Recent electrochemical experiments have shown that the reduction of O-2 can be driven backward to water oxidation, which is the first case that has been successfully demonstrated for an enzyme. To understand this ability of the enzyme, both the forward reduction and backward oxidation have been studied here. For the forward reaction, a mechanism similar to earlier studies was obtained. All steps of the full catalytic cycle were obtained for the first time, and it was shown that the explicit reduction steps contribute significantly to the rate-limiting step of the O-O bond cleavage. For the backward oxidation reaction, it was found that the mechanism of the O-O bond formation is not just the reverse of the reduction step where the O-O bond is cleaved for a protonated peroxide. The formation of two fully deprotonated oxo groups was found to be important, which leads to a large radical character for one of the oxo groups. For this possibility, it is important that the pK(a) of the water bound to the cofactor is quite high.