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 V-ee[rho] may be expressed in the form V-ee[rho]=<integral rho(r)delta V-ee[rho]/delta rho(r)dr-1/2 integral integral rho(r)rho(r')delta(2)V(ee)[rho]/delta(rho)(r)delta rho(r') drdr'. Also, V-ee[rho] + V-ee((1))[rho] + V-ee((2))[rho], where V-ee((1))[rho] and V-ee((2))[rho] are homogeneous functionals of degree 1 and 2 with respect to the density scaling, respectively, with V-ee((2))[rho] = -NVee(1)[rho]. (C) 1997 Elsevier Science B.V.