Atomistic modeling of electrocatalysis: Are we there yet?

Advancing CO2 Conversion with Cu-LDHs: A Review of Computational and Experimental Studies

Layered Double Hydroxides (LDHs) are versatile materials with tuneable properties. They show promising electro- and photo-catalytic activity in the activation and conversion of CO2. Their unique properties make LDHs pivotal materials in emerging sustainable strategies for mitigating the effect of CO2 emissions. However, the intricate structure-property relationship inherent to LDHs challenges their rational design. In this review, we provide a comprehensive overview of both experimental and computational studies about LDHs for photo- and electro-catalytic conversion of CO2, mainly focusing on Cu-based systems due to their superior performance in producing C2 products. We present a background framework, describing the essentials computational and experimental tools, designed to support both experimentalists and theoreticians in the development of tailored LDH materials for efficient and sustainable CO2 valorisation. Finally, we discuss future potential advancements, emphasizing the importance of new synergistic experimental-computational studies.

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.

Theory of Electro-Ionic Perturbations at Supported Electrocatalyst Nanoparticles

Nanoscopic heterogeneities in composition and structure are quintessential for the properties of electrocatalyst materials. Here, we present a semiclassical model to study the electrochemical properties of supported electrocatalyst nanoparticles (NP). The model captures the correlated electronic and ionic equilibration across NP, support, and electrolyte. It reveals peculiar trends in surface charging of the supported NP, validated by comparison with first-principles calculations. Support-induced perturbations in electronic and ionic charge densities at the NP's active surface manifest as distinct potentials of zero local electronic and ionic charges that could differ by more than 0.5 V in the studied system.

Practical Applications of Grand-canonical Electronic Structure Calculations in Electrochemical Simulation

Modeling electrified interfaces has long been a great challenge in electrochemistry. In recent years, the grand-canonical treatment for electrons has gradually been developed, and its combination with density functional theory has been widely used to simulate electrochemical processes on an atomistic scale. In this Perspective, we aim to discuss several practical applications of this powerful technique after a short review of necessary fundamentals. We will begin with capacitor-based parametrization method of grand-canonical calculated results. If considering the electrodes under different applied potentials as different materials, the parametrization can be viewed as a kind of "quadratic scaling relation", which might reduce the overall computational costs by data postanalysis rather than algorithm development. Following an example of the abnormal potential-independent energetic curve within the bandgap area, we turn the topic to the semiconducting electrodes. Meanwhile, the specific behaviors of the bandgap also indicate that besides the reaction thermodynamics and kinetics, the detailed electronic structure of the system can also be well described by the grand-canonical treatment on electrons. Several possibilities for further applications are proposed correspondingly and summarized at the end of paper. We believe that the grand-canonical treatment for electronic structure calculations can greatly enrich our understanding of the fundamental mechanisms under electrochemical environments.

Dataset for quantum-mechanical exploration of conformers and solvent effects in large drug-like molecules

We here introduce the Aquamarine (AQM) dataset, an extensive quantum-mechanical (QM) dataset that contains the structural and electronic information of 59,783 low-and high-energy conformers of 1,653 molecules with a total number of atoms ranging from 2 to 92 (mean: 50.9), and containing up to 54 (mean: 28.2) non-hydrogen atoms. To gain insights into the solvent effects as well as collective dispersion interactions for drug-like molecules, we have performed QM calculations supplemented with a treatment of many-body dispersion (MBD) interactions of structures and properties in the gas phase and implicit water. Thus, AQM contains over 40 global and local physicochemical properties (including ground-state and response properties) per conformer computed at the tightly converged PBE0+MBD level of theory for gas-phase molecules, whereas PBE0+MBD with the modified Poisson-Boltzmann (MPB) model of water was used for solvated molecules. By addressing both molecule-solvent and dispersion interactions, AQM dataset can serve as a challenging benchmark for state-of-the-art machine learning methods for property modeling and de novo generation of large (solvated) molecules with pharmaceutical and biological relevance.

Constant potential energetics of metallic and semiconducting electrodes: A benchmark study on 2D materials

Grand-canonical (GC) constant-potential methods within an implicit solvent environment provide a general approach to compute the potential-dependent energetics at electrified solid-liquid interfaces with first-principles density-functional theory. Here, we use a mindfully chosen set of 27 isostructural 2D metal halides MX2 to analyze the variation of this energetics when the electronic structure changes from metallic to semiconducting and insulating state. Apart from expectable changes due to the opening up of the electronic bandgap, the calculations also show an increasing sensitivity to the numerical Brillouin zone integration and electronic smearing, which imposes computational burdens in practice. We rationalize these findings within the picture of the total interfacial capacitance arising from a series connection of the electrochemical double-layer capacitance and the so-called quantum capacitance resulting from the filling of electronic states inside the electrode. For metals, the electrochemical double-layer capacitance dominates at all potentials, and the entire potential drop takes place in the electrolyte. For semiconductors, the potential drop occurs instead fully or partially inside the electrode at potentials within or just outside the bandgap. For 2D semiconductors, the increased sensitivity to numerical parameters then results from the concomitantly increased contribution of the quantum capacitance that is harder to converge. Fortunately, this understanding motivates a simple extension of the CHE + DL approximation for metals, which provides the approximate GC energetics of 2D semiconductors using only quantities that can be obtained from computationally undemanding calculations at the point of zero charge and a generic double-layer capacitance.

Activating Nitrogen for Electrochemical Ammonia Synthesis via an Electrified Transition-Metal Dichalcogenide Catalyst

The complex interplay between local chemistry, the solvent microenvironment, and electrified interfaces frequently present in electrocatalytic reactions has motivated the development of quantum chemical methods that can accurately model these effects. Here, we predict the thermodynamics of the nitrogen reduction reaction (NRR) at sulfur vacancies in 1T'-phase MoS2 and highlight how the realistic treatment of potential within grand canonical density functional theory (GC-DFT) seamlessly captures the multiple competing effects of applied potential on a catalyst interface interacting with solvated molecules. In the canonical approach, the computational hydrogen electrode is widely used and predicts that adsorbed N2 structure properties are potential-independent. In contrast, GC-DFT calculations show that reductive potentials activate N2 toward electroreduction by controlling its back-bonding strength and lengthening the N-N triple bond while decreasing its bond order. Similar trends are observed for another classic back-bonding ligand in CO, suggesting that this mechanism may be broadly relevant to other electrochemistries involving back-bonded adsorbates. Furthermore, reductive potentials are required to make the subsequent N2 hydrogenation steps favorable but simultaneously destabilizes the N2 adsorbed structure resulting in a trade-off between the favorability of N2 adsorption and the subsequent reaction steps. We show that GC-DFT facilitates modeling all these phenomena and that together they can have important implications in predicting electrocatalyst selectivity for the NRR and potentially other reactions.

Two-Dimensional Layered Heterojunctions for Photoelectrocatalysis

Two-dimensional (2D) layered nanomaterial heterostructures, arising from the combination of 2D materials with other low-dimensional species, feature a large surface area to volume ratio, which provides a high density of active sites for catalytic applications and for (photo)electrocatalysis (PEC). Meanwhile, their electronic band structure and high electrical conductivity enable efficient charge transfer (CT) between the active material and the substrate, which is essential for catalytic activity. In recent years, researchers have demonstrated the potential of a range of 2D material interfaces, such as graphene, graphitic carbon nitride (g-C3N4), metal chalcogenides (MCs), and MXenes, for (photo)electrocatalytic applications. For instance, MCs such as MoS2 and WS2 have shown excellent catalytic activity for hydrogen evolution, while graphene and MXenes have been used for the reduction of carbon dioxide to higher value chemicals. However, despite their great potential, there are still major challenges that need to be addressed to fully realize the potential of 2D materials for PEC. For example, their stability under harsh reaction conditions, as well as their scalability for large-scale production are important factors to be considered. Generating heterojunctions (HJs) by combining 2D layered structures with other nanomaterials is a promising method to improve the photoelectrocatalytic properties of the former. In this review, we inspect thoroughly the recent literature, to demonstrate the significant potential that arises from utilizing 2D layered heterostructures in PEC processes across a broad spectrum of applications, from energy conversion and storage to environmental remediation. With the ongoing research and development, it is likely that the potential of these materials will be fully expressed in the near future.

Computational chemistry for water-splitting electrocatalysis

Electrocatalytic water splitting driven by renewable electricity has attracted great interest in recent years for producing hydrogen with high-purity. However, the practical applications of this technology are limited by the development of electrocatalysts with high activity, low cost, and long durability. In the search for new electrocatalysts, computational chemistry has made outstanding contributions by providing fundamental laws that govern the electron behavior and enabling predictions of electrocatalyst performance. This review delves into theoretical studies on electrochemical water-splitting processes. Firstly, we introduce the fundamentals of electrochemical water electrolysis and subsequently discuss the current advancements in computational methods and models for electrocatalytic water splitting. Additionally, a comprehensive overview of benchmark descriptors is provided to aid in understanding intrinsic catalytic performance for water-splitting electrocatalysts. Finally, we critically evaluate the remaining challenges within this field.

h-MBenes: Promising Two-Dimensional Material Family for Room-Temperature Antiferromagnetic and Hydrogen Evolution Reaction Applications

Recently, a new class of two-dimensional (2D) hexagonal transition-metal borides (h-MBenes) was discovered through a combination of ab initio predictions and experimental studies. These h-MBenes are derived from ternary hexagonal MAB (h-MAB) phases and have demonstrated promising potential for practical applications. In this study, we conducted first-principles calculations on 15 h-MBenes and identified four antiferromagnetic metals and 11 electrocatalysts for the hydrogen evolution reaction (HER). Notably, the h-MnB material exhibited a remarkable Néel temperature of 340 K and a high magnetic anisotropy energy of 154 μeV/atom. Additionally, the hydrogen adsorption Gibbs free energies (ΔGH*) for h-ZrBO, h-MoBO, and h-Nb2BO2 are close to the ideal value of 0 eV, indicating their potential as electrochemical catalysts for HER. Further investigations revealed that the electronic structure, Néel temperature, and HER activity of the studied h-MBenes can be tuned by applying biaxial strains. These findings suggest that h-MBenes have wide-ranging applicability in areas such as antiferromagnetic spintronics, flexible electronic devices, and electrocatalysis, thereby expanding the potential applications of 2D transition-metal borides.

Modeling Interfacial Dynamics on Single Atom Electrocatalysts: Explicit Solvation and Potential Dependence

ConspectusSingle atom electrocatalysts, with noble metal-free composition, maximal atom efficiency, and exceptional reactivity toward various energy and environmental applications, have become a research hot spot in the recent decade. Their simplicity and the isolated nature of the atomic structure of their active site have also made them an ideal model catalyst system for studying reaction mechanisms and activity trends. However, the state of the single atom active sites during electrochemical reactions may not be as simple as is usually assumed. To the contrary, the single atom electrocatalysts have been reported to be under greater influence from interfacial dynamics, with solvent and electrolyte ions perpetually interacting with the electrified active center under an applied electrode potential. These complexities render the activity trends and reaction mechanisms derived from simplistic models dubious.In this Account, with a few popular single atom electrocatalysis systems, we show how the change in electrochemical potential induces nontrivial variation in the free energy profile of elemental electrochemical reaction steps, demonstrate how the active centers with different electronic structure features can induce different solvation structures at the interface even for the same reaction intermediate of the simplest electrochemical reaction, and discuss the implication of the complexities on the kinetics and thermodynamics of the reaction system to better address the activity and selectivity trends. We also venture into more intriguing interfacial phenomena, such as alternative reaction pathways and intermediates that are favored and stabilized by solvation and polarization effects, long-range interfacial dynamics across the region far beyond the contact layer, and the dynamic activation or deactivation of single atom sites under operation conditions. We show the necessity of including realistic aspects (explicit solvent, electrolyte, and electrode potential) into the model to correctly capture the physics and chemistry at the electrochemical interface and to understand the reaction mechanisms and reactivity trends. We also demonstrate how the popular simplistic design principles fail and how they can be revised by including the kinetics and interfacial factors in the model. All of these rich dynamics and chemistry would remain hidden or overlooked otherwise. We believe that the complexity at an electrochemical interface is not a curse but a blessing in that it enables deeper understanding and finer control of the potential-dependent free energy landscape of electrochemical reactions, which opens up new dimensions for further design and optimization of single atom electrocatalysts and beyond. Limitations of current methods and challenges faced by the theoretical and experimental communities are discussed, along with the possible solutions awaiting development in the future.

Importance of the Walden Inversion for the Activity Volcano Plot of Oxygen Evolution

Since the birth of the computational hydrogen electrode approach, it is considered that activity trends of electrocatalysts in a homologous series can be quantified by the construction of volcano plots. This method aims to steer materials discovery by the identification of catalysts with an improved reaction kinetics, though evaluated by means of thermodynamic descriptors. The conventional approach for the volcano plot of the oxygen evolution reaction (OER) relies on the assumption of the mononuclear mechanism, comprising the * OH, * O, and * OOH intermediates. In the present manuscript, two new mechanistic pathways, comprising the idea of the Walden inversion in that bond-breaking and bond-making occurs simultaneously, are factored into a potential-dependent OER activity volcano plot. Surprisingly, it turns out that the Walden inversion plays an important role since the activity volcano is governed by mechanistic pathways comprising Walden steps rather than by the traditionally assumed reaction mechanisms under typical OER conditions.

Controlled Electrochemical Barrier Calculations without Potential Control

The knowledge of electrochemical activation energies under applied potential conditions is a prerequisite for understanding catalytic activity at electrochemical interfaces. Here, we present a new set of methods that can compute electrochemical barriers with accuracy comparable to that of constant potential grand canonical approaches, without the explicit need for a potentiostat. Instead, we Legendre transform a set of constant charge, canonical reaction paths. Additional straightforward approximations offer the possibility to compute electrochemical barriers at a fraction of computational cost and complexity, and the analytical inclusion of geometric response highlights the importance of incorporating electronic as well as the geometric degrees of freedom when evaluating electrochemical barriers.

Modeling Single-Atom Catalysis

Electronic structure calculations represent an essential complement of experiments to characterize single-atom catalysts (SACs), consisting of isolated metal atoms stabilized on a support, but also to predict new catalysts. However, simulating SACs with quantum chemistry approaches is not as simple as often assumed. In this work, the essential factors that characterize a reliable simulation of SACs activity are examined. The Perspective focuses on the importance of precise atomistic characterization of the active site, since even small changes in the metal atom's surroundings can result in large changes in reactivity. The dynamical behavior and stability of SACs under working conditions, as well as the importance of adopting appropriate methods to solve the Schrödinger equation for a quantitative evaluation of reaction energies are addressed. The Perspective also focuses on the relevance of the model adopted. For electrocatalysis this must include the effects of the solvent, the presence of electrolytes, the pH, and the external potential. Finally, it is discussed how the similarities between SACs and coordination compounds may result in reaction intermediates that usually are not observed on metal electrodes. When these aspects are not adequately considered, the predictive power of electronic structure calculations is quite limited.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

Atomistic modeling of electrified interfaces remains a major issue for detailed insights in electrocatalysis, corrosion, electrodeposition, batteries, and related devices such as pseudocapacitors. In these domains, the use of grand-canonical density functional theory (GC-DFT) in combination with implicit solvation models has become popular. GC-DFT can be conveniently applied not only to metallic surfaces but also to semiconducting oxides and sulfides and is, furthermore, sufficiently robust to achieve a consistent description of reaction pathways. However, the accuracy of implicit solvation models for solvation effects at interfaces is in general unknown. One promising way to overcome the limitations of implicit solvents is going toward hybrid quantum mechanical (QM)/molecular mechanics (MM) models. For capturing the electrochemical potential dependence, the key quantity is the capacitance, i.e., the relation between the surface charge and the electrochemical potential. In order to retrieve the electrochemical potential from a QM/MM hybrid scheme, an electrostatic embedding is required. Furthermore, the charge of the surface and of the solvent regions has to be strictly opposite in order to consistently simulate charge-neutral unit cells in MM and in QM. To achieve such a QM/MM scheme, we present the implementation of electrostatic embedding in the VASP code. This scheme is broadly applicable to any neutral or charged solid/liquid interface. Here, we demonstrate its use in the context of GC-DFT for the hydrogen evolution reaction (HER) over a noble-metal-free electrocatalyst, MoS₂. We investigate the effect of electrostatic embedding compared to the implicit solvent model for three contrasting active sites on MoS₂: (i) the sulfur vacancy defect, which is rather apolar; (ii) a Mo antisite defect, where the active site is a surface bound highly polar OH group; and (iii) a reconstructed edge site, which is generally believed to be responsible for most of the catalytic activity. According to our results, the electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for the apolar system but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.

Understanding Electron Transfer Reactions Using Constrained Density Functional Theory: Complications Due to Surface Interactions

The kinetic rates of electrochemical reactions depend on electrodes and molecules in question. In a flow battery, where the electrolyte molecules are charged and discharged on the electrodes, the efficiency of the electron transfer is of crucial importance for the performance of the device. The purpose of this work is to present a systematic atomic-level computational protocol for studying electron transfer between electrolyte and electrode. The computations are done by using constrained density functional theory (CDFT) to ensure that the electron is either on the electrode or in the electrolyte. The ab initio molecular dynamics (AIMD) is used to simulate the movement of the atoms. We use the Marcus theory to predict electron transfer rates and the combined CDFT-AIMD approach to compute the parameters for the Marcus theory where it is needed. We model the electrode with a single layer of graphene and methylviologen, 4,4'-dimethyldiquat, desalted basic red 5, 2-hydroxy-1,4-naphthaquinone, and 1,1-di(2-ethanol)-4,4-bipyridinium were selected for the electrolyte molecules. All of these molecules undergo consecutive electrochemical reactions with one electron being transferred at each stage. Because of significant electrode-molecule interactions, it is not possible to evaluate outer-sphere ET. This theoretical study contributes toward the development of a realistic-level prediction of electron transfer kinetics suitable for energy storage applications.

Liquid-Liquid Phase Separation? Ask the Water!

Water is more than an inert spectator during liquid-liquid phase separation (LLPS), the reversible compartmentalization of protein solutions into a protein-rich and a dilute phase. We show that LLPS is driven by changes in hydration entropy and enthalpy. Tuning LLPS by adjusting experimental parameters, e.g., addition of co-solutes, is a major goal for biological and medical applications. This requires a general model to quantify thermodynamic driving forces. Here, we develop such a model based on the measured amplitudes of characteristic THz-features of two hydration populations: "Cavity-wrap" water hydrating hydrophobic patches is released during LLPS leading to an increase in entropy. "Bound" water hydrating hydrophilic patches is retained since it is enthalpically favorable. We introduce a THz-phase diagram mapping these spectroscopic/thermodynamic changes. This provides not only a precise understanding of hydrophobic and hydrophilic hydration driving forces as a function of temperature and concentration but also a rational means to tune LLPS.

Materials Screening by the Descriptor G max(η): The Free-Energy Span Model in Electrocatalysis

To move from fossil-based energy resources to a society based on renewables, electrode materials free of precious noble metals are required to efficiently catalyze electrochemical processes in fuel cells, batteries, or electrolyzers. Materials screening operating at minimal computational cost is a powerful method to assess the performance of potential electrode compositions based on heuristic concepts. While the thermodynamic overpotential in combination with the volcano concept refers to the most popular descriptor-based analysis in the literature, this notion cannot reproduce experimental trends reasonably well. About two years ago, the concept of G max(η), based on the idea of the free-energy span model, has been proposed as a universal approach for the screening of electrocatalysts. In contrast to other available descriptor-based methods, G max(η) factors overpotential and kinetic effects by a dedicated evacuation scheme of adsorption free energies into an analysis of trends. In the present perspective, we discuss the application of G max(η) to different electrocatalytic processes, including the oxygen evolution and reduction reactions, the nitrogen reduction reaction, and the selectivity problem of the competing oxygen evolution and peroxide formation reactions, and we outline the advantages of this screening approach over previous investigations.

Density-Potential Functional Theory of Electrochemical Double Layers: Calibration on the Ag(111)-KPF6 System and Parametric Analysis

The density-potential functional theory (DPFT) of electrochemical double layer (EDL) is upgraded by adopting (generalized) gradient approximations for kinetic, exchange, and correlation functionals of metal electrons. A new numerical scheme that is more stable and converges faster is proposed to solve the DPFT model. The DPFT model is calibrated with existing differential double-layer capacitance (C_dl) data of the EDL at Ag(111)-KPF₆ aqueous interface at five concentrations at room temperature. Metal electronic effects are essential to explain why the two peaks of the camel-shaped C_dl curves are almost symmetric in spite of the size difference of the hydrated cations and anions. A systematic parametric analysis is then conducted in terms of key EDL properties, including the potential of zero charge and the differential capacitance. The parametric analysis, on the one hand, elucidates how quantum mechanical behaviors of metal electrons as well as interactions between metal electrons and the electrolyte solution impact the EDL properties and, on the other hand, identifies key parameters of the DPFT model, which should be calibrated using first-principles calculations and/or advanced experiments in the future.

Exploring the Potential Energy Surface of Pt6 Sub-Nano Clusters Deposited over Graphene

Catalytic systems based on sub-nanoclusters deposited over different supports are promising for very relevant chemical transformations such as many electrocatalytic processes as the ORR. These systems have been demonstrated to be very fluxional, as they are able to change shape and interconvert between each other either alone or in the presence of adsorbates. In addition, an accurate representation of their catalytic activity requires the consideration of ensemble effects and not a single structure alone. In this sense, a reliable theoretical methodology should assure an accurate and extensive exploration of the potential energy surface to include all the relevant structures and with correct relative energies. In this context, we applied DFT in conjunction with global optimization techniques to obtain and analyze the characteristics of the many local minima of Pt₆ sub-nanoclusters over a carbon-based support (graphene)-a system with electrocatalytic relevance. We also analyzed the magnetism and the charge transfer between the clusters and the support and paid special attention to the dependence of dispersion effects on the ensemble characteristics. We found that the ensembles computed with and without dispersion corrections are qualitatively similar, especially for the lowest-in-energy clusters, which we attribute to a (mainly) covalent binding to the surface. However, there are some significant variations in the relative stability of some clusters, which would significantly affect their population in the ensemble composition.

Spectroscopic Fingerprints of Cavity Formation and Solute Insertion as a Measure of Hydration Entropic Loss and Enthalpic Gain

Hydration free energies are dictated by a subtle balance of hydrophobic and hydrophilic interactions. We present here a spectroscopic approach, which gives direct access to the two main contributions: Using THz-spectroscopy to probe the frequency range of the intermolecular stretch (150-200 cm-1 ) and the hindered rotations (450-600 cm-1 ), the local contributions due to cavity formation and hydrophilic interactions can be traced back. We show that via THz calorimetry these fingerprints can be correlated 1 : 1 with the group specific solvation entropy and enthalpy. This allows to deduce separately the hydrophobic (i.e. cavity formation) and hydrophilic contributions to thermodynamics, as shown for hydrated alcohols as a case study. Accompanying molecular dynamics simulations quantitatively support our experimental results. In the future our approach will allow to dissect hydration contributions in inhomogeneous mixtures and under non-equilibrium conditions.

Water electrolysis: from textbook knowledge to the latest scientific strategies and industrial developments

Replacing fossil fuels with energy sources and carriers that are sustainable, environmentally benign, and affordable is amongst the most pressing challenges for future socio-economic development. To that goal, hydrogen is presumed to be the most promising energy carrier. Electrocatalytic water splitting, if driven by green electricity, would provide hydrogen with minimal CO2 footprint. The viability of water electrolysis still hinges on the availability of durable earth-abundant electrocatalyst materials and the overall process efficiency. This review spans from the fundamentals of electrocatalytically initiated water splitting to the very latest scientific findings from university and institutional research, also covering specifications and special features of the current industrial processes and those processes currently being tested in large-scale applications. Recently developed strategies are described for the optimisation and discovery of active and durable materials for electrodes that ever-increasingly harness first-principles calculations and machine learning. In addition, a technoeconomic analysis of water electrolysis is included that allows an assessment of the extent to which a large-scale implementation of water splitting can help to combat climate change. This review article is intended to cross-pollinate and strengthen efforts from fundamental understanding to technical implementation and to improve the 'junctions' between the field's physical chemists, materials scientists and engineers, as well as stimulate much-needed exchange among these groups on challenges encountered in the different domains.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Theory-guided experimental design in battery materials research

A reliable energy storage ecosystem is imperative for a renewable energy future, and continued research is needed to develop promising rechargeable battery chemistries. To this end, better theoretical and experimental understanding of electrochemical mechanisms and structure-property relationships will allow us to accelerate the development of safer batteries with higher energy densities and longer lifetimes. This Review discusses the interplay between theory and experiment in battery materials research, enabling us to not only uncover hitherto unknown mechanisms but also rationally design more promising electrode and electrolyte materials. We examine specific case studies of theory-guided experimental design in lithium-ion, lithium-metal, sodium-metal, and all-solid-state batteries. We also offer insights into how this framework can be extended to multivalent batteries. To close the loop, we outline recent efforts in coupling machine learning with high-throughput computations and experiments. Last, recommendations for effective collaboration between theorists and experimentalists are provided.

Modeling Operando Electrochemical CO2 Reduction

Since the seminal works on the application of density functional theory and the computational hydrogen electrode to electrochemical CO₂ reduction (eCO₂R) and hydrogen evolution (HER), the modeling of both reactions has quickly evolved for the last two decades. Formulation of thermodynamic and kinetic linear scaling relationships for key intermediates on crystalline materials have led to the definition of activity volcano plots, overpotential diagrams, and full exploitation of these theoretical outcomes at laboratory scale. However, recent studies hint at the role of morphological changes and short-lived intermediates in ruling the catalytic performance under operating conditions, further raising the bar for the modeling of electrocatalytic systems. Here, we highlight some novel methodological approaches employed to address eCO₂R and HER reactions. Moving from the atomic scale to the bulk electrolyte, we first show how ab initio and machine learning methodologies can partially reproduce surface reconstruction under operation, thus identifying active sites and reaction mechanisms if coupled with microkinetic modeling. Later, we introduce the potential of density functional theory and machine learning to interpret data from Operando spectroelectrochemical techniques, such as Raman spectroscopy and extended X-ray absorption fine structure characterization. Next, we review the role of electrolyte and mass transport effects. Finally, we suggest further challenges for computational modeling in the near future as well as our perspective on the directions to follow.

Periodic DFTB for Supported Clusters: Implementation and Application on Benzene Dimers Deposited on Graphene

The interest for properties of clusters deposited on surfaces has grown in recent years. In this framework, the Density Functional based Tight Binding (DFTB) method appears as a promising tool due to its ability to treat extended systems at the quantum level with a low computational cost. We report the implementation of periodic boundary conditions for DFTB within the deMonNano code with k-points formalism and corrections for intermolecular interactions. The quality of DFTB results is evaluated by comparison with dispersion-corrected DFT calculations. Optimized lattice properties for a graphene sheet and graphite bulk are in agreement with reference data. The deposition of both benzene monomer and dimers on graphene are investigated and the observed trends are similar at the DFT and DFTB levels. Moreover, interaction energies are of similar orders of magnitude for these two levels of calculation. This study has evidenced the high stability of a structure made of two benzene molecules deposited close to each other on the graphene sheet. This work demonstrates the ability of the new implementation to investigate surface-deposited molecular clusters properties.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Photoredox Chemistry with Organic Catalysts: Role of Computational Methods

Organic catalysts have the potential to carry out a wide range of otherwise thermally inaccessible reactions via photoredox routes. Early demonstrated successes of organic photoredox catalysts include one-electron CO₂ reduction and H₂ generation via water splitting. Photoredox systems are challenging to study and design owing to the sheer number and diversity of phenomena involved, including light absorption, emission, intersystem crossing, partial or complete charge transfer, and bond breaking or formation. Designing a viable photoredox route therefore requires consideration of a host of factors such as absorption wavelength, solvent, choice of electron donor or acceptor, and so on. Quantum chemistry methods can play a critical role in demystifying photoredox phenomena. Using one-electron CO₂ reduction with phenylene-based chromophores as an illustrative example, this perspective highlights recent developments in quantum chemistry that can advance our understanding of photoredox processes and proposes a way forward for driving the design and discovery of organic catalysts.

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.

Cation Overcrowding Effect on the Oxygen Evolution Reaction

The influence of electrolyte ions on the catalytic activity of electrode/electrolyte interfaces is a controversial topic for many electrocatalytic reactions. Herein, we focus on an effect that is usually neglected, namely, how the local reaction conditions are shaped by nonspecifically adsorbed cations. We scrutinize the oxygen evolution reaction (OER) at nickel (oxy)hydroxide catalysts, using a physicochemical model that integrates density functional theory calculations, a microkinetic submodel, and a mean-field submodel of the electric double layer. The aptness of the model is verified by comparison with experiments. The robustness of model-based insights against uncertainties and variations in model parameters is examined, with a sensitivity analysis using Monto Carlo simulations. We interpret the decrease in OER activity with the increasing effective size of electrolyte cations as a consequence of cation overcrowding near the negatively charged electrode surface. The same reasoning could explain why the OER activity increases with solution pH on the RHE scale and why the OER activity decreases in the presence of bivalent cations. Overall, this work stresses the importance of correctly accounting for local reaction conditions in electrocatalytic reactions to obtain an accurate picture of factors that determine the electrode activity.

Critical Role of Thermal Fluctuations for CO Binding on Electrocatalytic Metal Surfaces

This work considers the evaluation of density functional theory (DFT) when comparing against experimental observations of CO binding trends on the strong binding Pt(111) and intermediate binding Cu(111) and for weak binding Ag(111) and Au(111) surfaces important in electrocatalysis. By introducing thermal fluctuations using appropriate statistical mechanical NVT and NPT ensembles, we find that the RPBE and B97M-rV DFT functionals yield qualitatively better metal surface strain trends and CO enthalpies of binding for Cu(111) and Pt(111) than found at 0 K, thereby correcting the overbinding by 0.2 to 0.3 eV to yield better agreement with the enthalpies determined from experiment. The importance of dispersion effects are manifest for the weak CO binding Ag(111) and Au(111) surfaces at finite temperatures in which the RPBE functional does not bind CO at all, while the B97M-rV functional shows that the CO-metal interactions are a mixture of chemisorbed and physisorbed species with binding enthalpies that are within ∼0.05 eV of experiment. Across all M(111) surfaces, we show that the B97M-rV functional consistently predicts the correct atop site preference for all metals due to thermally induced surface distortions that preferentially favor the undercoordinated site. This study demonstrates the need to fully account for finite temperature fluctuations to make contact with the binding enthalpies from surface science experiments and electrocatalysis applications.

Modelling electrocatalytic reactions with a concerted treatment of multistep electron transfer kinetics and local reaction conditions

A physicochemical model is developed for electrocatalytic reactions involving multiple electron transfer steps occurring in the electric double layer (EDL). The local reaction conditions are calculated using a mean-field EDL model, which is derived from a comprehensive grand potential that considers the steric effects, solvent polarization, and chemisorption-induced surface dipoles. Macroscopic mass transport in the so-called diffusion layer is controlled by the same set of controlling equations of the EDL model, without imposing the electroneutrality assumption as usual. The Gerischer's formulation of electron transfer theory, corrected with local reaction conditions, is used to describe the kinetics of elementary steps. Multistep kinetics of the electrocatalytic reaction is treated using microkinetics modelling, without resorting to the usual rate-determining step approximation. In formal analysis of the model, we retrieve canonical models with additional assumptions. Self-consistent numerical implementation of the model is demonstrated for oxygen reduction reaction (ORR) at Pt(111) in acidic solution, and the aptness of the model is verified by comparison with experimental data. A comparative study of the full model and its simplified versions allows us to examine how the ORR is influenced by asymmetric steric effects, finite concentration of ions, solvent polarization, surface charge effects, and metal electronic structure effects. We find that the difference in terms of the overpotential between the full model and the simplest model can be up to ∼0.1 V at a current density of -6 mAcm-2.

Interfacial Proton Transfer for Hydrogen Evolution at the Sub-Nanometric Platinum/Electrolyte Interface

Understanding the dynamic process of interfacial charge transfer prior to chemisorption is crucial to the development of electrocatalysis. Recently, interfacial water has been highlighted in transferring protons through the electrode/electrolyte interface; however, the identification of the related structural configurations and their influences on the catalytic mechanism is largely complicated by the amorphous and mutable structure of the electrical double layer (EDL). To this end, sub-nanometric Pt electrocatalysts, potentially offering intriguing activity and featuring fully exposed atoms, are studied to uncover the elusive electrode/electrolyte interface via operando X-ray absorption spectroscopy during the hydrogen evolution reaction (HER). Our results show that the metallic Pt clusters derived from the reduction of sub-nanometric Pt clusters (SNM-Pt) exhibit excellent HER activity, with an only 18 mV overpotential at 10 mA/cm² and one-magnitude-higher mass activity than commercial Pt/C. More importantly, a unique Pt-interfacial water configuration with a Pt (from Pt clusters)-O (from water) radial distance of approximately 2.5 Å is experimentally identified as the structural foundation for the interfacial proton transfer. Toward high overpotentials, the interfacial water that structurally evolves from "O-close" to "O-far" accelerates the proton transfer and is responsible for the improved reaction rate by increasing the hydrogen coverage.

Recent Progress toward Ab Initio Modeling of Electrocatalysis

Electrode potential is the key factor for controlling electrocatalytic reactions at electrochemical interfaces, and moreover, it is also known that the pH and solutes (e.g., cations) of the solution have prominent effects on electrocatalysis. Understanding these effects requires microscopic information on the electrochemical interfaces, in which theoretical simulations can play an important role. This Perspective summarizes the recent progress in method development for modeling electrochemical interfaces, including different methods for describing the electrolytes at the interfaces and different schemes for charging up the electrode surfaces. In the final section, we provide an outlook for future development in modeling methods and their applications to electrocatalysis.

Anion Modulation of Pt-Group Metals and Electrocatalysis Applications

Pt-group metal (PGM) electrocatalysts with unique electronic structures and irreplaceable comprehensive properties play crucial roles in electrocatalysis. Anion engineering can create a series of PGM compounds (such as RuP₂ , IrP₂ , PtP₂ , RuB₂ , Ru₂ B₃ , RuS₂ , etc.) that provide a promising prospect for improving the electrocatalytic performance and use of Pt-group noble metals. This review seeks the electrochemical activity origin of anion-modulated PGM compounds, and systematically analyzes and summarizes their synthetic strategies and energy-relevant applications in electrocatalysis. Orientation towards the sustainable development of nonfossil resources has stimulated a blossoming interest in the design of advanced electrocatalysts for clean energy conversion. The anion-modulated strategy for Pt-group metals (PGMs) by means of anion engineering possesses high flexibility to regulate the electronic structure, providing a promising prospect for constructing electrocatalysts with superior activity and stability to satisfy a future green electrochemical energy conversion system. Based on the previous work of our group and others, this review summarizes the up-to-date progress on anion-modulated PGM compounds (such as RuP₂ , IrP₂ , PtP₂ , RuB₂ , Ru₂ B₃ , RuS₂ , etc.) in energy-related electrocatalysis from the origin of their activity and synthetic strategies to electrochemical applications including hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR), hydrogen oxidation reaction (HOR), N₂ reduction reaction (NRR), and CO₂ reduction reaction (CO₂ RR). At the end, the key problems, countermeasures and future development orientations of anion-modulated PGM compounds toward electrocatalytic applications are proposed.

Ab initiomodelling of interfacial electrochemical properties: beyond implicit solvation limitations

First-principles calculations are an important tool to investigate the complex processes occurring at solid/liquid interfaces which are at the heart of modern technologies. Currently, capturing the whole electrochemical environment at an interface, including the applied potential and solvation, still remains challenging as it necessitates to couple different approaches whose interactions are not fully understood. In this work, a grand canonical density functional theory approach is coupled with solvation models to investigate the electrochemical interfaces under applied potential. We show that a parametrized polarizable continuum model (PCM) which represent solvation in a mean field approach by a continuous polarizable media, possesses catastrophic limitations for the modelling of ionic and charged interfaces. We reveal the origin of PCM instabilities under chemical or electrochemical strong oxidation to be the consequence of a phase transition in the surface Li electronic structure. Thus, PCM undergoes an unphysical response to this phase transition by penetrating within the atomic radius of surface Li atoms. To recover a physical response, an explicit first solvation shell has to be included in addition to the PCM in order to properly describe the electrochemistry of the interface. The Fukui functions show that the first solvation shell becomes involved in the redox process as solvent electron doublet is transferred to the acidic Li⁺. If another explicit solvent layer is added, the interface electrochemical properties become independent of the PCM parameters: in particular capacitance can then be computed from a parameter-free electrochemical approach. This is an important conclusion as the experimental electrochemical capacitance are not easily found and thus the parametrization of the PCM for electrochemical interface can be difficult. This approach can easily be applied to investigate electrochemical properties at the atomic scale and generalized to any electrochemical device for which interfaces play a crucial role.

First-principles description of electrocatalytic characteristics of graphene-like materials

Graphene-like materials (GLMs) have received much attention as a potential alternative to precious metal-based electrocatalysts. However, the description of their electrocatalytic characteristics may still need to be improved, especially under constant chemical potential. Unlike the case of conventional metal electrodes, the potential drop across the electrical double layer (ϕ_D) at the electrode-electrolyte interface can deviate substantially from the applied voltage (ϕ_app) due to a shift of the Dirac point (eϕ_G) with charging. This may in turn significantly alter the interfacial capacitance (C_T) and the relationship between ϕ_app and free-energy change (ΔF). Hence, accurate evaluation of the electrode contribution is necessary to better understand and optimize the electrocatalytic properties of GLMs. In this work, we revisit and compare first-principles methods available to describe the ϕ_app-∆F relation. Grand-canonical density functional theory is used to determine ΔF as a function of ϕ_app or electrode potential (ϕ_q), from which the relative contribution of eϕ_G is estimated. In parallel, eϕ_G is directly extracted from a density functional theory analysis of the electronic structure of uncharged GLMs. The results of both methods are found to be in close agreement for pristine graphene, but their predictions deviate noticeably in the presence of adsorbates; the origin of the discrepancy is analyzed and explained. We then evaluate the application of the first-principle methods to prediction of the electrocatalytic processes, taking the reduction (hydrogenation) and oxidation (hydroxylation) reactions on pristine graphene as examples. Our work highlights the vital role of the modification of the electrode electronic structure in determining the electrocatalytic performance of GLMs.

2H-MoS2 on Mo2CTx MXene Nanohybrid for Efficient and Durable Electrocatalytic Hydrogen Evolution

The development of highly efficient and durable earth-abundant hydrogen evolution reaction (HER) catalysts is crucial for the extensive implementation of the hydrogen economy. Members of the 2D MXenes family, particularly Mo₂CT_x, have recently been identified as promising HER catalysts. However, their inherent oxidative instability in air and aqueous electrolyte solutions is hindering their widespread use. Herein, we present a simple and scalable method to circumvent adventitious oxidation in Mo₂CT_x MXenes via in situ sulfidation to form a Mo₂CT_x/2H-MoS₂ nanohybrid. The intimate epitaxial coupling at the Mo₂CT_x/2H-MoS₂ nanohybrid interface afforded superior HER activities, requiring only 119 or 182 mV overpotential to yield -10 or -100 mA cm^-2_geom current densities, respectively. Density functional theory calculations reveal strongest interfacial adhesion was found within the nanohybrid structure as compared to the physisorbed nanohybrid, and the possibility to tune the HER overpotential through manipulating the extent of MXene sulfidation. Critically, the presence of 2H-MoS₂ suppresses further oxidation of the MXene layer, enabling the nanohybrid to sustain industrially relevant current densities of over -450 mA cm^-2_geom with exceptional durability. Less than 30 mV overpotential degradation was observed after 10 continuous days of electrolysis at a fixed -10 mA cm^-2_geom current density or 100,000 successive cyclic voltammetry cycles. The exceptional HER durability of the Mo₂CT_x/2H-MoS₂ nanohybrid presents a major step forward to realize practical implementation of MXenes as noble metal free catalysts for broad-based applications in water splitting and energy conversion.