Describing static correlation in bond dissociation by Kohn-Sham density functional theory

TL;DR

This paper demonstrates that RPA-based density functional theory accurately describes H₂ bond dissociation without symmetry breaking, highlighting static correlation effects and limitations of current approximations.

Contribution

It shows that RPA within Kohn-Sham DFT correctly captures static correlation in bond breaking and analyzes the limitations of RPA+X in dissociation.

Findings

RPA provides accurate adiabatic connection curves for H₂.

RPA+X exhibits unphysical repulsion at large bond lengths.

Absence of double excitations causes deficiencies in RPA+X.

Abstract

We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H$_2$ in a spin-restricted Kohn-Sham formalism, i.e. without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson-Fisher point. The strong curvature at large bond length implies important static (left-right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite and accurate around the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA+X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H$_2$ dissociation limit we show that the RPA+X is not size-consistent, in contrast to the RPA.