2322
`
`Chem. Mater. 1995, 7, 2322-2326
`
`An Ab Initio Approach to Crystal Structure
`Determination Using High-Resolution Powder
`Diffraction
`and Computational Chemistry Techniques:
`Application to 6,13-Dichlorotriphendioxazine
`Paul G. Fagan and Robert B. Hammond
`Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow G1 1XL, UK
`Kevin J. Roberts*-1"
`Department of Mechanical and Chemical Engineering, Heriot Watt University,
`Riccarton, Edinburgh EH14 4AS, UK
`Robert Docherty and Alan P. Chorlton
`Zeneca Specialties, Blackley, Manchester MA9 3AD, UK
`William Jones and Graham D. Potts
`Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, UK
`Received May 10, 1995. Revised Manuscript Received September 15, 1995s
`
`An alternative route for the crystal structure solution of molecular crystals is proposed
`and described. Using molecular and crystal modeling techniques in combination with high-
`the crystal structure of 6,13-dichlorotriphendioxazine, a
`resolution powder diffraction,
`commercially important dye molecule, has been solved. An independent single-crystal
`validation is performed by way of structure verification. The approach has particular
`application where, for example, sample size considerations preclude analysis by single-crystal
`techniques and provides an accessible alternative to existing strategies, especially where
`established powder methods fail.
`
`remains despite some notable successes,
`structure,
`elusive. Progress has been hindered by problems in
`both global minimisation and force field accuracy
`where the description of the electrostatic interactions
`has received much consideration.5 Concurrently we
`have witnessed the application of predominantly syn-
`chrotron X-radiation powder diffraction techniques for
`the structure solution of mainly inorganic crystals,6 and
`latterly organic molecular systems7 although conven-
`tional laboratory X-ray powder diffraction has been used
`for the solution of small-molecule systems.8 Crystal
`structures solved from powder X-ray data normally use
`the Rietveld refinement technique9 for which an ac-
`curate starting structure is needed.
`Starting models for structure solution from powder
`data have,
`to date, been obtained by Patterson10 or
`direct methods11 techniques which involve the separa-
`
`(4) See, for example: Perstin, A. J.; Kitaigorodsky, A. I. The Atom-
`Atom Potential Method·, Springer Verlag: Heidelberg, 1987. Busing,
`W. R. WMIN, a Computer Program to Model Molecules and Crystals
`in Terms of Potential Energy Functions; April 1981, Oak Ridge, TN
`37830
`(5) Price, S. L.; Stone, A. J. J. Chem. Phys. 1987, 86, 2859—2868.
`(6) Cox, D. E.; Hastings, G. B.; Thomlinson, W.; Prewitt, C. T. Nucl.
`Inst. Methods 1983,208, 573. Attfield, J. P.; Sleight, A. W.; Cheetham,
`A. K. Nature 1986, 322, 620.
`(7) Cernik, R. J.; Cheetham, A. K.; Prout, C. K.; Watkin, D. J.;
`Wilkinson, A. P. J. Appl. Cryst. 1991, 24, 222.
`(8) Lightfoot, P.; Tremayne, M.; Harris, K. D. M.; Bruce, P. D. J.
`Mater. Chem. 1992, 2, 1012.
`(9) Rietveld,  . M. J. Appl. Cryst. 1969, 2, 65.
`(10) Nolang, B. I.; Tergenius, L. E. Acta Chem. Scand. A 1980, 34,
`311.
`Published 1995 by the American Chemical Society
`
`Introduction
`Despite the importance of molecular engineering
`concepts in the development of novel speciality effect
`chemicals, our knowledge of the solid-state structure of
`such materials is surprisingly limited with less than 1%
`having a solved crystal structure. This has been due,
`in the preparation of
`in part, to difficulties inherent
`crystals of sufficient size and quality for single crystal
`structure determination. As the result of this the
`generation of structural data ab initio has become, in
`recent years, both a significant scientific goal1 and the
`subject of some controversy.2 The works of Gavezzotti3
`and Karfunkel1 represent considerable advances in this
`The increased sophistication of intermolecular
`area.
`force fields has meant that the interpretation of struc-
`tural models, via the well established atom-atom
`potential method,4 has in some cases, become routine.2
`However, the development of a reliable methodology
`which allows the prediction of the crystal structure of
`an organic material based solely on
`the molecular
`
`t Also CCRL Daresbury Laboratory, Warrington WA4 4AD, UK.
`8 Abstract published in Advance ACS Abstracts, November 1, 1995.
`(1) Karfunkel, H. R.; Gdanitz, H. J. J. Comput. Chem. 1992, 13,
`1171. Holden, J. R.; Du, Z.; Ammon, H. L. J. Comput. Chem. 1992,
`14, 422.
`(2) Maddox, J. Nature 1988, 335, 201. Cohen, M. L. Nature 1989,
`338, 291.
`(3) Gavezzotti, A. J. J. Am. Chem. Soc. 1991, 113, 4622—4629;
`Deem, M. W.; Newsam, J. Nature 1989, 342, 260-262. Halac, E.;
`Burgos, E.; Bonadeo, H.; D’Alessio, E. Acta. Crystallogr. 1977, A33,
`845.
`
`0897-4756/95/2807-2322$09.00/0
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`

`Ab Initio Approach to Crystal Structure Determination
`tion and integration of individual diffraction peaks.
`These approaches struggle to cope with systems of low
`symmetry where peak overlap is significant. Molecular
`mechanics and quantum chemical molecular modeling
`techniques, which can be utilized to provide sensible
`ab initio, will
`thus be of benefit
`starting structures
`where the above techniques fail. Molecular modeling
`techniques have in the past decade advanced to such a
`high level that
`the accurate prediction of molecular
`structures has become to an extent, albeit nontrivial,
`routine. Clearly molecules with a high degree of con-
`formational flexibility present the greatest challenge,
`but with modern computational facilities the torsional
`degrees of freedom, in the context of the crystal lattice,
`can be systematically searched on a reasonable time
`scale. The advantage is that the intramolecular coor-
`dinates of all atoms in the molecule can be predicted in
`to X-ray techniques where only the higher
`contrast
`electron density sites can be resolved before Rietveld
`refinement.12 Such effects can be significant when the
`scattering matrix is composed of similarly, poorly scat-
`tering atoms predominant in organic molecules. This
`contrasts with the analysis of inorganic materials where
`high scattering atom types dominate. For example
`McCusker,13 in her study of a clathrasil phase, was able
`to derive the Si and some O atomic sites but was not
`able to resolve the C atom intramolecular coordinates
`using direct methods.
`In this paper we report the application of a combina-
`tion of high-resolution powder diffraction and compu-
`tational chemistry techniques as a new ab initio ap-
`proach to crystal structure determination. We demon-
`strate the method through an application to the com-
`mercially important organic pigment 6,13-dichlorotri-
`phendioxazine. The work is validated through an inde-
`pendent single-crystal analysis. The specific aim of this
`the reliability of the technique in
`to assess
`study was
`cases where good single crystals cannot easily be
`obtained and to examine alternatives to other, equally
`viable, techniques.
`Crystal Structure Determination Using a
`Combination of Powder Diffraction
`and
`Molecular Modeling Techniques
`Basic Approach. Our overall approach to crystal
`structure determination using the new route involves
`essentially four main stages, each well established but
`never before utilized together in such a way to provide
`structure solution.
`Stage 1. Using standard modeling approaches with
`the aid of routinely available software packages,14’15
`molecular arrangements are obtained for the molecule
`under consideration.
`In turn the structure is optimized
`and refined using molecular mechanics and semiem-
`pirical quantum chemistry techniques to obtain preci-
`sion in bond lengths and angles. These calculations
`allow determination of the molecular geometry with
`respect to these two parameters with a high degree of
`
`(11) Berg, J. E.; Werner, P. E. Z. Kristallogr. 1977, 145, 310.
`(12) Rudolf, P. R.; Clearfield, A. Inorg. Chem. 1989, 28, 1706.
`(13) McCusker, L. J. Appl. Cryst. 1988, 21, 305.
`(14) CERIUS (Version 3.2), Molecular Simulations Limited, Cam-
`bridge, UK.
`(15) Bladon, P.; Breckenridge, R. INTERCHEM, a Program for the
`Graphical Display of Chemical Structures, Quantum Chemistry Pro-
`gram Exchange, 1994; 14, 47.
`
`Chem. Mater., Vol. 7, No. 12, 1995
`2323
`accuracy. By way of structure validation a comparison
`with a table of standard bond lengths and angles16 is
`in cases where the molecule
`performed. However,
`possesses internal conformational flexibility the model-
`ing of torsion bonds confers a nontrivial component. The
`use of an existing database of structures may provide
`an alternative route to the initial structure but cannot
`be considered as a routine approach to more
`complex
`systems and is thus not pursued in this paper.
`Stage 2. High-resolution (synchrotron) powder dif-
`fraction data are
`the sample material.
`collected on
`Following normalization, to account for beam decay,
`individual peaks are
`using the PODSUM17 program,
`identified visually before being modeled mathematically
`using PKFIT17 according to a prescribed peak-shape
`function. The peak positions so obtained are passed to
`a series of indexing programs which should in turn
`proffer the unit-cell dimensions for the system under
`test. From systematic absences the symmetry is ob-
`tained, and from density the number of molecules in the
`unit cell calculated. Synchrotron radiation is crucial in
`providing the peak resolution required (generally taken
`as 0.03°) for indexing in systems of low symmetry
`characteristic of organic materials.
`Stage 3. Using the information obtained from the
`it
`is possible to construct a series of
`above stages,
`starting crystal models for the system under test.
`Initially, with appropriate graphical display this can be
`achieved visually to obtain a sensible structure for
`energy minimization. After manual, but stepwise and
`systematic, variation of molecular orientation within the
`unit cell, by applying rotations and then translations
`to the rigid molecular framework, and adjusting torsion
`angles in flexible molecules, atom-atom potential mini-
`mization methods, using such programs as PCK8318 are
`used to calculate a series of possible low-energy crystal
`structures for further consideration. As a preliminary
`illustration of the method we treat here a centrosym-
`metric molecule; hence the inversion center
`is con-
`strained to lie at the unit-cell origin, and only rotations
`need be applied to the molecule. This, although serving
`as a useful example, does not imply that the methodol-
`as will be addressed in
`ogy is limited to such cases
`future work. Additionally, a computer algorithm to
`automate the search for starting structures by the
`systematic application of rotations,
`translations and
`molecular torsions is almost complete. The number of
`structures generated in the manual approach, it can be
`argued, is proportional to the time spent searching for
`them. Consequently, to ascertain the feasibility of one
`structure with respect to another, the powder diffraction
`profile for each is simulated and compared directly with
`the experimental data with respect
`to peak inten-
`sities—positions by virtue of indexing techniques must
`This is done quantitatively by refining the scale
`concur.
`factor and observing the difference spectrum. On
`comparing the theoretical structures in such a way, we
`obtain a rapid and reliable way of filtering out improb-
`able structures. Given that all the trial packing con-
`figurations have a low potential energy, a structure is
`
`(16) Allen, F. H.; Kennard, O.; Watson, D. G.; Brammer, L.; Orpen,
`A. G.; Taylor, R. J. Chem. Soc., Perkin Trans. 2 1987, 12, SI—S19.
`(17) Part of the Powder Diffraction Program Library, SERC Dares-
`bury Laboratory, Warrington, UK.
`(18) Williams, D. J. PCK83, Quantum Chemistry Programme
`Exchange programme, number 548.
`
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`

`2324 Chem. Mater., Vol. 7, No. 12, 1995
`
`Fagan et al.
`
`Figure 1. Results of the Rietveld refinement of DCTPD:
`(a)
`experimental high-resolution powder diffraction pattern; (b)
`residual plot showing the difference between experimental and
`theoretically modelled diffraction patterns; (c) marker points
`showing the location of diffraction points. The inset shows
`the molecular structure of DCTPD.
`if
`only considered for final
`refinement
`the powder
`diffraction simulation presents a good match with
`experimental data.
`In this, the final stage, the Rietveld method9
`Stage 4.
`is used to refine the theoretically produced structure.
`In this well-documented technique, a calculated diffrac-
`tion profile according to the proposed structure is fitted
`to the experimental data in a series of least-squares
`minimizations. Both structural (atomic positions, lat-
`tice and thermal) parameters and parameterized profile
`treated in the refinement.
`functions are
`Application to 6,13-Dichlorotriphendioxazine.
`6,13-Dichlorotriphendioxazine (C18H8N2O2CI2, see inset
`to Figure 1, hereafter referred to as DCTPD) is the basic
`chromophore unit of a number of commercially impor-
`It was prepared as a highly crystalline
`tant dyestuffs.
`powder following recrystallization from nitrobenzene
`and ground to a particle size of ca. 45 µ  .
`High-resolution powder diffraction data using a De-
`taken on beam-
`bye—Scherrer scattering geometry were
`line 2.319 at the Synchrotron Radiation Source (SRS)
`at CCRL Daresbury Laboratory in the UK. The storage
`ring operated at an energy of ca. 2 GeV with a stored
`beam current of ca. 175 mA. The incident beam
`wavelength was selected using a Ge(lll) monochroma-
`tor to provide photons at a wavelength of 1.202 29 A.
`Data were
`collected using an angular scanning range
`of 2  angle from 2° to 50° at a step size of 1 mdeg using
`a counting time of 1 s/point. Unit-cell dimensions were
`obtained from the first 30 reflections using the indexing
`programs of Werner et al.20 and refined using REFCEL.17
`The space group was determined by consideration of
`systematic extinction conditions. The lattice param-
`eters as determined were consistent with a bimolecular
`forcing the molecule to lie on
`a center of
`unit cell
`
`(19) Cernik, R. J.; Murray, P. K; Pattison, P. P.; Fitch, A. N. J.
`Appl. Cryst. 1990, 23, 292.
`(20) Werner, P. E.; Eriksson, L.; Westdahl, M. J.Appl. Cryst. 1985,
`18, 367. Visser, J. W. J. Appl. Cryst. 1969, 2, 89. Boulif, A.; Louér,
`D. J. Appl. Cryst. 1991, 24, 987.
`
`Figure 2. Experimental (—) and theoretical (---)
`powder
`diffraction patterns illustrating how comparison between two
`packing motifs (a and b) reveals a suitable starting structure
`for subsequent Rietveld refinement.
`(NB:
`(b)
`zero-point
`correction not applied).
`symmetry and thus halving the number of atoms
`involved in structure refinement.
`An approximate molecular model of DCTPD was gen
`erated via building modules within standard software,
`optimized using the molecular mechanics package
`MM2,21 and refined using semiempirical molecular
`orbital methods.22 The optimized molecular conforma-
`tion was placed in a proposed lattice from the unit-cell
`dimensions and by using molecular packing minimiza-
`tion methods together with the atom—atom technique
`a series of optimized lattice systems postulated. For
`these calculations we used the universal force field23
`together with charges calculated by the equilibrium
`method.24 Because of symmetry considerations, there
`no translational elements involved in the minimi-
`were
`zation.
`The hypothetical crystal structures derived from the
`then used to simu-
`molecular packing calculations were
`late the powder diffraction patterns25 which were,
`in
`turn, compared with the experimental data.
`In this
`through the on-line manipulation of the trial
`way,
`structures, a model structure having the best fit to the
`experimental data was obtained. For example, a struc-
`ture of feasible lattice energy of -46.9 kcal/mol was
`obtained in the first set of minimizations. Comparing
`the diffraction simulation data with the real profile
`the
`(Figure 2a) revealed reasonable agreement across
`2  range with only a few significant peaks missing. The
`
`(21) Sprague, J. T.; Tai, J. C.; Yuh, Y.; Allinger, N. L. J. Comput.
`Chem. 1987, 8, 581. Liljefors, T.; Tai, J. C.; Shusen, L.; Allinger, N.
`L. J. Comput. Chem. 1987, 8, 1051.
`(22) Stewart, J. P. P.; MOPAC 6.0, Quantum Chemistry Programme
`Exchange programme number 455.
`(23) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. J. Phys. Chem.
`1990 94 8897
`(24) Rappe, A. K; Goddard, W. A. J. Phys. Chem. 1991, 95, 58.
`(25) Yvon, K. J. Appl. Cryst. 1977, 10, 73.
`
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`

`Ab Initio Approach to Crystal Structure Determination
`
`powder
`
`ca. 45
`P2Vc
`8.717(1)
`4.887(1)
`17.147(2)
`97.865(3)
`723.59
`2
`
`298
`1.202 29
`2-50
`
`Figure 3. Overlay of the molecular structures which result
`from single-crystal (---)
`and combined modeling/powder
`diffraction (—) approaches.
`Table 1. Crystallographic Data for
`6,13-Dichlorotriphendioxazine“
`empirical formula
`C18H8N2O2CI2
`formula weight
`355.2
`density/mg cm-3
`1.646
`single crystal
`prism
`morphology
`370 x 150 x 70
`size/µ  
`P2\!c
`space group
`a/k
`8.700(2)
`b/k
`4.870(1)
`c/k
`17.064(3)
`97.50(3)
`ß/deg
`716.8
`voVA3
`Z
`2
`abs coeff/mm-1
`0.467
`298
`temp/K
`0.710 69
`wavelength/Á
`3-50
`2  range/deg
`standard reflections
`(306) and (10 10)
`R factor
`0.136
`0.073
`   |/ |  ß , where Y
` I Fobs -
`“ The R factor is defined as R =
`is diffracted intensity for the powder data and |F| for the single-
`crystal data.
`most significant of these (1 0 2) should have occurred
`at approximately 11°, 2 . The exaggerated presence of
`the (1 0 2) peak led the authors to rotate the minimized
`structure at 90° relative to the b axis. Subsequent
`minimization of the new arrangement led to a new
`structure of—47.2 kcal/mol which on pattern simulation
`thus
`presented a very close match (Figure 2b) and was
`selected, on both criteria, for Rietveld refinement. The
`used and yielded a structure
`program DEWS26 was
`solution with a final R factor of 0.1369 (for definition
`see Table 1). The mean
`isotropic temperature factor,
`based on all the atoms in the molecule, was
`refined to
`be 4.14(2) Á2. The resulting Rietveld fit to the data is
`In this the first two diffraction peaks
`shown in Figure 1.
`had to be omitted from the refinement because they
`occurred close to an area of residual low-angle scattering
`produced by the flat-plate sample holder. This produced
`a nonlinear background in the pattern which proved
`difficult to model.
`Verification
`of the Proposed Structure Using
`Single-Crystal Methods. Suitable crystals proved
`difficult to obtain using standard solution growth tech-
`sublimation at
`tem-
`niques. However, using vacuum
`perature ca. 400 °C, we were able to produce dark red
`
`(26) Sakthivel, A.; Young, R. A. DEWS, School of Physics, Georgia
`Institute of Technology, Atlanta, GA 30332.
`(27) The SHELX86 program is available from G. M. Sheldrick at
`the University of Gottingen, Germany.
`
`the
`
`2325
`
`f/12
`-2(5)
`10(5)
`4(5)
`-1(4)
`5(3)
`-2(4)
`10(3)
`2(4)
`3(3)
`0(4)
`3(3)
`11(1)
`form
`
`Chem. Mater., Vol. 7, No. 12, 1995
`Table 2. Anisotropic Temperature Factors (Á2 x 10s) As
`Refined from Single-Crystal Data"
`Un
`atom
`U22
`U23
`U13
`L/33
`Cl
`43(5)
`35(4)
`0(4)
`48(5)
`8(4)
`-5(4)
`C2
`4(4)
`54(5)
`42(5)
`28(4)
`-3(4)
`C3
`52(6)
`34(4)
`0(4)
`48(5)
`C4
`49(6)
`37(4)
`38(4)
`2(3)
`1(4)
`05
`52(4)
`38(3)
`41(3)
`7(3)
`7(2)
`-4(4)
`C13
`39(5)
`39(4)
`27(4)
`11(3)
`N14
`31(4)
`26(3)
`33(3)
`7(3)
`7(2)
`C14a
`34(5)
`21(4)
`43(4)
`0(3)
`3(3)
`-2(3)
`C4a
`33(5)
`23(4)
`46(4)
`5(3)
`-6(3)
`C13a
`37(5)
`23(3)
`37(4)
`2(3)
`-2(3)
`C5a
`32(5)
`32(4)
`31(4)
`5(3)
`52(1)
`74(2)
`24(1)
`44(1)
`C124
`18(1)
`temperature factor
`takes
`0 The
`exponent
`-2 2( / 31/ 2 *2 + ... + 2Uuhka*b*).
`Table 3.. Comparison of Non-Hydrogen Atom Positions
`for Two Methods (Coordinates Derived from Powder
`Technique Given First)
`atom
`y
`X
`z
`Cl
`0.7244(21)
`0.2040(7)
`0.1422(15)
`Cl
`0.1987(5)
`0.1394(10)
`0.7260(19)
`0.8774(21)
`0.2226(9)
`0.2782(13)
`C2
`0.2195(5)
`0.2711(10)
`0.8756(20)
`C2
`0.8428(22)
`0.1818(7)
`0.4053(13)
`C3
`0.1809(5)
`0.3988(10)
`C3
`0.8387(20)
`C4
`0.1220(7)
`0.3994(11)
`0.6534(22)
`C4
`0.1213(5)
`0.3972(9)
`0.6472(19)
`05
`0.0414(3)
`0.2665(8)
`0.3128(17)
`05
`0.0400(3)
`0.2634(6)
`0.3083(12)
`-0.0391(5)
`-0.0244(20)
`C13
`0.1351(11)
`-0.0380(4)
`-0.0407(17)
`C13
`0.1322(8)
`N14
`0.3727(18)
`0.1219(4)
`0.0000(9)
`N14
`0.0007(6)
`0.3807(14)
`0.1184(3)
`C14a
`0.1338(11)
`0.5300(22)
`0.1426(6)
`C14a
`0.1331(8)
`0.5323(16)
`0.1388(4)
`C4a
`0.1024(6)
`0.2643(12)
`0.4986(21)
`C4a
`0.2644(9)
`0.1009(4)
`0.4973(16)
`C13a
`0.0006(10)
`0.0644(7)
`0.1967(20)
`-0.0013(8)
`C13a
`0.0615(4)
`0.1980(17)
`C5a
`0.1336(11)
`0.0208(5)
`0.1567(22)
`C5a
`0.1360(8)
`0.0211(4)
`0.1549(16)
`-0.0881(2)
`-0.0562(9)
`0.2897(4)
`C124
`-0.0837(1)
`-0.0881(6)
`0.2942(2)
`C124
`Table 4. Comparison of Bond Lengths (Á) Obtained from
`the Powder and Single-Crystal Data
`powder data
`single-crystal data
`1.69
`1.71
`1.36
`1.39
`1.48
`1.47
`1.47
`1.39
`1.31
`1.32
`1.40
`1.37
`1.41
`1.39
`1.40
`1.36
`1.40
`1.39
`1.38
`1.38
`1.40
`1.37
`1.39
`1.39
`1.39
`1.34
`
`C124-C13
`C13-C12a
`C12a-C6a
`C6a-C6
`C6a-N7
`N7-C7a
`C7a—C8
`C8-C9
`C9-C10
`C10-C11
`Cll-Clla
`Clla-012
`012-C12a
`
`prism-shaped crystals of 6,13-dichlorotriphendioxazine.
`A suitable crystal of dimensions 0.37 x 0.15 x 0.07 mm
`selected for further analysis on an Enraf Nonius
`was
`CAD4 diffractometer using Mo   
`(0.710 69 Á) radia-
`tion. Data collection was carried out at ambient condi-
`tions with a 2  scan range of 3—50°. Of 1314 reflections
`measured 800 reflections were
`flagged as observed
`based on the criteria |F| > 3a|F0|. The (306) and (10 10)
`reflections were used as standard and measured after
`every 100 reflections. The structure was
`solved by
`
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`

`2326 Chem. Mater., Vol. 7, No. 12, 1995
`
`25 -
`
`15 -
`
`10 -
`
`5 J---------
`
`-
`
`0 0
`
`0.5
`
`1.0
`
`2.0
`
`2.5
`
`3.0
`
`1.5
`Expected   .
`Figure 4. Half-normal probability plot of differences in the
`fractional coordinates of the main-group atoms (with associ-
`ated standard deviations) for the two independently deter-
`mined structures.
`
`direct methods using SHELXTL/PC (version 4.1), a
`derivative of SHELX86,24 and refined 113 parameters
`using full-matrix least-squares. Hydrogen atoms not
`located from the Fourier difference maps were
`geo-
`metrically fixed. The final R factor for this structure
`0.073 (Table 1). The anisotropic temperature
`was
`factors refined from the single-crystal study are given
`in Table 2.
`Comparison between the results of the refinement
`from the powder and single crystal data is given in
`Tables 1, 3, and 4. The magnitudes of the differences
`between the cell parameters obtained from powder and
`single-crystal methods, although seemingly high in
`terms of the quoted standard deviations, are not unex-
`It is generally accepted that
`pected or unprecedented.
`cell parameters obtained from high-resolution powder
`diffractograms are more accurate than those obtained
`in the case of
`from single-crystal techniques, given,
`powder diffraction, a statistical averaging over
`a very
`large number of crystallites. A half-normal probability
`plot28 (Figure 4) was constructed for the two indepen-
`dently determined sets of 36 fractional coordinates of
`the main-group atoms. The ratio, <5p¿, of the ranked
`absolute differences in the fractional coordinates to the
`root of the average variance,
`the
`is plotted against
`expected value of <5p¿ given a normal probability distri-
`bution. This plot indicates that there are significant
`differences in three fractional coordinates. These cor-
`respond to the chlorine atom of the asymmetric unit.
`We believe that
`this is a subtle manifestation of a
`disorder effect operating in the single crystal, grown by
`
`(28) Abrahams, S. C.; Heve, E. T. Acta Crystallogr. 1972, A27, 157.
`
`Fagan et al.
`sublimation, but not manifest in the powdered sample,
`grown from solution. The disorder arises from an
`interchange in position of the nitrogen and oxygen
`atoms. The averaging of the molecular orientation
`the single-bond, double-bond char-
`effectively removes
`acter in the central ring of the molecule in the single
`crystal structure (note in Table 4 the equal carbon-
`carbon bond lengths C6a-C6 and C13-C12a). This has
`greatest effect on the positioning of the chlorine atoms
`attached to the central carbon atoms. Taking into
`this disorder effect
`that
`it can be seen
`the
`account
`atomic positions (Table 3) and intramolecular bond
`lengths (Table 4) derived from both approaches are
`in
`satisfactory agreement. The similarity in derived struc-
`tures can be easily illustrated through the overlay of
`the two molecular conformations shown in Figure 3
`which reflects the small value of 0.051 for the RMS15
`fit between the two structures expressed in Cartesian
`coordinates.
`
`Conclusions
`Although the molecular and crystallographic struc-
`tures of DCTPD are constrained via the ring systems
`there is much we
`and space-group symmetry,
`can
`conclude from this work with a view to the application
`of the technique for more
`complex systems.
`Despite the fact that ab initio prediction of crystal
`structures from calculations based purely on molecular
`modeling calculations remains a long-term goal, the use
`of high-resolution X-ray diffraction provides, perhaps,
`one of the key experimental benchmarks needed to test
`molecular modeling calculations and mitigate concerns
`over global minimization and force-field accuracy. This
`work demonstrates the utility of combining molecular
`modeling and diffraction techniques to solve molecular
`structure ab initio, particularly in the case of low-
`symmetry organic structures. Although, in the case
`presented here, validation is provided by single-crystal
`analysis, there are many examples within specialty fine
`chemicals, such as pharmaceutical materials, where
`single crystals of sufficient quality and size cannot be
`It is in the examination of such materials that
`obtained.
`our approach offers the most promise. Work is currently
`in hand to extend the methodology developed toward
`an approach for the routine consideration of molecules
`with conformationally flexibility. Results from this will
`be reported in future papers.
`Acknowledgment. We are grateful to the SERC
`and Zeneca Specialities for the financial support of a
`CASE studentship to P.G.F. to CCRL Daresbury Labo-
`ratory for beamtime on
`the SRS, and to the SERC/
`EPSRC for a research grant (GR/H/40891) and current
`support of a senior fellowship (K.J.R.).
`CM9402459
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