Richardson-Gaudin mean-field for strong correlation in quantum chemistry

TL;DR

This paper introduces a variational wavefunction ansatz based on Richardson-Gaudin eigenvectors to model strong electron correlation in quantum chemistry efficiently, matching DOCI results for atoms and dissociation curves.

Contribution

It presents a novel polynomial-cost variational approach using Richardson-Gaudin eigenvectors as a wavefunction ansatz for strong correlation in quantum chemistry.

Findings

Accurately reproduces DOCI data for atoms and dissociation curves.

Provides a polynomial-cost variational method for strong electron correlation.

Serves as a foundation for a many-body theory of pairs.

Abstract

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly-interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schr\"{o}dinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltionans and we present results for atoms and dissociation curves which are in agreement with doubly-occupied configuration interaction (DOCI) data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly-correlated electrons.