Kinetic reconstruction of free energies as a function of multiple order parameters

TL;DR

This paper introduces a method to reconstruct free energy surfaces involving multiple order parameters from steady state trajectories, enabling analysis of complex phenomena like phase transitions more efficiently.

Contribution

The authors develop a novel approach to estimate multi-parameter free energy surfaces from steady state data, extending previous single-parameter methods and applicable to unconstrained molecular dynamics.

Findings

Successfully reconstructed free energy surface for supercooled silicon.

Results are consistent with previous umbrella sampling studies.

Method improves efficiency in analyzing complex free energy landscapes.

Abstract

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analysed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.