Removal of Basis-Set Artifacts in Kohn-Sham Potentials Recovered from Electron Densities

Kohn-Sham effective potentials recovered from Gaussian-basis-set electron densities exhibit large oscillations and asymptotic divergences not found in exact potentials and in functional derivatives of approximate density functionals. We show that the detailed structure of these oscillations and divergences is almost exclusively determined by the basis set in terms of which the reference density is expressed, and is almost independent of the density-functional or wave function method used for computing the density. Based on this observation, we propose a smoothening scheme in which most basis-set artifacts in a Kohn-Sham potential recovered from a given density are removed by subtracting the oscillation profile of the exchange-only local-density approximation potential computed in the same basis set as the reference density. The correction allows one to obtain smooth Kohn-Sham potentials from electron densities even for small Gaussian basis sets and greatly reduces discrepancies between the original (input) density and the density obtained from the reconstructed potential.