Anisotropic charge screening and supercell size convergence of defect formation energies

Abstract

One of the main sources of error associated with the calculation of defect formation energies using plane-wave density functional theory (DFT) is finite size error resulting from the use of relatively small simulation cells and periodic boundary conditions. Most widely used methods for correcting this error, such as that of Makov and Payne, assume that the dielectric response of the material is isotropic and can be described using a scalar dielectric constant $\ensuremath{\epsilon}$. However, this is strictly only valid for cubic crystals, and cannot work in highly anisotropic cases. Here we introduce a variation of the technique of extrapolation based on the Madelung potential that allows the calculation of well-converged dilute limit defect formation energies in noncubic systems with highly anisotropic dielectric properties. As an example of the implementation of this technique we study a selection of defects in the ceramic oxide Li${}_{2}$TiO${}_{3}$ which is currently being considered as a lithium battery material and a breeder material for fusion reactors.