  The State--Specific Kohn--Sham Density Functional Theory
[arXiv:physics/0506037] is used to derive the Kohn-Sham exchange-correlation
potential $\vxc$ and exchange-correlation energy $\Eco$ as explicit functionals
of $v_s$ and $\phi_1$, where $v_s$ is the local, one-body potential from the
Kohn--Sham equations, and $\phi_1$ is the spinless one-particle density matrix
from the Kohn--Sham noninteracting state, say $|\phi_1\ran$. In other words,
$|\phi_1\ran$ is the ground state eigenfunction of the noninteracting
Schr\"odinger equation with the one-body potential $v_s$. For simplicity, we
only consider noninteracting states that are closed-shell states and
interacting states that are nondegenerate, singlet ground-states.
