Equation satisfied by the energy-density functional for electron-electron mutual Coulomb repulsion

It is shown that the electron- electron mutual Coulomb repulsion energy- density functional V-ee(gamma)[rho] satisfies the equation V-ee(gamma)[rho(1)(N)] - V-ee(gamma)[rho(gamma)(N-1)] = integral d(3)r delta V-ee(gamma)[rho(1)(N)]/delta rho(1)(N)(r)[rho(1)(N)(r) rho(gamma)(N-1) (r)], where rho(1)(N) (r) and rho(gamma)(N-1) N-electron and (N - 1)electron densities determined from the same adiabatic scaled external potential of the N-electron system at coupling strength gamma.