Describing Anions by Density Functional Theory: Fractional Electron Affinity

It is shown that the majority of commonly used exchange-correlation potentials in Kohn-Sham density functional theory describe anions as having only a fraction of the extra electron bound, while the remaining fraction drifts off to infinity when sufficiently flexible basis sets are employed. For systems with both cationic and anionic sites, this leads to fractional electron transfer, even when standard basis sets are used, and thus a qualitative incorrect description of the electronic structure. Exchange functionals without Hartree-Fock exchange display the largest effects, but hybrid functionals also show the phenomenon, except for strongly bound anions. The source of the error is the incorrect long-range behavior of the exchange potential and can be avoided by employing the long-range correction method. The results have consequences for density functional descriptions of systems with localized anionic or strong electron donor sites for almost all of the commonly employed exchange-correlation functionals.