Collective Variables for the Study of Crystallization

TL;DR

This paper introduces a machine learning-based approach to define collective variables for enhanced sampling in atomistic simulations of crystallization, enabling better exploration of slow crystallization processes.

Contribution

It presents a novel method using Deep Linear Discriminant Analysis to create collective coordinates based on structure factor peaks for crystallization simulations.

Findings

Successfully applied to NaCl crystallization

Effective in capturing slow degrees of freedom

Improves sampling efficiency in crystallization studies

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 crystallization is much larger than what can be explored in standard simulations. Enhanced sampling methods can overcome this time scale hurdle. Here we employ the on-the-fly probability enhanced sampling method that is a recent evolution of metadynamics. This method, like many others, relies 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 crystallization 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 apply the method to the study of crystallization of a multicomponent system, Sodium Chloride and a molecular system, Carbon Dioxide.