A similar choice can be made with respect to symmetries in real space. In open-shell atoms, for example, one can either require that the total density or the spin densities for the Kohn-Sham system and true electronic systems are identical or require that only their totally symmetric (i.e., spherical) real-space components are identical. Depending on the choice made, the Kohn-Sham Hamiltonian either has a symmetry lower than the spherical symmetry of the true Hamiltonian in real space or is spherically symmetric in real space like the Hamiltonian of the true electronic system.