Investigating Unused Hydrogen Bond Acceptors Using Known and

Investigating Unused Hydrogen Bond Acceptors Using Known and Hypothetical Crystal Polymorphism Thomas C. Lewis, Derek A. Tocher, and Sarah L. Price* Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom Received October 5, 2004;

CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 3 983-993

Revised Manuscript Received November 12, 2004

ABSTRACT: The crystal structures found in a manual search for polymorphs are discussed in conjunction with low energy crystal structures found in a computational search for minima in the lattice energy, for barbituric acid, cyanuric acid, alloxan, parabanic acid, and urazole. Since all these molecules, with the exception of urazole, have crystal structures in which there are carbonyl groups not used in conventional hydrogen bonding, these results and the electrostatic properties of the molecules are used to interpret this unusual behavior. It appears that there is no great difference between the strengths of the various N-H donors and CdO acceptors within these molecules, and the observed crystal structures result from the compromise between the intermolecular interactions of the molecules. Introduction “It is nearly axiomatic that a molecule with good hydrogen bonding functionalities will use them when it packs in crystals”.1 Certainly we expect molecules with N-H and CdO functional groups to form strong hydrogen bonds in crystals, with the classification “strong”2 implying that the hydrogen bond is dominated by the electrostatic interaction and the N‚‚‚O separation is less than the sum of the van der Waals radii. Such hydrogen bonds typify the term, and their reliable formation, strength, and directionality are central to understanding biological structures3-5 and strategies in crystal engineering.6-8 There has been considerable research effort on defining9 hydrogen bonds and quantifying10,11 their strength since Etter published general rules for hydrogen bonds as design elements in organic chemistry,12 and it is clear that CdO and N-H are among the donors and acceptors to which these rules are expected to apply. The first rule, that “all good proton donors and acceptors are used in hydrogen bonding”, is so reliable that although exceptions have long been known, particularly for acceptors,13 they are sufficiently rare as to deserve comment.1 The third rule, that “the best proton donors and acceptors remaining after intramolecular hydrogen-bond formation form intermolecular hydrogen bonds to one another”, implies a need to rank relative hydrogen bonding strengths.14,15 It also raises the question as to whether the lack of hydrogen bonds to a given donor or acceptor in the crystal structure implies that it is a poorer donor/ acceptor. This paper explores how computational modeling, including computational crystal structure prediction,16 can complement consideration of the range of crystalline forms of a molecule, in understanding unused hydrogen bonding capabilities. Alloxan has already been analyzed17 as an “exception that proves the rule”, as its crystal structure18 has no conventional length hydrogen bonds. The crystal structures of parabanic acid19 and both polymorphs of barbituric acid20 have an unused hydrogen bond acceptor. Although the crystal structure of cyanuric acid21 has all * To whom correspondence should be addressed. Tel: 020 7679 4622. Fax: 020 7679 7463. E-mail: [email protected].

its hydrogen bond donors and acceptors used in the hydrogen bonded sheet structure, there are unused acceptors in the dimethyl sulfoxide and dimethylformamide solvates,22 the 4,4′-bipyridyl, pyridine cocrystal,23 and both trans-1,2-bis(pyrid-4-ylethene) cocrystals.24 Notable unused hydrogen bonding capabilities are found in other crystal complexes, such as 9-ethyladenineparabanic-acid-oxaluric monohydrate complex,25 and derivatives, especially the barbiturate family.26 Indeed, it is the physiological activity20 of many of these compounds and their derivatives that makes it important to establish whether the unused hydrogen bonding capability in the crystals is intrinsic to the functional group or is just specific to the crystal structures. Intrinsic weakness of hydrogen bond donors and acceptors would affect the interactions in vivo, whereas the steric constraints of protein binding and so forth are very different from those in crystals. Computing the low energy crystal structures of a molecule can reveal whether there are alternative packings using different hydrogen bonding motifs that are competitive in energy. A recent study of barbituric acid20 showed that structures with hydrogen bonds to O4 and O6 were competitive in energy to the known structure (which uses O2 and O4) and led to the discovery of a new polymorph which has this hydrogen bonding motif. This polymorphism clearly demonstrates that any intrinsic difference in the hydrogen bonding capability of the unique and nonunique acceptor is a relatively insignificant factor in determining the crystal structure. In this study, we extend this approach by completing the investigations of the computational predictions of the hypothetical low energy crystal structures of the molecules in Chart 1, updating previous studies of alloxan17 and parabanic acid.27 We also seek to establish which polymorphs of these molecules can be readily found in a simple manual screen. Urazole is unique among the molecules in Chart 1, being the only one not to have examples of unused acceptors, according to the depositions in the Cambridge Structural Database,28 but was included in this study as a possible contrast, with only one anhydrate crystal structure29 known. These detailed computational and experimental investigations of the possible crystal structures of the

10.1021/cg049661o CCC: $30.25 © 2005 American Chemical Society Published on Web 01/11/2005

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Barbituric Acid (1), Cyanuric Acid (2), Alloxan (3), Parabanic Acid (4), and Urazole (5)

molecules are complemented by the calculation of the electrostatic potential around the gas phase molecules, to contrast the solid state behavior with the intrinsic contribution to the dominant electrostatic contribution to the hydrogen bonding energy. Methods Computational. The “gas phase” molecular models of barbituric acid, cyanuric acid, alloxan, parabanic acid, and urazole were obtained by optimization of the MP2/6-31G** energy using the program Gaussian 98.30 Corresponding wave functions were calculated for these molecular structures, and in each case, a distributed multipole analysis (DMA)31,32 of the ab initio charge density of the molecule was performed to provide an accurate description of the electrostatic contribution to the lattice energy in the rigid molecule crystal structure modeling. These atomic multipolar electrostatic models automatically represent the electrostatic effects of lone pair and π-electron density, and so give a realistic representation of the relative energies and directional preferences of hydrogen bonds.33,34 The DMA representations were used in the program ORIENT35 to calculate the electrostatic potential on a grid of points 1.4 Å from the van der Waals surface of each molecule, as defined by the Pauling van der Waals radii of 1.5 Å for N, 1.4 Å for O, and 2.0 Å for C. The hydrogen atoms had no explicit radius. The points were generated on the accessible surface at intervals of 0.3 Å and viewed using the program ESTGEN.36,37 As in the evaluation of the electrostatic contribution to the lattice energy from the DMA representations of the charge density, all terms in the electrostatic energy up to R-5 in the multipole series were included, involving atomic multipoles up to hexadecapole. The same DMA-based model was used to calculate the electrostatic contribution to the lattice energy in the computational crystal structure modeling. All other intermolecular contributions to the lattice energy were represented by an empirical repulsion-dispersion model of the form

U)

∑

i∈1,k∈2

Lewis et al.

1/2

(AιιAκκ)

exp(-(Bιι + Bκκ)Rik/2) -

(CιιCκκ)1/2 Rik6

where atom i in molecule 1 is of type ι, and atom k in molecule 2 is of type κ. The parameters for atomic types N, O, and Hc (nonpolar) were taken from the work of Williams,38,39 and those for HN from the extension of this potential in conjunction with a DMA-based electrostatic model to hydrogen bonded crystals.40 It proved necessary to make empirical adjustments to the carbon repulsion, as explained in the results section. For the theoretical polymorph searches, about 1500 initial close-packed crystal structures of each molecule were generated using MOLPAK,41 which performs a systematic grid search on orientations of the rigid central molecule in 29 common coordination geometries of organic molecules, belonging to the space groups P1, P1 h , P21, P21/c, Cc, C2, C2/c, P21212, P212121, Pca21, Pna21, Pbcn, and Pbca, with one molecule in the asymmetric unit. Approximately the 50 densest packings

in each of the 29 coordination types are then used as starting points for lattice energy minimization by DMAREL42 using the DMA-based model intermolecular potential and treating the molecule as a rigid body. The minimizations were constrained by space group symmetry, but if a negative eigenvalue of the second derivative matrix was present, indicating a transition state, the symmetry was lowered until a true minimum was found. The distinct low energy structures were established by considering the reduced cell parameters43 calculated using PLATON.44 Several properties of the unique low energy structures were considered. First, the hydrogen bond motif was established using graph set analysis12,45-48 within the program RPluto.49 The elastic tensor of each structure was estimated from the second derivative matrix50 and used to check whether any structures were so susceptible to shearing forces that they were unlikely to grow.51 The second derivative matrix was also used52 to estimate the k ) 0 phonon frequencies for the rigidbody motions within each lattice. The second derivative properties were used to estimate the zero-point intermolecular energy and the temperature dependence of the rigid-body internal energy and entropy, which added to the lattice energy provides an estimate of the Helmholtz free energy.52 It is hoped that the errors in these approximations to the free energy might be approximately the same when comparing the different lattice energy minimized crystal structures of the same rigid molecule, particularly when Z is constant.52 However this separate consideration of rigid-body motions will be unreliable for flexible molecules, as the different crystal structures will couple with the soft intramolecular modes to give very different atomic motions within the crystal.53 The morphologies of the low energy crystal structures and their relative growth rates54 were estimated using the attachment energy model, using GDIS55 and GULP.56 The same rigid molecular model and repulsion-dispersion potential were used, but using potentialderived atomic charges rather than the DMA of the molecular charge density. Experimental. The experimental search for polymorphs of cyanuric acid, alloxan, and urazole attempted crystallization by slow evaporation and slow cooling from a variety of solvents and by some appropriate vapor diffusion experiments, as detailed in Tables 7, 13, and 14 in the Supporting Information. The range of crystallization experiments that could be tried by this manual search was limited by solubility and the tendency of alloxan to react with moisture. Powder diffraction was used to determine whether any microcrystalline samples corresponded to a new solid form. When suitable crystals were grown, single-crystal X-ray diffraction data were performed on a Bruker SMART APEX diffractometer equipped with graphite-monochromated Mo KR radiation (λ ) 0.71073 Å) and a nominal crystal-to-area detector distance of 60 mm. The intensities were integrated using SAINT+,57 and the absorption correction was applied used SADABS.58 The structure was solved with direct methods (SHELXS97) and refined against F2 (SHELX97).59 All nonhydrogen atoms were refined with anisotropic displacement parameters. The hydrogen atoms were either added geometrically and refined using a riding model or refined independently. Details of the crystallographic studies are given in the Supporting Information.

Unused Hydrogen Bond Acceptors

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Figure 1. The ab initio optimized (“gas phase”) structures (red) superimposed on the molecular structures taken from the experimental crystal structures (blue) by aligning certain atoms and bonds. For barbituric acid, the two conformations found in form ii are shown in green and black, in addition to the form i conformation in blue. These qualitative overlays are supplemented by the smallest root-mean-square difference in the experimental and ab initio atomic coordinates, evaluated for the non-hydrogenic distance in Å, and in parentheses, for all atoms. The barbituric acid figure was produced using Cerius2 (ref 60); the others were produced using MOLDEN (ref 61).

Results Solid State versus Gas Phase Molecular Structure. The ab initio optimized molecular structure is contrasted with the best X-ray or neutron determined molecular structure from the known crystal structures of molecules in Figure 1. It is clear that the molecular structures of cyanuric acid, alloxan, and parabanic acid are well reproduced, with bond lengths and angles within a few percent of the experimental values when the hydrogen positions are taken from neutron data. Thus, these molecules can be effectively modeled as rigid. In contrast, barbituric acid is clearly quite flexible, with the planar conformation being a low energy transition state. This flexibility has a significant effect on the possible crystal packings.20 Thus, the significant differences between the ab initio and X-ray29 structures of urazole, with the torsion angles N1C2N3C4 decreasing from 5.5° to 1.4° and H1N1N5H5 from 94.8° to 65.5°, suggest that the crystal packing forces are having a significant effect on this molecular structure. The energy barrier is certainly small, as the MP2 energy difference between the molecule optimized with its torsion angles fixed at the X-ray values and the fully optimized structure is only 2.6 kJ mol-1. The electrostatic potential around the hydrogen bond donors and acceptors in this set of molecules shows some

variations (Figure 2). The potential 2.9 Å from each N atom is in the range 75-96 kJ mol-1 in approximately the direction of the bonded hydrogen in all cases (this is obscured by the nonplanarity of urazole in Figure 2). The potential 2.8 Å from each carbonyl oxygen shows more variation, in the range -42 to -73 kJ mol-1. The long-range nature of the electrostatic potential ensures that when two donors are adjacent, as in urazole, the potential maxima are larger and the potential is high between the two N-H bonds. Similarly, adjacent carbonyl groups reinforce the potential giving the bonded carbonyls in parabanic acid a more negative potential than the unique carbonyl, and the most negative potential around the central carbonyl (O5) in alloxan. These results suggest that the long-range effects more than compensate for any reduction in the CdO or N-H bond polarity caused by the competition for electron density when the functional groups are adjacent. Nevertheless, the high density of hydrogen bonding groups in these molecules probably does weaken their hydrogen bonds somewhat relative to more typical amide N-H and CdO groups. The corresponding62 potential maxima for formamide and N-acetyl alanine N′-methylamide (with R helix torsion angles) are 102 and 120 kJ mol-1, and the minima -86 and -142 kJ mol-1, respectively, indicating a stronger electrostatic contribution to their hydrogen bonds.

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Figure 2. The electrostatic potential V (kJ mol-1), as calculated on the water accessible surface from DMAs derived from the MP2/6-31G** wave functions for barbituric acid, cyanuric acid, alloxan, parabanic acid, and urazole. Color coded: white < -80 < gray < -60 < magenta < -40 < blue < -20 < cyan < 0 < green < 20 < yellow < 40 < orange < 60 < brown < 80 < red.

Computer Modeling of the Known Crystal Structures. The reproduction of the complete set of known crystal structures using the FIT potential38-40 was not satisfactory, using either the ab initio molecular models or the solid state molecular structures with the N-H and C-H bond lengths corrected to neutron values for the X-ray structures of barbituric acid and urazole. This appeared to be primarily due to an overestimate of the repulsion of the carbon atoms, which are predominantly carbonyl carbon atoms for these molecules, in contrast with the crystal structures used in the empirical fitting. We also considered the W99 potential63 as this has explicit C(dO) potentials; however it was found that the FIT potential gave a more accurate reproduction of the

lattice parameters and hydrogen bonds lengths for most of the crystal structures. An empirical scaling of the carbon repulsion by 75%, so that ACC ) 277180 kJ mol-1 (with all the other parameters in eq 1 from FIT38-40 unchanged), gave a reasonable compromise in the reproduction of the crystal structures. The structures of barbituric acid form i, barbituric acid form ii, cyanuric acid, and alloxan are well reproduced using both the solid state (Table 1 in the Supporting Information) and the gas phase molecular structures (Figure 3). The larger errors in reproducing the crystal structure of urazole are predominantly due to the difference in molecular conformation. The lattice energy minimum closest to the crystal structure of parabanic acid is very



Figure 3. Superimposed unit cells of barbituric acid form i, barbituric acid form ii, cyanuric acid, alloxan, parabanic acid, and urazole showing the experimental crystal structure (black) and the lattice energy minimized structure (red) using the gas phase molecular structure, and the FIT potential (25% reduction in carbon repulsion) and MP2 DMA in the wave function (ExptMinOpt). For barbituric acid form ii, the lattice energy minimum was obtained from the experimental structure using the ab initio envelope and transition state planar molecular structures (ref 20). The figures were produced using Cerius2 (ref 60).

sensitive to the intermolecular potential, and a better reproduction was previously obtained using a 25% reduction in the carbon repulsion in an alternative DMA-based potential.27 Hence, as usual, the relative energies of low energy hypothetical crystal structures generated in the search for lattice energy minima with the ab initio molecular model and the adjusted intermolecular potential are subject to uncertainties in the modeling of the inter- and intramolecular forces. However, in this case, despite the molecules being superficially similar, the variations in the reproduction of the known structures show that these errors vary between the molecules. Comparison of Low Energy Crystal Structures Found in Computational Search with Experimental Crystal Structures. (a) Cyanuric Acid. The search for crystal structures corresponding to minima in the lattice energy of cyanuric acid (Figure 4) found the experimental crystal structure21 around 5 kJ mol-1 from the global lattice minimum. The structure AB47 from the search is very similar to ExptMinOpt (Figure 4, Table 2 in the Supporting Information), the minimum obtained starting from the experimental structure using the same ab initio molecular model and intermolecular potential. The experimental crystal structure of cyanuric acid forms a hydrogen bonded sheet structure, using all the hydrogen bond donors and acceptors. The hypothetical structures that are predicted to be up to 5 kJ mol-1 more stable in lattice energy (4 kJ mol-1 in estimated free energy) are all based on a 3D hydrogen bonding network using all donors and acceptors. All these structures seem plausible, in that none have extremely low mechanical stability or faces predicted as having difficulty in growing in the vapor phase, according to

the attachment energy model. Therefore these alternative crystal structures for cyanuric acid seem thermodynamically and structurally plausible. The crystallization experiments did not find a new polymorph of cyanuric acid, with crystallization from the majority of solvents yielding the known structure,21 either in the microcrystalline or crystalline form (Table 7 in the Supporting Information). However, crystallization from ethanol solution gave crystals of a small block habit, while crystallization from the other solvents, including methanol, yielded long, needlelike crystals. The crystals grown from ethanol have more similar morphology to that predicted for vapor grown crystals by the attachment energy model (Table 8 in the Supporting Information), but nevertheless, it is clear that solvent plays a significant role in the growth of anhydrous cyanuric acid. The search also yielded crystals of cyanuric acid dihydrate and the dimethylformamide solvate which is unstable if removed from solution under ambient conditions. The crystal structures of these solvates22,64 were redetermined at 150 K (Tables 9-12 in the Supporting Information). The higher quality data confirmed that one donor of cyanuric acid did not form a conventional hydrogen bond in the dihydrate and one acceptor is unused in the DMF solvate. The pyridine23 and DMSO22 solvates also have unused cyanuric acid acceptors. Hence, for cyanuric acid, the calculations show that there are possible alternative crystal structures for the anhydrate which are competitive with the known sheet structure. The accuracy of the calculations does not confidently eliminate the possibility that the known structure is marginally the most thermodynamically stable. The 3D hydrogen bonded structures are signifi-

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Figure 4. Plot of lattice energy against cell volume per molecule for all the structures corresponding to lattice energy minima found using the gas phase molecular structure of cyanuric acid in the MOLPAK (ref 41) search. The corresponding minimum for the experimental structure (ExptMinOpt) is also shown for comparison. The minima are denoted by the space group of the MOLPAK starting structure.

cantly denser than the sheet structure and so may be unduly stabilized by the empirically estimated dispersion. The extent to which thermal effects may stabilize the sheet structure relative to the 3D structures may well be underestimated by the rigid-body harmonic model and hence might give questionable relative energies within the low energy crystal structures. However, the growth of the sheet crystal structure is strongly solvent dependent, as shown by the morphologies, and so it could be that the kinetics of crystallization is favoring the sheet structure over the thermodynamically competitive alternatives. Once the sheet structure was formed, it is unlikely to transform to one of the alternative 3D hydrogen bonding structures (assuming it was more stable) because of the hydrogen bonding rearrangements required. Although cyanuric acid has a crystal structure that uses all of its hydrogen bonding capabilities, the fact that there are energetically feasible rival structures and that cyanuric acid so readily crystallizes with other molecules, sometimes without using all its hydrogen bonding capabilities, demonstrates that the known structure is not particularly kinetically or thermodynamically favorable. (b) Alloxan Theoretical Results. The computational search for low energy crystal structures (Figure 5) gave qualitatively the same results as a previous study17 using a more limited search and a different, though DMA-based, model potential. The experimental crystal structure18 is found at the global lattice minimum, despite not having any conventional hydrogen bonds. This crystal structure is around 1.2 kJ mol-1 more energetically stable in lattice energy than the second lowest structure, AQ9, which contains both

hydrogen bonds to O2 and O4 and (CdO)‚‚‚(CdO) contacts (Table 3 in the Supporting Information). The difference in relative stability of these two polymorphs decreases with temperature, using harmonic estimates, but is still 1 kJ mol-1 at 298 K. This decrease is consistent with the known structure being denser than the hypothetical structures with hydrogen bonds. Thus, it seems highly probable that the known structure is the thermodynamically most stable structure. An analysis of the low energy structures (Table 3 in the Supporting Information) shows that those with conventional hydrogen bonds have O2 and/or O4 as the acceptors and also have close (CdO)‚‚‚(CdO) contacts, using the C5O5 carbonyl. The lack of low energy structures involving hydrogen bonds to C5O5 is almost certainly because of its geometrical position in the molecule and its involvement in carbonyl-carbonyl interactions being more advantageous in overall crystal packing. Such interactions can be energetically competitive with the formation of hydrogen bonds.65 The energy gap between the known structure and those involving hydrogen bonds is well within the range associated with polymorphism. None of the hypothetical low energy crystal structures can be discounted on mechanical stability grounds. Although the experimental crystal structure is predicted to have the highest growth rate (from the vapor), the predicted relative growth rate for a number of the low energy crystal containing hydrogen bonds is not dramatically less. Hence, if one of the hypothetical structures had a kinetic advantage in nucleation, possibly because of the hydrogen bonding, the packing differences suggest that there would be a significant kinetic barrier to transformation



Figure 5. Plot of the lattice energy against cell volume per molecule for all the structures corresponding to lattice energy minima found using the gas phase molecular structure of alloxan in the MOLPAK (ref 41) search. The corresponding minimum for the experimental structure (ExptMinOpt) is also shown for comparison. The minima are denoted by the space group of the MOLPAK starting structure.

to the known structure. Thus, the calculations do not eliminate the possibility of metastable polymorphs of alloxan. The majority of crystallizations of alloxan (Table 13 in the Supporting Information) yielded 5,5-dihydroxybarbituric acid, originally misnamed alloxan monohydrate,66,67 because alloxan is very sensitive to moisture.68 A new hydrate of 5,5-dihydroxybarbituric acid was found,69 and a redetermination of 5,5-dihydroxybarbituric acid trihydrate70 undertaken. Given that anhydrous alloxan is obtained by heating 5,5-dihydroxybarbituric acid, the simple laboratory experiments that can crystallize anhydrous alloxan are probably limited to sublimation.18 Thus, although no evidence was found for any polymorphs of alloxan, which is consistent with the known structure being the thermodynamic product, the results also reflect the severely limited range of practical solution crystallization conditions for this compound. Thus, the lack of polymorphs may simply reflect the reactivity of the compound with moisture under normal laboratory conditions. (c) Parabanic Acid. Previously, a theoretical polymorph search was performed on parabanic acid27 using the W99 potential63 (with the carbon repulsion parameters decreased by 25% and the hydrogen interaction sites displaced into the N-H bonds by 0.1 Å) and a SCF DMA. In that search, the experimental crystal structure19 was found at the global lattice minimum, with a plethora of low energy crystal structures. In the experimental crystal structure, there is no hydrogen bond to the unique acceptor O2, but many of the low energy crystal structures have a hydrogen bond to O2, and one of the nonunique acceptors is unused. Repeating the calculations with an alternative model potential

used throughout this paper changed the relative ordering of lattice energies (Table 4 in the Supporting Information) so that one structure that uses the O2 acceptor is 1.0 kJ mol-1 more stable and another is just slightly more stable than the known structure. However, the known structure is predicted as the most stable at 298 K by a small margin, despite its relative density. A parallel experimental search27 failed to find any polymorphs of parabanic acid, and neither has a recent high-pressure study.71 However a new sesquihydrate form of parabanic acid was found at the increased pressure range.71 (d) Urazole. The computational search with the ab initio optimized molecular structure (Figure 6) found the experimental crystal structure of urazole (ExptMinOpt) although it was predicted to be 9 kJ mol-1 above the global lattice minimum (Table 5 in the Supporting Information). With this ab initio optimized molecular structure, there are many more stable crystal structures which are 3D hydrogen bonding networks. However, given the conformational flexibility exhibited by urazole, an additional search was performed using the solid state molecular structure.29 The same model potential and DMA were used. This search did find the experimental crystal structure at the global lattice minimum (Figure 7 and Table 6 in the Supporting Information). The difference in the lattice energies found with the two molecular conformers, (Ulatt(ExptMinExpt) - Ulatt(ExptMinOpt)), is almost 20 kJ mol-1, much larger than the energy penalty involved in the distortion (estimated at less than 3 kJ mol-1), consistent with the conformational change being induced by the packing forces.

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Figure 6. Plot of lattice energy against cell volume per molecule for all the structures corresponding to lattice energy minima found using the ab initio optimized molecular structure of urazole in the MOLPAK (ref 41) search. The corresponding minimum for the experimental structure (ExptMinOpt) is also shown for comparison. The minima are denoted by the space group of the MOLPAK starting structure.

Figure 7. Plot of lattice energy against cell volume per molecule for all the structures corresponding to the lattice energy minima found using the solid state experimental molecular structure of urazole in the MOLPAK (ref 41) search using selected space groups. The corresponding minimum for the experimental structure (ExptMinExpt) is also shown for comparison. The minima are denoted by the spacegroup of the MOLPAK starting structure.

This complementary pair of results make it difficult to estimate the relative stability of the known and hypothetical structures within the limitations of current

techniques. Other low energy distortions of the molecule could well improve the relative stability of the hypothetical structures with respect to the observed struc-


ture. The relatively low density of the observed structure probably implies that it will be favored by entropic contributions, as shown by the rigid-body harmonic motion estimates, though the flexibility of the molecule makes the validity of the use of rigid-body modes highly questionable. Hence it is quite possible that the known structure may be the thermodynamically most stable, but there are definitely a range of low energy structures that are competitive thermodynamically. All the low energy structures use all the hydrogen bond donors and acceptors in 3D hydrogen bonded networks and are predicted to have reasonable mechanical stability and vapor growth rates. However, the differences in the graph set analyses of the hydrogen bonds (Tables 5 and 6 in the Supporting Information), which imply different acceptors and donors hydrogen bonded together in the crystal, give rise to some structures differing sufficiently from the known structure that a transformation would require the breaking of hydrogen bonds. Hence, if kinetic factors should produce some of these hypothetical low energy structures, they could be observed as metastable polymorphs even if the known structure was the thermodynamically most stable. In the urazole experimental search, the majority of crystallizations (Table 14 in the Supporting Information) yielded the known crystal structure of urazole.29 The usual morphology of the known form is long needles, typically around 1-1.5 mm in length (Table 15 in the Supporting Information), which grow on the crystallization vessel above the surface of some solvents. The attachment energy model (Table 15 in the Supporting Information) predicts the vapor grown morphology of urazole to be elongated block habit, rather than the thin needles found experimentally. This may indicate that the crystal growth is affected by the solvent. The only evidence of a new solid state form, formed by slow evaporation of a butan-2-ol solution of urazole (Figure 2 in the Supporting Information), is a reaction product between urazole and butan-2-ol as shown by poor quality X-ray data and from mass spectrometry. Thus, although the computational study points to the possibility of polymorphs of urazole, none were found in the limited experimental search. The results for urazole are similar to those for barbituric acid,20 in that both molecules show a degree of flexibility that affects the relative lattice energy sufficiently that there is a plurality of crystals within the energy range of polymorphism. The calculations differ in that, whereas for urazole all the low energy structures involve all the donors and acceptors in hydrogen bonding, most of the low energy structures for barbituric acid had one unused acceptor. The two possibilities are realized in the two polymorphs of barbituric acid, with form ii being discovered20 in a comparable experimental search. It seems possible that further polymorphs of barbituric acid may be found in the future. In contrast, the experimental search for polymorphs of urazole only found the known crystal structure,29 and the combination of theoretical and experimental results would suggest that this crystal structure could be the most thermodynamically stable form of urazole. Hence although our studies do not exclude the possibility of new polymorphs of urazole being found, this seems less likely than for barbituric acid.


Conclusions The variations in the electrostatic potential in the hydrogen bonding regions around this series of molecules (Figure 2) certainly do not show any correlation with the occurrence of hydrogen bonds in the solid state. Indeed, the only donor or acceptor that is not found in a hydrogen bond in low energy (real or hypothetical) crystal structures is the central carbonyl C5O5 of alloxan. This has one of the most negative regions of electrostatic potential. Hence, it seems reasonable that it is the position of C5O5 between two other carbonyls that makes its occurrence in strong CdO‚‚‚CdO interactions so likely and that accounts for the lack of hydrogen bonds, rather than any intrinsic weakness of this acceptor. Although parabanic acid has a slightly weaker electrostatic potential around the unique acceptor O2 that is unused in the known structure, hypothetical crystal structures that exhibit hydrogen bonding to O2, instead of one of the nonunique acceptors, have comparable lattice energies. Barbituric acid has two polymorphs, in both of which there are hydrogen bonds to two of the three acceptors. The electrostatic potentials suggest that if anything, hydrogen bonds to cyanuric acid would be among the weakest, but all donors and acceptors are used in both the known sheet and competitive 3D crystal structures. Urazole is predicted to have marginally stronger hydrogen bonds than cyanuric acid, again with all the donors and acceptors used in the low energy crystal structures. Overall, the solid state behavior is dominated by the total intermolecular potential, with the repulsion and dispersion forces enforcing the close-packing principle. For these small molecules, it is often not possible to use all the hydrogen bond donors and acceptors or completely optimize their geometries to obtain a dense structure. Molecular flexibility will be used to optimize the crystal packing and hydrogen bonding, as seen for barbituric acid and urazole. However, there are some molecules whose shape, flexibility, and disposition of polar functional groups imply that there is no good “selfstructure”, and so there will be a tendency to crystallize in structures that are exceptions to the normal “rules” and/or form solvates. Alloxan, barbituric acid, and parabanic acid are clear examples of exceptions to the normal hydrogen bonding rules12 for crystal structures. The ready formation of solvates of cyanuric acid with unused acceptors is consistent with its hydrogen bonding capabilities not being intrinsically different from those of the other molecules in the series. However, the cyanuric acid molecule happens to have a variety of compromise packings that satisfy all the hydrogen bonding functionality. Another example of such compromises is the different orientations and/or different conformations in vicinal diols, which hint at the packing compromises necessary to satisfy a full set of intermolecular O-H‚‚‚O hydrogen bonds.72 Thus our study also shows that “the observed crystal-packing arrangement does not have to be perfect, but just has to be better than the alternatives”.72 Given that none of the crystal structure prediction studies could clearly rule out the possibility of polymorphism, it is perhaps disappointing that the experimental searches yielded only one new polymorph. The interpretation of the distribution and structures of the

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hypothetical low energy crystal structures and the frequent limitations on the range of crystallization conditions that could be tried have led to individual conclusions about the possibilities of finding more polymorphs. However, it is perhaps worth emphasizing that these were limited, open laboratory studies on readily available compounds, and in the case of alloxan, the pure anhydrous form needed to be prepared from the “monohydrate” (5,5-dihydroxybarbituric acid), at high temperature. Given the well-known problems of reproducing the crystallization of many well characterized polymorphs,73 as evidenced by the phenomenon of “disappearing” polymorphs,74 it is worth noting that these studies were performed under conditions where seeding by the known structure could not be eliminated. The known structure is very likely to be the most thermodynamically stable form for alloxan and parabanic acid, and possibly for urazole and cyanuric acid. Hence, overall, we can only claim to have established the readily obtainable crystal forms of these molecules. As a set of computational crystal structure predictions, these studies clearly reflect the state-of-the-art of crystal structure predictions, consistent with that revealed by the series of blind tests organized by the Cambridge Crystallographic Data Centre.75-77 Although most success has been found with small rigid molecules, similar to those used in this study, the relative thermodynamic stability of the known and hypothetical structures is subject to uncertainties from the inter- and intramolecular potentials used and neglect of thermal effects. For the molecules in this study, these uncertainties were generally significant compared with the energy differences between the structures, as has been found in the majority of lattice energy minima searches.78 More significantly, kinetics plays a significant role in crystallization, severely hampering the hope of a generally applicable and reliable method of crystal structure prediction.79 This type of joint theoretical and experimental study contributes to clarifying the challenges faced in developing crystal structure prediction, most critically in establishing whether there are other readily obtainable polymorphs. However, more importantly for this current paper, consideration of what other crystal structures are energetically feasible complements the understanding of the crystallization behavior of a molecule. Although this often raises more questions, it does prevent the overinterpretation of the hydrogen bonding motifs found in individual crystal structures. Acknowledgment. This research was supported by the EPSRC in funding a studentship for T.C.L. and the provision of computing resources. The authors acknowledge the Research Councils UK Basic Technology Programme for supporting “Control and Prediction of the Organic Solid State”. For more information on this work, please visit http://www.cposs.org.uk/. Dr. D. S. Coombes at the Royal Institution is thanked for the calculation of morphologies and relative growth rates. Supporting Information Available: Results of the DMAREL lattice energy minimizations using the solid state molecular structures, Table 1. Low energy real and hypothetical crystal structures of cyanuric acid, Table 2; alloxan, Table 3; parabanic acid, Table 4; urazole, using the gas phase molecular structure, Table 5; and urazole, using the solid state molecular structure, Table 6. Experimental results on cyanuric

Lewis et al. acid, Table 7. Crystal morphologies of anhydrous cyanuric acid and the vapor grown morphology, Table 8. The crystal morphologies of cyanuric acid dihydrate and cyanuric acid DMF solvate, Figure 1. Crystallographic data for cyanuric acid dihydrate, Tables 9 and 10. Crystallographic data for DMF solvate of cyanuric acid, Tables 11 and 12. Experimental results on alloxan, Table 13. Experimental results on urazole, Table 14. The crystal morphology of anhydrous urazole with the vapor grown morphologies of ExptMinExpt and ExptMinOpt, Table 15. The morphology of the crystal obtained from slow evaporation of a butan-2-ol solution of urazole, Figure 2. X-ray crystallographic files (CIF) for cyanuric acid dihydrate and the DMF solvate of cyanuric acid. This material is available free of charge via the Internet at http:// pubs.acs.org.

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CG049661O

Investigating Unused Hydrogen Bond Acceptors Using Known and

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