The electric double layer at metal-water interfaces revisited based on a charge polarization scheme

Superdiffusive Rotation of Interfacial Water on Noble Metal Surface

Interfacial water on a metal surface acts as an active layer through the reorientation of water, thereby facilitating the energy transfer and chemical reaction across the metal surface in various physicochemical and industrial processes. However, how this active interfacial water collectively behaves on flat noble metal substrates remains largely unknown due to the experimental limitation in capturing librational vibrational motion of interfacial water and prohibitive computational costs at the first-principles level. Herein, by implementing a machine-learning approach to train neural network potentials, we enable performing advanced molecular dynamics simulations with ab initio accuracy at a nanosecond scale to map the distinct rotational motion of water molecules on a metal surface at room temperature. The vibrational density of states of the interfacial water with two-layer profiles reveals that the rotation and vibration of water within the strong adsorption layer on the metal surface behave as if the water molecules in the bulk ice, wherein the O-H stretching frequency is well consistent with the experimental results. Unexpectedly, the water molecules within the adjacent weak adsorption layer exhibit superdiffusive rotation, contrary to the conventional diffusive rotation of bulk water, while the vibrational motion maintains the characteristic of bulk water. The mechanism underlying this abnormal superdiffusive rotation is attributed to the translation-rotation decoupling of water, in which the translation is restrained by the strong hydrogen bonding within the bilayer interfacial water, whereas the rotation is accelerated freely by the asymmetric water environment. This superdiffusive rotation dynamics may elucidate the experimentally observed large fluctuation of the potential of zero charge on Pt and thereby the conventional Helmholtz layer model revised by including the contribution of interfacial water orientation. The surprising superdiffusive rotation of vicinal water next to noble metals will shed new light on the physicochemical processes and the activity of water molecules near metal electrodes or catalysts.

Revealing Interface Polarization Effects on the Electrical Double Layer with Efficient Open Boundary Simulations under Potential Control

A major challenge in modeling interfacial processes in electrochemical (EC) devices is performing simulations at constant potential. This requires an open-boundary description of the electrons, so that they can enter and leave the computational cell. To enable realistic modeling of EC processes under potential control we have interfaced density functional theory with the hairy probe method in the weak coupling limit (Zauchner et al. Phys. Rev. B 2018, 97, 045116). Our implementation was systematically tested using simple parallel-plate capacitor models with pristine surfaces and a single layer of adsorbed water molecules. Remarkably, our code's efficiency is comparable with a standard DFT calculation. We reveal that local field effects at the electrical double layer induced by the change of applied potential can significantly affect the energies of chemical steps in heterogeneous electrocatalysis. Our results demonstrate the importance of an explicit modeling of the applied potential in a simulation and provide an efficient tool to control this critical parameter.

Understanding electrochemical interfaces through comparing experimental and computational charge density-potential curves

Electrode-electrolyte interfaces play a decisive role in electrochemical charge accumulation and transfer processes. Theoretical modelling of these interfaces is critical to decipher the microscopic details of such phenomena. Different force field-based molecular dynamics protocols are compared here in a view to connect calculated and experimental charge density-potential relationships. Platinum-aqueous electrolyte interfaces are taken as a model. The potential of using experimental charge density-potential curves to transform cell voltage into electrode potential in force-field molecular dynamics simulations, and the need for that purpose of developing simulation protocols that can accurately calculate the double-layer capacitance, are discussed.

Laterally Resolved Free Energy Profiles and Vibrational Spectra of Chemisorbed H Atoms on Pt(111)

A scheme to compute laterally resolved free energy surfaces and spectral signatures of specifically adsorbed ions on electrode surfaces from their ab initio molecular dynamics (AIMD) trajectories is proposed. Considering H-covered Pt(111) electrodes, both in contact with water and vacuum and for various H coverages, we systematically explore the impact of explicit water and H-coverage on site occupancy, providing direct insight into the proportion of underpotential and overpotential deposited hydrogen adsorbates. Extending this approach further, we can obtain laterally resolved vibrational spectra of the Pt-H stretch modes. We discuss how the difference between the free energy basins of the on-top and fcc-hollow adsorption sites explains the features of the experimentally observed spectral fingerprints in this system. These fingerprints do not contain only information about the stable and metastable adsorption sites but also about intermediate short-lived adsorbate configurations. Our results also show that for these properties chemisorbed H2O acts as a spectator and does not qualitatively influence the relative stabilities of the adsorption sites and their spectral fingerprints.

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

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

Local reaction environment in electrocatalysis

Beyond conventional electrocatalyst engineering, recent studies have unveiled the effectiveness of manipulating the local reaction environment in enhancing the performance of electrocatalytic reactions. The general principles and strategies of local environmental engineering for different electrocatalytic processes have been extensively investigated. This review provides a critical appraisal of the recent advancements in local reaction environment engineering, aiming to comprehensively assess this emerging field. It presents the interactions among surface structure, ions distribution and local electric field in relation to the local reaction environment. Useful protocols such as the interfacial reactant concentration, mass transport rate, adsorption/desorption behaviors, and binding energy are in-depth discussed toward modifying the local reaction environment. Meanwhile, electrode physical structures and reaction cell configurations are viable optimization methods in engineering local reaction environments. In combination with operando investigation techniques, we conclude that rational modifications of the local reaction environment can significantly enhance various electrocatalytic processes by optimizing the thermodynamic and kinetic properties of the reaction interface. We also outline future research directions to attain a comprehensive understanding and effective modulation of the local reaction environment.

Impact of Pt(hkl) Electrode Surface Structure on the Electrical Double Layer Capacitance

The classical theory of the electrical double layer (EDL) does not consider the effects of the electrode surface structure on the EDL properties. Moreover, the best agreement between the traditional EDL theory and experiments has been achieved so far only for a very limited number of ideal systems, such as liquid metal mercury electrodes, for which it is challenging to operate with specific surface structures. In the case of solid electrodes, the predictive power of classical theory is often not acceptable for electrochemical energy applications, e.g., in supercapacitors, due to the effects of surface structure, electrode composition, and complex electrolyte contributions. In this work, we combine ab initio molecular dynamics (AIMD) simulations and electrochemical experiments to elucidate the relationship between the structure of Pt(hkl) surfaces and the double-layer capacitance as a key property of the EDL. Flat, stepped, and kinked Pt single crystal facets in contact with acidic HClO4 media are selected as our model systems. We demonstrate that introducing specific defects, such as steps, can substantially reduce the EDL capacitances close to the potential of zero charge (PZC). Our AIMD simulations reveal that different Pt facets are characterized by different net orientations of the water dipole moment at the interface. That allows us to rationalize the experimentally measured (inverse) volcano-shaped capacitance as a function of the surface step density.

Constant Potential Thermodynamic Integration for Obtaining the Free Energy Profile of Electrochemical Reaction

In this work, we advanced an efficient free energy sampling method based on constrained ab initio molecular dynamics (cAIMD) with a fully explicit solvent layer to depict the electrochemical reaction process at constant surface charge density, named the "Constant-Potential Thermodynamic Integration (CPTI)" method. For automatically adjusting surface charge density at different states, we built an "on-the-fly" procedure which is capable of managing all the necessary steps during cAIMD simulations, including the system pre-equilibrium, surface charge density updating, and force sampling. We applied it to predict the potential-dependent free energy profiles of CO2 adsorption on a single-atom catalyst. The results show that our method can not only account for changes in electrostatic potential energy associated with potential but also consider the potential-induced solvation effects. Our approach enables the accurate simulation of electrochemical environment by presenting the complete solid-liquid interface and efficient computation of electrocatalytic reaction energetics based on a robust potential descriptor.

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.

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.

Understanding the Effects of Electrode Material, Single Crystal Facet, and Electrolyte Ion on the Helmholtz Capacitance of Metal/Aqueous Solution Interfaces

The comprehensive interpretation of the measured differential Helmholtz capacitance curve is vital for advancing our understanding of the interfacial structure. While several possible physical effects contributing to the Helmholtz capacitance have been proposed theoretically, combining those factors to explain the experimentally observed potential-dependent capacitance profile remains a significant challenge. In this study, we employ ab initio molecular dynamics simulations to model various metal/solution interfaces. Our investigation primarily emphasizes the substantial effect of water chemisorption on the potential-dependent behavior of the Helmholtz capacitance. Additionally, we identify other critical factors that profoundly impact the Helmholtz capacitance: (1) Ions with low hydration energy hinder the availability of surface sites for water adsorption, resulting in a diminished enhancement of capacitance from water chemisorption. (2) Using large-sized ions leads to an expansion of the Helmholtz layer, causing a decrease in the Helmholtz capacitance. (3) Metal surfaces with higher affinity for water attract water adsorption at lower potentials, resulting in a lower peak potential for the differential Helmholtz capacitance curve.

A cell-electrode interface signal-to-noise ratio model for 3D micro-nano electrode

Objective. Three-dimensional micro-nano electrodes (MNEs) with the vertical nanopillar array distributed on the surface play an increasingly important role in neural science research. The geometric parameters of the nanopillar array and the cell adhesion state on the nanopillar array are the factors that may affect the MNE recording. However, the quantified relationship between these parameters and the signal-to-noise ratio (SNR) is still unclear. This paper establishes a cell-MNE interface SNR model and obtains the mathematical relationship between the above parameters and SNR.Approach. The equivalent electrical circuit and numerical simulation are used to study the sensing performance of the cell-electrode interface. The adhesion state of cells on MNE is quantified as engulfment percentage, and an equivalent cleft width is proposed to describe the signal loss caused by clefts between the cell membrane and the electrode surface.Main results. Whether the planar substrate is insulated or not, the SNR of MNE is greater than planar microelectrode only when the engulfment percentage is greater than a certain value. Under the premise of maximum engulfment percentage, the spacing and height of nanopillars should be minimized, and the radius of the nanopillar should be maximized for better signal quality.Significance. The model can clarify the mechanism of improving SNR by nanopillar arrays and provides the theoretical basis for the design of such nanopillar neural electrodes.

Accelerating explicit solvent models of heterogeneous catalysts with machine learning interatomic potentials

Realistically modelling how solvents affect catalytic reactions is a longstanding challenge due to its prohibitive computational cost. Typically, an explicit atomistic treatment of the solvent molecules is needed together with molecular dynamics (MD) simulations and enhanced sampling methods. Here, we demonstrate the utility of machine learning interatomic potentials (MLIPs), coupled with active learning, to enable fast and accurate explicit solvent modelling of adsorption and reactions on heterogeneous catalysts. MLIPs trained on-the-fly were able to accelerate ab initio MD simulations by up to 4 orders of magnitude while reproducing with high fidelity the geometrical features of water in the bulk and at metal-water interfaces. Using these ML-accelerated simulations, we accurately predicted key catalytic quantities such as the adsorption energies of CO*, OH*, COH*, HCO*, and OCCHO* on Cu surfaces and the free energy barriers of C-H scission of ethylene glycol over Cu and Pd surfaces, as validated with ab initio calculations. We envision that such simulations will pave the way towards detailed and realistic studies of solvated catalysts at large time- and length-scales.

Comparing Ab Initio Molecular Dynamics and a Semiclassical Grand Canonical Scheme for the Electric Double Layer of the Pt(111)/Water Interface

The theoretical modeling of metal/water interfaces centers on an appropriate configuration of the electric double layer (EDL) under grand canonical conditions. In principle, ab initio molecular dynamics (AIMD) simulations would be the appropriate choice for treating the competing water-water and water-metal interactions and explicitly considering the atomic and electronic degrees of freedom. However, this approach only allows simulations of relatively small canonical ensembles over a limited period (shorter than 100 ps). On the other hand, computationally efficient semiclassical approaches can treat the EDL model based on a grand canonical scheme by averaging the microscopic details. Thus, an improved description of the EDL can be obtained by combining AIMD simulations and semiclassical methods based on a grand canonical scheme. By taking the Pt(111)/water interface as an example, we compare these approaches in terms of the electric field, water configuration, and double-layer capacitance. Furthermore, we discuss how the combined merits of the approaches can contribute to advances in EDL theory.

Machine Learning Assisted Simulations of Electrochemical Interfaces: Recent Progress and Challenges

The electrochemical interface, where the adsorption of reactants and electrocatalytic reactions take place, has long been a focus of attention. Some of the important processes on it tend to possess relatively slow kinetic characteristics, which are usually beyond the scope of ab initio molecular dynamics. The newly emerging technique, machine learning methods, provides an alternative approach to achieve thousands of atoms and nanosecond time scale while ensuring precision and efficiency. In this Perspective, we summarize in detail the recent progress and achievements made by the introduction of machine learning to simulate electrochemical interfaces, and focus on the limitations of current machine learning models, such as accurate descriptions of long-range electrostatic interactions and the kinetics of the electrochemical reactions occurring at the interface. Finally, we further point out the future directions for machine learning to expand in the field of electrochemical interfaces.

Zooming into the Inner Helmholtz Plane of Pt(111)-Aqueous Solution Interfaces: Chemisorbed Water and Partially Charged Ions

The double layer on transition metals, i.e., platinum, features chemical metal-solvent interactions and partially charged chemisorbed ions. Chemically adsorbed solvent molecules and ions are situated closer to the metal surface than electrostatically adsorbed ions. This effect is described tersely by the concept of an inner Helmholtz plane (IHP) in classical double layer models. The IHP concept is extended here in three aspects. First, a refined statistical treatment of solvent (water) molecules considers a continuous spectrum of orientational polarizable states, rather than a few representative states, and non-electrostatic, chemical metal-solvent interactions. Second, chemisorbed ions are partially charged, rather than being electroneutral or having integral charges as in the solution bulk, with the coverage determined by a generalized, energetically distributed adsorption isotherm. The surface dipole moment induced by partially charged, chemisorbed ions is considered. Third, considering different locations and properties of chemisorbed ions and solvent molecules, the IHP is divided into two planes, namely, an AIP (adsorbed ion plane) and ASP (adsorbed solvent plane). The model is used to study how the partially charged AIP and polarizable ASP lead to intriguing double-layer capacitance curves that are different from what the conventional Gouy-Chapman-Stern model describes. The model provides an alternative interpretation for recent capacitance data of Pt(111)-aqueous solution interfaces calculated from cyclic voltammetry. This revisit brings forth questions regarding the existence of a pure double-layer region at realistic Pt(111). The implications, limitations, and possible experimental confirmation of the present model are discussed.

Potential-Dependent Pt(111)/Water Interface: Tackling the Challenge of a Consistent Treatment of Electrochemical Interfaces

The interface between an electrode and an electrolyte is where electrochemical processes take place for countless technologically important applications. Despite its high relevance and intense efforts to elucidate it, a description of the interfacial structure and, in particular, the dynamics of the electric double layer at the atomic level is still lacking. Here we present reactive force-field molecular dynamics simulations of electrified Pt(111)/water interfaces, shedding light on the orientation of water molecules in the vicinity of the Pt(111) surface, taking into account the influence of potential, adsorbates, and ions simultaneously. We obtain a shift in the preferred orientation of water in the surface oxidation potential region, which breaks with the previously proclaimed strict correlation to the free charge density. Moreover, the characterization is complemented by course of the entropy and the intermolecular ordering in the interfacial region complements the characterization. Our work contributes to the ongoing process of understanding electric double layers and, in particular, the structure of the electrified Pt(111)/water interface, and aims to provide insights into the electrochemical processes occurring there.

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

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

Modeling stepped Pt/water interfaces at potential of zero charge with ab initio molecular dynamics

It is worthwhile to understand the potentials of zero charge (PZCs) and structures of stepped metal/water interfaces, because for many electrocatalytic reactions stepped surfaces are more active than atomically flat surfaces. Herein, a series of stepped Pt/water interfaces are modeled at different step densities with ab initio molecular dynamics (AIMD). It is found that the structures of Pt/water interfaces are significantly influenced by the step density, particularly for the distribution of chemisorbed water. The step sites of metal surfaces are more preferred for water chemisorption than the terrace sites, and until the step density is very low, water will chemisorb on the terrace. In addition, it is revealed that the PZCs of stepped Pt/water interfaces are generally smaller than that of Pt(111), and the difference is mainly attributed to the difference in the work function, providing a simple way to estimate the PZCs of stepped metal surfaces. Finally, it is interesting to see that the Volta potential difference is almost same for Pt/water interfaces with different step densities, although their interface structures and magnitude of charge transfer clearly differ.

Essays on Conceptual Electrochemistry: I. Bridging Open-Circuit Voltage of Electrochemical Cells and Charge Distribution at Electrode–Electrolyte Interfaces

We ponder over how an electrochemical cell conforms itself to the open-circuit voltage (OCV) given by the Nernst equation, where properties of the electrodes play no role. We first show, via a pedagogical derivation of the Nernst equation, how electrode properties are canceled and then take a closer look into the electrode–electrolyte interface at one electrode by linking charge and potential distributions. We obtain an equilibrium Poisson–Nernst equation that shows how the charge distribution across an electrode–electrolyte interface can be dictated by the chemical potentials of redox species. Taking a H2/O2 fuel cell as an example, we demystify the formal analysis by showing how the two electrodes delicately regulate their “electron tails” to abide by the Nernst equation. In this example, we run into a seemingly counterintuitive phenomenon that two electrodes made of the same transition metal display two distinct potentials of zero charge. This example indicates that the double layer at transition metals with chemisorption can display distinct behaviors compared to ideally polarizable double layers at sp metals.

Structure and interactions at the Mg(0001)/water interface: An ab initio study

A molecular level understanding of metal/bulk water interface structure is key for a wide range of processes, including aqueous corrosion, which is our focus, but their buried nature makes experimental investigation difficult and we must mainly rely on simulations. We investigate the Mg(0001)/water interface using second generation Car–Parrinello molecular dynamics (MD) to gain structural information, combined with static density functional theory calculations to probe the atomic interactions and electronic structure (e.g., calculating the potential of zero charge). By performing detailed structural analyses of both metal–surface atoms and the near-surface water, we find that, among other insights: (i) water adsorption causes significant surface roughening (the planar distribution for top-layer Mg has two peaks separated by [Formula: see text]), (ii) strongly adsorbed water covers only [Formula: see text] of available surface sites, and (iii) adsorbed water avoids clustering on the surface. Static calculations are used to gain a deeper understanding of the structuring observed in MD. For example, we use an energy decomposition analysis combined with calculated atomic charges to show that adsorbate clustering is unfavorable due to Coulombic repulsion between adsorption site surface atoms. Results are discussed in the context of previous simulations carried out on other metal/water interfaces. The largest differences for the Mg(0001)/water system appear to be the high degree of surface distortion and the minimal difference between the metal work function and metal/water potential of zero charge (at least compared to other interfaces with similar metal–water interaction strengths). The structural information, in this paper, is important for understanding aqueous Mg corrosion, as the Mg(0001)/water interface is the starting point for key reactions. Furthermore, our focus on understanding the driving forces behind this structuring leads to important insights for general metal/water interfaces.

Electrochemical aspects of coinage metal nanoparticles for catalysis and spectroscopy

Down scaling bulk materials can cause colloidal systems to evolve into microscopically dispersed insoluble particles. Herein, we describe the interesting applications of coinage metal nanoparticles (MNPs) as colloid dispersions especially gold and silver. The rich plasmon bands of gold and silver in the visible range are elaborated using the plasmon resonance and redox potential values of grown metal microelectrode (GME). The gradation of their standard reduction potential values (E 0), as evaluated from the Gibbs free energy change for bulk metal, is ascribed to the variation in their size. Also, the effect of nucleophiles in the electrolytic cell with metal nanoparticles (MNPs) is described. The nucleophile-guided reduction potential value is considered, which is applicable even for bulk noble metals. Typically, a low value (as low as E 0 = +0.40 V) causes the oxidation of metals at the O2 (air)/H2O interface. Under this condition, the oxidation of noble metal particles and dissolution of the noble metal in water are demonstrated. Thus, metal dissolution as a function of the size of metal nanoparticles becomes eventful and demonstrable with the addition of a surfactant to the solution. Interestingly, the reversal of the nobility of gold (Au) and silver (Ag) microelectrodes at the water/electrode interface is confirmed from the evolution of normal and inverted 'core-shell' structures, exploiting visible spectrophotometry and surface-enhanced Raman scattering (SERS) analysis. Subsequently, the effect of the size, shape, and facet- and support-selective catalysis of gold nanoparticles (NPs) and the effect of incident photons on current conversion without an applied potential are briefly discussed. Finally, the synergistic effect of the emissive behaviour of gold and silver clusters is productively exploited.

Models of Electron Transfer at Different Electrode Materials

Electron transfer is the most important electrochemical process. In this review, we present elements of various aspects of electron transfer theory from the early work of Marcus and Hush to recent developments. The emphasis is on the role of the electronic, and to a lesser extent the geometrical, properties of the electrode. A variety of experimental works are discussed in light of these theoretical concepts. Because the field of electron transfer is so vast, this review is far from comprehensive; rather, we focus on systems that offer a special interest and illuminate aspects of the theory.

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.

Advancement of the Homogeneous Background Method for the Computational Simulation of Electrochemical Interfaces

Computational studies of electrochemical interfaces based on density-functional theory (DFT) play an increasingly important role in the present research on electrochemical processes for energy conversion and storage. The homogeneous background method (HBM) offers a straightforward approach to charge the electrochemical system within DFT simulations, but it typically requires the specification of the active fraction of excess electrons based on a certain choice of the electrode-electrolyte boundary location, which can be difficult in the presence of electrode-surface adsorbates or explicit solvent molecules. In this work, we present a methodological advancement of the HBM, both facilitating and extending its applicability. The advanced version requires neither energy corrections nor the specification of the active fraction of excess electrons, providing a versatile and readily available method for the simulation of charged interfaces when adsorbates or explicit solvent molecules are present. Our computational DFT results for Pt(111), Au(111), and Li(100) metal electrodes in high-dielectric-constant solvents demonstrate an excellent agreement in the interfacial charging characteristics obtained from simulations with the advanced HBM in comparison with the (linearized) Poisson-Boltzmann model (PBM).

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.

Ab Initio Simulations of Water/Metal Interfaces

Structures and processes at water/metal interfaces play an important technological role in electrochemical energy conversion and storage, photoconversion, sensors, and corrosion, just to name a few. However, they are also of fundamental significance as a model system for the study of solid-liquid interfaces, which requires combining concepts from the chemistry and physics of crystalline materials and liquids. Particularly interesting is the fact that the water-water and water-metal interactions are of similar strength so that the structures at water/metal interfaces result from a competition between these comparable interactions. Because water is a polar molecule and water and metal surfaces are both polarizable, explicit consideration of the electronic degrees of freedom at water/metal interfaces is mandatory. In principle, ab initio molecular dynamics simulations are thus the method of choice to model water/metal interfaces, but they are computationally still rather demanding. Here, ab initio simulations of water/metal interfaces will be reviewed, starting from static systems such as the adsorption of single water molecules, water clusters, and icelike layers, followed by the properties of liquid water layers at metal surfaces. Technical issues such as the appropriate first-principles description of the water-water and water-metal interactions will be discussed, and electrochemical aspects will be addressed. Finally, more approximate but numerically less demanding approaches to treat water at metal surfaces from first-principles will be briefly discussed.

Electrolyte pH-dependent hydrogen binding energies and coverages on platinum, iridium, rhodium, and ruthenium surfaces

The weakened Hatop binding strength and increased Hatop coverage are universal phenomena on Pt, Ir, Rh, and Ru surfaces from acidic to alkaline media, which are important factors in the pH-dependent hydrogen reaction kinetics.

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.

A molecular perspective on induced charges on a metallic surface

Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode-electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode-electrolyte interfaces.

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.

Unexpectedly High Capacitance of the Metal Nanoparticle/Water Interface: Molecular-Level Insights into the Electrical Double Layer

The electrical double‐layer plays a key role in important interfacial electrochemical processes from catalysis to energy storage and corrosion. Therefore, understanding its structure is crucial for the progress of sustainable technologies. We extract new physico‐chemical information on the capacitance and structure of the electrical double‐layer of platinum and gold nanoparticles at the molecular level, employing single nanoparticle electrochemistry. The charge storage ability of the solid/liquid interface is larger by one order‐of‐magnitude than predicted by the traditional mean‐field models of the double‐layer such as the Gouy–Chapman–Stern model. Performing molecular dynamics simulations, we investigate the possible relationship between the measured high capacitance and adsorption strength of the water adlayer formed at the metal surface. These insights may launch the active tuning of solid–solvent and solvent–solvent interactions as an innovative design strategy to transform energy technologies towards superior performance and sustainability.

Hydrogen Coupling on Platinum Using Artificial Neural Network Potentials and DFT

To date, the understanding of reactions at solid-liquid interfaces has proven challenging, mainly because of the inaccessible nature of such systems to current experimental techniques with atomic resolution. This has meant that many important features, including free energy barriers and the atomistic structure of intermediates, remain unknown. To tackle these issues, we construct and utilize a high-dimensional neural network (HDNN) potential for the simulation of hydrogen evolution at the HCl(aq)/Pt(111) interface, taking into consideration the influence of adsorbate-adsorbate, adsorbate-solvent interactions, and ion solvation explicitly. Long time scale MD simulations reveal coadsorbed H_ad/H₂O_ad on the surface. The free energy profiles for the Tafel and Heyrovsky type hydrogen coupling are extracted using umbrella sampling. It is found that the preferential mechanism can change depending on the surface coverage, highlighting the dual mechanistic nature for HER on Pt(111). Our work demonstrates the importance of controlling the solvent-substrate interactions in developing catalysts beyond Pt.

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.

Properties of the Pt(111)/electrolyte electrochemical interface studied with a hybrid DFT-solvation approach

Self-consistent modeling of the interface between solid metal electrode and liquid electrolyte is a crucial challenge in computational electrochemistry. In this contribution, we adopt the effective screening medium reference interaction site method (ESM-RISM) to study the charged interface between a Pt(111) surface that is partially covered with chemisorbed oxygen and an aqueous acidic electrolyte. This method proves to be well suited to describe the chemisorption and charging state of the interface at controlled electrode potential. We present an in-depth assessment of the ESM-RISM parameterization and of the importance of computing near-surface water molecules explicitly at the quantum mechanical level. We found that ESM-RISM is able to reproduce some key interface properties, including the peculiar, non-monotonic charging relation of the Pt(111)/electrolyte interface. The comparison with independent theoretical models and explicit simulations of the interface reveals strengths and limitations of ESM-RISM for modeling electrochemical interfaces.

Highly Heterogeneous Polarization and Solvation of Gold Nanoparticles in Aqueous Electrolytes

The performance of gold nanoparticles (NPs) in applications depends critically on the structure of the NP-solvent interface, at which the electrostatic surface polarization is one of the key characteristics that affects hydration, ionic adsorption, and electrochemical reactions. Here, we demonstrate significant effects of explicit metal polarizability on the solvation and electrostatic properties of bare gold NPs in aqueous electrolyte solutions of sodium salts of various anions (Cl^-, BF₄^-, PF₆^-, nitrophenolate, and 3- and 4-valent hexacyanoferrate), using classical molecular dynamics simulations with a polarizable core-shell model for the gold atoms. We find considerable spatial heterogeneity of the polarization and electrostatic potentials on the NP surface, mediated by a highly facet-dependent structuring of the interfacial water molecules. Moreover, ion-specific, facet-dependent ion adsorption leads to considerable alterations of the interfacial polarization. Compared to nonpolarizable NPs, surface polarization modifies water local dipole densities only slightly but has substantial effects on the electrostatic surface potentials and leads to significant lateral redistributions of ions on the NP surface. Besides, interfacial polarization effects cancel out in the far field for monovalent ions but not for polyvalent ions, as anticipated from continuum "image-charge" concepts. Far-field effective Debye-Hückel surface potentials change accordingly in a valence-specific fashion. Hence, the explicit charge response of metal NPs is crucial for the accurate description and interpretation of interfacial electrostatics (e.g., for charge transfer and interfacial polarization in catalysis and electrochemistry).

Cross-Sphere Electrode Reaction: The Case of Hydroxyl Desorption during the Oxygen Reduction Reaction on Pt(111) in Alkaline Media

Hydroxide ion is a common electrolyte when electrode reactions take place in alkaline media. In the case of oxygen reduction reaction on Pt(111), we demonstrate by ab initio molecular dynamics calculations that the desorption of hydroxyl (OH*) from the electrode surface to form a solvated OH^- is a cross-sphere process, with the OH* reactant in the inner sphere and the OH^- product directly generated in the aqueous outer sphere. Such a mechanism is distinct from the typical inner sphere and outer sphere reactions. It is dictated by the strong hydrogen bonding interactions between a hydroxide ion and water molecules and is facilitated by proton transfer through solvation layers. It should play a significant role whenever OH* desorption, or its reverse, OH^- adsorption, is involved in an electrochemical reaction.

Contact Electrification at the Liquid-Solid Interface

Interfaces between a liquid and a solid (L-S) are the most important surface science in chemistry, catalysis, energy, and even biology. Formation of an electric double layer (EDL) at the L-S interface has been attributed due to the adsorption of a layer of ions at the solid surface, which causes the ions in the liquid to redistribute. Although the existence of a layer of charges on a solid surface is always assumed, the origin of the charges is not extensively explored. Recent studies of contact electrification (CE) between a liquid and a solid suggest that electron transfer plays a dominant role at the initial stage for forming the charge layer at the L-S interface. Here, we review the recent works about electron transfer in liquid-solid CE, including scenerios such as liquid-insulator, liquid-semiconductor, and liquid-metal. Formation of the EDL is revisited considering the existence of electron transfer at the L-S interface. Furthermore, the triboelectric nanogenerator (TENG) technique based on the liquid-solid CE is introduced, which can be used not only for harvesting mechanical energy from a liquid but also as a probe for probing the charge transfer at liquid-solid interfaces.