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

Under certain assumptions, it is proved that for finite systems the electron-electron repulsion functional Vee[ϱ] may be expressed in the form Vee[ϱ] = Vee(1)[ϱ] + Vee(2)[ϱ], where Vee(1)[ϱ] and Vee(2)[ϱ] are homogeneous functionals of degree 1 and 2 with respect to the density scaling, respectively, with Vee(2)[ϱ] = −NVee(1)[ϱ].