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

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 (G3W 2) 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 G3W 2 contribution does not give consistent improvements over GW , taking the average of GW and GW + G3W 2 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. G0W0 quasiparticle energies evaluated with eigenvalue and orbitals from range-separated hybrids, however, are tremendously improved upon: The second-order corrected G0W0 outperforms all existing GW methods for the systems considered herein and also does not come with substantially increased computational cost compared to G0W0 for systems with up to 100 atoms.