Quasiparticle and fully self-consistent GW methods: An unbiased analysis using Gaussian orbitals

We present a comparison of various approximations to the self-consistent GW methods, including the oneshot G0W0 method, different quasiparticle self-consistent schemes, and the fully self-consistent GW (scGW ) approach. To ensure an unbiased and equitable comparison, we have implemented all the schemes with the same underlying Matsubara formalism, while employing Gaussian orbitals to describe the system. Aiming to assess and compare different GW schemes, we analyze band gaps in semiconductors and insulators, as well as ionization potentials in molecules. Our findings reveal that for solids, the different self-consistent schemes perform very similarly. However, for molecules, full self-consistency outperforms all other approximations, i.e., the one-shot and quasiparticle self-consistent GW methods. Our work highlights the importance of implementation details when comparing different GW methods. By employing state-of-the-art fully self-consistent, finite temperature GW calculations, we have successfully addressed discrepancies in the existing literature regarding its performance. Our results also indicate that when stringent thresholds are imposed, the scGW method consistently yields accurate results.