Outer-sphere Electron-transfer Reactions Research Articles

Rate-determining electron-transfer reactions in highly aqueous alcohol–water mixtures. A quantitative analysis of solvent effects on the oxidation of 4-methoxyphenylacetate by potassium 12-tungstocobaltate(III)

Kinetic solvent effects on the rate-determining outer-sphere electron-transfer reaction between 4-methoxy-phenylacetate and potassium 12-tungstocobaltate(III) in highly aqueous alcohol–water mixtures are quantitatively analysed in terms of pairwise Gibbs energy parameters for interaction of the initial and transition state with the cosolvent.

Comparative Kinetic Analysis of Reversible Intermolecular Electron-Transfer Reactions between a Series of Pentaammineruthenium Complexes and Cytochrome c.

In this kinetic and thermodynamic study, the reversible outer-sphere electron-transfer reactions between a series of Ru(NH(3))(5)L(3+/2+) complexes (L = etpy, py, lut) (etpy = 4-ethylpyridine; py = pyridine; lut = 3,5-lutidine) and cytochrome c were investigated as a function of ionic strength, buffer, pH, temperature, and pressure. Due to the low driving forces of these systems, it was possible to study all the reactions in both redox directions. The observed rate constants for various L are correlated on the basis of the ability of ligands on the ruthenium complex to penetrate the heme groove on cytochrome c. The measurements as a function of pressure enabled the construction of volume profiles for all investigated systems. The activation volumes for all of these processes are very similar: between -14.9 and -17.8 cm(3) mol(-)(1) for the reduction and between +14.7 and +17.8 cm(3) mol(-)(1) for the oxidation of the protein by Ru(NH(3))(5)L(2+/)(3+), respectively. The overall reaction volume varies between 27 and 35 cm(3) mol(-)(1), from which it follows that the transition state lies exactly halfway between reactant and product states on a volume basis in all cases. There is good agreement throughout between kinetic and thermodynamic data.

The role of solvent in inorganic reaction mechanisms, as elucidated by high pressure studies

Pressure effects on the rates of simple inorganic reactions in solution act primarily on intermolecular interactions, particularly solvation. They afford the possibility of “tuning” solvent properties without altering the solvent chemically. Outer-sphere self-exchange electron transfer reactions of transition metal complexes provide an opportunity to test this idea quantitatively, through an adaptation of Marcus-Hush theory. The theory is only moderately successful for organic solvents, as the solvent “seen” by the reactant behaves as if it is less compressible than bulk solvent. Furthermore, for multiply-charged ions or for solvents of low relative permittivity, the calculations become unstable even without the likely complication of ion pairing. For aqueous systems, the theory is successful except where one or more of the following complications applies: (a) changes in total spin multiplicity accompany the electron transfer process in complexes with flexible ligand systems; (b) cation-mediated pathways emerge in anion-anion self-exchange reactions; (c) the reactants are so small that the assumption that the solvent is a continuous dielectric fails; or (d) an inner-sphere sphere mechanism is operative.

Factors controlling electron transfer reactions and stabilisation of uncommon oxidation states of chromium

Some experimental approaches to seek semi-quantitative understanding of factors controlling outer sphere electron transfer reactions of some transition metal complexes have been made. The relative importance of nuclear and electronic factors to outer sphere processes has been examined. By the manipulation of Franck-Condon or nuclear factors, it has now been possible to gain access into the chemistry of chromium in unusual oxidation states. An example of a reorganisation controlled electron transfer reaction involving Cr(IV)-Cr(III) system has been demonstrated. The bimolecular rate of reduction of diperoxoaquaethylenediamine chromium(IV) and diperoxodiethylenetriamine chromium(IV) is independent of the nature of th reductant employed viz. Fe2+ or VO2+ indicating that the generation of6 coordinate Cr(IV) species from7 coordinate of diperoxochromium(IV) reactant may be rate limiting. Similarly by increasing the barrier for the6 coordinate to4 coordinate structures through equatorial coordination of macrocyclic ligands, it has now been possible to detect through cyclic voltommogram the formation of relatively stable Cr(IV) species in the electrochemical oxidation of Cr(Me4[14] tetraene)(H2O) 2 3+ in aqueous sulphuric acid media. The kinetics and mechanism of the cerium(IV) and iodosyl benzene oxidation of Cr(salen)(H2O) 2 + and Cr(salprn)(H2O) 2 + have been investigated and kinetic and spectroscopic evidence for the formation of Cr(IV) transients and stable Cr(V) products has been presented. The relative importance of Franck-Condon factors in the oxidation of Cr(III) to Cr(IV) and Cr(V) states in different macrocyclic and multidentate ligand environments has been discussed.

Oxidation and Reduction Reactions of Hydroperoxo Cobalt Macrocycles

The reduction of LCoOOH2+ (L = L' = [14]aneN4 and L2 = Me6[14]aneN4) by Cr2+, Fe2+, V02+, V2+, Ti3+, and Co(tim)*+ has been studied in acidic aqueous solution. The L'CoOOH2+/Fe2+ reaction takes place with a second-order rate constant 4.8 L mol-' s-' at 25 C and 0.10 M H@+. It is accompanied by a large negative entropy of activation, -122 J mol-' K-I. In the presence of a large excess of Fez+, this reaction proceeds with a 1:2 stoichiometry and produces L'Co3+ and Fe3+. A Fenton mechanism is proposed for this and other reduction reactions of LCoOOH2+. The oxidation of LCoOOH2+ by R~(bipy)3~+, Fe(~hen)3~+, IrChj2-, VO2+, and Fe3+ has also been investigated. The outer-sphere electron transfer reactions with Ru(bipy)j3+, Fe(~hen)3~+, and proceed with a 1:2 stoichiometry. The reaction of L'CoOOH2+ with Fe3+ produces 0 2 with a second-order rate constant 2.74 L mol-' s-' at 25 C and 0.10 M H@+. Unlike the reduction reactions, the kinetics of the oxidation of L'CoOOH2+ are acid-dependent.

Effects of solvent polarization relaxation on nonadiabatic outersphere electron transfer reactions in ultrafast dipolar solvents

Since the important work of Efrima and Bixon [J. Chem. Phys. 70, 3531 (1979)], it is believed that solvent polarization relaxation is usually too slow (compared to the rate of electron transfer) or the amplitude of energy fluctuation too large to have any noticeable effect on the dynamics of the nonadiabatic (NA) electron transfer reactions. On the other hand, recent studies have demonstrated that solvent polarization relaxation in several common dipolar liquids can proceed at a rate much faster than that anticipated in the earlier studies. This calls for a re-examination of the role of solvent dynamics on NA electron transfer reactions in these ultrafast solvents. In this paper, the results of such studies are presented for NA reactions in water and acetonitrile. It is found that because of ultrafast solvation, many NA reactions may lie in the dynamic region where the solvent effects are just beginning to be important. The present study further reveals the following new results. (i) In the case of high barrier reactions in solvents such as acetonitrile, the polarization relaxation in the reactant well can contribute significantly to the total rate of the nonadiabatic electron transfer reaction. (ii) In water, on the other hand, the reactive friction is still sufficiently high to make energy diffusion in the reactant well efficient and so, the solvent effects are predicted to be negligible. This is in accord with the earlier theoretical suggestions and is demonstrated here clearly for real systems. (iii) We find an interesting limiting situation where the long time rate can be significantly larger than the rate given by the Marcus expression.

Adiabatic and nonadiabatic outersphere electron transfer reactions in methanol: Effects of the ultrafast solvent polarization modes

Recent studies have demonstrated that the solvation dynamics in common dipolar liquids like water and acetonitrile is dominated by an initial ultrafast Gaussian component which seems to account for about 60%–70% of the total energy relaxation. Methanol, on the other hand, exhibits a rather different behavior with a much smaller amplitude of the initial Gaussian component and the relaxation is primarily caused by a much slower exponential decay. In the present study, we have investigated the role of these solvent modes on both adiabatic and nonadiabatic outersphere electron transfer reactions in methanol. It is found that the rate of the adiabatic barrier crossing is greatly enhanced due to the ultrafast solvation. For nonadiabatic reactions, the relative importance of the solvent dynamic modes increases enormously compared to the situation when only the slow, overdamped modes are included. Another important conclusion is that because of the dominance of the inertial modes, the rate of electron transfer reaction is almost independent of the longitudinal relaxation time, τL, of the solvent. The results of the present study are compared with those obtained earlier by us for water and acetonitrile to elucidate the underlying difference in the high frequency polar response of these liquids.

Volume profile analysis for intermolecular electron transfer between cytochrome c and Co(terpy) 22+/3+

The kinetics and thermodynamics of the reversible outer-sphere electron-transfer reaction between Co(terpy) 2 2+/3+ (terpy=2,2′:6′,2″-terpyridine) and horse-heart cytochrome c III/II was studied as a function of temperature and pressure. The activation volumes for the reduction of Co(terpy) 2 3+ and oxidation of Co(terpy) 2 2+ were found to be +18.4±1.3 and −18.0±1.4 cm 3 mol −1, respectively. The overall reaction volume for the reduction of Co(terpy) 2 3+ was determined to be +33±3 cm 3 mol −1. These data are used to construct a volume profile, from which it follows that the transition state lies exactly halfway between the reactant and product states on a volume basis. The experimental results are in good agreement with the rate constant and activation volume calculated from the Marcus-Hush-Stranks-Swaddle relationships.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

The effect of RuO 2/TiO 2 ratio on the rate of an outer-sphere electron transfer reaction on mixed oxide electrodes

The apparent heterogeneous rate constants can be determined by a special cv technique in solutions containing both the oxidized and the reduced forms of a redox couple. The electrode materials are characterized by the difference between the k 0 ox and k 0 red. The effect of RuO 2/TiO 2 ratio on the electrochemical effective surface area and the apparent rate constants of a redox system are investigated. The optimal composition of the RuO 2/TiO 2 electrode seems to be in the 0.6–0.9 RuO 2 mole fraction range.

Time dependent solution of generalized Zusman model of outersphere electron transfer reactions: Applications to various experimental situations

The Zusman model of the environmental effects on the outersphere electron transfer reaction has been widely used to study solvent effects on various important electron transfer reactions. We present here a generalized treatment of the Zusman model using a powerful Green’s function technique. This generalization enables us to obtain the time dependent solution of the model for various complicated situations often encountered in experiments. In addition, the present formulation allows for a unified description of the barrierless and the high barrier reactions for both the nonadiabatic and the weakly adiabatic limits of electron transfer reactions. A merit of the present description is that one need not assume an initial equilibrium population of the reactants and therefore, this method is particularly suitable for the treatment of photoelectron transfer reactions. The following four model situations have been studied. (a) Ground state, symmetric, and asymmetric electron transfer reactions. The reactant surface population exhibits a markedly nonexponential decay. (b) A low barrier, photoelectron transfer reaction where an additional photochemical reaction occurs from the charge transfer state. In this case, the decay of the reactant population is largely exponential when the funnel is efficient. (c) A high barrier photoelectron transfer reaction with a radiative decay from either or both of the reactant and product surfaces. In specific situations, the radiative decay can even compete with the electron transfer to give rise to a fractional dependence of the fluorescence quantum yield (of the locally excited state) on the average solvation time. (d) A multichannel nonradiative decay of population from an excited state surface having multiple sinks. Here an interesting nonlinear interaction between the sinks is observed. In all these cases, it is found that the average rate of electron transfer can be considerably different from the long time rate. The generality of the present formulation has been demonstrated by deriving the rate expressions of the theory of outersphere electron transfer reaction due to Zusman, that due to Rips and Jortner and also that due to Sumi, Nadler, and Marcus.

Investigation of excited state electron-transfer reactions. A search for other associative processes

Abstract The present investigations were carried out to reveal the nature of the photoinduced electron-transfer (ET) process within the electron donors 1,2,3,4-tetrahydroquinoline (THQ) and 1-methyl-1,2,3,4-tetrahydroquinoline (THMe), and widely used acceptor tetracyanoquinodimethane (TCNQ) in the highly polar solvent acetonitrile (ACN) at 300 K. Observations of considerable overlapping between the emission spectrum of the donor molecules studied in the present investigation and the electronic absorption spectrum of the acceptor TCNQ, coupled to a high negative value of Δ G [the energy gap between the locally excited (LE) and radical ion pair (RIP) states] when one of the chromophores is excited, indicate the possibility of concurrent occurrence of the two processes, e.g. energy and electron transfer. Surprisingly even when the donor chromophore is photoexcited, no spectral manifestation of energy transfer was observed, though both steady state and time resolved (in the time domain of nanosecond order) spectroscopic measurements strongly suggest the occurrence of a highly exothermic ET reaction within the present donor—acceptor systems. Furthermore such ET reactions have been suggested to occur between donor and acceptor separated by a large distance ( ∼ 7 A), and quenching of fluorescence emission of donor molecules is caused primarily due to outer sphere ET reactions with the acceptor. Measured electron transfer rates ( k ET ) were found to be of much lower value ( ∼ 10 7 s −1 ). It is demonstrated that loose structure of the transient geminate ion pair complex is formed due to the encounter between excited acceptor (or donor) and unexcited donor (or acceptor), and due to this structural property, a stable anionic species (TCNQ − ion) is produced due to the rapid dissociation (probably in the picosecond time domain) of this excited complex. It is hinted that synthesis of biochromophoric systems in which the present donor and acceptor chromophore would be linked by a polymethylene type (σ-type) spacer might be useful in building good photoconducting materials.

Electron transfer chemistry of hydride and carbanion donors. Hydride and carbanion transfer via electron transfer

The hydride transfer from 1,5-dihydroriboflavin-2′,3′,4′,5′-tetra-acetate (FlH 2) to various hydride acceptors (tetracyano- p-quinodimethane, tetracyanoethylene, and p-benzoquinone derivatives) in deaerated acetonitrile proceeds via electron transfer from FlH 2 to hydride acceptors followed by proton and electron transfer. The formation of transient radical ion pair has been detected directly in the reactions of 1,5-dihydroriboflavin-2′,3′,4′,5′-tetra-acetate (FlH 2) with some hydride acceptors in deaerated acetonitrile, providing unequivocal evidence for an electron transfer pathway in the overall two-electron redox reactions of FlH 2 with hydride acceptors. The formal carbanion transfer from alkylcobalt(III) complexes to cobalt(III) porphyrin has also been shown to proceed via electron transfer, followed by the cleavage of cobaltcarbon bonds of alkylcobalt(IV) complexes and the subsequent bond formation between alkyl radical and cobalt(II) porphyrin to yield alkylcobalt(III) porphyrins. The rate constants of the overall carbanion transfer from alkylcobalt(III) complexes to cobalt(III) porphyrin agree well with those predicted by the Marcus theory for the rates of outer-sphere electron transfer reactions. In contrast with the case of alkylcobalt(III) complexes, the rate constants of the carbanion transfer from tetraalkyltin compounds (R 4Sn) are 10 2–10 13 times faster than those predicted by the Marcus theory depending on the size of alkyl group of R 4Sn. The polar versus ET pathway is discussed in terms of the difference between outer-sphere versus inner-sphere electron transfer mechanisms based on the Marcus theory.

A molecular theory of electron transfer reactions in polar liquids

Outer sphere and inner sphere electron transfer reactions in the solvent of hard spheres with permanent dipoles are considered. The solvent reorganization energy has been shown to be the sum of the reorganization energy of reorientation of the permanent dipoles and the reorganization energy of changes in coordinates of solvent molecules. Analytical expressions for both contributions have been obtained. The free energy of activation appears to be temperature dependent, which can result in a negative activation enthalpy.

Solvent and temperature effects in the electron transfer quenching of triplet states of aromatic hydrocarbons by nitrobenzenes

The triplet quenching of anthracene and a,h-dibenzanthracene by four nitrobenzenes was studied by laser flash photolysis. Bimolecular quenching rate constants were determined in acetonitrile and methanol. They follow the expected free energy correlation for an outer sphere electron transfer process. The rate constants in methanol are generally higher than those in acetonitrile. The activation enthalpies and entropies were also measured in both solvents. The activation entropies are more negative in acetonitrile and the activation enthalpies are lower in acetonitrile with negative values being observed in some cases. Transient absorption spectra show that in the quenching process free radical ions are formed in methanol, but in acetonitrile free ions are almost absent. These results are compared with the current models for outer sphere electron transfer reactions. They cannot be explained if the solvent is considered as a dielectric continuum.

Mechanism of electron transfer during the course of oxidation of N-phenyl-p-phenylenediamine polythiophene and poly-3-methylthiophene coated electrodes: Redox catalysis versus outer-sphere heterogeneous electron transfer

Comparative studies of the mechanism of anodic oxidation of N-phenyl-p-phenylenediamine (NPPD) on a bare platinum electrode as well as on platinum coated with poly-3-methylthiophene (P3MT) or polythiophene (PT) films have been carried out. The shift of the voltammetric peak potential corresponding to the first one-electron oxidation step of NPPD on coated electrodes on varying the potential scan rate or the corresponding shift of half-wave potential towards more positive values in the series Pt < Pt/P3MT < Pt/PT have been observed. Two alternative models of kinetics of solute redox reactions such as the model of catalytic reactions mediated by conventional redox-polymers and the thermodynamic model of electrochemical doping of π-conjugated polymers with regard to the kinetics of outer-sphere electron-transfer reactions have been discussed in an attempt to account for the experimental results obtained. Evidence in favour of the applicability of the second model have been summarized.

Determination of the kinetic parameters for the electroreduction of fullerene C60 by scanning electrochemical microscopy and fast scan cyclic voltammetry

The electroreduction of the fullerene Cm in 1,2-dichlorobenzene (ODCB) and benzonitrile (PhCN) at a Pt electrode was studied by using scanning electrochemical microscopy and fast scan cyclic voltammetry. The former technique was employed for steady-state measurements in a thin-layer cell formed by an ultramicroelectrode tip and mercury pool substrate. The standard heterogeneous rate constants found in both solvents, 0.46 cm/s (ODCB) and 0.12 cm/s (PhCN), appeared to be lower than one would expect for an uncomplicated outer sphere electron-transfer reaction, probably because solvation and ion pairing affect the reaction kinetics. The diffusion coefficient of c60 in ODCB depends strongly on supporting electrolyte (TBABF4) concentration. a Ag wire quasireference electrode were used in the voltammetric ex- periments.

Kinetic salt effects on the outer sphere electron transfer reaction between hexacyanoferrate(II) and 4‐pyridinecarboxylatopentammine cobalt(III)

AbstractA study is made of the kinetic salt effects upon the outer‐sphere electron transfer reaction between hexacyanoferrate(II) and 4‐pyridinecarboxylatopentaamminecobalt(III). The observed salts effects are analyzed, taking into account the possible association of the reactants with the ions of the supporting electrolyte, though no conclusive results could be obtained. A correlation has been established between the logarithm of the observed second‐order rate constants and the logarithm of the rate constants for a related innersphere electron transfer reaction. From this correlation the conclusion can be drawn that the observed salt effects in concentrated electrolyte solutions are mainly due to the effects on the electron transfer step. © John Wiley &amp; Sons, Inc.

The general treatment of dynamic solvent effects in electron transfer at high temperature

A general treatment of dynamic solvent effects for outer-sphere electron transfer reactions based on the interactions between the electron transfer system and the solvent bath is presented. The electron transfer rate constant as a function of the solvent longitudinal relaxation time is categorized into the three solvent relaxation regions of adiabatic, normal, and fast. New nonadiabatic effects in the very fast solvent relaxation region are identified. A unified picture for adiabatic and nonadiabatic reactions, as well as a criterion for adiabaticity is given.

Theoretical Models of Hot Carrier Effects at Metal‐Semiconductor Electrodes

The physical and electrochemical properties of hot carriers at metallized semiconductor electrodes in contact with a redox electrolyte are described. Theoretical ballistic mean‐free paths, , for hot carriers in Ag, Cu, Au, Al, Ru, Pd, and Pt, were calculated as a function of excess energy above the Fermi energy. At 0.5 eV hot, was 580 Å for Ag, 420 Å for Cu and Au, 90 to 130 Å for the remaining metals, with Pt having the lowest value. Using the Marcus‐Gerischer model, currents at the equilibrium potential were calculated as a function of built‐in barrier, film thickness, and reorganization energy for Au and Pt. The current for a simple outer sphere electron transfer reaction is predicted to be enhanced when the film thickness becomes . For Au/n‐Si diodes, the enhancement for reorganization energy, , 100 Å Au and built‐in barriers of 0.4 to 0.6 eV are predicted to be 60 to 10 times. Larger enhancements are predicted for larger reorganization energies, the maximum effect being predicted for . The stage most likely to limit observation of hot carriers effects is slow vibrational or vibrational‐rotational relaxation of the redox acceptor or donor. By a combination of theoretical calculations and empirical data, we conclude that it is possible to observe hot carrier effects under real conditions. Experimental data that support the theoretical development and the hot carriers concept are presented in the following paper.