The outer-sphere reduction of oxygen to water according to O-2(g) + 4H(+)(aq) + 4e(-) - 2H(2)O(1) (1) and its reverse reaction are analyzed using self-consistent ab initio MP2/6-31G** calculations over the electrode potential range of U = 0-2 V (H+/H-2). Activation energies are calculated for each of the four one-electron steps: O-2 + H+ + e(-)(U) --> HOO. (2); HOO. + H+ + e(-)(U) --> H2O2. (3); H2O2 + H+ + e(-)(U) --> HO. + H2O (4); and HO. + H+ + e(-)(U) --> H2O (5). In the calculational model H+ is a hydronium ion with two water molecules hydrogen bonded to it. The electrode potential is given by U/V = phi/eV - phi(H+/H2)/eV (6) where phi and phi(H+/H2) are the thermodynamic work functions of the electrode surface and of the standard hydrogen electrode surface, respectively. Electron transfer is assumed to occur when the electron affinity, EA, of the reaction complex equals the ionization potential, IF, of the electrode and there is an equilibrium so that phi = IP = EA. The electron transfers to an RO ... H+... OH2(OH2) orbital that is H+... OH2 antibonding and RO ... H+ bonding and this orbital is greatly stabilized by the electric field due to the positive charge. Over the potential range considered, activation energies for the reduction reactions decrease in the sequence (4) > (2) > (3) > (5). For the reverse reactions the activation energies decrease according to (5) > (4) similar or equal to (3) > (2). It is found that calculated reversible potentials, U-o, as determined simply from reaction energies for reactions 1, 4, 5, 2 + 3 and reactions 4 + 5 differ from the measured values by a constant.