Duality of particle-hole and particle-particle theories for strongly correlated electronic systems

TL;DR

This paper introduces a new combined particle-hole and particle-particle approach within the RPA framework for multireference systems, improving correlation energy descriptions and outperforming individual methods in strongly correlated electronic systems.

Contribution

It establishes a formal duality between ph and pp theories and develops a combined method that avoids double counting, enhancing accuracy for strongly correlated states.

Findings

Combined ph-pp method outperforms individual approaches.

Fails to describe dissociation of multiple bonds with pp alone.

Achieves high accuracy with only one- and two-body density matrices.

Abstract

We propose a novel approach to electron correlation for multireference systems. It is based on particle-hole (ph) and particle-particle (pp) theories in the second-order, developed in the random phase approximation (RPA) framework for multireference wavefunctions. We show a formal correspondence (duality), between contributions to the correlation energy in the ph and pp pictures. It allows us to describe correlation energy by rigorously combining pp and ph terms, avoiding correlation double counting. The multireference ph, pp, and the combined correlation methods are applied to ground and excited states of systems in the intermediate and strong correlation regimes and compared with the multireference second-order perturbation method (MRPT2). It is shown that the pp approximation fails to describe dissociation of multiple bonds. The ph-pp combined method is overall superior to both ph and pp alone. It parallels good accuracy of the second-order perturbation theory for ground states and singlet excitation energies. For the singlet-triplet gaps of biradicals its accuracy is significantly better. This is impressive, taking into account that it relies only on one- and two-body density matrices, while MRPT2 methods typically require density matrices up to the four-body.