Asymmetric Marcus–Hush model of electron transfer kinetics: Application to the voltammetry of surface-bound redox systems

Ab Initio Kinetics of Electrochemical Reactions Using the Computational Fc0/Fc+ Electrode

The current state-of-the-art electron-transfer modeling primarily focuses on the kinetics of charge transfer between an electroactive species and an inert electrode. Experimental studies have revealed that the existing Butler-Volmer model fails to satisfactorily replicate experimental voltammetry results for both solution-based and surface-bound redox couples. Consequently, experimentalists lack an accurate tool for predicting electron-transfer kinetics. In response to this challenge, we developed a density functional theory-based approach for accurately predicting current peak potentials by using the Marcus-Hush model. Through extensive cyclic voltammetry simulations, we conducted a thorough exploration that offers valuable insights for conducting well-informed studies in the field of electrochemistry.

Interplay between element-specific distortions and electrocatalytic oxygen evolution for cobalt-iron hydroxides

A microscopic understanding of how Fe-doping of Co(OH)2 improves electrocatalytic oxygen evolution remains elusive. We study two Co1-x Fe x (OH)2 series that differ in fabrication protocol and find composition alone poorly correlates to catalyst performance. Structural descriptors extracted using X-ray diffraction, X-ray absorption spectroscopy, and Raman spectroscopy reveal element-specific distortions in Co1-x Fe x (OH)2. These structural descriptors are composition-dependent within individual sample series but inconsistent across fabrication protocols, revealing fabrication-dependence in catalyst microstructure. Correlations between structural parameters from different techniques show that Fe-O resists bond length changes, forcing distortion of Co environments. We find the difference in O-M-O bond angles between Co and Fe sites to correlate with electrocatalytic behavior across both sample series, which we attribute to asymmetric distortion of potential energy surfaces for the Co(iii) to Co(iv) oxidation. A Tafel slope consistent with a rate-limiting step without electron transfer emerges as the O-Co-O angle decreases, implying a distortion-induced transition in the rate-limiting step. The fabrication dependence of electronic and bonding structure in the catalysts should be considered in theoretical and high-throughput analyses of electrocatalyst materials.

Cu-P@silica-CNT-based catalyst for effective electrolytic water splitting in an alkaline medium with hydrazine assistance

In this study, we prepared a potential catalyst as an electrode modifier for electrolytic water splitting. In the preparation step, the amine was decorated with copper-phosphorus. It was immobilized over the silica surface, and the surface was engineered using N-(3-(trimethoxysilyl) propyl)ethylenediamine for the synthesis of the catalysts (AS). The morphological and structural aspects of the catalyst (AFS-Cu-P) were determined using FE-SEM/EDAX, FTIR, elemental analysis, BET, TGA, and XPS. The catalyst's efficacy for the oxygen evolution reaction (OER) was assessed in an alkaline medium with and without hydrazine. The hydrazine oxidation reaction enhanced the sluggish OER and facilitated water splitting. Detailed electrochemical measurements confirmed an increase in the kinetics of the process and a reduction in the activation energy needed to complete the process. The Tafel slopes, charge transfer coefficients, exchange-specific current densities, apparent rate constants, and diffusion coefficients are provided along with their respective values. The results showed that the presence of Cu and CNT is crucial in the conversion process.

Straightforward computational determination of energy-transfer kinetics through the application of the Marcus theory

Energy transfer (EnT) photocatalysis holds the potential to revolutionize synthetic chemistry, unlocking the excited-state reactivity of non-chromophoric compounds via indirect sensitization. This strategy gives access to synthetic routes to valuable molecular scaffolds that are otherwise inaccessible through ground-state pathways. Despite the promising nature of this chemistry, it still represents a largely uncharted area for computational chemistry, hindering the development of structure-activity relationships and design rules to rationally exploit the potential of EnT photocatalysis. Here, we examined the application of the classical Marcus theory in combination with DFT calculations as a convenient strategy to estimate the kinetics of EnT processes, focusing on the indirect sensitization of alkenes recently reported by Gilmour, Kerzig and co-workers for subsequent isomerization [Zähringer et al., J. Am. Chem. Soc., 2023, 145, 21576]. Our results demonstrate a remarkable capability of this approach to estimate free-energy barriers for EnT processes with high accuracy, yielding precise qualitative assessments and quantitative predictions with typical discrepancies of less than 2 kcal mol-1 compared to experimental values and a small mean average error (MAE) of 1.2 kcal mol-1.

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.

Local Field Induced Mass Transfer: New Insight into Nano-electrocatalysis

Unravelling the complex kinetics of electrocatalysis is essential for the design of electrocatalysts with high performance. Mass transfer and electron transfer are two primary factors that need to be optimized in order to enhance electrocatalytic reactions. The use of nanocatalysts proves to be a promising way of promoting the performance of electrocatalytic reactions, this improvement is usually attributed to their ability to enhance electron transfer. However, when catalysts are taken down to the nanoscale, their size is comparable to the thickness of an electrical double layer, so any curvature can lead to an inhomogeneous local electric field on the electrode, which then changes the mass transfer essentially. In this article, we introduce the new concept of local-field-induced mass transfer in nano-electrocatalytic systems, and provide a brief review of recent progress, revealing its effect on nano-electrocatalysis, which may bring new insight into the future design of nano-electrocatalysts.

Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory

The Marcus-Hush theory has been successfully applied to describe and predict the activation barriers and hence the electron-transfer (ET) rates in several physicochemical and biological systems. This theory assumes that in the ET reaction, the geometry of the free Gibbs energy landscape is parabolic, with equal curvature near the local minimum for both reactants and products. In spite of its achievements, more realistic models have included the assumption of the two parabolas having not the same curvature. This situation is analyzed by the Nelsen's four-point method. As a benchmark to compare the Marcus-Hush approximation to a precise calculation of the excitation energy, we studied the non-ET process of the electronic excitation of the aluminum dimer that has two local minima (³∑_g ^- and ³∏_u electronic states) and allows to obtain analytically the Marcus-Hush nonsymmetric parameters. We appraise the ability of the Marcus-Hush formula to approximate the analytical results by using several averages of the two reorganization energies associated with the forward and backward transitions and analyze the error. It is observed that the geometric average minimizes the relative error and that the analytical case is recovered. The main results of this paper are obtained by the application of the Nelsen's four-point method to compute the reorganization energies of a large set of potential π-conjugated molecules proposed for organic photovoltaic devices using the above-mentioned averages for the Marcus-Hush formula. The activation energies obtained with the geometric average are significantly larger for some donor-acceptor pairs in comparison with the previously employed arithmetic average, their differences being suitable for experimental testing.

Recent Advances in Voltammetry

Recent progress in the theory and practice of voltammetry is surveyed and evaluated. The transformation over the last decade of the level of modelling and simulation of experiments has realised major advances such that electrochemical techniques can be fully developed and applied to real chemical problems of distinct complexity. This review focuses on the topic areas of: multistep electrochemical processes, voltammetry in ionic liquids, the development and interpretation of theories of electron transfer (Butler-Volmer and Marcus-Hush), advances in voltammetric pulse techniques, stochastic random walk models of diffusion, the influence of migration under conditions of low support, voltammetry at rough and porous electrodes, and nanoparticle electrochemistry. The review of the latter field encompasses both the study of nanoparticle-modified electrodes, including stripping voltammetry and the new technique of 'nano-impacts'.

Access to enhanced differences in Marcus-Hush and Butler-Volmer electron transfer theories by systematic analysis of higher order AC harmonics

The potential-dependences of the rate constants associated with heterogeneous electron transfer predicted by the empirically based Butler-Volmer and fundamentally based Marcus-Hush formalisms are well documented for dc cyclic voltammetry. However, differences are often subtle, so, presumably on the basis of simplicity, the Butler-Volmer method is generally employed in theoretical-experimental comparisons. In this study, the ability of Large Amplitude Fourier Transform AC Cyclic Voltammetry to distinguish the difference in behaviour predicted by the two formalisms has been investigated. The focus of this investigation is on the difference in the profiles of the first to sixth harmonics, which are readily accessible when a large amplitude of the applied ac potential is employed. In particular, it is demonstrated that systematic analysis of the higher order harmonic responses in suitable kinetic regimes provides predicted deviations of Marcus-Hush from Butler-Volmer behaviour to be established from a single experiment under conditions where the background charging current is minimal.