Dependence Of Electron Transfer Rate Research Articles

Marcus model-based analysis of the photo-quenching mechanism of a boronic acid fluorophore: water concentration dependence of electron transfer rate.

The photo-quenching mechanism of 2-(4-phenylboronic acid)-1-pyrenemethamide (C1-APB), which has potential application as a saccharide-recognition sensor, was investigated. By performing temperature-dependent time-resolved photoluminescence measurements, we determined the mechanism responsible for the photo-quenching properties of C1-APB to be a photoinduced electron transfer (PET). Moreover, the dependence of the electron transfer rate (kPET) on the solvent water concentration was explored in detail, and it was found that kPET increased by many orders of magnitude with increasing water concentrations. This phenomenon was analyzed using the Marcus model, in which the electron transfer can be represented by a potential diagram involving the potential barrier (ΔGa) and frequency factor (A). With the aid of temperature-dependent measurements, the contribution of ΔGa and A to the increase in kPET was successfully analyzed independently, which allowed us to discuss the effect of water molecule orientation and change in molecular structure of C1-APB. The temperature-dependence measurements performed in this study offer a powerful research tool for investigating the PET process, and will contribute to the development of molecular recognition fluorescent sensors.

Surface-Ligand "Liquid" to "Crystalline" Phase Transition Modulates the Solar H2 Production Quantum Efficiency of CdS Nanorod/Mediator/Hydrogenase Assemblies.

This study reports how the length of capping ligands on a nanocrystal surface affects its interfacial electron transfer (ET) with surrounding molecular electron acceptors, and consequently, impact the H2 production of a biotic-abiotic hybrid artificial photosynthetic system. Specifically, we study how the H2 production efficiency of a hybrid system, combining CdS nanorods (NRs), [NiFe] hydrogenase, and redox mediators (propyl-bridged 2,2'-bipyridinium, PDQ2+), depends on the alkyl chain length of mercaptocarboxylate ligands on the NR surface. We observe a minor decrease of the quantum yield for H2 production from 54 ± 6 to 43 ± 2% when varying the number of methylene units in the ligands from 2 to 7. In contrast, an abrupt decrease of the yield was observed from 43 ± 2 to 4 ± 1% when further increasing n from 7 to 11. ET studies reveal that the intrinsic ET rates from the NRs to the electron acceptor PDQ2+ are all within 108-109 s-1 regardless of the length of the capping ligands. However, the number of adsorbed PDQ2+ molecules on NR surfaces decreases dramatically when n ≥ 10, with the saturating number changing from 45 ± 5 to 0.3 ± 0.1 for n = 2 and 11, respectively. These results are not consistent with the commonly perceived exponential dependence of ET rates on the ligand length. Instead, they can be explained by the change of the accessibility of NR surfaces to electron acceptors from a disordered "liquid" phase at n < 7 to a more ordered "crystalline" phases at n > ∼7. These results highlight that the order of capping ligands is an important design parameter for further constructing nanocrystal/molecular assemblies in broad nanocrystal-based applications.

Linkage dependence of charge separated lifetime in small donor-acceptor dyads system

Fast charge separation (CS) process and slow charge recombination (CR) process are critical for effective utilization of solar energy in artificial photosynthesis, photocatalysis and organic photovoltaic devices. Here we demonstrated in a model donor-acceptor (D-A) dyad of styrene based triphenylamine derivative (MTPA) as an electron donor (D), triazine group (TRC) as an electron acceptor (A) (MTPA-TRC) that the CS and CR process can be modulated by the linker groups between donor and acceptor. We synthesized a series of flexibly linked D-A dyads MTPA-TRC-n with different length of methylene units (n = 1, 2, 3, n stands for the number of methylene units) as the spacer and lifetimes of charge-separated states ranging from nanoseconds to milliseconds were observed. According to the Marcus charge transfer theory, MTPA-TRC-n have similar reorganization energies (λ) but decreased electronic coupling matrix element (V). V value is the key factor to dominate the charge transfer rate and charge-separated lifetime in this D-A dyads system. Additionally, the decay coefficient (β) of length dependence of electron transfer rate was decreased from 0.4 Å−1 to 0.3 Å−1 in methanol compared to acetonitrile. It revealed that electronic coupling between the donor and acceptor could be enhanced by the increasing solvent polarity in the non-conjugated linked D-A system.

On the Control of Electron Transfer Rates through the Morphology of Nanoparticles

It will be shown how the morphology and dimension of inorganic nanostructures in a solution should affect the rates of outer sphere electron transfer for nearby redox ions much differently than is predicted for a macroscopic planar interface. Simple Marcus theory and electrostatic evaluations of the self-energy of the ions near these nanostructures are used to calculate this effect, which is controlled by the degree to which the environment about the ion is the high dielectric permittivity of the solid rather than solution. A higher degree results in a lower reorganization energy for the ion and a smaller activation energy for electron transfer. The extreme of interest to this discussion is that of a redox ion within a spherical or cylindrical nanocavity of an inorganic solid.It has long been known how simple Marcus theory predicts electron transfer rates for donor and acceptor couples as a function of the difference in the free energy of the reaction and experimentation1 has confirmed the predicted parabolic form of transfer rates and the “inverted region,” where rates slow down. Variations in the outer sphere reorganization energies of donor-acceptor couples also result in changes of charge transfer rates predicted by this theory and also indicate this decrease in transfer rates.2 Recently, it has been demonstrated how the temperature dependence of electron transfer rates for a specific donor-acceptor couples also describes this parabolic behavior according to theory.3 This presentation on nanostructures and outer sphere electron transfer explores how the dielectric permittivity within Marcus theory may be an additional variable to control rates of electron transfer reactions.Geometric configurations will be examined in this work in the limits where the radius of the nanocavity of the solid varies from large compared to that of the redox ion within it to where it approaches the size of the redox ion. The electron transfer will be calculated as a self-exchange rate for reduced and oxidized forms of a redox couple to avoid considerations of electron exchange with the solid. To illustrate the principles involved, the solution will be taken as acetonitrile and the solid as ZnO. Spherical nanoshells will also be considered to illustrate how the same redox ion can have an accelerated electron transfer rate within the cavity while its rate for ions outside the shell slows down.4

On the origin of multiexponential fluorescence decays from 2-aminopurine-labeled dinucleotides.

The fluorescent probe 2-aminopurine (2Ap) has been used for decades to study local conformational fluctuations in DNA. Steady-state and time-resolved measurements of 2Ap fluorescence have been used to predict specific conformational states through suitable modeling of the quenching of the fluorescence of a 2Ap residue incorporated site-specifically into a DNA strand. The success of this approach has been limited by a lack of understanding of the precise factors responsible for the complex, multiexponential decays observed experimentally. In this study, dinucleotides composed of 2Ap and adenine were studied by the time-correlated single-photon counting technique to investigate the causes of heterogeneous emission kinetics. Contrary to previous reports, we argue that emission from 2Ap that is stacked with a neighboring base contributes negligibly to the emission signals recorded more than 50 ps after excitation, which are instead dominated by emission from unstacked 2Ap. We find that the decay kinetics can be modeled using a continuous lifetime distribution, which arises from the inherent distance dependence of electron transfer rates without the need to postulate a small number of discrete states with decay times derived from multiexponential fits. These results offer a new perspective on the quenching of 2Ap fluorescence and expand the information that can be obtained from experiments.

Charge Transfer Dynamics from Photoexcited Semiconductor Quantum Dots.

Understanding photoinduced charge transfer from nanomaterials is essential to the many applications of these materials. This review summarizes recent progress in understanding charge transfer from quantum dots (QDs), an ideal model system for investigating fundamental charge transfer properties of low-dimensional quantum-confined nanomaterials. We first discuss charge transfer from QDs to weakly coupled acceptors within the framework of Marcus nonadiabatic electron transfer (ET) theory, focusing on the dependence of ET rates on reorganization energy, electronic coupling, and driving force. Because of the strong electron-hole interaction, we show that ET from QDs should be described by the Auger-assisted ET model, which is significantly different from ET between molecules or from bulk semiconductor electrodes. For strongly quantum-confined QDs on semiconductor surfaces, the coupling can fall within the strong coupling limit, in which case the donor-acceptor interaction and ET properties can be described by the Newns-Anderson model of chemisorption. We also briefly discuss recent progress in controlling charge transfer properties in quantum-confined nanoheterostructures through wavefunction engineering and multiple exciton dissociation. Finally, we identify a few key areas for further research.

Unusual distance dependences of electron transfer rates.

Usually the rates for electron transfer (kET) decrease with increasing donor-acceptor distance, but Marcus theory predicts a regime in which kET is expected to increase when the transfer distance gets longer. Until recently, experimental evidence for such counter-intuitive behavior had been very limited, and consequently this effect is much less well-known than the Gaussian free energy dependence of electron transfer rates leading to the so-called inverted driving-force effect. This article presents the theoretical concepts that lead to the prediction of electron transfer rate maxima at large donor-acceptor distances, and it discusses conditions that are expected to favor experimental observations of such behavior. It continues with a consideration of specific recent examples in which electron transfer rates were observed to increase with increasing donor-acceptor distance, and it closes with a discussion of the importance of this effect in the context of light-to-chemical energy conversion.

The temperature dependence of the symmetry factor for a model Fe3+(aq)/Fe2+(aq) redox half reaction

The symmetry factor for the activation of an elementary electrode reaction is, in principle, potential dependent and temperature dependent. The variation with temperature is usually rationalised by an Arrhenius-type separation in an enthalpic and entropic contribution. This empirical scheme is investigated for a model aqueous ferrous–ferric oxidation half reaction, using Marcus theory based molecular dynamics simulations. These calculations are extended with umbrella integration and classical transition path sampling methods to verify the validity of the Marcus theory for our model reaction. We show that, in the framework of the Marcus theory, the empirical Arrhenius-type analysis of the symmetry factor is justified provided the activation entropy is evaluated from the temperature dependence of the activation free energy with the potential kept constant. Under these conditions the temperature derivative of the symmetry factor is directly equal to the potential derivative of the activation entropy. Both quantities in turn are proportional to the equilibrium reaction entropy which is the expected behaviour for asymmetric electron transfer of which the half reaction studied here is an example. The numerical simulation results are in good agreement with these theoretical relations confirming that the Marcus theory can be used to analyse the temperature dependence of electron transfer rates.

Enhanced Photoinduced Electron-Transfer Reduction of Li+@C60in Comparison with C60

Kinetics of photoinduced electron transfer from a series of electron donors to the triplet excited state of lithium ion-encapsulated C60 (Li(+)@C60) was investigated in comparison with the corresponding kinetics of the photoinduced electron transfer to the triplet excited state of pristine C60. Femtosecond laser flash photolysis measurements of Li(+)@C60 revealed that singlet excited state of Li(+)@C60 (λmax = 960 nm) underwent intersystem crossing to the triplet excited state [(3)(Li(+)@C60)*: λmax = 750 nm] with a rate constant of 8.9 × 10(8) s(-1) in deaerated benzonitrile (PhCN). The lifetime of (3)(Li(+)@C60)* was determined by nanosecond laser flash photolysis measurements to be 48 μs, which is comparable to that of C60. Efficient photoinduced electron transfer from a series of electron donors to (3)(Li(+)@C60)* occurred to produce the radical cations and Li(+)@C60(•-). The rate constants of photoinduced electron transfer of Li(+)@C60(•-) are significantly larger than those of C60 when the rate constants are less than the diffusion-limited value in PhCN. The enhanced reactivity of (3)(Li(+)@C60)* as compared with (3)C60* results from the much higher one-electron reduction potential of Li(+)@C60 (0.14 V vs SCE) than that of C60 (-0.43 V vs SCE). The rate constants of photoinduced electron transfer reactions of Li(+)@C60 and C60 were evaluated in light of the Marcus theory of electron transfer to determine the reorganization energies of electron transfer. The reorganization energy of electron transfer of Li(+)@C60 was determined from the driving force dependence of electron transfer rate to be 1.01 eV, which is by 0.28 eV larger than that of C60 (0.73 eV), probably because of the change in electrostatic interaction of encapsulated Li(+) upon electron transfer in PhCN.

Reorganization energy of supramolecular donor–acceptor dyad of octaethylporphyrin isomers and axial-coordinated acceptor: Experimental and computational study

The internal reorganization energy ( λ V) of photoinduced electron transfer (ET) in the supramolecular donor–acceptor dyads of 2,3,7,8,12,13,17,18-octaethylporphinatozinc(II) (ZnOEP) and electron acceptor ligands was compared with those of structural isomers, 2,3,7,8,11,12,17,18-octaethylhemiporphycenatozinc(II) (ZnHPc) and 2,3,6,7,12,13,16,17-octaethylporphycenatozinc(II) (ZnPcn). First, ET process of the supramolecular donor–acceptor dyads of ZnOEP was investigated by means of the transient absorption spectroscopy mainly. The formation of supramolecular dyads was confirmed by absorption spectral change, from which the association constant was estimated. The ET process was confirmed by the observation of radical cation of ZnOEP during the laser flash photolysis. The ET rates of these dyads are in the order of ZnOEP > ZnHPc > ZnPcn, when the driving forces for ET are similar to each other. From the free energy dependence of ET rates, the λ V values of OEP and its isomers were estimated. The estimated λ V value was in the order of ZnOEP < ZnHPc < ZnPcn. This tendency was reproduced by calculation at B3LYP/6-31G(d) and BHandHLYP/6-31G(d) levels. The origin of this tendency was discussed on the basis of the structural change during the ET process.

Study of photo-induced electron transfer in pyrene-(CH 2) n- N, N′-dimethylaniline system by molecular dynamic simulation

The dynamic behavior of pyrene-(CH 2) n - N, N′-dimethylaniline (PnD; n = 1–3) in acetonitrile and cyclohexane was investigated with molecular dynamic simulation (MD). Then, changes in distance ( R) between pyrene and N, N-dimethylaniline moieties with time were obtained at time intervals of 1 ps for P3D, 0.1 ps for P2D and 0.02 ps for P1D. Photo-induced electron transfer (ET) rates were evaluated with Kakitani, Yoshimori and Mataga theory (KYM theory) with R at each time. The observed fluorescence intensities with lifetimes, 11 ps for P3D, 6.1 ps for P2D and 1.7 ps for P1D were obtained from observed rise times of transient absorbance of pyrene anion radicals in PnD in acetonitrile. Parameters contained in KYM theory, frequency factor ( ν 0), coefficient for criterion of adiabatic and non-adiabatic processes ( β), critical distance between adiabatic and non-adiabatic processes ( R 0) and standard free energy change (Δ G 0) were determined by a non-linear least squares method, so as to fit the calculated fluorescence intensities obtained with the observed fluorescence intensities. The calculated intensities were in good agreement with the observed ones. The values of best-fit parameters, ν 0, β, R 0, and Δ G 0 were 82.04 ps −1, 5.56 nm −1, 0.568 nm and −2.12 eV, respectively, in P3D, 82.05 ps −1, 5.56 nm −1, 0.569 nm and −2.12 eV, respectively, for P2D, and 93.19 ps −1, 5.58 nm −1, 0.698 nm and −2.08 eV, respectively, for P1D. In all systems, the ET processes were non-adiabatic. The dependence of ET rate on R were calculated with these parameters, which suggests that ET rate also exhibits a “bell shape”, such as the one obtained in the variation of Δ G 0. Therefore, ET rate may decrease with R less than 0.55 nm for all PnD (n = 1–3) systems.

Electron-Transfer Fluorescence Quenching of Aromatic Hydrocarbons by Europium and Ytterbium Ions in Acetonitrile

To make the effects of molecular size on photoinduced electron-transfer (ET) reactions clear, the ET fluorescence quenching of aromatic hydrocarbons by trivalent lanthanide ions M3+ (europium ion Eu3+ and ytterbium ion Yb3+) and the following ET reactions such as the geminate and free radical recombination were studied in acetonitrile. The rate constant k(q) of fluorescence quenching, the yields of free radical (phi(R)) and fluorescer triplet (phi(T)) in fluorescence quenching, and the rate constant k(rec) of free radical recombination were measured. Upon analysis of the free energy dependence of k(q), phi(R), phi(T), and k(rec), it was found that the switchover of the fluorescence quenching mechanism occurs at deltaG(fet) = -1.4 to -1.6 eV: When deltaG(fet) < -1.6 eV, the fluorescence quenching by M3+ is induced by a long-distance ET yielding the geminate radical ion pairs. When deltaG(fet) > -1.4 eV, it is induced by an exciplex formation. The exciplex dissociates rapidly to yield either the fluorescer triplet or the geminate radical ion pairs. The large shift of switchover deltaG(fet) from -0.5 eV for aromatic quenchers to -1.4 to -1.6 eV for lanthanide ions is almost attributed to the difference in the molecular size of the quenchers. Furthermore, it was substantiated that the free energy dependence of ET rates for the geminate and free radical recombination is satisfactorily interpreted within the limits of the Marcus theory.

PH-Dependent Electron Transfer from Re-bipyridyl Complexes to Metal Oxide Nanocrystalline Thin Films

Photoinduced interfacial electron transfer (ET) from molecular adsorbates to semiconductor nanoparticles has been a subject of intense recent interest. Unlike intramolecular ET, the existence of a quasicontinuum of electronic states in the solid leads to a dependence of ET rate on the density of accepting states in the semiconductor, which varies with the position of the adsorbate excited-state oxidation potential relative to the conduction band edge. For metal oxide semiconductors, their conduction band edge position varies with the pH of the solution, leading to pH-dependent interfacial ET rates in these materials. In this work we examine this dependence in Re(L(P))(CO)3Cl (or ReC1P) [L(P) = 2,2'-bipyridine-4,4'-bis-CH2PO(OH)2] and Re(L(A))(CO)3Cl (or ReC1A) [L(A) = 2,2'-bipyridine-4,4'-bis-CH2COOH] sensitized TiO2 and ReC1P sensitized SnO2 nanocrystalline thin films using femtosecond transient IR spectroscopy. ET rates are measured as a function of pH by monitoring the CO stretching modes of the adsorbates and mid-IR absorption of the injected electrons. The injection rate to TiO2 was found to decrease by 1000-fold from pH 0-9, while it reduced by only a factor of a few to SnO2 over a similar pH range. Comparison with the theoretical predictions based on Marcus' theory of nonadiabatic interfacial ET suggests that the observed pH-dependent ET rate can be qualitatively accounted for by considering the change of density of electron-accepting states caused by the pH-dependent conduction band edge position.

Interference, Fluctuation, and Alternation of Electron Tunneling in Protein Media. 2. Non-Condon Theory for the Energy Gap Dependence of Electron Transfer Rate

Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.

Wire-like charge transport at near constant bridge energy through fluorene oligomers.

The study of photoinitiated electron transfer in donor-bridge-acceptor molecules has helped elucidate the distance dependence of electron transfer rates and behavior of various electron transfer mechanisms. In all reported cases, the energies of the bridge electronic states involved in the electron transfer change dramatically as the length of the bridge is varied. We report here, in contrast, an instance in which the length of the bridge, and therefore the distance over which the electron is transferred, can be varied without significantly changing the energies of the relevant bridge states. A series of donor-bridge-acceptor molecules having phenothiazine (PTZ) donors, 2,7-oligofluorene (FL(n)) bridges, and perylene-3,4:9,10-bis(dicarboximide) (PDI) acceptors was studied. Photoexcitation of PDI to its lowest excited singlet state results in oxidation of PTZ via the FL(n) bridge. In toluene, the rate constants for both charge separation and recombination as well as the energy levels of the relevant FL(n)(+.) bridge states for n = 1-4 are only weakly distance dependent. After the initial photo-generation of (1)(PTZ(+.)-FL(n)-PDI(-.)), radical pair intersystem crossing results in formation of (3)(PTZ(+.)-FL(n)-PDI(-.)) that recombines to give (3.)PDI. The dependence of the (3.)PDI yield on an applied magnetic field shows a resonance, which gives the singlet-triplet splitting, 2J, of the radical ion pair. The magnitude of 2J directly monitors the contribution of coherent charge transfer (superexchange) to the overall electron transfer rate. These data show that charge recombination through FL(n) is dominated by incoherent hopping at long distances.

Metal‐Assembled Modular Proteins: Toward Functional Protein Design.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Electron Transfer Rates in DNA Films as a Function of Tether Length

A homologous series of DNA-modified electrodes has been investigated in which the molecular tether length varies. Using intercalated, covalently bound daunomycin as a redox probe, an exponential dependence of electron transfer rates on the number of intervening methylene groups in the sigma-bonded tether is observed. In contrast, variation in DM position within DNA yields no detectable change in rate. These data confirm that overall electron transfer rates in DNA films are limited by the tether, not the DNA.

Metal-Assembled Modular Proteins: Toward Functional Protein Design

Metal-assembled parallel helix-bundle proteins have been used to investigate electron transfer through alpha-helical structures. Fermi Golden Rule distance dependence of electron transfer rates was established in a family of designed metalloproteins, and the contribution of intrahelical hydrogen bonding to the matrix tunneling element was explored. The first steps toward the design of functional proteins using dynamic combinatorial assembly of alpha-helical structural elements are described.

Effects of initial state preparation on the distance dependence of electron transfer through molecular bridges and wires

The dependence of electron transfer rates and yields in bridged molecular systems on the bridge length, and the dependence of the zero-bias conduction of molecular wires on wire length are discussed. Both phenomena are controlled by tunneling across the molecular bridge and are consequently expected to show exponential decrease with bridge length that is indeed often observed. Deviations from this exponential dependence for long bridges, in particular a crossover to a very weak dependence on bridge length, were recently observed experimentally and discussed theoretically in terms of thermal relaxation and dephasing on the bridge. Here we discuss two other factors that potentially affect the bridge length dependence of these phenomena. First, in experiments initiated by an initial preparation of a nonstationary “donor” state the initial energy is not well defined. A small contribution from initially populated eigenstates that are of mostly bridge-level character may dominate transmission for long bridges, resulting in weak or no bridge-length dependence. Second, in steady state experiments the distribution of initial states (for example, the Fermi distribution at the electrodes in conduction experiments) will cause deviations from exponential dependence on wire length because even a small population in higher energy states will dominate the transmission through long wires. For the first scenario we show that the crossover behavior observed for electron transfer in DNA between G and GGG species separated by AT chains can be largely reproduced just by initial state effects.

Rational design principle for modulating fluorescence properties of fluorescein-based probes by photoinduced electron transfer.

Fluorescence properties of fluorescein-based probes are shown to be finely controlled by the rate of photoinduced electron transfer from the benzoic acid moiety (electron donor) to the singlet excited state of the xanthene moiety (electron acceptor fluorophore). The occurrence of photoinduced electron transfer is clearly evidenced by transient absorption spectra showing bands due to the radical cation of the electron donor moiety and the radical anion of the xanthene moiety, observed in laser flash photolysis experiments. The photoinduced electron transfer rates and the rates of back electron transfer follow the Marcus parabolic dependence of electron transfer rate on the driving force. Such a dependence provides for the first time a quantitative basis for a rational design principle which has high efficiency in modulating fluorescence properties of fluorescein-based probes.