%0 Journal Article
%T A permutation invariant collective variable to track and drive vacancy dynamics in simulations of solids
%A Jan M. Knaup
%A Michael Wehlau
%A Thomas Frauenheim
%J Physics
%D 2013
%I arXiv
%R 10.1103/PhysRevB.88.220101
%X 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.
%U http://arxiv.org/abs/1307.3955v2