On pair functions for strong correlations

TL;DR

This paper explores how unrestricted Hartree-Fock (UHF) wave functions can serve as proxies for strong electron correlations through pair functions, demonstrated on hydrogen clusters and related to the Hubbard model.

Contribution

It introduces a method to analyze strong correlations via the overlap of alpha and beta orbitals in UHF solutions, connecting symmetry breaking to correlation strength.

Findings

UHF orbitals evolve smoothly from doubly occupied to symmetry-broken states.

Orbital pairing correlates with the degree of electron correlation.

Spin projection on UHF solutions addresses intermediate correlation challenges.

Abstract

The UHF wave function may be written as a spin-contaminated \textit{pair} wave function of the APSG form, and the overlap of the alpha and beta corresponding orbitals of the UHF solution can be taken as a proxy for the strength of the correlation captured by breaking symmetry. We demonstrate this with calculations on one- and two-dimensional hydrogen clusters and make contact with the well studied Hubbard model. The UHF corresponding orbitals pair in a manner that allows a smooth evolution from doubly occupied orbitals at small distance to one in which wave function breaks symmetry, segregating the $\alpha$ and $\beta$ electrons onto distinct sublattices at large distances. By performing spin projection on these UHF solutions, we address strong correlations that are difficult to capture at intermediate distances using a single determinant. Approved for public release: LA-UR-13-22691.