Density-Functional exchange-correlation potential and orbital eigenvalues for the Ne-atom

Using a numerical fitting scheme we construct the exact Density-Functional (DF) effective potential, corresponding wave-functions and orbital eigenvalues from an accurate correlated reference density for the neon atom. Our results compare well with those obtained later using a number of different methods, thus demonstrating the utility of the original and relatively simple fitting scheme. The exact DF quantities are then used to test the quality of different improvements (Langreth, Perdew, Mehl, Wang) of the local density approximation (LDA) to DF theory. The tested schemes are seen to considerably reduce the error in the LDA exchange-correlation energy. The density profile is also somewhat improved (particularly close to the core), while the effective potential is only marginally closer to its true DF counterpart.