Modeling the electrified solid–liquid interface

Thermodynamic phase control of Cu-Sn alloy electrocatalysts for selective CO2 reduction

In the electrochemical CO2 reduction reaction (CO2RR), Cu alloy electrocatalysts can control the CO2RR selectivity by modulating the intermediate binding energy. Here, we report the thermodynamic-based Cu-Sn bimetallic phase control in heterogeneous catalysts for selective CO2 conversion. Starting from the thermodynamic understanding about Cu-Sn bimetallic compounds, we established the specific processing window for Cu-Sn bimetallic phase control. To modulate the Cu-Sn bimetallic phases, we controlled the oxygen partial pressure (pO2) during the calcination of electrospun Cu and Sn ions-incorporated nanofibers (NFs). This resulted in the formation of CuO-SnO2 NFs (full oxidation), Cu-SnO2 NFs (selective reduction), Cu3Sn/CNFs, Cu41Sn11/CNFs, and Cu6Sn5/CNFs (full reduction). In the CO2RR, CuO-SnO2 NFs exhibited formate (HCOO-) production and Cu-SnO2 NFs showed carbon monoxide (CO) production with the faradaic efficiency (FE) of 65.3% at -0.99 V (vs. RHE) and 59.1% at -0.89 V (vs. RHE) respectively. Cu-rich Cu41Sn11/CNFs and Cu3Sn/CNFs enhanced the methane (CH4) production with the FE of 39.1% at -1.36 V (vs. RHE) and 34.7% at -1.50 V (vs. RHE). However, Sn-rich Cu6Sn5/CNFs produced HCOO- with the FE of 58.6% at -2.31 V (vs. RHE). This study suggests the methodology for bimetallic catalyst design and steering the CO2RR pathway by controlling the active sites of Cu-Sn alloys.

Toward Realistic Models of the Electrocatalytic Oxygen Evolution Reaction

The electrocatalytic oxygen evolution reaction (OER) supplies the protons and electrons needed to transform renewable electricity into chemicals and fuels. However, the OER is kinetically sluggish; it operates at significant rates only when the applied potential far exceeds the reversible voltage. The origin of this overpotential is hidden in a complex mechanism involving multiple electron transfers and chemical bond making/breaking steps. Our desire to improve catalytic performance has then made mechanistic studies of the OER an area of major scientific inquiry, though the complexity of the reaction has made understanding difficult. While historically, mechanistic studies have relied solely on experiment and phenomenological models, over the past twenty years ab initio simulation has been playing an increasingly important role in developing our understanding of the electrocatalytic OER and its reaction mechanisms. In this Review we cover advances in our mechanistic understanding of the OER, organized by increasing complexity in the way through which the OER is modeled. We begin with phenomenological models built using experimental data before reviewing early efforts to incorporate ab initio methods into mechanistic studies. We go on to cover how the assumptions in these early ab initio simulations─no electric field, electrolyte, or explicit kinetics─have been relaxed. Through comparison with experimental literature, we explore the veracity of these different assumptions. We summarize by discussing the most critical open challenges in developing models to understand the mechanisms of the OER.

Modeling Heterogeneous Catalysis and Electrocatalysis

With this special collection of articles with contributions from friends, former colleagues, collaborators, students, and postdocs, we celebrate Jens K. Nørskov′s belated 70th birthday. The studies reported here highlight just a small portion of the breadth and depth of Jens Nørskov's 40 years of influence in modeling heterogeneous catalysis and electrocatalysis. Many challenges remain in enabling in silico catalyst design, and the contributions in this special collection highlight the growing importance of machine learning approaches towards solving these challenges.

Emerging Atomistic Modeling Methods for Heterogeneous Electrocatalysis

Heterogeneous electrocatalysis lies at the center of various technologies that could help enable a sustainable future. However, its complexity makes it challenging to accurately and efficiently model at an atomic level. Here, we review emerging atomistic methods to simulate the electrocatalytic interface with special attention devoted to the components/effects that have been challenging to model, such as solvation, electrolyte ions, electrode potential, reaction kinetics, and pH. Additionally, we review relevant computational spectroscopy methods. Then, we showcase several examples of applying these methods to understand and design catalysts relevant to green hydrogen. We also offer experimental views on how to bridge the gap between theory and experiments. Finally, we provide some perspectives on opportunities to advance the field.

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.

Hydrogen evolution descriptors of 55-atom PtNi nanoclusters and interaction with graphite

Density functional simulations have been performed for PtnNi55-nclusters (n=0,12,20,28,42,55) to investigate their catalytic properties for the hydrogen evolution reaction (HER). Starting from the icosahedralPt12Ni43, hydrogen adsorption energetics and electronicd-band descriptors indicate HER activity comparable to that of purePt55(distorted reduced core structure). The PtNi clusters accommodate a large number of adsorbed hydrogen before reaching a saturated coverage, corresponding to 3-4 H atoms per icosahedron facet (in total ∼70-80). The differential adsorption free energies are well within the window of|ΔGH|<0.1 eV which is considered optimal for HER. The electronic descriptors show similarities with the platinumd-band, although the uncovered PtNi clusters are magnetic. Increasing hydrogen coverage suppresses magnetism and depletes electron density, resulting in expansion of the PtNi clusters. For a single H atom, the adsorption free energy varies between -0.32 (Pt12Ni43) and -0.59 eV (Pt55). The most stable adsorption site is Pt-Pt bridge for Pt-rich compositions and a hollow site surrounded by three Ni for Pt-poor compositions. A hydrogen molecule dissociates spontaneously on the Pt-rich clusters. The above HER activity predictions can be extended to PtNi on carbon support as the interaction with a graphite model structure (w/o vacancy defect) results in minor changes in the cluster properties only. The cluster-surface interaction is the strongest forPt55due to its large facing facet and associated van der Waals forces.

Comparative analysis of surface phase diagrams in aqueous environment: Implicit vs explicit solvation models

Identifying the stable surface phases under a given electrochemical conditions serves as the basis for studying the atomistic mechanism of reactions at solid/water interfaces. In this work, we systematically compare the performance of the two main approaches that are used to capture the impact of an aqueous environment, implicit and explicit solvent, on surface energies and phase diagrams. As a model system, we consider the magnesium/water interface with (i) Ca substitution and (ii) proton and hydroxyl adsorption. We show that while the implicit solvent model is computationally very efficient, it suffers from two shortcomings. First, the choice of the implicit solvent parameters significantly influences the energy landscape in the vicinity of the surface. The default parameters benchmarked on solvation in water underestimate the energy of the dissolved Mg ion and lead to spontaneous dissolution of the surface atom, resulting in large differences in the surface energetics. Second, in systems containing a charged surface and a solvated ion, the implicit solvent model may not converge to the energetically stable ionic charge state but remain in a high-energy metastable configuration, representing the neutral charge state of the ion. When these two issues are addressed, surface phase diagrams that closely match the explicit water results can be obtained. This makes the implicit solvent model highly attractive as a computationally-efficient surrogate model to compute surface energies and phase diagrams.

Surface Charge Effects for the Hydrogen Evolution Reaction on Pt(111) Using a Modified Grand-Canonical Potential Kinetics Method

Surface charges of catalysts have important influences on the thermodynamics and kinetics of electrochemical reactions. Herein, we develop a modified version of the grand-canonical potential kinetics (GCP-K) method based on density functional theory (DFT) calculations to explore the effect of surface charges on reaction thermodynamics and kinetics. Using the hydrogen evolution reaction (HER) on the Pt(111) surface as an example, we show how to track the change of surface charge in a reaction and how to analyze its influence on the kinetics. Grand-canonical calculations demonstrate that the optimum hydrogen adsorption energy on Pt under the standard hydrogen electrode condition (SHE) is around -0.2 eV, rather than 0 eV established under the canonical ensemble, due to the high density of surface negative charges. By separating the surface charges that can freely exchange with the external electron reservoir, we obtain a Tafel barrier that is in good agreement with the experimental result. During the Tafel reaction, the net electron inflow into the catalyst leads to a stabilization of canonical energy and a destabilization of the charge-dependent grand-canonical component. This study provides a practical method for obtaining accurate grand-canonical reaction energetics and analyzing the surface charge induced changes.

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.

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.

Origin of Solvent Dependency of the Potential of Zero Charge

Fundamental properties of the Au(111)-KPF6 interface, particularly the potential of zero charge (PZC), exhibit pronounced variations among solvents, yet the origin remains largely elusive. In this study, we aim to link the solvent dependency to the microscopic phenomenon of electron spillover occurring at the metal-solution interface in heterogeneous dielectric media. Addressing the challenge of describing the solvent-modulated electron spillover under constant potential conditions, we adopt a semiclassical functional approach and parametrize it with first-principles calculations and experimental data. We unveil that the key variable governing this phenomenon is the local permittivity within the region approximately 2.5 Å above the metal edge. A higher local permittivity facilitates the electron spillover that tends to increase the PZC on the one hand and enhances the screening of the electronic charge that tends to decrease the PZC on the other. These dual effect lead to a nonmonotonic relationship between the PZC and the local permittivity. Moreover, our findings reveal that the electron spillover induces a capacitance peak at electrode potentials that are more negative than the PZC in concentrated solutions. This observation contrasts classical models predicting the peak to occur precisely at the PZC. To elucidate the contribution of electron spillover to the total capacitance, we decompose the total capacitance into a quantum capacitance of the metal Cq, a classical capacitance of electrolyte solution Cc, and a capacitance Cqc accounting for electron-ion correlations. Our calculations reveal that Cqc is negative due to the promoted electron spillover at more negative potentials. Our work not only reveals the importance of local permittivity in tuning the electron spillover but also presents a viable theoretical approach to study solvent effects on electrochemical interfaces under operating 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.

What Is the Rate-Limiting Step of Oxygen Reduction Reaction on Fe-N-C Catalysts?

Oxygen reduction reaction (ORR) is essential to various renewable energy technologies. An important catalyst for ORR is single iron atoms embedded in nitrogen-doped graphene (Fe-N-C). However, the rate-limiting step of the ORR on Fe-N-C is unknown, significantly impeding understanding and improvement. Here, we report the activation energies of all of the steps, calculated by ab initio molecular dynamics simulations under constant electrode potential. In contrast to the common belief that a hydrogenation step limits the reaction rate, we find that the rate-limiting step is oxygen molecule replacing adsorbed water on Fe. This occurs through concerted motion of H2O desorption and O2 adsorption, without leaving the site bare. Interestingly, despite being an apparent "thermal" process that is often considered to be potential-independent, the barrier reduces with the electrode potential. This can be explained by stronger Fe-O2 binding and weaker Fe-H2O binding at a lower potential, due to O2 gaining electrons and H2O donating electrons to the catalyst. Our study offers new insights into the ORR on Fe-N-C and highlights the importance of kinetic studies in heterogeneous electrochemistry.

Electrochemical AFM/STM with a qPlus sensor: A versatile tool to study solid-liquid interfaces

Atomic force microscopy (AFM) that can be simultaneously performed with scanning tunneling microscopy (STM) using metallic tips attached to self-sensing quartz cantilevers (qPlus sensors) has advanced the field of surface science by allowing for unprecedented spatial resolution under ultrahigh vacuum conditions. Performing simultaneous AFM and STM with atomic resolution in an electrochemical cell offers new possibilities to locally image both the vertical layering of the interfacial water and the lateral structure of the electrochemical interfaces. Here, a combined AFM/STM instrument realized with a qPlus sensor and a home-built potentiostat for electrochemical applications is presented. We demonstrate its potential by simultaneously imaging graphite with atomic resolution in acidic electrolytes. Additionally, we show its capability to precisely measure the interfacial solvent layering along the surface normal as a function of the applied potential.

Realistic Modeling of the Electrocatalytic Process at Complex Solid-Liquid Interface

The rational design of electrocatalysis has emerged as one of the most thriving means for mitigating energy and environmental crises. The key to this effort is the understanding of the complex electrochemical interface, wherein the electrode potential as well as various internal factors such as H-bond network, adsorbate coverage, and dynamic behavior of the interface collectively contribute to the electrocatalytic activity and selectivity. In this context, the authors have reviewed recent theoretical advances, and especially, the contributions to modeling the realistic electrocatalytic processes at complex electrochemical interfaces,  and illustrated the challenges and fundamental problems in this field. Specifically, the significance of the inclusion of explicit solvation and electrode potential as well as the strategies toward the design of highly efficient electrocatalysts are discussed. The structure-activity relationships and their dynamic responses to the environment and catalytic functionality under working conditions are illustrated to be crucial factors for understanding the complexed interface and the electrocatalytic activities. It is hoped that this review can help spark new research passion and ultimately bring a step closer to a realistic and systematic modeling method for electrocatalysis.

Electric Double Layer Effects in Electrocatalysis: Insights from Ab Initio Simulation and Hierarchical Continuum Modeling

Structures of the electric double layer (EDL) at electrocatalytic interfaces, which are modulated by the material properties, the electrolyte characteristics (e.g., the pH, the types and concentrations of ions), and the electrode potential, play crucial roles in the reaction kinetics. Understanding the EDL effects in electrocatalysis has attracted substantial research interest in recent years. However, the intrinsic relationships between the specific EDL structures and electrocatalytic kinetics remain poorly understood, especially on the atomic scale. In this Perspective, we briefly review the recent advances in deciphering the EDL effects mainly in hydrogen and oxygen electrocatalysis through a multiscale approach, spanning from the atomistic scale simulated by ab initio methods to the macroscale by a hierarchical approach. We highlight the importance of resolving the local reaction environment, especially the local hydrogen bond network, in understanding EDL effects. Finally, some of the remaining challenges are outlined, and an outlook for future developments in these exciting frontiers is provided.

Substantial impact of surface charges on electrochemical reaction kinetics on S vacancies of MoS2 using grand-canonical iteration method

The surface charges of catalysts have intricate influences on the thermodynamics and kinetics of electrochemical reactions. Herein, we develop a grand-canonical iteration method based on density functional theory calculations to explore the effect of surface charges on reaction kinetics beyond the traditional Butler-Volmer picture. Using the hydrogen evolution reaction on S vacancies of MoS2 as an example, we show how to track the change of surface charge in a reaction and to analyze its influence on the kinetics. Protons adsorb on S vacancies in a tough and charge-insensitive water splitting manner, which explains the observed large Tafel slope. Grand-canonical calculations report an unanticipated surface charge-induced change of the desorption pathway from the Heyrovsky route to a Volmer-Tafel route. During an electrochemical reaction, a net electron inflow into the catalyst may bring two effects, i.e., stabilization of the canonical energy and destabilization of the charge-dependent grand-canonical part. On the contrary, a net outflow of electrons from the catalyst can reverse the two effects. This surface charge effect has substantial impacts on the overpotential and the Tafel slope. We suggest that the surface charge effect is universal for all electrochemical reactions and significant for those involving interfacial proton transfers.

Thermodynamic and kinetic modeling of electrocatalytic reactions using a first-principles approach

The computational modeling of electrochemical interfaces and their applications in electrocatalysis has attracted great attention in recent years. While tremendous progress has been made in this area, however, the accurate atomistic descriptions at the electrode/electrolyte interfaces remain a great challenge. The Computational Hydrogen Electrode (CHE) method and continuum modeling of the solvent and electrolyte interactions form the basis for most of these methodological developments. Several posterior corrections have been added to the CHE method to improve its accuracy and widen its applications. The most recently developed grand canonical potential approaches with the embedded diffuse layer models have shown considerable improvement in defining interfacial interactions at electrode/electrolyte interfaces over the state-of-the-art computational models for electrocatalysis. In this Review, we present an overview of these different computational models developed over the years to quantitatively probe the thermodynamics and kinetics of electrochemical reactions in the presence of an electrified catalyst surface under various electrochemical environments. We begin our discussion by giving a brief picture of the different continuum solvation approaches, implemented within the ab initio method to effectively model the solvent and electrolyte interactions. Next, we present the thermodynamic and kinetic modeling approaches to determine the activity and stability of the electrocatalysts. A few applications to these approaches are also discussed. We conclude by giving an outlook on the different machine learning models that have been integrated with the thermodynamic approaches to improve their efficiency and widen their applicability.

Approximating constant potential DFT with canonical DFT and electrostatic corrections

The complexity of electrochemical interfaces has led to the development of several approximate density functional theory (DFT)-based schemes to study reaction thermodynamics and kinetics as a function of electrode potential. While fixed electrode potential conditions can be simulated with grand canonical ensemble DFT (GCE-DFT), various electrostatic corrections on canonical, constant charge DFT are often applied instead. In this work, we present a systematic derivation and analysis of the different electrostatic corrections on canonical DFT to understand their physical validity, implicit assumptions, and scope of applicability. Our work highlights the need to carefully address the suitability of a given model for the problem under study, especially if physical or chemical insight in addition to reaction energetics is sought. In particular, we analytically show that the different corrections cannot differentiate between electrostatic interactions and covalent or charge-transfer interactions. By numerically testing different models for CO₂ adsorption on a single-atom catalyst as a function of the electrode potential, we further show that computed capacitances, dipole moments, and the obtained physical insight depend sensitively on the chosen approximation. These features limit the scope, generality, and physical insight of these corrective schemes despite their proven practicality for specific systems and energetics. Finally, we suggest guidelines for choosing different electrostatic corrections and propose the use of conceptual DFT to develop more general approximations for electrochemical interfaces and reactions using canonical DFT.

Electrochemical hydrogen evolution on Pt-based catalysts from a theoretical perspective

Hydrogen evolution reaction (HER) by splitting water is a key technology toward a clean energy society, where Pt-based catalysts were long known to have the highest activity under acidic electrochemical conditions but suffer from high cost and poor stability. Here, we overview the current status of Pt-catalyzed HER from a theoretical perspective, focusing on the methodology development of electrochemistry simulation, catalytic mechanism, and catalyst stability. Recent developments in theoretical methods for studying electrochemistry are introduced, elaborating on how they describe solid-liquid interface reactions under electrochemical potentials. The HER mechanism, the reaction kinetics, and the reaction sites on Pt are then summarized, which provides an atomic-level picture of Pt catalyst surface dynamics under reaction conditions. Finally, state-of-the-art experimental solutions to improve catalyst stability are also introduced, which illustrates the significance of fundamental understandings in the new catalyst design.

Inverse kinetic isotope effects in the oxygen reduction reaction at platinum single crystals

Although the oxygen reduction reaction (ORR) involves multiple proton-coupled electron transfer processes, early studies reported the absence of kinetic isotope effects (KIEs) on polycrystalline platinum, probably due to the use of unpurified D₂O. Here we developed a methodology to prepare ultra-pure D₂O, which is indispensable for reliably investigating extremely surface-sensitive platinum single crystals. We find that Pt(111) exhibits much higher ORR activity in D₂O than in H₂O, with potential-dependent inverse KIEs of ~0.5, whereas Pt(100) and Pt(110) exhibit potential-independent inverse KIEs of ~0.8. Such inverse KIEs are closely correlated to the lower *OD coverage and weakened *OD binding strength relative to *OH, which, based on theoretical calculations, are attributed to the differences in their zero-point energies. This study suggests that the competing adsorption between *OH/*OD and *O₂ probably plays an important role in the ORR rate-determining steps that involve a chemical step preceding an electrochemical step (CE mechanism).

The surface charge induced high activity of oxygen reduction reaction on the PdTe2 bilayer

Developing transition metal dichalcogenides as electrocatalysts has attracted great interest due to their tunable electronic properties and good thermal stabilities. Herein, we propose a PdTe₂ bilayer as a promising electrocatalyst candidate towards the oxygen reduction reaction (ORR), based on extensive investigation of the electronic properties of PdTe₂ thin films as well as atomic-level reaction kinetics at explicit electrode potentials. We verify that under electrochemical reducing conditions, the electron emerging on the electrode surface is directly transferred to O₂ adsorbed on the PdTe₂ bilayer, which greatly reduces the dissociation barrier of O₂, and thereby facilitates the ORR to proceed via a dissociative pathway. Moreover, the barriers of the electrochemical steps in this pathway are all found to be less than 0.1 eV at the ORR limiting potential, demonstrating fast ORR kinetics at ambient conditions. This unique mechanism offers excellent energy efficiency and four-electron selectivity for the PdTe₂ bilayer, and it is identified as a promising candidate for fuel cell applications.

Adaptive Electric Fields Embedded Electrochemical Barrier Calculations

Electrochemical interfaces are grand canonical ensembles of varying electrons. Simulating them by standard first-principles methods is a challenging task, since the number of electrons (or charge) is fixed in the calculation. Under the constant charge framework, we developed a constant potential simulation method realized by adding an adaptive electric field to a charge neutral system. Electric field is the controlling variable. In addition, we defined an internal reversible hydrogen electrode potential (ϕ_IRHE), which can ensure the model independence of our method. To validate our method, the reaction energies of some electrochemical reactions are calculated, the results are comparable with the computational hydrogen electrode model and experiments. At last, the evolution of transition state structures and charge transfer coefficients of some electrochemical reactions on Ag(111) surface were discussed by our method.

Copper-Based Catalysts for Electrochemical Reduction of Carbon Dioxide to Ethylene

Electrochemical reduction of CO₂ into high energy density multi-carbon chemicals or fuels (e. g., ethylene) via new renewable energy storage has extraordinary implications for carbon neutrality. Copper (Cu)-based catalysts have been recognized as the most promising catalysts for the electrochemical reduction of CO₂ to ethylene (C₂ H₄ ) due to their moderate CO adsorption energy and moderate hydrogen precipitation potential. However, the poor selectivity, low current density and high overpotential of the CO₂ RR into C₂ H₄ greatly limit its industrial applications. Meanwhile, the complex reaction mechanism is still unclear, which leads to blindness in the design of catalysts. Herein, we systematically summarized the latest research, proposed possible conversion mechanisms and categorized the general strategies to adjust of the structure and composition for CO₂ RR, such as tip effect, defect engineering, crystal plane catalysis, synergistic effect, nanoconfinement effect and so on. Eventually, we provided a prospect of the future challenges for further development and progress in CO₂ RR. Previous reviews have summarized catalyst designs for the reduction of CO₂ to multi-carbon products, while lacking in targeting C₂ H₄ alone, an important industrial feedstock. This Review mainly aims to provide a comprehensive understanding for the design strategies and challenges of electrocatalytic CO₂ reduction to C₂ H₄ through recent researches and further propose some guidelines for the future design of copper-based catalysts for electroreduction of CO₂ to C₂ H₄ .

Determining the hydronium pK[Formula: see text] at platinum surfaces and the effect on pH-dependent hydrogen evolution reaction kinetics

Electrocatalytic hydrogen evolution reaction (HER) is critical for green hydrogen generation and exhibits distinct pH-dependent kinetics that have been elusive to understand. A molecular-level understanding of the electrochemical interfaces is essential for developing more efficient electrochemical processes. Here we exploit an exclusively surface-specific electrical transport spectroscopy (ETS) approach to probe the Pt-surface water protonation status and experimentally determine the surface hydronium pKa [Formula: see text] 4.3. Quantum mechanics (QM) and reactive dynamics using a reactive force field (ReaxFF) molecular dynamics (RMD) calculations confirm the enrichment of hydroniums (H3O[Formula: see text]) near Pt surface and predict a surface hydronium pKa of 2.5 to 4.4, corroborating the experimental results. Importantly, the observed Pt-surface hydronium pKa correlates well with the pH-dependent HER kinetics, with the protonated surface state at lower pH favoring fast Tafel kinetics with a Tafel slope of 30 mV per decade and the deprotonated surface state at higher pH following Volmer-step limited kinetics with a much higher Tafel slope of 120 mV per decade, offering a robust and precise interpretation of the pH-dependent HER kinetics. These insights may help design improved electrocatalysts for renewable energy conversion.

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.

A caveat of the charge-extrapolation scheme for modeling electrochemical reactions on semiconductor surfaces: an issue induced by a discontinuous Fermi level change

(Photo)electrochemical surface reactions in realistic experimental systems occur under a constant-potential condition, while the ab initio simulations of electrochemical reactions are mostly performed under a constant-charge condition. A charge-extrapolation scheme proposed by earlier theoretical studies converts constant-charge reaction energies to constant-potential reaction energies for electrochemical reactions on metal surfaces, which is based on a capacitor-model assumption to approximate the surface electrical double layer. However, the charge-extrapolation approach may be problematic when applied to models of photoelectrochemical reactions on semiconductor surfaces with a cross-bandgap Fermi level change along the reaction path. We perform density-functional-theory calculations to show that the error is induced by an abrupt change of the modeling system's potential making the capacitor model assumption invalid. We further propose an approach to avoid the cross-bandgap Fermi level change in the simulations of semiconductor surface reactions, with which the charge-extrapolation scheme still can be employed to compute the constant-potential reaction energies for the semiconductor photoelectrode cases.

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.

Atomistic Understanding of Two-dimensional Electrocatalysts from First Principles

Two-dimensional electrocatalysts have attracted great interest in recent years for renewable energy applications. However, the atomistic mechanisms are still under debate. Here we review the first-principles studies of the atomistic mechanisms of common 2D electrocatalysts. We first introduce the first-principles models for studying heterogeneous electrocatalysis then discuss the common 2D electrocatalysts with a focus on N doped graphene, single metal atoms in graphene, and transition metal dichalcogenides. The reactions include hydrogen evolution, oxygen evolution, oxygen reduction, and carbon dioxide reduction. Finally, we discuss the challenges and the future directions to improve the fundamental understanding of the 2D electrocatalyst at atomic level.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Influence of an electrified interface on the entropy and energy of solvation of methanol oxidation intermediates on platinum(111) under explicit solvation

Liquid water and electric fields play significant roles in phenomena occurring at catalytic and electrocatalytic interfaces; however, how their interplay influences interfacial energetics remains uncertain. Electric fields control the orientations of water molecules, which we hypothesized would influence the solvation thermodynamics of surface species. To explore this hypothesis, we used multiscale simulations involving density functional theory and classical molecular dynamics. We computed the energies and entropies of solvation of surface species on Pt(111), specifically, adsorbed CH₃OH, COH, and CO, which are intermediates in the pathway of methanol oxidation, in the presence of electric fields spanning -0.5 to +0.5 V Å^-1. We found that both the energy and entropy of solvation depend on the strength and direction of the field, with the entropy of solvation being significantly impacted. Both the energy and entropy dependence on the field can be ascribed to water molecule orientations. Specifically, more positive fields orient water molecules so that they can more effectively hydrogen bond with surface species, which strengthens the energies of solvation. However, at more negative fields, competition with the surface species causes interfacial water molecules to reorient, which leads to disorder in the water structure and hence increased entropy.

Unveiling the role of 2D monolayer Mn-doped MoS2 material: toward an efficient electrocatalyst for H2 evolution reaction

Two-dimensional (2D) monolayer pristine MoS₂ transition metal dichalcogenide (TMD) is the most studied material because of its potential applications as nonprecious electrocatalyst for the hydrogen evolution reaction (HER). Previous studies have shown that the basal planes of 2D MoS₂ are catalytically inert, and hence it cannot be used directly in desired applications such as electrochemical HER in industry. Here, we thoroughly studied a defect-engineered Mn-doped 2D monolayer MoS₂ (Mn-MoS₂) material, where Mn was doped in pristine MoS₂ to activate its inert basal planes. Using the density functional theory (DFT) method, we performed rigorous inspection of the electronic structures and properties of the 2D monolayer Mn-MoS₂ as a promising alternative to noble metal-free catalyst for effective HER. A periodic 2D slab of monolayer Mn-MoS₂ was created to study the electronic properties (such as band gap, band structures and total density of states (DOS)) and the reaction pathways occurring on the surface of this material. The detailed HER mechanism was explored by creating an Mn₁Mo₉S₂₁ non-periodic finite molecular cluster model system using the M06-L DFT method including solvation effects to determine the reaction barriers and kinetics. Our study revealed that the 2D Mn-MoS₂ follows the most favorable Volmer-Heyrovsky reaction mechanism with a very low energy barrier during H₂ evolution. It was found that the change in the free energy barrier (ΔG) during the H˙-migration (i.e., Volmer) and Heyrovsky reactions is about 10.34-10.79 kcal mol^-1 (computed in the solvent phase), indicating that this material is an exceptional electrocatalyst for the HER. The Tafel slope (y) was lower in the case of the 2D monolayer Mn-MoS₂ material due to the overlap of the s-orbital of hydrogen and d-orbitals of the Mn atoms in the HOMO and LUMO transition states (TS1 and TS2) of both the Volmer and Heyrovsky reaction steps, respectively. The better stabilization of the atomic orbitals in the HER rate-limiting step Heyrovsky TS2 is the key for reducing the reaction barrier, and thus the overall catalysis, indicating a better electrocatalytic performance for H₂ evolution. This study focused on designing low-cost and efficient electrocatalysts for the HER using earth abundant transition metal dichalcogenides (TMDs) and decreasing the activation energy barriers by scrutinizing the kinetics of the reaction to achieve high reactivity.

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.

Design principles of noble metal-free electrocatalysts for hydrogen production in alkaline media: combining theory and experiment

Water electrolysis is a promising solution to convert renewable energy sources to hydrogen as a high-energy-density energy carrier. Although alkaline conditions extend the scope of electrocatalysts beyond precious metal-based materials to earth-abundant materials, the sluggish kinetics of cathodic and anodic reactions (hydrogen and oxygen evolution reactions, respectively) impede the development of practical electrocatalysts that do not use precious metals. This review discusses the rational design of efficient electrocatalysts by exploiting the understanding of alkaline hydrogen evolution reaction and oxygen evolution reaction mechanisms and of the electron structure-activity relationship, as achieved by combining experimental and computational approaches. The enhancement of water splitting not only deals with intrinsic catalytic activity but also includes the aspect of electrical conductivity and stability. Future perspectives to increase the synergy between theory and experiment are also proposed.

Stripping away ion hydration shells in electrical double-layer formation: Water networks matter

For centuries the double layer at the solid/electrolyte interface has been a central concept in electrochemistry. Today, it is still crucial for virtually all renewable energy storage and conversion technologies. Here, the double-layer formation is probed by THz spectroscopy with ultrabright synchrotron light as a source. Our results capture the molecular details of double-layer formation at positively/negatively charged Au electrodes for an NaCl electrolyte. We reveal a contrasting response applying positive versus negative bias, which is dictated by the interfacial water network and rationalized by accompanying molecular dynamics simulations and electronic-structure calculations. While Na⁺ is directly attracted toward the negatively charged electrode, stripping of the Cl⁻ hydration shell is observed only at larger potential values.

The double layer at the solid/electrolyte interface is a key concept in electrochemistry. Here, we present an experimental study combined with simulations, which provides a molecular picture of the double-layer formation under applied voltage. By THz spectroscopy we are able to follow the stripping away of the cation/anion hydration shells for an NaCl electrolyte at the Au surface when decreasing/increasing the bias potential. While Na⁺ is attracted toward the electrode at the smallest applied negative potentials, stripping of the Cl⁻ hydration shell is observed only at higher potential values. These phenomena are directly measured by THz spectroscopy with ultrabright synchrotron light as a source and rationalized by accompanying molecular dynamics simulations and electronic-structure calculations.

Static and dynamic water structures at interfaces: A case study with focus on Pt(111)

An accurate atomistic treatment of aqueous solid-liquid interfaces necessitates the explicit description of interfacial water ideally via ab initio molecular dynamics simulations. Many applications, however, still rely on static interfacial water models, e.g., for the computation of (electro)chemical reaction barriers and focus on a single, prototypical structure. In this work, we systematically study the relation between density functional theory-derived static and dynamic interfacial water models with specific focus on the water-Pt(111) interface. We first introduce a general construction protocol for static 2D water layers on any substrate, which we apply to the low index surfaces of Pt. Subsequently, we compare these with structures from a broad selection of reference works based on the Smooth Overlap of Atomic Positions descriptor. The analysis reveals some structural overlap between static and dynamic water ensembles; however, static structures tend to overemphasize the in-plane hydrogen bonding network. This feature is especially pronounced for the widely used low-temperature hexagonal ice-like structure. In addition, a complex relation between structure, work function, and adsorption energy is observed, which suggests that the concentration on single, static water models might introduce systematic biases that are likely reduced by averaging over consistently created structural ensembles, as introduced here.

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.

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.

Generalizable Trends in Electrochemical Protonation Barriers

Predicting activation energies for reaction steps is essential for modeling catalytic processes, but accurate barrier simulations often require considerable computational expense, especially for electrochemical reactions. Given the challenges of barrier computations and the growing promise of electrochemical routes for various processes, generalizable energetic trends in electrochemistry can significantly aid in analyzing reaction networks and building microkinetic models. Herein, we employ density functional theory and machine learning nudged elastic band models to simulate electrochemical protonation of *C, *N, and *O monatomic adsorbates from hydronium on a series of transition metal surfaces. We observe a consistent trend of decreasing protonation reaction energies yet increasing activation barriers from *O to *N to *C. Analysis of bond orders and reaction pathways provides insight into the origin of the observed trends in protonation energetics. We hypothesize that these results are relevant for polyatomic adsorbates, which can simplify analysis of reaction mechanisms and inform catalyst design.