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Adequacy of Approximations in GW Theory

We use an all-electron implementation of the GW approximation to analyze several possible sources of error in the theory and its implementation. Among these are convergence in the polarization and Green's functions, the dependence of QP levels on choice of basis sets, and differing approximations for dealing with core levels. In all GW calculations presented here, G and W are generated from the local-density approximation (LDA), which we denote as the \GLDA\WLDA approximation. To test its range of validity, the \GLDA\WLDA approximation is applied to a variety of materials systems. We show that for simple sp semiconductors, \GLDA\WLDA always underestimates bandgaps; however, better agreement with experiment is obtained when the self-energy is not renormalized, and we propose a justification for it. Some calculations for Si are compared to pseudopotential-based \GLDA\WLDA calculations, and some aspects of the suitability of pseudopotentials for GW calculations are discussed.