Levels of self-consistency in the GW approximation

We perform GW calculations on atoms and diatomic molecules at different levels of self-consistency and investigate the effects of self-consistency on total energies, ionization potentials, and particle number conservation. We further propose a partially self-consistent GW scheme in which we keep the correlation part of the self-energy fixed within the self-consistency cycle. This approximation is compared to the fully self-consistent GW results and to the GW(0) and the G(0)W(0) approximations. Total energies, ionization potentials, and two-electron removal energies obtained with our partially self-consistent GW approximation are in excellent agreement with fully self-consistent GW results while requiring only a fraction of the computational effort. We also find that self-consistent and partially self-consistent schemes provide ionization energies of similar quality as the G(0)W(0) values but yield better total energies and energy differences.