Exchange and correlation energies in density-functional theory: Bounds from available data

It is pointed out that the Kohn-Sham orbitals, for the exact interacting ground-state energy and density for the external potential of interest v(r), are simultaneously the optimum orbitals of the exact exchange?(hyonly computation for the modified external potential v(r)+$v_c$(r), where $v_c$(r) is the correlation potential. This theorem is used to derive necessary bounds that the exact density-functional-theory correlation energy must satisfy in terms of approximate correlation energies which are obtained from available data. Numerical examples of one of the bounds is given with respect to the surface correlation energies of jellium metal.