The symmetry-breaking charge transfer (SBCT) in quadrupolar molecules with normal and inverse level orders (LOs) (the lowest excited state is odd or even) is theoretically investigated. The effect of the locally excited state (LES) on SBCT and the transition dipole moment (TDM) is addressed in detail. The degree of symmetry breaking and the TDM between the lowest excited and ground states are examined in relation to the LO and solvent polarity. The parities of the lowest excited state and the LES are shown to have a profound effect on the degree of SBCT and the TDM magnitude. This opens up wide possibilities for managing the extent of SBCT and TDM. The key finding of this study is that the extent of SBCT is a critical factor governing the photophysics of molecules with inverse LO. A large SBCT magnitude is shown to lead to a pronounced enhancement in the oscillator strength of the lowest even excited state, resulting in a radiative efficiency that rivals that of systems with a normal LO. Furthermore, this work provides simple, practical formulas for quantifying the extent of symmetry breaking and the magnitudes of the key transition dipole moments. These analytical tools offer significant utility for experimentalists and facilitate the design of new studies and the interpretation of spectroscopic data. Together, these insights provide a foundation for advancing the rational design of optoelectronic materials, where precise control over symmetry-breaking processes is paramount.

In excited centrosymmetric donor-acceptor triads of type A-D-A or D-A-D, symmetry breaking charge transfer (SBCT) in polar media has been explored for a few decades. SBCT is accompanied by significant reorganization of the electronic structure of the molecule, which leads to a change in the fluorescence transition dipole moment (TDM). Previously, experiments revealed a 20%-30% reduction in TDM, which occurs on the timescale of SBCT. Simple SBCT models explain this reduction. Here, the effect of the interaction of a locally excited state with zwitterionic states on TDM is investigated. This interaction is shown to have a drastic impact on the TDM and its dependence on the solvent polarity. The magnitude of TDM can decrease monotonically, increase monotonically, and also pass through a maximum with an increase in the SBCT degree due to the locally excited state effect. The scale of changes in TDM in the course of SBCT increases greatly. The conditions for the implementation of a particular scenario have been determined. This work clearly demonstrates the observable influence of upper excited states on the photochemistry and photophysics of molecules. Methods for controlling the fluorescent characteristics of quadrupolar molecules are proposed.

The previously developed approach to the analysis of experimental spectra of non-stationary fluorescence has been improved by taking into account the effect of the duration of the gating pulse and a more accurate description of the initial stage of solvent relaxation. The exponential function used to describe the inertial component of relaxation has been replaced by the Gaussian function. This approach explicitly takes into account the reorganization and relaxation of the solvent and intramolecular vibrations. It includes an explicit description of the wave packet formation in the excited state of the fluorophore. The improvement of the approach made it possible to refine the relaxation characteristics of a number of solvents: ethylene glycol, dimethyl sulfoxide, butyronitrile, ethyl acetate, diethyl ether, dipropyl ether. Keywords: nonequilibrium of the nuclear subsystem, Stokes shift, relaxation of intramolecular vibrations, inertial component of solvent relaxation

The previously developed approach to the analysis of experimental spectra of nonstationary fluorescence has been improved by taking into account the effect of the duration of the gating pulse and a more accurate description of the initial stage of solvent relaxation. The exponential function used to describe the inertial component of relaxation has been replaced by the Gaussian function. This approach explicitly takes into account the reorganization and relaxation of the solvent and intramolecular vibrations. It includes an explicit description of the wave packet formation in the excited state of the fluorophore. The improvement of the approach made it possible to refine the relaxation characteristics of a number of solvents: ethylene glycol, dimethyl sulfoxide, butyronitrile, ethyl acetate, diethyl ether, dipropyl ether.

To elucidate the regularities inherent in the kinetics of ultrafast charge recombination following photo-induced 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.

In the framework of the stochastic approach, the effect of transitions between the vibrational sublevels of products on the ultrafast dynamics of “hot” (non-thermal) electron transfer in donor — acceptor complexes dissolved in a polar medium has been investigated. An analytical expression has been obtained for the probability of electron transfer, which takes into account the transition between the vibrational states of products and the mutual influence of sinks. Quantitative estimates of the scale of the mutual influence of sinks on the probability of electron transfer are made.

The dynamic solvent effect (DSE) in reactions of ultrafast proton-coupled electron transfer (PCET) under nonequilibrium conditions is studied. It is found in particular that the effect depends on angle φ between the directions of the reaction coordinates that correspond to the step of photoexcitation of the system, and to the step of product formation. Several trends characteristic of such reactions are established: (i) the highest DSE value should be observed in the region of the increased exergonicity of the reaction, and the effect is weak in the region of low exergonicity; (ii) upon an increase in the transition matrix element, the maximum in the curve of the dependence of the PCET rate constant on the reaction’s exergonicity shifts toward the region of lower values; (iii) the dependence of the effective reaction time on angle φ has a pronounced minimum, the position of which depends on the energy parameters of the reactants.

New data for the Early and Late Carboniferous sections of the Russian platform (Moscow syneclise and Donbass) are presented. Magneto-mineralogical studies are carried out to identify the magnetic minerals—carriers of natural remanent magnetization. Extensive Late Paleozoic remagnetization of Carboniferous rocks is revealed. The obtained paleomagnetic data allowed us to determine the average paleomagnetic poles for the Gzhelian, Serpukhovian, and Visean stages of Carboniferous deposits of the Moscow syneclise.

A model of photoinduced intramolecular proton-coupled electron transfer is derived. The model includes three states as follows: the ground, excited, and product states. The charge transfer is associated with both stages, photoexcitation and product formation. A larger part of the model parameters can be extracted from the stationary absorption and fluorescence spectra of a particular fluorophore. Two different reaction coordinates are associated with the two stages, which are not independent. The angle between the reaction coordinates strongly influences on the kinetics of ultrafast product formation. The stochastic multichannel approach is exploited for simulations of the kinetics. The simulations well reproduce the kinetics of ultrafast intramolecular proton- coupled electron transfer in 24(2-(2-hydroxyphenyObenzo[d]oxazol-6-yOmethylene)malononitrile in a few solvents. The transfer is shown to occur totally or partly, depending on the solvent, in the nonequilibrium regime. Analysis of the kinetics of the excited-state decay has uncovered a significant decrease in the magnitude of the reorganization energies of slow nuclear modes with increasing the solvent polarity. Such an unusual behavior of the total reorganization energy can be rationalized under the assumptions: (i) a slow intramolecular reorganization of a significant magnitude associates with the transition between excited and product states and (ii) intramolecular slow reorganization is accompanied by a change in the dipole moment of the fluorophore.

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 photo excited 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 effect on the free energy gap. In particular, theory predicts that in ultrafast charge recombination of excited complexes the dynamic solvent effect is weak in the area of weak exergonicity and becomes stronger in the 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.

The collections of Carboniferous rocks from sections of the Russian Platform (Gzhelian, Moscovian, Bashkirian, and Visean stages) are studied. The new mean paleomagnetic poles are obtained from the Gzhelian, Moscovian, and Visean layers of the Carboniferous of the Russian Platform. In the redbed Gzhelian and Moscovian rocks, the natural remanent magnetization (NRM) components with the inclination shallowing are revealed, which is due to the presence of the large hematite particles or particle aggregates associated with the interaction between the magnetic and clay particles. Based on the obtained determinations and the results contained in the World paleomagnetic database, the trajectory of the apparent polar wander path (APWP) for the East European Platform is constructed in the interval from the Devonian to Early Permian. The Carboniferous kinematics of the East European Platform is estimated.

Fast decay of both the reactant and product states is shown to strongly increase the intrinsic electron transfer rate in donor-acceptor dyads. The decay is associated with redistribution/relaxation of excited vibrational states that typically participate in the reaction. Although the role of the reorganization of high-frequency vibrational modes in electron-transfer dynamics is well understood and it is commonly accepted to strongly affect the ultrafast electron transfer dynamics, the influence of the relaxation of excited vibrational states on electron transfer is not accounted for in experimental data analysis. In photoinduced electron transfer, excited states of high-frequency vibrational modes are often produced by laser pump pulse so that the ultrafast charge separation, at least partly, occurs from excited vibrational states. The charge recombination accompanying the charge separation also essentially occurs from excited vibrational states of intermediates to form a final excited vibrational state. Since the decay of the reactant state and electron transfer are two elementary chemical reactions occurring in parallel, the influence of vibrational relaxation on the intrinsic electron-transfer rate constant is a clear manifestation of the violation of the fundamental principle of chemical kinetics postulating the independence of elementary chemical reactions. The mechanism of the violation is discussed in detail. The transition probability that better characterizes the efficiency of ultrafast nonequilibrium charge recombination than the rate constant is calculated. The dependencies of the electron-transfer rate constant and the transition probability on the product decay time are predicted to be identical while on the reactant decay time to be opposite.

Manifestation of the dynamic solvent effect (DSE) on the charge recombination (CR) kinetics of photoexcited donor-acceptor complexes in polar solvents has been investigated within the framework of the multichannel stochastic model. The model takes into account the reorganization of both the solvent and a number of intramolecular high-frequency vibration modes as well as their relaxation. The non-Markovian solvent dynamics is described in terms of two relaxation modes. The similarities and differences inherent to ultrafast charge transfer reactions occurring in the nonequilibrium and thermal regimes have been identified. The most important differences are as follows: (1) the DSE is strong in the area of weak exergonicity and is weak in the area of strong exergonicity for thermal reactions, whereas for the nonequilibrium reactions, the regions of strong and weak DSEs are reversed; (2) an increase in the electronic coupling value results in a decrease in the magnitude of DSE for nonequilibrium electron transfer and in its increase for the thermal reactions; and (3) the two-staged regime most clearly manifests if the reorganization energy of the relaxation modes noticeably exceeds the CR free-energy gap. With an increase in electronic coupling, the kinetics approaches the exponential regime because in the limit of strong electronic coupling, the reaction includes only single, nonequilibrium, stage.

Modern laser-based spectroscopy has provided methods for detection ultrafast photochemical transformations occurring on the timescale of intramolecular and solvent reorganization. Such processes usually proceed in non-equilibrium regime, in parallel with nuclear relaxation, and often manifest strong deviations from the Kasha–Vavilov rule. In particular, they offer a possibility to control the yield of photoinduced electron transfer (ET) by using different excitation wavelengths. In the last decade the non-equilibrium charge transfer (CT) processes have attracted considerable interest from the scientific community due to their determining role in photosynthesis, dye-sensitized solar cells and various molecular electronic devices. Non-equilibrium of nuclear (intramolecular and solvent) degrees of freedom can be created by a pump pulse or by photoreaction itself at some of its stages. In this review both situations are considered and illustrated by examples in which non-equilibrium effects are pronounced. It is shown that ultrafast charge recombination in photoexcited donor–acceptor complexes and photochemical processes in donor–acceptor1–acceptor2 molecular compounds proceed predominantly in non-equilibrium (hot) regime. It is important that kinetics and product yields of these reactions demonstrate regularities that considerably differ from that observed in thermal reactions. Among them, the lack of the Marcus normal region in the free energy gap law for charge recombination of the excited donor–acceptor complexes, extremely low quantum yields of the thermalized charge separated states in ultrafast CT from the second excited state of the donor are most known. Although there have been many efforts to clarify microscopic mechanisms of non-equilibrium photoreactions by using ultrafast time-resolved spectroscopy techniques, control of the rate and efficiency of photoinduced charge transfer reactions is still an open challenge. One of the most important applications here is a suppression of ultrafast charge recombination in CT systems, formed either by direct optical excitation or by the preceding ET step. In these systems charge recombination is often regarded as undesirable process, leading to the loss of energy and selectivity of photoreaction. In this review some strategies of ultrafast charge recombination suppression are discussed. The non-equilibrium effects are interpreted from a unified point of view in context of the multichannel point-transition stochastic model. This approach demonstrates similarities and differences in ET mechanisms in various donor–acceptor molecular systems and allows formulating general regularities inherent to these phenomena. We believe that new advances in this research area will not only help to discover new fundamental information about these regularities, but will also have impact on many emerging technologies where ultrafast CT plays the central role.

The influence of the torsional mode, simulating the twisting motion of the donor and acceptor moieties relative to the binding bridge on the dynamics of hot charge recombination with account of a deviation from the Condon approximation is examined. The second-order time-dependent perturbation theory in the electronic coupling parameter is used to derive an analytical expression for the hot charge recombination rate. The scale of the effect of deviation from the Condon approximation of the dynamics of the decay of the excited state of the donor-acceptor complex formed by photoexcitation with a short laser pulse at a charge transfer band frequency is evaluated. It is shown that, depending on whether the electronic coupling parameter increases or decreases during the oscillatory motion of the donor and acceptor moieties of the donor-acceptor complex, the deviation from the Condon approximation can either to accelerate or slow down the decay of the excited state of the complex.