We have investigated the magnetic interaction, the shape of the whole potential energy surface, and the electronic structure of realistic models of the active site in hemocyanin for the reversible dioxygen binding by UHF and DFT calculations. The results are discussed in relation to the effective exchange integrals and the charge and spin density distributions as well as the shape and symmetry of natural orbitals. The superexchange interaction via bridging dioxygen accounts for the strong antiferromagnetic interaction between the two copper ions. The shapes of the potential energy curve suggest that the structural change of hemocyanin controls dioxygen binding.