Quantifying Uncertainty in Activity Volcano Relationships for Oxygen Reduction Reaction

The oxygen reduction reaction (ORR) is an important electrochemical reaction and a major bottleneck for fuel cells. Due to the existence of a scaling relation between the adsorption energies of two key intermediates involved in ORR, OOH*, and OH*, the electrocatalytic activity for the ORR, to a first approximation, is determined by a single descriptor. This descriptor-based approach has been used to screen for electrocatalyst materials that have an optimal binding energy of oxygen intermediates. However, given that this descriptor-based search relies on several approximations, it is crucial to determine the overall predictability of the descriptor-based model to determine the activity of a catalyst. In this work, we develop a formalism for estimating uncertainty for the activity of a catalyst in an electrocatalytic reaction scheme and apply this framework to determine errors involved in describing the ORR activity. We perform density functional theory calculations using the Bayesian Error Estimation Functional with van der Waals exchange correlation functional to determine the adsorption energies of ORR intermediates on transition-metal fcc(111) and fcc(100) facets. We show that the error estimates for the adsorption energies calculated with a reference metal surface, chosen here to be Pt(111), are much smaller than those calculated with gas-phase molecules as reference. We demonstrate that Delta G(OH)., and Delta G(OOH) are the optimal descriptors for the 4e(-) and the 2e(-) ORR, respectively. We show that for the 4e(-) ORR with Delta G(OH) as the descriptor, the uncertainty in activity is determined by the error associated with the adsorption energy of OH* (similar to 0.1 eV) for materials that lie on the strong binding leg, and the error involved in the scaling relation between OOH* and OH* (similar to 0.2 eV) determines the uncertainty in activity for the weak binding leg. We propose a parameter, the expected limiting potential, U-EL, which is the expected value of U-L. The deviation of the expected limiting potential, U-EL, from the thermodynamic limiting potential, U-L, provides a qualitative estimate of the prediction error and can be used to identify trends in predictability. We believe that the concept of the expected limiting potential will be crucial in descriptor-based screening studies for multielectron electrochemical reactions.