It is first pointed out that in the jellium model of the homogeneous electron liquid, the correlation energyEc/Nper particle can be directly related to the ratio of the single-particle kinetic energyTsto the exchange energy A. The relevance of this result to the inhomogeneous electron liquid is then explored for light atoms. Such a relation again obtains, but with a markedly different coefficient of proportionality. With such a form of correlation energy, Ec, the Euler equation of density functional theory has somewhat reduced “coefficients” of δTs/δρ(r) and δA/δρ(r). The Hartree-Fock Euler equation is regained by puttingEc= 0. Modified Slater-Kohn-Sham equations are obtained, their use being illustrated by an atomic example.