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

Abstract

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 BEEF-vdW 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, surfacetransition 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 (ORR). 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 c-values to 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. arXiv:1710.08407v2 [cond-mat.mtrl-sci]

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

“…In order to construct overpotential‐dependent volcano plots for the CER and OER, a consistent data set needs to be analyzed. Herein, the DFT calculations of Viswanathan and co‐workers are used: this is mainly related to the fact that the authors quantified the confidence of their electronic structure calculations within the class of transition‐metal oxides by the application of the Bayesian error estimation functional with van der Waals correlation (BEEF‐vdW) . Hence, error bars of Δ E O and Δ G O−OH can be specified for RuO 2 (110) and IrO 2 (110) both.…”

“…Herein, the DFT calculations of Viswanathan and co-workers [36] are used: this is mainly related to the fact that the authors quantified the confidence of their electronic structure calculations within the class of transition-metal oxides by the application of the Bayesian error estimation functional with van der Waals correlation (BEEF-vdW). [72,73] Hence, error bars of ΔE O and ΔG OÀ OH can be specified for RuO 2 (110) and IrO 2 (110) both. Further information on the DFT calculations is given in the supporting information (SI), Section 1.…”

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

“…[10] While in the corresponding surface stability diagrams in heterogeneous catalysis [58,59] or in battery research [60,61] surface energies, γ, are used in order to comprehend on the stability range of the respective electrode material, Pourbaix diagrams are commonly constructed based on free energies, ΔG, rather than on surface energies, γ. [10,17,18,21,24,28,[54][55][56][57] This finding triggers to expand the Pourbaix approach by adopting the concept of surface energies from the neighboring research communities: [57] the electrode material is unstable, if in a certain (U, pH) range the surface energy γ(U, pH) of a surface phase falls below zero. It shall be noted that this criterion strongly depends on the chosen reference states when calculating surface energies.…”

Recent Advancements Towards Closing the Gap between Electrocatalysis and Battery Science Communities: The Computational Lithium Electrode and Activity–Stability Volcano Plots

“…In contrast, the adsorption and discharge of ac hloride anion on Ru cus constitutes ao ne-electronp rocess, with an energy gain of À1eU per adsorbed chlorine atom, whiche xplainsw hy chlorine does not directly adsorbo nR u cus ,s ince the number of electrons transferred stipulates the topology of the Pourbaix diagram under CER conditions. [61,62] Because the c value for the Ru cus -O ot phase in the potential range of CER is close to one, [63] the solventm ay have ad ecisive role on the energetics of the underlying adsorption process. [58] The formation of as ingle oxygen layer on the RuO 2 (110) surfacei nt he potentialr ange of the CER is ascribed to the competing oxygen evolution reaction( OER), which, from at hermodynamic point of view,i sp referred over the CER (U 0 OER = 1.23 Vv s. SHE).…”

“…In ar ecent ab initio study of Viswanathan and co-workers,t he concept of Pourbaixd iagrams was advanced by introducing a c value that allowed the confidence in predictions based on ab initio thermodynamics investigations to be quantified. [61,62] Because the c value for the Ru cus -O ot phase in the potential range of CER is close to one, [63] the solventm ay have ad ecisive role on the energetics of the underlying adsorption process. This finding clearly demonstrates the importance of an accuratet reatment of the surrounding solvation shell in the corresponding DFT calculations and emphasizes that ab initio studies without the inclusion of the surrounding electrolyte solution should be treated with caution.…”