Quantifying Confidence in DFT Predicted Surface Pourbaix Diagrams and Associated Reaction Pathways for Chlorine Evolution

Abstract

Catalytic activity predictions and the identification of active sites rely on precisely determining the dominant reaction mechanism. The activity governing mechanism and products could vary with the catalyst material, which can be described by material descriptor(s), typically the binding strength(s) of key intermediate species. Density functional theory calculations can be used to identify dominant reaction mechanisms. However, the dominant reaction mechanism is sensitive to choice of the exchange correlation functional. Here, we demonstrate using the example case of chlorine evolution reaction on rutile oxides, which can occur through at least three reaction mechanisms each mediated by different surface intermediates and active sites. We utilize Bayesian error estimation capabilities within the BEEF-vdW exchange correlation (XC) functional to quantify the uncertainty associated with predictions of the operative reaction mechanism by systematically propagating the uncertainty originating from DFT-computed adsorption free energies. We construct surface Pourbaix diagrams based on the calculated adsorption free energies for rutile oxides of Ru, Ir, Ti, Pt, V, Sn and Rh. We utilize confidence-value (c-value) to determine the degree of confidence in the predicted surface phase diagrams. Using the scaling relations between the adsorption energies of intermediates we construct a generalized Pourbaix diagram showing the stable surface composition as a function of potential and the oxygen binding energy on the cus site (∆E O c ). This is used to consistently determine activity volcano relationships. We incorporate the uncertainty in linear scaling relations to quantify the confidence in generalized Pourbaix diagram and the associated activity. This allows us to compute the expectation limiting potential as a function of ∆E O c , which provides a more appropriate activity measure incorporating DFT uncertainty. We show that the confidence in the classification problem of identifying the active reaction mechanism is much better than the prediction problem of determining catalytic activity. We believe that such a systematic approach is needed for accurate determination of activities and reaction pathways for multi-electron electrochemical reactions such as N 2 and CO 2 reduction.

Controlling Stability and Selectivity in the Competing Chlorine and Oxygen Evolution Reaction over Transition Metal Oxide Electrodes

“…Section 2) are scaled as function of the free formation energy of oxygen, Δ G 0 (O ot ) (cf. Figure ), which has been proven to serve as a descriptor for activity trends in the CER over transition metal oxide electrodes . I would like to emphasize that the discussed type of scaling differs from conventional linear scaling relationships in the literature: commonly, linear scaling relationships of an adsorbate as function of a descriptor are determined within a homologous series of materials .…”

Overpotential‐Dependent Volcano Plots to Assess Activity Trends in the Competing Chlorine and Oxygen Evolution Reactions

“…However, it is questionable, whether Δ E O is a suitable choice to describe the selectivity problem of the competing CER and OER adequately. In case of the CER, the usage of Δ E O appears justified, since for transition‐metal oxides, such as RuO 2 and IrO 2 , it has been shown that oxygen atoms in junction with the underlying metal atom (Me) serve as active sites for electrochemical chlorine formation: the adsorption and discharge of a chloride anion from the electrolyte solution results in the formation of an OCl adsorbate, reconciled as precursor for the formation of gaseous chlorine (cf. equation ). …”

Activity‐Stability Volcano Plots for Material Optimization in Electrocatalysis

“…The free energy diagram along the reaction coordinate (cf. Figure c) provides deep mechanistic insights into electrocatalytic processes, in this case the Volmer‐Heyrovsky mechanism, which has been confirmed for the CER over RuO 2 (110) by various experimental and theoretical studies . While for small overpotentials, that is, η CER <0.125 V, the Heyrovsky step is kinetically limiting according to the highest transition state free energy, the rate‐determining reaction step switches to the Volmer step if the applied overpotential exceeds 0.125 V. Since the change in the rate‐determining reaction step was quantified in the overpotential regime between 0.10 V and 0.15 V, the affiliated error bars for the determination of the threshold overpotential (0.125 V) may not exceed 25 mV if other error sources, such as the determination of the reversible equilibrium potential, are neglected.…”

“…As in case of prototypical activity‐based volcano plots, the construction of an activity‐stability volcano plot for the CER over RuO 2 (110) is based on linear scaling relationships for the involved active site O ot and the precursor OCl ot within the Volmer‐Heyrovsky mechanism (cf. Figure c) .…”