Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation

TL;DR

This paper investigates the correlation potentials within the random phase approximation for diatomic molecules, revealing key features and limitations of RPA in describing bond dissociation and fractional charges.

Contribution

It provides the first detailed analysis of self-consistent RPA correlation potentials for molecules, highlighting their strengths and shortcomings in modeling dissociation.

Findings

RPA correlation potential shows a peak at the bond midpoint.

RPA lacks the step feature for integer charge preservation.

RPA eliminates fractional spin error, explaining accurate dissociation energies.

Abstract

Self-consistent correlation potentials for H$_2$ and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the accurate total energy in the dissociation limit.