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X-ray crystallographic studies of four organic compounds Hughes, David Lewis 1971

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X-RAY CRYSTALLOGRAPHIC STUDIES OF FOUR ORGANIC COMPOUNDS by DAVID L. HUGHES B.Sc.(Hons.), University of Edinburgh; 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver 8, Canada Date H*~JL IS* 1111 ii ABSTRACT Supervisor: Professor James Trotter Single crystal X-ray diffraction methods have been used to investigate four organic compounds, two monosaccharide derivatives and two nitrobenzene compounds: 1. methyl 3-C-(carbomethoxymethyl)-4,6-di-0-p-chlorobenzoyl-2,3-dideoxy-a-D-ribo-hexopyranoside, C21+H21+C1208 • 2. 5-0-(p-bromobenzenesulphonyl)-2,2'-0-cyclohexylidene-3-deoxy-2-C-hydroxymethyl-D-erythro-pentono-1,4-lactone, C18rI21Br0yS. 3. 2,6-dichloro-4-nitroaniline, CH Cl N 0 . ' 6 4 2 2 2 4. ethyl 3,5-dinitrobenzoate, CgH8N206. Crystals of the di-(p-chlorobenzoate) derivative of a novel branched-chain sugar, methyl 3-C-(carbomethoxymethyl)-2,3-dideoxy-a-D-ribo-hexopyranoside, are monoclinic, space group , a = 5*752, b = 15*436, o c = 13*698 A., B = 93*74 and Z = 2. Intensity data have been measured on an automatic diffractometer, firstly with Mo-K radiation, then more a accurately with Cu-K^ radiation. Efforts to confirm the molecular structure of the derivative have been unsuccessful, although various methods of analysis have been employed; the principal approaches have been the examin ation of the Patterson and sharpened Patterson maps, and by direct methods, the application of the tangent formula in the phase determination procedures for noncentrosymmetric space groups. None of the methods has produced any encouraging, distinctive portions of the molecule, and at present, the investigation has been halted. The structure of "a"-D-isosaccharinic acid has been determined by crystal structure analysis of a derivative which was shown to be 5-0-(p-bromo-benzenesulphonyl)-2,2'-0-cyclohexylidene-3-deoxy-2-C-hydroxymethyl-D-erythro-pentono-l,4-lactone. Crystals are monoclinic, a = 5*757, b = 10*586, c = 16*021 A., 8 = 98*85°, Z = 2, space group ?2l. The intensities of 1319 reflections were measured with a scintillation counter and Cu-K radiation, the structure was derived from Patterson and electron-density maps, and refined by least-squares methods, the final R being 0*10 for 1140 observed reflections. The absolute configuration is established, since the compound was obtained by degradation of cellulose. Each of the two five-membered rings in the derivative has an envelope conformation, with one atom displaced from the plane of the other o four..In the 1,3-dioxolane ring, the displacement is 0*49 A.; the y-lactone o ring is less prominently bent, with displacement only 0*14 A. The bond distances and valency angles in the molecule do not differ significantly from the usual values, and the intermolecular distances correspond to van der Waals' interactions. Crystals of 2,6-dichloro-4-nitroaniline are generally twinned; they are monoclinic, space group P2j/c, a = 3*723, b = 17*833, c = 11*834 A., 8 = 94*12°, Z = 4. Intensity data were collected for one of the twins on an automatic diffractometer. The coordinates of the two chlorine atoms were found in a Patterson map and all the other atoms in electron-density and difference Fourier maps. The structure was refined by full-matrix least-squares methods to R = 0*038. There are only slight deviations from overall planarity of the molecule, the amino and nitro groups being rotated by 6*3 and 7*2° respect ively out of coplanarity with the benzene ring. The amino group appears-to be held nearly coplanar with the benzene ring by intermolecular N-H...0 and intramolecular N-H...C1 hydrogen bonds. The intermolecular hydrogen bonding also connects the molecules in long chains in the crystal. It is thought that the twins are congruent, related by a twin axis parallel to a; a possible arrangement of molecules at the twinning plane is suggested. Crystals of ethyl 3,5-dinitrobenzoate are colourless needles of o monoclinic space group P2^/c ; a = 13*856, b = 4*770, c = 18*354 A., B = 119*59° and Z = 4. The structure of this compound was determined from diffractometer data by direct methods, and was refined by full-matrix least-squares methods to R = 0*061. The substituent nitro groups are rotated 1*6 and 11*5°, and the carboxyl group 2*2°, out of coplanarity with the benzene ring; the molecular packing arrangement appears to determine that the rotation of one nitro group is considerably more than that of the other. The ethyl group is disordered randomly in the crystal in two orientations, with a ratio of populations approximately 7:3. V TABLE OF CONTENTS Page TITLE PAGE i ABSTRACT ii TABLE OF CONTENTS V LIST OF TABLES viLIST OF FIGURES ix ACKNOWLEDGEMENTS xi GENERAL INTRODUCTION 1 PART I. CRYSTALLOGRAPHIC STUDIES OF METHYL 3-C-(CARBOMETHOXYMETHYL)-4,6-DI-0-p-CHL0R0BENZ0YL-2,3-DIDE0XY-a-D-RIB0-HEX0PYRAN0SIDE . 8 A. Introduction 9 B. X-ray analysis 11 C. Attempts at Structure Analysis 14 D. Conclusions 27 PART II. THE STRUCTURE DETERMINATION OF 5-0-(p-BROMOBENZENESULPHONYL)-2,2*-0-CYCL0HEXYLIDENE-3-DE0XY-2-C-HYDR0XYMETHYL-D-ERYTHR0-PENTONO-1,4-LACTONE 29 A. Introduction 30 i B. X-ray analysis 1 C. Structure analysis 32 D. Discussion 4 PART III. THE STRUCTURE DETERMINATION OF 2,6-DICHL0R0-4-NITR0ANILINE .. 42 A. Introduction 43 B. X-ray analysisC. Structure analysis 45 D. Discussion 5vi Twinning 64 PART IV. THE STRUCTURE DETERMINATION OF ETHYL 3,5-DINITROBENZOATE 67 A. Introduction , 68 B. X-ray analysisC. Structure analysis 69 D. Discussion 86 PART V. THE COMPUTER PROGRAM "GESTAR" 95 A. Introduction 96 B. The program GESTAR 7 1. Diffractometer geometry . 97 2. Outline of the program 104 3. Data cards for the program 105 4. . Listing and example output 108 C. The subroutine TWIN Ill 1. Introduction2. Geometry of the second twin system 112 3. Listing and example output 116 BIBLIOGRAPHY 119 vii LIST OF TABLES Table Page Methyl 3-C-(carbomethoxymethyl)-4,6-di-0-p-chlorobenzoyl-2,3-dideoxy-a-D-ribo-hexopyranoside. I. Observed structure factors 13 II. Results from the Wilson Plot, and the distribution of |E|'S for the Cu-data 21 5-0-(p-bromobenzenesulphonyl)-2,2 *-0-cyclohexylidene-3-deoxy-2-C-hydroxymethyl-D-erythro-pentono-1,4-lactone. III. Final atomic parameters 35 IV. The measured and calculated structure factors 37 V. Mean planes in the molecule 38 VI. Bond lengths and valency angles 40 2,6-Dichloro-4-nitroaniline. VII. Final atomic parameters 47 VIII. The measured and calculated structure factors 48 IX. Bond lengths and valency angles 50 X. Mean planes 54 XI. Hydrogen bond distances and angles 55 XII. Nitroaniline derivatives and related compounds 56 XIII. Summary of.the effects of resonance and hybridisation on dimensions in 2,6-dichloro-4-nitroaniline 60 XIV. Shorter intermolecular distances 63 Ethyl 3,5-dinitrobenzoate. XV. Results from the Wilson Plot, and the E-statistics 71 XVI. Comparison of the 16 sets of phases generated by the phase determination program 74 viii XVII. The measured and calculated structure factors 77 XVIII. Final atomic parameters 79 XIX. Molecular dimensions; bond lengths and valency 'angles 83 XX. Mean planes 85 XXI. A comparison of the dimensions in nitrobenzene derivatives which have no substituted ortho groups 87 XXII. A comparison of the dimensions of the carboxyl group in benzoic acids and esters, and in related compounds ... 91 XXIII. Shorter intermolecular distances 93 ix LIST OF FIGURES Figure Page 5-0-(p-bromobenzenesulphonyl)-2,2'-0-cyclohexylidene-3-deoxy-2-C-hydroxymethyl-D-erythro-pentono-l,4-lactone. 1. View of the molecule . 33 2. Projection of the structure along a. 41 2,6-Dichloro-4-nitroaniline. 3. View of the molecule 49 4. Molecular dimensions, (a) bond lengths, and (b) valency angles 51 5. The thermal ellipsoids of the non-hydrogen atoms 53 6. The molecular packing arrangement, showing also the inter molecular hydrogen bonds 62 7. The suggested arrangement about the boundary plane (001) between the two twins 65 Ethyl 3,5-dinitrobenzoate. 8. A view of the molecule 81 9. Thermal ellipsoids of atoms, in plane of the benzene ring ... 82 10. Molecular dimensions, (a) bond lengths and fb) valency angles 84 11. The close neighbours of the N(9) nitro group 89 12. The molecular packing arrangement 90 The computer program GESTAR. 13. The unit cell 97 14. A portion of the reciprocal lattice 98 15. Diffractometer "normal-beam equatorial" geometry 100 X 16. Geometry in the equatorial plane 100 17. (a) Real and reciprocal axes in a reciprocal axis mounting .. 102 (b) The coordinates of the point hk£ in reciprocal space .... 102 18. The reciprocal unit cell 103 19. The axes of the twins of 2,6-dichloro-4-nitroaniline 112 20. Corresponding lattice points of the twins of 2,6-dichloro-4-nitroaniline 113 21. The plane, normal to the b* axes, containing the points (hkJi)1 and (hkJ02 115 ACKNOWLEDGEMENTS I wish to thank Professor James Trotter for his constant guidance and encouragement throughout the course of my research. I am indebted to many visiting professors, post-doctoral fellows and fellow graduate students for much stimulating discussion, and especially to Dr. Frank Allen for his assistance with new approaches involving direct methods. I am very grateful to the Standard Oil Company of British Columbia, Ltd., for a Fellowship in the year 1969-70. 1 GENERAL INTRODUCTION In 1912, von Laue proposed that X-rays might be diffracted by crystals, and shortly afterwards Friedrich and Knipping confirmed this experimentally. The next year, W.L. Bragg gave a mathematical explanation for the patterns and positions of the X-ray beams diffracted by a crystal, and the solution of simple crystal structures soon followed. Since that time, the science of X-ray crystallography has advanced rapidly. The development of computers and the automation of measurement of X-ray diffraction intensities have assisted the crystallographer greatly in recent years so that now the solutions of many structures, including several complex biological structures, are being reported annually. This thesis is concerned primarily with the crystallographic studies of four organic compounds, two monosaccharide derivatives and two nitrobenzene compounds. The structures of three of these have been deter mined, but that of one of the carbohydrate derivatives remains as yet unsolved. A description of the methods of structure analysis, and of the resulting molecular and crystal structures form the main parts of the thesis, Parts I-IV. Part V describes the up-dating of a program for the generation of diffractometer settings for a crystal mounted along a reciprocal axis, and the modification of this program to calculate the settings for a twinned crystal. The principles of X-ray crystallography are well established and are discussed in several standard texts 1-4. However, some of the symbols and formulae used and quoted in this thesis should perhaps be menti'oned here; in general, all the crystallographic nomenclature found in this thesis has its conventional meaning as described in "International Tables for X-ray Crystallography" 5. 2 The diffraction of an X-ray beam may be considered as reflection in a crystal plane. A crystal plane has indices hk£, and the spacing between planes of the same indices, d^^, is related by the Bragg Law to the diffraction angle 6, the angle between the incident beam and the reflecting plane: 2.djlk^.sin 6 = n X where n is an integer, and X is the wavelength of the X-radiation. The intensity, I^kl' °^ a diffracted beam is corrected by Lorentz and polarisation factors - these, respectively, allow for the method of intensity measurement (the scanning through a diffracted beam), and for the loss of beam intensity due to polarisation of the beam in the reflection; these are both geometrical factors, depending on the angle 9. The corrected *hk£ *s' *n 2eneral> related to the structure amplitude, |F| : ThkA " lFhkJ2 and this represents the measurable part of the structure factor, F^^^J which may be written: Fhk«, = ? fj .exp[2iri(hx;). + ky^ + SLz-)] where f^ is the scattering factor for atom j, with fractional coordinates (x^, y., Zj) in the unit cell; and the summation is over all the atoms in the unit cell. Thus the structure factor is a complex number and may also be written: F = A + iB or F = |F|(COS $ + i.sin <f>) where |F|2 = A2 + B2, and <f> is the phase of the structure factor. The atomic scattering factor, f. ., represents the scattering »J power of the stationary atom, j. Its value is characteristic of the type of 3 atom, and varies with (sin 8)/X. Calculated values of f for many atoms are tabulated in "International Tables", vol. Ill 5c and in more recent literature. These values of fQ should, however, be corrected for thermal motion - the atoms are always vibrating, and the scattering factors used in structure factor calculations have the form: fj = foJ.exp[(-B;j.sin2e)A2] where B.. is the temperature factor and is related to the mean square displacement, Uj2, of the atom j from its mean position: Bj = 8 IT2 Uj2 . In recent and more accurate structure determinations, it has been possible to describe the anisotropic vibrations of the atoms more fully, by means of thermal ellipsoids of electron distribution. These are determined from the squared amplitudes, U's, of vibration, in the general temperature factor expression: exp[-27r2(U h2a*2 + U k2b*2 + II £2c*2 + 2U. „hka*b* + XX ^ ^ 3 3 L 2U13h«,a*c* + 2U23k£b*c*)] The electron density, p, at a point (x, y, z) in the unit cell can be calculated to be: p(x,y,z) " \\ ll FhkA.exp[-2iri(hx •> ky + Zz)} i.e. the periodic electron density in a crystal can be represented by a three-dimensional Fourier series; the triple summation is over all values (-oo! to +oo) of each of h, k and I. The electron density at all points in the unit cell (hence the location of all the atoms) can be determined if the structure factors, F^^, are known. But only the amplitudes |F^^| can be measured; the phases, $y^^> °f the structure factors cannot be measured. This lack of data constitutes the phase problem, and the art of crystallography is in finding these phases. 4 Various methods have been used to solve the problem. One of the earliest was introduced by Patterson, who found that the expression: P(x,y,z) =?hU |F|2-exp[-2TTi(hx + ky + Iz)] (in which all the coefficients can be measured), represents the distribution of interatomic vectors in the unit cell, and in it, each vector peak is weighted according to the electron densities of the atoms involved. For simple structures, the whole molecule may be discernible in a Patterson map, but for larger structures the map becomes too complex. However, the Patterson map may be useful in determining the coordinates of one or two heavy atoms in a molecule containing many lighter atoms. In the first case, where an approximate solution has been determined, structure amplitudes may be calculated from the coordinates of the atoms in this structure and the results compared with the observed values. If the agreement is good, then the phase problem has been overcome and the structure is solved. In the second case, part of a structure has been determined, and phases can be calculated from the heavy atoms alone. In the heavy atom method, it is hoped that the heavy atom(s) dominate in the structure factors and that the magnitudes and phases due to the heavy atom(s) are an approxim ation to those of the whole structure. Then using the observed magnitudes, and the phases from the heavy atoms, an electron-density map is calculated, and it is hoped that the phases are a close enough approximation to show the positions of more of the atoms in the molecule. These new atom positions can be used to improve the phase calculations and another electron-density map can be drawn. This process is repeated until all the non-hydrogen atoms have been located. A more recent method of phase determination derives the phases directly by mathematical means from a consideration of the structure ampli-5 tudes 6. Rather than working with the usual structure factors, Fj^, it is common to use unitary structure factors, Uj^, or normalised structure factors, E^k^,' th656 latter put the structure factors on scales of relative importance after correction according to the diffraction angle, 8, for each reflection - the scattering matter is effectively concentrated at the atomic coordinates. The normalised structure amplitude, |E|, is defined 7: l£hkJ2 = where (i) fj is the atomic scattering factor for the jth atom in the unit cell for the value of G for the reflection hk£; it is corrected by the temperature factor; (ii) the summation is over all atoms in the unit cell; (iii) e is a symmetry factor which corrects for space group extinctions; normally e = 1, except e.g.: (a) in space group P2j for OkO reflections, e = 2, (b) in space group P2^/c for OkO and h0£, reflections, e = 2. Both and E^^ are complex numbers, and have the same phase as the. corresponding F^^. In 1948, Harker and Kasper showed that inequality relationships existed between the structure factors, and that sometimes one could obtain information on the phases of the structure factors from these inequalities. From considerations of symmetry elements, inequalities for various groups of reflections in many space groups have been derived, but in larger structures, the number of phases that can be determined from these relationships is limited. However, Sayre and others, in about 1952, developed probability expressions, by which a phase can be calculated and will be correct within a certain probability. 6 Most of the earlier work in these direct methods was concentrated on the solution of structures in centrosymmetric space groups, but more recently, attention has been paid, particularly by the Karles, to noncentro-symmetric space groups, and several phase-determining formulae have now been proposed for use in either case. The Karles have developed the determination of phases into a routine known as the symbolic addition procedure 7, which appears capable of solving fairly complex structures. Other methods of structure analysis include (i) trial and error methods - for simple structures in which, normally, the molecule is rigid, and (ii) the multiple isomorphous replacement method, particularly applicable to the large protein molecules. Crystals are prepared of the protein itself and of several heavy atom derivatives of the protein, all of which are isostructural. The heavy atom coordinates are calculated from a Patterson series of the difference between the structure amplitudes, (|F | - |F |)2, of the native protein crystals and their heavy atom derivatives. From a comparison of the data of at least two heavy atom derivatives and the native protein, the phases of all the structure factors can be determined unambigu ously. When all the non-hydrogen atoms of a molecule have been found, and their parameters partly refined (see below), it might be possible to locate any hydrogen atoms in the molecule. The best means of searching for these atoms, and for confirming that there are no other regions of residual electron density (perhaps solvent molecules), is by the computation of a Fourier difference synthesis: AP =^h k I ('F°bsl " IPcald^^P^^-^Pf-2771^ + ky + Zz)] where <j> is the phase of Fcalc> 7 The positional and thermal parameters of an approximate solution are refined, i.e. adjusted, normally by least-squares methods, until the calculated structure amplitudes agree as well as possible with the observed values. A measure of the average agreement between the amplitudes is the R factor: R = I iFobs 1 - lFcalcM * lFobsl Other measurements of accuracy of structural details are found in the standard deviations, statistically determined, for each of the atomic parameters. An analysis has been described as complete if a final differ ence synthesis shows nothing but random fluctuations. CRYSTALLOGRAPHIC STUDIES OF METHYL 3-C-(CARB0METH0XYMETHYL)-4,6-DI-0-p-CHL0R0-BENZOYL-2,3-DIDEOXY-a-D-RIBO-HEXOPYRANOSIDE. 9 A. INTRODUCTION. The title compound was prepared by Rosenthal and Catsoulacos 8 as a derivative of the product of a Wittig reaction on a 2-deoxy-3-ketose. The application of Wittig's reaction in this way provided another method of preparation of branched-chain sugars; these compounds, were of great interest after some antibiotics were found having branched-chain sugar substituent groups. The ketose I was mixed with phosphonoacetic acid trimethyl ester and potassium t-butoxide in anhydrous N,N-dimethyl formamide at room tempera ture for 20 hours. The product was II, in good yield; only one of the two expected unsaturated (cis/trans) isomers was produced, and p.m.r. studies indicated that the product was probably trans methyl 4,6-0-benzylidene-3-C-(carbomethoxymethylene)-2,3-dideoxy-a-D-erythro-hexopyranoside (as shown). Hydrogenation of II, using palladium on charcoal as catalyst, gave the reduced, and debenzylidated, product III. This was an oil and could not be crystallised, and its p.m.r. spectrum was indecipherable; therefore the di-(p-chlorobenzoate) derivative was prepared. Examination of the p.m.r. spectrum for this product indicated the structure IV. Microanalyses on compound IV gave the following results: , Calcd. for C2[tH2[t08Cl2 : C, 56«36 ; H, 4*69 % Found : C, 56-35 ; H, 4-70 %. For confirmation that the di-(p-chlorobenzoate) indeed has the structure IV, crystals of the compound were submitted for analysis by X-ray crystallographic methods. An account of the attempts made to determine the molecular structure of this compound is given below. 10 11 B. X-RAY ANALYSIS. The crystals of the title compound IV, from the laboratory of Drs. Rosenthal and Catsoulacos, had been recrystallised from ethanol, and were minute, colourless needles. Diffraction photographs were recorded on Weissenberg and precession cameras to determine the space group and approx imate cell dimensions of the crystal. The cell dimensions were obtained more accurately later from a least-squares refinement based on the 20 values of about 30 reflections measured on the diffractometer with Cu-KQ (X = 1*5418 A.) radiation. Crystal data: Methyl 3-C-(carbomethoxymethyl)-4,6-di-0-p-chlorobenzoyl-2,3-dideoxy-a-D-ribo-hexopyranoside, (compound IV), C^H^Clo^. M = 511*26 Monoclinic, a = 5*752(3), b = 15*436(3), c = 13*698(3) A., g = 93*74(3)°, (standard deviations in parentheses). Vc = 1213*6 P. Dm = 1*43 (by flotation in aqueous KI), Dc = 1*40 g.cm-3. with Z = 2. F(000) = 532. Absorption coefficients, v(Cu-KQ) = 28*1 ; yfMo-K^, X = 0*7107 A.) = 3*2 cm-1. Reflections absent: OkO when k is odd; hence space group is P2j or P21/m (but the latter is not possible since the compound is optically active). The X-ray photographs were not encouraging; even after many hours' exposure, the spots for reflections at angles corresponding to crystal plane o spacings of 1*7 A. were not visible, whereas, for example, ethyl 3,5- dinitro-benzoate (see part IV) gave patterns for spacings down to 0*9 A. Two sets of intensity data were collected on a G.E. XRD-6 automatic diffractometer, with scintillation counter, pulse-height analyser, and a 12 6-28 scan. The first collection was measured with Mo-Ka radiation (with Zr filter), since the absorption of Mo-radiation is considerably less than that of Cu-radiation; the measurements were made at a scanning speed of 4°/minute, and counting backgrounds for 10 seconds before and after the scan. The second collection was taken with Cu-Ka radiation (and Ni filter), which is the cleaner radiation; also the scanning speed was now l°/minute, and the background measurements were taken over 40 seconds. All the crystals of the sample examined were very small; the crystal mounted for the second collection of data had dimensions 0*25 x 0*05 x 0*04 mm3. Since this crystal was so small and approximately cylindrical, the absorption corrections would be small, and were therefore not applied. Lorentz and polarisation factors were applied to the measured intensities, and the structure amplitudes were calculated. The Mo-data was not very satisfactory; the intensities of 566 reflections were measured, and of these, 255 were considered unobserved. The second set of data, measured with Cu-Ka radiation, comprised 1028 independent reflections (i.e. for 26 ^ 90*0°, corresponding to a minimum interplanar spacing of 1*09 A.), of which 130 were classified as unobserved, having I/CTJ. < 2*0, where a^2 was defined: CTj2 = S + B + (0*02.S)2 where S = scan count, and B = background count over the same range. A list of the observed structure amplitudes, scaled from the measured intensities by Wilson's method 9, is given in Table I. 13 Table I. Measured structure amplitudes (scaled by Wilson's method to the absolute values). Unobserved reflections are marked by a negative sign. h k I l?0.oi 7s. 7 t. 10.? I 15.55 -1.9C ~ror 71. «?. 76.fc* ~5T.rr a.Ti -I .TB 17 . *C 27.C5 •*1 ."* 21.2 b B.CI) 11.6" 21.11 17.9*1 ii.rc 1 7.C* 9.6 3 26.10 T. t T 10-ri i i.*7 5.*7 i*,5* h.*7 H.5J t. 55 -*.3« ; -J.01 11 5.*i 1 14.7* : " i ic. 6 5.91 T -S.Cft n n'.e? S.B5 7 1.7t 7 -4.lt 1 8.2) 1 11."2 0 *0,*! 21.Rl ? s.a« 2 21.J* 3 -l.*C J 11.95 * 20.1' » 10. M 5 1*.|9 5 15.61 fc 13.5* i a.r< i 11 .oo 0 21.05 ) -1 lir.Mi 1 17.15 7 I'.CI 3 1 79.15 ) • * I ft. S T 19.72 l*.l* 1 *.6» 1 Ik.hi 1 -I a i. io D 16.41 15. 28 7 15.69 11 II 1 l». 61 16.21 15.5 1 5 H. 61 10.25 15. SO 11. Uf 5.*? ft. VI 10.*6 11.21 13.H* 2?.e* n. .1 it.'.i 0.25 76.65 o,57 61 H 1 8. 19 R. 01 6.02 \n.ti r -1. 1* -1.04 5.08 W.*5 l*.Jfl 13.67 8.11 1 I.H 1 1 j - J. 1 1 7.11 -3. 20 5. 68 6.06 * 0 0 * 0 1 * 0 -1 * 0 2 5 C 3 -1.73 B. i<; 9.C6 * ( -!• * 0 * * 0 • * 0 6 * fj -6 lC.t"> 0.0 o.n 20.C* fl. 76 10.15 *.!0 "TTTTc" 11.51 11.1 3 t.66 11 .58 9.C9 12. 69 10.5 1 -7.3" 11.31 14 C. ATTEMPTS AT STRUCTURE ANALYSIS. From the structure amplitudes, a three-dimensional Patterson map was calculated. In the first instance, with the Mo-data, this map consisted of several large, diffuse peaks; there were no small, sharp, discrete peaks. The Patterson map from the Cu-data showed little improvement over that of the Mo-data. A peak in a Patterson map can be regarded as representing an inter atomic vector, each such vector in the unit cell being removed so that one end lies at the origin of the map, the other end appearing as the peak. If there are n atoms in the unit cell, there will be n2 - n peaks in the unit cell of the Patterson map, plus a large peak at the origin representing the sum of vectors between each atom and itself. Since either end of each inter atomic vector can be removed to the origin, there is increased symmetry in the Patterson map (P2/m in our case) and this results in the asymmetric unit, which occupies half the unit cell in the molecular arrangement, now being only one quarter of the unit cell. Hence the Patterson map contains many more peaks and more symmetry than the fundamental unit cell, and it is from this more complex map that we wish to determine at least the coordinates of the chlorine atoms. The magnitude of the vector peaks depends upon the numbers of elect rons in the atoms responsible for that vector. If the atoms were point-size, the peak heights would be directly proportional to the product of the atomic numbers of the two atoms, e.g. a C1...C1 peak would stand clearly above a C...C peak by a ratio of 289:36. However, the atoms are not point-size, and two atoms with electron densities: f~\ /~\ I Electron / \ / \ density 15 will produce a vector peak: since vectors between all parts of the atoms are summed to give the vector peaks. Thermal motion also has the effect of spreading the electron density over wide regions, so that vector peaks involving atoms which are vibrating to any extent will appear smeared, and of much lower magnitude than the product of atomic numbers would indicate. In our di-(p-chloro-benzoate) compound, the chlorine atoms are located furthest from the centre of the molecule; both of the p-chlorobenzoyl groups are probably free to vibrate, and will vibrate considerably, so that the C1...C1 vectors could be very smeared and unrecognisable above the mass of vectors between the lighter atoms. A further complication arises from the presence of fairly rigid and symmetric groups in the molecule. For example, in the p-chlorobenzoyl groups, there are several vectors of approximately equal length and nearly parallel, e.g. the thickened bonds Cl and the dotted lines show two sets "^^^T^^N, of similar vectors: ^ 1. -0 Thus, large peaks, the sums of several vectors, will appear in the map. These are often most prominent around the origin, but may occur elsewhere when there are parallel groups or groups related by a centre of symmetry in the molecule or between molecules. Hence the location of C1...C1 vectors in the Patterson map was not straightforward; there were no outstanding peaks in the map - the chlorine atoms (i) were not heavy enough to stand out above the lighter atom vectors, and (ii) were far from the centre of the molecule and probably vibrating considerably. However, regions of high intensity in the Patterson map were investigated as containing possible C1...C1 vectors. There are two chlorine atoms in the molecule, and two molecules per unit cell. Let the two chlorine atoms in the molecule have coordinates (Xj, y^, Zj) and (x2, y2, z2) then, according to the symmetry of the space group P2j, there are chlorine atoms also at (xj, y^h, ZjO and (x2, yz+h, ^2^' Hence there are C1...C1 vectors at: 2x1} h, 2zj 1 These are Harker peaks, found on the Harker 2x2, h, 2z2 ( section at y = h xl-x2> >V>V zl"z2 xl+x2» yi^i*^' zi+z2 and in positions related to these by the symmetry of the vector map, P2/m. Several pairs of possible coordinates were determined for the chlorine atoms from the Mo-data Patterson map, and the best possibilities appeared to be: Cl(l) Cl(2) Pair A (0«03, 0-0, 0«16) (0*09, 0*48, 0-14) Pair B (0«0, 0«0, 0»0) (0*08, 0-07, 0«65) Each of these pairs was used in the calculations of structure factors and electron-density maps, but neither map produced any encouraging results. A further problem encountered here was that the chlorine atoms, in each case, have similar y-coordinates, and this feature gives rise to pseudo mirror-plane symmetry in the electron-density maps. Although no part of the molecule was really obvious in these maps, certain groups were found in not unreasonable positions, and these were used in phasing further electron-density maps. In these, certain peaks persisted, but no definite signs of the molecular structure were apparent. One would have thought that if the Cl-atoms were in approximately the correct positions, then at least the atoms close to the Cl-atoms would have appeared in the maps, but no complete benzene ring was ever seen. However, the computation of electron-density maps continued, using the persistent atoms (with scattering factors of oxygen atoms), the original chlorine atoms and some possible benzene ring atoms; but no real progress was made. There is one outstandingly strong reflection in the data, the 103 reflection. The interplanar spacing for the (103) plane is 3*53 A*., and it seems reasonable that both the p-chlorobenzoyl groups should lie in this plane. The Patterson function in this plane was examined and some peaks were found to correspond with possible interatomic vectors of the groups lying in this plane; there appeared to be peaks corresponding to only one orientation of the group, and it is therefore possible that if the two groups are in this plane, then they are either parallel or related by a centre of symmetry. An electron-density map was computed, based on two chlorine atoms in this plane at (0*0, 0*0, 0*0) and (0*124, 0*0, 0*292), and a benzoyl group from the first chlorine atom. But there were no other recognizable features in the map. Two attempts were made to "sharpen" the Patterson map. In this process, the scattering factors, f, for the atoms are adjusted so that they approximately represent point-atoms-at-rest, rather than atoms of finite size having some thermal motion. In a crystal containing only one kind of atom, the problem is quite easily overcome, but for most crystals, containing several types of atoms, the problem is not so straightforward. In our examples, the Mo-data was sharpened using a factor of 18 \2 fcl)0.exp[-B(sin26)/X2]j on the intensity data. This factor assumes that the chlorine atoms are the dominating atoms in the molecule, and that their vibrations are character istic of the other atoms in the molecule. This is only a rough approximation but a map of more discrete peaks was obtained. This map was superseded by an (|E|2 - 1) Patterson of the Cu-data. This function multiplies the intensities by the sharpening factor: Y I f2-j 3 where k is a constant which puts the data on an absolute scale, and is determined by Wilson's method 9; and where f\. is the scattering factor, corrected for thermal motion, for the jth atom in the unit cell, and the summation is over all the atoms in the unit cell. In this Patterson map, the origin peak has been removed, and the resolution of peaks which previously appeared as shoulders in the origin peak is now much improved. Investigation of the last map led to the computing of a series of electron-density maps which will be outlined here. Three pairs of possible chlorine atom coordinates were first determined: Cl(l) Cl(2) (i) (0-013, 0-0, 0-013) (0-14, 0-04, 0-297) (ii) (0-045, 0-48, 0-161) (0-225, 0-0, 0-136) (iii) (0-04, 0-02, 0-009) (0-31, 0-0, 0-306) Pairs (i) and (iii) have one chlorine atom with almost identical x- and z-coordinates, while the second chlorines of each pair are separated by about i L The peaks close to the origin indicated several vectors in a single plane, and the coordinates of all the carbon atoms in a benzoyl group were determined from these and other peaks in this plane. Since there was only one prominent plane of peaks in the Patterson map, it was assumed that both of the benzoyl groups lay in this plane (which was close to the (103) plane). Initially, electron-density maps were calculated using the seven carbon atoms attached to a chlorine atom in each of the two possible ways, with the chlorine atoms at (0*013, 0*0, 0-013) and then (0-225, 0-0, 0-136): Group C Group A b °2 sinp Group B Group D Group A's map had the strongest new peak appearing, as hoped, at (0«15, -0-004, 0- 298), but at only 1-7 eX'"3. The map of group B also showed its strongest new peak in the anticipated second chlorine position (0-12, 0-020, 0-297), at 1- 9 eXr3, Similarly for group C, the second chlorine showed at 2-2 eA~3. at (0-040, 0-495, 0-160). 20 However, when second electron-density maps were computed using, to determine the F0 phases, the two chlorine atoms plus the seven carbon atoms in arrangements A, B and C, there were negligible improvements in the R-factors, and no further parts of the molecule obvious in the electron-density maps. The initial map for group B (using one chlorine atom) showed the possibility of a second ring system starting from the second chlorine atom, but there was no sign of this ring in the second electron-density map. Also, having the second ring in that position appeared geometrically impossible -there was no way in which the rest of the molecule could reasonably be fitted into the system. After a comparison of the first maps of groups B and C, another map was calculated which had group B as before, with the second ring related by a centre of symmetry at (0*32, 0*178, 0*070), i.e. with the chlorine atom at (0*62, 0*355, 0*114), and the anticipated second chlorine of group B and a peak at (0*29, -0*005, 0*312) as the C=0 atoms of the carboxyl group. This arrangement looked geometrically feasible: cr ' ,''"J"< Also favouring this type of arrangement, in which there is a certain amount of centrosymmetry, are the "E-statistics" which are shown in Table II. Although the space group is undoubtedly P2-,, and therefore noncentrosymmetric, the statistics show values which indicate some centrosymmetry, e.g. the mean 21 Table II. Results from the Wilson Plot, for the Cu-data. Overall temperature factor, B = 5*42 A . E-Statistics: Theoretical Observed Centro- Noncentro-symmetric Mean |E| 0-860 0-798 0-886 Mean |E|2 1-028 1-000 1-000 Mean ||E|2 - 1| 0-844 0-968 0-736 Percentage of reflections with |E| > 3 0-29 0-30 0-01 " " |E| > 2 3-60 5-0 1-80 " |E| > 1 33-7 32-0 37-0 22 ||E|2 - l| value is close to the mean of the theoretical centrosymmetric and noncentrosymmetric values, and the proportions of the reflections with higher |E|'S correspond more to the centrosymmetry values. The relation of two p-chlorobenzoate groups by a centre of symmetry would probably help to explain the statistics' deviation from the theoretical values. However, again, the R-factor and structure factors appeared negligibly improved, and the electron-density map seemed to have peaks (about 1 eA .) scattered randomly with no obvious pyranose (or furanose) rings. Here the analysis by examination of the Patterson maps ended. The heavy atoms, the two chlorine atoms, were not sufficiently heavy. Even if we had, at some stage, determined the coordinates of the chlorine atoms fairly accurately, it is possible that these atoms were not sufficiently dominating in the structure, i.e. the phases based on the chlorine atoms alone were not a good enough approximation to the actual phases, and the: electron-density maps therefore could not indicate the rest of the molecule. A convenient guide as to how heavy the dominating atoms should be is the z2 ratio. A problem should be easily soluble by the heavy atom method if I z2 heavy =; \ y z2 "light In our case, the ratio is 0*41, when the chlorines were considered the heavy atoms. This result is low, but far higher than for some cases in which the problem has been solved (if with difficulty), e.g. vitamin B12, where the ratio was 0*17. The major problem in our case is probably that the coordin ates of the chlorine atoms cannot be determined accurately enough from the Patterson map, and this is primarily because these atoms are both located at the ends of large, vibrating groups. 23 An alternative approach to solution was then attempted using direct methods, the statistical determination of the phases of the structure factors directly from the structure amplitudes. The procedures for structure determination in the centrosymmetric case are well established 6 and fairly easy to apply; essentially, one determines the phases (which must be either 0 or IT) of the structure factors by consideration of the phases of reflections with related indices. The phases of 0 and TT correspond to the signs + and -of the structure factors. But in the noncentrosymmetric case, the phase determination is more complicated since each phase can take any value between -IT and +TT. In the last few years, J. Karle, H. Hauptman and I. Karle have developed the Symbolic Addition Procedure 7 for the phase determination for both centro symmetric and noncentrosymmetric crystals, and it was by using a computer program 10 based on this procedure, that we tried to solve the structure of our sugar derivative. The intensity data (with Cu-K^ radiation) of our compound were scaled to the absolute values of the structure amplitudes by Wilson's method 9. The normalised structure amplitudes, |E|'S 7, were then determined, and the E-statistics for the data were compared with theoretical values 11. These statistics are shown in Table II. A list of E-2 relationships amongst the reflections with |E| > 1*3 was prepared; for every reflection hk£, pairs of reflections h'k'£' and h-h",k-k',£-£' were recorded when |E| for each of the three reflections was greater than 1*3. The next step was the selection of three origin-determining reflections. In the space group P2l5 the origin may be put on any of the four lines (0, y, 0), (0, y, %), (%, y, 0) or Qi, y, %). One of these lines is chosen by selecting, and assigning phases to, two h0£ reflections in which the (odd-even) parities of hi.£i are different from h2£2, and neither have h and I both even. From a consideration of the real and imaginary terms 24 of the structure factors in the space group P2X, the phases of the hCH structure factors must be chosen as 0 or TT. The origin is then fixed at a point on the selected line by assigning any phase to any hkfl, reflection in which the index k is not zero; for convenience in the phase-determination procedure, it is suggested that h and i are both even, and that k=l for this third reflection. Having selected three origin-determining reflections, a further three (or more) reflections are chosen and assigned symbols a, b, c (etc.) for their phases. Reflections with high |E| values and with indices entering into as many E-2 relationships as possible are chosen here. The symbolic addition procedure calculates the phases of other reflections which have E-2 relationships with the reflections of known phase; and the phases are calculated in terms of the three assigned values for the origin-specifying reflections, and of the three (or more) symbols. In our examples, several triplets of reflections were used to specify the origin, e.g. (103, 201, 216), (103, 201, 136), (103, 106, 310), (103, 102, 310), (103, 201, 113) and , (103, 201, 016). Reflections selected to have symbols in the procedure included those with indices 023, 164, 201, 102 and others mentioned above. The computer program written to calculate the phases, determined sets of phases; the symbols a, b, and c were each given several values between -IT and +TT in the program and a series of computations was made, giving one set of phases for each combination of starting values of a, b, and c. One of the symbols was allowed starting values restricted to the range 0 to TT; this had the effect of selecting one of the two possible enantiomorphs allowed in the space group and by the data. The program had provision for the determination of phases for about 200 of the largest |E| reflections in the data. For our compound, the program was used several times, generally with the 182 reflections for which |E| > 1*3 (in the Cu-data). The phases for these reflections were calculated using the tangent formula of Karle and Hauptman 12: where: tan (j>. ~ h A = I lEkllEh-kl-sin Wk + +h-k5 B = J |Ek||Eh_k|.cos (t>k + *h_k) and the subscripts h, k and h-k correspond to the indices hk£, h'k'r, and h-h' ,k-k', l-V ; <j>k is the phase of reflection hk£, etc.; "~" means "probably equal to". Each reflection, h, in the list is examined in turn, and a phase is deter mined for it from the previously known phases of pairs of E-2 related reflections. After this initial examination of each reflection, the process is repeated, using, in the second cycle, those phases calculated in the first cycle. This "is continued through several cycles until most of the phases have been determined and there is little change from cycle to cycle in the values of the calculated phases. There are various criteria which must be satisfied for a new phase to be accepted - the consistencies th and a of the new angle have to exceed certain arbitrary values, nomally 0*25 and 1*25^ respectively (N is the' number of atoms in the unit cell); the consistencies are defined: _ A2 + B2 k id - lEh-kl t must have a value between 0 and 1. The consistency a is related to the n variance V of Karle and Karle 7, and is derived from the probability distrib ution of addition pairs of phases, <f)k + ^ k* ' If a new phase angle satisfies these criteria, it is used in the determination of phases of other reflections in the following cycle. Should the calculation of a phase angle in successive cycles differ by more than a certain amount (usually 125 millicycles, i.e. TT/4), the phase is considered unknown in the following cycle, i.e. it is not used in the determination of further phases, but will be recalculated during that following cycle. At the end of each cycle, the program computed average values of the consistencies, and an R-factor: and these values were compared in the several sets of phases produced by the program, to select the most likely correct set. was computed; an E-map is a Fourier synthesis in which the coefficients are E's rather than the usual structure factors, F's. It is hoped that some recognizable parts of the molecule will be apparent in the E-map, and that the more prominent peaks correspond to atoms. Sometimes, however, the first E-map computed does not show anything of sense, and it is recommended that one calculate E-maps using other sets of phases until the molecule is apparent. In each series of sets of phases calculated for our sugar derivative, there was never one set which stood out as being more consistent than the others, and there was often a choice between two or three sets as to which one might be most likely the correct set of phases. Consequently, several E-maps were computed and examined. In some maps, parts of p-chlorobenzoate groups could be discerned, and in others, pyranose rings were more obvious; but in no cases were there any real indications of the molecule. Some peaks were persistent from one map to another, and these were used, with possible ring fragments of the molecule, in subsequent structure factor and electron-density map calculations. appeared to be very similar to that of group B of page 19, but the other p-chlorobenzoate group and the pyranose ring were never apparent in any Then, using the calculated phases of the most likely set, an E-map The most probable position for one of the p-chlorobenzoate groups 27 geometrically suitable position relative to the first group. After considerable investigation by these methods, the structure determination of the branched-chain sugar derivative IV was halted for the present time. D. CONCLUSIONS. At the time of writing, the structure of the title compound, IV, has not been determined. Since considerable time and computing funds have already been spent on this analysis without any significant progress visible, alternative approaches to the problem of confirming the branch-chain configuration and the pyranose conformation of the compound are required. It was wondered, quite early in the investigation, whether an alternative derivative of the sugar was available. The di-(p-chlorobenzoate) was the end product of a series of reactions, and had been produced in minute quantities; the synthesis of, say, the di-(p-iodobenzoate), or the replace ment, of the two p-chlorobenzoate groups by some other group, was not feasible at the time. The removal of the huge p-chlorobenzoate groups and the preparation of crystals of a smaller, "equal atom" derivative molecule (the parent sugar was an oil), would possibly allow solution more easily by direct methods. One of the problems of using the direct methods as outlined in previous pages, was that the formulae used in the symbolic addition procedure had been developed for use in equal-atom structures (here the hydrogen atoms are ignored, and the carbon and oxygen atoms are considered to be equal). It has been argued 13 that, in general, the phase-determination amongst the reflections of high |E|'S should not be affected by the presence of unequal atoms; probability and consistency formulae will be affected a little, but this should not upset the actual calculation of phases. Other possible reasons why the structure has not been solved have been suggested in previous parts of this discussion. A further outstanding possibility is that there is disorder in the crystal. There is no overall rigidity in the molecular model of our compound, and one can readily suggest that there may be more than one arrangement of one or both of the large p-chlorobenzoate groups. If there is disorder involving the chlorine atoms, then, of course, one cannot expect to find C1...C1 vectors nor indeed any part of the p-chlorobenzoate group in the Patterson map. And in the E-maps, the search would be for several weak groups, some groups possibly overlapping others - very difficult to decipher. It has been assumed through most of this work that the monosacchar ide unit has the pyranose ring configuration; however, the possibility of a furanose ring configuration has not been disregarded and in electron-density and E-maps, any obvious five-member ring was considered as the basis of a furanose compound. Crystallographic investigation on the present derivative has been suspended; it is recommended that the structure of the branched-chain sugar be confirmed from an alternative derivative, or by some other method. PART II. THE STRUCTURE DETERMINATION OF 5-0-(p-BROMOBENZENESULPHONYL)-2,2'-0-CYC LOHEXYLIDENE-3-DE0XY-2-C-HYDROXYMETHYL-D-ERYTHRO-PENTONO-1,4-LACT0NE. 30 A. INTRODUCTION. The saccharinic acids are formed by treatment of reducing sugars with alkali, and their formation and chemistry have been reviewed 14>15. Since their preparation involves a rearrangement during which a new asymmetric centre is produced, there are two possible isomers of each type of saccharinic acid. Reaction of 4-0-substituted D-glucoses with alkali 16 yields "a"-D-isosaccharinic acid, 3-deoxy-2-C-hydroxymethyl-(D-erythro or D-threo)-pentonic acid (I or II), the configuration at C-2 being uncertain. The present crystal structure analysis of a derivative of the lactone of this acid, obtained by alkaline degradation of cellulose, was undertaken to determine the molecular structure, with particular interest in the configuration at C-2. The compound studied has been shown to be 5-0-(p-bromobenzenesulphonyl)-2,21-0-cyclohexylidene-3-deoxy-2-C-hydroxymethyl-D-erythro-pentono-l,4-lactone, so that "a"-D-isosaccharino-1,4-lactone has structure III, and "a"-D-isosacchar-inic acid has the D-erythro configuration I. While this work was in progress the D-erythro configuration was established independently by crystal struct ure analyses of calcium and strontium "a"-D-isosaccharates 17>18. C00H C00H H0CH2-C-0H HO C-CH20H CH2 CH2 H-C-OH H C-OH CH20H CH20H I. II. HOCH 2 0 III. OH 31 B. X-RAY ANALYSIS. a-D-isosaccharinic acid was obtained by alkaline degradation of cellulose, and a p-bromobenzenesulphonyl cyclohexylidene derivative of the y-lactone was prepared for X-ray analysis. Crystals of the derivative are colourless plates with (001) developed. Unit cell and space group data were determined from rotation, Weissenberg, and precession photographs, and the lattice parameters were obtained more accurately by least-squares refinement based on the 29 values for thirty reflections measured on the diffractometer with Cu-K (X = 1*5418 A.) radiation. Crystal data: 5-0-(p-bromobenzenesulphonyl)-2,2'-0-cyclohexylidene-3-deoxy-2-C-hydroxy-methyl-D-erythro-pentono-l,4-lactone, C18H21Br07S. M = 461-3 Monoclinic, a = 5-.757(2), b = 10-586(3), c = 16-021(6) A., B = 98-85(3)°, (standard deviations in parentheses). V = 964-7 A . c D = 1-58 (by flotation in aqueous KI), D =, 1-59 g.cm"3. with Z = 2. m c F(000) = 472. ' Absorption coefficient, y(Cu-Ka) = 45 cm"1. Absent reflections: OkO when k is odd. Space group is P2j^ (P2]ym is excluded since the crystals are optically active). The intensities of the reflections were measured on a Datex-automated G.E. XRD-6:Diffractometer, with a scintillation counter, Cu-K a radiation (Ni filter and pulse-height analyser), and a 6-26 scan. Of 1319 reflections with 26(Cu-Ka) J? 111° (minimum interplanar spacing 0-94 &.), 1140 (86-4%) had net intensities greater than half the minimum background, and these were treated as observed; the remaining 179 reflections were 32 classified as unobserved, and were included in the analysis with |F0| = 0•6.F(threshold). The crystal used was a plate, elongated along a with cross-section 0*2 x 0*03 mm2., and it was mounted with a* parallel to the <(>-axis of the goniostat. It was not possible to grow thicker specimens. Since the crystal is very thin, absorption errors are not serious, except in a few narrow regions of reciprocal space where errors of up to about 20% in |Fo| are possible. Since the errors for most reflections are much smaller, no absorption correction was made. Lorentz and polarisation factors were applied and the structure amplitudes were derived. C. STRUCTURE ANALYSIS. The bromine and sulphur atom positions were determined from the three-dimensional Patterson function, and all the carbon and oxygen atoms were located on an electron-density map. The structure was refined by block-diagonal least-squares methods, with minimisation of Z w(|FQ| - |Fc|)2, with /w = 1 for the unobserved reflections and when |FQ| ^ F*, and /w = F*/|FQ| when |FQ| > F*. F* was initially taken as 30, but examination of wA2 in the final stages of refinement indicated that F* = 20 was approp riate. The scattering factors of the International Tables 5C were used. Refinement with isotropic thermal parameters gave R = 0*14, and anisotropic refinement of all atoms gave a final R of 0*10. During the refinement, the isotropic temperature factors of two carbon atoms, C(14) and C(15) - see figure 1. - were noted to be abnormally low; these values were adjusted to 4*0 A2., but in subsequent least-squares cycles, they decreased again. The temperature factor for C(14) did increase before the refinement was complete, but that for C(15) remained low. A final difference synthesis revealed some of the hydrogen atoms, but these were not introduced into the refinement since many of them could not be positioned accurately, and other areas of equally high electron-Figure 1. View of the molecule. The positive direction of the a axis is towards the viewer, and the correct absolute configuration is shown. The atom numbering is for convenience in the crystal analysis. 34 O o density (~0«6 eA"3.) appeared spuriously in the difference map. The final positional and thermal parameters are in Table III, and the measured and calculated structure factors are recorded in Table IV. D. DISCUSSION. A view of the molecule is shown in Figure 1., where the atom numbering is for convenience in the crystal analysis. The compound was prepared by alkaline degradation of cellulose, via a series of reactions 11+>15 which involves no change in the configuration at C(13) of Figure 1. The absolute configuration of the molecule is therefore established, and is correctly depicted in Figure 1., and in the parameters of Table III referred to a right-handed set. The derivative studied is 5-0-(p-bromobenzene sulphonyl) -2,2 * -0-cyclohexylidene-3-deoxy-2-C-hydroxymethyl-D-erythro-pentono-1,4-lactone. Of particular interest is the configuration at C(15) of Figure 1. (C-2 in the chemical numbering system), and the analysis has established structure III for "a"-D-isosaccharino-l,4-lactone, and the D-erythro configuration, I, for "a"-D-isosaccharinic acid. This result is in agreement with the configuration determined by crystal structure analyses of calcium and strontium "a"-D-isosaccharates 17>18. Both of the five-membered rings in the molecule have envelope conformations, four of the atoms in each ring being approximately coplanar, with the fifth atom displaced. The relevant information about the planes is given in Table V. The envelope conformation of the 1,3-dioxolane ring is similar to that found in various cyclopentane derivatives, with atom 0(20) o deviating by 0*49 A. from the plane of the other four atoms of the ring. In the Y-lactone ring, C(15) [C-2 in the chemical numbering], is displaced by o 0*14 A. from the plane of the other four atoms - a less prominent envelope o conformation; 0(17) is displaced by 0*12 A. in the opposite direction, the configuration around C(16) being planar. The dihedral angle between the two Table III. Final atomic parameters. (a) Fractional atomic coordinates, (standard deviations in parentheses): X y z Br(l) -0 •5089(6) 0*4976(4) -0 •2814(2) S(2) 0 '0615(7) 0*8985(5) -0 •0324(3) C(3) -0 3281(32) 0*6091(19) -0 •2042(11) C(4) -0 1389(42) 0*6691(22) -0 •2289(14) C(5) -0 0072(36) 0*7552(22) -0 1751(12) C(6) -0- 0893(26) 0*7848(16) -0 0981(10) C(7) -0< 2826(29) 0*7253(20) -0 0777(12) C(8) -0< 4105(29) 0*6357(16) -0< 1290(11) 0(9) 0< 1784(22) 0*9796(15) -0 0811(8) 0(10) -0- 0928(23) 0*9474(12) 0« 0204(8) 0(11) 0 2670(19) 0*8198(13) 0 0225(7) C(12) 0-2075(29) 0*7467(21) 0< 0916(10) C(13) 0 4142(28) 0*6504(16) 0 1095(10) C(14) 0-3795(29) 0*5557(19) 0-1812(10) C(15) 0< 5810(22) 0*5969(16) 0-2545(9) C(16) 0-7250(25) 0*6892(16) 0< 2155(9) 0(17) 0< 9129(20) 0*7307(14) 0-2469(7) 0(18) 0-6233(18) 0*7203(11) 0-1373(6) 0(19) 0« 7142(19) 0*4884(13) 0-2865(7) 0(20) 0< 5130(21) 0*5496(13) 0-3900(7) C(21) 0« 5011(31) 0*6501(22) 0< 3356(12) C(22) 0< 7138(27) 0*4754(17) 0-3748(8) C(23) 0-6696(35) 0*3411(20) 0< 3952(12) C(24) 0' 6717(41) 0*3224(19) 0-4894(15) C(25) 0-9109(44) 0*3658(23) 0-5378(12) C(26) 0« 9424(42) 0*5089(30) 0< 5194(13) C(27) 0« 9404(35) 0*5262(20) 0* 4235(12) Anisotropic thermal parameters, in the form: exp [-2TT2. IO-^CUH h2a*2 + U22 k2b*2 + U33Jl2c*2 + 2U12hka• + 2U13h£a*c * + 2U23 ,k£b*c*)] "ll U22 "3 3 "12 "13 "2 3 Br(l) ;, 1232 592 842 -226 -310 - 83 S(2) 244 282 401 - 13 - 11 103 C(3) 510 394 366 51 -304 - 62 C(4) 821 382 689 -169 139 45 C(5) 586 508 453 - 63 -144 109 C(6) 243 270 336 42 - 5 113 C(7) 297 560 574 13 5 228 C(8) 403 257 446 147 - 14 -128 0(9) 450 564 618 - 22 - 76 305 0(10) 568 301 555 60 - 8 - 38 0(H) 342 542 338 70 83 239 C(12) 357 595 305 84 49 15 C(13) 340 256 413 -136 -139 132 C(14) 396 479 314 -165 - 87 159 C(15) 82 395 249 51 - 17 - 9 C(16) 252 256 333 30 74 - 93 0(17) 366 638 385 - 82 28 - 24 0(18) 291 307 287 80 - 38 8 0(19) 409 335 422 61 - 39 - 57 0(20) 554 465 410 116 136 127 C(21) 397 555 524 73 45 46 C(22) 386 411 156 - 44 125 - 28 C(23) 691 441 527 -323 77 178 C(24) 760 241 928 - 60 111 291 C(25) 1079 592 306 -265 -154 160 C(26) 838 808 503 - 76 -149 - 87 C(27) 580 421 527 - 17 -291 95 Table IV. Measured and calculated structure amplitudes. Measured values with negative sign indicate unobserved reflections, 37 k I F„ obi 'calc h = 0 57,5 10.8 22.1 68.2 67.1 JO.1 28.5 h = 1 h = 2 II.0 17.0. h = 3 12.8 13.2 27.2 26.-1 12.2 7t. ) 13.7 ~TfcTT a.7 12.0 h = 4 12.1 10.? h = 5 h = 6 38 Table V. Mean planes in the molecule. (a) Equations of mean planes. These are given in the form: AX1 + mY* + nZ' = p where X', Y' and Z' are coordinates in A. referred to ortho gonal axes a, b and c*. Ring % m n P Lactone -0-6137 0-6880 0-3873 4-0990 1,3-dioxolane 0-8104 0-5582 0-1782 6-4505 Cyclohexylidene • 0-7923 -0-6088 0-0399 0-3369 Aromatic -0-5197 0-7256 -0-4511 6-8673 (b) Displacements of the atoms from the planes; those underlined indicate the atoms included in calculating the equations of the planes. 1,3-dioxolane Cyclohexylidene Atom Aromatic ring Lactone ring ring ring Br(l) 0-126 S(2) 0-040 C(3) -0-011 C(4) 0-029 C(5) -0-019 C(6) 0-003 C(7) 0-004 C(8) -0-001 C(13) 0-012 C(14) -0-008 C(15) 0-141 -0-004 C(16) 0-007 0(17) -0-116 0(18) -0-005 0(19) 0-003 0(20) -0-489 C(21) 0-005 C(22) -0-003 -0-639 C(23) -0-002 C(24) 0-003 C(25) 0-751 C(26) -0-004 C(27) 0-002 39 four-atom planes is 88° (the angle between three^atom planes at C(15) is negligibly different). The cyclohexylidene six-membered ring has a normal chair conformation (Table V); the dihedral angles within the ring vary from 55° to 61°. The aromatic ring and the attached bromine and sulphur atoms are approximately planar (Table V). The bond distances and valency angles are in Table VI. None of the lengths or angles differ significantly from normal values. The mean dimen sions are: Br -"Car 1-90 C ar - C ar 1-39 s - Car 1-74 s - 0 1-59 s = 0 1-41 c - c 1-54 c - 0 1-42 c = 0 1-20 Angle in aromatic ring 120c Angle in cyclohexane ring 110° The bonds and angles at the sulphur atoms are close to previously reported values; in particular, the 0=S=0 angle (120*5°) is significantly larger than the other angles at the sulphur atom. A projection of the structure is shown in Figure 2. All the inter molecular distances correspond to van der Waals' interactions. The shortest contacts are 0...0, 2*99 A., and 0...C, 3*05 A. 40 Table VI. Bond lengths and valency angles. (a) Bond lengths (in A.; a = 0*02 - 0*04 A.): i j Length i j ij i j ij Br(l) - C(3) 1-90 C(7) - C(8) 1*39 C(16) - 0(18) 1-34 S(2) - C(6) 1-74 0(11) - C(12) 1*44 0(19) - C(22) 1-42 S(2) - 0(9) 1*40 C(12) - C(13) 1-56 0(20) - C(21) 1-37 S(2) - 0(10) 1«42 C(13) - C(14) 1*56 0(20) - C(22) 1-45 S(2) - 0(11) 1-60 C(13) - 0(18) 1*43 C(22) - C(23) 1-49 C(3) - C(4) 1-37 C(14) - C(15) 1-58 C(22) - C(27) 1*51 C(3) - C(8) 1*39 C(15) - C(16) 1-48 C(23) - C(24) 1*52 C(4) - C(5) 1-40 C(15) - 0(19) 1-43 C(24) - C(25) 1-54 C(5) - C(6) 1-42 C(15) - C(21) 1*55 C(25) - C(26) 1-56 C(6) - C(7) 1*36 C(16) - 0(17) 1-20 C(26) - C(27) 1*55 (b) Valency angles (in degrees; a =. 0*07 - 2*1°): i j k Angle (ijk) i j k Angle (i C(6) - S(2) - 0(9) 109 •0 C(14) - C(15) - 0(19) 109 •7 C(6) - S(2) - 0(10) 108 •3 C(14) - C(15) - C(21) 116 •4 C(6) - S(2) - 0(11) 103 •4 C(16) - C(15) - 0(19) 112 •1 0(9) - S(2) - 0(10) 120 •6 C(16) - C(15) - C(21) 111 •8 0(9) - S(2) - 0(11) 104 •4 0(19) - C(15) - C(21) 101 •7 0(10) - S(2) - 0(11) 109 •9 C(15) - C(16) - 0(17) 126 •2 Br(l) - C(3) - C(4) 118 •7 C(15) - C(16) - 0(18) 111 •4 Br(l) - C(3) - C(8) 117 •6 0(17) - C(16) - 0(18) 122 •4 C(4) - C(3) - C(8) 123 •3 CQ3) - 0(18) - C(16) 113 •0 C(3) - C(4) - C(5) 120 -3 C(15) - 0(19) - C(22) 110 •6 C(4) - C(5) - C(6) 117 •3 C(21) - 0(20) - C(22) 106 •1 S(2) - C(6) ~ C(5) 118 •4 C(15) - C(21) - 0(20) 105 •0 S(2) - C(6) - C(7) 121 •7 0(19) - C(22) - 0(20) 103 •8 C(5) - C(6) " C(7) 119 •9 0(19) - C(22) - C(23) 109 •7 C(6) - C(7) - C(8) 123 •5 0(19) - C(22) - C(27) 110 •2 C(3) - C(8) - C(7) 115 •5 0(20) - C(22) - C(23) 108 •2 S(2) - 0(11) - C(12) 117 •5 0(20) - C(22) - C(27) 111 •6 0(11) - C(12) - C(13) 103 •2 C(23) - C(22) - C(27) 112 •9 C(12) - C(13) - C(14) 112 •0 C(22) - C(23) - C(24) 111 •5 C(12) - C(13) - 0(18) 107 •6 C(23) - C(24) - C(25) 109 •3 C(14) - C(13) - 0(18) 107 •5 C(24) - C(25) - C(26) 108 •4 C(13) - C(14) - C(15) 102 •0 C(25) - C(26) - C(27) 108 •6 C(14) - C(15) - C(16) 105 •3 C(22) - C(27) - C(26) 110 •2 PART III. THE STRUCTURE DETERMINATION OF 2,6-DICHLORO-4-NITROANILINE. 43 A. INTRODUCTION. The determination of the structure of 2,6-dichloro-4-nitroaniline was carried out to investigate further the conformation of substituent groups in benzene derivatives. This molecule contains a nitro group whose orientation with respect to the benzene ring should not be affected by its ortho neighbours. The effect of the formation of hydrogen bonds or the proximity of other molecules might, however, rotate the group out of coplan-arity with the benzene ring. The orientation of the amino group should be decided by the formation of hydrogen bonds with the neighbouring chlorine atoms and/or the oxygen atoms of nitro groups of other molecules. The dimensions of the benzene ring are also of interest; these, with the C-N bond distances, should provide more information on the relevance of resonance forms and of hybridisation of carbon a orbitals in benzene derivatives. B. X-RAY ANALYSIS.. The sample of 2,6-dichloro-4-nitroaniline, supplied by Eastman Organic Chemicals (Eastman Kodak Co.), was recrystallised from 95% ethanol to yield fine yellow needles. The unit cell and space group data were determined initially from rotation, Weissenberg and precession photographs; the cell dimensions were later obtained more accurately from least-squares refinement methods based on the 26 values of 30 reflections measured on the diffractometer with Cu-K„ (X = 1*3922 A.) or Cu-K (X = 1-5405 A.) radia-tions. Crystal data: 2,6-dichloro-4-nitroaniline, C6HltCl2N202. M = 207*02. Monoclinic, a = 3*723(05), b = 17*833(1), c =11*834(1) A., 8 = 94*12(1)°, (standard deviations in parentheses). 44 V = 783*57 A3. c Dm = 1*74 (flotation in aqueous zinc chloride), Dc = 1*755 g.cm"3. with Z = 4. F(000) = 416. o Absorption coefficient, Cu-K^ (X = 1*5418 A.), u =71 cm"1. Reflections absent: OkO when k is odd, hO&'when I odd; hence space group is P2J7C. o The upper-level Weissenberg and the precession photographs showed that the crystal selected was twinned. The unit cells of the two twins had a common a. axis, and c* = -c| ; it was shown in the course of this work that the twins are probably congruent so that the b axes are colinear but opposite in direction, and this arrangement is assumed in the following description. Optical examination of a sample of the crystals, using polarised light, indicated that all the crystals were twinned, and that there might be only one twinning plane in each crystal, i.e. the crystal could, theoretic ally, be cut in two to yield two single crystals. The only examples of single crystals in the sample were minute, probably fragments of larger crystals. It was not possible to cut a crystal to provide a good single crystal and therefore a twinned crystal was used for the data collection. This crystal was a needle with a. as major axis and length 0*4 mm., cross-section 0*08 x 0*05 mm2. It was mounted with a* of one of the twins parallel to the goniostat <j>-axis. The intensities of the reflections were measured on a Datex-automated G.E. XRD-6 diffractometer with a scintillation counter, Cu-K^ radiation (Ni filter and pulse-height analyser), and a 6-20 scan. The intensities of 1160 reflections of one twin, with 20(Cu-K ) < 120° o (i.e. minimum interplanar spacing of 0*89 A.) were measured. The 323 reflections with indices 2kl were removed since these reflections included varying, unknown amounts of diffracted beams from (2k£+l) planes of the second twin. Weissenberg photographs first showed this possibility of over-lap in spots, and a chart recording of the collection of intensity data confirmed that often there were two diffracted beams measured in the 9-20 scan. The 837 remaining reflections were corrected for Lorentz and polar isation factors. There were 110 reflections (i.e. 13*2%) with I/o^ < 2*0, where a 2 is defined: I Oj2 = S + B + (0*02.S)2 where S = scan count, and B = background count over the same scan range; these reflections were treated as unobserved. The 0k£ intensities were then scaled down to correspond with those of other layers; the 0k£ reflections of one twin were coincident with the Okl" reflections of the other twin, and the intensity measured was thus the sum from the two twins. The required scale factor was determined by compar ing intensities of several general reflections in both twins; the first twin was found to be 1*034 stronger than the second, hence the scaling factor is 0*508. No corrections for absorption were made. The structure amplitudes were then derived. C. STRUCTURE ANALYSIS. A map of the Patterson function was calculated, and this indicated the coordinates of the two chlorine atoms. The other ten non-hydrogen atoms were found in an electron-density map. Scattering factors for chlorine, oxygen, nitrogen and carbon were taken from International Tables 5C, and for hydrogen from the values of Stewart, Davidson and Simpson 19. The structure was refined by a full-matrix least-squares procedure which minimised E w(|FQ] - |FC|)2, initially with w = 1 for all reflections. Refinement with isotropic thermal parameters gave R = 0*124. Further refine ment with anisotropic thermal parameters gave R = 0*060. A difference 46 Fourier at this stage showed the four hydrogen atoms clearly at 0«47 to 0*53 eA"3. above a maximum background of 0*42 eX"3. Final refinement of the coordinates of all atoms, anisotropic thermal parameters of all non-hydrogen atoms and isotropic thermal parameters of the hydrogen atoms, reduced R to 0*038. In the last stages of refinement, the strongest reflection, 102, suspected of extinction errors, was removed from the data and not included in any calculations. Also at this stage, a weighting scheme of the type: was found to be most suitable, from examination of the average values of W(|Fo| - |FC|)2 in ranges of |F0|; F* was put as 13*0 and G* as 8*0. Unobserved reflections were given a weight /w = 0*6. Reflections with indices 2ki were not included in any calculations. The resulting atomic parameters are listed in Table VII, and a list of structure factors, |FQ| and |FC|, (not including the 2k£ reflections), is given in Table VIII. A view of the molecule is given in Figure 3. The bond lengths and valence angles, calculated from the atomic coordinates of Table VII, are given in Table IX, and the angles are shown in Figure 4(b). Thermal motion corrections have been applied to the bond lengths (except to those bonds involving hydrogen atoms), and the corrected values are recorded also in Table IX and in Figure 4(a). In the determination of the thermal motion corrections, the thermal parameters of the atoms were converted to the thermal ellipsoids which describe the atomic vibrations in a molecule. Oscillation of the molecule in the molecule plane appears minimal - intermolecular hydrogen-bonding (see below) and other short intermolecular interactions restrict motion of this type; the ellipsoids of the carbon atoms indicate very little oscillation Table VII. Final atomic parameters, (a) Fractional atomic coordinates; standard deviations are in parentheses: X y z CCD 0 •5098(12) 0*3375(2) 0*3014(3) C(2) 0 3591(12) 0*3571(2) 0*1932(3) C(3) 0 •3431(12) 0*4296(2) 0*1545(3) C(4) 0 4766(13) 0-4856(2) 0*2249(3) C(5) 0 6248(12) 0*4712(2) 0*3330(3) C(6) 0 6414(12) 0*3984(2) 0*3694(3) Cl(7) 0 1942(4) 0*2852(1) 0*1060(1) Cl(8) 0-8261(3) 0*3783(1) 0*5049(1) N(9) 0« 5298(13) 0*2667(2) 0*3390(4) N(10) 0 4657(12) 0*5632(2) 0*1867(3) 0(11) 0 3037(14) 0*5778(2) 0*0953(3) 0(12) 0 6228(14) 0*6107(2) 0-2474(3) H(13) 0-251(13) 0*4419(23) 0*0805(35) H(14) 0< 738(11) 0*5098(20) 0*3821(30) H(15) 0« 599(16) 0*2557(29) 0*4124(46) H(16) 0< 459(15) 0*2326(28) 0*2909(39) (b) Thermal parameters of the atoms. Anisotropic thermal parameters are in the form: exp [-2u2.10-4(Unh2a*2 + U22k2b*2 + U33£2c*2 + 2U12hka*b* + 2U13hJla*c* + 2U23k£b*c*)] Standard deviations are given in parentheses; the value for the anisotropic thermal parameters is the mean for the six values. u22 "33 u12 U13 U23 Mean e.s.d. C(l) 331 292 351 30 40 -53 (20) C(2) 386 372 337 - 8 40 -133 (21) C(3) 365 430 304 53 36 -21 (21) C(4) 439 317 359 66 66 19 (21) C(5) 389 280 332 3 69 -47 (20) C(6) 338 • 296 315 3 10 - 4 (19) Cl(7) 529 491 459 -85 -24 -239 (6) Cl(8) 502 346 302 12 -50 13 (6) N(9) 700 274 481 -82 10 -52 (23) N(10) 631 380 439 112 88 67 (22) 0(11) 995 603 514 126 -73 199 (23) 0(12) 1052 293 656 -57 -16 54 (23) B (A2.) H(13) 3*0(9) H(14) 2*0(8) H(15) 5*8(14) H(16) 4*2(11) 48 Table VIII. Measured and calculated structure amplitudes. Measured values with negative sign indicate unobserved reflections. (N.B. 102 reflection, omitted from final calculations and list has |F I 1 o1 = 173«8 and |F | = 223»2) h k i F;bs r-c 0 c 0 4 9 24.6 24 5 -5 14.4 14.5 5 T 17.9 38.9 5 -T 2C.T 19.7 5 9 3.9 3.Z 5 -9 0.0 0.3 5 11 It.9 10.6 1 -8 4,4 3.T 1 13 -1 11 1» -1 14 6 11.1 11.0 B 6.9 8.J 8 6.1 6.1 I 15.T 35.8 1 17.3 17 2 IB.5 IB 4 18.4 18 0 -1.6 1.6 0 -2.4 0.9 2 -2.1 3.3 2 15.3 14.5 t 57.5 5T.8 0 0 0 c c 0 6 17.9 18 B 13.5 \Z 0 13.5 14 Z 5.0 5 1 45.8 47 3 21.T 21 14 -14 '. 14 14 . -1 14 I 6.9 5.6 1 14.8 14.5 3 31.6 31.4 5 6.8 6.0 5 12.8 12.5 7 10.9 10.9 0 0 0 0 C 0 0 0 1 0 0 I 1* 29 12 35 IT 4 3 I e 9 7 3 6 6 0 12.6 12.6 6 2 34. 9 33.3 b -2 27.1 28.3 6 4 11.2 9.8 6 -4 28.9 Ze.T 1 7C8 78.1 3 6.9 6.8 3 (.3 9.0 5 48.0 4B.B 5 13.9 14.5 7 11.5 12.3 0 0 5 6. T 6 7 22.9 22 9 13.3 12 1 1. 7 3 2 10.9 10 4 9.3 a 6 14.1 13 8 11.3 11 0 2.4 Z 2 9.9 9 1 13.4 IZ 1 5 3.3 52 9 0 a a B 1 14 -14 -I 15 I 19 1 15 -1 15 7 -3.0 2.6 9 13.5 14.1 0 25. 1 29.3 2 19.9 18.9 2 13.5 13.4 4 5.4 5.1 c c c 0 0 0 1 1 11 35 29 44 T 1 2 6 7 5 6 6 IT.7 IT.6 6 -6 25.0 24.5 6 8 -2.0 0.8 6 -B 4.2 3.6 « 10 5.2 4.5 6 -10 12.5 12.4 T 4B.4 *T.l 9 16.6 18.0 9 21. 5 21.1 1 9.1 9.1 1 16.4 16.4 1 4.1 4.0 3 6 i 6 I 15 -1 15 1 15 -15 -i 16 4 9.1 3.B 6 3.2 2.6 6 15.6 16.3 8 13.5 13.a 1 5.9 4.5 1 0.0 1.7 0 0 0 0 0 a * 7 ze 11 n 0 T 4 7 1 29 8 12 7 12 3 8 4 2 4 8 2 1 a c 0 0 6 12 4.4 5.0 6 -12 6.0 5.B 7 1 U.J 16.1 T -1 43.3 43.J 7 3 3 1. T 30.0 T -3 50.3 5C.3 0 70.1 70.6 2 «1.0 64.2 2 51.t 50.9 4 21.8 21.B 4 18.6 19.1 6 5.Z 5.6 0 0 0 0 c 5 26.6 26 T 20.1 20 9 7.5 7 1 4.6 4 2 6.5 5 4 -1.4 0 0 16 16 -16 -1 16 1 16 -3 6.1 5.7 3 IT.9 17.6 5 B.b B.l 5 6.6 5.T 7 6.2 6.5 7 9.6 9.9 0 0 0 0 0 s zc 12 52 14 C 13 A 6 9 21 3 33 9 54 C 13 0 5 0 9 T -5 12.5 12*3 7 7 32.0 32.8 7 -7 19.2 18.9 T S 18.4 19.2 7 -9 7.3 7.5 8 25.5 25.9 8 25.0 24.3 0 26.T 21.8 0 Zt.l 28.6 2 1.2 1.2 c 0 0 1 C 1 1 1 1 D 3 6 11.1 11 8 7.8 8 0 11.7 11 31.0 31 3 26.0 26 5 20.1 ZD 1 |T 1 17 I IT -1 IT 1 17 -1 IT 1 17 -1 IB 1 IB -1 18 I 18 -I 18 -0 12.6 12.2 2 17.0 16.7 2 -2.1 1.9 4 5.a 5.4 4 7.9 B.B 6 5.) 5.4 6 4.9 4.9 1 -2.7 0.6 1 6.3 6.5 3 "J.S 9.7 1 14.0 14.4 5 16.2 17.3 c 0 0 0 0 0 11 -0 12 31 7C 3 10 9 0 ft 13 6 4^ n 34 2 76 7 3 J 8 3 1 ' -11 -2.*J 2.3 B 0 4.6 2.1 8 2 38.0 35.7 8 -2 IC. 1 9.8 8 4 19.6 20.1 1 10.2 9.4 1 40.0 39.8 3 16.Z 15.5 3 25.3 25-8 5 31.8 14.0 a i 0 1 0 1 0 1 0 1 0 1 3 3 5 1 7 12.9 12 9 13.1 12 1 4.6 4 2 23.8 23 4 11.6 11 6 7.4 7 6 6 0 0 0 0 0 c 27 n 16 11 w *c 4 26 1 20 2 16 C 10 9 49 3 47 a 6 6 8 6 22.3 21.7 8 -6 19.3 19.1 8 8 -2.8 0.6 5 25.0 25.2 T 2B.4 29.6 T 3.6 1.7 9 24.5 26.2 9 -2.6 4.4 1 7.8 8.6 e i 0 1 C 1 C 1 0 1 0 1 B -2C.3 ZI 0 4.0 3 1Z.1 12 1 0.0 0 5 3.0 2 T 5.7 5 0 0 7 2 B -8 3.2 1.6 8 10 T.8 8.4 1 19 1 19 1 19 -3 0 3 0 3 0 ? P -0 3.5 2.9 2 7.1 B.l Z 13.4 13.6 0 25-1 Z4.9 2 17.0 17.9 2 12.5 12.6 4 -1.7 0.7 4 28.4 29.9 c 0 c 0 0 0 IT 41 5) 1 4 9 IT 9 42 1 6 * 61 3 11 1 5 0 B - 1U IL. • 1L.3 9 1 11.7 11.1 9 -1 3.1 2.Z 9 3 46.8 46.7 9 -3 5.9 5-0 9 5 17.6 16.9 0 16.1 16.4 2 60.1 tO.l 2 7.8 7.0 4 5.6 5.7 4 19.2 19.6 C 1 0 1 0 1 0 1 C 1 a i 9 7.8 7 2 31.9 32. 4 4.3 3 6 15.1 15 8 3.6 3 1 3.2 2 Z 1 2 6 0 c 0 c 0 19 1* 5 Tl 0 38 0 1 5 19 5 4 2 4 5 78 1 0 9 9 9 -5 19.6 IS.8 9 7 11.B 11.5 9 -7 4.4 3.3 9 9 8.Q 8.4 9 -9 11.8 11.6 9 11 15.4 16.2 9 -11 12.3 11.9 0 0 16.1 15.r 0 2 1C.3 s.a 0 -2 1 1.6 11.4 0 4 21.S 2C.9 D -4 B.C T.4 6 8. 0 7.9 6 15.6 15.4 8 27.1 28.7 8 ?t,l 2C.2 0 -1,3 C.8 0 17.7 17.) 2 6.5 6.1 2 -2.0 1.8 1 14.1 13.8 1 6.3 6.1 1 2Z.S 22.3 3 12.0 62-4 3 0 6 12.6 12.8 6 4.9 4.6 B 20.0 20.1 8 -2.9 2.4 1 12.5 12.4 7.1 7.4 C 1 C 1 C 1 C 1 0 1 0 I Z5.5 25 3 10.8 11 5 6.0 6 T 9,9 t 9 7.9 T 13.8 14 1 2 3 5 J 0 0 0 0 c 0 0 0 c 1 1*1 12 z* 39 11 r>2 Z5 3 3 7 5 3 1 18 8 12 7 21 3 19 2 12 2 52 2 25 1 33 B 9 3 6 1 5 7 1 2 T 3 18.4 18.4 3 8.3 fi.3 3 11.0 11.5 5 12.7 12.4 6.0 6,3 7 ICH 10.3 C 1 0 1 0 1 ' C 1 0 1 C 1 4 -Z.2 Z. t> B.4 8 8 11.5 11 7.5 8 10.1 9 5 11.7 13 5 2 3 0 -6 3.6 2.1 0 8 CC 0.2 0 -8 21.2 21.3 0 10 9.4 5.9 0 -10 12.6 12.3 5 4).6 45.Z T 17,8 18.) T 17.1 16.8 9 14.4 14.8 9 -Z.4 1.2 9 -l.T 0.8 J 20.3 19.6 2 6.9 6.3 2 10.0 10.B 17.B 17.8 4 ?C7 21.7 C 1 0 1 a i C 1 C 1 7 3.9 3 -1.3 0 4 12.) IZ. b 10.) 10 4.3 4 3 11.0 11. 5 c c c 0 D 2T 19 3* 2* 9 6 27 9 35 7 29 1 a 8 9 0 B 2 1 -I 12.B 12*.7 1 3 1B.Z 17.7 I -3 -1.4 2.3 1 5 6. 8 5.4 I -5 12.3 12.5 1 5.9 5.T 1 Z0.9 20.4 0 Z2.5 21,9 2 33.9 33.2 2 46.4 46.4 4 5.1 3.8 1 ).S 2.1 5 -2.6 1.3 1 f.3 6.2 0.0 1.) IZ.9 12.2 3.4 3.1 C I 5 -*• 4. 1 3 * 5.3 5. 3 101.7 1G6 10.0 9 4 14.5 14 4 5.5 5 6 Z4.2 25 b 45.2 44 B 40.9 42 8 6. Z 5 5 a 0 2 6 5 2 C 1 0 1 C 1 0 1 0 1 5... 1 IS 2 It 26 5 IB 2 I* 2 C 1 21 9 26 8 * 6 a 8 7 1 T 5.1 5.1 1 -7 B. 0 7.9 I 9 5.0 4.8 1 -9 4.0 0.9 2 0 27. 2 26.9 2 2 0.0 0.7 4 13,4 13.6 6 21.9 21.6 6 t.4 7.4 8 12,5 12.7 8 16.1 15.5 C 5.1 5.0 6.2 5.) -2.5 0.4 2 8.5 Z9.4 Z5.2 26.1 CO l.B T.J 6,1 0 1 e i C 1 o i o i C 1 « 20 21 I S 2 6 T 20 3 20 8 B 1 I 1 5 a 7 3 0 0 0 -2 -2 15.9 15.8 2 4 3.6 C.4 2 -4 5.5 4.7 Z 6 11.9 11.9 2 -fc -2.8 1.9 2 8 17.0 17.2 0 25.5 25 .0 2 3.C 0.7 1 5Z.0 50.) 1 9.) 4.8 3 15.4 14,1 3 9.2 8,4 -2.2 1.5 5.8 4.1 25.Z 24.2 15.B 15.2 2 5.B 2b.2 16.6 IT.2 14.4 14.0 19.1 19.fl -2.1 1.0 5.1 5.7 21.1 19.8 22. 8 23.0 0 -I 0 1 } 16.0 16 3 7.8 T 2 -2.5 2 9.9 10 30.1 10. 1 B.9 9 6 5 5 1 8 -ft 8 -C 1 0 1 0 1 O 1 C 1 C 1 2<i 10 15 S 2L l< T 29 9 30 1 15 8 S 2 21 5 IT 1 2 0_ 2 3 5 2~ ) 9 3 -1 2 -10 8.9 8.1 3 1 12.2 1Z.1 i -1 25.Z 24.9 3 3 6.5 6.2 1 -3 11.3 10.7 e 8 -8 5 32.2 31.4 7 3.1 3.8 7 15.6 15.6 9 6.5 6.2 9 26.) 25.6 3 31.9 3) 3 22.1 22 5 26.8 26 5 25.1 24 T -2.3 1 7 5.9 5 5 1 1 O 1 C 1 0 1 0 1 C I 9 I *2 7 IC 11 13 5 32 6 7 7 10 3 -5 CO Cl 3 7 18.2 17.8 3 -T -2.5 CO ) 9 3.5 3.4 ) -9 5.2 6.0 a -i 9 9 7.0 6.9 3 IB.9 1B.0 2 20.) 19,1 2 13.2 12.9 13.T 13.0 3.5 2.4 12.1 11.9 3.5 5.9 0.0 2.1 5.) 5.4 5 0 9 8 I 3 :| 9 -2.9 1 9 18.7 17 1 1Z.5 12 3.3 2 3 '-2.6 C. 0 18.2 3T 5 6 2 0 I C 1 0 1 0 1 p 1 C 1 -0 22 IC 11 12 4 2 19.7 19.9 4 -2 17.3 lb.9 4 4 14.6 14.2 4 -4 -l.fl 0.7 4 6 1.5 3.0 9 9 -9 -9 1 4 3.2 3.8 b 15.5 15.9 1, 9,4 9.6 B 7.1 6.7 22.9 23.1 6.9 B.l ; -7.7 7.5 -2.8 z'.S 6.9 6.7 -2.5 0.3 0.0 0,4 3 11 * '1 2 20.6 20 4 21.4 12 4 11.4 13 ft 2:8 l h 22.6 22 A 2 2 0 I C 1 0 1 C 1 C 1 0 1 2 -C 7* I * 5 T 6 0 1 15 4 28 a 9 a Z_ 2 1 5 5 a 9 0 0 4 8 16.5 17.5 4 -8 3.9 3.8 5 1 2 9.1 28.6 5 -1 3.5 2.0 5 3 11.8 11.3 10 10 -10 10 -10 3fl.4 37.9 56.9 56.4 «. ) 8.4 6.2 6.0 5 F.4 8.2 ;: 4.5 4.1 7.2 6.4 5.2 5.4 1C.2 10.4 >1.) 20.7 -2.0 3.5 B 20.Z 20 B 1C.2 10 1 11.3 10 ? 1C.4 9 2 10.Z 10 I 0 6 0 C 1 C 1 0 1 0 1 0 1 0 1 C I C 1 C 1 C 2 c c 2C 1 ) ) 3 17 3 9 -I lb a )8 5 2C 5 IJ 9 4 6 5 2 17 8 0 2 3 5 1 5 11.8 12.2 5 -5 16.2 16.5 7 7.a 8.1 -7 4.6 4.4 b a *.5 e.i b 2 19.1 19.1 h -2 T.9 8.1 5 4 11.4 11.0 b -4 4.1 4.1 6 6 -1.9 1.2 b -6 14.J 15.1 10 10 -10 10 -10 - t -11 11 -11 -2.2 1.2 -2.8 2.2 T 25.0 Z6.0 25.1 26.1 21.8 21.a 14.2 13.4 12.) 12.0 16.6 lb.) 8.8 T.b 3C.6 30.1 49.0 51.0 ! -9.0 9.a 1.6 3.1 •C.I 3.1 9.Z 9.1 4.1 6.0 10.5 10.5 i i:.z 14 1 19.8 19 3 51.9 51 3 7.0 7 5 -1.7 0 5 13.Z 13 1 9 2 1 5 • * IT.O 15.7 11.0 11.4 14.9 14.1 10.1 10.Z 1).9 13.a 10.2 10.7 3 a 6 a 7 14.5 14 7 IT.Z 16 9 3.0 8 9 -2.5 2 1 16.0 16 1 4.2 3 2 7 5 Z o (1 c c 0 c 1 1 17 1 3 11 34 22 7 6 T 2 0 5 3 3 2 6 8 J -1 ll.C 13.C 3 3,2 Z.8 -3 6.7 6.B 5 CO 0.0 -5 T.4 7.6 11 -11 1 11-1 12 -3.2 2.2 13.3 12.9 "3.7 3.1 -1.4 0.3 -1.8 0.5 ! -8.4 8.4 7.3 7.7 2).5 Z3.0 14.6 1».B 13.3 12.8 0 9.9 S 2 36.8 3T 2 4.7 3 4 2 7. B 28 6 19.3 19 5 a l 0 0 e 0 c • 1 2 1 46 7 0 1 5 0 2 1 8 a 9 5 1 1 Z 4.2 4. a -2 9.9 9.7 4 6.2 5.9 -4 CO 0.6 1 4.3 4.1 12 12 -12 12 -12 6. a 6.5 14.0 U.9 B. 7 8.2 5.6 5.1 0.0 1.6 10.4 11.1 5.C 5.2 -2.1 0.9 a.6 9,i 5.1 3.3 6 3C.5 30 8 4.2 4 8 5.4 4 0 8. 7 8 0 6.9 7 2 IB.5 19 Z 4 1 19.1 ia 1 5 3.4 54 3 14.1 13 3 -1.7 0 5 I 1 7 C 2 3 c 0 c 0 0 0 I 1 26 If 32 H •3 0 T 7 8" 1 4 0 16.4 16.4 2 11.7 12.7 -2 (2.7 89.2 4 44.6 47.2 1 -4 25.1 24.8 6 36.9 "9.0 -6 30.8 10.7 8 7.6 7.1 12 12 -11 .1 13 -1 3 —z±z± l.-L--2.0 2.1 3.2 1.6 15.9 15.6 ".0 T.4 4.9 4.) 24.1 24.2 -: •1.6 0.9 6.2 5.9 0.0 1.9 t.b 9.1 3.2 I.? c t 11 IT 9 7 0 11 " 1 3 34.4 35.9.0 8.3 a to.a ii.) 13.4 14.0 20.6 16.0 I). 5 50 Table IX. Bond lengths and valency angles. o (a) Bond distances (in A.). For bonds not involving a hydrogen atom, a = 0*004 - 0*006; for C-H bonds, a = 0*04; for N-H bonds, a = 0*05 A. Bond length Bond length Atoms Uncorr. Corr.* Atoms Uncorr. Corr.* CCD - c(2) 1-405 1*408 C(4) - N(10) 1*456 1*466 c(i) - c(6) 1*417 1*420 C(5) -C(6) 1*368 1*371 C(l) - N(9) 1*339 1*358 C(5) -H(14j 0*98 C(2) - C(3) 1*371 1*374 C(6) -Cl(8) 1*736 1*743 C(2) - Cl(7) 1*731 1*743 N(9) -H(15) 0*91 C(3) - C(4) 1*372 1*375 N(9) - H(16) 0*86 C(3) - H(13) 0*94 N(10) - 0(11) 1*227 1*257 C(4) - C(5) 1*381 1*384 N(10) - 0(12) 1*231 1*256 Bond lengths corrected for thermal motion. (b) Valence angles (in degrees). In angles involving (i) no hydrogen atoms a = 0*35, (ii) a ring hydrogen, a = 2*3, (iii) one amino hydrogen, a — 3*3, (iv) two amino hydrogens, a = 4*6°. i j k Angle (ijk) i j k Angle Cijk) C(2) - C(l) - C(6) 115*2 C(4) - C(5) - C(6) 118*3 C(2) - C(l) - N(9) 123*1 C(4) - C(5) -H(14) 123 C(6) - C(l) - N(9) 121*7 C(6) - C(5) - H(14) 118 C(l) - C(2) - C(3) 123*0 C(l) - C(6) - C(5) 122*9 C(l) - C(2) - Cl(7) 117*4 C(l) - C(6) - Cl(8) 117*7 C(3) - C(2) - Cl(7) 119*6 C(5) - C(6) - Cl(8) 119*5 C(2) - C(3) - C(4) 118*6 C(l) - N(9) - H(15) 122 C(2) - C(3) - H(13) 122 C(l) - N(9) -H(16) 116 C(4) - C(3) - H(13) 119 H(15) - N(9) - H(16) 122. C(3) - C(4) - C(5) 122*0 C(4) - N(10) - 0(11) 118*4 C(3) - C(4) - N(10) 120*2 C(4) - N(10) - 0(12) 118*1 C(5) - C(4) - N(10) 117*8 0(11) - N(10) - 0(12) 123*4 Figure 4. Molecular dimensions, (a) bond lengths, hydrogen-bond distances, and some shorter intermolecular interactions, and (b) valency angles. 52 in the plane of the benzene ring and the correction to the OC ring distances is 0*003 X.20 As can be seen from Figure 5., the shortest principal axis of the ellipsoid of each of the atoms Cl(7), 01(8), N(9), N(10), 0(11) and 0(12) is directed approximately along the bond connecting the atom to the centre of the molecule, and the component of vibration in the direction of the bond is approximately equal to that of the atom at the other end of the bond. There is considerably more vibration perpendicular to these bonds. This indicates that an appropriate model for the determination of thermal motion corrections to the bonds is the riding model of Busing and Levy21. The standard deviations in Table IX are for the uncorrected dimensions, and they indicate the precision in the determination of the centres of the scattering masses. Since the model for the estimation of thermal motion corrections is an approximation, the accuracy of the corrected bond lengths must be assumed to be less than that of the uncorrected values, and the standard deviations are probably of the order of twice those quoted for the uncorrected values. The equations of several atomic planes, and the angles between the planes are given in Table X. The distances and angles in the hydrogen-bonding systems of 2,6-dichloro-4-nitroaniline are given in Table XI. Figure 5. The thermal ellipsoids of the non-hydrogen atoms projected on to the plane of the benzene ring. 54 Table X. Mean planes. (a) Equations of mean planes, given in the form: AX' + mY' + nZ1 = p where X', Y» and Z1 are coordinates in A., referred to the orthogonal axes a, b and c*. Plane no. Plane £ m n P 1. Benzene ring -0-9265 0-1030 0-3618 0-3890 2. C-nitro group -0-8722 0-1499 0-4655 1-1545 3. Amino group -0-9615 0-1266 0-2440 -0-0405 4. C-amino group -0-9617 0-0619 0-2670 -0-2564 5. Bifurcated H-bond -0-9322 0-0336 0-3604 0-0321 (b) Angles between the planes: Plane q r Angle (qr) 1 2 7-2° 1 3 7-2 1 4 6-3 2 4 13-5 (c) Displacements from the planes; those underlined are the atoms used in calculating the equations of the plane. Atom Plane no. 1 2 3 4 5 CCD 0 003 -0-093 -0-000 C(?) -0 006 C(3) 0< 002 C(4) .• 0 004 0-001 C(5) -0- 005 C(6) . 0-002 Cl(7) -0- 001 0 Cl(8) -0< 010 N(9) 0-012 0 0-001 0 N(10) 0-017 -0-003 0(11) -0« 107 0-001 0(12) 0-165 0-001 Ot H(13) 0-037 H(14) 0-066 H(15) -0- 102 0 -0-032 H(16) 0« 072 0 -0-026 0-016 t Actually 0(12) of a neighbouring molecule, coordinates (1-x, y-%, %-z). 55 Table XI. Hydrogen bond distances and angles; standard deviations in parentheses. Atoms s t u V Distances CX.) Angles C°) su tu stu tuv N(9) - H(15).. .Cl(8) - C(6) 2-953C4) 2-56(5) 107(4) 71-6(12) N(9) - H(16).. •Cl(7) - C(2) 2-963(4) 2-52(5) 113C4) 70-0(11) N(9) - H(16).. .0(12) >- N(10) ' 3-004(5) 2-24(5) 148(4) 119-9(12) D. DISCUSSION. The plane of the benzene ring of the molecule of 2,6-dichloro-4~ nitroaniline lies inclined at 26-1° to the (100) plane. The chlorine atoms o are displaced 0-001 and 0-010 A. from the benzene ring plane, and the substituted amino and nitro groups are rotated by small angles, 6-3 and 7-2° respectively, out of coplanarity with the benzene ring. Table XII contains a comparison of bond lengths and angles in molecules similar to 2,6-dichloro-4-nitroaniline. For the benzene ring C-C distances, an average value is given for equal pairs of bonds; the maximum discrepancy of any of the recorded bond lengths from their mean value is 1-2 a. The precision of the final coordinates in these examples varies widely, but many similarities in the results can be seen. In the results for 2,6-dichloro-4-nitroaniline, there is a definite shortening and lengthening of the C-C bonds in the benzene ring; the angles at C(l) and C(4) are significantly different from 120° - smaller at the amino C(l) and larger at the nitro C(4); the C-N bonds both differ from the sum of o single-bond covalent radii, 1-47 A. But all these results agree well with those of similar compounds. The two principal factors affecting bond lengths and angles in Table XII. Nitroaniline derivatives and related compounds. Compound C-Nai dist Uncd. nino mce Corr.+ Meai Cj-C2, Uncd. 1 of Corr. Meai c2-c3, Uncd. 1 of Corr. Meai c3-c^, Uncd. 1 of c„-c5 Corr. C-Nn dist Uhcd. tro mce Corr. Mean °L * Ring angle at q Ring angle at Ck Mean o * A Rotn. ang.of C-NH2 Rotn. ang.of C-N02 c-dist Uncd. :i ance Corr. Ref. 2,6-dichloro-4-nitroaniline 1 339 1-358 1 411 1-414 1 369 1 372 1 377 1-380 1 456 1-466 0-005 115-2 122-0 0-4 6-3 7-2 1 733 1-743 This work p-nitroaniline 1 353 1-371 1 409 1-412 1 372 1 375 1 389 1-392 1 454 1-460 0-007 118-9 121-2 0-4 16 1-9 - - 22. 2,5-dichloroaniline 1 395 1-407 1 405 1-411 1 367 1 374 1 379 1-389 - - 0-017 117-8 - 1-1 ? - 1 737 1-744 23. 2-chloro-4-nitroaniline 1 382 1-386 1 407 1-412 1 393 1 398 1 394 1-399 1 466 1-471 0-013 116-7 122-9 1-1 M> ? 4-3 1 760 1-766 24. N,N-dimethyl-4-nitroaniline 1 352 1-358 1 432 1-435 1 372 1 375 1 397 1-400 1 400 1-405 0-019 117-1 121-0 1-2 7-3 5 2-8 - - 25. 2,6-dichloro-4-nitro-N,N-dimethylaniline 1 40 - 1 39 - 1 38 - 1 38 - 1 44 - 0-01 120 123 2 60-5 5 6 1 •72 - 26. nitrobenzene (at -30°C.) - - 1 363 - 1 426 - 1 367 - 1 486 - 0-014 - 125 - - 0 - - 27. p-nitrophenol (at 90°K.) - - 1 390 - 1 379 - 1 385 - 1 442 - 0-006 - 122-3 0-4 - 1-5 - - 28. l-(dinitro-2',4'-phenyl)-4-chloro-pyrazole 1 390 - 1 392 - 1 390 - 1 1 375 393 - 1 1 470 482 - 0-012 118-0 123-2 122-1 0-6 21-6 2-3 65-3 - - 29. 1-(trans-bicyclo[4.2.0]-octyl) 3,5-dinitrobenzoate - - - - 1 377 1 1 380 372 - 1 1 474 •489 - 0-004 - 122-8 122-6 0-2 - 1-4 4-3 - - 30. Bond distances are in A., angles in degrees. t bond lengths corrected for thermal motion. t Rotation angle of C-NMe2 group. * a - mean e.s.d. of bonds quoted involving C and N atoms, (N.B. o for uncorrected values). cr^ - mean e.s.d. of ring angles quoted. The compounds are numbered as derivatives of p-nitroaniline: i.e. the nitro group is always at C,,. In the last two compounds, each nitro group is considered, in turn, as being at C^. NO, benzene derivatives are resonance and hybridisation. The latter effect, in particular the non-equivalent or second-order hybridisation theories of Coulson 31, Trotter 27, Bent 32 and Carter, McPhail and Sim 33, have helped to explain many of the benzene ring distortions, especially the bond lengths and angles adjacent to a substituent group. The theories of ir-electron resonance can explain shortening of bonds in molecules capable of conjugation; in benzene derivatives, it is, of course, necessary for the substituent groups to be coplanar (or very nearly so) with the benzene ring if excited, resonance structures are to make any contribution to the overall structure. In molecules of type I, there are often several excited, resonance NH-, +NH, +0H + NH I II III IV forms possible, and it was concluded by Trueblood, Goldish and Donohue 22 that the quinoidal structure II has considerable importance in the overall structure of p-nitroaniline. The p-nitrophenol results 28 show that, similarly, structure III has importance. Our present study of 2,6-dichloro-4-nitroaniline shows the same characteristics, and an important contributor to the overall structure must be form IV. In these compounds, the C-N .. ^ ' nitro and C(2)-C(3) bonds are shorter than in nitrobenzene, and it is thus con cluded that the introduction of an electron-donating substituent in the para position to the nitro group does enhance the formation of excited, resonance forms as II - IV, and does shorten the c-Nn^tro bond slightly, and the C(2)-C(3) bond considerably. The C(l)-N(9) bond in 2,6-dichloro-4-nitroaniline is similar to 58 other C-N . bonds and considerably shorter than the C-N . distances, ammo ' nitro o It is, at 1*358 A. (amongst the shortest of recorded C-N . bonds), slight! ammo '' 5 shorter than that in p-nitroaniline. This is perhaps a result of the more coplanar amino group in our example, allowing increased ease of formation of the resonance structure IV. \ The benzene ring C-C distances in these two compounds are similar, and the shortening of the two bonds, C(2)-C(3) and C(5)-C(6) can be explained by the resonance theories above. The two other pairs of bonds - which the resonance theories say should be similar in length - are influenced more by "non-equivalent" hybridisation; for an atom using hybr-idised orbitals for bonding,the s-character of an atomic orbital is more concentrated in orbitals the atom uses towards electropositive substituents, and these bonds with more s-character are shorter and stronger than strictly equivalent hybridised bonds. Thus the nitro group, strongly electronegative, tends to attract the more diffuse 2p orbitals of the C(4) atom and the resulting hybridised bond ing orbital has less s-character, giving a long C-N bond; the adjacent ring C-C bonds have correspondingly more s-character, i.e. are shorter (i.e. opposing the resonance effect), with a ring angle of more than 120°. The less electronegative amine group at C(l) shows the opposite effect - a shortened C-N bond, longer ring C-C bonds and a ring angle of less than 120°. The electronegative effects of the two chlorine atoms ortho to the amine group will tend to shorten the ring C-C bonds adjacent to the C-Cl groups, i.e. opposing the amino group's effect on the C(l)-C(2) and C(l)-C(6) bonds, and enhancing the resonance effects on the C(2)-C(3) and C(5)-C(6) bonds; the ring angles at C(2) and C(6) are, as at C(4), greater than 120°. These resonance and hybridisation effects are found in most of the compounds of Table XII. Those molecules in which conjugation does not or cannot occur to any significant extent, e.g. nitrobenzene, 2,6-dichloro-4-nitro-N,N-dimethylaniline (in which the ~NMe2 group is rotated through 61° from coplanarity with the benzene ring), the pyrazole example (where the angle of rotation is 21'6°) and the dinitrobenzoate, have C-N . distances ammo o o of approximately 1*40 A., adjacent C-C(-N . ) distances of ^1*40 A., J ammo ' o o c"Nnitro distances between 1*44 and 1*49 A. (but mainly ^1*48 A.), and o adjacent C-C("Nni-tro^ distances of ^-1*38 A. The possibility of conjugation, as in p-nitrophenol, p-nitroaniline, 2,6-dichloro-4-nitroaniline, etc., adjusts the C-N^^ length to ^1*36 A. and the other bond lengths less markedly; significant differences can be observed only in the more accurate structure determinations. The ring angles at C-N . and C-N .... are ° ammo nitro approximately 117 and 122° respectively for all the examples. The C-H, N-H and C-Cl bond distances in 2,6-dichloro-4-nitroaniline all appear to be normal, within experimental error. Similarly, in the nitro o group, the N-0 distances of 1-257 A. and the O-N-O angle, 123*4°, are normal o and similar to those in p-nitroaniline (1*247 A. and 123*3 respectively). A summary showing how various bonds and angles in 2,6-dichloro-4-nitroaniline are affected by the resonance and hybridisation effects is given in Table XIII. In Table X, planes nos. 3 and 4 describe the C-NH2 group, showing it to be planar within the accuracy of the measurement of the hydrogen atom coordinates. This amino group should be approximately coplanar with the benzene ring if it is to be allowed to contribute to the formation of resonance structures; it is, in fact, 6*3° out of coplanarity with the benzene o ring plane. Hence the amino hydrogen atoms are only 2*56 and 2*52 A. (a = o 0*05 A.) from the neighbouring chlorine atoms. It seems likely, therefore, that there is intramolecular hydrogen bonding between H(15) and C*l(8), and H(16) and Cl(7); if.there was to be no bonding between the hydrogen and chlorine atoms, the amino group would have to be rotated much further about o the C(l)-N(9) bond so that the C1...H distances were approximately 3*0 A., Table XIII. Summary of the effects of resonance and hybridisation on normal benzene • ring,' C-N', and C-Cl dimensions in 2,6-dichloro-4-nitroaniline. ^-^amino bond C1-C2 Ci-c6 C2-C3 c5-c6 C3-Ci+ C_Nnitro C-Cl Ring angle at C! Ring angles at C2,C6 Ring angle at C4 Resonance shorten lengthen shorten lengthen shorten - - - -Hybridisation at C-NO - - - shorten lengthen - - - increase 11 " C-NH shorten lengthen - - - - decrease - -11 " C-Cl - shorten shorten - lengthen - increase -"Normal" dimensions 2,6-dichloro-4-nitro-aniline 1-475 * 1-358 1-395 + 1-411 1-395 + 1-372 1-395 + 1-380 1-475 * 1-466 1-7 * 1-743 120" + 115-2 120° + 122-9 120° + 122-0 The "normal" dimensions are taken from: * empirical sum of covalent radii, with allowances for differences in electronegativities, t dimensions of the benzene ring in benzene. 61 the sum of van der Waals' radii. Additional evidence, indicating that this short H...C1 distance is a hydrogen bond, is found in the angles at the C(2) and C(6) atoms; the chlorine atoms appear to be pulled slightly towards the amino group, rather than being pushed away by merely steric interactions. Any possible inter molecular interactions of the chlorine atoms, e.g. Cl(7)...Cl (8)', Cl(7)... H(15)', Cl(8)...Cl(7)•, and Cl(8)..,H(14)', would tend to push the chlorine atoms away from the amino group. The formation of a hydrogen bond, however, has the reverse, stronger effect. A similar type of intramolecular hydrogen bond has been noted for o-chlorophenol and other o-substituted phenols and anilines, etc. 31f; the evidence was found in spectroscopic studies, in particular in the 0-H and N-H stretching frequencies. Pimentel and McClellan 35 note that five-membered rings containing an intramolecular hydrogen bond are common and will normally be formed when two adjacent positions of a benzene ring have the proper substituents. The hydrogen atom, H(16), is also hydrogen-bonded to an oxygen atom, 0(12)', of a neighbouring molecule. Thus, H(16) is involved in a bifurcated hydrogen bond system - it is bonded intramolecularly with Cl(7), o and intermolecularly with 0(12)'; the hydrogen atom is located only 0*02 A. out of the plane through N(9), Cl(7) and 0(12)'. The angles at H(16) - 148, 113 and 98° - are similar in range to those of several examples of bifurcated hydrogen bonds, e.g;-those quoted by Parthasarathy 36, particularly the examples in glycylglycine hydrochloride monohydrate 36. The nitro group is rotated through 7.2° from coplanarity with the benzene ring; this rotation brings the 0(12) atom closer to the H(16)' atom of a neighbouring molecule, and allows the formation of the hydrogen bond 0(12)...H(16)' described above, connecting the molecules in long chains parallel to the b-axis. This is illustrated in Figure 6., which shows the 63 molecular packing arrangement in the crystal, looking down the very short a. axis. There are no other very short intermolecular distances; a list of the shorter distances is given in Table XIV. The Cl(7)...Cl(8)1 distance o of 3*40 A. is somewhat shorter than the sum of van der Waals' radii, but appears to correspond well with the C1...C1 distances in similar compounds, e.g. those quoted by Sakurai, Sundaralingam and Jeffrey 23. The C(2)-C1(7)...Cl(8)' angle is 164*0°, and this is also within the normal range for this type of interaction, but the angle at the other chlorine atom, i.e. C(6)-C1(8)...Cl(7)* is quite different, at 128*6°. Table XIV. Shorter intermolecular distances. Cl(7)r ..Cl(8)n 3*40 A. o(ii)r ..H(13)jJJ, 2*77 C1(7)T. ..H(15)n, 2*92 0(ll)r ..H(13)JJJ,, 2*85 Cl(8)r ..H(14)m: 2*84 0(12)r ..H(16)IV, 2*24 N(9)r. ..0(12)iv 3*00 * * Involved in a hydrogen bond. The Roman numerals refer to symmetry related molecules: I. x, y, z. II. x-i, h-y, z-h; II1.' x, h-y, z-%. III. 2-x, 1-y, 1-z; III'. 1-x, 1-y, . -z; III". -x, 1-y, -z. IV. 1-x, y-%, %-z; IV. 1-x, %+y, h-z. 64 Twinning. It will be observed from Figure 6. that the a-b plane seems sparsely populated - only the two Cl(8) atoms are close to this plane. This sparseness led to a consideration of the twinning in this crystal. In a monoclinic crystal, there are two possible ways in which the twins may be related 5^ -either by a twin axis or a twin-plane. The preliminary photographs for 2,6-dichloro-4-nitroaniline indicated that the twin axis would be [100], and the twin plane (001) . Both possibilities were examined here and it was found that only by rotation about the twin axis (followed by a translation along a) could one twin fit reasonably on to the other. The suggested arrangement about the (001) plane is shown in Figure 7., and the shortest estimated intermolecular distances are recorded thereon. To achieve this system of congruent twins, the unit cell of one twin was rotated through 180° about the a. axis and then shifted parallel to a. until the position of Cl(8) at the boundary plane (molecule II') coincides with that of Cl(8) in the original system. In the twinned cell, the y- and z-coordinates of the atoms are the same as those in the original cell. The o Cl(7)jjji atom is also found to be very close (within 0'09 A.) to the position of Cl(7) in the original arrangement. Some of the estimated intermolecular distances seem short, but none impossibly so. Hydrogen bonding probably controls the twinning across this plane, e.g. it seems likely that hydrogen bonds are formed between Cl(7) '' o and H(15) , (2*43 A.), and that there is some kind of hydrogen "liaison" The alternative mode of twinning, the formation of enantiomorphous twins by reflection through the twin plane (001), seems less likely. The and H(13) , (2-33 A.), 0(11). and H(13) III' (2-52 X.),; best arrangement again seemed to have Cl(8) II* on the boundary plane coincid-Figure 7. The suggested arrangement about the boundary plane (001) between the two twins. 66 ent with Cl(8) of the original system, (this involved translations parallel to a and to b), but this resulted in one impossibly short Cl(8)^... o 0(11) (1*67 A.) distance across the twin plane. PART IV. THE STRUCTURE DETERMINATION OF ETHYL 3,5-DINITROBENZOATE. t 68 A. INTRODUCTION. In 1961, Camerman and Trotter 37 recorded the crystallographic data for ethyl 3,5-dinitrobenzoate, but were unable to complete the determination of the structure at that time. A recent reinvestigation into this problem has produced an accurate solution of the molecular structure and is described here. This compound is of interest in that it has two nitro groups with almost identical intramolecular surroundings. The atoms in positions ortho to both the nitro groups are hydrogen atoms so that steric effects on the nitro group are minimal and equal. Hence we now have an opportunity to examine the orientation of the two nitro groups with respect to the benzene ring, and observe the effects of neighbouring molecules on the orientations. The C-N bond lengths and benzene ring dimensions in nitrobenzene compounds, and the relative importances of resonance and hybridisation theories in these compounds, have been discussed for a decade, and it was hoped that the results of this investigation might add some more accurate data for this discussion. B. X-RAY ANALYSIS. . The crystals- of ethyl 3,5-dinitrobenzoate, recrystallised from ethanol, are colourless needles elongated along the b axis and having a well-developed (100) face and lesser (001) face. The crystal selected had dimensions 0*07 * 0*8 x 0*2 mm . and was mounted with the b axis parallel to the <)>-axis of the goniostat. The unit cell dimensions and the space group were determined initially from rotation, Weissenberg and precession films, and the cell dimensions were later found more accurately from a least-squares refinement based on the diffractometer values of 26 for 30 reflections, determined with 69 Cu-K (A = 1-3922 A.) or Cu-K (X = 1«5405 A.) radiation. P «i • Crystal data: Ethyl 3,5-dinitrobenzoate, CgH^Og. M = 240*17. Monoclinic, a = 13*856(4), b = 4*770(1), c = 18*354(5) A., B = 119*59(2)°, (standard deviations in parentheses). V = 1054*75 A3. c Dm = 1*511 (flotation in aqueous KI), Dc = 1*512 g.cm"3. with Z = 4. F(000) = 496. Absorption coefficient, y (Cu-Ka, X = 1*5418 A.) = 11*4 cm"1. Reflections absent:. OkO when k is odd, hOJt when I is odd; hence space group is P21/c. The intensity measurements were made on a Datex-automated G.E. XRD-6 diffractometer with a scintillation counter and a 6-29 scan. Cu-K radiation o (Ni filter and pulse-height analyser) was used. The intensities of 1466 independent reflections with 26 < 120° (i.e. minimum interplanar spacing = o 0*89 A.) were measured. Of these, 166 (i.e. 11*3%) were treated as unobserv ed reflections, having I/aj < 2*0, where I is the corrected intensity count, and a^2 is defined: cjj2 = S + B + (0*02.S)2 where S = scan count, and B = background count over the same scan range. Lorentz and polarisation corrections were applied. No absorption corrections were made. The structure amplitudes were then calculated. C. STRUCTURE ANALYSIS. A Patterson map was drawn from the diffractometer data. Theoret ically, there should have been four outstanding peaks in this map, resulting from the sums of vectors between roughly centred portions of the molecule and their like portions related by a centre of symmetry, e.g. 70 and similarly for the other two C—X groups and for the benzene ring C 0 atoms. This assumes, of course, that the illustrated part of the molecule is approximately planar. A set of four possible peaks was found in the Patterson map, and the coordinates of nine atoms - the six carbons of the benzene ring, and three atoms (each taken as a nitrogen) attached to the ring in the 1,3,5 positions - were estimated, and used in a structure factor calculation and a Fourier synthesis. The resulting electron-density map was not encouraging, and indicated that the set of four chosen peaks was not the correct set. No alternative set of peaks was apparent and another means of approach was required. All the atoms of ethyl 3,5-dinitrobenzoate are light atoms and similar in size (not including the hydrogen atoms). The space group, ?2l/c, is a centrosymmetric one. Therefore the problem was a good candidate for solution by direct methods. Solution by direct methods: Wilson's method 9 was used to scale the structure amplitudes from their measured values to absolute values, and to determine an overall temperature factor for the structure. The structure amplitudes were then converted to the normalised structure amplitudes, |E|'S 7. The scattering factors for oxygen, nitrogen and carbon were taken from International Tables 5C, and for hydrogen from the values of Stewart, Davidson and Simpson *9. The results of the Wilson Plot and the E-statistics for ethyl 3,5-dinitrobenzoate, together with some theoretical values, are recorded in Table XV. There were 169 reflections with |E| > 1*50, and these were used in Table XV. Results from the Wilson Plot, and the E-statistics. Theoretical Observed Centro- Noncentro-symmetric Overall temperature factor 3' 98 Mean |E| 0* 787 0*798 0*886 Mean |E|2 •: 1*022 1*000 1*000 Mean ||E|2 - l| 1*032 0*968 0*736 Percentage of reflections with |E| > 3 1*02 0*30 0*01 " " |E| > 2 5*46 5*00 1*80 ti |E J > 1 27 «42 32*00 37*00 72 Long's program 38 for phase-determination in the centrosymmetric case. This program determines the signs (phases) of the normalised structure factors by applying Sayre's equation 39: s = s . s h h» h-h' where s means "the sign of", and h is the reflection hk£, etc. For this equation to hold, the normalised structure amplitudes of the reflect ions h, h1 and h-h' must all be large. More generally: s ^ s(E E .E ) h \t h» h-h'J where the symbol ^ means "probably equal to". This is known as the E-2 relationship. The probability, P, of the sign s, being correct is given for each n reflection, and is determined from: P = 0*5 + O'S.tanh e3. e2-x h h, h' h-h' • E, • E  ' where ^ is a constant depending on the contents of the unit : E2l cell, and is equal to V^N", where N is the number of atoms in the unit cell. The program prepares a list of reflections for the E-2 relationships, i.e. combinations of h' and h-h' for each reflection h in the input data. One of the eight centres of symmetry in the unit cell is then chosen as the origin by selecting, and arbitrarily assigning positive signs to, three reflections. The selection is made from the reflections with the highest |E|*S and with indices conforming to rules derived from the space group symmetry; here the indices of each reflection, the sums of indices of any pair, and the sum of indices of the three, must have odd-even parities other than (even, even, even). Four more reflections, each having large (E|'S and many E-2 relationships, are then selected and assigned each sign in turn so that there are sixteen (21*) starting sets of signs. The seven starting 73 reflections selected by the program were: h k I |E| 1 1 -4 3'27 0 1 3 3*35 0 2 11 3«65 2 2 -9 3*85 1 4 4 3-41 10 1 -13 3*59 9 0 2 3*41 In each of the sixteen sets, the signs of these seven reflections were not allowed to change. The program predicts the sign of each of the remaining reflections, h, by the application of Sayre's relationship to all the possible combinations of h' and h-h*, using the general equation above. After examining each reflection, and determining the signs of some, the program starts a second cycle, redetermining the signs and determining signs of additional reflections. There are various iteration procedures available in the program; in our case, newly determined signs were not used to deter mine signs of additional reflections until the next cycle. This procedure was continued through several cycles until there were no further changes in the signs of any of the reflections, and no new signs determined. A summary of the results of the sixteen sets of determinations is given in Table XVI. The consistency index, C, is defined as: c = <l'y£.VEh.h'l> where < > means the average over all h. The high consistency index of set no. 1, together with the results that only six cycles of iteration were required to complete the determination of all the signs, and that the numbers of positive and negative structure 74 Table XVI. Comparison of the 16 sets of phases generated by the Phase Determining program. Set no. No. of cycles No. of pluses No. of minuses Consistency, C 1 6 84 85 0*901 2 9 103 66 0*694 3 8 94 75 0*673 4 6 79 90 0-879 5 8 116 53 0*660 6 9 83 86 0*806 7 >12 90 79 0*720 8 11 89 80 0*681 9 9 97 72 0*860 10 9 89 80 0*656 11 7 98 71 0*624 12 7 80 89 0*866 13 7. 85 84 0*702 14 12 87 82 0*757 15 10 68 101 0*774 16 7 91 78 0*682 factors were almost equal, indicated that this set was most probably the correct set of signs. It was shown later that all 169 reflections had been assigned the correct signs. The normalised structure factors, with the phases of set no. 1, were then used in the calculation of an "E-map", a three-dimensional Fourier synthesis. The major part of the molecule of ethyl 3,5-dinitrobenzoate -the benzene ring and the three major substituent groups, -X02, at the 1,3,5 positions - was outstanding in the E-map. These fifteen atoms, with X designated as nitrogen in the three substituent groups, were used to calc ulate an electron-density map, and this showed, roughly, the positions of the ethyl group carbon atoms, and hence distinguished the carboxyl group from the two nitro groups. The structure was refined by full-matrix least-squares methods, 75 with minimisation of the sum EWC|Fq| - lFcl)2> initially with w=l for all reflections. The structure refined rapidly to R = 0*164 for the seventeen non-hydrogen atoms with isotropic temperature factors, and to R = 0*100 when all seventeen atoms were refined anisotropicly. The thermal parameters and the standard deviations of the ethyl group carbon atoms were not satisfactory at this stage, and the C-C bond length was very short. A difference Fourier map, computed to locate the hydrogen atoms, showed the three benzene ring hydrogen atoms clearly at 0*39 - 0*55 eA"3.; and in the region of the ethyl group, there were two major peaks of 0*78 and 0*39 eA"3. The high peak here led to the realisation that the ethyl group was randomly disordered in the crystal, and better refinement results were achieved when two ethyl group orientations were considered with a ratio of populations of 7/3. The occupancy ratio was determined from a consideration of the temperature factors of the ethyl group carbon atoms. If it is assumed that the pairs of carbon atoms, C(16) and C(16'), C(17) and C(17'), are in similar surroundings and are allowed to vibrate to similar extents, then the temper ature factors of the atoms of each pair should be approximately the same. The occupancies were varied until this equivalence was achieved. The presence of hydrogen atoms was not considered in the determination of this ratio. A later difference Fourier map indicated the positions Of the five hydrogen atoms of the major ethyl group. In the last stages of refinement, 15 non-hydrogen atoms (all except the ethyl group carbon atoms) were refined anisotropicly, and the ethyl carbon atoms and all the hydrogen atoms were refined isotropicly. A Hughes-type weighting scheme was. applied to the data, viz. for reflections with |FQ^s| « 10*0, i/w = 1; with . jFobs | > 10*0, /w = 10-0/1FQt)S I; and for unobserved reflections, /w = 0*6. 76 The 013 reflection was omitted from the final calculations since it was suspected of serious extinction errors. The refinement was complete with R = 0*061 for 1299 observed reflections, and 0*068 for all the reflections (except the 013). A list of the structure factors, |Fq| and |Fc|, is given in Table XVII. The final atomic parameters are recorded in Table XVIII, and a view of the molecule is shown in Figure 8. Corrections for thermal motion have been estimated from an examin ation of the thermal ellipsoids of the atoms with nos. 1 - 15, (Figure 9.). There seems to be very little oscillation in the plane of the ring, and this o results in a correction of approximately 0*003 A. to the C-C ring bond lengths 20. The riding model of Busing and Levy 21 appears to be an appropriate model for the determination of corrections to the bond lengths of the nitro groups. Similar corrections have been applied to the carboxyl group, but these results are perhaps not so reliable as for the nitro groups since the ellipsoid of the 0(13) atom is modified by the bonding of that atom to the ethyl group in one of two possible positions. Table XIX shows the bond lengths and valence angles as calculated from the final atomic coordinates, and some bond lengths after correction for thermal motion. : Standard deviations are quoted for the uncorrected values in Table XIX; since the thermal motion corrections were estimated from an approximate model, the final bond lengths probably have less precision than the uncorrected lengths. Figures 10(a). and 10(b). show the estimated final bond lengths and the valence angles. The equations of several planes through the molecule are in Table XX(a); in part (b), the distances of atoms from the benzene ring plane are recorded, and part (c) shows the angles between the normals of the benzene ring plane and the substituent group planes. Table XVII. Measured and calculated structure amplitudes. Measured values with negative sign indicate unobserved reflections. 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C 1 1 -5 3 8 .5 5.4 .0 9.4 .2 a.2 .4 2.2 .7 1.3 7 ? 1 3 * 4 2 11 3 -11 12 11 -1 2 -11 10 11 4 -11 6 5 ' 12. 0 0-5 11. 5 • 4. 5 6, -" 12 . 1 11.3 .7 1.9 .9 4.7 .0 0.3 .4 12.7 .9 3.4 S 5 b T a 2 11 -1 2 -11 5 11 1 2 -tl 1 2 -11 5 -n n 2 0. 8 5. 9 2. 6 5. 4 a. -1 4 .6 3.0 . >> 4.9 .5 2.7 .8 1 .8 .0 8.1 .7 15.7 10 11 12 13 I* 2 -11 6 -11 6 -11 10 7 -11 7 -11 1 ) -11 -1 3 6. 7 6. 7 9. 0 6. 9 1. 1 0. 1 J 1 " 14 26 I 0 .8 14.6 .0 2.2 .6 2.5 .2 26.4 . 1 3.) .2 10.0 1 1 2 13 » 2 13 5 2 -13 n 4 a. 3 5. f 13. Table XVIII. Final atomic parameters. Atomic fractional coordinates, (standard deviations in parentheses) X y z CCD 0< 1902(2) 0-3676(6) 0-1210(2) C(2) 0< 2814(3) 0-5167(6) 0-1794(2) C(3) 0 -2659(2) 0 7092(6) 0-2291(2) C(4) 0 1643(3) 0 7619(6) 0-2222(2) C(5) 0 0758(2) 0 6081(6) 0-1633(2) C(6) 0 0865(3) 0 •4120(6) 0-1128(2) C(7) 0 1995(3) 0 •1549(7) 0-0642(2) N(8) 0 3628(2) 0 •8728(7) 0-2902(2) N(9) -0 0341(2) 0 6555(6) 0-1545(2) 0(10) -0 0452(2) 0 •8580(5) 0-1904(1) 0(11) -0 •1078(2) 0 4906(5) 0-1128(2) 0(12) 0 1227(2) 0 •0269(5) 0-0126(2) 0(13) 0 3022(2) 0 •1242(6) . 0-0815(2) 0(14) 0-4507(2) 0 8324(8) 0-2941(2) 0(15) 0 3488(3) 1 •0433(7) 0-3328(2) C"(16) :• 0 3336(6) -0 1078(15) 0-0429(5) C(16') 0 2986(12) -0< 0303(32) 0-0053(11) C(17) 0" 3401(10) 0-0450(23) -0-0238(6) C(17') - 0-4157(18) -0-0512(51) 0-0290(15) H(18) 0« 158(3) 0< 894(9) 0-261(3) H(19) 0« 028(3) 0-326(7) 0-075(2) H(20) 0« 354(3) 0-488(7) 0-189(2) H(21) 0-277(3) -0' 252(10) 0-022(3) H(22) 0-414(4) -0« 177(11) . 0-071(3) H(23) 0-400(3) 0-152(9) 0-001(2) H(24) 0-369(8) -0-139(20) -0-036(6) H(25) 0 255(6) 0-063(14) -0-064(5) 80 (b) Thermal parameters; anisotropic thermal parameters are in the form: exp [^.lO^Cu^h-V2 + U22k2b*2 +'U33A?c*2 + 2U12hka*b* + 2U13hJla*c* + 2U23k£b*c*)] Ull U22 U33 U12 U13 U23 Mean e.s.d. CCD 513 388 459 4 234 42 (14) C(2) 497 484 539 14 242 53 C16) C(3) 530 458 454 -63 176 6 C15) CC4): 648 419 436 -21 256 20 C16) C(S) 505 410 437 28 245 63 (14) C(6) 518 368 431 0 212 48 (15) CC7) 564 513 594 -26 324 -19 (17) N(8> 631 687 592 -128 191 -88 (17) N(9) 597 510 520 39 295 25 (14) 0C10) 738 724 715 148 348 -165 (14) 0(1D 578 698 911 -91 395 -157 C14) 0(12) 705 769 728 -121 389 -263 C14) 0(13) 685 943 1222 -110 589 -490 C17) 0(14) 566 1354 1289 -254 297 -520 C21) 0(15) 964 1066 934 -306 399 -507 C20) B. C(16) 6»43(13) CC16-) 5-19(26) C(17) 9-02(19) C(17') 8-68(44) H(18) 6-4(10) H(19) 4-6(7) H(20) 4-7(7) H(21) 4-0(9) H(22) 4-9(11) H(23) 3-2(8) H(24) 14-1(26) H(25j 9-0(17) odo) 0(11) o 1 i i_ 0(14) H(20) y-t(6) H(19) 0(12) 4k. C(16')'-' H(22) N;C(17') £>H(23) H(24) H(25) Figure 8. View of the molecule. The positive direction of the b-axis is away from the viewer. 83 Table XIX. Molecular dimensions of ethyl 3,5-dinitrobenzoate; (standard deviations in parentheses). (a) Bond distances (in A.) Bond Uncorrected Corrected distance distance distance C(l) -C(2) 1 •383(4) 1 386 N(9) - 0(11) 1-215(3) C(l) - C(6) 1 •384 (4) 1 387 0(13) - C(16) 1-490(7) C(D - C(7) 1 •506(4) 1 •513 0(13) - C(16') 1-560(15) C(2) -C(3) 1 •384(4) 1 387 C(16) - C(17) 1-465(12) C(3) - C(4) 1 •372(4) 1 •375 C(16')- C(17') 1-461(26) C(3) -N(8) 1 •478(4) 1 •494 C(4) - C(5) 1 •379(4) 1 382 C(2) - H(20) 0-94(3) C(5) - C(6) 1 •376(4) 1 379 C(4) - H(18) 0-98(4) C(5) - N(9) 1 •467(4) 1 •473 C(6) - H(19) 0-87(3) C(7) - 0(12) 1 •186(4) 1 208 C(16) - H(21) 0-97(4) C(7) - 0(13) 1 •305(4) 1 346 C(16) - H(22) 1-02(5) N(8) - 0(14) 1 199(4) 1 257 C(17) - H(23) . 0-89(4) N(8) - 0(15) 1 209(4) 1< 251 C(17) - H(24) 1-03(9) N(9) - 0(10) 1 222(3) 1< 248 C(17)— H(25) 1-04(7) Bond Uncorrected Corrected distance 1-239 (b) Valence angles (in degrees) i j k Angle (ijk) i j k Angle (ijk) C(2) — c(D - C(6) 120 •5(3) C(7) — 0(13) - C(16') 106-7(6) C(2) — c(D - C(7) 121 7(3) 0(13) — C(16) - C(17) 100-4(6) C(6) — C(l) - C(7) 117 8(3) 0(13) — C(16')- C(17') 103-0(13) C(l) — C(2) - C(3) 118 2(3) C(2) — C(3) - C(4) 123 1(3) C(l) — C(2) - H(20) 124(2) C(2) — C(3) - N(8) 118 •2(3) C(3) — C(2) - H(20) 118(2) C(4) — C(3) - N(8) 118 7(3) C(3) — C(4) - H(18) 120(2) C(3) — C(4) - C(5) 116 8(3) C(5) — C(4) - H(18) 123(2) C(4) — C(5) - C(6) 122 '6(3) CCD — C(6) - H(19) 122(2) C(4) — C(5) - N(9) 118 •6(3) C(5) — C(6) - H(19) 119(2) C(6) — C(5) - N(9) 118 •8(3) 0(13) — C(16) - H(21) 110(3) C(D — C(6) - C(5) 118 8(3) 0(13) — C(16) - H(22) 120(3) C(l) — C(7) - 0(12) 123 4(3) C(17) — C(16) - H(21) 113(3) C(D — C(7) - 0(13) 111 •3(3) C(17) — C(16) - H(22) 95(3) 0(12) — C(7) - 0(13) 125 •3(3) H(21) — C(16) - H(22) 116(4) C(3) — N(8) - 0(14) 118 4(3) C(16) — C(17) - H(23) 107(3) C(3) — N(8) - 0(15) 118 0(3) C(16) — C(17) - H(24) 87(5) 0(14) — N(8) - 0(15) 123-6(3) C(16) — C(17) - H(25) 97(4) C(5) — N(9) - 0(10) 117 5(3) H(23) — C(17) - H(24) 103(6) C(5) — N(9) - 0(11) 118-3(2) H(23) — C(17) - H(25) 140(5) 0(10) — N(9) - 0(11) 124-2(3) H(24) — C(17) - H(25) 110(6) C(7) — 0(13)- C(16) 120-5(4) 1-1(23) H(25) 1-1(24) 0(15) (a) Cb) Figure 10. Molecular dimensions, (a) bond lengths, and (b) valency angles. 85 Table XX. . Mean planes. (a) Equations of mean planes, in the form: £X + mY + nZ = p where X, Y and Z are coordinates in X. referred to orthogonal axes a, b and c*. Plane no. Plane £ m n P 1. Benzene ring 0-1800 0-7089 -0-6819 0-2008 2. Carboxyl group, C-COO 0-2141 0-7151 -0-6654 0-3004 3. N(8) nitro group, C-N02 0-1573 0-7016 -0-6950 0-0841 4. N(9) nitro group, C-N02 0-1638 0-5592 -0-8127 -0-5656 (b) Displacements of atoms from the plane of the benzene ring. Underlined values indicate atoms included in the calculation of the equation of that plane. Atom Displacement Atom Displacement CCD 0-002 A. 0(12) 0-038 A. C(2) 0-004 0(13) -0-046 C(3) -0-007 0(14) 0-057 C(4) 0-005 0(15) 0-032 C(5) 0-001 C(16) -0-270 C(6) -0-004 C(16') 0-376 C(7) 0-017 C(17) 1-098 N(8) 0-023 C(17') 0-300 N(9) -0-003 H(18) -0-045 0(10) 0-204 H(19) 0-027 0(H) -0-223 H(20) -0-037 (c) Angles between the normals to the benzene ring plane and the substituent group planes: Plane q r Angle (qr)° 1 2 2-2 1 3 1-6 1 4 11-5 86 D. DISCUSSION. It has been concluded 22>27 that there is negligible contribution from excited resonance structures such as II and III in nitrobenzene comp-I II + III ounds, except when there is an electron-donating group in the ortho or para position to the nitro group. Table XXI shows the dimensions of nitro groups in several nitro benzene derivatives. Where there are appreciable contributions from resonance structures, as in p-nitrophenol and p-nitroaniline derivatives, o the C-Nn^tro bond distance, ^-1*46 A., is generally shorter than in compounds o not readily forming resonance structures, CC-Nn^trQ now 1*46 - 1*49 A.). Our results conform with the latter, but there is a significant difference between the C-N bond lengths in the two nitro groups in our molecule. The nitro group of N(8), 0(14) and 0(15) is rotated 1*6° out of the plane of the benzene ring, and the group of N(9), 0(10) and 0(11) is rotated 11*5°. The N-0 bonds are approximately equal in the two groups, with mean values 1*254 A. in the first group and 1*244 A. in the second group. But o the C-N bond length in the first group, 1*494 A., is significantly longer o than that in the second group, 1*473 A. This is the opposite effect to that expected from the rotations of the nitro groups out of coplanarity with the benzene ring since one of the requirements for the formation of resonance structures is that the planes of the nitro group and the benzene ring should be closely aligned; hence if any resonance effects are to be observed, they should be found in the N(8) nitro group. Table XXI. A comparison of the dimensions of nitro groups in nitrobenzene derivatives which have no substituted ortho groups. C-Nrntrn N-Oi N-02 Ang. in Rotn. A A J A A Mean Angle Angle Angle benzene Mean ang.of Compound Unc? Corr? Unc? Corr? Unc? Corr? °L* O-N-0 C-N-C^ C-N-0 2 ring a * A C-N02 Ref. Ethyl 3,5-dinitro- 1. 1*478 1-494 1-199 1-257 1-209 1-251 0-004 123-6 118-4 118-0 123-1 0-3 1-6 This benzoate 2 1*467 1-473 1-215 1-239 1-222 1-248 0-003 124-2 118-3 117-5 122-6 0-3 11-5 work Trans-bicyclo-[4.2.0]- 1. 1-489 1-218 1-213 0-004 125-4 117-4 117-2 122-6 0-2 4-3 octyl 3,5-dinitro- 2. 1-474 1-207 1-216 0-004 123-4 117-7 118-8 122-8 0-2 1-4 30. benzoate p-Nitrobenzoic acid 1-480 1-228 1-203 0-006 124-1 118-3 117-3 122-8 0-4 13-7 40. 2,6-Dichloro-4-nitro- 1-456 1-466 1-227 1-257 1-231 1-256 0-005 123-4 118-4 118-1 122-0 0-4 7-3 Part aniline III. 1:1 complex of s-trinitro- 1-462 1-463 1-232 1-247 1-207 1-222 0-006 124-0 117-1 118-9 122-6 0-4 9-9 benzene and 2. 1-464 1-466 1-222 1-233 1-238 1-247 0-006 122-9 118-5 118-6 122-8 0-4 0-9 41. s-triaminobenzene 3. 1-472 1-474 1-219 1-228 1-213 1-220 0-005 124-9 116-7 118-4 122-2 0-4 5-9 p-Nitroaniline 1-454 1-460 1-227 1-246 1-229 1-247 0-007 123-3 117-7 119-0 121-2 0-4 1-9 22. p-Nitrophenol (at 90°K.) 1-442 1-232 1-236 0-006 122-0 119-3 118-8 122-3 0-4 1-5 28. m-Dinitrobenzene 1. 1-484 1-491 1-243 1-276 1-197 1-220 0-009 125-1 116-6 118-3 123-1 0-6 13 42. 2. 1-487 1-494 1-214 1-230 1-227 1-266 0-009 126-5 116-8 116-1 124-0 0-6 13 a , a - e.s.d's of uncorrected bond lengths and valence angles. 88 The larger rotation of the N(9) group appears to result from packing forces - see Figures 11. and 12.; if this nitro group were rotated through a smaller angle, the N(9)...0(10)* distance would be shorter than the sum of van der Waals* radii, and other interactions, e.g. 0(10)...0(10)1, 0(11)... 0(12)' and 0(11)...C(7) would approach the minimum non-bonding distances. The angles around both the nitro groups compare well with those in other nitro compounds. In all cases, the O-N-O angle is larger than 120°. The angles in the benzene ring are similar to those in other comp ounds and as expected from second-order hybridisation effects 31~33, viz. ^123° at the carbons of -N02 substituents, three with a mean of 117*9° at the carbons bonded to hydrogens, and 120*5° at the carboxyl group carbon. o Similarly, the ring C-C distances about C(l), mean length 1*387 A., are perhaps slightly longer than those about C(3) and C(5), mean length 1*381 A. The plane of C(l) and the -C0.0- part of the carboxylic ester group is rotated 2*2° out of coplanarity with the benzene ring. The (uncorrected) dimensions of this group appear quite normal and are compared with those of other molecules in Table XXII. The angles about C(7) result from the repulsions between bonding electrons about the C(7) atom. The coordinates of the three hydrogen atoms on the benzene ring refined well, and these atoms are not significantly out of the plane of the ring. Their C-H bond lengths and the angles about their bonded carbon atoms are normal. The outer parts of the disordered ethyl group are not well defined and the lengths and angles are not very reliable. The hydrogen atoms H(21) and H(22) are well removed from the minor ethyl group, and their positions are thus reasonably well determined, but the methyl groups of C(17) and C(17') are overlapping and hence there is some confusion and a lack of definition. It is therefore not reasonable to discuss critically the dimensions of the Table XXII. A comparison of the dimensions of the carboxyl group in benzoic acids and esters, and in related compounds. Compound C-C coo C=0 C-0 Mean a * L C-C=0 C-C-0 0=C-0 Ang. in benzene ring Mean "A* Rotn. ang.of C-CO.O Ref. Benzoic acid derivatives: p-nitrobenzoic acid 1-501 1-222 1-319 0-007 121-1 115-0 123-9 121-2 0-5 3-3 40. 2-chloro-5-nitrobenzoic acid 1-489 1-220 1-294 0-008 121-3 114-0 124-8 117-7 0-6 23-0 43. o-chlorobenzoic acid 1-521 1-208 1-295 0-008 122-2 113-3 124-5 120-5 0-6 13-7 44. p-aminobenzoic acid, mol. A 1-455 1-236 1-315 0-006 123-5 115-6 120-8 118-1 0-4 1-5 45. " " , mol. B 1-464 1-248 1-293 0-006 121-4 116-5 122-1 118-5 0-4 2-5 45. Benzoic ester derivatives: ethyl 3,5-dinitrobenzoate 1-506 1-186 1-305 0-004 123-4 111-3 125-3 120-5 0-3 2-2 This work trans-bicyclo-[4.2.0]-octyl 3,5-dinitrobenzoate 1-507 1-200 1-323 0-004 122-0 111-1 126-9 119-8 0-2 8-9 30. complex of tricarbonyl-chromium:methyl benzoate 1-49 1-19 1-35 0-013 124 111 126 119 0-9 very small 46. Related compounds: o-nitroperoxybenzoic acid 1-495 1-214 1-337 0-007 125-1 109-9 124-7 118-6 0-5 58 47. 2-thio-amidopyridine 1-505 - - 0-005 122-9 113-9 123-0 123-3 0-3 10-5 48. 92 ethyl groups. The molecular packing arrangement is shown in Figure 12. The perpendicular distance between the planes of rings is 3*38 A., which appears general in benzene derivative crystals, and similar to the interplanar o distance of 3*35 A. in graphite. There are several short intermolecular distances and these are given o o in Table XXIII. The distances recorded (maximum 4*0 A.) are less than 0*3 A. greater than the sum of van der Waals* radii, which were taken as: o hydrogen 1*2 A. oxygen 1*4 nitrogen 1*5 o carbons of ethyl group 2*0 A. o other carbons: (a) radius in plane of benzene ring 2*0 A. (b) radius perpendicular to plane of o benzene ring 1*7 A. The N(9)...0(10)' distance of 2*870 A. and the 0(12)...H(19)' o distance of 2*54 A. correspond to van der Waals' interactions. The first nine interactions recorded of those involving carbons of the ethyl group have distances less than or equal to the sum of van der Waals' radii. The C(17')...C(17')" distance of 3*049 A. seems prohibitively short, but it must be remembered that the C(17') atoms may not be perfectly defined. It seems improbable, however, that two molecules each containing the minor ethyl group will be able to lie adjacent. When only one molecule of an adjacent pair contains the minor ethyl group, the C(17') to C(17)', H(23)' and H(24)' distances are still short but more reasonable; the C(17")...0(14)' and C(16') .. .0(11) ' distances are slightly less than the sum of van der Waals' radii, but this is allowable at certain orientations of the ethyl group bonds. The same applies to the 93 Table XXIII, Short intermolecular distances. (a) Distances from the ethyl group carbon atoms. Atom i is in molecule I *. Molecule ij Molecule ij i j of j * i 3 of j C(17') . .H(23) IIIc 2*90 A. C(16). ..0(11) Ilia 3-530 A. C(17') ..H(24) IIIc 3-06 C(17') ..0(15) He 3-556 C(17') .,C(17») IIIc 3-049 C(16') ..0(11) Illb 3-557 C(16). ..H(20) lb 3-21 C(17). ..0(11) Illb 3-570 C(16') ..0(11) Ilia 3*293 C(16») ..0(1C) Illb 3-667 C(17). ..0(15) IVa 3-333 C(16). ..0(14) lid 3-669 C(17') ..0(14) lid 3-373 C(16). ..C(l) lb 3-884 C(17). ..C(17») IIIc 3-432 C(16') ..C(2) lb 3-961 C(16). ..C(2) lb 3-434 (b) Distances involving hydrogen atoms: i j Molecule of j i j Molecule -jj of j 0(12)...H(19) Ilia 2-54 A. 0(14)...H(20) lie 2-68 0(11)..,H(21) Ilia 2-68 0(10)...H(25) Illb 2-70 0(11)...H(25) Illb 2-77 A. 0(11)...H(18) Ila 2-78 N(9) H(25) Illb 2-98 C(2) H(21) Ia 3-06 (c) Distances between non-hydrogen at ^ . Molecule ^. of j oms: i • Molecule • • of i N(9) 0(10) Ila 2-870 A. 0(10)...0(10) IIa,b 3-055 N(9) 0(12) Illb 3-080 C(5) 0(10) Ila 3-151 C(7)...0(11) Illb 3-310 A. C(2)...0(15) lb 3-362 C(6)...0(12) Ilia 3-390 C(3)...C(7) la 3-431 * Coordinates of adjacent molecules: I x, y, z Ia .x, 1+y, z lb x, y-1, z Ila -x, y-h, h-z lib -x, y+h, h-z lie 1-x, y+h, h-z lid 1-x, y-%, h-z lie 1-x, y-h, h-z Ilia -x, -y, -z Illb -x, 1-y, -z IIIc 1-x, -y, -z Illd 1-x, 1-y, -z IVa x, h-y, z-h 94 C(17)...0(15)' distance - the only really short intermolecular interaction of two adjacent, major ethyl group molecules. If, in fact, two molecules with minor ethyl groups are not able to lie adjacent, and there is no preference between major-major and major-minor pairs, then it is expected that the ratio of major to minor group molecules would be 67/33. Our results indicate approximately 30% occupancy of the minor group's sites. PART V. THE COMPUTER PROGRAM "GESTAR". 96 A. INTRODUCTION. In collecting the intensity data of the twinned crystal, 2,6-di-chloro-4-nitroaniline, data from both the twins was required. The crystal was mounted so that the a*-axis of one of the twins (the first twin) was parallel to the goniostat ij>-axis. A computer program which would calculate all the diffractometer settings for this twin, and which would punch out the instrument instructions on cards for use in the diffractometer, was avail able. It was considered that the best comparison between the intensity data of the first twin and that of the second twin would be obtained if the measurements could be made without altering the arcs of the goniometer head. But the second twin had neither a reciprocal axis nor a real axis parallel to the goniostat cj>-axis; therefore, a short computer program would have to be written to calculate the diffractometer settings for the collection of the second twin data. It was then thought worthwhile to bring the old program for the calculation of diffractometer settings - part one of the DATAPR program written for the IBM 1620 computer some years ago - more up-to-date, and to write a subprogram, which could be incorporated into the more general program, to calculate the second twin settings. The new version of DATAPR is named GESTAR, and; the subprogram for second-twin calculations is named TWIN. The program GESTAR will be described first, in section B, and the subprogram TWIN (and the slight modifications in the main GESTAR program) will then be described in section C. 97 B. THE PROGRAM "GESTAR". 1. Diffractometer geometry used in GESTAR. The basic diffractometer geometry used in the program DATAPR was used with little alteration in GESTAR, and is described below. A crystal has periodicity in the arrangement of its atoms and molecules in three dimensions. The small repeating unit is the "unit cell" which has edges of length a, b and c, and angles between the edges a, 6 and Y as shown in Figure 13. Figure 13. The unit cell. b Related to the unit cell is the Reciprocal Lattice which is a three-dimensional array of points with its origin placed at the centre of the crystal. The three major axes of the reciprocal lattice are the a*-, b*-and c*-axes, whose directions are defined as being: the a*-axis is normal to the b-c plane of the unit cell, If b*_ it II ft if it a_c ft ft if it II ancJ II C*_ II it . ti ti tt a„D ti ti tt tt ti The angles between these axes are a*, B* and y*, and their values are related to those of a, B and Y-The points- in the reciprocal lattice are indexed hk£, and they are 0 Figure 14. A portion of the reciprocal lattice. related to planes in the unit cell having Miller indices hkl. The mode of indexing the reciprocal lattice points is shown in Figure 14. The distances from the origin 0 to the points 100, 010 and 001 are a*, b* and c* respectively, and these lengths are defined: . b.c.sin a , . a.c.sin 8~ . a.b.sin y a v ' V ' V where V is the volume of the real unit cell and is calculated to be: V = a.b.c./ 1 + 2.cos a.cos 3.cos y - cos2a - cos23 - cos2y The angles a*, g* and y* are, in the general case: cos a* = cos g.cos y - cos a sin p.sin y 99 and similarly for cos g* and cos y*. It should be noted that all these expressions simplify considerably in crystal systems of higher symmetry than the triclinic system. The distance from the origin 0 to any reciprocal lattice point hkJl is d* , and hk£ hk£ in the real cell. Hence d* • = hkX, d where d,, is the perpendicular distance between (bki) planes A* _ o* = 1-a100 a —3^ 100 d* = L— = 3a* Q3oo -ar 300 do\o = 4b* etc-and the distance d*. for any point hk£ can be calculated from the dimensions of the reciprocal unit cell. Just as the a*-axis is perpendicular to the b-c plane, i.e. the (hOO) planes, and the distance of, say, the 200 point from the origin is the reciprocal of the distance between (200) planes in the real cell, so any vector hkl, from the origin of the reciprocal lattice to the point hkjl, is normal to the planes (hk£) in the real cell, and its length is the reciprocal of the interplanar spacing. The G.E. XRD-6 diffractometer employs the "Normal-beam Equatorial" method of diffraction geometry - the incident X-ray beam, the crystal and the X-ray detector for the diffracted beam, all lie in the equatorial plane of the instrument, and the incident beam is normal to the crystal oscillation axis io(= 9). The instrument geometry is illustrated in Figures 15. and 16. For a diffracted beam to be recorded, the crystal plane (hk£) must be perpendicular to the equatorial plane and inclined at 6 to the incident Figure 15. Diffractometer "normal-beam equatorial" geometry. Figure 16. In the equatorial plane. 101 beam, and the detector must be at 26 from the emergent non-diffracted beam. The 9 and 26 circles in the instrument are coordinated, and the required 29 value can be calculated from Braggfs Law (see below). The reciprocal lattice vector hkl, normal to the (hkJl) plane, is in the equatorial plane; if 6 and 26 are turned to 0, this vector is perp endicular to the incident X-ray beam. The diffractometer settings are thus calculated to bring the vector hkt initially into the equatorial plane and perpendicular to the incident X-ray beam; the 26 setting rotates the vector through 6 and the detector through 26 in the equatorial plane, to the correct diffracting position. The calculation of the 26 setting is made from the Bragg Law which expresses the condition under which a crystal plane will diffract an X-ray beam; the Law is: X = 2d.sin 6 where X is the wavelength of the radiation to be used, and d is the interplanar spacing. Hence: 26 = 2.sin-l(%d^ The program GESTAR calculates the instrument settings for crystals mounted with a reciprocal axis parallel to the <|>-axis of the goniostat. After the crystal is correctly aligned to the "initial" position - the settings of x and 26 at 0, and of <j> at the value of <j>o (so that the project ion on the equatorial plane of one of the reciprocal axes, a*, is normal to the incident beam) •- the situation is as in Figures 17(a). and 17(b). In order that the (hkl) planes might be in the correct diffracting orientation, the vector hkl (Figure 17(b).) must be rotated through x into the equatorial plane, and then through <j> into the <j>o position normal to the incident beam, (and then through 6 in the equatorial plane). To determine Figure 17(a). Positions of real and reciprocal axes in a reciprocal axis mounting. * hkl Figure 17(b). The coordinates of a point hk& in reciprocal space Figure 18. The reciprocal unit cell. N.B. the indices of • the corners of the cell are h^h^h^, where h1 is in the direction of a*, etc. X and <|>, we shall calculate X2 and X3, the distances parallel to the orthogonal axes - the c}>0-, a2~ and a*-axes, respectively. Consider a reciprocal unit cell, dimensions a*, a*, a* and a*, a* a*, as in Figure 18., shown in the same orientation as in Figure 17(a). The indices of the lattice points in Figure 18. are h,h h , where h is in r » 12 3 1 the direction of a*, etc. The six values - Rg can be calculated, by simple trigonometry, to be: In the Xj direction: Rj = a*.sin a* a* R2 = 2 .(cos a* - cos aj.cos a*) sin a* 2 104 In the X2 direction: R, = a2 ./l cos2a* - cos2ot* - cos2ct* + •5 . . 1 Z 3 sin a* 2.cos a*.cos a*.cos a* In the Xg direction: R^ = a*.cos a* R5 = a*.cos a* R6 = a3 The values of Xj, X2 and X3 for the general reflection hkJl are then determined from the increments Rj - Rg in the reciprocal unit cell: '•*"• Xl = hlRl + h2R2 X, = h2R3 X3 = h^ + h2R5 + h3R6 where h1, h2 and h3 are the indices of the point in reciprocal space, hj in the direction of a*, etc. The diffractometer settings are then calculated: X = tan"1/-^ ^ Ax2 + x22J 4 = tan-1/*^ Xl Also: d* = /X 2 + X 2 + X 2 hk£ 1 2 3 Hence: : 28 = 2.sin"1/r-./X 2 + X 2 + X 2 2 Ll "2 "3 2. Outline of the program GESTAR. The main program of GESTAR may be divided into several sections, and there is one subprogram (named ANGSRT); several library subroutines 105 are also called. An outline of the main program is: (i) The cell dimensions, either real or reciprocal, are read in and all the other dimensions are calculated. (ii) The values of Rx - Rg are calculated for the reciprocal unit cell (see subsection 1. above). (iii) The indices hkl are generated, and if they are within the required ranges (see subsection 3. below for the options available in the generation of hk£ indices), values of Xj, X2 and X3, the coordinates of the point hkl in reciprocal space, are calculated for each reflection. The results are written on file 3. (iv) The file 3 is read, selecting reflections according to their positive and negative indices, and the 28, x and <{i values for each reflection are calculated, printed out and written on file 8. (v) If "ij>-scaling" is required, the sorting subroutine ANGSRT is called and the values of if, x and 26 for the sorted reflections are listed. (vi) If required, the diffractometer instructions for each reflection are printed out and/or punched on cards; this section requires the "packing" of results, and some of the UBC CHAR character handling routines are called here. The subroutine ANGSRT is a sorting subprogram which sorts reflect ions on their values, of 26, x and tt so that tt decreases slowest, 26 fastest. The program calls the library routine ASORT which sorts partially complete arrays. The version of ASORT used here is new and its machine language deck is included with the deck of GESTAR. 3. Data cards for :program GESTAR. The input.instructions for the program GESTAR are given below, and 106 the various options available in the program are included here. PROGRAM GESTAR. Scratch files on units 3 and 8 must be named; if cards are to be punched, unit 7 must be assigned to the punch device. The program should therefore be called: $RUN XRAY:GESTAR 3=-A 7=*PUNCH* 8=-B or, if running the program from the source deck: $RUN -LOAD#+-SORT 3=-A 7=*PUNCH* 8=-B •:. NA A c|)-axis of goniostat OTHA CARD 1. (20A4) Title. CARD 2. (313) Col. 3 IPROG Type of output required: 0 - goniostat settings only. 1 - automatic diffractometer instuctions, cards punched plus listing of cards. 2 - A. D. instructions, listing only. 3-A. D. instructions, cards punched only. 6 WRORC Cell dimensions as supplied on Card 3: 107 0 - real dimensions. 1 - reciprocal dimensions. 9 ISRT Sorting for "^-scaling" (reflections sorted for 26 changing most rapidly, then x, <J> slowest): 0 - sorting required. 1 - sorting not required. CARD 3. (6F10.0) Cell dimensions, as for BUCILS2: a, b, c, a, 3, y, or a*, b*, c*, a*, 3*, y*. CARD 4. (513, 5X, 5F10.0) Col. 3 6 9 12 NA Goniostat axis PHI0A Axis along 4> 1 for a* ; 2 for b* ; 3 for c*, OTHA Third axis CENTT No. of tests to be made for centred cells; reflections for which EtL = 2n+l, (H = h,k,£), will be omitted, e.g. for A, B, C and I type cells, CENTT=1 and test k+&, h+£, h+k, or h+k+S,, respectively; for F cells, CENTT=2 and test h+k and k+X,. 15 SCSP Scan speed required in data collection: 1 - h degree per minute 2 - h ' " » 3- 1 " " 4- 2 " 5- 4 " 6 - Slew. it n it n II 21-30 MINTTH Minimum 26 value (in degrees) for reflections for data collection; if blank, 26 . taken as 4'0°. ' mm 31-40 MAXTTH Maximum 26 value (in degrees) for reflections; if blank, 26 taken as 160•0°. max 41-50 PHI0 Value of <|>0, (in degrees). 51-60 SCAN Constant k in calculation of scan range: 26 scan = 1'80 + k.tan 6 ; if hlank, k = 0»86. 108 61-70 WAVE Wavelength, of radiation to be used, (in A.) CARD 5. (1213) Values of h, k, £ required. Col. 1-3 4-6 7-9 -12 -15 -18 -21 -24 -27 -30 -33 -36 Lowest absolute value of h ^ ii •? " " k II II II tl £ No. of layers of h ' II it ti " k \ tt it it it ^ +1 indicates positive values only N.B. 000 reflection not generated. if blank, there is no restriction on the no. of layers. 0 indicates both positive and negative values •1 indicates negative values only in h in k in £ Interval in h ^ Interval in k > Interval in £ J CARD 6. (613). Required only if CENTT > 0. Col. 3 1 - if h, (Hx) 1 - if k, (H2) 1 - if £, (H3) J if blank, unit increments in h, k, £ are assumed. 6 9 12 15 18 is to be included in the test: m. = 2n + 1 \ ditto for second test, (if CENTT = 2). N.B. when CENTT = 2, both sums must have odd totals if the reflection is to be omitted. 4. A listing and an example output of GESTAR. A listing of the program GESTAR, followed by an example set of input data cards and the output for this test run are shown below: 109 Program listing INT ('.lift IP" (If., WRdflC, MA. PH10A, (IT H* I N T"? C, F H (NITI1). NLAYI3I. Pn«l3l. HH i K K, LL nn. UJ, IKK, P, o, H, RFIBI, anaiei, Nfl, j iNr-GF" I^TOl. M*Yl, NL AY 7, AY 31 HP, Kil, ]MFGt"» CENT!, 113,".J. N3, [XLFP IMtGFR HMH1JI, I AH 11 31 • IAW2f*l. J ftNGLC* •»» « INHGFR HH2 (1 I If AL *Wn7H, CHl, PHI, IISCAN cwr.citi S6Nr.(ii, OANG RFAL ASI13 BF AL •MN, ANJT.ST I > > , CANGSTI3I m. "1, a?. PHI3, SCAN, Bum R5, B6 HEAL R F Al ICCP, A>C n|fHY<i KiN T I TLe ( 201 OFtN. OF P F A L ANO PFCIPKnC/IL CFLL MANSIONS RF *p (5,M I I T ITLE 1 I I, I-l, 21) copf'AT I ?•?»*• J "IP I 11 I6,h7) I T I UP I I I, I- 1 .ZD Fflk^il UHO, 21AI.I ^Fi>1 I'.I'JI IP1UG, UKflBCi 1SKT Fl'O'lAt (113 1 IF (HI HOC GF.7 I GO 10 S FL r*6' 01: I *> F-1 LT . ,3)t 1AMU IIt, 1-1.3) 1 I * . 11 ANC,( I O'M; « A.'jr,< 11/1I.?V>TTI C»M-,( | I » CilSl<**«M S/HGI I I - S IWMMG I r.iKTlMJP 01 1*11 .(I* I I 1 ( I > .1 I I <• ANG I 1 • ' 1 • S 1NGI 1 I I'' <v.m .CO. "is. •'. AMI, MCI [MC CFLL V « Ail I ' AI ? I • A ( i 1*S(JC: .17) -r*n.; I 7 1-f «(1).Ee.«J .0 I G'T TO 71 • T, * 1 1 * A I I »? I'S »NGI I l/V L ' NG I 1 * 1 I ' C A '/<"•( I * 7 1 -C ANG I I I / I SANG I I* t >*5 ANC( 1*21) .7,TO-AKCistCAvr.su in •'I.i'.'I OH II 77 • I • Mil-IH tllrtlf. CFLL t -unr .Ff. • I UTTA" " . FB.l, 1 GAMMA* -t, fd.3 1 •*F *• . fo.t, 'CU. ( ITllA, C f NTT, SC5°. "INIIH, MAXTTH, PHlO, C11*> Cl?T 0128 C l?» PI 72 oi n 017'. |F IHH.FO.O.ANO.I (10 101 P«l ,7 oa 102 o»i,2 ;.EQ.O.AND.LL.E0.01 GO TO 6 i H(Pl»K(OI»L(°-) I I.G F,3 TO I CD TO mi HM.I2) - KID) HK LI 31 - LIP I It (CENTT.FO.01 on ' J-I.l KlO>M(2,JI»LtR|"TI3.. (CEP > IABS(HIP)-TI 1,J) i xcCP • KCtP/2. c*').oni AXCCP « 2-1 XC" niJ-r • XCFP-AXC.FPO.X'1 |F (ii|FF,r,F.O.SI N-) - HG*l CPHI!NUF [ F INU.Gt .CFNTT I GO TH 111 xl * Hi-MKL(PHI:A)*R7'HKLIOTMAI»C.0030001 IT > 1'3*H1L IOIHA I .,1 . " 4 * HM < P H IV 1 »R5'HKL(<JfHAI»P 6«HKL I NAI SINSC - .i.2.1»(Xl»*>*ii2**2*X**"2 t*NAVE*hAVE IF ISIN^'J.GP.FLII) GO Tn ICS IF I S INSD.LT .FIlNI f.d Til pi WMTF 1)1 MlPI, KCJI, OKI, I, SINSO. XI, Xi Gil T(l 1^3 THAU) • 1 CHNTINUF. CUNTIMJF CHMTINUE . 30Ci.0-<.nHAI I Gil TO 12 .ASD.|JJ.EO.1 . EO.l I G1 til < lan-THETA ANGLES MfcSQ. C'INT INUF Cr'NTlMJF. CONTINUF r>E TN. nF PHI , f NUF II C- 3 mi 71 J-l.fl Rf-INI) 3 «[AO (3.F.NO-2T) IMMHCII, 1-1,3). IF IS.1F..J) GO T'J 7.1 TWOTM « 1 l'..5<J156*ARSINIS(JFU IS INSQ I I CHI • S7. 79S7B'ATAN(I3/SORT<>1••2*X?-*2I> PHI • '.I.?'J?7t-Al AN( ).PHI') IF m.LT.O.^I PHI - PHI. 180.c IF ( > l.GC .f.'.i.AN), I2.LT.0.0) PHI • PHl»360.C IF (CHI .GT.-i..j i c,a m 4* IF IPIM .tiT.314.1.ni PHI • PHI-3hO.O WHITE IHHM(I), 1-1,3), PHI, FT'B 1 AT HH , Ml. 3F17.7I WHITE (HI IHhHIM, l-li3l, PHI, CH Hi, TWOTM TWOTH 77 C( NTJMIIE I S I M * I' (S IM "A' . BSTIPlU-dS T( -J4 ) PHICAI-CSACnrHAli/SNAIOTHAI Pur A)»*2-CSA IDT MA l»-2-CSAI N. l/SNA(OTHA) • CSA( P!ll •MNTTM, .FSSTIO.N OF )i,n i It IT 1 1 I I I I M I I ) , IF ICEMTF C't A*( I) . FT . ( I'-' I I 1 .CQ." :iTlMJf :in > Hit* INT ( 1 ) IF (-*«, CH.Ci Cl TO IF (PLill I .LF ,1 ) HI If (PI 'Mil. F'J. - 11 H • |MIT I?I-1NT|2) nr. £ I J J-l ,NL»Y2 .•S WITHIN 1*1.3), IN •. *AK, 2-THETA -•, F7.Z) II UU I RF D RANGE AYI1), |*1,?), lPOHtl). I-l.31, TWOTMETA',/I .171 ' MSI W > K(l I IF |MI,FJ.<*| GO TO 11 IF IPCHI71.IF.-M M7I . IF (P(M(J).FC.-ll Kill LL • l*MH 3l-I**T( II no h IK«-1.NIA/J L(?l * LL • IL•1NTI 31 ILL.t-O.II GO TO 16 |P| -I3I.LE.DI L(?l . I PCUU3 ) .1 0.-1 1 LII) wcnc (fc,15M Fn'«AT I'O H I r I IPROG.f U.') "It-ITF lb, 3SI I.I Sit t .FO. II GG TO 93 '. L PH| CHI , IPUGG.EO.31 GO TO 34 'DIFFRACTOHI-TrR INStfiUCTinNS'! T UOT HE T A*I A'l If, LiNP-'J'" I I HHH1 J I IE (b,l<-7) IHHH(J), kKAT | IH , 31 *, »F 12. 71 ( |PXfiG,E0.«l GO Ifl IVJ I (PH] ,GF . 3fi<). 9<>t-\ PHI • PHI Hi * PHI .fl . f ICllI .L T. 0.01CHI • CH1»36.J. PACK1\G OF OFSUlIS -. J>1,3), PHI, CHI, '1,31, PHI, CHI, TMI I'S IN BLANK SPAEES DO ' •1, 3 100-C AIL S= T (3. I API, 2*1) CML OFr.riM 11-1 M ( [ j, UB1I3)| CAlL PK (3, I4R1I1), WIHIII, PI CI.NT IMJF IF I Jf.AN.LT .'•.•"Ml I SCAN . 0.86 T.OTHE * THOfM/1 1*. S U%6 1TS(Af - L ,°,SCSNM»NI TwItTMEl >C. 5 U».GLEI 1 I - UiO .0-PHI lAMGl.r I 71 . 1 0' CHl UNI:LM3I • I TrffllH-'TSCAN I *10C.C lA^Ltl'.l - ITW0TH.TTSCANI-100.C' IC. I - 11 * CALL Stt IS, |AH2, 7*JI CALL DECCJ CIANGLFIII. IAR?ISII CALL P«U, IAR?tll, [AlvGLEIII, 01 CAl L PK I 1 , I A R? 15 I , UNI I ), 01 CONT I Ml? P"INT AND/OR PUNCH UUt OF RESULTS IF I IPRTC.FO. II GO TCI 46 KlITf 16.^11 IHHHIIII 1*1. 1|ANGL<(<>I, IANI4I, I ANGLE I F0R»AT UH*. 55x, •«', 343 1' S20Cf,' , A», Al , • SSOC • I IF (I PROG.EO.7 I GO TO 1« WITE (7,SO { HHH i I J, I-1.3I, ( IANGLE( II, llAMGLEU), I AN I i. I, IANGLEU). lA^CI FORMAT I'M', »A1, '/60Cb', A*. Al, 'Y6C06 IA), 'SSO?', II, A*,, Al, 'S2006'. A4, Al) ' CON1IMIF. STOP END ( IANGLEI II, IANI1I, I-I ANU) /6006', A4, Al, •Y60061 A4, Al, 'S23C61, A] 1,31, SCSP, •1,31. SCSP, •S20Db(, A*i 110 S'lBPfUJTINF ANGSUT IN I {.= " ""3 (.•: 3 7 . CHI• G PHI SD THAT PHI INT r r,TR li IMIrT.FP ANGLF(500n,6|. fj ANGL ( 50 C i 6 11 EANGL ( 50 • 6 I KKAI ANGL I snrOi 3) 111=9 nn i?n I=I,N UFAO C I II .E "Jl = 1211 I ANCLE I 1 • J 1 • J-4.6). IANGLU.JI. J-1.31 *>;CLE4 1 . COM INUC ^FulNIl III FALL ASC^I 10.}. C « ANGL { I . J t +0 . I JJ 1 UNCLE , -5nr.e. nn 123 J=2,N IF (AN11LF I J, 1] .F J. ANGLE U-l . 1 ) I JJ » JJ*l IF (AM1LF(J.1 I.NE.AMGI EIJ-l.1 I.AND.JJ.GE.2I GO TO 12* IF IJ.F1.N.AN0.JJ.GF.?! GO TO 132 fill T[) 12? 137 KJ = JU r.n m 135 12* «J * J 135 nri 125 K*1,JJ HANGLIK PANf.L I K PH 12*i H"3.6 U5 (iAMiLIH.H, = ANGLF(KJ-JJ-J* CALL ASHtT (flANCL. C, -50?. JJ. 6) on |?ft K*?,JJ IF (RANGLIK.1 I.FO.RANGL IK-I, 111 K K • KK*1 IF I <4 ANGL I K 11 l.NF.DANC. LIK-1 .11 . AN ri. KK . GF . 2 I GO TO 127 IF [K.FQ.JJ.AN0.KK.GE.21 CL) TP 131 Gf Til 126 CO •1 1 36 13ANGLI JK-K •  B*.NGL< JK-* K-1*1. 1 I 00*9 0050 pr M C057 03 5 7 r<?4p CT>9 COM 00*2 0"">3 00 6* 0365 0"ftft 16 7 CALL ASflttT IEANCL, 00 129 L-l.KK BANG11JK-Kd-l*L.I 1 RANGL(JK-KK-1+L,21 BANGL(JK-KH-1*L.31 nn 12Q H-*,6 BANGLIJK-KK-1»L .HI « EA IF (JK.GF.JJI r.o rn is* KK = 1 CONTINUE no 13" K-I,JJ ANCLEIK J-JJ-UH.l I - RBI ANGLE I KJ-JJ-i • K ,2 I - rtA 00 13r n=3.ft ANGLF.I K J-JJ-1 +K ,1 0, -50. KK« 6) - FANGL1 L. 3 I - EANGL< L t 2 I - EANGL (L, 1 ) (KJ.GF.NI Gfl TH 133 1 C'INTINUF On 1?2 IM.N HO 16* JM.3 4MGL (I,Jl * A1GLFII.Jl ANGLC.I.JI - 0.01*ANGL(I.Jl WRUF INI) IANGLFH.J). J-*.6). CUNTINUF E*-'!)FILE III REWIND III T KIRN END (ANGLtl.Jl. J-1.31 FXFCUT10N TFRMINATED ifiUN 'AS*»C SPUNr.H=-S1RT SPR INT»"-(>iJM"Y • FxfCUI ION TGINS EXECUTION TECMNATEO Input data cards tRIJN - I nAri»t -S pcT -» = -A 7" "PUNCH* 8»»fi Card I. T*Ml PUN 'IF "GESTAR" PRnr.RAM 2. 2 ' 3. 3.7227P 17.P?31' ll.*335» 90. Ol" 9*. HH52 90.00 4- 12 3 * 22.5C 27.00 20.14 1.5*18 5- .1 •! Printed output •PUNCH* TRIAL PUN OF "GESTAR1* PROGRAM REAL CELL: A - 3.723 1 - 17.833 C • 11.83* ALPHA - 90.000 BETA - 9*.119 GAMMA » 90.000 RFCIP. C<=LLi A" • 0.2fr>i2 B« - 0. 0560? C» « O.OP*72 ALPHA" « 90.000 6 FT A* - 85.B81 GAMMA* - 90.000 UNIT CEIL vni.iJWE • 7H3.5TCU. A. 27.00 2- TUP rA 22.sr. PH] 2-THFTA CHI TWOTMFTA NO. OF REFLECTIONS •• 3*3. : 3*3.1 32 3. : 3.77 2.*9 0. OP 1 .19 91-,01 72.9* TB .2* 69. TB 67. 39 -*. 1? -*. 02 -3.TT -2.*B -1. 19 72.2? 6H.93 61.92 72.20 -*.ll 72.9* *. 11 *.02 3. 76 f 9. 78 2.*4 1. 19 90.00 78.23 67. 39 -1. 19 WOTHFTA 01 FFflAC TOfETEP. INSTRUCTIONS 2 ft.59 WOOL 002101/60063*31*Y60060619252006O2558S5O0602759S200602759 25.03 HOOOC0*102/60063*31*V600635752520U602*03S500*026025200602602 25.12 WCOICOll01/6006323 TOY600606B935200602*125500*02611S200602611 2*.73 W0COCO2103/600631*OOY60063562*S2UU602373S500*02572S2006Q2572 23.15 UOOO0C1103/600630261Y60063559BS2G06022165500*02*13S200602*13 2*.61 MC01COOlOl/6C06290l*V6006072205200602361S500*025605200602560 22.60 WOOOCOO 10 3/60062901 *Y6D0635589S2006021615500*023585 200602358 2 5.66 WOC1000001/6DC61101*Y60060729*5200602*665500*02665S200602665 22.60 WOOOCeooa3/60C6llOl*Y600600*US20Q602161S500*02358S20060235B 23.15 WOCOOO100 3/610609766V600600*02S2006022165500*02*135200602*13 2*.73 wncOCO2OO3/6006Oflfe2 7Y6O06OO376S20O6U237iS50O*02 5T2S2006O2ST2 26.15 WOOK01001/6U0607657Y6P0606978S200602515S500*0271*S20060271* 25.03 WOOOCO*002/600605T13Y6006002*852U0602*03S500*02602S200602602 26.10 W0O0005OO 1/600603691Y600600119S200602510S5OO*02709S200602709 23.96 H001COnOOO/6006020l*Y60060900052006022965 500*02*955200602*95 2*.*B W00l001000/6006020l*Y6O0607B23520O602J*8S5O0*02 5*TS2O06O25*7 2 5.99 W00ir,02000/60060201*V600606T39S200602*99S500*02698S200602698 2*. 96 WOO0005000/60060201*T6006000005200602396S500*02595S200602595 26. 10 W000C0510l/600600136T600635B825200602 510S5aO*02709S2006O27O9 Ill C. THE SUBROUTINE "TWIN". 1. Introduction. This subprogram can be incorporated into the GESTAR program with only minor modifications in the latter parts of the main program. It was written specifically for the determination of the diffractometer settings for the reflections of the second twin of 2,6-dichloro-4-nitroaniline, a monoclinic crystal, mounted with the a*-axis of the first twin parallel to the goniostat <}>-axis; it may, however, be adapted for similar modes of twinning. The subprogram TWIN is called after the <J>, x and 20 values for each reflection of the first twin have been determined in GESTAR; it uses these results and calculates the ty and x settings (the 26 setting is unchanged) for the corresponding reflection in the second twin. The output of results in the main program has been altered a little from that described for GESTAR, section B.4 above. A listing of the sub program TWIN and of the latter part of the main program, and an example of the output, are shown below in subsection 3. The input data cards for the modified GESTAR/TWIN program are the same as for GESTAR, (section B.3), except that an extra card is required if diffractometer instructions are required for one or both of the twins: CARD 7. (13). Required only if IPROG is not zero. Col. 3 ITW 0 - if diffractometer instructions are required for both twins. 1 - for second twin only. 2 - for first twin only. 112 2. Geometry of the second twin system. In Figure 19., the major axes of the reciprocal lattices of the two twins of 2,6-dichloro-4-nitroaniline crystals are shown. The orientation of the diagram is the same as in Figure 17(a). and since the crystal system is monoclinic, the angles a* and a* of Figure 17(a). are 90° and the a*-axis of Figure 17(a). is now in the equatorial plane. In the labelling of the axes in Figure 19., the subscript refers to the twin number, ile. a*- is the a*-axis of the first twin. The a-axis is common to both twins and is therefore not given a subscript. It will be seen from Figures 19. and 20. that, in general, a recip rocal lattice point (hk£)^ of the first twin has a corresponding lattice 113 114 point (luU)2 of the second twin in the opposite quadrant on the same side of the equatorial plane. In order to calculate the x and <J> settings for the (hkl)2 point, the subprogram TWIN first calculates the settings for the (hkl)2 point; this latter point is equidistant with the (hk£)1 point from the a-b plane (the mirror plane M) and is on a line from (hk£)1 perpendicular to the plane M. The points (hk£)2 and (hkl)2 are related by the mirror plane N through the a- and c-axes - see Figure 20. The angles fy^ and (Figure 20.) are the settings determined in GESTAR for the point (hkJl) j. We wish to calculate, first, the angles X2 anc* <J)2. The angle x0 is defined as the angle between the a*-axes of the two twins in the plane N, i.e. X0 = 2(90 - g*)° Since the two twins' real unit cells, (and therefore also recip rocal unit cells), have identical dimensions, the distances dj and d2 are equal: dj = d2 = d Then: e1 = d.sin xx e2 = d.sin x2 h1 = d.cos Xi h2 = d.cos x2 fl = hj.sin <j>1 f2 = h2.sin <f>2 = d.cos Xi-sin ^ g = hrcos ^ = d.cos Xj • cos ij^ Figure 21. shows the points (hk£)^ and (hkl)^ in the plane that contains both points and which is normal to the b*-axes; this plane cuts the mirror plane M perpendicularly. About the plane M: Plane M Figure 21. The plane, normal to the b* axes, containing the points (hk£), and (hk£) Angle ?1 = £2 = ? Also: e1 + x = 90° . X0 + ? + e2 = 90° e2 = el x0 Now: e2 = j.sin E2 = j.sin (e1 - x0) • = j.(sin ercos x0 - sin xQ.cos = j.CjL-cos x0 - ^..sin x0) = d.sin Xi'COS x0 - d.cos x^sin (f^.sin x0 And: £2 = j.cos e2 = j.cos (e: - x0) = j. (cos e.j.cos x0 + sin Ej.sin x0) = j.(^l.cos x0 + %sin X0) j J = d.cos Xj-sin (f^.cos xQ + d.sin x^sin XQ 116 Hence; sin x = e2 2 ^ sin Xj.cos xQ - cos Xj-sin ij^.sin xQ And: f tan <j>2 = = d.(cos xx.sin cf^.cos xQ + sin Xj-sin xQ) d.cos Xj•cos ty = cos x0-tan ty1 + tan Xl-sin x0 cos tyl The x settings are the same for the (hkJl)2 and (hk«,)2 reflections. The ty setting for (hk£)2 is calculated from the <j>2 result above, and the three values, <J>, x and 20 , for the second twin reflection, hkA, are returned to the main program. For reflections with indices hOO and hOl, calculations of <J>2 are much simpler and are made separately from the general case; this avoids calculations of tan 90° (= °°) values in the computer. 3. A listing and example output of GESTAR/TWIN. The first parts of the main program are as listed in section B.3, except for line 94. • This line and the latter parts of the main program, and the subroutine TWIN are shown below; minor alterations in the subroutine ANGSRT are also shown. The library program ASORT is unchanged from section B.3. A listing of a sample set of input data cards, and the printed output, follow the program listing. 117 Program listing SHRRflllT INE ANGSRT i !-lHFtA ANGLES INT EGER H lti?w« «nr,irnn)t, REAL ANGL I 31 III * rt IF IIl.f0.2J III-'11 l?i |>l,it "'.11 II 11, E NO" 1211 FANGLIi'-CM, E»NGL(*C,fcl 1-4.61, IANGLU.JI, J* 1,31 If -1 ,i n,tN'l»?7l (l|HH(I|, 1-1,31, 5, SINSQ, XI. S.NF.JI >;n n 2i il . I 14.5"1 S6-ARS IM(S3KT{ SINSU II • '.">,?< ' 7C - AT AM »*/ignT I » 1*«2**2**2) I . •"7.>nsT'i*ATiNI>?/xil»PHi:. «] . L T .' I PH I • Ph I • I3r » l.H" .f.l. AN ). >2. LT.'j.-.'l PH| . PHI'SftC.O r-1 .ill .-4.M U) 111 4* PHI - PHI . ] n-.. --IF tPi-J .f.T.••'<••.'M PHI - PH(-»6C.f *»>III 11,I'M fHHtll. 1-1.31. PHI. CHI • HOIK FilW.Al I1H . U4, JF12.2I I-1T £ |i| (HUM II, 1-1,31, DHI, C"I. T WITH CALL Ixlr; (HhH i T1.11TH, CH|, PHI , PHI", ANGI2II «>• 1 I c I . CrfTI^lJi FM1F | L F RFWINO I TFTlMv FNO ' ANGLM1.J) ' r 1 • AN CL I (ANGLE I I.J IANGLII,JI. J-1,31 iH|jli J-l.31. PHI, CHI, TWOTH i.'Ul, J-1,31. PH?, CH2. T WOT 2 ). J=l.il. ""1. CH|, IHOTH I 1 .? I II . J-1,3 1, PH?, CH?, TWOU * IX ST T -' IN' , /) ' I .'..1 TO If] i[J1, J*l,31, PHI, CHI. TWDTH 'IJ), J-1,31,, OKI, CH] , TWHTH l^>y.':''/-| PHI . PHI-3f.;.0 .->ic."> • *'Hi*3t-: .<• 'F WFJIJI Ts - if^M'S IM HLANK S< sUHP.fMJl INF TWIN I HKL, ITHANr,, tHl, PHI I , PHIO. CHITI CALCULATING 01FFPAC TOMETEB SFTT1NGS FOR SECONO TWIN [NTf-C.rP HKL13I RfAt «NG( 3] , SANG C i I , ANG 11 I • PHI I-PHK-UNCI 31, TANG13 I ' CHI ' 'CHI ) IF I AMLIl I .IT .1 .0 I ANf.l 11 < 00 30 |«l,3 ni'l", • »NGi I I /57. ?'y«T79 CANGi [ 1 - CUSIflANGI SINIHNr.) ANGI 11 +360.( 1" L I.? .EG.' 2J TANGIN - S AN* I I I / C ANG I I C(INT|MJC CHi; • BJS|NISASGI2l»CANGI31-SANGI3 I*tANGI2I*S»NGI1))"S7.2957T9 IF limit 21..vF.n} r,n TO ?i |F |H«L 1 31 ."J."l PHlT - PHI9-9C.C IF I MIL Ii! .NF.3 ) PHlT • PHII-1H0.0 i\P TH 2? I HM | 2 • A T A"J I I S* NG I 3 > * TA NG I 2 I / C ANG t II 1*1 C ANG 131** TANG 111 II* 97.195 779 II- IHM.Ii I .LT.^I PH I T - »Hl?»PHI2 IT |HM(Jt.i;r."l PH|T - PHI 3+PH12-1 83.C ! IPHiT ,LT CHIT * PHllt36P.O IF I PH I T. <1E . 36'!. 'J I PHII • PHIT-3&;.0 WRITE I6.JTI IHULIHi 1*1,31, PHlT, CHI?, TTHANG cr,iPHAT I1H., K, 314, 3*12.21 -PIT' (11 (HKL(II, 1-1,31. PHlT. CHI2, TTHANG RFTUR' I 1 I ] r i si. A n sen' • |A |ANGL> 121 • 1 .••(."! lA'T.ll I'l - ITWlJjH-TTiCANI'lUl.U I»«MM - i r-fiiM.i T'CAN i-r..'.c <W 1-1.4 CAl I hr T IH, I A»?, ?4'.| CALL C'C-IN I lANHi (-( I I, |i"q?|4)l (.111 PKI4, [ANGLE1II, ' (Ml fill I A" ?l Si , liNl 1 ) . -J) CUM 1 '-'IE FX frilT IIIN 1 ER4IN*TFU LP I INCH*- MKT SF11N A t i A:.|4| , IANIII, [-1,31, SCSP, MbOO^1, A4. Al. I'SPr-r.', A'., Al, '55: ', II, A4, A), ' S?016', If I I PftM'L. rt'.? I Gil TP 14) , Wc I Tr I7,H| I HHH 111, 1-1,31, I IANGLF (II. IANIII, 1*1,3), SCSP, I I A^r.iH 4 I , I AMI 4), 1 4.JGI £ I 4 t, m(4l Fl P-'.l CW, 3A1, '/(..Iff.", 14, A) i 'rsO^h'i A4, Al, 'S2006', A4, lAi, "J*','. II. A4, Al, 'SKir'6', A4, All C':M urn. Input data cards *HllN -LPAO(*-SnKT 3*-A 7* * PUNCH" H"-H 9"-C C»rd 1. TJJAI fl'IN (IF "GtST•0/TWIN" PPOGOAN ' 2. ? J. i'. 7?? 7(. l7.H?31'i 1 1.^33^2 90. jr. «4,11H2 90.00 4. I 2 3 4 2C. 14 1.5418 5. ? ? 2 »1 6. (blink) Printed output *PUN' -L('.»n«»-SII".T 3=-A 7=«PHNCH>' o=-c CXFCUTlriN KTGINS TRIAL RUN OF " OF S T Ap /.T rl IM " PKn?;PAM PFA1 C F L I.: A =. 3.723 8 = 17.833 C = 11.134 ALPHA = 90.000 8 ETA = 94.119 GAMMA = 90.000 RFC IP. mi: »»• » 0.26932 H« - 0.OS60S C« = 0.08472 ALPHA* « 90.000 BETA* « 85.881 GAMMA* • 90.000 UNIT r F LL V'HUMO = 7Hl.57f.ll. A. MIN. 2-THFTA = 4.'.r-. MAX. 2-7HETA = 160.CO FMST TWIN SECUNO TWIN H K L PHI CHI TwOTHFTA H K L PHI CHI TWOTHETA c r l 1 10.14 4.12 7.49 0 ; 1 290.14 -4.12 7.49 l ' ?.~. 14 4. 96 0 1 0 20C.14 0.00 4.96 o I l 76. 5 7 3.43 8.93 0 I 1 256.57 -3.43 8.98 ! r r ?r . 1 t. 9r. .00 2 3.97 l 0 0 290. 14 81. 76 23.97 1 r I 11'.14 72. ^4 2?. 66 l CJ 1 2°0.14 64.70 25.66 1 I 2 ' . 1 4 T6.2'. 2 4.49 l 1 0 234.67 75.67 24.49 1 1 1 lb.hi 69.73 26. 15 l 1 1 265.65 62.56 26.15 C -1 29l . 14 -4.1? 7.49 0 -1 110.14 4.12 7.49 1 1 -1 32 3.71 -3.43 6.98 0 1 -1 143.7 1 3.43 8.98 I r-i 2'>r.14 72.2'' 24. 61 1 0 -1 110.14 80.44 24.61 l i-i 323.71 68.91 25.12 1 1 -1 160.83 75.11 25.12 -l o 20 ".I 4 -0 .!-1r1 4 .96 0 -1 0 20.14 -0.00 , 4.96 0-1 1 143.71 3. 43 8.98 0 - 1 1 323. 71 -3.43 8.98 i-i 20':. i 4 78.24 24.49 1 -1 0 345.61 75.67 24.49 I -1 ! 14'.71 69.73 26. 1 5 1 -1 l 314.63 62. 56 26.15 -• -1 -1 256.'7 -3. 4 3 3.98 o -1 -l 76.57 3.43 8.98 l -i -l 2 S 6. 5 7 68 25.12 1 -1 -l 59.45 75.11 25. 12 NO. OF p FFI FCTIONS = 1 7 FIRST Tfc'IN SECQNO TWIN H K L PHI CHI TWO THE TA H K L PHI CHI TWOTHETA 1 I -1 3? 7'. 68.93 25.12 1 -1 0 345.60 75.67 24.48 0 1 -1 3' ).7i -3.43 8. 98 0 - 1 1 323. 70 -3.43 8.98 1 <* -1 ?'••".. 14 72. 2 0 2 4.61 1 -1 1 314.63 62.55 26. 15 0 0 -1 2--0-.14 -4.11 7.49 1 0 0 290. 14 81. 76 2 3.96 l -l -i 255. 57 6R. 9' 25.12 1 0 1 290.14 64.70 25.66 r. -l -l 254. 57 -3.43 8.9P 0 0 1 290.14 -4.11 7.49 I -1 ?: 0.14 7H.23 24.48 1 1 1 265.64 62. 55 26. 15 ' -1 0 2" -.14 0. 0 4.95 0 1 1 256.57 -3.43 8.98 1-1 1 14 3. 7.1 6 9.73 26.15 1 1 0 234.67 75.67 24.48 r. .] 1 ) 4 » .7", 3.43 8.98 0 1 0 200. 14 0. 0 4. 95 1 1 11' . 14 72. 94 25. 66 1 1 -1 160.82 75.11 25.12 (' 1 11' .14 4.11 7.49 0 1 -1 143.70 3.43 8.98 1 I 1 7 * . 5 7 69. 71 26. 15 1 0 -I 110. 14 80.43 24.61 C 1 1 In. 57 3.4) 8 . 98 0 0 -1 110.14 4.11 7.49 I 2 0.! 4 9-" ,T. 23.96 0 -1 -1 76.57 3.43 8. 98 1 ! r 2" . 1 4 71-.23 24.48 1 -1 -1 59. 45 75.11 25.12 o i 2". 14 0. 0 4.95 0 -1 0 20.14 0.0 4.95 FIP.ST Till" W0C1 CO 11''! /6" 6323 h. Y6„06'-68 9 3S20.0 6 124125500402611 S2 006026 11 WO \ /6.-.;;6.3?3 7.'Y60OO356 57S2O"6C "604S5C 0 400991 S 2006009 91 HOC 10'-. l.'l / too629014V6:;06'• 7?20S2C'6',? 161 S5:.r 4 02 5 40S2 OC 60 2660 MO'-.r,.i_''l/600 62"014Y4'.'l. ', 35 5 89S2' ' 600.6 56SFr 0401' 84 I S20060L841 W"01 1:. 1! -,j /6"0 6256*7Y6<"..-6( 6H03S2 H 6'. 24 12S5.JC4 1261 IS2006026 11 MOT I.'.' 1 101 /6:' '62r>6 57Y6'.''6350 5 7S2C C60C804 S5 004 009 91 S2O06OO991 WOO] KKOC / 60 0 62.'--il4Y60r6r 78 Z3S2O0 6O2348S530 402547S200602547 WOOO 1 "10'0/6"t (2'.!."14Y60'r,.ir -«ns2'.0AC«4.'3SV 0 410 586S2 00 60C586 W001 1'' 10 01 / to.: 11 4 7 7'.Y6 \06< 6975S20C6.;2515S5( C4"2714S200602714 WW'l'") /6' :614?70Y6''f.'tr f 3 4 3 S 2 00 61'" 8 C 4 S 5C040"9 91 S2 006009 91 WOCl"'0l'.'• 1/6 0"61 1,'. 1 4 Y6''U6072 94 S2 3C 612466 S50.L4 02665 S2006C 2665 WOOOOt' 10'." 1/60061 1'. •14Y6T60041 1 S2 •"'6". 06 56 S 5l<" 4C 0 841 S 2 016 008 41 WOO! IH 10 .' 1 /f T.'60 7657V6 10601 978 S2 0'' 60 25 1 IS 5.0 4u 27 14S 200 60 27 14 WOOO'I'" 1001 /60 : '6.176 57 Y6 0C6OC 3 43 S2 006 3uP04 S5 004009 91 S2 006009 91 W1C]or 00 /6 0-16" 20 14 Y-i,! '.60<0 ;•'< S2C06-J22°'.S5Cl 40 2 496S2OC6O2495 Wi:oir(M0'H./6O",i6O2' 14Y6 ' 06''7 " 2 < S20 06" 2 3 4 8 S 5'JO 4 >2547S200602547 WOOO'lOC /6 00 6" 2; I COS2CJ4?n«03S5< 0 4.)'.5 86S2 006005 86 SFCONP TWIN W001 K'lo; i-/6v..63«56»Yftf-C60 756 7S2006'234 6S5r0 4S2 54 7S2CC602547 WOCOI i- l' 0) /OO'"*-'237' Y6' 06356 57S 2006' ( 3r4S5004')C991S200 6009 91 W001 l' K 0 1/6006?I 4h3Y6O06.'6255S2r060281 5S5::i.402714S200602714 WiOlO'. ...'."r/6'w- 629' 1'.Y6"C606170S200 60 2296S50C 4'J24O5S200602495 W001 Or : 1 / 6".V62 0"1 >.Y6.",.'6064 70S20r 6"!2466S 500402655S 20060 2665 WOOO"rO0': 1/6"''629' 14Y6f ''6.3s5 8iS2 0C60C6 56SSOC'4iH'841S2P06C0841 WOO 11' 1' 01/60.. 6 26 564Y6'.'06r '.'255S2',C6i2515S5(C 402 714S2OC602714 WOOO or 1001 /60"o2 5 6S7Y6' i 6 356 *7 S2006'1 ;&0 4S 500400991 S2 0 3 600991 WOO IOC 1C:'( /6'V 62 3467Y6OO6O75 67S2r.06O2 348S50C402 54 7S2r;C'602 547 WCOOO' 1 (>•'.( /6 0'. 6?i: (. 14Y6: 06 3' v'rjS21. 0 60 04 ) 3 S 500 400 5 85 S2 00 60 05 86 WOO 10" 1 1"! / 6 I0 6 1oi-82Y4C'.63 75 1L S2O.;60 24 12S5!.'C402611S2C0 60 26U WCOOO.: Ill 1/6':. 4 14 3 7"'Y6 ,060 03 4 3S2'0 6r'.804S5 0C 40099 1S20C 600991 WOO 10 ".'101/60 .61101 4Y.V.-.0603 • 43-S2"0 63 23 6 1 S 51 0402560S200 602560 WOCO'jiOlO 1/600 6110 14 Y6006T; 04 1 1 S2 f 0 60 06 5 6 S5'. 0 4008 41 S2P 060 0841 WOC 0 101 1 " 1 /60 'J60765 7 Y6' ('60 0 3 43S 2 "0 60080 4S 50C 400 9 91 S2 00 600991 W001 K'll 1 /60.- 40 5 945 Y60 0607 5 11 S2 0O6'^ 24 12S 500 40 261 1 S2C 360 2611 WOO-10 1 ( X Ik' ...'6,'20 14Y6' 06t 00 0" S200600403 S50040C"586S2006005 86 119 BIBLIOGRAPHY. 1. H. Lipson and W. Cochran, "The Crystalline State, vol. Ill: The Determination of Crystal Structures", 3rd. edn. G. Bell and Sons, Ltd., London (1966). 2. G.H. Stout and L.H. Jensen, "X-ray Structure Determination; A Practical Guide", The Macmillan Company, London (1968). 3. M.M. Woolfson, "X-ray Crystallography", Cambridge University Press, (1970). 4. M.J. Buerger, "Vector Space", J. Wiley and Sons, Inc., New York (1959) 5. "International Tables for X-ray Crystallography", (a) vol. I (1952); (b) vol. II (1959); (c) vol. Ill (1962). Kynoch Press, Birmingham. 6. M.M, Woolfson, "Direct Methods in Crystallography", Oxford University Press (1961). 7. J. Karle and I.L. Karle, Acta Cryst. (1966) 21, 849. 8. A. Rosenthal and P. Catsoulacos, Can. J. Chem. (1968) 46_, 2868. 9. A.J.C. Wilson, Nature (1942) 150, 151. 10. TANS program, written by M.G.B. Drew; see, for example, M.G.B. Drew, D.H. Templeton and A. Zalkin, Acta Cryst. (1969) B25, 261. 11. I.L. Karle, K.S. Dragonette and S.A.' Brenner, Acta Cryst. (1965) 19, 713. 12. J. Karle and H. Hauptman, Acta Cryst. (1956) 9_, 635. 13. W. Cochran, Acta Cryst. (1955) 8, 473. 14. J.C. Sowden, Advan. Carbohydrate Chem. (1957) 12^ 35. 15. R.L. Whistler and J.N. BeMiller, Advan. Carbohydrate Chem. (1958) 13, 289. 16. A.A.J. Feast, B. Lindberg and 0. Theander, Acta Chem. Scand. (1965) 1!9, 1127. 17. R. Norrestam, P.-E. Werner and M. v.Glehn, Acta Chem. Scand. (1968) 22, 1395. 18. P.-E. Werner, R. Norrestam and 0. RBnnquist, Acta Cryst. (1969) B25, 714. 19. R.F. Stewart, E.R. Davidson and W.T. Simpson, J. Chem. Phys. (1965) 42, 3175. 120 20. D.W.J. Cruickshank, Acta Cryst. (1956) 9^, 757. 21. W.R. Busing and H.A. Levy, Acta Cryst. (1964) 17_, 142. 22. K.N. Trueblood, E. Goldish and J. Donohue, Acta Cryst. (1961), 14, 1009. 23. T. Sakurai, M. Sundaralingam and G.A. Jeffrey, Acta Cryst. (1963) 16, 354. 24. A.T. McPhail and G.A. Sim, J. Chem. Soc. (1965) 227. 25. T.C.W. Mak and J. Trotter, Acta Cryst. (1965) 1_8, 68. 26. Ju.T. Struckov and T.L. Hocjanova, Structure Reports (I960) 24, 647. 27. J. Trotter, Tetrahedron (1960) 8, 13. 28. P. Coppens and G.M.J. Schmidt, Acta Cryst. (1965) 1_8, 62. 29. J.L.. Galigne" and J. Falgueirettes, Acta Cryst. (1970) B26, 380. 30. B.L. Barnett and R.E. Davis, Acta Cryst. (1970) B26, 326. 31. C.A. Coulson,."Valence", The University Press, Oxford (1963), chapter 8. 32. H.A. Bent, J. Inorg. Nuclear Chem. (1961) 19, 43. 33. O.L. Carter, A.T. McPhail and G.A. Sim, J. Chem. Soc. (A) (1966) 822. 34. L. Pauling, J. Am. Chem. Soc. (1936) 58, 94. 35. G.C. Pimentel and A.L. McClellan, "The Hydrogen Bond", W.H. Freeman and Co., San Francisco and London (1960), page 177. 36. R. Parthasarathy, Acta Cryst. (1969) B25, 509. 37. N. Camerman and J. Trotter, Can. J. Chem. (1961), 39, 2133. 38. R.E. Long, Ph:.D. thesis, (1965), U.C.L.A. 39. D. Sayre, Acta Cryst. (1952) 5_, 60. 40. T.D. Sakore and L.M. Pant, Acta Cryst. (1966) .21, 715. 41. F. Iwasaki and Y. Saito, Acta Cryst. (1970) B26, 251. 42. J. Trotter and C.S. Williston, Acta Cryst. (1966) 21^, 285. 43. G. Ferguson and G.A. Sim, J. Chem. Soc. (1962) 1767. 44. G. Ferguson and G.A. Sim, Acta Cryst. (1961) 1£, 1262. 45. T.F. Lai and R.E. Marsh, Acta Cryst. (1967) 22, 885. 121 46. O.L. Carter, A.T. McPhail and G.A. Sim, J. Chem. Soc. (A) (1967) 1619. 47. M. Sax, P. Beurskens and S. Chu, Acta Cryst. C1965) 18, 252. 48. W. Harrison, Ph.D. thesis, (1969), Newcastle-upon-Tyne Polytechnic, Newcastle-upon-Tyne. 

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