Quasiparticle self-consistent GW method:: a short summary

We have developed a quasiparticle self-consistent GW method (QSGW), which is a new self- consistent method to calculate the electronic structure within the GW approximation. The method is formulated based on the idea of a self- consistent perturbation; the non- interacting Green function G0, which is the starting point for GWA to obtain G, is determined self- consistently so as to minimize the perturbative correction generated by GWA. After selfconsistency is attained, we have G(0), W ( the screened Coulomb interaction) and G self- consistently. This G(0) can be interpreted as the optimum non- interacting propagator for the quasiparticles. We will summarize some theoretical discussions to justify QSGW. Then we will survey results which have been obtained up to now: e. g., band gaps for normal semiconductors are predicted to a precision of 0.1-0.3 eV; the selfconsistency including the off- diagonal part is required for NiO and MnO; and so on. There are still some remaining disagreements with experiments; however, they are very systematic, and can be explained from the neglect of excitonic effects.