Models of Electron Transfer at Different Electrode Materials

Electric Fields at Solid-Liquid Interfaces: Insights from Molecular Dynamics Simulation

In this review, we explore the electrostatic environment of the interface between a solid and dilute electrolyte solution, with an emphasis on the electric field profiles that these systems produce. We review the theoretical formalism that connects electrostatic potential profiles, electric field profiles, and charge density fields. This formalism has served as the basis for our understanding of interfacial electric fields and their influences on microscopic chemical and physical processes. Comparing various traditional models of interfacial electrostatics to the results of molecular dynamics (MD) simulation yields mutually inconsistent descriptions of the interfacial electric field profile. We present MD simulation results demonstrating that the average electric field profiles experienced by particles at the interface differ from the properties of traditional models and from the fields derived from the mean charge density of atomistic simulations. Furthermore, these experienced electric field profiles are species-dependent. Based on these results, we assert that a single unifying electrostatic potential profile-the gradient of which defines a single unifying electric field profile-cannot correctly predict the electrostatic forces that act on species at the interface.

Disentangling Multiple pH-Dependent Factors on the Hydrogen Evolution Reaction at Au(111)

Understanding how the electrolyte pH affects electrocatalytic activity is a topic of crucial importance in a large variety of systems. However, unraveling the origin of the pH effects is complicated often by the fact that both the reaction driving forces and reactant concentrations in the electric double layer (EDL) change simultaneously with the pH value. Herein, we employ the hydrogen evolution reaction (HER) at Au(111)-aqueous solution interfaces as a model system to disentangle different pH-dependent factors. In 0.1 M NaOH, the HER current density at Au(111) in the potential range of -0.4 V < E RHE < 0 V is up to 60 times smaller than that in 0.1 M HClO4. A reaction model with proper consideration of the local reaction conditions within the EDL is developed. After correcting for the EDL effects, the rate constant for HER is only weakly pH-dependent. Our analysis unambiguously reveals that the observed pH effects are mainly due to the pH-dependent reorganization free energy, which depends on the electrostatic potential and the local reaction conditions within the EDL. Possible origins of the pH and temperature dependence of the activation energy and the electron transfer coefficients are discussed. This work suggests that factors influencing the intrinsic pH-dependent kinetics are easier to understand after proper corrections of EDL effects.

Spatial correlation of desorption events accelerates water exchange dynamics at Pt/water interfaces

The altered solvation structures and dynamical properties of water molecules at the metal/water interfaces will affect the elementary step of an electrochemical process. Simulating the interfacial structure and dynamics with a realistic representation will provide us with a solid foundation to make a connection with experimental studies. To surmount the accuracy-efficiency tradeoff and provide dynamical insights, we use state-of-the-art machine learning molecular dynamics (MLMD) to study the water exchange dynamics, which are fundamental to adsorption/desorption and electrochemical reaction steps. We reproduce interfacial structures consistent with ab initio molecular dynamics (AIMD) results and obtain diffusion and reorientation dynamics in agreement with the experiment. We show that the hydrogen bonds at the interface become stronger than those in bulk water, which makes the diffusion, reorientation, and hydrogen-bond dynamics slower. Our findings reveal that the spatial correlation of desorption events, driven by the breaking and making of hydrogen bonds, accelerates water exchange dynamics. These dynamics occur on timescales of several hundred picoseconds at 337 K and 302 K. We take a solid step forward toward studying the in situ interface water dynamics and attribute the fast water exchange dynamics to the spatial correlation of the desorption events.

Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.

From 2e- to 4e- pathway in the alkaline oxygen reduction reaction on Au(100): Kinetic circumvention of the volcano curve

We report the free energy barriers for the elementary reactions in the 2e- and 4e- oxygen reduction reaction (ORR) steps on Au(100) in an alkaline solution. Due to the weak adsorption energy of O2 on Au(100), the barrier for the association channel is very low, and the 2e- pathway is clearly favored, while the barrier for the O-O dissociation channel is significantly higher at 0.5 eV. Above 0.7 V reversible hydrogen electrode (RHE), the association channel becomes thermodynamically unfavorable, which opens up the O-O dissociation channel, leading to the 4e- pathway. The low adsorption energy of oxygenated species on Au is now an advantage, and residue ORR current can be observed up to the 1.0-1.2 V region (RHE). In contrast, the O-O dissociation barrier on Au(111) is significantly higher, at close to 0.9 eV, due to coupling with surface reorganization, which explains the lower ORR activity on Au(111) than that on Au(100). In combination with the previously suggested outer sphere electron transfer to O2 for its initial adsorption, these results provide a consistent explanation for the features in the experimentally measured polarization curve for the alkaline ORR on Au(100) and demonstrate an ORR mechanism distinct from that on Pt(111). It also highlights the importance to consider the spin state of O2 in ORR and to understand the activation barriers, in addition to the adsorption energies, to account for the features observed in electrochemical measurements.

Choice of the Right Supporting Electrolyte in Electrochemical Reductions: A Principal Component Analysis

We present an analysis of a set of molecular, electrical, and electronic properties for a large number of the cations of quaternary ammonium salts usually employed as supporting electrolytes in cathodic reduction reactions. The goal of the present study is to define a measure for the quality of a supporting electrolyte in terms of the yield of the reaction considered. We performed a principal component analysis using the normalized values of the properties in order to lower the number of relevant reaction coordinates and find that the integral variance of 13 properties can well be represented by three principal components. The yield of the electrochemical hydrodimerization of acrylonitrile employing different quaternary ammonium salts as supporting electrolytes was determined in a series of experiments. We found only a very weak correlation between the yield and the values of the properties but a strong correlation between the yield and the values of the most important principal component. Very similar results are obtained for two further existing systematic experimental studies of the impact of the supporting electrolyte on the yield of cathodic reductions. For all three example reactions, a supervised regression using the two most important principal components as variables yields excellent values for the coefficients of determination. For comparison, we also applied our methodology to sets of purely structure-based features that are usually employed in cheminformatics and obtained results of almost similar quality. We therefore conjecture that our methodology in combination with a small number of experiments can be used to predict the yield of a given cathodic reduction on the basis of the properties of the supporting electrolyte.

Local reaction environment in electrocatalysis

Beyond conventional electrocatalyst engineering, recent studies have unveiled the effectiveness of manipulating the local reaction environment in enhancing the performance of electrocatalytic reactions. The general principles and strategies of local environmental engineering for different electrocatalytic processes have been extensively investigated. This review provides a critical appraisal of the recent advancements in local reaction environment engineering, aiming to comprehensively assess this emerging field. It presents the interactions among surface structure, ions distribution and local electric field in relation to the local reaction environment. Useful protocols such as the interfacial reactant concentration, mass transport rate, adsorption/desorption behaviors, and binding energy are in-depth discussed toward modifying the local reaction environment. Meanwhile, electrode physical structures and reaction cell configurations are viable optimization methods in engineering local reaction environments. In combination with operando investigation techniques, we conclude that rational modifications of the local reaction environment can significantly enhance various electrocatalytic processes by optimizing the thermodynamic and kinetic properties of the reaction interface. We also outline future research directions to attain a comprehensive understanding and effective modulation of the local reaction environment.

The pH-Induced Increase of the Rate Constant for HER at Au(111) in Acid Revealed by Combining Experiments and Kinetic Simulation

Origins of pH effects on the kinetics of electrocatalytic reactions involving the transfer of both protons and electrons, including the hydrogen evolution reaction (HER) considered in this study, are heatedly debated. By taking the HER at Au(111) in acid solutions of different pHs and ionic concentrations as the model systems, herein, we report how to derive the intrinsic kinetic parameters of such reactions and their pH dependence through the measurement of j-E curves and the corresponding kinetic simulation based on the Frumkin-Butler-Volmer theory and the modified Poisson-Nernst-Planck equation. Our study reveals the following: (i) the same set of kinetic parameters, such as the standard activation Gibbs free energy, charge transfer coefficient, and Gibbs adsorption energy for Had at Au(111), can simulate well all the j-E curves measured in solutions with different pH and temperatures; (ii) on the reversible hydrogen electrode scale, the intrinsic rate constant increases with the increase of pH, which is in contrast with the decrease of the HER current with the increase of pH; and (iii) the ratio of the rate constants for HER at Au(111) in x M HClO4 + (0.1 - x) M NaClO4 (pH ≤ 3) deduced before properly correcting the electric double layer (EDL) effects to the ones estimated with EDL correction is in the range of ca. 10 to 40, and even in a solution of x M HClO4 + (1 - x) M NaClO4 (pH ≤ 2) there is a difference of ca. 5× in the rate constants without and with EDL correction. The importance of proper correction of the EDL effects as well as several other important factors on unveiling the intrinsic pH-dependent reaction kinetics are discussed to help converge our analysis of pH effects in electrocatalysis.

Unified quantum theory of electrochemical kinetics by coupled ion-electron transfer

A general theory of coupled ion-electron transfer (CIET) is presented, which unifies Marcus kinetics of electron transfer (ET) with Butler-Volmer kinetics of ion transfer (IT). In the limit of large reorganization energy, the theory predicts normal Marcus kinetics of "electron-coupled ion transfer" (ECIT). In the limit of large ion transfer energies, the theory predicts Butler-Volmer kinetics of "ion-coupled electron transfer" (ICET), where the charge transfer coefficient and exchange current are connected to microscopic properties of the electrode/electrolyte interface. In the ICET regime, the reductive and oxidative branches of Tafel's law are predicted to hold over a wide range of overpotentials, bounded by the ion-transfer energies for oxidation and reduction, respectively. The probability distribution of transferring electron energies in CIET smoothly interpolates between a shifted Gaussian distribution for ECIT (as in the Gerischer-Marcus theory of ET) to an asymmetric, fat-tailed Meixner distribution centered at the Fermi level for ICET. The latter may help interpret asymmetric line shapes in x-ray photo-electron spectroscopy (XPS) and Auger electron spectroscopy (AES) for metal surfaces in terms of shake-up relaxation of the ionized atom and its image polaron by ICET. In the limit of large overpotentials, the theory predicts a transition to inverted Marcus ECIT, leading to a universal reaction-limited current for metal electrodes, dominated by barrierless quantum transitions. Uniformly valid, closed-form asymptotic approximations are derived that smoothly transition between the limiting rate expressions for ICET and ECIT for metal electrodes, using simple but accurate mathematical functions. The theory is applied to lithium intercalation in lithium iron phosphate (LFP) and found to provide a consistent description of the observed current dependence on overpotential, temperature and concentration. CIET theory thus provides a critical bridge between quantum electrochemistry and electrochemical engineering, which may find many other applications and extensions.

Understanding molecular and electrochemical charge transfer: theory and computations

Electron, proton, and proton-coupled electron transfer (PCET) are crucial elementary processes in chemistry, electrochemistry, and biology. We provide here a gentle overview of retrospective and currently developing theoretical formalisms of chemical, electrochemical and biological molecular charge transfer processes, with examples of how to bridge electron, proton, and PCET theory with experimental data. We offer first a theoretical minimum of molecular electron, proton, and PCET processes in homogeneous solution and at electrochemical interfaces. We illustrate next the use of the theory both for simple electron transfer processes, and for processes that involve molecular reorganization beyond the simplest harmonic approximation, with dissociative electron transfer and inclusion of all charge transfer parameters. A core example is the electrochemical reduction of the S2O82- anion. This is followed by discussion of core elements of proton and PCET processes and the electrochemical dihydrogen evolution reaction on different metal, semiconductor, and semimetal (say graphene) electrode surfaces. Other further focus is on stochastic chemical rate theory, and how this concept can rationalize highly non-traditional behaviour of charge transfer processes in mixed solvents. As a second major area we address ("long-range") chemical and electrochemical electron transfer through molecular frameworks using notions of superexchange and hopping. Single-molecule and single-entity electrochemistry are based on electrochemical scanning probe microscopies. (In operando) scanning tunnelling microscopy (STM) and atomic force microscopy (AFM) are particularly emphasized, with theoretical notions and new molecular electrochemical phenomena in the confined tunnelling gap. Single-molecule surface structure and electron transfer dynamics are illustrated by self-assembled thiol molecular monolayers and by more complex redox target molecules. This discussion also extends single-molecule electrochemistry to bioelectrochemistry of complex redox metalloproteins and metalloenzymes. Our third major area involves computational overviews of molecular and electronic structure of the electrochemical interface, with new computational challenges. These relate to solvent dynamics in bulk and confined space (say carbon nanostructures), electrocatalysis, metallic and semiconductor nanoparticles, d-band metals, carbon nanostructures, spin catalysis and "spintronics", and "hot" electrons. Further perspectives relate to metal-organic frameworks, chiral surfaces, and spintronics.

Anomalous Interfacial Electron-Transfer Kinetics in Twisted Trilayer Graphene Caused by Layer-Specific Localization

Interfacial electron-transfer (ET) reactions underpin the interconversion of electrical and chemical energy. It is known that the electronic state of electrodes strongly influences ET rates because of differences in the electronic density of states (DOS) across metals, semimetals, and semiconductors. Here, by controlling interlayer twists in well-defined trilayer graphene moirés, we show that ET rates are strikingly dependent on electronic localization in each atomic layer and not the overall DOS. The large degree of tunability inherent to moiré electrodes leads to local ET kinetics that range over 3 orders of magnitude across different constructions of only three atomic layers, even exceeding rates at bulk metals. Our results demonstrate that beyond the ensemble DOS, electronic localization is critical in facilitating interfacial ET, with implications for understanding the origin of high interfacial reactivity typically exhibited by defects at electrode-electrolyte interfaces.

Orientational Ordering in Nano-confined Polar Liquids

Water and other polar liquids exhibit nanoscale structuring near charged interfaces. When a polar liquid is confined between two charged surfaces, the interfacial solvent layers begin to overlap, resulting in solvation forces. Here, we perform molecular dynamics simulations of polar liquids with different dielectric constants and molecular shapes and sizes confined between charged surfaces, demonstrating strong orientational ordering in the nanoconfined liquids. To rationalize the observed structures, we apply a coarse-grained continuum theory that captures the orientational ordering and solvation forces of those liquids. Our findings reveal the subtle behavior of different nanoconfined polar liquids and establish a simple law for the decay length of the interfacial orientations of the solvents, which depends on their molecular size and polarity. These insights shed light on the nature of solvation forces, which are important in colloid and membrane science, scanning probe microscopy, and nano-electrochemistry.

A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics

The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces to transport through nanojunctions and offer a prime target for quantum computing applications. Here, we derive the set of conditions under which fermionic operators can be exactly replaced by bosonic operators that render the problem amenable to a large toolbox of dynamical methods while still capturing the correct dynamics of n-body operators. Importantly, our analysis offers a simple guide on how one can exploit these simple maps to calculate nonequilibrium and equilibrium single- and multi-time correlation functions essential in describing transport and spectroscopy. We use this to rigorously analyze and delineate the applicability of simple yet effective Cartesian maps that have been shown to correctly capture the correct fermionic dynamics in select models of nanoscopic transport. We illustrate our analytical results with exact simulations of the resonant level model. Our work provides new insights as to when one can leverage the simplicity of bosonic maps to simulate the dynamics of many-electron systems, especially those where an atomistic representation of nuclear interactions becomes essential.

Role of introduced Se element and induced anion vacancies in Mo(SSe)2-x/G van der Waals heterostructure for enhanced hydrogen evolution reaction

The Gibbs free energy of hydrogen adsorption at the edge of molybdenum disulfide (MoS₂) is close to that of Pt, meaning that MoS₂ is the best candidate to replace Pt-based materials. However, easy agglomeration between layers to mask active sites, lack of catalytic activity in the basal planes, and poor electronic conductivity make MoS₂ exhibit dissatisfactory hydrogen evolution reaction (HER) catalytic performance. Here, we successfully construct a van der Waals heterostructure stacked alternately with Mo(SSe)_2-x and graphene (Mo(SSe)_2-x/G) to enhance its catalytic ability. The introduction of Se into MoS₂ and the thermal treatment induce the sample to generate more anion vacancies. Theoretical and experimental results demonstrate the constructed van der Waals heterostructure, the introduced Se element, and the increased anion vacancies are in favor of promoting the number of active sites and improving the electronic conductivity of the catalyst. Therefore, Mo(SSe)_2-x/G exhibits superior HER catalytic performance (the overpotentials of 137 mV and 136 mV at a current of 10 mA cm^-2) and long-term stabilities (>90 h and 140 h at a current density of 20 mA cm^-2) in both acidic and alkaline media.

Access to Saturated Oxygen Heterocycles and Lactones via Electrochemical Sulfonylative Oxycyclization of Alkenes with Sulfonyl Hydrazides

A facile electrochemical sulfonylative cycloetherification of linear unsaturated alcohols with sulfonyl hydrazides under mild conditions has been accomplished. This catalyst- and oxidant-free protocol proceeds via electro-oxidation, followed by radical addition, as well as an intramolecular oxygen nucleophilic process. This methodology is compatible with a broad substrate scope and good functional group compatibility, which provides a valuable and convenient synthetic tool for the synthesis of saturated five-, six-, seven-, and eight-membered ring oxygen heterocycles. Furthermore, sulfonylative cycloesterification of linear unsaturated acids toward the lactone products has also been established under this electrochemical system. In addition, control experiments indicated that the N-H bonds of the sulfonyl hydrazide molecule are non-essential.