Fractional charge and spin errors in self-consistent Green's function theory

TL;DR

This paper investigates fractional charge and spin errors in self-consistent Green's function theory (GF2), showing it reduces errors compared to MP2 and hybrid density functionals, thus improving accuracy for strongly correlated systems.

Contribution

The study generalizes GF2 to open-shell systems and demonstrates its reduced fractional charge and spin errors compared to MP2 and other methods.

Findings

GF2 has very small fractional charge error, indicating low self-interaction error.

GF2 exhibits less fractional spin error than MP2 and hybrid density functionals.

GF2 improves upon MP2's limitations without losing desirable features.

Abstract

We examine fractional charge and spin errors in self-consistent Green's function theory within a second-order approximation (GF2). For GF2 it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Moller-Plesset theory (MP2) for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently little many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.