V nuc [ρ] can be obtained by numerical integration of Eq. ( ). The numerical evaluation of Ts [ρ] and Ẽxc [ρ] [Eqs. (10) and (11)] additionally requires the density gradient ∇ρ(r k ) at the grid points. Finally, for an efficient numerical integration of Eq. ( ), the Coulomb potential v Coul [ρ](r k ) at each grid point has to be calculated analytically.