Collective variables for the study of crystallisation

Abstract

The phenomenon of solidification of a substance from its liquid phase is of the greatest practical and theoretical importance, and atomistic simulations can provide precious information towards its understanding and control. Unfortunately, the time scale for crystallisation is much larger than what can be explored in standard simulations. Enhanced sampling methods can overcome this time scale hurdle. Many such methods rely on the definition of appropriate collective variables able to capture the slow degrees of freedom. To this effect, we introduce collective coordinates of general applicability to crystallisation simulations. They are based on the peaks of the three-dimensional structure factor that are combined non-linearly via the Deep Linear Discriminant Analysis machine learning method. We use these collective variables in the context of the on-the-fly probability enhanced sampling method that is a recent evolution of metadynamics. We demonstrate the validity of this approach by studying the crystallisation of a multicomponent system, Sodium Chloride, and a molecular system, Carbon Dioxide.