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 ΔG
OH and ΔG
OOH are the optimal descriptors
for the 4e– and the 2e– ORR, respectively.
We show that for the 4e– ORR with ΔG
OH as the descriptor, the uncertainty in activity
is determined by the error associated with the adsorption energy of
OH* (∼0.1 eV) for materials that lie on the strong binding
leg, and the error involved in the scaling relation between OOH* and
OH* (∼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.