Additional functional relations in the density functional theory of finite interacting electronic systems

It is argued that, for finite electronic systems, the total kinetic-energy density functional, T[ϱ], the Kohn-Sham kinetic-energy density functional, Ts[ϱ], and the kinetic-energy component of the correlation energy density functional, Tc[ϱ], may each be expressed as a functional homogeneous of degree one in density scaling. That is, T[ϱ] = ∫ϱ(r)(δT[ϱ]/δϱ(r)dr, and similarly with Ts[ϱ] and Tc[ϱ].