Molecular Modeling Study Of Chiral Drug Crystals: Lattice Energy Calculations

Molecular Modeling Study of Chiral Drug Crystals: Lattice Energy Calculations Z. JANE LI,1 WILLIAM H. OJALA,2 DAVID J. W. GRANT1 1

Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Weaver-Densford Hall, 308 Harvard Street SE, Minneapolis, Minnesota 55455-0343 2

Department of Chemistry, University of St. Thomas, St. Paul, Minnesota 55105

Received 10 May 2000; revised 27 February 2001; accepted 30 March 2001

ABSTRACT: The lattice energies of a number of chiral drugs with known crystal structures were calculated using Dreiding II force ®eld. The lattice energies, including van der Waals, Coulombic, and hydrogen-bonding energies, of homochiral and racemic crystals of some ephedrine derivatives and of several other chiral drugs, are compared. The calculated energies are correlated with experimental data to probe the underlying intermolecular forces responsible for the formation of racemic species, racemic conglomerates, or racemic compounds, termed chiral discrimination. Comparison of the calculated energies among ephedrine derivatives reveals that a greater Coulombic energy corresponds to a higher melting temperature, while a greater van der Waals energy corresponds to a larger enthalpy of fusion. For seven pairs of homochiral and racemic compounds, correlation of the differences between the two forms in the calculated energies and experimental enthalpy of fusion suggests that the van der Waals interactions play a key role in the chiral discrimination in the crystalline state. For salts of the chiral drugs, the counter ions diminish chiral discrimination by increasing the Coulombic interactions. This result may explain why salt forms favor the formation of racemic conglomerates, thereby facilitating the resolution of racemates. ß 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:1523±1539, 2001

Keywords: racemate; enantiomer; chiral drug; racemic compound; molecular modeling; lattice energy; intermolecular interactions; van der Waals energy; Coulombic interaction; enthalpy of fusion; melting point; chiral discrimination

INTRODUCTION Molecular modeling uses computational methods to study various chemical and biological systems. In recent years this technique has emerged as an important tool for predicting and correlating the energies and properties of molecules of known and unknown structures in chemical, biological, and Z. Jane Li's present address is P®zer Inc., Process R&D, PO Box 8156-111, P®zer Central Research, Eastern Point Road, Groton, Connecticut 06340. Correspondence to: D.J.W. Grant (Telephone: 612-624-3956; Fax: 612-625-0609; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 90, 1523±1539 (2001) ß 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association

pharmaceutical research.1,2 One of the major advantages of computer modeling over experiment is that the interaction energy and its variation with structure may be investigated at the atomic and molecular levels. Applications of molecular modeling in the solid state are very broad, ranging from investigation of the in¯uence of crystal packing on molecular structures to the determination of thermodynamic and dynamic properties of crystals.3 Not until the last few years have modeling techniques been applied in pharmaceutical research to polymorph predication, morphology modi®cation, crystal engineering, and more recently to the solution of crystal structures from powder patterns.4,5

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The modeling approach in materials research is greatly facilitated by improvements and accessibility of computer power and the emergence of user-friendly molecular modeling packages. Cerius2 is one of the software packages that provides a full suite of modeling and simulations, capable of solving diverse problems in materials research. Differences in intermolecular interactions between homochiral and racemic crystals, that is, chiral discrimination forces, are subtle and complex.6 The origin and magnitude of the intermolecular forces, although dif®cult to determine experimentally, may be revealed by the modeling approach. Understanding of the intermolecular interactions responsible for chiral discrimination in chiral drug crystals may ultimately lead to the rational design for optical resolution and puri®cation by crystallization. Industrial production of pure enantiomers involves either resolution or stereoselective synthesis. The resolution process may be carried out during any step of a multistep synthesis. A resolution earlier in the sequence is more desirable because of the higher ef®ciency of raw material production. Despite the advances made in enzymatic resolution and catalytic asymmetric synthesis, classical crystallization techniques will continue to play a major role in the industrial production of pure enantiomers, because of their

great potential and real economic importance in large scale optical puri®cation and resolution.7,8 However, this type of crystallization has been carried out by trial and error owing to a lack of fundamental understanding of the thermodynamics and kinetics of the technique. To optimize the resolution technique, it is essential to gain knowledge of the factors controlling the formation of enantiomers and racemic compounds at both the bulk and molecular levels. For a pair of enantiomers, the phase diagram of melting temperatures versus composition usually resembles one of the three shown in Figure 1.9 A racemic species, containing equimoles of two opposite enantiomers, can be either a racemic conglomerate (&10% occurrence), a racemic compound (&90% occurrence), or, rarely, a racemic solid solution (&1% occurrence). A racemic conglomerate is a physical mixture of both enantiomeric crystals, also termed homochiral crystals, while a racemic compound consists of racemic crystals in which the two enantiomers are paired up in the unit cells of the crystal lattice. When the racemic species is a racemic compound that melts at a higher temperature than the corresponding enantiomers, as in Figure 1a, it is impossible to resolve the racemic species and dif®cult to purify single enantiomers by crystallization. In Figure 1b, where the melting temperature of the racemic species as a racemic compound is lower

Figure 1. Typical phase diagrams of enantiomers and various cemic species. TA is the melting point of the enantiomer. TR is the melting point of the racemic compound. TE is the eutectic melting temperature. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

MOLECULAR MODELING STUDY OF CHIRAL DRUG CRYSTALS

than that of the enantiomers, puri®cation is facilitated and resolution is possible by entrainment (preferential crystallization induced by seeding).9 The most favorable case is that shown in Figure 1c, where the racemic species is a racemic conglomerate that provides spontaneous resolution. However, the racemic species in Figure 1c may be a racemic compound, of which the melting point is close to that of the eutectic temperature (TR & TE). In such cases, the racemic species may exist either as a racemic compound or as a racemic conglomerate, one of which is the metastable phase. Based on their melting behavior, racemic compounds may be divided into two types: Type I (TR > TA) and Type II (TR < TA). A Type II system is desirable for the puri®cation of enantiomers and the resolution of racemates by crystallization. A survey of over 100 chiral compounds by Jacques et al. 9 showed that the salts of organic acids or bases tend to form racemic conglomerates with a higher frequency than do the corresponding acids or bases; pharmaceutical compounds are not exceptions to this rule.9 The melting temperatures of the unionized and salt forms of ®ve pharmaceutical compounds are compiled, and the difference in melting point between the ionized base or acid and its chloride or salicylate salt are shown in Figure 2. In all cases the salt of a chiral drug displays a reduced difference in melting temperature, or, in other words, salt formation is likely to convert a chiral drug system from Type I to Type II.

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The formation of a salt introduces an additional complexity for chiral drugs as opposed to achiral drugs. If the counter ion is chiral, the resulting species is a diastereomeric salt. In fact, the formation of diastereomeric salts is a useful method for resolving racemates by crystallization based on the difference in their solubilities. Several molecular modeling studies have investigated the formation of diastereomeric salts for the resolution of racemates, suggesting the possibility of developing a predictive model.10,11 If the counter ion is achiral, the racemic solid phase diagram can be either a racemic compound or a racemic conglomerate. As can be deduced from Figure 2, the salts of chiral drugs may facilitate optical resolution and puri®cation. To develop an ef®cient resolution process, the roles of a chiral drug molecule and its counter ion in crystal packing, charge distribution, hydrogen bonding, and intermolecular interactions are worthy of investigation. The goal of the present study is to explore the factors of chiral discrimination in the crystalline state using a molecular modeling approach. The lattice energy and its components of the model compounds were calculated and compared with experimental data to reveal the intermolecular interactions governing the formation of homochiral and racemic crystals. The implications of the calculated thermodynamic parameters in the resolution process are discussed below in the section entitled ``Homochiral Crystals versus Racemic Compounds.''

Figure 2. Differences in melting points between homochiral and racemic species. (Acronyms are given in Table 1.) JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

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Lattice Energy Calculation Theory There are three levels of computation in molecular modeling, namely molecular mechanics (MM), semiempirical methods, and ab initio calculations. Among these levels, MM is the most widely applied in lattice energy calculations because of its simplicity and the possibility of handling large systems in the ground state. MM calculations employ an empirically derived set of equations based on classical mechanics.3,12,13 The set of potential functions, termed the force ®eld, contains adjustable parameters that are derived from experimental data, such as X-ray diffraction, infrared (IR) spectra, and nuclear magnetic resonance (NMR) spectra. The total MM energy (EMM) is calculated below in eq. 1 as the sum of the following readily identi®able energy components: bond stretch (Ebond), bond-angle bend (Ebond), dihedral angle torsion (Etorsion), van der Waals interaction (EvdW), and electrostatic interactions (Eelectrostatic): EMM ˆ Ebond ‡ Eangle ‡ Etorsion ‡ EvdW ‡ Eelectrostatic

…1†

EvdW is the energy of nonbonded van der Waals interactions, most commonly described by the Lennard-Jones function for repulsive and attractive forces. Eelectrostatic is the energy of nonbonded electrostatic interactions, often calculated by Coulombic potential. Because the differences in intramolecular interactions between enantiomers are usually rather small,10 the calculations presented in this work emphasize the intermolecular nonbonded interactions in the molecular crystals of chiral drugs. Molecular crystals consist of discrete molecules held together by intermolecular nonbonded forces that are weaker than the bonding energy. The lattice energy, ELatt, comprises primarily three nonbonded interactions: van der Waals (repulsive and attractive) forces (EvdW), electrostatic (Coulombic) forces (Eelectrostatic), and hydrogen-bonding energy (EH), as in eq. 2: ELatt ˆ EvdW ‡ Eelectrostatic ‡ EH

…2†

These interactions are computed by summing the interatomic energies between pairs of nonbonded atoms, that is, the atom-atom potentials.14 The basic assumptions underlying these calculations are the spherical symmetry assumption and the additivity assumption. As a ®rst approximation, JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

covalent bond lengths are independent of the state of matter in which they are measured and of the type of molecule in which they occur. For this reason, useful, albeit empirical, quantitative relationships between bond length and energy have been derived. Similarly, the nonbond interactions can be parameterized independent of the type of molecules involved. The mathematical expression of the lattice energy is: ELatt ˆ

n X 1 1X Eij …rij † 2 iˆ1 j

…3†

For each pair of atoms, the energy, Eij, is computed from the potential functions and parameters of an appropriate force ®eld. The most widely used potential function for the van der Waals term, EvdW, is the Lennard-Jones 12-6 potential,15 in eq. 4: ÿ Brÿ6 EvdW ˆ Arÿ12 ij ij

…4†

where A and B are empirical parameters, and rij is the interatomic distance between atoms i and j. The positive term, the ®rst term on the right, represents the repulsive force at a relatively short distance, while the negative rÿ6 term represents the attractive force at a relatively large distance. In MM, the summation of these two terms, EvdW, is referred to as the van der Waals interaction, although only the attractive term is, by de®nition, the van der Waals cohesive force. The Coulomb potential is the leading term for the calculation of electrostatic interactions by means of the atomic point-charge model: ÿ1 Ecoul ˆ qi qj rÿ1 ij "

…5†

where qi and qj are the atomic point charges and E is the dielectric constant. For organic molecules of pharmaceutical interest, this term is considered to be the major component of the hydrogenbonding energy for hydrogen-bonding functional groups, accounting for the majority of point charges. The calculated electrostatic energy, Ecoul, by eq. 5 may give rise to large variations due to differences in atomic charge assignments. Although considerable attention has been directed to the problem of selecting appropriate values for the atomic point charges, electrostatic potential calculations remain problematic.14,16 The method available in Cerius2, release 1.6, is the charge equilibrium (QEq) method based on the equilibrium potential.17In this study, the

MOLECULAR MODELING STUDY OF CHIRAL DRUG CRYSTALS

atomic charges assigned by the QEq method were comparable to those obtained by various ab initio methods, and were used for the calculations of the electrostatic energy. The total hydrogen-bonding energy, in theory, should include two components: the electrostatic energy, partially accounted for by the Ecoul term, and nonbonded van der Waals interactions. In MM, the van der Waals energy between two hydrogen-bonded atoms is de®ned as EH and is actually a partial hydrogen-bond energy. It is known that the distance between the hydrogen bond donor and acceptor atoms is usually less than the sum of the van der Waals radii, so that the Lennard-Jones 12-6 potential function may not be appropriate for calculating EH.16 For lattice energy calculations in Cerius2, the hydrogenbonding energy is calculated using a CHARMmlike hydrogen-bond energy, which is a 12-10 potential with an angular term: ! Cij Dij ÿ 10 cos4  …6† EH ˆ r12 rij ij where y is the angle between the donor, hydrogen, and acceptor atoms, and C and D are empirical parameters. The power of 10 in the attractive term is intended to correct for the shorter separation than the sum of the van der Waals radii between the hydrogen bond donor and acceptor atoms. However, accurate estimation of hydrogen-bonding energies may be dif®cult due to many factors. One such factor is the experimental error associated with the uncertainty of the positions of the hydrogen atoms derived from

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X-ray diffraction. The other is the strong angular dependence by the power of 4 in the cosine y term.The situation is further complicated by the nonadditive nature of these types of interactions. Unfortunately, there is still no better way to obtain the total hydrogen-bond energy without intensive computation. Correlation Between Calculated Lattice Energy and Experimental Data Kitaigorodski originally intended that the atomatom potentials would enable the calculation of the potential energy of particle interactions.17 The calculated energy is equal to the heat of sublimation of the crystal at the absolute zero, and is de®ned as the lattice energy in the absence of thermal vibrations. However, most crystal structures are determined at temperatures well above 0 K, whereas many experimental sublimation energies are measured at room temperature. To correlate the calculated value of lattice energy with the experimental enthalpy of fusion, a simple thermodynamic cycle between the solid and gas phases is considered, as shown in Figure 3. Based on this thermodynamic cycle, the enthalpy of sublimation, DHS, at temperature T, can be calculated from the following equation: S

ZT

…
H †T ˆ ÿELatt ÿ Eo ‡


Cp dT

…7†

0

where DCp is the difference between the heat capacities of the gaseous and solid state. Usually, the Eo term is less than 1% of ELatt, and the heat

Figure 3. Thermodynamic cycle for the heat of sublimation. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

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capacity contribution is no greater than 10% of ELatt. This fact partially explains why the enthalpy of sublimation may be approximated by the total lattice energy of a crystal with errors of up to 10%.18 Taking the difference of the sublimation energies between the racemic and homochiral crystals, eq. 8 can be obtained:

H s ˆ
H s …R† ÿ
H s …A†  ÿ
ELatt

…8†

where R and A in the parentheses represent the racemic and homochiral crystals, respectively. In eq. 8, the cancellation of Eo and the heat capacity term of the two species are assumed. It is likely that the errors in the calculated differences are actually further reduced in these chiral systems.19 The sublimation energy is the sum of the heat of vaporization (DHv) and the heat of fusion (DHf), while neglecting the contribution from the heat capacity (usually < 10 cal/mol while DHv and DHf are in the kcal/mol range). Because the interactions between homochiral and racemic species in the melt and vapor states are very similar for typical organic compounds, the difference in DHv between the racemic and the corresponding homochiral crystals is negligible. It is then plausible to derive eq. 9:

H f ˆ
H f …R† ÿ
H f …A† 
ELatt

…9†

Thus, the difference in enthalpy of fusion is the major contributor to the difference of lattice energy observed between the homochiral and racemic crystals. The enthalpy of fusion is a thermal quantity readily measurable by differential scanning calorimetry (DSC). This type of calculation applies quite well to chiral systems by the use of the aforementioned thermodynamic cycles, in which errors in the calculated values are likely cancelled out by taking the difference in the enthalpies of fusion between the homochiral and racemic crystals. Nevertheless, because eq. 9 is based on several approximations, the calculated energy terms should be cautiously evaluated.

EXPERIMENTAL SECTION The model compounds used in this work were selected based on the availability of crystal structural data, and are listed in Table 1 together with the acronyms that are employed in this report. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

Preparation of Salts and Single Crystals The salicylate salts of ephedrine, pseudoephedrine, and norephedrine were prepared by mixing equimolar solutions of the hydrochloride salt of the ephedrine derivatives and sodium salicylate. After cooling the solution, the precipitated salt was collected and recrystallized, when necessary, to ensure their purity, as indicated by a single melting exotherm in DSC and high performance liquid chromatography (HPLC). The hydrochloride salts and the free bases of the ephedrine derivatives, if of >99% purity, were used as received. The quality of the crystals, (ÿ)-methylephedrine and (ÿ) methylephedrine hydrochloride, from the suppliers was adequate for direct structural determination. The preparation of single crystals of many ephedrine derivatives with unsolved structures was attempted. Several compounds, (‡)- and (ÿ)-NE, ()-PE, (‡)- and (ÿ)-E, ()-E, and (‡)-NE
S, failed to form single crystals of adequate size and quality for structural analysis under various conditions. Suitable single crystals of ()-NE
Cl, ()-NE
S, ()-PE
Cl, and ()-E
Cl, were grown by slow evaporation from water ‡ methanol or water ‡ ethanol mixtures. Structural Determination of Ephedrine Derivatives Crystals of suitable size were selected and mounted on a glass ®ber. All measurements were made on a diffractometer (Rigaku AFC6S, Tokyo, Japan) with Cu Ka radiation and a graphite monochromator. The structures were solved by direct methods (SHELXS86).23,24 The ®nal unweighed agreement factors, R, were less than 0.07. All calculations were performed with TEXSAN software. Not all the hydrogen atoms could be located, and not all that were located could be re®ned. Three-dimensional coordinates and cell parameters in .res SHELX ®le format were used for the Cerius2 program. Structural Information on Other Chiral Drugs From the Cambridge Structural Database (CSD) Searches were made on the CSD (1994±1995) with the compound name and the reference code (REFCODE) of chiral compounds from the survey by Brock.25,26 Five chiral drugs were selected as model compounds based on the availability of

MOLECULAR MODELING STUDY OF CHIRAL DRUG CRYSTALS

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Table 1. List of Model Compounds, Their Acronyms, Structural Files, and Sources Compound

Acronyma

CSD REFCODEb

()-Norephedrine (ÿ)-Norephedrine
HCl ()-Norephedrine
HCl ()-Norephedrine
HS (ÿ)-Pseudonorephedrine-HCl (‡)-Pseudoephedrine (‡)-Pseudoephedrine
HCl ()-Pseudoephedrine
HCl (‡)-Pseudoephedrine
HS (ÿ)-Ephedrine
HCl ()-Ephedrine
HCl ()-Ephedrine
HS (ÿ)-Methylephedrine (ÿ)-Methylephedrine-HCl (ÿ)-Ibuprofen ()-Ibuprofen (ÿ)-Mandelic acid ()-Mandelic acid (ÿ)-Propranolol
HCl ()-Propranolol
HCl (ÿ)-Fen¯uramine
HCl ()-Propranolol
HCl (ÿ)-trans-Sobrerol ()-trans-Sobrerol ()-cis-Sobrerol

()-NE (ÿ)-NE
Cl ()-NE
Cl ()-NE
S (ÿ)-PNE
Cl (‡)-PE (‡)-PE
Cl ()-PE
Cl (‡)-PE
S (ÿ)-E
Cl ()-E
Cl ()-E
S (ÿ)-ME (ÿ)-ME
Cl (ÿ)-IB ()-IB (ÿ)-MA ()-MA (ÿ)-PN
Cl ()-PN
Cl (‡)-FA
Cl ()-FA
Cl (ÿ)-t-SB ()-t-SB ()-c-SB

NOREPH01 JASTUS JASVAA PSEPED(01) PEPHCL EPHECL01

JEKNOC10 IBPRAC FEGHAA DLMAND01 PROPDD BABCUC BUHCIQ BABCUC JOFKOE KPTDUS KUVVUS

Filec

Chemical Sourced

WH94 WH73

Sigma Sigma This work

WH89 SD1 WH90a SD2 WH81 WH97

Sigma Sigma This work Sigma This work Sigma Lancaster Ethyl Ethyl Sigma Sigma Sigma Sigma Sigma Sigma e e e

a

Cl and S represent the chloride and salicylate anions, respectively. The reference code names in the Cambridge Structural Database. c WH denotes SHELX ®le names for the structures solved in this work;20 SD denotes SHELX ®le names prepared from the coordinates from previous work by Duddu.21 d Sigma Chemical Co. (St. Louis, MO); Lancaster (Windham, NH); Ethyl Corporation (Baton Rouge, LA). e Data from Bettinetti et al.22 b

thermal data and crystal structures of both racemic and homochiral crystals. The threedimensional coordinates and cell parameters in .fdat ®le format were transferred to, and read by, the Cerius2 program. The structures and hydrogen-bond patterns were viewed with the threedimensional visualizer of this program. Thermal Analysis Measurements of melting point and enthalpy of fusion of the crystals were performed using a Du Pont 910 differential scanning calorimeter equipped with a data station (Thermal Analyst 2000; TA Instruments, New Castle, DE). The temperature axis and the cell constant were calibrated with indium (3 mg, 99.99%, peak maximum at 156.68C and heat of fusion 28.4 J/g). Samples of 3.0  0.2 mg in crimped aluminum pans were heated at a rate of 108C/min, and the peak melting temperature was recorded. All

determinations were carried out in triplicate and the arithmetic mean values and standard deviations are reported. Computational Method All lattice energy calculations were performed using Cerius2 software, release 1.6, program version 2.2 (Molecular Simulations Inc., San Diego, CA) running on commercial workstations: Silicon Graphics, Personal Iris 4D/20, Power Series 2 x R3000, and Indigo R4000. Energy minimization was performed using the Crystal Packer module of Cerius2, with the Dreiding II force ®eld, a generic force ®eld developed for inorganic and molecular crystals.13The atomic charges were assigned by the QEq method.27 The modi®ed Newton algorithm was used for minimization, convergence being reached when the gradient tolerance was less Ê .28 The periodic boundary then 0.01 kcal/mol.A JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

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Figure 4. Flow chart of the computational procedure used for lattice energy calculation.

condition was applied with a maximum cut-off Ê (the default value), and no radius of 7 A signi®cant difference in calculated energies was observed when larger cut-off radii were applied for selected model compounds. The general procedure of the computation is shown in Figure 4, the default values for setting energy calculation options being chosen from Cerius2 User's Reference, Property Prediction.29 During minimization, the molecules are held rigidly in the unit cell. The advantage of imposing rigidity is that the energy calculation and minimization can be carried out much faster because the number of degrees of freedom (Ebond, Eangle, Etorsion) is much reduced. If the molecules are considered to be rigid, the intramolecular enerJOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

gies, Ebond, Eangle, and Etorsion , are held constant and become irrelevant during the minimization. The computation method uses the atom-atom potential that is a function of radii, as shown in eqs. 3, 4, and 5. Calculation using radii greater Ê was performed, but no signi®cant change than 7 A (< 2%) in van der Waals energy was seen. Electrostatic interactions have a slow convergence and can ¯uctuate when the cut-off radius is changed. To solve this problem, Ewald summation was applied for a given cut-off radius in Cerius2. Ewald summation exploits the periodicity of the system by calculating part of the summation, the long range correction, in reciprocal space. When this method is used, the energy convergence is accelerated and a more accurate result can be obtained. A study of crystal packing has shown that there is a little in¯uence on the lattice parameters when the cut-off radius Ê . The absolute exceeds the minimum radius of 7 A energy of the minimized structure may change, but the difference between the homochiral and racemic crystals will not change signi®cantly. Therefore, a standard set of parameters was used for all calculations. The hydrogen-bonding energy was calculated with Exclude H±Acc preference, that is, any interactions for the atom-pairs involved in hydrogen bonding are not considered as van der Waals interactions in the Lennard-Jones 12-6 potential calculation. It was found that calculations by Exclude H±Acc result in smaller differences during minimization than the values obtained from Use H±Acc preference, which may overestimate the interaction energy between hydrogen and acceptor atoms. Therefore, all calculated values reported in this work were computed using Exclude H±Acc preference. Statistical Analysis The data were analyzed by multiple regression using the statistical analysis system (SAS version 6.12). Pearson's Correlation Coef®cient analysis was used to evaluate the correlation between a calculated energy term and experimental data.30

RESULTS AND DISCUSSION The crystal structures of a number of homochiral and racemic crystals are available either through structural determination reported in this work or through a search of the CSD (Table 1). Ephedrine

MOLECULAR MODELING STUDY OF CHIRAL DRUG CRYSTALS

and its N-methyl derivatives and their salts were used as structurally related model compounds, collectively termed ephedrine derivatives. Although the crystal structures of many chiral compounds are available, few have known structures for both the homochiral and racemic crystals, and even fewer for those of pharmaceutical relevance. Eight such pairs of chiral drugs were collected and used as model compounds. Molecular structures of the model compounds are shown in Figure 5. All of these compounds, except sobrerol, consist of an aromatic ring, phenyl or naphthyl, and a ¯exible side-chain with hydrogen-bonding func-

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tional groups. These types of structures are very common among many small drug molecules. Fen¯uramine and sobrerol were chosen as the model compounds in an attempt to test molecules with difference molecular structures. Fen¯uramine hydrochloride has a strong polar tri¯uoromethyl group attached to the phenyl ring, while sobrerol has a cyclohexane ring with available thermal analytical data.22 Validation of the Computational Procedure Lattice energy calculations may provide insight into the molecular forces governing the formation

Figure 5. Molecular structures of the model compounds. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

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of homochiral and racemic crystals, provided that the total energy and its components can be calculated accurately. The reliability of the energy calculations obtained using Cerius2 was ®rst evaluated in terms of the magnitude of the energy terms and the variations of the cell dimensions during minimization. The precise structural data available for the crystalline state, over 100,000 in CSD alone, provide a rich source of information for deriving energy parameters. Unfortunately, sublimation energies are known for only about 1000 organic crystals, and most of them have unsolved crystal structures.31 For pharmaceutical solids, such data are even scarcer. Among all the model compounds in this work, the sublimation energy of ibuprofen is the only one available.32 However, it is known that the sublimation energy for molecular crystals is within the range of 15±60 kcal/ mol for small organic molecules (MW < 500), and somewhat higher for their salts, which serves as a rough estimate of the magnitude of lattice energy.33,34 Previously reported lattice energy calculations of chiral crystals may also be used as references for the computational values employed with the current setup using Cerius2 software. During energy minimization, the molecules are assumed rigid but free to move within a unit cell. As a result, the unit cell parameters are allowed to vary slightly to accommodate the optimal intermolecular contacts with the minimum energy. The differences between the calculated unit cell

parameters and the corresponding experimental ones are generally expected to be 5 to 10%.18 The minimization procedure is routinely performed to obtain the best possible energy values with respect to the speci®c force ®eld employed. An indication of an appropriate choice of a force ®eld is the minimal changes of cell dimensions and lattice energies of the crystal structure before and after minimization. Two force ®elds, Dreiding II and Universal force ®eld,35 were employed to compute the lattice energies of the model compounds. Comparison of the values from the two force ®elds showed that the Dreiding II force ®eld gave overall smaller differences in both cell dimensions and lattice energies by minimization, and was therefore selected as the force ®eld for this study. Dreiding II is the default force ®eld for ELatt calculation in Cerius2. The changes in cell dimensions during minimization are summarized in Figure 6. Most values of Dx/x fall within 5%, with a few between 5 and 10%. The cell dimension after minimization, when plotted against that before minimization in Figure 6, shows a very good linear correlation, with a slope close to unity and a determination coef®cient of 0.991. The calculated values were compared with the previously reported values.32,36 An excellent agreement was achieved for ibuprofen between the calculated lattice energy (29.2 kcal/mol) and the experimental sublimation energy (28.92 kcal/ mol).32 Lattice energy calculations of a few chiral

Figure 6. Plot of unit cell dimensions before and after minimization. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

MOLECULAR MODELING STUDY OF CHIRAL DRUG CRYSTALS

compounds, alanine, valine, trans-1,2-cyclohexanecarboxylic acid, and two cinnamates salts, were reported to compare the differences between racemic compounds and racemic conglomerates.36 Reasonable agreements were found despite rather different force ®elds and procedures applied in these calculations. With these results, the reliability of the current force ®eld and the procedures was tested and was found satisfactory. Ephedrines and Their Derivatives: Base Versus Salt Because a number of crystal structures of ephedrine and its derivatives, both bases and their salts, were available, calculations were ®rst carried out for these compounds. The total lattice energies and their components were analyzed to describe the variations among the bases and salts with different counterions. The calculated lattice energies of ephedrine and its derivatives are summarized in Table 2. Some general trends are shown among the calculated values despite a few questionable calculated values of Ecoul and EH. For bases, the van der Waals energy is the dominant intermolecular force. For salts, contributions of the electrostatic interaction toward the total lattice energy increase substantially and may be greater than the van der Waals energy for highly charged ions. Statistical analysis of pair-wise correlation was performed between experimental data and the calculated values of Table 2 the results are shown

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in Table 3. No correlation was found between the experimental values of melting point and enthalpy of fusion, implying that the factors controlling these two properties are different. The increase in melting temperature is proportional to the energy of Coulombic interaction, while the enthalpy of fusion correlates well with the van der Waals energy. Although the goodness of ®t for these two linear relationships is modest (R  0.8), the p value obtained from statistical analysis implies that there are signi®cant correlations between the melting temperature and the Coulombic interaction, and between the enthalpy of fusion and the van der Waals interaction. The observed correlation explains the relative in¯uence of an energy component on the crystal property of interest. Between the chloride and salicylate salts, the differences in their van der Waals energies with the same cation average about 14 kcal/mol in Table 4. The salicylate anion gives rise to a rather large increment in the van der Waals interaction merely because of the greater number of atoms in the salicylate ion than in the chloride ion. The chloride salts, on the other hand, melt at appreciably higher temperatures and show signi®cantly greater electrostatic energies than the salicylate salts. The hydrogen-bonding energies, EH, of bases and salts account for 5 to 20% of the total lattice energy, depending on the number of available hydrogen-bond donors and acceptors in the molecule or ion. As shown in Table 2, the salicylate

Table 2. Lattice Energies and Thermal Properties of Ephedrine Derivatives Compounda

Tf (8C)

()-NE ()-NE
S (ÿ)-NE
Cl (ÿ)-PNE
Cl ()-NE
Cl (‡)-PE (‡)-PE
S ()-PE
Cl (‡)-PE
Cl) ()-E
S ()-E
Cl (‡)-E
Cl (ÿ)-ME (ÿ)-ME
Cl

101.5 119.0 172.8 181.037 195.9 119.2 131.3 166.0 182.9 145.6 190.8 219.1 88.0 192.6

DHf (kcal/mol)

ÿEvdW (kcal/mol)

ÿEcoul (kcal/mol)

ÿEH (kcal/mol)

ÿELatt (kcal/mol)

6.24 7.45 4.84

15.70 31.08 15.03 18.22 17.23 16.24 33.44 19.06 19.06 34.53 20.55 21.62 19.94 21.84

5.42 16.55 15.13c 18.71 24.67 3.59 12.19 29.30 24.67 14.30 24.84 22.51 3.56 43.46c

6.43 14.97 5.32 1.31c 10.29 3.51 11.96 7.14 1.92c 9.48 6.54 3.98 3.36 5.91

27.25 62.59 35.48 38.23 52.22 23.33 57.60 55.50 45.66 58.30 51.94 48.11 26.85 71.21

b

6.92 7.64 8.69 6.74 6.68 9.59 8.35 7.58 7.30 7.81

a

Acronyms are given in Table 1. The enthalpy of fusion of (ÿ)-PNE
Cl is unknown. The calculated value deviated signi®cantly from the general trend observed among the ephedrine derivatives.

b c

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LI, OJALA, AND GRANT

Table 3. Correlation of the Measured Thermal Properties and the Calculated Energies (n ˆ 13) Variable 1 Tf Tf Tf Tf DHf DHf DHf

Variable 2

Correlation, Ra

p Valueb

DHf EvdW Ecoul ELatt EvdW Ecoul ELatt

ÿ0.042 ÿ0.166 0.782 0.482 0.754 0.041 0.452

0.8918 0.5869 0.0016 0.0954 0.0029 0.8935 0.1207

a R value is the correlation coef®cient, which was obtained by linear regression of variable 2 against variable 1. b The p value is the Pearson correlation coef®cient for each pair of the variables. If the p value is greater than 0.1, there is no signi®cant correlation supporting the null hypothesis. If the p value is less than 0.05, there is a signi®cant correlation, as shown in bold, rejecting the null hypothesis.

salts have greater EH values than the chloride salts with the same cation. The calculated EH values for the chlorides seem questionable in a few cases because of the polarizability of the relatively large chloride ion, whose position sometimes deviated signi®cantly from the experimentally determined location during energy minimization. Optimization of the force ®eld parameters of the chlorine atom in these salts may improve the computational results, but was not carried out in this study. By comparison with the bases, the presence of the salicylate anion contributes greatly towards the van der Waals energy, and correspondingly increases the enthalpy of fusion signi®cantly, while elevating the melting point slightly. The chloride salts, on the other hand, displayed much higher melting temperatures because of strong electrostatic interactions, but showed slightly lower enthalpies of fusion than the corresponding bases. By de®nition, the enthalpy of fusion is the difference in enthalpy between the melt (liquid) and solid states. A smaller heat of fusion for salts, especially for chloride salts, implies a smaller

difference between the enthalpy of the liquid state, Hl, and that of the solid state, Hs. This situation likely applies to salts with counterions of strong acids when the electrostatic interactions persist in the melt state. Because the Coulomb potential is proportional to rÿ1, it has a long-range effect and therefore falls off slowly with increasing distance of separation in the melt state. However, the van der Waals interaction (/ rÿ6) has a relatively short range and is greatly reduced in the melt state. Among the ephedrine derivatives, these results suggest that the strong electrostatic forces elevate the melting temperature, perhaps by increasing the temperature required for total collapse of a crystal lattice from the ordered to the disordered state. The van der Waals interactions signi®cantly in¯uence the enthalpy of fusion by affecting the heat required to overcome the cohesive force over a short distance of separation. Homochiral Crystals Versus Racemic Compounds The lattice energies of eight pairs of homochiral and racemic crystals with known crystal structures were calculated and the results are summarized in Table 5. In all cases, DELatt(R ÿ A) is positive,38 indicating that the lattice energy of the racemic compound, R, is always greater than that of the corresponding enantiomers, A. This result suggests that all the existing racemic compounds are more stable than the corresponding enantiomers at absolute zero where the entropy term vanishes. Thus, the formation of racemic compounds is thermodynamically favorable under these circumstances. The marginal difference in ÿDELatt for propranolol hydrochloride indicates the possible formation of a conglomerate. This trend agrees well with the thermodynamic analysis, where the free energy of formation of racemic compounds from enantiomers is always positive.39

Table 4. Differences in Various Physical Properties Between the Salicylate and Chloride Salts of Ephedrine (E), Pseudoephedrine (PE), and Norephedrine (NE) Salicylate Salt

Chloride Salt

DDHf kcal/mol

ÿDEvdW kcal/mol

DTf 8C

ÿDEcoul kcal/mol

()-NE
S (‡)-PE
S ()-E
S

()-NE
Cl (‡)-PE
Cl ()-E
Cl

0.52 2.01 1.25

13.85 14.38 14.54

ÿ76.9 ÿ51.6 ÿ45.2

8.15 12.48 10.55

D ˆ Salicylate Salt ÿ chloride salt. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

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Table 5. Diffeences in Lattice Energy and Thermal Properties Between the Racemic Compound and the Corresponding Homochiral Crystals [DTfˆTf(R)ÿTf(A)] Compound Type I IB NE
Cl FA
Clb Type II PE
Cl MA E
Cl PN
Cl t-SB

a

f

DT (8C)

DDHf (kcal/mol)

ÿDEvdW (kcal/mol)

ÿDEcoul (kcal/mol)

ÿDEH (kcal/mol)

ÿDELatt (kcal/mol)

23.7 23.1 15.5

1.86 2.08 2.80

2.63 2.20 2.96 2.37

ÿ0.65 9.57 ÿ2.70 12.6

ÿ0.09 4.96 ÿ0.03 0.55

1.89 16.74 0.23 15.6

ÿ5.5 ÿ10.9 ÿ28.3 ÿ32.3 ÿ18.7

0.17 0.25 0.77 0.72 ÿ0.07c

ÿ0.00 ÿ1.00 ÿ1.06 ÿ0.09 0.64c

4.64 2.56 2.33 ÿ0.48 0.23

5.22 2.29 2.56 0.85 0.04

9.85 3.85 3.83 0.28 0.91

a

Acronyms are given in Table 1. The two energy values arise from two different sets of charge assignments obtained by selecting ion pairs (asymmetric unit) in different positions in the unit cell; more discussion is provided in the text. c This value has a sign opposite to those of the other compounds of Type II systems. b

Ibuprofen is a monocarboxylic acid that belongs to a family of well-studied mono- and dicarboxylic acids, for which the force ®eld parameters are well ®tted.40 The differences between the racemic and homochiral crystals in the total lattice energies and the enthalpies of fusion, ÿDELatt (1.864 kcal/mol) and DDHf (1.888 kcal/mol), agree almost perfectly. For other compounds, however, agreements between ÿDELatt and DDHf are not satisfactory because of the dif®culty in obtaining reliable Ecoul and EH energies, thereby affecting the reliability of the total lattice energy calculations. By pair-wise comparisons of the experimental and calculated quantities, two general trends were revealed. First, the signs of DEvdW and DTf agree very well, indicating that the species with the greater van der Waals energy display higher melting temperatures, such as those of Type I systems, whereas the reverse trend is observed for Type II systems, as Figure 7 clearly illustrates. Secondly, the van der Waals energy is favorable for Type I systems, for which the difference in EvdW is more than 2 kcal/mol, but is negative for Type II systems (or less than 1 kcal/mol for t-SB only), as shown in Figure 8. The exception of t-SB, which contains the cyclohexene ring, may indicate the necessity for modi®cation of the force ®eld parameters for different classes of compounds. Most importantly, both ®ndings suggest that the van der Waals forces play an important role in chiral discrimination.

The difference in the electrostatic interactions between homochiral and racemic crystals did not show a trend for Type I or Type II systems. One of the problems associated with accurate calculation of Ecoul arises from the strong dependence on the assignments of atomic point charges. A good example is the calculation of Ecoul of FA
Cl, of which the phenyl ring has the strongly polar CF3 substituent. Two rather different values of ÿDEcoul were obtained from two different charge assignments by selecting ions in different positions as asymmetric units. For other pairs of homochiral and racemic crystals, the same type of manipulations resulted in small differences of charge assignments and ÿDEcoul. In general, the differences in electrostatic interactions between the racemic and homochiral crystals are variable, and appear to be undiscriminating or nonstereoselective. However, this result requires further testing with a large number of chiral systems. Calculation of the hydrogen-bonding energy (van der Waals portion) is often problematic, as explained previously. The calculated values of EH are dif®cult to compare quantitatively between homochiral and racemic crystals. From a structural point of view, hydrogen-bond networks are actively involved in the architecture of the crystal lattices. Considering that a large portion of the hydrogen-bonding energy is electrostatic in nature, hydrogen-bond networks are more likely to in¯uence the melting temperatures through JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

Figure 7. Plot of differences in melting point and van der Waals energy between racemic and homochiral crystals. (Acronyms are given in Table 1.)

Figure 8. Plot of differences of enthalpy of fusion and van der Waals energy between racemic and homochiral crystals. (Acronyms are given in Table 1.) JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 10, OCTOBER 2001

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diastereomeric crystals, despite the interplay of various intermolecular forces in the solids.

electrostatic interactions, as discussed for ephedrine derivatives. Based on the lattice calculations in this work, the racemic compound, if it can exist, has a greater lattice energy than its homochiral counterpart. Although the racemic compound is usually thermodynamically favored, its melting temperature can be either higher than that of its corresponding enantiomer (Type I system) or lower (Type II system). Type II systems are favorable for resolution of racemates by crystallization. The fact that two systems show opposite trends of correlation between the van der Waals energy difference, DTf, and DDHf, suggests that the van der Waals interaction is the major chiral discriminating force between homochiral and racemic crystals. No correlation was found between the electrostatic and the hydrogen-bond energies with these two systems, indicating that they are not stereoselective. Agreements between DDHf and ÿDELatt cannot be tested due to the dif®culty in obtaining reliable calculated values of Ecoul and EH terms with the rather simple functions used in the Dreiding II force ®eld. More complicated functions with intensive computation may be needed to achieve accurate calculations, but these are beyond the scope of the present study.

CONCLUSION The contributions of the individual energy components, namely van der Waals interactions, electrostatic interactions, and hydrogen bonding, to the total lattice energy were calculated for a number of organic pharmaceutical crystals, and the individual correlations with their physical properties were investigated. Among the ephedrine bases and their salts, the electrostatic interaction correlates with the relatively large increases of melting temperatures of the salts, while the van der Waals interaction correlates with the enthalpies of fusion. Between the homochiral and racemic crystals, van der Waals forces appear to contribute signi®cantly to the differences in both melting behavior and enthalpy of fusion. The arrangement of complementary shapes of the paired enantiomers of covalent compounds probably provides more effective van der Waals interactions, resulting in greater discrimination between homochiral and racemic crystals. The greater tendency of salts of chiral compounds to form Type II (TR < TA) systems or racemic conglomerates can be explained by the decreased contribution of the van der Waals energy and the increased contribution of the electrostatic energy, consequently diminishing the chiral discrimination. Coulombic and hydrogen-bonding energies, although dif®cult to estimate accurately, are associated with electrostatic interactions and may not play an important role in chiral discrimination.

Diastereomers Among the model compounds, there are four pairs of diastereomers, for which Table 6 summarizes the differences in melting temperature, enthalpy of fusion, and van der Waals energy. The diastereoisomer with the higher melting temperature has the greater van der Waals energy and the higher enthalpy of fusion. The relationships between these properties, however, are not proportional, indicating the in¯uence of other intermolecular interactions. As between homochiral and racemic crystals, the van der Waals interaction plays a major role in discrimination between

Perspectives In many respects, molecular modeling has opened a new and exciting avenue for the study of

Table 6. Differences in the Physical Properties and the Calculated Energies Between Diastereomeric Pairs of the Model Compounds. (Acronyms are given in Table 1.) Diastereoisomer 1 (ÿ)-PNE
Cl (‡)-E
Cl ()-E
Cl ()-t-SB

fa

Diastereoisomer 2

DT (8C)

(ÿ)-NE
Cl (‡)-PE
Cl ()-PE
Cl ()-c-SB

8.2 36.2 24.8 26.0

DDHfa Kcal/mol)

ÿDEvdWa kcal/mol)

b

3.19 2.56 0.93 0.97

2.56 1.50 2.04

a

D ˆ 1ÿ2. DHf of (ÿ)-PNE
Cl is unknown.

b

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intermolecular interactions in crystals of chiral pharmaceuticals. The present work has taken a preliminary step toward applying the computational method in an attempt to understand intermolecular interactions and their roles in determining some crystal properties and the basis of chiral discrimination. Problems in the accurate estimation of the Coulombic interaction and hydrogen-bonding energy still persist. Nevertheless, through the molecular modeling approach, we have gained some insight into molecular interactions in certain crystalline chiral drugs and in some of their salts. With advances in theoretical methodologies for molecular modeling and in computational power, molecular simulation may soon become a valuable tool for the improved design and characterization of a variety of organic molecular crystals, including pharmaceutical solids.

ACKNOWLEDGMENTS The authors thank the following: Dr. William B. Gleason, Department of Laboratory Medicine and Pathology, University of Minnesota, for advice on crystal structure analysis of several compounds; Ms. Shuxuan Chao of 3M Pharmaceuticals for statistical analysis; the Pharmaceutical Research and Manufacturers of America Foundation for an Advanced Predoctoral Fellowship for Z. J. Li; and the Supercomputer Institute of the University of Minnesota for supporting our use of the Medicinal Chemistry/Supercomputing Institute VisualizationÐWorkshop Laboratory.

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