A general penalty method for density-to-potential inversion

A general penalty method is presented for the construction of of Kohn-Sham system for given density through Levy’s constrained-search. The method uses a functional $S[\rho ]$ of one’s choice. Different forms of $S[\rho ]$ are employed to calculate the kinetic energy and exchange-correlation potential of atoms, jellium spheres, and Hookium and consistency among results obtained from them is shown.