Article pubs.acs.org/JPCC
Pressure Effect on D,L-Mandelic Acid Racemate Crystallization Weizhao Cai, Jędrzej Marciniak, Michał Andrzejewski, and Andrzej Katrusiak* Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland S Supporting Information *
ABSTRACT: Mandelic acid, C6H5CHOHCOOH, (MA) is one of frequent exempts from the Wallach’s rule, as its racemate DL-MA is less dense than the enantiomers. This relation appears to be unfavorable for the racemate stability at high pressure; however, the racemate remains more stable than the conglomerate of enantiomers up to 1.36 GPa at least. The isochoric crystallization of DL-MA yields its orthorhombic form I, space group Pbca, and above 0.65 GPa, another centrosymmetric polymorph of monoclinic DL-MA form II, space group P21/c, becomes stable. Their structures have been determined by X-ray diffraction of the single crystals in situ grown in a diamond-anvil cell up to 1.36 GPa. Lattice-energy calculations by the semiempirical PIXEL method demonstrate that DL-MA form II is more stable than DL-MA form I, and both of these racemates are more stable than their enantiomer counterpart L-MA.
1. INTRODUCTION The efficient resolution of a racemate into enantiomers is one of the challenges for the synthesis and production of chiral compounds, with direct application in pharmaceutical and food industries.1 Usually only one enantiomer exhibits the required biological activity. The often cited examples of this are thalidomide2,3 and levothyroxine.3,4 The nutrition properties of enantiomers can be very different, too. For example, (−)-glucose tastes sweet but is not digested and can be used to fight obesity.5 Differences in bioactivity can be drastic, and the presence of unwanted enantiomer is harmful,6 hence the intensive research on resolution of enantiomers. Of the numerous methods of racemates resolution, none applied pressure. It was only considered in the book by Jacques, Collet, and Wilen,1 who estimated that compounds with positive molar volume difference between the racemate (VR) and enantiomer (VE) of several cubic angstroms should resolve between 0.1 and 1.0 GPa.7 The positive VR−VE difference for mandelic acid, C6H5CHOHCOOH, denoted MA, racemate DL-MA, and enantiomers D-MA or L-MA: Scheme 1 prompted Rietveld et al. to attempt the resolution of DL-MA into enantiomers by applying pressure. They claimed that the resolution proceeds at 0.65 GPa and 460 K.8 Their conclusions were based on the differential scanning calorimetry (DSC) signal splitting at high
pressure; however, no direct observation of the conglomerate formation was demonstrated. Mandelic acid is known for its bacteriostatic properties and is widely used in dermatology, especially for complexion diseases.9 For decades, it has also been applied for urinary tract treatment.10 MA ester derivatives are used in two drugs: cycladelate and homatropine. There are two known polymorphs of the DL-MA racemate: form I, of orthorhombic space group Pbca, denoted DL-MA-I;11−13 and form II, of monoclinic space group P21/c, denoted DL-MA-II.14 At 0.1 MPa, DL-MA-I is thermodynamically more stable than form II.14,15 Recently, our studies of the effect of pressure on the racemic crystallization and spontaneous resolution of enantiomers were reported to validate Wallach’s rule under high pressure. For example, racemic (±)-trans-1,2-diamonocyclohexane (DACH) crystallizes as the conglomerate up to 2.04 GPa, in the same phase as at low temperature.16 Also, high-pressure isochoric crystallization of racemic (±)-2-butanol and (±)-2,3butanediol still yields enantiomorphic conglomerates.17 Presently, we report the results of in situ high-pressure crystallization of DL-MA in a diamond-anvil cell (DAC) and X-ray diffraction study of so obtained samples, which is a straightforward method for revealing their crystalline form and structure.
2. EXPERIMENTAL SECTION D,L-Mandelic acid, DL-MA, purchased from Sigma-Aldrich with purity ≥99%, was used. High-pressure experiments were carried out in situ by isothermal and isochoric crystallizations of DLMA from a series of various solvents in a DAC, according to the experimental procedure previously described.18 Pressure was determined by a ruby fluorescence R1 line shift method with an accuracy of 0.03 GPa.19 The crystallizations of DL-MA
Scheme 1. Enantiomers of Mandelic Acid (MA)
Received: February 15, 2013 Published: March 18, 2013 © 2013 American Chemical Society
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dissolved in methanol and ethanol in the DAC led to the esterification reaction, and a series of other solvents were tried. Alcohols were substituted by water. Subsequently, a single crystal was successfully grown from aqueous solution at 0.05 GPa/296 K (Figure 1a−c). After measuring the X-ray
Figure 2. In situ isochoric crystallization of DL-MA-II dissolved in water−chloroform mixture (4:1 vol.): (a) one seed at 423 K; (b) 403 K; (c) 358 K, and (d) 0.86 GPa/296 K. Other needle-shaped small crystals appeared at the edge of the chamber wall. Six ruby chips for pressure calibration lie at the top left and bottom right sides of the chamber. Miller indices of crystal faces have been indicated in photograph (b). Figure 1. Isochoric crystallization of DL-MA-I of aqueous solution. A single crystal at (a) 305 K; (b) 305 K, and (c) 0.05 GPa/296 K. (d) The crystal sample at 0.65 GPa/296 K. Miller indices of crystal faces have been indicated in photograph (c).
diamond reflections were eliminated. The ambient-pressure structures were applied as the starting model for full-matrix least-squares refinement on high-pressure data.23 The hydrogen atoms were located from the molecular symmetry, with the C− H and O−H distances equal to 0.93 (aromatic ring), 0.98 Å (−CH group), and 0.983 Å (−OH group). The anisotropic factors Uij of nonhydrogen atoms were constrained to 1.5 (for hydroxyl hydrogen atoms) and 1.2 (for the C−H hydrogen atoms) times Ueq of their carriers. Because of the low completeness of high-pressure diffraction data, the anisotropic values of few carbon and oxygen atoms were restrained to approximate isotropic shape by using command ISOR 0.01. The selected crystal data are listed in Table 1 (cf. Table S1 of Supporting Information). The details of the structural determinations have been deposited in the form of CIF files in the Cambridge Crystallographic Database Center. They have been assigned reference codes CCDC 923825−923829 for the DL-MA-I structures at 0.05, 0.19, 0.33, 0.48, and 0.65 GPa and
diffraction data, pressure was increased to 0.19, 0.33, 0.48, and 0.65 GPa (Figure 1d), and for each step, crystallization was repeated and diffraction data were recorded again. All samples turned out to be the DL-MA-I racemate. All of our attempts to grow crystals from aqueous solution above 0.65 GPa yielded small grains of clearly monoclinic morphology. To optimize the conditions of crystallization, various solvents were used. The best crystals were obtained from the mixture of distilled water and chloroform used as the solvent and pressure-transmitting medium. Several small DLMA crystals were loaded in the DAC chamber, then topped off with the water−chloroform (4:1 vol.) mixture. Pressure was increased to 0.92 GPa, and the DAC was heated by a hot-air gun to 423 K when all crystals were dissolved. Then, temperature was slowly decreased to room temperature to allow a single crystal of MA to grow. Finally, it filled ca. 80% of the chamber, and the pressure stabilized at 0.86 GPa/296 K (Figure 2). Diffraction data collected for this single crystal revealed its form II DL-MA structure. Other single crystals of the same racemate form II were grown at 0.76, 1.09, and 1.36 GPa/296 K, and the X-ray diffraction data were subsequently measured for these samples. X-ray diffraction data of the single-crystals grown in the DAC have been measured with a KUMA KM4-CCD diffractometer and Oxford Diffraction Xcalibur Eos by applying the procedures for the DAC centering and high-pressure measurements.18 The CrysAlis software was used for collecting data and their initial reduction.20 After correcting intensities for the effects of DAC and sample absorption and sample shadowing by the gasket,21,22 the sample reflections overlapping with
Table 1. Selected Crystal Data of DL-MA-I and DL-MA-II and of L-MA
a
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form
DL-MA-I
DL-MA-II
L-MAa
pressure crystal system space group a/Å b/Å c/Å β/° V/Å3 Z Dcal (g cm−3)
0.65 GPa orthorhombic Pbca 9.637(2) 16.135(8) 9.365(2) 90 1456.1(8) 8 1.388
0.76 GPa monoclinic P21/c 5.825(2) 28.908(11) 8.224(6) 93.03(4) 1382.9(12) 8 1.462
0.1 MPa monoclinic P21 8.629(1) 5.861(1) 15.185(2) 102.76(1) 749.0 4 1.349
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Figure 3. Symmetry-independent MA molecules in (a) DL-MA-I, (b) DL-MA-II, and (c) L-MA, all viewed perpendicular to the phenyl ring (cf. Figure S2 in the Supporting Information). The same labeling scheme as in refs 12 and 32 for DL-MA-I and L-MA has also been adopted.
CCDC 923830−923833 for the DL-MA-II structures at 0.76, 0.86, 1.09, and 1.36 GPa, respectively. The intermolecular contacts have been compared using the Hirshfeld surface24 and 2D fingerprint analysis25 with the aid of Crystal Explorer.26 Theoretical calculations of the lattice energy were performed using the PIXEL method from the CLP program suite, with the condensation level set to 3.27 The crystal structures of two DLMA polymorphs and L-MA enantiomer under ambient conditions were selected. Molecular energies were calculated with the aid of Gaussian 09 with the Dunning’s correlation consistent quadruple-ζ basis set (cc-pvqz).28,29 For the calculations, torsion angles C1−C2−C3−C4/C8 and O1− C1−C2−O3 were fixed to the values observed experimentally in DL-MA-I, molecules A and B in DL-MA-II and molecules A and B in L-MA, whereas all other parameters were optimized (Figure 3). Two different DFT functions were chosen: B3LYP(cc-pvqz),30 as a standard functional widely used in calculations; and ωB97xd(cc-pvqz), as a long-range corrected functional, which includes empirical dispersion.31
Figure 5. Compression of unit-cell dimensions of DL-MA-I (blue full symbols) and DL-MA-II (black open symbols) related to the ambient condition 0.1 MPa/296 K. The crystal data of DL-MA-I at 0.1 MPa/ 150 K (blue half-filled symbols, ref 13) have been added for comparison.
3. RESULTS AND DISCUSSION Racemate DL-MA-I is less dense than enantiomer L-MA: 1.298 versus 1.349 g cm −3 (Figure S1 in the Supporting Information).12,32 Therefore, Jacques et al. postulated that this racemate should resolve into the more dense enantiomers
at high pressure.1 It is also known that racemate DL-MA exhibits two polymorphic forms at 0.1 MPa: orthorhombic form I12 and metastable monoclinic form II.14 The most dense is monoclinic racemate DL-MA-II (its density equals 1.356 g cm−3). Our in situ crystallizations have shown that DL-MA-I is stable up to 0.65 GPa, and above this pressure it is the DL-MAII racemate that becomes more stable. No signs of the enantiomers resolution and a conglomerate formation have been observed up to 1.36 GPa. The transition pressure between racemate DL-MA-I and DL-MA-II coincides with the pressure of 0.65 GPa detected by high-pressure DSC by Rietveld et al. and associated by them with the enantiomers resolution of DLMA racemate.8 According to our results, the transition at 0.65 GPa corresponds to the formation of DL-MA-II monoclinic racemate. This has been explicitly shown by solving the structure of the high-pressure crystals of DL-MA. This transition can be also observed optically because the morphology of racemates I and II can be easily distinguished by characteristic orthorhombic and monoclinic crystal habits (Figures 1 and 2). There is a clear volume difference of 4.3% between DL-MA-I and II at ambient pressure, which still persists up to 0.65 GPa, as shown in Figure 4. The unit-cell volume of DL-MA-I is compressed by ∼6.5% at 0.65 GPa before the transformation to DL-MA-II takes place. The unit-
Figure 4. Molecular volume Vm (V/Z, cf. Table S1 in the Supporting Information) of DL-MA as a function of pressure at 296 K for DLMA-I (blue squares) and DL-MA-II (black circles). Also, the DL-MA at 0.1 MPa/150 K (blue open square, ref 13) and L-MA (red triangle, ref 32) have been indicated. The insets show the crystal habits of DLMA-I and II, as observed in the DAC. 7281
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Figure 6. Hydrogen-bonded aggregates in the structure of (a) DL-MA-I, (b) DL-MA-II, and (c) L-MA. Symmetry codes in DL-MA-I: (a) (i) 1/2 − x, 1 − y, 1/2 + z, (ii) 1 − x, 1 − y, 2 − z; in DL-MA-II: (i) x − 1, y, z, (ii) 1 − x, −y, 1 − z; and in L-MA: (i) 1 − x, −1/2 + y, 1 − z, (ii) 1 − x, 1/2 + y, 1 − z.
Figure 7. Crystal structure of (a) DL-MA-I viewed along [010], (b) DL-MA-I viewed along [001], and (c) L-MA viewed along the [100] projection. The H-bonded chains in the top and bottom layers shown in drawings b and c have been discriminated by red and green dotted lines, respectively.
cell compression of DL-MA-I reveals an unusual negative linear compressibility33−35 along two axes aI and bI in a narrow pressure range to 0.2 GPa (Figure 5). Above 0.2 GPa, parameters aI and bI remain stiff and the crystal is compressed mainly along cI. Form DL-MA-II is compressed most along cII, then along bII, and least compressed along aII. Two DL-MA racemates and enantiomer L-MA have very different crystal structures, as illustrated in Figures 6 and 7. In the crystal, the molecules are linked by OH···O hydrogen bonds involving the carboxyl and hydroxyl groups. Interestingly, in none of these structures the carboxyl groups are bonded in the R22(8) motif, most characteristic of carboxylic acids.36−38 The smallest ring motifs are R22(10) in DL-MA-I and
Figure 8. Intermolecular contacts OH···O as the function of pressure in (a) DL-MA-I and (b) DL-MA-II. The crystal data of DL-MA-I at 0.1 MPa/150 K (open symbols, ref 32) have been added for comparison. Symmetry codes in DL-MA-I: (i) 1/2 − x, 1 − y, 1/2 + z, (ii) 1 − x, 1 − y, 2 − z, and (iii) 1/2 − x, 1 − y, −1/2 + z; in DL-MAII: (i) x − 1, y, z, (ii) 1 − x, −y, 1 − z; and (iii) 2 − x, −y, 2 − z.
DL-MA-II and the R33(11) ring in L-MA. In all of these structures the carboxyl group is OH···O bonded to the hydroxyl group into different structural motifs, as shown in Figure 6. The 7282
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Figure 9. Normalized intermolecular contacts mapped on the Hirshfeld surfaces of DL-MA-I and II at different pressures: (a) DLMA-I at 0.1 MPa, 0.05 GPa, and 0.65 GPa; (b) DL-MA-II molecule A at 0.1 MPa, 0.76 GPa, and 1.36 GPa; and (c) DL-MA-II molecule B at 0.1 MPa, 0.76 GPa, and 1.36 GPa, all at 296 K. The color scale describes distances longer than (navy blue), equal to (white), and shorter than (red) the van der Waals radii. The corresponding 2D fingerprint plots are given in Figure S4 in the Supporting Information.
Figure 10. (a) Molecular energy calculated by Gaussian at the B3LYP and ωB97xd levels of theory for the conformers present in DL-MA-I, DL-MA-II, and L-MA and (b) the lattice energy calculated by PIXEL.
intermolecular contacts mapped on the Hirshfeld surface for DL-MA-I and DL-MA-II at different pressures are depicted in Figure 9. On further increasing pressure, the H···H contacts and CH···H and OH···H hydrogen bonds became shorter in both forms I and II (Figure 8), which is apparent from larger red spots on the Hirshfeld surfaces shown in Figure 9 and shorter distances de and di (see Figure S4 in the Supporting Information). Notably, the Hirshfeld surfaces illustrate the similarity between the structure at 0.1 MPa and at 0.76 GPa in both molecules A and B of DL-MA-II and the fact that the OH···H contacts are hardly influenced by pressure (Figures 8 and 9). The 2D fingerprint plots of both of the two forms I and II contain a pair of sharp spikes corresponding to the strong OH···H hydrogen bond. At higher pressure, all H···H contacts become less prominent, whereas OH···H and CH···H hydrogen bonds are intensified (Figures S4 and S5 in the Supporting Information). The five symmetry-independent molecules in two racemic forms and enantiomer L-MA also differ in conformation, especially by the rotation angle of the carboxyl group toward to the aromatic ring. In DL-MA-I, torsion angle of C1−C2−C3− C4 is 55.0° at 0.1 MPa and increases gradually with pressure to 59.8(12)° at 0.65 GPa/296 K (Figure 3 and Table S2 in the Supporting Information). In DL-MA-II, two independent molecules A and B exhibit different conformations: their angle C1−C2−C3−C4 is 41.2 and 85.0°, respectively. They are similar to those in two independent molecules in L-MA: 90.4° in molecule A and 42.5° in molecule B under ambient conditions.32 Much more consistent is the mutual position of hydroxyl and carboxyl groups, described by torsion angle O1−
C1−C2−O3. It is −179.9 and −177.3° in molecules A and B in DL-MA-II and −176.8 and −179.8° in molecules A and B in LMA, respectively, but ∼20° smaller, −156.7°, in DL-MA-I. The potential energy of these five conformers differs from nearly 0 to 6 kJ mol−1, as calculated by different DFT functionals. According to these calculations, molecule B of DL-MA-II assumes the most energetically favorable conformation. Previous studies in the 260−320 K temperature range15,39 showed that the metastable racemate DL-MA-II and enantiomer L-MA have similar IR spectra and X-ray powder diffraction patterns (Figure S3 in the Supporting Information). The Gibb’s free energy of DL-MA-II is only −1.48 or −0.83 kJ mol−1 lower than that of enantiomer L-MA according to the different equations recommended by Jacques1and Brock,40 respectively. The calculated molecular energy and the lattice energy of DL-MA-I, DL-MA-II and L-MA are shown in Figure 10. Calculations using B3LYP and ωB97xd functionals yield similar energy diagrams for molecular energies in all three forms. The lowest energy Ep of the symmetry-independent molecule A in L-MA is nearly identical to that of molecule B in DL-MA-II (Figure 10 and Table S4 in the Supporting Information), and they both are the most favorable conformers. However, the other independent molecules, molecule A in DLMA-II and molecule B in L-MA, assume the least favorable conformations. The lattice-energy calculations indicate that the DL-MA-II is more stable by 10.4 kJ mol−1 than L-MA and by over 9.0 kJ mol−1 more stable than DL-MA-I (Table S4 in the Supporting Information). These theoretical results are consistent with the preferential racemic crystallizations of MA 7283
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(5) Garrett, R.; Grisham, C. Biochemistry; Cengage Learning, Inc: Boston, 2009. (6) Mori, K. Bioactive Natural Products and Chirality. Chirality 2011, 23, 449−462. (7) Collet, A.; Vigne-Maeder, F. Increase of the Occurrence of Spontaneous Resolution due to the Crystallization of Racemates under High Pressure. New J. Chem. 1995, 19, 877−880. (8) Rietveld, I. B.; Barrio, M.; Tamarit, J.-L.; Do, B.; Céolin, R. Enantiomer Resolution by Pressure Increase: Inferences from Experimental and Topological Results for the Binary Enantiomer System (R)- and (S)-Mandelic Acid. J. Phys. Chem. B 2011, 115, 14698−14703. (9) Taylor, M. Summary of Mandelic Acid for the Improvement of Skin Conditions. J. Cosmetic Dermatology 1999, 21, 26−28. (10) Putten, P. L. Mandelic Acid and Urinary Tract Infections. Antonie van Leeuwenhoek 1979, 45, 622. (11) Rose, H. A. Crystallographic Data. 61. dl-Mandelic Acid. Anal. Chem. 1952, 24, 1680−1681. (12) Wei, K.-T.; Ward, D. L. α-Hydroxyphenylacetic Acid: a Redetermination. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1977, 33, 797−800. (13) Mughal, R. K.; Gillon, A. L.; Davey, R. J. DL-Mandelic Acid: CCDC 602882, 2006. (14) Fischer, A.; Profir, V. M. A Metastable Modification of (RS)Mandelic Acid. Acta Crystallogr., Sect. E: Struct. Rep. 2003, 59, o1113− o1116. (15) Profir, V. M.; Rasmuson, Å. C. Influence of Solvent and the Operating Conditions on the Crystallization of Racemic Mandelic Acid. Cryst. Growth Des. 2004, 4, 315−323. (16) Cai, W.; Katrusiak, A. Enantiomeric Crystallization of (±)-trans1,2-Diaminocyclohexane under Pressure. CrystEngComm 2011, 13, 6742−6746. (17) Podsiadło, M.; Patyk, E.; Katrusiak, A. Chiral Aggregation Hierarchy in High-Pressure Resolved 2-Butanol and 2,3-Butanediol. CrystEngComm 2012, 14, 6419−6423. (18) Budzianowski, A.; Katrusiak, A. High-Pressure Crystallography; Katrusiak, A., McMillan, P. F., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2004; pp 101−112. (19) Piermarini, G. J.; Block, S.; Barnett, J. D.; Forman, R. A. Calibration of the Pressure Dependence of the R1 Ruby Fluorescence Line to 195 kbar. J. Appl. Phys. 1975, 46, 2774−2780. (20) Xcalibur CCD System, CrysAlisPro Software; Oxford Diffraction, Ltd.: Oxfordshire, U.K., 2004. (21) Katrusiak, A. Shadowing and Absorption Corrections of SingleCrystal High-Pressure Data. Z. Kristallogr. 2004, 219, 461−467. (22) Katrusiak, A. REDSHADE: A Program for Correcting Reflections Intensities for DAC Absorption and Gasket Shadowing; Adam Mickiewicz University: Poznań, Poland, 2003. (23) Sheldrick, G. M. A Short History of SHELX. Acta Crystallogr., Sect. A: Found. Crystallogr. 2008, 64, 112−122. (24) (a) Spackman, M. A.; Jayatilaka, D. Hirshfeld Surface Analysis. CrystEngComm 2009, 11, 19−32. (b) Dziubek, K. F.; Katrusiak, A. Compression of Intermolecular Interactions in CS2 Crystal. J. Phys. Chem. B 2004, 108, 19089−19092. (25) Spackman, M. A.; McKinnon, J. J. Fingerprinting Intermolecular Interactions in Molecular Crystals. CrystEngComm 2002, 4, 378−392. (26) Wolff, S. K.; Grimwood, D. J.; McKinnon, J. J.; Turner, M. J.; Jayatilaka, D.; Spackman, M. A. CrystalExplorer, version 3.0; University of Western Australia: Crowley, 2012. (27) Gavezzotti, A. Efficient Computer Modeling of Organic Materials. The Atom-Atom, Coulomb-London-Pauli (AA-CLP) Model for Intermolecular Electrostatic-Polarization, Dispersion and Repulsion Energies. New J. Chem. 2011, 35, 1360−1368. (28) Kendall, R. A.; Dunning, J. T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796−6806. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci,
at ambient and high-pressure conditions. It is possible that racemate DL-MA requires a recrystallization to transform from form I to form II. It was recently shown that imidazole does not transform between its phases α and β up to 2.7 GPa, whereas recrystallization yielded polar phase β at 1.2 GPa.41
4. CONCLUSIONS It can be concluded that mandelic acid preferentially crystallizes as racemate and that this preference is not changed by high pressure up to 1.36 GPa at least. We found that pressure above 0.65 GPa reverses the course of crystallization from racemate DL-MA-I to racemate DL-MA-II. However, in none of our high-pressure crystallizations was the conglomerate of enantiomers obtained. The structures of all crystallized samples were confirmed by single-crystal X-ray diffraction. The DL-MAII is stabilized at high pressure by a molecular-volume reduction of ∼3.61 cm3 mol−1 and abrupt density increase. Moreover, lattice-energy calculations reveal that DL-MA-II is more stable than enantiomer L-MA by 10.4 kJ mol−1. It is apparent that the pressure effects on resolution of enantiomers involving the relations between pressure and volume in racemates and enantiomers of chiral compounds1,8,42 still require further systematic studies.
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ASSOCIATED CONTENT
S Supporting Information *
Density of DL-MA as a function of pressure, symmetryindependent molecules in MA, comparison of simulated powder X-ray diffraction, 2D fingerprint plots of DL-MA-I and DL-MA-II at different pressures, relative contributions (%) to the Hirshfeld surface for the different contacts for DL-MA-I and DL-MA-II at different pressures, crystal data of DL-MA-I and DL-MA-II at varied pressures, torsion angles of DL-MA-I and DL-MA-II, shortest intermolecular contacts of DL-MA-I and II at different pressures, and molecular and lattice energies of DL-MA-I, DL-MA-II, and L-MA. This material is available free of charge via the Internet at http://pubs.acs.org.
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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 This study was supported by the Foundation for Polish Science, TEAM Grant 2009-4/6. Theoretical calculations were performed at the Poznań Supercomputing and Networking Center.
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REFERENCES
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related conglomerate: R(s)+S(s)⎯⎯⎯→RS(s). According to ref 1 by Jacques et al., the ΔGo is either ΔGo = ΔGoTfR = −ΔSfA(TfR − TfA) − TfRR ln 2 if TfR < TfA or ΔGo = ΔGoTAf = −ΔSfR(TfR − TfA) − TfAR ln 2 if TfR > TfA. It was argued that no entropy difference occurs due to the racemic and enantiomeric composition in ordered crystals: ΔGo = ΔHrac = (ΔHfA − ΔHfR) + (c1p − csp)(TfR − TfA). For details, see: Brock, C. P.; Schweizer, W. B.; Dunitz, J. D. On the Validity of Wallach’s Rule: on the Density and Stability of Racemic Crystals Compared with Their Chiral Counterparts. J. Am. Chem. Soc. 1991, 113, 9811−9820. (41) Paliwoda, D.; Dziubek, K. F.; Katrusiak, A. Imidazole Hidden Polar Phase. Cryst. Growth Des. 2012, 12, 4302−4305. (42) Cintas, P . Comment on “Enantiomer Resolution by Pressure Increase: Inferences from Experimental and Topological Results for the Binary Enantiomer System (R)- and (S)-Mandelic Acid”. J. Phys. Chem. B 2012, 116, 4403−4404.
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