Projected Quasiparticle Theory for Molecular Electronic Structure

TL;DR

This paper introduces a symmetry-projected Hartree-Fock-Bogoliubov method for molecular electronic structure, enabling a comprehensive treatment of strong correlations with mean-field computational cost.

Contribution

It develops and implements a self-consistent symmetry-projected HFB approach that restores multiple symmetries and captures strong correlations efficiently.

Findings

Method effectively handles strong correlations in molecules.

Wave function exhibits multireference character.

Demonstrated power through proof-of-principle examples.

Abstract

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of strong correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for electronic structure theory.