Levels of self-consistency in the GW approximation

TL;DR

This paper explores various levels of self-consistency in GW calculations for atoms and molecules, proposing a partially self-consistent scheme that balances accuracy and computational efficiency.

Contribution

It introduces a novel partially self-consistent GW scheme that maintains accuracy while reducing computational cost compared to fully self-consistent methods.

Findings

Partially self-consistent GW yields results close to fully self-consistent GW.

The new scheme improves total energies and energy differences over G0W0.

Results are in excellent agreement with more expensive GW calculations.

Abstract

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 on 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 $G W_0$ and the $G_0W_0$ 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 $G_0W_0$ values but yield better total energies and energy differences.