Average Local Ionization Energies in the Hartree−Fock and Kohn−Sham Theories

We explore the connection between average local ionization energies computed within the Hartree-Fock (HF) and the Kohn-Sham (KS) frameworks, focusing on exchange-only KS theory. We find that they are connected through a local quantity for which good approximations exist; I(HF)(r) = I(KS)(r) + DeltaV(X)(r). This allows determination of HF local ionization energies from exchange-only KS calculations without utilizing a nonlocal potential. We also suggest interesting research directions that emerge during our analysis.