First-principles molecular dynamics at a constant electrode potential

Alkali cation-induced cathodic corrosion in Cu electrocatalysts

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

Mechanism of surface oxygen-containing species promoted electrocatalytic CO2 reduction

Oxygen-containing species have been demonstrated to play a key role in facilitating electrocatalytic CO2 reduction (CO2RR), particularly in enhancing the selectivity towards multi-carbon (C2+) products. However, the underlying promotion mechanism is still under debate, which greatly limits the rational optimization of the catalytic performance of CO2RR. Herein, taking CO2 and O2 co-electrolysis over Cu as the prototype, we successfully clarified how O2 boosts CO2RR from a new perspective by employing comprehensive theoretical simulations. Our results demonstrated that O2 in feed gas can be rapidly reduced into *OH, leading to the partial oxidation of Cu surface under reduction conditions. Surface *OH accelerates the formation of quasi-specifically adsorbed K+ due to the electrostatic interaction between *OH and K+ ions, which significantly increases the concentration of K+ near the Cu surface. These quasi-specifically adsorbed K+ ions can not only lower the C-C coupling barriers but also promote the hydrogenation of CO2 to improve the CO yield rate, which are responsible for the remarkably enhanced efficiency of C2+ products. During the whole process, O2 co-electrolysis plays an indispensable role in stabilizing surface *OH. This mechanism can be also adopted to understand the effect of high pH of electrolyte and residual O in oxide-derived Cu (OD-Cu) on the catalytic efficiency towards C2+ products. Therefore, our work provides new insights into strategies for improving C2+ products on the Cu-based catalysts, i.e., maintaining partial oxidation of surface under reduction conditions.

On the Thermodynamic Equivalence of Grand Canonical, Infinite-Size, and Capacitor-Based Models in First-Principle Electrochemistry

First principles-based computational and theoretical methods are constantly evolving trying to overcome the many obstacles towards a comprehensive understanding of electrochemical processes on an atomistic level. One of the major challenges has been the determination of reaction energetics under a constant potential. Here, a theoretical framework was proposed applying standard electronic structure methods and extrapolating to the infinite-cell size limit where reactions do not alter the potential. Today, electronically grand canonical modifications to electronic structure methods, holding the potential constant by varying the number of electrons in a finite simulation cell, become increasingly popular. In this perspective, we show that these two schemes are thermodynamically equivalent. Further, we link these methods to capacitive models of the interface, in the limit that the capacitance of the charging components (whether continuum or atomistic) are equal and invariant along the reaction pathway. We benchmark the three approaches with an example of alkali cation adsorption on Pt(111) showing that all three approaches converge in the cases of Li, Na and K. For Cs, however, strong deviation from the ideal conditions leads to a spread in the respective results. We discuss the latter by highlighting the cases of broken equivalence and assumptions among the approaches.

Revealing Interface Polarization Effects on the Electrical Double Layer with Efficient Open Boundary Simulations under Potential Control

A major challenge in modeling interfacial processes in electrochemical (EC) devices is performing simulations at constant potential. This requires an open-boundary description of the electrons, so that they can enter and leave the computational cell. To enable realistic modeling of EC processes under potential control we have interfaced density functional theory with the hairy probe method in the weak coupling limit (Zauchner et al. Phys. Rev. B 2018, 97, 045116). Our implementation was systematically tested using simple parallel-plate capacitor models with pristine surfaces and a single layer of adsorbed water molecules. Remarkably, our code's efficiency is comparable with a standard DFT calculation. We reveal that local field effects at the electrical double layer induced by the change of applied potential can significantly affect the energies of chemical steps in heterogeneous electrocatalysis. Our results demonstrate the importance of an explicit modeling of the applied potential in a simulation and provide an efficient tool to control this critical parameter.

Activation Energies of Heterogeneous Electrocatalysis: A Theoretical Perspective

Heterogeneous electrochemistry is important for various applications. However, currently, there is limited information about activation energies. In this invited review, we review the challenges associated with calculating these activation energies. Specifically, we highlight three key difficulties in atomistic modeling: liquid structure, electrode potential, and electrolyte ions, along with state-of-the-art methods to address them. We aim to inspire more studies in the field of activation energies to better understand and design heterogeneous electrocatalysts.

Accelerating the Reaction Kinetics of CO2 Reduction to Multi-Carbon Products by Synergistic Effect between Cation and Aprotic Solvent on Copper Electrodes

Improving the selectivity of electrochemical CO2 reduction to multi-carbon products (C2+ ) is an important and highly challenging topic. In this work, we propose and validate an effective strategy to improve C2+ selectivity on Cu electrodes, by introducing a synergistic effect between cation (Na+ ) and aprotic solvent (DMSO) to the electrolyte. Based on constant potential ab initio molecular dynamics simulations, we first revealed that Na+ facilitates C-C coupling while inhibits CH3 OH/CH4 products via reducing the water network connectivity near the electrode. Furthermore, the water network connectivity was further decreased by introducing an aprotic solvent DMSO, leading to suppression of both C1 production and hydrogen evolution reaction with minimal effect on *OCCO* hydrogenation. The synergistic effect enhancing C2 selectivity was also experimentally verified through electrochemical measurements. The results showed that the Faradaic efficiency of C2 increases from 9.3 % to 57 % at 50 mA/cm2 under a mixed electrolyte of NaHCO3 and DMSO compared to a pure NaHCO3 , which can significantly enhance the selectivity of the C2 product. Therefore, our discovery provides an effective electrolyte-based strategy for tuning CO2 RR selectivity through modulating the microenvironment at the electrode-electrolyte interface.

Why efficient bifunctional hydrogen electrocatalysis requires a change in the reaction mechanism

Hydrogen evolution reaction (HER) and hydrogen oxidation reaction (HOR) are both two-electron processes that culminate in the formation or consumption of gaseous hydrogen in an electrolyzer or a fuel cell, respectively. Unitized regenerative proton exchange membrane fuel cells merge these two functionalities into one device, allowing to switch between the two modes of operation. This prompts the quest for efficient bifunctional electrode materials catalyzing the HER and HOR with reasonable reaction rates at low overpotentials. In the present study using a data-driven framework, we identify a general criterion for efficient bifunctional performance in the hydrogen electrocatalysis, which refers to a change in the reaction mechanism when switching from cathodic to anodic working conditions. The obtained insight can be used in future studies based on density functional theory to pave the design of efficient HER and HOR catalysts by a dedicated consideration of the kinetics in the analysis of reaction mechanisms.

Constant Potential Thermodynamic Integration for Obtaining the Free Energy Profile of Electrochemical Reaction

In this work, we advanced an efficient free energy sampling method based on constrained ab initio molecular dynamics (cAIMD) with a fully explicit solvent layer to depict the electrochemical reaction process at constant surface charge density, named the "Constant-Potential Thermodynamic Integration (CPTI)" method. For automatically adjusting surface charge density at different states, we built an "on-the-fly" procedure which is capable of managing all the necessary steps during cAIMD simulations, including the system pre-equilibrium, surface charge density updating, and force sampling. We applied it to predict the potential-dependent free energy profiles of CO2 adsorption on a single-atom catalyst. The results show that our method can not only account for changes in electrostatic potential energy associated with potential but also consider the potential-induced solvation effects. Our approach enables the accurate simulation of electrochemical environment by presenting the complete solid-liquid interface and efficient computation of electrocatalytic reaction energetics based on a robust potential descriptor.

Issues on DFT+U calculations of organic diradicals

The diradical state is an important electronic state for understanding molecular functions and should be elucidated for the in silico design of functional molecules and their application to molecular devices. The density functional theory calculation with plane-wave basis and correction of the on-site Coulomb parameter U (DFT+U/plane-wave calculation) is a good candidate of high-throughput calculations of diradical-band interactions. However, it has not been investigated in detail to what extent the DFT+U/plane-wave calculation can be used to calculate organic diradicals with a high degree of accuracy. In the present study, using typical organic diradical molecules (bisphenalenyl molecules) as model systems, the discrepancy in the optimum U values between the two electronic states (open-shell singlet and triplet) that compose the diradical state is detected. The calculated results show that the reason for this U value discrepancy is the difference in electronic delocalisation due to π-conjugation between the open-shell singlet and triplet states, and that the effect of U discrepancy becomes large as diradical character decreases. This indicates that it is necessary to investigate the U value discrepancy with reference to the calculated results by more accurate methods or to experimental values when calculating organic diradicals with low diradical character. For this investigation, the local magnetic moments, unpaired beta electron numbers, and effective magnetic exchange integral values can be used as reference values. For the effective magnetic exchange integral values, the effects of U discrepancy are partially cancelled out. However, because the effects may not be completely offset, care should be taken when using the effective magnetic exchange integral value as a reference. Furthermore, a comparison of DFT+U and hybrid-DFT calculations shows that the DFT+U underestimates the HOMO-LUMO gap of bisphenalenyls, although a qualitative discussion of the gap is possible.

Controlled Electrochemical Barrier Calculations without Potential Control

The knowledge of electrochemical activation energies under applied potential conditions is a prerequisite for understanding catalytic activity at electrochemical interfaces. Here, we present a new set of methods that can compute electrochemical barriers with accuracy comparable to that of constant potential grand canonical approaches, without the explicit need for a potentiostat. Instead, we Legendre transform a set of constant charge, canonical reaction paths. Additional straightforward approximations offer the possibility to compute electrochemical barriers at a fraction of computational cost and complexity, and the analytical inclusion of geometric response highlights the importance of incorporating electronic as well as the geometric degrees of freedom when evaluating electrochemical barriers.

What Is the Rate-Limiting Step of Oxygen Reduction Reaction on Fe-N-C Catalysts?

Oxygen reduction reaction (ORR) is essential to various renewable energy technologies. An important catalyst for ORR is single iron atoms embedded in nitrogen-doped graphene (Fe-N-C). However, the rate-limiting step of the ORR on Fe-N-C is unknown, significantly impeding understanding and improvement. Here, we report the activation energies of all of the steps, calculated by ab initio molecular dynamics simulations under constant electrode potential. In contrast to the common belief that a hydrogenation step limits the reaction rate, we find that the rate-limiting step is oxygen molecule replacing adsorbed water on Fe. This occurs through concerted motion of H2O desorption and O2 adsorption, without leaving the site bare. Interestingly, despite being an apparent "thermal" process that is often considered to be potential-independent, the barrier reduces with the electrode potential. This can be explained by stronger Fe-O2 binding and weaker Fe-H2O binding at a lower potential, due to O2 gaining electrons and H2O donating electrons to the catalyst. Our study offers new insights into the ORR on Fe-N-C and highlights the importance of kinetic studies in heterogeneous electrochemistry.

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.

Electric Double Layer Effects in Electrocatalysis: Insights from Ab Initio Simulation and Hierarchical Continuum Modeling

Structures of the electric double layer (EDL) at electrocatalytic interfaces, which are modulated by the material properties, the electrolyte characteristics (e.g., the pH, the types and concentrations of ions), and the electrode potential, play crucial roles in the reaction kinetics. Understanding the EDL effects in electrocatalysis has attracted substantial research interest in recent years. However, the intrinsic relationships between the specific EDL structures and electrocatalytic kinetics remain poorly understood, especially on the atomic scale. In this Perspective, we briefly review the recent advances in deciphering the EDL effects mainly in hydrogen and oxygen electrocatalysis through a multiscale approach, spanning from the atomistic scale simulated by ab initio methods to the macroscale by a hierarchical approach. We highlight the importance of resolving the local reaction environment, especially the local hydrogen bond network, in understanding EDL effects. Finally, some of the remaining challenges are outlined, and an outlook for future developments in these exciting frontiers is provided.

A Combined Reaction Path Search and Hybrid Solvation Method for the Systematic Exploration of Elementary Reactions at the Solid-Liquid Interface

We present a combined simulation method of single-component artificial force induced reaction (SC-AFIR) and effective screening medium combined with the reference interaction site model (ESM-RISM), termed SC-AFIR+ESM-RISM. SC-AFIR automatically and systematically explores the chemical reaction pathway, and ESM-RISM directly simulates the precise electronic structure at the solid-liquid interface. Hence, SC-AFIR+ESM-RISM enables us to explore reliable reaction pathways at the solid-liquid interface. We applied it to explore the dissociation pathway of an H2O molecule at the Cu(111)/water interface. The reaction path networks of the whole reaction and the minimum energy paths from H2O to H2 + O depend on the interfacial environment. The qualitative difference in the energy diagrams and the resulting change in the kinematically favored dissociation pathway upon changing the solvation environments are discussed. We believe that SC-AFIR+ESM-RISM will be a powerful tool to reveal the details of chemical reactions in surface catalysis and electrochemistry.

Grand Canonical Ensemble Modeling of Electrochemical Interfaces Made Simple

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

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.

Approximating constant potential DFT with canonical DFT and electrostatic corrections

The complexity of electrochemical interfaces has led to the development of several approximate density functional theory (DFT)-based schemes to study reaction thermodynamics and kinetics as a function of electrode potential. While fixed electrode potential conditions can be simulated with grand canonical ensemble DFT (GCE-DFT), various electrostatic corrections on canonical, constant charge DFT are often applied instead. In this work, we present a systematic derivation and analysis of the different electrostatic corrections on canonical DFT to understand their physical validity, implicit assumptions, and scope of applicability. Our work highlights the need to carefully address the suitability of a given model for the problem under study, especially if physical or chemical insight in addition to reaction energetics is sought. In particular, we analytically show that the different corrections cannot differentiate between electrostatic interactions and covalent or charge-transfer interactions. By numerically testing different models for CO₂ adsorption on a single-atom catalyst as a function of the electrode potential, we further show that computed capacitances, dipole moments, and the obtained physical insight depend sensitively on the chosen approximation. These features limit the scope, generality, and physical insight of these corrective schemes despite their proven practicality for specific systems and energetics. Finally, we suggest guidelines for choosing different electrostatic corrections and propose the use of conceptual DFT to develop more general approximations for electrochemical interfaces and reactions using canonical DFT.

Electrochemical hydrogen evolution on Pt-based catalysts from a theoretical perspective

Hydrogen evolution reaction (HER) by splitting water is a key technology toward a clean energy society, where Pt-based catalysts were long known to have the highest activity under acidic electrochemical conditions but suffer from high cost and poor stability. Here, we overview the current status of Pt-catalyzed HER from a theoretical perspective, focusing on the methodology development of electrochemistry simulation, catalytic mechanism, and catalyst stability. Recent developments in theoretical methods for studying electrochemistry are introduced, elaborating on how they describe solid-liquid interface reactions under electrochemical potentials. The HER mechanism, the reaction kinetics, and the reaction sites on Pt are then summarized, which provides an atomic-level picture of Pt catalyst surface dynamics under reaction conditions. Finally, state-of-the-art experimental solutions to improve catalyst stability are also introduced, which illustrates the significance of fundamental understandings in the new catalyst design.

Ab initio study of water dissociation on a charged Pd(111) surface

The interactions between molecules and electrode surfaces play a key role in electrochemical processes and are a subject of extensive research, both experimental and theoretical. In this paper, we address the water dissociation reaction on a Pd(111) electrode surface, modeled as a slab embedded in an external electric field. We aim at unraveling the relationship between surface charge and zero-point energy in aiding or hindering this reaction. We calculate the energy barriers with dispersion-corrected density-functional theory and an efficient parallel implementation of the nudged-elastic-band method. We show that the lowest dissociation barrier and consequently the highest reaction rate take place when the field reaches a strength where two different geometries of the water molecule in the reactant state are equally stable. The zero-point energy contributions to this reaction, on the other hand, remain nearly constant across a wide range of electric field strengths, despite significant changes in the reactant state. Interestingly, we show that the application of electric fields that induce a negative charge on the surface can make nuclear tunneling more significant for these reactions.

Frequency-Dependent Impedance of Nanocapacitors from Electrode Charge Fluctuations as a Probe of Electrolyte Dynamics

The frequency-dependent impedance is a fundamental property of electrical components. We show that it can be determined from the equilibrium dynamical fluctuations of the electrode charge in constant-potential molecular simulations, extending in particular a fluctuation-dissipation relation for the capacitance recovered in the low-frequency limit and provide an illustration on water-gold nanocapacitors. This Letter opens the way to the interpretation of electrochemical impedance measurements in terms of microscopic mechanisms, directly from the dynamics of the electrolyte, or indirectly via equivalent circuit models as in experiments.

Smart Graphene-Based Electrochemical Nanobiosensor for Clinical Diagnosis: Review

The technological improvement in the field of physics, chemistry, electronics, nanotechnology, biology, and molecular biology has contributed to the development of various electrochemical biosensors with a broad range of applications in healthcare settings, food control and monitoring, and environmental monitoring. In the past, conventional biosensors that have employed bioreceptors, such as enzymes, antibodies, Nucleic Acid (NA), etc., and used different transduction methods such as optical, thermal, electrochemical, electrical and magnetic detection, have been developed. Yet, with all the progresses made so far, these biosensors are clouded with many challenges, such as interference with undesirable compound, low sensitivity, specificity, selectivity, and longer processing time. In order to address these challenges, there is high need for developing novel, fast, highly sensitive biosensors with high accuracy and specificity. Scientists explore these gaps by incorporating nanoparticles (NPs) and nanocomposites (NCs) to enhance the desired properties. Graphene nanostructures have emerged as one of the ideal materials for biosensing technology due to their excellent dispersity, ease of functionalization, physiochemical properties, optical properties, good electrical conductivity, etc. The Integration of the Internet of Medical Things (IoMT) in the development of biosensors has the potential to improve diagnosis and treatment of diseases through early diagnosis and on time monitoring. The outcome of this comprehensive review will be useful to understand the significant role of graphene-based electrochemical biosensor integrated with Artificial Intelligence AI and IoMT for clinical diagnostics. The review is further extended to cover open research issues and future aspects of biosensing technology for diagnosis and management of clinical diseases and performance evaluation based on Linear Range (LR) and Limit of Detection (LOD) within the ranges of Micromolar µM (10^-6), Nanomolar nM (10^-9), Picomolar pM (10^-12), femtomolar fM (10^-15), and attomolar aM (10^-18).

Coupling nitrate capture with ammonia production through bifunctional redox-electrodes

Nitrate is a ubiquitous aqueous pollutant from agricultural and industrial activities. At the same time, conversion of nitrate to ammonia provides an attractive solution for the coupled environmental and energy challenge underlying the nitrogen cycle, by valorizing a pollutant to a carbon-free energy carrier and essential chemical feedstock. Mass transport limitations are a key obstacle to the efficient conversion of nitrate to ammonia from water streams, due to the dilute concentration of nitrate. Here, we develop bifunctional electrodes that couple a nitrate-selective redox-electrosorbent (polyaniline) with an electrocatalyst (cobalt oxide) for nitrate to ammonium conversion. We demonstrate the synergistic reactive separation of nitrate through solely electrochemical control. Electrochemically-reversible nitrate uptake greater than 70 mg/g can be achieved, with electronic structure calculations and spectroscopic measurements providing insight into the underlying role of hydrogen bonding for nitrate selectivity. Using agricultural tile drainage water containing dilute nitrate (0.27 mM), we demonstrate that the bifunctional electrode can achieve a 8-fold up-concentration of nitrate, a 24-fold enhancement of ammonium production rate (108.1 ug h^-1 cm^-2), and a >10-fold enhancement in energy efficiency when compared to direct electrocatalysis in the dilute stream. Our study provides a generalized strategy for a fully electrified reaction-separation pathway for modular nitrate remediation and ammonia production.

Dielectric Properties of Nanoconfined Water from Ab Initio Thermopotentiostat Molecular Dynamics

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

Unraveling the electrocatalytic reduction mechanism of enols on copper in aqueous media

Deoxygenation of aldehydes and their tautomers to alkenes and alkanes has implications in refining biomass-derived fuels for use as transportation fuel. Electrochemical deoxygenation in ambient, aqueous solution is also a potential green synthesis strategy for terminal olefins. In this manuscript, direct electrochemical conversion of vinyl alcohol and acetaldehyde on polycrystalline Cu to ethanol, ethylene and ethane; and propenol and propionaldehyde to propanol, propene and propane is reported. Sensitive detection was achieved using a rotating disk electrode coupled with gas chromatography-mass spectrometry. In-situ attenuated total reflection surface-enhanced infrared absorption spectroscopy, and in-situ Raman spectroscopy confirmed the adsorption of the vinyl alcohol. Calculations using canonical and grand-canonical density functional theory and experimental findings suggest that the rate-determining step for ethylene and ethane formation is an electron transfer step to the adsorbed vinyl alcohol. Finally, we extend our conclusions to the enol reaction from higher-order soluble aldehyde and ketone. The products observed from the reduction reaction also sheds insights into plausible reaction pathways of CO₂ to C₂ and C₃ products.

Understanding the electrochemical deoxygenation pathway of aldehydes and ketones is important yet challenging. Here the authors use acetaldehyde as a model system to elucidate the role of enols in the electroreduction of aldehydes and ketones, which may shed light on the reaction pathway of CO2 to C2 and C3 products.

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

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

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.

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.

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.

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

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

A molecular perspective on induced charges on a metallic surface

Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode-electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode-electrolyte interfaces.

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.

Recent Advances in Corrosion Science Applicable To Disposal of High-Level Nuclear Waste

High-level radioactive waste is accumulating at temporary storage locations around the world and will eventually be placed in deep geological repositories. The waste forms and containers will be constructed from glass, crystalline ceramic, and metallic materials, which will eventually come into contact with water, considering that the period of performance required to allow sufficient decay of dangerous radionuclides is on the order of 10⁵-10⁶ years. Corrosion of the containers and waste forms in the aqueous repository environment is therefore a concern. This Review describes the recent advances of the field of materials corrosion that are relevant to fundamental materials science issues associated with the long-term performance assessment and the design of materials with improved performance, where performance is defined as resistance to aqueous corrosion. Glass, crystalline ceramics, and metals are discussed separately, and the near-field interactions of these different material classes are also briefly addressed. Finally, recommendations for future directions of study are provided.

Origin of Selective Production of Hydrogen Peroxide by Electrochemical Oxygen Reduction

Oxygen reduction reaction (ORR) is one of the most important electrochemical reactions. Starting from a common reaction intermediate *-O-OH, the ORR splits into two pathways, either producing hydrogen peroxide (H2O2) by breaking the *-O bond or leading to water formation by breaking the O-OH bond. However, it is puzzling why many catalysts, despite the strong thermodynamic preference for the O-OH breaking, exhibit high selectivity for hydrogen peroxide. Moreover, the selectivity is dependent on the potential and pH, which remain not understood. Here we develop an advanced first-principles model for effective calculation of the electrochemical reaction kinetics at the solid-water interface, which were not accessible by conventional models. Using this model to study representative catalysts for H2O2 production, we find that breaking the O-OH bond can have a higher energy barrier than breaking *-O, due to the rigidity of the O-OH bond. Importantly, we reveal that the selectivity dependence on potential and pH is rooted into the proton affinity to the former/later O in *-O-OH. For single cobalt atom catalyst, decreasing potential promotes proton adsorption to the former O, thereby increasing the H2O2 selectivity. In contrast, for the carbon catalyst, the proton prefers the latter O, resulting in a lower H2O2 selectivity in acid condition. These findings explain the experiments and highlight the kinetic origins of the selectivity. Our work improves the understanding of ORR by uncovering the proton affinity as a new factor and provides a new model to effectively simulate the atomic-level kinetics of heterogeneous electrochemistry.

Thermodynamic cyclic voltammograms: peak positions and shapes

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

Molecular Simulation of Electrode-Solution Interfaces

Many key industrial processes, from electricity production, conversion, and storage to electrocatalysis or electrochemistry in general, rely on physical mechanisms occurring at the interface between a metallic electrode and an electrolyte solution, summarized by the concept of an electric double layer, with the accumulation/depletion of electrons on the metal side and of ions on the liquid side. While electrostatic interactions play an essential role in the structure, thermodynamics, dynamics, and reactivity of electrode-electrolyte interfaces, these properties also crucially depend on the nature of the ions and solvent, as well as that of the metal itself. Such interfaces pose many challenges for modeling because they are a place where quantum chemistry meets statistical physics. In the present review, we explore the recent advances in the description and understanding of electrode-electrolyte interfaces with classical molecular simulations, with a focus on planar interfaces and solvent-based liquids, from pure solvent to water-in-salt electrolytes.

Controlling potential difference between electrodes based on self-consistent-charge density functional tight binding

A proper understanding and description of the electronic response of the electrode surfaces in electrochemical systems are quite important because the interactions between the electrode surface and electrolyte give rise to unique and useful interfacial properties. Atomistic modeling of the electrodes requires not only an accurate description of the electronic response under a constant-potential condition but also computational efficiency in order to deal with systems large enough to investigate the interfacial electrolyte structures. We thus develop a self-consistent-charge density functional tight binding based method to model a pair of electrodes in electrochemical cells under the constant-potential condition. The method is more efficient than the (ab initio) density functional theory calculations so that it can treat systems as large as those studied in classical atomistic simulations. It can also describe the electronic response of electrodes quantum mechanically and more accurately than the classical counterparts. The constant-potential condition is introduced through a Legendre transformation of the electronic energy with respect to the difference in the number of electrons in the two electrodes and their electrochemical potential difference, through which the Kohn-Sham equations for each electrode are variationally derived. The method is applied to platinum electrodes faced parallel to each other under an applied voltage. The electronic response to the voltage and a charged particle is compared with the result of a classical constant-potential method based on the chemical potential equalization principle.

Dielectric Properties of Nanoconfined Water: A Canonical Thermopotentiostat Approach

We introduce a novel approach to sample the canonical ensemble at constant temperature and applied electric potential. Our approach can be straightforwardly implemented into any density-functional theory code. Using thermopotentiostat molecular dynamics simulations allows us to compute the dielectric constant of nanoconfined water without any assumptions for the dielectric volume. Compared to the commonly used approach of calculating dielectric properties from polarization fluctuations, our thermopotentiostat technique reduces the required computational time by 2 orders of magnitude.

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

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

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

Key role of chemistry versus bias in electrocatalytic oxygen evolution

The oxygen evolution reaction has an important role in many alternative-energy schemes because it supplies the protons and electrons required for converting renewable electricity into chemical fuels^1-3. Electrocatalysts accelerate the reaction by facilitating the required electron transfer⁴, as well as the formation and rupture of chemical bonds⁵. This involvement in fundamentally different processes results in complex electrochemical kinetics that can be challenging to understand and control, and that typically depends exponentially on overpotential^1,2,6,7. Such behaviour emerges when the applied bias drives the reaction in line with the phenomenological Butler-Volmer theory, which focuses on electron transfer⁸, enabling the use of Tafel analysis to gain mechanistic insight under quasi-equilibrium^9-11 or steady-state assumptions¹². However, the charging of catalyst surfaces under bias also affects bond formation and rupture^13-15, the effect of which on the electrocatalytic rate is not accounted for by the phenomenological Tafel analysis⁸ and is often unknown. Here we report pulse voltammetry and operando X-ray absorption spectroscopy measurements on iridium oxide to show that the applied bias does not act directly on the reaction coordinate, but affects the electrocatalytically generated current through charge accumulation in the catalyst. We find that the activation free energy decreases linearly with the amount of oxidative charge stored, and show that this relationship underlies electrocatalytic performance and can be evaluated using measurement and computation. We anticipate that these findings and our methodology will help to better understand other electrocatalytic materials and design systems with improved performance.

The electrochemical interface in first-principles calculations

First-principles predictions play an important role in understanding chemistry at the electrochemical interface. Electronic structure calculations are straightforward for vacuum interfaces, but do not easily account for the interfacial fields and solvation that fundamentally change the nature of electrochemical reactions. Prevalent techniques for first-principles prediction of electrochemical processes range from expensive explicit solvation using ab initio molecular dynamics, through a hierarchy of continuum solvation techniques, to neglecting solvation and interfacial field effects entirely. Currently, no single approach reliably captures all relevant effects of the electrochemical double layer in first-principles calculations. This review systematically lays out the relation between all major approaches to first-principles electrochemistry, including the key approximations and their consequences for accuracy and computational cost. Focusing on ab initio methods for thermodynamic properties of aqueous interfaces, we first outline general considerations for modeling electrochemical interfaces, including solvent and electrolyte dynamics and electrification. We then present the specifics of various explicit and implicit models of the solvent and electrolyte. Finally, we discuss the compromise between computational efficiency and accuracy, and identify key outstanding challenges and future opportunities in the wide range of techniques for first-principles electrochemistry.

Water dynamics at electrified graphene interfaces: a jump model perspective

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