Multi-reference GW approximation for strongly correlated molecules

TL;DR

The paper introduces the multi-reference GW (MR-GW) approximation, extending Green's function methods to strongly correlated molecules by incorporating non-perturbative correlation effects through a diagrammatic framework.

Contribution

It develops a rigorous diagrammatic framework for MR-GW, enabling accurate treatment of strong correlations in molecules beyond standard GW.

Findings

MR-GW accurately predicts ionization potentials in strongly correlated molecules.

It captures many-body satellites missed by standard GW.

MR-GW seamlessly combines strong and weak correlation effects.

Abstract

The GW approximation is a cornerstone of many-body perturbation theory for computing single-particle excitations, yet it fundamentally breaks down in strongly correlated systems where the single-reference picture fails. To overcome this long-standing limitation, we introduce the multi-reference GW (MR-GW) approximation, which incorporates strong correlation effects non-perturbatively into an interacting multi-determinantal zeroth-order reference. While the standard Dyson equation is inapplicable in this setting, we show that the GW approximation can be naturally generalized by developing a rigorous diagrammatic framework with an interacting reference. Specifically, we define the MR-GW self-energy using a diagrammatic expansion based on the generalized Dyson equation, and utilize a multi-reference random phase approximation for the screened interaction, which captures many-body processes absent in standard GW. Applications to challenging strongly correlated molecules demonstrate that MR-GW seamlessly captures both strong and weak correlations, yielding more accurate ionization potentials and recovering complex many-body satellites missed by standard $GW$. This work establishes a rigorous diagrammatic paradigm for extending ab initio Green's function methods into the strongly correlated regime.