Quantifying Confidence in DFT-Predicted Surface Pourbaix Diagrams of Transition-Metal Electrode–Electrolyte Interfaces

Density functional theory (DFT) calculations have been widely used to predict the activity of catalysts based on the free energies of reaction intermediates. The incorporation of the state of the catalyst surface under the electrochemical operating conditions while constructing the free-energy diagram is crucial, without which even trends in activity predictions could be imprecisely captured. Surface Pourbaix diagrams indicate the surface state as a function of the pH and the potential. In this work, we utilize error-estimation capabilities within the Bayesian ensemble error functional with van der Waals correlations exchange correlation functional as an ensemble approach to propagate the uncertainty associated with the adsorption energetics in the construction of Pourbaix diagrams. Within this approach, surface-transition phase boundaries are no longer sharp and are therefore associated with a finite width. We determine the surface phase diagram for several transition metals under reaction conditions and electrode potentials relevant for the oxygen reduction reaction. We observe that our surface phase predictions for most predominant species are in good agreement with cyclic voltammetry experiments and prior DFT studies. We use the OH* intermediate for comparing adsorption characteristics on Pt(111), Pt(100), Pd(111), Ir(111), Rh(111), and Ru(0001) since it has been shown to have a higher prediction efficiency relative to O*, and find the trend Ru > Rh > Ir > Pt > Pd for (111) metal facets, where Ru binds OH* the strongest. We robustly predict the likely surface phase as a function of reaction conditions by associating confidence values for quantifying the confidence in predictions within the Pourbaix diagram. We define a confidence quantifying metric, using which certain experimentally observed surface phases and peak assignments can be better rationalized. The probabilistic approach enables a more accurate determination of the surface structure and can readily be incorporated in computational studies for better understanding the catalyst surface under operating conditions.