Proton-coupled electron transfer in solution, proteins, and electrochemistry

Recent advances in the theoretical treatment of proton-coupled electron transfer (PCET) reactions are reviewed. These reactions play an important role in a wide range of biological processes, as well as in fuel cells, solar cells, chemical sensors, and electrochemical devices. A unified theoretical framework has been developed to describe both sequential and concerted PCET, as well as hydrogen atom transfer (HAT). A quantitative diagnostic has been proposed to differentiate between HAT and PCET in terms of the degree of electronic nonadiabaticity, where HAT corresponds to electronically adiabatic proton transfer and PCET corresponds to electronically nonadiabatic proton transfer. In both cases, the overall reaction is typically vibronically nonadiabatic. A series of rate constant expressions have been derived in various limits by describing the PCET reactions in terms of nonadiabatic transitions between electron-proton vibronic states. These expressions account for the solvent response to both electron and proton transfer and the effects of the proton donor-acceptor vibrational motion. The solvent and protein environment can be represented by a dielectric continuum or described with explicit molecular dynamics. These theoretical treatments have been applied to numerous PCET reactions in solution and proteins. Expressions for heterogeneous rate constants and current densities for electrochemical PCET have also been derived and applied to model systems.     

Microwave activation of electrochemical processes: enhanced electrodehalogenation in organic solvent media

The effect of high-intensity microwave radiation focused into a "hot spot" region in the vicinity of an electrode on electrochemical processes with and without coupled chemical reaction steps has been investigated in organic solvent media. First, the electrochemically reversible oxidation of ferrocene in acetonitrile and DMF is shown to be affected by microwave-induced thermal activation, resulting in increased currents and voltammetric wave shape effects. A FIDAP simulation investigation allows quantitative insight into the temperature distribution and concentration gradients at the electrode / solution interface. Next, the effect of intense microwave radiation on electroorganic reactions is considered for the case of ECE processes. Experimental data for the reduction of p-bromonitrobenzene, o-bromonitrobenzene, and m-iodonitrobenzene in DMF and acetonitrile are analyzed in terms of an electron transfer (E), followed by a chemical dehalogenation step (C), and finally followed by another electron-transfer step (E). The presence of the "hot spot" in the solution phase favors processes with high activation barriers.     

Evidence for concerted pathways in ion-pairing coupled electron transfers

Ion-pairing with electro-inactive metal ions may change drastically the thermodynamic and kinetic reactivity of electron transfer in chemical and biochemical processes. Besides the classical stepwise pathways (electron-transfer first, followed by ion-pairing or vice versa), ion-pairing may also occur concertedly with electron transfer. The latter pathway avoids high-energy intermediates but a key issue is that of the kinetic price to pay to benefit from this thermodynamic advantage. A model is proposed leading to activation/driving force relationships characterizing such concerted associative electron transfers for intermolecular and intramolecular homogeneous reactions and for electrochemical reactions. Contrary to previous assertions, the driving force of the reaction (defined as the opposite of the reaction standard free energy), as well as the intrinsic barrier, does not depend on the concentration of the ion-pairing agent, which simply plays the role of one of the reactants. Besides solvent and intramolecular reorganization, the energy of the bond being formed is the main component of the intrinsic barrier. Application of these considerations to reactions reported in recent literature illustrates how concerted ion-pairing electron-transfer reactions can be diagnosed and how competition between stepwise and concerted pathways can be analyzed. It provided the first experimental evidence of the viability of concerted ion-pairing electron-transfer reactions.     

Dynamical arrest of electron transfer in liquid crystalline solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.     

Electron transfer and dynamic infrared-band coalescence: it looks like dynamic NMR spectroscopy, but a billion times faster

Broadening and coalescence of infrared bands can occur due to chemical exchange processes occurring on very fast, femtosecond-to-picosecond timescales. One such fast process of recent investigation is intramolecular electron transfer in transition-metal complexes with strong communication between electron-donor and -acceptor sites. The observation of partial coalescence of metal-carbonyl stretching bands in hexanuclear ruthenium mixed-valence complexes due to electron-transfer rates on the order of 10(11)-10(12) s(-1) is chronicled here. Several important advances have been made with the aid of dynamic infrared-band coalescence in these complexes, including the observation of dynamic solvent relaxation effects on electron-transfer rates, the determination of the equilibrium constant between charge-transfer isomers, and a reconsideration of the theory of electron transfer and delocalization in bridged, near-delocalized electron-transfer systems.     

Energy gap law of electron transfer in nonpolar solvents

We investigate the energy gap law of electron transfer in nonpolar solvents for charge separation and charge recombination reactions. In polar solvents, the reaction coordinate is given in terms of the electrostatic potentials from solvent permanent dipoles at solutes. In nonpolar solvents, the energy fluctuation due to solvent polarization is absent, but the energy of the ion pair state changes significantly with the distance between the ions as a result of the unscreened strong Coulomb potential. The electron transfer occurs when the final state energy coincides with the initial state energy. For charge separation reactions, the initial state is a neutral pair state, and its energy changes little with the distance between the reactants, whereas the final state is an ion pair state and its energy changes significantly with the mutual distance; for charge recombination reactions, vice versa. We show that the energy gap law of electron-transfer rates in nonpolar solvents significantly depends on the type of electron transfer.     

Bottom-up view of water network-mediated CO2 reduction using cryogenic cluster ion spectroscopy and direct dynamics simulations

The transition states of a chemical reaction in solution are generally accessed through exchange of thermal energy between the solvent and the reactants. As such, an ensemble of reacting systems approaches the transition state configuration of reactant and surrounding solvent in an incoherent manner that does not lend itself to direct experimental observation. Here we describe how gas-phase cluster chemistry can provide a detailed picture of the microscopic mechanics at play when a network of six water molecules mediates the trapping of a highly reactive "hydrated electron" onto a neutral CO(2) molecule to form a radical anion. The exothermic reaction is triggered from a metastable intermediate by selective excitation of either the reactant CO(2) or the water network, which is evidenced by the evaporative decomposition of the product cluster. Ab initio molecular dynamics simulations of energized CO(2)·(H(2)O)(6)(-) clusters are used to elucidate the nature of the network deformations that mediate intracluster electron capture, thus revealing the detailed solvent fluctuations implicit in the Marcus theory for electron-transfer kinetics in solution.     

Chemical potential inequality principle

Regional density functional theory has been extended to treat irreversible thermodynamic electronic processes for application to adiabatic electron-transfer processes of chemical reactions. Onsager's local equilibrium hypothesis is slightly modified to take into account the quantum mechanical nature of the electron. The quantum mechanical interference effect has been demonstrated to be included in the entropy production rate formula associated with electron transfer through an interface. A new formula for the determination of the transition state of a chemical reaction has been postulated that corresponds to the maximum of the regional electron transferability. A quantum mechanical law of mass action has been established and applied to prove the regional electrochemical potential inequality principle. Received: 1 July 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

A Model Electron Transfer Reaction in Confined Aqueous Solution

Liquid water confined within nanometer-sized channels exhibits a strongly reduced local dielectric constant perpendicular to the wall, especially at the interface, and this has been suggested to induce faster electron transfer kinetics at the interface than in the bulk. We study a model electron transfer reaction in aqueous solution confined between graphene sheets with classical molecular dynamics. We show that the solvent reorganization energy is reduced at the interface compared to the bulk, which explains the larger rate constant. However, this facilitated solvent reorganization is due to the partial desolvation by the graphene sheet of the ions involved in the electron transfer and not to a local dielectric constant reduction effect.     

Glassy protein dynamics and gigantic solvent reorganization energy of plastocyanin

We report the results of molecular dynamics simulations of electron-transfer activation parameters of plastocyanin metalloprotein involved as an electron carrier in natural photosynthesis. We have discovered that slow, non-ergodic conformational fluctuations of the protein, coupled to hydrating water, result in a very broad distribution of donor-acceptor energy gaps far exceeding those observed for commonly studied inorganic and organic donor-acceptor complexes. The Stokes shift is not affected by these fluctuations and can be calculated from solvation models in terms of the linear response of the solvent dipolar polarization. The non-ergodic character of large-amplitude protein/water mobility breaks the strong link between the Stokes shift and the reorganization energy characteristic of equilibrium (ergodic) theories of electron transfer. This mechanism might be responsible for fast electronic transitions in natural electron-transfer proteins characterized by low reaction free energy.     

Studying and switching electron transfer: from the ensemble to the single molecule

We report here on the systematic investigation of photoinduced intramolecular electron transfer (IET) in a series of donor-bridge-acceptor molecules as a means of understanding electron transport through the bridge. Perylenebisimide chromophores connected by various oligophenylene bridges are studied because their electron-transfer behavior can readily be monitored by following changes in the fluorescence intensity. We find dramatic switching of the IET behavior as the solvent polarity (dielectric constant) is increased. By combining steady-state and time-resolved fluorescence spectroscopy in a variety of solvents at multiple temperatures with standard theories of electron transfer, we determine parameters governing the IET behavior of these dimers, such as the electronic coupling through the bridges. We also deploy available ab initio quantum chemical methods to calculate the through-space component of the electronic coupling matrix element. Single-molecule investigations of the electron-transfer behavior also show that IET can be switched reversibly by a similar mechanism in an isolated individual molecule.     

Salt and solvent effects on the kinetics of the oxidation of the excited state of the [Ru(bpy)3]2+ complex by S2O8(2-)

The title reaction was studied in different reaction media: aqueous salt solutions (NaNO3) and water-cosolvent (methanol) mixtures. The observed rate constants, k(obs), show normal behavior in the solutions containing the electrolyte, that is, a negative salt effect. However, the solvent effect is abnormal, because a decrease of the rate constant is observed when the dielectric constant of the reaction medium decreases. These effects (the normal and the abnormal) can be explained using the Marcus-Hush treatment for electron transfer reactions. To apply this treatment, the true, unimolecular, electron-transfer rate constants, k(et), have been obtained from k(obs) after calculation of the rate constants corresponding to the formation of the encounter complex from the separate reactants, k(D), and the dissociation of this complex, k(-D). This calculation has been carried out using an exponential mean spherical approach (EMSA).     

Femtosecond-Picosecond Laser Photolysis Studies on Photoinduced Electron Transfer Phenomena in Solutions

Results of our femtosecond-picosecond laser photolysis studies on photoinduced electron transfer phenomena in solutions including exciplex dynamics and its solvent dependences, energy gap dependences of photoinduced charge separation and charge recombination of various geminate ion pairs, mechanisms of chemical reactions via exciplexes and ion pairs, dynamics of photoinduced election transfer in hydrogen bonding complexes, dynamics and mechanisms of photoinduced electron transfer in fixed distance donor acceptor dyads and photosynthetic reaction center models, and mechanisms of electron ejection from solute fluorescent state in polar solutions are summarized and discussed.     

Charge-transfer mechanism for cytochrome c adsorbed on nanometer thick films. Distinguishing frictional control from conformational gating

Using nanometer thick tunneling barriers with specifically attached cytochrome c, the electron-transfer rate constant was studied as a function of the SAM composition (alkane versus terthiophene), the omega-terminating group type (pyridine, imidazole, nitrile), and the solution viscosity. At large electrode-reactant separations, the pyridine terminated alkanethiols exhibit an exponential decline of the rate constant with increasing electron-transfer distance. At short separations, a plateau behavior, analogous to systems involving -COOH terminal groups to which cytochrome c can be attached electrostatically, is observed. The dependence of the rate constant in the plateau region on system properties is investigated. The rate constant is insensitive to the mode of attachment to the surface but displays a significant viscosity dependence, change with spacer composition (alkane versus terthiophene), and nature of the solvent (H(2)O versus D(2)O). Based on these findings and others, the conclusion is drawn that the charge-transfer rate constant at short distance is determined by polarization relaxation processes in the structure, rather than the electron tunneling probability or large-amplitude conformational rearrangement (gating). The transition in reaction mechanism with distance reflects a gradual transition between the tunneling and frictional mechanisms. This conclusion is consistent with data from a number of other sources as well.     

Solvent reorganization of electron transitions in viscous solvents

We develop a model of electron transfer reactions at conditions of nonergodicity when the time of solvent relaxation crosses the observation time window set up by the reaction rate. Solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile is studied by molecular dynamics simulations at varying temperatures. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect, as discussed by the mode-coupling theory. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to the relaxation of the solvent dipolar polarization. An analytical theory proposed to describe this effect agrees well with both the simulations and experimental Stokes shift data. The theory is applied to the analysis of charge-transfer kinetics in a low-temperature glass former. We show that the reorganization energy is substantially lower than its equilibrium value for the low-temperature portion of the data. The theory predicts the possibility of discontinuous changes in the dependence of the electron transfer rate on the free energy gap when the reaction switches between ergodic and nonergodic regimes.     

Photoalkylation of 10-alkylacridinium ion via a charge-shift type of photoinduced electron transfer controlled by solvent polarity

A charge-shift type of photoinduced electron-transfer reactions from various electron donors to the singlet excited state of 10-decylacridinium cation (DeAcrH+) in a nonpolar solvent (benzene) is found to be as efficient as those of 10-methylacridinium cation (MeAcrH+) and DeAcrH+ in a polar solvent (acetonitrile). Irradiation of the absorption bands of MeAcrH+ in acetonitrile solution containing tetraalkyltin compounds (R(4)Sn) results in the efficient and selective reduction of MeAcrH+ to yield the 10-methyl-9-alkyl-9,10-dihydroacridine (AcrHR). The same type of reaction proceeds in benzene when MeAcrH+ is replaced by DeAcrH+ which is soluble in benzene. The photoalkylation of R'AcrH+ (R' = Me and De) also proceeds in acetonitrile and benzene using 4-tert-butyl-1-benzyl-1,4-dihydronicotinamide (Bu(t)BNAH) instead of R(4)Sn, yielding MeAcrHBu(t). The quantum yield determinations, the fluorescence quenching of R'AcrH+ by electron donors, and direct detection of the reaction intermediates by means of laser flash photolysis experiments indicate that the photoalkylation of R'AcrH+ in benzene as well as in acetonitrile proceeds via photoinduced electron transfer from the alkylating agents (R(4)Sn and Bu(t)BNAH) to the singlet excited states of R'AcrH+. The limiting quantum yields are determined by the competition between the back electron-transfer process and the bond-cleavage process in the radical pair produced by the photoinduced electron transfer. The rates of back electron transfer have been shown to be controlled by the solvent polarity which affects the solvent reorganization energy of the back electron transfer. When the free energy change of the back electron transfer (DeltaG(0)(bet)) in a polar solvent is in the Marcus inverted region, the rate of back electron transfer decreases with decreasing the solvent polarity, leading to the larger limiting quantum yield for the photoalkylation reaction. In contrast, the opposite trend is obtained when the DeltaG(0)(bet) value is in the normal region: the limiting quantum yield decreases with decreasing the solvent polarity.