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

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 Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of CoulombHamiltionans 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.

Correlating the Antisymmetrized Geminal Power Wave Function

“…Note also that while the pairing Hamiltonian is not particularly relevant for chemistry, its eigenstates can be useful in the description of molecular dissociation. 57 Geminal wave functions of various sorts have gone in and out of fashion over the years. At least in chemistry, AGP has not seen a huge amount of use in the past few decades.…”

Geminal replacement models based on AGP

“…Recently, Johnson et al have shown that the eigenfunctions of the pairing Hamiltonian can be used for the molecular Hamiltonian 61 . We believe that the tools and concepts developed in this work can be extended to describe seniority-breaking systems.…”