  We propose a way to improve energy density functionals (EDFs) in the density
functional theory based on the combination of the inverse Kohn--Sham method and
the density functional perturbation theory. Difference between the known EDF
and the exact one is treated as the first-order perturbation. As benchmark
calculations, we reproduce the theoretical exchange and correlation functionals
in the local density approximation. Systems of noble-gas atoms are used for
benchmark calculations, and the ground-state energies and densities, as well as
the functionals, are reproduced with good accuracies.
