On-the-fly meanfield transition-state theory for diffusive molecular dynamics

Abstract

We apply transition state theory to derive atomic-level master equations for mass transport from empirical interatomic potentials within the Diffusive Molecular Dynamics (DMD) framework. We show that meanfield approximation provides an exceedingly efficient and accurate means of computing free-energy barriers in arbitrary local atomic configurations, thus enabling long-term DMD ‘on-the-fly’ and on the sole basis of an underlying interatomic potential, without additional modeling assumptions. We apply and validate the resulting meanfield DMD paradigm in simulations of processes of hydrogenation and dehydrogenation of Mg using Angular-Dependent interatomic Potentials (ADP). We show that meanfield DMD correctly predicts hydrogen diffusivities in hcp Mg and vacancy diffusivities in rutile ${\mathrm{MgH}}_2$. We demonstrate the ability of meanfield DMD to predict evolution through calculations concerned with dilute concentrations of hydrogen in hcp Mg, and with dilute concentrations of hydrogen vacancies in rutile ${\mathrm{MgH}}_2$, including off-stoichiometry hydrogen concentrations and temperature effects. Remarkably, the time steps required by DMD are up to six orders of magnitude larger than those required by Molecular Dynamics (MD), which demonstrates the overwhelming superiority of the DMD paradigm in simulations of phenomena occurring on the diffusive time scale.