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

Exchange-correlation potentials (<i>v</i>_<i>xc</i>) and energy densities (<i>e</i>_<i>xc</i>) are derived for integer and fractional electron counts using an orbital-averaged (OA) Kohn-Sham (KS) inversion procedure. The reference densities for inversion come from full configuration interaction (FCI) in a Slater orbital basis. The OA potentials accurately capture key features of <i>v</i>_<i>xc</i>, including the asymptotic -1/<i>r</i> decay and the step discontinuity associated with integer electron transitions for the series of atoms He through Ne. Exchange-correlation energy densities <i>e</i>_<i>xc</i> are produced through an aufbau path integral. The energy densities reach good agreement with total <i>E</i>_<i>xc</i> values. By providing FCI-derived KS quantities─<i>v</i>_<i>xc</i>, <i>e</i>_<i>xc</i>, 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.