Relation between image charge and potential alignment corrections for charged defects in periodic boundary conditions

Charged defects are often studied within the periodic density functional theory (DFT), but this introduces strong finite-size artifacts. In this work, we develop an electrostatic image interaction correction (IIC) method based on the direct solution of the Poisson equation for charge models constructed directly from DFT calculations. These IICs are found to be detail-insensitive, depending almost entirely on bulk dielectric properties. As these IICs are not able to fully explain the observed finite-size scaling, we explore potential alignment in detail and introduce a novel decomposition to separate out different contributions. We find that the two main sources of potential alignment are defect image interactions and changes in the number of atoms present in the supercell. This first effect is accurately predicted by the periodic part of our IIC. The second contribution is unrelated to the IIC and justifies the common observation that the magnitude of finite-size dependence can strongly vary between vacancy and interstitial defects. It can be approximately predicted using atomic radius, but is strongly sensitive to the pseudopotential employed. Combined, these developments provide a new justification for known finite-size scaling rules. Our results suggest that for cubic supercells, the Lany-Zunger IIC, combined with simplified potential alignment between neutral systems, can yield accurate corrections in spite of the simplicity of the approach.