The problem is that F nor T s are everywhere discontinuous and therefore not differentiable 685 -more precisely, they are subdifferentiable but only on a (dense) subset of their domains and there is no reason to believe that these subsets are the same for the interacting and noninteracting problems. In short, we cannot hope to find a Kohn-Sham noninteracting system with exactly the same ground-state density as the interacting system.