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

Exchange-correlation potentials (v) and energy densities (e) 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 v, including the asymptotic -1/r decay and the step discontinuity associated with integer electron transitions for the series of atoms He through Ne. Exchange-correlation energy densities e are produced through an aufbau path integral. The energy densities reach good agreement with total E values. By providing FCI-derived KS quantities─v, e, 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.