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This paper describes an all-electron implementation of the self-consistent GW(sc-GW) approach -- i.e. based on the solution of the Dyson equation -- in anall-electron numeric atom-centered orbital (NAO) basis set. We cast Hedin'sequations into a matrix form that is suitable for numerical calculations bymeans of i) the resolution of identity technique to handle 4-center integrals;and ii) a basis representation for the imaginary-frequency dependence ofdynamical operators. In contrast to perturbative G0W0, sc-GW provides aconsistent framework for ground- and excited-state properties and facilitatesan unbiased assessment of the GW approximation. For excited-states, webenchmark sc-GW for five molecules relevant for organic photovoltaicapplications: thiophene, benzothiazole, 1,2,5-thiadiazole, naphthalene, andtetrathiafulvalene. At self-consistency, the quasi-particle energies are foundto be in good agreement with experiment and, on average, more accurate thanG0W0 based on Hartree-Fock (HF) or density-functional theory with thePerdew-Burke-Ernzerhof (PBE) exchange-correlation functional. Based on theGalitskii-Migdal total energy, structural properties are investigated for a setof diatomic molecules. For binding energies, bond lengths, and vibrationalfrequencies sc-GW and G0W0 achieve a comparable performance, which is, however,not as good as that of exact-exchange plus correlation in the random-phaseapproximation (EX+cRPA) and its advancement to renormalized second-orderperturbation theory (rPT2). Finally, the improved description of dipole momentsfor a small set of diatomic molecules demonstrates the quality of the sc-GWground state density.

Self-consistent GW: All-electron implementation with localized basis functions