The Gibbs free energies of key elementary steps for the electrocatalytic oxygen reduction reaction (ORR) are calculated with B3LYP type of density functional theory: O2 + M + H+ + e- (0 eV) --> HOO-M (deltaG1), HOO-M + M --> HO-M + O-M (deltaG2), O2 + 2M + H+ + e- (0 eV) --> O-M + HO-M (deltaG3), and HO-M + O-M + 3H+ + 3e- (0 eV) --> 2H2O + 2M (deltaG4), where H+ is modeled as H3(+)O(H2O)3 and M stands for the adsorption site of a metal catalyst modeled by a single metal atom as well as by an M3 cluster. Taking Pt as a reference, deltaG4 is plotted against deltaG1 for 17 metals from groups V to XII. It is found that no single metal has both deltaG1 and deltaG4 more negative than Pt, although some of them have either more negative deltaG1 or more negative deltaG4. This enables us to explain thermodynamically why no other single metal catalyzes the ORR as effectively as Pt does. Moreover, a thermodynamic analysis reveals that the signs of delta deltaG (the difference between deltaG of other metals and deltaG of Pt) strongly correlate with the valence electronic structure of metals, i.e., delta deltaG1 < 0 and delta deltaG4 > 0 for metals M with vacant valence d orbitals, whereas delta deltaG1 > 0 and delta deltaG4 < 0 for metals M' with fully occupied valence d orbitals. Thus, a simple thermodynamic rule for the design of bimetallic catalysts for the ORR is proposed: couple a metal M (delta deltaG1 < 0) with a second metal M' (delta deltaG4 < 0) to form an alloy catalyst MM'3. The rationale behind this selection is based on M being more efficient for the rate-determining step, i.e., for the formation of the adsorbed species M-OOH, while M' can enhance the reductions of O and OH in the last three electron-transfer steps.
