The electrochemical interface in first-principles calculations

Molecular dynamics of liquid-electrode interface by integrating Coulomb interaction into universal neural network potential

Computational understanding of the liquid-electrode interface faces challenges in efficiently incorporating reactive force fields and electrostatic potentials within reasonable computational costs. Although universal neural network potentials (UNNPs), representing pretrained machine learning interatomic potentials, are emerging, current UNNP models lack explicit treatment of Coulomb potentials, and methods for integrating additional charges on the electrode remain to be established. We propose a method to analyze liquid-electrode interfaces by integrating a UNNP, known as the preferred potential, with Coulomb potentials using the ONIOM method. This approach extends the applicability of UNNPs to electrode-liquid interface systems. Through molecular dynamics simulations of graphene-water and graphene oxide (GO)-water interfaces, we demonstrate the effectiveness of our method. Our findings emphasize the necessity of incorporating long-range Coulomb potentials into the water potential to accurately describe water polarization at the interface. Furthermore, we observe that functional groups on the GO electrode influence both polarization and capacitance.

Modeling interfacial electric fields and the ethanol oxidation reaction at electrode surfaces

The electrochemical environment present at surfaces can have a large effect on intended applications. Such environments may occur, for instance, at battery or electrocatalyst surfaces. Solvent, co-adsorbates, and electrical field effects may strongly influence surface chemistry. Understanding these phenomena is an on-going area of research, especially in the realm of electrocatalysis. Herein, we modeled key steps in the ethanol oxidation reaction (EOR) over a common EOR catalyst, Rh(111), using density functional theory. We assessed how the presence of electrical fields may influence important C-C and C-H bond scission and C-O bond formation reactions with and without co-adsorbed water. We found that electric fields combined with the presence of water can significantly affect surface chemistry, including adsorption and reaction energies. Our results show that C-C scission (necessary for the complete oxidation of ethanol) is most likely through CHxCO adsorbates. With no electric field or solvent present C-C scission of CHCO has the lowest reaction energy and dominates the oxidation of ethanol. But when applying strong negative fields (with or without solvent), the C-C scission of CH2CO and CHCO becomes competitive. The current work provides insights into how electric fields and water solvent affect EOR, especially when simulated using density functional theory.

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids-including the density response, surface tension and size-dependent cavitation free energies-for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

Accelerating QM/MM simulations of electrochemical interfaces through machine learning of electronic charge densities

A crucial aspect in the simulation of electrochemical interfaces consists in treating the distribution of electronic charge of electrode materials that are put in contact with an electrolyte solution. Recently, it has been shown how a machine-learning method that specifically targets the electronic charge density, also known as SALTED, can be used to predict the long-range response of metal electrodes in model electrochemical cells. In this work, we provide a full integration of SALTED with MetalWalls, a program for performing classical simulations of electrochemical systems. We do so by deriving a spherical harmonics extension of the Ewald summation method, which allows us to efficiently compute the electric field originated by the predicted electrode charge distribution. We show how to use this method to drive the molecular dynamics of an aqueous electrolyte solution under the quantum electric field of a gold electrode, which is matched to the accuracy of density-functional theory. Notably, we find that the resulting atomic forces present a small error of the order of 1 meV/Å, demonstrating the great effectiveness of adopting an electron-density path in predicting the electrostatics of the system. Upon running the data-driven dynamics over about 3 ns, we observe qualitative differences in the interfacial distribution of the electrolyte with respect to the results of a classical simulation. By greatly accelerating quantum-mechanics/molecular-mechanics approaches applied to electrochemical systems, our method opens the door to nanosecond timescales in the accurate atomistic description of the electrical double layer.

Theoretical Investigation of the Potential-Dependent CO Adsorption on Copper Electrodes

Despite the importance of CO adsorption in many electrocatalytic reaction mechanisms, there has been little investigation of the dependence of the free energy of CO adsorption on the applied potential. Herein, we report on the potential-dependent adsorption of CO on Cu electrodes using a grand-canonical density functional theory approach. We demonstrate that, within the working potential range of electrocatalytic CO2 reduction on Cu(111) and Cu(100), the CO adsorption strength can change by over 0.1 eV. Our analyses explain the potential dependence through an interfacial capacitance loss upon CO adsorption as well as orbital relaxation induced by the electrode potential. Via sensitivity analysis with respect to two electrolyte model parameters (solvent dielectric constant and Debye screening length), we find that the surface excess charge density is a useful descriptor of the CO adsorption free energy.

Constant potential energetics of metallic and semiconducting electrodes: A benchmark study on 2D materials

Grand-canonical (GC) constant-potential methods within an implicit solvent environment provide a general approach to compute the potential-dependent energetics at electrified solid-liquid interfaces with first-principles density-functional theory. Here, we use a mindfully chosen set of 27 isostructural 2D metal halides MX2 to analyze the variation of this energetics when the electronic structure changes from metallic to semiconducting and insulating state. Apart from expectable changes due to the opening up of the electronic bandgap, the calculations also show an increasing sensitivity to the numerical Brillouin zone integration and electronic smearing, which imposes computational burdens in practice. We rationalize these findings within the picture of the total interfacial capacitance arising from a series connection of the electrochemical double-layer capacitance and the so-called quantum capacitance resulting from the filling of electronic states inside the electrode. For metals, the electrochemical double-layer capacitance dominates at all potentials, and the entire potential drop takes place in the electrolyte. For semiconductors, the potential drop occurs instead fully or partially inside the electrode at potentials within or just outside the bandgap. For 2D semiconductors, the increased sensitivity to numerical parameters then results from the concomitantly increased contribution of the quantum capacitance that is harder to converge. Fortunately, this understanding motivates a simple extension of the CHE + DL approximation for metals, which provides the approximate GC energetics of 2D semiconductors using only quantities that can be obtained from computationally undemanding calculations at the point of zero charge and a generic double-layer capacitance.

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.

Incorporating Electrolyte Correlation Effects into Variational Models of Electrochemical Interfaces

We propose a way for obtaining a classical free energy density functional for electrolytes based on a first-principle many-body partition function. Via a one-loop expansion, we include coulombic correlations beyond the conventional mean-field approximation. To examine electrochemical interfaces, we integrate the electrolyte free energy functional into a hybrid quantum-classical model. This scheme self-consistently couples electronic, ionic, and solvent degrees of freedom and incorporates electrolyte correlation effects. The derived free energy functional causes a correlation-induced enhancement in interfacial counterion density and leads to an overall increase in capacitance. This effect is partially compensated by a reduction of the dielectric permittivity of interfacial water. At larger surface charge densities, ion crowding at the interface stifles these correlation effects. While scientifically intriguing already at planar interfaces, we anticipate these correlation effects to play an essential role for electrolytes in nanoconfinement.

An implicit electrolyte model for plane wave density functional theory exhibiting nonlinear response and a nonlocal cavity definition

We have developed and implemented an implicit electrolyte model in the Vienna Ab initio Simulation Package (VASP) that includes nonlinear dielectric and ionic responses as well as a nonlocal definition of the cavities defining the spatial regions where these responses can occur. The implementation into the existing VASPsol code is numerically efficient and exhibits robust convergence, requiring computational effort only slightly higher than the original linear polarizable continuum model. The nonlinear + nonlocal model is able to reproduce the characteristic "double hump" shape observed experimentally for the differential capacitance of an electrified metal interface while preventing "leakage" of the electrolyte into regions of space too small to contain a single water molecule or solvated ion. The model also gives a reasonable prediction of molecular solvation free energies as well as the self-ionization free energy of water and the absolute electron chemical potential of the standard hydrogen electrode. All of this, combined with the additional ability to run constant potential density functional theory calculations, should enable the routine computation of activation barriers for electrocatalytic processes.

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.

Electrocatalytic Mechanisms for an Oxygen Evolution Reaction at a Rhombohedral Boron Monosulfide Electrode/Alkaline Medium Interface

Rhombohedral boron monosulfide (r-BS) with a layer stacking structure is a promising electrocatalyst for an oxygen evolution reaction (OER) within an alkaline solution. We investigated the catalytic mechanisms at the r-BS electrode/alkaline medium interface for an OER using hybrid solvation theory based on the first-principles method combined with classical solution theory. In this study, we elucidate the activities of the OER at the outermost r-BS sheet with and without various surface defects. The Gibbs free energies along the OER path indicate that the boron vacancies at the first and second layers of the r-BS surface (VB1 and VB2) can promote the OER. However, we found that the VB1 is easily occupied by the oxygen atom during the OER, degrading its electrocatalytic performance. In contrast, VB2 is suitable for the active site of the OER due to its structure stability. Next, we applied a bias voltage with the OER potential to the r-BS electrode. The bias voltage incorporates the positive excess surface charge into pristine r-BS and VB2, which can be understood by the relationship between the OER potential and potentials of zero charge at the r-BS electrode. Because the OH- ions are the starting point of the OER, the positively charged surface is kinetically favorable for the electrocatalyst owing to the attractive interaction with the OH- ions. Finally, we qualitatively discuss the flat-band potential at a semiconductor/alkaline solution interface. It suggests that p-type carrier doping could promote the catalytic performance of r-BS. These results explain the previous measurement of the OER performance with the r-BS-based electrode and provide valuable insights into developing a semiconductor electrode/water interface.

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.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

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

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response

We demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation-dissipation method for water and acetonitrile. We examine this method's trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

Charged species redistribution at electrochemical interfaces: a model system of the zirconium oxide/water interface

Quantifying the local distribution of charged defects in the solid state and charged ions in liquid solution near the oxide/liquid interface is key to understanding a range of important electrochemical processes, including oxygen reduction and evolution, corrosion and hydrogen evolution reactions. Based on a grand canonical approach relying on the electrochemical potential of individual charged species, a unified treatment of charged defects on the solid side and ions on the water side can be established. This approach is compatible with first-principles calculations where the formation free energy of individual charged species can be calculated and modulated by imposing certain electrochemical potential. Herein, we apply this framework to a system of monoclinic ZrO₂(1̄11)/water interface. The structure, defect chemistry and dynamical behavior of the electric double layer and space charge layer are analyzed with different pH values, water chemistry and doping elements in zirconium oxide. The model predicts ZrO₂ solubility in water and the point of zero charge consistent with the experimentally-measured values. We reveal the effect of dopant elements on the concentrations of oxygen and hydrogen species at the surface of the ZrO₂ passive layer in contact with water, uncovering an intrinsic trade-off between oxygen diffusion and hydrogen pickup during the corrosion of zirconium alloys. The solid/water interface model established here serves as the basis for modeling reaction and transport kinetics under doping and water chemistry effects.

Hydrogen Bond Thermodynamics in Aqueous Acid Solutions: A Combined DFT and Classical Force-Field Approach

The thermodynamics of hydrogen bonds in aqueous and acidic solutions significantly impacts the kinetics and thermodynamics of acid reaction chemistry. We utilize in this work a multiscale approach, combining density functional theory (DFT) with classical molecular dynamics (MD) to model hydrogen bond thermodynamics in an acidic solution. Using thermodynamic cycles, we split the solution phase free energy into its gas phase counterpart plus solvation free energies. We validate this DFT/MD approach by calculating the aqueous phase hydrogen bond free energy between two water molecules (H₂O-···-H₂O), the free energy to transform an H₃O⁺ cation into an H₅O₂⁺ cation, and the hydrogen bond free energy of protonated water clusters (H₃O⁺-···-H₂O and H₅O₂⁺-···-H₂O). The computed equilibrium hydrogen bond free energy of H₂O-···-H₂O is remarkably accurate, especially considering the large individual contributions to the thermodynamic cycle. Turning to cations, we find the ion to be more stable than H₃O⁺ by roughly 1-2 k_BT. This small free energy difference allows for thermal fluctuation between the two idealized motifs, consistent with spectroscopic and simulation studies. Lastly, hydrogen bonding free energies between either H⁺ cation and H₂O in solution were found to be stronger than between two H₂O, though much less so than in vacuum because of dielectric screening in solution. Altogether, our results suggest the DFT/MD approach is promising for application in modeling hydrogen bonding and proton transfer thermodynamics in condensed phases.

How the Bioinspired Fe2Mo6S8 Chevrel Breaks Electrocatalytic Nitrogen Reduction Scaling Relations

The nitrogen reduction reaction (NRR) is a renewable alternative to the energy- and CO₂-intensive Haber-Bosch NH₃ synthesis process but is severely limited by the low activity and selectivity of studied electrocatalysts. The Chevrel phase Fe₂Mo₆S₈ has a surface Fe-S-Mo coordination environment that mimics the nitrogenase FeMo-cofactor and was recently shown to provide state-of-the-art activity and selectivity for NRR. Here, we elucidate the previously unknown NRR mechanism on Fe₂Mo₆S₈ via grand-canonical density functional theory (GC-DFT) that realistically models solvated and biased surfaces. Fe sites of Fe₂Mo₆S₈ selectively stabilize the key *NNH intermediate via a narrow band of free-atom-like surface d-states that selectively hybridize with p-states of *NNH, which results in Fe sites breaking NRR scaling relationships. These sharp d-states arise from an Fe-S bond dissociation during N₂ adsorption that mimics the mechanism of the nitrogenase FeMo-cofactor. Furthermore, we developed a new GC-DFT-based approach for calculating transition states as a function of bias (GC-NEB) and applied it to produce a microkinetic model for NRR at Fe₂Mo₆S₈ that predicts high activity and selectivity, in close agreement with experiments. Our results suggest new design principles that may identify effective NRR electrocatalysts that minimize the barriers for *N₂ protonation and *NH₃ desorption and that may be broadly applied to the rational discovery of stable, multinary electrocatalysts for other reactions where narrow bands of surface d-states can be tuned to selectively stabilize key reaction intermediates and guide selectivity toward a target product. Furthermore, our results highlight the importance of using GC-DFT and GC-NEB to accurately model electrocatalytic reactions.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

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.

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.

The Impact of the Surface Modification on Tin-Doped Indium Oxide Nanocomposite Properties

This review provides an analysis of the theoretical methods to study the effects of surface modification on structural properties of nanostructured indium tin oxide (ITO), mainly by organic compounds. The computational data are compared with experimental data such as X-ray diffraction (XRD), atomic force microscopy (AFM) and energy-dispersive X-ray spectroscopy (EDS) data with the focus on optoelectronic and electrocatalytic properties of the surface to investigate potential relations of these properties and applications of ITO in fields such as biosensing and electronic device fabrication. Our analysis shows that the change in optoelectronic properties of the surface is mainly due to functionalizing the surface with organic molecules and that the electrocatalytic properties vary as a function of size.

Piecewise Multipole-Expansion Implicit Solvation for Arbitrarily Shaped Molecular Solutes

The multipole-expansion (MPE) model is an implicit solvation model used to efficiently incorporate solvent effects in quantum chemistry. Even within the recent direct approach, the multipole basis used in MPE to express the dielectric response still solves the electrostatic problem inefficiently or not at all for solutes larger than approximately ten non-hydrogen atoms. In existing MPE parametrizations, the resulting systematic underestimation of the electrostatic solute-solvent interaction is presently compensated for by a systematic overestimation of nonelectrostatic attractive interactions. Even though the MPE model can thus reproduce experimental free energies of solvation of small molecules remarkably well, the inherent error cancellation makes it hard to assign physical meaning to the individual free-energy terms in the model, raising concerns about transferability. Here we resolve this issue by solving the electrostatic problem piecewise in 3D regions centered around all non-hydrogen nuclei of the solute, ensuring reliable convergence of the multipole series. The resulting method thus allows for a much improved reproduction of the dielectric response of a medium to a solute. Employing a reduced nonelectrostatic model with a single free parameter, in addition to the density isovalue defining the solvation cavity, our method yields free energies of solvation of neutral, anionic, and cationic solutes in water in good agreement with experiment.

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.

Adiabatic versus non-adiabatic electron transfer at 2D electrode materials

2D electrode materials are often deployed on conductive supports for electrochemistry and there is a great need to understand fundamental electrochemical processes in this electrode configuration. Here, an integrated experimental-theoretical approach is used to resolve the key electronic interactions in outer-sphere electron transfer (OS-ET), a cornerstone elementary electrochemical reaction, at graphene as-grown on a copper electrode. Using scanning electrochemical cell microscopy, and co-located structural microscopy, the classical hexaamineruthenium (III/II) couple shows the ET kinetics trend: monolayer > bilayer > multilayer graphene. This trend is rationalized quantitatively through the development of rate theory, using the Schmickler-Newns-Anderson model Hamiltonian for ET, with the explicit incorporation of electrostatic interactions in the double layer, and parameterized using constant potential density functional theory calculations. The ET mechanism is predominantly adiabatic; the addition of subsequent graphene layers increases the contact potential, producing an increase in the effective barrier to ET at the electrode/electrolyte interface.

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.

Structure and dynamics of nanoconfined water and aqueous solutions

This review is devoted to discussing recent progress on the structure, thermodynamic, reactivity, and dynamics of water and aqueous systems confined within different types of nanopores, synthetic and biological. Currently, this is a branch of water science that has attracted enormous attention of researchers from different fields interested to extend the understanding of the anomalous properties of bulk water to the nanoscopic domain. From a fundamental perspective, the interactions of water and solutes with a confining surface dramatically modify the liquid's structure and, consequently, both its thermodynamical and dynamical behaviors, breaking the validity of the classical thermodynamic and phenomenological description of the transport properties of aqueous systems. Additionally, man-made nanopores and porous materials have emerged as promising solutions to challenging problems such as water purification, biosensing, nanofluidic logic and gating, and energy storage and conversion, while aquaporin, ion channels, and nuclear pore complex nanopores regulate many biological functions such as the conduction of water, the generation of action potentials, and the storage of genetic material. In this work, the more recent experimental and molecular simulations advances in this exciting and rapidly evolving field will be reported and critically discussed.

Electric fields and potentials in condensed phases

The electric fields and potentials inside and at the interface of matter are relevant to many branches of physics, chemistry, and biology. Accurate quantification of these fields and/or potentials is essential to control and exploit chemical and physical transformations. Before we understand the response of matter to external fields, it is first important to understand the intrinsic interior and interfacial fields and potentials, both classically and quantum mechanically, as well as how they are probed experimentally. Here we compare and contrast, beginning with the hydrogen atom in vacuum and ending with concentrated aqueous NaCl electrolyte, both classical and quantum mechanical electric potentials and fields. We make contact with experimental vibrational Stark, electrochemical, X-ray, and electron spectroscopic probes of these potentials and fields, outline relevant conceptual difficulties, and underscore the advantage of electron holography as a basis to better understand electrostatics in matter.

Recent Progress toward Ab Initio Modeling of Electrocatalysis

Electrode potential is the key factor for controlling electrocatalytic reactions at electrochemical interfaces, and moreover, it is also known that the pH and solutes (e.g., cations) of the solution have prominent effects on electrocatalysis. Understanding these effects requires microscopic information on the electrochemical interfaces, in which theoretical simulations can play an important role. This Perspective summarizes the recent progress in method development for modeling electrochemical interfaces, including different methods for describing the electrolytes at the interfaces and different schemes for charging up the electrode surfaces. In the final section, we provide an outlook for future development in modeling methods and their applications to electrocatalysis.

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.

Ab initiomodelling of interfacial electrochemical properties: beyond implicit solvation limitations

First-principles calculations are an important tool to investigate the complex processes occurring at solid/liquid interfaces which are at the heart of modern technologies. Currently, capturing the whole electrochemical environment at an interface, including the applied potential and solvation, still remains challenging as it necessitates to couple different approaches whose interactions are not fully understood. In this work, a grand canonical density functional theory approach is coupled with solvation models to investigate the electrochemical interfaces under applied potential. We show that a parametrized polarizable continuum model (PCM) which represent solvation in a mean field approach by a continuous polarizable media, possesses catastrophic limitations for the modelling of ionic and charged interfaces. We reveal the origin of PCM instabilities under chemical or electrochemical strong oxidation to be the consequence of a phase transition in the surface Li electronic structure. Thus, PCM undergoes an unphysical response to this phase transition by penetrating within the atomic radius of surface Li atoms. To recover a physical response, an explicit first solvation shell has to be included in addition to the PCM in order to properly describe the electrochemistry of the interface. The Fukui functions show that the first solvation shell becomes involved in the redox process as solvent electron doublet is transferred to the acidic Li⁺. If another explicit solvent layer is added, the interface electrochemical properties become independent of the PCM parameters: in particular capacitance can then be computed from a parameter-free electrochemical approach. This is an important conclusion as the experimental electrochemical capacitance are not easily found and thus the parametrization of the PCM for electrochemical interface can be difficult. This approach can easily be applied to investigate electrochemical properties at the atomic scale and generalized to any electrochemical device for which interfaces play a crucial role.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Demystifying the Stern layer at a metal-electrolyte interface: Local dielectric constant, specific ion adsorption, and partial charge transfer

Electric double layer (EDL) represents one of the most basic concepts in electrochemistry and is pertinent to diverse engineering applications ranging from electrocatalysis to energy storage. Whereas phenomenological and coarse-grained models have been long established to describe ionic distributions in the diffuse layer, a faithful prediction of the physicochemical properties of the electrode-electrolyte interface from a molecular perspective remains a daunting challenge. In this work, we investigate the charging behavior of an Ag (111) electrode in NaF aqueous solutions leveraging experimental results and theoretical calculations based on the classical density functional theory for ion distributions in the diffuse layer and on the joint density functional theory (JDFT) for the electronic structure. When the Ag electrode is applied with a negative voltage, the surface charge density can be reasonably described by assuming a neutral Stern layer with the dielectric constant dependent on the local electric field as predicted by the Kirkwood equation. However, the specific adsorption of F^- ions must be considered when the electrode is positively charged and the fluoride adsorption can be attributed to both physical and chemical interactions. Qualitatively, F^- binding and partial charge transfer are supported by JDFT calculations, which predict an increased binding energy as the voltage increases. Our findings shed insight on the molecular characteristics of the Stern layer and the charge behavior of adsorbed species not specified by conventional EDL models.

Electronic structure behavior of PbO2, IrO2, and SnO2 metal oxide surfaces (110) with dissociatively adsorbed water molecules as a function of the chemical potential

A detailed analysis of the electronic structure of three different electrochemical interfaces as a function of the chemical potential (μ) is performed using the grand canonical density functional theory in the joint density functional theory formulation. Changes in the average number of electrons and the density of states are also described. The evaluation of the global softness, which measures the tendency of the system to gain or lose electrons, is straightforward under this formalism. The observed behavior of these quantities depends on the electronic nature of the electrochemical interfaces.

Resolving the Geometry/Charge Puzzle of the c(2 × 2)-Cl Cu(100) Electrode

Potential-induced changes in charge and surface structure are significant drivers of the reactivity of electrochemical interfaces but are frequently difficult to decouple from the effects of surface solvation. Here, we consider the Cu(100) surface with a c(2 × 2)-Cl adlayer, a model surface with multiple geometry measurements under both ultrahigh vacuum and electrochemical conditions. Under aqueous electrochemical conditions, the measured Cu-Cl interplanar separation (dCu-Cl) increases by at least 0.3 Å relative to that under ultrahigh vacuum conditions. This large geometry change is unexpected for a hydrophobic surface, and it requires invoking a negative charge on the Cl-covered surface which is much greater than expected from the work function and our capacitance measurements. To resolve this inconsistency we employ ab initio calculations and find that the Cu-Cl separation increases with charging at a rate of 0.7 Å/e- per Cl atom. The larger Cu-Cl bond distance increases the surface dipole and, therefore, the work function of the interface, contributing to the negative charge under fixed potential electrochemical conditions. Interactions with water are not needed to explain either the large charge or large Cu-Cl interplanar spacing of this surface under electrochemical conditions.

Quantifying Uncertainties in Solvation Procedures for Modeling Aqueous Phase Reaction Mechanisms

Computational quantum chemistry provides fundamental chemical and physical insights into solvated reaction mechanisms across many areas of chemistry, especially in homogeneous and heterogeneous renewable energy catalysis. Such reactions may depend on explicit interactions with ions and solvent molecules that are nontrivial to characterize. Rigorously modeling explicit solvent effects with molecular dynamics usually brings steep computational costs while the performance of continuum solvent models such as polarizable continuum model (PCM), charge-asymmetric nonlocally determined local-electric (CANDLE), conductor-like screening model for real solvents (COSMO-RS), and effective screening medium method with the reference interaction site model (ESM-RISM) are less well understood for reaction mechanisms. Here, we revisit a fundamental aqueous hydride transfer reaction-carbon dioxide (CO₂) reduction by sodium borohydride (NaBH₄)-as a test case to evaluate how different solvent models perform in aqueous phase charge migrations that would be relevant to renewable energy catalysis mechanisms. For this system, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations almost exactly reproduced energy profiles from QM simulations, and the Na⁺ counterion in the QM/MM simulations plays an insignificant role over ensemble averaged trajectories that describe the reaction pathway. However, solvent models used on static calculations gave much more variability in data depending on whether the system was modeled using explicit solvent shells and/or the counterion. We pinpoint this variability due to unphysical descriptions of charge-separated states in the gas phase (i.e., self-interaction errors), and we show that using more accurate hybrid functionals and/or explicit solvent shells lessens these errors. This work closes with recommended procedures for treating solvation in future computational efforts in studying renewable energy catalysis mechanisms.

A few basic concepts in electrochemical carbon dioxide reduction

In this perspective, I discuss a few basic concepts in fundamental mechanistic studies of electrochemical carbon dioxide reduction.

Electrochemical carbon dioxide (CO2) reduction has the potential to sustainably produce carbon-based fuels and chemicals while mitigating the increasing levels of CO2 in the atmosphere. In this comment, the author discusses a few basic concepts in the fundamental mechanistic studies of electrochemical CO2 reduction.

Theoretical Understandings of Graphene-based Metal Single-Atom Catalysts: Stability and Catalytic Performance

Research on heterogeneous single-atom catalysts (SACs) has become an emerging frontier in catalysis science because of their advantages in high utilization of noble metals, precisely identified active sites, high selectivity, and tunable activity. Graphene, as a one-atom-thick two-dimensional carbon material with unique structural and electronic properties, has been reported to be a superb support for SACs. Herein, we provide an overview of recent progress in investigations of graphene-based SACs. Among the large number of publications, we will selectively focus on the stability of metal single-atoms (SAs) anchored on different sites of graphene support and the catalytic performances of graphene-based SACs for different chemical reactions, including thermocatalysis and electrocatalysis. We will summarize the fundamental understandings on the electronic structures and their intrinsic connection with catalytic properties of graphene-based SACs, and also provide a brief perspective on the future design of efficient SACs with graphene and graphene-like materials.