Finding electron affinities with approximate density functionals

There has been a long discussion about the reliability of approximate density functionals for atomic anions. It is well known that the extra electron produces a strong self-interaction error, so strong that the extra electron is unbound. Despite this, electron affinities have been calculated using finite basis sets and very good results have been reported by Schaefer and others. We recently suggested how to resolve the contradicting viewpoints between theory and calculation. We calculate electron affinities using Hartree-Fock or exact exchange DFT densities which bind the extra electron correctly and show excellent results with well-defined basis-set limit. Here we give further data in support of our argument, and explain further how and why accurate densities and total energies of anions may be obtained from approximate density functional theory, despite positive HOMO energies.