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We proposed in Ref. [arXiv:1812.09285v2] a way to improve energy densityfunctionals in the density functional theory based on the combination of theinverse Kohn-Sham method and the density functional perturbation theory. Inthis proceeding, we mainly focus on the results for the $ \mathrm{Ar} $ and $\mathrm{Kr} $ atoms.

How to Improve Functionals in Density Functional Theory? ---Formalism and Benchmark Calculation---