Why Kohn-Sham and Hartree-Fock orbitals are very close to each other. Shell structure of exchange potential

TL;DR

This paper explains why Kohn-Sham and Hartree-Fock orbitals are very similar by showing that the local exchange potential in density functional theory closely matches shell-specific shifted Fock potentials, elucidating their proximity.

Contribution

It demonstrates that the exact local exchange potential is well approximated by shell-specific shifted Fock potentials, clarifying the close relationship between Kohn-Sham and Hartree-Fock orbitals.

Findings

Local exchange potential matches shell-specific shifted Fock potentials

Kohn-Sham and Hartree-Fock orbitals are highly similar in closed-l subshell atoms

Approximations like Krieger-Li-Iafrate are highly accurate for exchange potential

Abstract

It is found that, in closed-$l$-subshell atoms, the exact local exchange potential of the density functional theory is very well represented, within the region of every atomic shell, by each of the suitably shifted potentials obtained with the non-local Fock exchange operator acting on the Hartree-Fock (HF) orbitals that belong to this shell. This explains the outstanding proximity of Kohn-Sham and HF orbitals and the high quality of the Krieger-Li-Iafrate and localized HF (or, equivalently, common-energy-denominator) approximations to the exchange potential.