To describe the systematic error of DFAs, the concept of the delocalization error has been developed, and it can be understood from the perspective of fractional charges. For systems of small or moderate physical sizes, conventional DFAs usually have good accuracy in total energies for an integer number of electrons. For a fractional number of electrons, conventional DFAs, however, violate the Perdew-Parr-Levy-Balduz (PPLB) linearity condition , which states that the exact ground-state energy E(N) is a linear function of the fractional electron numbers connecting adjacent integer points. Inconsistent with the requirement of the PPLB linearity condition, E(N) curves from conventional DFAs are usually convex, with drastic underestimation to the ground-state energies of fractional systems. The convex deviation of conventional DFAs decreases when the systems become larger and vanishes at the bulk limit. However, the delocalization error is exhibited in another way, in which the error manifests itself in too low relative ground-state energies of ionized systems and incorrect linear E(N) curves with wrong slopes at the bulk limit. To reduce or eliminate the delocalization error, enormous efforts have been devoted to the development of new exchangecorrelation functionals. None of these developments are based on a semilocal form. All have nonlocal features in the functionals -see the development of the scaling approaches. In addition to the delocalization error characterized by fractional charges, commonly used DFAs also have a significant systematic static correlation error characterized by the violation of the constancy conditions on fractional spins. The combination of the exact fractional charge condition and the exact fractional spin condition leads to the general flat-plane condition, the satisfaction of which is a necessary condition for describing the band gap of strongly correlated Mott insulators. The flat-plane condition also leads to the conclusion that the exact exchange-correlation functional cannot be a continuous functional of the electron density or the density matrix of the noninteracting reference system everywhere. . To reduce or eliminate the static correlation error, one has to use nonlocal functionals (2.1.8) Savin : Warren Pickett said during a talk (Brisbane, 1996): "True, the density gives the potential, and this makes the Hohenberg-Kohn theorem sound so empty, because the potential, we know it anyhow". We do not need to start with an unknown function, ρ(r), when it is equivalent to using a known function of the position r -namely, the external potential, v(r). clear charges, hence the external potential v, hence the Hamiltonian. Also see Krylov's contribution (2.1.22) below.