Adiabatic Electron Transfer Reactions Research Articles

Calculation of solvent free energies for heterogeneous electron transfer at the water–metal interface: Classical versus quantum behavior

A computer simulation method is developed for the study of the adiabatic heterogeneous electron transfer reactions between an ion in solution and a metal electrode. The particular system studied is the Fe2+/Fe3+ electron transfer reaction with a Pt(111) electrode. The adiabatic classical free energy curve for the reaction is computed using umbrella sampling and molecular dynamics generated by the adiabatic solution to an Anderson–Newns-like Hamiltonian. Reactive flux calculations are then performed to determine the effect of transition state recrossings on the classical adiabatic rate constant. These effects are not found to be large (κ∼0.6). The water solvent model is next quantized using Feynman path integral techniques and the quantum adiabatic free energy curve for electronic transfer is calculated. The latter calculation shows that the solvent activation free energy barrier and thermodynamic driving force for the electron transfer process can be significantly affected by the water quantization. These results suggest that classical models for water may not be adequate, or at least need to be modified, for the accurate computer simulation of many heterogeneous electron transfer reactions.

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.

Well and barrier dynamics and electron transfer rates. A molecular dynamics study

Molecular dynamics simulations are carried out for model electronically adiabatic electron transfer (ET) reactions. The reactants are immersed in various model dipolar aprotic solvents, ranging from slightly overdamped to strongly overdamped. In all cases, the solvent barrier recrossings which give the solvent dynamical influence on the ET rate are determined by motion in the barrier top region, and not in the solvent wells as some current notions would have it. The MD reaction transmission coefficients are reproduced by Grote-Hynes theory to within the simulation error bars, while other analytic descriptions such as Zusman theory (in its range of applicability) and Kramers theory are less satisfactory, and fail significantly in the overdamped solvent regime. The reasons for these results as well as their implications for the interpretation of adiabatic ET rates are briefly discussed.

Dynamical solvent effects in inverted region electron transfer

The solvent dependence of the charge recombination (CR) electron transfer rate constants of cofacially linked magnesium/free base diporphyrin (MgH 2) and zinc porphyrin/modified free base chlorin (ZnH 2(=C(CN) 2)) complexes has been investigated by picosecond transient absorption spectroscopy. The photogenerated Mg +H − 2 and Zn +H 2(=C(CN) 2) − charge separated pairs undergo facile reaction in the Marcus inverted region to produce ground state species, with the latter exhibiting faster reaction rates owing to less activated CR. We find that the CR rate constants k obs(CR) are strongly solvent dependent in a homologous series of nitriles and acetates. Although they are slow with respect to solvent motion ( k obs(Mg +H − 2)=(0.6–4.0)×10 9 s −1; k obs(Zn +H 2(=C(CN) 2) −=(1.6–8.3)×10 10 s −1), a linear correlation is observed between k obs(CR) and the inverse of the solvent relaxation time (1/τ s=(1.5–9.1)×10 11 s −1). For the Mg +-H − 2 cofacial pair this correlation is observed only when solvents of the same series are considered, whereas for Zn +H 2(=C(CN) 2) − this linear correlation is independent of the solvent series. These observations are analyzed within the context of recent theoretical predictions for solvent-controlled adiabatic electron transfer reactions.

The multiconfigurational theory of adiabatic outersphere electron transfer reactions proceeding in polar solvent

This article outlines essential features of the continuum theory of outer-sphere electron transfer reactions as an illustration of recent ideas and approaches in the qualitative theoretical treatment of condensed phase reactions. A line of reasoning starting from a free-energy functional construction and ending with a rate-constant calculation in terms of the multidimensional Kramers-Grote-Hynes stochastic theory is followed. Special emphasis is placed on practical applications utilizing a conventional quantum chemical methodology.

Molecular theory of solvation and solvation dynamics in a binary dipolar liquid

Both the equilibrium and the dynamical aspects of solvation of a classical ion in a dense binary dipolar liquid are investigated by using a molecular theory. The theory properly includes the differing inter- and intramolecular correlations that are present in a binary mixture. As a result, the theory can explain several important aspects of the nonideality of equilibrium solvation energy (broadly known as preferential solvation) observed in experiments. We find that the nonideality of solvation depends strongly on both the molecular size and the magnitude of the dipole moment of the solvent molecules. The interactions among the solvent molecules play an important role in determining the extent of this nonideality. The dynamical calculations are based on a generalized Smoluchowski equation which has been used extensively for studies in one component liquid. For binary liquid, our study reveals rich and diverse behavior such as dependencies on the sizes, the transport coefficients and the polar properties of the components. The theory offers a detailed picture of the dependence of the solvation dynamics on the composition of the mixture. It is predicted that the dynamics of solvation in a binary liquid is, in general, nonexponential and that the details of the dynamics can be quite different from those in a one component liquid. In particular, the continuum model is found to be grossly inaccurate in describing the solvation dynamics in binary mixtures and rather extreme conditions are needed to recover the predictions of the continuum model which can be attributed to the nonideality of the solvation. The predicted results are used to study the dynamic solvent effects on the rate of an adiabatic electron transfer reaction in a binary liquid. The theoretical predictions are also compared with the available experimental results.

Stochastic Theory of Adiabatic Electron Transfer Reactions in Polar Media

Stochastic Theory of Adiabatic Electron Transfer Reactions in Polar Media

Dynamic solvent effects in adiabatic electron-transfer reactions: role of translational modes

A molecular theory of the dynamic solvent effects on an outer-sphere adiabatic electron transfer reaction is presented. The theory properly includes the role of the microscopic correlations present in a dense dipolar solvent in the dynamics of an electron-transfer reaction. The theory predicts that the translational modes of the solvent, hitherto neglected in most discussions on electron-transfer reactions, can significantly enhance the rate of an adiabatic electron-transfer reaction.

Molecular dynamics simulation of electron-transfer reactions in solution

Molecular dynamics simulation results are presented for model electronically adiabatic electron-transfer reactions in a model polar solvent. Transmission coefficients {kappa} characterizing the departure of the rate from the Marcus theory predictions are determined, and theoretical approaches to predicting {kappa} in terms of solvent dynamics are examined.

The analysis of solvent effects on the kinetics of simple heterogeneous electron transfer reactions

Abstract : A method for separating the solvent dependence of the pre-exponential factor from that in the free energy of activation is described for adiabatic electron transfer reactions in which the inner sphere contribution to the activation energy is much less than the outer sphere contribution. The analysis is applied to data published in the literature in which the heterogeneous electron transfer rate constant was measured in at least 4 different solvents. The resulting kinetic parameters are discussed with respect to current theory.

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.

A theory of adiabatic electron-transfer reactions

Abstract A theory for adiabatic electron-transfer reactions at metal electrodes is presented. The model Hamiltonian is similar to that of the Levich and Dogonadze theory for non-adiabatic reactions, but the rate is not calculated from perturbation theory but by techniques familiar from the Anderson-Newns model for adsorption. In the limit of comparatively weak interactions, this model reduces to the Marcus theory: for stronger interactions there are significant deviations. A possible classification of electrochemical electron-transfer reactions is discussed.

ChemInform Abstract: HETEROPOLYTUNGSTATES AS CATALYSTS FOR THE PHOTOCHEMICAL REDUCTION OF OXYGEN AND WATER

AbstractEine Reihe von Polywolframatanionen [XW,204"]"′ (X: P, Si, Fe, Co oder H2; n: 3 ‐ 6) werden in Gegenwart von organischen Elektronendonatoren, wie Alkoholen, photoreduziert.

ChemInform Abstract: THE INFLUENCE OF THE METAL ON THE KINETICS OF OUTER SPHERE REDOX REACTIONS

AbstractDie kinetischen Parameter des [Ru(NH3)6]2 ′3+‐Redoxpaares werden an verschiedenen Metallelektroden (Pt, Au, Pd, Cu, Ag, Hg) gemessen.

The Influence of the Metal on the Kinetics of Outer Sphere Redox Reactions

AbstractThe kinetic parameters of the outer sphere redox couple [Ru(NH3)6]2+/3+ were measured on six different metal electrodes. The reaction rate is independent of the substrate. The significance of these results for the electron transfer theory is discussed, and a new model for adiabatic electron transfer reactions is outlined.

Heteropolytungstates as catalysts for the photochemical reduction of oxygen and water

A series of polytungstate anions [XW12O40]n–(X = P, Si, Fe, Co, or H2; n= 3,4,5,6, and 6 respectively), spanning a range of reduction potentials, have been studied as sensitizers for the photoreduction of water and O2. [SiW12O40]4– was the most efficient sensitizer for H2 evolution in the presence of colloidal platinum. Saturation kinetics were found with respect to the concentrations of Pt,[SiW12O40]4–, and CH3OH as predicted by a simple kinetic scheme. The maximum rate depended on competition between the natural decay of the excited polyanion and quenching by alcohol. Electron transfer from photoreduced polyanions to O2 was also investigated by flash photolysis. Rate constants depended on the reduction potential of the polyanion and increased by a factor of 3 700 on going from [PW12O40]3– to [FeW12O40]5–, in line with the Marcus equation for adiabatic electron-transfer reactions.

On the theory of adiabatic electron-tranfers reactions in polar solvents

Abstract A theory describing the rate of adiabatic electron-transfer reactions in a polar medium with an arbitrary spectrum of the dielectric losses is presented. All results are given in terms of analytical expressions via integrals over the frequency-dependent dielectric permittivity of the solvent. The present work is a generalization of the well-known work of Kramers, concerning escape over a potential barrier, for the case where the motion on the reaction coordinate is an arbitrary normal random process, and it may serve as a substantiation of the transition-state method.