The effects of bonding to a platinum atom are calculated for the reduction of oxygen to water. The electron-correlation corrected MP2 method is used, and the electrode potential is modeled by variations in values for the electron affinities of the reaction centers. Potential-dependent transition state structures and activation energies are reported for the one-electron reactions [i] Pt-O-2 + H+(aq) + e(-)(U) --> Pt-OOH [ii] Pt-OOH + H+(aq) + e(-)(U) --> Pt-(OHOH) [iii] Pt-(OHOH)+ H+(aq)+ e(-)(U) --> Pt-OH + H2O [iv] Pt-OH + H+(aq) + e(-)(U) --> Pt-OH2 This is the predicted lowest energy pathway. An alternative, where step (ii) is replaced by [v] Pt-OOH + H+(aq) + e(-)(U) --> Pt-O + H2O is excluded by the high activation energy calculated for it, though reduction of [vi] Pt-O to Pt-OH Pt-O + H+(aq) + e(-)(U) --> Pt-OH has a very low activation energy. Compared to uncatalyzed outer-Helmholtz-plane values, bonding to the Pt has the effect of decreasing the calculated high reduction activation energies for O-2 and H2O2. Bonding to Pt also decreases the HOO . and increases the HO . activation energy values. The reverse reaction, oxidation of H2O to O-2, is also discussed in light of these results. The issues of potential-dependent double-layer potential drops and adsorbate bond polarizations are discussed, and it is pointed out that the results of this study can be used to estimate the effects of such potential drops.