In a recent study [J. Am. Chem. Sec. 121 (1999) 11855], an ab initio approach to calculate potential dependent activation energies was applied in studying the outer-sphere O-2 reduction and H2O oxidation. The purpose of this paper is to examine influences of changes in the calculational methodology and the reactant structural models. The first step in the overall four-electron reduction of O-2 to water, O-2(g) + H+(aq) + e(-)(U) reversible arrow HOO(aq) is the focus of this work. U is the electrode potential and H+(aq) is modeled by the [HOH2(OH2)(2)](+) cluster. For an electrode potential of 0.727 V on the hydrogen scale, the findings of this study are: 1. Determining the transition state structures constrained to using the product OOH angle is a satisfactory approximation. 2. The calculated activation energies are reduced for the forward reaction and increased for the reverse reaction when the hydronium ion structure is relaxed along the reaction coordinate. 3. Calculated reduction activation energies using the 6-31G** basis set are highest for the HF calculations, intermediate for MP2 calculations and lowest for B3LYP density functional calculations. Adding diffuse functions lowers all of the values. 4. Increasing the model size by coordinating another water molecule to the transferring proton increases the activation energy for the forward reaction. In addition to the above, the transfer coefficients in the Butler-Volmer equation relating current density to overpotential are calculated and discussed.