Self-interaction corrected Kohn--Sham potentials

Exchange-correlation potentials derived from conventional density-functional approximations fail to exhibit the slow Coulombic decay---a problem that is related to the self-interaction error in the potential. We show how the self-interaction error of standard semilocal approximations can be effectively reduced by employing modified electron densities to construct the corresponding Kohn--Sham potentials. Using this correction scheme in the framework of adiabatic time-dependent density-functional theory we obtain significantly improved electronic excitation energies, especially for Rydberg states.