Quasiparticle self-consistent GW method:: A basis for the independent-particle approximation

We have developed a type of self-consistent scheme within the GW approximation, which we call quasiparticle self-consistent GW (QSGW). We have shown that QSGW describes energy bands for a wide range of materials rather well, including many where the local-density approximation fails. QSGW contains physical effects found in other theories such as LDA+U, self-interaction correction, and GW in a satisfactory manner without many of their drawbacks (partitioning of itinerant and localized electrons, adjustable parameters, ambiguities in double counting, etc.). We present some theoretical discussion concerning the formulation of QSGW, including a prescription for calculating the total energy. We also address several key methodological points needed for implementation. We then show convergence checks and some representative results in a variety of materials.