Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations

TL;DR

This paper introduces a polynomial similarity transformation theory based on spin-projected Hartree-Fock, enabling a unified approach to correlated electronic structure calculations with analytic expressions and optimized excitation amplitudes.

Contribution

It presents a novel single-excitation polynomial similarity transformation framework that unifies projected Hartree-Fock and coupled cluster methods, with an analytic polynomial expansion and optimized amplitudes.

Findings

Analytic polynomial expansion for spin-projected Hartree-Fock.

Equivalence of amplitude optimization to orbital optimization.

Reproduction of variational results with pair excitations.

Abstract

Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.