Kohn-Sham theory and the representability problem

The representability problems related to the one-particle density ρ{variant}(1) and, more generally, to the 1-matrix γ(1,1') are discussed in the context of the Kohn-Sham (KS) formalism. It is shown that this formalism implies a projection (on a one-particle space) which does not preserve the representability conditions. A comparison between interacting and non-interacting systems is made, in the spirit of the Hohenberg-Kohn theorem, and it is shown that even though these systems may have the same one-particle densities they must necessarily have different 1- and 2-matrices. A more general approach based on a constrained variation is also outlined. The implications of this result on the energy functional are analysed.