Entropy as a tool for crystal discovery

The computational prediction of crystal structures has emerged as an useful alternative to expensive and often cumbersome experiments. We propose an approach to the prediction of crystal structures and polymorphism based on reproducing the crystallization process on the computer. The main hurdle faced by such an approach is that crystallization usually takes place in timescales much longer than those that can be afforded with standard molecular simulations. In order to circumvent this difficulty we construct a bias potential which is a function of one or more collective variables and whose role is to promote crystallization. This approach can only have true predictive power if the collective variable is crystal structure agnostic, that is to say, it does not include information about the geometry of any particular crystal structure. In order to achieve this goal, we take inspiration from thermodynamics and propose to use an entropy surrogate as collective variable. We use an approximation for the entropy based on the radial distribution function g(r). Using this collective variable we are able to explore polymorphism in simple metals and molecular crystals. We study the case of urea and find a new polymorph stabilized by entropic effects. We also propose a projection of the collective variable onto each atom that is useful to characterize atomic environments. Lastly, we introduce a generalized Kullback-Leibler divergence that measures the distance between two radial distribution functions. We apply this divergence to the automatic classification of the polymorphs that crystallize during the simulations.