Water structures on a Pt(111) electrode from ab initio molecular dynamic simulations for a variety of electrochemical conditions

Ab initio molecular dynamics investigation of the Pt(111)-water interface structure in an alkaline environment with high surface OH-coverages

In this study, we investigate the structure of the Pt(111)-water interface in an alkaline environment with large OH coverages of 1/3, 2/3 and 1 monolayer using a large well-equilibrated system. We observe that the OH coverage influences both the orientational distribution of the water molecules and their density, with more structure associated with higher coverage. At the same time, there is evidence of a highly dynamic hydrogen bond network on the lower coverage systems with substantial exchange of water between the surface and the solvent. In addition to OH and H2O species, which are preferentially located at the top sites, the 1/3 and 2/3 monolayer surfaces also contain O atoms, which are relatively stable and prefer the hollow sites. In contrast, the 1 monolayer surface shows none of these dynamics, and is unlikely to be active. The dynamic coexistence of O, OH and H2O on Pt(111) electrodes in alkaline conditions necessitates the investigation of several possible reaction paths for processess like ORR and water splitting. Finally, the exchange processes observed between the solvent and the interface underscore the need to explicitly include liquid water in simulations of systems similar to Pt(111).

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.

Cavity formation at metal-water interfaces

The free energy cost of forming a cavity in a solvent is a fundamental concept in rationalizing the solvation of molecules and ions. A detailed understanding of the factors governing cavity formation in bulk solutions has inter alia enabled the formulation of models that account for this contribution in coarse-grained implicit solvation methods. Here, we employ classical molecular dynamics simulations and multistate Bennett acceptance ratio free energy sampling to systematically study cavity formation at a wide range of metal-water interfaces. We demonstrate that the obtained size- and position-dependence of cavitation energies can be fully rationalized by a geometric Gibbs model, which considers that the creation of the metal-cavity interface necessarily involves the removal of interfacial solvent. This so-called competitive adsorption effect introduces a substrate dependence to the interfacial cavity formation energy that is missed in existing bulk cavitation models. Using expressions from scaled particle theory, this substrate dependence is quantitatively reproduced by the Gibbs model through simple linear relations with the adsorption energy of a single water molecule. Besides providing a better general understanding of interfacial solvation, this paves the way for the derivation and efficient parametrization of more accurate interface-aware implicit solvation models needed for reliable high-throughput calculations toward improved electrocatalysts.

Stay Hydrated! Impact of Solvation Phenomena on the CO2 Reduction Reaction at Pb(100) and Ag(100) surfaces

Herein, a comprehensive computational study of the impact of solvation on the reduction reaction of CO2 to formic acid (HCOOH) and carbon monoxide on Pb(100) and Ag(100) surfaces is presented. Results further the understanding of how solvation phenomena influence the adsorption energies of reaction intermediates. We applied an explicit solvation scheme harnessing a combined density functional theory (DFT)/microkinetic modeling approach for the CO2 reduction reaction. This approach reveals high selectivities for CO formation at Ag and HCOOH formation on Pb, resolving the prior disparity between ab initio calculations and experimental observations. Furthermore, the detailed analysis of adsorption energies of relevant reaction intermediates shows that the total number of hydrogen bonds formed by HCOO plays a primary role for the adsorption strength of intermediates and the electrocatalytic activity. Results emphasize the importance of explicit solvation for adsorption and electrochemical reaction phenomena on metal surfaces.

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.

Inverted Region in Electrochemical Reduction of CO2 Induced by Potential-Dependent Pauli Repulsion

Electrochemical CO₂ reduction reaction (eCO₂RR) is of great significance to energy and environmental engineering, while fundamental questions remain regarding its mechanisms. Herein, we formulate a fundamental understanding of the interplay between the applied potential (U) and kinetics of CO₂ activation in eCO₂RR on Cu surfaces. We find that the nature of the CO₂ activation mechanism in eCO₂RR varies with U, and it is the sequential electron-proton transfer (SEPT) mechanism dominant at the working U but switched to the concerted proton-electron transfer (CPET) mechanism at highly negative U. We then identify that the barrier of the electron-transfer step in the SEPT mechanism exhibits an inverted region as U decreases, which originates from the rapidly rising Pauli repulsion in the physisorption of CO₂ with decreasing U. We further demonstrate catalyst designs that effectively suppress the adverse effect of Pauli repulsion. This fundamental understanding may be general for the electrochemical reduction reactions of closed-shell molecules.

The ABC of Generalized Coordination Numbers and Their Use as a Descriptor in Electrocatalysis

The quest for enhanced electrocatalysts can be boosted by descriptor-based analyses. Because adsorption energies are the most common descriptors, electrocatalyst design is largely based on brute-force routines that comb materials databases until an energetic criterion is verified. In this review, it is shown that an alternative is provided by generalized coordination numbers (denoted by CN ¯ $\overline {{\rm{CN}}} $ or GCN), an inexpensive geometric descriptor for strained and unstrained transition metals and some alloys. CN ¯ $\overline {{\rm{CN}}} $ captures trends in adsorption energies on both extended surfaces and nanoparticles and is used to elaborate structure-sensitive electrocatalytic activity plots and selectivity maps. Importantly, CN ¯ $\overline {{\rm{CN}}} $ outlines the geometric configuration of the active sites, thereby enabling an atom-by-atom design, which is not possible using energetic descriptors. Specific examples for various adsorbates (e.g., *OH, *OOH, *CO, and *H), metals (e.g., Pt and Cu), and electrocatalytic reactions (e.g., O₂  reduction, H₂  evolution, CO oxidation, and reduction) are presented, and comparisons are made against other descriptors.

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.

Wetting of a Stepped Platinum (211) Surface

Steps stabilize water adsorption on metal surfaces, providing favorable binding sites for water during wetting or ice nucleation, but there is limited understanding of the local water arrangements formed on such surfaces. Here we describe the structural evolution of water on the stepped Pt(211) surface using thermal desorption, low-energy electron diffraction, and scanning tunneling microscopy to probe the water structure. At low coverage water forms linear structures comprising zigzag chains along the steps that are decorated by H-bonded rings every one or two units along the terrace. Simple 2-coordinate H-bonded chains are not observed, indicating the Pt step binds too weakly to compensate entirely for a low water H-bond coordination number. As the coverage increases, water chains assemble into a disordered (2 × 1) structure, likely made up of the same narrow water chains along the steps with little or no H-bonding between adjacent structures. The chain structure disappears as water adsorption saturates the surface to form an incommensurate, disordered network of water rings of different size. Although the steps on Pt(211) clearly stabilize water adsorption and direct growth, the surface does not support the simple 1D chains previously proposed or an ordered 2D network such as seen on other surfaces. We discuss reasons for this and the factors that determine the behavior of the first water layer on stepped metal surfaces.

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.

Cation-Coordinated Inner-Sphere CO2 Electroreduction at Au-Water Interfaces

Electrochemical CO₂ reduction reaction (CO₂RR) is a promising technology for the clean energy economy. Numerous efforts have been devoted to enhancing the mechanistic understanding of CO₂RR from both experimental and theoretical studies. Electrolyte ions are critical for the CO₂RR; however, the role of alkali metal cations is highly controversial, and a complete free energy diagram of CO₂RR at Au-water interfaces is still missing. Here, we provide a systematic mechanism study toward CO₂RR via ab initio molecular dynamics simulations integrated with the slow-growth sampling (SG-AIMD) method. By using the SG-AIMD approach, we demonstrate that CO₂RR is facile at the inner-sphere interface in the presence of K cations, which promote the CO₂ activation with the free energy barrier of only 0.66 eV. Furthermore, the competitive hydrogen evolution reaction (HER) is inhibited by the interfacial cations with the induced kinetic blockage effect, where the rate-limiting Volmer step shows a much higher energy barrier (1.27 eV). Eventually, a comprehensive free energy diagram including both kinetics and thermodynamics of the CO₂RR to CO and the HER at the electrochemical interface is derived, which illustrates the critical role of cations on the overall performance of CO₂ electroreduction by facilitating CO₂ adsorption while suppressing the hydrogen evolution at the same time.

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 Green's Function Approach for Determining Surface Induced Broadening and Shifting of Molecular Energy Levels

Upon adsorption of a molecule onto a surface, the molecular energy levels (MELs) broaden and change their alignment. This phenomenon directly affects electron transfer across the interface and is, therefore, a fundamental observable that influences electrochemical device performance. Here, we propose a rigorous parameter-free framework, built upon the theoretical construct of Green's functions, for studying the interface between a molecule and a bulk surface and its effect on MELs. The method extends beyond the usual wide-band limit approximation, and its generality allows its use with any level of electronic structure theory. We demonstrate its ability to predict the broadening and shifting of MELs as a function of intramolecular coupling, molecule/surface coupling, and the surface density of states for a molecule with two MELs adsorbed on a one-dimensional model metal surface. The new approach could help provide guidelines for the design and experimental characterization of electrochemical devices with optimal electron transport.

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.

Understanding the complementarities of surface-enhanced infrared and Raman spectroscopies in CO adsorption and electrochemical reduction

In situ/operando surface enhanced infrared and Raman spectroscopies are widely employed in electrocatalysis research to extract mechanistic information and establish structure-activity relations. However, these two spectroscopic techniques are more frequently employed in isolation than in combination, owing to the assumption that they provide largely overlapping information regarding reaction intermediates. Here we show that surface enhanced infrared and Raman spectroscopies tend to probe different subpopulations of adsorbates on weakly adsorbing surfaces while providing similar information on strongly binding surfaces by conducting both techniques on the same electrode surfaces, i.e., platinum, palladium, gold and oxide-derived copper, in tandem. Complementary density functional theory computations confirm that the infrared and Raman intensities do not necessarily track each other when carbon monoxide is adsorbed on different sites, given the lack of scaling between the derivatives of the dipole moment and the polarizability. Through a comparison of adsorbed carbon monoxide and water adsorption energies, we suggest that differences in the infrared vs. Raman responses amongst metal surfaces could stem from the competitive adsorption of water on weak binding metals. We further determined that only copper sites capable of adsorbing carbon monoxide in an atop configuration visible to the surface enhanced infrared spectroscopy are active in the electrochemical carbon monoxide reduction reaction.

Infrared and Raman spectroscopies are often assumed to provide similar insights into heterogeneous reaction mechanisms. This study shows that these techniques provide similar data when CO is strongly bound to a surface, yet distinct subpopulations of CO are probed when binding is weaker.

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.

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.

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.

Realistic Modelling of Dynamics at Nanostructured Interfaces Relevant to Heterogeneous Catalysis

The focus of this short review is directed towards investigations of the dynamics of nanostructured metallic heterogeneous catalysts and the evolution of interfaces during reaction—namely, the metal–gas, metal–liquid, and metal–support interfaces. Indeed, it is of considerable interest to know how a metal catalyst surface responds to gas or liquid adsorption under reaction conditions, and how its structure and catalytic properties evolve as a function of its interaction with the support. This short review aims to offer the reader a birds-eye view of state-of-the-art methods that enable more realistic simulation of dynamical phenomena at nanostructured interfaces by exploiting resource-efficient methods and/or the development of computational hardware and software.

A first principle study of water adsorbed on flat and stepped silver surfaces

The structural, electronic and vibrational properties of a water layer on Ag(100) and Ag(511) have been studied by first principles calculations and ab initio molecular dynamics simulations. The most stable...

Microscopic origin of the effect of substrate metallicity on interfacial free energies

We investigate the effect of the metallic character of solid substrates on solid-liquid interfacial thermodynamics using molecular simulations. Building on the recent development of a semiclassical Thomas-Fermi model to tune the metallicity in classical molecular dynamics simulations, we introduce a thermodynamic integration framework to compute the evolution of the interfacial free energy as a function of the Thomas-Fermi screening length. We validate this approach against analytical results for empty capacitors and by comparing the predictions in the presence of an electrolyte with values determined from the contact angle of droplets on the surface. The general expression derived in this work highlights the role of the charge distribution within the metal. We further propose a simple model to interpret the evolution of the interfacial free energy with voltage and Thomas-Fermi length, which allows us to identify the charge correlations within the metal as the microscopic origin of the evolution of the interfacial free energy with the metallic character of the substrate. This methodology opens the door to the molecular-scale study of the effect of the metallic character of the substrate on confinement-induced transitions in ionic systems, as reported in recent atomic force microscopy and surface force apparatus experiments.

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.

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.

CO2 activation at Au(110)-water interfaces: An ab initio molecular dynamics study

The electrochemical reduction of CO₂ into valuable chemicals under mild conditions has become a promising technology for energy storage and conversion in the past few years, receiving much attention from theoretical researchers investigating the reaction mechanisms. However, most of the previous simulations are related to the key intermediates of *COOH and *CO using the computational hydrogen electrode approach under vacuum conditions, and the details of the CO₂ activation are usually ignored due to the model simplicity. Here, we study the CO₂ activation at the Au-water interfaces by considering the dynamics of an explicit water solvent, where both regular ab initio molecular dynamics and constrained ab initio molecular dynamics simulations are carried out to explore the CO₂ adsorption/desorption reactions from the atomic level. By introducing K⁺ cations into Au(110)-water interfacial models, an electrochemical environment under reducing potentials is constructed, where the reaction free energy (0.26 eV) and activation energy (0.61 eV) are obtained for CO₂ adsorption based on the thermodynamic integration. Moreover, the Bader charge analysis demonstrates that CO₂ adsorption is activated by the first-electron transfer, forming the adsorbed CO₂ ^- anion initiating the overall catalytic reaction.

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.

Grand-Canonical Model of Electrochemical Double Layers from a Hybrid Density-Potential Functional

A hybrid density-potential functional of an electrochemical interface that encompasses major effects in the contacting metal and electrolyte phases is formulated. Variational analysis of this functional yields a grand-canonical model of the electrochemical double layer (EDL). Specifically, metal electrons are described using the Thomas-Fermi-Dirac-Wigner theory of an inhomogeneous electron gas. The electrolyte solution is treated classically at the mean-field level, taking into account electrostatic interactions, ion size effects, and nonlinear solvent polarization. The model uses parametrizable force relations to describe the short-range forces between metal cationic cores, metal electrons, and electrolyte ions and solvent molecules. Therefore, the gap between the metal skeleton and the electrolyte solution, key to properties of the EDL, varies consistently as a function of the electrode potential. Partial charge transfer in the presence of ion specific adsorption is described using an Anderson-Newns type theory. This model is parametrized with density functional theory calculations, compared with experimental data, and then employed to unravel several interfacial properties of fundamental significance in electrochemistry. In particular, a closer approach of the solution phase toward the metal surface, for example, caused by a stronger ion specific adsorption, decreases the potential of zero charge and elevates the double-layer capacitance curve. In addition, the ion specific adsorption can lead to surface depolarization of ions. The present model represents a viable framework to model (reactive) EDLs under the constant potential condition, which can be used to understand multifaceted EDL effects in electrocatalysis.

Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?

QM/MM simulations have become an indispensable tool in many chemical and biochemical investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chemistry, are there still "burning challenges" in QM/MM methods, especially for biomolecular systems? In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quantitative applicability of QM/MM simulations to many, if not all, biomolecules. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate additional developments that help push the field forward in meaningful directions.

Density Functional Theory and Thermodynamics Modeling of Inner-Sphere Oxyanion Adsorption on the Hydroxylated α-Al2O3(001) Surface

The inner-sphere adsorption of AsO₄^3-, PO₄^3-, and SO₄^2- on the hydroxylated α-Al₂O₃(001) surface was modeled with the goal of adapting a density functional theory (DFT) and thermodynamics framework for calculating the adsorption energetics. While DFT is a reliable method for predicting various properties of solids, including crystalline materials comprised of hundreds (or even thousands) of atoms, adding aqueous energetics in heterogeneous systems poses steep challenges for modeling. This is in part due to the fact that environmentally relevant variations in the chemical surroundings cannot be captured atomistically without increasing the system size beyond tractable limits. The DFT + thermodynamics approach to this conundrum is to combine the DFT total energies with tabulated solution-phase data and Nernst-based corrective terms to incorporate experimentally tunable parameters such as concentration. Central to this approach is the design of thermodynamic cycles that partition the overall reaction (here, inner-sphere adsorption proceeding via ligand exchange) into elementary steps that can either be fully calculated or for which tabulated data are available. The ultimate goal is to develop a modeling framework that takes into account subtleties of the substrate (such as adsorption-induced surface relaxation) and energies associated with the aqueous environment such that adsorption at mineral-water interfaces can be reliably predicted, allowing for comparisons in the denticity and protonation state of the adsorbing species. Based on the relative amount of experimental information available for AsO₄^3-, PO₄^3-, and SO₄^2- adsorbates and the well-characterized hydroxylated α-Al₂O₃(001) surface, these systems are chosen to form a basis for assessing the model predictions. We discuss how the DFT + thermodynamics results are in line with the experimental information about the oxyanion sorption behavior. Additionally, a vibrational analysis was conducted for the charge-neutral oxyanion complexes and is compared to the available experimental findings to discern the inner-sphere adsorption phonon modes. The DFT + thermodynamics framework used here is readily extendable to other chemical processes at solid-liquid interfaces, and we discuss future directions for modeling surface processes at mineral-water and environmental interfaces.

Potential-Induced Adsorption and Structuring of Water at the Pt(111) Electrode Surface in Contact with an Ionic Liquid

Water adsorption is important in many fields from surface electrochemistry to electrocatalysis, where molecular-level information is much needed in order to gain a detailed understanding of the role of interfacial water. Here we report on water at Pt(111) surfaces in contact with an [EIMIM][BF₄] ionic liquid, which was spectroscopically resolved by using in situ sum-frequency generation (SFG). O-H modes are used to study water adsorption and water structure as a function of electrode potential, while the analysis of C-H modes is used to infer orientational changes of [EMIM] cations at the interface. Different from the bulk where free water molecules are found, SFG spectra provide evidence that an interfacial layer with an extended network of hydrogen-bonded water molecules exists and grows with increasing absolute potential which is used to identify the potential of zero charge at +0.1 V SHE, where a pronounced minimum in O-H intensity is found.