Comparing Self-Consistent GW and Vertex-Corrected G₀W₀ (G₀W₀Γ) Accuracy for Molecular Ionization Potentials

We test the performance of self-consistent GW and several representative implementations of vertex-corrected G₀W₀ (G₀W₀Γ). These approaches are tested on benchmark data sets covering full valence spectra (first ionization potentials and some inner valence shell excitations). For small molecules, when comparing against state-of-the-art wave function techniques, our results show that full self-consistency in the GW scheme either systematically outperforms vertex-corrected G₀W₀ or gives results of at least comparative quality. Moreover, G₀W₀Γ results in additional computational cost when compared to G₀W₀ or self-consistent GW. The dependency of G₀W₀Γ on the starting mean-field solution is frequently more dominant than the magnitude of the vertex correction itself. Consequently, for molecular systems, self-consistent GW performed on the imaginary axis (and then followed by modern analytical continuation techniques) offers a more reliable approach to make predictions of ionization potentials.