Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory

TL;DR

This paper compares self-consistent GW and RPA methods for H2 dissociation, finding that RPA outperforms GW in bond-breaking scenarios due to differences in correlation energy treatment.

Contribution

It demonstrates that density-functional theory with RPA provides a more accurate description of bond-breaking than many-body perturbation theory with GW.

Findings

sc-RPA is superior to sc-GW in dissociation regions

DFT with RPA outperforms MBPT in bond-breaking scenarios

Differences are mainly due to correlation energy treatment

Abstract

For the paradigmatic case of H2-dissociation we compare state-of-the-art many-body perturbation theory (MBPT) in the GW approximation and density-functional theory (DFT) in the exact-exchange plus random-phase approximation for the correlation energy (EX+cRPA). For an unbiased comparison and to prevent spurious starting point effects both approaches are iterated to full self-consistency (i.e. sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with non-interacting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, the DFT framework outperforms the many-body framework when it comes to bond-breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.