Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems

TL;DR

This paper introduces a perturbative $G3W2$ correction to the $GW$ self-energy, improving total energies and charged excitations in finite systems, especially when combined with $GW$ or evaluated with range-separated hybrids.

Contribution

The study demonstrates that the $G3W2$ correction enhances $GW$ results for finite systems and shows that $G_0W_0$ with this correction outperforms existing methods without significant additional computational cost.

Findings

Second-order correction improves correlation energies over RPA.

Averaging $GW$ and $GW + G3W2$ yields excellent results.

Range-separated hybrid $G_0W_0$ with correction surpasses other $GW$ methods.

Abstract

Electron correlation in finite and extended systems is often described in an effective single-particle framework within the $GW$ approximation. Here, we use the statically screened second-order exchange contribution to the self-energy ($G3W2$) to calculate a perturbative correction to the $GW$ self-energy. We use this correction to calculate total correlation energies of atoms, relative energies, as well as charged excitations of a wide range of molecular systems. We show that the second-order correction improves correlation energies with respect to the RPA and also improves relative energies for many, but not all considered systems. While the full $G3W2$ contribution does not give consistent improvements over $GW$, taking the average of $GW$ and $GW + G3W2$ generally gives excellent results. Improvements over quasiparticle self-consistent $GW$, which we show to give very accurate charged excitations in small and medium molecules by itself, are only minor. $G_0W_0$ quasiparticle energies evaluated with eigenvalue and orbitals from range-separated hybrids, however, are tremendously improved upon: The second-order corrected $G_0W_0$ outperforms all existing $GW$ methods for the systems considered herein and also does not come with substantially increased computational cost compared to $G_0W_0$ for systems with up to 100 atoms.