  Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple
derivation of the density-functional correction of the Hartree-Fock equations,
the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated
view of quantum mechanical theories, in which the Kohn-Sham equations, the
Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation
formally stem from a common ground: density-functional theory, through its
Euler equation for the ground-state density. Along similar lines, the Kohn-Sham
formulation of the Hartree-Fock approach is also considered. Further, it is
pointed out that the exchange energy of density-functional theory built from
the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle
density functionals (N=1,2,...), forming a sequence of degree-two homogeneous
exchange-energy density functionals, the first element of which is minus the
classical Coulomb-repulsion energy functional.
