A survey of the potential energy surface for a 1:1 copper dioxygen complex, (C3N2H5)CuO2, reveals two distinct states in the valence region, a singlet ((1)A(1)) and a triplet (B-3(1)). The former spans a continuum from Cu-III-O-2(2-) to Cu-I-O-2((1)Deltag), while the latter spans Cu-II-O-2(1-) to Cu-I-O-2((3)Sigmag(-)). The point at which the potential energy curves for the two states cross marks an abrupt discontinuity in electron distribution, where the system shifts from dominant Cu-III-O-2(2-) character to Cu-II-O-2(1-). On this basis, we argue that there is no continuum between Cu-III-peroxide and Cu-II-superoxide: the two are represented by distinct states that differ both in symmetry and multiplicity.