A permutation invariant collective variable to track and drive vacancy dynamics in simulations of solids

TL;DR

This paper introduces a permutation invariant collective variable for tracking and driving vacancy dynamics in solid simulations, demonstrated through metadynamics of oxygen vacancies in TiO2, revealing insights into vacancy migration and free energy landscapes.

Contribution

A novel permutation invariant collective variable method for monitoring and influencing vacancy behavior in solid-state simulations, applied to TiO2 to explore vacancy migration pathways.

Findings

Effective tracking and driving of vacancies in simulations.

Free energy profiles align with minimum energy paths.

Migration governed by the most frequently realized jump.

Abstract

Vacancy dynamics in oxides are vital for understanding redox reactions and resulting memristive effects or catalytic activity. We present a method to track and drive vacancies which we apply to metadynamics simulation of oxygen vacancies (V$_{\mathrm{O}}$) in rutile, demonstrating its effectiveness. Using the density functional based tight binding method, it is possible to explore the free energy hyperplane of oxygen vacancies in TiO$_{2}$. We show that the migration of V$_{\mathrm{O}}$ in TiO$_{2}$ is governed by the jump with the higherst number of realizations. Free energy profiles are consistent with minimum energy paths.