Skip to main content

Quantifying Uncertainty in Activity Volcano Relationships for Oxygen Reduction Reaction

ACS Catalysis (2016)

Siddharth Deshpande, John R. Kitchin, and Venkatasubramanian Viswanathan, “Quantifying Uncertainty in Activity Volcano Relationships for Oxygen Reduction Reaction”, ACS Catalysis 6(8), 5251-5259 (2016). https://doi.org/10.1021/acscatal.6b00509

Read the paper

This summary was written by a language model from the paper and has not been checked line by line. Rely on the published paper for details.

Question

Descriptor-based screening for the oxygen reduction reaction (ORR) rests on a chain of approximations: DFT adsorption energies, a scaling relation between OOH* and OH*, and a thermodynamic volcano built on the computational hydrogen electrode. The authors ask how errors in the microscopic quantities propagate through the reaction network into the predicted activity (the limiting potential), which descriptor minimizes the resulting prediction error for the four-electron and two-electron ORR, and where on the volcano the predictions are least trustworthy (Deshpande et al. 2016).

Approach

Calculations used VASP with PAW potentials and the BEEF-vdW functional (450 eV cutoff, 0.1 eV Fermi smearing, forces below 0.05 eV/Å, four-layer slabs with the bottom two fixed). Free energies of O*, OH* and OOH* were computed on the fcc(111) and fcc(100) facets of Pt, Pd, Ag, Au and the alloy Pt3Ni, at 0 V versus the reversible hydrogen electrode, using the computational hydrogen electrode with zero point energy and entropy corrections. OH* and OOH* were stabilized by an explicit water layer (a √3 × √3 hydrogen-bonded layer at 1/3 ML on (111), and a 1/3 coverage water layer on a 2 × 3 cell for the unreconstructed (100) surfaces), while O* was placed at 1/4 ML without water (Deshpande et al. 2016).

Uncertainty came from the BEEF-vdW ensemble: 2000 perturbed sets of functional coefficients give 2000 energies per calculation. Rather than reference adsorption energies to gas-phase H2 and H2O, the authors referenced each surface’s ensemble to Pt(111), centered each distribution at zero, and pooled the distributions across all facets into a combined error distribution for each adsorbate (20 000 values for OH*). The uncertainty in the OOH*/OH* scaling intercept (slope fixed at 1) was obtained from the variances and covariance of the two ensembles. These spreads were then propagated through the volcano by treating the descriptor as a normal random variable around its computed mean, taking the limiting potential as the minimum over the two volcano legs, and building probability contours of the limiting potential versus the mean descriptor (Deshpande et al. 2016).

Key findings

Errors relative to gas-phase references were large, of the order of 0.3 to 0.4 eV for individual OH* and OOH* energies and up to about 0.5 eV in the Pt free energy diagrams, whereas errors relative to Pt(111) were about 0.1 eV: σOH = 0.11 eV and σOOH = 0.12 eV. The OH* spread stayed near 0.13 eV when other water structures were included and near 0.15 eV for Ni(111), Rh(111), Ru(0001) and Co(0001). The scaling intercept uncertainty was 0.19 eV, around the line ΔE_OOH = ΔE_OH + 3.2 eV (R² = 0.80; a free fit gave slope 0.943 and intercept 3.28). BEEF-vdW predicted O* to OH* as the potential-determining step on Pt(111), unlike earlier RPBE work, because it overstabilizes O*, but the difference was only about 0.05 V (Deshpande et al. 2016).

ΔG_OH is identified as the optimal descriptor for the 4e⁻ ORR: the strong-binding leg is limited by the ~0.1 eV OH* error and the weak-binding leg by the ~0.2 eV scaling error, and experimental activities of the selected Pt, Pd, Au, Ag and Pt3Ni facets fall within one standard deviation of the volcano. For the 2e⁻ route to H2O2, ΔG_OOH is the optimal descriptor, but ΔG_OH is accurate enough and lets the 2e⁻ and 4e⁻ volcanoes be compared directly; for example Au(100) appears about equally placed for both pathways, yet its 2e⁻ prediction is the more robust to error. The authors define the expected limiting potential, U_EL, as the mean of the limiting potential distribution at a given mean descriptor. U_EL tracks the thermodynamic volcano except near its apex, where samples fall on both legs and the expectation drops below the apex value; uncertainty therefore grows as candidates approach the volcano top. The most probable limiting potential U_ML differs from U_EL there because the distribution becomes non-normal (unequal leg errors for 4e⁻, and the 0.68 V equilibrium cap for 2e⁻) (Deshpande et al. 2016).

Significance

The paper gives a general recipe for carrying functional-ensemble uncertainty through a multistep electrochemical scheme and quantifies the familiar claim that DFT trends are more reliable than absolute values. The expected limiting potential offers a way to flag regions of a volcano where screening predictions are unreliable, and the authors suggest it for other multielectron reductions such as those of CO2 and N2. The extracted text was readable; the Supporting Information (OOH* distributions, U_ML contours) was not included.

Related

Concept articles: Uncertainty quantification, Volcano plot, Oxygen reduction reaction, and Adsorption scaling relations. Related summaries: norskov2004 (the thermodynamic ORR volcano and computational hydrogen electrode this work builds on), kitchin2012 (functional error as a limit of DFT in catalysis), ock2023 (correlated errors using BEEF-vdW ensembles), and medford2026 (BEEF-vdW ensembles propagated into microkinetic models).