A simple algorithm for the Kohn–Sham inversion problem applicable to general target densities

A simple algorithm for the Kohn–Sham inversion problem is presented. The method is found to converge toward a nearby ν$$\nu$$-representable Kohn–Sham density irrespective of the fact whether the initial target density has been ν$$\nu$$-representable or not. For the proposed procedure, the target density can be of general nature. The algorithm can handle Hartree–Fock and post-Hartree–Fock, spin-unpolarized and polarized states equally well. Additionally, experimental densities and even general gedanken densities can be treated. The algorithm is easy to implement and does not require an additional procedure to adjust eigenvalues.