Impact of Water Coadsorption on the Electrode Potential of H-Pt(1 1 1)-Liquid Water Interfaces

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.

Solvation Free Energies from Machine Learning Molecular Dynamics

The present work proposes an extension to the approach of [Xi, C; et al. J. Chem. Theory Comput. 2022, 18, 6878] to calculate ion solvation free energies from first-principles (FP) molecular dynamics (MD) simulations of a hybrid solvation model. The approach is first re-expressed within the quasi-chemical theory of solvation. Then, to allow for longer simulation times than the original first-principles molecular dynamics approach and thus improve the convergence of statistical averages at a fraction of the original computational cost, a machine-learned (ML) energy function is trained on FP energies and forces and used in the MD simulations. The ML workflow and MD simulation times (≈200 ps) are adjusted to converge the predicted solvation energies within a chemical accuracy of 0.04 eV. The extension is successfully benchmarked on the same set of alkaline and alkaline-earth ions.

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.

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.

Molecular understanding of the critical role of alkali metal cations in initiating CO2 electroreduction on Cu(100) surface

Molecular understanding of the solid-liquid interface is challenging but essential to elucidate the role of the environment on the kinetics of electrochemical reactions. Alkali metal cations (M+), as a vital component at the interface, are found to be necessary for the initiation of carbon dioxide reduction reaction (CO2RR) on coinage metals, and the activity and selectivity of CO2RR could be further enhanced with the cation changing from Li+ to Cs+, while the underlying mechanisms are not well understood. Herein, using ab initio molecular dynamics simulations with explicit solvation and enhanced sampling methods, we systematically investigate the role of M+ in CO2RR on Cu surface. A monotonically decreasing CO2 activation barrier is obtained from Li+ to Cs+, which is attributed to the different coordination abilities of M+ with *CO2. Furthermore, we show that the competing hydrogen evolution reaction must be considered simultaneously to understand the crucial role of alkali metal cations in CO2RR on Cu surfaces, where H+ is repelled from the interface and constrained by M+. Our results provide significant insights into the design of electrochemical environments and highlight the importance of explicitly including the solvation and competing reactions in theoretical simulations of CO2RR.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

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

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.

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.

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.

Addressing Dynamics at Catalytic Heterogeneous Interfaces with DFT-MD: Anomalous Temperature Distributions from Commonly Used Thermostats

Density functional theory-based molecular dynamics (DFT-MD) has been widely used for studying the chemistry of heterogeneous interfacial systems under operational conditions. We report frequently overlooked errors in thermostated or constant-temperature DFT-MD simulations applied to study (electro)catalytic chemistry. Our results demonstrate that commonly used thermostats such as Nosé-Hoover, Berendsen, and simple velocity-rescaling methods fail to provide a reliable temperature description for systems considered. Instead, nonconstant temperatures and large temperature gradients within the different parts of the system are observed. The errors are not a "feature" of any particular code but are present in several ab initio molecular dynamics implementations. This uneven temperature distribution, due to inadequate thermostatting, is well-known in the classical MD community, where it is ascribed to the failure in kinetic energy equipartition among different degrees of freedom in heterogeneous systems (Harvey et al. J. Comput. Chem. 1998, 726-740) and termed the flying ice cube effect. We provide tantamount evidence that interfacial systems are susceptible to substantial flying ice cube effects and demonstrate that the traditional Nosé-Hoover and Berendsen thermostats should be applied with care when simulating, for example, catalytic properties or structures of solvated interfaces and supported clusters. We conclude that the flying ice cube effect in these systems can be conveniently avoided using Langevin dynamics.

Electrochemistry under confinement

Although the term 'confinement' regularly appears in electrochemical literature, elevated by continuous progression in the research of nanomaterials and nanostructures, up until today the various aspects of confinement considered in electrochemistry are rather scattered individual contributions outside the established disciplines in this field. Thanks to a number of highly original publications and the growing appreciation of confinement as an overarching link between different exciting new research strategies, 'electrochemistry under confinement' is the process of forming a research discipline of its own. To aid the development a coherent terminology and joint basic concepts, as crucial factors for this transformation, this review provides an overview on the different effects on electrochemical processes known to date that can be caused by confinement. It also suggests where boundaries to other effects, such as nano-effects could be drawn. To conceptualize the vast amount of research activities revolving around the main concepts of confinement, we define six types of confinement and select two of them to discuss the state of the art and anticipated future developments in more detail. The first type concerns nanochannel environments and their applications for electrodeposition and for electrochemical sensing. The second type covers the rather newly emerging field of colloidal single entity confinement in electrochemistry. In these contexts, we will for instance address the influence of confinement on the mass transport and electric field distributions and will link the associated changes in local species concentration or in the local driving force to altered reaction kinetics and product selectivity. Highlighting pioneering works and exciting recent developments, this educational review does not only aim at surveying and categorizing the state-of-the-art, but seeks to specifically point out future perspectives in the field of confinement-controlled electrochemistry.

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.

Is the water/Pt(111) interface ordered at room temperature?

The structure of the water/Pt(111) interface has been a subject of debate over the past decades. Here, we report the results of a room temperature molecular dynamics study based on neural network potentials, which allow us to access long time scale simulations while retaining ab initio accuracy. We find that the water/Pt(111) interface is characterized by a double layer composed of a primary, strongly bound adsorption layer with a coverage of ∼0.15 ML, which is coupled to a secondary, weakly bound adsorption layer with a coverage of ∼0.58 ML. By studying the order of the primary adsorption layer, we find that there is an effective repulsion between the adsorbed water molecules, which gives rise to a dynamically changing, semi-ordered interfacial structure, where the water molecules in the primary adsorption layer are distributed homogeneously across the interface, forming frequent hydrogen bonds to water molecules in the secondary adsorption layer. We further show that these conclusions are beyond the time scales accessible to ab initio molecular dynamics.

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.

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.

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.