Crystal Structures with Many Symmetry ... - ACS Publications

May 2, 2008 - under which one polymorph or the other may be formed. Introduction ..... sensitive to minor detail than the real space one. (i) 5H-Diben...
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CRYSTAL GROWTH & DESIGN

Polymorphic Perversity: Crystal Structures with Many Symmetry-Independent Molecules in the Unit Cell† J. Bernstein,*,# J. D. Dunitz,*,§ and A. Gavezzotti*,‡ Chemistry Department, Ben Gurion UniVersity of the NegeV, Beer SheVa, Israel, Chemistry Department OCL, ETH-Hönggerberg HCI H333, Zurich, Switzerland, and Dipartimento di Chimica Strutturale e Stereochimica Inorganica, UniVersity of Milano, Milano, Italy

2008 VOL. 8, NO. 6 2011–2018

ReceiVed December 5, 2007; ReVised Manuscript ReceiVed January 18, 2008

ABSTRACT: An extensive analysis of polymorphic crystalline systems of organic compounds in which at least one member has a high number of molecules in the asymmetric unit (Z′ > 2) has been carried out. Crystal structures are compared by traditional methods based on crystallographic cell reductions and powder patterns, as well as from stability considerations by comparing the distribution of molecule-molecule energies in the packing coordination sphere. The combination of these methods allows a safer detection of genuine polymorphism, since real space and reciprocal space information are seen to be complementary. In many cases, a clear-cut difference between polymorphic structures appears. However, there are also cases where X-ray structure determinations of “new” polymorphs can be better interpreted merely as low-quality redeterminations of previously found phases. The present study provides improved crystal structure recognition methods and clarifies some details of the molecular organization in crystal structures with high Z′. We discuss problems of how polymorphs are to be defined and make some suggestions about the conditions under which one polymorph or the other may be formed. Introduction Crystal polymorphism of organic compounds seems to be currently a subject of great interest both for pure science and for its industrial consequences, especially for pharmaceutical production. The recent literature reports an increasing amount of work dedicated to the development of new skills in polymorph screening, recognition, production, and computer generation; firm predictions and documented examples of control over polymorphic perversity are nevertheless sparse. Increased instrumental accuracy and sensitivity of X-ray diffraction apparatus together with highly efficient computer programs for crystal structure solution and refinement now allow rapid studies in exquisite detail of materials that only 10 years ago would have been considered unsuitable for analysis. As a result, we now have more and more studies of very small, imperfect crystal specimens, and some of these studies have revealed large numbers of molecules in the asymmetric unit. While the instrumental and computational advances represent truly significant progress, they also bring home the lesson that caution is called for in interpreting results obtained from very small, poor quality crystal specimens, especially where polymorphism is involved. On the one hand, there is the understandable drive to produce and recognize new polymorphic systems and to document extreme cases of this phenomenon; on the other hand, one has surely to apply a parsimony principle, granting the status of crystal polymorph only to significantly different systems, thus excluding minor variants that often appear during the assembly of weakly bound molecules into crystals.1 After all, almost any two specimens of the same crystal are never quite identical. The key to this restrictive but scientifically justified attitude is, † This paper was intended to be published as part of the Special Issue “Facets of Polymorphism in Crystals” (Cryst. Growth Des. 2008, Vol. 8, issue 1). * To whom correspondence should be addressed. E-mail: [email protected] (J.B.); [email protected] (J.D.D.); [email protected] (A.G.). # Ben Gurion University. § ETH, Zurich. ‡ University of Milano.

obviously, the definition of “significantly different” by some readily applicable and objective method for comparing crystal structures. An analysis of the packing modes of organic crystals with two molecules in the asymmetric unit has been already presented.2 We now offer a systematic study of one-component polymorphic crystals in which at least one member of the polymorph system has more than two molecules in the asymmetric unit.3 Crystal data were retrieved from the Cambdrige Structural Database (CSD).4 In comparing crystal structures, the traditional reciprocal space approach, comparison of X-ray powder diffractograms, provides a quick and sometimes almost decisive method of comparison. In real space, inspection of unit cell parameters and their reduction is obviously called for, and, of course, visual comparison of packing motifs and diagrams can be most informative. Here, we place special emphasis on the calculation of molecule-molecule pair energies,5a,b using simple 6-exp atom-atom potentials.6 In one case of special interest to us, hypothetical crystal structures with Z′ ) 1/2 were generated by computer and compared with observed crystal structures with multimolecular asymmetric units. The combined application of real- and reciprocal-space methods of analysis leads the way towards an objective assessment of the degree of similarity between different crystal structures of the same compound, adding a more quantitative, energetic aspect to this task.7 The still distant goal is the identification and control of the physical factors that promote the formation of multimolecular asymmetric units in organic crystals.8 Computational Procedures The CSD was searched with the following query (ConQuest software): Z′ > 2 (where Z′ is the number of symmetry-independent molecules in the unit cell), organic, 3D coordinates present, “polymorph” qualifier present, no R-factor restriction, no atoms heavier than Cl. The entries were manually checked for those which also had other polymorphs with Z′ < 3, and these further polymorphs were also retrieved. The search is not exhaustive because polymorphs are sometimes designated as “form”, “phase”, or “modification”. Nevertheless, the size of the retrieved sample is more than adequate for the present purpose. The final data set of 138 crystal structures contains:

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38 groups of structures with 2 polymorphs; 8 groups of structures with 3 polymorphs; 4 groups of structures with 4 polymorphs; 2 single structures with Z′ > 3 that carry the “polymorph” qualifier but where the structures of other polymorphs are not known. Hydrogen-atom positions were reassigned by a recently developed protocol:2 briefly, C-H hydrogens were relocated using obvious geometrical criteria, with distances 1.08 Å; O-H and N-H hydrogens were relocated using CSD positions as starting point, with distances renormalized at 1.00 Å. A list of CSD refcodes and crystal data is deposited as Supporting Information, Table S1. To avoid the influence of the many factors that can affect experimental powder diffraction patterns, uniformly renormalized simulated powder spectra were generated as follows.5c Intensities Ihkl(θ) are calculated using an average thermal factor B ) 5.0 Å2, and the complete powder profile is then generated by placing each Bragg peak at its calculated position 2θ°, with an exponential spread:

I(θ) ) Σh,k,l Ihkl(θ°) exp(-t(θ - θ°)2) where t is an adjustable sharpening coefficient taken equal to 500 for high resolution, or 100 for low resolution. Renormalization is performed by setting the intensity of the strongest peak to a standard value. Real space comparisons were made by inspection of cell parameters and group-subgroup relationships, and by inspection of special projections. The main focus of this work is, however, on comparisons of molecule-molecule interaction energies in the crystal.5a For each crystal structure, distances between centers of mass of pairs of molecules, R(mol-mol), are collected and matched to the corresponding interaction energies, E(mol-mol), calculated with universal atom-atom potentials.6 For one compound of special interest to us, benzidine, hypothetical low-energy crystal structures with Z′ ) 1 or 1/2 were generated by computer search. All calculations were carried out with the OPiX computer program package,9 “Fc” module for structure factor calculation and powder pattern generation, “Oprop” module for lattice energies and molecule-molecule energies by the atom-atom potential method, “Prom” module for polymorph crystal structure generation.

Figure 1. (a) Scatterplot of differences in cell volume (Å3) between polymorph pairs and differences in Z′. (b) Same, differences in lattice energy (kJ mol-1). (c) Same, differences in crystallographic R-factor.

Scheme 1

Results The entire data set was first subjected to a general statistical study. For each polymorph pair, the following quantities were calculated: the difference in Z′ (∆Z′); the difference in conventional crystallographic R-factor (∆Rf); the difference in cell volume per molecule (∆V); and the difference in lattice energy (∆E). The ∆Z′/∆V plot (Figure 1a) shows a slight apparent tendency for larger volume (lower density) with increasing Z′. The ∆Z′/∆E plots (Figure 1b) show that there is no systematic trend in lattice energy as a function of Z′. Thus, a mild extrapolation would suggest that the presence or absence of symmetry relationships among the molecules in the crystal unit cell seems to have very little to do with the physical properties of the crystal. The ∆Z′/∆Rf plot (Figure 1c) shows no systematic trend in R-factor as a function of Z′. One might have expected that some structures with high Z′ would present refinement problems, arising from an unfavorable ratio between number of measured reflections and number of parameters. There may also be a tendency for high Z′ crystals to be of poorer quality than their low Z′ polymorphs.10 On the other hand, the lower Z′ structures may sometimes be disordered, leading to other kinds of refinement problems. One cannot expect a uniform, agreed approach to these problems. Indeed, for these nonroutine structure determination, one might imagine that a greater or lesser degree of time and effort might be applied, depending on the personal interests, capabilities, and limitations of the individual investigators. R/E plots were drawn for many groups of polymorphs. In such plots the horizontal axis is the distance between molecular centers of mass, and the vertical axis is the molecule-molecule interaction energy calculated by the standard atom-atom UNI

force-field formulation6 or by a Coulombic summation over empirical atomic point charges.6b A few typical cases are discussed below (see Scheme 1). (a) 3-Amino-5-(4-pyridyl)-1,2-dihydro-pyrid-2-one (1). The R/E plot in Figure 2a reveals the complete overlap of DUVZOJ11a and DUVZOJ03,11b which refer to the same polymorph (Z′ ) 4), as is evident from the close agreement between the cell dimensions

Crystal Structures with Symmetry-Independent Molecules

Figure 2. Typical examples of R/E plots for different polymorphs: (a) DUVZOJ (Z′ ) 4), DUVZOJ01 (Z′ ) 6), and DUVZOJ03 () DUVZOJ). (b) KOKQUW (Z′ ) 0.5) and KOKQUW01 (Z′ ) 6). Horizontal axis: distance between molecular centers of mass (Å). Vertical axis: molecule-molecule interaction energy calculated by the 6-exp UNI atom-atom potential functions.6

reported in two independent and almost simulataneous studies: there is no hint of obvious pseudosymmetry relating the independent molecules in this polymorph, called the R-modification. In contrast, DUVZOJ01 with Z′ ) 6 is seen to have a quite different R/E pattern. This structure, called the β-modification,11a has indeed a quite different packing. On the basis of powder diffraction patterns, an additional disordered version of the β-modification has been described (DUVZOJ0211a) with the c axis a third as long as in DUVZOJ01 and with Z′ ) 2; the weak superstructure reflections do not appear in the published powder diagram. No energy calculation is possible for the disordered structure. Renormalized powder patterns are shown in Supplementary Figure S1, Supporting Information. (b) 2,6-Di-t-butylnaphthalene (2).12 The patterns for the two polymorphs KOKQUW (P21/c, Z′ ) 0.5) and KOKQUW01 (P21, Z′ ) 6) (Figure 2b) are clearly different. While the KOKQUW structure gives a pattern of individual scattered points, the KOKQUW01 pattern consists of clusters, each containing six points. Nevertheless, the two molecular packings show some similarity as discussed in the original publications.12 The former has the higher density at 223 K (1.061 vs 1.018 g cm-3), and differential scanning calorimetry shows that it transforms to the Z′ ) 6 form above room temperature in what appears to be a nucleated first-order transition. NMR studies show that the dynamics of the t-butyl groups in KOKQUW01 are different from and more complex than those of KOKQUW. (c) 3-Phenyl-1H-indazole (3). The R/E plots shown in Figure 3a show some degree of similarity but clearly correspond to different polymorphs, UHENUQ (P1j, Z′ ) 6) and UHENUQ01 (C2/c, Z′ ) 3), as was recognized in the original publication.13 The similarity arises from the fact that both polymorphs are

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built from closely similar hydrogen-bonded N-H · · · N trimers differing only with respect to the arrangement of the phenyl groups. (d) 2,5-Diphenyl-1,3,4-oxadiazole (4).14 As in Figure 3a, the R/E plots in Figure 3b again show some cluster similarity but correspond to different polymorphs, NAXDIZ01 (P21/c, Z′ ) 1) and NAXDIZ04 (Cc, Z′ ) 6), described in detail in the original X-ray work.14b In both polymorphs the basic building blocks are molecular stacks, related by the short a translation (5.2 Å) in NAXDIZ01 but arranged in a more complex sequence along the [101] direction in NAXDIZ04. As in the KOKQUWKOKQUW01 example, it is the less densely packed Z′ ) 6 polymorph that is stable at high temperature. (e) N,N′-Bis(n-butyl)-1H-pyrrole-2,5-dithiocarboxamide (5). In the room-temperature structure, LANXOO15a (P21/n, Z′ ) 1) one of the n-butyl chains is disordered; on cooling the crystals to around 190 K, there is a first-order transition to a closely related, more ordered, denser superstructure (LANXOO02,15b P21, Z′ ) 12). The powder diagrams (Supplementary Figure S2, Supporting Information) are similar but clearly distinct, with the additional peaks expected for the superstructure in evidence. The R/E plot in Figure 4 shows that the points for the low Z′ structure are more or less at the center of clusters for the high Z′ structure. Other R/E plots (see below, Figures 5 and 6) share the same property. In these examples the high-Z′ structure can be regarded as a kind of “spreadout” version of the packing motif found in the low-Z′ structure. (f) Benzotriazole (6). The two crystal polymorphs of this compound are both high Z′ structures. In BZTRAZ16a (P21, Z′ ) 4), the molecules are assembled into chains via N-H · · · N hydrogen bonds, whereas in BZTRAZ0116b (P1j, Z′ ) 5), the molecules are linked into centrosymmetric 10-membered rings. Here the similarity between the R/E plots in Figure 5a does not emerge from any strong similarity between the crystal structures but is merely a consequence of the same general falloff of pairing energy with increasing intermolecular distance. The powder diagrams of the two BZTRAZ polymorphs (Supplementary Figure S3, Supporting Information) are distinctly different. (g) 4,5-Bis((benzylamino)carbonyl)-1H-imidazole (7).17 There is again a substructure-superstructure relationship between the two polymorphs, HUKHUQ 01 (Z′ ) 2) and HUKHUQ (Z′ ) 6, with similar cell dimensions but with one axis three times longer); here it is the high Z′ structure that is more stable at high temperatures and transforms to the more dense low Z′ structure on cooling. Note the identical behavior of UNI 6-exp and Coulombic point-charge energies in Figure 5b.The powder patterns (Supplementary Figure S4, Supporting Information) show clear differences in relative peak intensities, as well as as the small systematic 2θ-shift from the contraction of the unit cell in the low-temperature polymorph. In the three cases just mentioned, LANXOO, BZTRAZ, HUKHUQ, the high and low Z′ structures are related but show distinct differences in the way the molecules are packed. (h) 2,2-Aziridinedicaboxamide (8).18 The two polymorphs (BIPCOS, BIPCOS01) were obtained from different solvents, form A (P41212, Z ) 32, Z′ )4) from methanol, form B (P1, Z ) Z′ ) 16) from dimethylformamide. R/E plots in Figure 6 show close similarity. On examination of the structures, however, one sees that they are built from nearly identical layers in different stacking patterns. The R/E plots reveal the similarities rather than the differences. The powder patterns (Supplementary Figure S5, Supporting Information) show some similarity with respect to the strong peaks but there are distinct differences in the distribution

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Figure 3. Typical examples of R/E (distance-energy) plots for polymorphs with partial coincidence: (a) UHENUQ (Z′ ) 6) and UHENUQ01 (Z′ ) 3); (b) NAXDIZ01 (Z′ ) 1) and NAXDIZ04 (Z′ ) 6). See also captions to Figure 2.

Figure 4. Typical example of R/E (distance-energy) plots for polymorphs where the low-Z′ phase has one point close to a cluster for the high-Z’ phase: LANXOO (Z′ ) 1) and LANXOO02 (Z′ ) 12). See also caption to Figure 2.

of minor features. Here the reciprocal space comparison is more sensitive to minor detail than the real space one. (i) 5H-Dibenz[b,f]azepine-5-carboxamine (Carbamazepine) (9). This compound has a rich polymorphic history. There are at least four polymorphs:19a the first, CBMZPN10 (P21/n, Z′ ) 1) was described almost simultaneously in two laboratories.19b,c Other polymorphs include a trigonal form CBMZPN03 (R3j, Z′ ) 1),19d a second monoclinic form CBMZPN12 (C2/c, Z′ ) 1),19d and a high-temperature triclinic form CBMZPN11 (P1j, Z′ ) 4).19a The structural units are all centrosymmetric (or in CBMZPN11 nearly centrosymmetric) dimers, linked across the amide groups. Figure 7 shows R/E plots for the triclinic and two monoclinic forms, calculated with 6-exp and also with Coulombic point-charge energies. The three polymorphs clearly show differences and similarities in the R/E patterns for both models (the calculated powder patterns, Supplementary Figure S6, are clearly different). Notice how the points at R ) 8.3 Å in Figure 7 (centrosymmetric molecular pairs with the two CdO · · · H-N hydrogen bonds) appear as a distinct cluster in both plots. The cluster at R ≈ 5.2 Å corresponds to stacking by pure translation (Figure 8a), while the cluster at R 5.8 to 6.2 Å corresponds to centrosymmetric pairs in which one phenylene group of each molecule makes a parallel stack interaction with its partner and a T-interaction with the other phenylene group (Figure 8b). These dispersive interactions have a stabilizing energy only in the 6-exp energy plot (Figure 7a). The hydrogen-

bonded cluster at R ≈ 8.3 Å has stabilizing components in both the 6-exp and the Coulombic plots. This is an example where R/E plots based on different energy schemes can give an impression of the nature and relative strength of the various types of packing forces in a crystal. It is noteworthy that in the examples discussed in Figure 7, the high Z′ polymorph is sometimes the low-density, hightemperature structure, while in other cases it is the high density, low-temperature form. (j) More High Z′ Cases; Perverse Polymorphism? We now discuss in more detail two selected high Z′. structures. Benzidine (10) (henceforth BZD) is reported to crystallize in four different crystal forms, I, II, III, IV, with a rather bewildering variety of molecular conformations.20 Of special interest here is the fact that two of these forms, I and IV, crystallize with 4.5 molecules in the asymmetric unit! Our second example is 4,4-diphenyl2,5-cyclohexanedione (11) (henceforth DPCD, refcode HEYHUO),21 which is also reported to crystallize in four crystal forms, A, B, C, D; of special interest here is the fact that two of these forms, B and C, crystallize in the same space group P1j with 4 and 12 molecules in the asymmetric unit, respectively.We concentrate our attention here on these egregious pairs BZD/I-IV and DPCD/B-C. Figure 9 shows the R/E plot for the BZD I-IV pair. The obvious scatter in this plot demonstrates that the molecular organization in these two crystal structures is different. For example, form I uses three molecule-molecule contacts at R ) 4.75, 5.25, and 5.90 Å, with energies of about -28 kJ mol-1, while form IV uses a set of contacts at 5 < R < 5.8 Å, with energies of -22 to -26 kJ mol-1. The corresponding plot of Coulombic interaction energies (not shown for economy of space) is also completely different in the 4.5–7 Å range of intermolecular distance. The two structures are obviously different, as is also confirmed by the powder pattern in Supplementary Figure S7, Supporting Information. Figure 10 shows the R/E plots for the DPCD/B-C pair: there is total overlap of recognition modes/energies, up to the finest detail of organization between molecules separated by 13 Å. The powder patterns (Supplementary Figure S8b, Supporting Information) clearly demonstrate the essential identity of the two structures, as was indeed already apparent in the simulated powder patterns shown in the Supporting Information of the original report.21 We believe that the putative Z′ ) 12 structure (Form C) is actually a defective sample of Form B. Presumably, the relevant diffraction data were collected from a (possibly imperfect) specimen of the Z′ ) 4 polymorph. Taking into

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Figure 5. R/E (distance-energy) plots for (a) BZTRAZ (Z′ ) 4), BZTRAZ01 (Z′ ) 5), (b) HUKHUQ (Z′ ) 6), HUKHUQ01 (Z′ ) 2). For the latter pair, the figure shows both the regular 6-exp energy and the point-charge Coulombic energy (Eqq).

Figure 6. R/E (distance-energy) plots for BIPCOS (Z′ ) 4) and BIPCOS01 (Z′ ) 16). See also caption to Figure 2.

account the higher standard deviations, the torsion angles derived for the molecules in Form C merge into those of Form B so the conformations are identical within the limited accuracy of the analysis; likewise, the two networks of intermolecular C-H · · · O contacts22 cannot be really distinguished from one another. Discussion The kind of analysis described in the preceding paragraphs obviously provides no answer to the fundamental question: why should such simple (chemically and structurally speaking) compounds crystallize in many polymorphs with high and/or noninteger numbers of molecules in the asymmetric unit, including sometimes widely different conformations? For example, benzidine crystallizes with a planar aromatic skeleton in the cocrystal with hydroquinone23 (CSD refcode PITYEW, P21/c, Z ) 2, Z′ ) 1/2), and a quick computer simulation of possible crystal structures easily afforded a number of very stable crystal structures with Z′ ) 1/2 also for the pure compound (see Figure S9, Supporting Information), a further demonstration, if need be, that the problem of predicting by theory the temperature-dependent, stable polymorph of an organic compound is far from being solved, in spite of much progress made in the last years. Is it a failure of theory? We do not know how to calculate what is the stable polymorph of

benzidine around ambient temperature. Or is it a failure of experiment? We have not yet succeeded in obtaining the stable polymorph. The distance-energy R/E plot describes the molecular coordination sphere in an organic crystal and can be a useful indicator of the similarity between crystal structures. One of its advantages is that the energy calculations need not be very accurate: in fact these “energies” need not correspond to any physical quantity and, in the simplest application of the method, may be taken merely as real-space indicators of the similarity in recognition modes between pairs of molecules. These energies can be calculated in a matter of seconds with ordinary computers and simple software.9 Of course, if a more realistic force field is used, more detailed information on the type of recognition mode can be gained.5a,b This is not to claim that R/E plots are the only or the best way of identifying polymorphs and assessing the degree of similarity or difference between them. In some obvious cases, for example, DUVZOJ and DUVZOJ03, identity or close similarity among the cell dimensions is enough to make a strong case for assuming the same crystal structure. Another straightforward and nowadays rapid test is the comparison of powder patterns simulated from the single-crystal information stored in the CSD.7a This comparison does away with the problem of different cell reductions, choices of origin, and the like, but suffers from a degree of subjectivity when the patterns are similar but yet slightly different or when the structures are determined at different temperatures with consequent changes in cell dimensions. There remain the questions concerning subcells and supercells, ordered and disordered structures, modulated and demodulated structures, all involving closely similar crystal packings in which strict periodicity and other symmetry relationships may hold only imperfectly. We speak here of timeaveraged structures, not instantaneous ones, which are never strictly periodic. We further exploit the case of DPCD polymorphism to bring up a few points related to the caution that needs to be exerted in the handling of crystallographic data. Inspection of the b* projection of the Z′ ) 12 structure (HEYHUO02) could raise the suspicion that there may be an approximate, 3-fold translational repeat, so that intensities of reflections that do not belong to the reduced cell are systematically weak (in case of exact periodicity they would be systematically absent). However, the rule for such symmetry

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Figure 7. R/E (distance-energy) plots for CBMZPN10 (Z′ ) 1), CBMZPN11 (Z′ ) 4), and CBMZPN12 (Z′ ) 1). Left: 6-exp energies, right: point-charge Coulombic energies, Eqq. See also caption to Figure 2.

Figure 8. Two frequent association modes in crystals of carbamazepine. (a) Stacking by pure translation (amino hydrogens not shown). (b) Inversion center. The distances between centers of mass are 5.2 and 5.8-6.2 Å, respectively. The corresponding molecule-molecule energies are shown in Figure 7. Figure 10. R/E (distance-energy) plots for HEYHUO01 (Z′ ) 4) and HEYHUO02 (Z′ ) 12). See also caption to Figure 2.

Figure 9. R/E (distance-energy) plots for two polymorphs of benzidine, both with Z′ ) 4.5. See also caption to Figure 2.

absences may not be simple and hence the systematic nature of the absences not immediately obvious. For example, a simple transformation24 converts the Z′ ) 12 unit cell into a reduced unit cell almost indistinguishable from the published one for the Z′ ) 4 phase. Since two-thirds of the reflections of the putative Z′ ) 12 unit cell must be systematically absent or extremely weak, the atomic positions and vibrational parameters of 12 formally independent molecules need to be derived essentially from the diffracted intensities from a cell containing only four actually independent molecules. In such conditions, the least-squares normal equations matrix becomes badly behaved, and, in the extreme case, singular: each of the three individual molecules in the corresponding triad undergoes

random shifts in the atomic parameters, leading to apparently distinct molecular structures. A contributing factor in this difficulty is that in modern X-ray crystal structure analysis, the experimental diffraction data are measured automatically with minimal intervention by the scientist. In particular, weak, random, above-background intensity noise at positions between the Bragg reflections can easily be taken by an automatic indexing program as indication of a larger unit cell. This is especially likely to occur with poorly developed crystal specimens with possible inclusions of solvent (liquid, not just interstitial) and other defects and impurities, possibly with some twinning in the bargain. A careful observer, either in the old days of X-ray photographs or even better with modern 2D detectors which allow for the possibility of reconstructing selected slices of reciprocal space from the original frames, would surely notice if a revealing fraction of the X-ray reflections from a wrongly assigned unit cell were associated with intensities not significantly above background. Examples must be plenty; we may point to the putative polymorph of anthracene25 (ANTCAN17) with Z′ ) 1 (2 × 1/2) rather than Z′ ) 1/2, as in the usual, old-established crystal form, which turned out7a to be merely the original crystal structure with the c axis doubled. In the opposite case, failure to recognize genuine superstructure reflections or omission of such reflections from the structure analysis process or from the least-squares refinement solution must lead to a structure that is the averaged superposition of

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the several individual molecules that make up the genuine asymmetric unit. In the former case, wrong information was generated; in the latter, genuine information is lost. Wrong or nearly wrong cell assignments are essentially harmless as long as the purpose of the structure determination has to do with molecular geometry and conformation or with a gross determination of the packing modes. We emphasize here that what used to be merely a minor imprecision may turn today into a major nuisance, because the drive to discover new polymorphs or to construct new theories of molecular packing with a view to polymorph screening may sometimes be propelled by imagination rather than based on fact. We have already mentioned the HEYHUO example,21 and there is also the case of the questionable evidence for polymorph II of aspirin,26 recently reinterpreted in terms of domain intergrowths.27 The construction of shaky theories from erroneous data has examples also in the past: the reported crystal structure of the highly carcinogenic compound 10-methyl-l,2-benzanthracene with Z′ ) 10, was used to suggest that high values of Z′ (then known as the aggregation factor, not a bad descriptor) in crystals of aromatic hydrocarbons went together with carcinogenic activity.28 When the crystals were re-examined by Herbstein29 the high Z′ value was shown to be an artifact of unrecognized crystal twinning. Mistakes can always happen, but one factor contributing to the increasing frequency of this kind of mistake is automatic data processing without human intervention: computers do not think, they only process numbers. Concluding Remarks In the end, we have more questions than answers. (a) How should polymorphs be defined? In our opinion, subcell and supercell variants of the same underlying molecular arrangement should not be counted as distinct polymorphs, otherwise the number of reported polymorphs of what is essentially the same molecular arrangement can increase without bound. This brings us to a first basic problem: when are two crystals, or the same crystal under different conditions of temperature and pressure, to be counted as polymorphs? How are polymorphs to be recognized, characterized, distinguished, and described? We might as well start with McCrone’s wellknown definition: “A polymorph is a solid crystalline phase of a given compound resulting from the possibility of at least two different arrangements of the molecules of that compound in the solid state”.30 The wording suggests that “compound” is to be interpreted in the context of the phase rule, that is, as “component”. Thus, according to this definition, rapidly equilibrating structures such as conformational isomers or tautomers count as a single component. The definition is not perfect but we may agree to accept it. When the crystal structures are known, we can accept the close identity of computed powder patterns from crystal structure data as evidence that the structures are the same, that we are dealing with the same polymorph.7a What if we do not know the crystal structures? Clearly, differences in physical properties (color, density, hardness, solubility, optical and electric propertiessalthough not crystal shape!) provide obvious indicators to differences in molecular arrangement in the underlying crystal structure. Also, in the absence of any knowledge about the underlying crystal structure, similarities and differences among powder diffraction patterns from different crystalline products can provide useful guidance. Here, however, we need to take into account that differences in the samples (particle size, preferred orientation, etc.) and in experimental conditions can lead to powder diffraction patterns with different peak shapes and relative intensities from the same

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polymorph. Thus, although close identity of experimental powder diffraction patterns from two samples is evidence of the same underlying crystal structure, differences in peak shape and relative intensity are not infallible indicators that the structures are different. Furthermore, the answer to the question whether or to what extent two powder diffraction patterns are significantly different, similar, or identical is one that surely depends on the point of view of the observer.31 In the end, therefore, although we shall continue to talk and write about polymorphs and polymorphism, we have no better suggestion than to continue to struggle on with McCrone’s definition. However inadequate it may be, it still seems to offer the best basis we have for mutual understanding. (b) Why do high-Z′ crystal structures arise? High-Z′ structures have been described as “snapshot pictures” and also as “fossil relics”8b of early stages in crystallization. Such descriptions have a certain charm. However, as we are almost totally ignorant of the nucleation process, the early stages in crystallization, these picturesque descriptions have the disadvantage that they are almost impossible to confirm or to refute. It is important to remember that crystal nucleation is a nonequilibrium process, that is, that it takes place only under conditions of high supercooling or supersaturation. We must not confuse the metaphor with the real thing. In describing our results for low and high Z′ polymorphs we noted a slight tendency for the high Z′ polymorph to have a lower density and therefore, when phase transformations could be observed, to correspond in general to the high-temperature form. When the opposite is true, for example, for LANXOO where the high Z′ polymorph has a higher density and corresponds to the low-temperature form, then it is usually a matter of a relationship between a disordered substructure and an ordered superstructure. When the structures are very similar, it becomes arguable whether they should be regarded as distinct polymorphs or merely as modulated and demodulated versions of the same basic molecular arrangement. Many crystallographers are aware that when crystals are cooled below room temperature, additional weak reflections often appear in the X-ray diffraction pattern and disappear again on warming, indications of this type of temperature-dependent order–disorder change. As for the high-temperature polymorphs: rather than telling us about early stages in crystallization, the occurrence of such high-Z′ high-temperature polymorphs may simply be a consequence of the way crystals are frequently obtained, that is, by cooling a warm solution of the compound in question. In such experiments with polymorphic systems, the first crystals to appear may very well be those not of the polymorph stable at room temperature but those of a polymorph stable at the higher temperature in question. This could be considered as a kind of paraphrase of Ostwald’s Rule, more appropriate for crystallization experiments. If our results may serve as a guide: when the polymorphs have different Z′ values (and are not mere modulated-demodulated variants of the same basic structure), then the one stable at high temperature is likely to be the high Z′ polymorph. Differences in rates of cooling in crystallization experiments could of course well lead to preferential formation of one polymorph or the other. (c) We have used here R/E plots which, with due allowance for the approximations in the force fields, provide at least a glimpse of the physics of the interaction. Simulated powder patterns involve only the geometry of the unit cell and of the molecular arrangement, and are sensitive to minor changes in them. But all methods of comparison of crystal structures

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Bernstein et al.

involve a certain amount of subjectivity in the definition of how large a difference must be present in order to consider two phases as genuine polymorphs. A sensible mix of powder diffraction patterns and R/E-plot energy calculations may be the best approach to the recognition of crystal identity and difference, and hence to the elimination of the most perverse cases from the polymorph landscape. Lattice energy calculations in any form seem to have very little to say about the reasons why high Z′ structures are adopted. 32

Acknowledgment. Figure 8 was drawn by Schakal.

Supporting Information Available: Table S1 with all refcodes and crystal data for the compounds considered; simulated powder patterns mentioned in the text, Figures S1-S8; plot of computer-generated crystal structures for benzidine (Figure S9) and Table S2, crystal coordinates for the best Z′ ) 1/2 structure. This material is available free of charge via the Internet at http://pubs.acs.org.

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NAXDIZ03, NAXDIZ. Franco, O.; Reck, G.; Orgzall, I.; Schulz, B. W.; Schulz, B. J. Mol. Struct. 2003, 649, 219. (a) Zielinski, T.; Jurczak, J. Tetrahedron 2005, 61, 4081. (b) LANXOO01, LANXOO02. Dobrzycki, L.; Zielinski, T.; Jurczak, J.; Wozniak, K. J. Phys. Org. Chem. 2005, 18, 864. (a) Escande, A.; Galigne, J. L.; Lapasset, J. Acta Crystallogr. 1974, B30, 1490. (b) Krawczyk, S.; Gdaniec, M. Acta Crystallogr. 2005, E61, o2967. Baures, W.; Rush, J. R.; Wiznycia, A. V.; Desper, J.; Helfrich, B. A.; Beatty, A. M. Cryst. Growth Des. 2002, 2, 653. Bruckner, S. Acta Crystallogr. 1982, B38, 2405. (a) Grzesiak, A. L.; Lang, M.; Kim, K.; Matzger, A. J. J. Pharm. Sci. 2003, 92, 2260. (b) Himes, V. L.; Mighell, A. D.; De Camp, W. H. Acta Crystallogr. 1981, B37, 2242. (c) Reboul, J. P.; Cristau, B.; Soyfer, J. C.; Astier, J. P. Acta Crystallogr. 1981, B37, 1844. (d) Lowes, M. M. J.; Caira, M. R.; L¨otter, A. P.; van der Watt, J. G. J. Pharm. Sci. 1987, 76, 744. (e) Lang, M.; Kampf, J. W.; Matzger, A. J. J. Pharm. Sci. 2002, 91, 1186. Rafilovich, M.; Bernstein, J. J. Am. Chem. Soc. 2006, 128, 12185. Senthil Kumar, V. S.; Addlagatta, A.; Nangia, A.; Robinson, W. T.; Broder, C. K.; Mondal, R.; Evans, I. R.; Howard, J. A. K.; Allen, F. H. Angew. Chem., Int. Ed. 2002, 41, 3848. Roy, S.; Banerjee, R.; Nangia, A.; Kruger, G. J. Chem. Eur. J. 2006, 12, 3777. Ermer, O.; Eling, A. J. Chem. Soc. Perkin Trans. 2 1925, 1194. Matrix [0–1/3–1/3; 0–2/3 1/3;-1–1/3–1/3] transforms the Z′ ) 12 unit cell of HEYHUO02, a ) 18.379 Å, b ) 19.970 Å, c ) 24.442 Å, R ) 95.01°, β ) 111.69°, γ ) 105.22 °, V ) 7872 Å3 into a Z′ ) 4 unit cell a ) 10.061 Å, b ) 16.204 Å, c ) 16.251 Å, R ) 88.12°, β ) 85.17°, γ ) 83.83°, V ) 2624 Å3, almost identical with the published data for HEYHUO01, a ) 10.094 Å, b ) 16.259 Å, c ) 16.292 Å, R ) 88.26°, β ) 85.34°, γ ) 83.65°, V ) 2648 Å3. Marciniak, B.; Pavlyuk, V. Mol. Cryst. Liq. Cryst. Sci. Technol. 2002, A373, 237. Vishweshwar, P.; McMahon, J. A.; Oliveira, M.; Peterson, M. L.; Zaworotko, M. J. J. Am. Chem. Soc. 2005, 127, 16802. Bond, A. D.; Boese, R.; Desiraju, G. R. Angew. Chem. Int. Ed. 2007, 46, 618. Mason, R. Acta Crystallogr. 1958, 11, 329. Herbstein, F. H. Acta Crystallogr. 1964, 17, 1094. McCrone, W. Polymorphism. In Physics and Chemistry of the Organic Solid State; Fox, D., Labes, M. M., Weissberger, A., Eds.; WileyInterscience: New York, 1965; Vol. 2, pp 725–767. Identity of experimental powder patterns from two crystal samples is evidence of the same underlying crystal structure, but differences in peak shape or intensity are not infallible indicators that the structures are different, not to mention that “identity” and “difference” surely depend on subjective judgment. Polymorphs are often identified and characterized by listing the positions and relative intensities of prominent peaks as compiled in the Powder Diffraction file maintained by the International Centre for Diffraction Data. This practice is common in pharmaceutical patents, but may be inadequate for cases where the structures share some common features (e.g., layer stacking as in BIPCOS) with identity of strong peaks and differences in weak ones. Characterization of crystal forms by a variety of physical and analytical techniques is to be strongly encouraged (see Bernstein, J. Polymorphism in Molecular Crystals; Oxford University Press: Oxford, 2002). Keller, E. SCHAKAL92, A Program for the Graphic Representation of Molecular and Crystallographic Models; University of Freiburg, Germany, 1993.

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