Importance of complex orbitals in calculating the self-interaction-corrected ground state of atoms

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.