Comparison between various finite-size supercell correction schemes for charged defect calculations

We present a comparison of the most common finite-size supercell correction schemes for charged defects in density functional theory calculations. Considered schemes include those proposed by Makov and Payne (MP), Lany and Zunger (LZ), and Freysoldt, Neugebauer, and Van de Walle (FNV). The role of the potential alignment is also assessed. Supercells of various sizes are considered and the corrected formation energies are compared to the values obtained by extrapolation to large supercells. For defects with localized charge distributions, we generally find that the FNV scheme slightly improves upon the LZ one, while the MP scheme generally overcorrects except for point-charge-like defects. We also encountered more complex situations in which the extrapolated values do not coincide. Inspection of the defect electronic structure indicates that this occurs when the defect Kohn-Sham states are degenerate with band-edge states of the host.