  We show that the Hartree-Fock (HF) results cannot be reproduced within the
framework of Kohn-Sham (KS) theory because the single-particle densities of
finite systems obtained within the HF calculations are not $v$-representable,
i.e., do not correspond to any ground state of a $N$ non-interacting electron
systems in a local external potential. For this reason, the KS theory, which
finds a minimum on a different subset of all densities, can overestimate the
ground state energy, as compared to the HF result. The discrepancy between the
two approaches provides no grounds to assume that either the KS theory or the
density functional theory suffers from internal contradictions.
