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.

Quantum yield and energy efficiency of photoinduced intramolecular charge separation.

Kinetics of photoinduced intramolecular charge separation (CS) and the ensuing ultrafast charge recombination (CR) in electron-donor-acceptor dyads are studied numerically, taking into account the excitation of charge-transfer active intramolecular vibrations and multiple relaxation time scales of the surrounding polar solvent. Both energetic and dynamic properties of intramolecular and solvent reorganization are considered, and their influence on the CS/CR kinetics and quantum yield of ultrafast CS is explored. Particular attention is paid to the energy efficiency of CS, as one of the most important parameters indicating the promise of using a molecular compound as a basis for emerging optoelectronic devices. The CS quantum yield and the energy efficiency of CS are shown to depend differently on the key model parameters. Necessary conditions for the highly efficient CS are evaluated using analytic formulae for the electron transfer rates and derived from numerical simulation data. The reasons why low-exergonic CS taking place in the Marcus normal region can be much slower than CR in the deep inverted region are discussed.

Magnetic field effect on ion pair dynamics upon bimolecular photoinduced electron transfer in solution.

The dynamics of the ion pairs produced upon fluorescence quenching of the electron donor 9,10-dimethylanthracene (DMeA) by phthalonitrile have been investigated in acetonitrile and tetrahydrofuran using transient absorption spectroscopy. Charge recombination to both the neutral ground state and the triplet excited state of DMeA is observed in both solvents. The relative efficiency of the triplet recombination pathway decreases substantially in the presence of an external magnetic field. These results were analyzed theoretically within the differential encounter theory, with the spin conversion of the geminate ion pairs described as a coherent process driven by the hyperfine interaction. The early temporal evolution of ion pair and triplet state populations with and without magnetic field could be well reproduced in acetonitrile, but not in tetrahydrofuran where fluorescence quenching involves the formation of an exciplex. A description of the spin conversion in terms of rates, i.e., incoherent spin transitions, leads to an overestimation of the magnetic field effect.

Solvent-assisted multistage nonequilibrium electron transfer in rigid supramolecular systems: Diabatic free energy surfaces and algorithms for numerical simulations.

An approach to the construction of diabatic free energy surfaces (FESs) for ultrafast electron transfer (ET) in a supramolecule with an arbitrary number of electron localization centers (redox sites) is developed, supposing that the reorganization energies for the charge transfers and shifts between all these centers are known. Dimensionality of the coordinate space required for the description of multistage ET in this supramolecular system is shown to be equal to N - 1, where N is the number of the molecular centers involved in the reaction. The proposed algorithm of FES construction employs metric properties of the coordinate space, namely, relation between the solvent reorganization energy and the distance between the two FES minima. In this space, the ET reaction coordinate znn' associated with electron transfer between the nth and n'th centers is calculated through the projection to the direction, connecting the FES minima. The energy-gap reaction coordinates znn' corresponding to different ET processes are not in general orthogonal so that ET between two molecular centers can create nonequilibrium distribution, not only along its own reaction coordinate but along other reaction coordinates too. This results in the influence of the preceding ET steps on the kinetics of the ensuing ET. It is important for the ensuing reaction to be ultrafast to proceed in parallel with relaxation along the ET reaction coordinates. Efficient algorithms for numerical simulation of multistage ET within the stochastic point-transition model are developed. The algorithms are based on the Brownian simulation technique with the recrossing-event detection procedure. The main advantages of the numerical method are (i) its computational complexity is linear with respect to the number of electronic states involved and (ii) calculations can be naturally parallelized up to the level of individual trajectories. The efficiency of the proposed approach is demonstrated for a model supramolecular system involving four redox centers.

Efficiency of intramolecular charge separation from the second excited state: suppression of the hot charge recombination by electron transfer to the secondary acceptor.

Ultrafast intramolecular charge transfer induced by the Soret-band excitation of the donor-acceptor1-acceptor2 molecular triads has been explored within the stochastic point-transition model. It is shown that nonthermal (hot) charge transfer from the primary to the secondary acceptor, assisted by relaxation of solvent polarization, can effectively screen ultrafast back electron transfer into the first excited state of the donor. Ways to increase the quantum yield of the charge-separated states are discussed. The dependencies of the quantum yield of the charge-separated states on the main electron transfer parameters: the free energy gaps, the reorganization energy of the solvent and intramolecular vibrational modes, the electronic couplings, and the solvent relaxation timescale are revealed. The important role of the geometry of the donor-acceptor1-acceptor2 triad in charge separation effectiveness is emphasized. For the zinc-porphyrin-imide1-imide2 triad, the charge-transfer parameters maximizing the quantum yield of the charge separated states are estimated.

Kinetics of nonequilibrium electron transfer in photoexcited ruthenium(II)-cobalt(III) complexes.

Kinetics of photoinduced electron transfer reactions in [Ru(II)(L-L)Co(III)](5+) complexes have been investigated in the framework of the stochastic point-transition model. The model involves the medium and intramolecular nuclear reorganization as well as fast relaxation of intramolecular high frequency vibrations and description of the medium relaxation in terms of two time scales. The model has allowed reproducing the experimental data (Torieda, H.; Nozaki, K.; Yoshimura, A.; Ohno, T. J. Phys. Chem. A2004, 108, 4819) of forward and backward electron transfer kinetics, including the low yield of electron transfer products and its variation with solvent. These results have lent support to the important role of hot backward electron transfer in the formation of low yield of electron transfer products. The experimentally observed significant decrease of the product yield in more viscous solvents has been shown to be a direct consequence of the hot transition efficiency increase. A weak opposite dependence, also revealed in experiments, has been elucidated in terms of two time scales of the solvent relaxation. Solvent relaxation is well-known to involve at least two stages: the inertial one (fast) and the diffusive one (slower) with the time scales weakly dependent on and proportional to solvent viscosity, respectively. When hot transitions are terminated at the stage of the inertial relaxation, the yield of the electron transfer products is nearly independent of the diffusive time scale; otherwise a strong increase of the yield in more viscous solvents should be observed.

The Efficiency of Photoinduced Intramolecular Charge Separation from the Second Excited State: What Factors Can Control It?

The efficiency of photoinduced charge separation (CS) in electron donor-acceptor compounds is commonly limited due to fast deactivation processes, such as the excited-state internal conversion and ultrafast hot reverse electron transfer to the acceptor, charge recombination (CR). A traditional way to avoid undesired energy losses due to CR is to put the reverse electron transfer into the Marcus inverted region, thus effectively suppressing it. This method, however, is not generally applicable when considering CS from the second locally excited state because the driving force of CR to the first excited state is small, and thus charge recombination is ultrafast and efficient. In this paper, we study the kinetic features of CS/CR from the second locally excited state of the donor using a semiclassical stochastic model of electron transfer. Particular attention is paid to the CS efficiency as well as the influence of the polar environment and intramolecular high-frequency vibrational modes on the kinetics of the charge-separated state. The influence of a number of model parameters on the CS yield and the energy efficiency has been analyzed using the results of numerical simulations. Several simple practical recipes for creating molecular compounds with high CS yields have been suggested. Simulations have also revealed a strong and non-monotonous (double-humped) dependence of both the yield and energy efficiency of CS on the driving force.

Double-channel photoionization followed by geminate charge recombination/separation.

The photoionization of perylene by tetracyanoethylene (TCNE) in liquid solutions is reconsidered within the corrected energy scheme for a double channel electron transfer: to the ground and excited states of the produced ion pair. The complex space dependence of a total (double channel) rate of multiphonon transfer is specified and compared to the recently proposed monoexponential model. The fitting of the forward electron transfer (ionization) is essentially improved, and the real electron coupling and tunneling parameters are firmly established. The same has been done for the geminate recombination/separation kinetics, accounting theoretically for the hot recombination experienced by 2/3 of the initially produced ion pairs. Only 1/3 of them is left for subsequent thermal recombination and even less are left for their separation into free ions. The yields of the latter, strongly dependent on the initial concentration of TCNE, are brought into reasonable coincidence with the theoretical predictions by a renormalization of the empirically calibrated ion densities especially at large concentrations. Altogether, this is a precedent spin-less treatment of photoionization well-fitted to the experimental data at all times (from the excitation until charge separation), with a single set of varying parameters.

Solvent and spectral effects in the ultrafast charge recombination dynamics of excited donor-acceptor complexes.

The charge recombination dynamics of excited donor-acceptor complexes consisting of hexamethylbenzene (HMB), pentamethylbenzene (PMB), and isodurene (IDU) as electron donors and tetracyanoethylene (TCNE) as electron acceptor in various polar solvents has been investigated within the framework of the stochastic approach. The model accounts for the reorganization of intramolecular high-frequency vibrational modes as well as for the solvent reorganization. All electron-transfer energetic parameters have been determined from the resonance Raman data and from the analysis of the stationary charge transfer absorption band, while the electronic coupling has been obtained from the fit to the charge recombination dynamics in one solvent. It appears that nearly 100% of the initially excited donor-acceptor complexes recombine in a nonthermal (hot) stage when the nonequilibrium wave packet passes through a number of term crossings corresponding to transitions toward vibrational excited states of the electronic ground state. Once all parameters of the model have been obtained, the influence of the dynamic solvent properties (solvent effect) and of the carrier frequency of the excitation pulse (spectral effect) on the charge recombination dynamics have been explored. The main conclusions are (i) the model provides a globally satisfactory description for the IDU/TCNE complex although it noticeably overestimates the spectral effect, (ii) the solvent effect is quantitatively well described for the PMB/TCNE and HMB/TCNE complexes but the model fails to reproduce their spectral effects, and (iii) the positive spectral effect observed with the HMB/TCNE complex cannot be described within the framework of two-level models and the charge redistribution in the excited complexes should most probably be taken into account.

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.

Hot recombination of photogenerated ion pairs.

The recombination dynamics of ion pairs generated upon electron transfer quenching of perylene in the first singlet excited state by tetracyanoethylene in acetonitrile is quantitatively described by the extended unified theory of photoionization/recombination. The extension incorporates the hot recombination of the ion pair passing through the level-crossing point during its diffusive motion along the reaction coordinate down to the equilibrium state. The ultrafast hot recombination vastly reduces the yield of equilibrated ion pairs subjected to subsequent thermal charge recombination and separation into free ions. The relatively successful fit of the theory to the experimentally measured kinetics of ion accumulation/recombination and free ion yield represents a firm justification of hot recombination of about 90% of primary generated ion pairs.

Effect of the excitation pulse carrier frequency on the ultrafast charge recombination dynamics of donor-acceptor complexes: Stochastic simulations and experiments.

The influence of the excitation pulse carrier frequency on the ultrafast charge recombination dynamics of excited donor-acceptor complexes has been explored both theoretically and experimentally. The theoretical description involves the explicit treatment of both the optical formation of the nuclear wave packet on the excited free energy surface and its ensuing dynamics. The wave packet motion and the electronic transition are described within the framework of the stochastic point-transition approach. It is shown that the variation of the pulse carrier frequency within the absorption band can significantly change the effective charge recombination dynamics. The mechanism of this phenomenon is analyzed and a semiquantitative interpretation is suggested. The role of the vibrational coherence in the recombination dynamics is discussed. An experimental investigation of the ultrafast charge recombination dynamics of two donor-acceptor complexes in valeronitrile also is presented. The decays of the excited state population were found to be highly nonexponential, the degree of non-exponentiality depending on the excitation frequency. For one complex, the charge recombination dynamics was found to slow down upon increasing the excitation frequency, while the opposite behavior was observed with the other complex. These experimental observations follow qualitatively the predictions of the simulations.