CRYSTAL GROWTH & DESIGN
Monte Carlo Calculations for the Solid-State Properties of Warfarin Sodium 2-Propanol Solvate Wick,*,†,‡
Collin D. Sami Karaborni⊥
J. Ilja
Siepmann,*,‡
Agam R.
Sheth,§,|
David J. W.
Grant,|
2006 VOL. 6, NO. 6 1318-1323
and
Departments of Chemistry and Chemical Engineering and Materials Science and Department of Pharmaceutics, UniVersity of Minnesota, Minneapolis, Minnesota 55455, and Pharmaceutical Research & DeVelopment, Merck & Company Inc., P.O. Box 4, WP78-304, West Point, PennsylVania 19486 ReceiVed October 13, 2005; ReVised Manuscript ReceiVed March 31, 2006
ABSTRACT: Monte Carlo simulations in the isotension-isothermal and Gibbs ensembles were carried out to investigate the structural properties of warfarin sodium 2-propanol and the ability of this compound to retain 2-propanol as a function of vapor pressure and in the presence of water. At full loading, the simulations yield a stable solvate structure that is in good agreement with the experimentally determined crystal structure. 2-Propanol is well-retained by the warfarin sodium host, and full loading is observed for partial pressures as low as 1% of its saturated vapor pressure, while water does not substantially replace 2-propanol from the crystalline interior even at 100% relative humidity. Radial distribution functions show strong binding of 2-propanol’s hydroxyl hydrogen with the 2-keto oxygen and the oxygen atom of the coumarin ring of warfarin and strong binding of 2-propanol’s oxygen to a single sodium ion. Thus, the spatial position of 2-propanol is highly confined, supporting the experimental observation that the 2:1 adduct of warfarin sodium and 2-propanol is a true solvate and not a clathrate. In contrast, water molecules would be less constrained and two water molecules would fit into 2-propanol’s binding site, but there is no channel for the transport of water or 2-propanol molecules. I. Introduction Warfarin sodium 2-propanol solvate (W), the 2-propanol solvate of the sodium salt of 4-hydroxy-3-(3-oxo-1-phenylbutyl)2H-1-benzopyran-2-one (see Chart 1), is a pharmaceutical lowdose blood thinner that inhibits Vitamin K dependent coagulation factors.1 The crystallization of W is performed in the presence of 2-propanol, in which warfarin sodium forms a 2:1 adduct with 2-propanol and the asymmetric unit contains one each of the R and S enantiomer of the warfarin anion (see Chart 1).2 The warfarin sodium 2-propanol adduct was originally described as a clathrate,3 which is considered to be a combination of two types of molecules, one being a relatively rigid host and the other a mobile guest, but confined to a “caged” region in all directions. Recently, the crystal structure of the warfarin sodium 2-propanol adduct was solved,4 and Sheth et al. demonstrated that 2-propanol is well localized in a specific solvate environment and not in a clathrate cage, as previously suggested. A solvate differs from a clathrate in that it contains a guest molecule with strong and specific coordination (usually attributed to hydrogen bonding) to the host molecule(s). This specific coordination was found to arise from the donation of a hydrogen bond from 2-propanol to the 2-keto and the coumarin ring’s oxygens of the warfarin anion and a close contact of the hydroxyl oxygen of 2-propanol with the sodium counterion.4 Although water could in principle exhibit a similar bonding pattern, it does not induce crystallization. Furthermore, high humidity levels have been shown to significantly affect the stability of W, causing deliquescence of the crystal.5,6 * To whom correspondence should be addressed. E-mail: collin.wick@ pnl.gov (C.D.W.);
[email protected] (J.I.S.). † Current address: Chemical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352. ‡ Departments of Chemistry and Chemical Engineering and Materials Science, University of Minnesota. § Current address: Pharmaceutical Research & Development, Merck & Company Inc., P.O. Box 4, WP78-304, West Point, PA 19486. | Department of Pharmaceutics, University of Minnesota. ⊥ Merck & Company Inc.
Chart 1. Structure Formula for Warfarin Sodium 2-Propanol Solvate
Particle-based simulations are an excellent tool for studying a variety of chemical and pharmaceutical systems at the microscopic level. Once a simulation has been validated through comparison of macroscopic properties with experiment, the trajectory of the simulation can be analyzed to provide a molecular-level understanding of the system of interest. For the case of W, molecular simulations can provide valuable insight into the mobility of 2-propanol and the strength and specificity of its interaction with warfarin sodium. Additionally, the simulations allow us to investigate whether there is a thermodynamic driving force and a kinetic pathway for replacing 2-propanol in warfarin sodium with water at high humidity levels. II. Models The united-atom version of the transferable potential for phase equilibria (TraPPE-UA) force field7-12 was used to model the warfarin anion and 2-propanol, and water and sodium were modeled through the TIP4P and OPLS force fields,13,14 respectively. The TraPPE-UA force field utilizes pseudo-atoms located at carbon centers to model alkyl groups, while treating all other atoms explicitly. The TraPPE-UA force field is fit to reproduce the vapor-liquid coexistence curves from near the triple to the critical point for a set of low-molecular-weight test compounds for which reliable experimental data are available. Utilizing this fitting strategy, the TraPPE-UA model has been shown to accurately model retention in chromatographic systems,15,16 water-octanol partitioning,17 the solubility of polymers,18 and solid-vapor phase equilibria, including the triple points of various molecules.19,20
10.1021/cg050542y CCC: $33.50 © 2006 American Chemical Society Published on Web 05/20/2006
Warfarin Sodium 2-Propanol Solvate
Crystal Growth & Design, Vol. 6, No. 6, 2006 1319
The TraPPE-UA, OPLS, and TIP4P force fields utilize Lennard-Jones (LJ) 12-6 potentials to account for repulsive and dispersive interactions and Coulombic potentials of partial charges for first-order electrostatic interactions:
uinter(rij) ) 4ij
[( ) ( ) ] σij rij
12
-
σij rij
6
+
qiqj 4π0rij
(1)
where rij, ij, σij, qi, and qj are the site-site separation, LJ well depth, LJ diameter, and partial charges on beads i and j, respectively. For unlike LJ interactions, the standard LorentzBerthelot combining rules were used.21 For the LJ interactions, a site-site-based spherical potential truncation at 14 Å was used together with analytical tail corrections for the energy and pressure.22,23 Electrostatic interactions were computed using the Ewald summation technique with tin-foil boundary conditions.23 The structures of the two enantiomeric warfarin anions were kept rigid, with bond lengths, bond angles, and torsional angles set to those found in the crystal structure of W.4 The sodium ion was treated as an independent site, and its motion was not constrained to a specific position relative to the warfarin anions. The 2-propanol molecule was modeled as semiflexible, with fixed bond lengths but with flexible bending and torsional degrees of freedom governed by harmonic bond bending and Fourier cosine series potentials, respectively,11 The TIP4P water model consists of a rigid four-site structure, with positive charges located at the hydrogen atoms, an LJ site located at the oxygen site, and a negative charge located along the bisector of the two oxygen-hydrogen bond vectors.13 Previous simulations have shown that explicit accounting of the quadrupole moment of benzene is important to stabilize the benzene I crystal structure with its T-shaped arrangement of neighboring molecules.20 In the TraPPE-UA model, the quadrupole moment is represented by three off-planar partial charges that do not carry LJ interactions.10 The lack of any repulsive interactions on benzene’s π-cloud charges and on the polar hydrogen in TIP4P water and TraPPE-UA 2-propanol leads to a problem for the simulation of W, because the hydrogen bond between these polar hydrogens and the arene ring would be unphysically strong. To remedy this problem, a purely repulsive interaction potential of the form
Urep ) Arij-B
Chart 2. Resonance Structures of the Warfarin Aniona
a The labels 2kO, 4hO, crO, and 3oO identify the 2-keto oxygen (exocyclic ester oxygen), the 4-hydroxy oxygen, the oxygen of the coumarin ring, and the 3-oxo oxygen, respectively.
Table 1. Oxygen-Sodium Coordination Distances and Selected Bond Lengths (in Å) Taken from the Experimental Crystal Structure4 param
R enantiomer
S enantiomer
r(2kO-Na) r(4hO-Na) r(crO-Na) r(3oO-Na) l(2kO-C2) l(C2-C3) l(C3-C4) l(C4-4hO)
2.25 2.30 3.98 2.61 1.22 1.42 1.40 1.27
2.23 2.23 3.59 2.51 1.24 1.40 1.40 1.25
and are close to the bond length in benzene,26 and (iii) the coordination distances to the nearest sodium cation are quite similar for 2kO and 4hO, it can be concluded that all three resonance structures contribute to the structure of the warfarin anion. Because of this, the TraPPE-UA LJ parameters for a ketone oxygen12 were used for both 2kO and 4hO, and the negative charge was evenly distributed between these two oxygen atoms. Actually, a short test run with the full negative charge added to the regular 4hO quickly led to substantial structural disorder. III. Simulation Details
(2)
was fit using the TraPPE-UA benzene-TIP4P water dimer. A choice of A/kB ) 4700 K and B ) 4 yields a binding energy of -16.31 kJ/mol and a hydrogen to benzene center-of-mass distance of 3.34 Å, in very good agreement with the ab initio (at the MP2 level) binding energy of -16.32 kJ/mol24 and the experimentally observed distance of 3.32 ( 0.07 Å.25 Special attention was given to the distribution of the negative charge of the warfarin anion. Although the 4-hydroxy oxygen is often shown to contain all of the negative charge (see Chart 1), a resonance structure and a resonance hybrid structure can be drawn that lead to a redistribution of the negative charge. These three structures for the warfarin anion are schematically shown in Chart 2 together with the labeling of the four oxygen atoms. To test whether the warfarin anion exists preferentially in one form, the coordination distances to the nearest sodium cation and the lengths of four bonds involved in the resonance structures are compared in Table 1. From the observations that (i) the carbon-oxygen bond lengths for both the 2kO and 4hO fall between values typical for the carbon-oxygen bond lengths of ketones and hydroxy anions,26 (ii) both carbon-carbon bond lengths fall between values typical for single or double bonds
Coupled-decoupled configurational-bias Monte Carlo (CBMC)8,27,28 simulations in the isotension-isothermal ensemble29,30 were carried out at T ) 173 K and p ) 1 atm to validate the force field and to compute the equilibrium crystal structure. Rigid-body translational and rotational moves were used to sample the corresponding degrees of freedom for the warfarin anion and 2-propanol, while only translation moves were applied to the positions of the sodium cations. Coupled-decoupled CBMC moves were performed to sample the vibrational degrees of freedom of the 2-propanol molecules. The volume and shape of the simulation box were allowed to fluctuate in contact with an external pressure bath. This has been achieved through Monte Carlo moves on the six nonzero elements of the H matrix that describe the three lattice vectors defining the simulation box.30 The simulation box can also be specified by the lengths of the three lattice vectors a, b, and c and the angles R (between b and c), β (between a and c), and γ (between a and b). While the experimental crystal structure of W is monoclinic (R ) γ ) 90°), these angles were not constrained throughout the Monte Carlo simulations. To investigate the strength of the interactions of 2-propanol and water in warfarin sodium, Monte Carlo simulations in the constant-pressure Gibbs ensemble were carried out at T ) 298.15 K and for varying external pressures to obtain adsorption isotherms. The Gibbs ensemble simulations utilized two periodic simulation boxes without an explicit interface but with thermodynamic contact. Use of the Gibbs ensemble approach offers the advantage that it allows for changes in the volume and shape of the crystalline phase in response to changes of the gas
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Wick et al.
Table 2. Crystal Data for W at T ) 173 Ka
a
param
exptl4
simulation
a/Å b/Å c/Å R/deg β /deg γ/deg V/Å3
15.393(2) 11.2392(17) 22.124(3) 90.0 107.424(3) 90.0 3651.9(9)
15.727(16) 11.469(8) 21.481(34) 89.99(6) 107.91(10) 90.01(12) 3686.8(8)
Numbers in parentheses give the uncertainties in the last digit(s).
pressure, whereas the more common grand canonical Monte Carlo approach would require constraining the cell parameters throughout the simulation. CBMC particle swap moves27,28 of 2-propanol and water were performed in order to equilibrate their chemical potential between the solid and vapor phases. It should be emphasized here that the Gibbs ensemble simulations probe the adsorption isotherm under thermodynamic control; i.e., the particle swap moves allow guest molecules to jump directly from the crystalline interior to the vapor phase and vice versa without the need for an explicit pathway through which guest particles could diffuse. Thus, although kinetic barriers are ignored, the adsorption isotherms obtained from the Gibbs ensemble simulations allow us to probe the strength of the interactions of warfarin sodium with 2-propanol and water. The isotension-isothermal and Gibbs ensemble simulations used 96 warfarin anions and 96 sodium cations, and the initial dimensions of the solid-phase simulation boxes correspond to two, three, and two unit cells of the experimental W structure in the a, b, and c directions, respectively. The isotension-isothermal simulations were carried out at full loading: i.e., with 48 2-propanol molecules. A total of 64 2-propanol and/or 128 water molecules were used for the Gibbs ensemble simulations, and all guest molecules were allowed to swap between the solid and vapor phases. For the calculation of the adsorption isotherms, the simulations were run at varying external pressures below the saturated vapor pressure of 4.0 kPa for the TraPPE-UA 2-propanol model and 4.7 kPa for the TIP4P water model. All simulations were equilibrated for a minimum of 10 000 Monte Carlo cycles (1 cycle consists of N Monte Carlo moves, where N is the total number of molecules in the system), and production runs of 100 000 MC cycles were performed for each system.
Figure 1. Overlay of the ensemble-averaged atomic positions of W predicted by the simulations (shown as solid, small spheres) and the experimentally determined crystal structure (shown as translucent, large spheres).
IV. Results and Discussion A. Crystal Structure. The cell parameters for W predicted from the isotension-isothermal simulations at T ) 173 K are compared to their experimental counterparts4 in Table 2. The simulated system maintains a monoclinic structure throughout the run; i.e., the angles R and γ show only the usual thermal fluctuations around their equilibrium value of 90°. The calculated value for β is 0.5° too large. The deviations for the cell lengths are somewhat larger, with an overprediction of the a and b parameters by about 2% and an underprediction of the c parameter by 3%: i.e., the simulated system shows an expansion of the molecular sheets that are found in the ab plane and a contraction in the c direction that is governed by van der Waals contacts.4 Overall, the crystal volume is well reproduced with an overprediction by about 1%. These results show good agreement between the experimental and calculated crystal cell parameters, especially considering the difficulties often encountered in modeling ionic systems with empirical pair potentials.23 Figure 1 shows a graphic comparison of the ensembleaveraged structure for W and its experimental counterpart, both at T ) 173 K. It is evident that not only the cell parameters but also the placement of the molecules in the unit cell are well reproduced by the simulations. To provide a more quantitative evaluation of the crystal structure obtained from the simulation, powder patterns were calculated for the experimental and simulated crystal structures. As is evident from Figure 2, if the ensemble-averaged simulation
Figure 2. Comparison of the powder patterns for W generated from the experimental crystal structure (black line), determined directly from the simulation data (red line, shifted upward by 50 units), and obtained using the fractional coordinates from the simulation but scaled with the experimental cell parameters (blue line, shifted upward by 100 units). The bottom part shows the intensity differences (not shifted) between the (direct or scaled) simulation data and the experimental data.
structure is used directly, then the differences between the two powder patterns are rather significant. However, it should be noted that the larger differences arise from displacements in peak position and not changes in peak intensities: i.e., the larger deviations are paired with deviations of similar magnitude but opposite sign. The regularity of these displacements points to the small changes in the cell parameters as the main cause for these differences. When the powder pattern is calculated using the ensemble-averaged fractional coordinates from the simulations in conjunction with the experimental cell parameters, then the differences are reduced by an order of magnitude and most of the differences are now due to changes in intensity and no longer to changes in peak position. Thus, the relative packing of the molecules in the unit cell is very well reproduced by the simulations. B. Adsorption Isotherms. The adsorption isotherms for 2-propanol and water obtained from the Gibbs ensemble simulations are shown in Figure 3. It needs to be emphasized
Warfarin Sodium 2-Propanol Solvate
Figure 3. Adsorption isotherms for 2-propanol (O) and water (0) in warfarin sodium as a function of fractional pressure. A Langmuir fit is applied to the 2-propanol results (s). One additional state point is shown (b, 9) for the competitive adsorption of 2-propanol at 0.6% of its saturated vapor pressure and water at 100% relative humidity.
again that these Gibbs ensemble Monte Carlo simulations probe the thermodynamic strength of the interactions but not the kinetics of the adsorption/desorption processes. That is, in these Monte Carlo simulations a guest molecule can directly enter or leave any site in the host framework without the need for a diffusion channel. The adsorption isotherm for 2-propanol shows Langmuir-type behavior: i.e., pointing to specific adsorption sites with negligible interference between adsorbates at neighboring adsorption sites. There are four adsorption sites per unit cell of warfarin sodium for 2-propanol, and full loading is reached at about 1% of 2-propanol’s saturated vapor pressure. This is an indication of the very favorable interactions of 2-propanol with warfarin sodium and might explain why warfarin sodium has been known to crystallize only as the 2-propanol solvate. The adsorption isotherm for water is shifted to much higher relative saturation pressures, and full loading (i.e., a plateau) is not observed even at 100% humidity. Thus, the interaction of water with the warfarin sodium host are thermodynamically much less favorable than those for 2-propanol. On the side, it should be noted that at 100% humidity more than four water molecules are adsorbed per warfarin sodium unit cell. This is a reflection of the much smaller molar volume of water. An additional simulation was carried out to investigate the competitive adsorption of 2-propanol at a partial vapor pressure close to the OSHA exposure limit34 and 100% humidity. As can be seen in Figure 3, under thermodynamic control high humidity has only a limited influence on the amount of adsorbed 2-propanol molecules. In fact, only about 5% fewer 2-propanol molecules are adsorbed for this gas mixture, whereas the amount of adsorbed water is about a factor of 20 less than is observed for neat water at 100% humidity. Again, the competitive adsorption indicates that the interactions of 2-propanol with warfarin sodium are much more favorable than those for water. Previous experimental studies have pointed to the exchange as well as coexistence of 2-propanol and water in the crystal lattice of warfarin sodium.3,5,35 However, a more recent investigation indicates that such an exchange cannot occur; water can neither find channels to enter the crystal lattice nor does it replace 2-propanol.6 Below the critical relative humidity (RH0) of W, mimimal uptake of water takes place due to surface adsorption, whereas above RH0 deliquesence occurs.6 Our
Crystal Growth & Design, Vol. 6, No. 6, 2006 1321
Figure 4. Radial pair distribution functions for the 2-propanol hydrogen and the four oxygens of the warfarin anion: (s) H-crO; (‚‚‚) H-2kO; (- - -) H-4hO; (- ‚ -) H-3oO.
simulation study also does not support the presence of a significant amount of water in the crystalline warfarin sodium host. As shown by Sheth et al.,6 deliquesence of W begins at the surface. However, the infinitely periodic model system mimics only the interior of crystalline W and does not contain any surfaces. As a result, deliquescence cannot be investigated here. C. Structural Analysis of the Adsorption Sites. To address the question of whether the 2-propanol molecules occupy a solvate-type or clathrate-type environment, the structure of the adsorption sites was analyzed for the Gibbs ensemble simulation at 1% of 2-propanol’s saturated vapor pressure (full loading). Figure 4 shows the radial distribution functions (RDFs) for the hydrogen atom of 2-propanol with the four distinct oxygen atoms of the warfarin anion. These RDFs support the notion that the 2-propanol hydrogen possesses a strong interaction with the two ester oxygens (2kO and crO) of the coumarin ring. The peak with 2kO is stronger and is located at about 1.8 Å, the usual distance for a strong hydrogen bond,36 whereas the peak with crO is somewhat weaker and is shifted to about 2.5 Å. Hydrogen bonding to the 2kO and crO is also found in the experimental crystal structure, but the proximity order is reversed with values of 2.3 and 2.6 Å for crO and 2kO, respectively.4 4hO and 3oO are not involved in the binding of 2-propanol but are coordinated to sodium cations (see Table 1). In addition to 2-propanol’s involvement as a hydrogen-bond donor, its partially negative oxygen atom is strongly coordinated to a nearest-neighbor sodium cation at a distance of about 2.4 Å and is weakly coordinated to a second sodium cation at about 3.9 Å, as can be seen from two sharp peaks in the oxygensodium RDF and two well-defined steps in the corresponding number integral (see Figure 5). Again, the simulation data are in good agreement with the experimental crystal structure, which shows oxygen-sodium distances of 2.4 and 4.5 Å.4 The number integral for 2-propanol pairs indicates that 2-propanol molecules are separated by at least 7 Å. This large separation between the adsorption sites explains why there are negligible interactions between adsorbates and a Langmuir-type adsorption isotherm is found. Overall, the structural data demonstrate that all 2-propanol molecules interact with the host framework through hydrogen bonding to 2kO and crO of the warfarin anion and through a
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hydrogen-bonding and two dipole-ion interactions. Overall, the agreement with the experimental crystal structure is good, but the simulations predict slightly different unit cell lengths and a switch in the proximity to the two hydrogen-bond acceptors of the warfarin anion. Adsorption isotherms were computed for 2-propanol and water and clearly demonstrate that 2-propanol has interactions with the warfarin sodium host framework more favorable than those found for water. The simulations indicate that channels are not present in the crystal lattice of W and that, even under thermodynamic control, water molecules cannot replace 2-propanol molecules in W.
Figure 5. Radial pair distribution function for 2-propanol oxygen with (s) sodium cations, (- - -) its number integral, and (‚‚‚) the oxygenoxygen number integral for 2-propanol pairs.
Figure 6. Contour surface containing the 2-propanol oxygen with 99% probability (blue) shown together with the nearest warfarin and sodium ions (purple).
dipole-ion interaction with two sodium cations. Figure 6 depicts the 99% probability contour for the 2-propanol oxygen atom. Its high localization gives conclusive evidence that, for these simulations, 2-propanol is in a solvate environment. In contrast, if water molecules would be able to enter the warfarin sodium framework as in the Gibbs ensemble simulations, then their location is less restrained (as observed from broadening of the first peak in the guest-host hydrogen-oxygen RDFs and guest oxygen-sodium RDFs) and sometimes two water molecules occupy the same adsorption site (as can be seen from the adsorption isotherm). Thus, this mobility points to a clathrate environment for adsorbed water molecules. However, it should be noted that these clathrate cages are well separated and that there is no pathway for water molecules (and, of course, also 2-propanol molecules) to diffuse through the crystalline warfarin sodium host. Thus, uptake of water can only occur at the crystal surface, in agreement with the experimental observation that deliquesence is surface-mediated.6 V. Conclusions Monte Carlo simulations for W in the isotension-isothermal ensemble yield a monoclinic crystal with the 2-propanol molecule being in a solvate environment characterized by two
Acknowledgment. Financial support from the National Science Foundation (Grant No. CTS-0138393), a DOE Computational Science Graduate Fellowship (C.D.W.), and an NSFMPS Distinguished International Postdoctoral Fellowship (C.D.W.) is gratefully acknowledged. Part of the computer resources were provided by the Minnesota Supercomputing Institute. References (1) Majerus, P. W.; Broze, G. J.; Miletich, J. P.; Tollefsen, D. M. Goddman and Gilman’s The Pharmacological Basis of Therapeutics, 9th ed.; Hardman, J. G., Limbird, L. E., Eds.; McGraw-Hill: New York, 1996. (2) Shroeder, C. H.; Link, K. P. U.S. Patent 3 077 481, 1963. (3) Haleblian, J. K. J. Pharm. Sci. 1975, 64, 1269-1288. (4) Sheth, A. R.; Young, V. G.; Grant, D. J. W. Acta Crystallogr., Sect. E 2002, 58, m197-m199. (5) Gao, D.; Maurin, M. B. AAPS PharmSci 2001, 3(1), article 3 (8 pages). (6) Sheth, A. R.; Brennessel, W. W.; Young, V. G.; Muller, F. X.; Grant, D. J. W. J. Pharm. Sci. 2004, 93, 2669-2680. (7) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 25692577. (8) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1999, 103, 45084517. (9) Wick, C. D.; Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 2000, 104, 8008-8016. (10) Wick, C. D.; Siepmann, J. I.; Schure, M. R. J. Chromatogr. A 2002, 954, 181-190. (11) Chen, B.; Potoff, J. J.; Siepmann, J. I. J. Phys. Chem. B 2001, 105, 3093-3104. (12) Stubbs, J. M.; Potoff, J. J.; Siepmann, J. I. J. Phys. Chem. B 2004, 108, 17596-17605. (13) Jorgensen, W. L.; Chandrasekhar, J. D.; Madura, R. W.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926-935. (14) Kaminski, G. A.; Friesner, R. A.; Tirado-Rives, J.; Jorgensen, W. L. J. Phys. Chem. B 2001, 105, 6474-6487. (15) Wick, C. D.; Siepmann, J. I.; Schure, M. R. Anal. Chem. 2002, 74, 37-44. (16) Wick, C. D.; Siepmann, J. I.; Schure, M. R. Anal. Chem. 2004, 76, 2886-2892. (17) Chen, B.; Siepmann, J. I. J. Phys. Chem. B 2006, 110, 3555-3563. (18) Wick, C. D.; Siepmann, J. I.; Theodorou, D. N. J. Am. Chem. Soc. 2005, 127, 12338-12342. (19) Chen, B.; Siepmann, J. I.; Klein, M. L. J. Phys. Chem. B 2001, 105, 9840-9848. (20) Zhao, X. Z.; Chen, B.; Karaborni, S.; Siepmann, J. I. J. Phys. Chem. B 2005, 109, 5368-5374. (21) Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A. Intermolecular Forces; Oxford University Press: Oxford, U.K., 1987; p 519. (22) Wood, W. W.; Parker, F. R. J. Chem. Phys. 1955, 27, 720-733. (23) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, U.K., 1987. (24) Feller, D. J. Phys. Chem. A 1999, 103, 7558-7561. (25) Stoicheff, B. P. Can. J. Phys. 1954, 32, 339. (26) CRC Handbook of Chemistry and Physics, 72nd ed.; Lide, D. R. Ed.; CRC Press: Boca Raton, FL, 1991; pp 9-22. (27) Siepmann, J. I.; Frenkel, D. Mol. Phys. 1992, 75, 59-70. (28) Frenkel, D.; Mooij, G. C. A. M.; Smit, B. J. Phys.: Condens. Matter 1992, 4, 3053-3076. (29) Parrinello, M.; Rahman, A. Phys. ReV. Lett. 1980, 45, 1196-1199.
Warfarin Sodium 2-Propanol Solvate (30) Yashonath, S.; Rao, C. N. R. Mol. Phys. 1985, 54, 245-251. (31) Panagiotopoulos, A. Z. Mol. Phys. 1987, 61, 813-826. (32) Panagiotopoulos, A. Z.; Quirke, N.; Stapleton, M.; Tildesley, D. J. Mol. Phys. 1988, 63, 527-545. (33) Smit, B.; de Smedt, P.; Frenkel, D. Mol. Phys. 1989, 68, 931-950. (34) U.S. Department of Labor Occupational Safety & Health Administration Standards (http://www.osha.gov).
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CG050542Y
