The density, ρ = ∑ i f i |φ i | 2 , is defined using orbitals with allowed fractional occupation factors, f i , that reflect the nature of the ensemble. Ensembles are thus amenable the same machinery as standard DFT -that is, by approximating E Hxc [ρ] and then finding a set of self-consistent orbitals and density. Accommodating ensembles in Kohn-Sham DFT not only extends approximations to new problems (like excited states), but can also remedy deficiencies in standard approximations. A major difficulty in treating ensembles is that the minimizing wave functions and ensembles are not guaranteed to be unique and cannot be used explicitly to define functionals -the "nonuniqueness disaster". 427 This is related to issues raised in contribution (3.7.1). One must thus resort to more foundational relationships to further break E Hxc into useful pieces that may then be approximated. A rigorous separation into Hartreeexchange and correlation terms is achieved by using,