Spontaneous Resolution of Enantiomers by Crystallization: Insights

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DOI: 10.1021/cg9014306

Spontaneous Resolution of Enantiomers by Crystallization: Insights from Computed Crystal Energy Landscapes

2010, Vol. 10 1749–1756

Emiliana D’Oria,† Panagiotis G. Karamertzanis,‡ and Sarah L. Price*,† †

Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, U.K., and ‡Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K. Received November 16, 2009; Revised Manuscript Received February 10, 2010

ABSTRACT: We used crystal structure prediction methods to generate racemic and homochiral crystal structures of benzo(c)phenanthrene, 3,4-dehydroproline anhydride, and 2,6-dimethylglycoluril, which are all known to spontaneously resolve. The known homochiral crystal structures were found at or near the global minimum in lattice energy; however, in all three cases there were hypothetical racemic crystal structures within a few kJ mol-1 in energy. The comparison of hypothetical racemic structures with the known homochiral crystal structures showed structural similarities, despite the symmetry differences, suggesting that most molecules are very unlikely to crystallize in a chiral crystal structure that is markedly more stable than any racemic crystal. Thus the experimentally observed asymmetry in the thermodynamic favorability of racemic and homochiral crystal structures is not due to experimental bias; that is, any thermodynamic drive for spontaneous resolution is genuinely small. Hence, whereas the formation of a racemic crystal can have a significant enthalpic stability advantage over all possible homochiral crystal structures and be more readily predicted, spontaneous resolution cannot be predicted without careful consideration of entropic effects and accurate computational models.

*To whom correspondence should be addressed. Tel: 020 7679 4622. Fax: 020 7676 7463. E-mail: [email protected].

observed and manually separated the hemihedral crystals of sodium ammonium tartrate.9,10 However, little progress has been made in explaining8 why only a minority of chiral molecules form conglomerates11 despite the industrial importance of the phenomenon and its implications in the origin and evolution of life.2,12 It is also not understood why conglomerate formation is more likely for organic salts than neutral molecules.13-15 The rarity of conglomerate formation is reflected in the prevalence of racemic space groups16 in the Cambridge Structural Database (CSD)17 that has been attributed to the ability of the inversion center to mediate stabilizing intermolecular interactions18 without like-like contacts,19 facilitate denser crystal packing,20 and allow favorable, centrosymmetric hydrogen bond motifs, such as carboxylic acid and amide R22(8) dimers.21 The frequency of chiral space groups decreases further for significantly flexible molecules16 and is linked to the type of hydrogen bond donors and acceptors present.13 However, analyses solely based on observed crystals are biased in that an enantiomerically pure crystal can in principle be produced by crystallizing a chirally pure sample (obtained naturally or by other means of separation), but a racemic crystal cannot be grown if it is significantly less stable than a homochiral crystal. Crystal structure prediction (CSP)22 provides the ability to generate plausible structures with all desired symmetry relationships and hence compare the differences between the low-energy structures in chiral and nonchiral space groups. Therefore, the predicted crystal energy landscape can show whether there are hypothetical crystal structures energetically competitive with the observed structures, raising the question as to whether these structures could be as yet undiscovered polymorphs. In this work, we generated hypothetical crystal structures for three conglomerate-forming molecules and compared the crystal packing, hydrogen bonding patterns, and relative thermodynamic stability of homochiral and racemic crystal structures.

r 2010 American Chemical Society

Published on Web 02/26/2010

Introduction A racemic mixture of a chiral molecule can exist in the solid state as a racemic crystal (both enantiomers in the unit cell in equal stoichiometry), a conglomerate (mechanical mixture of equimolar quantity of the two homochiral crystals), or, more rarely, a racemic solid solution (both enantiomers in the unit cell but with no fixed stoichiometry). The nature of the racemic solid defines to a large extent the type of crystallization process needed to separate a solution or melt that contains both enantiomers. The pharmaceutical industry has been concerned with producing optically pure products since regulatory requirements restricted the use of racemic drugs in 1990,1 as the physiological effect of the two enantiomers can be markedly different.2 Manufacturing a racemic mixture, followed by chiral separation of the two enantiomers, is often preferred over the more expensive direct synthesis of an optically pure molecule (stereoselective synthesis), which often does not provide sufficient purity.3 Crystallization of a racemic solution or melt can sometimes lead to a conglomerate, which is known as spontaneous resolution.4 Industrially, such a mechanical mixture of chiral crystals can be separated by entrainment,5-7 that is, the cyclic crystallization of pure enantiomers initiated by adding a quantity of one enantiomer to the starting racemic solution. Molecules with readily interconverting enantiomers (achiral) can pack in any of the 230 space groups that produce stable crystals. On the other hand, optically pure samples of molecules whose enantiomers do not readily interconvert (referred to as chiral molecules hereafter) are limited to crystallizing in the 65 chiral space groups with only rotational and translational symmetry.8 The spontaneous resolution of a racemic mixture or melt has been known since Louis Pasteur

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Scheme 1. The Atomic Numbering of Conglomerate-Forming Molecules Studied and the CSD17 Refcode of Their Experimentally Determined Crystal Structures

Provided thermodynamics control crystallization, spontaneous resolution corresponds to a positive free energy of formation for the racemic crystal: 1=2mol R-crystal þ 1=2mol S-crystal f 1mol RS-crystal

ð1Þ

that is, the racemic crystal has higher Gibbs free energy (and is less stable) than the homochiral crystal. It has been suggested4,23 that conglomerate formation is penalized by RT ln 2, that is, around 0.5 kcal mol-1 (2 kJ mol-1) at ambient conditions, arising from the entropically unfavorable separation of the two enantiomers in a homogeneous racemic liquid into a mechanical mixture of two homochiral crystals. We accept the view8 that this contribution is not present because both racemic crystals and conglomerate mixtures of enantiomers are in equilibrium with the same racemic liquid and hence the entropic penalty applies equally.24 Entropy differences between predicted low-energy crystal structures are generally small.25 Hence, lattice energy calculations can provide insights4,26,27 into spontaneous resolution by estimating the enthalpy difference of racemic and homochiral crystals.28 However, it was previously found that this requires a highly accurate model for the intermolecular forces and conformational distortions.29-31 In this work, we study conglomerate forming molecules of limited flexibility, so that the use of a limited number of rigid-body conformations would provide a reasonable search for stable crystals. This allows the determination of a set of energetically feasible, unique structures, whose relative lattice energies are then calculated more accurately by accounting for the effect of molecular distortions. In these calculations, the intramolecular energy penalty for conformational changes and the conformation-dependent model for the intermolecular electrostatic interactions are

directly computed from the isolated-molecule wave function during lattice energy minimization. We chose three conglomerate forming molecules of different sizes and hydrogen bonding abilities (Scheme 1): benzo(c)phenanthrene, 3,4-dehydroproline anhydride, and 2,6-dimethylglycoluril. Although benzo(c)phenanthrene does not possess a chiral center, we established that the intramolecular energy barrier for interconversion of the helical enantiomers is sufficiently high that racemization in solution or melt is unlikely. All three molecules have been observed to spontaneously resolve and their chiral crystal structures have been determined by X-ray diffraction.32-34 Although the literature was carefully surveyed to ensure that these three molecules only formed conglomerates, the range of experimental crystallization conditions reported is too narrow to unequivocally exclude the possibility of a (probably metastable) racemic crystal. Computational Method Isolated-molecule optimizations and conformational scans were performed at the MP2/6-31G(d,p) level using GAUSSIAN03.35 The most stable gas-phase conformation for 2,6-methylglycoluril was found to have N1C4C2N3 = 147.7° (referred to as the “more open conformation” or OC), whereas the minimization of the experimental conformation led to a local minimum with N1C4C2N3 = 97.7° (referred to as the “more closed conformation” or CC). Both conformations were used in separate rigid-body CSP searches. Benzo(c)phenanthrene and 3,4-dehydroproline have a unique gas phase minimum. Detailed investigations to assess the extent of molecular flexibility and barriers of interconversion are reported in Supporting Information (Section S1, Figures S1-S3, Table S1). The model for the intermolecular forces to evaluate the intermolecular lattice energy, Uinter, included a conformation-dependent electrostatic model derived from the distributed multipole analysis36 (calculated using GDMA)37 of the molecular charge density computed

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at MP2/6-31G(d,p) level of theory. This model improves the accuracy in modeling hydrogen bonding and π-π interactions38,39 of systems containing lone pairs and π-electron density. The remaining contributions to Uinter were modeled with an atom-atom exp-6 model parametrized to reproduce the structure and sublimation energies of organic crystals. We used a parametrization due to Williams40,41 for benzo(c)phenanthrene, since this potential is more suitable for hydrocarbons. For the other, more polar molecules, we used an alternative set of parameters that has been parametrized in conjunction with a distributed multipole electrostatic model.42 Details on the accuracy of these models in reproducing the known crystal structures are given in Supporting Information (Section S2, Table S2). The generation of hypothetical crystal structures was performed with MOLPAK.43 The search was restricted to hypothetical crystal structures with one molecule in the asymmetric unit (Z0 = 1) in common packing types, covering the chiral (P1, P21, C2, P21212, P212121) and racemic (P1, Cc, P21/c, P21/n, C2/c, Pbcn, Pbca, Pca21, Pna21) space groups. MOLPAK generated of the order of 1000 chiral and 2000 racemic densely packed crystals, which were then lattice energy minimized using DMACRYS44,45 without relaxation of the molecular conformations. The second derivatives were used to confirm that each structure was a true minimum: saddle points were reminimized in the appropriate subgroup. The most stable rigid-body lattice energy minima were then used as starting points for reminimization using CrystalOptimizer46 (a significantly enhanced version of the DMAflex47 algorithm). This approach accounts for molecular flexibility by minimizing the lattice energy Elatt = Uinter þ ΔEintra with respect to the lattice parameters, molecular positions and orientations and all torsion angles. The intermolecular energy Uinter was computed as in the rigid-body minimizations, but the MP2/6-31G(d,p) atomic multipole moments were rotated with their local environment and recomputed from the quantum-mechanical charge density after significant conformational changes (5° in torsions and 2° in bond angles) during lattice energy minimization. The intramolecular energy was computed using a local approximate model based on a second-order Taylor expansion that was updated simultaneously with the distributed multipole model. The intramolecular energy was calculated at the HF/6-31G(d,p) level, except in the case of benzo(c)phenanthrene for which MP2/6-31G(d,p) energies were used. For the discussion of certain structures, we made crude estimates of the free energy at 298 K48 from the elastic constants49 and k = 0 phonons50 calculated in the rigid-body harmonic approximation, with the detailed results shown in Supporting Information. This also contains (Section S5) the morphology and relative growth rate of selected crystal structures computed using the attachment energy model51 and assuming that the proportionality between growth rate and attachment energy is independent of crystal structure. Crystal structure comparisons were performed using the Compack52 procedure in Mercury53 and expressed in terms of the root-mean-square deviation in the position of non-hydrogen atoms in the n-molecule coordination sphere (rmsdn).

Results The search for low-energy crystal structures (Figure 1) located a structure that overlaid with the experimental crystal with rmsd15 of less than 0.2 A˚ for all three systems. However the rigid-body search did not predict the experimentally observed conglomerate structure to be the most thermodynamically stable for any of the three systems. The searches generated racemic structures that were denser and more stable than the known homochiral crystal, although the energy differences were small. Hence, reminimizing the lattice energy of the most stable crystal structures by allowing the conformation to change in response to the intermolecular forces gave a significant reranking of the predicted crystal structures (Figure 2) but only subtle changes to the structures (Supporting Information Section S3). The observed crystal structure of benzo(c)phenanthrene becomes the most stable structure, albeit by just 0.33 kJ mol-1

Figure 1. Lattice energy landscape for the rigid-body search of (a) benzo(c)phenanthrene, (b) 3,4-dehydroproline anhydride, and (c) 2,6-methylglycoluril. Full and empty symbols correspond to homochiral and racemic crystal structures, respectively. The red diamond highlights the “observed” structure, that is, the lattice energy minimum obtained starting from the experimental structure using the same computational model as in the search. The insets show the overlay of the experimental (blue) and the optimized conformations (red and black) used in the search. For (c) the structures obtained with the local conformational minimum (CC, shown in red) are shown with larger symbols, with the lattice energies including the ΔEintra = 1.19 kJ mol-1 energy penalty relative to the OC conformation (smaller symbols).

(Figure 2a) relative to the most favorable racemic crystal. The observed crystal structure of 3,4-dehydroproline anhydride becomes the most stable in chiral space groups and is only 1.8 kJ mol-1 less stable than the most stable hypothetical racemic crystal (Figure 2b). The extent to which relaxing the molecular conformation stabilizes the lattice energy varies

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Comparison of Observed Homochiral and Hypothetical Racemic Crystal Structures

Figure 2. Relative lattice energy of the most stable structures from the rigid-body search (in blue) and after CrystalOptimizer refinement (in red) with respect to the corresponding global minimum, for (a) benzo(c)phenanthrene, (b) 3,4-dehydroproline anhydride, and (c) 2,6-methylglycoluril. Solid bars correspond to homochiral structures and textured bars correspond to racemic crystals. The structures are labeled using their MOLPAK packing type and number and for (c) * indicates crystal structures whose conformations approximate the CC conformation, which is also present in the experimental crystal structure.

more markedly for the low-energy crystal structures of 2,6-dimethylglycoluril (Figure 2c). The observed homochiral structure becomes the most stable structure with the CC conformation and is 3.8 kJ mol-1 less stable than the global minimum (structure ac11), which is also a homochiral structure but contains the OC conformation.

For these three spontaneously resolving systems, the energy difference between the known homochiral and the most stable, hypothetical racemic structure is less than a few kJ mol-1. We compared the crystal packings to understand the relationship between this small energy difference and packing similarity. For benzo(c)phenanthrene, the observed homochiral and the most stable racemic crystal structures (Figure 3) exhibit a similar columnar arrangement of molecules in which the molecules of the same chirality are related by translation. The stacking of the slightly helical molecules within the columns of the chiral structure has less π 3 3 3 π overlap but closer contacts than in the racemic structure. The inversion relationship between the columns gives the racemic structure a slightly greater density, but the terminal benzene ring in the homochiral structure packs in the herringbone structure of benzene and many small aromatic structures.54 The observed homochiral and most stable racemic structure of 3,4-dehydroproline anhydride are both based on R22(10) rings formed by C-H 3 3 3 O = C contacts (Supporting Information, Figure S5), but these involve C-H groups with different carbon hybridizations. As shown in Figure 4, this difference results in limited packing dissimilarity, with the racemic crystal being approximately 3% denser than the observed homochiral structure. Although lattice energies do not predict spontaneous resolution, our attachment energy calculations51 show that the observed homochiral structure may be kinetically favored as it is predicted to grow four times faster than the lowest energy racemic crystal (Supporting Information Section S5). The most stable structure of 2,6-dimethylglycoluril (ac11) is a homochiral crystal structure that contains the OC conformation. The molecules form CdO 3 3 3 H-N chains that create parallel ribbons as shown in Figure 5a. This arrangement is also present in the experimental structure (bb12) and in the second lowest energy racemic crystal (fa24), in which the hydrogen bonds are only slightly longer (Figure 5b,c). The most stable predicted homochiral structure (ac11) and the second lowest energy racemic structure (fa24) have a double layer of molecules in common, resulting in a striking similarity in the crystal packing (Figure 6) and a lattice energy difference of only 1.1 kJ mol-1. In the observed structure (bb12), the parallel ribbons are hydrogen bonded and form a 3-dimensional hydrogen bonded framework. These additional hydrogen bonds are facilitated by the CC conformation in the observed crystal, where the smaller N1C4C2N3 torsion angle allows the carbonyl to point to the amide hydrogen of the upper ribbon (Figure 5b). The dihydrate cocrystal of 2,6-methylglycoluril with 2,8methylglycoluril,55 which also crystallizes from water, contains the OC geometry and suggests that both OC and CC conformations can give thermodynamically plausible crystals. Although the experimental CC conformation was calculated to be 1-2 kJ mol-1 less stable than OC in isolation (see Supporting Information, Section S2), it could be dominant in aqueous solution as the relative stability of the two conformations is reversed when calculated in a dielectric field corresponding to water. Metastable crystals may form because of the preferred conformation in solution,56,57 if the barrier for conformational interconversion is

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Figure 3. Crystal packings of benzo(c)phenanthrene: (a) observed homochiral structure aq21 (left) view down c and (right) the columns of molecules viewed down a; the close contacts shown are C9 3 3 3 C6 3.240, C10 3 3 3 C6 3.241, and C10 3 3 3 C5 3.448 A˚. (b) The most stable racemic structure (left) viewed down a and (right) the columns of molecules viewed down c, the close contacts shown are C2 3 3 3 C3 3.466 and C13 3 3 3 C14 3.469 A˚. In the racemic crystal, different colors distinguish the two enantiomers. The hydrogen atoms have been omitted for clarity.

Figure 4. Crystal packings of 3,4-dehydroproline anhydride: (a) observed homochiral structure aq88 (left) view down a and (right) view down c; (b) most stable racemic structure cb30 (left) view down b and (right) view down c. In the racemic crystal, different colors distinguish the two enantiomers.

high compared with thermal energy. The barrier separating the two 2,6-methylglycoluril conformations varies strongly (between 4 and 11 kJ mol-1) depending on the ab initio method and dielectric constant. Hence, establishing whether the rate of conformational interconversion during crystallization, and consequently sample history, influences the poly-

morphic outcome warrants further theoretical and experimental investigation. Discussion Examination of the hypothetical structures reveals that for all three conglomerate forming molecules studied, there is no

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Figure 5. Crystal packing of 2,6-methylglycoluril: (a) most stable homochiral structure, ac11, viewed perpendicular to the 101 plane (left) and perpendicular to the bc plane (right); (b) observed homochiral structure, bb12, viewed perpendicular to the bc plane (left) and perpendicular to the ab plane (right); (c) the second lowest-energy racemic structure, fa24, viewed perpendicular to the bc plane (left) and perpendicular to the ab plane (right). The hydrogen atoms have been omitted for clarity.

Figure 6. Overlay of a 14-molecule cluster of 2,6-methylglycoluril for the most stable structure (ac11, shown in yellow), which is homochiral, and the second lowest-energy structure (fa24, colored by element), which is racemic with rmsd14 =0.18 A˚. Both structures contain the OC conformation. The overlaid double layer of molecules (in yellow) repeats along the horizontal b direction by translation in the homochiral crystal (b = 15.8 A˚) and inversion center in the racemic crystal, leading to an approximate doubling of the b axis (31.3 A˚).

qualitative distinction in the packings of the lowest-energy hypothetical racemic structure and the known homochiral crystal structure. The distinguishing symmetry elements result in differences in some aspects of the packing, but overall produce structures that are close in energy as the intermolecular

interactions are similar relative to the marked differences between dimers and chains, as observed for carboxylic acids and amides. Hence this first examination of the possible racemic structures of spontaneously resolving systems is fully consistent with the arguments18-21 for the rarity of spontaneous resolution and prevalence of racemic space groups16 in the Cambridge Structures Database. From the packing in our three examples, it seems likely that most conglomerate forming systems will have a possible racemic structure with dominant intermolecular interactions similar to the observed homochiral structure. Even when molecules of one hand form a good one or two-dimensional packing motif, “...control in the third dimension, which is necessary for the separation of enantiomers, has not been conquered.”6 This is possibly because the chiral motif will pack more densely in a racemic than a chiral crystal structure, reducing the thermodynamic advantage. Thus, only if a molecule specifically designed so that packing by rotational and translational symmetry is particularly favorable along all three crystal axes, would it have a significant thermodynamic driving force for spontaneous resolution. The qualitative similarity in intermolecular contacts between the hypothetical racemic and known homochiral crystal structures (Figures 3-6) is consistent with the small lattice energy difference of less than about 4 kJ mol-1 between the known homochiral and possible racemic structures (Figure 2).

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A different theoretical approach based on a hybrid molecular mechanics and solid-state density functional method showed31 that the homochiral crystal structures of 2-(4-hydroxyphenyl)2,5,5-trimethylpyrrolidine-1-oxy and 5-hydroxymethyl-2-oxazolidinone were only 0.4 and 2.7 kJ mol-1 more stable than hypothetical racemic crystals, respectively. Hence, the differences in energy between observed homochiral and hypothetical racemic crystals are so small that they challenge the assumption29-31 that lattice energy alone can be used for the reliable computational prediction of spontaneous resolution. Lattice energy differences are equivalent to enthalpy differences at 0 K if we ignore the infinitesimally small PΔV contribution and assume that the zero-point energies of all crystal structures are equal. Hence, comparing lattice energies to predict the stability order at crystallization conditions assumes that the free energy difference of predicted crystal structures does not depend on temperature; that is, the lattice entropy of all crystal forms is the same. This is known to be a crude assumption because homochiral crystals often have lower frequency vibrational modes58 (due to lower density8) that typically gives greater entropic stabilization. Approximate free energy estimates (Supporting Information Section S4, Table S3) based on rigid-body, k = 0 vibrational modes and elastic constants show that the variations in zero-point energies and thermal energies are small but significant relative to the calculated lattice energy difference between the lowest energy racemic and known homochiral structures. Indeed, it is experimentally observed that the free energy difference can be so small that it may change sign with temperature, with some compounds (including Pasteur’s tartrate salts9) crystallizing as a racemic crystal at one temperature and as a conglomerate at another.59 The interplay of enthalpy and entropy has been experimentally determined from thermal measurements of racemic and homochiral pairs of crystals,8,15,23 with the latest measurements of heats of fusion and melting points being reported for 25 such pairs.23 These include four conglomerate-forming systems, for which the observed homochiral crystal is only on the order of ∼0.5 kJ mol-1 more stable in Gibbs free energy than the racemic crystal at the melting point of the lower melting crystal. On the other hand, the relative entropic contribution can be up to 1 kcal mol-1 (∼4 kJ mol-1). Thus the determined entropic contribution to the free energy in favor of conglomerate formation can be comparable to the predicted 0 K lattice energy difference between the known homochiral and putative racemic crystals in this and other studies.31 In contrast, these experiments show that when a racemic crystal is formed, this can be up to 2 kcal mol-1 more stable in free energy compared with the homochiral crystal, and even more stable in enthalpy.4,23 Hence, our computational results are fully consistent with the well-documented asymmetry in the relative thermodynamic stability of homochiral and racemic crystals.8 The computationally generated racemic crystals for conglomerate-forming systems studied here confirm that this asymmetry is genuine and not due to experimental bias. Designing and optimizing a crystallization process for chiral separation depend not only on the thermodynamic relation of the various forms depicted in the ternary phase diagram, which could include solvates,60 but also on kinetic aspects. The first crystalline solid obtained from a racemic melt or solution may contain chirally pure crystals but may not necessarily correspond to the thermodynamically more stable crystal that is racemic,61 as occurs for racemic mandelic

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acid62 and for felodipine.63 Moreover, crystallization by entrainment is inherently a kinetic process that depends crucially on the extent of metastable zone widths,64 which is determined by the nucleation rates. Our results show that kinetic effects may be of importance for 3,4-dehydroproline anhydride, whose known homochiral crystal structure has surfaces that are predicted to grow faster than those of the marginally more stable predicted racemic crystals (Supporting Information, Section S4). Moreover, the known homochiral crystal of 2,6dimethylglycoluril is the most stable predicted crystal structure with the experimental conformation, and so the barrier to conformational change could prevent the formation of the computationally generated crystal structures with lower lattice energy. Conclusions Crystal structure prediction shows that there are hypothetical racemic crystal structures close in energy to the known homochiral crystal for three systems that are known to spontaneously resolve. The small difference in lattice energy between these structures is consistent with the similarity in packing despite the different symmetry elements. Hence, the enthalpic driving force for spontaneous resolution is so small that entropic and kinetic effects are likely to strongly influence the crystallization process. Thus, if computational chemistry is to assist the design of chiral separation by spontaneous resolution, it needs to address the far more complex issues of kinetics and reliable prediction of small free energy differences. In contrast, experimental studies show that racemic crystal formation can be significantly favored over spontaneous resolution. Hence, generating the crystal energy landscape with a good model for intermolecular forces and molecular flexibility can demonstrate that crystallization of enantiomers in a racemic crystal is likely but only provide an indication of possible conglomerate formation. Nonetheless, such calculations could be a useful complement to the design of entrainment processes for enantiomer separation, by revealing energetically competitive crystal structures that may otherwise unexpectedly appear in the enantiomers-solvent ternary phase diagram. Acknowledgment. The authors acknowledge Prof. Alan Jones, Dr. Peter Cains and Mr. Miguel Ardid Candel for useful discussions and EPSRC for funding under the Chemistry and Chemical Engineering program EP/F006721. All predicted crystal structures are stored in SHELX format in the CPOSS database (www.cposs.org.uk) hosted by the NGS, and are available from the authors on request. Supporting Information Available: Molecular conformational analysis, choice of model potential for intermolecular repulsion-dispersion interactions, comparison of the experimental and predicted structures, harmonic, rigid-body free energy estimates of known and hypothetical crystal structures for the three conglomerate-forming molecules, morphology and growth rate predictions for the experimental and hypothetical crystal structures of 3,4dehydroproline anhydride. This material is available free of charge via the Internet at http://pubs.acs.org.

References (1) Development of New Stereoisomeric Drugs; Guidance Document; U.S. Food and Drug Administration: Silver Spring, MD, January 5, 1992; http://www.fda.gov/Drugs/GuidanceComplianceRegulatoryInformation/ Guidances/ucm122883.htm. (2) Viedma, C. Origins Life Evol. Biospheres 2001, 31, 501–509.

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