Assessment of density functional approximations: long-range correlations and self-interaction effects

TL;DR

This paper evaluates how well common density functional approximations handle long-range electron correlations and self-interaction effects, revealing significant inaccuracies in their predictions of electron densities and potentials.

Contribution

It provides a critical assessment of the performance of various density functional approximations on a simple two-electron system, highlighting their limitations in capturing non-local correlations.

Findings

Local and semi-local functionals show significant errors in potentials and densities.

Even the best functionals fail to accurately describe long-range correlations.

Self-interaction effects are inadequately modeled by common approximations.

Abstract

The complex nature of electron-electron correlations is made manifest in the very simple but non-trivial problem of two electrons confined within a sphere. The description of highly non-local correlation and self-interaction effects by widely used local and semi-local exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles.