Oxygen Vacancies in the Anatase (101) Surface: Formation Energies and Finite Size Effects

We present a study of oxygen vacancies in the anatase TiO$_{2}$ (101) surface. We take great care to minimise the impact of periodic boundary conditions on our results. We make use of the ONETEP\footnote{Skylaris C K, Haynes P D, Mostofi A A and Payne M C 2005 \emph{J. Chem. Phys} \textbf{122}} linear scaling DFT code to study defects in large (order 800 atom) simulation cells, to reduce long range strain interactions. We also make use of a scheme to correct for spurious periodic electrostatic interactions in the case of charged defects\footnote{Komsa, H-P and Pasquarello A 2013 \emph{Phys. Rev. Lett.} \textbf{110}:095505}. Finally we study the behaviour of defect formation energies as a function of distance from the surface, and demonstrate convergence to bulk formation energies with depth. We also present novel functionality for EELS calculations within LS-DFT, suitable for large nanomaterials systems.