Charged defect in GaSb by selective occupation in density functional theory

In a density functional theory (DFT) approach, the transition energy of an acceptor-like defect is typically calculated by the total energy difference between E(N$+$1) and E(N), where N is the total number of the valence electrons of the defected system. Effectively, in this scheme, the hole in the valence band is simulated by a uniform positive background charge or a plane wave. A scheme closer to the reality would be to move one electron from the valence band maximum (VBM) to the defect level, because the VBM state usually is quite different from a plane wave. We apply this selective occupation scheme to a defect problem, an antisite defect of Ga on Sb in GaSb, and compare the results of two schemes with varying supercell size, using a pseudopotential DFT theory.