Lattice defects in semiconductors and wide-gap materials which create deep levels in an open-shell electronic configuration could give rise to so-called defect bound small polarons. This type of defects present a challenge for electronic structure methods because the localization of the defect state and the associated energy levels depended sensitively on the ability of the total-energy functional to satisfy the physical condition that the energy E(N) must be a piecewise linear function of the fractional electron number N. For practical applications the requirement of a linear E(N) was re-cast as a generalized Koopmans condition. Since most functionals do not fulfil this condition accurately, parameterized perturbations were used that cancel the non-linearity of E(N) and recovered the correct Koopmans behaviour. Starting from standard density functionals, two types of parameterized perturbation were compared: the addition of on-site potentials and the mixing of non-local Fock exchange in hybrid functionals. After surveying a range of acceptor-type defects in II–VI and III–V semiconductors, a classification scheme was presented that described the relation between hole localization and the lattice relaxation of the polaronic state.

Predicting Polaronic Defect States by Means of Generalized Koopmans Density Functional Calculations. S.Lany: Physica Status Solidi B, 2011, 248[5], 1052–60