where (v | ρ) = v(r)ρ(r)dr. Since E and F can be calculated from each other, they contain the same information, only expressed in different ways. However, although the Lieb variation is a powerful tool for analysis and method development, it is not a practical tool for computation. Instead, the power of DFT derives from Kohn-Sham theory, making it possible to approximate F[ρ] (sufficiently) accurately and inexpensively for densities ρ of interest to us by introducing orbitals.