Quasiparticle self-consistent G W 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 $GW$ (QS$GW$). We have shown that QS$GW$ describes energy bands for a wide range of materials rather well, including many where the local-density approximation fails. QS$GW$ contains physical effects found in other theories such as $mathrm{LDA}+U$, 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 QS$GW$, 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.