Determination of Kohn-Sham effective potentials from electron densities using the differential virial theorem

We present an accurate method for constructing the Kohn-Sham effective potential corresponding to a given electron density in one-dimensional and spherically symmetric systems. The method is based on the differential virial theorem--an exact relation between the effective potential, the electron density, and the kinetic energy density. A distinctive feature of the proposed technique is that it employs a size-consistent bosonic reference potential to ensure the correct asymptotic behavior of the resulting Kohn-Sham potential. We describe a practical implementation of our method and use it to obtain high-quality exchange-correlation and correlation potentials of the neon and argon atoms from ab initio densities generated in large Slater- and Gaussian-type basis sets.