The activation of dioxygen at typically isolated two-electron reduced centers can lead to the formation of electrophilic superoxo or peroxo species, providing an essential route to form reactive O-2-derived species in biological, organometallic, and heterogeneous catalysts. Alternatively, O-2 activation can proceed via outer sphere routes, circumventing the formation of bound peroxo (OO*) species during oxidation catalysis by forming H2O2(g), which can react with another reduced center to form H2O. The electronic and binding properties of metal oxides that determine the relative rates of these activation routes are assessed here by systematic theoretical treatments using density functional theory (DFT). These methods are combined with conceptual frameworks based on thermochemical cycles and crossing potential models to assess the most appropriate descriptors for the activation barriers for each route using Keggin polyoxometalates as illustrative examples. In doing so, we show that inner sphere routes, which form OO* species via O-2 activation on the O-vacancies (*) formed in the reduction part of redox cycles, are mediated by early transition states that only weakly sense the oxide binding properties. Outer sphere routes form H2O2 (g) via O-2 activation on OH pairs (H/OH*) formed by dissociation of H2O on O-vacancies; their rates and activation barriers reflect the rates of the first H-atom transfer from H/OH* to O-2. The activation barriers for this H-transfer step depend on the binding energy of more weakly-bound H-atom in H/OH* pairs (HAE(2)) and on the center dot OOH-surface interaction energy at its product state (E-int(0)). The E-int(0) values are similar among oxides unless a large charge-balancing cation is present and interacts with center dot OOH; consequently, HAE(2) acts as an appropriate descriptor of the outer sphere dynamics. HAE(2) also determines the thermodynamics of H2O dissociation on O-vacancies, which influence the inner and outer sphere rates by setting the relative coverage of * and H/OH*. These results, in turn, show that HAE(2) is a complete descriptor of the reactivity and selectivity of oxides for O-2 activation; the O-atoms in more reducible oxides (more negative HAE(2)) exhibit a greater preference for the inner sphere routes and for the formation of electrophilic OO* intermediates that mediate epoxidation and O-insertion reactions during catalytic redox cycles. Large charge-balancing cations locally modify E-int(0) values that determine the outer sphere rates and thus can be used to alter the preference of O-atoms to either inner or outer sphere routes. (C) 2019 Elsevier Inc. All rights reserved.