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.

Modeling the Effect of H-Bonding of Excited Quadrupolar Molecules with a Solvent on Charge Transfer Symmetry Breaking.

A model of the H-bonding effect on charge transfer symmetry breaking in excited quadrupolar dyes is proposed. A dye is assumed to have two symmetrically arranged H-bond acceptors. The effect of H-bonding is described in terms of two quantities: (i) the free energy of H-bond formation by an excited symmetric dye with a protic solvent and (ii) a parameter that determines the susceptibility of the H-bond strength to the charge of the H-bond acceptor. The model assumes that an increase in dye dissymmetry results in a charge shift from one acceptor to the other, making one acceptor more negative and the other less negative. As a result, the strength of the H-bond on one branch increases, while on the other branch, it decreases. An analytical solution of the mathematical model is obtained. Regardless of the strength of the H-bond, the effect of the H-bonding on the symmetry breaking degree is shown to be small, as long as the free energy of formation of the weaker H-bond is negative. A strong effect is expected only if this free energy becomes positive, that is, when the H-bond is formed on only one arm. An unexpected result of weakening of the dissymmetry degree caused by the strengthening of the H-bond is predicted and discussed. An approach for quantitative determination of the susceptibility of the H-bond strength to the charge of the H-bond acceptor is proposed.

Effect of Symmetry Breaking in Excited Quadrupole Molecules on Transition Dipole Moment.

Manifestations of charge transfer symmetry breaking in excited quadrupolar molecules in optical spectra are theoretically studied. The molecules are supposed to have π-conjugated structures of A-π-D-π-A or D-π-A-π-D character, where electron acceptors (A) or electron donors (D) are identical. A theory describing the effect of symmetry breaking and solvent fluctuations on the dipole moments of optical transitions associated with absorption by a quadrupolar dye in the ground and excited states, as well as fluorescence, is developed. Simple equations describing the influence of the symmetry breaking extent on the transition dipole moments are found. The orientational solvent fluctuations are predicted to decrease the transition dipole moment of the ground state absorption. The decrease does not exceed 10%. A considerably larger effect of symmetry breaking and the solvent fluctuations on the emission dipole moment is found. Equations describing dependencies of the transition dipole moment associated with excited state absorption on the solvent polarity and the parameters of the dye are derived. The scale of the changes in the transition dipole moments due to symmetry breaking in the excited state are determined. The influence of the polar solvent fluctuations is also taken into account. The theoretical findings are shown to be consistent with the available experimental data.

Symmetry Breaking in an Excited Quadrupolar Acridine-Dione Derivative Driven by Hydrogen Bonding.

An acridine-dione derivative (3,3,11,11-tetramethyl-8,16-diphenyl-3,4,8,10,11,12,13,16-octahydroacridino[4,3-c]acridine-1.9(2H,5H)dion) with quadrupolar motif has been synthesized and its stationary and transient spectra have been measured. Stationary absorption and fluorescence spectra as well as nonstationary spectra show no signs of symmetry breaking (SB) in aprotic solvents, even of high polarity. The specific features of SB are revealed in alcohol solvents through a considerable red shift of stationary fluorescence spectra and the appearance of a new excited state absorption band in transient absorption spectra. SB is due to the formation of asymmetric strong hydrogen bonds, mainly on one side of the molecule. An unexpected regularity of symmetry breaking is found in mixtures of aprotic dimethylformamide and protic methanol, where methanol acts as a fluorescence quencher. It is revealed that there is no quenching as long as the methanol concentration is less than the critical value of 9 M. This leads to the conclusion that SB in such mixtures is possible only if the concentration of the protic solvent exceeds a certain threshold value.

Nonstationary Theory of Excited State Charge Transfer Symmetry Breaking Driven by Polar Solvent.

A consistent theory of electron transfer symmetry breaking (SB) dynamics in excited quadrupolar molecules in polar solvents is developed. The interaction of the electronic subsystem of the molecule with intramolecular degrees of freedom and solvent polarization is taken into account and is divided into interaction with inertial and inertialess degrees of freedom. A strong influence of the inertialess polarization of the solvent on the extent of symmetry breaking is revealed. The theory is nonlinear due to the equilibration of inertialess degrees of freedom to the solute electronic state. The interaction of a molecule with the inertial solvent polarization is described in terms of a single variable-the reaction coordinate, for which a rigorous definition is given. The free energy of the system is derived, and the motion of the system along the reaction coordinate is modeled by the Smoluchowski equation. The theory is adapted to describe the dynamics of SB in real solvents characterized by several relaxation time scales. Conditions for the applicability of a much simpler stationary SB model are formulated. The role of thermal fluctuations in the solvent polarization is clarified. Instead of the magnitude of the dissymmetry parameter, a distribution function of molecules over this parameter is introduced. An analysis of the Franck-Condon state created by a short pump pulse shows that it has distinct features of a state with broken symmetry for a wide range of parameters. Thermal fluctuations of the solvent polarization are shown to crucially affect SB.

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.

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.

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.

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.

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.

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.

Verification of Nonequilibrium Mechanism of Ultrafast Charge Recombination in Excited Donor-Acceptor Complexes.

Control of charge transfer requires knowledge of its detailed mechanism. Due to the large number of known mechanisms, the identification of the mechanism in specific systems is a challenge so far. In this article we propose the idea of how to distinguish between thermal and nonequilibrium modes of charge recombination in excited donor-acceptor complexes. Simulations of the effect of solvent relaxation time scale on ultrafast charge recombination kinetics in photoexcited donor-acceptor complexes within the framework of the multichannel stochastic model have shown that a series of regularities inherent to the thermal and nonequilibrium charge transfer can strongly differ. Among them there are opposite regularities, for example, the dependence of the dynamic solvent effect on the free energy gap. In particular, theory predicts that in ultrafast charge recombination of excited donor-acceptor complexes the dynamic solvent effect is weak in the area of weak exergonicity and becomes stronger in the area of stronger exergonicity whereas for the thermal reactions an opposite trend is expected. Comparison of such trends with experimental data implemented in this article allowed establishing the regime in which the reaction proceeds. It is shown that observation of dynamic solvent effect in the region of strong exergonicity for ultrafast charge recombination is decisive evidence in favor of nonequilibrium mechanism.

Free-Energy-Gap Law for Ultrafast Charge Recombination of Ion Pairs Formed by Intramolecular Photoinduced Electron Transfer.

In this article, regularities of ultrafast charge recombination (CR) kinetics in photoinduced intramolecular electron transfer in polar solvents are studied. The kinetics of charge separation and ensuing ultrafast CR are simulated within the framework of the multichannel stochastic model. This model accounts for the reorganization of both the solvent and a number of intramolecular high-frequency vibrational modes. The solvent relaxation is described in terms of two relaxation modes. For ultrafast CR, the free-energy-gap law strongly depends on the parameters: the electronic coupling, reorganization energy of intramolecular high-frequency vibrational modes, and the vibrational and solvent relaxation times. The semilog dependence of the CR rate constant on the free-energy gap varies from a parabolic shape to a nearly linear one with increasing the electronic coupling and decreasing the vibrational relaxation time. The dynamic solvent effect in CR is predicted to be large in the area of strong exergonicity and small in the area of weak exergonicity. This regularity is opposite to that observed for the thermal reactions.

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.