Density functional theory (B3LYP) has been applied to large models of the Fe(II)-Cu(I) binuclear center in cytochrome oxidase, investigating the mechanism of O-O bond cleavage in the mixed valence form of the enzyme. To comply with experimental information, the O-2 molecule is assumed to be bridging between iron and copper during the O-O bond cleavage, leading to the formation of a ferryl-oxo group and a cupric hydroxide. In accord with previous suggestions, the calculations show that it is energetically feasible to take the fourth electron needed in this reaction from the tyrosine residue that is cross-linked to one of the copper ligands, resulting in the formation of a neutral tyrosyl radical. However, the calculations indicate that simultaneous transfer of an electron and a proton from the tyrosine to dioxygen during bond cleavage leads to a barrier more than 10 kcal/mol higher than that experimentally determined. This may be overcome in two ways. If an extra proton in the binuclear center assists in the mechanism, the calculated reaction barrier agrees with experiment. Alternatively, the fourth electron might initially be supplied by a residue in the vicinity other than the tyrosine.