Standard Potential Research Articles

Neutrino oscillations in matter using the adjugate of the Hamiltonian

We revisit neutrino oscillations in constant matter density for a number of different scenarios: three flavors with the standard Wolfenstein matter potential, four flavors with standard matter potential and three flavors with non-standard matter potentials. To calculate the oscillation probabilities for these scenarios one must determine the eigenvalues and eigenvectors of the Hamiltonians. We use a method for calculating the eigenvalues that is well known, determination of the zeros of determinant of matrix (λI-H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\lambda I -H)$$\\end{document}, where H is the Hamiltonian, I the identity matrix and λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} is a scalar. To calculate the associated eigenvectors we use a method that is little known in the particle physics community, the calculation of the adjugate (transpose of the cofactor matrix) of the same matrix, (λI-H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\lambda I -H)$$\\end{document}. This method can be applied to any Hamiltonian, but provides a very simple way to determine the eigenvectors for neutrino oscillation in matter, independent of the complexity of the matter potential. This method can be trivially automated using the Faddeev–LeVerrier algorithm for numerical calculations. For the above scenarios we derive a number of quantities that are invariant of the matter potential, many are new such as the generalization of the Naumov–Harrison–Scott identity for four or more flavors of neutrinos. We also show how these matter potential independent quantities become matter potential dependent when off-diagonal non-standard matter effects are included.

Optimization of ultrasound-assisted extraction of phenolics from Cordia dichotoma leaves using response surface methodology

In this study, ultrasound-assisted extraction (UAE) was employed to extract phenolic compounds from Cordia dichotoma (C. Dichotoma) leaves. The extraction process was optimized using response surface methodology (RSM). The C. Dichotoma tree is found in tropical and subtropical areas and has medicinal properties. The obtained extracts were subjected to phytochemical screening using standard tests, antioxidant potential, and total phenolic content (TPC) of C. Dichotoma leaf extract by 2,2-diphenylpicrylhydrazyl assay and Folin-Ciocalteu assay respectively. The impact of process parameters like different solvents, solute-to-solvent ratio, ultrasonic power, and sonication time on TPC and antioxidant activity were studied. UAE offers a more rapid and efficient extraction process when compared to conventional extraction techniques such as Soxhlet extraction due to effective mass transfer. RSM models identified that ultrasonic power of 200 W and 30:1 (mL/g) solvent-to-solute ratio, using methanol, and a sonication time of 15 min are the optimal conditions for extraction of phenolics. FTIR analysis of methanolic extract confirmed the presence of phenolic functional groups. The compounds obtained from C. Dichotoma leaf extracts were identified by GCMS. UAE proves to be a promising technique for obtaining bioactive compounds with antioxidant potential from Cordia dichotoma leaves which can be potential applications in pharmaceutical, nutraceuticals, and functional food industries.

Novel Green Screen-Printed Potentiometric Sensor for Monitoring Antihistamine Drug Chlorphenoxamine HCl in Various Matrices

The pharmaceutical sector is seeking cost-effective analyzers that deliver precise, real-time data. This study aims to establish a correlation between the pharmaceutical industry and advancements in solid-contact ion-selective electrodes for quantifying chlorphenoxamine hydrochloride (CPX) concentration in various matrices. A comparative analysis of the performance between solid contact and liquid contact sensors showed that solid contact sensors outperformed their liquid contact counterparts in terms of durability, handling, and ease of integration. A sensor was developed using MWCNT and calix[8]arene as ionophore, resulting in a Nernstian potentiometric response for CPX across a linear range of 5.0 × 10−5 to 1.0 × 10−8 M. The slope of the response was 57.89 ± 0.77 mV/decade, and the standard potential was determined to be 371.9 ± 0.8 mV. The developed sensor exhibits notable intrinsic advantages, such as a rapid response time of 12 ± 2 s and an extended lifespan of 3 months. The sensor exhibiting optimal performance has been effectively employed for the analysis of CPX in different matrices, including pharmaceutical formulations, urine, and plasma. The developed method underwent validation in compliance with ICH requirements. Finally, the method’s greenness and whiteness were evaluated using five different tools and successfully compared to those obtained from the established reported method.

Assessing the potential of functionalized cobalt-doped graphyne-like boron nitride as an efficient and accessible catalyst for oxygen reduction reaction in fuel cells

Due to its exorbitant expense and scarcity on Earth, there is a need to anticipate a cost-effective and widely accessible catalyst that can effectively replace platinum, which is known for its efficiency in fuel cells. In this context, catalysts such as OH, H, and COOH group-functionalized cobalt-doped Graphyne-like boron nitride (referred to as BNyen) are being examined to enhance the mechanism of oxygen reduction reaction (ORR) via direct 4e− reduction. According to findings derived from DFT, it has been observed that reactions predominantly take place above Co metal center rather than edge site of BNyen. Additionally, the thermochemical characteristics point to the fact that these reactions release a significant amount of heat, suggesting their feasibility. By examining reversible potential of products and intermediates on phthalocyanines as well as adsorption energy (Eads), it has been determined that Co-BNyen(OH) serves as a superior catalyst for ORR process. In conclusion, this research affirms that BNyen materials hold significant promise as catalysts for ORR, a crucial process in fuel cell applications.

Exploring the thermal and mechanical properties of PAI-Graphene monolayers and nanotubes: Insights from molecular dynamics simulations

Two-dimensional (2D) materials are widely applicable in emerging technologies, with graphene remaining a focal point of interest. Among the computationally designed 2D carbon allotropes is PAI-Graphene (PAI-G), formed through the lateral polymerization of molecules containing 5- and 6-membered rings, specifically Polimerized as-Indacene. This study employs reactive molecular dynamics simulations to explore the thermal and mechanical properties of PAI-G monolayers and nanotubes using the AIREBO-M potential. The results reveal that the melting point of PAI-G is 3200 K, significantly lower than that of graphene. Anisotropic behavior in elastic properties is observed in PAI-G monolayers, with similar trends seen in nanotubes of varying chiralities. The Young’s modulus values for these systems range between 650 and 900 GPa. Furthermore, the analysis of nanotubes across different diameters unveils a correlation between diameter and elastic constants. A Machine Learning Interatomic Potential (MLIP) was trained to confirm the appropriateness of the standard parameterized AIREBO-M potential for describing the thermomechanical behavior of PAI-G.

Zigzag phase transition of electrons confined within a thin annulus region

We consider a semiclassical approach to study the possible stabilization of a zigzag phase for a system of interacting electrons confined within a thin annulus region with infinite inner/outer walls. The electrons are considered spinless and interact via the standard Coulomb interaction potential. The classical minimum energy configuration of the system due to the Coulomb repulsion between electrons is accurately determined by using the simulated annealing method. As the number of electrons increases we see the appearance and stabilization of a two-ring structure with zigzag patterns. Further increase of the number of electrons appears to eventually lead to the collapse of the two-ring zigzag structure. A simple quantum treatment of the nodal features of the free many-particle wave function shows the appearance of nodal domain patterns that are consistent with the zigzag features that were observed in the classical model.

Simple and Accurate One-Body Energy and Dipole Moment Surfaces for Water and Beyond.

Water is often the testing ground for new, advanced force fields. While advanced functional forms for intermolecular interactions have been integral to the development of accurate water models, less attention has been paid to a transferable model for intramolecular valence terms. In this work, we present a one-body energy and dipole moment surface model, named 1B-UCB, that is simple yet accurate and can be feasibly adapted for both standard and advanced potentials. 1B-UCB for water is comparable in accuracy to those with much more complex functional forms, despite having drastically fewer parameters. The parametrization protocol has been implemented as part of the Q-Force automated workflow and requires only a quantum mechanical Hessian calculation as reference data, hence allowing it to be easily extended to a variety of molecular systems beyond water, which we demonstrate on a selection of small molecules with different symmetries.

An Investigation into Electrolytes and Cathodes for Room-Temperature Sodium–Sulfur Batteries

In the pursuit of high energy density batteries beyond lithium, room-temperature (RT) sodium–sulfur (Na-S) batteries are studied, combining sulfur, as a high energy density active cathode material and a sodium anode considered to offer high energy density and very good standard potential. Different liquid electrolyte systems, including three different salts and two different solvents, are investigated in RT Na-S battery cells, on the basis of the solubility of sulfur and sulfides, specific capacity, and cyclability of the cells at different C-rates. Two alternative cathode host materials are explored: A bimodal pore size distribution activated carbon host AC MSC30 and a highly conductive carbon host of hollow particles with porous particle walls. An Na-S cell with a cathode coating with 44 wt% sulfur in the AC MSC30 host and the electrolyte 1M NaFSI in DOL/DME exhibited a specific capacity of 435 mAh/gS but poor cyclability. An Na-S cell with a cathode coating with 44 wt% sulfur in the host of hollow porous particles and the electrolyte 1M NaTFSI in TEGDME exhibited a specific capacity of 688 mAh/gS.

Formation of Be13Ln intermetallics by codeposition of Be and Ln from molten NaF-BeF2-LnF3 (Ln = Pr, Nd, Gd)

The electrodeposition of Be and Ln from NaF-BeF2-LnF3 (Ln = Pr, Nd, Gd) molten salts on various electrodes, including W, Mo, Ni, Cu, and brass (70 %Cu-30 %Zn alloy), is systematically investigated using cyclic voltammetry (CV), stripping chronopotentiometry (SCP), square wave voltammetry (SWV), chrono-amperometry (CA), galvanostatic electrolysis, and microanalytical analysis of the deposits. Underpotential deposition (UPD) of Be is observed on all electrodes, while UPD of Ln is selectively observed on certain electrodes like Ni, Cu, and brass. Furthermore, the codeposition of Be and Ln is observed on all electrodes at a potential between −0.090 to −0.190 V vs Eeq,Be(II)/Be. SEM-EDS and XRD analysis confirm the intermetallic compound Be13Ln as the predominant phase in the deposits. The current–time transient behavior indicates a 3D instantaneous nucleation for Be electrodeposition, followed by a progressive nucleation process for the codeposition of Be-Gd on the W electrode. The standard Gibbs free energy of various Be-containing intermetallics is calculated based on the determined standard potentials. A novel strategy for Ln separation from BeF2-based molten salt is proposed based on the insights gained from this study.

Recovery of Metal Ions (Cd2+, Co2+, and Ni2+) from Nitrate and Sulfate on Laser-Induced Graphene Film Using Applied Voltage and Its Application.

The urgent removal of Cd, Co, and Ni from nitrate and sulfate is essential to mitigate the potential risk of chemical pollution from large volumes of industrial wastewater. In this study, these metal ions were rapidly recovered through applying voltage on nitrate and sulfate, utilizing laser-induced graphene/polyimide (LIG/PI) film as the electrode. Following the application of external voltage, both the pH value and conductivity of the solution undergo changes. Compared to Co2+ and Ni2+, Cd2+ exhibits a lower standard electrode potential and stronger reducibility. Consequently, in both nitrate and sulfate solutions, the reaction sequence follows the order of Cd2+ > Co2+ > Ni2+, with the corresponding electrode adsorption quantities in the order of Cd2+ > Co2+ ~ Ni2+. Additionally, using the recovered Co(OH)2 as the raw material, a LiCoO2 composite was prepared. The assembled battery with this composite exhibited a specific capacity of 122.8 mAh g-1, meeting practical application requirements. This research has significance for fostering green development.

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models.

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

Typology and Design of Parametric Cat-in-a-Box and Cat-in-a-Grid Triggers for Tropical Cyclone Risk Transfer

The insurance industry has used parametric solutions to transfer catastrophe risks since the 1990s. Instead of relying on a lengthy process to assess a claim, these products pay the insured a pre-agreed amount if the physical characteristics of the event fulfill pre-defined conditions. Cat-in-a-box or cat-in-a-circle triggers, commonly used tools for tropical cyclone risk transfer, provide a payout to the insured if the track of a hurricane crosses the perimeter of a geographic area defined by a polygon or a circle with a certain intensity. Cat-in-a-grid solutions are novel and more sophisticated. They rely on a set of multiple cat-in-a-box triggers arranged on an orthogonal grid. The consideration of multiple geographic domains instead of a single box or circle is helpful to reduce basis risk, i.e., the difference between the parametric loss estimate and the target loss. In the case study for Miami presented here, for instance, a cat-in-a-grid solution showed 18.5% less basis risk than a typical cat-in-a-box alternative. To organize the different types of triggers within a common framework, we classify the existing alternatives based on whether they use a single geographic domain (like a box or a circle) or multiple domains (like a grid). We discuss their advantages and disadvantages and describe the process required to calibrate any one solution with the help of a catastrophe-risk model. We focus, in particular, on the analysis and construction of cat-in-a-grid triggers, the alternative that we believe offers the greatest potential for global standardization and adoption.

Interaction Between Uranium Trifluoride and the Mixture of Lithium and Beryllium Fluorides

Equilibrium potentials of uranium (U3+/U0) have been measured in the LiF-BeF2-UF3 melt as a function of temperature and uranium fluoride concentration. The empirical equation of uranium potential isotherms and polytherms have been obtained. Cathode polarization of uranium in the molten mixture of beryllium and lithium fluorides has been measured using the current switch off method form the stationary state. Uranium ions were found to have primarily the-valence of three in the LiF-BeF2 electrolyte in the studied temperature and uranium fluoride concentration ranges. A conditional standard potential of uranium (U3+/U0) in the molten mixture of lithium and beryllium fluorides was calculated relative to the reference fluorine electrode according to the experimentally obtained data on the equilibrium potentials of the uranium electrode in the LiF-BeF2-UF3 melt. Standard conditional changes in the Gibbs energy, enthalpy and entropy at the formation of uranium trifluoride from the elements in the form of dilute solutions were determined. The enthalpy of mixing of liquid uranium fluoride and the 0.73LiF–0.27BeF2 melt was calculated.

Tunable photocatalytic and optoelectronic properties of SiTe/SiH heterostructure as a photocatalytic water splitting with high hydrogen production

The development of appropriate photocatalysts based on semiconductors is crucial for overcoming energy and environmental challenges. Especially, photocatalysts of water splitting are attractive nanomaterials. In the present work, a new β-SiTe/SiH van der Waals heterostructure has been produced by stacking the SiTe monolayer on top of the SiH monolayer. The electronic band structure, optical characteristics, photocatalytic capabilities and stability of the SiTe/SiH heterostructure were comprehensively examined based on the density functional theory. The obtained results indicated that biaxial strain is an effective strategy for improving the properties under consideration. These results demonstrated that the stable SiTe/SiH heterostructure exhibits a type II band alignment and possesses an indirect band gap of 1.725 eV/2.307 eV according to the PBE/HSE06 method. When the biaxial strain increases, the band gap of SiTe/SiH decreases linearly, reaching a minimum band gap when subjected to a strain of −6 %. Moreover, the SiTe/SiH heterostructure reveals an upward trend in optical properties within the visible spectrum, peaking in the visible and violet regions. Furthermore, the photocatalytic characteristics conserved at strains from −4% to +6 % because the band edges satisfy the reduction and oxidation standard potentials. A biaxial strain influence may be used to regulate the SiTe/SiH heterostructure, which smoothly enhances photogenerated carrier segregation. Consequently, the heterostructure is a perfect choice for photovoltaic application and photocatalysis due to its high optical absorption, and adjustable photocatalytic and electronic properties.

Composite ellipsoids to model charge anisotropy in particle-scale simulations of kaolinite

This paper outlines a new approach to use coarse-grained molecular dynamics (CGMD) and the Gay–Berne (GB) potential to simulate the compression of kaolinite saturated with water at an acidic pH ( = 4) in a low (1 mM) ion concentration solution. To overcome the limitations of the standard GB potential and capture the charge heterogeneity on the surface of kaolinite particles under acidic pH conditions, each clay platelet is modelled using a two-ellipsoid composite particle. The molecular dynamics software Large-scale Atomic/Molecular Massively Parallel Software was employed to generate virtual monodisperse samples containing 1000 composite particles and to simulate isotropic compression at 100 kPa. The observed macro-scale response in void ratio–effective stress space lay above the response obtained in a simulation that used an equivalent CGMD model developed to simulate alkaline (pH = 8) pore water conditions. This is in qualitative agreement with available experimental data for one-dimensional compression. A post-compression qualitative observation of two virtual samples revealed a book-house-type fabric in the sample with acidic pore fluid, whereas a turbostatic-type fabric was observed when an alkaline pore fluid was simulated. These observations are also in qualitative agreement with scanning electron microscopy data reported in the literature.

The anodic dissolution kinetics of Mg alloys in water based on ab initio molecular dynamics simulations

AbstractThe corrosion susceptibility of magnesium (Mg) alloys presents a significant challenge for their broad application. Although there have been extensive experimental and theoretical investigations, the corrosion mechanisms of Mg alloys are still unclear, especially the anodic dissolution process. Here, a thorough theoretical investigation based on ab initio molecular dynamics and metadynamics simulations has been conducted to clarify the underlying corrosion mechanism of Mg anode and propose effective strategies for enhancing corrosion resistance. Through comprehensive analyses of interfacial structures and equilibrium potentials for Mg(0001)/H2O interface models with different water thicknesses, the Mg(0001)/72 H2O model is identified to be reasonable with −2.17 V vs. standard hydrogen electrode equilibrium potential. In addition, utilizing metadynamics, the free energy barrier for Mg dissolution is calculated to be 0.835 eV, enabling the theoretical determination of anodic polarization curves for pure Mg that aligns well with experimental data. Based on the Mg(0001)/72 H2O model, we further explore the effects of various alloying elements on anodic corrosion resistance, among which Al and Mn alloying elements are found to enhance corrosion resistance of Mg. This study provides valuable atomic‐scale insights into the corrosion mechanism of magnesium alloys, offering theoretical guidance for developing novel corrosion‐resistant Mg alloys.

Relationship between the Thermodynamic Quantities and Coordination Structure of Oxide Ions in CaCl2-Based Chloride Melts.

Measuring the thermodynamic quantities and coordination structure of oxide ions in CaCl2-based melts is essential for comprehensively understanding the relationship between the thermodynamic and microscopic behaviors of high-temperature molten salts. In this study, the standard formal chemical potentials of oxide ion, μO2- o', and activity coefficient, γO2- , in NaCl-CaCl2, NaCl-KCl-CaCl2, and LiCl-KCl-CaCl2 melts at 873 K, were evaluated by measuring the dependence of potential of O2/O2- on the oxygen partial pressure by using non-consumable ceramic electrodes; the μO2- o' was -527 ± 0.3, - 535 ± 0.1, and -538 ± 0.2 kJ mol-1 and the γO2- was 0.10, 0.30, and 0.45 for each melt. In addition, the coordination structure of oxide ions in each melt was investigated by combining high-temperature Raman spectroscopy and density functional theory calculations. The coordination structures of oxide ions were identified as [NaO2]3- and [CaOCl3]3- in the NaCl-CaCl2 melt, [CaOCl2]2- in the NaCl-KCl-CaCl2 melt, and [LiCaO]+ and [Li3KO]2+ in the LiCl-KCl-CaCl2 melt, revealing that the stable structure was significantly different depending on the melt composition. The activity coefficients showed a tendency to depend on the nearest-neighbor cation coordinated with the oxide ion. The reported data will provide insights into the physicochemical properties of high-temperature melts and contribute to controlling the compatibility of materials and melts in pyrochemical engineering processes.

Evaluation of the Xtb Semiempirical Method for the Prediction of Antioxidant Properties in Alzheimer’s Disease: Salen-Type Ligands

Alzheimer’s disease (AD) stands as the predominant form of dementia, accounting for up to 70% of all cases worldwide. AD is a complex disease with various contributing factors. Evidence suggests that the metalliccomplexes formed by the β-amyloid peptide (Aβ) and extraneuronal copper can catalyze the generation ofreactive oxygen species, consequently increasing oxidative stress and contributing to the decline of neurons. This interaction underscores the significance of bioavailable copper as a crucial redox-active target in exploring protocols for multifunctional agents in AD treatment. In the field of computational chemistry, density functional theory (DFT) is widely accepted as a standard method across different disciplines. Despite this, DFT presents computational challenges, particularly in screening extensive molecular sets during the initial phases of drug research. Recent advances in semiempirical quantum mechanical methods (SQM) offer a promising alternative, providing rapid molecular geometry optimization and approximate estimation of thermodynamical properties, being at least two orders of magnitude faster than traditional DFT calculations. In this work, we present an evaluation of the GFNn-xTB SQM methods in the rapid screening of antioxidant properties in AD, performed on a set of salen ligands by calculating the standard reduction potentials of their copper complexes as key property. Results show that the implementation of GFNn-xTB SQM calculations before DFT evaluations is

Competitive response of maize against glyphosate-resistant Digitaria insularis and Eleusine indica

To optimize integrated weed management, it is essential to understand the competitive ability of maize hybrids with new traits when coexisting with the weed community. Thus, the aim of this study was to evaluate the competitive ability of the maize against E. indica and D. insularis weeds under greenhouse (controlled conditions) and in the field by additive and replacement series designs, with different densities for each condition. In greenhouse experiments, maize coexisting with E. indica resulted in negative relative growth for leaf area and shoot dry mass, indicating damage to both species. However, maize with D. insularis did not exhibit negative relative growth, suggesting a different interaction. The analysis of relative competitiveness and aggressiveness revealed significant values for maize with D. insularis, indicating a competitive relationship. In contrast, maize with E. indica showed non-significant values, suggesting a less competitive interaction. In field experiments, the full model and reduced models showed good fit to the data, with non-significant differences between them, indicating that the interference of these weed species on maize yield were similar. The Principal Component Analysis identified four principal components. For PCs 1 and 2, chlorophyll-related variables exhibited a high relative contribution, showing a positive correlation with cases involving high density of D. insularis. Variables related to ear insertion height, plant height, stem diameter, and stand of plants had greater relative importance for PC 1, especially for cases with higher density of E. indica. This highlights the resilience of maize to competitive conditions and suggests that its capacity for rapid growth in height makes this crop effective in competition for light, even against other C4 species.

Replacing a Cysteine Ligand by Selenocysteine in a [NiFe]-Hydrogenase Unlocks Hydrogen Production Activity and Addresses the Role of Concerted Proton-Coupled Electron Transfer in Electrocatalytic Reversibility.

Hydrogenases catalyze hydrogen/proton interconversion that is normally electrochemically reversible (having minimal overpotential requirement), a special property otherwise almost exclusive to platinum metals. The mechanism of [NiFe]-hydrogenases includes a long-range proton-coupled electron-transfer process involving a specific Ni-coordinated cysteine and the carboxylate of a nearby glutamate. A variant in which this cysteine has been exchanged for selenocysteine displays two distinct changes in electrocatalytic properties, as determined by protein film voltammetry. First, proton reduction, even in the presence of H2 (a strong product inhibitor), is greatly enhanced relative to H2 oxidation: this result parallels a characteristic of natural [NiFeSe]-hydrogenases which are superior H2 production catalysts. Second, an inflection (an S-shaped "twist" in the trace) appears around the formal potential, the small overpotentials introduced in each direction (oxidation and reduction) signaling a departure from electrocatalytic reversibility. Concerted proton-electron transfer offers a lower energy pathway compared to stepwise transfers. Given the much lower proton affinity of Se compared to that of S, the inflection provides compelling evidence that concerted proton-electron transfer is important in determining why [NiFe]-hydrogenases are reversible electrocatalysts.