Analysis of Enantiospecific and Diastereomeric Cocrystal Systems by

Article pubs.acs.org/crystal

Analysis of Enantiospecific and Diastereomeric Cocrystal Systems by Crystal Structure Prediction Matthew Habgood* Department of Chemical Engineering, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom ABSTRACT: Cocrystals offer two novel variants on the classic salt formation method of chiral resolution. Diastereomeric cocrystal pairs are directly analogous to salts but without the requirement for proton transfer. Conversely, a coformer that cocrystallizes with one enantiomer but not the other (enantiospecific cocrystallization) has recently been shown to give high enantiomeric yield. For either variant an understanding of intermolecular interactions is vital. In this study computational crystal structure prediction (CSP) is applied to three recently reported examples: levetiracetam with mandelic acid and with tartaric acid, which display enantiospecific cocrystallization, and tartaric acid with malic acid, which forms a diastereomeric cocrystal pair. The ability of CSP techniques to predict the experimental cocrystal structures is demonstrated. The chirally selective interactions are determined using the unique capabilities of CSP, with reference to alternative structures for each cocrystal system, including the hypothetical diastereomeric twins of the levetiracetam cocrystals. In each case, chiral selectivity can be described in terms of the dominant R22(8) dimer’s response to the change in enantiomer. It is concluded that when designing a coformer for chiral resolution a predilection toward a single, orientationally restrictive intermolecular motif, with minimal ability to form alternative motifs, is the best strategy.

1. INTRODUCTION In a wide variety of applications, including the pharmaceutical, agrochemical, and food industries, it is a necessity to obtain enantiomeric compounds in an optically pure form,1 because only one out of a pair of enantiomers may display desirable activity, and because of regulation such as the FDA’s requirement for optically pure drugs.2 For a high proportion of molecules a fully asymmetric synthesis (i.e., synthesis of just one enantiomer) will not be possible or will not be economical;3 hence postsynthesis resolution to separate the enantiomers will be necessary. A widely used method is diastereomeric salt formation,4 in which the target molecule is reacted with a chiral acid or base. The two diastereomers of the resultant salt will have different stabilities and hence different solubilities, allowing in principle for crystallization of a product with high enantiomeric excess. Choice of counterion is vital to the success of this approach. Formation of a solid solution (in which both enantiomers of the molecule are accommodated in a disordered way at identical crystal sites) and formation of a double salt (in which both enantiomers are incorporated in a ternary crystal structure) must be avoided.5,6 The most fundamental requirement, though, is that the difference in stability between the salts be as large as possible. However, it remains unclear how a counterion might be rationally selected or designed to produce such a gap.7 There have been several studies examining the specific intermolecular interactions by which a particular compound or family of compounds is able to resolve the enantiomers of another (the set of interactions is referred to as the “resolution mechanism”). This is usually achieved by examining the crystal structures of the salts, although detailed discussion is often © XXXX American Chemical Society

hampered by an inability to resolve the crystal structure of the less stable (more soluble) of a salt pair. Various hydrogen bonding motifs have been identified and suggested to be important in preferentially stabilizing the more stable (less soluble) of a salt pair, including 21 columns,8−11 sheets,12 double chains,13,14 and single chains.15 In general, the details of the connection between any one of these motifs and strong discrimination between salts are not clear. Hence it is difficult to say whether, and for which molecules, pursuing the formation of these motifs (e.g., by crystal engineering16) would lead to strong chiral resolution. In many cases, it appears that a combination of a strong hydrogen bonding motif with the formation of various weaker interactions must be considered to explain the difference in stability of a salt pair. The disruption of C−H···π interactions in the less stable salt in order to maintain a dominant hydrogen bonding motif common to both salts has been identified as the source of chiral resolution in some systems.9,11 In other cases, no such hydrogen bonding motif is observed; the hydrogen bonding is completely different between the two salts.8,10,14 Cases have even been identified in which a “weak” packing motif, for example, the interaction of an NO2 group with a hydrophobic layer, has been maintained between two salts, forcing the formation of different hydrogen bonding motifs and hence giving chiral discrimination.17 In summary, it is not yet clear how to determine which intermolecular interaction motifs will Received: July 10, 2013 Revised: August 16, 2013

A

dx.doi.org/10.1021/cg401040p | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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been used to interpret and explain differences in cocrystal behavior between structurally similar molecules.37,38 In this study, CSP was applied to three recently reported chiral cocrystal systems. Two of these are the cocrystals of S-2(2-oxopyrrolidin-1-yl)butyramide (Figure 1a; “levetiracetam”,

be most useful in achieving chiral resolution for a given molecule. The same problem applies to the analogous, but much less studied, field of cocrystals between chiral molecules (i.e., the constituent molecules are noncharged). Cocrystals in general have become a focus of attention in recent years18,19 as a route to tuning the solid state properties of molecules of interest by addition of selected “coformers”. For chiral resolution, cocrystallization offers an alternative to salt formation for molecules that are not readily ionized. Diastereomeric cocrystal formation is the direct analogue of salt formation. Alternatively cocrystallization may be enantiospecific, occurring only between an enantiopure coformer and one enantiomer of the target molecule. Enantiospecific cocrystallizations have been reported sporadically over the last 20 years,20−22 including a recent example23 that has been developed to give chiral resolution with high enantiomeric excess.24 The same quandary is found for diastereomeric cocrystal pairs as for salts: how to select or design a coformer that will give a sufficiently large stability gap between the pair to strongly resolve the two enantiomers. The selection of an enantiospecific coformer has slightly different requirements. In thermodynamic terms, one cocrystal of the pair must be more stable than crystals of the separate components, while the other must be less stable, regardless of the absolute stability difference between the pair. Nonetheless aiming for as large a stability difference as possible appears to be a valid design principle in this case as well, since a larger difference gives more scope for the component crystal stabilities to lie in the gap. A computational approach that may be useful in selecting a coformer or counterion is crystal structure prediction (CSP).25 In CSP, the diagram of a molecule or molecules are is to predict the hypothetical most stable set of crystal structures that they can form, based on global minimization of a model of the crystal lattice energy (as an approximation to free energy). As well as identifying the single most stable crystal structure and specific alternative structures, the set of stable hypothetical structures, referred to as the “crystal energy landscape”, can be interpreted to give a very broad overview of the molecules’ solid state behavior.26 CSP has been shown to be capable of predicting the most stable crystal structure for small organic molecules,27,28 for model pharmaceutical compounds,29 and also for hydrates30 and cocrystals,31,32 with the potential to predict simple disordered crystal structures.33,34 It has two possible roles in finding a chirally selective coformer or counterion. One role is in straightforward candidate screening. The other is a more detailed study of known systems. Alternative cocrystal structures and structures for diastereomeric partners that cannot be measured experimentally (due to forming poor-quality crystals, for example) or do not form at all can be generated. Hence, structural elements and intermolecular interactions can be studied not just for what a given system did in reality but for what it might alternatively have done. By examining additional hypothetical crystal structures of a given cocrystal or salt system, the details of how each part of the molecules interacted in reality or could alternatively interact can be examined. In this way, CSP allows a wealth of information to be extracted on the favorable or unfavorable aspects of each system, and what attributes should be looked for to find improved coformers (or counterions). Previous results suggest that CSP is suitable for both roles. Successful predictions have been made for the crystal structures of diastereomeric salts,35,36 and crystal energy landscapes have

Figure 1. (a) Levetiracetam (S-2-(2-oxopyrrolidin-1-yl)butyramide, lev), the racemic form of which is referred to as etiracetam, (b) Smandelic acid (S-mand), (c) (2S,3S)-tartartic acid (S-tar), and (d) Smalic acid (S-mal).

an antiepilepsy drug,39 the racemic form of which is called “etiracetam”40−42) with mandelic acid (Figure 1b) and with tartaric acid (Figure 1c). These are enantiospecific, with levetiracetam only cocrystallizing with S-mandelic acid and (2S,3S)-tartaric acid.23 The third system is tartaric acid with malic acid (Figure 1d) which, contrastingly, forms a diastereomeric cocrystal pair.43 The ability of CSP to correctly predict the experimental crystal structures was assessed, and the crystal energy landscapes (i.e., alternate stable crystal structures) were examined along with the known crystal structures and with reference to the calculated stabilities (lattice energies) to obtain detailed information on the intermolecular interactions responsible for the observed chirally selective behavior (or lack of such behavior) of these systems. The study serves to revisit and clarify these very interesting recent experimental results in the little-developed area of chirally selective cocrystallization and addresses the broader issue of chiral resolution mechanisms. For brevity in designation of cocrystals, levetiracetam is designated lev, mandelic acid as S/R-mand, malic acid as S/Rmal, and (2S,3S)- and (2R,3R)-tartaric acid as S/R-tar.

2. METHODS Crystal Structure Prediction and Lattice Energy Model. Crystal structure prediction was carried out to identify the most stable hypothetical crystal structures for each of six cocrystal systems with a 1:1 stoichiometry: lev/S-mand, lev/R-mand, lev/S-tar, lev/R-tar, Smal/S-tar, and S-mal/R-tar. The CSP methodology employed was among those used successfully in the recent blind test of crystal structure prediction.28 For each cocrystal system, 1 000 000 crystal structures were generated, with varying conformations, in the five most common chiral space groups found in the Cambridge Structural Database (CSD)44 (P1, P21, P21212, P212121, C2), using the program CrystalPredictor.32,45 These were ranked according to an approximate model of lattice energy based on point charges and a simple exponential-6 potential, and the most stable were relaxed, and their energies were refined, using the program CrystalOptimizer46 to apply a more computationally expensive but much more accurate model of the lattice energy. B



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CrystalOptimizer and its accompanying lattice energy model have proven very accurate in ranking experimentally known crystal structures favorably relative to other hypothetical structures under blind test conditions.27,28 The crystal structure is simultaneously relaxed with respect to the lattice parameters and molecular orientation, and the internal degrees of freedom of the molecule. Internal energies were calculated using parabolic local approximate models (LAMs) based on ab initio calculations on the isolated molecule at the PBE0/6-31G(d,p) level of theory. Intermolecular energies were calculated as the sum of interactions between atomcentered distributed electrostatic multipoles, representing electrostatic interactions, and an atom−atom exp-6 term representing all other interactions, particularly dispersion. Distributed multipoles were calculated from Stone’s distributed multipole analysis (DMA) using the program GDMA2.2,47 based on analysis of a wave function calculated at the PBE0/6-31G(d,p) level of theory using Gaussian09.48 Multipole interactions are handled by DMACRYS,49 called internally by CrystalOptimizer. The exp-6 potential was taken from a set of parameters fitted to crystallographic and thermodynamic data, referred to as the “FIT potential”.50−52 To model the behavior of electrondepleted “polar” hydrogen atoms, exp-6 terms were used that had been specifically fitted for hydrogen atoms bonded to nitrogen53 and oxygen,54 as parts of the FIT potential. Mandelic acid, tartartic acid, and malic acid are all capable of forming intramolecular hydrogen bonds between an alcohol group and a carboxylic acid group. It is to be expected that any crystal structures generated by CSP will include some that form this intramolecular hydrogen bond. It has been noted that the combination of intermolecular electrostatics calculated using distributed multipoles combined with internal energies calculated ab initio tends to overestimate the stability of internal hydrogen bonds relative to intermolecular hydrogen bonds, effectively overestimating the stability of this kind of structure.55 The polarizable continuum model56 (PCM) has been shown to resolve this difficulty. Recalculating multipoles and internal energies in a continuum that approximates a crystalline environment polarizes the molecule and balances the energies of internal and intermolecular hydrogen bonds.57 The energies of the crystal structures in this landscape and of the experimental structure were hence recalculated after CrystalOptimizer relaxation using the PCM, with ε = 3, a value typical of organic crystals. As an initial test of the validity of these lattice energy models, the experimentally determined crystal structures for each of the known cocrystals and of each of the pure species were relaxed using CrystalOptimizer. The relaxed crystal structures were compared to the original experimental structures by calculating the root-mean-square difference of atomic positions on 15 nearest-neighbor molecules (RMSD15) using58 Mercury 3.0. Table 1 shows that in every case the relaxed structure closely matches the experimental structure, suggesting that the lattice energy model is a good representation of these molecules. To examine the stabilities of specific intermolecular interaction motifs (see Discussion), the participating molecules were extracted from the crystal structure using Mercury 3.0, and energies were calculated using the same potential energy function, within the program Orient.71

Table 1. Reproduction of Experimental Crystal Structures by the Same Structures Minimized in CrystalOptimizer, Measured by the Root-Mean-Square Distance between Atoms over 15 Nearest-Neighbor Molecules (RMSD15) experimental crystal structure

CSD refcode

RMSD15 (Å)

levetiracetam etiracetam, I etiracetam, II mandelic acid, chiral mandelic acid, racemic, I (Pbca) mandelic acid, racemic, II (P21/c)c tartaric acid, chiral tartaric acid, racemic malic acid, chiral malic acid, racemic, I (α, Cc)d malic acid, racemic, II (β, P21/c)d lev/S-mand lev/S-tar S-mal/S-tar S-mal/R-tar

OMIVUB59 CCDC 859779a CCDC 859780a FEGHAA60 DLMAND03b DLMAND0261 TARTAL0462 ZZZDUI0163 COFRUK1064 DLMALC65 DLMALC1166 YASGIK23 YASGEG23 NIVYOG67 CCDC 897408a

0.16 0.13 0.19 0.31 0.28 0.18 0.30 0.36 0.18 0.2 0.16 0.22 0.20 0.36 0.18

a

The structures of racemic 2-(2-oxopyrrolidin-1-yl)butyramide (etiracetam) and S-mal/R-tar do not yet have full CSD refcodes; their submission codes are given, for structures taken from Herman et al.68 and Eddleston et al.43 bDLMAND03 was submitted to the CSD as a private communication. cForm II (P21/c) of mandelic acid was assumed to correspond to the metastable racemic69 form, based on that form’s reported resemblance to the chiral crystal structure and the root-mean-square-difference of 0.34 Å between a coordination sphere of 10 nearest neighbor molecules between structures DLMAND02 and FEGHAA as measured in Mercury 3.0. dThis study follows the CSD in referring to the Cc form of malic acid as “α” and the P21/c form as “β”, but it should be noted that other studies70 reverse this designation.

cocrystal to form at all.72,73 As important for purposes of chiral resolution is whether the cocrystal (A/B) plus a chiral crystal of component A is more stable than a chiral crystal of component B plus a racemic crystal of component A. This will dictate whether B can resolve A on the basis of pure crystal thermodynamics. The corresponding thresholds are marked in Figures 2−4. These are calculated as Ethresh = (EB,chir + EA,rac − EA,chir)/2, the lattice energy required for a cocrystal (A/B) to enable the resolution of A. As can be seen in Figures 2−4, the experimentally known cocrystal structure for each system is found by the crystal structure prediction search, is calculated to be more stable than the separate chiral components, and is found to be one of the most stable structures in the landscape. For the levetiracetam cocrystals and S-mal/R-tar, the experimental crystal structure is the most stable crystal structure. For S-mal/S-tar, the experimental structure is second ranked, by ∼0.5 kJ mol−1. This may indicate a small error in the lattice energy model, or there may be a second polymorph of this cocrystal that has not been observed yet. (It was also observed that the S-mal/S-tar and S-mal/R-tar crystal structures are isomorphous with those of racemic tartaric acid and chiral malic acid, respectively. If molecular differences are ignored, Mercury 3.0 gives an RMSD15 of 0.24 Å for the former and 0.13 for the latter.) Furthermore, the most stable generated cocrystals of levetiracetam with R-mandelic and (2R,3R)-tartaric acid are less stable than the separate chiral components, consistent with the experimental observation that cocrystals do not form from these systems.

3. RESULTS The six crystal energy landscapes are plotted in terms of lattice energy and density for each hypothetical crystal structure in Figures 2−4. Lattice energy indicates stability while density is a convenient physical quantity to differentiate between crystal structures of similar stability. Each figure also shows the combined lattice energies for the crystals of the separate components, divided to give the average energy for one molecule. The combined lattice energies of the separate chiral components dictates whether (according to the model used in this study) each chiral cocrystal will be thermodynamically stable; generally, this is taken to be the criterion for the C



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Figure 2. Crystal energy landscapes for levetiracetam with S-mandelic acid and with R-mandelic acid (lev/S-mand, “S” and lev/R-mand, “R”). The generated structure corresponding to the experimental crystal structure is marked with a gray circle. The more stable polymorphs of racemic mandelic acid69 (form I, Pbca) and etiracetam42 (form I) were used to calculate the cutoffs shown here for resolution of racemic mixtures by cocrystal formation.

Figure 3. Crystal energy landscapes for levetiracetam with (2S,3S)-tartaric acid and with (2R,3R)-tartaric acid (lev/S-tar, “S” and lev/R-tar, “R”). The generated structure corresponding to the experimental crystal structure is marked with a gray circle. The more stable polymorph of etiracetam42 (form I) was used to calculate the cutoffs shown here for resolution of racemic mixtures by cocrystal formation.

In Figure 4, it is shown that racemic malic acid can be resolved by the formation of an S-mal/S-tar cocrystal. By simple symmetric inversion of the enantiomers, it follows from these results that R-malic acid left over from this resolution would also form an R-mal/S-tar cocrystal with the tartaric acid “resolving agent”, hence giving resolution of racemic malic acid by chiral tartaric acid with formation of the diastereomeric cocrystal pair. Conversely Figure 4 shows that chiral malic acid would not resolve racemic tartaric acid. These results exactly match the experimental findings43 of Eddleston et al. The only significant discrepancy between these calculations and experimental observation is the result (Figure 2) that resolution of etiracetam by chiral mandelic acid would not be viable, at least on the grounds of pure crystal thermodynamics, whereas this has in fact been demonstrated24 by Springuel et al. This could indicate a deficiency in the potential model used here, or it could be because the success of Springuel et al. resulted from careful measurement and exploitation of the

ternary phase diagram, including interactions with the solvent, which cannot be represented in these calculations. Despite this cautionary result, it seems that overall the CSP procedure and the lattice energy model adopted here are for the most part well suited to describing these systems and fully able to predict the crystal structures of these cocrystals or their inability to form.

4. DISCUSSION The usefulness of CSP as a complement to laboratory screening of coformers is reaffirmed by the results presented here. The correct reproduction and high relative stability (low energy) of the experimental crystal structures also indicates a high level of confidence in the more general trends in intermolecular interactions and chiral selectivity that can be inferred from the computationally generated crystal structures in these crystal energy landscapes. An important factor in improving chiral selection by cocrystal formation will be achieving a large stability difference between D



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Figure 4. Crystal energy landscapes for S-malic acid with (2S,3S)-tartaric acid and with (2R,3R)-tartaric acid (S-mal/S-tar, “S” and S-mal/R-tar, “R”). The generated structures corresponding to the experimentally known crystal structures are marked with a gray circle. The more stable69,74 polymorph of racemic malic acid (β, P21/c) was used to calculate the cutoffs shown here for resolution of racemic mixtures by cocrystal formation.

formed with each enantiomer, ΔER−S = E(X/YR) − E(X/YS), was 2.0 kJ mol−1 for levetiracetam/mandelic acid, 5.7 kJ mol−1 for levetiracetam/tartaric acid, and 4.5 kJ mol−1 for S-malic acid/tartaric acid. In terms of intermolecular interactions, it should first be noted that all four experimentally known structures include an eight-membered, double hydrogen bonded (R22(8) in Etter’s notation75) dimer between the two molecular species. An example is shown in Figure 5a for the lev/S-mand system. Table 2 shows that the most stable lev/R-mand structure has much lower electrostatic energy, suggesting that it contains a more stable hydrogen bonding motif(s) than its diastereomeric counterpart. Examination of the structure reveals a ninemembered ring (R22(9)) dimer (Figure 5b). The stabilities of both this dimer and the experimental R22(8) dimer were calculated using Orient (it should be noted that these are not the hypothetical stabilities of these dimers in a vacuum, but strictly their contribution to the lattice energy as calculated in CrystalOptimizer), giving values of −57.1 kJ mol−1 with −71.3 kJ mol−1 of electrostatic energy for the R22(8) dimer and −64.9 kJ mol−1 with −87.0 kJ mol−1 of electrostatic energy for the R22(9) dimer. Hence the greater electrostatic stability of the most stable lev/R-mand structure and the small ΔER‑S for the lev/mand system are the result of the strong R22(9) dimer. Contrastingly, the most prominent hydrogen bonding motif in the most stable lev/R-tar structure is a R33(12) trimer (Figure 6a), which is evidently much less stable than the experimental R22(8) dimer (Table 2, electrostatic energies). The question arises of why a R22(9) dimer like that found in the lev/R-mand global minimum does not equivalently stabilize any lev/R-tar structures. Examination of the crystal energy landscape reveals that an equivalent dimer is found in the sixth ranked crystal structure. In this system, though, the geometry of the dimer and the levetiracetam molecule means that the second alcohol group of the tartaric acid molecule is blocked from forming any hydrogen bonds (Figure 6b), giving an overall less stable crystal structure. Hence in this system, the R22(9) dimer is less competitive with the R22(8) dimer. A more fundamental question is why the R22(8) dimer itself, which is evidently very important to the S-cocrystals in lev/ mand and lev/tar systems, does not equivalently stabilize any Rcocrystal structures. Structures containing this motif are found

the crystal structures formed between one chiral molecule and the two enantiomers of another. As well as achieving better resolution in the case of diastereomeric cocrystal formation, a larger energy gap can be expected to increase the likelihood of enantiospecific cocrystal formation. To study the influence of molecular structure and intermolecular interactions on this stability gap, selected structures of interest from each search (including the experimental structures) were analyzed in terms of contributions to its lattice energy, as extracted from CrystalOptimizer. Table 2 shows the intermolecular electroTable 2. Electrostatic (Eelec), Repulsion−Dispersion (Er‑d), and Intramolecular Energies (ΔEintra) for Selected Structures of Interest from the Crystal Energy Landscapes, Figures 2−4 structurea

Eelecb (kJ mol−1)

S-1 (exp) R-1 R-8

−78.3 −88.5 −85.1

S-1 (exp) R-1 R-6 R-11

−120.0 −104.5 −107.9 −100.1

S-2 (exp) R-1 (exp)

−152.0 −135.5

Er‑db (kJ mol−1)

ΔEintrab (kJ mol−1)

levetiracetam/mandelic acid −46.8 6.5 −33.0 4.9 −39.3 12.1 levetiracetam/tartaric acid −25.1 6.9 −31.9 3.9 −23.7 5.3 −27.7 2.9 S-malic acid/tartaric acid −16.5 13.6 −21.1 6.2

Elattb (kJ mol−1)

Hbondingc

−118.6 −116.6 −112.3

R22(8) R22(9) R22(8)

−138.2 −132.5 −126.3 −124.9

R22(8) R33(12) R22(9) R22(8)

−154.9 −150.4

R22(8) R22(8)

a

S/R-N indicates the Nth most stable generated cocrystal between one enantiomer (levetiracetam, S-malic acid) and the indicated enantiomer of the coformer. bAll energies are per molecule. cH-bonding indicates the principle hydrogen bonding motif in this structure, conveyed in Etter’s notation.

static energy (which will largely be accounted for by hydrogen bonds), intermolecular repulsion−dispersion potential (which, in the parametrization used here, will implicitly include thermal effects and additional polarization effects but still broadly indicates the contribution of dispersion and hence of good packing to the crystal stability), and intramolecular energy (relative to the gas phase molecular structure). The lattice energy difference between the most stable crystal structures E



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Figure 6. Hydrogen bonding motifs in (a) the most stable generated levetiracetam/(2R,3R)-tartaric acid structure (R33(12)) and (b) the sixth ranked levetiracetam/(2R, 3R)-tartaric acid structure (R22(9)). Hydrogen bonds are shown by blue lines.

mol−1 of electrostatic energy for the R-tar dimer. Nonetheless, the experimental mal/R-tar structure has a higher (less stable) electrostatic energy, suggesting weaker hydrogen bonding. The reason for this is that in the S-tar structure the dimers are reciprocally linked by alcohol−carboxyl hydrogen bonds (Figure 7a), whereas the R-tar structure has dimers linked only by single alcohol−alcohol hydrogen bonds (Figure 7b). Hence, as with the lev/tar system, formation of the R22(8) dimer in the mal/R-tar system is only achieved at the cost of other hydrogen bonding interactions, in this case a secondary motif that is geometrically impossible to maintain. In this system, the difference leads directly to the relatively large ΔER−S. At a qualitative level, these case studies suggest some principles that could be used in the selection or design of coformers (or counterions) to maximize the energy gap between diastereomeric cocrystal or salt pairs. These principles are broadly supported by previous studies on interactions leading to resolution in salts. The first principle is to aim for a strong interaction motif that places serious restrictions on the orientations of the molecules, to prevent reorientation that would accommodate a different enantiomer. The R22(8) dimer plays this role in the systems studied here, but previous salt studies suggest that other hydrogen bonding motifs8−15 or sufficiently specific packing interactions can also achieve this.17 A strong interaction motif will also help to secure the basic aim of a stable cocrystal system (with one enantiomer or the other). The second principle is to aim for a number of weaker “secondary” interactions that will be disrupted if one

Figure 5. Hydrogen bonding motifs in (a) the experimental levetiracetam/S-mandelic acid crystal structure (R22(8)) and (b) the most stable generated levetiracetam/R-mandelic acid structure (R22(9)). Hydrogen bonds are shown by blue lines.

ranked eighth in the lev/R-mand landscape and 11th in the lev/ R-tar landscape. The breakdown of their energies (Table 2) shows that the eighth ranked lev/R-mand structure has a relatively stabilizing electrostatic energy but poor packing and a high intramolecular energy compared with the experimental Smand crystal structure. Conversely the 11th ranked lev/R-tar structure has an uncompetitive electrostatic energy. Hence for both systems, the R22(8) dimer can form the basis of crystal structures but at the cost of destabilizing other intermolecular interactions or the molecular geometry that stabilizes the Scocrystals. The mal/tar system displays a very different set of resolving interactions. The R22(8) dimer is found in both the experimental structures, giving rise to very similar chains of molecules (Figure 7). Orient calculations confirm that the motif contributes roughly the same stability to both structures, with values of −67.7 kJ mol−1 with −89.5 kJ mol−1 of electrostatic energy for the S-tar dimer and −65.5 kJ mol−1 with −89.4 kJ F



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to other groups) leads to a relatively small stability gap between the cocrystal structures of its enantiomers with levetiracetam. The results24 of Springuel et al. suggest that enantiospecific cocrystallization in particular may give high enantiopure yields. In this context, it is worth noting that a larger ΔER−S does not guarantee enantiospecific cocrystallization. Only if the combined stability of pure crystals of the component molecules lies within the ΔER−S gap will enantiospecificity be achieved. This is illustrated in the results of this study by the lev/mand system, which is enantiospecific despite having the smallest ΔER−S, as opposed to the S-mal/tar system, which has a larger ΔER−S but forms a diastereomeric cocrystal pair. It is therefore worth asking whether any molecular selection principles might specifically target enantioselectivity. As noted above, in the Smal/tar system, the stable R22(8) dimer is found in both the experimental structures, whereas in the lev/R-mand and lev/Rtar systems, structures including the R22(8) dimer are relatively unstable. The S-mal/tar system is more able to accommodate the change of one enantiomer for the other within the R22(8) dimer. Comparison of the S-mal/S-tar and S-mal/R-tar crystal structures (Figure 7) shows that this is achieved by the formation of internal hydrogen bonds in the S-mal/R-tar structure, replacing intermolecular hydrogen bonds in the Smal/S-tar structure (in Table 2, this is expressed as a more stable intramolecular energy). In all three systems, the R22(8) dimer is evidently critical to the formation of the cocrystal in terms of its stability relative to crystals of the separate components. The implication of these results is therefore that it is the ability of the S-mal/tar system to accommodate enantiomeric differences in the critical intermolecular interaction (the R22(8) motif) through rearrangement of secondary interactions (switching from intermolecular to intramolecular hydrogen bonds) that leads to diastereomeric crystal formation. To encourage enantiospecific behavior, it is suggested that an addendum be added to the third principle outlined in the previous paragraph: that as limited as possible a set of secondary interaction motifs should be compatible with the chosen primary interaction motifs, to avoid accommodation of different enantiomers. Directional, spatially restrictive interactions will also be important in this context. The molecular design goals of a large ΔE R−S and enantiospecific cocrystal formation are clearly closely connected. The results presented here suggest that the approaches required may differ in the emphasis on stronger or weaker interaction motifs. A large ΔER−S emphasizes the need for a strong “primary” motif with no competitors; the lev/mand system has a competing motif and hence a relatively small ΔER−S. By comparison enantiospecific cocrystallization emphasizes the need for secondary motifs that are destabilized by the replacement of one enantiomer with another within the primary motif. The lev/R-mand system cannot accommodate the R22(8) dimer, and hence lev/mand is enantiospecific, whereas the S-mal/R-tar system can, and hence S-mal/tar is diastereomeric. These principles could be pursued by various methods of approximate, qualitative screening, such as synthon analysis,76 hydrogen bond parameter calculation,77 or calculation of critical molecular descriptors,78 and in general an application of crystal engineering tools and expertise. The result would be a tightly focused pool of candidate molecules that could be easily approached with a combined experimental/CSP screen.

Figure 7. Hydrogen bonding motifs in (a) the experimental S-malic acid/(2S,3S)-tartaric acid crystal structure and (b) the experimental Smalic acid/(2R,3R)-tartaric acid structure. Hydrogen bonds are shown by blue lines. R22(8) motifs are seen in both structures.

enantiomer is exchanged for another while maintaining the “primary” interaction. Clearly, directional interactions are the most likely to be sensitive in this way, so classical hydrogen bonding networks or C−H···π interactions9,11 are good candidates, although it is worth noting that generic packing interactions played this role for lev/mand. The third principle is to avoid alternative interaction motifs that are strong enough to be competitive with the chosen primary motif. For example, the ability of mandelic acid to form the R22(9) dimer without disrupting other hydrogen bonding possibilities (as opposed to tartaric acid, in which the same motif blocks hydrogen bonding G



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5. CONCLUSIONS The experimental crystal structures of levetiracetam with Smandelic acid and (2S,3S)-tartaric acid, and S-malic acid with (2R,3R)-tartaric acid have been generated as the most stable structures by computational crystal structure prediction, while the structure of S-malic acid with (2S, 3S)-tartaric acid was generated as a close second ranked structure. A wide variety of alternative, hypothetical crystal structures was also generated for each of these systems and for their diastereomeric counterparts, in the process confirming the nonviability of cocrystals of levetiracetam with R-mandelic and (2R, 3R)tartaric acid. Examination of the real and hypothetical crystal structures strongly suggested that the differences of stability between cocrystals with different enantiomers, the so-called “resolution mechanism”, could be rationalized for these three systems with reference to the highly stabilizing eight-membered doublehydrogen-bonded ring (R22(8)) motif. In the case of tartaric acid with malic acid or levetiracetam, the large changes in other interaction motifs forced by exchange of one enantiomer for another while maintaining this motif led to a sizable energy gap. In the case of levetiracetam with mandelic acid, the availability of an alternative highly stabilizing motif led to a relatively smaller gap. Contrariwise, the ability of the system to rearrange the set of secondary interactions to give moderately stable structures containing the R22(8) motif with either enantiomeric combination meant that tartaric acid with malic acid produced a diastereomeric cocrystal pair, whereas the lack of such rearrangement led to levetiracetam with mandelic acid being enantiospecific. Based on these observations, and previous observations of diastereomeric salts, qualitative principles were proposed for the selection of resolving coformers. These include aiming for a strong, orientationally restrictive interaction motif (e.g., double hydrogen bonding), the avoidance of competitive motifs, and the presence of multiple weaker “secondary” motifs that will be disrupted by the exchange of one enantiomer for the other within the “primary” motif. The author looks forward to these ideas being put to the test in the laboratory.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author acknowledges Claire Adjiman, Louise Price, Mark Eddleston, and Tom Leyssens for useful discussions, Sally Price for useful discussions and the use of DMACRYS, and the EPSRC for funding through Grants EP/E016340/1 and EP/ J014958/1.

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