HSE hybrid functional tuned to generalized Koopmans condition for defect calculations in GaN

Generalized Koopmans condition can be used to tune HSE hybrid functional to enforce the linearity of total energy with respect to the occupation. In such tuned HSE the defect state eigenvalues are equal to the electron addition energies. The latter are related to the optical transition levels. Therefore a Koopmans tuned HSE allows using the unoccupied defect state eigenvalues to calculate defect photoluminescence peaks. Lattice relaxation energies can be used to calculate zero phonon lines. This approach does not rely on any correction scheme for the electrostatic interactions in a charged supercell and is less sensitive to other artificial interactions. We describe the HSE tuning procedure based on the generalized Koopmans condition and demonstrate the accuracy of this approach using several acceptors in GaN.