  We investigate from a practitioner's point of view the computation of the
ionization potential (IP) within density functional theory (DFT). DFT with
(semi-)local energy-density functionals is plagued by a self-interaction error
which hampers the computation of IP from the single-particle energy of the
highest occupied molecular orbital (HOMO). The problem may be cured by a self
interaction correction (SIC) for which there exist various approximate
treatments. We compare the performance of the SIC proposed by Perdew and Zunger
with the very simple average-density SIC (ADSIC) for a large variety of atoms
and molecules up to larger systems as carbon rings and chains. Both approaches
to SIC provide a large improvement to the quality of the IP if calculated from
the HOMO level. The surprising result is that the simple ADSIC performs even
better than the original Perdew-Zunger SIC (PZSIC) in the majority of the
studied cases.
