Limitations of empirical supercell extrapolation for calculations of point defects in bulk, at surfaces, and in two-dimensional materials

The commonly employed supercell approach for defects in crystalline materials may introduce spurious interactions between the defect and its periodic images. A rich literature is available on how the interaction energies can be estimated, reduced, or corrected. A simple and seemingly straightforward approach is to extrapolate from a series of finite supercell sizes to the infinite-size limit, assuming a smooth polynomial dependence of the energy on inverse supercell size. In this work, we demonstrate by means of explict density-functional theory supercell calculations and simplified models that wave-function overlap and electrostatic interactions lead to more complex dependencies on supercell size than commonly assumed. We show that this complexity cannot be captured by the simple extrapolation approaches and that suitable correction schemes should be employed.