Rationalization of Racemate Resolution: Predicting Spontaneous

CRYSTAL GROWTH & DESIGN

Rationalization of Racemate Resolution: Predicting Spontaneous Resolution through Crystal Structure Prediction

2007 VOL. 7, NO. 1 56-63

Matthew D. Gourlay, John Kendrick, and Frank J. J. Leusen* Institute of Pharmaceutical InnoVation, UniVersity of Bradford, Bradford BD7 1DP, United Kingdom ReceiVed June 16, 2006; ReVised Manuscript ReceiVed October 5, 2006

W This paper contains enhanced objects available on the Internet at http://pubs.acs.org/crystal. ABSTRACT: Crystal structure prediction simulations are reported on 5-hydroxymethyl-2-oxazolidinone and 4-hydroxymethyl-2oxazolidinone to establish the feasibility of predicting the spontaneous resolution of racemates of small organic molecules. It is assumed that spontaneous resolution occurs when the enantiomorph is more stable than the racemic solid. The starting point is a gas phase conformational search to locate all low-energy conformations. These conformations are used to predict the possible crystal structures of 5- and 4-hydroxymethyl-2-oxazolidinone. In both cases, the racemic crystal structure is predicted to have the lowest energy. The energy differences between the lowest-energy racemic solids and the lowest-energy enantiomorphs are 0.2 kcal mol-1 for 5-hydroxymethyl-2-oxazolidinone and 0.9 kcal mol-1 for 4-hydroxymethyl-2-oxazolidinone. In the case of 4-hydroxymethyl2-oxazolidinone, where the racemic crystal is known to be more stable and the experimental crystal structures of both the racemate and the enantiomorph are available, the simulation results match the observed data. For 5-hydroxymethyl-2-oxazolidinone, where only enantiopure crystals are observed experimentally, the known experimental structure is found 1.6 kcal mol-1 above the lowestenergy predicted structure. This work shows that it is possible to predict whether the racemate of a small chiral molecule can be resolved spontaneously, although further advances in the accuracy of lattice energy calculations are required. Introduction The two enantiomers of a chiral compound have identical physical properties until placed in a chiral environment. As nature uses R-amino acids, the environment of the cell is chiral. As a consequence, the enantiomers of a pharmaceutically active compound have different biological actions. Therefore, the production of pure enantiomers is of fundamental importance in pharmaceutical and agrochemical applications. Stereoselective synthesis is expensive and rarely provides 100% enantiomeric excess. It is often more economical to manufacture the racemate and then separate it into pure enantiomers. Current separation techniques include liquid chromatography (HPLC) and crystallization. Because of the expense and relatively small scale of chromatographic separations, crystallization is the preferred method for racemate resolution on an industrial scale. The most common resolution method is the formation of diastereomeric salts. However, choosing the optimum resolving agent and crystallization conditions is difficult and time consuming.1,2 Diastereomeric salts are formed by the interaction of a chiral base with a racemic acid or by the interaction of a chiral acid with a racemic base; however, the technique does not work for all compounds. An emerging method involves the addition of a chiral inhibitor to the racemate in solution, preventing the crystallization of one of the enantiomers by stereoselective inhibition of the nucleation and/or growth of that enantiomorph. An example of such an inhibitor is poly-(N-methacryloyl-lysine) interacting with glutamic acid.3 The major disadvantage of these methods is the deliberate addition of an impurity requiring additional steps to remove it from the end product. A small percentage of chiral compounds crystallize as conglomerate crystals (mechanical mixtures of enantiopure R and S crystals). These compounds can be resolved using preferential enrichment crystallization methods4 in batch reactors. Obviously, no additives are required. * To whom correspondence should be addressed. Phone: +44 (0)1274 236144. Fax: +44 (0)1274 236155. E-mail: [email protected].

Figure 1. Molecular structures of 5-hydroxymethyl-2-oxazolidinone (1) and 4-hydroxymethyl-2-oxazolidinone (2).

The driving force for conglomerate formation is not fully understood; however, some links have been made with molecular symmetry5 and hydrogen-bonding patterns. In a recent paper6 looking at the derivatives of 2-oxazolidinone shown in Figure 1, it was found that compound 1 did form conglomerate crystals, but compound 2 did not. Compound 1 is used as a precursor in the manufacture of the antimicrobial linezolid and the antidepressant befloxatone. This paper examines the feasibility of predicting conglomerate crystallization by crystal structure prediction. Both isomers of hydroxylmethyl-2-oxazolidinone are studied, one of which is an example of a conglomerate forming system. By choosing two very similar systems with differing crystallization behavior, we hope to focus on the intermolecular interactions that cause the enantiomer separation. Crystallization is a complex process where the main contribution to crystal stability comes from the lattice energy. Thermodynamics suggests that the more stable crystal, i.e., the structure with the lower lattice energy, will be found experimentally. To predict whether a molecule crystallizes as a conglomerate or a racemate therefore involves the prediction of the most stable enantiomorph and the most stable racemic solid. If the enantiomorph is more stable than the racemate, spontaneous resolution will occur. If the racemate is more stable, then the compound will not resolve spontaneously. Methodology Two 4-hydroxymethyl-2-oxazolidinone (4HMO) and one 5-hydroxymethyl-2-oxazolidinone (5HMO) crystal structures were obtained from the Cambridge Structural Database (CSD),7 which was searched using

10.1021/cg060364o CCC: $37.00 © 2007 American Chemical Society Published on Web 12/13/2006

Rationalization of Racemate Resolution

Crystal Growth & Design, Vol. 7, No. 1, 2007 57

Table 1. The Different Calculations Used to Determine PDCsa code

package

basis set

functional

charges

DFT1 DFT2 DFT3 DFT4

GAMESS-UK GAMESS-UK GAMESS-UK DMol3

6-311G** 6-311G** 6-31G** DNP

B3LYP B3LYP PBE PBE

expt. conformation averaged averaged averaged

a

DNP ) Double zeta numerical basis set with polarization functions.

Table 2. Conformations 1-9 Minimized with a 6-311G** Basis Set and B3LYP Functional in GAMESS-UKa 5HMO S 5HMO Conf 1 Conf 2 Conf 3 Conf 4 Conf 5 Conf 6 Conf 7 Conf 8 Conf 9

T1 (°)

T2 (°)

56.7 60.5 56.7 60.4 176.9 -57.5 -63.4 -179.3 -62.2 -75.0 -63.9 85.7 169.0 154.5 53.8 -82.8 178.9 60.0

∆ energy (kcal mol-1) 0.00 0.00 1.64 3.15 3.27 3.65 4.44 5.01 5.51

ring torsions (°) OCCN CCNC

hydrogen bond

-22.4 -22.2 -1.4 -0.5 -0.1 -23.6 -22.4 4.8 -0.2

OH‚‚‚O< OH‚‚‚O< OH‚‚‚O< no no no no no no

22.8 22.6 2.2 0.6 0.6 23.4 22.9 -3.2 0.3

4HMO

Figure 2. Definition of torsion angles: C-C-C-O (highlighted in bold) defines torsion 1; C-C-O-H (highlighted in bold) defines torsion 2. Torsions O-C-C-N (not highlighted) and C-C-N-C (not highlighted) in the five-membered ring are used to measure ring deformation. 5HMO is shown on the left, and 4HMO is shown on the right. name and structural parameters. Geometry optimization and lattice parameter optimization were performed using the Forcite module in Materials Studio v 3.2.8 For isolated molecules, the nonbonded interactions at a distance greater than 15.5 Å were smoothly set to zero using a cubic spline potential. For calculations involving periodic boundary conditions, the Ewald method was used to accelerate the convergence of the Coulomb and dispersive nonbonded interactions. The force fields used in this study include Dreiding,9 COMPASS,10 CVFF,11 PCFF,12 and the Universal13 force field. For all the force fields tested, a variety of methods for calculating charges was explored: charge equilibration (QEq),14 Gasteiger charges as implemented in Materials Studio, and potential derived charges (PDCs) obtained from fitting to the ab initio electrostatic potential.15,16 Ab initio density functional theory (DFT) calculations were performed on the molecules using GAMESS-UK17 and DMol3.18 In all cases, the geometry was fully optimized before calculating the electrostatic potential (ESP). Table 1 summarizes the basis set and functionals used in the DFT calculations. The DFT1 charge set was obtained by starting with a single molecule from the experimental structure, minimizing the energy with respect to geometry and determining the ESP.15 This approach assumes that the experimental structure is known in advance, so biasing the charge set toward the experimental structure. The DFT2, DFT3, and DFT4 charges were determined by taking the nine conformations generated in the conformational analysis (see below) and re-minimizing them with GAMESS-UK or, in the case of DFT4, with DMol3. The final atomic charges were then obtained by averaging the PDCs of the nine conformations using Boltzmann weighting19 (at 298 K) calculated from their relative conformational stabilities. Conformational analysis was performed in Cerius2.20 Both HMO structures were drawn and then geometry optimized using the Dreiding force field with Gasteiger charges as implemented in Cerius2. Using the same force field, a grid scan conformational search was done with the two torsions, shown in Figure 2, exploring the flexibility of the hydroxylmethyl group. This resulted in nine distinct low-energy conformations for each molecule. These conformations were used as starting points for further geometry optimization using molecular mechanics and ab initio methods. Atomic charges were calculated as described above, and the conformations were re-minimized with the Dreiding force field and PDCs. This produced the starting conformations used in the subsequent crystal structure prediction stage. The Materials Studio Polymorph module8,21-23 was used with the Dreiding force field and DFT2 charges as described above. The 13 most common space groups24 were used in the polymorph search, which represents 87.3% of the crystal structures entered in the CSD. These groups (with their occurrence in the CSD) were: P21/c (35.9%), P1h (13.7%), P212121 (11.6%), P21 (6.7%), C2/c (6.6%), Pbca (4.3%), Pnma (1.9%), Pna21 (1.8%), Pbcn (1.2%), P1 (1%), Cc (0.9%), C2 (0.9%), and Pca21 (0.8%). Five runs were conducted for each conformation to ensure adequate sampling of crystal packing alternatives. A Microsoft

R 4HMO Conf 1 Conf 2 Conf 3 Conf 4 Conf 5 Conf 6 Conf 7 Conf 8 Conf 9

T1 (°)

T2 (°)

57.0 49.6 171.3 -170.6 168.7 74.0 173.0 -79.2 -65.7 -72.1 -65.1 -174.5 61.8 -61.5 52.7 -178.9 -69.4 85.4

∆ energy (kcal mol-1) 0.00 1.14 1.69 2.01 2.05 2.41 2.53 3.04 3.46

ring torsions (°) OCCN CCNC

hydrogen bond

-21.7 24.3 23.1 -21.6 25.5 3.2 27.3 17.6 1.5

OH‚‚‚NH no no no no no no no no

22.1 -24.2 -23.4 21.8 -24.3 -0.7 -26.7 -19.7 0.5

a The torsion angles OCCN, CCNC, T1, and T2 are defined in Figure 2. OH‚‚‚NH and OH‚‚‚O< are intramolecular hydrogen bonds. O< is the oxygen contained in the ring.

Table 3. Gas Phase Conformations Minimized Using the Dreiding Force Field and Charges Derived from the DFT2 Calculationa 5HMO S 5HMO Conf 4 Conf 2 Conf 3 Conf 5 Conf 6 Conf 1 Conf 7 Conf 9 Conf 8

T1 (°)

T2 (°)

-91.9 -179.0 60.0 59.6 177.3 -52.5 -63.4 -69.1 -65.3 74.1 52.1 174.8 -172.5 -177.2 179.6 56.3 61.7 -60.4

ring torsions (°) ∆ energy (kcal mol-1) OCCN CCNC 0.00 0.68 0.82 1.18 2.16 2.56 3.45 3.81 4.34

-0.2 -1.2 0.0 -0.2 -0.3 0.3 -0.2 0.1 2.1

0.3 1.1 0.0 0.3 0.3 0.3 0.2 0.1 -1.6

hydrogen bond no OH‚‚‚O< no no no no no no no

4HMO R 4HMO Conf 6 Conf 5 Conf 1 Conf 2 Conf 8 Conf 3 Conf 9 Conf 4 Conf 7

T1 (°)

T2 (°)

-61.8 -179.8 -62.7 -68.1 54.8 60.4 179.8 179.2 54.2 177.0 179.3 65.3 -66.1 74.4 -179.0 -69.7 64.5 -61.3

ring torsions (°) hydrogen ∆ energy (kcal mol-1) OCCN CCNC bond 0.00 1.21 1.31 1.39 1.93 2.13 2.13 2.63 3.57

0.1 -0.2 -0.3 -0.4 -0.8 -0.8 -0.2 1.0 1.1

-0.1 0.1 0.1 0.3 0.3 0.7 0.1 -1.0 -1.1

no no no no no no no no no

a Torsion angles OCCN, CCNC, T1, and T2 are defined in Figure 2. OH‚‚‚O< is an intramolecular hydrogen bond in which O< is the oxygen contained in the ring.

Excel macro was used to cluster the results from all the runs, based on space group, energy, density and Crystal Similarity Measure.23

Results and Discussion The gas phase conformations after minimization in GAMESSUK with the 6-311G** basis set and B3LYP functional (DFT2) are shown in Table 2. The results of minimizing these gas phase conformations with the Dreiding force field and DFT2 charges

58 Crystal Growth & Design, Vol. 7, No. 1, 2007

Gourlay et al.

Table 4. CSD Entries for the Three Crystal Structures6 a CSD code

space group

HMO molecule

EXEWAF EXEWEJ EXEVUY

P21/c P212121 P21

4 race 4 pure 5 pure

ring torsions (°) OCCN CCNC 2.6 9.3 -0.8

-1.1 -6.6 -0.6

T1 (°)

T2 (°)

a (Å)

53.1 53.0 53.3

82.9 69.7 -87.6

5.13 6.91 5.57

unit cell parameters b (Å) c (Å) 8.21 8.08 7.90

12.25 9.21 6.24

β (°)

hydrogen bond pattern

92.6 90.0 105.0

1D 3D 2D

a The column labeled “HMO molecule” describes the composition of the crystal with “race” meaning a racemic crystal and “pure” an enantiopure crystal structure. Torsions OCCN, CCNC, T1, and T2 are defined in Figure 2. “Hydrogen bond pattern” describes the dimensionality of the hydrogen-bonding network. 1D indicates that the hydrogen bonding propagates in a column, 2D indicates that the hydrogen bonding occurs in layers, and 3D indicates that the hydrogen bonding occurs in all directions in the crystal structure.

Table 5. Deviations in Lattice Parameters Caused by Minimization of the Experimental Crystal Structures with Different Force Fields and Atomic Chargesa % deviations from expt. crystal lattice

torsion angle (°)

% rms

force field

charge set

crystal

a

b

c

β

T1

T2

abc

COMPASS COMPASS COMPASS CVFF CVFF CVFF PCFF PCFF PCFF Universal Universal Universal Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding Dreiding

COMPASS COMPASS COMPASS CVFF CVFF CVFF PCFF PCFF PCFF QEq QEq QEq QEq QEq QEq DFT1 DFT1 DFT1 DFT2 DFT2 DFT2 DFT3 DFT3 DFT3 DFT4 DFT4 DFT4

EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY EXEWEJ EXEWAF EXEVUY

-2.2 -2.5 -1.5 1.6 3.6 -5.0 -3.0 1.0 -6.2 -10.7 9.6 13.5 -1.3 -1.3 7.6 -1.2 -1.1 2.1 -1.6 -0.4 0.7 -1.0 -0.8 1.9 -1.1 -1.2 5.0

-1.4 0.2 -0.6 -2.8 -2.9 0.8 -0.4 -3.9 0.8 8.3 -2.7 -0.3 0.3 1.5 -1.1 2.0 1.7 0.7 2.5 1.1 0.7 2.4 1.5 0.8 1.7 1.9 0.7

1.2 -0.7 -5.8 0.2 -1.3 1.0 3.1 0.5 -1.4 11.3 0.9 -10.5 3.5 2.0 -5.3 4.5 3.6 1.7 4.5 3.6 1.8 4.4 4.0 1.0 4.7 3.9 -1.7

0.0 1.4 0.6 0.0 -6.9 -3.9 0.0 -6.5 -2.3 0.0 -1.4 -1.4 0.0 -0.9 0.1 0.0 -2.5 1.3 0.0 -3.2 0.3 0.0 -3.1 -0.2 0.0 -2.7 -0.6

45.7 46.2 51.2 51.7 55.3 57.1 48.8 52.2 44.7 52.1 50.3 69.0 48.5 54.8 59.2 50.2 57.7 54.2 49.9 57.9 54.2 50.3 58.5 55.6 50.1 58.2 57.3

73.4 73.3 -80.3 52.3 62.9 -87.8 61.8 69.6 -80.5 66.4 63.2 -80.7 57.9 59.9 -79.5 60.6 65.3 -89.3 61.2 65.8 -87.7 61.0 65.6 -86.6 60.3 64.8 -84.1

2.39 2.58 2.91 8.85 3.49 2.38 2.29 2.37 2.89

a The last column contains the root-mean-square of the percentage deviations in the a, b, and c lattice parameters. An extended table showing further parameters tested, is available as Supporting Information.

are shown in Table 3. In Table 2a, conformations 1 and 2 are identical. This is because GAMES-UK minimized these two conformations to the same minimum, although the starting conformations differed in the rotation of the hydroxyl group after the Cerius2 grid scan conformational analysis. Minimizations of the molecular conformations found in the experimental crystal structures led to conformation 8 for 5HMO and conformation 1 for 4HMO, with energies relative to the lowest-energy gas-phase conformations of 4.3 and 1.3 kcal mol-1, respectively (see Table 3). The large energy difference for 5HMO is caused by the difference in ring distortion found in the gas-phase DFT results (distortions of about 22 degrees, see Table 2) in comparison to the experimental solid-state conformations (distortions of less than 1 deg; see Table 4). The large distortions in the gas-phase in both ring torsions for the two lowest-energy conformations have a significant effect on the calculated atomic charges. Because of the Boltzmann weighting used in averaging the atomic charges over the 5HMO conformations, these two distorted conformations have the largest contribution to the molecular electrostatics and thus the molecular energy. Hence, the electrostatic part of the force field model does not represent the undistorted experimental conformation well, thus explaining the large energy difference. In the case of 4HMO, the difference in ring distortion between the gas-phase DFT results and the experimental solid-state confor-

mations is less pronounced. Therefore, the electrostatic part of the force field model for 4HMO is more appropriate for the solid-state conformation of 4HMO, leading to a smaller energy difference between the gas-phase conformation and the solidstate conformation. The lattice parameters of the three experimental crystal structures are shown in Table 4. The results of the minimizations of these crystal structures using the various force fields are shown in Table 5. In this table, the deviations caused by the force field minimizations are shown as percentage changes in the unit cell parameters; a negative sign indicates a reduction in the lattice parameter. The COMPASS force field provides its own charge set and predicts a large deviation for crystal EXEVUY along the “c” direction. CVFF and PCFF, similarly, provide their own charge sets and show large deviations in the “a” axis dimension of EXEVUY and in the β angle of EXEWAF. The Universal force field was used with various charge sets, but all performed poorly. QEq charges, which are much quicker to calculate, do not provide as good results as DFT charges when used with any of the force fields. Only the Dreiding force field with DFT charges produces acceptable results with lattice deviations of less than 5%25 for the three crystals. Our results show that the Dreiding force field with ab initio charges outperforms the other charge and force field sets tested

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Crystal Growth & Design, Vol. 7, No. 1, 2007 59

Table 6. Twenty-Five Lowest-Energy Predicted Crystal Structures of 5HMO in Enantiopure Space Groupsa 5HMO enantiopure

hydrogen-bonding pattern

torsion angle

rank

space group

density (g cm-3)

relative energy (kcal mol-1)

starting conformation

type

dimension

T1 (°)

T2 (°)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

P212121 P212121 P212121 P212121 P21 P212121 P21 P21 P212121 P21 P21 P21 P212121 P212121 C2 P21 P212121 P212121 P212121 P21 P212121 P21 C2 P212121 P212121

1.43 1.37 1.36 1.44 1.41 1.32 1.40 1.35 1.39 1.41 1.38 1.37 1.37 1.30 1.35 1.39 1.29 1.34 1.36 1.36 1.37 1.42 1.36 1.30 1.31

0.21 0.62 0.63 0.71 0.82 0.83 0.83 0.85 0.90 1.06 1.10 1.11 1.16 1.20 1.20 1.24 1.38 1.55 1.57 1.59 1.60 1.64 1.70 1.72 1.79

1,2,6,8 1,2,8 4,6,7 1,2,6 2,4,6 1,2,6,8 3,7,9 1,2,6,8 4,6,9 3,7,9 3,7,9 1,2,8 1,2,8 4,5,6 4,5,6,9 3,7 4,5,6 1,2,6 3,5,7,9 4,5,6 2,7,9 1,8 4,5,6,9 1,2,8 1,2,6,8

010100 100100 100100 100100 100100 010100 010100 010100 100100 010100 011100 100100 010100 100100 100100 011100 010100 010100 010100 010100 010001 100100 100100 001100 100100

2D 3D 2D 2D 3D 1D 2D 1D 2D 1D 1D 2D 3D 3D 2D 1D 3D 1D 2D 2D 3D 2D 2D 3D 3D

58.5 50.3 -75.1 53.5 -71.8 63.0 -172.3 60.5 -71.1 -178.4 -176.3 56.6 54.4 -63.8 -73.4 -177.0 -61.6 56.0 -170.2 -61.2 177.5 54.2 -73.4 56.5 52.7

73.1 167.9 58.0 66.1 85.9 66.7 -68.6 66.8 75.8 -60.0 -59.3 67.6 165.7 172.8 63.0 -57.8 179.1 64.4 -66.8 176.7 63.1 -87.7 70.4 175.9 62.8

a

See text for explanation of hydrogen-bonding types. The predicted structure that corresponds to the experimentally observed structure (#22) is boldfaced.

(see Table 5 and Supporting Information). As crystal structure predictions should not assume prior knowledge of the crystal structure, an averaged charge set based on the calculated conformations was required (DFT2, DFT3, or DFT4). Overall, the DFT2 charges with the Dreiding force field have the lowest root-mean-square deviation from the experimental lattice parameters (abc), with DFT3 a very close second. A decision was made to use the DFT2 charge set (6-311G** basis set with a B3LYP functional) for the rest of the work. Although the Dreiding force field proved the better energy parametrization for this system, the use of DFT PDCs also led to improvements with other force fields (see Supporting Information). This finding is in agreement with previous work in this area.26 Using DFT PDCs in combination with the COMPASS force field, on the other hand, showed little or no improvement in the predicted lattice parameters. A total of 1170 simulation runs generated 100 000 possible crystal structures for each molecule, of which around 40 000 are unique and 1000 are within 3 kcal mol-1 of the global minimum for each molecule and can therefore be considered as potential polymorphs.21 Tables 6-9 show the lowest-energy predicted crystal structures for racemic and enantiopure 5HMO and 4HMO. The three experimental structures are present in the crystal structure prediction results. The results for 4HMO are in perfect agreement with experiment: both experimental structures are predicted as the lowest-energy racemic and enantiopure crystals, with an energy difference of 0.9 kcal mol-1 in favor of the racemic solid. The 5HMO prediction is less successful. Experimentally, only enantiopure crystals are observed, but according to the simulations, the lowest-energy racemic structure is more stable than the lowest-energy enantiopure crystal by 0.2 kcal mol-1. The experimentally observed crystal structure is ranked 22nd in the list of predicted enantiomorphs, 1.6 kcal mol-1 above the lowest-energy (racemic) structure. A comparison of the gas-phase conformations used as starting points for the crystal structure predictions with the conformations

in the predicted structures produces some interesting results. Both low-energy and high-energy conformations can form lowenergy predicted crystal structures. For 5HMO, the experimentally observed structure is predicted starting from conformations 1 and 8. In the gas-phase calculations using Dreiding with PDCs, these conformations have energies of 2.6 and 4.3 kcal mol-1 above the lowest-energy conformation 4 (see Table 3a). The lowest-energy predicted 5HMO crystal structure, which is racemic, is reached by starting from conformations 4 and 6, with conformation 6 being 2.2 kcal mol-1 above conformation 4, which is the global minimum. The lowest-energy enantiopure 5HMO structure is reached starting from conformations 1, 2, 6, and 8, with conformation 2 being 0.7 kcal mol-1 above the global minimum. A similar pattern occurs for 4HMO. Comparison of the starting conformations to those contained in the predicted crystal structures reveals that torsion 1 is tightly constrained, whereas torsion 2 is much less constrained. This analysis indicates that there is no identifiable link between the energy of the initial gas-phase conformations and the energy of the resulting predicted crystal structures. In the paper in which the experimental crystal structures were reported,6 it was suggested that moving the OH from the 5 to the 4 position hinders the transfer of chirality from the molecular to the supermolecular structure. This was assumed to be due to a change in the hydrogen-bonding pattern. The main hypothesis was that enantiopure crystals have a higher dimensionality in their hydrogen-bonding network with more molecules hydrogen bonded to each other, thus leading to more stable structures than their racemic counterparts. Similar differences in the hydrogen-bonding pattern in other compounds also affect the selectivity, favoring crystallization of the enantiopure compound over the racemic.27,28 In Tables 6-9 the hydrogen bonding is described by a binary code, in which 1 indicates that the hydrogen bond is present and 0 means that the hydrogen bond is absent. The six positions represent the six types of hydrogen bonds possible in these crystal structures. The first three represent hydrogen bonding

60 Crystal Growth & Design, Vol. 7, No. 1, 2007

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Table 7. Twenty-Five Lowest-Energy Predicted Crystal Structures of 5HMO in Racemic Space Groupsa 5HMO racemic

hydrogen-bonding pattern

torsion angle

rank

space group

density (g cm-3)

relative energy (kcal mol-1)

starting conformation

type

dimension

T1 (°)

T2 (°)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

P21/c P21/c Cc C2/c P21/c P21/c P21/c P21/c Pca21 Pna21 P21/c P21/c P21/c P21/c P1h P21/c P1h P21/c C2/c Pna21 Pbca C2/c Pna21 Pbca P21/c

1.39 1.43 1.33 1.39 1.36 1.40 1.40 1.37 1.38 1.33 1.36 1.41 1.44 1.39 1.40 1.33 1.39 1.42 1.38 1.36 1.45 1.35 1.34 1.39 1.39

0.00 0.23 0.29 0.37 0.39 0.42 0.42 0.44 0.44 0.53 0.55 0.56 0.57 0.57 0.65 0.66 0.66 0.67 0.69 0.70 0.70 0.74 0.74 0.76 0.86

4,6 4,6 1,4,6 4,6 3,4,5,6,7,9 4,6 1,2,6,8 3,5,7,9 4,5,6,7 1,2,6,8 6 1,2,8 4,7 4,5,6,9 4,5,6 4,5 3,5,7,9 3,5,7,9 5 1,2,6,8 3,7,9 4,6,9 4,5 4,6 1,2

100100 100100 100100 100100 100100 100100 010100 100100 100100 010100 010100 100100 100100 100100 100100 010100 010100 100100 100100 010100 001100 100100 100100 100100 010100

2D 2D 3D 2D 3D 2D 1D 2D 2D 3D 2D 2D 3D 2D 2D 3D 1D 1D 3D 1D 3D 2D 3D 2D 1D

-75.1 -72.1 -64.6 -74.2 -68.8 -75.5 60.4 178.3 -62.2 -69.2 56.9 -76.9 59.5 -63.2 -75.8 -68.1 -64.1 176.7 -58.9 65.2 175.8 -74.5 -56.8 -47.6 59.7

61.1 79.3 -168.8 63.3 -67.1 66.8 66.7 -68.2 174.3 -179.7 67.8 74.2 70.2 162.7 68.5 -174.7 -170.7 -70.7 -60.5 66.4 -64.1 67.9 -64.1 84.6 70.9

a

See text for explanation of hydrogen-bonding types. Table 8. Twenty-Five Lowest-Energy Predicted Crystal Structures of 4HMO in Enantiopure Space Groupsa 4HMO enantiopure

hydrogen-bonding pattern

torsion angle

rank

space group

density (g cm-3)

relative energy (kcal mol-1)

starting conformation

type

dimension

T1 (°)

T2 (°)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

P212121 P21 P212121 P21 P21 P212121 P212121 P212121 P212121 P212121 P212121 P21 P212121 P212121 P212121 P212121 P212121 P212121 P212121 P212121 P212121 P212121 P21 P212121 P212121

1.43 1.34 1.35 1.32 1.44 1.29 1.43 1.30 1.33 1.36 1.40 1.41 1.38 1.38 1.41 1.33 1.38 1.34 1.38 1.39 1.34 1.39 1.39 1.27 1.29

0.87 0.92 1.17 1.37 1.60 1.65 1.70 1.71 1.75 1.75 1.75 1.78 1.82 1.83 1.85 1.94 1.98 2.02 2.11 2.15 2.15 2.18 2.33 2.33 2.33

1,7,8 5,6,9 5,6,9 6,5 5,6,9 5,6,9 2,3,4 4,5,6,9 1,7,8 2,5,6,9 1,7,8 5,6,9 5,6,9 5,6,9 5,6,9 2,5,6,8,9 1,7,8 5,6,9 7,8 5,6,9 5,6,9 1,7,8 2,3,4 5,6 1,8

100100 010100 010100 010100 010100 010100 010100 100100 001100 010100 100100 010010 010110 010100 010010 100100 100100 010100 100100 010100 001100 100100 011100 100100 010100

3D 2D 2D 2D 2D 3D 1D 2D 3D 3D 3D 1D 3D 3D 1D 3D 2D 3D 3D 3D 2D 3D 1D 3D 2D

49.9 -61.1 -59.5 -60.2 -52.4 -59.5 -175.1 -60.4 53.6 -54.9 48.7 -63.4 -62.8 -55.7 -64.5 -56.3 52.7 -55.0 53.9 -58.4 -51.6 56.0 -169.6 -60.5 49.9

61.2 -170.2 -168.3 -169.2 177.5 171.6 -62.3 -63.7 -178.9 178.3 72.4 -173.2 -171.6 -173.0 -170.5 -170.8 -174.7 -174.2 -82.4 -55.5 -173.1 164.3 -55.5 -70.2 -177.4

a

See text for explanation of hydrogen-bonding types. The predicted structure that corresponds to the experimentally observed structure (#1) is boldfaced.

with NH as a donor, and the last three represent hydrogen bonding with OH as a donor. Position 1 ) NH‚‚‚OH, position 2 ) NH‚‚‚OdC, position 3 ) NH‚‚‚O