Validation of Koopmans' theorem for density functional theory binding energies

Both initial state effects, to a good approximation the electrostatic potential at the nucleus, and final state effects, due to the response of the electrons to the presence of the core-hole, contribute to core-level binding energies, BE's. For Hartree-Fock, HF, wavefunctions, Koopmans' theorem, KT, which states that the initial state BE = -epsilon ?s rigorous. However, the KT relationship is commonly used for Kohn-Sham, KS, epsilon's. We review that the KT relationship with KS epsilon's fails to give the absolute initial state contribution to the BE. However, we demonstrate that the shifts of initial state BE's from a reference value are accurately obtained from the shifts of the KS epsilon's. Thus the initial state contributions to BE shifts can be obtained from KT using KS epsilon's. This result validates a large body of work where KT has been used with KS epsilon's to define initial state contributions to BE shifts.