Dynamics of adiabatic electron transfer reactions at metal electrodes

We have investigated the dynamics of adiabatic electron transfer reactions at metal electrodes using a Hamiltonian suggested by Schmickler (J. Electroanal. Chem., 204 (1986) 31). We show that in the adiabatic limit the problem reduces to that of dynamics of a single variable, the shift of the ionic orbital caused by its interaction with the solvent. This variable is identified as the reaction co-ordinate for the problem and we show that in certain limits, it obeys a non-linear Volterra type integral equation, with a stochastic inhomogeneous term. For an inhomogenous term with the autocorrelation function decaying exponentially, this may be converted into a differential equation for Brownian motion. This equation can be analysed to obtain the rate, through the associated Fokker-Planck equation. The rate so obtained, has a correction to the pre-exponential factor obtained by Schmickler. A possible extension to inner sphere reactions is also discussed.     

Approximate critical conditions in thermal explosion theory for a two-step kinetic model

Approximate critical conditions for a thermal explosion problem is developed for a two-step reactions based on theories of Semenov and Frank-Kamenetskii. The aim is to examine the contributions of the radical termination step and the temperature dependent pre-exponential factor on the critical parameters within the framework of classical stationary and non-stationary theories. In the non-stationary case, a more general expression for the critical Semenov parameter (Ψ _cr ) and critical temperature (θ _cr ) were obtained by asymptotic procedure. In the stationary case, numerical estimates for the critical Frank-Kamenetskii parameter (δ _cr ) and the critical temperature (θ _cr ) were obtained by variational method technique. It was observed that the Semenov and Frank-Kamenetskii parameters are greatly influenced by the termination step and the variable pre-exponential factor. Apart from elucidating hitherto unknown features in the theory of thermal explosion, the results are more general as some known results are easily recovered.     

Effects of Electron Correlations in a Simple Model for Adiabatic Electrochemical Reactions: The Diagram of Kinetic Regimes

In the framework of the surface-molecule model for adiabatic electrochemical reactions of electron transfer previously suggested by the authors, a diagram of kinetic regimes (DKM) in the space of model parameters is obtained. The diagram comprises critical regions that correspond to various feasible electron transfer processes (transfer of one electron, simultaneous transfer of two electrons, transfer of two electrons in the presence of an intermediate state) and a region corresponding to electroadsorption of the reagent in certain charge states. Analytical expressions for boundary curves of DKM are obtained for a number of simple cases. A DKM for the general case of the surface-molecule model with an exact allowance for electron–electron correlations is constructed and analyzed.     

Concerted proton-electron transfers. Consistency between electrochemical kinetics and their homogeneous counterparts

The concerted proton-electron transfer (CPET) oxidation of phenol with water (in water) and hydrogen phosphate as proton acceptors provides a good example for testing the consistency of the electrochemical and homogeneous approaches to a reaction, the comprehension of which raises more mechanistic and kinetic challenges than that of a simple outer-sphere electron transfer. Comparison of the intrinsic kinetic characteristics (obtained at zero driving force of the CPET reaction) shows that consistency is indeed observed after a careful identification and quantitation of side factors (electrical work terms, image force effects). Water (in water) appears as a better intrinsic proton acceptor than hydrogen phosphate in both cases in terms of reorganization energy and pre-exponential factor, corroborating the mechanism by which electron transfer is concerted with Grotthus-type proton translocation in water. Detailed compared analysis of the approaches also revealed that modest but significant electric field effects may be at work in the electrochemical case. Comparison with phenoxide ion oxidation, taken as a reference outer-sphere electron transfer, points to a CPET precursor complex that possesses a precise spatial structure allowing the formation of one or several H-bonds as required by the occurrence of the CPET reaction, thus decreasing considerably the number of efficient collisions compared with those undergone by structureless spherical reactants.     

Solvent effects on simple electron transfer reactions: A comparison of results for homogeneous and heterogeneous systems

Solvent effects on the rate constants for both homogeneous and heterogeneous electron transfer reactions have been analyzed on the basis of current models which consider the role of dynamic relaxation processes in determining the magnitude of the pre-exponential factor. A statistical method for separating the effects of the solvent longitudinal relaxation time τ_L from those of the solvent permittivity parameter γ is described and applied to 15 sets of experimental data for which results are available in at least four solvents. The degree to which the explained variation in the logarithm of the rate constant could be attributed to either of these effects varied all the way from 0 to 100% depending on the degree of reaction adiabaticity and the relative sizes of the inner and outer sphere components of the Gibbs energy of activation. Data for the limiting cases in which there is no τ_l dependence in the pre-exponential factor or in which the pre-exponential factor is proportional to τ_L⁻¹ were analyzed further to obtain the size-distance parameter and the components of the pre-exponential factor relevant to the encounter pre-equilibrium model. These parameters have been discussed with respect to current developments in electron transfer theory. Problems in estimating the longitudinal relaxation time in the solvent, required for the analysis, are also considered.     

Regression Analysis of Rate Parameters for the Photoinduced Electron Transfer Reaction

The dependence of the rate constant for the quenching of the triplet state of xanthene dyes by cyanide complexes of transition metals on the free energy change of the photoinduced electron transfer reaction is correlational, rather than functional, in character. Experimentally, it was proved that there is no spin forbiddance in the photoinduced electron transfer reaction between these reactants. For the photoreactions with reactants in which dyes are electron acceptors, the values of the intrinsic barrier of electron transfer and the pre-exponential factor of the reaction rate constant were determined. A method for the determination of calculation errors for these values was proposed.     

Water (in water) as an intrinsically efficient proton acceptor in concerted proton electron transfers

The oxidation of PhOH in water by photochemically generated Ru(III)(bpy)(3) is taken as prototypal example disclosing the special character of water, in the solvent water, as proton acceptor in concerted proton-electron transfer reactions. The variation of the rate constant with temperature and driving force, as well as the variation of the H/D kinetic isotope effect with temperature, allowed the determination of the reaction mechanism characterized by three intrinsic parameters, the reorganization energy, a pre-exponential factor measuring the vibronic coupling of electronic states at equilibrium distance, and a distance-sensitivity parameter. Analysis of these characteristics and comparison with a standard base, hydrogen phosphate, revealed that electron transfer is concerted with a Grotthus-type proton translocation, leading to a charge delocalized over a cluster involving several water molecules. A mechanism is thus uncovered that may help in understanding how protons could be transported along water chains over large distances in concert with electron transfer in biological systems.     

Protonation of anion radicals and dianions of some dinitro aromatics

A simple electrochemical method developed to study reactions of reactive intermediates (neutralfree readical, cation-, anion- radicals etc.) was employed to study the protonation reaction of anion radicals and dianions of some dinitroaromatics. Rate constants thus obtained and the mechanism of protonation reaction invesitgated, are reported. It is suggested that the reactions do not involve a direct electron transfer. The possible role of various ion-pairs was investigated. Positions of nucleophilic attack were investigated through M.O. calculations.     

Acid/base-regulated reversible electron transfer disproportionation of N–N linked bicarbazole and biacridine derivatives

Regulation of electron transfer on organic substances by external stimuli is a fundamental issue in science and technology, which affects organic materials, chemical synthesis, and biological metabolism. Nevertheless, acid/base-responsive organic materials that exhibit reversible electron transfer have not been well studied and developed, owing to the difficulty in inventing a mechanism to associate acid/base stimuli and electron transfer. We discovered a new phenomenon in which N–N linked bicarbazole (BC) and tetramethylbiacridine (TBA) derivatives undergo electron transfer disproportionation by acid stimulus, forming their stable radical cations and reduced species. The reaction occurs through a biradical intermediate generated by the acid-triggered N–N bond cleavage reaction of BC or TBA, which acts as a two electron acceptor to undergo electron transfer reactions with two equivalents of BC or TBA. In addition, in the case of TBA the disproportionation reaction is highly reversible through neutralization with NEt₃, which recovers TBA through back electron transfer and N–N bond formation reactions. This highly reversible electron transfer reaction is possible due to the association between the acid stimulus and electron transfer via the acid-regulated N–N bond cleavage/formation reactions which provide an efficient switching mechanism, the ability of the organic molecules to act as multi-electron donors and acceptors, the extraordinary stability of the radical species, the highly selective reactivity, and the balance of the redox potentials. This discovery provides new design concepts for acid/base-regulated organic electron transfer systems, chemical reagents, or organic materials.     

Effects of Electron Correlations in a Simple Model for Adiabatic Electrochemical Reactions: The General Relationships

General relationships for adiabatic free-energy surfaces (AFES) for electrochemical reactions of electron transfer are derived in the framework of exactly solvable model of the so-called surface molecule, which is a limiting case of Anderson's Hamiltonian and may be applied to transition metals. As opposed to earlier models for adiabatic reactions, the model exactly allows for the effects of electron–electron correlations. The obtained results constitute a basis for calculating AFES and plotting diagrams that correspond to different kinetic regimes of one- and two-electron processes.     

H-bond relays in proton-coupled electron transfers. Oxidation of a phenol concerted with proton transport to a distal base through an OH relay

Four molecules comprising a phenol moiety and a distal pyridine base connected by an intermediary H-bonding and an H-bonded alcohol group have been synthesized and their electrochemistry has been investigated by means of cyclic voltammetry. The molecules differ by the substituent at the alcohol functional carbon and by methyl groups on the pyridine. The reaction follows a concerted proton-electron transfer pathway as confirmed by the observation of a significant H/D kinetic isotope effect in all four cases. The standard rate constants characterizing each of the four compounds are analyzed in terms of reorganization energy and pre-exponential factor. Intramolecular and solvent reorganization energies appear as practically constant in the series, in which a previously investigated aminophenol is included, whereas significantly different pre-exponential factors are observed. That the latter, which is a measure of the efficiency of proton tunneling concerted with electron transfer, be substantially smaller with the H-bond relay molecules than with the aminophenol is related to the fact that two protons are moved in the first case instead of one in the second. Within the H-bond relay molecules, the pre-exponential factor varies with the substituent present at the alcohol functional carbon in the order CF(3) > H > CH(3), presumably as the result of a fine tuning of the balance between the H-bond accepting and H-bond donating properties of the central OH group. The kinetic H/D kinetic isotope effect increases accordingly in the same order.     

Electron Correlation Effects for Adiabatic Electrochemical Reactions of Electron Transfer in a Model for an Electrode with an Infinitely Wide Conduction Band: Diagrams of Kinetic Modes

For adiabatic electrochemical reactions, within the framework of a model for an electrode with an infinitely wide conduction band, exact results are obtained for critical regions that correspond to different possible types of electron transfer processes (transfer of a single electron with and without an intermediate state, simultaneous transfer of two electrons) and regions that correspond to electroadsorption of the reactant in certain charge states. These regions form a diagram of kinetic modes (DKM) in the space of model parameters. Analytical expressions for outermost curves of DKM are obtained for some extreme cases. For the general case of a model for an electrode with an infinitely wide conduction band, a DKM is constructed and investigated with exact allowance for the effects of electron–electron correlations.     

On the theory of tunnelling in electron and proton transfer reactions

The concept of tunnelling in the theory of electron and proton transfer reactions has recently been questioned on the ground that the situation is a non-stationary one. It has been suggested that time-dependent perturbation theory should be applied to obtain the quantum mechanical transition probability. We have done this for a square barrier. The result for most reactions is the same as obtained by the WKB approximation.     

Charge transfer dynamics of donor-acceptor systems in solutions and sol-gel matrices

Charge transfer reactions are photoinduced by exciting with UV and visible light strongly coupled donor acceptor pairs. The systems investigated are composed either of porphyrin and phthalocyanine mixed dimers. In this case, the proton transfer competes with the electron transfer process.The results obtained in sol-gel matrices are compared to the ones in solutions and organized media, and discussed in terms of the effect of the confinement of the reactants and degree of organization of the environment on the efficiency of charge transfer reactions.     

Photoinduced electron-transfer reactions in a host-guest assembly of mono-6-p-nitrobenzoyl-β-cyclodextrin with N-(1-naphthylacetyl)-1-adamantanamine

Photoinduced electron transfer was studied in a supramolecular complex assembled by an electron-donating substrate (N-(1-naphthylacetyl)-1-adamantanamine (1)) and an electron-accepting receptor (p-nitrobenzoyl--cyclodextrin (NBCD)), which was stabilized by hydrophobic interactions in water/methanol (9 : 1) binary solvents. Fluorescence quenching results indicated that the electron transfer process occurred in a intra-supramolecular system. The electron transfer reactions of 1- or 2-naphthyl acetate with NBCD were also studied, and upward Stern-Volmer curves were obtained. It is concluded that two different electron transfer pathways, intra-supramolecular and inter-molecular electron transfer processes, exist.     

鎓盐的固液相转移平衡研究(Ⅰ)——溴化四丁铵和羧酸钾的平衡常数测定

目前广泛应用的液-液相转移催化反应有两个主要的缺点:一是有一些水分子会随着离子对一起萃入有机相并在其周围形成水化膜[1,2],这不仅会降低反应速度有时还会引起种种副反应[3,4]。     

生物体系中电子转移机理的理论研究Ⅰ: 一种计算电子转移 的方法及在螺环化 合物中的应用

应用"相应轨道变换"和"广义"密度矩阵的方法,向MOPAC程序包中加入了新的功能,使其能处理电子转移反应中的部分参数。然后用此程序包中AM1方法对具有螺环结构的分子进行处理,计算了化合物在不同外加电场强度下的势能面、反应热ΔE,重组能λ及电子转移矩阵元V~A~B,结果表明,λ,V~A~B受外加电场的影响较小,而ΔE则与之成正比。对标题化合物1的计算结果也同abinitio法的结果进行了比较,发现其变化趋势完全一致,这说明本方法在计算电子转移方面是可靠的。与abinitio方法相比,本程序不仅适用于计算较大体系(如生物大分子),而且还具有速度快,耗时少的优点。     

Light‐Triggered,Spatially Localized Chemistry by Photoinduced Electron Transfer

It is of immense interest to exert spatial and temporal control of chemical reactions. It is now demonstrated that irradiation can trigger reactions specifically at the surface of a simple colloidal construct, obtained by adsorbing polyethyleneimine on fluorescent colloidal particles. Exciting the fluorescent dye in the colloid affords photoinduced electron transfer to spatially proximal amine groups on the adsorbed polymer to form free radical ions. It is demonstrated that these can be harnessed to polymerize acrylic acid monomer at the particle surface, or to break up colloidal assemblies by cleaving a cross‐linked polymer mesh. Formation of free radical ions is not a function of the size of the colloid, neither is it restricted to a specific fluorophore. Fluorophores with redox potentials that allow photoinduced electron transfer with amine groups show formation of free radical ions.     

Structure�Creactivity relationships in inorganic electrochemistry

Relationships between structure and electron transfer reactivity underlie many important electrochemical applications and provide fundamental insight to chemical and biological processes. The vast array of experimental techniques developed during the latter half of the twentieth century helped greatly to foster progress in this area, and the advent of powerful computational techniques such as density functional theory promises even more far-reaching developments. It is evident that molecular composition, geometric and electronic structure, and changes in these features influence the thermodynamics and kinetics of transition metal electron transfer reactions in predictable and understandable ways. Several examples drawn from the author??s research program to illustrate this premise include the influence of sulfur versus oxygen donation on molybdenum-centered electron transfer, reactions in which a change in metal atom spin state accompanies electron transfer, and concomitant multi-electron transfer and metal?Cmetal bond cleavage in binuclear, ligand-bridged complexes.