Quantum critical benchmark for density functional theory

TL;DR

This paper provides a highly accurate benchmark for density functional theory using a two-electron ion near the ionization threshold, highlighting challenges for approximations and correlation effects.

Contribution

It introduces a precise computational benchmark for DFT at the critical ionization point and discusses the implications for functional approximations.

Findings

Accurate density and energy components for the two-electron ion near critical charge

Parametrization of the critical density

Discussion of correlation strength and DFT challenges

Abstract

Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. A pseudospectral method yields a very accurate density of the two-electron ion with nuclear charge close to the critical value. Highly accurate energy components and potentials of Kohn-Sham density functional theory are given, as well as a useful parametrization of the critical density. The challenges for density functional approximations and the strength of correlation are also discussed.