Projected Hartree-Fock Theory

TL;DR

This paper develops a new variation after projection Hartree-Fock method that is computationally efficient, applicable to various symmetries, and produces high-quality multireference wavefunctions, with applications to dissociation and spin splitting.

Contribution

It introduces a novel PHF approach with simple expressions, broad symmetry applicability, and benchmark validation, reviving and extending classical PHF techniques.

Findings

PHF wavefunctions show high multireference character.

Energy in PHF is not lower than broken-symmetry HF in the thermodynamic limit.

Method is computationally modest and versatile for different symmetries.

Abstract

Projected Hartree-Fock theory (PHF) has a long history in quantum chemistry. PHF is here understood as the variational determination of an N-electron broken symmetry Slater determinant that minimizes the energy of a projected state with the correct quantum numbers. The method was actively pursued for several decades but seems to have been abandoned. We here derive and implement a "variation after projection" PHF theory using techniques different from those previously employed in quantum chemistry. Our PHF methodology has modest mean-field computational cost, yields relatively simple expressions, can be applied to both collinear and non-collinear spin cases, and can be used in conjunction with deliberate symmetry breaking and restoration of other molecular symmetries like complex conjugation and point group. We present several benchmark applications to dissociation curves and singlet-triplet energy splittings, showing that the resulting PHF wavefunctions are of high quality multireference character. We also provide numerical evidence that in the thermodynamic limit, the energy in PHF is not lower than that of broken-symmetry HF, a simple consequence of the lack of size consistency and extensivity of PHF.