The performance of a large number of hybrid density functional theory methods is evaluated toward calculating potential-dependent activation energies for uncatalyzed and Pt-catalyzed oxygen reduction and hydroperoxyl oxidation. This reaction is the first step and the rate-determining step in the electrochemical oxygen reduction, which is the cathodic process in electrolyte-based fuel cells. Special focus is put on determining methods that allow results comparable to those previously calculated using MP2 method with the 6-31G(d,p) basis set for 0 and H and the LANL2DZ basis set for Pt. This level of theory was shown to reproduce well, within the model used here, key features of experimental data. It is found that hybrid density functional theory methods with small (less than 30%) Hartree-Fock exchange contributions give less accurate results mainly due to underestimated calculated activation energies while methods with higher (around 50%) Hartree-Fock exchange contributions give results closer to the target ones. New hybrid density functional theory methods with specific reaction parameters that give superior results are proposed. The best overall performance is found for the method denoted as BIB95-50 in which the Hartree-Fock exchange contribution is half. This method is computationally affordable and offers promise as a reliable method in applications to larger systems. (c) 2006 Elsevier Ltd. All rights reserved.