  In past decades the scientific community has been looking for a reliable
first-principles method to predict the electronic structure of solids with high
accuracy. Here we present an approach which we call the quasiparticle
self-consistent GW approximation (QpscGW). It is based on a kind of
self-consistent perturbation theory, where the self-consistency is constructed
to minimize the perturbation. We apply it to selections from different classes
of materials, including alkali metals, semiconductors, wide band gap
insulators, transition metals, transition metal oxides, magnetic insulators,
and rare earth compounds. Apart some mild exceptions, the properties are very
well described, particularly in weakly correlated cases. Self-consistency
dramatically improves agreement with experiment, and is sometimes essential.
Discrepancies with experiment are systematic, and can be explained in terms of
approximations made.
