  A generalization of the Kohn--Sham approach is derived where the
correlation-energy functional depends on the one-particle density matrix of
noninteracting states and on the external potential from the interacting
target-state. The one-particle equations contain the exact exchange potential,
a nonlocal correlation potential, and an additional operator involving the
correlation density. The electronic-energy functional has multiple solutions:
Any one-particle density matrix delivering the target-state density yields a
solution. In order to obtain the Kohn--Sham solution, the nonlocal operators
are converted into local ones using an approach developed by Sala and Gorling.
Since the exact exchange-potential is used, and the N--representability problem
does not arise--in contrast to the Kohn--Sham approach--errors from Coulomb
self-interactions do not occur, nor the need to introduce functionals defined
by a constraint search. Furthermore, the approach does not use the
Hohenberg-Kohn theorem. A density functional formalism is also derived that
assumes that the one-particle density matrices of interest have v-representable
(non-interacting) densities and that these density matrices can be written as
an explicit functional of the electron density. For simplicity, we only
consider noninteracting closed-shell states and target states that are
nondegenerate, singlet ground-states.
