Excitation energies from density-functional orbital energies

It is shown that the exact difference between the ground-state and first-excited-state electronic energies can be obtained, in principle, as the difference of highest occupied orbital energies from two separate Kohn-Sham calculations. Alternatively, this excitation energy may be taken as the difference between the lowest unoccupied and highest occupied orbital energies of a single Kohn-Sham calculation, provided that one corrects for a certain derivative discontinuity in the exchange-correlation potential that is analogous to the one for the band gap in solids.