Predicting polymorphism in molecular crystals using orientational entropy

Abstract

We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant polymorphs. This idea, however, conflicts with the fact that crystallization has a timescale much longer than that of molecular simulations. To bring the process within affordable simulation time, we enhance the fluctuations of a collective variable by constructing a bias potential with well-tempered metadynamics. We use as a collective variable an entropy surrogate based on an extended pair correlation function that includes the correlation between the orientations of pairs of molecules. We also propose a similarity metric between configurations based on the extended pair correlation function and a generalized Kullback-Leibler divergence. In this way, we automatically classify the configurations as belonging to a given polymorph, using our metric and a hierarchical clustering algorithm. We apply our method to urea and naphthalene. We find different polymorphs for both substances, and one of them is stabilized at finite temperature by entropic effects.

Keywords: crystal structure prediction; enhanced sampling; molecular simulation; polymorphism; urea.

Fig. 1.

$g\left(r,\theta \right)$ for the liquid and polymorph I of urea at 450 K. Snapshots of the system in each of the phases are shown. Polymorph I is viewed down the c axis. C, O, N, and H atoms are shown in orange, gray, blue, and white, respectively.

Fig. 2.

Tree diagram resulting from the clustering according to the distance in Eq. 4 of the trajectory of urea at 450 K. The threshold distance used to join clusters is shown with a gray dashed line. Configurations at 450 K for selected clusters are shown.

Fig. 3.

Enthalpy, entropy, and free energy for selected polymorphs of urea at 450 K and naphthalene at 300 K. All quantities have the liquid as reference state.

Fig. 4.

Crystal structures of form B of urea and form A of naphthalene. C, O, N, and H atoms are shown in cyan, red, blue, and white, respectively. Images were obtained with Visual Molecular Dynamics (VMD) (29).