Symmetry breaking charge transfer and control of the transition dipole moment in excited octupolar molecules.

The structure of the energy levels of excited symmetric donor-acceptor octupolar molecules suggests a completely symmetric state and a degenerate doublet. For most molecules, the doublet is the first excited state, which is called the normal level order, but there are molecules with the reverse level order. Symmetry breaking charge transfer (SBCT) and its effect on the transient dipole moment in these structures are studied. It has been established that for reverse level order, SBCT is possible only if the reorganization energy exceeds a certain threshold, whereas for the normal level order, there is no such threshold. The lowest completely symmetric excited state is shown to become bright after SBCT. The dependence of the fluorescence transition dipole moment on the SBCT extent is calculated. It was established that the direction and magnitude of the transition dipole moment change similarly to the change in the dipole moment for the reverse level order, whereas for the normal level order, the changes are opposite. The effect of solvent thermal fluctuations on the transition dipole moment is simulated and discussed. A way for controlling the direction of the transition dipole moment by an external electric field is suggested.

Controlling the symmetry breaking charge transfer extent in excited quadrupolar molecules by tuning the locally excited state.

The effect of a locally excited state on charge transfer symmetry breaking (SBCT) in excited quadrupolar molecules in solutions has been studied. The interaction of a locally excited state and two zwitterionic states is found to either increase or decrease the degree of SBCT depending on the molecular parameters. A strategy on how to adjust the molecular parameters to control the extent of SBCT is presented. The influence of level degeneracy on SBCT is identified and discussed in detail. The level degeneracy is shown to lead to the existence of a hidden dipole moment in excited quadrupolar molecules. Its manifestations in SBCT are analyzed. The main conclusions are consistent with the available experimental data.

Electric dipole flip in a quadrupolar molecule with broken symmetry upon excited state absorption.

The nature of the second excited state in a quadrupolar molecule of the A-D-A structure, where A and D are an electron acceptor and an electron donor, respectively, has been studied. The orthogonality condition of the wave functions requires that the direction of the molecular dipole moment arising due to the charge transfer symmetry breaking be opposite in the first and second excited states. The dipole moment flip leads to large reorganization energy of the solvent upon excited state absorption. The manifestations of dipole flip are discussed. The dependence of the energy gap on the solvent polarity is found. The symmetry breaking effect on the transition dipole moment suppression is calculated. The available experimental data confirm the main conclusions.

The effect of energy level degeneracy on symmetry-breaking charge transfer: Excited octupolar dyes.

A three-level model of symmetry-breaking charge transfer (SBCT) in excited octupolar molecules is developed. The model describes the joint dynamics of the solvent and the dye in the excited state. For this, a distribution function in the space of two reaction coordinates is introduced. An evolution equation of this function is derived. A strict definition of the reaction coordinates is given, and its dynamic characteristics are determined. The free energy surface in the space of these coordinates is calculated. To quantify the symmetry-breaking degree, a two-dimensional dissymmetry vector is introduced. The model predicts the absence of SBCT in apolar solvents and an abrupt increase in its degree to half the maximum value in weakly polar solvents. The dye dipole moment is revealed to be directed along a molecular arm independently of the direction and the strength of the electric field of the solvent created by its orientational polarization. The conditions for the occurrence and nature of this effect are discussed. The effect of the degeneracy of excited states, which is inherent in octupolar dyes in the excited state, on SBCT is revealed. Degeneracy of energy levels is shown to lead to a significant increase in the symmetry-breaking degree. The effect of SBCT on the dependence of the Stokes on the solvent polarity is calculated and compared with the available experimental data.

Minimal model of excited-state symmetry breaking in symmetric dimers and covalently linked dyads.

A model of symmetry breaking (SB) charge separation in symmetric excited dyads and dimers is presented. The minimal model should include at least four basis electronic states due to a small energy gap between the locally excited and charge separated (zwitterionic) states of the chromophores. There are electronic couplings between all these states. The model includes the following interactions: (i) the Coulomb interaction between charges on the chromophores of the dyad, (ii) the interaction of the dipole moment of the asymmetric dyad with the solvent polarization, and (iii) the electronic-vibrational interaction. SB becomes possible only if the intensity of these interactions exceeds a threshold value. The threshold vanishes if there is a degeneration of the levels. Unusual resonant dependencies of the dissymmetry degree on the model parameters are revealed. Resonances arise due to the degeneration of energy levels. The ranges of the parameters in which energy level crossings occur are established. The oddity lies in the dependence of the resonance shape on the parameters of the model. A variation in the electronic couplings and the energy gap between the locally excited and ionic states, which leads to a broadening of the resonance, simultaneously leads to an increase in the resonant height. This opens up wide possibilities for controlling the charge separation degree. The predictions of the theory agree with the available experimental data. The charge separation SB is predicted to accompany by SB in the excitation distribution on the branches of dyads.

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.

Spectral Dynamics of Nitro Derivatives of Xanthione in Solutions.

Nitro derivatives of xanthione, 2,7-dinitro-9 H-xanthene-9-thione and 2,4,7-trinitro-9 H-xanthene-9-thione, have been first synthesized and their stationary and transient spectra have been measured. The stationary spectra show that the attachment of the nitro groups to the xanthione scaffold leads to strong quenching of S2 → S0 fluorescence and the decrease of the oscillator strength of the S2 ← S0 electronic transition. Analysis of the transient absorption spectra uncovers the ultrafast stimulated emission quenching from the second excited state, S2, in the both derivatives. A kinetic scheme has been suggested to rationalize the complex spectral dynamics of the transient absorption signal. The kinetic scheme is deduced from the analysis of the transient spectra and supported by the quantum-chemical calculations, which predict the existence of a dark state and S2 state splitting into two close levels. The ultrafast transitions between S2 state sublevels and the transition into the dark state play a crucial role in spectral dynamics. These new features discovered in the nitro derivatives of xanthione distinguish essentially their spectral dynamics from that observed in xanthione.

Exact solution of three-level model of excited state electron transfer symmetry breaking in quadrupolar molecules.

An analytical solution of a three-level model of symmetry breaking in excited AL-D-AR quadrupolar triads with an electron donor D and identical electron acceptors AL and AR is derived, in particular, an analytical expression for the dissymmetry parameter (difference in charges, in electron charge units, on the left and right arms of the molecule) is obtained. The model predicts the threshold dependence of the symmetry breaking degree on the parameters of the molecule and its interaction with the solvent. It is shown that for typical molecular parameters, symmetry breaking occurs as a charge transfer from one arm of the molecule to the other with nearly invariable donor charge. A considerable variation of the donor charge in the course of symmetry breaking is predicted for triads with small energy gap between the ground and first excited states. Analysis of the results shows that for a large parameter area, they are very similar to those obtained in a much simpler two-level model, which suggests that instead of a more realistic three-level model, we can use a two-level model to describe symmetry breaking in excited quadrupole molecules. The theory of symmetry breaking effect on the intramolecular vibrational spectra is developed. A comparison of the effect of solvent polarity on IR spectra changes due to an increase in the degree of symmetry breaking with the available experimental data shows that the model adequately describes this phenomenon.

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.

The effect of solvent relaxation time constants on free energy gap law for ultrafast charge recombination following photoinduced charge separation.

To elucidate the regularities inherent in the kinetics of ultrafast charge recombination following photoinduced charge separation in donor-acceptor dyads in solutions, the simulations of the kinetics have been performed within the stochastic multichannel point-transition model. Increasing the solvent relaxation time scales has been shown to strongly vary the dependence of the charge recombination rate constant on the free energy gap. In slow relaxing solvents the non-equilibrium charge recombination occurring in parallel with solvent relaxation is very effective so that the charge recombination terminates at the non-equilibrium stage. This results in a crucial difference between the free energy gap laws for the ultrafast charge recombination and the thermal charge transfer. For the thermal reactions the well-known Marcus bell-shaped dependence of the rate constant on the free energy gap is realized while for the ultrafast charge recombination only a descending branch is predicted in the whole area of the free energy gap exceeding 0.2 eV. From the available experimental data on the population kinetics of the second and first excited states for a series of Zn-porphyrin-imide dyads in toluene and tetrahydrofuran solutions, an effective rate constant of the charge recombination into the first excited state has been calculated. The obtained rate constant being very high is nearly invariable in the area of the charge recombination free energy gap from 0.2 to 0.6 eV that supports the theoretical prediction.

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.

Simulations of the Ultrafast Transient Absorption Dynamics of a Donor-Acceptor Biaryl in Solution.

A model for simulating the transient electronic absorption spectra of donor-acceptor dyads undergoing ultrafast intramolecular charge transfer in solution has been developed. It is based on the stochastic multichannel point-transition approach and includes the reorganization of high-frequency intramolecular modes (treated quantum mechanically) and of low frequency intramolecular and solvent modes (described classically). The relaxation of the slow modes is assumed to be exponential with time constants taken from experiments. The excited-state dynamics is obtained by simulating the population distribution of each quantum state after optical excitation and upon electronic and vibrational transitions. This model was used to simulate the transient electronic absorption spectra measured previously with a pyrylium phenolate in acetonitrile. A very good agreement between the simulated and measured spectra was obtained assuming a three-level model including the ground state, the optically excited state, and a dark state with large charge-transfer character and a substantially different geometry relative to that of the optically excited state. The merit of this approach to disentangle the contributions of both population changes and relaxation processes to the ultrafast spectral dynamics will be discussed.

A simple model of solvent-induced symmetry-breaking charge transfer in excited quadrupolar molecules.

A simple model has been developed to describe the symmetry-breaking of the electronic distribution of AL-D-AR type molecules in the excited state, where D is an electron donor and AL and AR are identical acceptors. The origin of this process is usually associated with the interaction between the molecule and the solvent polarization that stabilizes an asymmetric and dipolar state, with a larger charge transfer on one side than on the other. An additional symmetry-breaking mechanism involving the direct Coulomb interaction of the charges on the acceptors is proposed. At the same time, the electronic coupling between the two degenerate states, which correspond to the transferred charge being localised either on AL or AR, favours a quadrupolar excited state with equal amount of charge-transfer on both sides. Because of these counteracting effects, symmetry breaking is only feasible when the electronic coupling remains below a threshold value, which depends on the solvation energy and the Coulomb repulsion energy between the charges located on AL and AR. This model allows reproducing the solvent polarity dependence of the symmetry-breaking reported recently using time-resolved infrared spectroscopy.

Dynamics of ground state absorption spectra in donor-acceptor pairs with ultrafast charge recombination.

A theoretical approach to simulation of the transient spectra in molecular systems with ultrafast photoinduced nonradiative electronic transitions is developed. The evolution of the excited and ground state populations as well as the nonradiative transitions between them are calculated in the framework of the stochastic multichannel point-transition model involving the reorganization of the medium and the intramolecular high frequency vibrational modes. Simulations of transient spectra of donor-acceptor pairs excited in the charge-transfer band that are accompanied by ultrafast charge recombination into the ground state demonstrate a possibility of positive band appearance in the transient absorption spectrum caused by those systems in the ground state, which returned there from the excited state. The region of the parameters of the donor-acceptor systems where a positive ground state absorption signal can be observed is discussed. A qualitative comparison of the simulated transient spectra with the experimental data on betaine-30 is presented.

Diffusion affected magnetic field effect in exciplex fluorescence.

The fluorescence of the exciplex, (1)[D(+δ)A(-δ)], formed at contact of photoexcited acceptor (1)A(*) with an electron donor (1)D, is known to be very sensitive to an external magnetic field, reducing the spin conversion efficiency in the resulting geminate radical ion pair, (1, 3)[D(+)…A(-)]. The relative increase of the exciplex fluorescence in the highest magnetic field compared to the lowest one, known as the magnetic field effect, crucially depends on the viscosity of the solvent. This phenomenon first studied experimentally is at first reproduced here theoretically. The magnetic field effect is shown to vanish in both limits of high and low solvent diffusivity reaching a maximum in between. It is also very sensitive to the solvent dielectric constant and to the exciplex and radical-ion pair conversion rates.

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.

Dynamics of charge separation from second excited state and following charge recombination in zinc-porphyrin-acceptor dyads.

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 and the ground states has been investigated in the framework of a model incorporating four electronic states (the first and the second singlet excited, the charge separated, and the ground states) as well as their vibrational sublevels. Kinetics of the transitions between these states are described in terms of the stochastic point-transition approach involving reorganization of a number of high frequency vibrational modes. The influence of the model parameters (the number of high frequency vibrational modes, the magnitude of the reorganization energies of the medium and the high frequency intramolecular vibrations, the solvent polarity) on the kinetics of population of the second and first singlet excited states as well as the charge separated state has been investigated. Simulation of the kinetics of the charge separated state population allows quantitative reproducing of the distinctive features of the two-humped kinetic curve observed in the experiment.

Hyperfine interaction mechanism of magnetic field effects in sequential fluorophore and exciplex fluorescence.

The magnetic field effect on the fluorescence of the photoexcited electron acceptor, (1)A∗, and the exciplex, (1)[D(+δ)A(-δ)] formed at contact of (1)A∗ with an electron donor (1)D, is theoretically explored in the framework of Integral Encounter Theory. It is assumed that the excited fluorophore is equilibrated with the exciplex that reversibly dissociates into the radical-ion pair. The magnetic field sensitive stage is the spin conversion in the resulting geminate radical-ion pair, (1, 3)[D(+)...A(-)] that proceeds due to hyperfine interaction. We confirm our earlier conclusion (obtained with a rate description of spin conversion) that in the model with a single nucleus spin 1/2 the magnitude of the Magnetic Field Effect (MFE) also vanishes in the opposite limits of low and high dielectric permittivity of the solvent. Moreover, it is shown that MFE being positive at small hyperfine interaction A, first increases with A but approaching the maximum starts to decrease and even changes the sign.

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.; Hammarström, 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.

Reorganization of intramolecular high frequency vibrational modes and dynamic solvent effect in electron transfer reactions.

The possibility of the multichannel stochastic model to adequately describe all principal regularities observed in thermal electron transfer kinetics has been demonstrated. The most important are as follows: (i) the model predicts the solvent controlled regime in the Marcus normal region and its almost full suppression in the Marcus inverted region as well as a continuous transition between them in the vicinity of the activationless region; (ii) the suppression of dynamic solvent effect (DSE) is principally caused by the reorganization of high frequency vibrational modes; (iii) an additional factor of the DSE suppression stems from fast solvent relaxation component; (iv) in the inverted region, the multichannel stochastic model predicts the apparent activation energy to be much less than that calculated with Marcus equation. The exploration of the multichannel stochastic model has allowed one to conclude that the reorganization of high frequency vibrational modes can (i) raise the maximum rate constant above the solvent controlled limit by 2 and more orders of magnitude, (ii) shift the rate constant maximum to larger values of the free energy gap, and (iii) approach the electron transfer kinetics to the nonadiabatic regime.