Atomic-Scale Simulation of Electrochemical Processes at Electrode/Water Interfaces under Referenced Bias Potential

Revealing the Size and Potential Dependent D2O Microkinetics on Pt Nanoparticles Using Grand Canonical Ensemble Modeling

Revealing the potential and nanoparticle size effect is significant for understanding the electrochemical microkinetic behaviors under real reaction conditions. Herein, an efficient strategy of combining the robust fully converged constant potential (FCP) algorithm and the size dependent site distribution rule assumption was proposed. A simple reaction of isotopic D2O/H2O adsorption and dissociation on Pt nanoparticles was set as the model reaction. The results show that the cathodic negative potential and the anodic positive potential would result in the D2O orientation of the D-down/O-down physisorption configuration. Microkinetic simulations by this strategy obtained electrochemical widows for D2O/H2O dissociation, and the optimal Pt nanoparticle diameter was predicted to be 1.8 nm, which agrees well with the experimental observation of ∼2 nm threshold. The kinetic isotope effect (KIE) rate constant ratio at the optimal potential of -0.80 V vs SHE was calculated to be ∼1.83. This work provides a guideline in studying electrochemical electrode-electrolyte interactions on nanoparticles.

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.

Alkali cation-induced cathodic corrosion in Cu electrocatalysts

The reconstruction of Cu catalysts during electrochemical reduction of CO2 is a widely known but poorly understood phenomenon. Herein, we examine the structural evolution of Cu nanocubes under CO2 reduction reaction and its relevant reaction conditions using identical location transmission electron microscopy, cyclic voltammetry, in situ X-ray absorption fine structure spectroscopy and ab initio molecular dynamics simulation. Our results suggest that Cu catalysts reconstruct via a hitherto unexplored yet critical pathway - alkali cation-induced cathodic corrosion, when the electrode potential is more negative than an onset value (e.g., -0.4 VRHE when using 0.1 M KHCO3). Having alkali cations in the electrolyte is critical for such a process. Consequently, Cu catalysts will inevitably undergo surface reconstructions during a typical process of CO2 reduction reaction, resulting in dynamic catalyst morphologies. While having these reconstructions does not necessarily preclude stable electrocatalytic reactions, they will indeed prohibit long-term selectivity and activity enhancement by controlling the morphology of Cu pre-catalysts. Alternatively, by operating Cu catalysts at less negative potentials in the CO electrochemical reduction, we show that Cu nanocubes can provide a much more stable selectivity advantage over spherical Cu nanoparticles.

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.

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.

Water molecules mute the dependence of the double-layer potential profile on ionic strength

We present the results of molecular dynamics simulations of a nanoscale electrochemical cell. The simulations include an aqueous electrolyte solution with varying ionic strength (i.e., concentrations ranging from 0-4 M) between a pair of metallic electrodes held at constant potential difference. We analyze these simulations by computing the electrostatic potential profile of the electric double-layer region and find it to be nearly independent of ionic concentration, in stark contrast to the predictions of standard continuum-based theories. We attribute this lack of concentration dependence to the molecular influences of water molecules at the electrode-solution interface. These influences include the molecular manifestation of water's dielectric response, which tends to drown out the comparatively weak screening requirement of the ions. To support our analysis, we decompose water's interfacial response into three primary contributions: molecular layering, intrinsic (zero-field) orientational polarization, and the dipolar dielectric response.

Fundamental Drivers of Electrochemical Barriers

We find that ion creation and destruction dominate the behavior of electrochemical reaction barriers, through grand-canonical electronic structure calculations of proton deposition on transition metal surfaces. We show that barriers respond to potential in a nonlinear manner and trace this to the continuous degree of electron transfer as an ion is created or destroyed. This explains both Marcus-like curvature and Hammond-like shifts. Across materials, we find the barrier energy to be driven primarily by the charge presented on the surface, which, in turn, is dictated by the native work function, a fundamentally different driving force than in nonelectrochemical systems.

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.

Molecular understanding of cation effects on double layers and their significance to CO-CO dimerization

Cation effects have been shown in numerous experiments to play a significant role in electrocatalysis. To understand these effects at the molecular level, we systematically investigate the structures and capacitances of electric double layers with a variety of cations as counter charges at Pt(111)-COad/water interfaces with ab initio molecular dynamics. It is encouraging to find that the computed Helmholtz capacitances for different cations are in quantitative agreement with experiments, and that the trend of cation effects on capacitances shows clear correlation with the structures of interface cations of differing sizes and hydration energies. More importantly, we demonstrate the Helmholtz capacitance as the key descriptor for measuring the activity of CO-CO dimerization, the rate-determining step for C2+ formation in electroreduction of CO and CO2. Our work provides atomistic insights into cation effects on electric double layers and electrocatalysis that are crucial for optimizing electrode and electrolyte materials.

Grand Canonical Ensemble Modeling of Electrochemical Interfaces Made Simple

Grand canonical ensemble (GCE) modeling of electrochemical interfaces, in which the electrochemical potential is converged to a preset constant, is essential for understanding electrochemistry and electrocatalysis at the electrodes. However, it requires developing efficient and robust algorithms to perform practical and effective GCE modeling with density functional theory (DFT) calculations. Herein, we developed an efficient and robust fully converged constant-potential (FCP) algorithm based on Newton's method and a polynomial fitting to calculate the necessary derivative for DFT calculations. We demonstrated with the constant-potential geometry optimization and Born-Oppenheimer molecular dynamics (BOMD) calculations that our FCP algorithm is resistant to the numerical instability that plagues other algorithms, and it delivers efficient convergence to the preset electrochemical potential and renders accurate forces for updating the nuclear positions of an electronically open system, outperforming other algorithms. The implementation of our FCP algorithm enables flexibility in using various computational codes and versatility in performing advanced tasks including the constant-potential enhanced-sampling BOMD simulations that we showcased with the modeling of the electrochemical hydrogenation of CO, and it is thus expected to find a wide spectrum of applications in the modeling of chemistry at electrochemical interfaces.

Molecular understanding of the Helmholtz capacitance difference between Cu(100) and graphene electrodes

Unraveling the origin of Helmholtz capacitance is of paramount importance for understanding the interfacial structure and electrostatic potential distribution of electric double layers (EDL). In this work, we combined the methods of ab initio molecular dynamics and classical molecular dynamics and modeled electrified Cu(100)/electrolyte and graphene/electrolyte interfaces for comparison. It was proposed that the Helmholtz capacitance is composed of three parts connected in series: the usual solvent capacitance, water chemisorption induced capacitance, and Pauling repulsion caused gap capacitance. We found the Helmholtz capacitance of graphene is significantly lower than that of Cu(100), which was attributed to two intrinsic factors. One is that graphene has a wider gap layer at interface, and the other is that graphene is less active for water chemisorption. Finally, based on our findings, we provide suggestions for how to increase the EDL capacitance of graphene-based materials in future work, and we also suggest that the new understanding of the potential distribution across the Helmholtz layer may help explain some experimental phenomena of electrocatalysis.

Dielectric Properties of Nanoconfined Water from Ab Initio Thermopotentiostat Molecular Dynamics

We discuss how to include our recently proposed thermopotentiostat technique [Deissenbeck et al. Phys. Rev. Lett. 2021, 126, 136803] into any existing ab initio molecular dynamics (AIMD) package. Using thermopotentiostat AIMD simulations in the canonical NVTΦ ensemble at a constant electrode potential, we compute the polarization bound charge and dielectric response of interfacial water from first principles.

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.

Platinum-Water Interaction Induced Interfacial Water Orientation That Governs the pH-Dependent Hydrogen Oxidation Reaction

Understanding the electrode-water interface structure in acid and alkali is crucial to unveiling the underlying mechanism of pH-dependent hydrogen oxidation reaction (HOR) kinetics. In this work, we construct the explicit Pt(111)-H₂O interface models in both acid and alkali to investigate the relationship between the HOR mechanism and electrode-electrolyte interface structure using ab initio molecular dynamics and density functional theory. We find that the interfacial water orientation in the outer Helmholtz layer (OHP) induced by the Pt-water interaction governs the pH-dependent HOR kinetics on Pt(111). In alkali, the strong Pt-interfacial water electrostatic interaction behaves as a narrow OHP, which increases the proportion of "H-down" interfacial water and leads to less adsorbed water entering the inner Helmholtz plane (IHP), decreasing the work function of Pt(111). Furthermore, the more "H-down" interfacial water stabilizes the H_ad adsorption, prevents H_ad desorption, and suppresses the Volmer step of HOR by forming the solvated [H_ad···H₂O···H₂O] complex. Our work provided a visualized molecular-level mechanism to understand the nature of pH-dependent HOR kinetics.

Electrochemistry from the atomic scale, in the electronically grand-canonical ensemble

The ability to simulate electrochemical reactions from first-principles has advanced significantly in recent years. Here, we discuss the atomistic interpretation of electrochemistry at three scales: from the electronic structure to elementary processes to constant-potential reactions. At each scale, we highlight the importance of the grand-canonical nature of the process and show that the grand-canonical energy is the natural thermodynamic state variable, which has the additional benefit of simplifying calculations. We show that atomic forces are the derivative of the grand-potential energy when the potential is fixed. We further examine the meaning of potential at the atomic scale and its link to the chemical potential and discuss the link between charge transfer and potential in several situations.

Multilevel Computational Studies Reveal the Importance of Axial Ligand for Oxygen Reduction Reaction on Fe-N-C Materials

The systematic improvement of Fe-N-C materials for fuel cell applications has proven challenging, due in part to an incomplete atomistic understanding of the oxygen reduction reaction (ORR) under electrochemical conditions. Herein, a multilevel computational approach, which combines ab initio molecular dynamics simulations and constant potential density functional theory calculations, is used to assess proton-coupled electron transfer (PCET) processes and adsorption thermodynamics of key ORR intermediates. These calculations indicate that the potential-limiting step for ORR on Fe-N-C materials is the formation of the Fe^III-OOH intermediate. They also show that an active site model with a water molecule axially ligated to the iron center throughout the catalytic cycle produces results that are consistent with the experimental measurements. In particular, reliable prediction of the ORR onset potential and the Fe(III/II) redox potential associated with the conversion of Fe^III-OH to Fe^II and desorbed H₂O requires an axial H₂O co-adsorbed to the iron center. The observation of a five-coordinate rather than four-coordinate active site has significant implications for the thermodynamics and mechanism of ORR. These findings highlight the importance of solvent-substrate interactions and surface charge effects for understanding the PCET reaction mechanisms and transition-metal redox couples under realistic electrochemical conditions.

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.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Revealing Elusive Intermediates of Platinum Cathodic Corrosion through DFT Simulations

Cathodic corrosion of metals discovered more than 120 years ago remains a poorly understood electrochemical process. It is believed that the corrosion intermediates formed during cathodic polarization are extremely short-lived species because of their high reactivity. Together with the concurrent vigorous hydrogen evolution, this makes it challenging to investigate the reaction mechanism and detect the intermediates experimentally. From a computational standpoint, the process also presents a serious challenge as it occurs at rather low negative potentials in concentrated alkaline solutions. Here, we use density-functional-theory calculations to elucidate the identity of reaction intermediates and their reactivity at the Pt(111)/electrolyte interface. By controlling the electrode potential in an experimentally relevant region through constant Fermi-level molecular dynamics, we reveal the formation of alkali cation-stabilized Pt hydrides as intermediates of cathodic corrosion. The results also suggest that the found Pt anions could discharge at the interface to produce H₂ by reacting with either surface-bound hydrogen species or solution water molecules.

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.

Double-layer structure of the Pt(111)-aqueous electrolyte interface

We present detailed measurements of the double-layer capacitance of the Pt(111)-electrolyte interface close to the potential of zero charge (PZC) in the presence of several different electrolytes consisting of anions and cations that are considered to be nonspecifically adsorbed. For low electrolyte concentrations, we show strong deviations from traditional Gouy-Chapman-Stern (GCS) behavior that appear to be independent of the nature of the electrolyte ions. Focusing on the capacitance further away from PZC and the trends for increasing ion concentration, we observe ion-specific capacitance effects that appear to be related to the size or hydration strength of the ions. We formulate a model for the structure of the electric double layer of the Pt(111)-electrolyte interface that goes significantly beyond the GCS theory. By combining two existing models, namely, one capturing the water reorganization on Pt close to the PZC and one accounting for an attractive ion-surface interaction not included in the GCS model, we can reproduce and interpret the main features the experimental capacitance of the Pt(111)-electrolyte interface. The model suggests a picture of the double layer with an increased ion concentration close to the interface as a consequence of a weak attractive ion-surface interaction, and a changing polarizability of the Pt(111)-water interface due to the potential-dependent water adsorption and orientation.

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.

Water-Assisted Chemical Route Towards the Oxygen Evolution Reaction at the Hydrated (110) Ruthenium Oxide Surface: Heterogeneous Catalysis via DFT-MD and Metadynamics Simulations

Notwithstanding that RuO2 is a promising catalyst for the oxygen evolution reaction (OER), a plethora of fundamental details on its catalytic properties are still elusive, severely limiting its large-scale deployment. It is also established experimentally that corrosion and wettability of metal oxides can, in fact, enhance the catalytic activity for OER owing to the formation of a hydrated surface layer. However, the mechanistic interplay between surface wettability, interfacial water dynamics and OER across RuO2 , and what degree these processes are correlated are still debated. Herein, spin-polarized Density Functional Theory Molecular Dynamics (DFT-MD) simulations, coupled with advanced enhanced sampling methods in the well-tempered metadynamics framework, are applied to gain a global understanding of RuO2 aqueous interface (explicit water solvent) in catalyzing the OER, and hence possibly help in the design of novel catalysts in the context of photochemical water oxidation. The present study quantitatively assesses the free-energy barriers behind the OER at the (110)-RuO2 catalyst surface revealing plausible pathways composing the reaction network of the O2 evolution. In particular, OER is investigated at room temperature when such a surface is exposed to both gas-phase and liquid-phase water. Albeit a unique efficient pathway has been identified in the gas-phase OER, a surprisingly lowest-free-energy-requiring reaction route is possible when (110)-RuO2 is in contact with explicit liquid water. By estimating the free-energy surfaces associated to these processes, we reveal a noticeable water-assisted OER mechanism which involves a crucial proton-transfer-step assisted by the local water environment. These findings pave the way toward the systematic usage of DFT-MD coupled with metadynamics techniques for the fine assessment of the activity of catalysts, considering finite-temperature and explicit-solvent effects.

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.

Linear Correlation between Water Adsorption Energies and Volta Potential Differences for Metal/water Interfaces

Potential of zero charge (PZC) is an important reference for understanding the interface charge and structure at a given potential, and its difference from the work function of metal surface (Φ_M) is defined as the Volta potential difference (ΔΦ). In this work, we model 11 metal/water interfaces with ab initio molecular dynamics. Interestingly, we find ΔΦ is linearly correlated with the adsorption energy of water (E_ads) on the metal surface. It is revealed that the size of E_ads directly determines the coverage of chemisorbed water on the metal surface and accordingly affects the interface potential change caused by electron redistribution (ΔΦ_el). Moreover, ΔΦ is dominated by the electronic component ΔΦ_el with little orientational dipole contributing, which explains the linear correlation between ΔΦ and E_ads. Finally, it is expected that this correlation can be helpful for effectively estimating the ΔΦ_el and PZC of other metal surfaces in the future work.

The Fermi level as an energy reference in liquid jet X-ray photoelectron spectroscopy studies of aqueous solutions

To advance the understanding of key electrochemical and photocatalytic processes that depend on the electronic structure of aqueous solutions, X-ray photoemission spectroscopy has become an invaluable tool, especially when practiced with liquid microjet setups. Determining vertical ionization energies referenced to the vacuum level, and binding energies referenced to the Fermi level, including the much-coveted reorganization energy of the oxidized species of a redox couple, requires that energy levels be properly defined. The present paper addresses specifically how the vacuum level "just outside the surface" can be known through the energy position of the rising edge of the secondary electrons, and how the Fermi level reference is uniquely determined via the introduction of a redox couple. Taking the case of the ferricyanide/ferrocyanide and ferric/ferrous couples, this study also tackles issues related to the electrokinetic effects inherent to the production of a liquid jet in a vacuum, which has become the standard water sample environment for photoemission experiments.

Water at charged interfaces

The ubiquity of aqueous solutions in contact with charged surfaces and the realization that the molecular-level details of water-surface interactions often determine interfacial functions and properties relevant in many natural processes have led to intensive research. Even so, many open questions remain regarding the molecular picture of the interfacial organization and preferential alignment of water molecules, as well as the structure of water molecules and ion distributions at different charged interfaces. While water, solutes and charge are present in each of these systems, the substrate can range from living tissues to metals. This diversity in substrates has led to different communities considering each of these types of aqueous interface. In this Review, by considering water in contact with metals, oxides and biomembranes, we show the essential similarity of these disparate systems. While in each case the classical mean-field theories can explain many macroscopic and mesoscopic observations, it soon becomes apparent that such theories fail to explain phenomena for which molecular properties are relevant, such as interfacial chemical conversion. We highlight the current knowledge and limitations in our understanding and end with a view towards future opportunities in the field.

Thermodynamic cyclic voltammograms: peak positions and shapes

Based on a mean-field description of thermodynamic cyclic voltammograms (CVs), we analyze here in full generality, how CV peak positions and shapes are related to the underlying interface energetics, in particular when also including electrostatic double layer (DL) effects. We show in particular, how non-Nernstian behaviour is related to capacitive DL charging, and how this relates to common adsorbate-centered interpretations such as a changed adsorption energetics due to dipole-field interactions and the electrosorption valency - the number of exchanged electrons upon electrosorption per adsorbate. Using Ag(111) in halide-containing solutions as test case, we demonstrate that DL effects can introduce peak shifts that are already explained by rationalizing the interaction of isolated adsorbates with the interfacial fields, while alterations of the peak shape are mainly driven by the coverage-dependence of the adsorbate dipoles. In addition, we analyze in detail how changing the experimental conditions such as the ion concentrations in the solvent but also of the background electrolyte can affect the CV peaks via their impact on the potential drop in the DL and the DL capacitance, respectively. These results suggest new routes to analyze experimental CVs and use of those for a detailed assessment of the accuracy of atomistic models of electrified interfaces e.g. with and without explicitly treated interfacial solvent and/or approximate implicit solvent models.

Modeling Electrified Pt(111)-Had/Water Interfaces from Ab Initio Molecular Dynamics

Unraveling the atomistic structures of electric double layers (EDL) at electrified interfaces is of paramount importance for understanding the mechanisms of electrocatalytic reactions and rationally designing electrode materials with better performance. Despite numerous efforts dedicated in the past, a molecular level understanding of the EDL is still lacking. Combining the state-of-the-art ab initio molecular dynamics (AIMD) and recently developed computational standard hydrogen electrode (cSHE) method, it is possible to realistically simulate the EDL under well-defined electrochemical conditions. In this work, we report extensive AIMD calculation of the electrified Pt(111)-Had/water interfaces at the saturation coverage of adsorbed hydrogen (Had) corresponding to the typical hydrogen evolution reaction conditions. We calculate the electrode potentials of a series of EDL models with various surface charge densities using the cSHE method and further obtain the Helmholtz capacitance that agrees with experiment. Furthermore, the AIMD simulations allow for detailed structural analyses of the electrified interfaces, such as the distribution of adsorbate Had and the structures of interface water and counterions, which can in turn explain the computed dielectric property of interface water. Our calculation provides valuable molecular insight into the electrified interfaces and a solid basis for understanding a variety of electrochemical processes occurring inside the EDL.

Effects of applied voltage on water at a gold electrode interface from ab initio molecular dynamics

Electrode–water interfaces under voltage bias demonstrate anomalous electrostatic and structural properties that are influential in their catalytic and technological applications. Mean-field and empirical models of the electrical double layer (EDL) that forms in response to an applied potential do not capture the heterogeneity that polarizable, liquid-phase water molecules engender. To illustrate the inhomogeneous nature of the electrochemical interface, Born–Oppenheimer ab initio molecular dynamics calculations of electrified Au(111) slabs interfaced with liquid water were performed using a combined explicit–implicit solvent approach. The excess charges localized on the model electrode were held constant and the electrode potentials were computed at frequent simulation times. The electrode potential in each trajectory fluctuated with changes in the atomic structure, and the trajectory-averaged potentials converged and yielded a physically reasonable differential capacitance for the system. The effects of the average applied voltages, both positive and negative, on the structural, hydrogen bonding, dynamical, and vibrational properties of water were characterized and compared to literature where applicable. Controlled-potential simulations of the interfacial solvent dynamics provide a framework for further investigation of more complex or reactive species in the EDL and broadly for understanding electrochemical interfaces in situ.

Ab initio molecular dynamics of an aqueous electrode interface reveal the electrostatic, structural, and dynamic effects of quantifiable voltage biases on water.

Thermodynamic Cyclic Voltammograms Based on Ab Initio Calculations: Ag(111) in Halide-Containing Solutions

Cyclic voltammograms (CVs) are a central experimental tool for assessing the structure and activity of electrochemical interfaces. Based on a mean-field ansatz for the interface energetics under applied potential conditions, we here derive an ab initio thermodynamics approach to efficiently simulate thermodynamic CVs. All unknown parameters are determined from density functional theory (DFT) calculations coupled to an implicit solvent model. For the showcased CVs of Ag(111) electrodes in halide-anion-containing solutions, these simulations demonstrate the relevance of double-layer contributions to explain experimentally observed differences in peak shapes over the halide series. Only the appropriate account of interfacial charging allows us to capture the differences in equilibrium coverage and total electronic surface charge that cause the varying peak shapes. As a case in point, this analysis demonstrates that prominent features in CVs do not only derive from changes in adsorbate structure or coverage but can also be related to variations of the electrosorption valency. Such double-layer effects are proportional to adsorbate-induced changes in the work function and/or interfacial capacitance. They are thus especially pronounced for electronegative halides and other adsorbates that affect these interface properties. In addition, the analysis allows us to draw conclusions on how the possible inaccuracy of implicit solvation models can indirectly affect the accuracy of other predicted quantities such as CVs.

Molecular origin of negative component of Helmholtz capacitance at electrified Pt(111)/water interface

Electrified solid/liquid interfaces are the key to many physicochemical processes in a myriad of areas including electrochemistry and colloid science. With tremendous efforts devoted to this topic, it is unexpected that molecular-level understanding of electric double layers is still lacking. Particularly, it is perplexing why compact Helmholtz layers often show bell-shaped differential capacitances on metal electrodes, as this would suggest a negative capacitance in some layer of interface water. Here, we report state-of-the-art ab initio molecular dynamics simulations of electrified Pt(111)/water interfaces, aiming at unraveling the structure and capacitive behavior of interface water. Our calculation reproduces the bell-shaped differential Helmholtz capacitance and shows that the interface water follows the Frumkin adsorption isotherm when varying the electrode potential, leading to a peculiar negative capacitive response. Our work provides valuable insight into the structure and capacitance of interface water, which can help understand important processes in electrocatalysis and energy storage in supercapacitors.

Water dynamics at electrified graphene interfaces: a jump model perspective

The reorientation dynamics of water at electrified graphene interfaces was recently shown [J. Phys. Chem. Lett., 2020, 11, 624-631] to exhibit a surprising and strongly asymmetric behavior: positive electrode potentials slow down interfacial water reorientation, while for increasingly negative potentials water dynamics first accelerates before reaching an extremum and then being retarded for larger potentials. Here we use classical molecular dynamics simulations to determine the molecular mechanisms governing water dynamics at electrified interfaces. We show that changes in water reorientation dynamics with electrode potential arise from the electrified interfaces' impacts on water hydrogen-bond jump exchanges, and can be quantitatively described by the extended jump model. Finally, our simulations indicate that no significant dynamical heterogeneity occurs within the water interfacial layer next to the weakly interacting graphene electrode.

Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces

Understanding microscopic mechanism of multi-electron multi-proton transfer reactions at complexed systems is important for advancing electrochemistry-oriented science in the 21st century.

Scaled and Dynamic Optimizations of Nudged Elastic Bands

We present a modified nudged elastic band routine that can reduce the number of force calls by more than 50% for bands with nonuniform convergence. The method, which we call "dyNEB", dynamically and selectively optimizes images on the basis of the perpendicular PES-derived forces and parallel spring forces acting on that region of the band. The convergence criteria are scaled to focus on the region of interest, i.e., the saddle point, while maintaining continuity of the band and avoiding truncation. We show that this method works well for solid state reaction barriers-nonelectrochemical in general and electrochemical in particular-and that the number of force calls can be significantly reduced without loss of resolution at the saddle point.

Simulating Electrochemical Systems by Combining the Finite Field Method with a Constant Potential Electrode

A better understanding of interfacial mechanisms is needed to improve the performances of electrochemical devices. Yet, simulating an electrode surface at fixed electrolyte composition remains a challenge. Here, we apply a finite electric field to a single electrode held at constant potential and in contact with an aqueous ionic solution, using classical molecular dynamics. The polarization yields two electrochemical interfaces on opposite sides of the same metal slab. The net charge on one electrode surface is the opposite of the net charge on the other, maintaining overall charge neutrality of the metal. The electrode surface charge fluctuations are compensated by the adsorption of ions from the electrolyte, forming a pair of electric double layers with aligned dipoles. This opens the way towards the efficient simulation of electrochemical interfaces using any flavor of molecular dynamics, from classical to first-principles-based methods.

Quantum-to-Classical Transition of Proton Transfer in Potential-Induced Dioxygen Reduction

We report an observation of a quantum tunneling effect in a proton-transfer (PT) during potential-induced transformation of dioxygen on a platinum electrode in a low overpotential (η) region at 298 K. However, this quantum process is converted to the classical PT scheme in the high η region. Therefore, there is a quantum-to-classical transition of the PT (QCT-PT) process as a function of the potential, which is confirmed by theoretical analysis. This observation indicates that the quantum tunneling governs the multistep electron-proton-driven transformation of dioxygen in the low η condition.