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An approach is developed that allows estimation of excited quadrupole molecule parameters responsible for changes in vibration frequencies in states with symmetry breaking by charge transfer from time-resolved IR spectra. The approach is tested on a molecule like A-π-D-π-A composed of an electron-accepting group A coupled with electron-donating group D by means of π-conjugated bonds, a D pyrrolopyrrole core, and two cyanophenyl acceptors. The expression derived for the IR spectrum of a molecule with symmetry breaking is shown to perfectly describe experimental data. The numerical values of the parameters of asymmetry in a series of solvents with different polarities and the solvent-independent parameters of the molecule itself are determined.

A significant number of quadrupolar dyes with a D-$pi$-A-$pi$-D or A-$pi$-D-$pi$-A structure, where D and A are electron donor and acceptor groups, were shown to undergo symmetry breaking (SB) upon optical excitation. During this process, the electronic excitation, originally distributed evenly over the molecule, concentrates on one D-$pi$-A branch, and the molecule becomes dipolar. This process can be monitored by time resolved infra-red (TRIR) spectroscopy and causes significant spectral dynamics. A theoretical model of excited-state SB developed earlier ( extit{J. Phys. Chem. C}, extbf{2018}, extit{132}, 29165) is extended to account for the temporal changes taking place in the IR spectrum upon SB. This model can reproduce the IR spectral dynamics observed in the $-mathrm{C}equiv mathrm{C}-$ stretching region with a D-$pi$-A-$pi$-D dye in two polar solvents using a single set of molecular parameters. This approach allows estimating the degree of asymmetry of the excited state in different solvents as well as its change during SB. Additionally, the relative contribution of the different mechanisms responsible for the splitting of the symmetric and antisymmetric $-mathrm{C}equiv mathrm{C}-$ stretching bands, which are both IR active upon SB, can be determined.

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.

FSDS is Fluorescence Spectral Dynamics Simulator, designed to investigate photoinduced charge transfer and its manifestations in time-resolved fluorescence spectra of a dye in a solvent. The project is implemented in C, using the MPI library. The computer model simulates stationary absorption and fluorescence spectra, as well as the time evolution of population distributions along the solvent reaction coordinate, to calculate spectral dynamics. Excitation and relaxation of intramolecular high-frequency vibrations are described at the quantum level. FSDS can fit the physical parameters of the dyes to experimental data. The dye excitation is consistently described accounting for the finite duration of the pump pulse. The program code implements two evolutionary models: a spin-boson model within the harmonic potential and a stochastic model based on the Smoluchowski diffusion operator for an arbitrary free energy surface. Computer simulation shows the numerical coincidence of the calculations performed in the framework of these models for the harmonic free energy surface. The detail description of the code and numerical schemes are presented. Program summary Program Title: Fluorescence Spectral Dynamics Simulator (FSDS) CPC Library link to program files: https://doi.org/10.17632/d39rrrkvhr.1 Code Ocean capsule: https://codeocean.com/capsule/6544976 Licensing provisions: GPLv3 Programming language: C Supplementary material: Sample configuration files, User Manual Nature of problem: The time-resolved spectra contain reach information about photochemical processes. However, the chemically important information about separate elementary processes is entangled due to they proceed in parallel. Time-resolved spectra modeling allows extracting information about these processes. The presented program code makes it possible to determine the relaxation characteristics of the solvent and the times of intramolecular relaxation. Solution method: Finite-difference time-domain and Brownian dynamics simulation methods.

A general analytical expression for the transient fluorescence spectrum is derived. The formation of a wave packet in the excited state of a fluorophore is described, assuming that the pump pulse has a Gaussian time-profile. The expression explicitly connects the relaxation characteristics of the medium with the spectral dynamics of a fluorophore. Fitting the expression to experimental spectral dynamics allows obtaining the solvent relaxation function. So far this approach was applicable for the analysis of experimental data when the pump pulse does not populate excited sublevels of intramolecular high-frequency vibrational modes. Here, the approach is generalized to include vibrational relaxation in the excited electronic state. In this case, fitting to the experimental spectral dynamics provides reliable information not only on the solvent relaxation, but also on the relaxation time constants of intramolecular high-frequency vibrational modes. This approach is applied to the excited state dynamics of coumarin 153 in multiple solvents, obtained from broadband fluorescence upconversion spectroscopy.

Regularities of ultrafast charge recombination kinetics in photoinduced intramolecular electron transfer in polar solvent are investigated. The multichannel stochastic model is used to simulate kinetics of charge separation and ensuing ultrafast charge recombination. The rate constant of ultrafast charge recombination occurring in non-equilibrium mode is shown to depend on the free energy gap of the preceding charge separation stage. This is a clear demonstration of violation of one of the fundamental principles of formal chemical kinetics, namely, the postulate of independence of elementary chemical reactions. The simulations revealed two main trends: (i) the charge recombination rate constant typically increases with decreasing the charge separation free energy gap, (ii) the maximum of the charge recombination rate constant, as a function of the charge recombination free energy gap, |ΔGCR|, shifts toward smaller values of |ΔGCR| with decreasing the free energy gap at the previous, charge separation, stage of the reaction. The prediction of ultrafast charge recombination in donor–acceptor dyads with small charge recombination free energy gap is shown to be supported by the experimental data on the kinetics of charge recombination into the first excited state followed the charge separation from the second excited state.

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

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.

We introduce bsmKinetic , an implementation of the stochastic multichannel point-transition approach to simulation of the charge transfer kinetics in molecular systems with reorganization of many intramolecular high-frequency vibrational mode in solvents with several relaxation timescales. The software provides simulation of the charge transfer kinetics in the molecular systems with many electronic states involved in photochemical transformations. It also allows simulating the charge transfer occurring in both equilibrium and nonequilibrium regimes. bsmKinetic is open-source software distributed under the terms of the GPL without additional components. Software is implemented on multiple computing platforms. It exploits Matsumoto and Nishimura source code for pseudorandom number generator and a hierarchy of custom parallelization of the stochastic trajectories built on MPI . Program summary Program Title: bsmKinetic Program Files doi: http://dx.doi.org/10.17632/ywd9cwzzx9.1 Licensing provisions: GPLv3 Programming language: C++ Supplementary material: MPI Nature of problem: Simulation of dynamics and kinetics of charge transfer in solution. Solution method: Brownian simulation method for diffusional dynamics, stochastic point-transition approach for electronic and vibronic transitions. Additional comments including Restrictions and Unusual features: Binary search of transition-points for each diffusion step on crosses of vibrational manifolds, initial electron-vibrational distribution includes pump pules characteristics, classical description of the solvent fluctuations, description of the vibronic states in terms of populations ignoring the quantum coherence, usage of the diabatic basis, parabolic terms. Reference: [1] M. Matsumoto, T. Nishimura Dynamic Creation of Pseudorandom Number Generators, in book Monte Carlo and Quasi-Monte Carlo Methods, 1998, Springer, 2000, 56–69.

We study the fluorescence spectral dynamics of a molecule with two excited fluorescent states (called the precursor and product) within the stochastic point transition model, which includes a consistent description of the dynamics of the particles distribution in excited states and transitions between them. Crucial changes in spectral dynamics with increasing the transition rate between the precursor and the product are discovered. Analysis of the results of spectral dynamics modeling allows us to determine how the transition rate between the precursor and the product affects the isoemissive point in the spectra collected with an increasing time delay. The following main regularities were revealed: fluorescence spectra with a short delay not exceeding several solvent relaxation times ( τ L ) may not pass through the isoemissive point; the isoemissive point shifts to the red with a decrease in reaction time constant ( τ eff ). The shifted isoemissive point exists in the range 10 τ L τ eff 40 τ L . For faster reactions with 5 τ L τ eff 10 τ L , the isoemissive point blurs. When the reaction proceeds in the ultrafast regime τ eff 5 τ L , the fluorescence spectrum shifts from a vicinity of the precursor spectrum to the product spectrum as a whole, changing its shape.

A model of photoinduced ultrafast charge separation and ensuing charge recombination into the ground state has been developed. The model includes explicit description of the formation and evolution of nonequilibrium state of both the intramolecular vibrations and the surrounding medium. An effect of the high-frequency intramolecular vibrational mode excitation by a pumping pulse on ultrafast charge separation and charge recombination kinetics has been investigated. Simulations, in accord with experiment, have shown that the effect may be both positive (the vibrational mode excitation increases the charge-transfer rate constant) and negative (opposite trend). The effect on charge separation kinetics is predicted to be bigger than that on the charge recombination rate but nevertheless the last is large enough to be observable. The amplitude of both effects falls with decreasing vibrational relaxation time constant, but the effects are expected to be observable up to the time constants as short as 200 fs. Physical interpretation of the effects has been presented. Comparisons with the experimental data have shown that the simulations, in whole, provide results close to that obtained in the experiment. The reasons of the deviations have been discussed.