrepancy between the observed and c a l c u l a t e d structure amplitudes.  123 terms ( i n c l u d i n g F(000)) were used i n a Fourier  synthesis, which gave good r e s o l u t i o n of a l l the atoms^  R e c a l c u l a t i o n of the  structure f a c t o r s w i t h atomic coordinates determined from the electron-density map reduced R t o 0.288.  Refinement of p o s i t i o n a l and"temperature parameters  proceeded by computing successive ( F - F ) syntheses, and a f t e r f i v e cycles R 0  c  dropped t o 0.150. At t h i s p o i n t , the c o n t r i b u t i o n s of the hydrogen atoms were considered. The p o s i t i o n a l parameters were obtained by measurement on a molecular model. An i s o t r o p i c temperature f a c t o r of 5-°A^ was assigned t o each of t h e s i x hydrogen atoms.  The i n c l u s i o n of these hydrogen-atom c o n t r i b u t i o n s l e d to a  s i g n i f i c a n t improvement i n the agreement of the low-order data, e s p e c i a l l y the OkO r e f l e x i o n s , and the R f a c t o r was lowered t o 0.139Measured and c a l c u l a t e d structure f a c t o r s are compared i n Table A-5, and the f i n a l hkO F ClOO]  Q  synthesis i s shown i n Figure 22.  Projection  Since the number of observed Ok-t r e f l e x i o n s was smaller than the number of parameters t o be determined good r e s o l u t i o n was not expected i n t h i s projection.  Approximate z coordinates f o r the carbon and oxygen atoms were  obtained by measurement on a molecular model.  The i n i t i a l 0k£. discrepancy  was 0.190 f o r the observed r e f l e x i o n s , and t h i s was reduced by an ( F - F ) 0  c  - 71  0  1  1 1 1 1 1 1 1 ' 111  Figure 22.  -  2 i  i  3 i  A  I  Electron-density p r o j e c t i o n along foOll. Contour l i n e s o-2 Q-2 are drawn at i n t e r v a l s of 1 e.A s t a r t i n g with 1 e.A .  - 73  synthesis to 0.116.  -  Hydrogen-atom c o n t r i b u t i o n s were not considered.  and c a l c u l a t e d Okt structure f a c t o r s are included in-Table A-5-  Measured  The f i n a l  e l e c t r o n density projection.along [ [ l O O j i s shown i n Figure 23Coordinates and Molecular Dimensions The f i n a l p o s i t i o n a l and i n d i v i d u a l temperature 'parameters are l i s t e d i n Table IX where the atomic coordinates are r e f e r r e d to the space group o r i g i n and expressed as f r a c t i o n s of the u n i t - c e l l edges.  The coordinates of  the carbon and oxygen atoms can be f i t t e d to the equation 0.3284X + O.35U8Y - O.875UZ - 2.3951 = 0  o where X,Y,Z  are coordinates expressed i n Angstrom u n i t s .  The deviations of  the-atoms from t h i s plane are l i s t e d i n the l a s t column of Table IX. The bond lengths and valency angles, c a l c u l a t e d "from the x,y,z 1  coordinates of Table IX, are shown i n Table X.  There are no s i g n i f i c a n t  d i f f e r e n c e s between chemically equivalent bonds, and the average dimensions symmetry, are shown i n Figure 2k.  of the molecule, assuming Cg  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 XI i n terms of the angles  76^  f , L  <*> ; T^M, L  V%  W  M;  811(1  ^N,  V%  °°N  which the molecular axes L, M (see Figure 2k) and the plane normal K make with the c r y s t a l l o g r a p h i c axes.  The a x i s L was"taken through the mid-points  of the C3-C1+ and Cy-Cg bonds, and axis M through atom C^ the C 1 - C 2 bond. ^ LM = 88. 5 ° ,  a  and the centre of  L, M and N are thus not e x a c t l y orthogonal, the angles being ^MW  = 9 0 . 9 ° , and ^-LW  = 89.9°.  of the molecule and the (OOl) plane i s 2 8 . 9 ° .  The angle between the plane  - 7k Table IX. F i n a l Parameters* Atom  X  y  ,o2.  z  B(A )  (X)  Cl  0.7542  0.1556  0.296  5-2  +0.032  c  O.7852  0.1025  0.170  5-2  +0.028  O.6267  0.0864  -0.005  4-3  +0.057  0.5745  0.0427  -0.143  4.1  -0.030  0.4006  0.0407  -0.276  4-9  -0.047  0.2910  0.0802  -0.262  4-5  +0.003  2  c  2a  C  3  c  k  c  5  C  5a  0.3437  0.1242  -0.109  4.1  +0.044  C6  0.2390  0.1659  -0.062  4-5  +0.016  0. 048  0.2052  0.118  4.9  -0.045  C8  0.4779  0.2097  0.253  4.1  -0.013  c  8a  0-5757  O.1683  0.201  4-3  +0.016  c  8b  O.5086  0.1256  O.O37  • 3.6  -0.012  Cl  0.8533  0.1793  0.457  5-7  -0.029  °2  O.9168  O.O805  0.223  •5-7  -0.024  O.658  0.013  5.0  O.364  0.006  5-0  0.l6l  O.O73  5-0  T  C  3  H  3  H  4  H  5  H  6  0.111  O.163  5.0  H  ,0.237  0.236  5.0  0.517  0.240  5.0  H  ?  8  * Subscripts o f theoxygen,and hydrogen atoms i n d i c a t e the-carbon atoms to which they are attached.  - 75  Table X. Atoms  -  Bond Lengths and Valency Angles  Bond Lengths  Atoms  Bond Lengths  1-2  1-533  2-2a  1.473  5a-6  1.403  2a-8b  1.413  6-7  1.368  8b-8a  1.415  7-8  1.452  8a-l  1.482  8-8a  1.369  2a-3  .1-357  8b-5a  1.406  A  5-5a  1.389  3-4  1.474  1-Oi  1.180  4-5  1.369  2-0  1.204  Atoms  Valency Angles  2  ft  > Atoms  Valency Angles  l-2-2a  106.9°  8a-8b-5a  122.7°  2-2a-8b  105-5  8b-5a-6  117.4  2a-8b-8a  115-2  5a-6-  7  118.0  8b-8a-l  105.7  6-7-  8  125.8  8a-l- 2  106.7  7-8-  8a  114.2  2a-3- 4  117.2  8-8a-8b  121.6  3-4-  5  122.9  1-2  -0  2  122.9  4-5-  5a  119-8  2a-2  -0  2  I3O.3  5-5a-8b  117.6  2-1-  0  5a-8b-2a  121.6  8a-l-  0  8b-2a-3  120.0  1  124.7  ±  128.4  F i g u r e 2h.  "Numbering and average  dimensions o f the  molecule.  - 77  Table XI.  co  L  =  -  Molecular O r i e n t a t i o n i n the C r y s t a l  81.0°  21.7°  159-3°  V-VL = 89-8°  108.5°  ^M  109.2° V'N  = 68.4°  = 110.8° =  28.9  0  Standard Deviations The standard d e v i a t i o n s f o r the x and y coordinates, c a l c u l a t e d from the hkO data using Cruickshank's formulae, are C (x).= CX^y)^ r  0.011A f o r oxygen.  0.015°v f o r carbon,  CT(z) was not c a l c u l a t e d from the 0k£ s t r u c t u r e f a c t o r s ,  which are few i n number, but i s c e r t a i n l y somewhat greater.  The standard  d e v i a t i o n of the bond lengths are about 0.02ift f o r C'-C bonds and 0.01c;ft f o r c=0 bonds.  These values may be compared w i t h the root mean square d e v i a t i o n o  of the i n d i v i d u a l bond lengths from the mean distances, which i s only 0.007A. A l l valency angles have a standard d e v i a t i o n of approximately 1 . 3 ° . Intermolecular Distances A l l the intermolecular distances correspond t o normal van der Waals interactions.  The perpendicular distance between molecules r e l a t e d by  t r a n s l a t i o n c i s 3-37ft-  Packing of the molecule and some shorter l a t e r a l  intermolecular contacts are i l l u s t r a t e d i n Figure 25D.  Discussion  The acenaphthenequinone molecule i s probably planar w i t h i n the l i m i t s of experimental error.  The maximum d e v i a t i o n from the mean molecular plane  i s 0.057ft f o r carbon atom Cga* but t h i s and another apparently large deviations from p l a n a r i t y are due t o the f a c t that the z coordinates have been determined somewhat imprecisely. Since the c-axis i s only 3-851ft long, s l i g h t e r r o r s i n z w i l l not however have a s i g n i f i c a n t e f f e c t on the measured bond lengths and valency angles.  -  0  1 Figure 25*  7  8  -  1  2  3  4  5  I  I  I  I  1  A  P r o j e c t i o n of the structure along [ 0 0 l ] the shorter intermolecular contacts.  , showing  -  79  -  I t i s i n t e r e s t i n g to compare the dimensions of the acenaphthenequinone molecule (Figure 24) found i n the present work with those of naphthalene, acenaphthene, 5>6-dichloroacenaphthene, and pyracene (Figure 19).  The  v a r i a t i o n of bond lengths i n the aromatic nucleus i s very s i m i l a r i n a l l four molecules.  Fusion of one (or two) five-membered ring(s) to the system  causes d i s t o r t i o n of the valency angles, which i s shared out by the e n t i r e molecule.  The apex Cg -C8-b-C a  2a  angle of the p e r i - r i n g has a mean value of  1 1 4 ° , which i s j u s t midway between the i n t e r i o r angles, 108° and  120°  r e s p e c t i v e l y , of a regular pentagon and a regular hexagon. In acenaphthenequinone the a l i p h a t i c C^-C^  bond has a length of  1. 53+P-02^, which agrees w e l l with the value reported f o r acenaphthene; the angles i n the p e r i - r i n g are a l s o s i m i l a r . bond i s 1.48ft ( CT = O.Oli+ft).  The length of the 02~^2B.  On the b a s i s of the standard d e v i a t i o n , t h i s  bond s h r i n k i n g i s p o s s i b l y s i g n i f i c a n t and would seem to i n d i c a t e some conjugation between the aromatic nucleus and the carbonyl groups.  Shortening  of bonds i n a s t r a i n e d system -as a r e s u l t of conjugation has been observed previously.  In cis-l,2-dichlorobenzocyclobutene, f o r example, a mean  length of 1.452. has been reported f o r the peri-bonds The C=0 distance of I.19X  (80).  i s quite s i m i l a r to the length: found i n  p-benzoquinone ( 8 l ) and most ketones ( 5 l ) .  The C=0 bonds make e x t e r i o r  angles of 124° and 129° with the p e r i - r i n g ; t h e i r o r i e n t a t i o n s are such that the intramolecular distances 02-• •  and 0 . . . . C 2 2  length (2.41ft), and the O 1 . . . . O 2 distance i s 2. 86ft.  a  have the same  - 80  III.  -  cis-1,2-ACENAPHTHENEDIOL A.  Introduction  For cis-1,2-acenaphthenediol molecular models show that the oxygen-oxygen distance i s l e s s than the normal van der Waals separation.  There i s some  evidence that an i n t e r n a l hydrogen "bond e x i s t s between the e c l i p s e d OH  groups.  Study of the i n f r a r e d spectrum of cis-1,2-acenaphthenediol i n d i l u t e carbon t e t r a c h l o r i d e s o l u t i o n by Moriconi and co-workers (82) revealed two absorption bands f o r bonded hydroxyl groups: broad shoulder at l) = 35^3 to a weak OH. . . . TT  c m  a w e l l - r e s o l v e d peak at l) = 3584 cm 7 and a  ~ Moriconi et_ a l assigned the higher frequency  i n t e r a c t i o n and the lower frequency to stronger i n t r a -  molecular hydrogen bonding between vie-OH groups.  S i m i l a r l y , Csizmadia and  Hayward(64) examined the i n f r a r e d spectrum of the c r y s t a l l i n e s o l i d and found two OH absorption bands of approximately equal i n t e n s i t y :  the lower frequency  at 3190 cm7"^ i n d i c a t i n g i n t r a m o l e c u l a r hydrogen bonding of considerable strength, i n agreement w i t h the assignment of Moriconi et_ a l , and the higher frequency at 3333 crn"^: being a s c r i b e d , more a p p r o p r i a t e l y i n t h i s case, to intermolecular -  hydrogen bonding. Simple c o n s i d e r a t i o n s of molecular geometry, however, suggest that the hydrogen bond between OH groups on adjacent carbon atoms, i f formed at a l l , can at most be a weak one.  For the five-membered intramolecular chelate r i n g  H  C  C  the angle ft between the 0-H bond and the 0 . . . . 0 l i n e i s 35-40° i f standard values (-^O-C-C — 1 1 2 ° , ^ C-O-H =± 1 0 7 ° , 0 - H ^ 1 . 0 A , 0  0 — 2-7A) are assumed  - 81  -  f o r the "bond distances and valency angles, leading t o a "contour" hydrogen "bond length of at l e a s t 3°^  The formation of a banana-type intramolecular  hydrogen bond between the oxygen atoms would seem t o c o n t r a d i c t the generally accepted view that fi i s not greater than about 1 5 ° ( 8 3 ) .  On the other  hand,,if  the proton were a c t u a l l y close to t h e - i n t e r n u c l e a r 0 . . . . 0 l i n e , a large s t r a i n energy would be expected f o r the excessive deformation of the .bond angle.  These arguments s t r o n g l y suggest,that  C-O-H  c h e l a t i o n i s rather  u n l i k e l y , e s p e c i a l l y i n a c r y s t a l which a f f o r d s ample o p p o r t u n i t i e s f o r intermolecular hydrogen-bond formation.  To t e s t t h i s hypothesis and t o obtain  f u r t h e r s t r u c t u r a l data f o r the acenaphthene nucleus, the c r y s t a l structure of cis-1,2-acenaphthenediol  i  was determined.  - 82 -  B.  Experimental  A sample o f cis-1,2-acenaphthenediol  c o n s i s t e d of c o l o u r l e s s needles  elongated along the b - a x i s , w i t h the (OOl) f a c e - w e l l developed. c r y s t a l s examined were twinned on (100). i n aqueous potassium iodide.  A l l the  The density was measured by f l o t a t i o n  The u n i t - c e l l dimensions and space group were  determined from r o t a t i o n and o s c i l l a t i o n photographs o f a c r y s t a l mounted about the b - a x i s , hot  and hit  Weissenberg f i l m s , and hkO and Okt  precession  •films. c i s - 1 , 2 - A c e n a p h t h e n e d i o l , C12H10O2; M=l86.2; m.p. 218-219-5°C.  C r y s t a l Data,  p=lll°50'+5'.  M o n o c l i n i c , a=12.77+0.02, b=4.8U5+O.003, c=15-74+0.02A, U=90U.O^. X-rays,  D ( w i t h Z=U)=1.368, x  ^=1.5^l8°v, u=8.93cm~7  D =1.35g.cm"? m  Absorption c o e f f i c i e n t f o r Absent s p e c t r a : hOl  F(000)=392.  odd, OkO when k i s odd. Space group i s P 2 ^ c  when £ i s  •  For the c o l l e c t i o n of i n t e n s i t y data a needle c r y s t a l of c r o s s - s e c t i o n O.O9XO.O6 mm. was mounted about the b-axis. hit  The i n t e n s i t i e s o f the h0£ and  r e f l e x i o n s were recorded on Weissenberg photographs, using CuK^ r a d i a t i o n ,  and m u l t i p l e - f i l m s t o c o r r e l a t e strong and weak r e f l e x i o n s . hOt  and hit  The ranges of  i n t e n s i t i e s were about 7^60 t o 1 and 18U00 t o 1 r e s p e c t i v e l y ,  . the estimates being made v i s u a l l y .  Twinning o f the c r y s t a l r e s u l t e d i n the  appearance of,two sets o f r e f l e x i o n s on a Weissenberg f i l m ( d i f f e r e n t c* a x i s ) with o c c a s i o n a l overlap.  Fortunately one component o f the twin was appreciably  bigger than the-other ( i n t e n s i t y r a t i o 8 to 3)* so that the spots from the two components could be d i s t i n g u i s h e d , although often w i t h some d i f f i c u l t y . absorption c o r r e c t i o n s were considered necessary.  No  The s t r u c t u r e amplitudes  were derived by the usual formulae,.the absolute scale being established- l a t e r by c o r r e l a t i o n with the c a l c u l a t e d s t r u c t u r e f a c t o r s . r e f l e x i o n s and 2^6 hit  I 3 8 independent hOt  r e f l e x i o n s were observed, representing 56$ and 1+9$  r e s p e c t i v e l y o f the p o s s i b l e number observable under the experimental conditions..  - 83 -  C  Structure-Analysis  [OlO] P r o j e c t i o n Since the b-axis i s reasonably short  a good view of the molecule  i s expected i n t h i s p r o j e c t i o n . The o r i e n t a t i o n o f the aromatic  nucleus  was deduced f i r s t from the weighted r e c i p r o c a l l a t t i c e and confirmed  later  from examination of the Patterson p r o j e c t i o n along the b-axis (Figure 26). The w e l l - r e s o l v e d intramolecular 0-0 vector peak i n d i c a t e d that the p r o j e c t i o n of the molecular a x i s M.(see Figure 28) must be almost p a r a l l e l to the a-axis. The highest peak on the Patterson map corresponded t o the i n t e r a c t i o n between naphthalene r i n g s r e l a t e d by symmetry and l e d t o the coordinates ZQ=0.276  XQ=0.207,  f o r the molecular o r i g i n , defined as the centre o f the C^-Cg^ bond.  (The f i n a l coordinates of the molecular o r i g i n are XQ=0.2008,  ZQ=0.276I).  The  x and z parameters were then obtained from the p r o j e c t i o n o f a CENCO Petersen molecular model h e l d i n the deduced o r i e n t a t i o n .  Structure amplitudes f o r the  h0£, r e f l e x i o n s were c a l c u l a t e d using the carbon and oxygen s c a t t e r i n g f a c t o r s from Tabellen zur Rontgenstrukturanalyse ,  (50) and an o v e r a l l i s o t r o p i c  o  temperature f a c t o r B=4-5A.  The discrepancy f a c t o r f o r 193 r e f l e x i o n s ,  i n c l u d i n g 55 unobserved r e f l e x i o n s with i n t e n s i t i e s taken a t h a l f the minimum observable l i m i t , was somewhat high (R=0.517)*  However, there were no serious  disagreements between the observed and unobserved s t r u c t u r e amplitudes and t h e i r c a l c u l a t e d values.  I t was p o s s i b l e t o a l l o c a t e signs t o 9^ observed  r e f l e x i o n s f o r a F o u r i e r synthesis, and the r e s u l t i n g map-showed good r e s o l u t i o n of a l l the atoms.  R e c a l c u l a t i o n o f the h0£ s t r u c t u r e f a c t o r s with the x and z  coordinates o f the e l e c t r o n - d e n s i t y maxima lowered R (observed r e f l e x i o n s only) to O.344.  Refinement of the atomic parameters was c a r r i e d out by means of  successive ( F - F ) syntheses, and a f t e r s i x c y c l e s R was 0.148. 0  c  The f i n a l d i f f e r e n c e map had a number of e l e c t r o n density maxima which could be a t t r i b u t e d t o the presence of hydrogen atoms.  Although the e l e c t r o n  F i g u r e 26.  P a t t e r s o n p r o j e c t i o n a l o n g [oio]. Contours are drawn a t a r b i t r a r y A diagram o f two m o l e c u l e s i s superimposed.  intervals.  --8  5  -  density was negative.in the region between oxygen atoms i n the same molecule and p o s i t i v e i n the proximity o f the intermolecular 0....G l i n e s , t h i s should not be taken as d e f i n i t e evidence against i n t e r n a l hydrogen bonding since hydrogen atoms i n 0-H....0 bonds are d i f f i c u l t t o l o c a t e by X-ray methods. Since the l o c a t i o n s o f the hydroxyl hydrogens were uncertain, p o s i t i o n a l parameters were deduced only f o r the eight hydrogen atoms attached t o the carbon skeleton.  When these hydrogen atoms were included i n the structure  f a c t o r c a l c u l a t i o n , R was lowered t o 0.131. hO-6  The measured and c a l c u l a t e d  structure f a c t o r s are l i s t e d i n Table A-6,.and the f i n a l e l e c t r o n -  density p r o j e c t i o n on (010) , i s shown i n Figure 27y Parameters and F i n a l Refinement As good r e s o l u t i o n of the i n d i v i d u a l atoms could not be expected i n the [lOO] data.  and [OOI] p r o j e c t i o n s , the y coordinates were deduced from the h i t Approximate y parameters r e f e r r e d t o the molecular o r i g i n were  derived from a molecular model, and the y-coordinate o f the molecular o r i g i n was  then v a r i e d u n t i l reasonable•agreement was obtained between the  c a l c u l a t e d and observed structure f a c t o r s f o r a few low-order h i t r e f l e x i o n s . Structure f a c t o r s were c a l c u l a t e d f o r a l l the h i t r e f l e x i o n s , using the y coordinates refinement.  thus determined and the x,z and B parameters from the h O t R was 0.2^2.  For f u r t h e r refinement i t would be advantageous to use the complete three-dimensional data.  However, indexing of the h2t  and h3£  l a y e r s was  d i f f i c u l t as a r e s u l t o f the twinning, and i n any case the proportion o f observable r e f l e x i o n s on these upper l e v e l s became i n c r e a s i n g l y smaller. Since the observed h0£-  and hl-E, r e f l e x i o n s c o n s t i t u t e d a large part o f  the observable three-dimensional data, refinement was completed by computing cosine and sine d i f f e r e n c e generalised p r o j e c t i o n s , using the hl£ data and  \  - 87 -  r e f i n i n g a l l the x,y,z and B parameters simultaneously. ' A f t e r s i x c y c l e s R was 0.173 f o r "the observed h i t  reflexions.  The i n c l u s i o n of the  c o n t r i b u t i o n s from the eight hydrogen atoms p r e v i o u s l y considered l e d t o a s i g n i f i c a n t improvement i n the agreement of the observed and c a l c u l a t e d structure amplitudes, and R was lowered t o 0.155-  Measured and  c a l c u l a t e d h i t , structure f a c t o r s are l i s t e d i n Table A-7Molecular Dimensions and O r i e n t a t i o n The f i n a l p o s i t i o n a l and temperature parameters are l i s t e d i n Table X I I , where the atomic coordinates, are expressed as f r a c t i o n s o f the u n i t - c e l l edges, and x,z and B are the mean of h o t  and h i t  values.  The equation o f  the mean plane f o r the carbon atoms i s o.7039X'+o.7i07Y+o.oi52Z'-2.5902=0 ,  where X',Y and Z' are coordinates expressed i n % and r e f e r r e d t o orthogonal axes a, b and c'.  The deviations of the atoms from t h i s plane a r e . l i s t e d i n  the l a s t column of Table X I I . The dimensions o f the molecule, c a l c u l a t e d from the atomic coordinates of Table X I I , are given i n Table X I I I .  Since -differences between chemically  equivalent bonds are o f doubtful s i g n i f i c a n c e , mean values f o r the bond distances and valency angles were obtained by assuming symmetry C  s  f o r the  molecule (Figure 2 8 ) .  ,  The o r i e n t a t i o n o f the molecule i n the u n i t c e l l i s given i n Table XIV i n terms o f the angles  -/^  W . L  7^  f  M>  <*>. ^  cO  M  N  which the molecular a x i s L, M (see Figure 28), and the plane normal N make w i t h the orthogonal system a, b and c . The a x i s L was taken through the 1  centres o f the C^-C^, and C^-Cg bonds, and a x i s M through atom C^ and the mid-point of the C]_-C2 bond.  L, M and N are thus not e x a c t l y  perpendicular to one another, the angles being ^-LM=90.4 , 0  ^ LN=90.0 . G  a  ^-MN=89-8 , and Q  - 88 -  Table X I I . Atom  F i n a l Parameters*  y  z  B(f)  0.3922  0.101+  0.3255  l+.l  +0.021+  0.3366  0.110  0.2161+  1+.6  -0.029  0.21+81+  0.320  O.193I  ^•5  -0.008  0.1718  0.1+37  0.1113  5-3  +0.025  O.O9U8  0.6kQ  0.1173  1+.8  +0.036  O.O887  0.737  O.I9I+7  k.k  -0.011+  0.l6l9  0.61+0  O.2789  l+.l;  -0.018  O.1687  0.720  O.3705  •k.k  -0.038  0.21+90  0.619  0.1+1+22  5-^  +0.057  C8  0.3291  0.391  0-1+393  5-5  +0.002  C8a  0.3228  0.309  0.3522  l+.l  +0.003  8b  0.2396  0.1+23  0.2733  l+.l  -0.01+1+  Ol  0.5109  0.167  0.3596  1+.6  +1-175  °2  0.1+182  0.170  0.17I+2  k.k  +I.075  %  O.386  -0.100  0-351  6.0  H  0.305  -0.083  0.191  6.0  3  O.179  0.329  0.053  6.0  ?1+  ,0.01+0  0.750  0.055  6.0  0.027  0.889  0.202  6.0  0.110  •0.871+  0-377  6.0  0.721  O.505  6.0  0.289  0.1+93  6.0  l  C  c  2  c  2a  C  3  c  k  c  5  C  5a ,  C6 c  c  H  H  7  2  5  H6 H  X  ?  H8  0.399  * Subscripts o f the oxygen and hydrogen atoms i n d i c a t e the carbon atoms t o which they are bonded.  - 89 -  Table X I I I .  Bond Lengths, Valency Angles and Some Intramolecular Approach Distances  Atoms  Bond Lengths  Bond Lengths  Atoms  1-2  1.596ft  2-2a  1.1+61  5a-6  1.1+61+  2a-8b  1.1+00  6-7  1.306  8b-8a  1.1+13  7-8  1.519  8a-l  1-^93  ,8-8a  1.1+01  2a-3  l.klk  8b-5a  1.1+71  5-5a  .1.389ft  3-h  1.1+1+6  1-0!  1.1+58  h-<?  1.322  2-0  1.1+1+0  Atoms  Valency Angles  2  Atoms  —  Valency Angles  l-2-2a  106.0°  8a-8b-5a  122.1°  2-2a-8b  IO9.6  8b-5a-6  117.0  2a-8b-8a  111.5  5a-6 -7  119. k  8b-8a-l  110.1  6-7 - 8  12k. 6  8 a - l -2  102.6  7-8 - 8 a  116.2  2a-3 -k  118.8  8-8a-8b  120.0  3-k -5  121+.5  1-2 - 0  2  112.7  1+-5 - 5 a  121.3  2a-2 - 0  2  111.2  5-5a-8b  111+. 5  2-1 -Ox  .112.5  •8a-l - 0 !  lll+.O  5a-8b-2a  126.2  8b-2a-3  111+.7  Selected Intramolecular Approach Distances Distances  Atoms  Distances  Oi-C-2 1 -o  2.7lft  8a-0i  2.l+6ft  2. 54  2a-0  2.1+1  2 -  2.53  2  0  l  Atoms 2  - 90 -  tM  F i g u r e 28.  Numbering and average dimensions o f the m o l e c u l  - 91 -  Table XIV . Molecular O r i e n t a t i o n - i n the C r y s t a l 9^ f  L  L  co  L  =  90-9°  7^  =  87-8°  ^  = 177.6  M  «o  0  M  M  =  hh.5°  = 13^.5° = 91.8  = ^5-3° ^  0  = UU.8°  N  cO  . N  = 89. l  e  Standard Deviations The standard d e v i a t i o n s of the mean x and z coordinates are C7"(x) = 0~(z) =0.010A f o r carbon, O.OO9A f o r oxygen.  cT'(y) i s c e r t a i n l y somewhat greater  but since most o f the bonds l i e c l o s e t o the (010) plane and are therefore not very dependent on y, the standard deviations o f the measured bond distances are about O.Ol^ft, and o f the valency angles about 0 . 9 ° . D.  Discussion  The packing of the molecules i s i l l u s t r a t e d i n Figure 29 w i t h the main short approach distances i n d i c a t e d .  I t i s seen that molecules r e l a t e d by a  screw a x i s a r e • l i n k e d together by intermolecular hydrogen bonds t o form i n f i n i t e zigzag chains extending i n the d i r e c t i o n o f b.  The 6 - H . . . . 0 distances  of 2.72 and 2.7OA are s i m i l a r to those found i n alcohols (84).  A perspective  diagram, Figure 30, i l l u s t r a t e s the mode o f hydorgen bonding i n the c r y s t a l . I t i s evident from the zigzag chain molecular packing that there i s no intramolecular hydrogen bonding between the vie-OH groups.  The interatomic  0-J.....02 distance i s short (2.71%) only as a consequence o f the geometry.  molecular  A p l a u s i b l e explanation o f the two i n f r a r e d absorption peaks may  be the d i f f e r e n t angles and environments of the intermolecular hydrogen bonds (Figure 30). The carbon skeleton of the cis-1,2-acenaphthenediol'molecule planar.  i s probably  Some o f the apparently s i g n i f i c a n t deviations from p l a n a r i t y  (maximum value 0.057ft f o r atom C7) are due t o the f a c t that the y coordinates  - 92  0  1  2  -  3  4  5  A  1 I I I I I  Figure 29-  P r o j e c t i o n o f the s t r u c t u r e a l o n g the hydrogen "bonds and the s h o r t e r contacts.  (|oio]  , ohowing intermolecular  F i g u r e 30.  Perspective  diagram showing the hydrogen b o n d i n g .  - 9^  have been determined l e s s p r e c i s e l y .  -  Since the b-axis i s short, t h i s should  not s i g n i f i c a n t l y a f f e c t the measured bond lengths and valency angles. Comparison of the molecular dimensions of cis-1,2-acenaphthenediol with the data f o r other acenaphthene d e r i v a t i v e s (Figure 19) shows that the valency angles are very s i m i l a r .  The a l i p h a t i c C]_-C2 bond, however, i s  s i g n i f i c a n t l y lengthened (bond length 1.59g+0.Ol^A, p r o j e c t i o n on (010) 1.59^°i) probably due to the combined e f f e c t of r i n g s t r a i n and s t e r i c r e p u l s i o n of the non-bonded oxygen atoms. unexpected.  The short peri-bond length of 1.U8+0.01Q°I i s  I t may be pointed out, however, that a s i m i l a r  bond-shortening  e f f e c t has been observed i n cis-1,2-dichiorobenzocyclobutene, which has an average peri-bond distance of 1.1+5+0.012. (80). 1.1+5+0.OLQA  r i n g s the  The C-0 bond has a length of  which i s t y p i c a l of a l i p h a t i c a l c o h o l s ( 5 l ) -  C3-CI1  and  CI4.-C5  In the naphthalene  bonds are r e s p e c t i v e l y the longest and the shortest,  i n agreement w i t h the bond-length v a r i a t i o n s observed i n a l l acenaphthene d e r i v a t i v e s so f a r examined.  - 95 -  IV.  cis-1,2-ACENAPHTHENEDIOL DINITRATE A.  Introduction  Recently i t has been demonstrated that o-dinitrosobenzene ( X V I I l ) has the benzofurazan-N-oxide (XIX) structure i n the s o l i d state (85).  A  tautomeric form (XX) i n which the n i t r o x y groups are d i r e c t l y l i n k e d together has also been suggested f o r n i t r o g l y c e r i n e t o e x p l a i n the mechanism o f i t s polarographic  reduction ( 8 6 ) . Furthermore, much evidence  has been found f o r the s t e r i c i n t e r a c t i o n of contiguous n i t r o x y groups i n c y c l i c and a c y c l i c p o l y n i t r a t e s (6k). speculate that r i n g formation  I t therefore seems reasonable to  i s sometimes favoured i n organic  structures  containing -NO, -NO2 and -ONO2 groups on s u i t a b l e oriented carbon atoms.  R e l a t i v e l y l i t t l e i s known about the c r y s t a l and molecular structures of n i t r a t e esters.  The only published X-ray work i s that on p e n t a e r y t h r i t o l  t e t r a n i t r a t e (87,88) i n which no bonding between n i t r o x y groups was found. However, the compound i s rather unique among n i t r a t e e s t e r s , and can hardly be regarded as a t y p i c a l example.  -  (xxi)  96  -  (XXII)  (XXIII)  (xxrv)  cis-1,2-Acenaphthenediol d i n i t r a t e ( X X l ) , f i r s t synthesised  by  Csizmadia and Hayward(6U), provides a rigorous t e s t of the p o s s i b i l i t y of intramolecular bonding between n i t r o x y groups.  In structures (XXIl) and  ( X X I I l ) . t h e steriochemical configurations can be e a s i l y assumed by r o t a t i o n about s i n g l e bonds, and the non-planar eight- and seven-membered r i n g s thus formed are completely free of s t r a i n .  A s t r a i n e d structure (XXIV) would be  analogous to one proposed f o r d i n i t r o g e n t e t r o x i d e (89).  To decide between  these s t r u c t u r e s , an X-ray i n v e s t i g a t i o n of the c r y s t a l l i n e m a t e r i a l  was  .carried out. B.  Experimental  C r y s t a l s of cis-1,2-acenaphthenediol d i n i t r a t e are c o l o u r l e s s needles elongated along the b-axis with the (OOl) face w e l l developed. was measured by f l o t a t i o n i n aqueous potassium iodide.  The  density  The c e l l constants  and space group were determined from r o t a t i o n and o s c i l l a t i o n photographs of a c r y s t a l r o t a t i n g about the b - a x i s , h0€ 0k&  and hkO precession f i l m s .  and hl£.  Weissenberg f i l m s , and  C r y s t a l Data,  cis-1,2-Acenaphthenediol  m.p.l28.0-130.5°C p>=122°12'+5'.  10  2  2  ; M=276.20;  M o n o c l i n i c , a=17-10+0.02, b=4.242+0.005, c=19.l8+0.02%,  D ( w i t h Z=4)=1.557> D =l-53 gm.cmT  U=1177.3^ . 3  c o e f f i c i e n t s f o r X-rays, F(000)=568.  d i n i t r a t e , . C Hg(CH0N0 )  x  "X =1. 5U18A, |u=12.70 cm!"  Absent spectra:  hOt  3  m  when tis  1  Absorption  ; ?v. =0. 7IO7A, /u=1.57  odd, OkO when k i s odd.  cmT  1  Space  group i s P 2 / - c | . 1  c  h  For the c o l l e c t i o n of i n t e n s i t y data a needle c r y s t a l of c r o s s - s e c t i o n 0.07x0.11 mm.  was mounted about the b-axis.  photographs of the hOt  and hit  E q u i - i n c l i n a t i o n Weissenberg  l a y e r s were taken w i t h CuK^  radiation.  To  extend the i n t e n s i t y range the data f o r each zone were c o l l e c t e d on two sets of four f i l m s r e l a t e d by time exposures.  The i n t e n s i t i e s of the various  r e f l e x i o n s were estimated v i s u a l l y and corrected as usual f o r Lorentz and polarization factors. 246 hOt  Wo absorption c o r r e c t i o n s were considered  necessary.  (excluding the 100 and 102 r e f l e x i o n s which were cut o f f by the beam  trap) and 443 bit - independent r e f l e x i o n s were found to be of measurable 1  magnitude; these represent 75$ and 76$, r e s p e c t i v e l y , , o f the t o t a l number t h e o r e t i c a l l y observable. C  Structure A n a l y s i s  The f i r s t attempts to derive an approximate structure made use of the set of h0£  data.  A Patterson synthesis projected down the short b-axis  (Figure 3l),was computed.  The highest peaks on t h i s map were r e a d i l y  i d e n t i f i e d as m u l t i p l e vector peaks between naphthalene r i n g s r e l a t e d by symmetry, l e a d i n g to a p o s i t i o n of x =0.258, z =0.196 or x =0.242,. z =0.304 Q  Q  o  f o r the molecular o r i g i n , defined as the centre of the 0^ -CQ^ bond. a  o  The  o r i e n t a t i o n of the aromatic nucleus i n d i c a t e d by the Patterson map was i n agreement w i t h that deduced from an examination of the weighted r e c i p r o c a l lattice.  The extended peak marked w i t h a cross (about 3.4°v from the o r i g i n )  - 99 c o u l d be r e a s o n a b l y groups.  ascribed to<interactions  On t h i s b a s i s  structure  (XXIl),  between  w i t h i t s many c o n f o r m a t i o n s  r o t a t i o n s a b o u t C-0 a n d 0 - N s i n g l e b o n d s , , w a s the p r e c i s e [OlO]  location of  non-bonded n i t r o x y involving  t a k e n as a s t a r t i n g p o i n t  for  atoms b y F o u r i e r m e t h o d s .  Projection The s h o r t n e s s  projection.  o f t h e b - a x i s p r o m i s e d a good v i e w o f the  The x a n d z c o o r d i n a t e s  structure  in  o f t h e c a r b o n atoms were o b t a i n e d  t h e p r o j e c t i o n o f a CENCO P e t e r s e n m o l e c u l a r m o d e l ' ( F i g u r e 36)  this  from  held in  the  deduced o r i e n t a t i o n , the m o l e c u l a r o r i g i n b e i n g a r b i t r a r i l y p l a c e d a t  x =0.258,  z =0.196.  oxygen  V a r i o u s s e t s o f x and z parameters were p o s t u l a t e d f o r the  Q  and n i t r o g e n atoms,  a l l o w i n g f o r the f a c t  that  t h e two n i t r o x y g r o u p s must be  .O  M  a p p r o x i m a t e l y 3-^A a p a r t , the molecule  i n the  and o r i e n t e d i n such a w a y , t h a t  [ O l O ] d i r e c t i o n was n o t e x c e s s i v e .  s t r u c t u r e s w e r e t e s t e d b y c a l c u l a t i n g hO-t  structure  them w i t h t h e o b s e r v e d v a l u e s .  scattering  the  o  International Tables,  B=U.5?L was u s e d . 2  The a t o m i c  Vol.Ill,  Finally  factors  a s t r u c t u r e w h i c h gave r e a s o n a b l e  o n l y ) was 0 . 6 l 8 , a r a t h e r h i g h v a l u e ,  atoms c o u l d be d e n s i t y map.  t o 155  observed  the c o r r e c t  the u n i t c e l l .  reflexions  O.UO.  but  with  factor  the  R  i t was  possible  for a Fourier synthesis.  A l l the  structure  This suggested that  i n the  electron-  s h i f t e d to the  R e c a l c u l a t i o n o f t h e hOE.  the molecule  had  a n d o r i e n t a t i o n , b u t was w r o n g l y p l a c e d  New x a n d z c o o r d i n a t e s  the molecular o r i g i n  agreement  factor  f u r t h e r r e f i n e m e n t p r o v e d l e s s e n c o u r a g i n g and R c o u l d  n o t be improved b e l o w about essentially  were t a k e n from  The d i s c r e p a n c y  i d e n t i f i e d , and t h e r e were no s p u r i o u s d e t a i l s However,  trial  and an o v e r a l l i s o t r o p i c t e m p e r a t u r e  (observed  signs  of  a m p l i t u d e s and comparing  was c h o s e n f o r r e f i n e m e n t .  to allocate  the'thickness  The d i f f e r e n t  low-order reflexions reflexions  M  structure  in  f o r a l l t h e a t o m s w e r e now d e d u c e d w i t h  a l t e r n a t i v e p o s i t i o n x =0.2k2, Q  factors  gave an R v a l u e  z =0.304. o  o f O.523 a n d i n  Figure 32.  Electron-density p r o j e c t i o n along [oio] are drawn at i n t e r v a l s of 1 e.A  -2  .  Contour l i n e s  s t a r t i n g with 1 e . i  .  - 101  -  f i v e c y c l e s of refinement by- d i f f e r e n c e synthesis, t h i s was reduced to 0 . l 6 0 . The f i n a l e l e c t r o n - d e n s i t y p r o j e c t i o n on ( 0 1 0 ) , i s shown i n Figure 32y Parameters, and F i n a l Refinement To"determine the y coordinates of the atoms,, a t t e n t i o n was turned,to the hit  data.  Approximate y, parameters r e f e r r e d to the molecular o r i g i n were  derived from a molecular model (Figure 36), and the y, coordinate of the molecular o r i g i n was chosen as that which gave the best agreement between the c a l c u l a t e d and observed structure-amplitudes f o r a few low order data. Structure f a c t o r s were now c a l c u l a t e d f o r a l l hlE* r e f l e x i o n s , , using the y coordinates thus determined and the x, z ,and B parameters from the h O t refinement.  The i n i t i a l value of R f o r the observed r e f l e x i o n s was 0.3^7-  Refinement of a l l the p o s i t i o n a l and temperature parameters proceeded by computing cosine and sine d i f f e r e n c e generalized p r o j e c t i o n s , and a f t e r f i v e c y c l e s R dropped t o 0.169-  The observed values f o r the very intense  211,  312, 212, 313,.and 213 r e f l e x i o n s were c o n s i d e r a b l y • l a r g e r than F , probably due to e r r o r s , i n i n t e n s i t y estimation, and these planes were omitted i n evaluating R. Structure f a c t o r s were again c a l c u l a t e d f o r the h O t r e f l e x i o n s with the parameters determined from the hl£. refinement; the R value was reduced s l i g h t l y from 0.160 to 0.1^5.  Measured and c a l c u l a t e d h O t  1  and h i t  structure  f a c t o r s a r e ' l i s t e d i n Tables A-8 and A-9 r e s p e c t i v e l y . Coordinates, Molecular Dimensions, and Orientations The f i n a l p o s i t i o n a l and temperature parameters are given i n Table XV, where the atomic coordinates are expressed as f r a c t i o n s of the u n i t - c e l l - e d g e s . The dimensions of the molecule, c a l c u l a t e d from these coordinates, are shown i n Table XVI. symmetry C  s  Mean bond lengths and valency angles were obtained by assuming  f o r the cis-1,2-acenaphthenediol p o r t i o n of the molecule (Figure 33)*  - 102 -  Table-XV. Atom  X  y  F i n a l Parameters ,' z  .02.  B(A )  A (A)  Cl  0.323^  0.1+55  O.2289  U-3  -0.003  C  2  O.2187  O.387  O.I56I+  k>3  +0.038  C  2a  O.17I+6  0.193  O.19I+I  1+.1+  -0.031+  C  3  O.0871  0.080  0.1617  5.0  <+0.008  O.0681  -0.08l  0.2181  5.8  -0.002  0.1336  -0.116  0.3015  5-6  -0.023  O.2230  0.021+  O.33I+I  5-2  +0.020  C6  O.29I+3  0.008  O.I+I72  7  0.3780  0.11+0  o.UUoo  C8  0.3982  O.306  0.3852  +0.035  0.3268  0.298  0.3019  -0.053  0.21+09  0.171  0:2786  1+.8  -0.006  0.3882  0.273  0.2168  1+.6  +0.007  N  0.1+070  0.398  0.1592  h.9  -0.030  02  0.3660  O.63I  0.1230  6.1  •+0.010  0.1+675  0.262  0.1605  5-7  +0.011  0.2216  0.191  0.091+7  5.0  -0.015  0.1530  0.257  0.0120  5-2  +0.058  O.0915  0.1+21+  0.0009  7.2  -0.025  O.1636  0.082  -0.0333  6.8  -0.021  c  h  c  c  C  5  8a  C8b  °1  °3  ° i  N" °2 °3  +0.019  h.9  -+0.005  - 103 Table XVI.  Bond :Lengths, Valency, Angles and Some :Intramolecular Approach Distances  . /Atoms  Bond Lengths  Bond Lengths  Atoms  Bond Lengths  • Atoms  1-2  1.603ft  k-5  1.388ft  2-2a  1-533  5-5a  I.436  2a-8b  •1.401  5a-6  1.401  N-0  8b-8a  1-396  6-7  1-373  N-O3  1-173  8a-l  I.523  7-8  1.451  2-0j_  1.468  2a-3  1-365  8-8a  1.402  1.455  8b-5a  1-0!  0i-N  ,1.408  t  2  1  0 -N  1.401  N'-O . 2  t  Atoms  Valency Angles  l-2-2a  106.9°  1.196  1.410  1  1  N -O3  Atoms  1.U67&  Valency'Angles  8b-2a-3  121.2°  2-2a-8b  106.5  8a-8b-5a  123.2  2a-8b-8a  114.4  8b-5a-6  118.4  Atoms 1  t  f  >  i  1  0 -N - 0 2  ,116.5°  2  1  Oi-N -O3 t  ,1.227  Valency- Angles  •Oi-N - 0 t  I.189  109.2 133-1  3  -7  118.1  0 -l  101.3  6-7 -8  125.2  Oi-1 - 8 a  104.7  -h  116.8  7-8 - 8 a  114-5  1 -Oi-N  115-7  3-k -5  123.O  8-8a-8b  120.2  Oi-N - 0  4-5 - 5 a  118.4  0i-2  107.4  Oi-N -O3  •111.5  5-5a-8b  117.8  0[-2 - 2 a  108.2  0 -N -O3  131.0  5a-8b-2a  122.6  2  115-h  8b-8a-l  110.9  8 a - l -2 2a-3  ,5a-6  -1  -Oi-N  1  ±  2  110.9  -2  2  117-3  continued on page 108  - 104 -  F i g u r e 33.  Numbering and average  dimensions o f the  molecule.  - 105  -  37)•  and by, averaging corresponding values f o r the two n i t r o x y groups (Figure The equations of the mean planes are Carbon atoms  :  Unprimed 0N0 Primed 0N0  2  2  -O.U699X' + O.8658Y + 0.1720Z'  - O/813I+ = 0,  :  0.3583X' + 0.5907Y' + O.7229Z' - U.8051 = 0,  :  0.6638X' + O . 7 U 5 U Y - 0 . 0 6 l 6 Z '  - 2-3966 = 0,  where X', Y, Z' are coordinates expressed i n % and r e f e r r e d to orthogonal axes a, b and c . T  The deviations of the atoms from these planes are l i s t e d  i n the l a s t column of Table XV. (Figure 35) +71-2°  The unprimed and primed 0N0  groups  2  are i n c l i n e d to the plane of carbon atoms at angles of + 6 2 . 1 ° and  respectively.  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 may be i n d i c a t e d by g i v i n g the angles 9^>  V'and ^  (Table' X V I l ) , which the molecular axes L,M  (Figure 33) and the carbon-plane normal N make with the a and b c r y s t a l axes, and t h e i r perpendicular c'.  The axes L'was taken through the mid-points of  bond C-^-C^ and Cy-Cg, and axis M through C^  a  and the centre of the C]_-C bond. 2  L, M, and N are thus not mutually orthogonal, the angles being -LM=90.6°, /  ^LN=90.2°, and ^MN=90.0°.  - 106 -  Table XVII. 128.9° 101.4° co L  Molecular O r i e n t a t i o n i n the C r y s t a l 51-5°  T^N - 118.0°  62.5  y- -  30.0°  <*> =  8o.i°  ^M = ^M  138.7°  =  0  H  129.1°  M  N  Standard Deviations The standard d e v i a t i o n s f o r the x and z coordinates, c a l c u l a t e d using Cruickshank's formulae, are cT(x),=  (7(Z),=  0.009ft f o r N, and 0.010ft f o r 02 and O3. greater.  0.010ft f o r C, 0.00&A f o r ©i,  tT(y) ,is expected t o be somewhat  The standard d e v i a t i o n s of the measured bond distances are about  0.0l4ft f o r C-C and N=0 bonds, 0.013ft f o r C-0 and 0.012 f o r 0-N .bonds. • A l l valency angles have a standard d e v i a t i o n , o f approximately 0.9°Intermolecular Distances A l l the intermolecular distances correspond t o normal van der Waals interactions.  Packing of the molecules i n the u n i t c e l l and some shorter  l a t e r a l intermolecular contacts are shown i n Figure 3^> D.  Discussion  The y coordinates have not been determined t o a high degree of accuracy so that t h e apparent d e v i a t i o n s from the mean planes of the•acenaphthene nucleus (maximum value 0.053 f o r 0 3 ) and of the n i t r o x y groups (maximum a  value O.O58 f o r N') are probably not s i g n i f i c a n t .  Since the b-axis i s short  small e r r o r s i n the y parameters should not s e r i o u s l y a f f e c t the measured bond lengths and valency angles. The molecular s t r u c t u r e of cis-1,2-acenaphthenediol i n perspective i n Figure 35-  d i n i t r a t e i s shown  The n i t r o x y groups are w e l l separated from eac t o  other, the two shortest contacts between them being O1-O1 =2-57A and 0]_-02 =2.9lft-  The planes of the n i t r o x y groups are i n c l i n e d i n the same  I— 1  o  Figure 3^,  Projection of the str.uc.ture along ,[oio]  - 108 -  Figure 35.  Perspective diagram of the molecular s t r u c t u r e .  Selected Intramolecular Approach Distances Atoms  Distances  Atoms  0  0  0J^-2a  0 _-8a ]  Distances  Atoms  2-57A  °1"  2  2-53A  1-N  2.^3  2  -W  2A3  i-o  2.1+8  2 -0>  2.60  2-37  Distances ,  0  2.1+3A 2  °i-°2  2.61 2.91  Fig. 36.  CENCO P&tersen arbitrary  molecular  directions  to  model  show  "its  photographed general  in  Snape.  two  - 110 -  ( b )  0  3  (c)  F i p u i - 37. Dimensions of the n i t r o x y group i n (a) c i s - 1 , 2 a c e n a p h t h e n e d i o l d i n i t r a t e , (b) p e n t a e r y t h r i t o l t e t r a n i t r a t e , and ( c ) n i t r i c a c i d .  - Ill -  sense w i t h respect to the plane of carbon atoms.  Figure 36 shows a CENCO  molecular model viewed i n two a r b i t r a r y d i r e c t i o n s . The dimensions of the acenaphthene nucleus of cis-1,'2-acenaphthenediol d i n i t r a t e are very s i m i l a r to those found i n other acenaphthene d e r i v a t i v e s . The lengths of bondB C 2 - C , C^-Cip. C^-Ctj • vary i n the order short-long-short, a  3  as do'the corresponding distances i n naphthalene. o The a l i p h a t i c C1-C2 (010)  1.57Q°Y),  bond has a length of I.6O3+O.Ol^A ( p r o j e c t i o n on  which agrees w e l l w i t h the value 1. 59g+0.Ol^X found i n  cis-1,2-acenaphthenediol. compared to the values l.^kk  The s i g n i f i c a n t lengthening of t h i s bond, as o o and 1-53-A found i n acenaphthene and  acenaphthene-  quinone r e s p e c t i v e l y , may be ascribed to s t e r i c r e p u l s i o n of the non-bonded 1  oxygen atoms 0-j_ and 0-]_. The bond lengths and valency angles of the n i t r o x y group found i n the present study are compared w i t h those of p e n t a e r y t h r i t o l t e t r a n i t r a t e (88) and n i t r i c a c i d (90) i n Figure 37-  There i s e x c e l l e n t agreement among  corresponding values, and i n both n i t r a t e s ^-O^NC^ i s s i g n i f i c a n t l y l a r g e r than ^0iN03 as a consequence of s t e r i c i n t e r f e r e n c e between atoms C and C^The appreciably l a r g e r temperature f a c t o r f o r atoms Cgand O3 than f o r N and Oi suggest t o r s i o n a l o s c i l l a t i o n of the n i t r o group .about the 0-N bond, i n a manner s i m i l a r to the motion observed i n U - n i t r o a n i l i n e (91)•  It'is  a l s o probable that the n i t r o x y group, as a whole, executes t o r s i o n a l o s c i l l a t i o n about the C-0 bond.  These l i b r a t i o n a l movements are expected to  cause an apparent diminution of the measured Ef=0 distance (92), and i t i s suggestive that the present measured value of 1.19^+0.00^2. i s s l i g h t l y smaller than the corresponding l e n g t h ( l . 2 1 ^ + 0 . 0 l 2 ) ,in p e n t a e r y t h r i t o l t e t r a n i t r a t e f o r which thermal motion i s smaller.  Since a n i s o t r o p i c thermal f a c t o r s have not  been determined i n the present a n a l y s i s , no attempt has been made to c o r r e c t the bond distances f o r r o t a t i o n a l o s c i l l a t i o n e r r o r s .  - 112 V.  GENERAL CONCLUSIONS  From a c r i t i c a l examination of the s t r u c t u r a l data o f acenaphthene and i t s d e r i v a t i v e s , the f o l l o w i n g conclusions may.be drawn: (a) .The carbon skeleton i s planar. (b)  The s t r a i n , i n the p e r i - r i n g i s a l l e v i a t e d p r i n c i p a l l y by the  d i s t o r t i o n of bond.angles,. both i n the; p e r i - r i n g and i n the naphthalene  rings.  In c i s - 1 , 2 - d i s u b s t i t u t e d .acenaphthenes the C\-C2 bond i s  (c)  s i g n i f i c a n t l y longer than the corresponding distance i n acenaphthene, probably as a consequence of s t e r i c r e p u l s i o n between the non-bonded substituents. (d)  In acenaphthenequinone the short peri-bonds C-j_-Cg and..C2"C2 a  a  suggest some degree of conjugation between.the carbonyl groups and the aromatic nucleus.  The s i g n i f i c a n t s h r i n k i n g of these bonds i n c l s - 1 , 2 -  acenaphthenediol i s l e s s w e l l understood. (e)  The average dimensions of the naphthalene moiety of the acenaphthene  system,. derived from the data f o r acenaphthene,. 5>6-dichloroacenaphthene- and the three compounds studied i n the present work, are shown i n F i g u r e - 3 8 ; :  t h e i r d e v i a t i o n s from the corresponding v a l u e s . i n naphthalene•are a l s o indicated.  The standard.deviations of the mean bond distances-are about :  .0 ^o O.OOoA f o r bond C^-Cg^ and 0.006A f o r other bonds,, and of the valency, angles  about 0.4°.  I t i s seen that formation ..of the p e r i - r i n g r e s u l t s p r i m a r i l y , i n  compression of the C -Cgk bond, s t r e t c h i n g of the 0 2 3 - 0 ^ bond,.. and widening 2a  of the 02 -Cg^-C^ angle. a  a  In general the bond distances are a f f e c t e d t o a  l e s s e r extent than.are the valency angles.  - 113  F i g u r e 38.  -  Average dimensions o f the naphthalene m o i e t y o f the acenaphthene system. D e v i a t i o n s from the c o r r e s p o n d i n g v a l u e s i n naphthalene are shovm i n "brackets; f o r t h e b o n d d i s t a n c e s the d e v i a t i o n s are g i v e n i n 10 A. Q  APPENDIX I  STRUCTURE FACTOR TABLES  - 115 Table A - l .  h  k  £  Zc(2)  0  h  Biphenylene  k  h h  2 4 6 8 10 12 3 1 2 3 4 5 6 7 8 9 10 11 12 13 6 0 1 2 3 4 5 6 7 8 9 10 0  97.8 9.4 42.9 4.2 14.0 18.9 45.0 116.7 89.1 21.7 24.7 <3.1 3.2 7.0 5.2 11.4 < 3.4 <3.0 8.6 46.8 48.6 2.1 3.1 <2.5 30.7 31.2 <3.3 3.6 <3.6 3.6  +112,1 + 11.2 + 54.7 - 1.7 + 14.8 + 17.2 + 53.8 +134.0 + 95.5 - 26.9 + 20.6 + 1.0 + 3.3 + 1.9 + 3.0 - 15*9 - 1.7 + 1.8 + 4.9 - 53.2 - 48.1 + 6.6 0 - 4.1 + 26.6 - 28.9 - 1.2 - 4.1 + 0.7 - 2.6  +111.0 + 9.7 + 50.6 - 0.3 + 17.2 + 19.9 + 55.5 +134.6 + 96.1 - 22.1 + 20.4 + 1.4 + 4.7 + 3.1 + 4.0 - 16.5 - 0,8 + 2.6 + 6.6 - 49.5 - 47.1 + 8.9 + 1.0 - 3.1 + 29.0 - 30.9 - 0.3 - 4.0 + 1.5 - 2.0  6 11 12 13 9 1 2 3 4 5 6 7 8 9 10 11 12 12 0 1 2 3 4 5 6 7 8 9 10 11 12 15 1 2  5.9 4.0 2.6 2.8 2,1 2.5 2.2 2.8 4.4 8.8 3.1 6.2  0 0 0 0 0 0 0 0 0 0 0 0  + + + + + +  0 1.3 4.0 0 1.3 0.9 1.1 1.8 1.5 0.6 0 1.5  10 2 11 16 2 3 4 5 7 8 10 13 17 4 4  =  4.4 4.1 5.2 10.6 2.1 6.2 3.5 6.3 3.6 3.4 5.3 1.6  /  k  lo  IcCD P (2) c  3n - 6.9 - 4.7 - 7.5 + 4.4 +36.9 -28.9 +25.4 -12.8 0 - 5.3 -15.3 - 0.7 - 5.9 + 2.2 - 0.7 -27.5 0 - 8.4 + 9.2 +13.4 + 7.9 +16.2 - 4.7 + 5.4 - 3.5 - 2.9 - 2.9 - 0.1 - 3.0 - 2.5  10.4 <2.7 5.1 4.9 30.8 34.7 32.8 12.4 <3.3 6.2 15.6 < 3.7 9.7 <3.0 <2.3 30.4 <3.0 11.8 10.9 14.0 8.8 19.4 4.5 6.4 6,9 6.5 3.0 <-1.4 <3.5 3.5 h  5 0 8 10 11 2 1 4 7 8 16 2 2 4 5  hkO  - 7.5 - 5.0 - 7.9 + 1.4 +30.8 -33.0 +28.4 -14.2 + 1.3 - 6.6 -14.2 - 1.9 - 6.0 + 2.0 - 0.8 -30.1 + 0.5 - 9.4 +11.2 +13.7 + 8.9 +17.1 - 3.8 + 5.3 - 3.8 -. 4.8 - 2.6 - 0.5 - 0.6 - 2.3  3 4 5 6 7 8 9 10 11 18 0 1 2 3 4 5 6 7 8 9 21 1 2 3 4 5 6 7 24 0 1 2 3  21.9 5.2 3.7 <3.7 6.2 9.5 <3.0 < 2.4 <1.4 30.2 11.7 14.0 <3.7 5.8 7.1 10.5 < 3.0 <2.6 <2.0 19.8 16.8 5.5 <3.0 <2.8 7.2 <2.0 10.4 2.9 3.7 6.2  + + + .+ + + -  5 4 7 8 5 5 7 8 16 1 6 5 7 10 8 11  6.9 4.6 3.4 6.7 2.1 5.3 2.7 7.0 5.7 6.0 3*8 5.3  15  -19.1 - 6.7 + 2.6 + 3.1 + 4.1 + 4.8 0 - 2.1 + 2.7 -28.3 +11.4 -11.3 + 2.8 - 6.9 - 6.0 -10.0 + 1.1 + 0.5 - 1.8 -13.5 -11.7 - 2.6 + 2.7 - 2.8 - 1.0 - 2.2 + 9.6 - 1.4 - 1.1 - 2.8  -18.4 - 6.1 + 3*7 + 3.0 + 5.4 + 5.7 + 0.8 - 2.2 + 3.2 -29.6 +12.5 -11.4 + 3.3 - 6.0 - 7.1 -10.2 + 1.1 + 0.6 - 2.2 -16.9 -14.0 - 4.0 + 2.6 - 4.5 - 0.9 - 3.3 + 9.5 - 1.6 - 2.7 - 3.1  0 0 0 0 0 0 0 0 0 0 0 0  + 0.8 + 0.1 - 0.5 - 1.6 + 0,6 + 1.7 + 0.8 - 0.8 - 0.6 - 1.3 - 0.9 - 0.3  32 0 0 0 0 0 0 0 0 0 0 0 0  0.3 3.0 1.1 0.7 1.3 1.7 1.4 1.1 2.1 1.4 1.5 1.2  116 -  Table A-2. h  k  -20 0 -18 -16 -14 -12 -10 - 8 - 4 - 2 0 2 4 6 8 10 12 14 16 18 20 -22 1 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4  lo 4.2 16.6 12.2 <4.0 3.6 <3.2 <2.7 27.6 16.7 Not Not Not 16.0 29.8 <2.8 4.5 5.1 11.4 9.7 30.4 6.0 8.9 <4.0 <4.2 10.7 4.4 6.3 <4.3 4.2 <4.0 26.5 22.9 4.8 7.8 20.6 18.6 18.2 21.5 5.6 50.2 109.9 18.2 Not Not Not 61.4 70.2 25.1  lc + + + + + +  4.2 11.4 12.6 0.7 6.0 2.8 2.0 29.6 24.1 obs. obs. obs. + 21,7 - 37.5 + 3.8 + 6.5 + 4.1 8.2 7.7 + 23.1 - 8.1 7.2 + 6.5 - 3.6 - 8.2 + 1.4 - 9.5 + 5.4 + 4.7 + 1.3 - 19.8 - 22.0 - 7.3 + 5.2 - 18.7 + 7.4 + 13.9 +. 14.1 + 8.4 + 50.9 -101.2 +. 26.8 obs. obs. obs. + 60.4 + 72.1 + 34.3  h  Biphenylene  k  5 1 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 -18 2 -17 -16 -15 -14 -13 -12 -11 -10 - 9 -8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 11 12  lc 26.0 16.9 2.6 <2.8 20.6 <3.2 10.8 25.0 10.9 4.0 4.2 <4.4 15.3 <4.4 <4.4 5.1 5.6 4.4 6.3 12.4 7.4 13.0 3.9 3.7 5.0 8.1 26.8 <2.9 10.1 47.5 4.7 80.6 74.9 <1.9 33.0 4.3 5.7 9.6 26.2 44.1 22.9 23.2 3.9 8.3 25.1 7.0 <3.5 3.7  + + + + + + + + + + + + + + + + + -  + + + + + + + + + +  25.4 12.1 3.5 3.1 19.4 1.8 13.6 25.2 11.3 3.2 3.5 0.3 15.4 4.7 3.2 5.4 4.9 4.7 6.5 13.8 10.1 11.4 7.9 4.7 4.3 12.3 23.2 2.3 4.8 45.6 0.6 83.8 74.4 0,8 30.2 3.1 8,0 14.7 36.6 49.5 20.7 21.4 6.2 4.3 29.4 9.4 1.8 4.8  hkl h  k  lo  13 14  2  7.9 21.0 13.5 9.8 <4.5 6.3 <4.3 <4.1 6.7 4.3 <4.4 4.4 <4.4 11.4 <4.2 9.9 3.9 7.3 9.2 30.1 7.6 27.8  15 16 17 18 19 20 21 -19 3 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0  1  2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  lc  + 7.5. - 21.4 - 15.7 - 5.9 + 6.9 + 5.5 - 1.1 + 2.0 + 6.1 + 5.7 + 3.4 - 2.4 - 3.1 - 12.2 + 4.0 - 14.9 - 10.8 - 0.2 + 7.7 + 24.4 + 13.3 + 29.0 23.1 - 14.0 2.6 + 8.5 28.8 + 29.5 47.7 - 52.0 5.6 6.2 24.3 - 28.5 21.5 - 19.9 14.1 - 13.8 11.2 - 5.9 21.7 + 27.2 20.1 + 18.6 33.9 + 42.2 <2.8 4.7 21.0 + 19.0 24.5 + 23.6 24.5 - 24.8 <3.5 + 3.9 11.1 - 8.1 + 4.6 <3.9 9.1 - 5.9 <4.2 + 7.7 32.1 + 25.8 <4.4 - 2.3 < 4.5 - 3.6 <4.4 - 1.3 <4.2 + 1.4  - 117  h  k  20 3 -19 4 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 -6 - 5 _4 - 3 - 2 - 1 0  1  2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 -16 5 -15 -14 -13 -12 -11 -10 - 9 - 8  lo 4.0 5.9 <4.3 <4.4 <4.5 4.4 7.5 5.9 <4.0 5.5 7.4 <3.5 <3.3 31.2 58.5 11.0 23.9 3.9 6.0 24.0 9.8 9.8 10.7 8.2 14.4 17.4 37.1 24.5 19.1 < 3.5 3.7 7.8 5.7 4.2 13.0 <4.4 <4.5 4.4 6.3 4.4 4.4 <4.3 10.3 <4.1 5.6 3.8 <3.6  h  lc _  3.3 4.4 + 1.1 3.4 1.3 + 3.3 9.9 9.0 + 2.3 + 5.6 8.3 3.4 + 4.1 + 41.0 57.2 5.3 + 27.2 + 1.3 2.0 26.9 + 6.8 11.6 2.6 + 13.8 + 18.7 + 18.9 + 43.6 + 22.3 + 12.5 5.3 6.9 + 9.8 + 3.9 + 2.9 13.7 2.0 + 0.7 8.4 5.3 10.1 + 1.9 2.6 + 8.1 0.6 + 9.7 3*7 + 5.6  -  -  -  -  -  -  -  -  -  -  k  -  7 5 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 - 9 6 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0  1 2 3 4 5 6 7 8 9 10 11 - 9 7 - 8 - 7  h k  lc 22.2 28.4 9.8 3.2 8.2 4.3 9.1 7.4 9.6 21.0 23.1 <3.2 18.0 <3.4 10.0 18.7 <3.8 7.9 <4.1 16.9 <4.3 <4.4 6.3 5.8 4.0 <3.8 26.7 <3.6 14.3 3.5 <3.5 6.8 8.4 4.8 <3.5 <3.5 <3.6 5.2 22.2 <3.8 6.0 <44 <4.2 64 12.2 <4.2 <4.1  + 17.5 - 17.2 - 16.2 - 2.9 - 15.8 - 12.1 + 15.8 '+ 10.8 + 9.4 - 19.9 + 23.6 - 2.1 - 20.1 + 2.9 + 10.0 + 15.8 - 0.6 +. 5.1 - 3.1 - 15.4 - 1.0 + 1.9 + 7.6 - 5.3 + 1.2 + 2.7 - 19.8 + 0.1 - 19.1 - 1.0 - 3.2 + 11.1 - 6.8 + 6.6 - 2.1 - 2.2 - 5.7 + 1.7 + 23.4 + 1.6 + 7.2 + 0.6 + 3.2 + 6.6 - 4.8 - 4.0 - 4.6  6 7  -5  -4 3 -2 -1  0  1  2 3 4 5 8 8 7 6 5 4 3 2  -1  0 1 2 3 4 5 6 4 9 3 2  -1  0  1  -  2 3 4 5 4 10 3 2  -1 - 3 11 -2 -1 0  1  2  lo <4.1 9.8 3.7 13.5 12.2 <3.8 10.8 <3.8 21.8 26.6 5.6 8.0 <4.2 14.0 12.4 <4.3 12.7 <4.2 <4.2 9.3 < 4.2 7.2 5.9 10.3 7.4 6.1 17.3 8.9 16.5 < 4.4 15.3 <4.4 <4.4 6.2 17.7 4.4 7.7 6.2 <4.4 <4.4 4.4 11.5 < 4.1 5*8 5.8 7.1 5.8  lc + + + + + + + + + + + -  + + + + + + -  7.8 8.2 7.7 13.2 8.8 0 12.4 0.3 22.0 19.6 3.6 7.2 0.8 11.0 16.1  1.1 13.7 0.4 7.6 10.4 0 6.2 11.9 6.9 9.0 3.0 13.2 5.7 18.9 2.7 14.1 0 0 5.0 16.4 4.8 9.1 7.0 7.0 4.9 7.5 10.3 3,3 6.6 3.9 4.4  7.1  00  O rH + +  V  CM CM +  vo  rH t-  + ?  CTl VO <Ti O rH rH  +  cr. vo 8  CM tO CMrH  CM  00  VO VO VO VO  COO  o  CM  O O O O  o  o o  vo  s  8 i  Tt  rH  1  1  tO tO  Tt  in vo vo CM to «t to to 1 1 1 1 1  Tt  CM  vo in  CM  W  CM CM  V  V V  o o  o o o o  CO 00 tto CM tO CT> rH  ?  tO rH COVO Q  vo Tt  Tt  to  o o  Y?  in V V V CO  Tt  o o  O O  in o  to  1024  q O  O O  t~  s Tt  o  in o CO rvo t o in  1 1  +  O CM  o rH CM  t  to to tO CM V v V V  T  O O  CM CM CM  CM  VO CO  to in  rH rH  O o  1  CT> CM c- VO 00 rH CT» VO VO rH Tt  in in to "<*-  rr vo  O  CTv  (Tv  cr> cr, cr.  O  O  o q  o oo o o  CM  cr.  *? ?  CM 1 + +  in to  CTl  CM rH  1  o mo  c- to  Tt  in  Tt  +  +  in in  VO  in  Tt  «t  Tt  Tt  Tt  Tt  11  +  Tt  v  Tt w  Tt  VO  rH IO  CT. rH rH + +  +• H-  O  00 in +  +  Tt  1 1 1 CM rH Tt vo in cr. in vo CO in vo Tt CO to CO VO oS o in t o to CM rH rH V O to to O O O O O O o o o 9 °o CM Tt VO C O O Tt vo CO O CMTt  o rH rH rH rH CM CM CM o O O O o o o O o o oo o  rHvO  +  +  Tt  +  VO IH  TT  in t-  CM + +  • . ?  <V  cr. go rt- to in CO rHTt rH CM  O  O  rH tO H  ri  O in  o  r-  CM  O O O  o  O  vo  CM rH  c—  rH rH  o  o CTv  m to  + to VO VO IO rH rH rH  *t vo oo  I  r-  + 1  1  vo vO vO VO  00  CO  to  t~  CT> rH rH  o  O O O  C-- to  1 1 1 1 1 cr. cr. to H rH tO V v in in to w  CO  o  o o o  rH O  O O  CT.  in  O O O  1  vo vo  VO CM  ^  O  1  t-  to  o  CTl rH rH CM  rH rH rH rH rH rH H rH rH rH rH rH  rH  Tt  +  R  VO VO VO VO VO VO  i C-  o o o  CM  tr vo to to IH  +  +  +  in in CM  1 1 1  O vo  in +  O  vo *=r rin in  C~ C>-  t- c- t~  CM CM rH  00  1  +  +  o o o oo o o vo CD CO o CM rH rH rH rH o T*-  rH CM CM CM CM CM CM CM CM CM CM CM CM  +  + +  H  in in LO  to in t- cr.  in in m in in Tt to V V V V V V V V V  O  +  VO  CT\ rH to in rH rH rH  in in vo 1 1 1 CT. H CM to c- cr. en vo in to to c- ^ V rH rH rH rH  in  +"  rt-  as  Tt  in rH  r-  in  rH rH CVJ  B.  vo O  VO VO VO  O O O O  CM  ?? Tt  VO  o  rH +  1  O o 00  vO vo vo vo 00 S r H  o o o  cr. CM cr. to in rH cr.  rH rH +  VO  s  P  +  +  +  cr. cr. oo c- in rH  o o O o o CM  Tt  CO CO  vO oo o rH  CO 00 CO  to T}- vo H VO H to vo Tt Tt in CTl ft to rH rH H M <H 1 1 1  vo to  T  92  o-  CM enin rH CM rH co T J - in vo Tt rH rH rH rH H rH rH  O  CO CO  O O O O O O O  c—CM  rH IO  00 00 00  to in r-  rH  vo CM O CM rH rH rH rH CM CM  +  +  in cr. VO CM rH CM rH rH rH rH"  q O o oo o oo  +  in  +  rH  o o o o o o oo o o VO VO C o CM M O COOrH CrH rH rH rH  1 1 1 +  1 1  rH  vo  CM  Tj-  VO  cr. cr. cr.CO to CM to  in oo tO CM m vo  1 to oo vo in  t-  3 CMCT.  vo in  to to in in in in in in V V V V V V V v V V  VO VO  o  V 1  H  l  O O O o cr. rH to in rH  in  CO  CTl rH VO CM + + +  in o oo tn  a CM3 to rH rH  CM rH  CM  Tt  in  to  tf +  m  cr.  t  O  + ' +  CM  COvo in  rH VO rH  CM * * CM CM CM  +  rH rH rH rH rH  in in  O  Tt  O  rH O t- CM rH CM CM  o o  3 2  o  t- S  in  O o o in c- cr.rH to in  03  CTv rH to rH rH  to to  r-  to VO  "51-  l>  to  o o  +  Tt  to in to •?  cr*  O  CM  t-  CO 3 o  in  CM to CO VO rH CM CM CM CM rH  o o O O  to  V  in  CO rH in rH CO rH VO  Tt  CM  CO  r-  vo O  tn in in in in in tn in in  Tt  +  CO OrH  o oo o o  IO CM 8 Pi vo  i i i  CM  rH  1 +  +  in  CM CM CM CM CM CM CM CM CM CM CM CM CM  rH rH  rH  Tt  tO  O O O O  TJ-  Tt  Tl-  Tt  CM  vo  VO  CM  CT. rH rH  & ocr. in OCMtoincr. toin  O  CM  o  rH H rH CM rH  1  ?  CM  to  O  Tt  V  rH rH CM  o oo o  t~ t-  00 to to 1  in vo to  rH  O o t- cr. rH  rH rH  ?  o  tO Lf\  rH  CO  f  to to rH to to to H  rH rH  cr. CO rH rH 1  H  IO r— t- to C OC M Ttto CM CT. Cvoto CM VO CM  o  00 vo  Tt  Tt  Tt  Tt w  CO00  o o oo o o o o o o o vo CO o o CM vo o rH a CM rH Tt  CM VO  +  CO  vo  CM  V V CM Tt rH rH CO CO  fCM  CO CO CO CO  rH rH rH CM  Tt  vo.to  O O O to in  OO o  § rH  O  CVJ CM  ^  V  o O O  c- cr. to to to to to to to to to to to rH  CTv rH rH to in rH rH rH rH rH CM  - 119 -  Table  h k Z 0 0 0 0 0 2 0 0 4 0 0 0 0  0 0 0 1  6 8 10 1  0 1 2 0 1 3 0 1 4 0 0 0 0 0 0 0 0 0  1 1 1 1 1 1 1 2  5 6 7 8 9 10 11 12 0  0 2  1  0 0 0 0 0 0 0 0 0 0  1  2 2 2 2 2 2 2 2 2 2  2 3 4 5 6 7 8 9 10 11  lo 12.6 (21.1) 18.3 (28.9) 4.8 <0.6 3.6 13.6 (16.3) 19.4 (42.5) 11.6 (15.0) 16.2 (16.8) 4.8 7.5 12.9 0.6 1.6 2.1 1.3 4.7 15.8 (18.6) 16,1 (22.2) 7.8 12.5 10,3 15.1 12.4 0.6 2,1 5.8 5.3 0.8  A-4.  P  —c 160 +24.3 -34.3 - 9.2 + 3.7 - 2.4 +12.4 -43.4 +21.2 +12.4 - 0.8 +10.3 - 8.9 + 2.5 - 2.1 - 1.3 + 1.3 + 3.6 -16.9 +25.8 + 7.5 +12.4 - 8.8 -13.6 - 9.1 - 1.8 + 0.8 + 7.3 + 4.9 + 1.9  JD-Chloronitrobenzene  h k 0 3 0 3 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0  3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7  Okl  and  hOt  h k 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 1 2 3 4 5  2.0 1.7 19.6 (23.2) 10.3 6.1 <0.6 9.8 2.8 0.7 4.7 1.3 6.1 1.6 1.7 4.0 1.3 7.4 1.1 4.3. 3.5 1.7 2.7 1.3 <0.8 <0.8 2,4 <0.8 <0.8 2.4 <0.8 <0.8 <0.8 2.5 0.8 1.1 <0.8 <0.8 1.8 <0.8 0.7  - 0.9 - 1.6 -25.6 + + + + + + + + + + + + + + + + + + + + -  6.9 4.9 2.3 9.9 1.1 4.1 3.4 6.6 4.5 2.0 1.4 5.0 3.1 3.1 0.4 4.8 3.3 1.4 4.9 3.4 0.6 1.6 3.7 1.3 1.4 0.1 6.0 2.0 2.0 1.7 2.6 0.9 1.1 1.0 0.6 0.4 0.3  1 2 3 4 5 -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3 -2 -1 0 1 2 3 0 1 2 -1 0 1  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  lo 0 9.3 0 <1.1 0 3.4 0 3.0 0 <1.5 2 2.5 4.2 2 2 37.0 2 23.0 2 11.7 2 9.0 2 5.5 2 2.1 4 4.9 4 3.9 2.2 4 4 34.7 4 9.1 6.0 4 3.2 4 6 2.1 6 <1.4 6 3.1 6 16.7 6 4.7 6 2.3 6 2.3 6" 5.1 8 6.4 8 5.8 8 <1.2 2.2 8 8 6.3 8 3.4 10 3.7 10 3.9 10 4.2 12 3.5 12 <1.5 12 2.1  lc - 7.3 + 5.8 + 2.1 - 3.1 + 0.3 + 3.2 -15.7 +70.0 +24.3 -10.3 +12.6 - 8.5 - 0.3 - 6.2 + 5.5 +11.8 -34.3 +11.8 - 7.6 - 1.9 - 1.3 - 1.5 + 0.8 -17.7 - 9.2 + 2.8 - 3.9 + 2.4 - 3.8 - 9.0 + 3.7 - 2.7 + 4.0 + 2.4 - 2.4 - 2.4 + 4.2 - 1.9 - 2.4 + 2.1  - 120 -  Table A-5.  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 I 1 1 1 1 1 1  0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34  0 Not 0 obs. 0 75.9 0 <0.6 0 60.8 0 10.6 0 14.6 0 6.0 0 16.2 0 2.7 0 9.5 0 <1.3 0 29.5 0 <1.3 0 <1.2 0 <1.2 0 <0.9 0 <0.7  1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 200 21 6 22 23 24 25 26 0  14.7 62.3 9.7 <0.5 19.4 20.2 6.5 13.7 15.5 52.1 30.6 2.0 6.3 19.6 21.9 4.0 <1.1 12.7 < 1.2 2.1 10.6 11.3 <1.3 <1.3 4.5 10.3  lc  h  376 - 4.6 -85.8 1.8 -55.6 12.2 16.6 - 8.4 -16.1 - 1.4 -12.2 1.7 29.4 -1.8 - 2.9 - 0.9 -2.3 - 0.3  1 1 1 1  -15.9 -55.7 11.4 - 1.3 21.0 -20.5 - 8.4 -13.2 17.0 -48.4 -29.8 4.0 - 6.9 20.6 20.6 5.4 - 1.1 12.0 - 0.0 - 1.9 -10.3 12*8 1.8 - 1.0 7.8 -12.0  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  3 3 3 3 3 3 3 3  k I 27 28 29 30  8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  hkO and Okl  Acenaphthenequinone  0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  h  lo <1.3 - 4.1 <1.2 1.3 <1.2 1.5 < 1.1 - 0.5 17.5 38.8 16.3 8.9 30.8 2.6 11.1 <0.7 3.7 21.4 4.1 17.7 30.7 7.0 <1.0 3.1 6.8 12.7 3.5 <1.2 5.7 2.2 4.5 <1.3 9.1 <1.3 1.6 2.2 <1.2 3.5 <1.1  21.4 -38.9 -15.2 -12.7 -28.1 - 2.3 13.4 1.8 - 4.8 20.4 6.9 -16.8 29.4 6.6 - 2.2 4.5 - 8.1 ?11.8 3.4 - 1.1 5.5 4.3 - 5.8 3.2 - 6.5 2.0 1.7 1.1 - 0.8 - 3.2 0.9  37.5 31.8 8.4 11.1 15.7 -14.9 38.8 -32.9 3.7 - 3.5 <0.9 1.8 7 0 27.3 -26.7 11.6 8 0 11.1  k I  3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  0 1 2 3 4 5 6 7 8  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  9 10 11 12 13 14 15 16 17 18  19  20 21 4 22  lc  25.2 -22.5 <0.9 - 2.3 26.0 26.0 5.5 6.4 16.0 15.5 4.2 - 2.9 <1.2 - 2.5  13.7 -14.0  <1.2 <1.2  0.7  2.9 12.1 -12.7  4.7 3.9 - 6.5 1.1 <1.3 10.4 11.3 4.0 2.2 6.5 4.9 3.0 - 4.3 2.1 - 3.5 3.4 - 3.1 <1.1 - 0 . 3 <1.3  <0.9 -1.5 26.2 -24.0 22.8 -21.6 2.8 - 5.5 5.9 - 6.7 15.7 14.5 6.1 5.9 2.7 - 6.1 16.2 14.4 <1.1 - 0.4 <1.1 - 1.0 6.0 -6.4 5.5 - 5.3 <1.2 - 3.0 10.6 8.2  12.8  10.6 4.3 - 5 . 0  3.5 3.1 4.2 6.9 3.6 - 2.1 4.6 6.5 1.1 <1.4  10.4 -11.0  h  k£  —0  4 4 4 4  23 0 24 0 25 0 26 0  <1.3 <1*3 <1.2 <1.2  5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5  1 2 3 4 5 6 7 8  9 10 11  12  13  14 15  16 17 18  19 20 21 22  23 24 25 26  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  P  lc  1.6  -  0.3 2.9 2.2  7.9 - 8.5 5.0 - 5.2 <1.1 - 3.1 6.0 7.3 17.6 13.5 <1.2 1*5 7.6 -10.1 17.7 20.5 2.5 - 2.7 <1.2 - 2.1 12.8 13.0 5.0 6.5 3.0 <1.3 7.0 7.2 <1.3 - 1.2 19.3 -18.6 <1.4 - 1.1 9.1 - 8 . 0 4.0 - 1.9 2.8 - 2 . 3 0.2 < 1.3 5.2 4*9 <1.2 1.4 < 1.2 2.3 2*3 -3.7  <1.0  6 0 0 8.5 6 1 0 3.7 6 20 8.6 6 3 0 5.7 6 4 0 <1.2 6 5 0 8.1 2.2 6 6 0 6 7 0 11.1 6 8 0 11.9 6 9 0 15.2 6 10 0 14.2 6 11 0 2.2 6 12 0 16.3  7.4 - 4,3 10.1 - 3.5 Q.9 - 7.4 2.0 11.1 -11.6 14.6 -13.3 - 2.9 13*8  - 121 -  Ho  lc  h 7 7 7 7 7 7 7  16 17 18 19 20 21 22  0 0 0 0 0 0 0  4.1 3.9 4.9 5.3 2.0 <1.1 1.0 <1.0 mm <1.0 1.6 1.2 3.3 <0.9 0.3  8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  <1.3 1.5 2.2 6.1 4.3 5.2 4.2 5.2 6.5 1.4 <1.2 <1*2 <1.1 <1.1 <1.0 3.5 <1.2 <1.0 <0.9 4.0 <0.7  6 6 6 6 6 6 6 6 6 6 6 6 6 6  13 14 15 16 17 18 19 20 21 22 23 24 25 26  0 0 0 0 0 0 0 0 0 0 0 0 0 0  <1.4 3.2 14.7 14.5 <1.3 <1.3 6.5 2.9 <1.2 <1.1 <1.0 <0.9 <0.9 4.2  0.8 - 4.9 -12.3 -12.3 - 0.7 2.9 5.0 4.0 - 3.2 0.8 1.3 1.2 - 0.5 3.3  7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 90 10 0 ii 0 12 0 13 0 14 0 15 0  4.0 5.0 3.2 7.2 <1.4 13.8 4.5 10.4 <1.3 10.4 <1.3 <1.3 3.8 <1.3 3.7  -3.2 4.8 4.9 4.0 1.5 -12.7 6.0 - 8.8 - 4.4 6.7 - 1.8 - 0.2 - 3.4 - 0.4 - 4.0  lo  lc  lo  -  -  3.0 2.7 1.9 6.2 4.5 5.3 2.2 5.1 3.2 2.2 0.5 0.9 1.2 0.9 0.5 2.9 0.2 0.0 0.2 3.1 1.3  lc  0 0 0 0 0 0 0 0 0 0 0 0  2 4 6 8 10 12 14 16 18 20 22 24  0 ODS. 5.3 0 86.7 -95.9 0 <2.8 - 1.4 0 65.7 -60.6 0 14.1 -13.2 0 15.5 10.9 0 9.6 6.9 0 18.2 -17.1 0 <4.5 2.0 0 12.3 -12.1 0 <5.1 - 1.8 0 34.9 29.3  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  43.8 33.9 47.0 67.6 <3.9 <4.0 27.5 32.8 <4.4 18.5 14.3 <4.7 9.6 18.8 7.0 11.5 <5.4 6.7  43.3 40.1 -49.0 58.6 - 2.1 - 4.8 29.0 30.7 4.5 -21.1 -13.3 - 4.4 - 9.0 16.1 - 4.5 -11.5 - 2.6 - 5.5  lo  lc  0 0 0 0 0 0 0 0 0  19 20 21 22 23 24 25 26 27  1 1 1 1 1 1 1 1 1  <5.7 13.9 <5.9 <5.9 12.9 <6.2 10.7 <6.4 <6.5  0.3 -14.7 - 2.9 2.6 11.0 0.1 9.9 - 1.5 - 5.9  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0  16.7 <5.2 <5.2 <5.2 <5.2 <5.3 12.3 14.7 10.5 10.6 <5.4 7.5 <5.5 <5.8 7.8 <5.9 16.2 <5.9 <6.0 <6.1 8.5  -21.0 - 2.6 13.0 - 2.5 - 8.3 - 6.1 -15.3 15.6 13.5 15.0 - 3.5 -7.8 - 1.8 2.3 9.3 - 4.1 15.6 - 6.8 - 1.2 - 2.0 - 6.2  The phases of the hkO and Qk£ structure factors are referred to the respective origins of the (OOl) and (lOO) projections. The calculated OkO structure amplitudes are not the same since hydrogen-atom contributions are not included i n computing 0k€ structure factors.  - 122 Table A-6. h  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5  6  7 8 9 10 11 12 13 -14 -13 -12 -11  lc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 4 4 4 4  not ODS.  52.8 22.3 14.2 7.4 2.3 13.4 2.5 4.6 £ 2.2 11.6 29.4 £2.0 10.9 4.2 10.1 •£1.8 £2.1 4.6 3.3 £2.1 3.7 13.4 5.3 £1.6 30.9 X1.2 60.5 37.5 £0.8 93.5 22.5 24.7 30.5 17.7 38.8 17.3 8.5 3.1 4.3 4.3 £2*3 14.4 4.5 7.7 £2.2 8.8 8.7  392 -30.1 -61.5 -22.5 -19.4 - 7.3 2.1 - 9.4 2.3 - 3.5 - 1.2  -5.5  24.4 2.4 - 7.5 - 2.8 6.9 - 0.5 - 1.3 - 3.0 5.6 - 2.9 - 4.9 -13.3 - 8.2 - 0.0 25.6 4.4 55.9 41.4 - 1.7 -93.1 25.3 -25.9 -31.8 19.7 -33.7 17.4 8.6 5.8 5.1 4.6 1.3 -11.5 - 2.6 6.4 - 2.2 - 8.9 9.2  h  -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 -16 -15 -14 -13  I 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 66 6 8 8 8 8  lo  lc  32.2 13.4 24.5 12.8 8.4 18.8 7.2 35.6 2.3 13.4 53.2 44.0 52.6 31.2 28.4 32.9 22.9 £2.0 3.3 4.6 5.7 6.2 £1.8 3.7 £2.3 4.7 10.5  -26.1 12.7 24.4 12.5 - 9.2 -16.4 - 7.7 36.6 - 5.7 -18 -51.0 44.4 -55.2 27.6 25.7 30.1 -19.5 - 4.6 - 4.7 5.8 - 3.6 - 5.9 0.5 3.3 - 3.5 5.8 -2.0.7 22.2 -16.6 1.2 9.4 -14.4 - 0.3  24.9  18.5 £2.0 11.6 14.0 £1.6 9.7 10.0 16.0 48.4 30.9 34.0 39.9 2.4 15.6 4.1 7.9 £2.2 4.9 £1.7 £1.9 £2.0  hOt  cis-1.2-Acenaphthenediol  9.8  15.6 19.0 ^5.9 26.6 -31.2 39.0 - 2.2 -18.1 7.5 - 9.6 - 0.7 - 5.3 - 0.9 1.8 - 2.3  h  -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 -14 -13 -12 -11 -10  -9 -  8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 -14 -13 -12 -11 -10  8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 12 12 12 12 12  lc  lc  4.1 3.3 £2.2 £2.0 5.0 13.5 39.6 6.0 32.4 35.8 11.9 £1.7 8.1 20.2 £1.8 16.3 15.1 15.0 16.5 <2.3 5.0 4.2 4.8 £2.1 3.3 24.0 <2.3 £2.2 15.1 £2.1 14.6 £2.0 8.6 <1.9 9.4 14.3  - 4.7 4.7 2.7 - 2.5 5.6 - 9.9 32.4 6.4 -27.4 -38.6 17.2 2.0 - 9.0 20.4 - 1.2 -19.3 17.4 -15.2 18.3 0.4 - 6.0 - 5.7  <2.1  17.8 £2.2 6.8 12.5 £2.3 5.7 8.2 10.1 8.3 26.3 11.5  -  3.7  1.9 0.8 21.5 - 5.3 1.7 ^15.3 3.8 -14.7 - 2.1 8.0 1.2 -12.0 13.2 - 2.7 21.6 6.0 - 6.5 -16.7 6.3 - 7.2 8.4 8.0 - 7.5 -21.0 10.0  h  -  9 8 7 6 5 4 3 2 1 0 1 2 3 -14. -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - i 0 I  2 3 4 5 6 -11 -10 - 9 - 8 - 7 - 6 - 5 - 5 - 4 - 3 - 2 - 1 0 - 5  I  lo  lc  12 12 12 12 12 12 12 12 12 12 12 12 12 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 16 16 16 16 16 16 16 18 18 18 18 18 18 20  £2.3 £2.3 4.5 12.6 12.4 < 2.2 £ 2.2 12.5 11.5 11.7 29.9 £2.3 7.5 6.3 £1.8 9.2 £2.2 3.2 <2.3 £2.3 £2.3 17.4 16.6 4.1 £2.3 9.5 5.3 3.6 £ 2.2 £ 2.1 £2.0 £1.8 £1.6 5.6 2.6 £2.0 4.7 £2.2 4.7 £2.2 4.7 5.4 3.7 £1.8 £1.7 £1.5 3.2 4.2  - 3.1 - 0.1 4.0 -14.8 15.5 - 1.1 3.2 16.5 13.0 -12.9 -31.2 - 0.2 10.6 - 4.3 - 2.7 5.2 - 4.9 - 2.9 2.6 5.7 1.0 17.9 -16.8 4.9 - 0.6 -11.5 - 6.7 4.6 2.0 0.5 1.3 4.9 - 2.2 6.6 5.3 - 0.4 6.2 - 2.2 - 6.6 - 5.0 3.9 7.0 - 2.6 2.2 - 3.1 - 1.2 3.0 - 6.9  - 123  Table A-7.  h  e  1 2 3 4 5 6 7  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  8  9 10 11 12 13 14 15 -15 -14 -13 -12 -11 -10 - 9 -  8  -  7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8  9 10 11  h  I  12 13 14 -14 -13 -12 -11 -10 - 9  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 2 2 3 3 3 3 3 3 3 3 3 3 3 3  —Fc  14.2 _ 21.3 112.7 106.1 16.6 17.8 4l.O — 3.2 3.2 2.7 12.2 - 11.2 3.1 2.5 3.0 4.6 42.7 3.3 21.1 - 18.9 5.8 4.0 3.0 3.2 0.2 42.1 5.4 4.4 40.8 3.2 2.0 3.3 4.0 — 4.0 8 . 2 — 4.5 42.8 3.3 43.0 1.4 42.9 1.5 0.8 42.6 1.8 42.4 0.2 41.8 5.7 5.5 9.0 - 8.3 15.2 13.7 74.4 70.3 95.2 — 81.9 35.7 - 51.2 4.4 5.3 22.5 20.2 25.7 26.8 5.6 5.9 42.4 1.3 5.8 6.3 5.7 7.9 6.8 6.4 6.9 - 6.9 10.9 13.8 10.5 9.0 9.6 7.7  -  -  -  -  -  -  8  7 6 5 4 3 2 l 0 1 2 3 4 5 6 7 8  9 10 11 12 -13 -12 -11 -10. - 9 -  8  -  7 6 5 4 3 2  cis-1,2-Acenaphthenediol  So  2.5 2.9  hl£-  h  h  He  0.5 3.0 4.8 3.0 2.2 3.2 0.2 4 2.4 4 2.9 - 0.9 4 3.0 0.6 42.9 4.8 42.6 1.5 4.9 4.0 9.7 -10.7 2.8 3.5 81.6 -75.0 8.5 7.1 46'.0 47.3 93.1 83.9 39.3 -38.4 11.2 10.3 6.5 il.8 0.8 1.9 2.0 1.9 41.3 - 1.9 26.6 -21.4 10.4 12.7 35.6 -32.7 7.1 5.0 9.0 8.5 14.9 17.2 3.9 - 4.3 4 2.4 - 2.4. 4 2.5 - 2.3 5.0 - 3.3 3.2 4 3.0, 5.6 5.6 42.5 - 3.6 20.8 18.4 22.6 -22.5 3.9 - 3.2 8.5 9.5 9.1 - 8.7 26.9 -23.9 24.1 21.8  4  -  - 1 0 1 2 3 4 5 6 7 8  9 io -13 -12 -11 -10 - 9 -  8  -  7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8  9 10 11 12 13 -13 -12 -11  3 34.2 ^32.5 3 13.7 16.2 3 23.1 20.2 3 4.6 - 4.0 0.6 3 < 1.2 3 13.1 14.7 3 15.7 -15.3 3 5.8 - 5.2 1.9 3 4 2.4 3 42.7 4.4 3 8.7 - 8 . 8 3 4 3.0 3.6 4 42.6 - 1.7 4 4.6 4.6 1.2 4 4 3.0 4 14.4 -13.7 4 9.5 10.4 4 20.1 -20.0 4 9.7 13.4 4 41.5 0.4 4 25.8 24.3 4 12.1 -10.8 4 5.0 9.0 4 4.2 7.7 4 9.3 - 9.2 4 6.9 6.2 4 11.2 -15.2 4 19.2 -21.8 2.9 4 1.9 4 3.4 - 4.8 4 4.6 7.0 4 4 2.3 3.3 4 9.8 11.3 1.8 4 42.9 4 4 3.0 - 1.8 4 4 2.8 - 1.2 4 42.4 - 2.5 1.0 4 4"1.8 4 2.8 - 3.3 5 42.7 - 2.2 5 7.4 8.6 5 3.8 5.0  -10 - 9 -  8 7  -  6 5 4 3 2. 1 0 1 2 3 4 5 6 7 8  -14 -13 -12 -11 -10 - ,9 -  8  -  7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8  £c  5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 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  5.6 2.6 13.5 17.0 4.3 12.7 6.6 12.1 6.5 13.7 27.9 22.0 12.7. 12.1 6.6 4.6 7*8  - 6.7 - 0.6 -13.9 15.8  -  1.5  8.9  2.1  -10.8  11.8  -16.1 32.0 26.0 -13.0 -14.6 -ll 2 5.6 10.4 f  7.1 - 8 . 1 1.0 4 3.0 4 2.1 - 0.3 4.4 4.7 8.2 - 6.0 4.7 3.8 8.5 7.9 7.5 - 8.3 2.4 3.9 7.6 - 7.4 4 1.7 0.7 22.2 22.7 29.6 -30.2 11.5 10.9 23.6 -20.3 37.8 39.6 18.6 -21.3 8.5 8.0 11.7 14.9 5.7 - 6.9 3.4 - 3.0 5.9 6.4 3.8 - 2.6 8.0 7.0 8 . 7 -10.7  - 124 -  h  9 -13 -12 -11 -10 - 9  -  8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8  9-  10 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3  Ho  6 7 7 7 7 7 7 7 7 7  42.8 2.7 8.2 4.1 42.9 8.5 4 2.4 5.6 2.8 41.7 1 19.9 7 20.8 7 9.8 7 16.6 7 37.0 7 2.6 7 3.6 7 9.7 7 7.5 7 4.7 7 5.7 7 4.1 7 4.0 7 2.6 7 3.4 8 3.4 8 3.7 8 4 3.0 8 42.9 8 4 2.7 8 4.1 8 4.2 8 30.1 8 8.9 8 16.9 8 5.9 8 5.5 8 20.8 8 9.7 8 42.0 8 8.8 8 3.7  —Fc  0.5 2.6 - 7.6 4.0 0.7 - 7.9  1.9  5.8 - 3.4 2.8 -23.a  23.4 10.4 19.9 -32.0 - 5.9 4.8 - 9.7 7.5 5.2 - 6.3 5.8 - 6.6 2.2 3.4 - 3.5 3.5 - 2.7 - 0.9 - 4.2 - 6.3 - 5.6 31.2 - 8.6 17.8 - 9.5 4.8 -24.2 12.5 2.8 - 9.8 7.6  h  e  h  So  4 8 5.2 5 8 42.9 6 8 12.7 7 8 2.8 8 8 ^2.7 - 9 9 4 2.8 - 8 9 5.1 - 7 9 8.8 - 6 9 2.4 - 5 9 9.2 - 4 9 4 2.0 - 3 9 5.5 - 2 9 2.8 - 1 9 5.2 0 9 42.1 1 9 42.3 2 9 4.2 3 9 4.7 4 9 4 2.9 -13 10 42.5 -12 10 2.5 -11 10 7.8 -10 10 4.1 - 9 10 16.7 - 8 10 11.5 - 7 10 3.9 - 6 10 14.3 - 5 10 3.7 - 4 10 1.9 - 3 10 11.3 - 2 10 6.6 - 1 10 7.4 0 10 4.3 1 10 6.4 2 10 4.9 3 10 5.5 4 10 11.9 5 10 7.4 6 10 6.3 7 10 4 2.4 -13 11 5.7 -12 11 5.5  - 9.7 - 5.5 13.1 - 1.7 2.9 - 1.6 8.7 - 7.1 2.6 8.6 3.1 - 5.7 3.2 - 6.9 - 1.2 1.6 - 5.5 5.3 - 0.5 - 3.8 0.1 - 6.1 - 0.1 19.8 12.5 - 3.9 -18.2, 3.6 1.7 -11.8 7.6 - 9.9 1.6 - 7.6 6.8 7.8 16.6 - 6.7 -10.2 0.3 - 5.4 - 4.9  -11 -10 - 9 - 8 - 7  11 4 2.9 11 17.6 11 4 3.0 11 11.4 11 7.8 - 6 11 4 2.6 - 5 11 3.3 - 4 11 14.2 - 3 11 12.6 - 2 11 3.7 - 1 11 4 2.6 0 11 11.0 1 11 4" 2.8 2 11 19.7 3 11 4 3.0 4 11 5*0 5 11 4 2.8 -13 12 8.5 -12 i2 2.6 -11 12 14.5 -10 12 4 3.0 - 9 12 14.3 - 8 12 4.6 - 7 12 4 2.9 - 6 12 4 2.8 - 5 12 3.5 _ 4 12 14.6 - 3 12 6.6 - 2 12 4 2.8 - 1 12 13.5 0 12 4.6 1 12 4.0 2 12 4 3.0 3 12 7.0 4 12 42.8 -15 13 1.4 -14 13 2.0 -13 13 8.4 -12 13 42.3 -11 13 4 2 . 6 -10 13 42.9 - 9 13 4 3.0  h  Ic  0.2 13.4 2.1 - 9.7 6.2 - 1.9 - 4.6 12.2 -12.1 7.8 - 4.8 -11.4 - 0.4 18.0 1.1 - 4.7 - 1.8 6.8 - 2.3 9.2 - 3.6 - 9.1 4.2 - 1.7 - 6.5 3.0 -19.3 10.6 4.8 19.3 - 4.7 -  4.6  2.1 9.3 2.1 2.0 2.7 6.0 1.3 - 0.1 - 3.0 1.8  -  8 7 6 5 4 3 2 1 0 1 -14 -13 -12 -11 -10  Z  Ho  13 3.7 13 2.9 13 43.0 13 3.6 13 6.4 13 43.0 13 8.6 13 9.7 13 7.7 13 4 3.0 14 4.3 14 41.6 14 <2.1 14 4 2.4 14 42.7 - 9 14 42.9 - 8 14 6.5 - 7 14 5.1 - 6 14 43.0 - 5 14 43.0 - 4 14 19.6 - 3 14 3.7 - 2 14 8.7 - 1 14 43.0 0 14 2.8 1 14 4 2.8 2 14 3.4 3 14 4 2.3 4 14 41.8 5 14 2.8 -14 15 2.1 -13 15 2.4 - 8 15 7.4 4 15 4.7 -13 16 3.7 -10 17 3.0 - 8 17 3.0 - 3 18 4.2 - 3 19 3.3  2c  3.0 - 4.5 - 0.6 3.6 - 5.6 0.7 -11.3 10.9 10.3 - 3.3 - 2.6 0.1 1.6 - 1.9 - 0.5 - 4.2 - 5.5 4.6 - 0.8 2.7 21.2 - 4.6 - 9.7 - 2.3 0.3 0.0 - 5.1 1.6 - 3.2 4.0 - 1.9 1.4 - 5.8 - 4.0 - 3.6 - 3.1 3.5 4.9  3.4  0  - 125  Table A-8.  h  P  2c  — o  0 1 2 5 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 -18 -17 -16 -15 -14 -13 -12  -11  -10 - 9 - 8 - 7 - 6 - 5 - 4 -3 - 2 - 1 0 1 2 3  0 0 net ODS. 0 88.9 0 29.6 0 106.4 0 37.1 0 19.2 0 35.5 0 9.7 0 3.3 0 8.9 0 14.3 0 £2.6 0 26.8 0 4.8 0 £2.3 0 5.5 0 £1.7 0 2.0 2 £1.7 2 2.1 2 5.0 2 £2.4 2 11.6 2 £2.4 2 5.0 2 16.4 2 16.9 2 15.2 2 29.8 2 35.8 2 52.6 2 22.6 2 59,1 2 4.3 2 2 not 2 ODS. 73.3 2 11.2 2 £1.0 2 75.7  568  -20.6  -89.7 -31.3 -95.1 43.4 -19.5 -39.9 9.8 - 8.5 9.2 -12.5 2.8 29.0 - 3.9 - 0.4 - 6.4 - 1.1 3.4 - 1.9 - 2.6 - 5.8 -  4.1  12.3  1.1  3.2 21.6 -14.2 -15.3 -35.1 26.9 54.0 24.4 -59.2 3.2 10.9 80.0 -70.3 16.2 3*2 -73.5  h 4 5 6 7 8 9 10 11 12 13 14 15 16 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9  -  cis-1,2-Acenaphthenediol Dinitrate  £  lo  lc  2 9.6 12.4 2 34.7 28.9 2 17.0 12.5 2 17.3 17.4 2 29.5 29.4 2 4.7 10.5 2 5.2 6.5 2 10.2 8.4 2 2.6 4.8 2 2.1 5.5 2 6.0 5.8 2 9.9 10.4 2.2 2 £1.7 0.1 4 £ 2.0 4 4.5 5.1 8.0 4 7.4 4 2.4 5.1 7.8 14.7 4 6.1 4 7.5 4 21.8 27.5 4 14.9 11.9 4 26.4 57.1 8.8 .6.7 4 48.2 4 59.5 4 24.6 21.5 4 25.5 22^5 4 52.6 51.5 4 56.6 52.5 4 113.5 - 1 1 4 . 9 41.0 4 45.2 4 50.2 58.9 2.0 2.4 4 4 115.5 108.7 57.1 4 41.2 4 56.1 55.4 59.9 4 47.1 4 56.1 55.1 24.0 4 18.6 4 21.6 19.9 8.6 4 9.5 16.2 4 20.5  -  -  -  -  -  -  -  h  £  10 11 12 15 14 15 16 -20 -19 -18 -17 -16 -15 -14 -15 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 5 - 2 - 1 0 1 2 5 4 5 6 7 8 9 10 11 12  4 4 4 4 4 4 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  15  Zo  lc  55.6 7.2 6.2 5.0 £ 2.1 £ 1.7 4.5 £1.5 5.2 £2.1 £2.5  -55.7 7.4  £  7.1  2.4 £2.4 10.5 8.4 10.7 20.6 25.5 24.5 7.1 4.5 5.5 17.8 59.4 29.5 6.5 59,9 65.6 28.0 72.1 18.5  11.2  5.6 £2.2 15.5 14.5 7.9 £2.4 5.7 5.5  9.1  5.8 1.8 0.8 4.0 - 0.9 5.7 - 0.1 - 5.6 -  -  8.1  5.5 6.7 14.8 11.9 14.7 -17.2 -27.5 20.2 4.5 0.0 2.4 -14.6 -57.7 55.0 - 6.0 55.7 58.5 28.2 -67,6 -18.5 -10.7 - 1.9 - 0.8 -15.7 15.2 5.0  1.1  5.8 - 2.5  hOt  h £ 14 15 -21 -20 -19 -18 -17 -16 -15 -14 -15 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2  6 6 8 88 8 8  8 8 8  8 8 8 8 8 8 8 8  8 8  8 8  - 1 8 0  1  2 3 4 5 6 7 8 9 -17 -16 -15 -14  8 8  8  8  8  8 8 8 8 8 10 10 10 10 -13 10 -12 10 -11 10 -10 10  Zo  Zc  2.2 2.3 £1.1 2.1 £ 1 . 2 - 0.9 2.4 8.0  3.6  -  8.1  -  0.1 2.1  1.2 £ 2 . 4 - 0.5 5.1 - 5.9 4.8 5.9 £ 2 . 4 - 3.5 8.9 8.5 8.8 4.5 8.7 13.2 5.0 5.2 5.0 5.2 5.5 9.5 16.0 - 2 0 . 6 76.0 - 7 2 . 4 55.1 26.5 25.1 -19.2 20.9 26.5 5.0 £1.5  £2.1  7,1  £1.7 6.9 15.5 4.5 7.4 9.6 9.2 £2.4 5.4 £2.4 £2.4 14.4 3.4 4.0 19.7 £2.1  £2.1 8.6  5.2 15.2  - 2.1 - 7.2 -11.4 11.6 0.4 5.2 - 0.7 2.9 9.5 - 5.7 5.5 -18.7 5.4 -  1.7  6.5  - 126 -  h I -  9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4  F  Ic  10 4 1 . 9 1.7 10 1.8 2.5 10 12.0 3.7 10 23.8 20.2 10 40.4 -41.9 i o 25.7 17.8 10 8.7 11.2 10 45.4 -45.4 10 33.2 31.6 10 21.4 19.0 10 6.4 7.5 10 6.0 4.8 10 4.9 - 4.8 10 22.1 -24.7 10 8.1 7.1 10 4 2o4 1.3 12 <1.8 0.0 3.0 12 2.4 12 3.1 - 3.5 12 5.8 4.7 12 30.3 -32.3 12 4 2.4 - 3.1 12 19.8 24.0 12 2.3 - 3.3 12 5.5 8.7 12 12.0 - 8.1 12 12.0 12.1 12 44.4 44.8 12 12.8 -14.9 12 10.9 -11.8 12 U . 6 .-13.5 12 7.5 -15.8 12 23.6 19.4 12 36.2 -41.1 12 21.7 13.8 12 2.7 2.9 12 4.8 4.1 12 8.6 5.5 12 10.2 - 9.6 12 4 2 . 4 1.0 12 15.5 18.5  h I 5 6 7 8 9 10 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 -22 -21 -20 -19 -18 -17  12 12 12 12 12 12 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 16 16 16 16 16 16  F  F  — oQ  7.5 9.2 42.1 3.4 2.1 5.6 41.8 2.8 4.9 6.2 28.1 5.4 8.6 17.8 28.2 5.1 16.5 5.9 42.1 10.4 11.1 6.2 8.0 27.4 4.0 14.1 7.5 4.3 6.8 7.8 4 2.3 <2.1 3.4 41.7 2.3 40.8 2.4 41.7 2.7 42.1 7.8  — cC  -  5.1 8.2 0.0 3.4 1.2 4.5 1.3 - 0.9 - 6.5 -10.5 22.3 7.7 - 7.7 16.3 -25.8 6.5 18.3 - 7.7 - 5.6 - 8.3 -16.4 - 7.3 -10.3 27.6 - 1.3 13.7 10.6 -11.4 4.0 - 4.5 - 1.7 - 1.7 - 1.9 - 0.1 3.0 - 0.9 5.0 1.8 1.9 - 2.8 - 8.1  h _I  mm*  -16 16 -15 16 -14 16 -13 16 -12 16 -11 16 -10 16 - 9 16 - 8 16 - 7 16 - 6 16 - 5 16 - 4 16 - 3 16 - 2 16 - 1 16 0 16 1 16 2 16 3 16 4 16 -17 18 -16 18 -15 18 -14 18 -13 18 -12 18 -11 18 -10 18 - 9 18 - 8 18 - 7 18 - 6 18 - 5 18 am 4 18 - 3 18 - 2 18 - 1 18 0 18 1, 18 -20 20  F  He  6.9 4 2.4 5.4 17.3 4 2.4 11.4 12.0 4 2.4 10.2 42.4 24.6 6.2 29.7 6.8 14.4 42.4 11.3 42.3 42.1 2.9 41.9 <2.1 3.8 42.3 3.3 9.4 4.1 14.4 4.2 6.8 15.5 4.8 28.3 4.1 42.4 4.0 2.3 5.3 7.4 41.9 41.1  6.4 - 2.9 4.4 -13.1 - 1.6 13.2 -11.2 - 2.9 13.6 0.0 26.0 - 6.0 -28.0 5.5 10.1 0.4 -11.7 1.4 - 0.4 2.4 0.2 1.1 - 4.5 0.5 - 3.2 12.2 6.6 -12.6 5.9 6.8 13.4 - 3.9 -25.2 - 6.7 2.8 2.2 6.3 - 5.5 8.1 - 1.9 - 1.2  h  t  Ho  -19 -18 -17 -16 -15 -14 -13  20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 24 24 24 24 24  3.3 41.7 41.8 42.0 8.2 4 2.1 42.1 3.9 2.3 4.5 3.9 2.3 2.2 5.3 42.1 2.1 42.0 1.8 3.8 4 1.4 41.2 4.4 41.6 <1.7 4.0 41.8 41.9 3.3 41.9 41.9 41.9 3.1 41.7 <1.6 41.4 5.3 40.9 41.2 5.2 41.2 2.5 <1.1  -ia -ii  -IQ - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 -13 -12 -11 -10 - 9  He _  -  -  -  -  -  -  2.9 0.8 1.7 1.9 7.1 1.6 1.6 2.7 1.5 3.4 3.6 0.6 1.5 3.8 0.6 0.7 0.5 1.2 3.1 0.7 2.2 4.3 1.7 0.6 3.2 0.7 0.8 2.6 X Q2 0.4 0.0 3.4 0.2 1.2 1.1 3.8 2.1 0.2 4.9 1.0 2.9 0.2  - 127 -  Table A-g.  h L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 i 2 3 4 5 6 7 8 9 10 11  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  2c 148.0 -148.9 19.5 15.4 18.6 20.9 68.1 69.6 10.8 6.3 20.5 20.9 4.8 5.9 2.8 3.1 2.6 4.8 £1.4 2.4 4.4 5.9 22.0 20.0 15.0 15.3 6.2 — 7.3 0..4 0.3 £1.3 2.3 6.4 6.9 £0.7 0.4 2.2 3.1 1.8 £1.2 2.1 £1.3 3.8 2.5 2.0 3.1 6.1 7.9 8.8 6.2 £1.4 2.9 16.3 17.9 2.9 4.3 18.6 20.5 0.6 7.3 14.8 14.4 41.6 39.4 22.3 20.5 45.2 42.1 120.8 84.7 34.8 34.4 46.8 47.8 17.4 13.5 70.7 67.1 21.8 20.1 1.6 0.3 20.2 17.5 22.1 23.7 16.8 16.7 1.6 — 3.3 6.1 6.2 2.1 £1.4 2.1 2.4  -  -  -  -  -  -  -  -  -  -  -  l  k 12 13 14 15 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7  cis-1,2-Acenaphthenediol Dinitrate hit  k  So  2  1  5.7 3.4 6.0 ^1.3 <1.2 5.6 6.3 £1.5 15.3 4.7 2.4 3.7 4.2 20.3 £1.0 5.1 21.9 32.1 121.0 83.7 23.9 37.2 2.4 67.3 42.9 36.5 10.1 19.1 2.9 £1.3 11.2 2.1 5.7 1.9 6.7 2.8 3.6 2.4 £0.7 £1.5 2.7 2.1 6.8 10.5 2.2 7.7 13.0 21.3  7.1 4.2 - 6.0 - 0.2 - 0.7 5.5 5.7 1.4 -15.9 5.4 - 2.0 - 7.3 - 8.1 19.9 0.6 - 5.6 -23.8 -35.1 87.6 70.8 -23.1 -35.2 - 3.8 -65.9 45.4  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 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3  h  C  -30.5  11.8 16.6 1.0 - 1.6 -11.7 - 1.9 6.8 1.2 5.0 - 2.2 - 5.1 3.9 - 1.6 - 1.1 5.0 1.0 - 9.5 - 8.9 0.9 - 8.1 8.9 22.0  -  6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5  Z  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 4 4 4 6 4 7 4 8 4 9 4  2o  2c  5.0 58.4 43.2 61.4 125.2  6.9 57.2 40.1 -49.9 -90.5 -33.9 31.9 -37.4 - 5.6 7.0 -11.1 34.6 20.1 1.4 12.0 10.3 - 9.0 ^•17.8 - 3.2 - 0.5 -<3.5 3.6 - 1.4 - 3.3 0.9 8.0 - 1.2 0.3 - 1.9 -15.0 29.0 ii.9 5.2 -32.8 -28.8 -17.3 39.0 - 8.9 51.7 -46.6 24.7 -22.5 -42.9 49.0 2.0 6.1 - 3.3 -22.0  30.8 33.3 39.9 6.7 5.4 8.6 36.5 19.1 £1.2 7.4 8.3 9.1 19.3 £1.5 £1.0 2.3 £1.4 <1.5 2.2 £1.5 5.6 4.5 £1.3 3.1 14.9 35.4 7.5 2.8 36.7 33.6 22.0 38.0 9.0 56.2 50.9 28.8 30.9 47.6 49.3 £1.2 7.6 3.5 20.4  h 10 11 12 13 14 15 16 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -16 -15 -14 -13 -12 -11  Z  p  12.4 11.1 4.5 £1.4 1.5 2.5 £0.6 <1.0 2.2 £1.4 £1.5 2.7 <1.5 4.7 £1.4 5 32.8 9.0 5 5 27.5 5.1 5 5 19.7 5 48.5 5 5.1 5 13.6 5 35.8 5 40.3 2.2 5 5, 11.8 5, 8.1 5 32;8 6.5 5 5 2.5 9.1 5 2.7 5 8.8 5 5 11.3 5 11.0 5 £1.5 2.6 5 5 £1.4 5 £1.3 1.6 5 £ 0 .8 5 6 <1.5 6 5.3 6, 2.1 6 8.9 8.0 i 14.2  4 4 4 4 4 4 4 5 5 5 5 5 5 5 5  2c 11.4 12.4 - 6.2 6.8 - 6.3. 3.2 0.0 - 0.6 2.0 4.1 1.0 - 3.2 - 0.3 -10.1 - 4.1 28.6 -11.1 -23.2 - 7.5 -17.7 48.5 10.5 - 8.7 33.8 -40.7 - 2.2 -11.3 - 8.6 35.8 4.8 1.0 -11.1 2.0 12.6 -10.8 -12.4 - 0.5 3.0 0.7 2.7 2.1 - 1.6 - 1.0 5.2 2.4 10.3 7.9 -14.9  - 128  h  I  Ho  2c  -10 6 22.7 -24.9 - 9 6 26.7 25.3  -  8 7 6 5 4 3 2  - 1  0 1 2 3 4 5 6 7 8  9 10 11  12 13  14 15  -19  -18 -17 -16  -15 -14 -13 -12  -11  -10 - 9 -  8 7 6 5 4 3 2 1 0 1 2  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  19.2 -22.7 16.3 14.3 44.4 -40.7  29.7 -25.2 43.8 43.5 31.1 29.0 11.4 12.5 30.1 26.1 7.0 - 8.2 7.9 1.7 34.3 -28.3 19.6 -53.1  43.8 35.2 13.2 -11.4  8.3 9.7 18.2 -19.1 4 1.5 - 4.6  13.1  <1.5 41.5 41.3  12.2 1.0  41.1 14.1 23.0  0.4 1.6 - 2.0 1.4 - 2.4 - 1.4 - 3.5 0.4 9.1 - 3.7 - 4.9 - 0.9 - 0.7 2.3 - 2.9 - 0.3 -11.1 17.8  13.8  17.1  41.2  1.6 40.4 41.2 3.8  41.4  6.4  2.9  2.3 41.5 41.4  1.9 1.7  27.6  31.2 35.3 -28.2  32.4 29.3 30.2 -21.5  7.1 -11.6  13.4 -11.2  9.5 - 9*9 2.3 - 1.1  h  3 4 5 6 7 8 9 10 11 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 11 12 -19 -18 -17 -16 -15 -14  e  2o  7 1.7 7 6.6 7 2.4 7 5.7 7 10.9 7 5.5 7 2.2 7 41.5 7 41.4 8 41.0 8 4.2 8 5.4 8 4.2 8 7.2 8 41.5 8 41.5 8 3.9 8 17.5 8 3.0 8 23.0 8 9.1 8 24.3 8 16.1 8 8*7 8 37.9 8 22.1 8 8.8 8 5.8 8 4.1 8 9.0 8 12.9 8 34.8 8 41.3 8 5.3 8 2.9 8 7.7 8 4.1 8 41.5 8 41.5 8 <1.4 8 2.2 8 1.8 9 41.2 9 1.7 9 3.6 9 41.5 9 41.5 9 3.7  j?  —c  0.7 - 9.5 - 4.5 5.2 13.0 7.0 - 3.3 0.4 - 0.1 - 2.4 - 4.8 6.8 - 5.9 ! 8.2 1.4 - 1.2 - 1.5 -17.5 - 4.3 22.2 -10.7 21.1 -15.3 -10.6 35.1 -18.7 7.6 9.4 0.0 -12.4 12.9 -31.5 1.0 - 4.9 5.3 10.8 4.8 - 1.5 - 1.9 - 1.1 0.7 - 0.2 - 0.6 2.9 6.3 Q.4 2.2 3.0  h  1  p £.0  -13 9 9.2 -12 9 41.4 -11 9 19.4 -10 9 5.6 - 9 9 6.7 - 8 9 11.5 - 7 9 9.0 - 6 9 16.4 - 5 9 53.2 - 4 9 37.0 - 3 9 7.7 - 2 9 9.3 - 1 9 45.1 0 9 41.2 1 9 18*0 2 9 41.3 3 9 2.4 4 9 3.5 5 9 11.5 6 9 2.4 7 9 41.5 8 9 41.5 9 9 2.0 10 9 41.3 11 9 2.0 12 9 4 0.9 ^21 10 4 0.8 -20 10 2.0 -19 10 2.2 -18 10 3.9 -17 10 4.2 -16 10 3.1 -15 10 4.9 -14 10 4.3 -13 10 6.2 -12 10 2.5 -11 10 2.7 -10 10 41.3 - 9 10 1.8 - 8 10 4.8 - 7 10 13.1 - 6 10 41.1 - 5 10 3.6 - 4 10 11.7 - 3 10 22.3 - 2 10 <1.2 - 1 10 13.8 0 lb 13.7  2c  6.9 - 5.6 -21.0 7.0 - 5.7 -11.8 - 7.8 -13.9 50.8 29.9 - 6.4 - 7.3 -42.7 - 0.8 17.2 0.9 - 4.9 3.4 9.8 - 5.2 - 0.3 3.4 - 1.4 1.3 - 2.1 - 3.9 - 0.7 - 1.9 2.4 - 4.1 3.6 - 2.7 - 4.0 5.8 9.1 1*6 - 3.6 1.0 - ,4.3 3.4 -13.5 2.6 - 9.1 13.4 -22.8 4.1 13.0 16.9 1  h  Z  P  Zc  1 10 10.8 -11.5  2 10 2.2 3 10 41.4 4 10 5.0 5 10 3.1 6 10 8.8 7 10 3.7 8 10 41.4 9 10 2.6 10 10 41.1 11 10 1.3 -19 11 41.2 -18 11 3.9 -17 U 1.9 -16 11 4 1.5 -15 11 41.5 -14 11 24.2 -13 11 41.5 -12 11 2.7 -11 2.9 -10 i i 5.9 - 9 ii 7.4 - 8 ii 9.2 - 7 i i 13.2 - 6 ii 3.7 - 5 i i 22.4 - 4 ii 3.9 - 3 ii 8.2 - 2 i i 41.3 - 1 i i 17.6 0 ii 1.9 1 ii 2.4 2 ii 6.2 3u 5.2 4 ii 6.1 5 n 41.5 6 n 41.5 7n 2.5 8 n <1.3 -21 12 3.1 -20 12 4.1 -19 12 41.2 -18 12 41.4 -17 12 41.5 -16 & 6.4 -15 12 23.4 -14 12 4.9 -13 12 8.2  - 3.3 0.6 6.4 6.6 - 7.5 - 4.6 - 2.3 3.4 - 1.4  1.9  1.6 4*8  - 2.1 5.2 1.2 -19.0 - 1.4 - 5.1 - 8.3 9.4 8.0 11.4 - 8*8 4.5 24.7 - 6.6 9.0 - 2.0 -20.5 - 0.7 - 5.7 - 8.0 6.6 4.4 1.0 3.4 - 3.0 0*2 - 3.3 4.8 - 3.0 - 0.1 - 1.6 - 6.1 23.3 - 6.1 -13.5  -  h  £  -12 12 -11 12 -10 12 - 9 12 - 8 12 - 7 12 - 6 12 - 5 12 - 4 12 - 3 12 - 2 12 - 1 12 0 12 1 12 2 12 3 12 4 12 5 12 6 12 7 12 8 12 9 12 -19 13 -18 13 -17 13 -16 13 -15 13 -14 13 -13 13 -12 13 -11 13 -10 13 - 9 13 - 8 13 - 7 13 - 6 13 - 5 13 - 4 13 - 3 13 - 2 13 - 1 13 0 13 1 13 2 13 3 13 4 13 5 13 6 13 7 13  F 2.9 1.8  13.9 5.4 23.0 3.2 5.4 6.6 5.8 21.1 20.6 7.6 2.0 14.4 £1.5 6.1 £1.5 6.4 <1.4 £ 1.3 2.4 <1.0 £1.2 6,7 5.8 £1.5 £1.5 9.3 6.4 <1.5 17.7 2.2 4.7 <1.4 1.9 <1.4 1*9 <1.4 5.6 7.8 3.6 20.0 <1.5 6.9 3.1 2.1 < 1.4 <1.3 <1.2  £c - 1.3 0.3 13.5 7.6 -26.5 2.5 - 8,6 9.1 - 8.3  19.6 22.8 - 9.8 - 1.3 -15.7 - 0.9 6.0 - 0.8 - 5.3 1.2 - 0.5 2.6 - 0.0 - 0.8 - 6.3 - 3.7 5.6 6.2 11.0 - 8.6 - 5.8 15.5 - 5.1 - 4.7 - 0.0 - 3.6 0.2 - 3.3 0.3 - 7.1 9.8 6.7 -16.6 2.3 9.7 3.5 - 2.7 - 3.0 - 0.6 - 0.9  h  £  8 -20 -19 -18 -17 -16 -15 -14  13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15  -13 -12  -11  -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1  to  ,2  129  C  3.8 3.7 £ 1 . 0 - 1.3 4.3 - 4.9 2.3 - 4.3 6.2 2.5 8.4 11.5 8.4 - 8.1 5.0 5.3 -10.2 8.4 2.3 3.5 8.8 9.6 6.9 - 6.9 0.1 £1.4 5.3 - 4.4 <1.4 2.4 2.5 4.5 8.3 - 8.7 7.8 10.5 2.1 2.5 2.3 - 7.0 16.0 13.9 22.2 -17.5 6.0 5.3 3.1 3.3 2.1 - 4.2 2.0 2.4 0.8 1.9 £ 1 . 2 - 0.1 3.2 4.3 2.1 - 2.5 <1.2 - 0.6 7.6 6.4 4.5 5.3 4.7 . - 3.1 2.4 5.8 £ 1 . 5 - 0.7 5.3 - 6.7 1.9 3.1 11.7 -15.4 <1.5 - 4.4 7.6 5.1 5.7 - 7.2 £ 1 . 5 - 0.6 2.1 0.9 6.0 9.6 13.8 17.9 2.1 3.7 2.2 - 4.1 3.1 - 4.5  h  I  0 1 2 3 4 5 6 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 P -20 -19 -18 -17 ^16 -15 -14 -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0  15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17  2  0  1.9 2.1 <1.5 2.8 3.2 1.6 <1.0 £1.0 4.3 <1.3 <1.4  £1.4 £1.5 5.0 <1.5 8.2 6.1 <1.5 £1.5 £1.5 2.6 7.8 13.1 14.1 11.2 2.7 10.3 <1.5 3.5 4.4 £1.2 £1.3 <1.4 £1.5£1.5 £1.5 4.9 £1.5 5.5 2.2 11.9 11.9 11.9 7.9 2.2 £1.5 2.1 £1.4 4.4  2c - 0.9 - 5.9 - 4*5 1.8 0.6 0.2 1.7 - 2.4 2.4 - 1.7 2.2 0.8 - 1.1 - 4.5 - 0.4 9.7 - 6.9 - 2.5 2.7 1.8 2.3 - 5.6 -15.5  14.3 7.8 5.4 - 9.3 - 3.3 3.9 - 3.1 - 1.1 1.6 - 0.8 1.6 - 1.6 - 1.1 - 6.0 0.6 5.7 - 3.5 10.5 11.1 - 6.7 - 5.9 - 0.5 - 0.9 - 2.7 0.6 - 3.5  h  Z  1 17 2 ,17 3 17 4 17 5 17 -20 18 -19 18 -18 ,18 -17 18 -16 18 -15 18 -14 18 -13 18 -12 18 -11 18 -10 18 - 9 18 - 8 18 - 7 18 - 6 18 - 5 18 - 4 18 - 3 18 - 2 18 - 1 18 0 18 1 18 2 18 3 18 -18 19 -14 19 - 8 19 - 6 19 - 5 19 - 3 19 - 2 19 - 1 19 -13 20 - 8 20 -17 21 -15 21 -14 21 -11 21 - 9 21 -13 22 -10 22 - 7 22 - 9 23 - 7 23  II  —  Q  £1.3 <1.2 2.2 1.5 1.3 2.7 2.5 £1.2 <1.3 £1*5' £1.4 £1.4 4.2 16.9 7.7 2.6 6.5 6.1 25.1 2.3 8.7 £1.5 7.9 4.9 £1.3 2.5 4.9 2.9 2.3 1.9 4.0 6.3 3.6 3.5 3.6 3.1 1.7 2.7 4.4 3.1 4.3 2.4 5.1 5.1 3.2 7.9 1.5 1.6 2.0  F - 1.1 3.2 - 0.8 2.7 1.8 - 3.9 - 3.7 1.3 0.7 1.6 0.4 2.0 4.7 -15.6 7.4 4.6 5.8 6.0 -19.1 - 5.0 10.6 - 2.8 6.1 - 3.8 - 0.8 4.6 - 5.0 2.8 - 2.3 - 2.1 3.3 - 5.7 4.7 - 2.7 3.2 2.8 - 0.0 - 3.6 - 3.9 3.8 - 4.7 2.0 - 4.0 3.5 - 2,8 5.6 - 1.4 1.8 - 1.9  APPENDIX. I I CRYSTALLOGRAPHIC DATA^ FOR SEVERAL ORGANIC COMPOUNDS  - 131 -  trans-l,2-Acenaphthenediol C r y s t a l s obtained by c r y s t a l l i z a t i o n from aqueous methanol are t h i n c o l o u r l e s s p l a t e s p a r a l l e l to (OOl) and bounded by (lOO) and. ('010). C r y s t a l Data trans-l,2-Acenaphthenediol, C H 8 ( 0 H ) 1 2  2  ; M=l86.20;.m.p. • l 6 0 . 0 - I 6 3 . 0 ° C .  Orthorhombic, a=ll.37+0.02, b=ll.37+0.02,. c=28.9^+0.03A. D ( w i t h Z=l6) = 1.322, 0 = 1 , 2 9 gm.cm"? x  F(000)=1568.  U=37l+lft . 3  Absent spectra: hkl  when h+k i s odd, hOt when L i s odd, hhO when h i s odd. •A p o s s i b l e space 17 group i s Cmcm-D^ provided the l a s t c o n d i t i o n f o r systematic absences i s regarded as a c c i d e n t a l . The t e n t a t i v e space group assignment t o trans-l.)2-acenaphthenediol requires .some comment.  Weissenberg and precession phtotgraphs were taken,  with CuK^ and MoK^ r a d i a t i o n s r e s p e c t i v e l y , of a c r y s t a l mounted about the c-axis.  Since the hkO and h k l f i l m s displayed p e r f e c t tetragonal symmetry, a  p r i m i t i v e tetragonal l a t t i c e with a=b=8.0l+ft was chosen i n i t i a l l y . Systematic absences were hh(L- f o r & odd,. hOO f o r h.odd,. and OkO f o r k odd.  However,, i t  was soon discovered that l(hh£, )^l(hh-C ) so that the c r y s t a l system could not be tetragonal.  Accordingly, the photographs were indexed i n terms, of a  centered orthorhombic l a t t i c e with a=b = ^2'x 8.01+2= 11.37ft. I t i s p o s s i b l e to v i s u a l i z e the general arrangement of.molecules - i n the u n i t c e l l , . although an accurate a n a l y s i s w i l l probably prove t o be d i f f i c u l t . In the c r y s t a l the arrangement of the carbon skeleton must conform c l o s e l y to tetragonal symmetry, the small deviations, being due t o the presence of the hydroxyl groups.  An i d e a l i s e d . s t r u c t u r e can be obtained i n the f o l l o w i n g way.  Since the c-axis is. 28.9I+A' long,. i t has enough . room to accommodate a.set of four molecules stacked on top o f one another.  The sixteen molecules • i n ..the  u n i t c e l l may be d i v i d e d i n t o four such sets, each l y i n g .on a .screw.axis  - 132 p a r a l l e l t o the c-axis and midway between m i r r o r planes.  The molecules have  t h e i r molecular planes (planes containing carbon atoms) on ^220} so that p e r f e c t tetragonal symmetry i s achieved i n the [oGl] p r o j e c t i o n .  In such an  arrangement the structure w i l l only be s l i g h t l y d i f f e r e n t when viewed along the  TlOO] and [blOj d i r e c t i o n s .  This explains rather w e l l the f a c t that the  0k£. and ho£- precession f i l m s bear a s t r i k i n g resemblance. trans-l,2-Acenaphthenediol D i n i t r a t e C r y s t a l s obtained from heptane s o l u t i o n are transparent p l a t e s p a r a l l e l to (010).  Other faces such as (lOO) and (110) are also w e l l developed.  C r y s t a l Data trans-l,2-Acenaphthenediol d i n i t r a t e , C Hg(CH0N0 ) ;"M=276.20, 10  m.p. 98.O-99. 5°C. f3 =113°lV+5' .  2  2  Monoclinic, a=10. 56+O. 03, b=7.77+0.02, C=7.85+0.02A',  U=591-9A.  D ( w i t h Z=2)=1.550, D =1.53 gm.cm . F(000)=28U. x  2  .  Absent spectra: OkO when k i s odd. Space groups i s P2-]_-C • (The p o s s i b l e 2  space group T?2.-Jm i s r u l e d out because i t requires the molecule t o have symmetry m o r l ) . p-Chloroaniline C r y s t a l s of p - c h l o r o a n i l i n e (Eastman Kodak), obtained by slow c r y s t a l l i s a t i o n from aqueous ethanol, are sand-coloured octahedra bounded by ( i l l ) • They are h i g h l y v o l a t i l e and must be sealed i n Lindemann-glass c a p i l l i a r i e s f o r measurements l a s t i n g a day or longer. C r y s t a l Data p - C h l o r o a n i l i n e , CL CgH^NHg ; M=127-57; m.p.71°C +0.01, b=9.26+0.01, c=7.39+0.01A. U=592.6A . 3  D ( w i t h Z=4)=1.U27, x  Absent spectra: 0k£ when k+£ i s odd, hot when 9 16 Space group,is e i t h e r Pna2i-C2v or Pnam-D2h'  D =1.1+3 gm.cm". F(000)=2l+8. 3  h i s odd.  Orthorhombic, a=8.66  - 133 N,N-Dimethyl-p-nitroaniline C r y s t a l s o f N,N-dimethyl-p-nitroaniline (Eastman Kodak) grown from ethanol s o l u t i o n are yellow prisms with the (lOO) and (010) faces w e l l developed. C r y s t a l Data N,N-Dimethyl-p-nitroaniline, (CHg^NCgH^NC^ ;'M=l66.l8; m.p. l 6 3 ° C Monoclinic, a=9.73+0.01, b=10.56+O.01, c=3-96U+O.OO5X, p> =91°28*+5 . 1  U=l+07.2& . 3  D ( w i t h Z=2)=l-355> m ' 3 3 gm.cmT D  F(000)=176.  3  = 1  x  2  .  Absent spectra: 2  OkO when k i s odd. Space group may be e i t h e r P2-j_-C2 or P2!/m-C2h • A p r e l i m i n a r y i n v e s t i g a t i o n o f the c r y s t a l s t r u c t u r e (93) has e s t a b l i s h e d the c o r r e c t space group as P2i/m, which requires that the molecule possesses a m i r r o r plane o f symmetry perpendicular t o the plane of the benzene r i n g . A c l e a r l y resolved e l e c t r o n - d e n s i t y p r o j e c t i o n along the short c-axis shows that the molecule ( n e g l e c t i n g the hydrogen atoms o f the methyl groups) probably has symmetry mm2-C2y Naphtho I b^ cyclobutene (9U) C r y s t a l s grown from ethanol s o l u t i o n by slow evaporation occur as transparent p l a t e s , the p r i n c i p a l face being (lOO); twinning on (lOO) i s common.  The-crystals are h i g h l y v o l a t i l e - a n d slowly turn milky on exposure  to a i r , presumably due t o surface decomposition.  The high-angle  reflexions  were a l l too weak t o be recorded on Weissenberg photographs,•and t h i s i n d i c a t e s unusually large-thermal v i b r a t i o n s of the atoms i n the c r y s t a l . C r y s t a l Data Naphtho [ b ] cyclobutene, C  1 2  % 0 ' M=15^.20; , m.p. 8^.5-86°C.  a=l8.0U+0.02, b=5.91+0.01, c=8.13+p.01A, / 3 = 9 2 0 ' + 6 ' . o  = l . l 8 l , 1^=1.19 gm.cm"  3  h0&  F(000)=328.  Monoclinic,  U=866-3A . 3  D ( w i t h Z=U) x  Absent s p e c t r a : h k ^ when h+k i s odd,  ^ when -t i s odd. Space group i s Cd-C . g  6 (The p o s s i b l e space group C2/c-C2^  - 13U -  i s excluded since i t requires the two-fold symmetry a x i s of the molecule (length ~ 6.3°0 t o he p a r a l l e l t o the b c r y s t a l a x i s ) . Benzocyclobutadienoquinone C r y s t a l s obtained from n-propanol  (95)  s o l u t i o n are yellow prisms bounded  by ( l 0 0 \ . The {lio} faces are also w e l l developed.  The c r y s t a l s slowly  decompose i n t o a powder on prolonged exposure t o X-rays. C r y s t a l Data Benzocyclobutadienoquinone, CgHi (C0) ; M=132.11 ; m.p. 132.5°C. |  2  Orthorhombic, a=10.72+0.01, b=7.94+0.01, c=7-15+0.Oli. U=608.6& . 3  D ( w i t h Z=4)=1.442, Dm=lA5 gm- cmT x  3  F(000)=272.  Absent spectra: h O l when 5  11  ,h i s odd, 0k£ when t i s odd. Space group,is Pca2]_-C2 or Pcam-Dgft. v  cis-1,2-Benzocyclobutenedior D i n i t r a t e (95) C r y s t a l s grown from a benzene/petroleum ether mixture are transparent prisms elongated along the a-axis, with the (010) and (OOl) faces w e l l developed. C r y s t a l Data cis-1,2-Benzocyclobutenediol d i n i t r a t e , C6H^(CH0N0 ) ; M=226.l4; 2  c=8.14+0.01A, jS =98°2'+5 .  m.p.110 C.  M o n o c l i n i c , a=7-41+0.01,  U=938.3A .  D ( w i t h Z=4)=1.601, Dm=1.57 gm.cm"? F(000)=464.  3  hOc-  x  b=15.71+0.02,  2  1  Absent spectra: 5  when h+C, i s odd, OkO when k i s odd. Space group i s P2i/n-C ^. 2  REFERENCES  -  136  -  1.  I n t e r n a t i o n a l Tables f o r X-r.ay Crystallography. V o l . 1 , 1952; V o l . 1 1 , 1959; V o l . I l l , 1962. Kynoch Press, Birmingham.  2.  A.J.C. Wilson, Acta Cryst. 2, 318 (19^9); E.R. Howells, D.C. P h i l l i p s and D. Rogers, i b i d . 3, 210 (1950).  3.  M.J. Buerger, "X-Ray Crystallography". Wiley,-New York, 19^2; " C r y s t a l - S t r u c t u r e A n a l y s i s " . Wiley, New York, I96O; N.F.M. Henry, H. Lipson and W.A. Wooster, "The I n t e r p r e t a t i o n of X-ray D i f f r a c t i o n Photographs", Second E d i t i o n . Macitiillan, London, i 9 6 0 .  k.  H. Lipson and W. Cochran, "The Determination o f C r y s t a l Structures", p.ll+7. B e l l , London, 1957.  5.  J.M. Robertson, J.Chem.Soc, 615 (1935); H95 (1936); J.M. Robertson and I. Woodward, i b i d . , 219 (1937)-  6.  A.L. Patterson, Phys.Rev. k6, 372 (l93h);  7.  M.J. Buerger, "Vector Space and I t s A p p l i c a t i o n i n C r y s t a l - S t r u c t u r e Investigation".  Z. K r i s t .  £0, 517  Wiley, • New York, 1959-  8.  D. Harker and J.S. Kasper, Acta Cryst.  1,  9.  J . Karle and H. Hauptmann, Acta Cryst.  3_, l 8 l (1950);  ibid.  (1935)-  70 (19U8).  J.A. Goedkoop,  3, 37^ (1950).  10.  D. Sayre, Acta Cryst.  11.  W. Cochran, Acta Cryst.  12.  W.H. Zachariasen, Acta Cryst. 5_, 68 (1952). H. Hauptmann and J . K a r l e , " S o l u t i o n of the Phase Problem. I. The Centrosymmetric C r y s t a l " , Am.Cryst.Assoc.Monograph No.3- Edwards, Ann Arbor, 1953; J- Karle and H. Hauptmann, Acta Cryst. %  13-  635  5, 60 (1952). _5, 65  (1952).  (1956).  lU.  A.D. Booth, Trans.Faraday Soc. k2,.hkk,  15.  A.D. Booth, Nature 156, 51 (19U5); J . Donohue, J. Am.Chem.Soc. 9h9  617 (19U6). 72,  (1950).  16.  E.W. Hughes, J.Am.Chem.Soc. 63, 1737 ( l 9 ^ l ) -  17.  A.D. Booth, Nature l 6 l , 765 (19U8).  18.  W. Cochran, Acta Cryst.  19.  C J . B . Clews and W. Cochran, Acta Cryst. 2, h6 (19U9); W. Cochran and H.B. Dyer, i b i d . 5, 63k (1952). M.G. Rossmann and H.M.M. Shearer, Acta Cryst. -11, 829 (1958).  20.  h, kOQ ( l 9 5 l ) .  - 137  -  21.  D.W.J. Cruickshank, Acta Cryst.  22.  S. von Niementowski, Ber.  23.  W. Baker, J.Chem.Soc, 258 (19U5); W. Baker and J.F.W. McOmie i n "Chemical Society Symposia B r i s t o l 1958". S p e c i a l Publ. No.12. The Chemical Society, London, 1958; i n "Non-Benzenoid Aromatic Compounds". Interscience, New York, 1959-  2k.  W.C. Lothrop, J.Am.Chem.Soc.  25.  W. Baker, M.P.V. Boarland and J.F.W. McOmie, J.Chem.Soc, IU76 (19 5*0; J. C o l l e t t e , D. McGreer, R. Crawford, F. Chubb.and R.B. Sandin, J.Am.Chem.Soc. 78, 3819 (1956).  26.  W.S. Rapson andR.G. Shuttleworth, J.Chem.Soc, U87 (19U1); W.S. Rapson, R.G. Shuttleworth and J.N. van Niekerk, i b i d . , 326 (19U3); G. W i t t i g and W. Herwig, Ber. , 8 7 , 1511 (195*0; G. W i t t i g and L. Pohmer, i b i d . 89, I33U (1956).  27.  W. Baker, Nature 15_0, 210 (19^2).  28.  C A . Coulson, Nature 150, 577 (19^2).  29.  J . Waser and V. Schomaker, J. Am.Chem. Soc.  30.  J . Waser and C.-S. Lu, J. Am.Chem.Soc.  31.  W. Baker, M.P.V. Boarland and J.F.W. McOmie, J.Chem.Soc, IU76 (195I+); W. Baker, J.W. Barton and J.F.W. McOmie, i b i d . , 2666, 2685 (1956).  32.  R.D. Brown, Trans. Faraday S o c  33-  J . I - Fernandez Alonso and R. Domingo, • Anales r e a l s o c e s p a n . f i s . y quim. (Madrid) 50B, 253 (195*0; 51B, - ^ 7 (1955)-  3k.  E.P. Carr, L.W. P i c k e t t and D. V o r i s , J.Am.Chem.Soc  35.  J . Chatt, R.G. Guy and H.R. Watson, J.Chem.Soc, 2332 (1961).  36.  H.C. Longuet-Higgins, Proc.Chem.Soc, 157  37-  W. Baker, J.F.W. McOmie, D.R. Preston and V. Rogers, J.Chem.Soc, klk  2, 65  (19U9).  3J+, 3331 (1901).  63,-1187  (19I+I).  6_5_, ll+51 (19U3).  66, 2035' ( 1 9 W ) .  U6, lU6  (1950).  63, 3231  (19U1).  (1957).  (i960).  38.  H.R". Bosshard and Hch. Z o l l i n g e r , Helv.Chim.Acta kk,  39-  J . J . deLunge, J.M. Robertson and I. Woodward, Proc.Roy.Soc. 171A, 398 (1939); J-M. Robertson, J . S c i . I n s t r . 20, 175 (19^3); J . I b a l l , i b i d . 31, 71 (195*0 •  kO.  J . Berghius, I J . M. Haanappel, M. P o t t e r s , B.O. Loopstra, C.H. MacGillavry and A.L. Veenendaal, Acta Cryst. 8, U78 (1955).  1985.(1961).  - 138  -  hi.  L. P a u l i n g , "The Nature of the Chemical Bond", p.171. Press, Ithaca, 1948.  42.  C.A.  Coulson i n the "V. Henri Memorial Volume".  43.  H.N.  Shrivastava and J.C. Speakman, Proc.Roy.Soc  44.  A. A l i and C.A.  45-  W.  46.  W. Manchot, Ber. 53,  47.  W.  48.  N.V.  Coulson, Tetrahedron 10,  S c h o e l l e r , W.  4l  S c h o e l l e r , 53B,  2144  Dosoer, • Liege, 19*1-8. 257A, 477  (i960).  (i960).  Schrauth and W. Essers, Ber. 46, 984  Cornell University  2864 ( l 9 1 3 ) »  (1920). (1920); W.  Manchot, i b i d .  54B,  571  (l92l).  Sidgwick, "Chemical Elements and Their Compounds", V o l . 1 ,  p.306.  Oxford U n i v e r s i t y Press, London,> 1950. 49.  J . Halpern and S.F.A. K e t t l e , Chem. and Ind., 668  (1961).  50.  K. Sagel, "Tabellen zur Rontgenstrukturanalyse".  Springer, Berlin,,1958-  51. 52.  "Tables of Interatomic Distances and Configurations i n Molecules and Ions". S p e c i a l Publ. No.11. The Chemical Society,• London,,1958. H. Braekken.and C.A.W. Schol'ten, Z. K r i s t . 89, 448 (193*0; A.F. Wells, " S t r u c t u r a l Inorganic Chemistry", pp.119, 632. Oxford U n i v e r s i t y Press, London, 1950.  53.  J . Toussaint, Mem.Soc.Sci.Liege  12,  (3),  1  (1952); Structure  Reports,  1 6 , . 5 1 7 (1952), Utrecht i Oosthoek. 54.  P.R.  Pinnock, C.A.  55.  S.B.  Hendricks, Z. K r i s t .  56.  0.  57-  M. B e r t h e l o t , Jahresber., 594  58.  I.U.P.A.C.  Hassel and E.H.  1957  Taylor and H. Lipson, Acta Cryst. 9_, 173 84,.85 (1933).  Vihovde, Acta Chem.Scand.  Rules.  (1956).  7,,1164  (1953).  (1867).  "Nomenclature of Organic Chemistry 1957".  Butter-worths, London, 195859.  M. B e r t h e l o t , Bull.soc.chim.  9,  265  (l868).  60.  M. B e r t h e l o t , Bull.soc.chim.  l8,  11  (1872).  61.  C  62.  C. Graebe, Ber. 5, 15 ( 1 8 7 2 ) ; , i b i d . 20, 237 (1887); C Graebe and J . Jequire,-Ann. 290, 195, 205 IT896); C. Graebe, i b i d . 32J_, 77 (19O3). D.A. Hahn and H.E. Holmes, Ind.Eng.Chem. 13, 822 ( l 9 2 l ) .  Graebe, Ber. 20, 652  63.  657  (1887); C  (1892); Ann.•276, 1  Graebe and E. G f e l l e r , Ber.  25,  (1893).  - 139  -  6h.  I.G-. Csizmadia, M.Sc. Thesis, Univ. of B r i t . Col. , , 1 9 5 9 ; and L.D. Hay-ward. To he published i n Tetrahedron.  65.  W.H.  66.  E. H e r t e l and H. Kleu, Z.Phys.Chem. B l l , 59 (1930).  67.  K. Banerjee-and K.L. Sinha, Ind.J.Phys. 11,  68.  A.I. K i t a i g o r o d s k i i , Zhur.Fiz.Khim. 21,, IO85 (19I+7).  69.  A.I. K i t a i g o r o d s k i i , Izv.Akad.Nauk S.S.S.R.,•Otdel.Khim.Nauk, 278  70.  A.I. K i t a i g o r o d s k i i , , Zhur.Fiz.Khim. 23,  71.  H.W.W. E h r l i c h , Acta Cryst. 10,  72.  D.W.J. Cruickshank, Acta, Cryst. 10,  73.  R.L. Avoyan and Yu. T. Struchkov, Zhur.Strukt.Khimi 2, 719  7I+.  G.L.  Simmons and E.C. L i n g a f e l t e r , Acta Cryst. 1J+, 872  75.  E.W.  E h r l i c h and C A .  76.  J . I b a l l and S.G.G. MacDonald, Z. K r i s t . Ilk,  77.  J.D. Dunitz and L. Weissman, - Acta Cryst. 2, , 62 (19I+9).  78.  R.L. Avoyan and Yu. T. Struchkov,-Zhur.Strukt.Khimi 3_, 99 (1962).  79.  M.J. Buerger, E. Barney and T. Hahn, Z. K r i s t . 108,,130 (1956).  80.  G.L.  81.  J . T r o t t e r , Acta Cryst.  82.  E.J. M o r i c o n i , W.F. O'Connor, L.P. Kuhn, E.A. Keneally and F.T. J.Am.Chem.Soc. 8 l , 61+72 (1959)-  83.  J . Donohue, J.Chem;Phys. 56, 502 (1952); G.C. Pimentel and A. L. McClleland, "The Hydjrogen Bond", p.265Freeman, • San Francisco, ,1960; L. Pauling,•"The Nature of the Chemical*Bond", P.U53. C o r n e l l U n i v e r s i t y Press, Ithaca, i 9 6 0 .  81+.  G.C.  85.  R. Hulme, Chem.& Ind., 1+2 (1962).  86.  J.S. Hetman, Talanta 5, 267  87.  A.D.  Bragg, Proc.Phys.Soc. London 3j+,  699  33  Csizmadia  (l92l).  21  (1937).  (19I+8).  IO36 (19U9).  (1957) •  50I+ (1957)-  (1961).  (1961).  Beevers, Acta Cryst. 9, 602 (1956). 1+39  (i960).  Hardgrove, Thesis, U n i v e r s i t y of C a l i f o r n i a , Berkeley (1959); G.L. Hardgrove and D.H. Templeton, Programs and Abstracts, Am.Cryst.Assoc.Annual Meeting, 1961. 13,  86  (i960).  Pimentel and A. L. McClelland, "The Hydrogen Bond", p. 271. Freeman, San F r a n c i s c o , , i 9 6 0 .  (i960).  Booth and F.J. L l e w e l l y n , J.Chem. S o c , 837 (19I+7).  Wallenberger,  - iko 88.  J . Trotter.  89.  P. Gray, "The Chemistry of D i n i t r o g e n Tetroxide". The Royal I n s t i t u t e  To be published i n Acta Cryst.  of Chemistry.  Lectures,- Monographs and Reports, No.k, 1958.  90.,  D.J. M i l l e n and J.R. Morton, J.Chem.Soc.,.1523 . ( i 9 6 0 ) .  91.  K.N. Trueblood, E. Goldish and J . Donohue, - Acta Cryst.  92.  D.W.J. Cruickshank, Acta Cryst.  93.  J . T r o t t e r and T.C.W. Mak.  94.  M.P. Cava and R.L. S h i r l e y , J. Am.Chem.Soc.  95.  M.P. Cava and D.R. Napier, J.Am.Chem.Soc.  9, 757  lU,,1009  (1956).  Unpublished r e s u l t s . 82, 6<?k ( i 9 6 0 ) . 79,  3606  (1957)-  (1961).  - 6 -  f7  i  a}  LTWCUNIC  3 . SIDE-CENTERED MOMOCLINIC  2. SIMPLE MONOCLINIC  4=71  4Z7I  rTIJ\  4 SIMPLE 0RTHORH0MBIC  6. END-CENTERED ORTHORHOMBtC  6. FACE-CENTERED ORTHORHOMBtC  7 BODY-CENTERED ORTHORHOMBIC  A7\ AA V  V 9.RHOMBOHEDRAL 10. SIMPLE TETRAGONAL  8. H6XASONAL  11. BOSY'CENTE RED TETRAGONAL  l i d7 12. SIMPLE CUBIC  Figure 1.  IS. BOPYCEHTEREP CUBIC  14. F A C E CENTERED CUBIC  The Ik Bravais l a t t i c e s .  • Figure 8.  (a) Measured- bona lengths and (b) valency angles.  F i g u r e 10.  P r o j e c t i o n o f the s t r u c t u r e a l o n g JjDOl] , showing the s h o r t e r i n t e r m o l e c u l a r c o n t a c t s . .'.  1-55  Figure 19•  159  Mean "bond lengths and valency angles i n (a) acenaphthene, (b) naphthalene, (c) 5 , 6 - d i c h l o r o acenaphthene, (d) pyracene, (e) 2.13-benzfluoranthene, and ( f ) 20-methylcholanthrene.  - 67 -  c  —  Figure 20.  Table V I I I .  Space Group Coordinates x  ,  W  * h  itt\  R e l a t i o n of the o r i g i n of space group ~?2-\2-\2-± t o the o r i g i n s of i t s p r o j e c t i o n s on the pinacoids (100), (OlO), and (OOl). The several o r i g i n s are i n d i c a t e d by dots. A f t e r Buerger, Barney and Hahn(79)»  Transformations between Space Group and P r o j e c t i o n Coordinates.  (OOl) x'=x-£  P r o j e c t i o n Coordinates (lOO)  (010)  - 76  Figure 2k.  -  Numbering and average dimensions of the molecule.  -  0  2  1 iv  II II  .i,  ise"  4  3 •  l  78  -n—m  -  5  A  J  Figure 25 • P r o j e c t i o n of the structure along £oOl] > showing the shorter intermolecular contacts.  - go  -  tM  Figure 28.  Numbering and average dimensions of the molecule.  - 92 -  Figure 29.  P r o j e c t i o n , o f the s t r u c t u r e a l o n g the hydrogen bonds and t h e s h o r t e r contacts.  £oio]  , showing intermolecular  Figure 30.  Perspective diagram showing the hydrogen bonding.  - 104 -  F i g u r e 33-  Numbering and average dimensions o f the m o l e c u l e . t  I  Figure 32+,  L__l  l_J  P r o j e c t i o n of the structure along ,[6lo]  - 110  -  C  a 17,  115.5  (a)  -N  1-41  '32  a  0, 2-6 •404  IT-  N  1304  Cb)  0,  (C)  F i g u r e 37. Dimensions o f the n i t r o x y group i n (a) c i s - 1 , 2 a c e n a p h t h e n e d i o l d i n i t r a t e , (b) p e n t a e r y t h r i t o l t e t r a n i t r a t e , and ( c ) n i t r i c a c i d .  - 113  Figure 38•  -  Average dimensions of the naphthalene moiety of the acenaphthene system. Deviations from the corresponding values i n naphthalene are shown i n brackets; f o r the bond distances the d e v i a t i o n s are given i n 10 A. Q  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062271/manifest

Comment

Related Items