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

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.