Racemic Naproxen: A Multidisciplinary Structural and Thermodynamic

ARTICLE pubs.acs.org/crystal

Racemic Naproxen: A Multidisciplinary Structural and Thermodynamic Comparison with the Enantiopure Form Doris E. Braun,† Miguel Ardid-Candel,‡ Emiliana D’Oria,† Panagiotis G. Karamertzanis,§ Jean-Baptiste Arlin,|| Alastair J. Florence,|| Alan G. Jones,‡ and Sarah L. Price†,* †

Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom § Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, 27 Taylor Street, Glasgow G4 0NR, United Kingdom

)

‡

bS Supporting Information ABSTRACT: Following the computational prediction that (RS)-naproxen would be more stable than the therapeutically used and more studied homochiral (S)-naproxen, we performed an interdisciplinary study contrasting the two compounds. The crystal structure of the racemic compound was solved from powder X-ray diffraction data (Pbca) and showed no packing similarity with the homochiral structure (P21). The binary melting point phase diagram was constructed to confirm the nature of the racemic species, and differential scanning calorimetric and solubility measurements were used to estimate the enthalpy difference between the crystals (ΔHR+SfRScry) to be
1.5 ( 0.3 kJ 3 mol
1 at T ∼ 156 °C and
2.4 ( 1.0 kJ 3 mol
1 in the range 10
40 °C. A comparison of the different approximations involved in estimating ΔHR+SfRScry implied that the difference in the lattice energies overestimated the stability of the (RS) crystal. The naproxen lattice energy landscape confirmed that all the practically important crystal structures have been found and characterized and provided insights into the crystal growth problems of the racemic form. This highlights the complementarity of computational modeling in investigating chiral crystallization.

1. INTRODUCTION Chiral molecules and their mixtures are of great fundamental scientific interest: how does a mere stereochemical change affect how the molecules self-assemble in different phases? This can be particularly complex for the solid phase where racemic compounds and mechanical mixtures of enantiomers (conglomerates) and occasionally solid solutions (pseudoracemates) may be found, as well as polymorphs of all the fixed stoichiometry racemic and enantiopure compounds. Control of chiral crystallization has long been of great industrial interest, particularly after the 1992 Food & Drug Administration (FDA) guideline stipulated that no racemates are allowed to enter the market as new medicines.1 The demand for enantiotropically pure drugs has prompted the development of efficient preparation methods, with resolution by crystallization2
6 being the most important and most economical process. In combination with other industrial preparation methods, such as asymmetric synthesis, enzymatic resolution, and chiral chromatography,1,7 this has resulted in a dramatic increase in the number of chiral drugs sold as single enantiomers to more than half of all marketed drugs.8,9 For a rational design of resolution and purification processes,10 it is essential to know the nature of the solid phases formed by crystallizing a racemic mixture. While X-ray powder diffraction r 2011 American Chemical Society

and spectroscopic techniques are commonly applied to identify the structural differences between a racemate and its enantiomers,7 obtaining a complete picture of the atomic arrangement and thermodynamic stability across the entire phase diagram and all metastable phases is, at best, very laborious and often frustrated by problems in obtaining suitable crystals for singlecrystal X-ray diffraction. Hence there has been considerable interest in developing computer modeling to predict chiral crystallization behavior.11
16 Crystal structure prediction (CSP) methods are capable of generating thermodynamically feasible homochiral and racemic crystal structures and estimating their relative stability. For example, the crystal energy landscapes of benzo[c]phenathrene, 3,4-dehydroproline anhydride, and 2,6dimethylglycoluracil showed13 that there were hypothetical racemic compounds which had structural similarities and were only slightly less stable than the observed spontaneously resolving enantiopure crystal structures. In principle, such computational models could predict the quantitative thermodynamic data required for the rational design of crystallization processes, Received: September 14, 2011 Revised: November 1, 2011 Published: November 02, 2011 5659

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the ultimate aim of developing computational methods for predicting the experimentally observed structures and thermodynamic stability of chiral crystals without relying on experimental data.

2. MATERIALS AND METHODS Figure 1. Molecular diagram of naproxen (C14H14O3, Mr = 230.26), with the three main torsion angles defined by ϕ1 = C14
O1
C7
C8, ϕ2 = C12
C11
C2
C1, and ϕ3 = O2
C12
C11
C2.

though this depends on the accuracy of the calculated relative energies and various thermodynamic assumptions. For example, the resolution efficiency of diastereomeric salt pairs could be estimated by comparing the diastereomers’ static lattice energies,12 by assuming that the solubility ratio correlates well with the enthalpy difference,6 (i.e., that the entropies of the diastereomers are approximately equal and that the zero-point energy and specific heats of the two diastereomers are similar). Thus developing reliable computer models for the design of chiral separation processes requires careful validation of the assumptions and accuracy by comparison with experimental studies. Hence, this interdisciplinary study characterizes the binary phase diagram for a pharmaceutical system, determining the nature and structure of the racemic compound and comparing different estimates of the relative stability of the enantiopure and racemic compounds. The nonsteroidal anti-inflammatory drug (NSAID) (S)-naproxen [(+)-2-(6-methoxy-2-naphthyl)propionic acid, NPX, Figure 1] is marketed only as the (S)-enantiomer, although other NSAIDs such as ketoprofen and flurbiprofen are marketed as racemic compounds. The (S)-enantiomer of NPX is 28-fold more active than the (R)-enantiomer, which is obtained by separation after the synthesis of the racemate.17,18 However, only the enantiopure phase has been characterized: its crystal structure has been deposited in the Cambridge Structural Database (CSD),19 under the refcode family COYRUD.20,21 Similarly, solution studies22
29 have been reported only for (S)-NPX. Solubility data are available for common organic solvents (methanol, ethanol, acetone, ethyl acetate, 2-propanol, octanol, isopropyl myristate, chloroform, cyclohexane, benzene, lower alcohols up to n-octanol, and water22,24,28,29), water cosolvents,22,27 and propylene glycol cosolvents.25,26 The thermal properties available for (S)-NPX are the melting point,30
32 heat/entropy of fusion,30,32 and solid and liquid heat capacities,30 and for (RS)-NPX, the melting point and heat/entropy of fusion.32 Furthermore, Perlovich et al.29 determined the enthalpy of sublimation for (S)-NPX and contrasted it with crystal lattice energy calculations using two different force fields. The crystal energy landscape of NPX unequivocally predicted that crystallization of a 1:1 racemic solution should form a racemic compound with a very different crystal packing from (S)-NPX. This led us to obtain racemic and enantiopure NPX, characterize the binary melting phase diagram, and contrast the thermal and solution behavior of the two compounds. Since we could not obtain suitable crystals of (RS)-NPX, for single-crystal structure determination, its structure was solved from powder diffraction data. The derived structural and thermodynamic data were then used to assess the ability of state-of-the-art computational modeling, based on lattice energy minimization, to reproduce the crystal structures and experimentally determined relative stability. This allowed an assessment of progress toward

2.1. Computational Generation of the Crystal Energy Landscape. Isolated molecule optimizations and conformational scans were performed at the HF/6-31G(d,p), MP2/6-31G(d,p), and PBE/ 6-31G(d,p) levels by use of Gaussian03.33 Eight conformational minima produced by varying the torsion angles ϕ1, ϕ2, and ϕ3 (Figure 1; Supporting Information section 1) were considered in the CSP searches. The model for intermolecular forces used to evaluate the intermolecular lattice energy, Uinter, included a conformation-dependent electrostatic model derived from the distributed multipole analysis34 (using GDMA235) of the ab initio charge density computed at the MP2/6-31G(d,p) level of theory. The remaining contributions to Uinter were modeled with an atom
atom exp-6 model parametrized to reproduce the structure and sublimation energies of organic crystal structures.36 Hypothetical crystal structures were generated by MOLPAK,37 which performs a systematic grid search on orientation for the rigid central molecule in 39 common coordination geometries of organic molecules, belonging to the space groups Cc, C2, C2/c, P1, P1, P2/c, P21, P21/c, P21212, P212121, Pba2, Pc, Pca21, Pna21, Pbcn, Pbca, Pma2, Pmn21, and Pnn2 with one molecule in the asymmetric unit. A more extensive search in the space group Pbca, indicated by indexing the powder X-ray diffraction (PXRD) pattern of (RS)-NPX, was performed with CrystalPredictor,38 which uses a low-discrepancy sequence for searching the crystal packing space of unit cell dimensions, molecular orientations, and positions, followed by rigid molecule lattice energy minimization. Approximately 3000 of the densest packings (∼1000 chiral and ∼2000 racemic) from the MOLPAK search, and all Pbca structures within 20 kJ 3 mol
1 of the lowest structure generated by CrystalPredictor, were then used as starting points for lattice energy minimization by DMACRYS,39 using distributed multipoles without relaxation of the molecular conformation. The second derivatives were used to confirm that each structure was a true minimum; saddle points were reminimized in the appropriate subgroup. The most stable rigid-body lattice energy minima were then refined with CrystalOptimizer40 to allow small changes in conformation (dihedrals ϕ1, ϕ2, and ϕ3, aromatic ring, methyl groups, and the C14
O1
C7 angle; Figure 1) by minimizing the lattice energy, Elatt = Uinter + ΔEintra, where ΔEintra is the conformational energy penalty (with respect to the global conformational minimum) paid to improve the intermolecular interactions, calculated at the HF/6-31G(d,p) level of theory. The final estimate of the lattice energies of these structures used a polarizable continuum around the molecule, as implemented in the PCM41 module in Gaussian03, during a final rigid-body MP2/6-31G(d,p) electron density calculation, using ε = 3, a value typical for organic crystals.41
43 The relative energies of the conformations within this dielectric continuum, ΔEintra, were derived from the same PCM calculation and do not include the interaction energy between the molecule and the polarizable continuum. The effect of the surrounding molecules within the crystal is approximated by the changes in the distributed multipole moments due to the dielectric continuum. An analysis of the sensitivity of the relative lattice energies of the experimental structures, (RS)- and (S)-NPX, to different wave functions for the geometry optimization and charge density calculations, including variations in the PCM model, is given in the Supporting Information, Table S2. The relationships between crystal structures were examined by use of the XPac program,44,45 and differences were quantified via the overlay46 of a n molecule cluster, rmsdn, as calculated by the Molecular Similarity Module in Mercury.47 The XPac results described were obtained with all 5660

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Figure 2. Powder X-ray diffraction pattern and Rietveld fit of final structure for (RS)-NPX at 25 °C. non-hydrogen atoms and routine medium cutoff parameters (δang = 10°, δtor and δdhd = 18°). 2.2. Materials and Crystallization Experiments. (S)-NPX (purity >98%) and (RS)-NPX (purity >97%) were purchased from Sigma
Aldrich and Manchester Organics, respectively. The samples were recrystallized for purification from ethanol. Optical sample purity was determined by HPLC on a chiral (R,R)Whelk-01 column under isocratic conditions with hexane/2-propanol (60:40) + 0.1% acetic acid as eluent at a flow rate of 1 mL 3 min
1. All organic solvents used were of analytical quality and were purchased from either Fluka or Aldrich. Slow evaporation experiments were conducted by preparing a saturated solution at room temperature and subsequent evaporation from vials covered with a pierced lid at 25 and 4 °C. Slow cooling crystallization was performed by preparing a hot saturated solution close to the boiling point of each solvent and slowly cooling down to room temperature over a period of a day. Approximately 30 cooling crystallization or evaporation experiments were performed with (S)- and (RS)-NPX in methanol, ethanol, 2-propanol, 2-butanol, acetone, acetonitrile, dioxane, tetrahydrofuran, ethyl acetate, and diethyl ether.

2.3. Crystal Structure Determination from Powder X-ray Diffraction Data. (RS)-NPX was loaded in a rotating 1.0 mm borosilicate glass capillary and mounted on a Bruker AXS D8 powder X-ray diffractometer equipped with primary monochromator (Cu Kα1, l = 1.54056 Å) and Lynxeye position-sensitive detector. Data were collected at room temperature via a variable-count-time scheme48,49 (Supporting Information, Table S5). The diffraction pattern indexed to an orthorhombic unit cell, and the space group was determined to be Pbca from a statistical assessment of systematic absences,50 as implemented in the DASH structure solution package.51 [The possibility of (RS)-NPX being a Z0 = 2 Pca21 structure was also investigated but was ruled out by solid-state NMR spectroscopy (Supporting Information, Figure S8).] The data were background-subtracted and truncated to 40° 2θ for Pawley fitting52 (Pawley χ2 = 5.57). Simulated annealing was used to optimize the (RS)-NPX model against the diffraction data set (112 reflections) in direct space. The internal coordinate (Z-matrix) description was derived from the MP2/6-31G(d,p) gas-phase global conformational minimum starting from the S-enantiomer single-crystal structure (COYRUD11),21 with O
H distances normalized to 0.9 Å and C
H distances to 0.95 Å. This ab initio optimization of the molecular model was required as the naphthalene ring is unusually bent in the (S)-enantiomer. The structure was solved using 20 simulated annealing

runs of 2.5  107 moves/run as implemented in DASH, allowing nine degrees of freedom (six external and three internal). The best solutions returned a χ2 ratio of ca. 4.66 (profile χ2/Pawley χ2). A restrained Rietveld refinement53 was carried out on the best solution returned from the simulated annealing in TOPAS v4.1.54 The final refinement included a total of 137 parameters (24 profile, 3 cell, 1 scale, 1 isotropic temperature factor, 15 preferred orientation, 93 positions), yielding a final Rwp = 4.547 (Figure 2). [Crystal data for (RS)-NPX: C14H14O3, Mr = 230.259, orthorhombic, space group Pbca, T = 298 K, sample formulation powder, specimen shape 12  1.0  0.7 mm, wavelength 1.54056 Å, a = 25.8301(13) Å, b = 15.4939(4) Å, c = 5.9465(2) Å, volume = 2379.85(16) Å3, Z = 8, density = 1.285 g 3 cm
3, 2θ range for data collection 3
70°, Chebyshev polynomial background treatment, 525 measured reflections, Rietfeld refinement method, 525 data/137 parameters/87 restraints, goodness-of-fit 2.344 (on yobs), Rwp = 4.547, Rexp = 1.940, Rp = 4.037. Atomic positions were refined, subjected to a series of restraints on bond lengths, bond angles, and planarity of the O-naphthalene and carboxylic acid functionalities.] 2.4. Thermal Analysis. Thermomicroscopic investigations were carried out with a polarizing microscope (Reichert, A) fitted with a Kofler hot-stage (Reichert, A). Differential scanning calorimetry (DSC) experiments were performed on two instruments: (i) The first instrument was a TA Instruments Q2000 system using the TA Universal Analysis 2000 software (Manchester, U.K.). The instrument was calibrated for temperature and energy in the respective temperature range with pure indium (mp 156.6 °C, heat of fusion 28.45 J 3 g
1). Approximately 3
4 mg of sample was accurately weighed (AD-6 microbalance, Perkin-Elmer, Norwalk, CT) into sealed aluminum Tzero pans with a hermetic Tzero lid. Dry helium was used as a purge gas (purge 20 mL 3 min
1). (ii) The second instrument was a DSC 7 (Perkin-Elmer, Norwalk, CT) using Pyris 2.0 software. Approximately 1
3 mg sample (UM3 ultramicrobalance, Mettler) was weighed into aluminum pans (25 μL). Dry nitrogen was used as the purge gas (purge 20 mL 3 min
1). The instrument was calibrated for temperature with pure benzophenone (mp 48.0 °C) and caffeine (mp 236.2 °C), and the energy calibration was performed with pure indium. A heating rate of 10 K 3 min
1 was used for both instruments. The errors of the stated temperature and enthalpy values (Table 1) are calculated at 95% confidence intervals based on at least five measurements on (i), and confirmed by a measurement with (ii). 5661

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Table 1. Values of Thermodynamic Parameters of Enantiomer, Racemic Compound, and Eutectic of NPXa (S)-NPX

(RS)-NPX

eutectic

Δ[(S)
(RS)]b

Thermal Measurements (155
156 °C) Tfus, °C

156.2 ( 0.1

155.8 ( 0.3

lit. values, °C

157.3c, 155.4d, 158.1e

155.4c

ΔHfus, kJ 3 mol
1

145.5 ( 0.5

0.4 ( 0.3 1.9c

31.7 ( 0.1

33.2 ( 0.3


1.5 ( 0.3

lit. values, kJ 3 mol
1

31.3c, 31.5 ( 0.7d

32.3c


1.0c

ΔSfus,f J 3 mol
1 3 K
1

73.8 ( 0.3

77.4 ( 0.7


3.6 ( 0.8

ΔHsol°, kJ 3 mol
1

31.4 ( 0.3

33.8 ( 1.0


2.4 ( 1.0

ΔSsol°, J 3 mol
1 3 K
1 ΔGsol°, kJ 3 mol
1

62.8 ( 0.3 12.7 ( 0.1

66.4 ( 1.0 14.0 ( 0.1


3.6 ( 1.0
1.0 ( 0.1


Elatt, kJ 3 mol
1

143.8

Solubility Measurements (10
40 °C, Ethanol/Water, Thm = 25 °C)

Lattice Energy Calculations (∼0 K) a

150.3


6.1 to
9.2

Parameters were obtained from differential scanning calorimetry and van’t Hoff plots. The experimentally determined values are contrasted to literature values and calculated lattice energies. b These are simple differences between the quantities, which are compared with more elaborate treatments in the text. c Reference 32. d Reference 30. e Reference 31. Peak maximum and not onset temperature was used for melting point determination. f Entropies of fusion are calculated from ΔH
TΔS at the transition temperature being zero.

2.5. Determination of Solubility. The solubility of (S)- and (RS)-NPX as a function of temperature was established at 10, 15, 20, 25, 30, 35, and 40 °C in an ethanol/water mixture (4:1 v/v). The solubility apparatus consisted of a jacketed glass vessel maintained at a constant temperature by water circulated from a water bath (Grant LTC 12-50). The jacket temperature could be maintained within (0.01 °C in the temperature range used. An excess of substance was added to 50 mL of the cosolvent mixture and stirred with a magnetic stirrer (800 rpm) for 5 days to reach equilibrium (the equilibration time was established by quantifying the drug concentration). Three samples were withdrawn from each suspension and temperature at 12 h intervals with volumetric pipettes attached to filter holders (Swinnex, Millipore) and 0.22 μm membrane filters (Millipore). To maintain the sample temperature during sampling, the filter attachments were conditioned in an empty vessel in the water bath. Samples withdrawn at 25 °C and above were diluted after filtration by a factor of 2 to be within the concentration range of the HPLC calibrations. (S)-NPX samples withdrawn at 40 °C had to be diluted by a factor of 3. HPLC was performed with a Shimadzu LC-2010CHT system (Milton Keynes, U.K.).

3. RESULTS 3.1. Crystallization Results. The limited crystallization screen using 10 solvents for (S)- and (RS)-NPX always resulted in the same anhydrous form of the homochiral or racemic compound, respectively, as confirmed with infrared spectroscopy and powder X-ray diffractometry (Supporting Information, Figures S4 and S5). The therapeutic form, (S)-NPX, readily crystallized with either a plate or needle morphology, whereas the (RS)-NPX crystallized very slowly in the shape of needles or multilayered plates (as illustrated in Supporting Information, Figure S7), unsuitable for laboratory X-ray single diffraction studies. 3.2. Crystal Structures of Enantiomeric and Racemic Naproxen. The monoclinic P21 Z0 = 1 crystal structure of the (S)-enantiomer is deposited in the Cambridge Structural Database, and we used COYRUD1121 for the structure comparisons. The racemate (RS)-NPX crystallizes in space group Pbca (Z0 = 1). The molecular conformations in the two crystal structures differ in the dihedral angles ϕ2 and ϕ3 by 27.8° and 29.9°, respectively,

Figure 3. Packing diagrams of (a) (RS)-NPX and (b) (S)-NPX (COYRUD11). (S)-NPX molecules are colored by element, and (R)NPX is shown in blue.

but both have the methoxy group approximately coplanar with the naphthalene moiety (ϕ1 ∼ 180°). The naphthalene ring in the (S)-enantiomer is markedly nonplanar, and was assumed to be planar in the (RS) structure refinement (see section 3.3). Strong intermolecular interactions are formed only between carboxylic acid groups, with infinite C11(4) chains mediated by 21 symmetry in the homochiral crystal and inversion-related R22(8) acid dimers of the two hands in the racemic crystal (Figure 3). Both structures exhibit weak C
H 3 3 3 π interactions between the naphthalene rings and the layers containing the strong hydrogen bonding, but XPac analysis44,45 gave no packing similarity between the two experimental forms. 3.3. Crystal Energy Landscape. The most stable structure on the crystal energy landscape for NPX (Figure 4) corresponds to the observed structure of the racemic compound, and the observed structure of the (S)-enantiomer is the most stable homochiral structure. All the low-energy structures have approximately the same conformation of the methoxy and carboxylic acid groups as found in the experimental structures. The majority of the computed low-energy structures (Figure 4) exhibit the R22(8) carboxylic acid dimer motif,55 but there are also C11(4) carboxylic acid catemers. A previous study56 of crystal energy landscapes of simpler carboxylic acids showed that the crystal packing and steric interactions of the other functional groups in 5662

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Figure 4. Lattice energy landscape for NPX (Elatt = Uinter + ΔEintra) classified by the most extensive common packing motif, shown in Figure 5. Each symbol denotes a crystal structure which is a lattice energy minimum. (4) Lower symmetry version of the experimental racemic crystal structure.

Figure 5. Illustration of the packing similarities and differences in structures on the crystal energy landscape (Figure 4) with the two hands, (R) and (S), colored differently. All fragments shown are present in either the experimental racemic or homochiral structure. Supporting Information Table S4 identifies all the structures in Figure 4 and their hydrogen-bonding motifs.

the molecule play a major role in determining the relative stability of dimer and catemer carboxylic acid hydrogen-bonding motifs. At higher energies there are C11(11) chains where the carboxylic acid is hydrogen-bonded to the methoxy group. More detailed analysis of the packing types (Figure 5; Supporting Information Table S4) shows that the most stable structures, within 5 kJ 3 mol
1 of the global minimum, are based on the same 2D layer fragment and differ only in the hydrocarbon packing between adjacent layers. These racemic layers of dimers (depicted in Figure 5) are the most stable building block for NPX crystals. The three lowest-energy homochiral structures exhibit carboxylic acid chains with the same C11(4) motif found in racemic structures of comparable energy. The 1D stack and COOH C11(4) catemer packing arrangements (Figure 5) are

both found in the experimental structure of (S)-NPX and one or the other in the next two homochiral structures. 3.3.1. Comparison of Predicted and Observed Structures. The therapeutically used (S)-NPX is calculated to be the most stable of the computationally generated homochiral structures (rmsd15 = 0.380 Å, Figure 6). The modeling of the (S)-NPX crystal structure reproduces the bending of the naphthalene ring: the calculated angle between the two aromatic rings was 175.61°, compared with the experimental value of 174.88°. It is notable that this chiral structure has the molecule in a less stable conformation than the racemic structure, but the energy difference, ΔEintra, is sensitive to the wave function. (Supporting Information, Table S3). The global minimum structure provides a worse match to the PXRD structure of (RS)-NPX, with rmsd15 = 0.70 Å and a smaller 5663

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Figure 6. Structure overlays of experimental (black) and calculated (gray) NPX structures: (a) (S)-NPX viewed along the c-axis; (b) modeling of the bending observed in (S)-NPX; (c) (RS)-NPX and saddle-point structure viewed along the b-axis; (d) (RS)-NPX and global minimum structure. The braces in panels c and d indicate the layers in Figure 5.

bend in the naphthalene ring of the predicted structure, calculated as 177.02°. This and the fact that the planar conformation gives a lower profile χ2 fit to the data support the assumption that the molecule could be modeled as planar in the PXRD determination. The (RS) structure was found to correspond to a saddle point structure on the potential energy surface. Relaxing the structure to a true minimum lowers the Pbca symmetry (Z0 = 1) to Pca21 (Z0 = 2), giving a minor shifting and slipping of the layers that changes the lattice parameters by less than 1.2% and changes the conformations of the two symmetrically independent NPX molecules to give a rmsd1 difference of 0.004 Å (when one molecule is inverted). The two calculated structures are essentially the same; the Pca21 (Z0 = 2) model has a slightly worse overlay with the experimental structure with an rmsd15 of 0.86 Å. The lower symmetry structure is 1 kJ 3 mol
1 more stable than the Pbca symmetry (Z0 = 1) transitionstate structure (Figure 4). An estimate57 of the zero-point energy for the Pca21 (Z0 = 2) structure within the zone-center, rigid-body harmonic approximation is 2.9 kJ 3 mol
1, about 3 times greater than the barrier of the Pbca Z0 = 1 saddle point. Therefore a zero-point and thermal motion average over symmetrically equivalent lower symmetry structures (Pca21, Z0 = 2) would be expected to result in the Pbca Z0 = 1 structure.58 Solid-state NMR (Supporting Information, Figure S8) verified that (RS)-NPX is a Z0 = 1 structure, and the fits to the PXRD were unable to distinguish between the Z0 = 1 and Z0 = 2 structures. Thus the layer structure of (RS)-NPX is unusually sensitive to the static lattice approximation, as there is a shallow potential well for small shifts in the C
H 3 3 3 π contacts. 3.3.2. Relative Stability of the Racemic Compound from Calculations. The stability of a racemic compound can be defined through the free energy difference, ΔGcry R+SfRS, which corresponds to the “reaction” between the crystalline (R)- and (S)-enantiomers in the racemic conglomerate that gives rise to the crystalline racemic compound (RS):60 SðcrystalÞ þ RðcrystalÞ f RSðcrystalÞ

ð1Þ

The simplest estimate for this free energy difference is to note that the lattice energy of each crystal is the energy required to separate

the static lattice into infinitely separated molecules in their lowestenergy conformation. The energy gap between the most stable homochiral and racemic structures, derived from static 0 K lattice energy calculations as 7.1 kJ 3 mol
1 (
ΔElatt, Figure 4), provides a first estimate of
ΔUcry R+SfRS for this reaction. The approximations used in calculating the lattice energy in the CSP search, such as the quality of the ab initio method and use of the polarization continuum model (PCM), were tested (Supporting Information, Table S3) and give a range of values of ΔUcry R+SfRS from
6.1 to
9.2 kJ 3 mol
1 providing an estimate of the modeling uncertainties. The usual thermodynamic comparison is between the heat of sublimation and the lattice energy, as a simple thermodynamic cycle11 relates the enthalpy of sublimation at the temperature T, ΔHsubl,T: ΔHsubl, T ¼
Elatt
E0 þ

Z T 0

ΔCp dT

ð2Þ

where Elatt and E0 are the lattice energy and zero-point energy, respectively, and ΔCp is the heat capacity difference between the gaseous and solid states. Usually E0 is less than 1% of Elatt, and the ΔCp contribution is not greater than 10% of Elatt.11 Since it is rather difficult to measure temperature-dependent values for the heat capacity of the gas and crystal, approximate relationships have been proposed, by use of either a constant value for ΔCp of
60 to
40 J 3 K
1 3 mol
1 61 or empirical forms,62 implying that the stability of Elatt may be overestimated with error of up to 10% if contrasted to ΔHsubl. Perlovich et al.29 measured the heat of sublimation (ΔHsubl) of (S)-NPX as 128.3 ( 0.5 kJ 3 mol
1 and estimated the lattice energy with two different empirical force fields to be
128 and
145 kJ 3 mol
1, whereas variations in Elatt within our approach (Supporting Information, Table S3) vary from
125 to
147 kJ 3 mol
1. Thus the calculation of ΔUcry R+SfRS assumes that the errors in the absolute lattice energies, due to the model for the intermolecular forces, are the same for the two structures. If the zero-point energies and heat capacities are the same for racemic and homochiral crystals, then the enthalpy of formation 5664

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all other enantiomeric compositions. The first endothermic peak represented the fusion of the eutectic. The second peak represented the melting of the excess phase in the melting process, the liquidus temperature. The data could be well represented as a solid
liquid equilibrium in ideal binary systems (Figure 7) calculated by use of the equations of Schroeder
Van Laar and Prigogine
Defay69 in simplified forms:   ΔHfus ðSÞ 1 1 ln x ¼
ð4Þ R Tfus ðSÞ Tfus ln 4xð1
xÞ ¼ Figure 7. Binary (melting point) phase diagram of naproxen enantiomer showing racemic compound formation. Black circles represent the eutectic temperature, gray circles show the liquidus or melting temperatures, and the dotted line indicates the average eutectic temperature (145.5 °C), measured with DSC. The dashed line represents eq 4 and the solid line represents eq 5, calculated with DSC thermal data from Table 1.

of the racemic crystal from the two crystalline enantiomers (eq 1), can be calculated: cry

ΔHR þ S f RS ¼ ΔΔHsubl ¼ ΔHsubl ðSÞ
ΔHsubl ðRSÞ ≈
ΔElatt

ð3Þ

However, as noted in section 3.3.1 and Figure 6, there is a qualitative difference between the effects of zero-point motion in (RS)- and (S)-NPX. In addition, homochiral crystals often have lower frequency modes,63 due to lower density,64 that typically give greater entropic stabilization. NPX conforms to Wallach’s rule as the racemic compound is denser than the enantiomeric crystal.64 Approximations of the free energies at 298 K65 based on rigid body, zone-center vibrational modes66 and elastic constants67 shows that the difference in calculated zero-point and thermal energies are small, with (S)-NPX being stabilized over (RS)-NPX by 0.1 and 0.6 kJ 3 mol
1, respectively. This estimate excludes thermal expansion, which will be anisotropic in both crystals.68 The difference in cell volume at room temperature is 8.404 Å3/molecule, so the PΔV contribution to
4 ΔHcry R+SfRS for the racemization reaction is a negligible 5  10 kJ 3 mol
1 . This consideration of the approximations in equating the differences in lattice energies with the difference in sublimation enthalpies does not significantly reduce the energy difference between (RS)- and (S)-NPX. 3.4. Thermal Measurements and Binary Melting Point Phase Diagram. Differential scanning calorimetric investigations of the thermal behavior of (S)-NPX, (RS)-NPX, and mixtures thereof produced the thermodynamic data in Table 1 and the binary phase diagram in Figure 7. The DSC curves of the racemate (0.5 mol) and single (S)-enantiomer (1.0 mol) exhibited one sharp endothermic peak at 155.8 ( 0.3 and 156.2 ( 0.1 °C, respectively (Supporting Information, Figure S6), corresponding to the melting of the two compounds. The racemic compound has a slightly lower melting point (0.4 °C) and slightly higher heat and entropy of fusion than the enantiopure crystal. However, the differences are small relative to our error estimates, which are smaller than those in previous studies of (S)NPX30 (Table 1). The binary phase diagram (Figure 7) was constructed from the temperatures of the two distinct peaks seen in the DSC traces at

  2ΔHfus ðRSÞ 1 1
R Tfus ðRSÞ Tfus

ð5Þ

where x is the mole fraction of the more abundant enantiomer of the mixture; R is the gas constant (8.314 J 3 K
1 3 mol
1); Tfus(S), Tfus(RS), and Tfus are the melting temperatures of the enantiomer, racemic compound, and mixture, respectively; and ΔHfus(S) and ΔHfus(RS) are the enthalpies of fusion of the enantiomer and racemic compound (Table 1). The eutectic point corresponds to the point of intersection of the curves obtained by eqs 4 and 5. Hot-stage microscopy (Kofler’s contact method70) gave the eutectic temperature, confirmed the melting temperatures, and confirmed the existence of the racemic compound. The phase diagram excludes the existence of a racemic conglomerate, a physical mixture of both enantiomeric crystals, as this would have a theoretical eutectic melting point (eq 4) of 125.1 °C, far below with the experimental value of 155.8 ( 0.3 °C. The presence of a eutectic between (RS)- and (S)-NPX excludes not only a conglomerate but also the occurrence of a pseudoracemate,71 and no signs of any phases apart from (S)-NPX, (RS)-NPX, and their eutectic were observed. 3.4.1. Relative Stability of the Racemic Compound from Thermal Measurements. The thermodynamic quantities, ΔG°R+SfRS,Tfus (RS), ° ° and ΔSR+SfRS,T , for the hypothetical ΔHR+SfRS,T fus (RS) fus (RS) reaction (eq 1) within the crystal cannot be directly measured, but they can be determined from our data in Table 1, at the melting point of (RS)-NPX, Tfus(RS), the maximum temperature at which the “reaction” of the racemic compound from its enantiomers in the solid state may occur. The relationships, due to Jacques et al.69 and Li et al.,72 are ΔHR° þ S f RS, Tfus ðRSÞ ¼ ΔHfus ðSÞ
ΔHfus ðRSÞ þ ðCl
CS s Þ½Tfus ðRSÞ
Tfus ðSÞ

ð6Þ

ΔS°R þ S f RS, Tfus ðRSÞ ¼ ΔSfus ðSÞ
ΔSfus ðRSÞ þ R ln 2 þ ðCl
CS s Þ ln

Tfus ðRSÞ Tfus ðSÞ

  Tfus ðRSÞ
Tfus ðRSÞR ln 2 ΔG°R þ S f RS, Tfus ðRSÞ ¼ ΔHTfus ðSÞ 1
Tfus ðSÞ   Tfus ðRSÞ þ ðCl
CS s Þ Tfus ðRSÞ
Tfus ðSÞ
Tfus ðRSÞ ln Tfus ðSÞ

ð7Þ

ð8Þ

We assumed a typical heat capacity difference between racemic and enantiopure forms of 0.08 kJ 3 mol
1 3 K
1 for (Cl
CSs),73 but since the differences in melting temperatures are small, this contribution is negligible. For NPX, the enthalpy, entropy, and free energy of formation of the racemic compound from the pure enantiomers (eqs 6
8) are
1.6 kJ 3 mol
1, 2.1 J 3 mol
1 3 K
1, and
2.4 kJ 3 mol
1, respectively, confirming that formation of 5665

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Table 2. Experimental Solubility of (S)- and (RS)-NPX a (S)-NPX temp (°C) 10

mol 3 L
1 0.0684 (0.0003)

15

0.0832 (0.0010)

20

0.1009 (0.0026)

25

0.1255 (0.0010)

30

0.1522 (0.0016)

35

0.1867 (0.0011)

40

(RS)-NPX

0.2383 (0.0058)

2.757 (0.014)  10


3

3.375 (0.040)  10


3

4.107 (0.109)  10


3

5.174 (0.044)  10


3

6.265 (0.067)  10


3

7.641 (0.162)  10


3

10.14 (0.260)  10


3

17.426  10


3

b

25 (ideal) a

mol 3 L
1

mole fraction

0.0434 (0.0002)

1.738 (0.008)  10
3

0.0517 (0.0043)

2.172 (0.036)  10
3

0.0676 (0.0005)

2.743 (0.020)  10
3

0.0840 (0.0003)

3.412 (0.014)  10
3

0.1027 (0.0006)

4.260 (0.025)  10
3

0.1298 (0.0005)

5.355 (0.022)  10
3

0.1693 (0.0077)

7.033 (0.010)  10
3

mole fraction

14.449  10
3 b

in EtOH/water (4:1 v/v) expressed in molarity and mole fraction at several temperatures. Ideal solubility calculated according to eq 10.

the racemic compound from its enantiomers in the solid state is exothermic. The configurational entropy of mixing term in eqs 7 and 8, R ln 2, favoring the racemic melt makes a significant relative contribution to the entropy and free energy difference for racemization. However, behind this treatment is the assumption that the enantiopure and racemic melts differ only by the entropy of mixing, R ln 2. This is assuming that the two melts have the same structure in order that the enthalpy of mixing is zero. This is not true in general for enantiomers, though the differences in the melts are likely to be less than in the crystalline form because of the lack of long-range order and decreased density. In the specific case of NPX, significant differences between enantiopure or racemic clusters or melts are unlikely because of the molecular flexibility of the carboxylic acid (Supporting Information section 1) or the possibility of proton exchange within carboxylic acid dimers. 3.5. Solubility Measurements and Solution Thermodynamics. The experimental solubilities of (S)- and (RS)-NPX in EtOH/water (4:1 v/v) were measured between 10 and 40 °C (Table 2) and exhibit the usual pattern of increasing solubility with temperature. There is good agreement with the published values27 for (S)-NPX. For both (S)- and (RS)-NPX, a linear van’t Hoff plot of ln X2 against (1/T
1/Thm) is obtained (Figure 8), showing that ΔHsol is constant over the range Thm ( 15 °C, where Thm, the mean harmonic temperature, is 25 °C. This is consistent with the IR spectra of the solid residuals from the solubility measurement not indicating any phase transformation at any temperature for any of the samples. The apparent standard enthalpy change, ΔHsol°, and standard free energy, ΔGsol°, of solution were obtained by the Krug approach74 for both solids (Table 1). The enthalpies and entropies of solution are positive for (S)-NPX and greater for (RS)-NPX; therefore the process is always endothermic and driven by solution entropy. 3.5.1. Relative Stability of the Racemic Compound from Solubility Measurements. The enthalpy of solution (ΔHsol) can be described as the sum of contributions from the intermolecular interactions that are broken when the crystal lattice breaks up (ΔHsubl) and the interactions formed when the molecules are solvated (ΔHsolvation). If the solvation energy is the same for (S)- and (RS)-NPX, then the lattice energy difference between (RS) and (S) is approximately the difference in the heat of solution difference of the two compounds.

Figure 8. Temperature dependence for solubility of (S)- and (RS)NPX in EtOH/water (4:1 v/v) expressed in mole fraction. The gradient is
ΔHsol°/R and the intercept is
ΔGsol°/RThm..

Hence, the difference in the heats of solution between (RS)- and (S)-NPX,
2.4 ( 1.0 kJ 3 mol
1, could be taken as an estimate for the hypothetical reaction (eq 1) within the crystal (eq 3) if we assume that there is no thermodynamic difference in the stability of the chiral and racemic solutions. This assumption is reasonable if the solvents are achiral and the saturated concentrations are too low to have significant solute
solute interactions. We note that the latter assumption is not reasonable for cocrystallization from solution: measurements of the transfer enthalpy involved in cocrystal formation from solution are significant (on the order of (1 kJ 3 mol
1) for the difference between dissolving carbamazepine and analogues in methanol, with or without the presence of saccharine in the solution.75 Transfer energies would be zero for ideal solutions and reflect the different interactions of the solutes with each other and the solvent. Are our measurements of the solubility of (S)-NPX in the solvent equivalent to dissolving it in a solution with (R)-NPX already dissolved, so both solutions are comparable? We can estimate the ideal solubility of a crystalline solute as a mole fraction X2id in an unspecified liquid solvent by ΔHfus ðTfus
TÞ RTfus T     ΔHfus ðTfus
TÞ T þ ln þ T Tfus RTfus

ln X2 id ¼


cry

ΔΔHsol ¼ ΔHsol ðSÞ
ΔHsol ðRSÞ ≈
ΔElatt ≈ ΔHR þ S f RS

ð9Þ 5666

ð10Þ

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Figure 9. Diagrammatic summary of the measured and computationally calculated thermodynamic quantities (thick lines) and other enthalpic contributions (thin lines) relating the solid forms to the gas phase. Contributions that are probably negligible for naproxen but could be significant for other chiral systems with a more distinctive shape difference are indicated by yellow boxes.

where T is the absolute solution temperature, using our values in Table 1. The measured solubilities are considerably lower than ideal (Table 2), implying significant solvent
solute interactions. At 25 °C, the solubility corresponds to 158 water and 131 ethanol molecules per NPX molecule for the (RS) racemic solution and 106 and 86 for the enantiopure solution. From the published solubility data for (S)-NPX, the number of solvent molecules per NPX varies from 38 for ethyl acetate,24 in which it is most soluble, to over 3500 for water.27 Thus the solvation shell is likely to be sufficient to even out the small differences in molecular shapes between the two enantiomers in our solubility measurements, and the transfer energy is likely to be negligible. This may be less true for other solvents or for other chiral molecules, but transfer energies involving the two hands of a chiral molecule would generally be much lower than those involved in cocrystal formation.

4. DISCUSSION 4. 1. Lattice Energy Landscape. This interdisciplinary study on NPX proved that (RS)-NPX forms a racemic compound, which is more stable than the therapeutically used (S)-enantiomer. The computationally generated lattice energy landscape successfully predicted the racemic compound and the homochiral structure at the global minimum and the lowest homochiral structure in lattice energy, respectively. No signs of polymorphs were observed in our limited screen.76 This is consistent with an energy gap of almost 4 kJ 3 mol
1 between the observed and second lowest homochiral structures (Figure 4). The smaller energy differences between different packings of the carboxylic acid layers in (RS)-NPX may be more indicative77 of the likelihood of stacking faults than true polymorphs, as found for progesterone78 and aspirin79 in contrast to aprepitant.80 A tendency for stacking faults would account for the difficulty in growing good quality single crystals (see Supporting Information Figure S7), suitable for structural determination from singlecrystal diffraction. Thus, although (RS)-NPX is more stable, the nature of its crystal packing makes characterizing the structure

intrinsically more difficult, with the independent computational prediction adding confidence to the solution from powder diffraction data. 4.2. Comparison of Calculated and Experimental Energy Differences between Racemic and Enantiopure NPX. The calculations and thermal and solubility measurements all give the same qualitative result that the racemic compound is more stable than the homochiral phase, consistent with the expectation that formation of a racemic crystal can have significant enthalpic stability advantage over homochiral crystal structures.7,69 The analysis of the naproxen system is relatively straightforward, as no other solid forms have been detected.81 However, the three estimates (Figure 9) are comparing breaking up the racemic and enantiopure crystals into different phases at different temperacry was found to be tures. The experimentally derived ΔHR+SfRS
1 approximately
1.5 ( 0.3 kJ 3 mol (Table 1) when calculated from thermal measurements at T ∼ 156 °C and
2.4 ( 1.0 kJ 3 mol
1 when calculated from solubility measurements in the range of 10
40 °C, respectively. The lattice energy difference gives an estimate of
7.1 kJ 3 mol
1, which is significantly more stabilizing, although the neglect of zero-point and thermal effects is likely to reduce the difference by approximately 1 kJ 3 mol
1. There is a variation of at least 1 kJ 3 mol
1 depending on the wave function used to compute the charge density and conformational energies. Hence, the calculations are overestimating the energy difference between the two idealized crystal structures by a few kilojoules per mole. This error is small as a percentage of the lattice energy, and also is sufficiently accurate for this crystal energy landscape (Figure 4) to give reliable ordering of the different structural types. However, the error is too large for other applications, as the free energy of formation of racemic compounds from chirally pure crystals is normally on the order of
0.8 to
4 kJ 3 mol
1 but can be as high as
8 kJ 3 mol
1.69 NPX was studied in order to characterize the racemic phase of a pharmaceutical, and there are features of the two structures that are particularly challenging to the accurate calculation of relative lattice energies. The unusual bending of the naphthalene ring in (S)-NPX and inability to determine this exactly for the racemic 5667

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Crystal Growth & Design structure introduce uncertainties into the estimate of the conformational contribution to lattice energy. The two structures differ in their hydrogen-bonding motifs, and the differential polarization of carboxylic acid groups in the two motifs is not well represented by the empirically fitted isotropic atom
atom potentials. Moreover, the empirical fitting of the repulsion
dispersion parameters to known crystal structures and sublimation energies partially absorbs some of the approximations in the thermodynamics and form of the model potential. Hence, we can hope that more accurate modeling of the intermolecular forces, by use of molecule-specific intermolecular potentials82 and including molecular polarizability and flexibility or dispersioncorrected periodic density functional calculations,83 may improve the reliability of relative energies. However, we note that the flexibility of most chiral molecules means that good estimates of thermal effects are also needed. Hence, the experimental measurements of both absolute and relative thermodynamic quantities provide an essential validation target for emerging computational chemistry methods.84

5. CONCLUSIONS The structure of (RS)-naproxen has been solved by powder X-ray diffraction, and its solubility and thermal melting behavior are contrasted with those of the therapeutically used (S)-naproxen. The binary melting point phase diagram, solubility measurements, limited solid-state screening, and calculated crystal energy landscape are all consistent with the racemic Pbca and enantiopure P21 compounds being the only practically relevant solid phases of the free acid naproxen. The racemic compound is more stable than the enantiopure by a few kilojoules per mole. This degree of consistency within this interdisciplinary study significantly increases the confidence in the experimental findings, particularly in supporting the determination of the crystal structure of the racemic compound. This study has reproducibly shown that the thermodynamic driving force for the industrially important separation of (S)naproxen from the racemate is small, only a few kilojoules per mole, defining the target accuracy needed if computational methods are to assist in the design of chiral separation processes. The assumptions made in calculating the relative lattice energies and the many approximations often used to estimate the thermodynamic differences between racemic and enantiopure solids, solutions, and melts at practical temperatures have uncertainties that are significant. This study, by providing the structures and thermodynamic measurements, sets a benchmark for the challenge of developing a quantitative predictive model for the thermodynamics of chiral resolution. ’ ASSOCIATED CONTENT

bS

Supporting Information. Additional text, eight figures, and six tables showing conformational analysis of naproxen; representation of experimental naproxen structures; computationally generated crystal energy landscape; Fourier-transform infrared and Raman spectroscopy, powder X-ray diffractometry, and differential scanning calorimetry for (S)- and (RS)-naproxen; crystal growth and solid-state NMR for (RS)-naproxen; and values for ideal solubility calculated in the range 10
40 °C. This material is available free of charge via the Internet at http://pubs.acs.org/.

ARTICLE

’ AUTHOR INFORMATION Corresponding Author

*Tel +44(0)20 7679 4622; fax +44(0)20 7679 7463; e-mail [email protected].

’ ACKNOWLEDGMENT We thank Professor Ulrich J. Griesser for access to the instrumentation in the University of Innsbruck, Martin Vickers for early stage powder-ray diffraction experiments, Rajni Miglani for additional simulated annealing PXRD fitting work, and the EPSRC National Solid-state NMR Research Service for solidstate NMR measurements of (RS)-naproxen. The EPSRC funded this project through EP/F006721 and EP/F03573X (www.cposs.org.uk). ’ REFERENCES (1) Announcement. Chirality 1992, 4, 338
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