A series of ab initio calculations were carried out for the O-2.benzene complex and its anions to determine their structures and the O-2.benzene adiabatic electron affinity. The calculations revealed interesting differences between the electronic and molecular structures of the anion and the neutral complex, and between the free and complexed O-2(-). While for O-2.benzene the calculations predict two equilibrium structures, one planar and one with O-2 located above the benzene and interacting with its pi electrons, for [O-2.benzene](-) only the planar structure was predicted to be stable. Analysis of the [O-2.benzene](-) wave function shows some delocalization of the excess electron from O-2(-) to the region of the sigma electrons in benzene. This delocalization may explain the predicted increase of the adiabatic electron affinity (A.E.A) by 0.59 eV upon O-2 complexation with benzene. This increase is consistent with A.E.A. shift reported in the accompanying paper by Le Barbu [J. Chem. Phys. 116, 9663 (2002)].