Simple model for the spherically- and system-averaged pair density: Results for two-electron atoms

TL;DR

This paper extends a model for pair density from uniform to nonuniform two-electron systems, achieving highly accurate short-range properties and correlation energies, with promising implications for density functional theory.

Contribution

It introduces a simple model for the pair density in nonuniform systems, demonstrating high accuracy for two-electron atoms and potential for DFT applications.

Findings

Accurate short-range pair densities for two-electron atoms.

Kohn-Sham correlation energies with errors less than 4 mHartree.

Short-range correlation energies with an order of magnitude better accuracy.

Abstract

As shown by Overhauser and others, accurate pair densities for the uniform electron gas may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion. In this work we explore the extension of this approach to nonuniform systems, and we discuss its potential for density functional theory. For the spherically- and system-averaged pair density of two-electron atoms we obtain very accurate short-range properties, including, for nuclear charge $Z\ge 2$, ``on-top'' values (zero electron-electron distance) essentially indistinguishable from those coming from precise variational wavefunctions. By means of a nonlinear adiabatic connection that separates long- and short-range effects, we also obtain Kohn-Sham correlation energies whose error is less than 4 mHartree, again for $Z\ge 2$, and short-range-only correlation energies whose accuracy is one order of magnitude better.