  The ground state of atoms from H to Ar was calculated using a
self-interaction correction to local and gradient dependent density
functionals. The correction can significantly improve the total energy and
makes the orbital energies consistent with ionization energies. However, when
the calculation is restricted to real orbitals, application of the
self-interaction correction can give significantly higher total energy and
worse results, as illustrated by the case of the Perdew-Burke-Ernzerhof
gradient dependent functional. This illustrates the importance of using complex
orbitals for systems described by orbital density dependent energy functionals.
