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In 1972, Trasatti compiled the exchange current densities j0 and work functions 𝚽 for the hydrogen evolution reaction (HER) on 31 polycrystalline metals at pH 0. Exchange current density measures the HER rate and the work function measures the energy required to remove an electron from the surface of the metal to a point outside the metal. Trasatti showed a plot of log j0 vs 𝚽 linear for the so called d metals and for the sp metals. The slopes are statistically the same for the d and sp metals (6.44 and 6.6 excludes Hg) but the intercepts differ (-35.4 and -38). Here, a thermodynamic specification for the slope of log j0 versus 𝚽 is suggested as 𝛂F/RT, where 𝛂 is the transfer coefficient for heterogeneous electron transfer. Electrochemical potentials for species i in phase j have been used to derive the rates of heterogeneous electron transfer within a transition state context for Butler Volmer kinetics (Bard and Faulkner). The standard chemical potential, activity, and ion charge for species i are 𝝁i 0,j, ai j, and zi is the electrical potential is 𝝓j. Extrapolation of the electrochemical potential to include 𝚽 and derive a rate expression for j0 yield: The electrode potential and the work function group into a common term. The slope of log j0 versus 𝚽 as 𝛂F/RT. An explanation of how Pt with the highest energetic cost to remove an electron 𝚽 yields the highest log j0 is presented. At 25 oC, F/RT = (0.05916 V)-1. Within the electrochemical potential model for log j0 versus 𝚽, the slopes of 6.44 and 6.6 for the d and sp metals at room temperature yield 𝛂 of 0.381 and 0.39. Across 30 metals, 𝛂 is estimated the same. The value of 0.4 is common in measurements of 𝛂 found for the potential dependent term in Butler Volmer kinetics. References Trasatti, S. Work Function, Electronegativity, and Electrochemical Behavior of Metals. III. Electrolytic Hydrogen Evolution in Acid Solution. Electroanalytical Chemistry and Interfacial Electrochemistry 39, 163-184 (1972). A.J. Bard and L. R. Faulkner, Electrochemical Methods, 1980, wiley and Sons, Chapter 2. Acknowledgments This work was supported by the National Science Foundation and the Army Research Office. The University of Iowa Obermann Center for Advanced Studies is acknowledged.

Here we describe the synthesis, structures, and reactivity of Ru complexes containing a triaryl, redox-active S2N2 ligand derived from o-phenylenediamine and thioanisole subunits. The coordination chemistry of N,N′-bis[2-(methylthio)phenyl]-1,2-diaminobenzene [H2(MeSNNSMe)] was established by treating RuCl2(PPh3)3 with H2(MeSNNSMe) to yield {Ru[H2(MeSNNSMe)]Cl(PPh3)}Cl (1). Coordinated H2(MeSNNSMe) was sequentially deprotonated to form Ru[H(MeSNNSMe)]Cl(PPh3) (2) followed by the five-coordinate, square pyramidal complex Ru(MeSNNSMe)(PPh3) (3). Single-crystal X-ray diffraction (XRD) studies revealed that the ligand structurally rearranged around the metal at each deprotonation step to conjugate the adjacent aryl groups with the o-phenylenediamine backbone. Deprotonation of 2 with NaBH4 or treatment of 3 with BH3·tetrahydrofuran (THF) yielded Ru[(μ-H)BH2](MeSNNSMe)(PPh3) (5) with BH3 bound across a Ru–N bond in a metal–ligand cooperative fashion. The cyclic voltammogram of 3 in THF revealed three redox even...

Square wave voltammetry (SWV) is used to investigate fast electron transfer kinetics across a wide range of redox active species. SWV is an inherently faster, frequency dependent method as compared to most potential sweep methods. Sweep methods commonly implement an applied potential as a staircase of small potential steps. The frequencies of SWV can be related to sweep methods as the product of SWV frequency and the potential increment at each staircase step. Recent work in our group has shown that k0 measurements for tris-bipyridine transition metal complexes can be made using SWV as the wave morphology changes with k0. Heterogeneous electron transfer rates are not reliably measured at the slower voltage perturbations (scan rates) available with cyclic voltammetry (CV). The heterogeneous electron transfer rates k0 for M(bpy)3 z+ complexes, where M = Ru2+, Os2+, Cr3+, Co2+, Co3+, and Fe2+ are sufficiently rapid that k0 is not reliably measured by CV for most of these complexes. Analysis of the SWV data is possible but not as facile as analysis of CV data. To better evaluate k0 measurements, an alternative data analysis algorithm for quasireversible heterogeneous electron transfer is developed based on classical finite difference simulations. The algorithm can be envisioned as converting voltammograms between CV and SWV. Because CV and SWV both contain a potential parameter and a time parameter (mV/s in CV; frequency and step height in SWV), the algorithm uses a “universal scan rate” to convert between all of the other potential and time-dependent parameters. The purpose of the algorithm is to simplify quantitative SWV data analysis and present information in context of the more commonly used CV.

Technologically, the hydrogen evolution reaction (HER) is the foundation of many electrochemical energy systems. Fundamentally, HER is important as 2H+ + 2e ⇌ H2 defines the standard reference potential E0 H = 0.000 V in thermodynamics. All evolutions in kinetic theory are critically tested against HER. In electrocatalysis, the HER mechanism is historically specified in three steps. The first step, Volmer, couples concerted adsorption and reduction of proton to form electrochemically adsorbed hydrogen. H+ + e ⇄ Hads (Volmer) (1) Once the first proton electroadsorbs, H2 forms by two parallel pathways. The Heyrovsky step proceeds as a second proton is electroadsorbed to the same metal atom and hydrogen gas desorbs from the common metal center. Hads + H+ + e ⇄ H2 (Heyrovsky) (2) In the Tafel step, electrochemically adsorbed hydrogen forms on an adjacent metal center and H2 desorbs. Hads + Hads ⇄ H2 (Tafel) (3) Commonly, HER electrode kinetics are evaluated according to the Volmer-Heyrovsky-Tafel scheme, where rate is measured as exchange current densities j₀. For HER at metal electrodes, log j₀ depends strongly on the electrode metal where log j₀ falls between -3 for Pt, Re, and Pd and -12 for Hg. Although metals are not explicit in the Volmer-Heyrovsky-Tafel scheme, j₀ is evaluated in view of Steps (1) to (3). Here, metal electrode properties are introduced as the standard potential E0 M of the electrode metal. For metal cation reduction to metal M⁰, Mz+ + ze ⇌ M⁰ E0 M log j₀ values are cataloged in a paper by Trasatti (Electroanalytical Chemistry and Interfacial Electrochemistry 1972, 39, 163-184), where he partitioned 31 metal electrodes into d and sp metals. For the transition metals, the d metals, log j₀ is well and linearly correlated with E0 M . For the sp metals, there is little to no correlation of log j₀ with E0 M . For the transition metals, several observations and a model sketch are noted. HER rates as log j₀ increase with more positive values of E0 M . For the initial step of the metal dependent HER process, it is sketched that electron(s) release from M0 to form Mz+ immediately at the electrode surface. For this initial step, formation of Mz+ immediately at the electrode solution interface yields log j₀ linearly dependent on E0 M . Within transition state or activated complex theory, a proposed transition state is formed of electron(s) shared between Mz+ and H+. Formation of the transition state [(1/z)Mz+⋯e⋯H+]‡ precedes the Volmer step, and where applicable, is a rate determining step. Overpotential η pinned by E0 M may characterize the counter intuitive observation that rate (log j₀) increases as E0 M is more positive. This sketch of HER yields a kinetic model where a component of the activation energy is set by F(E0 H -E0 M ). The sketch of an electrode dependent transition state may pose a general approach to characterizing electrocatalysis and interfacial electron transfers. The proposed transition state introduces physical properties of specific electrode materials into the rate expressions a priori.

The hydrogen evolution reaction (HER) is critical technologically in electrochemically energy systems. HER is also important fundamentally as 2H⁺ + 2e ⇌ H₂ provides the standard reference potential E0 H = 0.000 V in thermodynamics and HER serves as a primary and critical test case for kinetics theory. For HER electrocatalytic rates, the mechanism is historically broken down into three steps. The reaction sequence begins with adsorption and reduction of proton to form electrochemically adsorbed hydrogen. This is the Volmer step. H⁺ + e ⇄ Hads (Volmer) After the first Hads is formed, H2 can be formed by two pathways. In the Heyrovsky pathway, a second proton undergoes electrochemical hydrogen adsorption at the same metal atom to form hydrogen gas. Hads + H⁺ + e ⇄ H2 (Heyrovsky) In the Tafel pathway, electrochemically adsorbed hydrogens on adjacent metal atoms react to form H2. Hads + Hads ⇄ H2 (Tafel) HER electrode kinetics measured as exchange current densities j₀ are evaluated in accord with the Volmer-Heyrovsky-Tafel scheme. For HER at metal electrodes, log j₀ is known highly dependent on the metal of the electrodes with rates that vary > 10 orders of magnitude. HER data are evaluated according to these three steps, despite that properties of the metal are not explicit in the Volmer-Heyrovsky-Tafel scheme. Here, properties of the metal electrode are introduced through the standard potential E0 M. For metal M0, Mz+ + ze ⇌ M⁰ E0 M Data for log j₀ are taken from a paper by Trasatti (Electroanalytical Chemistry and Interfacial Electrochemistry (1972) 39, 163-184). Trasatti grouped the 31 metal electrodes into d and sp metals. For the d metals (transition metals), log j₀ is well and linearly correlated with E0 M, whereas for the sp metals, little to no correlation is found. Several points are considered. Higher HER rates are observed at transition metal electrodes with more positive values of E0 M. It is sketched that the initial step in the metal dependent HER process is release of electron(s) to form Mz+ immediately at the electrode surface. Where formation of Mz+immediately at the electrode solution interface is the initial step, log j₀ is anticipated linearly dependent on E0 M. The behavior is sketched within transition state or activated complex theory and is based on a transition state formed of electron(s) shared between the metal cation Mz+ and the proton H+. Formation of the transition state [(1/z)Mz+⋯e⋯H+]‡ precedes the Volmer step, and where applicable, is a rate determining step. Implications for overpotential η pinned by E0 M are considered. This may account for the counter intuitive observation that higher log j₀ are found on metals such as Pt where E0 M is more positive. A kinetic model is sketched where a component of the activation energy is set by F(E0 H-E0 M). Finally, the process of proposing an electrode dependent transition state and evaluating the thermodynamic and kinetic consequences may yield a general method for modeling interfacial electron transfer and electrocatalysis. Such a process may introduces electrode specific properties into the rate expressions a priori.