Temperature Accelerated Monte Carlo (TAMC): a method for sampling the free energy surface of non-analytical collective variables

TL;DR

The paper presents TAMC, a novel simulation method for rare events involving complex or non-analytical collective variables, demonstrated through crystallization studies in Lennard-Jones particles.

Contribution

It introduces TAMC, extending Temperature Accelerated Molecular Dynamics to handle non-analytical collective variables for free energy surface sampling.

Findings

Successfully computed free energy barriers and critical nucleus size.

Validated the method with Lennard-Jones crystallization data.

Observed a monotonic free energy increase in the liquid phase.

Abstract

We introduce a new method to simulate the physics of rare events. The method, an extension of the Temperature Accelerated Molecular Dynamics, comes in use when the collective variables introduced to characterize the rare events are either non-analytical or so complex that computing their derivative is not practical. We illustrate the functioning of the method by studying the homogeneous crystallization in a sample of Lennard-Jones particles. The process is studied by introducing a new collective variable that we call Effective Nucleus Size $\mathcal N$. We have computed the free energy barriers and the size of critical nucleus, which result in agreement with data available in literature. We have also performed simulations in the liquid domain of the phase diagram. We found a free energy curve monotonically growing with the nucleus size, consistent with the liquid domain.