Mixed quantum-classical treatment of electron transfer at electrocatalytic interfaces: Theoretical framework and conceptual analysis

Hierarchical Modeling of the Local Reaction Environment in Electrocatalysis

ConspectusElectrocatalytic reactions, such as oxygen reduction/evolution reactions and CO2 reduction reaction that are pivotal for the energy transition, are multistep processes that occur in a nanoscale electric double layer (EDL) at a solid-liquid interface. Conventional analyses based on the Sabatier principle, using binding energies or effective electronic structure properties such as the d-band center as descriptors, are able to grasp overall trends in catalytic activity in specific groups of catalysts. However, thermodynamic approaches often fail to account for electrolyte effects that arise in the EDL, including pH, cation, and anion effects. These effects exert strong impacts on electrocatalytic reactions. There is growing consensus that the local reaction environment (LRE) prevailing in the EDL is the key to deciphering these complex and hitherto perplexing electrolyte effects. Increasing attention is thus paid to designing electrolyte properties, positioning the LRE at center stage. To this end, unraveling the LRE is becoming essential for designing electrocatalysts with specifically tailored properties, which could enable much needed breakthroughs in electrochemical energy science.Theory and modeling are getting more and more important and powerful in addressing this multifaceted problem that involves physical phenomena at different scales and interacting in a multidimensional parametric space. Theoretical models developed for this purpose should treat intrinsic multistep kinetics of electrocatalytic reactions, EDL effects from subnm scale to the scale of 10 nm, and mass transport phenomena bridging scales from <0.1 to 100 μm. Given the diverse physical phenomena and scales involved, it is evident that the challenge at hand surpasses the capabilities of any single theoretical or computational approach.In this Account, we present a hierarchical theoretical framework to address the above challenge. It seamlessly integrates several modules: (i) microkinetic modeling that accounts for various reaction pathways; (ii) an LRE model that describes the interfacial region extending from the nanometric EDL continuously to the solution bulk; (iii) first-principles calculations that provide parameters, e.g., adsorption energies, activation barriers and EDL parameters. The microkinetic model considers all elementary steps without designating an a priori rate-determining step. The kinetics of these elementary steps are expressed in terms of local concentrations, potential and electric field that are codetermined by EDL charging and mass transport in the LRE model. Vital insights on electrode kinetic phenomena, i.e., potential-dependent Tafel slopes, cation effects, and pH effects, obtained from this hierarchical framework are then reviewed. Finally, an outlook on further improvement of the model framework is presented, in view of recent developments in first-principles based simulation of electrocatalysis, observations of dynamic reconstruction of catalysts, and machine-learning assisted computational simulations.

The decisive role of electrostatic interactions in transport mode and phase segregation of lithium ions in LiFePO4

Understanding the mechanism of slow lithium ion (Li+) transport kinetics in LiFePO4 is not only practically important for high power density batteries but also fundamentally significant as a prototypical ion-coupled electron transfer process. Substantial evidence has shown that the slow ion transport kinetics originates from the coupled transfer between electrons and ions and the phase segregation of Li+. Combining a model Hamiltonian analysis and DFT calculations, we reveal that electrostatic interactions play a decisive role in coupled charge transfer and Li+ segregation. The obtained potential energy surfaces prove that ion-electron coupled transfer is the optimal reaction pathway due to electrostatic attractions between Li+ and e- (Fe2+), while prohibitively large energy barriers are required for separate electron tunneling or ion hopping to overcome the electrostatic energy between the Li+-e- (Fe2+) pair. The model reveals that Li+-Li+ repulsive interaction in the [010] transport channels together with Li+-e- (Fe2+)-Li+ attractive interaction along the [100] direction cause the phase segregation of Li+. It explains why the thermodynamically stable phase interface between Li-rich and Li-poor phases in LiFePO4 is perpendicular to [010] channels.

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.

The electrostatic effect and its role in promoting electrocatalytic reactions by specifically adsorbed anions

The adsorption of anions and its impact on electrocatalytic reactions are fundamental topics in electrocatalysis. Previous studies revealed that adsorbed anions display an overall poisoning effect in most cases. However, for a few reactions such as the hydrogen evolution reaction (HER), oxidation of small organic molecules (SOMs), and reduction of CO₂ and O₂, some specifically adsorbed anions can promote their reaction kinetics under certain conditions. The promotion effect is frequently attributed to the adsorbate induced modification of the nature of the active sites, the change of the adsorption configuration and free energy of the key reactive intermediate which consequently change the activation energy, the pre-exponential factor of the rate determining step etc. In this paper, we will give a mini review of the indispensable role of the classical double layer effect in enhancing the kinetics of electrocatalytic reactions by anion adsorption. The ubiquitous electrostatic interactions change both the potential distribution and the concentration distribution of ionic species across the electric double layer (EDL), which alters the electrochemical driving force and effective concentration of the reactants. The contribution to the overall kinetics is highlighted by taking HER, oxidation of SOMs, reduction of CO₂ and O₂, as examples.

Theory for nanoscale curvature induced enhanced inactivation kinetics of SARS-CoV-2

We develop a novel theory for the nanomorphology dependent outer sphere heterogeneous electron transfer (ET) rate constant () based on an energy level alignment approach. is modelled through the activation free energy, which is a product of the water monolayer covered metal work function (WF) and the fractional electronic charge exchanged at the transition state (attained through the alignment of the metal Fermi and HOMO/LUMO energy levels of the electroactive species). The theory shows that is an exponentially increasing and decreasing function of the mean curvature in concave and convex nanomorphologies, respectively, for electroactive species or proteins involving their HOMO energy. For the specific spike protein of SARS-CoV-2, we have estimated the half lifetime (t_1/2) and degree of inactivation as a function of the metal WF, nanostructure mean curvature, spike protein HOMO energy, and the environmental temperature (T). By varying the metal from Ag to Au, t_1/2 is reduced from 7 h to 4 min, respectively. The reduction in the copper nanoparticle size from 50 to 5 nm increases the degree of inactivation from 60 to 99.6% (with a reduction factor of 10 in t_1/2). Similarly, the increase in T from 10 °C to 65 °C causes a 100 times lowering of the t_1/2 and t_99.9% of SARS-CoV-2 on Cu metal. The theory predicts that involving the HOMO energy level of a protein follows the surface nanostructure shape dependent order as follows: spherical nanoparticle > cylindrical nanorod > cylindrical nanopore > spherical nanocavity, while the opposite trend is observed in the case of the LUMO energy level participation. Finally, the theory shows agreement with the reported experimental data of the degree of inactivation of SARS-CoV-2 on Ag and Cu nanoparticles.

Cation Overcrowding Effect on the Oxygen Evolution Reaction

The influence of electrolyte ions on the catalytic activity of electrode/electrolyte interfaces is a controversial topic for many electrocatalytic reactions. Herein, we focus on an effect that is usually neglected, namely, how the local reaction conditions are shaped by nonspecifically adsorbed cations. We scrutinize the oxygen evolution reaction (OER) at nickel (oxy)hydroxide catalysts, using a physicochemical model that integrates density functional theory calculations, a microkinetic submodel, and a mean-field submodel of the electric double layer. The aptness of the model is verified by comparison with experiments. The robustness of model-based insights against uncertainties and variations in model parameters is examined, with a sensitivity analysis using Monto Carlo simulations. We interpret the decrease in OER activity with the increasing effective size of electrolyte cations as a consequence of cation overcrowding near the negatively charged electrode surface. The same reasoning could explain why the OER activity increases with solution pH on the RHE scale and why the OER activity decreases in the presence of bivalent cations. Overall, this work stresses the importance of correctly accounting for local reaction conditions in electrocatalytic reactions to obtain an accurate picture of factors that determine the electrode activity.

Modelling electrocatalytic reactions with a concerted treatment of multistep electron transfer kinetics and local reaction conditions

A physicochemical model is developed for electrocatalytic reactions involving multiple electron transfer steps occurring in the electric double layer (EDL). The local reaction conditions are calculated using a mean-field EDL model, which is derived from a comprehensive grand potential that considers the steric effects, solvent polarization, and chemisorption-induced surface dipoles. Macroscopic mass transport in the so-called diffusion layer is controlled by the same set of controlling equations of the EDL model, without imposing the electroneutrality assumption as usual. The Gerischer's formulation of electron transfer theory, corrected with local reaction conditions, is used to describe the kinetics of elementary steps. Multistep kinetics of the electrocatalytic reaction is treated using microkinetics modelling, without resorting to the usual rate-determining step approximation. In formal analysis of the model, we retrieve canonical models with additional assumptions. Self-consistent numerical implementation of the model is demonstrated for oxygen reduction reaction (ORR) at Pt(111) in acidic solution, and the aptness of the model is verified by comparison with experimental data. A comparative study of the full model and its simplified versions allows us to examine how the ORR is influenced by asymmetric steric effects, finite concentration of ions, solvent polarization, surface charge effects, and metal electronic structure effects. We find that the difference in terms of the overpotential between the full model and the simplest model can be up to ∼0.1 V at a current density of -6 mAcm-2.

Impedance response of electrochemical interfaces: part II-chemisorption

Physical modeling helps to acquire fundamental insights from experimental data when electrochemical impedance spectroscopy is employed for mechanistic understandings of electrocatalytic reactions. Herein, we report an analytical model for chemisorption impedance with a consistent treatment of ion transport in the solution and electron transfer on the electrode surface. Our formulation avoids botha prioridecoupling of double-layer charging and electron transfer reaction, and a strict separation of double-layer charging and ion transport. Ion transport in the entire solution region is described by the Poisson-Nernst-Planck theory and electron transfer kinetics on the electrode surface by the Frumkin-Butler-Volmer theory. Surface dipoles caused by partially charged chemisorbates are considered. The classical Frumkin-Melik-Gaikazyan model for chemisorption is retrieved as a limiting case. The obtained formula is validated using experimental data of hydrogen adsorption at Pt(111). Characteristic frequencies and asymptotic behaviors of chemisorption impedance are analyzed.

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

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