One-electron self-interaction and the asymptotics of the Kohn-Sham potential: an impaired relation

TL;DR

This paper investigates the limitations of current density functionals in accurately describing one-electron systems, highlighting issues with self-interaction correction and asymptotic behavior of the Kohn-Sham potential, and suggests the need for reevaluation of existing strategies.

Contribution

It demonstrates that self-interaction-free energies do not guarantee correct potential asymptotics and reveals limitations of the iso-orbital indicator near nodal planes, prompting reconsideration of correction methods.

Findings

Self-interaction-free energies do not ensure correct potential asymptotics.

The iso-orbital indicator can fail near orbital nodal planes.

Strategies for self-interaction correction need reevaluation.

Abstract

One-electron self-interaction and an incorrect asymptotic behavior of the Kohn-Sham exchange-correlation potential are among the most prominent limitations of many present-day density functionals. However, a one-electron self-interaction-free energy does not necessarily lead to the correct long-range potential. This is here shown explicitly for local hybrid functionals. Furthermore, carefully studying the ratio of the von Weizs\"acker kinetic energy density to the (positive) Kohn-Sham kinetic energy density, $\tau_\mathrm{W}/\tau$, reveals that this ratio, which frequently serves as an iso-orbital indicator and is used to eliminate one-electron self-interaction effects in meta-generalized-gradient approximations and local hybrid functionals, can fail to approach its expected value in the vicinity of orbital nodal planes. This perspective article suggests that the nature and consequences of one-electron self-interaction and some of the strategies for its correction need to be reconsidered.