Potential-dependent activation energies are calculated quantum mechanically, using a local reaction center model, for the hydrogen reduction-oxidation reaction over platinum by the Volmer-Heyrovsky mechanism, Pt-H + H+ + e(-)(U) <----> Pt + H-2 (i), modeled by Pt-(HH)-H-...+(OH2)(OH2)(2) + e(-)(U) <----> Pt...H-H...OH2(OH2)(2) (ii). A contribution from the electrolyte to the potential of the reaction centers in ii is included in the ab initio Hamiltonian. The reversible potential predicted for i based on model ii is 0.04 V, close to the standard hydrogen electrode value of 0 V, and the predicted activation energy at the predicted reversible potential is 0.076 eV, close to the literature value of 0.12 eV for the apparent activation energy. The theoretical results validate the possibility of the Volmer-Heyrovsky mechanism being followed on platinum.