Exchange-Correlation Potentials and Energy Densities through Orbital Averaging and Aufbau Integration

TL;DR

This paper develops a method to derive accurate exchange-correlation potentials and energy densities for atoms using orbital-averaged Kohn-Sham inversion based on full configuration interaction data, aiding functional development.

Contribution

It introduces an orbital-averaged inversion procedure and aufbau integration to obtain detailed xc potentials and energy densities from wavefunction data, enhancing DFT accuracy.

Findings

Accurately captures asymptotic decay of vxc

Reproduces step discontinuities at integer electron counts

Achieves good agreement with total Exc values

Abstract

Exchange-correlation potentials vxc and energy densities exc are derived for integer and fractional electron counts using an orbital-averaged Kohn-Sham inversion procedure. The reference densities for inversion come from full configuration interaction in a Slater orbital basis. The orbital-averaged potentials accurately capture key features of vxc, including the asymptotic negative one over r decay and the step discontinuity associated with integer electron transitions for the series of atoms He through Ne. Exchange-correlation energy densities exc are produced through an aufbau path integral. The energy densities reach good agreement with total Exc values. By providing full configuration interaction-derived Kohn-Sham quantities, including vxc, exc, and step contributions, this workflow can be instrumental in the development of improved XC functionals that bridge wavefunction-level accuracy with the computational efficiency of density functional theory.