Correspondence of defect energy levels in hybrid density functional theory and many-body perturbation theory

We demonstrate the correspondence between charge transition levels of localized point defects in hybrid density functional theory and in G(0)W(0) many-body perturbation theory. To achieve this correspondence, it is necessary to properly combine the treatments of the finite-size effect, the delocalization error, and the path dependency in the G(0)W(0) scheme. In particular, we introduce a beyond-monopole finite-size electrostatic correction for the eigenvalue which is fully consistent with the analogous correction for the total energy. We illustrate how the comparison with experiment is affected by the calculated band-edge positions, which unlike the defect levels are sensitive to the adopted electronic-structure method.