Efficient GW calculations for SnO2, ZnO, and rubrene: The effective-energy technique

In a recent Rapid Communication [J. A. Berger, L. Reining, and F. Sottile, Phys. Rev. B 82, 041103(R) (2010)], we presented the effective-energy technique to evaluate, in an accurate and numerically efficient manner, electronic excitations by reformulating spectral sum-over-states expressions such that only occupied states appear. In our approach all the empty states are accounted for by a single effective energy that can be obtained from first principles. In this work we provide further details of the effective-energy technique, in particular, when combined with the GW method, in which a huge summation over empty states appears in the calculation of both the screened Coulomb interaction and the self-energy. We also give further evidence of the numerical accuracy of the effective-energy technique by applying it to the technological important materials SnO2 and ZnO. Finally, we use this technique to predict the band gap of bulk rubrene, an organic molecular crystal with a 140-atom unit cell.