Nonequilibrium Electron Transfer Research Articles

Semiclassical Theory of Multistage Nonequilibrium Electron Transfer in Macromolecular Compounds in Polar Media with Several Relaxation Timescales

Many specific features of ultrafast electron transfer (ET) reactions in macromolecular compounds can be attributed to nonequilibrium configurations of intramolecular vibrational degrees of freedom and the environment. In photoinduced ET, nonequilibrium nuclear configurations are often produced at the stage of optical excitation, but they can also be the result of electron tunneling itself, i.e., fast redistribution of charges within the macromolecule. A consistent theoretical description of ultrafast ET requires an explicit consideration of the nuclear subsystem, including its evolution between electron jumps. In this paper, the effect of the multi-timescale nuclear reorganization on ET transitions in macromolecular compounds is studied, and a general theory of ultrafast ET in non-Debye polar environments with a multi-component relaxation function is developed. Particular attention is paid to designing the multidimensional space of nonequilibrium nuclear configurations, as well as constructing the diabatic free energy surfaces for the ET states. The reorganization energies of individual ET transitions, the equilibrium energies of ET states, and the relaxation properties of the environment are used as input data for the theory. The effect of the system-environment interaction on the ET kinetics is discussed, and mechanisms for enhancing the efficiency of charge separation in macromolecular compounds are analyzed.

Ultrafast Dynamics of Nonequilibrium Short-Range Electron Transfer in Semiquinone Flavodoxin.

Short-range protein electron transfer (ET) is crucially important in light-induced biological processes such as in photoenzymes and photoreceptors and often occurs on time scales similar to those of environment fluctuations, leading to a coupled dynamic process. Herein, we use semiquinone Anabaena flavodoxin to characterize the ultrafast photoinduced redox cycle of the wild type and seven mutants by ultrafast spectroscopy. We have found that the forward and backward ET dynamics show stretched behaviors in a few picoseconds (1-5 ps), indicating a coupling with the local protein fluctuations. By comparison with the results from semiquinone D. vulgaris flavodoxin, we find that the electronic coupling is crucial to the ET rates. With our new nonergodic model, we obtain smaller values of the outer reorganization energy (λoγ) of environment fluctuations and the reaction free energy force (ΔGγ), a signature of nonequilibrium ET dynamics.

Modeling and Experimental Study of the Electron Transfer Kinetics for Non-ideal Electrodes Using Variable-Frequency Square Wave Voltammetry.

The knowledge of nonequilibrium electron transfer rates is paramount for the design of modern hybrid electrocatalysts. Herein, we propose a general simulation-based approach to interpret variable-frequency square wave voltammetry (VF-SWV) for heterogeneous materials featuring reversible redox behavior. The resistive and capacitive corrections, inclusion of the frequency domain, and statistical treatment of the surface redox kinetics are used to account for the non-ideal nature of electrodes. This approach has been validated in our study of CoII/CoI redox transformation for Co tetraphenylporphyrin (CoTPP) immobilized on carbon cloth and multiwalled carbon nanotubes (CNTs) - one of the most active heterogeneous molecular catalysts in carbon dioxide (CO2) electroreduction. It is demonstrated that the modeling of experimental data furnishes the capacitance of the surface double layer C, uncompensated resistance Ru, symmetry coefficients α, kinetic constants k0, and equilibrium redox potentials E0 in one experiment. Moreover, the proposed method yields a stochastic map of the redox kinetics rather than a single value, thus exposing the inhomogeneous nature of the electrochemically active layer. The computed parameters are in excellent agreement with the results of the classic methods such as cyclic voltammetry and fall in line with the reported CoTPP catalytic activity. Thus, VF-SWV is suitable for the study of high-level composites such as covalent organic frameworks and organometallic-CNT mixtures. The resulting insights into the electron transfer mechanisms are especially useful for the rational development of the catalyst-support interfaces and immobilization methods.

Effects of nonequilibrium fluctuations on ultrafast short-range electron transfer dynamics

A variety of electron transfer (ET) reactions in biological systems occurs at short distances and is ultrafast. Many of them show behaviors that deviate from the predictions of the classic Marcus theory. Here, we show that these ultrafast ET dynamics highly depend on the coupling between environmental fluctuations and ET reactions. We introduce a dynamic factor, γ (0 ≤ γ ≤ 1), to describe such coupling, with 0 referring to the system without coupling to a “frozen” environment, and 1 referring to the system’s complete coupling with the environment. Significantly, this system’s coupling with the environment modifies the reaction free energy, ΔGγ, and the reorganization energy, λγ, both of which become smaller. This new model explains the recent ultrafast dynamics in flavodoxin and elucidates the fundamental mechanism of nonequilibrium ET dynamics, which is critical to uncovering the molecular nature of many biological functions.

Understanding Short-Range Electron-Transfer Dynamics in Proteins.

Short-range electron-transfer (ET) reactions in biological systems are usually ultrafast, having transfer rates comparable to or even faster than corresponding environmental fluctuations, and often display nonexponential behaviors. To understand these nonequilibrium ET dynamics, we carried out detailed theoretical analyses based on the Sumi-Marcus model. It is shown that the ET dynamics is largely determined by the relative time scales of the ET reaction and its surrounding motions. Significantly, different environmental fluctuations can produce a variety of apparent ET dynamics even with the same driving force, Δ Go, and reorganization energy, λ. We applied our analyses to an ultrafast ET process in DNA repair by (6-4) photolyase and directly obtained the inner and outer reorganization energies (λi and λo) as well as the free energy Δ Go of various mutants, providing mechanical insight into ultrafast short-range ET reactions in proteins.

Dynamic Solvent Effect on Ultrafast Charge Recombination Kinetics in Excited Donor-Acceptor Complexes.

Manifestation of the dynamic solvent effect (DSE) on the charge recombination (CR) kinetics of photoexcited donor-acceptor complexes in polar solvents has been investigated within the framework of the multichannel stochastic model. The model takes into account the reorganization of both the solvent and a number of intramolecular high-frequency vibration modes as well as their relaxation. The non-Markovian solvent dynamics is described in terms of two relaxation modes. The similarities and differences inherent to ultrafast charge transfer reactions occurring in the nonequilibrium and thermal regimes have been identified. The most important differences are as follows: (1) the DSE is strong in the area of weak exergonicity and is weak in the area of strong exergonicity for thermal reactions, whereas for the nonequilibrium reactions, the regions of strong and weak DSEs are reversed; (2) an increase in the electronic coupling value results in a decrease in the magnitude of DSE for nonequilibrium electron transfer and in its increase for the thermal reactions; and (3) the two-staged regime most clearly manifests if the reorganization energy of the relaxation modes noticeably exceeds the CR free-energy gap. With an increase in electronic coupling, the kinetics approaches the exponential regime because in the limit of strong electronic coupling, the reaction includes only single, nonequilibrium, stage.

Electric-field-driven electron-transfer in mixed-valence molecules.

Molecular quantum-dot cellular automata is a computing paradigm in which digital information is encoded by the charge configuration of a mixed-valence molecule. General-purpose computing can be achieved by arranging these compounds on a substrate and exploiting intermolecular Coulombic coupling. The operation of such a device relies on nonequilibrium electron transfer (ET), whereby the time-varying electric field of one molecule induces an ET event in a neighboring molecule. The magnitude of the electric fields can be quite large because of close spatial proximity, and the induced ET rate is a measure of the nonequilibrium response of the molecule. We calculate the electric-field-driven ET rate for a model mixed-valence compound. The mixed-valence molecule is regarded as a two-state electronic system coupled to a molecular vibrational mode, which is, in turn, coupled to a thermal environment. Both the electronic and vibrational degrees-of-freedom are treated quantum mechanically, and the dissipative vibrational-bath interaction is modeled with the Lindblad equation. This approach captures both tunneling and nonadiabatic dynamics. Relationships between microscopic molecular properties and the driven ET rate are explored for two time-dependent applied fields: an abruptly switched field and a linearly ramped field. In both cases, the driven ET rate is only weakly temperature dependent. When the model is applied using parameters appropriate to a specific mixed-valence molecule, diferrocenylacetylene, terahertz-range ET transfer rates are predicted.

Geometric effects in nonequilibrium electron transfer statistics in adiabatically driven quantum junctions

Cyclic Pancharatnam-Berry (PB) and adiabatic noncyclic geometric (ANG) effects are investigated in a single electron orbital system connected to two metal contacts with externally driven chemical potential and/or temperatures.The PB contribution does not affect the density matrix evolution, but has quantitative effect on the statistics (fluctuations) of electron transfer. The ANG contribution, on the other hand, affects the net flux across the junction. Unlike the PB, the ANG contribution is non-zero when two parameters are identically driven. Closed analytical expressions are derived for the ANG contribution to the flux, and the PB contribution to the first two leading order fluctuations. Fluctuations can be modified by manipulating the relative phases of the drivings. Interestingly, we find that the fluctuations of the pumped charge do not satisfy the steady state fluctuation theorem in presence of nonzero geometric contribution, but can be recovered for a vanishing geometric contribution even in presence of the external driving.

Effect of geometrical parameters of dyad D–A and triad D–A1–A2 on the efficiency of ultrafast intramolecular charge separation from the second excited state

Ultrafast intramolecular charge transfer induced by the Soret-band excitation of molecular dyads, donor–acceptor, and triads, donor–acceptor1–acceptor2, has been explored within the stochastic point-transition model. The influence of the effective radii of the donor, acceptors, distances between them, and the angle between the directions of two sequential electron transfers on the quantum yield of thermalized charge separated states has been studied. A bell-shaped dependence of the quantum yield of the charge separated state on the center-to-center distance between the donor and acceptor is revealed for dyads. This dependence is a result of competition between two processes suppressing formation of the charge separated state. At short distances the electronic coupling is strong and the non-equilibrium charge recombination into the first excited state is very effective. At large distances the charge separation is slow and can not compete with internal conversion. This is the reason why the quantum yield is expected to be small in both limits. In triads the non-equilibrium electron transfer from the primary to the secondary acceptor can effectively compete with ultrafast back electron transfer into the first excited state of the donor and considerably increase the quantum yield of thermalized charge separated state. The strategy of maximizing the quantum yield is discussed. The regions of spatial parameters of triads and dyads maximizing the quantum yield of the charge separated states have been estimated for typical charge transfer parameters.

Excitation wavelength dependence of the charge separation pathways in tetraporphyrin-naphthalene diimide pentads

The excited-state dynamics of two multichromophoric arrays composed of a naphthalene diimide centre and four zinc or free-base porphyrins substituted on the naphthalene core via aniline bridges has been investigated using a combination of stationary and ultrafast spectroscopy. These pentads act as efficient antennae as they absorb over the whole visible region, with a band around 700 nm, associated with a transition to the S1 state delocalised over the whole arrays, and bands at higher energy due to transitions centred on the porphyrins. In non-polar solvents, population of these porphyrin states is followed by sub-picosecond internal conversion to the S1 state. The existence of a charge-separated state located above the S1 state could enhance this process. The decay of the S1 state is dominated by non-radiative deactivation on the 100 ps timescale, most probably favoured by the small S1-S0 energy gap and the very high density of vibrational states of these very large chromophores. In polar solvents, the charge-separated state lies just below the S1 state. It can be populated within a few picoseconds by a thermally activated hole transfer from the S1 state as well as via sub-picosecond non-equilibrium electron transfer from vibrationally hot porphyrin excited states. Because of the small energy gap between the charge-separated state and the ground state, charge recombination is almost barrierless and occurs within a few picoseconds. Despite their very different driving forces, charge separation and recombination occur on similar timescales. This is explained by the electronic coupling that differs considerably for both processes.

Ultrafast Dynamics of Nonequilibrium Electron Transfer in Photoinduced Redox Cycle: Solvent Mediation and Conformation Flexibility

We report here our systematic characterization of a photoinduced electron-transfer (ET) redox cycle in a covalently linked donor-spacer-acceptor flexible system, consisting of N-acetyl-tryptophan methylester as an electron donor and thymine as an electron acceptor in three distinct solvents of water, acetonitrile, and dioxane. With femtosecond resolution, we determined all the ET time scales, forward and backward, by following the complete reaction evolution from reactants to intermediates and finally to products. Surprisingly, we observed two distinct ET dynamics in water, corresponding to a stacked configuration with ultrafast ET in 0.7 ps and back ET in 4.5 ps and a partially folded C-clamp conformation with ET in 322 ps but back ET in 17 ps. In acetonitrile and dioxane, only the C-clamp conformations were observed with ET in 470 and 1068 ps and back ET in 110 and 94 ps, respectively. These relatively slow ET dynamics in hundreds of picoseconds all showed significant conformation heterogeneity and followed a stretched decay behavior. With both forward and back ET rates determined, we derived solvent reorganization energies and coupling constants. Significantly, we found that solvent molecules intercalated in the cleft of the C-clamp structure mediate electron transfer with a tunneling parameter (β) of 1.0-1.4 Å(-1) and the high-frequency vibration modes in the product(s) couple with the back ET process, leading to the ultrafast back ET dynamics in tens of picoseconds. These findings provide mechanistic insights of nonequilibrium ET dynamics modulated by conformation flexibility, mediated by unique solvent configuration, and accelerated by vibrational coupling.

Photoinduced intramolecular charge separation in a polymer solid below the glass transition temperature

Photoinduced intramolecular charge separation (CS) in a polar polymer glass, cyanoethylated pullulan (CN-PUL), was studied below the glass transition temperature (Tg=395 K). A series of three carbazole (Cz: donor)-cyclohexane (S: spacer)-acceptor (A: acceptor) molecules (Cz-S-A) was used as intramolecular donor-acceptor dyads. The photoinduced CS rate was evaluated by the fluorescence decay measurement at temperatures from 100 to 400 K. The CS rate (kCS) increased above 200 K even far below Tg where micro-Brownian motions of the whole polymer chain are frozen. Below 200 K, on the other hand, kCS showed weak dependence on temperature. The temperature dependence of kCS is discussed in terms of the dielectric relaxation time of the polymer matrix. Consequently, CS below Tg was well explained by a thermally nonequilibrium electron transfer (ET) formula above 200 K and by a two-mode quantum-mechanical ET formula below 200 K. The increase in kCS above 200 K is mainly caused by a thermally activated low-frequency matrix mode originating from the side-chain relaxation of polar cyano groups. The weak temperature dependence of kCS can be explained by a nuclear-tunneling effect caused by a high-frequency matrix mode (variant Planck's over 2piomegH=250 cm-1) and an intramolecular vibrational mode (variant Planck's over 2piomegaQ=1300 cm-1). The high-frequency mode of the polymer matrix was attributed to a vibrational or librational motion of polar groups in the CN-PUL glassy solid.

On Charge Separation at the Phase Boundary Molecular Crystal/Aqueous Electrolyte

Abstract Analysis of the electrostatics of charge carrier injection into molecular crystals during nonequilibrium electron transfer reactions demonstrates the unique advantage of aqueous or similar electrodes in measuring limiting currents which yield the rate constant of the injection process. At the phase boundary molecular crystal/aqueous electrolyte image forces are negligible due to the slow orientation polarization of water molecules with respect to the hopping frequency of injected charge carriers. Coulomb forces arising from slowly mobile or localized counter charges are shown to be effectively screened by water as a consequence of its relatively higher static dielectric constant as compared to that of the crystal.