For the paradigmatic case of bond-breaking in molecular dissociation, I compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. For an unbiased comparison and to prevent spurious starting point effects, both approaches are iterated to full self-consistency (i.e., scRPA and scGW). The exchange-correlation diagrams in both approaches are topologically identical, but in scRPA they are evaluated with noninteracting and in scGW with interacting Green's functions. This has a profound consequence for the dissociation region, where scRPA is superior to scGW. While RPA and scRPA dissociate the H2 molecule correctly, they do worse for N2 and C2 and fail completely for H2+. To improve on this situation, we start from the Bethe–Goldstone equation (BGE) to derive a simple orbital-dependent correlation functional (BGE2) which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair correlations. BGE2 is size consistent and one-electron ‘self-correlation’ free. The self-consistent coupling ensures the correct H dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap. To make BGE2 applicable to polyelectronic systems, we incorporate a screened version into a double hybrid density-functional, termed ZRPS. ZRPS excels at bond-breaking as exemplified by a good performance for N2 and C2 dissociation. At the computational cost of MP2, ZRPS provides a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.

Self-consistent many-body methods for bond-making and breaking

253rd National Meeting (2017)

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