Effect of high-frequency modes and hot transitions on free energy gap dependence of charge recombination rate

The charge recombination (CR) dynamics of geminate ion pairs formed by excitation of the ground-state donor-acceptor complexes in polar solvent have been investigated within the framework of stochastic approach. It is shown that for low exergonic reactions these dynamics critically depend on the reorganization energy of intramolecular high-frequency mode. Even moderate reorganization energies (0.1-0.2 eV) significantly accelerate the excited-state population decay making it nearly exponential. In the solvent-controlled regime, the majority of the excited donor-acceptor complexes recombine at nonthermal (hot) stage when the nonequilibrium initial wave packet passes through a number of term crossings corresponding to the transitions with creation of several vibrational quanta. Analysis of this mechanism allows to conclude (i) the CR in viscous solvents proceeds much faster than the diffusive relaxation of solvent, (ii) under certain conditions, the CR rate becomes practically independent of the diffusive component of solvent relaxation which is determined by solvent viscosity, (iii) in contrast to predictions of Marcus theory, the CR rate decreases monotonically with the rise of reaction exergonicity even at small free energy gaps, in accordance with experimental results. Two semiquantitative approaches providing rather simple analytical expressions for the hot charge recombination dynamics are suggested. These approximations give a good reproduction of the excited-state decay in the wide area of model parameters.     

Charge recombination in excited donor-acceptor complexes with two absorption bands

The dynamics of charge recombination in a photoexcited donor-acceptor complex comprising 1,2,4-trimethoxybenzene (electron donor) and tetracyanoethylene (electron acceptor) in several polar solvents (acetonitrile, valeronitrile, and octanonitrile) was studied in terms of the stochastic approach. The Gibbs energy of charge recombination and the reorganization energies of the medium and quantum and vibrational degrees of freedom were found by fitting the stationary absorption spectrum. The electronic couplings were determined by analyzing the time dependences of the population of the ionic state in acetonitrile. A comparison of the numerical simulation results with the experimental data showed that the nonstationary model under consideration quantitatively described the dynamics of charge recombination and its dependence on the carrier frequency of excitation pulses and the relaxation properties of solvents. Original Russian Text ? V.N. Ionkin, A.I. Ivanov, E. Vauthey, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 4, pp. 791–797.     

Nonequilibrium charge recombination from the excited adiabatic state of donor-acceptor complexes

A model of nonequilibrium charge recombination from an excited adiabatic state of a donor-acceptor complex induced by the nonadiabatic interaction operator is considered. The decay of the excited state population prepared by a short laser pulse is shown to be highly nonexponential. The influence of the excitation pulse carrier frequency on the ultrafast charge recombination dynamics of excited donor-acceptor complexes is explored. The charge recombination rate constant is found to decrease with increasing excitation frequency. The variation of the excitation pulse carrier frequency within the charge transfer absorption band of the complex can alter the effective charge recombination rate by up to a factor 2. The magnitude of this spectral effect decreases strongly with increasing electronic coupling.     

Charge recombination in excited donor-acceptor complexes

The influence of the excitation pulse carrier frequency on the dynamics of ultrafast charge recombination in donor-acceptor complexes was studied in the limit of strong electron coupling. An increase in the carrier frequency of excitation pulses invariably decreased the effective rate constant. The dependence of the degree to which the decay of the excited state deviated from the exponential law on reaction exothermicity and the dynamic characteristics of the medium was revealed.     

What factors control product yield in charge separation reaction from second excited state in zinc-porphyrin derivatives?

Intramolecular charge separation from the second singlet excited state of directly linked Zn-porphyrin-imide dyads and following charge recombination into the first singlet excited state has been investigated in the framework of a model involving three electronic states (the first and the second singlet excited and charge separated states) as well as their vibrational sublevels. Kinetics of the transitions between these states are described in terms of the stochastic point-transition approach. The influence of the model parameters (free energy change of charge separation, magnitude of the reorganization energies of the medium and the high frequency intramolecular vibrations, the rate of relaxation of the medium and the intramolecular high frequency vibrational mode) on the kinetics of population of both the charge separated and the first singlet excited states has been explored. Simulations of the kinetics of the charge separated state population have allowed reproducing the distinctive features of the kinetics observed in the experiment [Wallin, S.; Monnereau, C.; Blart, E.; Gankou, J.-R.; Odobel, F.; Hammarstr?m, L. J. Phys. Chem. A 2010, 114, 1709]: (i) two maxima on short time scale (hundreds of femtoseconds) and long time scale (tens of picoseconds), (ii) the magnitudes of both maxima, and (iii) the depth of the notch between the maxima.     

Acceleration of the Recombination of Photoexcited Donor—Acceptor Complexes with a High-Frequency Vibrational Mode

The recombination dynamics of ion pairs formed by the photoexcitation of donor—acceptor complexes in a polar solvent was investigated using the stochastic approach. The reorganization of high-frequency intramolecular vibrational modes plays an important role in these reactions. It was shown for the perylene—tetracyanoethylene complex in acetonitrile solution that the overwhelming majority of ion pairs recombined at the hot stage, during solvent polarization relaxation.     

Reorganization asymmetry of electron transfer in ferroelectric media and principles of artificial photosynthesis

This study considers electronic transitions within donor-acceptor complexes dissolved in media with macroscopic polarization. The change of the polarizability of the donor-acceptor complex in the course of electronic transition couples to the reaction field of the polar environment and the electric field created by the macroscopic polarization. An analytical theory developed to describe this situation predicts a significant asymmetry of the reorganization energy between charge separation and charge recombination transitions. This result is proved by Monte Carlo simulations of a model polarizable diatomic dissolved in a ferroelectric fluid of soft dipolar spheres. The ratio of the reorganization energies for the forward and backward reactions up to a factor of 25 is obtained in the simulations. This result, as well as the effect of the macroscopic electric field, is discussed in application to the design of efficient photosynthetic devices.     

Effect of the relaxation of high-frequency vibrational modes on the kinetics of charge separation and recombination

The processes of intramolecular electron transfer from the second excited electron state accompanied by superfast reverse transfer to the first excited state are studied. The kinetics of the populations of the first and second excited states, along with that the charge-separated states, is calculated within the generalized stochastic model, taking into account the reorganization of the medium and intramolecular high-frequency vibrations. It is shown that variations in the relaxation rate of the high-frequency vibrational modes can change the population of the quenching products by a factor of two to three. It is established that in the case of the weak exothermicity of the charge separation process, the population of the charge-separated states declines upon an increase in the vibrational relaxation rate, while the population of the first excited state increases; in the region of high exothermicity, these dependences change to ones that are opposite. To reveal the scales of these effects in real systems, the kinetics of the photo-induced processes in the zinc-porphyrin derivatives, including electron-acceptor imide groups covalently coupled with porphyrin rings, are calculated. It is shown that the results from calculating the kinetics of the population of the first and the second excited states agree well with the experimental data on the kinetics of the fluorescence of these states. The absolute values of the population of the charge-separated state and the first excited state are determined. The key role of the hot electron transitions that occur in parallel with the relaxation of the medium and intramolecular vibrations in the considered process is shown.     

Simultaneous generation of different types of ion pairs upon charge-transfer excitation of a donor-acceptor complex revealed by ultrafast transient absorption spectroscopy

The excited-state dynamics of the methylperylene/tetracyanoethylene (MPe/TCNE) donor-acceptor complex has been investigated in various solvents using femtosecond transient absorption spectroscopy. The transient spectra reveal the formation of two types of ion pairs: The first (IP1), constituting the major fraction of the total ion-pair population, is characterized by a broad and red-shifted absorption spectrum compared to that of the free MPe cation and by a subpicosecond lifetime, whereas the second (IP2) has a spectrum closer to that of MPe cation and a lifetime of a few picoseconds. A substantial polarization anisotropy was observed with IP1 but not with IP2, indicating a relatively well-defined structure for the former. The reaction scheme that best accounts for the observed dynamics and its solvent dependence involves the simultaneous excitation of complexes that differ by their electronic coupling. The more coupled complexes have a high absorption coefficient and thus yield IP1, which undergoes ultrafast charge recombination, whereas the less coupled complexes have a lower probability to be excited and lead to the longer-lived IP2.     

Temperature dependence of charge separation and recombination in porphyrin oligomer-fullerene donor-acceptor systems

Electron-transfer reactions are fundamental to many practical devices, but because of their complexity, it is often very difficult to interpret measurements done on the complete device. Therefore, studies of model systems are crucial. Here the rates of charge separation and recombination in donor-acceptor systems consisting of a series of butadiyne-linked porphyrin oligomers (n = 1-4, 6) appended to C(60) were investigated. At room temperature, excitation of the porphyrin oligomer led to fast (5-25 ps) electron transfer to C(60) followed by slower (200-650 ps) recombination. The temperature dependence of the charge-separation reaction revealed a complex process for the longer oligomers, in which a combination of (i) direct charge separation and (ii) migration of excitation energy along the oligomer followed by charge separation explained the observed fluorescence decay kinetics. The energy migration is controlled by the temperature-dependent conformational dynamics of the longer oligomers and thereby limits the quantum yield for charge separation. Charge recombination was also studied as a function of temperature through measurements of femtosecond transient absorption. The temperature dependence of the electron-transfer reactions could be successfully modeled using the Marcus equation through optimization of the electronic coupling (V) and the reorganization energy (λ). For the charge-separation rate, all of the donor-acceptor systems could be successfully described by a common electronic coupling, supporting a model in which energy migration is followed by charge separation. In this respect, the C(60)-appended porphyrin oligomers are suitable model systems for practical charge-separation devices such as bulk-heterojunction solar cells, where conformational disorder strongly influences the electron-transfer reactions and performance of the device.     

Model system-bath Hamiltonian and nonadiabatic rate constants for proton-coupled electron transfer at electrode-solution interfaces

An extension of the Anderson-Newns-Schmickler model for electrochemical proton-coupled electron transfer (PCET) is presented. This model describes reactions in which electron transfer between a solute complex in solution and an electrode is coupled to proton transfer within the solute complex. The model Hamiltonian is derived in a basis of electron-proton vibronic states defined within a double adiabatic approximation for the electrons, transferring proton, and bath modes. The interaction term responsible for electronic transitions between the solute complex and the electrode depends on the proton donor-acceptor vibrational mode within the solute complex. This model Hamiltonian is used to derive the anodic and cathodic rate constants for nonadiabatic electrochemical PCET. The derivation is based on the master equations for the reduced density matrix of the electron-proton subsystem, which includes the electrons of the solute complex and the electrode, as well as the transferring proton. The rate constant expressions differ from analogous expressions for electrochemical electron transfer because of the summation over electron-proton vibronic states and the dependence of the couplings on the proton donor-acceptor vibrational motion. These differences lead to additional contributions to the total reorganization energy, an additional exponential temperature-dependent prefactor, and a temperature-dependent term in the effective activation energy that has different signs for the anodic and cathodic processes. This model can be generalized to describe both nonadiabatic and adiabatic electrochemical PCET reactions and provides the framework for the inclusion of additional effects, such as the breaking and forming of other chemical bonds.     

Hole transfer in a C-shaped molecule: conformational freedom versus solvent-mediated coupling

The electronic coupling matrix elements attending the charge separation reactions of a C-shaped molecule containing an excited pyrene as the electron acceptor and a dimethylaniline as the donor are determined in aromatic, ether, and ester solvents. Band shape analyses of the charge-transfer emission spectra (CT --> S(0)) provide values of the reaction free energy, the solvent reorganization energy, and the vibrational reorganization energy in each solvent. The free energy for charge separation in benzene and toluene solvents is independently determined from the excited state equilibrium established between the locally excited pyrene S(1) state and the charge-transfer state. Analyses of the charge separation kinetics using the spectroscopically determined reorganization energies and reaction free energies indicate that the electronic coupling is solvent independent, despite the presence of a cleft between the donor and acceptor. Hence, solvent molecules are not involved in the coupling pathway. The orientations of the donor and acceptor units, relative to the spacer, are not rigidly constrained, and their torsional motions decrease solvent access to the cleft. Generalized Mulliken-Hush calculations show that rotation of the pyrene group about the bond connecting it to the spacer greatly modulates the magnitude of through-space coupling between the S(1) and CT states. The relationship between the torsional dynamics and the electron-transfer dynamics is discussed.     

Excitation Frequency Dependence of Ultrafast Photoinduced Charge Transfer Dynamics

The dependence of the photoinduced charge transfer rate constant on the pump pulse carrier frequency is shown to be strong, and it is considerably affected by the value of the reorganization energy of low‐frequency modes at the stage of excitation. In the area of small values of the reorganization energy, the dependence of the charge transfer rate constant on the pump pulse carrier frequency is strongly nonmonotonic that is caused by vibrational resonances and variation of the initial position of the wave packet on the term of the locally excited state. Increasing the reorganization energy smoothes the dependence. The smoothing is caused by the broadening of the vibrational resonances and their overlapping. The high‐frequency vibrational mode excitation typically accelerates the charge transfer in both areas of high and low exergonicity and decelerates it in the vicinity of the Marcus barrierless region.     

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.