Qualitative breakdown of the unrestricted Hartree-Fock energy

TL;DR

This paper examines the limitations of unrestricted Hartree-Fock and density functional methods in accurately modeling certain two-electron molecules, highlighting issues with symmetry breaking and potential energy surface inaccuracies.

Contribution

It introduces specific two-electron molecules that exacerbate symmetry-breaking problems in UHF and DFT, revealing significant inaccuracies in potential energy surfaces.

Findings

UHF fails with certain two-electron molecules, causing incorrect energy surfaces.

DFT with B3LYP also exhibits symmetry breaking and delocalization errors.

The study highlights fundamental limitations in common electronic structure methods.

Abstract

The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also fail with unrestricted density-functional calculations where a functional such as B3LYP gives both symmetry breaking and an unphysically low energy due to the delocalization error. The implications for density functional theory are also discussed.