Density functional theory from spherically symmetric densities.

In a recent paper, Theophilou [J. Chem. Phys 149 , 074104 (2018)] proved that in molecules and solids, a set of spherically symmetric densities determines uniquely the external potential. Here an alternative derivation of Theophilou's new theorem is presented. A somewhat more general version is also proved via constrained search. Euler equations and Kohn-Sham equations are derived for spherically symmetric densities.