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Atomistic modeling of electrocatalysis: Are we there yet?

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Stephan N. Steinmann, Zhi Wei Seh, Kang Rui Garrick Lim, Nawras Abidi

Published Online: Aug 26 2020

DOI: 10.1002/wcms.1499

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Abstract Electrified interfaces play a prime role in energy technologies, from batteries and capacitors to heterogeneous electrocatalysis. The atomistic understanding and modeling of these interfaces is challenging due to the structural complexity and the presence of the electrochemical potential. Including the potential explicitly in the quantum mechanical simulations is equivalent to simulating systems with a surface charge. For realistic relationships between the potential and the surface charge (i.e., the capacity), the solvent and counter charge need to be considered. The solvent and electrolyte description are limited by the computational power: either molecules or ions are included explicitly or implicit solvent and electrolyte descriptions are adopted. The first option is limited by the phase‐space sampling that is at least 10 times too small to reach convergence, while the second is missing a realistic structuring of the interface. Both approaches suffer from a lack of validation against directly comparable experimental data. Furthermore, the limitations of density functional theory in terms of accuracy are critical for these metal/liquid interfaces. Nevertheless, the atomistic insight in electrocatalytic interfaces allows insights with unprecedented details. The joint theoretical and experimental efforts to design non‐noble hydrogen evolution catalysts are discussed as an example for the success of theory to spur and accelerate experimental discoveries. This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Electronic Structure Theory > Density Functional Theory

Left: Scaling relationship for OH* and OOH* over various oxides, superposed on a heat map of activity as a function of these two variables. Note that the optimum (brightest color) is does not lie on the scaling line (a). Right: Examples of how to overcome the scaling relation by introducing adsorbate specific stabilizations. Bifunctionality (b) on alloys or mixed metal/oxide/sulfide catalysts, promoters in terms of specifically adsorbed ions (c), ligands (d), or electrolyte molecules (e) can stabilize various adsorbates specifically. Three‐dimensional active sites such as interfaces between two materials (f) or confinement (g) can also provide opportunities to break scaling relationships. Differently colored circles indicate distinct elements. Reproduced from Reference 54. Copyright Nature Publishing Group

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Reconciling theory with experiment results for hydrogen evolution reaction (HER) electrocatalysts. (a) (top) Experimental i₀ plotted against theoretically calculated ΔG_H for various transition metal surfaces, compared against the proposed kinetic model (below). Open circles represent single crystal data. Reproduced from Reference 46. Copyright IOP science. (b) Experimental HER data of Pt (black), BiPt alloy precursor (Pt‐Bi_ir, red dash), and the synthesized BiPt alloy (blue dots). Modified from Reference 47. Copyright Nature Publishing Group. (c) Color contour plot of stability (measured by surface energy per unit cell γ) with varying levels of strain and S vacancies. Black line illustrates combinations of strain and S vacancies for ΔG_H = 0. (d) HER data of Au substrate, Pt control, and 2H‐MoS₂ (pristine and with various treatments). (c) and (d) reproduced from Reference 229. Copyright Nature Publishing Group. (e) (left) Theoretical volcano plot of MXenes (Ti₂C and Mo₂C marked out with red stars) and (right) HER activity of Ti₂CT_x and Mo₂CT_x. Modified from Reference 246. Copyright American Chemical Society. (f) Comparison of theoretical and experimental overpotential at −10 mA cm⁻² for various MXenes after considering –F coverage on basal planes. Dashed line indicates complete agreement. Reproduced from Reference 247. Copyright American Chemical Society

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Mean average deviations (MADs) for eight diverse test sets. The performance for PBE (blue) and the dispersion corrected PBE‐dDsC (pink) are shown. The data for surface adsorption is taken from Reference (206). The E_adsPt_Small refers to H, O, and CO adsorption on Pt.¹¹¹ E_adsPt_Org. contains methane, ethane, ethylidyne, cyclohexene, benzene, and naphtalene on Pt(111). The other test sets are extracted from GMTKN24.²⁰⁷ The PBE‐dDsC data were published in Reference (208). ISOL22 assesses isomerization energies of large organic molecules. DARC stands for Diels‐Alder reaction energies, while AL2X contains dimerization energies of AlX3 species. ISO34 determines isomerization energies of small organic molecules while S22 is dedicated to weak intermolecular interactions. BSR36 measures bond separation energies of alkanes, that is, hydrogenation reactions of alkanes to methane

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Model Free Energy surface in terms of the adsorbate, nuclear coordinate (x‐axis), and the electrolyte arrangement coordinate (y‐axis). Early and late transition states with respect to the electrolyte coordinate can be distinguished

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Comparison of computational hydrogen electrode (CHE) (horizontal lines and solid points) and grand‐canonical density functional theory (GC‐DFT) (empty crosses and thick lines) results for the energy difference of two intermediates during the oxygen evolution reaction (OER) over CoOOH (a semiconductor) in basic conditions. The intermediate in pink (crosses) has O₂ bound to the catalyst, while O₂ is desorbed in the intermediate in blue (plus signs). The desorbing O₂ molecule is highlighted in pale red in the structural representation, which also exemplifies the use of symmetric unit cells to avoid surface dipole moments and obtain unambigious workfunctions. The data is taken from Reference 64

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Schematic plot of the overpotential (η) versus the logarithm of the current density (pink). The Tafel slope and the exchange current density i₀ as determined by the linear fit (Tafel approximation) are indicated (blue)

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Representation of the key contributions introducing various descriptions of the electrocatalytic interface. The superscript refers to the reference to the corresponding article, while the year is given below the lead author name. The gray scale highlights the chronological ordering. Note, that other groups have applied these techniques in various contexts and some of the methods have been developed several times independently with slight variations, but we have tried to highlight the earliest contributions. The horizontal axis is indicative of the treatment of the solvent, with the black line symbolizing the electrostatic potential. (a) corresponds to vacuum, (b) the combination of a small number of solvent molecules at the vacuum interface, (c) the use of an implicit solvent, (d) the combination of implicit solvent (light blue) and explicit solvent molecules, and (e) the use of a fully explicit description of the liquid phase. The computational hydrogen electrode (CHE) cornerstone is highlighted in bold. The vertical axis represents the description of the electrochemical potential. Constant charge approaches typically work with neutral surfaces. Constant electric fields can be used as a proxy for the electrochemical potential under certain assumptions (typically the thickness of the double layer). Truly constant potential approaches are typically relying on grand‐canonical density functional theory (GC‐DFT)

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