Improvement of functionals in density functional theory by the inverse Kohn?Sham method and density functional perturbation theory

We propose a way to improve energy density functionals (EDFs) in 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.