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Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 75-11,374 KERSHAW, Richard Allen, Jr., 1947- THE CRYSTAL AND MOLECULAR STRUCTURES OF SEVERAL BICYCL0[5.1.0]0CTANES. The Ohio State University, Ph.D., 1974 Chemistry, physical
Xerox University Microfilms,Ann Arbor, Michigan 48106
© 1975
RICHARD ALLEN KERSHAW, JR.
ALL RIGHTS RESERVED THE CRYSTAL AND MOLECULAR STRUCTURES
OF SEVERAL BICYCLO[5. 1. 0]OCTANES
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Richard Allen Kershaw, Jr., B.Sc., M.S.
#
The Ohio State University
197^
Reading Committee:
Dr. G. G. Christoph
Dr. P.G. Gassman
Dr. C.W. Mathews Department of Chemistry ACKWOVILEDGEMENTc
I would like to thank friends and family for their generous support throughout this project. Special thanks, however, must go to
Dr. P.W.R. Corfield for his counsel and guidance during my graduate career and to Dr. Gary G. Christoph who helped bring this work to its conclusion. Most of all, I must thank my wife, Gladys, however, for her understanding through the many rough places and whose nimble fingers typed the finished copy. VITA
Richard Allen Kershaw, J r ., the son of Richard Allen and Betty
Barbara, was horn in Cleveland, Ohio on May 2k , 19^7- He received his elementary and secondary education in Euclid, Ohio. In September, 1 9 6 5 , he entered the Ohio State University where he received the B. Sc. degree in Chemistry in June, 19^9* He then went on to graduate study at that university in the fall of 1 9 6 9. 0n March 21, 1970 he married
Gladys McIntosh of South Lebanon, Ohio, whom he had met while an under graduate at Ohio State University. In December, 1972, he received the
M.S. degree in physical Chemistry from the Ohio State University. His thesis was entitled "The Crystal and Molecular Structure of Potassium trans-Bicyclo[5*l*0]octane-U-carboxylate Monohydrate". During the course of his graduate studies he held appointments as a teaching associate except during the period when he was a research assistant under his advisor, Dr. P.W.R. Corfield. During the 1971-1972 school year he was given the additional responsibilities of special assistant in charge of the physical chemistry laboratories. His graduate career was temporarily interrupted so that he might attend several m ilitary schools for the U.S. Army where he holds a commission as Second Lieuten ant in the Chemical Corps which is now part of the Ordnance Corps.
i i i TABLE OF CONTENTS
ACKNOWLEDGEMENTS...... i i VITA...... i i 'i LIST OF TABLES...... v i LIST OF FIGURES...... x I . INTRODUCTION A. The Twist Bent Bond ...... 1 B. S y n th e tic M ethods ...... 5 C. S t r a i n ...... 8 D. Anchimeric Assistance ...... 13 I I . SURVEY OF STRUCTURES...... 19 I I I . cis-BICYCLO[5. 1» OlQCTA-ex o -YL p-BROMOBENZENE SULFONATE A. Photographic Preliminaries, Space Group, and Density..26 B. Alignment ...... 28 C. Intensity Collection ...... 35 IV. DATA REDUCTION A. Attenuator Corrections ...... 3^ B. B ackground C o rre c tio n s ...... 35 C. Lorentz and Polarization Corrections ...... 39 1. The Lorentz Factor 2. The Polarization Factor D. Evaluation of Check Reflections-Decomposition ...... 4 l E. Absorption Corrections ...... ^9 F. Deletions and Averages ...... 51 G. The Wilson Plot ...... 52 V. SOLUTION OF THE STRUCTURE A. The Patterson Function ...... 57 B. The T r i a l S tr u c t u r e ...... 62 C. Initial Refinement ...... 65 TABLE OF CONTENTS (continued)
D. Anisotropic Refinements ...... 69 E. Full Matrix Refinements and Hydrogen Atoms ...... 72 F. Extinction ...... 73 VI. DISCUSSION OF THE STRUCTURE A. The Crystal Structure ...... 82 B. The Molecular Structure ...... 96 V II. t r a n s -BICYCLOf3 .1 . 01OCTANE-4-CARBOXYLIC ACID A. Photographic Prelim inaries, Space Group and Density.. 1^0 B. Intensity Collection ...... 1^3 C. Data Reduction ...... Ikk V III. SOLUTION OF THE STRUCTURE A. The Patterson and Superposition Functions ...... 152 B. In itial Refinements - The Isotropic Model ...... 156 C. Anisotropic Refinements ...... 159 IX. trans-B IC Y C L 0r5.1. OlOCTANE-U-METHAtTOL p-BROMOBENZENE SULFONATE A. Photographic Prelim inaries, Space Group and Density.. 164 B. Data Collection...... 167 C. Data Reduction ...... 170 X. SOLUTION OF THE STRUCTURE A. The Patterson Function and the Trial Structure ...... 178 B. Refinement of the Structure ...... 182 XI. STRUCTURES OF THE tra n s-B IC Y C L 0 [5 .1. 0]0CTANES A. The Crystal and Molecular Structure of trans-Bicyclo- [5.1. 0]octane-4- carboxylic Acid ...... 194 B. The Crystal and Molecular Structure of trans-Bicyclo- [5.1. Opjoctane-4-methanol p-Bromobenzene Sulfonate.... 206 APPENDIX...... 224 REFERENCES...... 225
v LIST OF TABLES
T a b le Page
1. Survey of Compounds Studied ...... 20
2. cis-Bicyclo[ 5 -1 • 0 3oct-H-endo-yl p-Bromobenzene Sulfonate ...... 2k
3. cis-Bicyclo[5.1.0joct-^-exo-yl p-Bromobenzene Sulfonate ...... 31
k. Full Width at Half Height for Several Reflections ...... J>2
5. Summary of Attenuator Corrections for cis-Bicyclo[5.1.0]oct- U-exo-yl p-Bromobenzene Sulfonate ...... 37
6. Summary of Data above Background for cis-Bicyclo[5-l-0]oct- U-exo-yl p-Bromobenzene Sulfonate ...... 38
7. Statistics on E for cis-Bicyclo[5*1.0]oct-U-exo-yl jo- Bromobenzene Sulfonate ...... 55
8. List of the Strongest Peaks in the Patterson Function ...... 6 l
9. Initial Coordinates Obtained from the Minimum Function ...... 6k
10. Initial Hydrogen Atom Posisitons for cis-Bicyelo[3.l.O joct- U-exo-yl p-Bromobenzene Sulfonate ...... 71
11. Summary of Refinements ...... 73
12. Final Heavy Atom Coordinates for cis-Bicyclo[5.1.0]oct-U- exo-yl p-Bromobenzene Sulfonate...... 76
13. Anisotropic Thermal Parameters for cis-Bicyclo[5-l-0]oct- U-exo-yl p-Bromobenzene S u lfo n ate.' ...... ?8 lU. Final Hydrogen Parameters ...... 80
15* Observed and Calculated Structure Factors for cis-Bicyclo [5-1.0]oct-U-exo-yl _p-Bromobenzene Sulfonate ...... 8 l
16. Honbonded Interactions in cis-Bicyclo[5■1■03oct-^-exo-yl p-Bromobenzene Sulfonate ...... 85
17- Analysis of Benzene Planarity ...... 91
vi LIST OF TABLES (continued)
18. Bond Lengths in cis-Bicyclo[5•1•03oct-^-exo-yl p-Bromo benzene Sulfonate ...... 100
19. C-H Bond Lengths in cis-Bicyclo[5.1.0]oct-H-exo-yl p-Bromohenzene Sulfonate ...... 102
20. Bond Angles in cis-Bicyclo[5.1.0]oct-^-exo-yl p-Bromo- benzene Sulfonate ...... 101
21. Bond Angles Involving Hydrogen in cis-Bicyclo[5.1.0]oct-U- exo-yl p-Bromobenzene Sulfonate ...... 105
22. Dihedral Angles in cis-Bicyclo[5.1.0]oct-l|-exo-yl _p-Bromobenzene Sulfonate ...... 107
23. Rigid Body Thermal Parameters for cis-Bicyclo[5-1.0]oct- U-exo-yl p-Bromobenzene Sulfonate ...... 112
2k. Bond Lengths in Some Bromine and Sulfur Containing Benzene Derivatives ...... 119
25. Bond Lengths in Cyclopropane Derivatives ...... 1 2 5
26. Relative Solvolytic Rates ...... 153
27. Intramolecular Contacts in cis-Bicyclo[5.1.0]oct-It-exo-yl p-Bromobenzene Sulfonate ...... 137
28. Crystal Data for trans-Bicyclo[5.1.0]octane-U-carboxylic A c id ...... 1^2
29. Summary of Attenuator Corrections for trans-Bicyclo[5.1.0]- octane-i*-carboxylic Acid ...... 1^5
30. Summary of Data above Background for trans-Bicyclo[5.1.0]- octane-U-carboxylic Acid ...... lk6
31. Summary of Check Reflections for trans-Bicyclo[5.1.0]octane- U-carboxylic Acid ...... 1^7
32. Statistics on E for trans-Bicyclo[5.1.0]octane-^-carboxylic A c id ...... 77777...... 151
33. Initial Coordinates for trans-Bicyclo[5.1.0]octane-lf- c a rb o x y lic A c id 777777’...... 155
v ii LIST OF TABLES (continued)
3*+. Atomic Coordinates for trans-Bicyclo[5.1.0]octane-U- carboxylic Acid ...... 157
35. Anisotropic Thermal Parameters for trans-Bicyclo[5.1.0]- octane-U-carboxylic Acid ...... 158
36 . Positions Calculated for Hydrogen Atoms in trans- Bicyclof5.1.0]octane-l+-carboxylic Acid ...... IbO
37. Summary of Refinements for trans-Bicyclo[5.1.0]octane-l+- carboxylic Acid ...... l 6l
38. Observed and Calculated Structure Factors for trans- Bicyclo[5.1.0]octane-lj—carboxylic Acid ...... l6 2
39* Crystal Data for trans-Bicyclo[5.1.0]octane-U-methanol p-Bromobenzene Sulfonate ...... 166
1+0. Instrument Settings During Data Collection ...... Ib 8
1*1. Summary of Data above Background for trans-Bicyclo- [5.1.0]octane-U-iiiethanol p-Bromobenzene Sulfonate ...... 172
1+2. Summary of Check Reflections for trans-Bicyclo[5.1.0]octane- methanol p-Bromobenzene Sulfonate ...... 173
1*3. Statistics on E for trans-Bicyclo[5-1.0]octane-l+-methanol p-Bromobenzene Sulfonate...... Ij6
1+1*. In itial Coordinates for trans-Bicyclo [5.1.0] octane-1*- methanol p-Bromobenzene Sulfonate ...... l 8l
1+5. Final Heavy Atom Coordinates for trans-Bicyclo[5.1.0]octane- l+-methanol p-Bromobenzene Sulfonate ...... 186
1*6. Final Thermal Parameters for _trans-Bicyclo[5.1.0]octane-l+- methanol p-Bromobenzene Sulfonate ...... 188
1*7. Calculated Hydrogen Positions for trans-Bicyclo[5.1.0] octane-l+-methanol p-Bromobenzene Sulfonate ...... 190
1*8. Summary of Refinements for Jtrans_-Bicyclo[5*1.0]octane- l*-methanol p-Bromobenzene Sulfonate ...... 191
1+9. Observed and Calculated Structure Factors for trans- Bicyclo[5.1.0]octane-l*-methanol p-Bromobenzene Sulfonate.. 192 LIST OF TABLES (continued)
50. ilonbonded Contacts in trans-Bicyclo[5.1.0]octane-^- carboxylic Acid ...... 19T
51. Bond Lengths in trans-Bicyclo[5.1.0]octane-U- carboxylic Acid ...... 202
52. Bond Angles in trans~Bieyelo[5-1.0]octane-^- carboxylic Acid ...... 203
53. Dihedral Angles for trans-Bicyclo[5.1.0]octane-^- carboxylic Acid ...... 20^4-
5^. ilonbonded Contacts in trans-Bicyclo[5.1.03octane-^- methanol p-Bromobenzene Sulfonate ...... 210
55. Analysis of Benzene Planarity in trans-Bicyclo[5.1.0]- octane-U-methanol p-Bromobenzene Sulfonate ...... 211
56 . Bond Lengths in trans-Bicyclo[3»1•01octane-U-methanol p-Bromobenzene Sulfonate ...... 213
57. Bond Angles in trans-Bicyclo[5.1.0]octane-^-methanol p-Bromobenzene Sulfonate ...... 21^
58 . Dihedral Angles in trans-Bicyclo[5.1.O^octane-^-methanol p-Bromobenzene Sulfonate ...... 2 l6
ix LIST OF FIGURES
Figure Page
1. Schematic View of Several Carbon-Carbon a B onds ...... 3
2. The Data Crystal Used for cis-Bicyclo[5.1.0]oct-U-endo-yl p-Bromobenzene Sulfonate ...... 25
3. The Data Crystal Used for cis-Bieyclo[5.1.0]oct-U-exo-yl p-Bromobenzene Sulfonate ...... 30
4. Check Reflections ...... k2
5. A Plot of In I/I vs. sin 20/X2 ...... 46 o 6 . The Wilson Plot ...... 56
7. A Schematic Representation of the Numbering System Used for cis-Bicyclo[5.1.03oet-4-exo-yl -p-Bromobenzene S u lf o n a te ...... 63
8. The Crystal Packing of cis-Bicyclo[5.1•0]oct-4-exo-yl p-Bromobenzene Sulfonate Viewed Down b_ ...... 83
9. The Crystal Packing of cis-Bicyclo[5.1.0]oct-4-exo-yl p-Bromobenzene Sulfonate Viewed Down c ...... 84
10. Van der Waals Radius of Double Bonded Oxygen from Contacts Involving 02 and 03 as a Function of the S=0*»»X Angle.. 90
11. Two Views of the Bromobenzene Sulfonate Group ...... 93
12. cis-Bicyclo[ 5 • 1 •0]oct-4-exo-yl p-Bromobenzene Sulfonate.... 97
13. Selected Bond Lengths and Angles in cis-Bicyclo[5-1.0]oct- 4-exo-yl ^-Bromobenzene Sulfonate ...... 98
14. A Detailed View of the Bromobenzene Sulfonate Group ...... I l 6
15. c i s -B i cy clo [ 5« 1 .0 ] oc t an e ...... 124
16. Conformations of Two Molecules ...... 139
x LIST OF FIGURES (continued)
17. The Morphology of trans-Bicyclo[5.1.0]octane-H-carboxylic A c id ...... lA l
18. Wilson Plot for trans-Bicyclo[5.1.Q]oetane-^-carboxylic A c id ...... 150
19. A Schematic Representation of trans-Bicyclo[5-l«0]octane- 4-carboxylic Acid Illustrating the Numbering System Em ployed ...... 152
20. The Data Crystal Used for trans-Bicyclo[5.1•0]octane-H- methanol p-Bromobenzene Sulfonate ...... 1&5
21. The Wilson Plot for trans-Bicyclo[5.1.0]octane-U- methanol p-Bromobenzene Sulfonate ...... ITT
22. A Schematic Representation of trgns-Bicyclo[5.1.0]oetane- ^-methanol p_-Bromobenzene Sulfonate ...... l8 0
23. trans-Bicyclo[5.1.01octane-^-methanol p-Bromobenzene Sulfonate. View Down b_ Axis ...... l 8U
2k. The Crystal Structure of trans-Bicyclo[$.1.0]octane-U- carboxylic Acid Viewed Down the a_ Axis ...... 195
25. The Crystal Structure of trans-Bicyclo[5.1.0]octane-U- carboxylic Acid Viewed Down the b_ Axis ...... 196
26. An ORTEP Drawing of trans-Bicyclo[5.1.0]octane-^- carboxylic Acid ...... - ...... 200
27. An ORTEP Drawing of the Anion in Potassium trans-Bicyclo- [5*1* 0 ]octane-lj—carboxylate Monohydrate ...... 201
28. A Schematic Representation of Some Bond Lengths and Angles in trans-Bicyclo [5.1.0] octane-l-carboxylic Acid ...... 205
29. Packing Diagram for trans-Bicyclo[5•1»03octane-^- methanol p_-Bromobenzene Sulfonate Viewed Down the a_ A x is ...... 207
30. Packing of trans-Bicyclo[5.1.0]octane-U-methanol p- Bromobenzene Sulfonate Viewed Down c_*...... TTT...... 208
31. A General View of the Packing of trans-Bicyclo[5.1.0]octane- ^-methanol p_-Bromobenzene Sulfonate ...... 209
xi LIST OF FIGURES (continued)
32. An Isolated View of the Bromobenzene Sulfonate Group in trans-Bicyclo 5.1.0 octane-^-methanol_pjBromoben zene Sulfonate ...... 217
33. Summary of Geometry in trans Compounds ...... 221 I
I . INTRODUCTION
A. The Twist Bent Bond
Although cyclopropane itse lf is a highly strained molecule, even more highly strained molecules obtain when cyclopropane becomes part of a polycyclic system. Moreover, because the unusual geometries imposed by strained systems distort normal bonds, such systems serve as a probe of the lim itations of such bonds. Gassman 1 has recently suggested that, in certain cases, the extra strain can work to alter the nature of the cyclopropyl bent bonds sufficiently to produce a distinct, new type of bond, the tw ist bent bond.
In most of the known polycyclic derivatives of cyclopropane, represented schematically as 1 , the classical bent or banana bond 2 *3
suffices to represent the bonding. The bond must bow outward, since even pure p orbitals cannot accommodate bond angles less than 90° and still maintain maximum overlap along the internuclear axis. Coulson and Mof- f i t t 2 ’ 3 predicted that the cyclopropyl bond is formed from hybrid orbi tals which have their maximum overlap some 22° off the internuclear axis. Experimental verification that excess bonding density exists out side the internuclear axis has been claimed in X-ray diffraction
1 2 experiments involving cis-tricyanocyclopropane,4 2, 5 -dimethyl-7,7- dicyanonorcaradiene5 and tetracyanoethylene oxide.6 When the extra strain incorporated into a polycyclic molecule tw ists the cyclopropyl bridge bond, a-b, however, Gassman suggests that a new, "twist bent bond" may result. Trans-bicycloTn.l.Ol and tricyclo[ n.m.O]alkanes, represented schematically as 2 and ^ are the type of molecules which should possess the torque necessary to produce such a bond when n, and in the latter case n and m, are sufficiently s m a ll.
(CH2 ) m n n J s
Schematically, the bonding picture for various types of cr bonds are shown in figure 1. When viewed from above the plane of the ring, the classical bent bond and the proposed tw ist bent bond look identical, but the view edge on exposes a difference. In the twist bent bond, the bonding orbitals no longer overlap as well as in the classical bent bond. Thus the tw ist bent bonds may be expected to be somewhat more reactive than other bent bonds. Structurally, the twist bent bond may manifest itself as a shorter than normal bond, just as the classical bent bond is shorter (1.51 A)T than a normal a bond (1.5^ A)8. In
each case the degree of overlap is smaller in the shorter bond,
countervailing the usual trend. Such anomolous behavior arises because above edge
norm al cr bond
c l a s s i c a l e n t bond
twist bent bond
F ig u re 1 . Schematic views of several carbon-carbon ct bonds. k we generally define the hond length as the straight line distance between internuclear centers, while what we understand to be the bond in these cases is more realistically a curved line.
Structurally, ^ is unknown, and only a preliminary report has been made on a structure like 2- In that report, Kershaw 9 elucidated the structure of potassium trans-bicycloC5.l.Oloctane-^-carboxvlate. but disorder prevented detailed analysis of the structure. Moreover, in spite of a wealth of data about the cyclopropane system, very few accurate structural studies have been carried out in the solid state.
Vapor phase methods such as microwave spectroscopy and gas phase electron diffraction suffer at times because they do not retain the spatial repetition of the crystal, and structural information must be deconvoluted from a radial distribution function. Apart from any lack of a unique structural solution from a possibly non-congruent homometric set of scattering centers , 103 the one dimensional projec tion of the structure derived from gas phase diffraction can also suf fer from a lack of resolution. Correlations between parameters can obscure small variations in bond lengths within a structure, especially if such differences are smaller than the amplitudes of vibration of the atoms involved . 10*3 Thus further investigation of both cis and trans- b ic y clo C 5 . 1 -0 ]octanes was initiated.
Before turning to the structures involved in this study, however, let us look at the synthesis, strain and reactions of the b icy clo T 5 . 1 . 0 ] a lk a n e s . 5
B. Synthetic Methods
Cis-fused bicyclc[ n.l.O]alkanes are known where n achieves its lim iting value, 1 , but the extra strain inherent in a trans-fused derivative lim its the size of the n-membered bridge to a larger value.
Three different approaches have provided routes to trans- bicyclo[5.1.0]octanes. Kirmse and Hase 11 turned the carbene insertion reaction to their advantage, to produce the trans-fused parent hydro carbon directly.
N H S O ,- c t / 0 CH=N Cl o Diglyme/160 1
o th e r p ro d u c ts
12$ 37$
In this reaction, steric factors favor a transition state which leads to a trans-substituted cyclopropane . 12 However, the increased strain of a trans-fused, bicyclic product becomes increasingly important as the size of the molecule decreases, trans-BicycloC6.1.0]nonane dominates the cis product by a 2 :1 margin in the product mixture from cyclooctyl carbene, but the difference in strain between trans-bicyclo
[ 5 . 1 . 0 ]octane and the cis isomer becomes the overriding factor when cycloheptyl carbene is the precursor. In the latter case, the cis- fused isomer is favored, ^'.lyOYev trans-bicyclof 5 . 1 . 0 ]octane among 6 the products. Cyclohexyl carbene and cyclopentyl carbene yield only cis-fused products.
Several investigators 13"15 have made use of photochemical ring
contractions to reduce a more readily available bicyclo[ 6. 1. O]nonane to a b ic y c lo [ 5 . 1 . O]octane.
CH3OH
In this scheme, the trans-fused character of the system is already pre sent in the trans-bicyclo[ 6 . 1 . 0 ]nonane and is carried over to the final product in good yield. In general, the precursors in this synthetic route involve a trans-substituted double bond which leads to the trans substituted cyclopropane ring via the Simmons-Smith reaction . 18 A r e lated synthesis has been proposed by Williams . 17 in that proposal, the starting material is the trans-bicyclo[ 6 . 1 . 0 ]n o n an - 2 -one reported by
DePuy, 18 but the method remains untried. 7
The trans-fused brosylate used in our structural study, is obtained from the carboxylic acid in a two step synthesis.
W j > 1 Hq / 2. p-bromobenzene ^ sulfonyl chloride/pyridine
Finally,Paukstelis and Kao 19 have reported a synthesis which leads not only to trans-bicycloT 5 .l.Oloctane, but also to the even more strained trans-bicyclo[ 4.1.0]heptane. Their scheme takes advan tage of the stereospecificity of the glycol monotosylate rearrangement, which can be run under mild conditions. 0Ti o
p o ta ssiu m t-butoxide (l eq)
THF 10 min.
0* H OH HO p o ta ssiu m t-butoxide (l eq)
p o ta ssiu m tri-t-butoxy aluminum hydride/ THF 8
C. S tr a in
The increased strain at a trans-fused, zero member bridge is reflected in the chemistry of these compounds. Cyclopropyl ring opening of trans-bicyclof5.l.oloctane 20 leads to rupture of the trans fused bridge 7]$ of the time, and the rate of reaction is 18 tim es
OAc CH20Ac 0. 005M OTs in HAc 800>
that for trans-bicyclof6.1.0]nonane. Conversely, the same reaction generally leads to rupture of one of the exocyclic bonds in the less strained, cis-bicyclof 5 . 1. Oloctane, as well as in both the cis- and trans-bicyclof b. 1. 0 ]nonane . 14,20
!Hs OAc Ac
a
2%
OAc
OAc HCH3 ach=ch2
0 . 5% 9
Acid catalysed addition of acetic acid to trans-bicyclof5.1.01 o c t - 3 -en e 21 yields a complex array of products which indicate that the product determining protonation occurs exclusively at the bridgehead positions rather than at the non-bridgehead cyclopropyl carbon or at the double bond. cr h2oh is$
1. HOAc :H20H +
2. LiAlH4 O 1# o cd>“ 'ft 3 3 Another reflection of the increased strain in the parent compound, trans-bicyclef 5 . 1 . 0 ]octane, appears in the catalytic hydrogenation of that compound to methylcycloheptane22, which proceeds quantatively.
^ y c n 3 HOAc/pentane ...... ■ 1 ■'■■■ 1 ■■'■"I H2(l atm. )/PtC >2
Under the same conditions, only 1<3?° of the less strained cis-fused isomer is converted, while 9C$ remains unchanged. 10
The total strain in any compound is the result of many factors, but for any pair of isomeric bicycloC n .l. 0 ]alkanes, cis and trans, the angle strain 23 imposed by stretching an n-membered bridge across the cyclopropyl ring rapidly becomes the major part of that total as n gets small.
Even in bicycloC 6 .1.0]nonane, a trans-fused bridge adds some strain relative to the cis isomer. Depuy and Marshall 18 have shown that in base, trans-bicycloC 6 . 1 . 0 ]n o n an - 2 -one. is converted almost entirely to the cis isomer
0 0
1. 5M NaOCH3 in
CH30H a t RT 87 h r s . which illustrates the thermodynamic stability of the cis isomer relative to the trans isomer. Neither ketone reacts under mildly acidic condi tions. A similar result was obtained by Wiberg and Meijere 1 4 ’24 who found that the trans compound is converted, to its cis isomer when treated with sodium methoxide in ether. The half life of the reaction is approximately 8 hours. Furthermore, when they allowed the cis isomer to react under these conditions, 0 .^$ of it eventually converted to the trans isomer. From this data, these investigators estimated that AG of isomerization for this system is roughly 3*5 kcal/mol. In a somewhat more precise experiment, Pirkle and Lunsford 25 m easured 11 the thermal equilibrium between a trans and a cis-spirof 6.1.0lnonane and found AG=-2.9 kcal/mol at 158°in cyclohexane. 0 n
T herm al
For comparison, the difference between cis and trans-cyclooctene is ' much greater. Turner and Meador28 estimate that Ah of isomerization for the two alkenes is -9*2 kcal/mol at 25 r .
When the spiro[5.1.0]octanes were equilibrated, almost none of the trans isomer was left and an equilibrium constant could not be de- te rm in e d .
0 0
However, Ah of isomerization was determined to be -9.011.0 kcal/mol from data provided by differential scanning calorimetry. Benson, et al.^have established that the heat of formation, Ah^ , of cis-bicvclo
[ 5 .1.0]octane is - 3-87 kcal/mol, but the corresponding quantity for the trans isomer has not been measured. 12
While no direct measure of the strain in trans-bicycloT h . 1 . O l■ heptane relative to the cis isomer has been forthcoming, Paukstelis and Kao did report that trans-bicyclo[U.1.0]heptane-2-one 19 w ill isomerize to the cis isomer when exposed to excess potassium tertbutoxide under the conditions which lead to its synthesis.
Potassium t-butoxide » (2 eq. )/THF 19 hrs. 1 3
D. Anchimeric Assistance
There is no doubt that a suitably oriented cyclopropyl bond can lend effective neighboring group assistance 28 in solvolysis reactions, that is, it can form a bond or a partial bond which stabilizes the transition state. The term, anchimeric assistance, was coined for such phenomena by W instein 29 from the Greek words "anchi" and "meros", meaning "pertaining to the neighboring or adjacent part". When a re action mechanism involves anchimeric assistance, new substituents need not appear in the same place as the leaving group, there is a tendency toward retention of configuration in the products, and because the reaction intermediate is stabilized, the rate of reaction may be greatly enhanced 30 and show a special salt effect . 3 0 ’31
When the leaving group is adjacent to the cyclopropyl ring, the interaction between the developing cationic center and the cyclopropyl ring, the interaction is mainly of a jt character 32 and the most effi cient intermediate in such reactions is the bishomoallylic cation with a bisected configuration . 33 ih
When the leaving group is at a greater distance, a a type inter
action is more likely, involving the back lobe of the developing p
orbital of the incipient carbonium ion and the bent cyclopropyl bond.
A classic example of long range, neighboring group participation has
been the norbornane system, where rate enhancements of as much as lU
orders of magnitude have been ascribed to anchimeric assistance 3 2 ’34 37
k. r e l X
10la- via formation of the nonclassical homoallylic cation . 38 Even when the
developing carbonium ion is tertiary and adjacent to a p-anisyl group,
a properly oriented cyclopropane ring can provide an accelerating factor
of three orders of magnitude , 39 and the effect has been seen to operate 15
c h 3 o CH30
OPBN OPBN
over a distance of as many as four bonds . 4 0 ’41 Molecular models indicate
OBs OBs
1 105 that the interaction in this case must occur across a distance of o approximately 2.5 A.
When the leaving group is not attached to the highly strained bridge, anchimeric assistance, if it operates at all, has a much smaller impact on the reaction rate. For example the solvolysis rate of two ethyl norbornane derivatives 47 (Bs = jD-bromobenzene sulfonate) differ only by a factor of 3 S although backside participation is strongly indi cated by the nature of the products. Similar trends among rates and
BSOCH2 CH0 CHsCHsOBs
5 1 16 products were observed for various cyclopropylethyl brosylates , 48 In th e cycloheptane system, a double bond does provide moderate rate enhance ment when the leaving group is separated from the strained ring system
CH2OBs CH2OBs CH2 OBs
r e l
CH'sOBs <
3 .7 1.1 by an intervening methylene group , 17,49550 but the acceleration is no where near that observed when the leaving group is attached directly to the strained ring, and a cyclopropyl group provides almost no enhance ment at all in this type of molecule. The trend is also seen in the bicyclo[3.1.0]hexylethyl system 52 (PBN = p - n it r o b e n z o a te ) .
CH2CH2OEBN CHjjCHjSOEBN ch 2ch 2oebn
1 87
In each of these cases, however, the effect of neighboring group assis tance is moderated not only by the conformational flexibility of the molecules, but also by strong,nonbonded H---H repulsions 51 not present when the leaving group is attached to the ring system.
By analogy to the effects observed in the norbornane and related systems, one might .expect the bicyclo[ 5 . 1 . 0 ]octanes to exhibit a simi- lar pattern of increased reactivity. Models indicated, and a prelimi nary study of potassium trans-bicyclo[5 . 1 . 0 ~1octane-^-carboxvlate 9 con firmed, that the distance between the incipient carbonium ion and the cyclopropyl bond is 2.5 I . However, solvolysis studies showed that neither a double bond nor a cyclopropyl bent bond lead to the expected enhancement in the reaction rate. Neither do the products of the reac tion support a mechanism which proceeds through an intermediate which
OBs OBs
1 2.1 3 .0
OBs OBs
27.8 is stabilized via backside participation . 1 3 ’ 17 Rather, only a slight rate depression is observed which may be ascribed to inductive 42 e f f e c t s .
Cycloheptane itself has four possible stable conformations, a chair, a boat, a twist-boat and a twist-chair. in the gas phase, the last of these has been shown to be the most stable , 43 45 with the molecule under going rapid pseudorotations among several tw ist-chair conformations.
When the cycloheptane ring is fused to a cyclopropyl ring, the conforma tional flexibility of the parent molecule is lost. In their studies,
Gassman and W illiams 46 postulated that trans-bicyclor5.l.Oloctane. or rather the carbonium ion derived during solvolysis, adopted the tw ist- boat conformation. With this postulate, the lack of solvolytic reactiv ity could be ascribed to the improper geometry which would exist between 18 the p-orbital and the cyclopropyl ring. Instead of intersecting the center of the ring, the axis of that orbital would be parallel to it.
Thus,as the ion developed, the overlap between that lobe and the cyclo propyl bond would not increase. Even more important, as a schematic of the interaction indicates, any bonding overlap is cancelled by an equal
antibonding component to give overall a nonbonding interaction.
In the first structure of a trans-bicyclo[5.1.0]octane derivative elucidated by X-rays in the solid state , 9 the conformation proved to be derived from the chair conformer not the tw ist-chair and the axis of the substituent in the b position pointed directly toward the cyclopropyl twist-bent bond. This result (confirmed here) showed that a conformation favorable to anchimeric assistance was at least attainable, albeit, in the solid state. Therefore, it was no longer clear why such a mechanism could not be operative. II. SURVEY OF STRUCTURES
A number of compounds have been examined 52 in the course of our
investigations. As we have already noted, one of these, potassium
trans-bicyclor 5 . 1 .Oloetane-^-carboxvlate monohydrate,has been described
in a preliminary report . 9 Three of the structures are reported here:
c.is-bicyclof 5 .1.0]oct-U-exo-yl p-bromobenzene sulfonate, trans-bicyclo-
[ 5 . 1 . 0 ]octane -4-carboxylic acid and trans-bicyclo[ 5 > 1. 0 ]octane-^-methanol
p-bromobenzene sulfonate. However, several other derivatives were also
examined and their space groups determined. The data for all the com pounds are summarized in Table 1.
Among the compounds whose molecular structures were not eluci
dated are the two cis alcohols. The endo alcohol gives needle-like
crystals in the tetragonal system with the unique axis along the length
of the needle, which is bounded by the form [l 1 0}. The space group,
determined photographically, was either 1^ , l5", lb/m. with unit cell
parameters a =17.09 and c = 5*5^ A* The exo alcohol was available
only as a crystaline mass. Microscopic examination indicated the crys
tals may have formed as plates which later melted and fused together.
As might be expectedjboth alcohols exhibit rather high vapor pressures
and low melting points but the endo derivative scattered well enough
even at room temperature to indicate that, it could possibly provide an
accurate structure at low temperature.
19 TABLE i
SURVEY OF COMPOUNDS STUDIED cis-bicyclo[5.1.0]octan-4-endo-ol 14, l£ , Ik/m a = 17.0936 c = 5-36
cis-bicyclo[5.1.0]oct-4-endo-yl p-bromo- P I , pT a = 6.593(1) a = 94.14(1) benzene sulfonate b = 8 . 2 9 5 (2 ) p = 1 0 3 . 2 2 (1 ) c = 6 . 9 2 5 (1 ) Y = 9 7 .7 6 (1 ) cis-bicyclor 5. 1 . 0]oct-4-exo-yl p-bromo- P 2x/c a = 1 2 . 829(1 ) benzene sulfonate b = 9 -7 5 9 (1 ) P = 95-74(1) c = 1 1 .7 3 0(2 ) trans-bicyclor 5.l.Oloctane-4-carboxvlic acid P2i / c a = 7-094(1) b = 6.165(1) p =. 104.344(7) c = 2 0 . 80U(3 ) potassium trans-bicyclo[5.1.0loctane-4- P c a 2 i, Pcam a = 8.631(9) carboxylate b = 16.14(1) c = 7.674(10) trans-bicyclor 5.l.Oloctane-4-methanol P 2 i/c a = 6.662(3) p-bromobenzene sulfonate b = 21.310(7) p = 1 2 7. 2 6(2 ) c = 14.047(5) trans-b icyclo[ 5 •1 . 0 ]o c ta n e - 4 -bromobenzene f i , pI a = 1 2 .1 8 a = 108.31 s u lf o n a te b = 11.30 P = 117.32 c = 7 .2 1 y = 106.03
ro o 21
Crystals of trans-bicyclo[5.1. 0]oct-4-yl _p-"bromobenzene sulfonate were supplied from a crude mixture of reaction products grown in ether solution. Microscopic examination showed they were poorly formed plates.
When a sample was recrystallized from hexane, well-formed needles with triclin ic morphology resulted. 53 Furthermore, the new crystals exhibited a different crystal IR spectrum and melted 2° lower than the original sample. Thus, it is probable that the compound crystallizes differently from the two solvents.
The crystals from the recrystallized sample were observed to ex tinguish at an angle to each of the needle edges. A series of diffrac tion pictures exhibited no symmetry. Thus, the triclinic crystal system was established. The unit cell was chosen such that a = 12.18 A, b =
11.30 A, c = 7. 21 A, o' = 108.31°, 3 = 117.32° and y = 106.03°. With two molecules in the unit cell, the calculated density becomes 1 .5 6 g cm 3 which is in good agreement with the values found for the isomeric, cis- fused brosylates. Scans along a*, b#, c# and the 10 1 directions indi cated the crystal did not scatter appreciably above 28 = 20° and high background scattering was also observed.
Although the space group of the crystals in the original sample was not determined, tria l scans were made on the Picker diffractometer and the scattering from these crystals was also found to die off rapidly and give high background scattering. Since these symptoms portend a disorder problem, no further investigations were carried out with this compound.
Crystals of cis-bicyclof!?. 1. Oloct-4-endo-yl bromobenzene sulfonate grow as thick plates with only one of the axes of the optical indicatrix 22 coincident with a crystal edge. After mounting, a sample crystal was placed on a precession camera, and a strong row of diffracted intensities was made coincident with the axis of the camera. Thirty-six photographs were made at 10° intervals around the azimuth angle and no symmetry was observed in any of the zones thus recorded. As before, this established that the crystal class was triclinic. Unit cell parameters were chosen from two of the stronger zones, then 18 high order reflections were carefully aligned on the Picker diffractometer with Mol^, radiation
c (X = O.7O926 A). Unit cell parameters determined from these reflections refined to a = 6.593(1) A, b = 8 . 2 9 5 (2 ) A, c = 6.952(1) A, or = 9l . l ^ ( l ) ° ,
P = 103.22(l)0, and y = 97. 7 6(1 )°. A complete summary of the crystallo- graphic data for this compound is given in Table 2.
Although a set of diffracted intensities was collected for this compound, the structure could not be elucidated. Probable coordinates for bromine, sulfur and the three oxygen atoms were established, but attempts to find and refine the complete molecule failed. Two positions were derived for the benzene ring from a difference Fourier function phased on the basis of the bromine, sulfur and oxygen positions, but neither trial structure refined adequately or led to probable coordinates for the rest of the molecule. In addition, the distribution of the diffracted intensities itself was more consistent with the centric space group, PI, than the noncentric space group, PI, but density measurements indicated there was only one molecule in the unit cell. Since the molecule itself cannot have a center of symmetry, there have to be two centrosymmetrically related molecules in general positions to satisfy the requirements of the centric space group. Lastly, the diffraction pattern was observed to die off very rapidly and. the background scattering was very high. All of these considerations indicated that the crystal structure of this compound was disordered. Figure 2 shows the data crystal used for the investigation. 2b
TABLE 2
cis-BICYCLO[5• 1. 0 ] 0CT-J|-endo-YL_ 2-BR0M0BENZENE SULFONATE
P-BrC6H4 S O2OCQH13
T r i c l i n i c
Possible Space Groups
PI x y z
P I x y z x y z
a = 6 .5 9 3 (1 ) A a' = 9 b. l ^ ( l ) °
b = 8. 2 9 5 (2 ) A P = 103.22(1)° at 25° C
c = 6.925(1) A y = 9 7 .7 6 (1 )°
cell volume = 363-23(20) A3
1.539 g cm 3 Dc = 1. 578 g cm 3
M = 3^5. 256 Z = 1
Fooo = 176
E ff = 219*1. 1 25
2 i I
F ig u re 2. The data crystal used for cis-bicvclor5.1. Oloct-4-
endo-yl jo-broaobenzene sulfonate. I I I . cis-B IC Y C L 0[5.1. 0 jOCT-^-exo-YL p-BROMOBENZENE SULFONATE
A. Photographic Prelim inaries, Spcae Group and Density
A sample of cis-bicyclo[5. 1. Oloct-^-exo-yl p-bromobenzene sulfonate was supplied by Dr. Gassman. The crystals grow as chunky needles bounded by the form {0 1 1} with the needle axis along a-*. Precession photographs of several crystals established that the crystal structure was monoclinic
(C^). In addition, the 0 k 1, h 0 jJ, h 1 jl, hkO and h k X nets were photographed during these studies. The following conditions for dif fraction were observed:
h k X no conditions h k 0 no conditions h O i X = a i 0 k X no conditions h 0 0 no conditions 0 k 0 k = 2n 0 0 X (X = 2n)
These conditions establish the space group uniquely.
The density was measured with a density gradient column , 54 w hich was made by layering a saturated solution of potassium tartarate on top of a solution of potassium iodide. After slight mixing to establish the gradient, the column was allowed to settle. A ground sample of cis- b i c y c l o f 5 . 1 .Oloct-^--exo-yl p-bromobenzene sulfonate was mixed with some of the saturated tartarate solution until it was wetted and then the mixture was added to the column. This too was allowed to settle, then 2 7 the column was calibrated using drops of solutions of bromobenzene in
carbon tetrachloride whose density had been previously determined. The measured density was found to be D = 1.566 g cm 3, which is in good
agreement with the value 1.5 6 9 g cm 3 calculated for four molecules in the unit cell. 28
B. A lignm ent
The crystal used for data collection was cut from a needle and
mounted with Eastman 910 adhesive on a glass fiber approximately 0.2 mm
in diameter. The a# axis was approximately coincident with that of the
glass fiber. Figure 3 is a schematic representation of this crystal.
The crystal was aligned photographically, then transferred to a
Picker four circle diffractometer where it remained for the rest of the
investigation. Keeping track of the crystal orientation, the arcs of
the goniometer head were adjusted to zero to provide better stability,
reduce the chance of accidental collisions between the goniometer head
and the instrument itself, and to avoid multiple reflections as far as
possible.55 The crystal was then carefully centered on the instrument
and the angles 20, 0 and x accurately determined for lb high order (20
> 60°) reflections, with graphite monochromatized copper radiation
(\CuK = -.5^051 A). Since the graphite monochrometer affected the <*1 apparent instrument zeroes, all investigations were carried out with the monochrometer crystal in place. The Bragg angle for the monochrometer
crystal and x were 2b.66° and 13.3^°, respectively. A least squares fit56
of the unit cell parameters, angular zeroes, and orientation angles for
these high angle reflections gave a = 7. 09 M 1 ) A, b = 6. 1 6 5 (1 ) A, c =
20.840(3) A and £ = 104.344(7)°. A summary of a ll the crystal data is g iv e n in T ab le 3-
With the diffractometer set to monitor the 1 0 4 reflection, the take-off angle of the X-ray source was adjusted to give 80f> of the maxi mum intensity in the diffracted beam. Because of slippage in the scale,
the value of this angle was not well determined, but it was probably about 4°. A 1 ram incident beam collimator and a 1 mm receiving col limator were chosen. The crystal to source distance was 21.2 cm and the crystal to counter distance was 23.0 cm. Previous work had shown the pulse height analyzer window should be set at 9 * 30/ 3*20 which corres ponds to upper and lower level lim its of 2 9 .^- and 9 .6 kev.
The full width at half height for several reflections with 9 -
20 and ou scans is given in Table 4 . 50
o / /
F ig u re 5 . The data crystal used for cis-blcyclo[5.1.0] octA-
exo-yl jD-bromobenzene sulfonate. 31
TABLE 3 cis-BICYCLOflL 1. 0~]0CT-4-exo YL p-BROMOBENZENE SULFONATE
M o n o clin ic
Space Group P2i/c x y z x 2 ~y i+ z
x y z x i+y i-z
a = 12.829(1) A at 2^°
b = 9.759(1) A p= 95.7^(1)°
c = 11.730(2) A
cell volume = 1^61.3(3) A3
D = 1 .5 6 5 (2 ) g cm”3 Dc = 1.5692(3) g cm 3
M = 3^5.256 Z = b
nCuK^ = 55*77 cm 1
Fooo = 176
£ f f = 219^ 32
TABLE 4
FULL WIDTH AT HALF HEIGHT FOR SEVERAL REFLECTIONS
Reflection 9-20 Scan cu Scan
0 6 0 0.1 5 0 .1 5
0 0 ¥ 0.2 5 0 .1 1
9 0 0 0 .5 2 0 .1 6
9 0 2 0 .5 2 ------
k 0 0 0 .2 2 0 .1 1 C. Intensity Collection
Using graphite monochromatized copper radiation, 21+9T mostly unique reflections, not including systematic absences, were monitored from the quadrant +h, +k, , out to 28 = 126.8° (sin 0/1 = O .58 A- 1 ).
This is essentially the maximum allowable angle imposed by the geometry of the Picker diffractometer if collisions are to be avoided. Because
0 k & and 0 k I are equivalent reflections in the monoclinic system,
2581 unique reflections were eventually available for this problem.
The duplicates were averaged after the data was corrected for absorp tion and were used to assess the validity of that correction, as well as the self-consistency of the data as a whole.
The integrated intensities were obtained using the 8-20 scan techniques with scans 2 . 2 ° wide centered on the position calculated for each peak with CuK^ radiation. The peaks were scanned at 2°/ min. and background scattering was monitored for 20 seconds on either side of the peak. After each 100 peaks were scanned, a set of 3 check reflections, the 211, 12 0 2, 035 were monitored. These provide a measure of inter nal consistency for the data set and help to assess crystal decomposition.
Throughout the investigation the data crystal was subjected to a total of 95*5 hours of X-radiation. Of the total, 0 .5 hours of the ex posure was unfiltered MoK radiation, used in the in itial photographic line up, and 1 3 .5 hours of exposure was graphite monochromatized CuK^ radiation used during alignment and various checks prior to data collection.
The data collection itself exposed the sample to 81.5 hours of CuK^ r a d i a t i o n . IV. DATA REDUCTION
A. Attenuator Corrections
In order to avoid coincidence losses, the data collection program automatically inserts layers of brass foil, each 0.0 0 1 inch thick, be tween the crystal and the counter whenever the counting rate during a scan exceeds 12,000 cps. Successive layers of foil are inserted and the reflection rescanned until the entire scan is successfully completed.
The to tal raw counts, and each background were corrected with program
A1TEN57 by multiplying each by 2.99 (for CuK radiation) raised to the O' "fcii n power, where n is the number of attenuators used. A summary of these corrections is given in Table 5- 35
B. Background Corrections
If one assumes that the background intensity is a linear func tion of 29, at least within the lim its of a given peak scan, then the net integrated intensity, I for a particular reflection is given as
1=1 - G(B1 + B2) (1) o w here I q is the net raw count accumulated during the scan, G is the ratio of time spent scanning the reflection to the total time spent counting backgrounds, and B1 and B2 are the raw counts accumulated for the first and second backgrounds respectively. In this experiment
G = I . 6 5 . The standard deviation of the net integrated intensity a^ is given by the semiempirical equation
1 o T = [lo + 9-00 + G2 (B1 + B2 + 1 8 .0 ) + ( p i )2 ]2 (2) where the terms in Iq and the backgrounds represent the statistical variance appropriate to a Poisson distribution in the counting statis tics. The final term, which was first introduced by Busing and Levy ,58 allows for errors proportional to the net count such as fluctuations in the beam intensity or uncertainty about the extinction correction, and helps to avoid an unrealistically low estimate of the standard deviation for strong reflections. The numerical constants 9*0 and 18.0 arise be cause the EMR computer does not read the last digit of the scaler. A v a lu e o f 0 .0 6 was chosen for p when the data was initially processed with program BCOKR57. Subsequent investigations have shown that this value may have been too large, and the strong data underweighted in the least squares refinements. After subtracting background, 2kb’J r e f l e c tions were found to be observed above background and the intensity of
2357 reflections was greater than a^. Because some reflections were measured more than once (see below, p . 31 ), the number of unique re flections ultimately available in this study was somewhat smaller. In
Table 6 , the data is broken down into 10 shells corresponding to in creasingly larger values of the Bragg angle. Each shell is of equal volume in reciprocal space and should roughly contain an equal number of reflections. Although there is some indication that the data dies off with increasinging angle, there are s till many strong data in even the highest shell. 37
TABLE 5
SUMMARY OF ATTENUATOR CORRECTIONS FOR
cis-BICYCLO[5.l.OIOCT-4-exo-YL jd-BROMOBENZENE SULFONATE
Number of Attenuators Number of Reflections
0 2kkk
1 b’J
2 13
3 l 3 8
TABLE 6
SUMMARY OF DATA ABOVE BACKGROUND FOR
cis-BICYCLOH. 1 . OlQCT-4 -exo-YL _p-BROMOBENZENE SULFONATE
Number greater Range Number th a n
1 2 3 4 5 6 7 8 9 10 A ll
Oct 265 248 2^5 241 250 241 239 260 223 235 2447
I ct 263 247 242 231 242 228 229 247 20 6 222 2357
2ct 262 244 235 226 233 220 218 235 191 199 2263
3a 261 2^3 229 225 218 207 206 222 184 186 2181
4c 261 243 225 219 212 203 202 214 176 172 2127
5^ 261 242 224 213 207 192 195 208 162 160 2064
6a 261 239 220 207 204 185 189 198 15^ 150 2007
lo 261 234 214 204 199 181 184 188 144 142 1951
8 a 259 230 212 203 196 174 178 183 134 133 1902
9o 25 4 226 205 195 194 168 169 175 126 127 1839 lOcr 250 222 203 187 182 163 153 161 115 122 1758
0 max imum s in 9 /\ = 0.58 A 1
crystal volume = 0 .0 1 1 mm3
Cul^ radiation 39
C. Lorentz and Polarization Corrections
Program PLPIC 57 applied corrections for Lorentz and polariza tion effects.
1. The Lorentz Factor
The Lorentz factor, L ,59 accounts for the rate at which a recip rocal lattice point passes through the diffracting position. For the normal beam geometry employed in the. Picker diffractom eter, L is a simple function of the Bragg angle
L - s i r s r
This function is evaluated exactly and does not introduce any extra un certainty into the observed structure factor.
2. The Polarization Factor
The polarization factor, p , 59 reflects the power loss due to partial polarization of the diffracted X-ray beam. Because a graphite monochrometer was employed, the X-ray beam was polarized by both the monochrometer crystal and by the specimen crystals, and the polarization factor must take both into account. Azaroffs°a has derived a general formula for p which reduces toe .60^
p = CO S2 2QW + cos 2 20 p p i + cos 20 ^ ' m when the plane normal of the monochrometer crystal is perpendicular to that of the specimen crystal. This is the geometry used in the Picker diffractometer. The variables 0 and 0 represent the Bragg angles of in o the monochrometer and specimen crystals respectively. For graphite ko
monochromatized Cu K radiation, 29^ = 2 6. 55 °. Equation (*0 assumes
that both the specimen crystal and the monochrometer crystals are
ideally mosaic, which may not be an entirely valid assumption for the
monochrometer. If the monochrometer crystal is ideally perfect rather
than ideally mosaic, then the expression for the polarization factor becom es 61
cos 20 + cos 2 29 m______e P = ------(5 ) 1 + cos 20 m
When 29^ = 0 or 180° equation (1) and ( 5 ) are identical. The differ
ence between them reaches a maximum at 29 = 90°. For Cu K radiation, c Q? ’ the two expressions give p = O.UU 5 and p = 0.kj22, respectively, at
20 = 90°. In this experiment, the monochrometer crystal was assumed to be ideally mosaic.
The observed structure factor magnitude on a relative scale is
g iv e n as
|F ( h ) | 2 = 1(h) /Lp ( 6 )
and the standard deviation of | F(h ) | 2 i s
a |F(h)|2 = a l / l p E V (7) In addition to applying the above corrections to the observed data and
their standard deviations, program PLPIC takes the square root of equa
t i o n ( 6 ) and stores the structure factor magnitudeJf‘ '(b) \ At the same
time, the standard deviation of the structure factor
CT|F(h)| / 2 h-)l =aF (8) is calculated and stored. h i
D. Evaluation of the Check Reflections - Decomposition
During data collection, a set of three check reflections, the
2 1 1 , and 0 3 5 , and th e 12 0 2 , were monitored after each 100 d a ta points. The 2 1 1 at 20 = 18.8°, was very strong, averaging 79,800(160) counts with two attenuators in place ( 7 1 3, 0 0 0 (1 * 1 0 0 ) counts after the attenuator correction was applied). Figure la charts the measured intensity of this reflection as a function of the sequence number
IWHEN which is roughly proportional to the amount of time the crystal had been exposed to X-rays during data collection. The best straight line through the data had a slope of -0.27(10) counts/lWHEN and an intercept, 1^ = 7-996(13) x 10 3 counts. The standard deviation of the residuals was 355 counts. At the end of the data collection if 1^
(2 1l)= 0.9916. Figure lb illustrates the behavior of the 0 3 5
(20 = 1 7-9 0 ) and figure 1 c shows the 12 0 2 (20 = 9 2 . 9°)* The best straight line through the data for the first of these reflections had slope = -1.08(12) counts/lWHEN and intercept, I^n= 7-905(18) x 10^ counts while the second reflection gave slope = -0.20 counts/rWHEN and intercept, I = l.l!0(8) x 10 4 counts. At the end of the data collec tion, 1/ I^n was O .966 and 0.97° counts- respectively for the two reflec tions. The standard deviations of the residuals were 181 and 2ll counts for the two reflections.
Decomposition affects the long term order in a crystal, thus high order reflections are more sensitive to its effect than low order reflections. One model for a correction term which compensates for de composition is Figure 4. Cheek reflections for cis_-bicyclo[5. 1 . 0 ] - oct-4-exo-yl jD-bromobenzene sulfonate.
k2 o * INTENSI TV 8.0 - 9 7 8.1 - - + + + •I- + 800 mIn 2 I I WHEN 0 0 S I 2400 ' 4 INTENS I TY * I O I * TY I INTENS oo ^ o j ■Nl ■Nl W N ->j ?> oo o * I I WHEN 0 2
+
-h + + +
800 1600 2400
I WHEN vn k6
?(t) = I = A#(t) exp (- B S2) (9 ) where A*( t ) describes the amount of crystal decay as a function of time S 0 and B accounts for the dependence of the effect on S = —-— . If we A assume that the amount of decay increases linearly with time, that is,
A'(T) = AT, then
STt ) = AT exp (- B S2) (lO)
If we take the natural logarithm of both sides of equation ( 8 ) we get
ln(l(T)) = In (AT) - B S 2 ( l l ) s in 2 Q and at any given time, T, a plot of ln(T) versus for several X2 reflections w ill have slope -B and intercept, In AT. In Figure 5 we plot
In T(T) at the end of the data collection versus (sin2©/ X2) for the three check reflections. These reflections do not yield a linear rela tionship. In fact, highest angle reflection shows a slightly smaller loss of intensitythan the intermediate reflection. In any case, it was felt that the form of any decomposition factor was indeterminate from the three data points available. Moreover, decomposition was relatively un important in this study, amounting at most to an error of ^ in I or 1.5^ in F which is less than the uncertainty in the measurement itself or in the absorption correction.
In the data reduction, the factor p (eqn. (2)) used in the calcu lation of the estimated standard deviation was set arbitrarily at 0. 06.
However, further examination of the check reflections reveals that this figure may have been somewhat overestimated. If we identify the standard deviation of the eesiduals calculated for the least squares lines men tioned above with the standard deviation calculated via equation ( 2 ), th e 8 -
*0
16
24
+ 32 4-
i —r~ 0 .1 sin2 Q 0.2 A*
Figure 5. A plot of In I/I vs. sin20/X2. •p- o -3 factor p may "be adjusted to bring about equality. For the three stan dards, this procedure gave p = 0. 01. h9
E. Absorption Corrections
As outlined above, the data crystal is best described by the id e a liz e d fig u re shown in F igure 3 (p. 3 0 ). A complete description of the crystal, however, includes not only a list of the indices of the bounding planes, but also the perpendicular distance of each to some point. For the crystal used in this study, the following description was employed
1 0 0 0.1187 mm O i l 0.0875 mm
1 0 0 0.1187mm O i l 0 .0 8 7 5 mm
0 1 1 0.11+37 mm 1 1 1 0 .1150 mm
O i l 0.11+37 mm where the first three numbers refer to the Miller indices of the crystal face and the distance refers to the distance from each face to the hypo thetical center of mass of the crystal without the chipped edge. The absorbance, A, of the crystal for any reflection is given as 62
A = J | exp[-^(rp + rd)3 dV (12) where V is the volume of the crystal, and r and r^ are the path lengths within the crystal of the primary and the diffracted beams for that part of the beam diffracted by the volume element dV. The linear mass ab so rp tio n c o e f fic ie n t, jx, is NA I (1 3 ) i= l , u s 63 where p = the crystal density, g^ = the mass fraction and ( — )^ = the mass absorption coefficient of the i ^*1 atom. The summation is evaluated 50 over the NA atoms of the unit cell. For c is-b icy clod 5 .l.Oloct-^-exo-vl p-bromobenzene sulfonate m> = 55-77 cm "1 for Cu 1^, radiation.
The in te g ra l ( j ) was not evaluated d ir e c tly , but was approxi mated in program PICABS 64 which applied the correction as a summation of terms evaluated at a series of points throughout the crystal. After several trials, the summation was found to converge adequately for a grid of points 7x 7 x 7 *
The structure factor,|Fre^(h)|, corrected for absorption, is given as:
2 = |p'(h)|2/ A(h) (lit)
ctf = ctf/ /A(h) (15) where F/(h) is the structure factor before correction. The minimum and maximum corrections on |F/ (h ) | 2 were A 1 = 2.191. and 3-7^7, respectively. 51
F. Deletions and Averages
Because of the nature of the data collection routine, the data set included the reflections 0 k 0 , where k was an odd integer, and the zone h 0 ±&. The former are systematically absent in space group P2i/c and were expunged from the data set before further processing. None were observed above background scattering.
Moreover, in monoclinic space groups, the reflections h 0 Z and h 0 jI are equivalent, thus they were averaged by program MERGE ? 7 a f te r the absorption correction, leaving a total of 2381 structure factors in the data set, of which 215^ were significant at the 2j level. For the h 0 SL zone, th e average d e v iatio n from the mean was 11° for the structure factors with the absorption applied. Without the correction, the average deviation from the mean would have been . This implies that absorption effects, which do not necessarily affect symmetry related reflections equally, had been reduced by the correction.
While the data was being averaged, a preliminary scale factor was also applied to place the data on a more nearly absolute scale. The scale factor, h . 6 8 was derived by multiplying the approximate average absorption correction (on F), 1.79s by a preliminary scale factor, 2.6l, derived from a rough Wilson plot (see below) done at an earlier stage of processing. G. The Wilson P lo t
The average value of the structure factor squared, on an absolute
scale is related to the scattering material in the unit cell as 65 NA
factor of the i ^*1 atom in the unit cell. The pwys factor allows for the
fact that the average intensity of the reflections from certain zones is
abnormally high. The unusual averages for these zones is a reflection of the underlying symmetry of the unit cell. In space group P2i/c, p = 2 for the zones 0 k 0 and h 0 I; otherwise p = 1 .
The thermally averaged scattering factor, g^(h), reflects the "fcil true scattering from the i 1 atom. The scattering is attenuated because
of the thermal motion of the atom.
g.(h) = f.(h)*T.(h) (IT) where f^(h) is the stationary-atom scattering factor and. T^(h) is a
function to allow for the thermal motion. If the atom is assumed to
execute simple, isotropic, harmonic motion, then T^(h) is the Fourier
transform of a spherically symmetric, three-dimensional, normal proba
bility distribution function
T ,(h) = exp (- B SiBf®. ) (18) 1 ” \ s
Equation ( 1 3 ) provides a means to link the structure factors
derived from the intensity data on a relative scale with the scale factor which will put them on an absolute scale. The scale factor, K, is 53
defined from the equation
k b Ste >|2 “kel^l2/ K («)
Equations (1*0, (15) and (16) can be combined with equation ( 1 3 ) to
give
Equation ( 1 3 ), which is a direct consequence of the central limit
theorem, is valid not only for the average taken over all of reciprocal
space, but also for any unbiased sample of reciprocal space. If we
divide the data up into shells where sin 9/ X is constant, or nearly so,
and if we assume that B is the same for all the atoms, then equation (IT)
becomes < . ) K exp (_2B sirf_e (2I) P ° z n X2
where the subscript n denotes that the average applies to the shell,
and we have defined
ct2 = J f f ( h ) (2 2 )
Taking the natural logarithm of both sides, we get Wilson's equation
K e l ^ l 2 , > = In K - 2B Silf-® (23) p a 2 n
which says that a plot of In (|Fre 2 (]l)j2/ P CT2 )n vs. sin 2 9 / X2 should
be a straight line with slope -2B and intercept In K.
Program WILPLT66 performed the necessary computations.
And, then, aft;er dividing reciprocal space into a series of concentric
shells of equal volume, the quantity in ^ |^re^(ll)| 2 / P CT2 ^ an<^
average value of sin 2 0 / X2 Were calculated for each shell. These values are then fit to a least squares line to find K and B, and K' is applied
to the observed structure factors to place them on an absolute scale.
We shall refer, hereafter, to the observed, scaled structure factors as
F0 (h)
In the calculations, the scattering factor for bromine was taken from the tabulation of Cromer and Waber , 67 while the scattering factors for the remaining non-hydrogen atoms, sulfur, oxygen, and carbon, were those derived by Hanson, Hermon, Lea, and Skillman . 68 For hydrogen, the tabulation derived by Stewart, Davidson, and Simpson 69 was chosen.
At the same time that the data was scaled, the normalized struc ture factors, E(h), were calculated and stored
The Wilson plot, Figure 6 , indicated that a scale factor /K =
should be applied to the structure factors, |F(h)|, to put them on an absolute scale and that the average temperature factor, B = 4.51(13)
A2. However, with these values for/K and B, the average value of E 2
is 0.984. It has been pointed out 70 that to get meaningful statistics involving E, (Je|2) must be close to the theoretical value of 1.00. Thus, before scaling the data, /k was adjusted to 0.934 so that ((eJ2 ) was forced to attain its theoretical value. The observed statistics on|E| are listed in Table 7, along with the theoretical values for a centric and an acentric distribution of the diffracting power in the crystal.
Because 55 *8/° of the scattering power is concentrated in one atom, bromine, the basic premise of the Wilson statistics, that is, that the 55 distribution of the scattering power is essentially random, cannot be completely valid. Thus, it is not surprising that the observed distri bution of the normalized structure factors is somewhat different from that which is predicted for a centric structure. However, the distri bution is in better agreement with the statistics for a centrosymmetric structure than with those for a noncentrosymmetric structure which is as it should be for a structure in the centrosymmetric space group
P 2 ; l / c . The concentration of the scattering power in the bromine atom also manifests itself as ripples in the Wilson plot itself. 56
TABLE T
STATISTICS ON E
cis-BICTCLOr5.1. OlOCT-4-exo-YL £ - BROMOBENZENE SULFONATE
Experimental Acentric Centric
< |e |2 > 1 .0 0 0 1 .0 0 0 1.0 0 0
(I e 2 -i|> 0 .9 2 1 0.7 3 6 0 .9 6 8
<|e|> 0 .8 1 7 0 .8 8 6 0 .7 9 8
Values of | e | greater than Number F ra c tio n Acentric Centric
0.5 1517 O.637OOO O.799OOO O.618OOO
1 .0 816 0 . 31+2000 O.368OOO O.317OOO
1-5 323 0.135000 0.105000 O.I3I+OOO
2 .0 81+ O.O35 OOO 0.018000 0 .01+5000
2.5 16 O.OO67OO 0.001900 0.012000
3.0 1 0 . 000t 20 0.000120 0.002700
5-5 _ 0 0.000000 0.000005 0 .0001+50
1+.0 0 0.000000 0.000000 0.000060 0 . 0 1
-I.O'
Cb> L- CL
- 2.0 + ,
- 3.0 \ 0.1 0.2 0.3
s i n 2 9 Figure 6. The Wilson P lo t X 2 VJ1 V. SOLUTION OF THE STRUCTURE
A. The Patterson Function
A sharpened Patterson 71 function ( 2 5 ) was c alcu lated using p ro gram FOUR57 with the normalized structure factors, |E(h)|, as coefficients
P(u) = |E(h)| 2 cos 2fl(h*u) ( 2 5 )
In the space group P2a/c, the four symmetry elements
x,y,z x,y,z x,|+y,|-z x,i-y,|-+z give rise to the following Harker vectors72in the Patterson function
(with their relative weights given in parenthesis).
1 2x 2y 2z (1) 2x 2 2 +2z (2)
1 -2x -2y -2z (1) -2x 2 -2z (2)
1 2x -2y 2z (1) .0 i+2y 2 (2)
1 -2x 2y -2z (1) 0 i-2 y 2 (2)
In addition, the center of symmetry implies that any Patterson peak (not
Harker) will in general be doubly degenerate. The weights of the various single weight vectors is :
origin 4 £f? 2= &[j6 Br-Br = 1225 Br-S = 560(but these will be S-S = 256 double weight) 59
Table 8 lists the highest peaks found on the Patterson function along with their height on a relative scale. The first three of these repre sent bromine Harker vectors and fix the bromine position at
0 .0 1 0 0 .1 7 0 0.105
There are eight peaks in the Patterson function (four in the asymetric unit) which correspond to the Br - S vectors. If we call the bromine coordinates xls yx, zx, and the sulfur coordinates x2, y 2 , z2 , we may re p re se n t th ese v ecto rs as
Ax Ay A z ■Ax *Ay -Az
Ex s y Ez -Ex -Ey -Zz Ex • i-*A y -Ex i-A y I'-Zz
Ax i-£ y ■^hAz -Ax i-E y i-Az where Ax = xj. - x2 , Ex = xi + x2 , and so on for each of the other variables. Each vector is two-fold degenerate, and should in general have a relative height approximately equal to that of a single weight
Br-Br vector. Peaks U through 7 in Table 8 represent the Br-S vectors in this map, and from these, the sulfur position was fixed at
-0 .2 6 0.625 -0.040
With these coordinates, peaks 8 through 10 were identified as the sulfur
Harker peaks. Peak 9} which lies on the Harker line, is anomolously small because it lies in the interference fringe of a bromine Harker peak. 6o
In order to place both of the atoms on one molecule, the coordi- nates were transformed to
* Z z a b c
Br 1.010 O.33O -O .395
s 0.71*0 0.625 -0.0U 0 6 l
TABLE 8
LIST OF THE STRONGEST PEAKS IN THE PATTERSON FUNCTION
u V w relative type height
1. 0 .0 0 .1 6 0 0 .5 + Br-Br Harker
2 . 0.98 0 .5 O.29 + Br-Br Harker
3- 0 .0 2 O.54 0 .2 1 23 Br-Br Harker
k. 0.255 0 .0 5 0 0 .1*3 23 Br- S vector
5- 0.75 0 .2 0 0 .0 7 2k Br- S vector
6 . 0.73 0 .3 0 0 .3 6 25 Br- S vector
7- 0.265 O.Ui-5 0.1k 23 Br- S vector
8 . 0 .U8 0 .5 0 .1*25 19 S - S Harker
9- 0 .0 O.25 0 .5 10 S - S Harker
1 0 . 0 .5 2 O.25 0 .0 8 7 S - S Harker 62
B. The T ria l S tru ctu re
It can be shown, that the Patterson function can be interpreted as a repeated superposition of the electron density function onto itself with the origin of each copy of the density function shifted in turn to one of the atomic centers. Based on the positions of the four symmetry related bromine atoms and the four symmetry related sulfur atoms in the u n it c e ll , a minimum fu n ctio n 73 was constructed by superimposing the
Patterson function on itself, with relative displacements of each "copy*' equal to one of the bromine-bromine or bromine-sulfur vectors. The value of the function was determined by averaging the two smallest of the eight terms found for each point. The necessary computations were carried out by program SUPER .74
The minimum fu n c tio n generated in th is manner was very clean.
The positions of the nineteen atoms of the complete structure (without hydrogen) were identified from the twenty-three largest peaks in the function. The few spurious peaks were mostly near the bromine atom.
They were easily eliminated, not only because they were not in accord with the molecular geometry, but also because they were among the weaker peaks on the map and they were poorly shaped.
The numbering system used for this molecule is illustrated in
Figure 7 and the initial atomic coordinates derived from the minimum function are listed in Table 9 • H3
HI 2 H* HI3 \C C2 C8 BHI BH2 0 2 BC BCV C4
BC4 Br
BC6 BC5 0 3 BH3 BH4
Figure 7. A schematic representation of the numbering system used for cis-bicvclo
[ 5 . 1. 0 ]oct-4-exo-yl _p-bromobenzene sulfonate.
CT\ V>J 64
TABLE 9
INITIAL COORDINATES OBTAINED FROM THE MINIMUM FUNCTION
X Z z a b c
B r 1.010 0.330 -0 .3 9 5 S 0.740 0 .6 2 5 - 0 . o 4 o 01 0 .7 0 0 0 .5 0 0 0. 020 02 0.815 0 .7 0 0 0 .0 3 5 03 0.655 0 .7 0 0 -0 .0 9 5 BC1 0 .8 1 0 0.535 -0 .1 3 0 BC2 o. 885 0. 445 - 0.100 BC3 0.940 0. 385 -0 .1 8 0 BC4 0 .9 2 0 0. 420 - 0 .2 8 0 BC5 0 .8 5 5 0.515 -0 .3 2 0 BC6 0 .8 0 0 0 .6 0 0 - 0. 240 C l 0 .6 5 0 0.335 0 .3 7 0 C2 O .750 0. 415 0 .3 4 0 C3 0 .7 6 0 o . 4 oo 0 .2 0 5 c 4 0 .6 8 0 0 .5 0 5 0 .1 6 0 C5 0 .5 7 0 0 .5 0 5 0 .1 5 0 c 6 0.5^0 0.500 0.280
ct 0 .5 5 0 0 .3 8 5 0 .3 5 0 c 8 O.bOO 0.375 0 .4 7 0 C. Initial Refinement
Structure factors calculated for the trial structure as m F (b) -I f^(h) T^(h) cos 2ir h*r (26) i= l gave R = 0.21, and WR = 0.3 6 . The agreement factors, R and WR, provide
an index of the goodness of fit between the observed structure factors,
Fo(h), and the calculated structure factors based on the proposed model
s tru c tu re
R (27) 2 lF 0 (h)l
£w I A | 2 WR = (2 8) £w | F0 (h)l
In these equations, A = |Fo(h)l - lFc(h)|, and the weighting function , w = l/CTp • For the in itial structure factor calculation, the atoms were
assumed to vibrate isotropically (see equation (15)). The temperature
factor, B, was set at 4.5 A2, for all of the atoms. The scattering
factors 67 69 used here and throughout the refinements, were the same
as those used in the Wilson plot. At a later stage, during the full ma
trix refinements, the anomolous dispersion effects calculated by Cromer75
for bromine and sulfur were added.
The initial least squares refinements of the structural parameters
were carried out on the same EMR 6130 computer which had controlled the
data collection and which had carried out the data reduction. The four
program package, SFLS,57 provided the necessary computations. The first
program, SFLS1, reads and stores the input parameters, which are used in 66 turn by SFLS2 to calculate structure factors and set up the normal ma trix. SFLSJ inverts the matrix, then SFLSU calculates the discrepancy between the observed and calculated structure factors, tests for conver gence, and applies the appropriate shifts to the parameters to improve the fit between the two. The function minimized in these refinements was 2w (lF0 (h)| -k |F c (h)} )2 where k is a scale factor. The programs assume convergence has been achieved when WR does not decrease from one cycle to the next, but in practice, the magnitude of the parameter shifts is also considered before assuming convergence. Although the refinements were carried out on Fo(h), only the planes where FoCh)5^ ^ were included.
The entire normal matrix was used in the first cycle of the re finement, but a block diagonal approximation was used in all succeeding cycles on the EMR 6130 computer. In the approximation, the normal matrix is reduced to a series of 4xU matrices along the diagonal of the full matrix. Each block corresponds to the coordinates and the temperature factor of one isotropic atom. In addition, a 2x2 block contains the scale factor and the overall temperature factor. All other elements of the matrix are set identically equal to zero. In effect, this means that correlations between the parameters from different atoms are ignored.
Parameter shifts were damped by a factor of 0.8 in the first cycle but later cycles had the full shift applied. A total of 6 cycles were needed to achieve convergence at R = O.I 38 and WR = 0.217, for 22hb d ata.
After the refinement converged., a difference Fourier function was constructed
D(x) = ^ ^ (Fo(h) - Fc(h) ) exp[- 2 n h*x] ( 2 9 ) Since the observed data only yield the structure factor magnitudes di rectly, Fo(h) is given the same sign as F (_h) in this function. The largest features in the map were associated with the bromine atom and clearly indicated that the thermal motion of that atom was not adequately described by the isotropic model discussed above (see p.52 ). In addi tion, similar features of lesser magnitude indicated that the thermal model was inadequate for the sulfur and. oxygen atoms as well. Residual features associated with the carbon atoms were less than the background noise in the map and hydrogen atoms were not evident in the map.
A better approximation to the thermal motion of the atom allows for simple anisotropic, harmonic motion. In this case, T^(h) is the
Fourier transform of a three dimensional, normal probability distribution function-76
Ti (h)=exp [-(Pnh2 + £ 2 2 ^ + P3312 + 2p12hk +
2(313hl + 2p23kl)3 = exp [-h^ ph ] (50) where p is a 3X3 symmetric tensor with elements 0... An initial estimate of the tensor is derived from the temperature factor coefficient,B , via the relation
(31) -1 where A is the inverse metric tensor for the crystal 68
The parameters P .. are not easily interpretable in terms of physi- X J cal vibrations and we shall find use for a related definition of T (h):
T.(h) = exp [-27t2(u1ih2a* + Uaak 2^!-2 + U33je2c* 2 + 1 “ (33) 2Ui2hka*b# cos y* + SUishla^c* cos P# + SUaakXb^c^cos cv*)] where the thermal parameters, U.are expressed in terms of root mean XJ square amplitudes of vibration in angstroms. 69
D. Anisotropic Refinements
After converting the bromine temperature factor coefficient, B to the appropriate p tensor, five additional cycles of block diagonal refinement brought R = 0.0823, and WR = 0.1301. The additional param eters of the anisotropic atom were refined as a 9X9 block in the approx imate normal matrix. The dramatic decrease in WR evidenced the validity of the extra parameters needed to describe the anisotropy of the bromine thermal motion. Four more cycles with an anisotropic sulfur atom reduced
R to O.O785 and WR to 0.0922. Then, with all the atoms anisotropic, R and WR dropped to 0.0559 and 0.0922 before the refinement diverged slightly. The divergence arose, no doubt, because the block diagonal approximation ignors correlations between parameters in different blocks.
While WR decreased at each stage of the refinement, the quanti tative significance of the decrease should be tested in view of the cor responding increase in the number of parameters used in each case. Table
11 summarizes the refinements. Following Hamilton's 77 procedure, we may test the hypothesis:
Hq: All atoms vibrate isotropically.
In this case we compare WR at the end of the first stage of the refine ment with all atoms anisotropic. The appropriate R-factor ratio is
which must be compared,with the tabular value = 1.0297 95,2071,0.005 which says that we may reject the hypothesis at the 0 .«$ le v e l. TO
For the hypothesis
Ho: Only Br has an anisotropic temperature factor,
the appropriate statistics are:
_ = 1 J a o 8 0.0927
= 1.0285 *9 0 , 2071, 0.005 and the hypothesis is rejected at the 0.005 l e v e l .
F i n a l l y we t e s t th e h y p o th e s is
Ho: Only Br and S have anisotropic temperature factors,
and the statistics are:
0.1261 8 - a t m = 1 ° 60
= 1.0275 £8 5 ,2071, 0.005
Once ag ain , th is hypothesis must be re je c te d a t th e 0.005 le v e l. Thus we
are confident that the thermal motion of the non-hydrogen atoms was not
is o tro p ic .
A difference Fourier (equation ( 2 9 )) constructed at the end of
th e anisotropic refinements had residual peaks with densities between 0 .5
and 0 .8 e/A 3 which were in accord with the positions predicted for hydro
gen atoms. Every feature in the map above 0.2 e/A3, was associated with
one of the hydrogen atoms. Table 10 lists the initial hydrogen coordi n a te s . 71
TABLE 10
THE INITIAL HYDROGEN ATOM POSITIONS FOR cis-B IC Y C L 0[5.1. QlOCT-4-exo-YL p-BROMOBENZENE SULFONATE X z z a b c
HI 0 .6 6 0 0.195 0 .3 8 0 H2 O.8 3 0 o .4 oo 0 .3 8 0 H3 O.'fkO 0 .5 4 0 0 .3 7 0 h4 0.7 3 0 0.325 0 .1 8 0 H5 0.835 0 .4 5 0 0.205 h6 0.700 0.6 1 2 0 .1 8 0 H7 0.5^5 0.3 9 0 0 .1 2 0 h8 0.525 0 .5 6 5 0.095 H9 0.5 5 5 0 .0 2 0 0. 240 ELO 0. J+ifO 0 .0 9 0 0 .1 8 0 H ll 0 .4 9 0 0 .5 0 0 0 .3 1 0 H12 0.6 2 0 0 . 1»85 0 .5 0 0 H13 0 .5 6 5 0.315 0 .5 3 0 BEL 0.895 0 . 44 o - 0 .0 2 5 BH2 0 .0 0 0 0.325 - 0 .1 4 5 BH3 0.835 0.5 2 5 - 0 .415 m b 0 .7 3 0 0.625 - 0 .2 8 0 72
E. Full Matrix Refinements and Hydrogen Atoms
At this point, the data was transferred to the IBM 37° computer at the Ohio State University and the refinements continued with the complete normal matrix. The computations were carried out by program
NUGLS? ,78 which is a local version of the Oak Ridge program ORFLS. The scattering factors used previously were retained .,67 69 but anomalous dispersion corrections for bromine and sulfur were added .75 Five cycles of refinement gave R = O.O 56 H and WR = O.O 89I. After hydrogen was added to the refinement, five more cycles of refinement led to conver gence a t R = O.O 3 8 8, and WR = 0.05^8. As before, the function
£ w (|F0 (h)[-k|Fc(h)| )2 was minimized. 73
F. Extinction
At the end of the foregoing refinements, a detailed examination of the observed and calculated structure factors revealed that the data
set suffered significantly from the effects of secondary extinction.
Secondary extinction reflects the attenuation of the incident beam as it passes through the crystal which occurs because some of the incident beam goes into the diffracted beam. This is in addition to the attenua tion due to absorption. Strong, low order planes are particularly sensi tive to the effect, which causes them to be systematically underestimated.
If the mosaic character of the crystal is assumed to be isotropic, then the formalism due to Zachariasen 79 may be used to correct for secon dary extincation. In this case, the structure factor, corrected for secondary extinction is given as
Fcorr(h) w K F0 (h ) [ 1 + p '( 2 0 ) g 1 (h ) ] (3k) w here
(1 + cos2 20 ) (1 + cos2 29 cos4 29 ) C dA-1/c!(i 3OB „0 , , p'(28)=------—------2------(35 ) ( 1 + cos 2 2 9 m cos 2 2 0 c )2 [dA~ /dn-3 20 _ Qo and g is the secondary extinction parameter, which is a characteristic of each particular crystal.
In order to accomodate the effects of secondary extinction, Lar son,'s8
After four cycles of refinement the residuals were R = 0.03533 an(3 WR =
0 . 0 5 1 1 2 . The statistics
f l - s tiit =1-°r20 reject the hypothesis that extinction was not important.
With the inclusion of secondary extinction in the refinements, the parameters most affected were the scale factor and the thermal parameters. The former increased "by while was approximately
0.0 0 0 3 for all of the atoms.
The atomic parameters from the final least-squares cycle are given in Tables 12 through lb. The observed and calculated structure factors are given in Table 15- TABLE 11
SUMMARY OF REFINEMENTS b m a NO R WR GOFC
( Block diagonal refinements on EMR 6130 )
All atoms isotropic 78 2244 O.138O 0.2169 6 .0 k
Anisotropic Br 83 2244 O.O839 O.I307 3 .6 k
Anisotropic S 88 2244 0.0800 0.1261 3 .5 2
All atoms anisotropic 173 2 2 kb 0.0573 O.O927 2 .6 4
( Full matrix refinements on IBM 370 )
All atoms anisotropic 172d 2244 0.0564 O.O89I 2 .3 k
Add hydrogen 240 2244 O.O388 0.0548 I .50
Add e x tin c tio n p a ra m e te r 24-1 2244 0.0333 0.0511 1 .4 8 a. NV = the number of parameters allowed to vary. b. NO = the number of observed data included in the refinement. c. The goodness of fit (or standard deviation of an observation of unit weight) i s d e fin e d as Ew( | Fq ( h ) | - 1 Fc ( h.) | )^
NO-NV d. One less parameter was refined because an overall temperature factor is not necessary in full matrix refinements. TABLE 12
FINAL HEAVY ATOM COORDINATES FOR cis-BICYCLO[5 .1 . OlOCT-^-exo -YL p-BROMOBENZENE SULFONATE
Atom X 1 z_ a b c
1 Br 1 . 00991(3 ) 0 .3 2 8 9 1 (4 ) -0.39346(3) 2 S 0 .7 4 0 8 4 (5 ) 0. 62678( 6 ) - 0 . 03762(5 ) 3 01 0 . 6960( 2 ) 0 .5 0 3 7 (2 ) 0 . 0253 ( 2 ) 4 02 0 . 8 1 3 4 (2 ) o„ 7004 ( 2 ) 0 . 0397( 2 ) 5 03 0 .6 5 7 9 (2 ) 0 . 7022( 3 ) -0 . 0975 ( 2 ) 6 BC1 0 . 8 0 8 9(2 ) 0. 5380 (3 ) -0 .1 3 7 4 (2 ) 7 BC2 0 . 8 8 6 2(2 ) 0 .4 4 6 6 (3 ) -0 .0 9 7 9 (2 ) 8 BC3 0 . 9458 (3 ) 0.3835(3) -0.1744(3) 9 BC4 0 . 9262( 2 ) 0 .4 1 3 9 (3 ) -0 . 2898( 2 ) 10 BC5 0 .8 lt8 6 (2 ) 0 . 5034 (3 ) - 0. 3291( 2 ) 11 bc6 0 . 7 8 9 1(2 ) 0 .5 6 5 7 (3 ) - 0 . 2527 ( 2 ) TABLE 1 2 (CONTINUED)
z Atom c
12 C l 0 .6 6 0 9 (4 ) 0 .3 3 2 3 (4 ) 0.3787 (4 )
13 C2 0 . 7492 (3 ) 0 . 4 i 67( 5 ) 0. 3419 ( 5 )
l 4 C3 0. 7558 ( 3 ) 0 . 4157 ( 4 ) 0. 2112( 3 )
15 c 4 0 .6 7 9 6 (2 ) 0. 5149 (3 ) 0. 1499 ( 2 )
16 C5 0 .5 6 3 7 (2 ) 0 .4 9 0 1 (3 ) 0. 1547 ( 2 )
17 C6 0 .5 3 0 0 (2 ) 0. 5029 ( 3 ) 0. 2760(2)
18 C7 0 .5 5 0 1 (3 ) 0 . 3765(3 ) 0 . 3453 (5 )
19 c8 0. 5956 ( 4 ) 0. 3822( 5 ) 0. 4686( 3 )
K (scale factor) = 1.082(4) g (extinction parameters) = 0.l8(l) x 10"4 cm.
=3 TABLE 13
ANISOTROPIC THERMAL PARAMETERS FOR cis-BICYCLOP5 . 1. QlOCT-4 -eKo -YL t>-BROMOBENZENE SULFONATE
3h ?22 P33 P 12 613 623
Br o .00850(3) 0.011+60(6) 0. oo86i ( 4 ) 0.00152(2) 0.00269(2) -0.00237(2)
S 0. 00577(5 ) 0.00885(8) 0.00667(5) -0.00034(4) 0. 00151 (4 ) -0. 00028(4 )
01 0.0101+6(18) 0 .01179(?4 ) 0.00638(14) -0.00379(16) 0 00350(13) -0. 00173( 14 )
02 0.00851(26) 0.01185(23) 0.00810(16) -0.00299(16) 0.00199(13) -0. oo?6o(i6)
03 0. 00855 ( 18) 0.01661(30) 0. 01054 (? l) 0.00471(19) 0.00170(15) 0.00086(20)
BC1 0.00509(15) 0.00881(26) 0.00551(16) -0.00036(16) 0.00067(13) 0.00034(17)
BC2 0.00680(19) 0. 01307(310 0.00505(18) 0.00151(21) 0.00063(15) 0.00138(20)
BC3 0.00643(20) 0 .01254 (36) 0.00743(2?) 0.00287(2?) 0.00030(17) 0. 00049 (22) b c 4 0.00556(16) 0.00990(39) 0.00648 (18) -0.00023(17) 0. 00100( 14 ) -0.00051(18)
BC5 0. 00812(22) 0 .01229(34 ) 0.00554(19) 0. 00140 (22) 0.00058(17) 0.00062(19) b c 6 0.00689(19) 0.01153(55) 0.00628(19) 0.00176(21) 0.00037(16) 0.00095(20) TABLE 13 (CONTINUED)
Cl 0 .01359 (39) 0 .01350 (44 ) 0.00900(29) 0.00340(32) 0.00283 (£T) 0.00310(27)
C2 0.00883(27) 0 .01798(55 ) 0.00827(26) 0.00388(31) -0.00074(21) 0. 00046 (30)
C3 0.00693(22) 0.01686( 48 ) 0.00852(25) 0.00207(27) 0.00154(19) -0.00032(28)
C4 0.00678(18) 0.01034(30) 0.00546(18) -0.00111(18) 0. 00183(14 ) - 0 .00089(14 )
C5 0.00682(19) 0.01116(34) 0.00639(19) -0.00039(20) 0.00099(15) -0.ooo4 i ( 21) c6 0.00623(19) 0.01292(37) 0.00685(21) -0.00015(21) 0.00161(16) -0.00079(22)
CT 0.01065(29) 0.01203(37) 0.00900(26) -0.00150(27) 0.00339(23) 0.00108(26) c8 0 .01596(1+6) 0.01881(59) 0.00831(29) 0. 00246 (44 ) 0.00403(30) 0.00422(36)
The expression -used for the temperature factor was exp[-Pnh2 + f322k2 + P 33^2 + 2f312hk +
23i3h X + 80
TABLE l 4
FINAL HYDROGEN PARAMETERS
X z Z B a b c
HI o. 6 7 1(5 ) 0. 2 2 6 (4 ) 0. 3 6 6(3 ) 6 .4 ( 9 )
H2 0 .8 1 4 (3 ) 0. 3 8 9(5 ) 0 .3 7 9 (3 ) 7 .1 (1 0 )
H3 0 .7 4 7 (3 ) 0 . 5 1 1 (4 ) 0 .3 6 4 (3 ) 4 .7 (7 )
H4 0.743(3) 0.327(3) 0 . 172(3 ) 4 .9 (8 )
H5 0. 8 2 6(3 ) 0. 447 ( 3 ) 0 .1 9 7 (3 ) 5 .1 (7 ) h6 0 . 7 0 0( 2 ) 0. 6 0 6( 3 ) 0 .1 7 5 (2 ) 3 .5 (5 )
HT 0 .5 4 7 (3 ) 0.4 0 2 (4 ) 0. 1 2 7(3 ) 5 .0 ( 7 ) h8 0 .5 2 6 (3 ) 0 .5 7 1 (4 ) 0 . 101 ( 3 ) 6 .0 ( 9 )
H9 0 .4 5 2 (3 ) 0 .5 2 2 (4 ) 0 . 269(3 ) 5 .9 (8 )
HLO 0 . 567 ( 2 ) 0 .5 8 4 (3 ) 0 .3 1 5 (2 ) 3 .3 (5 )
H ll 0 .4 9 4 (4 ) 0. 3 0 0 (5 ) 0 .3 1 6 (4 ) 8 .3 (1 2 )
H12 0.6 2 4 (4 ) 0 .4 8 8 (5 ) 0.496(4) 7.8(11)
H13 0 .5 7 5 (5 ) 0 . 3 2 0 (6 ) 0. 5 2 6 (5 ) 1 1 .9 (1 9 )
BH1 0. 902( 2 ) 0 .4 3 3 (3 ) - 0 . 01 9 ( 3 ) 4 .8 (7 )
BH2 0 .9 9 5 (3 ) 0 .3 3 6 (4 ) - 0 . 153 ( 4 ) 5 .5 ( 9 )
BH3 0 .8 3 5 (3 ) 0 .5 2 7 (3 ) -0 .4 2 0 (3 ) 4 .9 (7 )
BH4 0 .7 3 9 (3 ) 0. 6 2 4 (4 ) - 0 . 280( 3 ) 5 .0 (7 ) TABLE 15
OBSERVED AND CALCULATED STRUCTURE FACTORS FOR cis_-BICYCLO[ 5. 1, OlOCT-^-exo-YL p-BROMOBENZENE SULFONATE
The column headings a.re:
h 1 10 F 10 F 100 ct(F ) o c o
8 l ii ii'
!: :: ii i: : ft 5' ii! i
:: :::
:: ii:: ii :■ ii' i: ii ?■ !' £
a: s.
w ;;; va = 11 a si
•ii ii! ::: :
I
2 ::: :::
:: :i: t. r.:::: ::: ^ ii s. H. »•ii .<> !■:■iti Li- i!
::: VI. DISCUSSION OF THE STRUCTURE
A. The Crystal Structure
Figures 8 and 9 illustrate the crystal packing viewed down the b
and c_ axes respectively. The molecules pack with the bromohenzene stacked around one two-fold screw axis yielding the fam iliar herringbone pattern, and bicyclo[5.l.Ojoctane around the second screw axis. No single fea ture appears to dominate the packing and the molecular crystal is basi cally arranged to achieve closest packing82’83 which minimizes the free energy of the crystal lattice.83
The more important intermolecular contacts are set out in Table l6, along with the sums of the van der Waals radii proposed by Bondi84 for the atoms involved in each contact. The Br*»» 02 contact is particularly short (3.229(2) a ) and deserves further comment. Bondi84 has postulated that double-bonded oxygen may reflect its ir electron density with a shorter (l.l+O a ) van der Waals radius along the bond axis, and a longer
(1.6 to 1.7 a ) radius normal to it. Pauling85 set the radius at l.H A.
If the bromine-oxygen contact is determined by the van der Waals radii of the two atoms, then the difference between the observed contact dis tance and the bromine van der Waals radius should be a measure of the oxygen van der Waals radius. Bondi84 sets 1.85 1 as the van der Waals radius for bromine and the intermolecular contact distance, 3.229(2) A, was well determined from our experiment. This leaves an oxygen radius of
82 83
Figure 8. The crystal packing of cis-bicyclo[5.1.Oloct -J - e x o - y l
p-bromobenzene sulfonate viewed down b. 84
l 7
i 7
_i_ 4
Figure 9. The crystal packing of cis-bicyclo[5.1.Oloct 4-exo-yl
p-bromobenzene sulfonate viewed down c. 85
TABLE 16
NONBONDED INTERACTIONS IN
cis-BICYCLO[5 .1.0]0C T -4-exo-Y L p-BROMOBENZENE SULFONATE
a tom 1 Atom 2 Symmetry8 D ista n c e D istan c e ^ A ngle 0 r w obs c a lc
02 Br 75404 3 . 2 2 9(2 ) 3 .2 5 -3 .5 5 1 0 7 .8 I .38
02 BC5 56503 3 .2 8 3 (3 ) 3 -1 7 -3 -^ 2 142.3 1-51
02 bc 6 56503 3 -3 7 5 (3 ) 3 .1 7 -3 .4 2 1 3 4 .2 1 .6 0
02 BC3 76502 3 .4 2 5 (4 ) 3 . 17- 3 .4 2 132.3 I .65
02 BH2 76502 2.69(4) 2.4 - 2 .7 143 1 .6 9 OJ OJ 02 BH3 56503 2 .7 1 (3 ) 1 130 1 .7 1
02 bh4 56503 2 -9 6 (4 ) 2 .4 -2 .7 120 1-95
03 H10 561+03 2 .5 5 (3 ) 2 .6 - 2 .9 155-5 1-35
03 HT 66502 2 .8 0 (4 ) 2 .6 - 2 .9 120 1 .6 0
03 H ll 65502 3 . 0 6(5 ) 2 .6 - 2 .9 142 1 .8 6
03 H3 56403 3 -0 7 (4 ) 2 .6 - 2 .9 105 1 .8 7
Br BC1 74404 3-664(2) 3 .6 2
Br BC2 55403 3 -8 3 9 (3 ) 3 .6 2
01 HI 55403 2 .9 1 (4 ) 2 .7 2
BC1 HI 55403 3 -1 2 (4 ) 2 .9 7
BC2 BH1 76502 3 -1 4 (3 ) 2 .7 7
BC2 Hl 55403 3 -2 2 (4 ) 2.9 7
BC2 BC2 75502 3 . 6 8 0(6 ) 3.5 4
BC3 H2 55403 3-24(5) 2 .9 7 TABLE l6 (continued) a b ;om 1 Atom 2 Symmetry- Distance D is ta n c e obs c a lc
bc6 H9 66502 3. 19(4 ) 2.97
C5 HL1 665 o4 3. 1M 5 ) 2.90
c 6 ELI 65504 3. 10(5 ) 2.90
c8 c8 66602 3.^93(10) 3.40
h8 ELI 66504 2. 46 (6) 2.40
HT H13 55403 2 .51 (7 ) 2.40
ELO H ll 66504 2.68(6) 2. 40
H5 BH3 55601 2.68(5) 2.20
H2 BH3 55601 2 .71(5 ) 2.20
h6 BH4 56503 2 .73(5 ) 2. 20
HT h8 66502 2. 76(5 ) 2.40
HL2 BH3 55601 2.81(6) 2. 20
BEL BEL 76502 2.81(6) 2. 20
H9 bh4 66502 2. 84 (5 ) 2. 20
HLO EL3 66602 2.89(7) 2. 40
H13 H9 66602 2 .90(7) 2. 40 TABLE 16 (continued)
The first three numbers express unit cell translations along a, b and _c respectively which are applied after atom 2 is transformed according to the symmetry element designated by the last digit. The symmetry transformations are: 01 x y z 03 x i - y i+ z 02 x y "z Ob x ^+y \ - z th e screw The origin is taken at 555 and unit cell translations along the crystal axes are added or subtracted for integers larger or smaller th a n 5 respectively. For example, the symmetry element 65^03 w ould transform atom 2 according to the glide then add one unit cell translation along a and subtract one along c.
The distances were calculated as the sum of the van der Waals radii, r , proposed by Bondi:
1.85 A Br 1. bO a 0(=) along the bond axis 1.6 to 1.7 A 0(=) normal to the bond axis 1. 52 A 0(<) ether 1.77 A C(aromaric) 1.70 A C(a iphatic)
1 .0 0 a H(aromatic)
1 .2 0 a H(aliphatic)
Because of the proposed variation in the van der Waals radius of double-bonded oxygen, a range of values is given for contacts in v o lv in g 02 and 03.
T h is i s th e S=rO®*«X a n g le .
r = the van der Waals radius of oxygen after subtracting out the radius of the second atom. 88
1.38 J[, which is precisely the lim it proposed for contacts along the
"bond a x is and 0 .2 f less than the lim it proposed for contacts normal to the bond. However, in this case, the S=0«**Br angle is 107.8°. that is, the contact is more less normal to the S=0 bond.
At first we felt that this observation refuted Bondi's anisometric van der Waals radius for double-bonded oxygen, however, the work of Has- sel and Romming37- provides a second interpretation. These authors have pointed out that a donor atom possessing a lone pair of electrons in con cert with a halogen acceptor atom can give rise to charge transfer inter actions . In such cases, the carbon-halogen donor linkage is nearly linear and the weakly bonding interaction causes the contact distance to decrease from the expected van der Waals distance. In this structure, the BCii-Br*..02 interaction is indeed approximately linear, 1 o 9 . 8 ° , th u s the short contact may belie any explanation couched merely in terms of van der Waals forces. A Br«*«02 link would tie molecules together in the crystal structure in infinite chains parallel to the b axis.
Short bromine••• oxygen contacts have previously been reported in
N-(p-bromophenyl)-syndone, 3.16 A ,88 oxalyl bromide, 3 .2 7 A ,89 and 3-^p- bromophenyl-l-nitroso-2-pyrazoline, 3.298 A .90 In each case, the C-Br***
0 linkage was essentially linear, 1 6 3. 2° , 169° and 1 7 6. 2 °, respectively.
In each case, the short contacts were explained in terms of a weakly bonding charge transfer interaction.
Three other features of the present structure argue in favor of a weakly bonding interaction between bromine and 02. First, the S = 0 2 bond is slightly, but significantly, longer than the S.= 03 bond and second, the Br-BC^-BC5 angle is slightly distorted from a strictly trigonal 89
value and more importantly, the distortion is such that the Br***0
distance is decreased. And finally, in order to approach bromine, 02
is pulled to a position where the intramolecular 02***h6 and S***h6
contacts are only 2.kk and 2.60 A, respectively, which is 0.2 to 0 .It 1
less than the contacts predicted from van der Waals contacts (see below).
All of the close contacts involving 02 and 03 are summarized in
Figure 10. Just as with bromine, the van der Waals radius of the second
atom was subtracted from the observed contact distance and the result plotted as a function of the S = 0***X angle. As the figure shows, with
the exception of the bromine contact, there is a rough correlation between this angle and the observed oxygen radius, but the result is not
so decisive as to clearly confirm Bondi's prediction. On the other hand, we cannot reject his proposal either.
The contacts involving the benzene ring are also of interest, in
that it is somewhat distorted. Table 17 lists the least squares plane91
through the benzene ring and lists the deviations of various atoms from
the plane. Two views of the bromobenzene sulfonate group are shown in
f i g u r e 11. Both sulfur and bromine are bent significantly out of the
plane determined by the six benzene carbon atoms. The deviations are both in the same direction and a trend among all the atoms is consistent with a bowed molecule.
Numerous substituted benzene derivatives have been reported in
the literature, and where bending has been observed, two explanations
have been advanced. First, the molecule may be inherently bowed because a quinoid type structure is making a significant contribution to the resonance forms associated with the substituted benzene molecule, and c
Figure 10. Van der Waals radius of double bonded oxygen from
contacts involving 02 and 05 as a function of the
S=0» • *X angle. 91
TABLE 17
ANALYSIS OF BENZENE PLANARITY
The equation of the best plane through the benzene ring with coordinates g SX, SY, SZ relative to the orthogonal coordinate system a_, b, c*.
A(SX) + B(SY) + C(SZ) + D = 0
Coefficients:
A = 0.61*956 D = 10.62659
B = 0.75325 £ A2= 0.00095
c = 0 . 1051*2
Deviations:
BC1 0.007 A BH1 O.O76 A Br 0.052 A
BC2 -0.002 A BH2 0.1 1 9 I S 0 .1 5 7 A
BC5 - 0 .0 0 5 A BH5 0 .0 1 9 A 01 - 1 .1 1 5 A
BCl* 0.005 A bhA - 0 .0 0 2 k 02 I .519 A
BC5 -0 .0 0 1 A 03 -0 .0 2 6 A
B06 -0 .0 0 5 A
a. The orthogonalized coordinate system is chosen such that the first axis is along a_, the second along b* and the third along the cross product of a_ and b* . In the monoclinic system these axes are along a_, b, c.*. In general, the transformation matrix from fractional to orthogonal coordinates for this choice of axes is: 92
TABLE IT (continued)
a sin Y 0 -c sin O' cos P a cos Y b c cos a 0 0 c sin or sin P
and the inverse transformation is:
a s in Y 0 -c s in a cos P a cos Y b c cos a 0 0 c s in a s in P
for cis-hicyclof^. 1. O'joct-^-exo-yl p-bromobenzene sulfonate these matrices are:
12.829 0 -1.173 ^ 9 .7 5 9 0 o 1 1.671
7.7 9 5 0 0.7835 10. 2^7 0 0 8.568
b. Only the six carbon atoms of the benzene ring were used to determine the plane. 93
Figure 11. Two views of the bromobenzene sulfonate group. 9b second, crystal packing forces may deform the molecule. Among recent structures, 3-sulfanilamide,92 p-nitroaniline ,93 the a and 3 forms of p- nitrophenol 94 p-aminobenzoic acid,95 p-toluenesulfonate 96 >97and sulph - thiazole II 98 all show a marked shortening of the bonds parallel to the long molecular axis of the benzene ring and a concomitant lengthening of the remaining bonds which has been construed to indicate that the quinoid type structure is making a significant contribution. Even so, this may not be the source of the observed bowing. More to the point, the bending in the metastable, 3-modification of p-nitrophenol was claimed94 to decrease intermolecular distances relative to the values observed in the a-modification. Although we might argue for an inher ently bowed molecule based on this evidence, we should note that the contact distances which decrease are s till greater than the sums of the van der Waals radii for the atoms involved, and several of the contacts which were not considered appear to be more important. On the other hand, the bending in the two modifications of the crystal structure is different, which is good evidence that crystal packing forces cause the distortion. Differing amounts of bending have also been reported in two structures containing the p-toluenesulfonate group,96,97 which adds cre dence to the importance of crystal packing forces in bending the benzene m o le c u le .
In cis-bicyclo[5•1.0]oct-U-exo-yl p-bromobenzene sulfonate, sev eral of the more severe intermolecular contacts are consistent with crystal packing forces which would cause the observed distortion. In particular, the contacts between bromine and both screw related 02
(3 .2 2 9 (2 ) t) and BC1 (3.66U(2)A ), as well as the contact between BC5 and glide related 02 (3.283(3) A),could contribute to a bowed molecule.
We should note, however,, that the small Br-BC^-BCJ angle, ll8.U (2)°J
does bring bromine closer to 02. B. The Molecular Structure
The geometry of eis-bicyelo[5. 1. Q~loct -^-exo-yl p-bromobenzene sul fonate, derived from the final least squares parameters is set out in
Tables 18 through 22 and Figure 12, and some of the more significant bond lengths and angles are summarized schematically in Figure 13. Since a rigid body analysis of the thermal parameters was carried out following the procedure of Schomaker and Trueblood," the corrected bond lengths and angles99’100 which were derived101 for the two different assumptions about the thermal motion appear in the various tables along with the re sults of a conformational analysis carried out by Schleyer102 for cis- bicyclo[5.1. O]octane.
The first thermal analysis (Scheme 41) assumed that the thermal motion of the entire molecule could be adequately interpreted in terms of the librations and vibrations of a single rigid body. The results are summarized in Table 23a. In the second analysis (Scheme #2), the molecule was broken down into two rigid groups: bromobenzene sulfonate and bicyclo
[5.1. 0Joctane. The results of that study are given in Tables 23b and 23c.
The dramatic decrease in the r.m. s. AU. . for the two parts of the id molecule in Scheme #2, indicates that a model which assumes two rigid fragments provides a more satisfactory description of the thermal motion than one which assumes a single, rigid molecule. In addition, the mean a(U. .) was also in better accord with r.m. s. AU. . in Scheme 42 (r.m . s. id id AU. . = 0. 004l and 0.0035 A2 vs. cr(U. .) = 0.0013 and 0.0023 A2, respec- tively for the two fragments) then in Scheme #1 (r.m. s. AU. . = 0.OO 72 v s.
0.0017 A2). Both models indicate that the bond lengths derived directly Figure 12. Cis-blcyclo[5.1.0]oct-fr-exo-yl p-bromobenzene sulfonate. 1.380
1.330 1.89 3
1.373
Figure 13a. Selected bond lengths in cis-bicyclo[5.1.0]oct-U-exo-yl jo-bromobenzene
s u lf o n a te .
vo oo 121.4 1 20.8
F ig u re 13b. Selected bond angles in cis -bicyclo[$. 1.Q]oct--U-exo-yl £-bromobenzene
s u lf o n a te . 100
TABLE 18
BOND LENGTHS IN
cis-B IC Y C L0[5 .1 .0 ]0 C T -4 -ex o -Y L p-BROMOBENZENE SULFONATE
C o rre c ted C o rre c t Uncorrected Scheme #1 Scheme :
Br -BC4 1 -8 9 3 (3 ) 1.894 1.895
S - 01 1 .5 5 0 (2 ) 1-554 1 .5 5 8
S - 02 1 .4 2 8 (2 ) 1 .4 3 2 1 .4 3 6 CO KA O 1 1 .4 2 0 (2 ) 1 .4 2 3 1 .4 2 7
Avg. S = 0 1.4 2 4 1 .4 2 8 1 .4 3 2
S -BC1 1 .7 5 7 (2 ) 1-759 I. 76O
BC1-BC2 1 .3 8 0 (4 ) 1.385 I .388
BC2-BC3 1 .3 8 0 (4 ) I .381 1 .3 8 2
BC5-BCU 1 .3 8 4 (4 ) 1.387 1 .3 9 0
BC4-BC5 1 -3 7 0 (4 ) 1 .3 7 4 1-378
BC5-B06 1 -3 7 5 (4 ) 1 .3 7 6 1 .3 7 8
BC6-BC1 1 -3 7 8 (4 ) 1 .3 8 0 1 .3 8 4
Avg. C - C l-379t0.006 1 . 38( ^ 0.005 i . 385 to.O( a r a r 1 H 9- 0 1 -5 0 1 (3 ) 1.5 0 2 101
TABLE l 8 (continued)
C o rrected C o rre c te d Uncorrected Scheme #1 Scheme #2 S c h le y e r
C1-C2 1 .4 9 8 (6 ) 1.5 0 1 1 .5 1 0 1.5 4 1
C6-C7 1 .4 8 5 (4 ) 1.4 9 0 1.495 1 .5 4 0
C2-C5 1 .5 4 5 (5 ) 1.5 4 6 1 .5 5 2 1 .5 4 4
05-06 l.5 3 3 (* 0 1 .53k 1 .5 4 0 1 .5 4 0
03-cU 1 .5 0 6 (4 ) 1.512 1.5 1 7 1 .5 4 3
C4-C5 1.515 0 0 1 .5 1 9 1.527 1 .5 ^ 3 c i - c 8 1 .4 9 3 (6 ) 1.4 9 4 1 .5 0 0 1-539
C7-C8 1 .5 0 6 (5 ) 1.5 0 9 1.514 1-539 c i - o r 1 . 4 9 9 (6 ) I .503 1 .5 1 1 1-53^
Avg. C - C (cyclopropane) 1 .49910.006 1 . 50210.007 1 . 50810.007 102
TABLE 19
C - H BOND LENGTHS IN cis-BICTCLOF^. 1. OlOCT-^-exo-YL £-BROMOBENZENE SULFONATE
Uncorrected
BC2-BH1 0 .9 l|( 3 )
BC3-BH2 0 .8 l(U )
BC5-BH3 1 -0 8 (3 )
bo 6-bh!+ 0 . 8 9(1+)
Avg. C “ H 0.93±0.11 a r
C l-H I 1 . 0 6( 1+
C2-H2 0 .9 3 (^
C2-H3 0 . 96(3
C3-H1+ 0 . 98(3
C3-H5 0 . 9 8(1+
c!+-h 6 0 .96 (3
C5-HT 0 . 91+ ( 1+
C5-H8 1.09(1+
06-H9 1 . 0 1 ( 1+
c6 -h io 1 .0 1 (3
CT-HLl 1 .0 7 (5
C8-H12 1 . 13(5
C8-H13 0 . 96(6 - H 1.01±0.06 Avg. Csp3 103
TABLE 20
BOND ANGLES IN
cis-B IC Y C L 0[5.1. 0]0C T-4-exo-Y L _p-BROMOBENZENE SULFONATE
C o rre c te d C o rre c ted Uncorrected Scheme #1 Scheme #2
03 S - 02 1 1 7 -5 (1 1 1 7 .6 1 1 7 .6
03 S - 01 110. 1(1 1 0 9 .9 110.0
02 S - 01 1 0 9 .7 (1 109 .8 1 0 9 .8
03 S -BC1 1 0 8 .9 (1 1 0 8 .9 108 .9
02 S -BC1 1 0 9 . 6 (1 109 .6 1 0 9 .4
01 S -BC1 9 9 -7 (1 99-5 99-6
Br -BC4-BC3 1 1 8 .4 (2 1 1 8 .2 11 8 .2
B r -BC4-BC5 1 2 0 . 2 (2 120.3 120.2
S -BC1-BC2 1 1 9 . 0 (2 1 1 8 .9 11 8 .9
S -BC1-B06 120. 1(2 120.1 120.0
BC2-BC1-BC6 120. 8(2 120.9 121.0
BC3-BC2-BC1 1 1 9 . 8(2 1 1 9 .8 1 1 9 .7
BC4-BC3-BC2 1 1 8. 8(3 1 1 8 .7 118.7
BC5-BC4-BC3 1 2 1 .4 (2 121.5 121.6
B06-BC5 -bc4 1 1 9 . 6 (2 1 1 9 .6 1 1 9 .6
BC1-B06-BC5 1 1 9 .6 (3 119.5 119.4
Avg. 1 2 0 . 0 1 0 .9 1 2 0 . O i l . 0 120.011.1 10b
TABLE 20 (continued)
C o rre c ted C o rre c ted Uncorrected Scheme #1 Scheme #2 S c h le y e r
S -Ol-Cb 120. 1 (2 ) 120.1
C1-C2-C3 1 1 3 .6 (3 113.5 113.5 112.8
CT-C6-C5 1 1 3 . 0 (3 1 1 3 .0 1 1 3 .0 1 1 1 .1
C2-C3-CU 1 1 1 .9 (3 1 1 1 .9 111.9 11U.3
C6-C5-C4 112.9 (2 112.8 112.9 11 3 .3
C3-C&-C5 118.2(3 11 8 .2 118.2 11 5 .1
C2-C1-C8 121.2(k 121.1 121.1 1 1 7 .8
C6-C7-C8 121.6(3 121.6 121.6 118.7
C2.-C1-CJ 1 1 9 . b (3 1 1 9 .^ 1 1 9 . b 1 1 8 .0
CS-CT-C1 1 1 9 .3 (3 1 1 9 .^ 1 1 9 .3 1 1 6 .8
C8-C1-CT 6 0. 1^(3 60 .5 6 0 .3 6 0 .1 c i-c r -c 8 5 9 -6 (3 59.5 59 .5 6 0 .1
C7-C8-C1 6 0 . 0 (3 6 0 .1 60.2 59-8
C3 -c4 -o i 1 0 5 .7 (2
C5-C&-01 105.0(2 TABLE 21
BOND ANGLES INVOLVING HYDROGEN IN c is -BICYCL0[5.1. 0~|0CT-4-exo-YL p-EROMOEENZENE SULFONATE
The Benzene Ring
BH1-BC2 -BC1 120(2 ) BH3-BC5-BC^ 1 2 1(2 )
BH1-BC2 -BC3 1 2 0 (2 ) BH3-BC5-BC6 1 2 0 (2 )
BH2-BC3 -BC2 1 2 1 (2 ) BH4-B06-BC5 1 1 8(2 )
BH2-BC3 -BC4 120(2 ) BH4-BC6-BC1 122(2 )
The Bicyclo[5.1.0]Octane System
O bserved S c h le y e r Observed Schleyer
H1-C1-C2 113(2 ) 11 8 .6 H ll-O T-C6 10 9 (3 ) 118.6
H1-C1-CT 112(2 ) 1 1 3 .8 H i i - o r - c i 118(3) 11 3 .9
H1-C1-C8 120(2 ) 1 1 5 .3 H11-C7-C8 121(3 ) 11 5 .3
H2-C2-H3 102(3 ) 1 0 7 .8 H9-C6-H10 108(3) IO3 .6
H2-C2-C1 111( 3 ) IO8 .3 H9-C6-C7 108(2 ) IO8 .3
H3-C2-C1 114(2) 117.5 H10-C6-C7 110(2 ) 112.4
H2-C2-C3 109(2 ) IO9 .7 H9-C6-C5 108(2 ) 1 1 0 .1
H3-C2-C3 106(2 ) 10 0 .2 H10-C6-C5 109(2 ) 11 1 .0 TABLE 21 (continued)
O bserved S c h le y e r Observed Schleyer
H4-C3-H5 108(3) 1 0 4 .2 H7-C5-H8 1 1 3 (3 ) 1 0 4 .2
H4-C3-C2 1 1 6(2 ) 11 0 .4 H7-C5-C4 109 (2 ) 110.5
H5-C3-C2 108(2 ) 109.0 H8-C5-C4 104(2) 108.6
H4-C3-C4 1 0 6(2 ) 110.4 H7-C5-06 1 0 8(2 ) 1 1 0 .9
H5-C3-C4 1 0 6(2 ) 1 0 7 .9 H8-C5-C6 109(2 ) 1 0 9 .0
H6-C4-C3 108(2 ) 1 0 9 .0 H12-C8-H13 H 9 ( 4 ) 1 1 8 .9
H6-C4-C5 1 1 2(2 ) 108.7 H12-C8-C7 113( 2 ) 1 1 6 .8 h6 - c4 - o i 107(2 ) H12-C8-C1 108(2 ) 116.5
H12-C8-C7 1 2 3 (4 ) 11 6 .0
H12-C8-C1 1 2 0 (4 ) 11 5 .3 107
TABLE 22
DIHEDRAL ANGLES IN
C is -BICYCLOr 5 .1 . 0~l0CT-4-exo-YL p-BROMOBMZENE SULFONATE
O bserved S c h le y e r C8-C1-C2-H5 17 (2 ) 2 3 .3
C8-C1-C2-C3 138.5 b) 1 3 9 .0
C8-C1-C2-H2 -98 3) -99 -b -54
C7-C1-C2-C5 6 7 .2 5) 7 0 .0 -9 8 -3" \ T L 1 C7-C1-C2-H3 2 ) -4 5 .8 67.2
C7-C1-C2-H2 -169 3) - 1 6 8.b
-68 H1-C1-C2-H2 56 b) kj.k 56
H1-C1-C2-H3 170 3) 1 7 0 .1
H1-C1-C2-C3 -68 2 ) -7 ^ .1
c8- c t - c 6 -h io -15 2 ) - 1 3 .2
C8-C7-C6-C5 - 1 3 6 .9 b) - 1 3 8 .3
C8-C7-C6-H9 103 2 ) 1 0 0 .6
C1-C7-C6-C5 - 6 6 .5 h) -6 9 .3 13,
C1-C7-C6-H10 56 2 ) 5 5 .8 103
C1-C7-C6-H9 174 2 ) 1 6 9 .6 - 66.5
H11-C7-06-H9 -b6 3) -4 8 .0 -4 6 73 H11-C7-C6-H10 -164 3) - 1 6 1 .8
H11-C7-C6-C5 73 3) 7 3 -0 a. The dihedral angles were defined according to the convention proposed by Klyne and Prelog, Experimentia. lb, 521 (l9b0). 108
TABLE 22 (continued)
C1 -C2 -C3 -CH -8 i.o h) -82.5
C1 -C2 -C5 -HU hi 2) 42.7
C1 -C2 -C3 -H5 162 2) 156.6
H2 -C2 -C3 -C4 154 3 ) 156.6 43 - 81.0 H2-C2-C3-H4 - 8b -78.1 - 7 2 H2 -C2 -C3 -H5 35-8 37 *) 41 H3-C2-C3-CJ+ b3 2) b$.2 37 -84 H3 -C2 -C3 -H4 167 3 ) 168.5
H3 -C2 -C3 -H5 -72 3 ) -77.6
cr-c6-c?-ck 82.1 3 ) 88.3
CT-C6 -C5 -H7 -39 2) -36.5 ot-o6 -C5 -h8 162 2) -150.6
H9 -o6 -C5 -cii 158 2) 151.6 -41 82.1 H9-06-C5-HT 80 3 ) 83.5 74 H9 -o6 -C5 -h8 -b3 3 ) -30.6 -3 9 h io -c6 -c5 -c 4 -bl 2) - 37-5 -4 3 H10-06-C5-HT 162 3 ) -I62.I1 80 h io - o 6-c 5 -h 8 7^ 3 ) 83.5 TABLE 22 (continued)
C2-C3-C4-C5 6 3 .5 (4 ) 6 0 .5
C2-C3-C4-h6 -65 (2 ) -6 4 .2
C2-C3-C4-01 -1 7 9 -3 (3 ) -1 7 7 -0 53 -65
H4-C3-C4-C5 -64 (2 ) -6 4 .7
-6 2 H4-C3-C4-H6 168 (3 ) 170.6 63.4 h4 - c3 - c4 - o i 53 (2 ) 5 7 .7 53 H5-C3-C4-C5 -179 (2 ) - 1 7 8 .0 -6 4
H 5-C3-c4 - h6 53 (3 ) 57-3
H5-C3-C^-0! -62 (2 ) -55-5
c6-C5-c4-c3 - 6 4 .7 ( 3 ) -6 4 .1
0 6-C 5-c4 - h6 61 (2 ) 6 0 .7 c6 - c5 - c4 - o i 1 7 8 .7 (2 ) 1 7 3 .3 -5 7 H7-C5-C4-C3 56 (2 ) 6 1 .O
H7-C5-C4-H6 -178 (3 ) -1 7 4 .2 59 - 64.7 H7-C5-C4-01 -61 (2 ) - 6 1 .6
H8-C5-C4-C3 177 (2) 1 7 4 .6 56 -61 h8 - c5 - c4 - h6 -57 (3 ) -6 0 .5
H8-C5-C4-01 59 (2 ) 5 2 .O 1 1 0
TABLE 22 (cont irrued )
H12-C8-C1-H1 -154 3> - 1 9 4 .0 .-i
H13-C8-C1-H1 -13 5 ) - 2 .6 106
H13-C8-C1-C2 134 5 ) 1 4 5 .3 134 H12-C8-C1-C2 -2 3 ) - l . l
H12-C8-C1-C7 106 3 ) 1 0 7 .0 ,-113 -1 3' H13-C8-C l-C r -113 5 ) - 106.6
H12-C8-C7 -HU 155 4 ) 1 4 9 -3
H13-08-07-H ll 2 5 ) 1 .2 / h i 2 - c 8-err-06 9 3 ) -0 .3
H13-C8-CT-C6 -144 5 ) -1 4 8 .4
H12-C8-CT-C1 -9 9 3 ) - 106.5
H13-C8-CT-C1 108 5) 105.4 -9 9
C2-C1-C7-C8 1 1 1 .3 4 ) 107.6 — 144 0 2 - c i -C 7 - c6 - 0 .3 5 ) 1 06 C2-C1-C7-H11 -137 3 )
H1-C1-CT-C8 -113 2 )
H1-C1-C7-H11 - l 4 ) c8-ci-cr-c6 - 111.6 4 ) - 10 9 .3 Ill
TABLE 2 2 (continued)
h6 - c4 - o i - s -1 (2 )
C3-C4-01-S 113.7(2)
C5-C4-01-S - 1 2 0 . 5 (2 ) 120.5 113.7
C t-0 l-S -0 2 -3 3 -5 (2 )
C4-01-S-BC4 -146.9(2)
C 4-01-S-03 9 7 -2 (2 )
9 7 ?
01-S-BC4-BC3 '5 4 .7 (2 ) 146.9
01-S-BC4-BC5 - 1 2 2 .7 (2 )
/ 02-S-BC4-BC3 -6 0 .4 ( 2 )
02-S-BC4-BC5 1 2 2 . 1 (2 )
03-S-BC4-BC5 1 7 1. 0 (2 )
- 6 .4 ( 2 ) 03-S-BC4-BC5 54.7
- 6 0.4
122.5 TABLE 23
RIGID BODY THERMAL PARAMETERS FOR
cis-BICYCLO[5*1. O^OCT-^-exo-YL p-BROMOBENZENE SULFONATE
Scheme #1: The Whole Molecule
95(14) 15(8) -1 0 8 (1 7 ) -1 L = 3 0 (7 ) 2 5 (1 0 ) x 10 deg2
> 1 6 1(2 8) ,
533(28) -9 (2 5 ) -7 4 (2 2 ) 1 -4 2 T 500(29) - 1 3 ( 2 2 ) x 10 A
436(20) ,
Principles axes o f L
r.m. s. amplitude (deg) direction cosines (x 103 )
4.95 588 -132 -798
I .65 270 962 4o
1. 21 762 -239 602
Principle axes o f T r.m. s. amplitude (A) direction cosines (x 103 )
0.239 -881 27 471
0 .2 2 4 -45 989 -142
0 .1 9 9 -470 -i4 6 -870
r.m . s. AU. . = O.OO72 I2 iJ avg. ct(U. .) = 0.0017 I.2 a. Calculations were carried out relative to the orthogonal coordinate system a,b,c . 113
TABLE 25 (continued)
Scheme * 2 : cis-Bicyclo[5-1.Oloctane
196(49) -3 5 (2 6 ) -6 4 (2 9 ) 195(32) . 6 (4 0 ) x 10 deg2 389(73)
6 3 4 (2 2 ) - 2 (2 1 ) -1 2 (1 7 ) 466(45) 1 3 ( 26) x 10 4 2 2 (2 1 )
Principle axes of L amplitude (deg) direction cosines (x 103 6 .4 0 -297 78 952 4.6 7 -563 791 -240 3 .9 1 -771 -607 -191 \ \ Principle axes of T
a m p litu d e (a ) direction cosines (x 103 0. 254 -998 7 57 0.2 1 7 -17 913 -4 o8 0 . 209 -55 4 o8 -911
r.m. s. AU. . = 0. OO35 i j
ayg. ct(U. .) = 0.0023 A2 J TABLE 23 (continued)
Scheme #2: Bromobenzene Sulfonate
139( 2 8) - 7 1( 20) -1 5 0 (2 4 ) - 2 L = 159(21) 1 3 3 (2 0 ) x 10 deg2 257(33)
4 66(21) - 3 0 ( 2 0 ) -5 7 (1 7 ) — ^ w 0 1— X 1 T 4 50(23) 27(17) 384(18)
Principle axes o f L m. s . ampli tude (deg) direction cosines (x 10s ) ..^ '6 7 7 1 \ 469 -460 -7 5 4 N 2 .9 0 460 856 -236 1 .9 7 754 -235 613
Principle axes of T r.m .s. amplitude ( a ) direction cosines (x 103 ) 0. 228 755 -502 -422 0 .2 0 7 503 856 -117 0 .1 8 8 420 -123 899
r.m . s. AU. . = 0 . 0 0 4 l K2 i j
avg. o (u. .) = 0.0013 I s 115 from the least squares parameters are foreshortened, as expected; some by more than twice their estimated standard deviation.
1. jD-Bromobenzene sulfonate
Isolated views of the bromobenzene sulfonate group are shown in
F ig u re lh . Examination of the thermal ellipsoids for this fragment shows that the thermal motion is mainly a rocking motion around the long axis of the molecule and some wagging about a fixed sulfur atom. The three oxygen atoms seem to undergo larger rotations about the BC1-S bond than the remainder of the group, and perhaps should not have been included in the rigid body analysis described above.
The C-C bond lengths in the benzene ring average 1.379 A before
corrections were applied for thermal motion, and 1.3 8 3 H after the cor rections derived from Schemed were applied. Estimates of the standard
deviation of the C-C bond lengths ( 0 . 0 0 k a) derived from the inverse of the normal matrix are somewhat smaller than the value derived from the ob
served variations in the calculated bond lengths (0.006 a). After correc
tion for thermal motion, the variations decreased and the estimated stan
dard deviation of a bond length fell to 0. 005a • Following Hamilton’s 103
procedure, (see Appendix B), a x 2 test shows that the carbon-carbon bonds
are all equal within experimental error. In detail, S^/cr2, for these bonds is 7.31 even before any corrections for thermal effects. Thus we
cannot reject the hypothesis that a ll the bond lengths are equivalent
= )i 2 6 ulfonate group 117 a t th e 1$ significance level since y 2 = 15.08 or even at the $ 5 , 0 * 01 significance level since y 2 = 11.07. Corrections for thermal mo- 5 , 0. 05 tion only make this result more certain.
TThe average, even after correction for thermal motion, is some what less than the v ’.lue observed by Cox 104 for crystalline benzene,
1.392(*0 A, or the average listed in Sutton’s 105 survey, 1.39M5); but it is within the range of values observed for various substituted ben zene derivatives. Among the bromine and sulfur substituted benzene derivatives selected for Table 2h} the average C-C bond ranges from 1.371 to 1. tol A.
The average C-C bond angle in the benzene ring is 120° but the estimated standard deviation based on the variations of the observed angles is ±0.9° before corrections for thermal motion. After the cor rections derived from the thermal model in Scheme #2? the estimate rises -to 1.1°. Both values are considerably greater than the estimates derived from the inverse of the normal matrix. When we test the hypo thesis that all the bonds are equal , 103 we f in d S^/o -2 = 2 9 .3 w h ile v 2 = 15.08. Thus we may reject the hypothesis at the 3$ level, "•5 ,0.01 that is, there are probably significant differences among the bond angles. These differences, no doubt, reflect the distortion of the molecule by crystal packing forces as discussed above.
The C-Br distance found in this study, 1.895(3) 'A, is also typi cal of the values found in bromobenzenes. For comparison, the C-Br bonds listed in Table 2U range from 1 .8 6 7 to 1.919 with an average of
I .8 9 6 A. The value, 1 .8 5 A listed in the "International Tables for
X-ray Crystallography" probably underestimates the best value for 118
this bond length. The S-BC1 bond, 1.760(2) a, is also typical of the
value found for this bond. Among the compounds sampled in Table 2b,
the observed values range from 1.75 to 1.77 A with an average of 1.758(9).
The value is also typical of the S-C g bond lengths surveyed by sp Jackobs and Sundaralingam 107 and significantly shorter than the accepted
values for the S-C 3 bond given by Sutton , 104 1.80 a, or by Sutherland sp and Young , 108 1.805(12) A. O’Connell and Maslen928, have claimed that
the shortness of a sim ilar bond in a P-sulphanilamide is indicative of
significant rt character in the S-C bond.
Surveys of various sulfonates by Sundaralingam9sa and of various
sulfones by Herdklotz 100 and by Hargittai and H argittai 110 have estab
lished that the geometry around sulfur in these cases is dependent on the nature of the substituents involved and is explained in terms of
Gillespie’s 111 valence shell electron pair repulsion theory. In the sulfonates, the C-S-0 angles are smaller and the O-S-O angles are larger than the tetrahedral value to allow for the added size of the partially doubly bonded oxygen. Among the sulfones, the double bond is more local- lized on the two oxygens and the o = S=0 angle increases further while
X-S-Y is forced to collapse. The more electronegative the various sub stituents become, the shorter a ll the bonds become.
The geometry found around sulfur in the present study is closely akin to that found in various sulfones in the two surveys mentioned above, and more especially in (CH^^SOg 112 and (CH 3 )C1 SO2113. In our compound, 119
TABLE 2h
BOND LENGTHS IN SOME BROMINE AND SULFUR CON
CONTAINING BENZENE DERIVATIVES
r e f C-C C-Br C-S cis-bicyclo[5.1. Q~loct-^-exo-yl a 1 . 3 8 5 ( 5 ) 1 .8 9 5 (3 ) 1 . 7 6 0( 2 ) p-bromobenzene sulfonate trans-bicyclor5.1.Oloctane-4-metha a 1. 5 7 6 (7 ) 1 .8 9 0 (7 ) 1. 7 6 8( 6 ) nol p-bromobenzene sulfonate anti-8-tricyclo[3. 2. 1. 02,4-]octyl b 1 .3 9 (2 ) 1. 9 0 (1 ) 1 .7 7 (1 ) p-bromobenzene sulfonate 2 - 0 -(p-bromobenzenesulfonatyl)- 1 , c 1. hi 1 .9 2 1 .7 9 h: 3,6-dianhydro-D-glucitol 5-nitrate cyclohexyltosylate d 1.3 7 5 (1 8 ) 1. 7 6( 2 ) cis-4-tert-butylcyclohexyl p- P 1 .3 8 6 1 .7 5 5 (3 ) toluene sulfonate trans-4-tert-butylcyclohexyl f 1 .3 8 2 1 .7 5 9 p-toluene sulfonate cis, trans- 2 , 5 -di-t-butyl-cyclo- g 1.3 8 9 1 .7 5 6 hexanol p-toluenesulfonate p o l y - [ l . 2-bis-(p-tolysulfonyloxy- h 1.3 7 1 1 .7 5 2 m e th y le n e ) -1 -b u te n -3 - in y le n ] 3a, 33 -dimethoxy- 5 cv -o e s tr a n -173 -o 1 i 1 .3 9 0 1 .7 ^ 9 p-toluene sulfonate 3 -oxo -5cv-andro s t an -173 -o l 3 1.3 8 7 1 .7 6 2 p-toluenesulfonate sulphathiazole II k 1. 3 8 6( 1 0 ) 1 .7 5 9 (3 ) p-toluenesulfonic acid 1 1 .3 8 0 1 .7 5 8 (2 ) 1 , 5 -endomethylenequinolizidinium m 1 .3 8 7 1 .7 8 0 p-toluenesulfonate t o s y l - 1 -pro lyl-l-hydroxytroline n 1.387(35) 1.777(H)
3 -sulfamilamide o 1 .3 9 8 (1 5 ) 1 .7 5 (2 ) P 1 .3 9 0 (9 ) l . 7 5 (2 ) orthanilic acid <1 l . 7 7M 3) p-bromophenyl-R r l.3 7 7 (* 0 1 . 8 9 1(1 0 ) 1 2 0
TABLE 2k (continued)
r e f C-C C-Br £-bromopheny limino (triphenyl) s 1. 383 1 .8 9 M 8 ) phosphorane b romophenyldephenylpho sphine t 1-397 1. 891(7) o x id e bromobenzoate u 1.371(19) 1.901(7)
P03 (C6H5 ) 4 (C6H4 B r)C5 H2 V 1 .3 8 2 (9 ) 1. 9 0 5 (9 ) 3 -£-bromo phenyl -1 n i t r o s o - 2 - w l.*+ 0 l 1 . 8 6 7(1 2 ) p y ra z o le n e N- (p-bromophenyl) syndone X 1 .3 9 (9 ) 1. 89 Ryanodol p-bromobenzyl ether J 1.3 7 1 1 .9 1 5 brom o- 2, 3 -dimethylbenzo[b]- z 1 .9 0 3 (1 0 ) th io th e n e k '-bromoflacanone aa 1 . 9 1 0 (6 ) retigeranic acid bb 1. 910 benzene c c 1.392(U )
a. This work. b. A.C. MacDonald and J. Trotter, Acta Cryst. , l 8 , 2*+3 ( 1965 ). c. A. Camerman, N. Camerman and J. Trotter, ibid. , 19, *+*+9 (19^5 )• d. V, J. Janies and J. F. McConnell, Tetrahedron, 27 , 5*15 (l9 T l). e. P. L. Johnson, J. P. Schaefer, V. J. James and J. F. McConnell, ib id . , 28 , 2901 (1972). f. P. L. Johnson, C. J. Sheer, J. P. Schaefer, V. J. James and F. H. Moore, ibid. , 28, 2895 (1 9 7 2 ). g. D. H. Farber and C. Altona, Acta Cryst. , B30, *+*+9 (197*0. h. D. Cobelt andE.F. Paulus, ibid., B5£, 232 (197*0- i. R. A.G. de Graff. C. A. M. van der Ende and C. Romers, ib id ., B30, 2034 (197*+). j. R. A.G. de Graff and C. Romers, ib id ., B3£, 2029 (197*0. k. G. J. Kruger and G. Gafher, ibid. , B27, 326 (1971). 1. S.K. Arora and M. Sundaralingan, ibid. , B27, 1273 (1971). m. C. S. Huber, ibid. , B25, 11^0 ( 1969X n. M.N. S abesan and X. V an k ateso n , ib id . , B27, 1879 (1971). o. A.M. O’Connell and E.I. Maslen, ibid. , 22, 13*+ ( 1967). p. M. Alleaume and J. Decap, ibid. , 22, 731 (1967). q. S. R. Hall and E.N. Maslen, ibid. , 22, 216 (1 9 6 7). r. G.B. Ansell, D.¥. Moore and A.T. Nielson, J. Chem. Soc. (b ), 2376 (1967). s. M.J.E. Hewlins, ibid. , 9*+2 (1971). t. W. Dreissig and K. Plieth, Acta Cryst. , B27, 11*1-0 ( l9 7 l ) . 1 2 1
TABLE 2b (continued) u. E. Thom and A. T. Christensen, ibid. , B27, 573 (l97l). v. D.D. Swank, C.N. Caughlan, P. Ramirez and J.P. Pilot, J. Am. Chera. Soc., 93, 523b (1971). * w. M.N. S abesan and K. V e n k ate sen , A cta C r y s t ., B27, 986 (1971)• x. H. Bamighausen, F. Jellinek, J. Munnik and A. Vos, ibid., l 6, *71 (1963). “ y. S. IT. Srivastava and M. Przybyloka, ibid. , B26. 707 (1970). z. J. H.C. Hogg and H. H. Sutherland, ibid., B30, 2058 (197* )• aa. J. S. Cantrell, R. A. Stalzer and T. L. Becker, ibid., B30,15* (I#*),. bb. M. Kanida, Y. Iitaka and S. Shibata, ibid. , B30, 358 (197*0. 1 2 2
the angles C-S-0 and O-S-O are'99.7(1)° and 1 1 7 . 5(l)° respectively while
the S—0 bonds average 1. b2k A before correction for thermal motion and
1. ^ 3 2 A after the corrections derived from Scheme # 2 have been applied.
As we mentioned before, however, the bonds S=02 and S =03 do
differ by a small but significant amount. Before thermal corrections,
the bond to 0 3 , which lies in the plane of the benzene ring, is shorter
by approximately four standard deviations, than that to 02. After the
corrections in Scheme #2, the difference increases slightly. In view of
the closeness of the Br»»*02 contact and the linear arrangement of the
interaction, a partially-bonding, charge transfer interaction is a
plausible rational for the difference. Such an interaction could reduce
the bonding density between S and 02, weakening and lengthening that b o n d .
While the double bonding character in the sulfate group is concen trated mainly in the bonds to 02 and 03, we have already mentioned that
some rt character has also been claimed92 for bonds like S-BC1. The S-01 bond shows some double bond character as well. Cruickshank114 has calcu
lated from the Schomaker-Stevenson equation115 that a sulfur-oxygen
single bond should be 1. 69 h} while the value observed in this study,
1 .5 5 0 ( 2 ) A, is considerably less than that value. From Cruickchank’s work the bond lengths observed here correspond to it-bond orders of 0 .7 and 0.5 for the S = 02,03 and the S-01 bonds respectively.
For comparison, the values 1. 6 0 5 (7 ) A a n d 1. 6 1 1( 3 ) A h a v e b e e n r e ported for the shortened S-0 "single" bond in potassium ethyl sulfate 116
117 and A-tyrosine sulfate and -similar shortening of an analogous S-N 123 bond is seen in the structures of portual p-bromophenylhydrazone , 118
f3-sulphanilamide 92 and sulphathiazole II . 98 The effects of the partial double bond between sulfur and 01 are also seen in the S-01-C4 angle which is more appropriate to trigonal oxygen and considerably larger than the value found, for example, in dimethyl ether , 119 111° .
2. cis-Bicyclo[5.1. Oloctane
This work represents the first structural elucidation of the cis- bicyclo[5.1.Oloctane moiety. A similar structure in syn- 8 , 8 -dichloro-U- phenyl-3,5-dioxabicyclo[5.1. Oloctane 120 has been reported, and the struc tures are related , but there are differences between the two com pounds. Figure 15 isolates the bicyclooctane found in this study, and
lists some of its more important bond lengths and angles. As before, a complete listing of all the structural information is given in Tables 18 th ro u g h 2 2 .
Any strain in our cis isomer had little effect on the cyclopro pane ring. The bond lengths a ll equal and average 1.^99(6) A, before correction for thermal motion and 1. 5°8 A after the correction with
Scheme #2. The latter value is virtually identical with the bond lengths observed in cyclopropane , 121 1.510(1) A, and is well within the range of values observed for various substituted cyclopropanes. The known struc tures of cyclopropane and its derivatives are summarized in Table 25.
Among the structures in that table, few accurate studies in the solid state are reported and we have already considered briefly the uncertain ties involved in a gas phase study. Because of these uncertainties, the
structures reported for cicyclopropyl X-ray (at -100° c)122 and electron 123
TABLE 25
BOOT) LENGTHS IN CYCLOPROPANE DERIVATIVES
Compound Method Interior E x te r io r E x o c y c lic Type Bond Bond Bonds trans-bicyclof5.1. Oloctane-4- X 1 .3 i a l.b9 1 .5 2 C-C 3 carboxylic acid sp trans-bicycloF5.1.Oloctane-4- X 1 . 20( )b 1. *H( ) l . ^ ( ) C-C 3 methanol-jD-bromobenzene sulfonate sp potassium trans-bicycloF5. 1.01 X 1 .4 6 M )c 1. 509 ( ) 1. 503 ( ) C-C 3 octane-4-carboxylie sv
1 .^9 1 C-C 3 cis-bicyclo[5.1. Oloct-^-exo-yl p- X 1 .5 0 1 (7 )d sp bromobenzene sulfonate
l.kQ(2) 1 .5 2 C-C 3 sy n - 8 , 8 -dichloro-^—pnenyl-3j5- X 1-53(2)® dioxabicyclo[5.1. Oloctane 1.765 C-Cl
2 , 5 -d im e th y l- 7, 7 -d icy an o X 1. l£ o C-C 2 l . 501(3 )f 1 .5 5 6 (3 ) sp norcaradiene
I.U 36 C-CN b enz ocyclopropa pyran X C-C 2 l . 5 i( )s l . ^5 sp
i .4 o C-0 . e t 1 .5 2 C-C 3 axivalin hydrate X l . 5 l ( l ) h i.'oti) so H VJlrv> TABLE 25 (continued)
Compound Method I n t e r i o r Escfcerior E x o c y c lic Type Bond Bond Bonds
6, 6-diphenyl-3,3-diethyl-3- X 1 .5 2 0 (5 )i 1 .5 0 3 C-C 3 azabicyclo[3.1.0]hexane spJ
1 .5 0 3 C-C a r a n t i - 8- t r i c y c l o [ 3 , 2 , l , 0 2 ,4 ] o c ty l X 1. 5 M 3 )5 1 .5 1 (3 ) 1 .5 3 (3 ) C-C 3 p-bromobenzene sulfonate sp b ic y c l o [ 2. 1. 0 ]p e n ta n e ed 1 .^ 5 9 (1 5 ) 1 .5 2 1 (1 1 ) 1.5^3(11) C“C^p3 bicyclo[l. 1. 0 ] MW 1 . 4 9 8 (3 )1 cyclopropane MW 1 .5 1 0 (l)m cyclopropane MW l^ O O 11 1.515 chloro cyclopropane MW 1. 5 ik(k)° 1 .7 ^ 0 (3 ) C-Cl
1 , 1 -dichlorocyclopropane MW 1 . 5 3 3 (iOp 1 .7 3 ^ (2 ) C-Cl cyclopropane- 1, 1 -dicarboxylie acid X l.462(4)q- 1.53M3) 1 . ^ ( 5 ) C-C 2 sp sr bicyclopropyl X 1. b8 7(ky 1. 5 10(^) C-C 3 3 1. 501(3) sp a t 100° C
ed 1.5 1 7 suffers from lack of resolution t cyclopropane carboxamide X 1 . *181(7 ) 1 . *(87(7) C-C 2 1 .5 0 7 (7 ) sp TABLE 25 (continued)
Compound Method Interior E x te r io r Exocyclic Type Bond Bond Bonds cyclopro pane carb ohjnir axi de X 1. 501 ( )U 1 .4 8 C-C f i l m v cis-1,2,3-tricyanocyclopropane X 1. 518
1 , 2 , 3 -tri sdimethylamino cyclopro- X 1 .3 6 3 ( 1.3 3 3 C-N pinium io n x exo-ant i -tri cyclo [3.1.1.O2’4] l . W ( ) 1.57( ) c-csp3 heptan-S-yl p-nitrobenzoate
8,8-dichlorotricyclo[3. 2. 1 . 0 1’ 5 ] X l . 572 ( 1 5 )y 1 .4 5 8 (1 2 ) 1 .4 8 3 (1 2 ) C-C 3 sp o c ta n e 1. 526 ( 1 2 ) C-C 3 sp 1. 760( 1 2 ) C-Cl TABLE 25 (continued)
T h is -work
T h is work.
R. A. Kershaw, Masters Thesis, The Ohio State University, 1972.
T h is work.
G. R. Clark and G. J. Palenik, J. C. S. Perkin II, 194 (1973)-
C.J. Fritchie, Jr., Acta Cryst. , 20, 27 ( 1966).
L.J. Guggenberger, R. A. Jacobson, Acta Cryst. , B25, 888
G.D. Anderson, R. S. McEwen and W. Hertz, Acta Cryst. , B29, 2783 (1973).
F.R. Ahmed and E. R. Gabe, A cta C ry s t. , 1 , 603 (1964).
A. C. Macdonald and J. Trotter, Acta Cryst. , 18, 243 ( 1965 ).
R. K. Bohn and Y.H. T a i, J . Am. Chem. S o c ., 92, 6bkrJ (1970).
K.W. Cox and M.D. Harmony, J. Chem. Phys. , 5£, 1976 ( 1969).
0. Bastiansen, F.N. Fritsch and K. Hedberg, Acta Cryst. , 17, 538 (1964).
P.H. Kasai, R. J. Meyers, D. F. Eggers and K.W. Wiberg, J. Chem. Phys. , 30, 512 (1959)*
R. H. Schwendeman, G.D. Jacobs and T.M. Krigas, J. Chem. Phys. . 40, 1022 (1964).
W.H. F ly g a re , A. H a ra th and W. D. Gwinn, J . Chem. Phys. , 36, 200 ( 1962).
M.A. M. Meester, H. Schenk and C.H. MacGillavry, Acta Cryst. , B27, 630 (1971). TABLE 25 (continued) r. J. Eraker and C. Romming, Acta Chem. Scand. , 21, 2721 ( 1967). s. 0. Bastiansen and A. de Meijere, Acta Chem. Scand., 20, 5 1 6 (1966). t. R.E. Long, H. Maddox and K.N. Trueblood, Acta Cryst. , B25, 208j ( 1969)- u. D.B. Chestnut and R.E. Marsh, Acta Cryst. , 11, I 13 (1 9 5 8 ). y. A. Hartman and F.L. Hirshfield, Acta Cryst., 20, 80 ( 1 9 6 6). w. A.T. Ku and M. Sundaralingam, J. Am. Chem. Soc., , 1688 (1 9 7 2 ). x. S. Masamune, R. Vukov, M.J. Bennett and J.T. Purdham, J. Am. Chem. Soc. , 9^, 8239 (^972). y. K.B. Wiberg, G.J. Burgmaier, K. Shen, S.J. La Placa, W.C. Hamilton and M.D. Newton, J. Am. Chem. S o c ., 9b, 7^02 (1972).
H $ 130
diffraction are strikingly different. Nevertheless, trends can be found
among these derivatives and their origin explained.
In chlorocyclopropane 124 and 1,1-dichloroeyelopropane , 125 th e
three carbon-carbon bonds are nearly equal. Hybridization parameters
derived by Wiberg 126 suggest that although the electron withdrawing
substituent, chlorine, results in a significant increase in the s charac
ter of the bond hybrid at the substituted carbon, a rehybridization in
the opposite sense is induced into the bond hybrids at the remaining
carbons. The first effect by itself would shorten the C-C bond, but the
second compensates by lengthening it and the results overall balance
each other out.
W iberg’ s 126 calculations also show that, when the cyclopropyl
ring is fused into a polycyclic system, the bridgehead-bridgehead bond
is formed from relatively pure p orbitals increasing the s character of
a ll the orbitals involved, in the remaining bonds. Similar calculations
for bicyclo[l. 1. 0 ]b u ta n e , 130 by other authors confirm this result.
Within the cyclopropyl ring, the bridgehead-bridge bonds are
shorter than, equal to, or longer than the bridgehead-bridgehead bond, depending on whether substituents on the bridge carbon induce more or
less s character into the bridge carbon bonding orbitals. In syn- 8 , 8 - dichloro-^—phenyl- 3 , 5 -dioxabicyclo[ 5 . 1. 0 ]octane12° as well as 8, 8 -dichloro- t r i c y c l o [ 3 * 2. 1. 0 1:i5 ] o c ta n e , 126 the chloro substituent increases the s
character of the bridge orbitals and the bridgehead-bridge bond is signifi
cantly shorter than the bridgehead-bridgehead bond. On the other hand, *L P9 cyano substituents on the bridge in dimethyl- 7, 7 -dicyanoorcaradiene
I 131 presumably induce greater p character into the bridge carbon orbitals,
causing the bridgehead-bridge bond to be longer than the bridgehead- bridgehead bond. In our compound, added p character in the bridge carbon
compensates just enough to keep all the bonds equal. The increased s
character in the exocyclic bond, which was originally pointed out by
Coulson and M offitt 2 in their pioneering paper, causes that bond to be shorter than we might otherwise expect. Among the compounds surveyed in
T ab le 2 5 , for example the ^CyCp 0propyp -<^sp 3 ^on^s average 1*508 A and only the bonds in bicyclo[ 2. 1 . O lo c ta n e 127 and 8 ,8 dichlorotricyclo
[ 5 . 2. l.O1’5] octane 126 deviate markedly from this value, presumably in each case because of the strain in the four membered ring. The average of the exocyclic bonds, C1-C2 and Cb-CT is 1.^91 A before correction for
o thermal motion and 1. 502 A after the correction and fits well with the other values. The central bonds C2-C3 and C5-C6 average 1.539 A before and 1.5^6 A after correction for thermal motion, which is normal for
C 3 -C 3 b o n d s .1SB sp sp The bonds eminating from C^, however, are rather unusual. The bonds CJ-Cb and C^-C5 average 1. 51O(*0 A before and 1.522 A after thermal corrections which is more like the values observed for C 2 -C 3 s in g le sp sp bonds. In conjunction with the shortened bonds, the angle C3-C4-C5 has opened up to 118.2(3)°. The bond C^-01, on the other hand, measures
1.501(3) A which is longer than the value listed for a C 3 -0 single bond sp b y Brown , 128 1.^38 A or by Lide , 131 1 .^ 3 A.
The deviations from the expected geometry around has an impor tant bearing on the observed solvolysis rate of this molecule. While the 152 conformation of the molecule does not allow the cyclopropane' ring to pro vide anchimeric assistance as the brosylate group leaves (see below), the observed geometry of the molecule implies that the structure is ideally suited for the brosylate group to leave. The geometry at C^t- is essentially that of the trigonal carbon in the ionic transition state, and that along with the long C^-01 bond, may imply some partial ionization has already occurred. L ittle or no additional strain need be introduced into the structural framework as the leaving group departs and the molecule passes into the transition state.
Strain, especially at the sight of the incipient carbonium ion is oftentimes devastating in terms of the solvolytic rate. Norbomane, whose derivatives provide extraordinary .examples of the impact of anchimeric assistance is just as remarkable for the lack of solvolytic activity of the parent molecule. Compared to most simple alkanes (see Table 26 ), the solvolytic rate of this molecule is depressed by at least seven orders of magnitude. The origin of this effect lies in the constricted bridgehead a n g le , 132 9b°, which cannot open up as the carbonium intermediate develops.
The geometry of the norbomane skeleton is essentially invarient, espe-
*L go, 1 3 3 cially at the bridgehead position in all of its derivatives, 7 i n c lu d in g th e n o rb o m e n y l1333, and e n d o - a n ti- 8 - t r i c y c l o [ 3« 2. 1. 0 2’ 4 joctyl133^ derivatives, and explosive solvolytic rates 3 2 ’ 34 37 associated with these last two compounds, are possible only because anchimeric assistance pro vides an alternate mechanism for the reactions.
In view of the geometry found at C^, then, the solvolytic rate of the cis-bicyclo[5.1.0]octane is something of a surprise. Because it is TABLE 2b
RELATIVE SOLVOLYTIC RATES FOR SEVERAL COMPOUNDS
o X 2 0 .0C 10 4 c X
o X 2.bs 10
X bb.a X 60 f ’
X 1 . 0 0 l O- X X b.5 s
a i . 5 X T . l
■X
-r c ,d g 10 6.5
10 e h Table 26 (continued)
S. Winstein and J . Sonnenberg, J_. Am. Chem. Soc. , 83_, 3235 (l96l).
A.H. Fainberg and S. Winstein, ibid. , 78. 2780 (1956).
H. Tanida, T. Tsuji and T. Irie, i b i d . , 8 9, 1953 ( 1 9 6 7)*
M.A. B attiste, J.L. Deyrup, R.E. Pincock and J. Haywood-Farmer, i b i d . , 8 9, 195 U (1 9 6 7 ).
S. W instein, M. Shatavsky, C. Norton and R.B. Woodward, ibid. , 77, Ul83 (1955).
H.C. Brown and G. Ham, i b i d . , 78., 2735 (1956).
F . J . Williams, Ph.D. Thesis, The Ohio State Univ., 1 9 6 9*
S. Masamune, R. Vukov, M.J. Bennett and J.T. Purdham, J. Am. Chem. Soc., 9b, 8239 (1972). 135
so favorable to the transition state, one might expect some enhancement of the solvolytic rate, but the compound is quite ordinary compared to other cycloalkanes. Its rate lies slightly below the values found for
cyclopentyl 134 and cycloheptyl 135 model compounds, but the unfavorable nonbonded interactions which arise in the transition state of cyclohexyl derivatives 23 to lower its solvolytic rate 136 relative to cycloalkanes are unlikely to operate here. Thus, we are forced to conclude that some other factor slows its solvolysis, for example, inductive effects from I the cyclopropyl ring.
Schleyer has estimated 102 that the strain energy in cis-bicyclo-
£5 . 1. O]octane amounts to 3 1 .1 1 kcal/mol from a conformational analysis employing the Westheimer method . 137 Similar calculations 138 in d ic a te that the strain energy of cyclopropane itself amounts to 28 .1 3 k c a l/m o l and of cycloheptane, 7. 57 kcal/mol. This implies that cis-fusion adds little new strain to the product.
With the exception of the geometry at C^, the bicyclo[5.1. O^octane shows little evidence of strain and is in accord with what was observed in the 3,5-dioxabicyclo[5-1. 0]octane . 120 The angles C2-C1-C8 and C6-C7-C8 average 121. V3 while C2-C1-C7 and C6-C7-C1 average 119.3° which is slightly larger than the value 117.3° found in the C-C-H angle of cyclo p ro p an e. 121 The corresponding angle in most mono and disubstituted cyclo- propanes is also around 118° but values of 120° have been seen. Thus any distortion at the cyclopropyl ring is no larger than that which might be caused by replacing hydrogen with carbon in any cyclopropane. 136
Although the positions of hydrogen atoms are not well determined by X-ray methods, the consistency of the angles involving HI and PHI provide some support for a hypothesis bending these atoms toward each other and away from C 8. The angles H1-C1-C2 and H11-C7-C6 average 111°, and H1-C1-C8 and HU-C7-C8 average 120°.
The remaining interior angles which average 113.3° and 112. are also normal, and close to the "strainless” value, 112.4 ° , 138 p r o posed by Schleyer 138 f o r th e C-CH 2 -C a n g le .
The conformation of the bicyclo[5.1. Oloctane is basically deter mined by the interactions of H3, H 6 , H10 and H12 which approach each other to essentially the sum of their van der Waals radii (see Table 27), and is sim ilar to the conformation observed in 3 , 5 -dioxabicyclo[ 5 . 1. Of o c ta n e . 120 In the latter molecule, oxygen replaces C3 and C5, which means several H* • *H nonbonded interactions are eliminated. However, the conformation about C3-C b and C4-C5 is already staggered and elimination of hydrogen atoms cannot make some new conformations more stable, nor do the hydrogen atoms on C3 and C5 make any close contacts, in the first p la c e .
The most severe interaction occurs between H 6 and sulfur, which are eclipsed. This brings both sulfur and 02, 0.2 to 0.4& closer to H 6 than van der Waals forces predict, and the only driving force for such crowding seems to be to move 02 closer to bromine. 137
TABLE 27
INTRAMOLECULAR CONTACTS IN c i s - BICTCLO[5.1. 0]OCT-4-e: :o-YL % -BROMOBENZENE SULFONATE
HI H ll 2. 4 0 (6 )
HI h4 2 .7 2 (5 ) H ll H7 2. 5 7 (b )
H^ H7 3. 6 2 (5 )
H3 HIO 2.k2(b)
H3 h 6 2. k2(k) HIO h 6 2.b9(b)
H3 H12 2. 3M 5) HIO H12 2. 3 6 (5 ) h 6 02 2. kk(3) p r e d ic t 2. 6 - 2.9 h 6 03 3 .3 2 (3 ) h 6 S 2. 6 0(3 ) p r e d i c t 3. 0 138
F ig u re l 6 shows a schematic representation of cis-bicyclof^. 1. 0~I-
oct-4-exo-yl jD-bromobenzene sulfonate and for comparison, a sim ilar
representation of exo-anti-tricyclof" 3« 1 . 1 . 02 ’ 4 ]h e p ta n - 6 -yl p-nitro-
b e n z o a te *39 As the picture shows, the conformation of the latter
compound is such that when it solvolyses, the developing p orbital of
the incipient carbonium ion is well suited to overlap with the orbitals
of the cyclopropane bent bond. Rupture of the cyclopropyl bent bond
can occur via an upward disrotary process in accord with the rules
proposed by Woodward and Hoffman . 140 In the bicyclooctane on the other
hand, the conformation of the molecule is very poorly suited for any
interaction between the orbitals of the leaving group and of the cyclo
propane ring. If the cyclopropyl orbitals were to rupture in a manner
which would increase this overlap, then severe steric interactions between HI and Hll would rapidly lead to prohibitively large strain
energies. Thus it is no surprise that anchimeric assistance operates
in the solvolysis of the tricyclic compound but not in our bicyclo
o c ta n e . 139
119
109
OPNB
O l
F ig u re l 6. (a) The conformation of exo-ant.i-tricyclor3»1«1»0 1 heptan-b-yl p-nitrobenzoate. (b) The conformation of cis-bicyclof"5.1. Oloct-fr-exo-yl p-bromobenzene sulfonate V II. tTM is-BICYCL0[5.1. 0]0CTAKE-4-CAEB0XYLIC ACID
A. Photographic Prelim inaries, Space Group and Density
Crystals of trans-bicyclo[5.1.0]octane-4-carboxylic acid grow as needles bounded by the forms {0 1 1} and {0 0 1} with the latter form more pronounced. The crystals tend to cleave along the 10 0 face, but the cleavage is generally poor. Figure 17 illustrates the general morphology observed for these crystals.
Precession photographs of the crystals revealed that the crystal belongs to the monoclinic system, and the space group V2.xfc was uniquely established by the systematic absences displayed in the diffraction pat tern (see above p. 25). In all, the zones h04, hlj0 and hkO were photo graphed and the diffraction pattern was observed to die off somewhat more rapidly along b* than along a*'or c*.”
Unit cell parameters at 24° C were established after aligning 16 high angle (20 > l 6°) reflections on the Picker diffractometer using o graphite monochromatized MoK radiation (AMoK^ = O. 70926 A). A least squares fit of the unit cell parameters , 56 angular zeroes and orientation angles for these high reflections gave a = 7. 09^ ( 1 ) A, b = 6. 165 (1 ) A, c =
20,840(3) A and [3 = 104. 344(7)°. density 1.1599(2) g cm 3 calculated assuming 4 molecules in the unit cell is in accord with the value 1.1 5 g cm 3 determined by floatation in a solution of sodium iodide in water.
A summary of all the crystal data is given in Table 28.
l40 ik l
Figure 17. Morphology of trans-bicyclo[5.1.0]octane-U-carboxvlic
a c id . Ih2
TABLE 28
CRYSTAL DATA t r a n s -BICYCLOP5. 1 .0 ]OCTAME- 4 -CARBOXYLIC ACID
C9H14 02
M o n o clin ic
Space Group P2i/c x y z x jn-y \~ z
x y z x -k-y i+ z
a = 7.09U(l) A 24° C
b = 6 .1 6 5 (1 ) A p = IOU. 5 ^ ( 7 ) °
c = 20.8^0(5) A
cell volume = 885 . 0 (1 ))
D = 1 .1 5 g cm-3 m Dc = 1 .1 5 9 9 (2 ) g cm 3
M = 15b. 21 g m ol 1 Z = k
^MoK 0, 870 cm
Pooo = 336
Zff = 186U 1 ib j,
B. Intensity Collection.
Because this compound exhibits a rather high vapor pressure, the
crystal used for data collection was sealed in a capillary tube in order
to minimize the effects of sublimation. After placing the crystal on the
Picker diffractometer the take-off angle was adjusted to give 8($ o f th e maximum possible diffracted beam from the 5 0 0 reflection.
The diffracted intensities out to a maximum 20 of 60° (sin 0/A -
0.7 A 1) were monitored with graphite monochromatized MoK^ radiation
(A = O .7IO69 A). Inadvertently, the maximum I index was set at 20 w hich
cuts the data off at ^+1° in that direction. The truncated quadrant of data collected along h k ± j2 included a total of 22^9 reflections. Each o o reflection was scanned for 1 .9 0 at a rate of 2 /min. , with the scan
centered on the position calculated based on the wavelength of molybdenum
K radiation (A = 0 .70926 A). Background scattering was monitored for
10 sec. on either end of each scan. In order to monitor any loss in scattering power due to crystal decay or sublimation, check reflections were remeasured at intervals of 25 O data points while the first IO 79 d a ta were collected and thereafter at intervals of once every bOO data points.
Nine reflections, hk C. Data Reduction As before (see above, Ch.IV), the data set was corrected for any attenuators used, background scattering was subtracted, and Lorentz and polarization factors were applied to reduce the observed intensities to a set of structure factor magnitudes, |F '(h)| and their standard devia tions, CTp. In the calculations, the attenuator factor was 2.84, the ratio of time spent scanning to time spent counting background, G, was 2.25, and Busing and Levy's factor, p, was 0.06. Tables 29 and ~$Q sum marize the attenuator corrections and the data observed above background. No corrections were made for absorption. The l 8 check reflections col lected at intervals throughout the data collection did not show any loss in intensity over the period of the experiment (see Table 3l). The Because the data set was truncated along £*and because of the rapid die off of the data at high angles, especially along b* the Wilson plot tailed off above sin 0/X = 0 .5 6 A 1 (see figure 1 7 ). The overall tempera ture factor, B, and the scale factor, /K , derived from the Wilson plot w e r e it.2 (7 ) A2 a n d 1 .7 ( 1 ) respectively. These parameters were used to scale the data and calculate normalized structure factors, E (h ). I t would probably have been more rea listic, however, to exclude the data a b o v e s i n 0/X = 0 .56 A 1 from our calculations. With that lim itation, the estim ate of the overall temperature factor becomes 6. 8(4 ) a n d t h e scale factor 2 .7 2 (2 ). 1^5 TABLE 29 SUMMARY OF ATTENUATOR CORRECTIONS FOR t ran s-3lCYCLO[9.1. 0]OCTANE-4-CARBOXYLIC ACID Number of Attenuators Number of Reflections 0 2 2 1 1 1 15 2 1 2 3 ■ 9 4 2 l b6 TABLE 30 SUMMARY OF DATA ABOVE BACKGROUND FOR trans-BICYCLO[5.1 .0]0CTAHE-4-CARB0XYLIC ACID Number greater Range Number th a n 1 2 3 k 5 6 7 8 9 10 A ll Oct 233 233 199 173 1^3 123 129 93 110 95 1531 l a 9.2b 206 164 110 63 k8 58 25 i+8 28 97^ 2a 210 183 125 63 15 15 6 8 lb b 6b 3 3a 201 169 98 35 6 2 0 1 1 0 513 *KT 19 ^ i b i 72 18 5 1 0 1 0 0 k 3 2 5° 190 131 58 12 0 0 0 0 0 0 392 & 186 119 b3 k 0 0 0 0 0 0 357 7a l 8l 103 38 3 0 0 0 0 0 0 325 173 8k 29 2 0 0 0 0 0 0 288 op 170 73 28 1 0 0 0 0 0 0 272 1CP 159 65 20 1 0 0 0 0 0 0 2I+5 14 t TABLE 31 SUMMARY OF CHECK REFLECTIONS FOR t r a n s -B I CYCLOf 5 .1 . 0]OCTANE-4-CARBOXYLIC ACID R e f l e c t i o n IW I R e f l e c t i o n IW I i / i . ^ i n l t ' in : 2 0 0 355 10670 1 .0 0 0 2 1 3 365 12670 1. 000 648 IO38O 0 .9 7 3 658 12910 1.019 953 io64o 0 .9 9 7 963 12980 1. 024 1341 10730 1.0 0 6 1351 13020 1.028 1775 10360 0 .9 7 1 1785 12820 1.0 1 2 2212 10390 0 .9 7 4 2222 12760 1.007 2 0 4 355 9630 1.0 0 0 0 1 7 365 19825 1 .0 0 0 648 9560 0.9 9 3 658 19480 O.983 953 9650 1 .0 0 2 963 1341 9610 O.9 9 8 1351 19125 0.965 1775 9650 1. 002 1785 19820 1. 000 2212 9700 1.007 2222 19430 0.980 I 1 0 555 15980 1 . 000 1 1 8 365 10870 1 .0 0 0 648 15570 O.9 7 4 658 10670 0 .9 8 2 953 15980 1 .0 0 0 963 10750 0 .9 8 7 1341 15580 0 .975 1351 10820 0.995 1775 15630 0.978 1785 11000 1.0 1 2 2212 15520 0 .9 7 1 2222 10680 0 .9 8 3 TABLE 31 (continued) Reflection IW I R e f le c tio n IW I I / I i n i t 2 1 3 365 12950 1. 000 5 1 0 371 9530 1 . 000 658 12690 0 .9 8 0 664 9630 1. 010 963 12768 0.986 969 9500 0.9 9 7 1351 13150 1.015 1357 9580 1.005 1785 12650 0.977 1791 9510 0 .9 9 8 2222 12U90 0.9 6 4 2228 9640 1 .0 1 2 0 1 7 365 19570 1.000 0 0 10 371 9865 1 .0 0 0 658 19360 0.9 8 9 664 9830 0 .9 9 6 963 19510 0.997 969 9860 0 .9 9 9 1351 19250 0 .9 8 4 1357 9860 0.9 9 9 1785 19280 0.985 1791 9720 0.985 2222 18850 0 .9 6 3 2228 9930 1 .0 0 7 T i f f 365 11000 1. 000 2 2 0 371 5640 1 .0 0 0 658 10680 0. 971 664 5800 1 .0 2 8 963 IO78OO.98O 969 5660 1. oo4 1351 11010 1. 001 1357 5630 0 .9 9 8 1785 10860 O.9 8 7 1791 5800 1 .0 2 8 2222 10730 0.975 2228 5640 1 .0 0 0 2 2 0 371 5728 1. 000 5 1 0 371 9700 1 .0 0 0 664 5695 0. 9 9 4 664 9680 0 .9 9 8 969 5610 0.9 7 9 969 9550 0.9 8 5 1357 5690 0.993 1357 9590 0 .9 8 9 1791 5653 0 .9 8 7 1791 9800 1 .0 1 0 2228 5600 0.978 2228 9220 0 .9 5 1 149 TABLE 31 (continued) R e f l e c t i o n IW I Reflection IW I i/i. ' m i t 0 0 10 371 io o4 o 1. 000 355 9790 1 .0 0 0 664 io o4 o 1. 000 648 9500 0 .9 7 0 969 984o 0 .9 8 0 953 9730 0 .9 9 4 1357 10000 0 .9 9 6 1341 9720 0.993 1791 9780 0. 974 1775 9720 0.993 2228 9720 0 .9 6 8 2212 9770 0 .9 9 8 2 0 0 355 i o44 o 1 .0 0 0 355 16090 1 .0 0 0 648 10310 0 .9 8 8 648 15610 0 .9 7 0 953 10500 1 .0 0 6 953 16310 i . o i4 134 i 10570 1 .0 1 2 1341 16030 0 .9 9 6 1775 1775 15710 0 .9 7 6 2212 10260 0 .9 8 3 2212 lb l6 0 1. oo4 + + - 2.0 + + + + + + \ \ 0.1 0.2 5iq Q 0.3 0.4 A* F ig u re 1 8. The Wilson plot for trans-bicyclo[5.1.Oloctane-4-carboxylic acid. \-TI o TABLE 32 STATISTICS ON E FOR tr a n s -BICTCLOf 5 • 1. 0]OCTANE-4-CARBOXYLIC ACID < |e | s ) 1 .2 6 0 1 . OOO 1 . 000 < |e 2- i I > 1 .2 9 0 0 .7 3 6 0 .9 6 8 <|E|> 0 .7 8 0 0 .8 8 6 0 .7 9 8 Values of |E| greater than Num ber F r a c t i o n A c e n t r i c C e n t r i c 0 .5 1 2 6 4 0.562 0.799000 0 .6 1 8 1 . 0 7 66 0 .3 4 0 0 .3 6 8 0 0 0 0 .3 1 7 1 .5 400 0 .1 7 8 0 .1 0 5 0 0 0 0 .1 3 4 2 .0 1 8 7 0 .0 8 3 0 .0 1 8 0 0 0 0 .0 4 5 2 .5 86 0 .0 3 8 o. 0 0 1 9 0 0 0 . 0 1 2 3 .0 4 i 0 .0 1 8 0.000120 0.0027 3 .5 17 0 .0 0 7 0 .0 0 0 0 0 5 0 .0 0 0 4 5 0 4 .0 5 0 . 0 0 2 0 .0 0 0 0 0 0 0 .0 0 0 0 6 0 V III. SOLUTION OF THE STRUCTURE A. The Patterson and Superposition Functions Once again a sharpened Patterson function (eqn. 25) was calcula ted with the normalized structure factors, E ( h ) , used as coefficients. Unlike the bromobenzene sulfonate derivatives discussed above, no heavy atoms are present in a carboxylic acid derivative, so peaks in the Pat terson function are a ll approximately equal. In this case, a clue to the disposition of the m olecule was deconvoluted from the Patterson function with the aid of a symmetry minimum function. The symmetry min imum function uses superposition methods74 based only on the symmetry elements of the unit cell. Since carboxylic acids generally dimerize about a center of symmetry in the solid state, a peak at 0.167, 0 . 0 , 0. 08 in the symmetry minimum function provided a lik ely candidate for the oxygen-oxygen vector. A considerably larger peak at 0 . 0 5 , 0 . 8 0 , 0 . 0 1 was also considered as a likely candidate for the same vector and because of its magnitude, tria l structures based on that assumption dominated much of the in itia l, unsuccessful effort toward an elucidation of the structure. With the proper oxygen-oxygen vector, however, a vector super position map was constructed which lead to the ultim ate resolution of the entire structure. The vector superposition map is constructed by superimposing successive copies of the Patterson function onto itse lf 152 153 with the copies shifted along the defining vector and along each of its symmetry related vectors. The oxygen atoms and two carbon atoms of the carboxylic acid group were identified from this map, and with their coordinates, a third minimum function was computed, this one based only on the interatomic vectors in this functional group. Neither this function, nor the vec tor superposition function which preceded it contained a clearly re solved picture of the entire molecule. However, by combining the strongest peaks on each map, subject to the constraint that only peaks consistent with a chemically reasonable structure should be included, tria l coordinates for all but one of the atoms of the complete non- hydrogen structure were established. The coordinates resolved from these maps are listed in Table 33.-, and th e num bering sy stem i s shown schematically in Figure 1 9 . 154 02 oi H ll KL C2 HIO H2 Cl H3.2 HL3 Figure 19. A schematic representation of trans-bicyclo[5.1.0]- octane-4-carboxylic acid illustrating the numbering system employed for that molecule. 155 TABLE 33 INITIAL COORDINATES FOR t r a n s -BICYCLoT5 .1.0]0CTANE-4-CARB0XYLIC ACID X y z a b c Cl O.63O 0.540 0.170 C2 0.^33 0.600 0.180 C3 O.3OO 0.480 0.120 c4 O.38O 0.280 0.100 C5 O.55O 0.233 0.080 c6 0.767 O.267 0.110 c r O.767 0.400 0.210 c8 - - - C9 0.220 0.160 0.045 0 1 0.150 0.000 0.080 0 2 0.150 0.200 0 .0 0 0 156 B. Initial Refinements - The Isotropic Molecule Structure factors (eqn. 26) calculated based on the coordinates listed in Table 32 gave R = 0.50 and WR = O. 5 5 . Each atom was given a temperature factor of 4.0 A 2 for the calculation. The scattering factors for carbon and oxygen were taken from the tabulation compiled by Hanson, Herman, Sea and Skillman . 68 Full matrix refinement of the positions and thermal parameters associated with this model lead to convergence at R = 0.37 and WR = 0.42, and a difference Fourier (eqn. 2 9 ) phased on the basis of the ten atoms clearly indicated the position of the remaining atom , C8 , at 0.167, 0.133, 0.295- Structure factors calculated on the basis of a model which included c 8 gave the residual indices R = 0.33 and WR = 0.40 which supported the basic correctness of the model. Ten cycles of full matrix refinement further reduced these indices to R = 0.27 and WR = 0 . 3 1 , before the refinement converged. The isotropic temperature factors at this point ranged from 5-6 A 2 to 9-3 an^ the geometry was s till somewhat unsettled, but the structure was basically reasonable. With such large residual indices, the estimated standard deviation of a o bond length was s till approximately 0.03 A. Although equivalent bonds were within 2a of each other, at that level of resolution, few structural details could be firmly established but it was already apparent that the bridgehead-bridgehead bond C1-C7 was very short at 1.34(3) A. The largest features on a difference Fourier function calculated at this point were O 1 . 6e/A 3 high and clearly indicated anisotropic thermal motion for the two carboxylic oxygen atoms. Indications of hydrogen atom positions and anisotropic thermal motion in the carbon atoms were mixed together throughout the map. 157 TABLE 34 ATOMIC COORDINATES FOR t r a n s -BICYCLO[5.1. Q]OCTANE-4-CARBO:XYT.TO ACID X Atom £ a b c 01 0. 1656(9 ) -0 . 0095 ( 15 ) 0. 0758(4 02 0.1378(10) 0 . 2271(1*0 -0. 0053(4 Cl 0.6326(16) 0 . 5944 (19) 0. i6 4 o (7 C2 0.4349(14) 0 . 5 868(1 8) 0. 1797(5 C3 0.3203(1*0 0 . 4250 (24 ) 0.1326(6 c4 0.3876(12) 0 . 2868( 2 0 ) 0.0929(5 C5 0.5614(12) 0 . 2246 (18) 0. 0736(5 c6 0.7671(13) 0.3058(20) 0.1071(6 C7 0.7501(15) 0.4304(23) 0 . 1697(6 C8 0.8397(16) 0 . 6334 (18) 0.2031(5 C9 0. 2219(13) 0.1613(18) 0.0518(5 TABLE 35 ANISOTROPIC THERMAL PARAMETERS FOR tfans-BICYCLO[5 . 1 .0]OCIANE-4-CARBOXYLIC ACID P n P22 P33 Pl2 ^23 P31 01 0 .0408 (20) 0.0725(55) 0.0071(5) -0 .008l ( 2 5 ) -0.0028(9) -0.0018(6) 02 0.0501(22) 0.0871(59) 0 .0064 (5 ) -0 . 0264 (27) -0.0028(9) 0.0055(6) Cl 0.0598(31) 0 .0584 (55 ) 0.0107(6) -0.0055(32) -0.0149(16) -o.oo4 i ( i i ) C2 0.051+6(27) o.o64 o(i+7 ) 0.0057(4) -0.0001(51) -0.0065(11) 0.0015(8) C3 0.0274(26) 0.0966(71) 0.0091(6) -0.0151(54) -0.0149(17) 0.0026(9) c4 0.0225(21) 0.0862(56) 0.0081(5) -0.0155(30) -0.0195(14) o.oo4 o (8) C5 0.0252(21) 0 .0679(46 ) 0.0075(4) -0.0057(50) -0.0074(15) 0.0049(8) o6 0.0280(25) 0.0698(50) 0.0079(5) -0.0116(52) -0.0095(14) 0.0014(9) C7 0.0558(50) 0.0896(75) 0 .0084 (5 ) 0.0019(57) -0.0098(17) -0.0012(9) c8 0.01+82(55) 0.0542(45) 0.0052(4) -0.0157(52) -0.0027(11) -0.0009(8) C9 0.0568(27) 0.0549(42) 0.0055(4) 0.0009(28) -0.0045(10) 0.0052(8) VJH1 CD 159 C. Anisotropic Refinements On the basis of the foregoing observations, further refinements were undertaken with anisotropic temperature factors for each of the atoms. Eleven cycles of refinement brought the residuals to R = 0. l4 and WR = 0.17. Tables 33 and 3k- list the positional and thermal param eters after these refinements. The largest feature remaining on a dif ference map computed just before convergence was achieved was a peak 0 . 6 l e/A 3 at 0.17, 0. 50 and 0.13. That peak and a number of others corresponded well to the postions calculated for hydrogen atoms in the structure (see Table 35). However, when hydrogen atoms were added to the model structure, the indices R and WR increased to 0 .1 5 and 0.21 and an attempted re finement of the structure with hydrogen atoms diverged. Since only 6 k3 data above 2cy were available for the refinements, the divergence could F be an indication that the problem was not sufficiently overdetermined for the 153 parameters involved in the model with hydrogen atoms. A summary of all refinements is given in Table 36. ? i6 o TABLE 36 POSITIONS CALCULATED FOR HYDROGEN ATOMS IN trans-BICYCLOD-l.OlOCTANE-U-CARBOXYLIC ACID X y z a b c Hl 0.5 4 4 0 .6 9 2 0 .1 3 0 H2 0 .4 5 3 0 .5 4 9 0.225 H3 O.38O 0 .7 4 3 0 .1 7 1 H4 O.252 0 .3 5 2 0 .1 6 1 H5 0 .2 2 2 0 .5 3 0 0 .1 0 1 H6 0 .4 8 2 0.327 0.134 HT 0 .5 4 1 0 .2 7 3 0.025 H8 0 .5 7 0 0 .0 6 2 0.075 H9 0 .8 1 9 0.405 0.079 HIO 0 .8 5 9 0 .1 8 1 0 .1 2 2 H ll 0.775 0 .2 8 2 0 .1 9 0 H12 0 .8 7 0 0 .6 4 2 0 .2 5 3 H13 0 .9 2 9 0 .7 2 0 0.182 TABLE 37 SUMMARY OF REFINEMENTS FOR tr a n s -BICYCLOf^. 1. Q]0CTANE-4-CARB0XYLIC ACID Description NY a m h R WR GOF C The Trial Structure 4 l 643 0.5049 0.5492 11. 22 Converged Isotropic 45 643 0 .3745 0.4235 8.6 5 with 10 Atoms Converged Isotropic 45 643 o . 2663 0 .3 0 9 2 6 .3 4 with 11 Atoms Converged Anisotropic 100 643 0.1429 0.1665 3 .5 8 With T rial Hydrogen 153 643 0.1547 0.2056 4 .6 2 Atom P o s itio n s a. NV = the number of parameters allowed to vary. b. HO = the number of observed data included in the refinement. c. The goodness of fit (or standard deviation of an observation of unit weight) is defined as: rw (lF 0 ( h ) j - |F c ( h ) | ) 2 NO - NV o\ TABLE 38 OBSERVED AND CALCULATED STRUCTURE FACTORS FOR t r a n s -BICYCLOP. 1. 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Photographic Prelim inaries, Space Group and Density Crystals of trans-bicyclo|"5.1. 0 ]octane -4-methano 1 -_d-bromobenzene sulfonate were grown by slow evaporation from hexane at 0 ° c . The c r y s tals grow as flat needles, bounded by {0 1 0 } and {1 1 0 } with the needle axis along a#. Figure 20 illustrates the morphology of the crystal cut for use in this investigation. After mounting the crystal approximately along a*, precession photographs established that the crystal structure was monoclinic (C^)* Systematic absences observed on the nets hOi, hi i , hkO and h k l e s ta b lis h e d the space group P2x/c uniquely (see above p. 2 5 ). Subsequent investiga tion showed a = 6.662(3 ) A, b = 21.310(7 ) A, c = l4. 0^7( 5 ) A and p = 127.26(2). Although an alternate choice of a# along 1 0 1 would cause P to take on a more normal value, 98. 5 °, in the non-standard space group, P2 i/n, it was decided to work in the standard space group. The density measured with a density gradient column 54 was 1.50(1) g cm 3, which is in good agreement with the value 1 . 509 ( 1 )) g cm 3 c a lc u lated from the unit cell parameters assuming four molecules in the unit cell. The crystal data for this compound is summarized in Table 39* 164 165 0 / 0 / 0 l o Figure 20. The data crystal used for trans-btcvclo[5.1. Oloctane- ^-methanol-jj-bromobenzene sulfonate. 166 TABLE 39 CRYSTAL DATA FOR t r a n s - BICYCLQ[g.l.O]PCTANE-U-METKAIIOL p-BROMOBENZENE SULFONATE p-BrC6H4S020CH2CaHi3 M o n o clin ic Space Group P2j/c x y z x Jr-y |+z x y z x |r+y ^--z a = 6. 662 ( 3 ) A b = 21.310(7 ) A p = 127.26(2) c = l 4 . 0 i*7 (5 ) .A cell volume = 1592 . 2h A3 D - 1 . 5 0 ( l ) g cm 3 D = 1 .5 0 9 g cm 3 c M = 359. 29 g mol 1 Z = k 28 .8 3 cm 1 %oK O' £Fooo = 736 £ f i s = 8928 2emax = 50° B. Data Collection A second crystal was mounted on a Syntex PI automated diffrac tometer for measurement of the diffracted intensities. The sample crys ta l was positioned 45 mm from the collim ator (diameter = 0 . 5 mm) a n d 90 mm from the counter (aperture diameter = 2.0 mm). Previous work had shown the pulse height analyzer would produce adequate resolution of the diffracted radiation from machine noise and from harmonics at the set tings given in Table 40. Ten reflections were autom atically aligned 141 and used to deter mine the orientation of the crystal and the unit cell parameters used for data collection. A somewhat more precise estim ate of the 'unit cell parameters, however, was made from the data provided by the alignment of 15 reflections (20 > 22°) chosen at the end of the data collection. The diffracted intensities were monitored using 0-20 s c a n s with the diffractom eter in the bisecting mode. With graphite monochroma- tized molybdenum radiation, a to tal of 2803 of which 2481 were above background unique reflections were available out to 20 of 50° (sin Q/X = 0 .5 9 A- 1 ). Each peak was scanned from 1° in front of the position calculated for MoK radiation to 1° beyond the position calculated for MoK radi a l as ation. The scan rate was chosen for each reflection based on a prelim i nary, two second count at the peak position. If the initial survey showed less than 20 counts, and effective rate scan rate of l°/min. was u sed . When more th a n 20 counts were recorded during the preview, the effective scan rate was increased linearly up to a maximum of 24°/min., when the in itia l preview exceeded 20 0 0 counts. Backgrounds were moni- 168 TABLE UO INSTRUMENT SETTINGS DURING DATA COLLECTION High Voltage Power Supply 900 v Pulse Height Analyser 22b counts machine noise in 500 s e c . Course Gain = b F in e G ain = 5 Window = 2. 0/ 0. 3 Discrimination Mode: differential Lower Level Reference: internal Tube 50 kV 20 mA Take-off Angle = 6° 169 to r e d f o r l/b of the scan time on either side of the peak. Each peak was step scanned through 9 6 equal increments with the counting time in each increment adjusted to give the appropriate effective scan rate. When the counting rate in any step exceeds 5000 counts/sec., coinci dence losses become important. Corrections for coincidence losses in the detector and associated circuitry were made via the approximation: 1 - / 1 - ^ t I o" t = ------( 3 6) t 2 t where I. = the true count t I = the observed count o T = the dead time for an isolated event before each increment was added to the net count for the scan. The ap proximation remains valid up to an intensity of 50000 cps and no reflec tions were strong enough to exceed the lim it. Nonetheless, reflections were recollected at the end of the data collection with the intensity of the X-ray source reduced. The number of counts in each increment, the total counts observed in each background and during the scan, the effec tive scan rate, the net integrated intensity normalized to a scan rate of l°/m in., and the standard deviation of the integrated intensity based on Poisson counting statistics was recorded for each reflection. After each 100 data points, seven check reflections were monitored. 170 C. D ata R ed u ctio n Recent investigations 61 have shown that a graphite monochrometer crystal should be considered to be partly ideally mosaic and partly per fect. Like the Picker diffractometer, the Syntex PI diffractometer adopts a configuration with the diffracting plane of the graphite mono chrometer crystal perpendicular to that of the specimen crystal. The polarization factor which allows for the intermediate character of the monochrometer crystal is a combination of equations (k) and ( 5 ): c o s 220 + c o s 220 c o s 20 + c o s 220 P = F ------S------+ ( i - F ) ------a ------£ - (3 7 ) 1 + cos 20 1 + cos 20 m m The factor F which describes the ratio of mosaic to perfect character in the monochrometer crystal was set at 0.5 in this investigation. The Lorentz factor (eqn. 3) is unchanged. Program P I 142 was written primarily to read the data tape and apply the Lorentz and polarization factors to the observed intensi ties to give structure factor magnitudes on a relative scale, |F'(h)|. In addition, the program reevaluates the data to check for such anomalies as high backgrounds, negative net counts in any step, or ratemeter over flows during the scan. If the background counts differ from another by more than four times the square root of the smaller value, the pro gram resets the larger background to the lower one and recalculates the net integrated intensity. Since different scan rates, u), were employed for the various reflections, equation (l) for the net integrated 171 intensity becomes I = u)[I0 - G(B1 + B2 ) ] (3 8) to adjust the net integrated intensity to an effective scan of l°/min. As before Io is the net raw count accumulated during the scan, G is the ratio of time spent scanning the reflection to the total time spent counting backgrounds and B1 and B2 are the raw counts accumulated during the first and second backgrounds. In this investigation, G was set a t 0 . 5 . If negative counts were found in any step, the number of counts in that step was reset to a value interpolated from the steps immediate ly preceding and following that increment. No ratemeter overflows were detected. The extra error suggested by Busing and Levy , 58 was also added to Oj at this point so that the effective standard deviation becomes .1 a = { 10 [ I o + G2 (B1 + B2) ] + (pi )2 } 2 (3 9 ) I where the factor p was set at 0 . 01. Table 39 summarizes the observed intensities from the unique set of data (i.e., without any recollected data and with no h 0 I d a ta ) . The diffraction patterns of both the cis and trans brosylates were measured to essentially the same lim it (sin Q/X = 0.59 A 1) and the crys tals used in the two investigations were of comparable volume, but dif ferent radiation was used in each case. Because the net integrated in tensity of the diffracted beam is proportional to X3} intensities moni tored with molybdenum radiation are smaller by a factor of 10 than those monitored with copper radiation. Although this effect is offset to some 172 TABLE 41 SUMMARY OF DATA ABOVE BACKGROUND FOR t r a n s - BICYCLO [ 5 .1 .0 3 OCTANE-4-METHANOL E.-BROMOBENZENE SULFONATE Number g greater Range Number th a n 1 2 3 4 5 6 7 8 9 10 A ll Oct 298 281 268 267 260 245 223 248 209 182 2481 l a 288 265 241 227 226 208 161 172 13b 120 2044 2j 281 250 221 202 184 173 119 112 90 66 1698 3a 273 236 203 187 156 138 93 76 54 42 1458 4cr 265 231 194 173 135 109 75 59 35 24 1300 5 ct 261 225 183 165 116 86 59 42 23 11 1171 6ct 256 218 173 156 101 70 45 30 16 5 1070 7ct 250 209 168 144 88 61 42 23 12 5 1002 8a 244 200 157 136 80 54 33 15 9 2 930 9CT 240 191 151 123 76 44 28 11 7 1 872 maximum s in 0/ l = 0 .5 9 A -1 crystal volume = 0. 0113 mm3 a- radiation 173 TABLE 42 SUMMARY OF CHECK REFLECTIONS FOR t r a n s - BICYCLOfg.l. 0]OCTANE-4 -METHANOL p-BROMOBENZENE SULFONATE h c F a CT s m x IO3 d F 6 0 2 5 1 5 8 .1 2 1.0 4 0 .9 1 - 0 .0 ( 4 ) 5 8 .1 (3 ) 0 2k 0 43-34 l . 88 1 .3 0 + 8 (7 ) ^ 2 .9 (5 ) 2 5 1 b2. 68 0 .7 6 O.9 6 + 4(3) 42. 4 (2 ) 3 15 1 75 .5 9 l . 38 1 .1 1 -2 (5 ) 7 5 .7 (4 ) 0 l 7 7 1 .8 4 1 .3 6 1 .0 5 -8 (5 ) 7 2 .4 (4 ) 0 k 6 76 .1 8 l . 21 1. 01 -K5) 7 6 .3 (3 ) 0 7 5 100.98 1 . 14 1 .0 8 + 2 (4 ) 100. 9 ( 3 ) b. a = / l 0 * 1 V n -1 C. S = 1 / ffp d. m = the slope of the least squares line. e. Fq = the intercept of the least squares line. 174 extent because data monitored with shorter wavelength radiation lie at lower values of the Bragg angle, the intensities for the cis compound (Table 6) were significantly stronger than those for the trans-compound (Table 3 9 ). The seven check reflections which were monitored throughout the data collection are summarized in Table 42. Plots of |F(h)| as a func tion of exposure time for these reflections indicated that none of them gained or lost significant intensity during l44 hours of exposure to MoK^ radiation. In addition, each standard was averaged and its stan dard deviation was computed from the acc mulated remeasurements. In each case, this standard deviation was in good agreement with the value derived from equation ( 3 9 ), indicating that the scatter in the observed intensities is adequately accounted for from counting statistics plus a 3$ contribution from machine noise. The remainder of the data reduction, the solution of the structure t 43 and the in itial refinements were carried out with the CRYM package of X-ray computer programs. Absorption corrections were made based on a crystal with the form illustrated in Figure 17. The crystal was defined for the absorption program, however, in terms of the diffractometer angles ^ and X 0 0 1 0 4. 58 17k 82 0. 075 mm 0 . 1 0 355 . 42 3 54.82 0 . O75 mm 1 1 0 1 6 .3 4 251.56 0 .1 5 0 mm 1 1 0 l4 . 04 280.54 0 . 15 O mm 175 X 0 1 1 0 3 5 4 .9 6 100.54 0.1125 mm Top 6 5 . 55- O.138 mm Bottom 291. 302. 0 .138 mm The M iller indices of the side faces are included only for convenience. The top and bottom faces were rather crudely cleaved and not readily in dexed. Following the procedure of Busing and Levy , 62 the absorption factor was evaluated over an 8x 8x 8 grid interval. The linear mass ab sorption coefficient for the compound is 2 8 .8 3 cm 1. In order to test the validity of the absorption correction, ^ scans were made for 12 reasonably intense, we 11-separated reflections. Figure illustrates the behavior of these reflections before and after the absorption correction. As the figures show, large systematic errors in the data were effectively removed after the correction was applied. At this point, the system atically absent reflections were removed from the data set and equivalent reflections averaged, leaving 2798 unique reflections. A Wilson plot (Figure 21) for the data indicated that the overall temperature factor was 4.35 and that the scale factor /K = 0.1+640 would place the observed structure factor magnitudes |F 7(h)| on an ap proximately absolute scale. Statistics derived from the normalized structure factors, E(h), and summarized in Table 1+3, were in excellent agreement with the values expected for a centric distribution of diffrac ted intensities. 176 TABLE 1*3 STATISTICS ON E FOR trans_-BICYCLO[ 5 . 1. 0 ]OCTANE-4 -METHANOL £ -BROMOBENZENE SULFONATE Experimental A c e n t r i c C e n t r i c 1 . Ol4 1. 000 1.0 0 0 < |e 2 - i |> o. 965 0 .7 3 6 O.968 < |E |> 0 .7 9 1 0 .8 8 6 0.7 9 8 Values of |E| greater than Num ber Fraction Acentric Centric 1 .0 908 0.3 2 5 0 .3 6 8 0 .3 2 0 2 .0 125 0.01*5 0 .0 1 8 0 .0 5 0 3 .0 11 O.OOl* 0 .0 0 0 1 0 .0 0 3 < |e 2 - i | 2 > = 2.088 < (e 2 - i )3 > = 8 .8 8 9 d 0.1 sin 0 0.2 0.3 AJ Figure 21. The Wilson plot for trans-bicyclo[5.1.0]octane-H-methanol jD-bromobenzene sulfonate. ^ X. SOLUTION OF THE STRUCTURE A. The Patterson Function and the Trial Structure The ten highest peaks in a sharpened Patterson function corre sponded to the bromine and sulfur Harkers vectors and to the bromine- sulfur cross vectors just as they had in the Patterson function for the cis isomer discussed above. The bromine and sulfur atoms were located a t : x y z a b c Br 0.625 0.635 0.^38 s 0.500 0.495 0.205 In this case, the coefficients used to sharpen the Fourier summation w ere: F ( h )2 = (E(h) -1) x 10 4 x (-S-1”/ 9) x E(h) x (-19.36 ) (40) ?2 The isotropic temperature factor of the bromine atom was set at 3-5 A^, and structure factors calculated. The R factor with only this atom in the structure was 0.54. A difference Fourier confirmed the position of the sulfur atom. In addition, two peaks were identified as oxygen atoms and four peaks were chosen as carbon atoms, but the complete structure was was not yet obvious at this point. The difference map also showed a large negative density at the bromine position which indicated that the in itial temperature factor was too small. 178 179 The temperature factor of the bromine atom was increased to 3.7 A 2 and sulfur, the two oxygen atoms and the four carbon atoms were added to the trial structure. The initial temperature factors chosen for these atoms were 3.7 A2 (sulfur), U.5 A2 (oxygen) and 5*0 A 2 (carbon), respec tively. The R factor for structure factors based on this model without refinement was 0.H8. A Fourier summation based on the phases generated by this fragment showed 20 peaks which corresponded uniquely to the total structure (aside from hydrogen). The initial coordinates are listed in Table UU and the numbering scheme is illustrated in figure 22. Hll HLO KL CIO H2 Cl C2 01 !12 Cl HI! >H1? I n k B r C15 in.6 h i s H1T F ig u re 22. A schematic representation of trans-hicyclor5.1. 0]octane-4-methanol £-hromobenzene sulfonate. H co o l8l TABLE 44 IN ITIAL COORDINATES FOR t r a n s - BICYCLO[5.1. 0 ] OCTANE-METHANOL j^-BROMOBENZENE SULFONATE X X z a b c B r 0.375 o. 365 0.562 S o. 500 0.495 0.205 0 1 0.540 0. 445 o . i4 o 02 0.750 0.535 0.270 03 o. 248 0 .55 ^ 0.102 Cl 0.475 o .46 o 0.300 C2 o. 66 o 0.445 0 .4 io C3 o. 66o 0.425 0.495 c4 0 . 420 o .4 io 0 . 46o C5 0 .2 2 0 0.425 0.347 c 6 0 . 220 0.450 0.265 CT o. 340 0.405 0.060 C8 0.375 0.136 0.477 C9 0 .1 0 1 0.167 0.385 CIO 0.113 0.210 0.298 c n o. 293 0.2325 0.328 C12 0.499 0.254 0.295 C13 0.570 0.206 0.338 cib 0.732 0. 204 0.507 ci5 o. 6oo 0.180 0.559 1 8 2 B. Refinement of the Structure Structure factors calculated from the unrefined coordinates led to R = 0.336j WR = 0.559 for all the data, which fell to 0. 18^ and 0.237 re spectively after b cycles of isotropic refinement. While further refinements were carried out in the CRYM 143 sy stem , difficulties in the refinement led us to suspect the CRYM program package, so parallel refinements were initiated with the program MJGLS5 78 u sed earlier for the cis isomer. Refinements with that program, however, led to the same difficulties, the source of which we now see is the disorder in the crystal itself. The same quantity, Z w i2, defined above, was minimized in each set of refinements, but the weighting function, w, was 1/6 p for the refinements with the CRYM program and 1,6 22 for the refine ments with MJGLS5. In addition, the refinements in the CRYM system in cluded a ll of the data, whereas refinements with MJGLS5 restricted the data set to those data where I was greater than a Because the two sets of refinements were so similar, only the latter set w ill be discussed in detail. Both sets of refinements are summarized in Table ^ 8 . F o r b r o mine, the scattering factors used in both refinements were taken from the tabulations of Cromer and Waber , 67 those for sulfur, oxygen and carbon from from tables given by Hanson, Hermon, Lea and Skillman 68 and the table used for hydrogen came from Stewart, Davidson and Simpson. 69 Anomolous dispersion corrections were taken from the tables published by Cromer . 75 Starting with parameters derived from earlier refinements, an iso tropic model converged at R = 0 .1 5 3 and WR = 0.118 for data above S p At this point, the isotropic temperature factor for bromine was 5.8 A 2 and a difference Fourier indicated the bromine should be given an anisotropic 183 temperature factor. The temperature factors for the remainder of the bromobenzene sulfonate group ranged from 5-3 to 3*5 A2, while temperature factors for the bicyclooctane were much larger, ranging from 4.8 to 1 0 .6 A2, with the largest values observed at the two bridgehead carbons, Cll and C13* Difference Fourier functions computed from phases based on a model without the cyclopropane ring, however, did not show any marked elongation of tlie peaks for these atoms. When anisotropic temperature factors were introduced into the model structure, the indices rapidly fell to R = 0.O 78 and WR = 0 .06l. The parameters derived at the end of this refinement are given in Tables 1*5 and kG . The largest feature in a difference Fourier map was a peak e/A 3 high near the cyclopropane ring. Hydrogen atom positions were calculated on the basis of the geom etry of the carbon skeleton of the molecule, but peaks corresponding to these atoms were not readily identifiable in the difference Fourier map. When the scattering from these atoms was added as a fixed contribution to the model structure, the residual indices immediately dropped to 0.06l0 and O.O 388 respectively. Refinements with this model, however, were meaningless. After three cycles of refinement, the geometry of the cyclopropane ring had become distorted to the point that the bridgehead- bridgehead bond Cl-Cll was only 1.2 A long and the residual indices R and WR had not improved. When the molecular parameters were graphically interpreted (see fig. 23 ), disorder was clearly indicated as the source of the difficulties. 184 F ig u r e 23 . Trans-bicyclo[ 5.1.0"!octane-*!—methanol- p-bromobenzene sulfonate. View down b s c a l e d t o \ inch/angstrom, 5 0 a! probability thermal ellipsoids, 3 0 " view distance. 185 In particular, the thermal ellipsoids at Cl and Cll are very elongated prependieular to the molecular plane, while the ellipsoid for C8 is equally elongated in the plane of the molecule. Such thermal motion is physically unreasonable and must arrise as an artifact reflect ing a disordered crystal rather than real thermal motion. Thus refinements were term inated and the parameters observed at the end of the anisotropic refinements were adopted as the best estimate of the true parameters. The observed and calculated structure factors for this model are given in T a b le USl TABLE 1*5 FINAL HEAVY ATOM COORDINATES FOR t r a n s - BICYCLO [ 5 . 1 . 0 ] OCTANE-4-METHANOL jj-BROMOBENZENE SULFONATE x y z Atom a b c 1 Br 0 .3 7 3 3 (2 ) 0 . 13086( 4 ) 1.0 6 4 4 5 (6 ) 2 S 0 . 5 l4 2 (4 ) - 0 . 00162( 8 ) 0.7000 (2 ) 3 01 0 .5 4 7 7 (7 ) 0 .0 5 4 7 (2 ) 0.6393 (3) 4 02 0 .7 5 2 5 (8 ) - 0.0329 ( 2 ) 0.7669 (3) 5 03 0 .2 8 8 4 (8 ) - 0.0 3 5 6 (2 ) 0.6132 (4 ) 6 Cl 0 .4 7 3 5 (1 2 ) 0.0 3 5 4 (3 ) 0.8002 (5 ) 7 02 0 . 6811( 1 2 ) 0.0517 (3) 0.9126 ( 6 ) 8 C3 0 .6 5 3 6 (1 3 ) 0.0802 (3 ) 0.9916 (5) 9 ck 0 . 4138 ( 1 5 ) 0.0920 (3 ) 0.9559 ( 6 ) 10 C5 0 .2 0 4 4 (1 2 ) 0 .0 7 6 4 (3 ) 0.8449 ( 6 ) 11 c6 0. 2325 ( 1 2 ) 0.0470 (3 ) 0.7657 (5) 12 CT 0. 3322(1 1 ) 0.0947 ( 3) 0 .5 566 (5) 13 08 0 .3 8 2 4 (1 1 ) 0 .1 3 3 2 (3) 0.4832 ( 5) lb 09 0. i4 o 4 (1 3 ) 0.1695 (3) 0.3923 ( 6 ) TABLE it5 (continued) Atom X y z a b c 15 CIO 0.1101(15) 0. 1998( 4 ) 0 .2 8 6 3 (6 ) 16 C ll 0. 3459 ( 20) 0. 2298(5) 0 .3 3 2 0 (9 ) 17 Cl 2 0. 4911 ( 16) 0 .2 5 ^ ( 3 ) 0 .2 9 8 5 (6 ) 18 C13 0 .5 6 0 9 (2 0 ) 0 .2 1 1 6 (5 ) 0 .3 8 7 6 (9 ) 19 c i 4 0. 7515 ( 13) . 0. 1994 (3 ) 0. 5141(b) 20 c i 5 0 .6 1 8 0 (1 3 ) 0 . 1751 (3 ) 0 .5 6 5 1 (5 ) i H 00 TABLE 46 FINAL THERMAL PARAMETERS FOR trans-B IC Y C L0[5.1.0]0CTA N E-U -M ETH A N 0L p-BROMOBENZENE SULFONATE P l l 622 £ 3 3 P 12 P i 3 6 2 3 B r 0.08465(52) 0 . 00317(2 ) 0 . 01308( 8) - 0 . 00133(9 ) 0 . 02613(1 9 ) -0.00043(4) S 0 . 04057 (9 1 ) 0 . 00192(4 ) 0 . 00907(1 7) 0 . 00035 (1 8) 0.01239(36) 0 . 00028( 8 ) 01 0 . 03858 (2 0 9 ) 0 . 00234 (1 2 ) 0.00942(44) 0.00174(41) 0 . 01262(8 6) 0 . 00133(1 9 ) 02 0.04710(246) 0 . 00274 (1 3 ) 0.01159(48) 0.00468(46) 0 . 01533 (9 8) 0 . 00163(2 0 ) 03 0 . 05116 (2 4 0 ) 0 . 00254 (1 2 ) 0.01093(46) - 0 . 00302(4 7 ) 0.01484(96) -0.00142(20) Cl 0 . 03310(3 2 8) 0 . 00182(1 7) 0.00696(64) -0.00048(65) 0 . 00870(1 3 2 ) 0 . 00049 (2 8) C2 0 . 02968(3 3 9 ) 0 . 00285 (2 1 ) 0.00935(76) 0 . 00069(6 7) 0 . 00809(1 4 3 ) 0 . 00040 (3 3 ) C3 0 . 03751 (3 6 9) 0 . 00312(2 3 ) 0.00702(69) 0.00048(73) 0.00702(141) - 0 . 00032(3 1 ) C4 0 . 05506 (41 8) 0 . 00212( 1 9 ) 0.00784(71) - 0 . 00059 (7 4 ) 0 . 01502 (1 5 5 ) 0 . 00038(2 9 ) C5 0 . 03918(3 6 4 ) 0 . 00362(2 3 ) 0.01047(79) -0.00100(74) 0 . 01452 (15 2 )- 0 . 00019(3 6) c 6 0 . 03197(3 4 6 ) 0 . 00313(2 2 ) 0.00740(68) - 0 . 00136(6 8) 0 . 00810(1 3 6) 0 . 00007(3 0 ) C7 0 . 03790(3 4 8 ) 0 . 00281(1 9 ) 0 . 01016(7 1) 0 . 00186(6 8) 0 . 01227(14 3 ) 0 . 00108(3 2 ) C8 0 . 03099(3 0 7) 0 . 00260(1 8) 0 . 00731(5 8 ) 0 . 00013(6 9) 0 . 01027(12 1 ) 0 . 00030(3 1 ) C9 0 . 03751 (3 8 6) 0 . 00543 (2 9 ) 0 . 01660(9 6) 0.00426(85) 0 . 01602(16 8) 0 . 00501 ( 4 5 ) TABLE 46 (continued) P n P22 P 33 P i 2 P 1 3 P 2 3 CIO 0.05513(^55) 0 . 00549 (3 1 ) 0 . 01240 (9 1 ) 0.00394(100) 0.01167(177) 0.00422(44) C ll 0 . 05580 (5 6 1 ) 0 . 01071(5 7 ) 0.02010(141) 0.00472(153) 0 . 02161(2 5 9 ) 0 . 01033(7 3 ) C12 0.09986(553) 0 . 00277(2 3 ) 0 . 01260(8 8) - 0 . 00387(9 1 ) 0 . 02588 (1 9 8) - 0 . 00159 (3 6) C13 0.05312(565) 0.01118(48) 0.02374(148) 0.01069(137) 0.02432(267) 0 . 01393(6 9) Cl4 0 . 04795 (4 0 0 ) 0 . 00366(2 3 ) 0 . 01131( 8 2)- 0 . 00503 (8 0) 0.01305(158) -0.00008(37) 015 0 . 06209(4 2 8 ) 0 . 00360(2 4 ) 0 . 00786(6 8) - 0 . 00399(8 2) 0 . 01381(1 5 0 ) - 0 . 00036(3 3 ) H CD VO TABLE 47 CALCULATED HYDROGEN POSITIONS FOR t r a n s - BICYCLO[ 5 .1 .0 ] OCTANE-4-METHANOL J 3-BROMOBENZENE SULFONATE HI o. 85546 0.04170 0.95890 H2 0 .8 0 6 5 7 0.09085 1.07551 H5 0 . 05704 0.08540 0.82510 h 4 0 . 0 8 l4 0 0.54600 0.68726 H5 0.29091 0.12558 0.59720 H 6 0.17585 0.06995 0.50252 H7 0.45656 0.10889 0. 44249 h 8 0.12766 0.20522 0.45598 H9 - 0 .00220 0.14156 0 .56542 HIO - 0.04627 0 .2 2 5 9 2 0.25896 KL1 0.07551 0.16656 0 . 22875 H12 0. 21202 0.2 5 5 4 2 0.54220 H13 0. 55721 0 .29797 0.51809 Elk 0 . 4 b l4 2 0.24569 0.22586 H15 0.65400 0.17055 0.41498 H l6 0.8 5 4 4 2 0 . 25652 0 .55855 H17 0.87851 0.16701 0.55116 H18 0.56485 0. 21196 0.58719 H19 0 .7 5 7 9 7 0.15285 0. 6 4 i4 i TABLE kQ SUMMARY OF REFINEMENTS FOR trans-BICYCLO[ 5 . 1. 0]OCTANE-^-METHANOL p-BROMOBENZENE SULFONATE NVa NOb R WR GOFC (Refinements using CRYM system) Trial Structure 8l 2798 0 .336 0.5 5 9 All Atoms Isotropic 81 2798 0. 18^ 0 .2 3 7 Anisotropic Br, 0, S 106 2798 0.1 1 9 0. 1606 All atoms anisotropic l 8l 2798 (Refinements using Program EUGLS5) All atoms isotropic 81 1700 0 .1 5 3 0 . 118 TABLE h9 OBSERVED AND CALCULATED STRUCTURE FACTORS FOR t r a n s -BICYCLOr 5- 1. OIOCTAME-^-METHANOL p-BROMOBENZENE SULFONATE The column headings are: }c 1 10 F 10 F 100 a (F ) 192 ;;; Iii iHi i: iii ii! u» n» i»« :: r, :::: iii :ii ;;i :: ■::: I ^ !j| iji >) . . ii. ii; i:ii!i i» -ic i>* i»r i:» iii ...... : ;;; ::: !:: :: -* 110 joo i. ::: :: I: 5 iii ii i;; ::: ih iii H: ii i: ::: ;r,a ii :: • i: ‘i; ii: ii it: in .ii ii: iii ::: ;; ii: iii :ii iii iii»i ! i i i n: iii Hi ::::: i ii S H : iii !ii iii ; :: i i i iii «■£ I Hi ii; :ii ;i: HiS ■s ::: iu1:; i iii Ii ii H !ii : ii !:::::: « r.: iiiiiiiiiiii r id //• ii i :!i iii ii: • >1 ir» I .iii: iii!i; XI. STRUCTURES OF THE t rans-BICYCLO [5.1.0] OCTMES A. The Crystal and Molecular Structure of trans-Bicyclo[j?.1.0 Joctane- U-carboxylic Acid The crystal structure viewed down the a and b_ axes is illu s trated in Figures 2b and 25. Like many 144 carboxylic acids, trans-bicy- c l o [ 5 . 1 . 0 ]octane-U-carboxylic acid crystallizes as a dimer about the centers of symmetry. Carboxylic hydrogen bonds generally range from 2.6 * t o 2 .7 A144 and the bond in the present structure is no exception. The - 0 hydrogen bonds linking each pair of molecules together are 2.63 A long. The dimeric nature of the molecules is reflected by the elevated melting point of the crystals, 85-37°C . 46 Such a melting point is more consistent with a hydrocarbon with twice the molecular weight of this compound, like trans-bicyclo[ 5 . 1 . 0 ]oct-U-yl p-nitrobenzoate, for exam ple, which melts around 70°C.4S For comparison, trans-bicyclo[5.1.0]- octan-^-ol, with a molecular weight just under that of the carboxylic acid is a liquid at room temperature, reflecting the more monomeric nature of the molecule. Aside from the hydrogen bonds linking the molecules into dimers, only van der Waals forces serve to hold the crystal together. Table 50 lists the more important contacts involving hydrogen atoms based on the positions calculated for those atoms assuming normal geometry observed in carbon compounds. The molecule is arranged to achieve a closest packing configuration, but few of the contacts are particularly close. 19^ 195 _l_ 4 4 V c si nP _l_ 4 4 Figure 2h. The crystal structure of trans-bicyclo[5.1.0]■ octane--J|-carboxylic acid viewed down the a a x i s . 196 f Figure 25. The crystal structure of trans-bicyclo[5.1. O*]octane- l|-carboxylic acid veiwed down the b axis. The scale i s \ inch / A with an infinite view distance. 197 TABLE 50 NONBONDED CONTACTS IN trans-BICZCL 0[ 5 . 1- 0 ]OCTANE- 4 -CARBOXYLIC ACID ;om 1 Atom 2 Symmetry8, D is ta n c e D is ta n c e obs c a lc 01 H3 54501 2 .6 6 2. 6 -2 . 9 02 H9 66502 2 .8 0 2. 6 - 2. 9 HI h 8 56501 2 .5 7 2 .4 H2 H3 64503 2 .9 0 2 .4 h4 H12 64503 2 .5 5 2 .4 H5 H9 45501 2 .8 8 2 .4 H5 02 56502 5 .1 9 2. 6- 2. 9 H7 H8 65502 2 .9 0 2 .4 H ll H12 . 74503 2. 65 2 .4 198 Figure 26 graphically interprets the parameters derived for this molecule at the end. of the anisotropic refinements, and the most strik ing feature of that illustration is the magnitude of the thermal param eters derived, for this model, which are indicative of disorder in the crystal structure. While the disorder apparently affects the crystal structure of the carboxylic acid more severely than it does the brosy- late which we shall discuss shortly, or the potassium salt investigated earlier, and. illustrated for comparison in Figure 27, the nature of the problem is exactly the same in each case. The disorder arises in each of these structures because the forces in the crystal lattice are not great enough to force the left and right handed molecules of the racemic mix ture into left and right handed sites respectively in the crystal lat tice at the time the crystal is formed. This is a static disorder problem and it is frozen into the crystal lattice. Because of the disorder, the diffracted intensities reflect the average of a left and a right handed molecule at each lattice site. Atoms not involved in the cyclopropane ring apparently can occupy the same positions in the unit cell for either enantiomer and can be well resolved, as they were in the brosylate and in the potassium salt. But in the carboxylic acid, however, all of the atoms are somewhat displaced from one enantiomer to the other and the entire molecule is poorly resolved. The molecular geometry for the mole cule is presented in Table 51 through 53 and illustrated in Figure 28 . Dunitz and Strickler 145 have pointed out that the C = 0 bond in carboxylic acids is generally synplanar with respect to the C -CQ bond. a p This configuration not only reduces the nonbonded interactions of CQ and P its attached hydrogen atoms with the two oxygen atoms, but also corre- 199 sponds to a staggered conformation about the C-C bond if the C=0 double bond is decomposed into two bent bonds in the manner suggested by- P a u lin g . 146 Both trans-bicyclo[5.1. octane-4-carboxylic acid and its potassium salt, however, adopt a conformation where the carboxyl group bisects the C3-C4-C5 angle. While it is not apparent why these compounds should behave any differently than the carboxylic acids surveyed by the foregoing authors, the observed configuration is s till in accord with the model they have proposed. The observed configuration is actually the third position for which the bent bonds of the Cn: 0 double bond are in the staggered conformation. The 01* **hU and 01***h8 intermolecular are 2.83 and 2.92 A while the 02• • • and 02 •••HT contacts are 2.79 and 2.86 O A respectively all of which are greater than the sums of the van der Waals radii for the atoms involved. Because of the overall disorder, the dimensions of the carboxylic acid group are not well resolved. The two C-0 bonds are equal within ex perimental error and average 1. 27(l) A, precisely the average of the C v a lu e s 1. 23 and 1. 31 A generally observed in carboxylic acids for the C 0 and C-OH bonds respectively, while the C9~Cb bond, 1. * 1-9 ( 2 ) A, i s typical of the C-C bond observed in carboxylic acids. The remainder of the molecule w ill be discussed further below. FIGURE 26 An ORTEP drawing of t ra ns—bi cy c lo [ 5 .1.0 ] oc t a n e — 4 — ca r b o x y I i c acid. Atoms are represented with 50% probability ellipsoids FIGURE 27 An ORTEP drawing of the onion in potassium trans- bicyclo [ 5.1.0] octane — 4 - carboxy lote monohydrate 201 2 0 2 TABLE 51 BOND LENGTHS IN tran s-B iC Y C L 0 [5 .1. 0]OCTANE- 4 -CARBOXYLIC ACID C1-C2 1. 5 2 (2 C6-C7 1 .5 5 (2 C2-C5 1 .4 9 (2 C5-Cb 1 .5 4 (2 C3-C4 1 .3 5 (2 C4-C5 1. 44(2 C1-C8 1. 51(2 C7-C8 1. 5 0 (2 C1-C7 1. 3 0 (2 C4-C9 1 .4 9 (2 09-01 l . 27(1 C9-02 1 . 26(1 203 TABLE 52 BOND ANGLES IN trans.-BICYCLO[5 -1 . 0]OCTABE- 4 -CARBOXYLIC ACID C1-C2-C3 106. 2 (7 ) CT-C6-C5 1 0 5 .7 (7 ) C2-C3-C4 126. 8 (8 ) c6-C5-C4 126. 0 (7 ) C3-C4-C5 l4l.5(7) C3-C4-C9 1 0 9 .6 (7 ) C5-C4-C9 108. 8 (7 ) C2-C1-CT 123. 2 (1 1 ) C6-CT-C1 121. 5 ( 1 1 ) C2-C1-C8 13 6 .5 C6-C7-C8 1 3 4 .6 c8 - c i - c7 6 4 .3 (7 ) C1-C7-C8 6 3 .7 (7 ) C1-C8-C7 5 2 .0 (6 ) c4 - c9 - o i 1 1 9 .7 (9 ) C4-C9-02 1 1 9 .9 (9 ) 01-C 9-02 120. 3 (7 ) 20b TABEE 53 DIHEDRAL ANGLES FOR tr a n s - BICTCLOf5.1. OlOCTANE-^-CARBOXYLIC ACID 01-C9-C4-C3 8 5 ( 1 )° 01-C9-CU-C5 98(1)° 02-C9-CU-C3 9M i )° 02-C9-C4-C5 83(1)° C9-C4-C3-C2 178(1 )° C9-C^-C5-C6 176( i )° CU-C3-C2-C1 12(2)° C^-C5-Cb-C7 9(2)° C3-C2-C1-C7 6i ( i ) ° C5-C6-C7-C1 59(l)° C3-C2-C1-C8 1^7(1)° C5-C6-C7-C8 l4l(l)° C2-C1-C7-Cb 102(1)° C2-C1-C8-C7 112(2)° c 6-c 7 -c 8 - c i 109( 2 )° C2-C3-C^-C5 3(3)° C3-C4-C5-C6 9(2)° C8-C7-C 1 -C2 130( 1 )° C6-C7-C1-C2 102(1)° c 6- c 7- c 8- c i 109( 2 )° 205 Oi Figure 28. A schematic representation of some bond lengths and angles in trans-bicyclof 5 . 1. Oloctane-^t-carboxylic acid. 206 B. The Crystal and Molecular Structure of Trans-bicyclo[5.1.0]octane- 4-methanol-p-bromobenzene Sulfonate Figure 29 illustrates the packing of trans-bicvclot^.l.Oloctane- l|-methanol-p~bromobenzene sulfonate viewed down the a_ axis and Figure 30 gives a second view down c*. The major feature of the packing is the arrangement of the aromatic rings in pairs about the inversion centers. As Figure 31 shows, the overlapping rings are separated by J.68 A and many of the more important nonbonded contacts occur between the two rings. A complete summary of all the nonbonded contacts is given in T ab le 5U. Perhaps the most striking characteristic of the packing of this molecule, in view of the structure observed in the cis isomer discussed above, is the lack of a really short bromine-oxygen contact. In this structure, bromine and 02 are separated by 3 *65 A, which is slightly more than the sum of the van der Waals radii for these atoms using the maximum double bonded oxygen radius . 84 Like the cis compound discussed above, the contact is essentially normal to the S = 0 bond, 95*T ° 3 b u t the C-Br***0 angle is also almost perpendicular, , rather than linear as before, and there is no evidence of any formation of a charge transfer complex. The S=02 bond if anything is shorter than the S = 03 bond and bromine is equidistant from C3 and C 5 (and in the plane of the benzene ring). Because the benzene rings pack together, there are no intermolecu- lar forces (crystal packing forces) trying to bend the ring and as Table 55 shows, the benzene molecule is planar within experimental error. Bro mine and sulfur, which were bent out of the plane of the benzene ring by 207 c s Figure 29. Packing diagram for trans-bicyclof^. 1. Oloctane-^- methanol-bromobenzene sulfonate viewed down the a axis. The scale is % inch / A with an infinite irl st.annp. 208 F ig u re 30. Packing of trans_-bicyclo[ 5. 1 .0]octane-U-methanol p-bromobenzene sulfonate viewed down c_*. Infinite view distance, ^inch/angstrom. F ig u r e 3 1 . A general viev of the packing of trans-bicyclo[5.1.0] octane-i+-wethanol jv-broi;iobenzene sulfonate. Infinite viev distance, J inch/angstron. PLEASE NOTE: This page not included in material received from the Graduate School. Filmed as received. UNIVERSITY MICROFILMS 211 TABLE 55 ANALYSIS OF BENZENE PLANARITY tr a n s -BICYCL 0C5 • 1 • O] OCTANE-4 -METHANOL BROMOBENZENE SULFONATE The equation of the best plane through the benzene ring 'with coordinates SX, SY, SZ relative to the orthogonal coordinate system 3 a, b , c*. A(SX) + B(SY) + C(SZ) + D = 0 Coefficients: A = 0.17590 ■ D = - 2 . 1U819 B = O.96O82 ZA2 = 0.0001 C = - 0 . 21^122 D e v ia tio n s Cl 0.0 0 6 Br 0 .0000 C2 - 0 .0 0 2 - S 0 .0 1 0 C3 -0 .0 0 3 01 0.966 cfc 0 .0 0 3 02 -0.3^ 3 C5 0 .0 0 1 03 -0 .3 1 9 c6 -0 .0 0 6 a. See above, p. 91 for an explanation of the orthogonal co ordinate system. b. Only the six atoms of the benzene ring were used to deter mine the plane. 212 o • O.Oj52 and O .I 57 A respectively in the cis-isomer,are coplanar with the aromatic ring in this structure. Thus it seems clear that the bromoben- zene sulfonate group is by nature planar, but that it can be deformed by the forces of the crystal lattice. A complete summary of the geometry of the molecule is given in T ab les 56 th ro u g h 5 8 - Because of the disorder problem, corrections for rigid body motion were not made. The dimensions of the bromobenzene sulfonate group are consistent with the values derived above for the cis-isomer. An isolated view of the group is shown in Figure 52. The average C-C bond in the benzene ring was 1.593(16) k which is essentially the value observed by Cox 104 for benzene and is consistent v/ith' the range of values observed for vari ous substituted benzene derivatives listed in Table 2h. While the bond lengths in the benzene ring are all equal within experimental error, the bond angles are distinctly distorted. The standard deviation of the six angles is 4.1° and the statistic S^/cr 2 is 8 b .1 (see Appendix )• Since X 4 0.01 = 1 5 * 0 8, we clearly reject the hypothesis that all the angles in 3 the benzene ring are equal. Because the angles at Cl and are so wide and there is some indication that the bond lengths along the long axis of the benzene molecule are shorter than the remaining bonds, it is tempting to ascribe a significant amount of quinoid type structure to the bromobenzene sulfonate group observed here. However, if this is really true, then it is unclear why sim ilar distortions were not observed on the corresponding cis-derivative discussed earlier. Moreover, the Br-CU, and S-Cl bonds 213 TABLE 56 BOND LENGTHS IN trans-BICYCLO [ 5 .1 .0 ] OCTANE-4-METHANOL v -BROMOBENZENE SULFONATE Br-C4 1 .9 1 1 (1 0 ) 0 1 -C7 1.495(10) S -01 1. 576(6) C7-C8 1.539(11) S-02 1 . 428(7) C8-C9 1.576(12) S-03 1 .4 3 5 (8 ) C8-C15 1.568(12) Average S-0 = 1.789(10) C9-C10 1.561(14) C14-C15 1 .5 4 8 (1 3 ) S -C l 1 .7 8 9 ( H ) C.10-C11 1.4 0 8 ( 1 8) C1-C2 1 .4 0 3 (1 1 ) C13-C14 1 .46 o (16) C2-C3 1. 380( 1 2 ) C3-Ch 1. 400(15) C11-C12 1.537(18) C4-C5 1 .3 7 9 (1 3 ) C12-C13 1.495(17) C5-C6 1 .3 7 9 (1 2 ) c6- c i 1. 4 l7 ( l4 ) C11-C13 1.381(19) Average C -C = 1.393 ± 0. Ol 6 I cLic a r 21k TABLE 57 BOND ANGLES IN t r a n s - BICYCLOF5.1. 0 ]OCTANE -4 -METHANOL P-BROMOBENZENE SULFONATE 0 5 -S -02 119. 7 (5 ) 03 -s-o i 109. 5 ( 4 ) 0 2 -S -01 104 . 5 ( 4 ) 03 -S-C 1 109. 3 ( 5 ) 0 2 -S-C1 108. 6 ( 5 ) O l-S -C l 104 . 0 ( 4 ) Br-C4 -C3 116. 5 (9 ) Br-C4 -C5 1 1 7 .1 (1 0 ) S-C1-C2 1 1 8 .6 (9 ) S-C1 -C6 1 1 8 .2 (8 ) C2 -C1 -C6 1 2 3 .2 (9 ) C3-C2-C1 119. 7 ( 1 0 ) C4 -C3 -C2 115 . 4 ( 1 0 ) C5 -C4 -C3 126. 4 ( 1 0 ) c 6-C5 - c 4 1 1 8 .2 (1 0 ) C1 -C6-C5 117. 1 (9 ) A verage 120 ± 4 ° S-01 -C7 1 1 7 .8 (6 ) 01 -C7-C8 105 . 5 ( 8 ) TABLE 57 (continued) C7-C8 -C9 1 0 1 .0 (8 ) C7 -C8 -C15 1 0 9 .0 (8 ) C9 -C8 -C15 114 . 6 (9 ) C8 -C9 -C10 1 1 6 .6 (9 ) 0 8 -0 1 5 - c i 4 114 . 4 (8 ) C9 -C1 0 -C11 1 0 2 .3 (1 1 ) c i5 - c i4 - c i3 1 0 4 .6 (1 0 ) C10 -C11-C13 1 2 9 .3 (1 7 ) C14 -C13-C11 132. 9 ( 1 4 ) C1 0 -C11-C12 l 4 o .i( i4 ) C1U-C13-C12 l 4 o. 2(1 3 ) 012-011-013 6 1. 4(H ) 012-013-011 .64 . 4 ( 1 0 ) CH-C12-BC13 54 . 2 (8 ) 216 TABLE 58 DIHEDRAL ANGLES IN t r a n s -BICYCLOP5-1. OlOCTANE-4-METHANOL £ -BROMOBENZENE SULFONATE CT-C8-C9-C10 163. 1 (1 0 ) C2-C1-S-01 86. 8 (8 ) C7-C8-Cl5-Cl4 - 160. 4 (9 ) C2-C1-S-02 -2 4 .1 (8 ) C2-C1-S-03 - 156 . 4 (7 ) C8-C9-C10-C11 5 1 (2 ; C6-C1-S-01 -94 .4 ( 8 ) 08- 015 - c i 4 - c i 3 - 3 6(1 ) C6-C1-S-02 15 ^ .6 ( 7 ) C9-C10-C11-C12 -1 5 5 (2 ) C6-C1-S-03 2 2 .3 (9 ) C15-C1^-C13-C12 - 137(2 ) 02-S-01-C 7 - 175 . 5 (6 ) C9-C10-C11-C13 -6 4 (2 ) 03 S-01-07 - 4 6 .1 (7 ) C1-S-01-C7 70. 6 (7 ) C15-C14-C13-C11 - 3 6(2 ) C9-C8-C15-Cl4 8 7(1 ) S-01-C7-C8 163. 7 (6 ) C10-C9-C8-C15 -8 0( 1 ) C15-08-07-01 62. 0 (1 0 ) 09 -0 8- 07-01 - 176. 9 (7 ) Figure 32. An isolated view of the bromobenzene sulfonate group in trans-bicyclo [ 5 .l.O^octane-l-methanol p-bromobenzene sulfonate. 2l8 are both somewhat longer in the present structure than they were in the cis-compound. If this structure had a significantly greater contribution from a quinoid resonance form than did the cis-structure, then these bonds should be shorter rather than longer. o The C^-Br bond, 1.911(10) A, has the same value within experimental error observed in the cis-isomer and lies at the upper end of the range of values reported in Table 2k. The Cl-S bond, 1 .7 8 9(H) A, is significantly longer than the value observed in that former study and in the compounds listed in Table 2k. Rather, it is more like the values reported by S u tto n 104 or by Southerland and Young 108 for an S-C 3 bond. These o o authors set 1.80 A and 1.805 A, respectively, for such a bond. The remaining bonds around sulfur are also longer than in the cis isomer but the general dimensions of the group are still fairly similar to the values observed previously. In particular, the S-01 bond is still short enough to have some partial jt character and the 02=S = 03 bond angle has opened up at the expense of the 01—S—Cl angle. The geometry at CJ bears a striking resemblance to the geometry observed in the cis-isomer discussed earlier. At this junction between the sulfonate group an the carbon skeleton, the 0-C-C angle is only 105-7° 0 while the 0-C bond is I .50 A. Such an angle is significantly smaller than the value 11 2 . 1° found in straight chain hydrocarbons or 111° found in typical ethers. Moreover, the C-0 bond is considerally longer than the value expected for a C 3 -0 bond 128 131 Just as in the cis-isomer, such sp J observations are consistent with a molecule that is partially ionized and based on our structural studies it appears that such ionization may be characteristic of all bromobenzene sulfonates. 219 Bromobenzene sulfonates are generally not the derivatives of choice in structural studies, thus the geometry of this group has net been well characterized. While it was not perhaps completely exhaustive, our survey of benzene derivatives containing bromine and sulfur indicated that only one such structure had been elucidated in the last ten years (see Table 2^). That structure, anti- 8 -tricyclc[ 3. 2.1.02’ ^octyl p- i qoQ bromobenzene sulfonate, has some bearing on the present studies, OBs however, in that the brosylate group is attached to the 7 position of the norbomane type cage in the molecule. As we discussed earlier, the angle strain at the 7 position makes ionization there very difficult, which gives rise to the remarkably depressed solvolytic rates for norbomane derivatives where anchimeric assistance is not operative. This inability to ionize stands in opposition to the penchant for ionization we have seen in our bromobenzene sulfonates and the norbomyl compound reflects it in its structure. In the norbomane structure, the C-C-0 angles at the point of substitution are wider than in our bromobenzene sulfonates, a v e ra g in g 110.5 , and is more like the values observed in typical ethers. The C-0 bond length, at 1. b8 A, is at least closer to the expected value f o r a Cg^ 3 -0 bond. Thus it appears that the strain which inhibits the formation of a carbonium ion translates into a less ionized molecule in the solid state as well. 220 Three trans-bicyclo[5.1. °]octanes have now been elucidated but all three have suffered from the disorder problem delineated above. Several features of the molecule have become clear, however. A conformational analysis of the parent molecule which predicts the observed geometry 1 A p fairly well has been carried out by Schleyer. That study indicated that the trans isomer is strained by 5 .7 0 kcal/mol relative to the cis isomer, and that k. 53 kcal/mol of that total arises :from angle strain. In view of the experimental difference 9-0 ± 1.0 kcal/mol observed by Pirkle and Lunsford (see above p. 11), the magnitude of the total strain may have been underestimated, but angle strain is certainly the major component of the observed deformation of the molecule. The three struc tures are summarized along with the structure predicted by Schleyer in Figure 33 • The large angles in the carboxylic acid reflect the poorly resolved geometry in that compound and are clearly unreasonable. In ad dition, the averaged positions for the C2-C3-Cb-C5-C6 fragment in that molecule makes all of the atoms almost coplanar. In the remaining two structures, this part of the molecule is less disordered as the smaller thermal parameters for these atoms attest. These two structures indi cate that the interior angles of the cycloheptane ring have opened up by above 3° each but that the major strain occurs at the bridgehead. The exocyclic bonds C10-C11-C12 and C14-C13-C12 are 1^0° in the brosylate and average 132° in the carboxylic salt and 136° in the carboxylic acid. Even the smallest of these reflects a 11° increase from the value 121. observed in the cis fused derivative and a 1.4° increase relative to the value observed in most substituted cyclopropanes. 221 oo 06 106 \0 6 1.30 5 8 . 115 ut 117 «o 113 oo 1.38 1.54 60 Figure 33. Summary of geometry in trans compounds. 222 The disorder affects the bridgehead-bridgehead bond most severely and causes it to appear foreshortened. Models indicate that the trans fused ring makes an angle of about 30° with respect to the mean plane of the ring. Roughly speaking, what we see is a projection onto that plane. With this estimate, what we see as the bond has been foreshortened by a factor of cos 30° or about O. 8 7, and the true bond length is on the order of 1.5 A. The most reliable estimate of the bond length s till comes from the potassium salt, 1. b6 A, since the disorder in that struc ture was at least partially resolved. The conformations of a ll three trans-derivatives, correspond to the conformation of the cycloheptane system. An incipient car- bonium ion derived from this configuration provides better overlap be tween the back lobe of a developing p orbital and the bent bond of the cyclopropane ring (see Figure 35) than it did in the cis fused deriva tive. But as the leaving group departs and the ionic site becomes more trigonal, that lobe w ill be carried up and away from the cyclopropane ring. Thus we can rationalize the lack of anchimeric assistance. Although the angle at the b position in the trans -bicyclo|~5« 1. 01 octane system seems to have opened up somewhat because of the strain in the trans-fused system, it apparently has not favored the trigonal tran sition state to any great extent, since its rate of solvolysis differs little from that of the two cis-isomers. In view of the extensive re hybridization at that position evident in the exo-cis-isomer, however, this observation is hardly surprising. What is surprising is the de creased solvolytic activity of all of these derivatives relative to the cycloheptyl system. Again steric factors do not seem to be the 223 cause, rather the source must lie elsewhere, perhaps in an inductive effect from the cyclopropyl ring. 22k APPENDIX Statis-cical Tests If we assume the bond lengths and angles quoted in the tables above each represent the class mean, y^ of a sample from a single normal population and that the errors quoted for them, a(y^), are estimates of the standard deviation of the mean based on many degrees of freedom, then following Hamilton we may define the statistic = spjfoi. ' y)’ which is distributed as x*f -L where p., the weight of the i mean is g iv e n as: P.- = o2(y.) and y, the weighted overall mean of n class means is: n 2 p . y . 1 1 i = l y = n E p k k = l Then the hypothesis that a ll the means y^ are equal Ho: y± = y2 « ••• = yn may be tested by consulting a table of x2- 225 REFERENCES 1 . P.G . Gassman, Chem. Commun. , 793 (1 9 6 7 ). 2. C.A. Coulson and W.E. M offitt, Phil. Mag., Ser. 7, 1 (1949). 3- C.A. Coulson, "Valence", Second Ed., Oxford University Press, London, E n g lan d , 1963, p .H 5 - 4. A. Hartman and F.L. Hirshfeld, Acta Cryst. , 20, 80 ( 1966). 5 . C.J. Fritchie, Jr., ibid., 20, 27 (1966). 6 . D.A. Mathews, J. Swanson, M.H. Mueller and G.D. Stuckey, J. Am. Chem. Soc., 93, 5945 (1971). 7« K.W. Cox and M.D. Harmony, J . Chem. P h y s. , 5 0 , 1976 ( 1 969). 8 . H.A. B e n t, Chem. R eview s, 6l, 275 (1961). 9* R .A . Kershaw, Jr., M.S. Thesis, The Ohio State University, 1 9 7 2 . 10. A.L. Patterson, Z. Cryst. , Ago, 517 (1935). 11. W. Kirmse and C. Hase, Angew. Chem. Internatl. Ed., 7 , 891 (1968). 12. W. Kirmse and G. Wachtershauser, Tetrahedron, 22, 63 (1966). 13* P.G. Gassman, F.J. Williams and J. Seter, J. Am. Chem. Soc. , 90, 6893 (1 9 6 8). 14. K.B. Wiberg and A. de Meijere, Tetrahedron L ett., 519(1969)* 1 5 . A. Ashe, ibid., 523 (1969). 16. H.E. Simmons and R.D. Smith, J. Am. Chem. Soc. , 8l , 4256 (1959)* 1 7. F.J. Williams, Ph.D. Thesis, The Ohio State University, 197°. 18. C.H. DePuy and J.L. Marshall, J. Org. Chem. , 33, 3326 ( 1968). 1 9 . J.V. Paukstelis and J. Kao, J. Ami. Chem. Soc. , 94, ^783 ( 1 9 7 2 ) . 2 0 . R .T . LaLonde and L .S . F o rn ey , J . O rg. Chem. , 2 9 , 2 9 1 1 ( 1 9 6 4 ) . 21. P.G. Gassman and F.J. Williams, J. Am. Chem. Soc. , 93, 5199 (1971)* 226 22. W. Kirm se and C. H ase, Angew. Chem. I n t e r n a t l . Ed. , 7 , 891 (1 9 6 8). 23. The effect of nonbonded interactions can also make a significant contribution, however. For example, the heat of hydrogenation of cyclopentene is 1 .7 kcal/mol less than that of cyclohexene even though the double bond in the smaller ring introduces more strain and should release more energy when broken. This surprising re sult arises because the product of the first reaction, cyclopentane, s till forces the C-H bonds to be extensively eclipsed, whereas the relief via elimination of the double bond is obscured by the strain which is due to onbonded interactions (j. B. Conn, G. B. Kistiakow- sky and E. A. Smith, J. Am. Chem. Soc. , 6l , 1868 (1939) and refer ences contained therein"]"]* 24. K. P. Wiberg and A. de Meijere, Tetrahedron Lett. , 59 (1969)- 25. W.H. P ir k le and W.B. L u n sfo rd , J . An. Chem. S oc. , 9b, 7 2 0 1 (1 9 7 2 ). 26. R.B. Turner and W.R. Meador, ibid. , 79, 4133 (1957). 27. S.W. Benson, F.R. Cruickshank, D.M. Golden, G.R. Hangen, H.E. O’Neal, R. Shaw and R. W alsh, Chem. Rev. , 69, 279 ( 1969). 28. S. Winstein and R.E. Buckles, J. Am. Chem. Soc. , 64, 278O (1942). 29. S. Winstein, C.R. Lindegren, H. Marshall and L.L. Ingraham, ibid., 75, 1^7 (1953). 30. (a) S. Winstein, J. Sonnenberg, L. deVries, ibid. . 8l , 6523 (19 5 9 ); (b) S. Winstein, ibid. , 8l, 6524 (1959); (c) S. Winstein and J. Son n e n b e rg , ib id . . 83, 3235"Tl96l); (d) S. Winstein and J. Sonnenberg, ib id . , 8 3, 32l47l96l). 31. (a) S. W instein, E. Clippinger, A. H. Fainberg and G. J. Robinson, ib id . , 76, 2597 (195*0; (t) S. Winstein, E. Clippinger, A.H. Fain berg and G. J. Robinson, Chemistry and Industry, 6 6 b (1954); (c) S. Winstein Experimentia Suppl. II, 137 (1955); (d) S. Winstein and G. C. Robinson, J. Am. Chem. Soc. , 80, 169 (1958). 32. J. S. Haywood-Farmer and R. E. Pincock, J. Am. Chem. Soc., 91, 3020 (1969). ~ 33- For a complete discussion and leading references see (a) B.R. Ree and J. C. Martin, J. Am. Chem. Soc. , 92, 1662 (l970);see also (b) P. v.R. Schleyer and V. Buss, ibid. . 9T, 588O (l9o9);(c) C. J. Martin and R. Ree ibid. , 91, 5882 ( 1969); (d)E. C. Fredrich and M. A. Saleh, Tetrahedron L ett., 1373 (l97l); (e) G.H. Schmidt and A. Brown, ibid., 4695 (1968); (f) R.N. Me Donals and G.E. Davis, J. Am. Chem. Soc. , 9 4 , 5078 (1972); (g) L.A. Paquette, 0. Cox, M. Oku and R. P. Henzel, i b i d . , 9 6, 4892 (1974); (h) R. Hoffman and R.B. Davidson, ibid. , 93, 5b99 (1971). 227 3h. H. Tanida, T. Tsugi and T. Irie, ibid., 8 9, 1953 (19&7) • 35• M.A. B attiste, C.L. Deyrup, R.E. Pincock and J. Haywood-Farmer, ibid., 89, 195^ (1967). 3 6. J. Haywood-Farmer, R.E. Pincock and. J.I. Wells, Tetrahedron, 22, 2007 (1 9 6 6). 37* (a) S. Winstein, M. Shatavsky, C. Norton and R.B. Woodward, J. Am. Chem. S o c. , 7 7, 4183 (1955); (b) S. Winstein, A.H. Levin, K.C. Pande, ibid.. , 85_, 232U (1963). 3 8. The existence of such an intermediate was first postulated, from solvolytic studies with the more conforraationally flexible 3 - substituted bicyclo[ 3 * 1 . 0 ]hexyl system (see ref. 3 5 ); since then, the results of numerous other studies of 3 -substituted bicyclo [ 3 - l* 0 ]hexyl derivatives have generally been interpreted in terms of the nonclassical homoallylic cation. Haywood-Farmer and Pin cock (see above ref. 3 2 ) give extensive references to these studies and the whole area has been reviewed by Winstein, see: S. Winstein, Special Publication No. 21, The Chemical Society, London, 1967. For an alternate point of view, however, see: E.J. Corey and H. Uda, J . Am. Chem. S oc. , 8 5 , 1788 (1 9 6 3); E.J. Corey and R.L. Dawson, i b i d . , 8 5 , 1782 (1 9 5 3 ). 3 9 . P.G. Gassman and A.F. Fentiman, J. Am. Chem. Soc. , 92, 2551 (197O). 40. M.A. B attiste, J. Haywood-Farmer, H. Malkus, P. Seidl and S. Win s t e i n , J . Am. Chem. S oc. , 9 2, 21kh ( I 97O). See also M.A. Martin and W. P a rk e r, Chem. Commun. , 955 (19&7 • hi. This example would be classified as V5 by Schleyer since 5 carbon atoms are involved between the reaction site and the ring bonds. See footnote 10 in ref. k j . • h2. hj. J.B. Hendrickson, R.K. Boeckman, Jr., J.D. Glickson and E. Grunwald, J. Am. Chem. Soc. , 95., ^9^ (1973)* ^4. J. B. Hendrickson, ibid., 8 9, JOk^ (1967)* ^5 • For a discussion of the conformation of cycloheptane and leading references, see: N.L. Allenger and J.T. Sprague, ibid., 9h, 573^ (1 9 7 2 ). h6 . P.G. Gassman, J. Seter and F.J. Williams, ibid, 93, 1&73 (1971)* 47. R. Muneyuki, T. Yano and H. Tanida, ibid., 9 1 , 2408 ( 1 969). 228 *£. M.J. S. Dewar and J.M. Harris, ibid. , 92, 6557 (1970). b9. G. LeNey, Compt. Rend. , 251, 1526 ( i 9 6 0). 50. M. Hanack, W. Krause, W. Rothenwohrer, W. Kaiser and G. Wentrop, L ie b ig s Ann. Chem. , 703. ^ ( 1967). 51. G.D. Sargent, R. L. Taylor, W.F. Demish, Tetrahedron Le tt. , 18, 2275 ( 1968). 52. All of the compounds used in this study were supplied by Professor P.G. Gassman and, in general, were used just as they came to us. However, as we have already reported (see ref. 9) crystals of the potassium salt of trans_-bicyclo[5.1. O^octane were grown from a solution after titratin g the acid with KOH in MeOH. 53- We wish to thank Professor Gassman for recrystallizing this com pound and determining the melting point and crystal IR. 5*k International Tables for Crystallography, Vol. Ill, C. H. Mac Gil- lavary et. al. , Ed. , Kynoch Press, Birmingham, England, 1968, p p . 17- 20. 55- For further discussion of multiple reflections and an algorithm to predict where they occur and to eliminate them, see: P. Coppens, A cta C ry s t. , A24, 255 (1968). 56.—-The program COZLS wa-s—written by Dr. G. J. Gainsford and Professor P.W. R. Corfield for a least squares fit of unit cell parameters. Much o f the logic is based on the program PICK3 written by J . A. I b e r s . 57. The following programs were w ritten for the EMR 6130 computer by Professor P.W.R. Corfield: the attenuator correction program, ATTEN; correction for background scattering, BCORR; conversion of raw data to structure factors, PLF1C; data sort and averaging program, MERGE; structure factor least squares refinement, SFLS1, SFLS2, SFLS3, SFLS*)-; Fourier summation, FOUR and FPRNT; bond distance and angle programs, GEOM, DIST1, DIST1A, ANG1. 58 . W. R. B using and H. A. L evy, J . Chem. Phys. , 26, 563 (1957). For a direct estimate of the magnitude of the errors which arise from this source and their effect on the derived structural parameters, see: S.C. Abrahams, Acta Cryst. . 17, 1190 (196*0; J.W. Jeffrey and K.M. Rose, ibid. ,if, 3^3 ( 1 9 6 k ); S.C. Abrahams, ibid. , 17, 1327 (196*0; J.W. Jeffrey, ibid. , 17, 1329 (196*0* For experimenatal measurements, see L.E. Alexander and G.S. Smith, ibid., 17, 1195 (196*0. 59. M. J. Buerger, "Crystal Structure Analysis", Wiley, Hew York, pp 152-19*)-. See also: R.W. James, "The Optical Principles of the Diffraction of X-rays", Cornell University Press, 1965, PP-29-31. 229 60. (a) L.V. Azaroff, Acta Cryst., 8 , 701 (1955)- For a derivation of equation 4 which is valid for the geometry employed for both the Picker and Syntex diffractometers used in these studies, see Ruble, M.S. Thesis, The Ohio State University, 1972, pp. 27-3°. 61. (a) S. Miyake, S. Togawa, and S. Hosoya, Acta Cryst. , 17, IO 83 (19 6 4 ); (b) P. Suortti, and T. Paakkari, J. Appl. Cryst. , 1, 121 ( 1968); (c ) H. Hope, Acta Cryst. , A27, 392 ( 1971), 62. W. R. Busing and H. A. Levy, Acta Cryst. , 10, 180 (1937). 63. op. c it., ref. 54, pp. 162- 163. 64. The program PICABS was w ritten by Dr. G.W. Gainsford and Professor P.W.R. Corfield following the method discussed in ref. 62. 65 . (a) A. J. C. Wilson, Nature, 130, 151 (1942) (b) D. Rogers in ''Computing Methods in Crystallography", J.S. R ollett, Ed., Pergamon Press, Oxford, 1965, p, 117 ff. 6b. Program WILPLT was w ritten mainly by R.A. Kershaw. 67. D. T. Cromer and J . T. Waber, Acta Cryst. , 1 8 , 104 ( 1965 ). 68. H. P. H a n so n , F. H erm an, J.D . L e a , S. S k illm a n , ibid., 17, 1040 (1964). 69. R. F. S te w a rt, E.R . D av id so n , and W. T. Sim pson, J . Chem. Phys. , 42, 3175 (1965). 70. C. Tsai and W.E. Streib, Acta Cryst. , 26, 835 (1970). 71. A.L. Patterson, Z. K rist., A90, 517 (1935). 72. D. Harker, J. Chem. Phys., 4, 381 (1 9 3 6 ). 73- 74. Program SUPER was w ritten mainly by Professor P.W.R. Corfield. 75* D.T. Cromer, Acta Cryst. , 18, 17 ( 1965 )• 7 6. P.W. H ig g s, i b i d . , 6 , 232 (1953)- 77* (a) W. C. Hamilton, "Statistics in Physical Science", The Ronald Press, New York, 1964, pp. 157-162; (b) W.C. Hamilton, Acta Cryst., 1 8, 502 (1 9 6 5 ). 7 8. Program NUGLS5 is an updated, local version of the Doedens-Ibers program by the same name and thus corresponds basically to a highly modified version of ORFLS. 230 79. W.H. Zachariasen, Acta Cryst. , 16, 1139 (1963). For further dis cussion see also: W. H. Zachariasen, ibid. , 23, 558 (1967); P. Coppens and W. C. Hamilton, ib id ., A26, 71 (1970). 80. (a) A.C. Larson, ibid. , 2 3 , 664 ( 1967); (b) A. C. Larson in "Crystal- lographic Computing", F.R. Ahmed, Ed., Munksgaard, Copenhagen, 1970, pp 291-294. 81. A. I. Kitajgorodskij, J. Phys. USSR, 9, 351 (1945). 82. A.I. Kitajgorodskij, "Chemical Organic Crystallography", Consultants B ureau, N. Y. , 1959. 83. A.I. Kitajgorodskij, Acta Cryst. , 18, 585 ( 1965 ). 84. a. B ondi, J . Phys. Chem. , 6 8, 44l (1964). 85 . L. Pauling, "The Nature of the Chemical Bond", Cornell University P r e s s , I th a c a , New Y ork, i 960, p. 2b0. 8 6. R. M. Miasnikova and A. I. Kitiagorodskij, Sov, Phys. Cryst., 3, 157 (1958). 87. 0. Hassel and Chr. Romming, Quart. Rev. (London), lb, 1 ( 1962). 88. H. Barnighausen, F. Jellinek, J. Munnik and A. Vos, Acta Cryst. , 16, 471 (1963). 89. P. Groth and 0. Hassel, Acta Chem. Scand. , 16, 2311 ( 1962). • 90. M.N. Sabesan and K. Venkatesan, Acta Cryst. , B27, 98b (1971). 91. The least squares plane was determined using a program written by G. J. Palenik. 92. (a) A.M. O’Connell and E.N. Maslen, Acta Cryst. . 22, 134 ( 1967); (b ) M. Alleaume and J. Decap, ibid. , 2£, 731 ( 1967). 93. K.N. Trueblood, E. Goldish and J. Donohue, ibid., l4, 1009 ( 1962). 94. (a) P. Coppens and G. M. J. Schmidt, ibid., 18, 62 (1 9 6 5 ); (b) P. Coppens and G.M.J. Schmidt, ibid. , 18 , 654 TE 9 6 5 ). 95* T.F. Lai and R.E. Marsh, ibid. , 22, 885 ( 1967). 96. (a) S.K. Arora and M. Sundaralingam, ibid. , B27, 1293 (1971). See also (b) D. D. Dexter, Z. Kristallogr. , 134, 350 (1971). 97. C. S. Huber, Acta Cryst. , B25, ll4o ( 1969). 231 98. G. J. Kruger and G. Gafner, ibid. , B27, 326 ( 1971). 99. V. Schoraaker and K. H.. Trueblood, Acta C ryst., B24, 63 ( 1968). 100. (a) D.W. J. Cruickshank, ib id.,9, 757 (1956)j (b) D.W. J. Cruickshank, ibid. , 14, 896 (1 9 6 1). 101. The appropriate calculations were carried out with program MGTLS, which was w ritten mainly by P. K. Gantzel and K. W. Trueblood. 102. Provate communication from P. v. R. Schleyer to P. G. Gassman. 103 . W.C. Hamilton, "Statistics in Physical Science", Ronald Press, Hew York, 1964, p. 113 f f . 104. E.G. Cox, D.W. Cruickshank and J. A. S. Smith, Proc. Roy. Soc., A247, 1 (1958). 105. L.E. Sutton, Ed., "Tables of Interatomic Distances and Configurations of Molecules and Ions", Supplement, London: The Chemical Society (1956-1959). 10b. "The International Tables for X-ray Crystallography", Vol. Ill, C. H. MacGillavry and G.D. Rieck, Ed., Kynoch Press, Birmingham, England, 1968, p. 275. 107. J. Jackobs and M. Sundaralingam, Acta Cryst. , B25, 2487 ( 1969). 108. H. H. Southerland and D.W. Young, ibid. , lb, 897 (1963). 109. J. Herdklotz and R. L. Sass, Acta Cryst. , B25, lbl4 ( 1969). 110. I . H argittai and M. H argittai, J. Mol. Struct. , 13, 399 (1973). 1 1 1 . R. J. G il l e s p i e , J. Chem. Educ. , 40 , 2 9 5 ( 1 9 6 3). 112. (a) E.J. Jacob and D.R. Lide, Jr., J. Chem. Phys. , 34, 4591 (l97l)j (b) S. Saito and F. Makino, Bull. Chem. Soc. Jap. ,~45, 9 2 (1971). 113. M. Hargittai and I . H a r g i t t a i , J . Chem. Phys. ,5 9 , (1973). 114. D.W. J . C ru ick sh an k , J . Chem. Soc. , 5487 ( i 9 6 0). 115. V. Schomaker and D. P. Stevenson, J. Am. Chem. Soc. , 6 3, 37 (l94l). 116. (a) J. Jarvis, Acta Cryst., 6 , 327 (1953). (b) Truter, ibid., 11, 680 (1958 ). ~ ~ 117. D.C. Fries and M. Sundaralingam, ibid. , B27, 401 (1971). 232 118. S. Yamazaki, S. Tamura, F. Marumo and Y. Saito, ibid. , B27, 2097 (1971). 119. (a) K. Kimura and M. Kubo, J. Chem. Phys., 30, 151 (1959); (b) L. P a u lin g and L. 0. Brockway, J . An. Chem. Soc. , 37 , 2684 (1935). 120. R.G. Clark and G.J. Palenik, J.C. S. Perkin II, 194 (1973). 121. 0. Bastiansen, F.N. Fritsch and K. Hedberg, Acta Cryst. , 17, 538 (1964). 1 2 2 . J. Eraker and C. Romming, Acta Chem. Scand. , 2 1 , 2 7 2 1 ( 1 9 6 7). 123. 0. Bastiansen and A. de Meijere, ibid., 20, 516 ( 1966). 124. R. H. Schvendem an, G. D. Jaco b s and T.M. K rig a s, J. Chem. Phys. , 40, 1022 (1964). 125 . W.H. F ly g a re , A. N a ra th and W.D. Gwinn, i b i d . , 36, 280 ( 1962). 12b, K.B. Wiberg, G.J. Burgamaier, K. Shen, S. J. LaPlaca, W.C. Hamilton and M.D. Newton, J . An. Chem. Soc. , 94, 7402 ( 1972). 127. R.K. Bohn and Y. H. Tai, J. An. Chem. Soc. , 92 , 6447 (1970). 128. M. G. Brown, Trans. Faraday Soc. . 55. 694 (1959). 129. C.J. Fritchie, Jr., Acta Cryst., 20, 27 ( 1966). 130. K.W. Cox, M.D. Harmony, G. N elson and K.B. W iberg, J . Chem. Phys. . 50, 1976 (1969). 131. Dr. R. Lide, Tetrahedron, 17, 125 ( 1962). 132. (a) J.F. Chang, C.F. Wilcox, Jr. and S.H. Bauer, J. An. Chem. Soc. , 90, 3149 (1968)* (b) Y. Morino, K. Kuchitsu and A. Yokozeki, Bull. Chem. Soc. J a p . , 4-0, 1552 ( 1 9 6 7); (c) G. Dallinga and L. H. Taneman, Reel. Trav. Chim. Pays-Bas. , 8 7, 795 ( 1968); (d) W. C. Hamilton, Ph.D. Thesis, California Institute of Technology, 1954. 133. (a) A. C. MacDonald and J. Trotter, Acta Cryst., 19 , 456 ( 1965 ); (b) A.C. MacDonald and J. Trotter, ibid. , 18, 243 (1965); (c) G. Ferguson, C. J. Fritchie, J. M. Robertson and G. A. Sim, J. Chem. Soc. , 1976 ( 1961); (d) D. A. Brueckner, T. A. Hamor, J.M. Robertson and G. A Sim, ibid. , 799 (1962)* (e) G. Gallinga and L. H. Toneman, Reel. Tray. Chim. , P av s-Bas. , 8 7, 0O5 (1967); (f) A.F. Cesur and D. F. Grant, Acta C ry st. , 1 8, 55 (19^5); (g) R. Destro, G. Filippini, C.M. Gramaccioli and M. Simonetta, Tetrahedron L ett., 3223 ( 1969); (h) G. Filippini, C.M. Gramaccioli, C. Rovere and M. Simonetta, Acta Cryst. , B28 ,2872 233 (1972). (i) A. V. Fratini, K. B ritts and I.L. Karle, Jl Phys. Chem. , 7 1, 2ko2 ( 1967); (j) M. Przybylasks, Acta cryst. , B2£T, 2mJT (i'972'); 7 k ) E.M. G o p a lak rish n a , ib id . 5 B28, 275 k (1972). 13^. S. Winstein and J . Sonnenberg, J . Am. Chem. Soc. , 8 3, 3235 (1961). 135. H. C. Brown and G. Ham, i b i d . , 7 8, 2735 (1956). Gives whole series. 136. A.H. Fainberg and S. Winstein, ibid., 7 8, 2780 (1956 ); S. Winstein, H.M. W alborsky and K. S c h re ib e r, i b i d . . 7 2 , 5795 (1950). 137. F.H. Westheimer in Steric Effects in Organic Chemistry, M.S. Newman Ed. , John Wiley and Sons, Inc. New York, 1956, Ch. 12. 138. P. v.R. Schleyer, J.E. Williams and K.R. Blanchard, J. Am. Chem. Soc., 92, 2377 (1970). 139. S. Masamune, R. Vukov, M. J. Bennett and J. T. Purdham, ibid. , 9**-. 8239 (1972). l*tO. R.B. Woodward and R. Hoffmann, ibid. , 8 7, 396 ( 19651 . l* n . The package of programs supplied by Syntex was used to automatical ly align the data sample and collect the set of diffracted inten s i t i e s . 1U2. Program PI was w ritten by Professor G.G. Christoph and R.A. Kershaw to decipher the raw intensity data on the magnetic tape derived from the Syntex PI diffractometer and to carry out the in itial stages of the data reduction process. The logic in part is based on the programs BCORR and PLPIC w ritten by Professor P.W.R. Corfield. l*i3. (a) D.J. Duchamp, Program and A bstracts, Amer. Cryst. Assoc. Meeting, Bozeman, Montana, Paper B~-lf, 196^ , p. 2§- (b) D.J. Duchamp, Ph. D. Thesis, Calif. Institute of Tech. ( 1965 ). ihh. J. Donohue, Acta Cryst. , B2*j_ 1558 ( 1968). 1*1-5. J. D. Dunitz and P. Strickler in "Structural Chemistry and Molecular Biology" A. Rich and N. Davidson, Ed. , W. H . Freem an and Co. , San Francisco, 1968, p. 595 ff- 1^6. L. Pauling in "Theoretical Organic Chemistry',1, IUPAC Kekuli Sym posium, Buttersworth London, 195 9-