This paper is published as part of a CrystEngComm themed issue on:
Computational contributions to crystal engineering Guest edited by Angelo Gavezzotti Università di Milano
Published in issue 4, 2008 of CrystEngComm
Images reproduced by permission of Peter Wood (left) and Mark Spackman (right)
Papers published in this issue include: Analysis of the compression of molecular crystal structures using Hirshfeld surfaces Peter A. Wood, Joshua J. McKinnon, Simon Parsons, Elna Pidcock and Mark A. Spackman, CrystEngComm, 2008, DOI: 10.1039/b715494a
Electrostatic potentials mapped on Hirshfeld surfaces provide direct insight into intermolecular interactions in crystals Mark A. Spackman, Joshua J. McKinnon and Dylan Jayatilaka, CrystEngComm, 2008, DOI: 10.1039/b715227b
Structure and energy in organic crystals with two molecules in the asymmetric unit: causality or chance? Angelo Gavezzotti, CrystEngComm, 2008, DOI: 10.1039/b714349d
Discovery of three polymorphs of 7-fluoroisatin reveals challenges in using computational crystal structure prediction as a complement to experimental screening Sharmarke Mohamed, Sarah A. Barnett, Derek A. Tocher, Sarah L. Price, Kenneth Shankland and Charlotte K. Leech, CrystEngComm, 2008, DOI: 10.1039/b714566g
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PAPER
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An optimized force field for crystalline phases of resorcinol Jittima Chatchawalsaisin,†a John Kendrick,a Sigrid C. Tubleb and Jamshed Anwar*a Received 31st October 2007, Accepted 12th February 2008 First published as an Advance Article on the web 10th March 2008 DOI: 10.1039/b716868n The two known crystalline phases of resorcinol and their phase transitions are of considerable interest. The crystals exhibit pyro- and piezo-electricity and, remarkably, the higher temperature b phase is the denser phase. Furthermore, crystals of the a phase, by virtue of having a polar axis, have played a crucial role in investigating fundamental issues of crystal growth. We report an optimized force field for the molecular simulation of crystalline phases of resorcinol. The hydroxyl groups of the resorcinol molecule have a torsional degree of freedom and the molecule adopts a different conformation in each of the two phases of resorcinol. The torsional barrier, therefore, was considered to be critical and has been characterized using ab initio methods. Although the atomic partial charges showed some dependence on the molecular conformation, a single set of partial charges was found to be sufficient in describing the electrostatic potential for all conformations. The parameters for the van der Waals interactions were optimized using sensitivity analysis. The proposed force field reproduces not only the static structures but also the stability of the crystalline phases in extended molecular dynamics simulations.
Introduction Resorcinol (1,3-benzenediol) (Fig. 1) exhibits two crystalline phases, a and b, that continue to attract significant interest. The a-phase of resorcinol, in particular, has played a crucial role as a model for investigating fundamental issues in crystal growth. Crystals of a-resorcinol exhibit a polar axis, growth along which has been observed to be asymmetric in aqueous solutions.1,2 This observation has served as a basis for disentangling the relative contributions of the intrinsic crystal structure and the various external factors (such as the effects of solvent) that determine the morphology of a crystal.3,4 The asymmetric growth was attributed largely to solvent effects on the basis that, to a first approximation, the rate of growth could be considered to be proportional to the layer attachment energy and that this would be identical for the two opposite faces terminating the polar axis. Recently, it has been reported that the asymmetric growth along the polar axis of a-resorcinol also occurs in the vapour phase,5 with the implication that our understanding of how solvents affect crystal growth of resorcinol, particularly along the polar axis, needs to be reviewed. The resorcinol crystalline phases also exhibit other interesting properties including pyro- and piezo-electricity.6 Furthermore, remarkably, the higher temperature b phase is the denser phase.6,7 The a–b transformation is reconstructive and involves a change in the hydrogen bonding network in going from one phase to another,7 and hence could serve as a model for reconstructive transformations in
a Computational Biophysics, Institution of Pharmaceutical Innovation, University of Bradford, Bradford, West Yorkshire, UK, BD7 1DP. E-mail:
[email protected] b Cardiac Surgery Research Group, Cardiac and Thoracic Surgical Unit, Flinders Medical Centre, Bedford Park, SA 5042, Australia † Permanent Address: Department of Industrial Pharmacy, Faculty of Pharmaceutical Sciences, Chulalongkorn University, Bangkok 10330, Thailand.
This journal is ª The Royal Society of Chemistry 2008
more complex systems such drug molecules. The a–b transformation can be induced by both temperature and pressure.8 At ambient temperature and pressure the a-phase is the stable phase. The a-phase transforms to the b-phase above about 347 K at ambient pressure,9 or at or above a pressure of 5 kbar at ambient temperature.8 At a pressure of 40 kbar the crystalline phases become amorphous.10 The crystal structures of the a and b phase are shown in Fig. 2. Both forms belong to the orthorhombic space group Pna21 and contain four molecules in the unit cell. The respective lattice ˚, b ¼ parameters at room temperature are Z ¼ 4, a ¼ 10.530 A ÿ3 11 ˚ ˚ 9.530 A, c ¼ 5.600 A, r ¼ 1.278 g cm (a phase), and Z ¼ 4, ˚ , b ¼ 12.606 A ˚ , c ¼ 5.511 A ˚ , r ¼ 1.327 g cmÿ3 a ¼ 7.934 A (b phase).12 A key difference between the two forms is in the molecular conformation adopted by the resorcinol molecule. In a-resorcinol both of the hydroxyl groups on the molecule are pointing downwards, whilst for b-resorcinol one of the hydroxyl
Fig. 1 Conformational isomers of resorcinol. Conformation (a) occurs in a-resorcinol while conformation (c) occurs in b-resorcinol.
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area of crystal engineering, and indeed applications include studies of the crystal growth of resorcinol.13–16 To date it has not been possible to represent the two known crystalline phases of resorcinol using a single transferable force field, which has prevented the exploration of the various possible solid phases of resorcinol and simulations of phase transitions between the phases. Most simulation studies have focused on the a-phase13–16 with only one study on the b-phase.17 The force field developed and employed in the latter assumed the resorcinol molecule to be rigid (in the conformation appropriate for the b-phase), hence restricting this force field just to the b-phase. We report here an optimized force field for the two crystalline phases of resorcinol. The development of the parameters comprising the force field is not trivial, as the resorcinol molecule and its crystalline phases exhibit some uncommon features that include a conformational change in the molecule on going from one phase to another and the higher temperature phase being more dense. The conformational change involves rotation of the hydroxyl groups, which suggests the need to accurately characterize this rotational barrier. The conformational change also implies that the partial charges on the atomic sites (which characterize the electrostatic interactions) could show significant dependence on conformation. The choice of the form of the van der Waals potential could also be critical as the a–b transformation can be induced by pressure. High pressure causes increased sampling of the repulsive part of the potential, in view of which the softer and theoretically more acceptable exponential (Buckingham) form might be preferable. The optimization of the van der Waals parameters has been carried out using the method of sensitivity analysis.
Methods Determination of the H–O–C–C torsional barrier
Fig. 2 Crystal structures of a(11) and b(12) forms of resorcinol projected in the b–c (top), a–c (middle) and a–b (bottom) planes.
groups points upwards while the other points downwards (Fig. 1). The molecular packing in a-resorcinol is an open arrangement which is enforced by the directional forces of the hydrogen bonds. In contrast, the molecular packing in the denser b phase is much more compact with the molecules lying more parallel to each other akin to that in hydrocarbons. In the b phase the hydroxyl bond angles are 97 and 123 , i.e. significantly distorted from the expected tetrahedral value; for the a phase the corresponding angles are 102 and 106 . On going from the a to the b phase, it appears that the van der Waals and polarization energies are increased at the expense of strain energy. Whilst experimental methods such as diffraction offer atomic resolution, such data typically yield a time and space averaged picture and usually only for periodic systems such as crystals. An alternative approach is molecular simulation, which is proving to be a powerful tool for investigating molecular level processes. Molecular simulations have been employed extensively in the 438 | CrystEngComm, 2008, 10, 437–445
The H–O–C–C torsional barrier was determined from the potential energy surface calculated using density functional theory (B3LYP) with a triple zeta cc-pVTZ basis set18 within Gaussian98.19 We carried out a 2-d search in which a series of structures were generated with the two H–O–C–C dihedral angles being rotated in increments of 45 . For each calculation, the dihedral angles were held rigid while the rest of the atoms in the molecule were allowed to relax. In defining the molecular mechanics force constant for the H–O–C–C dihedral angle we excluded 1–4 non-bonded interactions for the atoms involved. Determination of partial charges As the resorcinol molecule involves a conformational change involving rotation of the hydroxyl arms, the atomic partial charges are likely to depend on the conformation. The ab initio torsion scan (detailed above) revealed that there are four distinct low energy conformations (Fig. 1): where both hydroxyls are pointing up, both pointing down, and two (degenerate) conformations in which one hydroxyl points up while the other points down. We determined the atomic partial charges for each of these individual conformations from the wavefunction using the electrostatic potential fitting method20 with a 6-31G** basis set and the B3LYP density functional. In addition to developing atom-centred charges which were specific to each conformation, This journal is ª The Royal Society of Chemistry 2008
we explored the ability of an atom-centred charge model to represent the electrostatic potential of all of the conformers. Towards this end the fitting was extended so that a single set of charges was determined which minimized the least squares deviation of the point charge model and the quantum-mechanical electrostatic potential for all four minimum energy conformations simultaneously. The conformations were weighted equally as their energy differences are small. Using an exponential potential form for the non-bonded interactions coupled with FIT21–23 and W9924 parameters we explored the influence of the partial charges in reproducing each of the crystalline phases by employing charges that were appropriate for the molecular conformation present in the particular phase. The influence of the charges was not significant to warrant a force field with an explicit dependency of the partial charges on the conformation. Consequently, we proceeded by using the single set of partial charges determined simultaneously for the four lowest energy states of the resorcinol molecule. Assessment of force fields Various force fields, that included AMBER,25 CHARMM,26 Gavezzotti and Filippini’s (GF)27 chargeless force-field, and FIT + W9921–24 non-bonded parameters (O from ref. 21, C from ref. 24, H bonded to O from ref. 22, aromatic H from ref. 23) coupled with valence terms from AMBER, were assessed with respect to their ability to reproduce the crystal structures of the two phases of resorcinol. The lattice optimizations for CHARMM and GF force fields were carried out earlier28 using the code GULP29 with Ewald summation and a real space cutoff of 1.0 nm for both the van der Waals and the electrostatic interactions. For AMBER and FIT + W99 force-fields, we investigated the stability of the two phases of resorcinol in a molecular dynamics simulation in a NPT ensemble with Parrinello– Rahman boundary conditions30,31 (which allow the individual cell lengths and angles to vary independently according to the stress within the cell and the set external (ambient) pressure) and at 10 K over 30 ps using the code GROMACS.32 The electrostatic interactions were calculated using Particle-Mesh Ewald with a precision of 1 10ÿ5. The cutoffs for the real space Ewald and the van der Waals interactions were both 1.2 nm. All bonds were constrained using the SHAKE algorithm which allowed a timestep of 0.002 ps. The molecular dynamics simulation at 10 K is akin to potential energy minimization as the thermal energy is very low. The simulations converged rapidly and the equilibrium lattice parameters were averaged over the 10–30 ps period.
The FIT + W9921–24 parameters were taken as a starting point, which were then optimized. We optimized the parameters using sensitivity analysis wherein the influence of a 5% change in each of the potential parameters on the lattice parameters of the two phases was determined in molecular dynamics simulations at 10 K as detailed above. This enabled the identification of the critical potential parameters, that is, those that had the most significant effect in reproducing the lattice parameters of the crystalline phases. The identified critical parameters were then varied in small increments. The set of parameters that best reproduced the two crystalline phases were selected for the definitive force-field. Molecular dynamics simulations of a- and b-resorcinol The quality of the optimized potential parameters was verified in extended molecular dynamics simulations of the a and the b phase at 298 and 360 K, respectively, both at ambient pressure (0.001 kbar). The chosen temperatures represent conditions where the respective phases are known to be stable. The simulation box contained 180 molecules (3 3 5 unit cells) for the a-phase, and 288 molecules (4 3 6 unit cells) for the b phase. The molecular dynamics simulations were carried out in an NPT ensemble with Parrinello–Rahman boundary conditions30,31 using the code GROMACS.32 For the electrostatic interactions we employed Particle-Mesh Ewald with a precision of 1 10ÿ5. The cutoffs for the real space Ewald and the van der Waals interactions were both 1.2 nm. All bonds were constrained using the SHAKE algorithm which allowed a timestep of 0.002 ps. Simulations were carried out for 500 ps with averages being collected for the 200–500 ps period.
Results and discussion The potential energy surface (PES) for the rotation of the hydroxyl groups is shown in Fig. 3, which reveals four energy minima corresponding to angles of 0/0 , 0/180 , 180/0 , and 180/180 for the two H–O–C–C dihedral angles f1 and f2, respectively. The lowest energy structure amongst these is the
Optimization of non-bonded parameters None of the force fields tested were able to reproduce both of the crystalline phases of resorcinol. In deriving our force field we opted for the exponential form of the non-bonded potential, that is, Uij ¼ Aexp(ÿBr) ÿ Crÿ6, where A, B and C are the parameters that characterize the interaction between atoms i and j, and r is the separation distance. The repulsive component of the exponential form has a stronger theoretical basis and is somewhat softer than the Lennard Jones repulsive wall and is therefore more appropriate for simulation of crystalline phases. This journal is ª The Royal Society of Chemistry 2008
Fig. 3 Potential energy surface of resorcinol as a function of the hydroxyl group dihedral angles f1 and f2. The energy scale in the legend is in kJ molÿ1, with the zero of energy being defined by the lowest energy structure, the b-resorcinol conformation (Fig. 1c).
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0/180 conformation i.e. the b-resorcinol conformation (Fig. 1c). Conformations where the hydroxyl arms are out of the plane appear to be unstable. These finding indicate that the potential energy surface of a given hydroxyl group is dependent on the dihedral angle of the other hydroxyl group, i.e. there is some correlation. The potential energy associated with a torsion scan shows a variation of between 5 and 25% depending on the value of the second torsion angle, the highest variation being at the minimum where one of the angles is 180 . However, the overall form of the energy surface i.e. two maxima and two minima, remains unchanged. In view of this, for the purposes of deriving a torsion potential, the two torsions were considered independent. The barrier to rotation was found to be 18.19 kJ molÿ1, with the highest energy corresponding to the conformation where the hydroxyl hydrogen is in an out-of-plane geometry. It appears that the planar geometry is stabilised by the nonbonding electrons of the oxygen being in resonance with the aromatic ring. Partitioning the barrier height value amongst the two torsional terms that characterize the rotation about the Table 1 Atomic partial charges for the three distinct conformational isomers of resorcinol and the charges fitted simultaneously to all four conformations. The partial charges for the individual conformers were derived by fitting to their electrostatic potential. The charges fitted to all four conformers are the result of a least squares fit to the electrostatic potential to all conformers simultaneously Atomic partial charge / electrons Atom Conformer Conformer Conformer Fitted to all Atoma typeb (a) (b) (c) four conformers 1 (H) 2 (C) 3 (C) 4 (C) 5 (C) 6 (C) 7 (C) 8 (O) 9 (O) 10 (H) 11 (H) 12 (H) 13 (H) 14 (H)
HA CA CA CA CA CA CA OH OH HO HO HA HA HA
0.213 ÿ0.394 0.467 ÿ0.434 0.043 ÿ0.434 0.467 ÿ0.594 ÿ0.594 0.420 0.420 0.155 0.155 0.110
0.182 ÿ0.640 0.553 ÿ0.334 ÿ0.082 ÿ0.334 0.553 ÿ0.609 ÿ0.609 0.423 0.423 0.172 0.172 0.130
0.200 ÿ0.509 0.513 ÿ0.420 ÿ0.025 ÿ0.328 0.472 ÿ0.582 ÿ0.577 0.406 0.407 0.154 0.169 0.120
a
The atom numbers refer to those given in Fig. 1. corresponding to the atom indices given in Fig. 1.
0.197 ÿ0.473 0.444 ÿ0.346 ÿ0.046 ÿ0.346 0.444 ÿ0.523 ÿ0.523 0.366 0.366 0.159 0.159 0.122 b
Atom types
C–O bond, e.g. torsions 2–3–8–10 and 4–3–8–10 (where the indices are atom numbers), yields a force constant of k ¼ 4.55 kJ molÿ1 as defined by the torsional form Udihed ¼ k[1 + cos(nf ÿ 180)], where f is the dihedral angle and n the periodicity (¼2). We exclude the 1–4 interactions of the atoms involved in these torsions and assume that other higher order interactions are insignificant. The atomic partial charges determined for each of the distinct resorcinol conformations and the charges fitted simultaneously to all four conformations are given Table 1. It is clear that the partial charges do vary with conformation. The overall variation is however not too marked with the exception of the carbon atom (atom 2) that lies between the two OH groups, which appears to be particularly sensitive showing a change of 0.25 electrons on changing from conformation (a) to (b). Since the two crystalline phases of resorcinol contain different conformations of the resorcinol molecules, we investigated whether the conformation-specific atomic partial charges were able to reproduce each of the two crystal phases. Here we employed W99 + FIT21–24 parameters for the non-bonded interactions. The deviation between the calculated and experimental lattice parameters, shown in Table 2, was found to be relatively large, being in excess of 5% for the b-axis of both phases. These data suggest that whilst the conformational dependence of the charges could be an issue, the actual gain in adopting such an approach is very little. This was probably because the carbon atom (atom 2) that showed the greatest variation in partial charge as a function of conformation is somewhat embedded, and hence does not much influence the molecular packing. For comparison, Table 2 also presents lattice deviations obtained with a single set of conformation-independent charges. These charges reproduce the a phase reasonably well but for the b phase yield a deviation of about 6.5% in the b-axis. Clearly, the single set of conformation-independent charges is hardly any worse than the conformation-specific charges. Consequently, we proceeded with the single set of fixed partial charges that were independent of the molecular conformation. The evaluation of the various force fields in reproducing the experimental structures of a and b resorcinol are summarized in Table 3, which details the percentage deviation of the calculated lattice parameters from the experimental values. For these calculations we used the partial charges that had been fitted simultaneously to all four conformations of resorcinol. For comparison we also present the published results of Day
Table 2 Optimization of lattice parameters using conformation-specific atomic partial charges for resorcinol. Percentage deviations of the calculated lattice parameters from the experimental values are given in the parentheses a form
Experimentala FIT + W9921–24 with partial charges specific for the particular conformation present in the phase FIT + W9921–24 with single set of partial charges fitted to all four conformations simultaneously
b form
˚ a/A
˚ b/A
˚ c/A
˚ a/A
˚ b/A
˚ c/A
10.530 10.70 (1.58)
9.530 10.01 (5.02)
5.600 5.63 (0.55)
7.811 7.86 (0.69)
12.615 13.30 (5.42)
5.427 5.42 (ÿ0.10)
10.69 (1.54)
9.70 (1.81)
5.78 (3.25)
8.01 (2.56)
13.44 (6.50)
5.33 (ÿ1.88)
a
The experimental lattice parameters of the a phase are for a room temperature structure whilst those for the b phase correspond to the structure determined at 4 K.
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Table 3 Comparison of various force fields in their ability to reproduce crystal structures of a and b resorcinol. Percentage deviations of the calculated lattice parameters from the experimental values are given in parentheses. The atomic partial charges employed were those derived by fitting to all four resorcinol conformations simultaneously (see Table 1) a form
b form
Force field
˚ a/A
˚ b/A
˚ c/A
˚ a/A
˚ b/A
˚ c/A
Experimental11,12c FIT + DMA17 CHARMM26 GF27 ab AMBER25 FIT + W9921–24 a
10.530 — 10.71 (1.6) 10.00 (ÿ5.0) 10.59 (0.55) 10.69 (1.54)
9.530 — 9.15 10.50 9.14 9.70
5.600 — 5.71 (1.9) 5.20 (ÿ8.1) 5.77 (3.11) 5.78 (3.25)
7.811 7.78 (ÿ0.4) 9.08 (16.2) 8.20 (5.0) 8.99 (15.07) 8.01 (2.56)
12.615 12.87 (2.0) 12.65 (0.3) 12.00 (ÿ4.9) 12.88 (2.09) 13.44 (6.50)
5.427 5.46 (0.6) 4.64 (ÿ14.5) 4.70 (ÿ13.4) 4.69 (ÿ13.50) 5.33 (ÿ1.88)
(ÿ3.9) (10.1) (ÿ4.10) (1.81)
a For these force fields the parameters for the valence terms i.e. bonds, bond angles and torsions were taken from AMBER.25 b The GF27 force field is chargeless and does not contain electrostatic interactions. c The experimental lattice parameters of the a phase are for a room temperature structure whilst those for the b phase correspond to the structure determined at 4 K.
Table 4 Sensitivity analysis of the non-bonded potential parameters in reproducing the crystalline phases a and b of resorcinol. The form of the potential is Uij ¼ Aexp(ÿBr) ÿCrÿ6, where A, B and C are parameters that characterize the interaction between atoms i and j, and r is the separation distance. The table presents the % deviation of the lattice parameters from the experimental structures11,12 for the un-optimised force field (FIT + W9921–24) and for systematic 5% increments in each of the individual potential parameters. The un-optimised force field shows a large deviation in reproducing the c-axis of the a-phase and the b-axis for b-phase. The critical parameters are those that minimize the lattice deviations for both phases simultaneously in a significant way, and are identified to be the B-parameters for the OH/OH and OH/HO interactions (highlighted in bold) Deviation of lattice parameters from experimental structure (%)a a form Interaction Unoptimised parameters (FIT + W99) CA/CA CA/OH CA/HO CA/HA OH/OH OH/HO OH/HA HO/HO HO/HA HA/HA
a
Parameter
A B C A B C A B C A B C A B C A B C A B C A B C A B C A B C
˚ a/A
b form ˚ b/A
˚ c/A
˚ a/A
˚ b/A
˚ c/A
1.54
1.81
3.25
2.56
6.50
ÿ1.88
1.60 0.87 1.40 1.68 ÿ1.08 1.36 1.62 0.52 1.51 1.71 ÿ0.16 1.46 1.60 0.74 1.49 1.27 1.34 1.53 1.53 1.40 1.48 1.54 1.57 1.54 1.47 1.98 1.57 1.49 1.85 1.56
1.87 0.65 1.61 1.91 2.18 1.61 1.85 1.87 1.73 1.89 1.27 1.66 1.83 2.01 1.83 2.34 0.94 1.77 1.97 0.43 1.73 1.81 1.78 1.80 1.96 0.73 1.72 1.96 0.84 1.75
3.37 2.73 3.20 3.24 2.92 3.25 3.20 3.68 3.29 3.58 ÿ0.14 3.14 3.37 1.99 3.16 3.20 2.11 3.21 3.19 3.49 3.27 3.26 3.23 3.25 3.24 3.34 3.27 3.22 3.48 3.25
2.64 20.96 2.31 2.74 0.46 2.18 2.64 2.09 2.49 2.90 2.01 2.30 2.86 ÿ0.35 2.53 2.74 1.39 2.49 2.83 0.47 2.41 2.57 2.50 2.55 2.59 2.39 2.53 2.61 2.31 2.52
6.48 3.64 6.42 6.63 5.71 6.33 6.51 6.08 6.45 6.37 6.77 6.47 6.55 5.31 6.32 6.70 4.48 6.40 6.64 5.38 6.37 6.50 6.49 6.50 6.51 6.36 6.49 6.50 6.47 6.50
ÿ1.61 ÿ17.85 ÿ2.15 ÿ1.83 ÿ1.88 ÿ1.90 ÿ1.92 ÿ1.62 ÿ1.87 ÿ1.50 ÿ5.65 ÿ2.08 ÿ1.99 0.20 ÿ1.85 ÿ1.98 ÿ0.88 ÿ1.83 ÿ1.78 ÿ2.21 ÿ1.92 ÿ1.88 ÿ1.83 ÿ1.87 ÿ1.87 ÿ2.00 ÿ1.88 ÿ1.88 ÿ1.85 ÿ1.88
The lattice deviations are with respect to the room temperature structure for the a phase and a 4 K structure for the b phase.
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et al.17 that used FIT + W9921–24 parameters coupled with the Distributed Multiple Analysis (DMA) model for the electrostatics and treated the molecule as a rigid body. In general, the force-fields have some success with a-resorcinol but not for the b-phase. Both the AMBER25 and CHARMM26 force fields are respectable in reproducing the a-resorcinol structure with less than 4% deviation. The GF27 force field does a poor job giving about 10% deviation, a result which might be expected as this force field contains no explicit electrostatics. For b-resorcinol, none of the force fields tested were able to satisfactorily reproduce the crystal structure. For this form, the published results of Day et al.17 using the DMA approach for the electrostatics and FIT + W9921–24 parameters do a good job with less than 2% deviation. There are, however, no results using the DMA approach for a-resorcinol. From the force fields tested we decided to proceed with the exponential form coupled with FIT + W9921–24 parameters for the non-bonded interactions. The results of the sensitivity analysis, in which we explored the influence of a 5% variation in each of the non-bonded parameters in the ability of the force field to reproduce the two crystalline phases of resorcinol, are presented in Table 4. In the first instance we focused only on the homo-parameters as variables with the hetero-interactions being derived as required using standard mixing rules. The critical parameter was determined to be the B-parameter of the O/ O (in terms of atom types OH/OH) interaction. This was incremented up to 12%, first individually in isolation and then together with some other parameters to reproduce both resorcinol phases simultaneously. This approach proved to be unsuccessful, presumably because the coupling between the homo- and hetero-interactions was limiting. In view of this we extended the variable space by including all hetero- and homo-interactions explicitly. In this case the critical parameters were the B-parameters of the O/O (atom types OH/OH) and O/H–O (atom types OH/HO) interactions, with the B-parameter of O/H–O interaction dominating. In view of this, the B-parameter of the O/H–O interaction was varied incrementally, for which the lattice deviations are presented in Table 5. The results indicate that a 12% increase in the B-parameter for the O/H–O interaction is optimal and sufficient to reproduce both phases of resorcinol at the ~2% level lattice deviation. The original and the optimized interaction potential for the O/H–O interaction are
plotted in Fig. 4. It appears that to reproduce the crystalline phases of resorcinol it is necessary to reduce the effective contact distance between the hydroxyl hydrogens (donor) and the oxygen (acceptor) atoms that define the hydrogen bonds. In this respect this would bring these interactions in line with other force fields, e.g., AMBER,25 where hydrogen-bonding hydrogens do not have any effective radius. The other required change is a significant increase in the well depth of the potential, i.e., the hydrogen bonds are strengthened. The success of the DMA electrostatics model for describing b-resorcinol17 suggests that this optimization of the hydrogen bonding parameters probably compensates for the lack of directionality in the isotropic point charge model employed. The excellent quality of the optimized force field is illustrated in Fig. 5 and 6 in which the predicted structure for each phase is superposed on the experimental structure, yielding an almost perfect match for each phase. The definitive set of non-bonded parameters is tabulated in Table 6. The achievement of good results in the fitting of potential parameters does not always guarantee success in molecular dynamics simulations. There are various issues that need to be considered. In empirical fitting, the parameters are optimized at 0 K (or low temperature as in our case) which means that thermal motion is non existent (or limited). However, in MD, simulations are done at finite temperature and pressure, and
Fig. 4 Potential energy curve for the original (W99 + FIT21–24) and the optimized O/H–O (in terms of atom types OH/HO) non-bonded interaction as a function of separation distance.
Table 5 Systematic optimization of the B-parameter of the non-bonded potential for OH/OH and OH/HO interaction (see Table 1) to reproduce the a and b structures of resorcinol. The form of the non-bonded interaction is Uij ¼ Aexp(ÿBr)ÿCrÿ6 Deviation of lattice parameter from experimental structure (%)a a form
b form
Increase in B parameter (%)
˚ a/A
˚ b/A
˚ c/A
˚ a/A
˚ b/A
˚ c/A
Unoptimised parameters (FIT + W9921–24) OH/OH 5 10 OH/HO 5 10 12 15
1.54 0.74 0.15 1.34 0.78 0.58 0.29
1.81 2.01 2.32 0.94 1.16 1.31 1.37
3.25 1.99 0.90 2.11 0.07 ÿ0.72 ÿ1.74
2.56 ÿ0.35 ÿ1.50 1.39 0.31 ÿ0.04 ÿ0.40
6.50 5.31 4.49 4.48 2.32 1.57 0.31
ÿ1.88 0.20 0.93 ÿ0.88 ÿ0.29 0.01 0.63
Interaction
a
The lattice deviations are with respect to the room temperature structure for the a phase and a 4 K structure for the b phase.
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Fig. 5 Superposition of the a-resorcinol structure from experiment11 (in blue) and the average calculated structure (ball and stick) obtained from a molecular dynamics simulation at 10 K using the optimized force field.
molecules will interact in orientations that are not sampled in the experimental structures employed in the 0 K (or low temperature) optimization. Therefore, to be able to verify the quality of the parameters that have been developed, MD simulations were performed for both phases of resorcinol at the temperatures at which they are stable. If the fitted parameters are respectable, then it is expected that the simulated structure would not differ much from the experimental structure taking lattice expansion into account. The variation in the cell vectors as a function of simulation time for both a-resorcinol (at 298 K) and b-resorcinol (at 360 K) is shown in Fig. 7. The plot shows that both phases are stable over the 500 ps simulation time. The % deviations between the averaged lattice parameters from the MD simulations and the experimental lattice parameters are given in Table 7. It can be seen that the difference between the experimental and calculated structures is reasonable, the predicted lattice parameters deviating by less than about 5%. A large part of this percentage deviation can be attributed to the expected expansion of the cell. A close comparison of the structures, rather than the lattice parameters, revealed that the simulated structures were similar to the experimental structures with the appropriate conformation of the resorcinol molecule being preserved within each phase. The molecular simulations carried out yield a number of thermodynamics quantities that can be compared with experiment, although the temperatures at which studies have been carried out do not correspond exactly. The heat and entropy of transition and the latent volume have been reported as DHa/b ¼ 1.56 0.07 kJ molÿ1, DSa/b ¼ 4.64 0.14 J Kÿ1 molÿ1, and
Fig. 6 Superposition of the b-resorcinol structure from experiment12 (in blue) and the average calculated structure (ball and stick) obtained from a molecular dynamics simulation at 10 K using the optimized force field.
Table 6 Non-bonded potential parameters for the optimized force field. The form of the non-bonded interaction is Uij ¼ Aexp(ÿBr)ÿCrÿ6. The parameters optimized as part of this work are shown in bold Interaction
A/kJ molÿ1
B/nmÿ1
C/nm6 kJ molÿ1
CA/CA CA/OH CA/HO CA/HA OH/OH OH/HO OH/HA HO/HO HO/HA HA/HA
2.38577e +05 2.34282e +05 3.46416e +04 5.34416e +04 2.30064e +05 3.40180e +04 5.24795e +04 5.03000e +03 7.75978e +03 1.19710e +04
3.6000e +01 3.7700e +01 4.0600e +01 3.6700e +01 3.9600e +01 4.7936e +01 3.8500e +01 4.6600e +01 4.1500e +01 3.7400e +01
1.64270e 1.35858e 1.87931e 4.73354e 1.12360e 1.55427e 3.91483e 2.15000e 5.41535e 1.36400e
This journal is ª The Royal Society of Chemistry 2008
ÿ03 ÿ03 ÿ04 ÿ04 ÿ03 ÿ04 ÿ04 ÿ05 ÿ05 ÿ04
Fig. 7 Variation of the simulation cell dimensions of the a and b forms of resorcinol as a function of time in a molecular dynamics simulation with anisotropic boundary conditions (each of the cell dimensions and angles is allowed to vary) at their respective temperatures of stability, 293 K and 360 K, and 0.001 kbar. The cell angles (not shown) remained orthogonal with minor fluctuations throughout the simulations.
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Table 7 Comparison of experimental and averaged lattice parameters from extended molecular dynamics simulations of a and b-resorcinol at their respective temperatures of stability, 298 K for a phase and 360 K for b phase. The calculated lattice parameters were averaged over the period 200–500 ps of the trajectory. Percentage deviations of the averaged lattice parameters from the experimental values are given in parentheses
Experimentala Molecular dynamics a
˚ a/A
a form ˚ b/A
˚ c/A
˚ a/A
b form ˚ b/A
˚ c/A
10.530 10.68 (1.43)
9.530 10.00 (4.91)
5.600 5.58 (ÿ0.29)
7.934 8.28 (4.36)
12.606 12.83 (1.76)
5.511 5.56 (0.90)
The experimental lattice parameters for both phases correspond to room temperature structures.
DVa/b ¼ ÿ2.91 0.01 cm3 molÿ1 at 337 K, respectively.9 The corresponding predicted values are DHa/b ¼ 6.60 kJ molÿ1, DSa/b ¼ 18.44 J Kÿ1 molÿ1 and DVa/b ¼ ÿ2.92 cm3 molÿ1 but at 360 K. Whilst there is perfect agreement with respect to the latent volume, the predicted heat of transition is somewhat higher which is also reflected in the entropy change. The reported sublimation energy is DHsub ¼ 85.3 0.5 kJ molÿ1 at 334 K33 which is a little higher than the predicted lattice energy DHcry ¼ 76.4 kJ molÿ1 calculated for the a form at 10 K. This small disparity may reveal itself in the resorcinol model having a lower melting point than the real system. The published enthalpy of fusion for the a phase is DHa,fus ¼ 18.9 kJ molÿ1 at 383 K,34 which is a little lower than the predicted value of DHa,fus ¼ 24.5 kJ molÿ1 at 390 K. Overall, the extent of disparity observed obtained between the predicted and observed thermodynamics quantities is typical of force field simulation methods. In conclusion, an optimized force field that utilizes the exponential form for the non-bonded interactions has been derived for the crystalline phases of resorcinol using both ab initio calculations (for the torsional force constants) and empirical fitting to experimentally-determined crystal structures. The force field has been shown to maintain the stability of both crystalline phases of resorcinol in extended molecular dynamics simulations. The proposed force field should enable us to address a number of fundamental and outstanding issues concerning growth and dissolution of resorcinol crystals (and possibly phase transitions) by molecular simulation with confidence. Indeed a recent application of the proposed force field has provided much needed insight into the cause of asymmetric growth of resorcinol crystals along the polar axis from the vapour phase.35
Acknowledgements J.C. would like to thank the Institute of Pharmaceutical Innovation (IPI) and Faculty of Pharmaceutical Sciences, Chulalongkorn University, for supporting her stay at the IPI.
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