  Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set
of spherically symmetric densities determines uniquely the external potential
in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations
are derived. The spherical densities can be expressed with radial wave
functions. Expression for the total energy is also presented.
