Central to theories of electron transfer (ET) is the idea that nuclear motion generates a transition state that enables electron flow to proceed, but nuclear motion also induces fluctuations in the donor-acceptor (DA) electronic coupling that is the rate-limiting parameter for nonadiabatic ET. The interplay between the DA energy gap and DA coupling fluctuations is particularly noteworthy in biological ET, where flexible protein and mobile water bridges take center stage. Here, we discuss the critical timescales at play for ET reactions in fluctuating media, highlighting issues of the Condon approximation, average medium versus fluctuation-controlled electron tunneling, gated and solvent relaxation controlled electron transfer, and the influence of inelastic tunneling on electronic coupling pathway interferences. Taken together, one may use this framework to establish principles to describe how macromolecular structure and structural fluctuations influence ET reactions. This framework deepens our understanding of ET chemistry in fluctuating media. Moreover, it provides a unifying perspective for biophysical charge-transfer processes and helps to frame new questions associated with energy harvesting and transduction in fluctuating media.

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Fluctuations in Biological and Bioinspired Electron-Transfer Reactions

A rate constant expression for charge transfer reactions mediated by flexible bridges is presented as a series of terms of decreasing importance. The leading term corresponds to the static limit obtained from the Condon approximation. Corrections due to finite time fluctuations are evaluated explicitly, assuming a Gaussian shape of the coupling autocorrelation function and the Marcus model with a one-dimensional harmonic thermal bath. The use of this model for the interpretation of experimental data and the expected magnitudes of the fluctuation effects are discussed.

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A rate constant expression for charge transfer through fluctuating bridges

The influence of static and dynamic torsional disorder on the kinetics of charge transfer (CT) in donorbridge-acceptor (D-B-A) systems has been investigated theoretically using a simple tight-binding model. In such systems, variations of the torsion angle often give rise either to static changes in the magnitude of electronic coupling along the bridge length or to dynamic fluctuations of this quantity on the certain characteristic time scale τrot. These lead to the functional breakdown of the Condon approximation. Modeling of CT beyond the Condon approximation reveals two types of non-Condon (NC) effects. If τrot is much less than the characteristic time, τCT, of CT in the absence of disorder, the NC effects was shown to be static. Due to self-averaging of electronic coupling in this fast fluctuation limit, the breakdown of the Condon approximation manifests itself as a static correction to the time-independent rate coefficient calculated for the ordered bridge with the same time-averaged electronic coupling for all pairs of adjacent subunits. As a consequence, the CT process exponentially evolves with time and therefore can be characterized by a time-independent rate coefficient wa for the charge arrival on the acceptor (also termed the rate constant). For larger τrot, however, the NC effects become purely kinetic. In this case, the process of CT in the tunneling regime exhibits time scale invariance, the corresponding decay curves become dispersive, and the rate coefficient wa turns out to be time dependent. In the limit of very slow dynamic fluctuations, where τrot . τCT, the NC effects in kinetics of CT are found (as anticipated) to be very similar to the effects revealed for bridges with the static torsional disorder. Both analytical and numerical results obtained within this limit allow the conclusion that for very slow fluctuations and/or for static disorder, the nonexponential time evolution of the CT process is due to the configuration averaging of electronic coupling. Several consequences of our theoretical findings for the interpretation of experimentally observed transients are briefly discussed. In particular, we argue that the minimal value of the falloff parameter describing the distance dependence of the time-independent rate coefficient in tunneling regime can not be less than 0.2-0.3 A -1 and that the smaller experimental value of this parameter reported in the literature for several D-B-A systems must be attributed to the multistep hopping mechanism of charge motion rather than to the mechanism of single-step tunneling.

Charge Transfer in Donor-Bridge-Acceptor Systems: Static Disorder, Dynamic Fluctuations, and Complex Kinetics

The temperature-dependent fluorescence anisotropy decay (orientational relaxation) of perylene and sodium 8-methoxypyrene-1,3,6-sulfonate (MPTS) were measured in a series of 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (alkyl = ethyl, butyl, hexyl, octyl) organic room temperature ionic liquids (RTIL). The two fluorescent probe molecules display markedly different rotational dynamics when analyzed using Stokes−Einstein−Debye theory, demonstrating that they are located in distinct environments within the RTILs and have very different interactions with their surroundings. Perylene rotates with subslip behavior, becoming increasingly subslip as the length of ionic liquid alkyl chain is increased. The dynamics approach those of perylene in an organic oil. In contrast, MPTS shows superstick behavior, likely reflecting very strong coordination with the RTIL cations. These results are consistent with different elements of rotational friction within the ionic liquid structure, which are available...

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Dynamics in Organic Ionic Liquids in Distinct Regions Using Charged and Uncharged Orientational Relaxation Probes

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.

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Solvent reorganization energy of electron-transfer reactions in polar solvents

Rotational diffusion of organic solutes: the role of dielectric friction in polar solvents and electrolyte solutions

The temperature dependence of intramolecular electron-transfer rate constants for a C-shaped donor-bridge-acceptor molecule was measured in a series of solvents of differing electron affinities. The rate data was analyzed using a semiclassical version of the Marcus equation. The reaction free energies were characterized using a molecular model for solvation. The electronic coupling between the electron donor and acceptor groups is enhanced in solvents with more positive electron affinity. This enhancement arises from solvent occupation of a cleft between the donor and acceptor groups, resulting in an increase of the electronic coupling via an enhancement of the superexchange interaction. Solvents with more positive electron affinity provide mediating, superexchange states whose energies are closer to that of the resonant, initial, and final states.

Solvent Mediated Superexchange in a C-Clamp Shaped Donor-Bridge-Acceptor Molecule: The Correlation between Solvent Electron Affinity and Electronic Coupling

Two recent investigations into electron trans fer reactions are described. The first study probes solvent effects on intramolecular electron transfer of donor-bridge-acceptor systems. The study compares a molecule which possesses a molecular cleft between the donor and acceptor moiety to one without such a cleft. The influence on the electronic coupling of a solvent molecule between the donor and acceptor is discussed. The second study concerns heterogeneous electron transfer through self-assembled monolayer films on InP electrodes. The data show that the film inhibits oxidation of the semiconductor. Electron tunneling through the film is explored, and the chemical functionalization of the film is shown to modify the charge recombination processes in the electrode.

Studies into the character of electronic coupling in electron transfer reactions

The charge separation (S1 → CT) and charge recombination (CT → S1) rate constants for a C-shaped, donor−bridge−acceptor molecule in the solvent 1,3-di-isopropylbenzene are found to increase, reach a maximum, and then decrease as the temperature is raised from 215 to 360 K. The reaction free energy change for the charge separation and charge recombination processes are determined from the ratio of the two rate constants. The charge separation and the charge recombination rate constants also display a maximum when plotted against the experimental reaction free energy (Marcus plot). This behavior can be quantitatively modeled in two different ways:  (i) using a small and temperature-independent value of the solvent reorganization energy, which results in transitions between the Marcus normal and the Marcus inverted region as the reaction free energy changes with temperature and (ii) allowing a decrease in the magnitude of the donor−acceptor electronic coupling at elevated temperatures. The latter explanation...

Electron Transfer Reactions of C-shaped Molecules in Alkylated Aromatic Solvents: Evidence that the Effective Electronic Coupling Magnitude Is Temperature-Dependent

A direct temporal measurement of the internal motion of a host−guest bimolecular complex is reported. Time-resolved polarization spectroscopy is used to monitor the motion of a guest chromophore, anthracene-1,3-dicarboxylate, bound to a bis(guanidinium) host molecule through a combination of hydrogen bonding and electrostatic forces. The dynamics of the bound chromophore is well described by an overdamped oscillator model. Through simple modeling, it is possible to estimate the frequency of the host−guest potential and the range of the guest chromophore's angular displacement.

Ian Read

Papers

Rotational diffusion of organic solutes: the role of dielectric friction in polar solvents and electrolyte solutions

Solvent Mediated Superexchange in a C-Clamp Shaped Donor-Bridge-Acceptor Molecule: The Correlation between Solvent Electron Affinity and Electronic Coupling

Studies into the character of electronic coupling in electron transfer reactions

Electron Transfer Reactions of C-shaped Molecules in Alkylated Aromatic Solvents: Evidence that the Effective Electronic Coupling Magnitude Is Temperature-Dependent

Experimental Measurements of Low-Frequency Intermolecular Host−Guest Dynamics