The ground-state anion of perfluorobenzene is investigated by means of equation-of-motion (EOM) methods. It is found that at the geometry of the neutral, the excess electron is bound by 0.135 eV. This anion state is nonvalence in nature with the excess electron bound in a very diffuse orbital with dispersion-type interactions between the excess electron and the valence electrons being pivotal to the binding. The diffuse correlation-bound state is shown to evolve into a more stable compact valence-bound anion state with a budded structure having an adiabatic EA of 0.5 eV. Results are also presented for the bound anion states of the C6F6 dirtier.