(451b) Ab Initio Prediction of Crystal Structure and the Effects of Temperature On the Relative Stability of Enantiotropic Polymorphs

A given molecule may lead to more than one crystal structure and the term polymorph describes each of the many possible -long ranged- spatial arrangements in which the molecule may crystallise [1]. Different polymorphs have different physical properties, rendering polymorphism a phenomenon of industrial interest since most solid products of practical interest are in crystalline form e.g. pharmaceuticals or agrochemicals. As a result the identification of possible polymorphs and their relative stability is an important challenge which must be addressed in order to engineer products and processes.

In recent years, there has been a growing effort to predict the number and structure of the polymorphs a compound forms. Successful predictions have been achieved for several small [2] molecules and more recently for large molecules exhibiting extended flexibility [3]. Most of the currently used crystal structure prediction techniques are based on lattice energy minimisation algorithms [4], thus restricting calculations to 0K and limiting our ability to assess reliably the relative stability of different polymorphs. Furthermore, based on those approaches, it is not possible to study enantiotropic polymorphs, i.e., polymorphs whose stability order is a function of temperature.

In this study, a methodology to include quantum and temperature effects within an existing crystal structure prediction methodology [3], based on the CrystalPredictor [5] and CrystalOptimizer [6] algorithms, is presented. It is based on fully atomistic lattice dynamics under the harmonic approximation [7], using an energy model that is consistent with the CrystalOptimizer algorithm. The approach is applied to tetracyanoethylene (TCNE), which is known to exhibit enantiotropic polymorphs [8,9]. TCNE possesses two resolved polymorphs, the cubic form, which is stable at low temperatures, and the monoclinic form, which is stable at more elevated temperatures. The free energies of the low lattice energy structures of TCNE identified by CrystalOptimizer are calculated at various temperatures using. The intra-molecular interactions are computed using isolated molecule quantum mechanical calculations and the electrostatic interactions are modeled using ab-initio derived distributed multipole moments [10]. An Ewald type summation technique is employed for divergent and poorly convergent sums. The effect of temperature on the predicted landscape is investigated and a reversal of stability is correctly predicted between the two enantiotropic polymorphs at higher temperatures. The impact of the approximations inherent in the harmonic approximation is assessed through comparison with experimental data.  

[1]     J. Bernstein, “Polymorphism in Molecular Crystals”. Clarendon Press, Oxford, (2002)

[2]     G.M. Day, T.G. Cooper, A.J. Cruz-Cabeza, K.E. Hejczyk et.al. , Acta Cryst. B, 65, 107-205

[3]     A.V. Kazantsev, P.G. Karamertzanis, C.S. Adjiman, and C.C. Pantelides et.al., International Journal of Pharmaceuticals, 418, 168-178, (2011)

[4]     G.M. Day, Cryst. Rev.  17, 3-52, (2011)

[5]     P.G. Karamertzanis and C.C. Pantelides, Molecular Physics, 105(2-3), 273-291 (2007)

[6]     A.V. Kazantsev, P.G. Karamertzanis, C.S. Adjiman, and C.C. Pantelides, J. Chem. Theory Comput., 7, 1998-2016 (2011)

[7]     M.T. Dove, “Introduction to lattice dynamics”, Cambridge University Press, (1993)

[8]     J. Murgich and S. Pissanetzky, J. Chem. Phys., 62, 92-93 (1975)

[9]     R. Mukhopadhyay, S.L. Chaplot and K.R. Rao, Physca Status Solidi A: Applied Research, 92, 467-474 (1985)

[10]   A.J. Stone, J. Chem. Theory Comput., 1, 1128-1132, (2005)