In the Kohn-Sham treatment, we then have a choice: (i) We can require the spin density to be identical in the Kohn-Sham and true electronic systems. This choice amounts to a spin-polarized Kohn-Sham calculation with a Kohn-Sham Hamiltonian operator that is no longer rotationally invariant in spin space. Spin is then no longer a good quantum number for the Kohn-Sham determinant -that is, spin poisoning occurs. (ii) Alternatively, we can require the total density but not the individual spin densities of the Kohn-Sham system to be identical to the true electronic system. The Kohn-Sham Hamiltonian operator then remains rotationally invariant in spin space and we get identical spin-up and -down orbitals. As a result, the orbitals and the Kohn-Sham wave function can be chosen to have well-defined spin but the individual Kohn-Sham spin-up and -down densities are no longer identical to those of the true electronic system. In practice, approach (i) is typically taken -however, approach (ii) is equally correct from a formal perspective, a point Walter Kohn made from time to time.