Direct Demonstration of Unified Brønsted-Evans-Polanyi Relationships for Proton-Coupled Electron Transfer Reactions on Transition Metal Surfaces
Brønsted-Evans-Polanyi (BEP) relationships, which relate elementary reaction barriers to reaction thermodynamics, have long been discussed in electrochemical science, but demonstration of their existence in heterogeneous electrocatalysis, across many different catalyst surfaces and voltages, is lacking. In this contribution, the BEP model is demonstrated to describe both multiple catalyst surfaces and variable voltages in electrochemical environments. For proton-coupled electron transfer (PCET) to surface nitrogen (N*) and nitric oxide (NO*), reaction energies and activation barriers are calculated using Density Functional Theory (DFT) on a parallel plate capacitor model at three different potentials and for nine different transition metal surfaces. Linear BEP relations that describe all potentials and catalyst surfaces are obtained for these elementary reactions, and the slopes of the correlations are shown to be directly related to the fractional coordinate of the transition states (FCTS) of the reactions. The results, which are explained in terms of Marcus Theory, prove a direct equivalence between unified BEP coefficients, describing both variable catalyst surfaces and voltages, and electrochemical symmetry factors and provide a straightforward means of estimating this quantify for PCET reactions on transition metal surfaces. The resulting relationships, in turn, could lead to predictions of electrocatalytic reactivity trends of enhanced accuracy and efficiency.