To account for changes in composition n of each element i, the DFT total energy of a standard elemental reference E ref i is combined with a relative value of chemical potential µ i . Post-processing supercell corrections are applied to counteract the effects of using a finite supercell, and consist of: potential alignment correction, to account for the shift in eigenvalues between a charged and noncharged supercell; anisotropic image charge correction, developed by Murphy and Hine from the Makov-Payne method, a finite-size correction that removes the Coulombic repulsion between periodic images of defective supercells by treating the defect as a periodic point charge in a dielectric medium; and a band filling correction, which counteracts the unrealistic filling of the conduction band (emptying of the valence band) in a finite-sized supercell. At a given E F , the lowest energy charge state dominates for that defect, and a "transition level" is the point at which two charge states are in thermodynamic equilibrium.