Towards constant potential modeling of CO-CO coupling at liquid water-Cu(1 0 0) interfaces

Non-Nernstian Effects in Theoretical Electrocatalysis

Electrocatalysis is one of the principal pathways for the transition to sustainable chemistry, promising greater energy efficiency and reduced emissions. As the field has grown, our theoretical understanding has matured. The influence of the applied potential on reactivity has developed from the first-order predictions based on the Nernst equation to the implicit inclusion of second-order effects including the interaction of reacting species with the interfacial electric field. In this review, we explore these non-Nernstian field effects in electrocatalysis, aiming to both understand and exploit them through theory and computation. We summarize the critical distinction between Nernstian and non-Nernstian effects and outline strategies to address the latter in theoretical studies. Subsequently, we examine the specific energetic contributions of the latter on capacitive and faradaic processes separately. We also underscore the importance of considering non-Nernstian effects in catalyst screening and mechanistic analysis. Finally, we provide suggestions on how to experimentally unravel these effects, offering insights into practical approaches for advancing the field.

Fleeting-Active-Site-Thrust Oxygen Evolution Reaction by Iron Cations from the Electrolyte

Oxygen evolution reaction (OER) is key to sustainable energy and environmental engineering, thus necessitating rational design of high-performing electrocatalysts that requires understanding the structure-performance relationship with a possible dynamic nature under working conditions. Herein, we uncover a novel type of OER mechanisms thrust by the fleeting active sites (FASs) dynamically formed on Ni-based layered double hydroxides (Ni-LDHs) by Fe cations from the electrolyte under OER potentials. We employ grand-canonical ensemble methods and microkinetic modeling to elucidate the potential-dependent structures of FASs on Ni-LDHs and demonstrate that the fleeting-active-site-thrust (FAST) mechanism delivers superior OER activity via the FAST intramolecular oxygen coupling pathway, which also suppresses the lattice oxygen mechanism, leading to improved operando stability of Ni-LDHs. We further reveal that introducing only trace-level loadings (10-100 ppm) of FASs on Ni-LDHs can significantly boost and govern the catalytic performance for OER. This underscores the crucial importance of considering the novel FAST mechanism in OER and also suggests the electrolyte as a key part of the structure-performance relationship as well as an effective design strategy via engineering the electrolyte.

Origin of copper as a unique catalyst for C-C coupling in electrocatalytic CO2 reduction

High yields of C2 products through electrocatalytic CO2 reduction (eCO2R) can only be obtained using Cu-based catalysts. Here, we adopt the generalized frontier molecular orbital (MO) theory based on first-principles calculations to identify the origin of this unique property of Cu. We use the grand canonical ensemble (or fixed potential) approach to ensure that the calculated Fermi level, which serves as the frontier orbital of the metal catalyst, accurately represents the applied electrode potentials. We determine that the key intermediate OCCO assumes a U-shape configuration with the two C atoms bonded to the Cu substrate. We identify the frontier MOs that are involved in the C-C coupling. The good alignment of the Fermi level of Cu with these frontier MOs is perceived to account for the excellent catalytic performance of Cu for C-C coupling. It is expected that these new insights could provide useful guidance in tuning Cu-based catalysts as well as designing non-Cu catalysts toward high-efficiency eCO2R.

On the Thermodynamic Equivalence of Grand Canonical, Infinite-Size, and Capacitor-Based Models in First-Principle Electrochemistry

First principles-based computational and theoretical methods are constantly evolving trying to overcome the many obstacles towards a comprehensive understanding of electrochemical processes on an atomistic level. One of the major challenges has been the determination of reaction energetics under a constant potential. Here, a theoretical framework was proposed applying standard electronic structure methods and extrapolating to the infinite-cell size limit where reactions do not alter the potential. Today, electronically grand canonical modifications to electronic structure methods, holding the potential constant by varying the number of electrons in a finite simulation cell, become increasingly popular. In this perspective, we show that these two schemes are thermodynamically equivalent. Further, we link these methods to capacitive models of the interface, in the limit that the capacitance of the charging components (whether continuum or atomistic) are equal and invariant along the reaction pathway. We benchmark the three approaches with an example of alkali cation adsorption on Pt(111) showing that all three approaches converge in the cases of Li, Na and K. For Cs, however, strong deviation from the ideal conditions leads to a spread in the respective results. We discuss the latter by highlighting the cases of broken equivalence and assumptions among the approaches.

S.O.S: Shape, orientation, and size tune solvation in electrocatalysis

Current models to understand the reactivity of metal/aqueous interfaces in electrochemistry, e.g., volcano plots, are based on the adsorption free energies of reactants and products, which are often small hydrophobic molecules (such as in CO2 and N2 reduction). Calculations played a major role in the quantification and comprehension of these free energies in terms of the interactions that the reactive species form with the surface. However, solvation free energies also come into play in two ways: (i) by modulating the adsorption free energy together with solute-surface interactions, as the solute has to penetrate the water adlayer in contact with the surface and get partially desolvated (which costs free energy); (ii) by regulating transport across the interface, i.e., the free energy profile from the bulk to the interface, which is strongly non-monotonic due to the unique nature of metal/aqueous interfaces. Here, we use constant potential molecular dynamics to study the solvation contributions, and we uncover huge effects of the shape and orientation (on top of the already known size effect) of small hydrophobic and amphiphilic solutes on their adsorption free energy. We propose a minimal theoretical model, the S.O.S. model, that accounts for size, orientation, and shape effects. These novel aspects are rationalized by recasting the concepts at the base of the Lum-Chandler-Weeks theory of hydrophobic solvation (for small solutes in the so-called volume-dominated regime) into a layer-by-layer form, where the properties of each interfacial region close to the metal are explicitly taken into account.

Cation-Induced Interfacial Hydrophobic Microenvironment Promotes the C-C Coupling in Electrochemical CO2 Reduction

The electrochemical carbon dioxide reduction reaction (CO2RR) toward C2 products is a promising way for the clean energy economy. Modulating the structure of the electric double layer (EDL), especially the interfacial water and cation type, is a useful strategy to promote C-C coupling, but atomic understanding lags far behind the experimental observations. Herein, we investigate the combined effect of interfacial water and alkali metal cations on the C-C coupling at the Cu(100) electrode/electrolyte interface using ab initio molecular dynamics (AIMD) simulations with a constrained MD and slow-growth approach. We observe a linear correlation between the water-adsorbate stabilization effect, which manifests as hydrogen bonds, and the corresponding alleviation in the C-C coupling free energy. The role of a larger cation, compared to a smaller cation (e.g., K+ vs Li+), lies in its ability to approach the interface through desolvation and coordinates with the *CO+*CO moiety, partially substituting the hydrogen-bonding stabilizing effect of interfacial water. Although this only results in a marginal reduction of the energy barrier for C-C coupling, it creates a local hydrophobic environment with a scarcity of hydrogen bonds owing to its great ionic radius, impeding the hydrogen of surrounding interfacial water to approach the oxygen of the adsorbed *CO. This skillfully circumvents the further hydrogenation of *CO toward the C1 pathway, serving as the predominant factor through which a larger cation facilitates C-C coupling. This study unveils a comprehensive atomic mechanism of the cation-water-adsorbate interactions that can facilitate the further optimization of the electrolyte and EDL for efficient C-C coupling in CO2RR.

Preventing Alloy Electrocatalyst Segregation in Air Using Sacrificial Passivating Overlayers

Many alloy electrocatalysts, including intermetallics, are exceptionally sensitive to segregation in air due to the electronic dissimilarity of the constituent metals. We demonstrate that even alloys with strong cohesive energies rapidly segregate upon air exposure, completely burying the less reactive constituent metal beneath the surface. To circumvent this issue, we develop and validate a new experimental approach for bridging the pressure gap between electronic structure characterization performed under ultrahigh vacuum and electrocatalytic activity testing performed under ambient conditions. This method is based on encapsulation of the alloy surface with a sacrificial passivating overlayer of aluminum oxide. These passivating overlayers protect the underlying material from segregation in the air and can be completely and rapidly removed in an alkaline electrochemical environment under potential control. We demonstrate that alloy surfaces prepared, protected, and introduced into the electrolyte in this manner exhibit near-surface compositions consistent with those of the bulk material despite prior air exposure. We also demonstrate that this protection scheme does not alter the electrocatalytic activity of benchmark electrocatalysts. Implementation of this approach will enable reliable correlations between the electrocatalytic activity measured under ambient conditions and the near-surface electronic structure measured under ultrahigh vacuum.

Data-driven discovery of electrocatalysts for CO2 reduction using active motifs-based machine learning

The electrochemical carbon dioxide reduction reaction (CO2RR) is an attractive approach for mitigating CO2 emissions and generating value-added products. Consequently, discovery of promising CO2RR catalysts has become a crucial task, and machine learning (ML) has been utilized to accelerate catalyst discovery. However, current ML approaches are limited to exploring narrow chemical spaces and provide only fragmentary catalytic activity, even though CO2RR produces various chemicals. Here, by merging pre-developed ML model and a CO2RR selectivity map, we establish high-throughput virtual screening strategy to suggest active and selective catalysts for CO2RR without being limited to a database. Further, this strategy can provide guidance on stoichiometry and morphology of the catalyst to researchers. We predict the activity and selectivity of 465 metallic catalysts toward four expected reaction products. During this process, we discover previously unreported and promising behavior of Cu-Ga and Cu-Pd alloys. These findings are then validated through experimental methods.

Tuning Surface Reactivity and Electric Field Strength via Intermetallic Alloying

Many electrosynthesis reactions, such as CO2 reduction to multicarbon products, involve the formation of dipolar and polarizable transition states during the rate-determining step. Systematic and independent control over surface reactivity and electric field strength would accelerate the discovery of highly active electrocatalysts for these reactions by providing a means of reducing the transition state energy through field stabilization. Herein, we demonstrate that intermetallic alloying enables independent and systematic control over d-band energetics and work function through the variation of alloy composition and oxophilic constituent identity, respectively. We identify several intermetallic phases exhibiting properties that should collectively yield higher intrinsic activity for CO reduction compared to conventional Cu-based electrocatalysts. However, we also highlight the propensity of these alloys to segregate in air as a significant roadblock to investigating their electrocatalytic activity.

Charting C–C coupling pathways in electrochemical CO 2 reduction on Cu(111) using embedded correlated wavefunction theory

The electrochemical CO 2 reduction reaction (CO 2 RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C 2+ ) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO 2 RR electrocatalysts is mechanistic analysis of the best metal catalyst thus far identified, namely, copper (Cu), via quantum mechanical computations to complement experiments. Here, we apply embedded correlated wavefunction (ECW) theory, which regionally corrects the electron exchange-correlation error in density functional theory (DFT) approximations, to examine multiple C–C coupling steps involving adsorbed CO (*CO) and its hydrogenated derivatives on the most ubiquitous facet, Cu(111). We predict that two adsorbed hydrogenated CO species, either *COH or *CHO, are necessary precursors for C–C bond formation. The three kinetically feasible pathways involving these species yield all three possible products: *COH–CHO, *COH–*COH, and *OCH–*OCH. The most kinetically favorable path forms *COH–CHO. In contrast, standard DFT approximations arrive at qualitatively different conclusions, namely, that only *CO and *COH will prevail on the surface and their C–C coupling paths produce only *COH–*COH and *CO–*CO, with a preference for the first product. This work demonstrates the importance of applying qualitatively and quantitatively accurate quantum mechanical method to simulate electrochemistry in order ultimately to shed light on ways to enhance selectivity toward C 2+ product formation via CO 2 RR electrocatalysts.

A unifying mechanism for cation effect modulating C1 and C2 productions from CO2 electroreduction

Electrocatalysis, whose reaction venue locates at the catalyst-electrolyte interface, is controlled by the electron transfer across the electric double layer, envisaging a mechanistic link between the electron transfer rate and the electric double layer structure. A fine example is in the CO₂ reduction reaction, of which rate shows a strong dependence on the alkali metal cation (M⁺) identity, but there is yet to be a unified molecular picture for that. Using quantum-mechanics-based atom-scale simulation, we herein scrutinize the M⁺-coupling capability to possible intermediates, and establish H⁺- and M⁺-associated ET mechanisms for CH₄ and CO/C₂H₄ formations, respectively. These theoretical scenarios are successfully underpinned by Nernstian shifts of polarization curves with the H⁺ or M⁺ concentrations and the first-order kinetics of CO/C₂H₄ formation on the electrode surface charge density. Our finding further rationalizes the merit of using Nafion-coated electrode for enhanced C2 production in terms of enhanced surface charge density.

Force-Based Method to Determine the Potential Dependence in Electrochemical Barriers

Determining ab initio potential-dependent energetics is critical to the investigation of mechanisms for electrochemical reactions. While methodology for evaluating reaction thermodynamics is established, simulation techniques for the corresponding kinetics is still a major challenge owing to a lack of potential control, finite cell size effects, or computational expense. In this work, we develop a model that allows for computing electrochemical activation energies from just a handful of density functional theory (DFT) calculations. The sole input into the model are the atom-centered forces obtained from DFT calculations performed on a homogeneous grid composed of varying field strengths. We show that the activation energies as a function of the potential obtained from our model are consistent for different supercell sizes and proton concentrations for a range of electrochemical reactions.

Understanding the complementarities of surface-enhanced infrared and Raman spectroscopies in CO adsorption and electrochemical reduction

In situ/operando surface enhanced infrared and Raman spectroscopies are widely employed in electrocatalysis research to extract mechanistic information and establish structure-activity relations. However, these two spectroscopic techniques are more frequently employed in isolation than in combination, owing to the assumption that they provide largely overlapping information regarding reaction intermediates. Here we show that surface enhanced infrared and Raman spectroscopies tend to probe different subpopulations of adsorbates on weakly adsorbing surfaces while providing similar information on strongly binding surfaces by conducting both techniques on the same electrode surfaces, i.e., platinum, palladium, gold and oxide-derived copper, in tandem. Complementary density functional theory computations confirm that the infrared and Raman intensities do not necessarily track each other when carbon monoxide is adsorbed on different sites, given the lack of scaling between the derivatives of the dipole moment and the polarizability. Through a comparison of adsorbed carbon monoxide and water adsorption energies, we suggest that differences in the infrared vs. Raman responses amongst metal surfaces could stem from the competitive adsorption of water on weak binding metals. We further determined that only copper sites capable of adsorbing carbon monoxide in an atop configuration visible to the surface enhanced infrared spectroscopy are active in the electrochemical carbon monoxide reduction reaction.

Infrared and Raman spectroscopies are often assumed to provide similar insights into heterogeneous reaction mechanisms. This study shows that these techniques provide similar data when CO is strongly bound to a surface, yet distinct subpopulations of CO are probed when binding is weaker.

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

The rational design of high-performance catalysts is hindered by the lack of knowledge of the structures of active sites and the reaction pathways under reaction conditions, which can be ideally addressed by an in situ/operando characterization. Besides the experimental insights, a theoretical investigation that simulates reaction conditions-so-called operando modeling-is necessary for a plausible understanding of a working catalyst system at the atomic scale. However, there is still a huge gap between the current widely used computational model and the concept of operando modeling, which should be achieved through multiscale computational modeling. This Perspective describes various modeling approaches and machine learning techniques that step toward operando modeling, followed by selected experimental examples that present an operando understanding in the thermo- and electrocatalytic processes. At last, the remaining challenges in this area are outlined.

The role of hydrophobic hydration in the free energy of chemical reactions at the gold/water interface: Size and position effects

Metal/water interfaces catalyze a large variety of chemical reactions, which often involve small hydrophobic molecules. In the present theoretical study, we show that hydrophobic hydration at the Au(100)/water interface actively contributes to the reaction free energy by up to several hundreds of meV. This occurs either in adsorption/desorption reaction steps, where the vertical distance from the surface changes in going from reactants to products, or in addition and elimination reaction steps, where two small reactants merge into a larger product and vice versa. We find that size and position effects cannot be captured by treating them as independent variables. Instead, their simultaneous evaluation allows us to map the important contributions, and we provide examples of their combinations for which interfacial reactions can be either favored or disfavored. By taking a N₂ and a CO₂ reduction pathway as test cases, we show that explicitly considering hydrophobic effects is important for the selectivity and rate of these relevant interfacial processes.