Variationally enhanced sampling with permutationally invariant collective variables

Abstract

Molecular dynamics (MD) simulations have become an indispensable tool in understanding the physical world at a resolution of molecular details. Currently, MD simulations are still limited to the microsecond timescale in most circumstances. When there is a high free energy barrier between metastable states, sampling is easily trapped in a local free energy minimum. A variety of enhanced sampling methods and algorithms have been developed to overcome such issues. In this thesis, we present our work on both developments of algorithms and methods. In terms of algorithm development, we have created an interface between PLUMED 2, a software package that has implemented some of the most prominent enhanced sampling methods, and the MD engine ESPResSo++. We used the combination of the two packages to study the first-order phase transition of the 128 monomer single-chain smooth square-well polymer. In terms of method development, based on the variationally enhanced sampling method, we have created the variationally enhanced sampling with permutationally invariant collective variables method so that such local collective variables can be used in biased simulations. We have demonstrated the effectiveness of the new method in phase transition studies of seven Lennard- Jones particles in two-dimensional space and crystallization of bulk sodium. We have also explored crystallization of ice and urea from melt with the new method and discussed the limitations of the current implementation encountered in these works.