Fully self-consistent GW calculations for atoms and molecules

TL;DR

This paper performs fully self-consistent GW calculations for atoms and molecules, demonstrating improved ionization potentials and the reliability of the Luttinger-Ward functional for testing self-energy approximations.

Contribution

It introduces a fully self-consistent GW approach for atoms and molecules and shows the effectiveness of the Luttinger-Ward functional in evaluating energy differences.

Findings

Self-consistent GW yields accurate ionization potentials.

Total energies differ from exact values but energy differences are reliable.

Self-consistent GW often outperforms non-self-consistent G0W0 results.

Abstract

We solve the Dyson equation for atoms and diatomic molecules within the GW approximation, in order to elucidate the effects of self-consistency on the total energies and ionization potentials. We find GW to produce accurate energy differences although the self-consistent total energies differ significantly from the exact values. Total energies obtained from the Luttinger-Ward functional E_LW[G] with simple, approximate Green functions as input, are shown to be in excellent agreement with the self-consistent results. This demonstrates that the Luttinger-Ward functional is a reliable method for testing the merits of different self-energy approximations without the need to solve the Dyson equation self-consistently. Self-consistent GW ionization potentials are calculated from the Extended Koopmans Theorem, and shown to be in good agreement with the experimental results. We also find the self-consistent ionization potentials to be often better than the non-self-consistent G0W0 values. We conclude that GW calculations should be done self-consistently in order to obtain physically meaningful and unambiguous energy differences.