Electron transfer rates and Franck–Condon factors: an application to the early electron transfer steps in photosynthetic reaction centers

Mechanistic aspects of some of the early electron transfer steps occurring in photosynthetic reaction centers are discussed. Starting from the normal modes of the redox cofactors involved in the electron transfer processes, we show how a series of quantities which regulate electron transfer rates, such as (i) the electron transfer active modes, (ii) the intramolecular reorganization energy, and (iii) the mutual couplings between the vibronic states of the donor and the acceptor, can be obtained and used to draw qualitative conclusions on ET rates.     

On the role of nuclear motions in electron and excitation transfer rates: Importance of transfer-integral dependence upon nuclear coordinate

The role of nuclear degrees of freedom in modifying the electron or exciton transfer rates between molecules is investigated. In addition to the usual Franck-Condon overlap factors which arise from the overlaps of initial and final vibrational states, we discuss a dependence of the transfer integral upon nuclear motions, a dependence which has been often cited, but nearly always ignored, in the usual dynamical theories of transfer processes. We show, within a Bom-Oppenheimer treatment, that the transfer integral dependence upon librational, rotational and vibrational modes can profoundly change both the rate itself and its functional dependences (upon temperature, upon orientation, etc.). Using a simple cosine form for the dependence of the transfer integral upon the modifying nuclear mode and a simple displaced-oscillator transformation, we obtain a closed-form solution for the transfer rate, which includes a new overlap factor arising from the dependence of the transfer integral upon nuclear coordinates. Some general remarks about the role of this dependence are made, and applications to particular transfer systems are briefly discussed.     

Monte Carlo simulations of heterogeneous electron transfer: New challenges

We report results of MC simulations of electron transfer across a metal electrode/electrolyte solution interface. The model presumes the Landau–Zener theory and a random walk on a two-dimensional lattice formed by crossing parabolic reaction free energy surfaces along the solvent coordinate. Emphasis is put on investigating the activationless discharge regime; the bridge-assisted electron transfer is also partially addressed. We have calculated effective electronic transmission coefficient as a function of the electrode overpotential and temperature in a wide range of orbital overlap. The dependence of the transmission coefficient on the electronic density of states is analyzed as well.     

Reversible Switching of Redox‐Active Molecular Orbitals and Electron Transfer Pathways in CuA Sites of Cytochrome c Oxidase

The Cu_A site of cytochrome c oxidase is a redox hub that participates in rapid electron transfer at low driving forces with two redox cofactors in nearly perpendicular orientations. Spectroscopic and electrochemical characterizations performed on first and second‐sphere mutants have allowed us to experimentally detect the reversible switching between two alternative electronic states that confer different directionalities to the redox reaction. Specifically, the M160H variant of a native Cu_A shows a reversible pH transition that allows to functionally probe both states in the same protein species. Alternation between states exerts a dramatic impact on the kinetic redox parameters, thereby suggesting this effect as the mechanism underlying the efficiency and directionality of Cu_A electron transfer in vivo. These findings may also prove useful for the development of molecular electronics.     

The femtosecond dynamics of electron transfer in a modified photosynthesis reaction center: Quantum, classical, and kinetic analyses

The dynamics of electron transfer in a modified photosynthesis reaction center in which electron transfer from the bridge to the acceptor is blocked is considered. A microscopic model of the process is suggested. Within this model, the diabatic electronic states of the donor and bridge are described by one-dimensional displaced harmonic oscillators. The dynamics of the population of electronic states is calculated by the quantum method of wave packets and classical and kinetic modeling. The suggested model is used to study the qualitative dependence of the dynamics of electron transfer on the nonadiabatic interaction potential. The parameters of the model are determined by comparing the experimental and calculated absorption spectra of the product of electron transfer. It is shown that kinetic models can be used to approximately describe the dynamics of electron transfer in reaction centers. The boundaries of the applicability of the kinetic method are considered.     

Influence of thermal fluctuations on interfacial electron transfer in functionalized TiO2 semiconductors

The influence of thermal fluctuations on the dynamics of interfacial electron transfer in sensitized TiO2-anatase semiconductors is investigated by combining ab initio DFT molecular dynamics simulations and quantum dynamics propagation of transient electronic excitations. It is shown that thermal nuclear fluctuations speed up the underlying interfacial electron transfer dynamics by introducing nonadiabatic transitions between electron acceptor states, localized in the vicinity of the photoexcited adsorbate, and delocalized states extended throughout the semiconductor material, creating additional relaxation pathways for carrier diffusion. Furthermore, it is shown that room-temperature thermal fluctuations reduce the anisotropic character of charge diffusion along different directions in the anatase crystal and make similar the rates for electron injection from adsorbate states of different character. The reported results are particularly relevant to the understanding of temperature effects on surface charge separation mechanisms in molecular-based photo-optic devices.     

Identification of the optically active vibrational modes in the photoluminescence of MEH-PPV films

The temperature dependence of the photoluminescence properties of a thin film of poly[2-methoxy-5-(2(')-ethylhexyloxy)-p-phenylene-vinylene], MEH-PPV, fabricated by spin coating, is analyzed. The evolution with temperature of the peak energy of the purely electronic transition, of the first vibronic band, of the effective conjugation length, and of the Huang-Rhys factors are discussed. The asymmetric character of the pure electronic transition peak and the contribution of the individual vibrational modes to the first vibronic band line shape are considered by a model developed by Cury et al. [J. Chem. Phys. 121, 3836 (2004)]. The temperature dependence of the Huang-Rhys factors of the main vibrational modes pertaining to the first vibronic band allows us to identify two competing vibrational modes. These results show that the electron coupling to different vibrational modes depends on temperature via reduction of thermal disorder.     

Effect of group electronegativity on electron transfer in bis(hydrazine) radical cations

The radical cation of 4,10-ditert-butyl-5,9-diisopropyl-4,5,9,10-tetraazatetracyclo[6.2.2.2]-tetradecane (sBI4T(+)), as well as its substituted bis(hydrazine) radical cations, is chosen for the investigation of the electronegativity dependence of its intramolecular electron transfer. To do so, two parameters, reorganization energy and electronic coupling, are calculated with several ab initio approaches. It is found that the electronic couplings decrease with the increase of the group electronegativity while the reorganization energies do not show an explicit dependency. Furthermore, Marcus formula is employed to reveal those effect on the electron transfer rates. The predicted rates of electron transfer generally decrease with increasing group electronegativity, although not monotonically.     

On the theory of electron transfer reactions. The naphthalene−·/TCNQ system

A theory for electron transfer reactions involving large free energy changes is presented. The energy distribution between inner-sphere vibrational modes and the outer-sphere polar continuum modes is analyzed and formulas are presented which are particularly suited to treat polyatomic systems. The temperature dependence is of the exponential type for strongly exoergic transitions. We treat explicitly a complete set of possible channels for the naphthalene ion radical/TCNQ system and discuss the competition between transitions falling into the so-called normal region with those falling into the abnormal region.     

The Influence of Dissipation on Vibrational Dynamics in a System of Two Interacting Electronic States

The vibrational dynamics of a nonadiabatic transition between two interacting electronic states in a molecular system in a thermal environment was considered. Two models were used. In one of these, both states, and in the other, only one state interacted with the environment. The electronic states were described by one-dimensional harmonic oscillators on the assumption that the interaction amplitude with the environment (bath) linearly depended on the coordinates of the bath and system. Model parameters typical of electron transfer in photosynthesis reaction centers were selected. The numerical solutions to the Redfield equations for the reduced density matrix were used to calculate the time characteristics of the system, including the mean vibrational energy, product population, and the degree of vibrational motion coherence. The influence of temperature and intensity of interactions with the bath on the time dependence of these values was studied. The character of vibrational dynamics had features common to both models, namely, (1) the vibrational energy monotonically decreased with the time, and this dependence was close to one-exponential in the majority of cases and (2) the time dependence of reaction yield, i.e., product population, was a step function, and the probability of the electron transition decreased as the temperature increased. It was found that there was a fundamental difference between the models under consideration: if only the reaction product interacted with the bath, vibrational coherence was retained for a long time (up to 2000 fs).     

A nonmonotonic dependence of standard rate constant on reorganization energy for heterogeneous electron transfer processes on electrode surface

In the present work a nonmonotonic dependence of standard rate constant (k(0)) on reorganization energy (lambda) was discovered qualitatively from electron transfer (Marcus-Hush-Levich) theory for heterogeneous electron transfer processes on electrode surface. It was found that the nonmonotonic dependence of k(0) on lambda is another result, besides the disappearance of the famous Marcus inverted region, coming from the continuum of electronic states in electrode: with the increase of lambda, the states for both Process I and Process II ET processes all vary from nonadiabatic to adiabatic state continuously, and the lambda dependence of k(0) for Process I is monotonic thoroughly, while for Process II on electrode surface the lambda dependence of k(0) could show a nonmonotonicity.     

Electron tunneling through sensitizer wires bound to proteins

We report a quantitative theoretical analysis of long-range electron transfer through sensitizer wires bound in the active-site channel of cytochrome P450cam. Each sensitizer wire consists of a substrate group with high binding affinity for the enzyme active site connected to a ruthenium-diimine through a bridging aliphatic or aromatic chain. Experiments have revealed a dramatic dependence of electron transfer rates on the chemical composition of both the bridging group and the substrate. Using combined molecular dynamics simulations and electronic coupling calculations, we show that electron tunneling through perfluorinated aromatic bridges is promoted by enhanced superexchange coupling through virtual reduced states. In contrast, electron flow through aliphatic bridges occurs by hole-mediated superexchange. We have found that a small number of wire conformations with strong donor–acceptor couplings can account for the observed electron tunneling rates for sensitizer wires terminated with either ethylbenzene or adamantane. In these instances, the rate is dependent not only on electronic coupling of the donor and acceptor but also on the nuclear motion of the sensitizer wire, necessitating the calculation of average rates over the course of a molecular dynamics simulation. These calculations along with related recent findings have made it possible to analyze the results of many other sensitizer-wire experiments that in turn point to new directions in our attempts to observe reactive intermediates in the catalytic cycles of P450 and other heme enzymes.     

Cross sections for low-energy electron scattering from adenine in the condensed phase

Measurements of the vibrational and electronic excitation of a sub-monolayer up to a monolayer film of adenine were performed with a high resolution electron energy-loss (HREEL) spectrometer. The integral cross sections (over the half-space angle) for excitation of the normal vibrational modes of the ground electronic state and electronically excited states are calculated from the measured reflectivity EEL spectra. Most cross sections for vibrational excitation are of the order of 10(-17) cm(2), the largest being the out-of-plane wagging of the amino-group and the six-member ring deformations. A wide resonance feature appears in the incident energy dependence of the vibrational cross sections at 3-5 eV, while a weak shoulder is present in this dependence for combined ring deformations and bending of hydrogen atoms. For the five excited electronic states, at 4.7, 5.0, 5.5, 6.1 and 6.6 eV, the cross sections are of the order of 10(-18) cm(2), except in the case of the state at the energy of 6.1 eV, for which it is two to three times higher.     

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.     

Temperature dependence of photoinduced electron transfer within self-associated porphyrin: guanine monophosphate complexes

In the current report, the temperature dependence of photoinduced electron transfer between tetrakis-(4-tetramethylpyridyl)porphine (T4MPyP) and guanine monophosphate (GMP) has been examined. In the presence of GMP the fluorescence lifetime analysis reveals a Lorentzian distribution of lifetimes centered at 0.7 ns with a width of 0.9 ns displaying significant temperature dependence. Fitting temperature dependent data to the Marcus equation gives a reorganizational energy (λ) for the electron transfer reaction of 0.6 eV and an electronic coupling factor (H_AB) of 3×10⁻³ eV. These results suggest conformational regulation of electron transfer within the non-covalent porphyrin:nucleotide complex.     

Role of adenine in thymine-dimer repair by reduced flavin-adenine dinucleotide

We present a study of excited-state behavior of reduced flavin cofactors using femtosecond optical transient absorption spectroscopy. The reduced flavin cofactors studied were in two protonation states: flavin-adenine dinucleotide (FADH2 and FADH-) and flavin-mononucleotide (FMNH2 and FMNH-). We find that FMNH- exhibits multiexponential decay dynamics due to the presence of two bent conformers of the isoalloxazine ring. FMNH2 exhibits an additional fast deactivation component that is assigned to an iminol tautomer. Reduced flavin cofactors also exhibit a long-lived component that is attributed to the semiquinone and the hydrated electron that are produced in photoinduced electron transfer to the solvent. The presence of adenine in FADH2 and FADH- further changes the excited-state dynamics due to intramolecular electron transfer from the isoalloxazine to the adenine moiety of cofactors. This electron transfer is more pronounced in FADH2 due to pi-stacking interactions between two moieties. We further studied cyclobutane thymine dimer (TT-dimer) repair via FADH- and FMNH- and found that the repair is much more efficient in the case of FADH-. These results suggest that the adenine moiety plays a significant role in the TT-dimer repair dynamics. Two possible explanations for the adenine mediation are presented: (i) a two-step electron transfer process, with the initial electron transfer occurring from flavin to adenine moiety of FADH-, followed by a second electron transfer from adenine to TT-dimer; (ii) the preconcentration of TT-dimer molecules around the flavin cofactor due to the hydrophobic nature of the adenine moiety.     

Proton-coupled electron transfer in soybean lipoxygenase

The proton-coupled electron transfer reaction catalyzed by soybean lipoxygenase-1 is studied with a multistate continuum theory that represents the transferring hydrogen nucleus as a quantum mechanical wave function. The inner-sphere reorganization energy of the iron cofactor is calculated with density functional theory, and the outer-sphere reorganization energy of the protein is calculated with the frequency-resolved cavity model for conformations obtained with docking simulations. Both classical and quantum mechanical treatments of the proton donor-acceptor vibrational motion are presented. The temperature dependence of the calculated rates and kinetic isotope effects is in agreement with the experimental data. The weak temperature dependence of the rates is due to the relatively small free energy barrier arising from a balance between the reorganization energy and the reaction free energy. The unusually high deuterium kinetic isotope effect of 81 is due to the small overlap of the reactant and product proton vibrational wave functions and the dominance of the lowest energy reactant and product vibronic states in the tunneling process. The temperature dependence of the kinetic isotope effect is strongly influenced by the proton donor-acceptor distance with the dominant contribution to the overall rate. This dominant proton donor-acceptor distance is significantly smaller than the equilibrium donor-acceptor distance and is determined by a balance between the larger coupling and the smaller Boltzmann probability as the distance decreases. Thus, the proton donor-acceptor vibrational motion plays a vital role in decreasing the dominant donor-acceptor distance relative to its equilibrium value to facilitate the proton-coupled electron transfer reaction.     

Photoinduced electron transfer and geminate recombination in liquids on short time scales: Experiments and theory

The coupled processes of intermolecular photoinduced forward electron transfer and geminate recombination between the (hole) donor (Rhodamine 3B) and (hole) acceptors (N,N-dimethylaniline) are studied in three molecular liquids: acetonitrile, butyronitrile, and benzonitrile. Two color pump-probe experiments on time scales from approximately 100 fs to hundreds of picoseconds give information about the depletion of the donor excited state due to forward electron transfer and the survival kinetics of the radicals produced by forward electron transfer. The data are analyzed with a model presented previously that includes distance dependent forward and back electron transfer rates, donor and acceptor diffusion, solvent structure, and the hydrodynamic effect in a mean-field theory of through solvent electron transfer. The forward electron transfer is in the normal regime, and the Marcus equation for the distance dependence of the transfer rate is used. The forward electron transfer data for several concentrations in the three solvents are fitted to the theory with a single adjustable parameter, the electronic coupling matrix element Jf at contact. Within experimental error all concentrations in all three solvents are fitted with the same value of Jf. The geminate recombination (back transfer) is in the inverted region, and semiclassical treatment developed by Jortner [J. Chem. Phys. 64, 4860 (1976)] is used to describe the distance dependence of the back electron transfer. The data are fitted with the single adjustable parameter Jb. It is found that the value of Jb decreases as the solvent viscosity increases. Possible explanations are discussed.     

Influence of a weak hydrogen bond on vibrational coherence probed by photon echoes in DCl dimer trapped in solid nitrogen

The dynamics in the ground electronic state of the two intramolecular D-Cl stretching modes of (DCl)2 in nitrogen solid has been probed by degenerate four wave mixing experiments. Accumulated photon echoes on the "free" nu1 and "bonded" nu2 modes have been performed by means of the free electron laser of Orsay (CLIO). The analysis of the time-resolved signals provides information on the various processes responsible for the loss of vibrational coherence, in particular intra- and intermolecular vibrational energy transfer and pure dephasing. The influence of the weak hydrogen bond is clearly observed on the coherence times of the two stretching modes. Whatever the temperature, the homogeneous width of nu2 lines is almost twice that of nu1 lines. Contrary to the case of isolated DCl trapped in solid nitrogen, no obvious effect of the nitrogen lattice can be extracted from the temperature dependence of the coherence times.