Kohn–Sham orbitals and orbital energies: fictitious constructs but good approximations all the same

Abstract

Kohn and Sham introduced orbitals into density–functional theory (DFT) as a set of physically meaningless auxiliary quantities useful only for calculating the total energy and charge density. While the traditional view is that Kohn–Sham orbitals do not approximate anything, Duffy et al. [ Phys. Rev. A 50 (1994) 4707] showed that Kohn–Sham orbitals calculated using approximate exchange-correlation (xc) potentials could provide excellent approximations to spherically averaged momentum distributions, despite the fact that the corresponding Kohn–Sham orbital energies do not provide good approximations to ionization potentials when typical common present-day functionals are used. Since the original conclusions were based upon approximate xc potentials, the question arises as to how these conclusions might change when the same orbitals and orbital energies are calculated using an exact (or nearly exact) xc potential. For example, it has long been known that the highest occupied molecular orbital energy should give the exact ionization potential when the DFT xc functional is exact, but that this is not observed for approximate potentials. What about the other orbital energies? Long regarded as artifactual, we show that (1) Kohn–Sham orbital energies calculated using the exact Kohn–Sham exchange potential are actually better approximations to experimental ionization potentials than are Hartree–Fock orbital energies calculated via Koopmans’ theorem. We also show that (2) there are only negligable differences between spherically averaged momentum distributions calculated from HF orbitals and from Kohn–Sham orbitals calculated using the exact Kohn–Sham exchange potential, thus partially addressing the question of how the use of the exact Kohn–Sham potential will affect predictions for electron momentum spectroscopy. In addition to the two numbered observations above can be added that (3) it is quite remarkable that a nominally initial state theory such as DFT can do so well in describing ionization, a phenomenon which one expects to be sensitive to both initial and final states (before and after the ionization event).