Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation

TL;DR

This paper compares the static correlation and delocalization errors in self-consistent GW and RPA methods during molecular dissociation, revealing that RPA better captures static correlation while GW exhibits significant delocalization errors.

Contribution

It provides a detailed analysis of static correlation and delocalization errors in GW and RPA, including explicit formulas and insights into their differences during molecular dissociation.

Findings

RPA yields larger correlation energies, better describing static correlation.

GW shows significant delocalization errors, especially at dissociation.

Explicit formulas for GW Green's function and energy are derived for a simplified model.

Abstract

We investigate static correlation and delocalization errors in the self-consistent GW and random-phase approximation (RPA) by studying molecular dissociation of the H_2 and LiH molecules. Although both approximations contain topologically identical diagrams, the non-locality and frequency dependence of the GW self-energy crucially influence the different energy contributions to the total energy as compared to the use of a static local potential in the RPA. The latter leads to significantly larger correlation energies which allow for a better description of static correlation at intermediate bond distances. The substantial error found in GW is further analyzed by comparing spin-restricted and spin-unrestricted calculations. At large but finite nuclear separation their difference gives an estimate of the so-called fractional spin error normally determined only in the dissociation limit. Furthermore, a calculation of the dipole moment of the LiH molecule at dissociation reveals a large delocalization error in GW making the fractional charge error comparable to the RPA. The analyses are supplemented by explicit formulae for the GW Green's function and total energy of a simplified two-level model providing additional insights into the dissociation limit.