Many-electron self-interaction and spin polarization errors in local hybrid density functionals

Errors for systems with noninteger occupation have been connected to common failures of density functionals. Previously, global hybrids and pure density functionals have been investigated for systems with noninteger charge and noninteger spin state. Local hybrids have not been investigated for either of those systems to the best of our knowledge. This study intends to close this gap. We investigate systems with noninteger charge to assess the many-electron self-interaction error and systems with noninteger spin state to assess the spin polarization error of recently proposed local hybrids and their range-separated variants. We find that long-range correction is very important to correct for many-electron self-interaction error in cations, whereas most full-range local hybrids seem to be sufficient for anions, where long-range-corrected density functionals tend to overcorrect. On the other hand, while all hitherto proposed long-range-corrected density functionals show large spin polarization errors, the Perdew–Staroverov–Tao–Scuseria (PSTS) functional performs best of all local hybrids in this case and shows an outstanding behavior for the dependence of the energy on the spin polarization.