Validity of the Slater-Janak transition-state model within the LDA+U approach

Known with the name of the Slater-Janak transition-state model, Janak's theorem allows a calculation of charge transition levels by analyzing the Kohn-Sham eigenvalues of the density-functional theory without the need of explicitly comparing differently charged systems. Unfortunately, the usual local-density approximation (LDA) and its gradient extensions fail in describing the Kohn-Sham eigenvalues sufficiently well. In this work we show that the Slater-Janak transition state becomes a powerful tool if applied self-consistently within an LDA+U approach. We first explain this fact analytically and then present a numerical validation, calculating the Slater-Janak transition state for a selection of representative examples in GaN. The formalism is found to be valid for all the investigated examples, which are, besides oxygen donors (O-N) and carbon acceptors (C-N), also systems with negative-U effect (nitrogen vacancies, V-N) and strongly correlated electrons (europium substitutionals, Eu-Ga).