Density-functional theory for ensembles of fractionally occupied states. I. Basic formalism

A density-functional theory for ensembles of unequally weighted states is formulated on the basis of the generalized Rayleigh-Ritz principle of the preceding paper. From this formalism, two alternative approaches to the computation of excitation energies are derived, one equivalent to the equiensemble method proposed by Theophilou J. Phys. C 12, 5419 (1979), the other grounded on an expression relating the excitation energies to the Kohn-Sham single-particle eigenvalues.