Accurate DFT computations have been carried out to investigate the mechanism of oxygen binding to hemocyanins using two different model systems. The simpler model (model 1) is formed only by a Cu+-Cu+ dimer and by the approaching oxygen molecule, while the more complex model (model 2) involves also four ammonia molecules (bonded to the metal atoms) which emulate the real histidine ligands of the protein matrix. The computational results point out the inadequacy of model 1 in describing the oxygen binding process and show that the greater stability of the singlet versus the triplet state of the final complex (experimentally observed) is not an intrinsic property of the oxygenated copper dimer but is due to the presence of the copper ligands which are responsible for the occurrence of an intersystem crossing along the reaction coordinate. Tne ligand effect has been rationalized using a simple hiIO model which considers the interactions occurring between the nitrogen lone pairs of the ligands and the orbitals that describe the bonding in the Cu+(O-OCu+ fragment.