A Metadynamics-Based Framework for Free Energy Surface Mapping of Multiparticle Diffusion in Crystals

Abstract

We propose two metadynamics (MetaD)-based methodologies for efficiently mapping free energy surfaces (FESs) of multiple interacting carriers diffusing in crystalline solids. Our approaches circumvent the challenges of high-dimensional collective variables (CVs) by employing replica state exchange MetaD and parallel bias MetaD, both of which decompose the high-dimensional CVs into multiple lower-dimensional ones. As a benchmark, we investigate two-dimensional lithium (Li) diffusion in LixTiS2 across a wide range of Li concentrations. The Li jump frequencies estimated from the obtained FESs exhibit concentration- and temperature-dependent trends consistent with previous kinetic Monte Carlo simulations and nuclear magnetic resonance measurements. Our approaches provide a promising framework for capturing the slow dynamics of diffusive carriers that are typically inaccessible to conventional molecular dynamics simulations.