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

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