Accuracy of Electron Affinities of Atoms in Approximate Density Functional Theory

Most approximate density functionals do not bind small atomic; anions because of large self interaction errors. Yet atomic electron affinities are often calculated using finite basis sets with surprisingly good results, despite positive highest occupied molecular orbital (HOMO) energies. We show that excellent results (better than for ionization potentials) can be obtained using standard approximate functionals evaluated on Hartree-Fock or exact-exchange densities for which the extra electron is bound. Although these good results found with limited basis sets are not accidental, we argue that this method cannot be used in general. Thus a positive HOMO indicates that the total energy should not be disregarded, only treated with caution.