  The delocalization error of popular density functional approximations (DFAs)
leads to diversified problems in present-day density functional theory
calculations. For achieving a universal elimination of delocalization error, we
develop a localized orbital scaling correction (LOSC) framework, which unifies
our previously proposed global and local scaling approaches. The LOSC framework
accurately characterizes the distributions of global and local fractional
electrons, and is thus capable of correcting system energy, energy derivative
and electron density in a self-consistent and size-consistent manner. The
LOSC-DFAs lead to systematically improved results, including the dissociation
of cationic species, the band gaps of molecules and polymer chains, the energy
and density changes upon electron addition and removal, and photoemission
spectra.
