Adequacy of approximations in GW theory

Following the usual procedure of the $GW$ approximation (GWA) within the first-principles framework, we calculate the self-energy from eigenfunctions and eigenvalues generated by the local-density approximation. We analyze several possible sources of error in the theory and its implementation, using a recently developed all-electron approach based on the full-potential linear muffin-tin orbital (LMTO) method. First we present some analysis of convergence in some quasiparticle energies with respect to the number of bands, and also their dependence on different basis sets within the LMTO method. We next present a new analysis of core contributions. Then we apply the GWA to a variety of materials systems to test its range of validity. For simple $sp$ semiconductors, GWA always underestimates band gaps. Better agreement with experiment is obtained when the renormalization $(Z)$ factor is not included, and we propose a justification for it. We close with some analysis of difficulties in the usual GWA procedure.

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