(685a) Improving Intermolecular Force-Fields for Crystal Structure Prediction

A given molecule may crystallise in several crystal forms called polymorphs. Different polymorphs exhibit differences in physical properties and as a result polymorphism is a phenomenon of great industrial importance, especially for pharmaceutical and agrochemical industries where most solid products are crystalline. Thus the development of techniques for the prediction of the possible crystal structures of a given compound has great practical benefits, helping to avoid possible manufacturing problems and allowing the improvement of the properties of the stable structures.

There have been significant advances in recent years in computational methods for the prediction of the crystal structures of small organic molecules, based on lattice energy minimization at 0 K [1]. Reliable predictions of possible crystal structures have been obtained for many rigid molecules [2] and for flexible molecules of molecular weight up to 500 g/mol [3]. However, while known polymorphs are usually found as low-energy minima, there is evidence that in many cases the relative energy of the minima is not in agreement with experimental data [4]. The development of more accurate lattice energy models is thus necessary to enhance prediction capabilities, especially when relative stabilities of different polymorphs differ by only a few kJ/mol.

In our computational approach, based on the Crystal Predictor [5] and Crystal Optimizer [6] algorithms, the lattice energy is calculated following a classical approach in which the energy is partitioned into intramolecular and intermolecular pairwise contributions; the latter can be further partitioned into repulsive/dispersive and electrostatic terms. The intramolecular energy is derived using isolated molecule quantum mechanical calculations, the electrostatics are modelled through atomic charges or distributed multipole moments derived from the ab initio charge density [7] and the repulsive/dispersive energy using an empirical exp-6 potential with parameters taken from the literature [8, 9, 10, 11].

In this study, the impact of the modelling choices made for each component is investigated: the level of theory for the quantum mechanical calculations and the values of the repulsion/dispersion potential parameters used to model crystals of the ROY molecule are varied and the resulting changes in lattice energy, crystal structure and relative stability of two polymorphs are reported. The sensitivity analysis reveals the need to re-estimate the parameters of the exp-6 potential, which were originally derived based on levels of theory and electrostatic models that are now rarely used in crystal structure prediction. A re-parameterization is thus expected to produce an optimized set of parameters consistent with any changes in the lattice energy model and to capture remaining errors and approximations elsewhere in the model [12].

A method for deriving parameters for atom-atom exp-6 potential for crystals has been developed and is presented. The method is based on the minimization of deviations between experimental and minimized experimental crystal structures and deviations of their lattice energies from the experimental heats of sublimation. Experimental structures are compared with the minimized experimental structures using as measure of similarity the root mean square deviation of the 15 molecule coordination sphere of the two structures. The proposed method is applied to a set of hydrocarbons and the effect of the new set of parameters on the quality of the predictions is discussed.

References

[1] G.M. Day. Current approaches to predicting molecular organic crystal structures. Crystallography Reviews, 17(1):3-52, 2011.

[2] G.M. Day, T.G. Cooper, A.J. Cruz-Cabeza, K.E. Hejczyk, H.L.  Ammon, S.X. M.  Boerrigter, J.S. Tan, R.G. Della Valle, E. Venuti, J. Jose, S.R. Gadre, G.R. Desiraju, T. S. Thakur, B.P. van Eijck, J.C. Facelli, V.E. Bazterra, M.B. Ferraro, D.W. M. Hofmann, M.A. Neumann, F.J. J. Leusen, J. Kendrick, S.L. Price, A.J. Misquitta, P.G. Karamertzanis, G.W. A. Welch, H.A. Scheraga, Y.A. Arnautova, M.U. Schmidt, J. van de Streek, A.K. Wolf, and B. Schweizer. Significant progress in predicting the crystal structures of small organic molecules - a report on the fourth blind test. Acta Crystallographica Section B, 65(2):107-125, Apr 2009.

[3] A.V. Kazantsev, P. G. Karamertzanis, C. S. Adjiman, C.C. Pantelides, S.L. Price, P.T.A. Galek, G.M. Day,and A.J. Cruz-Cabeza. Successful prediction of a model pharmaceutical in the fifth blind test of crystal structure prediction. International Journal of Pharmaceutics, 418(2):168-178, 2011. A priori Performance Predictions.

[4]  M. Vasileiadis, A.V. Kazantsev, P.G. Karamertzanis, C.S. Adjiman, and C.C. Pantelides. The polymorphs of ROY: application of a systematic crystal structure prediction technique. Acta Crystallographica Section B, 68(6):677{685, Dec 2012.

[5] P. G. Karamertzanis and C. C. Pantelides.  Ab initio crystal structure prediction. II. Flexible molecules. Molecular Physics, 105(2-3):273-291, 2007.

[6] A.V. Kazantsev, P.G. Karamertzanis, C.C. Pantelides, and C.S.  Adjiman. CrystalOptimizer: An Efficient Algorithm for Lattice Energy Minimization of Organic Crystals Using Isolated-Molecule Quantum Mechanical Calculations, pages 1-42. Wiley-VCH Verlag GmbH & Co. KGaA, 2011.

[7] A.J. Stone. The Theory of Intermolecular Forces. Clarendon Press, Oxford,1996.

[8] D. E. Williams and S. R. Cox. Nonbonded potentials for azahydrocarbons:the importance of the Coulombic interaction. Acta Crystallographica Section B, 40(4):404-417, Aug 1984.

[9] S. R. Cox, L.-Y. Hsu, and D. E. Williams. Nonbonded potential function models for crystalline oxohydrocarbons. Acta Crystallographica Section A,37(3):293-301, May 1981.

[10] D. E. Williams and D. J. Houpt. Fluorine nonbonded potential parameters derived from crystalline perfluorocarbons. Acta Crystallographica Section B,42(3):286-295, Jun 1986.

[11] L.-Y. Hsu and D. E. Williams. Intermolecular potential-function models for crystalline perchlorohydrocarbons. Acta Crystallographica Section A,36(2):277-281, Mar 1980.

[12] C.C. Pantelides, C.S. Adjiman, and A.V. Kazantsev. General computational algorithms for ab initio crystal structure prediction for organic molecules. In Sule Atahan-Evrenk and Alan Aspuru-Guzik, editors, Prediction and Calculation of Crystal Structures, volume 345 of Topics in Current Chemistry, pages 25-58. Springer International Publishing, 2014.