Solvation at metal/water interfaces: An ab initio molecular dynamics benchmark of common computational approaches

Correcting implicit solvation at metal/water interfaces through the incorporation of competitive water adsorption

Conventional continuum solvation models are ubiquitous in computational catalysis, including for describing metal/water interfaces, which are relevant to both solution-phase heterogeneous catalysis and electrocatalysis. Nonetheless, we find that such continuum models qualitatively fail to describe both the adsorption free energy and conformational preference for many organic molecules at such interfaces, largely due to the failure of continuum models to incorporate the role of competitive water adsorption. We develop a simple phenomenological model that accounts for competitive water adsorption and show that the model, when used in conjunction with continuum solvation, provides a dramatic improvement in the description of both adsorption and conformational preference. The model is also extended to additionally incorporate the influence of applied potential at the electrode surface, thus facilitating computationally efficient applications to scenarios including electrocatalysis.

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.

Toward Realistic Models of the Electrocatalytic Oxygen Evolution Reaction

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

Advancing H2O2 electrosynthesis: enhancing electrochemical systems, unveiling emerging applications, and seizing opportunities

Hydrogen peroxide (H2O2) is a highly desired chemical with a wide range of applications. Recent advancements in H2O2 synthesis center on the electrochemical reduction of oxygen, an environmentally friendly approach that facilitates on-site production. To successfully implement practical-scale, highly efficient electrosynthesis of H2O2, it is critical to meticulously explore both the design of catalytic materials and the engineering of other components of the electrochemical system, as they hold equal importance in this process. Development of promising electrocatalysts with outstanding selectivity and activity is a prerequisite for efficient H2O2 electrosynthesis, while well-configured electrolyzers determine the practical implementation of large-scale H2O2 production. In this review, we systematically summarize fundamental mechanisms and recent achievements in H2O2 electrosynthesis, including electrocatalyst design, electrode optimization, electrolyte engineering, reactor exploration, potential applications, and integrated systems, with an emphasis on active site identification and microenvironment regulation. This review also proposes new insights into the existing challenges and opportunities within this rapidly evolving field, together with perspectives on future development of H2O2 electrosynthesis and its industrial-scale applications.

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).

Benchmarking water adsorption on metal surfaces with ab initio molecular dynamics

Solid-water interfaces are ubiquitous in nature and technology. In particular, technologies evolving in the green transition, such as electrocatalysis, heavily rely on the junction of an electrolyte and an electrode as a central part of the device. For the understanding of atomic-scale processes taking place at the electrolyte-electrode interface, density functional theory (DFT) has become the de facto standard. The validation of DFT's ability to simulate the interfacial solid/water interaction is crucial, and ideal simulation setups need to be identified in order to prevent avoidable systematic errors. Here, we develop a rigorous sampling protocol for benchmarking the adsorption/desorption energetics of water on metallic surfaces against experimental temperature programmed desorption, single crystal adsorption calorimetry, and thermal energy atom scattering. We screened DFT's quality on a series of transition metal surfaces, applying three of the most common exchange-correlation approximations: PBE-D3, RPBE-D3, and BEEF-vdW. We find that all three xc-functionals reflect the pseudo-zeroth order desorption of water rooted in the combination of attractive adsorbate-adsorbate interactions and their saturation at low and intermediate coverages, respectively. However, both RPBE-D3 and BEEF-vdW lead to more accurate water adsorption strengths, while PBE-D3 clearly overbinds near-surface water. We relate the variations in binding strength to specific variations in water-metal and water-water interactions, highlighting the structural consequences inherent in an uninformed choice of simulation parameters. Our study gives atomistic insight into water's complex adsorption equilibrium. Furthermore, it represents a guideline for future DFT-based simulations of solvated solid interfaces by providing an assessment of systematic errors in specific setups.

Cation Effects on the Adsorbed Intermediates of CO2 Electroreduction Are Systematic and Predictable

The electrode-electrolyte interface, and in particular the nature of the cation, has considerable effects on the activity and product selectivity of the electrochemical reduction of CO2. Therefore, to improve the electrocatalysis of this challenging reaction, it is paramount to ascertain whether cation effects on adsorbed intermediates are systematic. Here, DFT calculations are used to show that the effects of K+, Na+, and Mg2+, on single carbon CO2 reduction intermediates can either be stabilizing or destabilizing depending on the metal and the adsorbate. Because systematic trends are observed, cation effects can be accurately predicted in simple terms for a wide variety of metals, cations and adsorbed species. These results are then applied to the reduction of CO2 to CO on four different catalytic surfaces (Au, Ag, Cu, Pd) and activation of weak-binding metals is consistently observed by virtue of the stabilization of the key intermediate *COOH.

The Impact of Electron Donating and Withdrawing Groups on Electrochemical Hydrogenolysis and Hydrogenation of Carbonyl Compounds

The hydrogenolysis or hydrodeoxygenation of a carbonyl group, where the C═O group is converted to a CH2 group, is of significant interest in a variety of fields. A challenge in electrochemically achieving hydrogenolysis of a carbonyl group with high selectivity is that electrochemical hydrogenation of a carbonyl group, which converts the C═O group to an alcohol group (CH-OH), is demonstrated not to be the initial step of hydrogenolysis. Instead, hydrogenation and hydrogenolysis occur in parallel, and they are competing reactions. This means that although both hydrogenolysis and hydrogenation require adding H atoms to the carbonyl group, they involve different intermediates formed on the electrode surface. Thus, revealing the difference in intermediates, transition states, and kinetic barriers for hydrogenolysis and hydrogenation pathways is the key to understanding and controlling hydrogenolysis/hydrogenation selectivity of carbonyl compounds. In this study, we aimed to identify features of reactant molecules that can affect their hydrogenolysis/hydrogenation selectivity on a Zn electrode that was previously shown to promote hydrogenolysis over hydrogenation. In particular, we examined the electrochemical reduction of para-substituted benzaldehyde compounds with substituent groups having different electron donating/withdrawing abilities. Our results show a strikingly systematic impact of the substituent group where a stronger electron-donating group promotes hydrogenolysis and a stronger electron-withdrawing group promotes hydrogenation. These experimental results are presented with computational results explaining the substituent effects on the thermodynamics and kinetics of electrochemical hydrogenolysis and hydrogenation pathways, which also provide critically needed information and insights into the transition states involved with these pathways.

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

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

Transferable Water Potentials Using Equivariant Neural Networks

Machine learning interatomic potentials (MLIPs) have emerged as a technique that promises quantum theory accuracy for reduced cost. It has been proposed [J. Chem. Phys. 2023, 158, 084111] that MLIPs trained on solely liquid water data cannot accurately transfer to the vapor-liquid equilibrium while recovering the many-body decomposition (MBD) analysis of gas-phase water clusters. This suggests that MLIPs do not directly learn the physically correct interactions of water molecules, limiting transferability. In this work, we show that MLIPs using equivariant architecture and trained on 3200 liquid water structures reproduces liquid-phase water properties (e.g., density within 0.003 g/cm3 between 230 and 365 K), vapor-liquid equilibrium properties up to 550 K, the MBD analysis of gas-phase water cluster up to six-body interactions, and the relative energy and the vibrational density of states of ice phases. We show that potentials developed using equivariant MLIPs allow transferability for arbitrary phases of water that remain stable in nanosecond long simulations.

Computational chemistry for water-splitting electrocatalysis

Electrocatalytic water splitting driven by renewable electricity has attracted great interest in recent years for producing hydrogen with high-purity. However, the practical applications of this technology are limited by the development of electrocatalysts with high activity, low cost, and long durability. In the search for new electrocatalysts, computational chemistry has made outstanding contributions by providing fundamental laws that govern the electron behavior and enabling predictions of electrocatalyst performance. This review delves into theoretical studies on electrochemical water-splitting processes. Firstly, we introduce the fundamentals of electrochemical water electrolysis and subsequently discuss the current advancements in computational methods and models for electrocatalytic water splitting. Additionally, a comprehensive overview of benchmark descriptors is provided to aid in understanding intrinsic catalytic performance for water-splitting electrocatalysts. Finally, we critically evaluate the remaining challenges within this field.

Cation-Induced Interfacial Hydrophobic Microenvironment Promotes the C-C Coupling in Electrochemical CO2 Reduction

The electrochemical carbon dioxide reduction reaction (CO2RR) toward C2 products is a promising way for the clean energy economy. Modulating the structure of the electric double layer (EDL), especially the interfacial water and cation type, is a useful strategy to promote C-C coupling, but atomic understanding lags far behind the experimental observations. Herein, we investigate the combined effect of interfacial water and alkali metal cations on the C-C coupling at the Cu(100) electrode/electrolyte interface using ab initio molecular dynamics (AIMD) simulations with a constrained MD and slow-growth approach. We observe a linear correlation between the water-adsorbate stabilization effect, which manifests as hydrogen bonds, and the corresponding alleviation in the C-C coupling free energy. The role of a larger cation, compared to a smaller cation (e.g., K+ vs Li+), lies in its ability to approach the interface through desolvation and coordinates with the *CO+*CO moiety, partially substituting the hydrogen-bonding stabilizing effect of interfacial water. Although this only results in a marginal reduction of the energy barrier for C-C coupling, it creates a local hydrophobic environment with a scarcity of hydrogen bonds owing to its great ionic radius, impeding the hydrogen of surrounding interfacial water to approach the oxygen of the adsorbed *CO. This skillfully circumvents the further hydrogenation of *CO toward the C1 pathway, serving as the predominant factor through which a larger cation facilitates C-C coupling. This study unveils a comprehensive atomic mechanism of the cation-water-adsorbate interactions that can facilitate the further optimization of the electrolyte and EDL for efficient C-C coupling in CO2RR.

Ab Initio-Based Modeling of Thermodynamic Cyclic Voltammograms: A Benchmark Study on Ag(100) in Bromide Solutions

Experimental cyclic voltammograms (CVs) measured in the slow scan rate limit can be entirely described in terms of the thermodynamic equilibrium quantities of the electrified solid-liquid interface. They correspondingly serve as an important benchmark for the quality of first-principles calculations of interfacial thermodynamics. Here, we investigate the partially drastic approximations made presently in computationally efficient calculations for the well-defined showcase of an Ag(100) model electrode in Br-containing electrolytes, where the nontrivial part of the CV stems from the electrosorption of Br ions. We specifically study the entanglement of common approximations in the treatment of solvation and field effects, as well as in the way macroscopic averages of the two key quantities, namely, the potential-dependent adsorbate coverage and electrosorption valency, are derived from the first-principles energetics. We demonstrate that the combination of energetics obtained within an implicit solvation model and a perturbative second order account of capacitive double layer effects with a constant-potential grand-canonical Monte Carlo sampling of the adsorbate layer provides an accurate description of the experimental CV. However, our analysis also shows that error cancellation at lower levels of theory may equally lead to good descriptions even though key underlying physics such as the disorder-order transition of the Br adlayer at increasing coverages is inadequately treated.

Electrochemical Potential-Driven Shift of Frontier Orbitals in M-N-C Single-Atom Catalysts Leading to Inverted Adsorption Energies

Electronic structure is essential to understanding the catalytic mechanism of metal single-atom catalysts (SACs), especially under electrochemical conditions. This study delves into the nuanced modulation of "frontier orbitals" in SACs on nitrogen-doped graphene (N-C) substrates by electrochemical potentials. We observe shifts in Fermi level and changes of d-orbital occupation with alterations in electrochemical potentials, emphasizing a synergy between the discretized atomic orbitals of metals and the continuous bands of the N-C based environment. Using O2 and CO2 as model adsorbates, we highlight the direct consequences of these shifts on adsorption energies, unveiling an intriguing inversion of adsorption energies on Co/N-C SAC under negative electrochemical potentials. Such insights are attributed to the role of the dxz and dz2 orbitals, pivotal for stabilizing the π* orbitals of O2. Through this exploration, our work offers insights on the interplay between electronic structures and adsorption behaviors in SACs, paving the way for enhanced catalyst design strategies in electrochemical processes.

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.

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

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

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

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

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.

Evaluating Adsorbate-Solvent Interactions: Are Dispersion Corrections Necessary?

Incorporating solvent-adsorbate interactions is paramount in models of aqueous (electro)catalytic reactions. Although a number of techniques exist, they are either highly demanding in computational terms or inaccurate. Microsolvation offers a trade-off between accuracy and computational expenses. Here, we dissect a method to swiftly outline the first solvation shell of species adsorbed on transition-metal surfaces and assess their corresponding solvation energy. Interestingly, dispersion corrections are generally not needed in the model, but caution is to be exercised when water-water and water-adsorbate interactions are of similar magnitude.

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.

Molecular Dynamics Investigation of Nanoscale Hydrophobicity of Polymer Surfaces: What Makes Water Wet?

The wettability of a polymer surface─related to its hydrophobicity or tendency to repel water─can be crucial for determining its utility, such as for a coating or a purification membrane. While wettability is commonly associated with the macroscopic measurement of a contact angle between surface, water, and air, the molecular physics that underlie these macroscopic observations are not fully known, and anticipating the relative behavior of different polymers is challenging. To address this gap in molecular-level understanding, we use molecular dynamics simulations to investigate and contrast interactions of water with six chemically distinct polymers: polytetrafluoroethylene, polyethylene, polyvinyl chloride, poly(methyl methacrylate), Nylon-66, and poly(vinyl alcohol). We show that several prospective quantitative metrics for hydrophobicity agree well with experimental contact angles. Moreover, the behavior of water in proximity to these polymer surfaces can be distinguished with analysis of interfacial water dynamics, extent of hydrogen bonding, and molecular orientation─even when macroscopic measures of hydrophobicity are similar. The predominant factor dictating wettability is found to be the extent of hydrogen bonding between polymer and water, but the precise manifestation of hydrogen bonding and its impact on surface water structure varies. In the absence of hydrogen bonding, other molecular interactions and polymer mechanics control hydrophobic ordering. These results provide new insights into how polymer chemistry specifically impacts water-polymer interactions and translates to surface hydrophobicity. Such factors may facilitate the design or processing of polymer surfaces to achieve targeted wetting behavior, and presented analyses can be useful in studying the interfacial physics of other systems.

Recent advances in the theoretical studies on the electrocatalytic CO2 reduction based on single and double atoms

Excess of carbon dioxide (CO2) in the atmosphere poses a significant threat to the global climate. Therefore, the electrocatalytic carbon dioxide reduction reaction (CO2RR) is important to reduce the burden on the environment and provide possibilities for developing new energy sources. However, highly active and selective catalysts are needed to effectively catalyze product synthesis with high adhesion value. Single-atom catalysts (SACs) and double-atom catalysts (DACs) have attracted much attention in the field of electrocatalysis due to their high activity, strong selectivity, and high atomic utilization. This review summarized the research progress of electrocatalytic CO2RR related to different types of SACs and DACs. The emphasis was laid on the catalytic reaction mechanism of SACs and DACs using the theoretical calculation method. Furthermore, the influences of solvation and electrode potential were studied to simulate the real electrochemical environment to bridge the gap between experiments and computations. Finally, the current challenges and future development prospects were summarized and prospected for CO2RR to lay the foundation for the theoretical research of SACs and DACs in other aspects.

Thermal transport across copper-water interfaces according to deep potential molecular dynamics

Nanoscale thermal transport at solid-liquid interfaces plays an essential role in many engineering fields. This work performs deep potential molecular dynamics (DPMD) simulations to investigate thermal transport across copper-water interfaces. Unlike traditional classical molecular dynamics (CMD) simulations, we independently train a deep learning potential (DLP) based on density functional theory (DFT) calculations and demonstrated its high computational efficiency and accuracy. The trained DLP predicts radial distribution functions (RDFs), vibrational densities of states (VDOS), density curves, and thermal conductivity of water confined in the nanochannel at a DFT accuracy. The thermal conductivity decreases slightly with an increase in the channel height, while the influence of the cross-sectional area is negligible. Moreover, the predicted interfacial thermal conductance (ITC) across the copper-water interface by DPMD is 2.505 × 10⁸ W m^-2 K^-1, the same order of magnitude as the CMD and experimental results but with a high computational accuracy. This work seeks to simulate the thermal transport properties of solid-liquid interfaces with DFT accuracy at large-system and long-time scales.

Using micro-solvation and generalized coordination numbers to estimate the solvation energies of adsorbed hydroxyl on metal nanoparticles

Solvent-adsorbate interactions have a great impact on catalytic processes in aqueous systems. Implicit solvent calculations are inexpensive but inaccurate toward hydrogen bonds, while a full incorporation of explicit solvation is computationally demanding. Micro-solvation attempts to break this dilemma by including only those solvent molecules directly interacting with the solute and any nearby interfaces, thereby providing a compromise between accuracy and computational expenses. Here, we show that micro-solvation of *OH and its relation to adsorption sites is largely transferable across late transition metal nanoparticles. Solvation energies for *OH on nanoparticles of Ir, Pd, and Pt range from -0.63 ± 0.04 eV to -0.67 ± 0.12 eV, while those on Au and Ag are -0.75 ± 0.07 eV and -1.01 ± 0.05 eV, respectively. These results enable the use of average solvation corrections for *OH on late transition metal nanostructures.

Adsorbate chemical environment-based machine learning framework for heterogeneous catalysis

Heterogeneous catalytic reactions are influenced by a subtle interplay of atomic-scale factors, ranging from the catalysts' local morphology to the presence of high adsorbate coverages. Describing such phenomena via computational models requires generation and analysis of a large space of atomic configurations. To address this challenge, we present Adsorbate Chemical Environment-based Graph Convolution Neural Network (ACE-GCN), a screening workflow that accounts for atomistic configurations comprising diverse adsorbates, binding locations, coordination environments, and substrate morphologies. Using this workflow, we develop catalyst surface models for two illustrative systems: (i) NO adsorbed on a Pt₃Sn(111) alloy surface, of interest for nitrate electroreduction processes, where high adsorbate coverages combined with low symmetry of the alloy substrate produce a large configurational space, and (ii) OH* adsorbed on a stepped Pt(221) facet, of relevance to the Oxygen Reduction Reaction, where configurational complexity results from the presence of irregular crystal surfaces, high adsorbate coverages, and directionally-dependent adsorbate-adsorbate interactions. In both cases, the ACE-GCN model, trained on a fraction (~10%) of the total DFT-relaxed configurations, successfully describes trends in the relative stabilities of unrelaxed atomic configurations sampled from a large configurational space. This approach is expected to accelerate development of rigorous descriptions of catalyst surfaces under in-situ conditions.

Liquid-Phase Effects on Adsorption Processes in Heterogeneous Catalysis

Aqueous solvation free energies of adsorption have recently been measured for phenol adsorption on Pt(111). Endergonic solvent effects of ∼1 eV suggest solvents dramatically influence a metal catalyst's activity with significant implications for the catalyst design. However, measurements are indirect and involve adsorption isotherm models, which potentially reduces the reliability of the extracted energy values. Computational, implicit solvation models predict exergonic solvation effects for phenol adsorption, failing to agree with measurements even qualitatively. In this study, an explicit, hybrid quantum mechanical/molecular mechanical approach for computing solvation free energies of adsorption is developed, solvation free energies of phenol adsorption are computed, and experimental data for solvation free energies of phenol adsorption are reanalyzed using multiple adsorption isotherm models. Explicit solvation calculations predict an endergonic solvation free energy for phenol adsorption that agrees well with measurements to within the experimental and force field uncertainties. Computed adsorption free energies of solvation of carbon monoxide, ethylene glycol, benzene, and phenol over the (111) facet of Pt and Cu suggest that liquid water destabilizes all adsorbed species, with the largest impact on the largest adsorbates.

Comparing interfacial cation hydration at catalytic active sites and spectator sites on gold electrodes: understanding structure sensitive CO2 reduction kinetics

Hydrated cations present in the electrochemical double layer (EDL) are known to play a crucial role in electrocatalytic CO2 reduction (CO2R), and numerous studies have attempted to explain how the cation effect contributes to the complex CO2R mechanism. CO2R is a structure sensitive reaction, indicating that a small fraction of total surface sites may account for the majority of catalytic turnover. Despite intense interest in specific cation effects, probing site-specific, cation-dependent solvation structures remains a significant challenge. In this work, CO adsorbed on Au is used as a vibrational Stark reporter to indirectly probe solvation structure using vibrational sum frequency generation (VSFG) spectroscopy. Two modes corresponding to atop adsorption of CO are observed with unique frequency shifts and potential-dependent intensity profiles, corresponding to direct adsorption of CO to inactive surface sites, and in situ generated CO produced at catalytic active sites. Analysis of the cation-dependent Stark tuning slopes for each of these species provides estimates of the hydrated cation radius upon adsorption to active and inactive sites on the Au electrode. While cations are found to retain their bulk hydration shell upon adsorption at inactive sites, catalytic active sites are characterized by a single layer of water between the Au surface and the electrolyte cation. We propose that the drastic increase in catalytic performance at active sites stems from this unique solvation structure at the Au/electrolyte interface. Building on this evidence of a site-specific EDL structure will be critical to understand the connection between cation-dependent interfacial solvation and CO2R performance.

Applying Classical, Ab Initio, and Machine-Learning Molecular Dynamics Simulations to the Liquid Electrolyte for Rechargeable Batteries

Rechargeable batteries have become indispensable implements in our daily life and are considered a promising technology to construct sustainable energy systems in the future. The liquid electrolyte is one of the most important parts of a battery and is extremely critical in stabilizing the electrode-electrolyte interfaces and constructing safe and long-life-span batteries. Tremendous efforts have been devoted to developing new electrolyte solvents, salts, additives, and recipes, where molecular dynamics (MD) simulations play an increasingly important role in exploring electrolyte structures, physicochemical properties such as ionic conductivity, and interfacial reaction mechanisms. This review affords an overview of applying MD simulations in the study of liquid electrolytes for rechargeable batteries. First, the fundamentals and recent theoretical progress in three-class MD simulations are summarized, including classical, ab initio, and machine-learning MD simulations (section 2). Next, the application of MD simulations to the exploration of liquid electrolytes, including probing bulk and interfacial structures (section 3), deriving macroscopic properties such as ionic conductivity and dielectric constant of electrolytes (section 4), and revealing the electrode-electrolyte interfacial reaction mechanisms (section 5), are sequentially presented. Finally, a general conclusion and an insightful perspective on current challenges and future directions in applying MD simulations to liquid electrolytes are provided. Machine-learning technologies are highlighted to figure out these challenging issues facing MD simulations and electrolyte research and promote the rational design of advanced electrolytes for next-generation rechargeable batteries.

Atomistic Understanding of Two-dimensional Electrocatalysts from First Principles

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

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.

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.

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.

Trends in oxygenate/hydrocarbon selectivity for electrochemical CO(2) reduction to C2 products

The electrochemical conversion of carbon di-/monoxide into commodity chemicals paves a way towards a sustainable society but it also presents one of the great challenges in catalysis. Herein, we present the trends in selectivity towards specific dicarbon oxygenate/hydrocarbon products from carbon monoxide reduction on transition metal catalysts, with special focus on copper. We unveil the distinctive role of electrolyte pH in tuning the dicarbon oxygenate/hydrocarbon selectivity. The understanding is based on density functional theory calculated energetics and microkinetic modeling. We identify the critical reaction steps determining selectivity and relate their transition state energies to two simple descriptors, the carbon and hydroxide binding strengths. The atomistic insight gained enables us to rationalize a number of experimental observations and provides avenues towards the design of selective electrocatalysts for liquid fuel production from carbon di-/monoxide.

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.

Theories for Electrolyte Effects in CO2 Electroreduction

Electrochemical CO₂ reduction (eCO₂R) enables the conversion of waste CO₂ to high-value fuels and commodity chemicals powered by renewable electricity, thereby offering a viable strategy for reaching the goal of net-zero carbon emissions. Research in the past few decades has focused both on the optimization of the catalyst (electrode) and the electrolyte environment. Surface-area normalized current densities show that the latter can affect the CO₂ reduction activity by up to a few orders of magnitude.In this Account, we review theories of the mechanisms behind the effects of the electrolyte (cations, anions, and the electrolyte pH) on eCO₂R. As summarized in the conspectus graphic, the electrolyte influences eCO₂R activity via a field (ε) effect on dipolar (μ) reaction intermediates, changing the proton donor for the multi-step proton-electron transfer reaction, specifically adsorbed anions on the catalyst surface to block active sites, and tuning the local environment by homogeneous reactions. To be specific, alkali metal cations (M⁺) can stabilize reaction intermediates via electrostatic interactions with dipolar intermediates or buffer the interfacial pH via hydrolysis reactions, thereby promoting the eCO₂R activity with the following trend in hydrated size (corresponding to the local field strength ε)/hydrolysis ability: Cs⁺ > K⁺ > Na⁺ > Li⁺. The effect of the electrolyte pH can give a change in eCO₂R activity of up to several orders of magnitude, arising from linearly shifting the absolute interfacial field via the relationship U_SHE = U_RHE - (2.3k_BT)pH, homogeneous reactions between OH^- and desorbed intermediates, or changing the proton donor from hydronium to water along with increasing pH. Anions have been suggested to affect the eCO₂R reaction process by solution-phase reactions (e.g., buffer reactions to tune local pH), acting as proton donors or as a surface poison.So far, the existing models of electrolyte effects have been used to rationalize various experimentally observed trends, having yet to demonstrate general predictive capabilities. The major challenges in our understanding of the electrolyte effect in eCO₂R are (i) the long time scale associated with a dynamic ab initio picture of the catalyst|electrolyte interface and (ii) the overall activity determined by the length-scale interplay of intrinsic microkinetics, homogeneous reactions, and mass transport limitations. New developments in ab initio dynamic models and coupling the effects of mass transport can provide a more accurate view of the structure and intrinsic functions of the electrode-electrolyte interface and the corresponding reaction energetics toward comprehensive and predictive models for electrolyte design.

Understanding Adsorption of Organics on Pt(111) in the Aqueous Phase: Insights from DFT Based Implicit Solvent and Statistical Thermodynamics Models

Adsorption of organics in the aqueous phase is an area which is experimentally difficult to measure, while computational techniques require extensive configurational sampling of the solvent and adsorbate. This is exceedingly computationally demanding, which excludes its routine use. If implicit solvent could be applied instead, this would dramatically reduce the computational cost as configurational sampling of solvent is not needed. Here, using statistical thermodynamic arguments and DFT calculations with implicit solvent models, we show that semiquantitative values for the free energy and entropy change of adsorption in the aqueous phase (ΔG_ads^solv and ΔS_ads^solv) for small organics can be calculated, for a range of coverages. We parametrize the soft sphere based solute dielectric cavity to an approximated free energy of solvation for a single Pt atom at the (111) facet, forming upper and lower bounds based on the entropy of water at the aqueous metal interface (ΔG_solv(Pt) = -4.35 to -7.18 kJ mol^-1). This captures the decrease in ΔG_ads^solv compared to the free energy of adsorption in the vacuum phase (ΔG_ads^vac), while solvent models with electron density based cavities fail to do so. For a range of oxygenated aromatics, the adsorption energetics using horizontal gas phase geometries significantly overestimate ΔG_ads^solv compared to experiment by ∼100 kJ mol^-1, but they agree with ab initio MD simulations using similar geometries. This suggests oxygenated aromatic compounds adsorb perpendicular to the metallic surface, while the ΔG_ads^solv for vertical geometries of furfural and cyclohexanol agree to within 20 kJ mol^-1 of experimental studies. The proposed techniques provide an inexpensive toolset for validation and prediction of adsorption energetics on solvated metallic surfaces, which could be further validated by the future availability of more experimental measurements for the aqueous entropy/free energy of adsorption.

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.

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.

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.

Generation of Quantum Configurational Ensembles Using Approximate Potentials

Conformational analysis is of paramount importance in drug design: it is crucial to determine pharmacological properties, understand molecular recognition processes, and characterize the conformations of ligands when unbound. Molecular Mechanics (MM) simulation methods, such as Monte Carlo (MC) and molecular dynamics (MD), are usually employed to generate ensembles of structures due to their ability to extensively sample the conformational space of molecules. The accuracy of these MM-based schemes strongly depends on the functional form of the force field (FF) and its parametrization, components that often hinder their performance. High-level methods, such as ab initio MD, provide reliable structural information but are still too computationally expensive to allow for extensive sampling. Therefore, to overcome these limitations, we present a multilevel MC method that is capable of generating quantum configurational ensembles while keeping the computational cost at a minimum. We show that FF reparametrization is an efficient route to generate FFs that reproduce QM results more closely, which, in turn, can be used as low-cost models to achieve the gold standard QM accuracy. We demonstrate that the MC acceptance rate is strongly correlated with various phase space overlap measurements and that it constitutes a robust metric to evaluate the similarity between the MM and QM levels of theory. As a more advanced application, we present a self-parametrizing version of the algorithm, which combines sampling and FF parametrization in one scheme, and apply the methodology to generate the QM/MM distribution of a ligand in aqueous solution.

Hydrogen adsorption on doped graphene investigated by a DFT-based tight-binding method

DFTB is a tight binding model based on density functional theory (DFT); it is less exact than the latter, but much faster, and allows calculations for much larger ensembles and timescales. Here we explore its possibilities for electrochemistry, taking hydrogen adsorption on pristine and doped graphene as an example. The speed and the flexibility of DFTB enabled us to provide a broad panorama incorporating not only the effects of various dopants, but also of ionic adsorption and double-layer charging. With the exception of graphene doped with boron, our results agree well with literature data based on DFT where they exist, and with a few control DFT calculations performed by us. DFTB is well suited to perform molecular dynamics for the electrochemical interface. As an example, we have investigated the effect of water on hydrogen adsorption on pristine graphene.

Elastic Collision Based Dynamic Partitioning Scheme for Hybrid Simulations

In hybrid simulations, such as the QM/MM approach, the system is partitioned into regions that are treated at different levels of theory. The key question then becomes how to evaluate the interactions between particles on opposite sides of the boundary. One approach is to place the boundary in such a way that particles near the boundary on both sides are of the same type, thus simplifying the evaluation of the interactions. If mobile particles are present, such as solvent molecules, and particles are allowed to cross the boundary, the conservation of energy and atomic forces is problematic unless the computational effort is increased significantly. By preventing particles from crossing the boundary but allowing the boundary to be flexible, an accurate estimate of average thermodynamic properties is obtained in principle as illustrated by the flexible inner region ensemble separator (FIRES) method [C. Rowley and B. Roux, J. Chem. Theory Comput. 2012, 8, 3526]. In FIRES, a harmonic restraint is applied to particles near the boundary. Therefore, it can occur that particle cross the boundary to some extent resulting in anomalies in the particle density. Here, a constraint approach is presented where particles instantaneously scatter from the boundary. This scattering-adapted FIRES (SAFIRES) implementation makes use of a variable-time-step propagation algorithm where the time step is scaled automatically to identify the moment a collision should occur. If the length of the time step is kept constant, this propagator reduces to a regular Langevin dynamics algorithm, and to the velocity Verlet algorithm for conservative dynamics if the friction coefficient is set to zero. Correct average ensemble statistics are obtained as demonstrated in simulations where, for testing purposes, the particles in the two regions are treated at the same level of theory, namely, a homogeneous Lennard-Jones (LJ) liquid and liquid water based on the TIP4P potential function. In order to illustrate this approach in solid-liquid interface simulations, a LJ liquid in contact with the surface of a crystal is also simulated. The simulations using SAFIRES are shown to reproduce the unconstrained reference simulations without significant deviations in the particle density and the dynamics are shown to conserve energy when coupling to the heat bath is turned off.