  In effective single-electron theories, self-interaction manifests itself
through the unphysical dependence of the energy of an electronic state as a
function of its occupation, which results in important deviations from the
ideal Koopmans trend and strongly affects the accuracy of electronic-structure
predictions. Here, we study the non-Koopmans behavior of local and semilocal
density-functional theory (DFT) total energy methods as a means to quantify and
to correct self-interaction errors. We introduce a non-Koopmans
self-interaction correction that generalizes the Perdew-Zunger scheme, and
demonstrate its considerably improved performance in correcting the
deficiencies of DFT approximations for self-interaction problems of fundamental
and practical relevance.
