V. A. Morozov

On applicability of optical Bloch equations to simulation of photochemical reaction dynamics

61 Recent progress in theoretical photochemistry is attributed to advances in quantum theory, which treats the chemical reaction as a non optical transition between the reagent and product states (see [1] and references therein). In this theory, the reacting system is considered a closed system. In simulation of its state population dynamics, different variants of the optical Bloch equations are used, describing the elements of the population matrix of the reacting molecular com plex and the radiation field; this matrix is reduced tak ing into account the states of secondary and spontane ous emission photons (reduced density matrix (RDM), see, e.g., [2]).

Mathematical simulation of dual fluorescence quenching

The dynamic quenching of dual fluorescence is simulated based on solving a system of equations for matrix elements of the statistical operator of a five-level model molecule three levels of which belong to its excited states. It is assumed that one of the excited states is resonantly populated by monochromatic irradiation, while the other two states are populated as a result of subsequent relaxation processes. These two states are initial states for transitions that emit dual fluorescence photons. Expressions for the population of the excited molecular states in the case of steady-state fluorescence are obtained taking into account their decay (quenching) due to collisions with foreign molecules of the environment. As applied to molecules with intramolecular hydrogen bonds, the dual fluorescence quenching is described more completely and in more detail compared to the description given in the literature based on the molecular model with two excited levels.

Modeling of quantum beats of the state populations of a molecule

Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.

Mathematical modeling of the dynamics of photoreactions of a five-level molecule

A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given.

Mathematical modeling of the population dynamics of “dark” states of a three-level system

Mathematical modeling of the population dynamics is performed for states of a three-level system (atom) with a V-type configuration transforming a light pulse. It is assumed that the excited eigenstates of the atom are degenerate and coupled by coherent interaction, one of the states being radiating (radiative), while the other state is nonradiating (“dark”). The population dynamics of atomic states is described on the basis of numerical solutions of equations for the matrix elements of the density operator. The dependence of the efficiency of population of the atomic dark state from the values of the parameters of an irradiation pulse and from the ratio of the period of population oscillations of excited atomic states (caused by their coherent interaction) to the lifetime of the atomic radiating state is determined. Typical examples of the time dependence of the population of states of the atom considered are presented for the cases of irradiation by a short (as compared to the lifetime of the radiating state) sinusoidal light pulse and by a long rectangular light pulse with the resonance carrier frequency.

Simulation of intramolecular dynamics at transformation of two light pulses by molecules of active media of photochemical lasers

Using a numerical solution of a system of equations for matrix elements of file-level model molecule density operator time dependencies of population on its states at different values of two irradiation pulses parameters (the pump pulse and the dump (or probe) pulse) and constants, determining rates of induced radiative transitions of the molecule, and radiative and nonradiative decays of the molecular states are calculated. The values of these constants were taken, in particular, close to these of the corresponding constants of molecules with intramolecular hydrogen bond as the 3-hydroxyflavone (3-HF) molecule. Values of irradiation pulses parameters are obtained, at which after enol-keto photoisomerization, induced by pump pulse, dump pulse induces molecular transition from excited electronic state in keto-form to ground state in this (ldquotautomericrdquo) form. This transition is accompanied by stimulated emission with a frequency of ldquotautomericrdquo fluorescence. Examples of periodic change of intensity of the stimulated emission are given, the frequency of oscillations of fluorescence intensity being proportional to dump pulse intensity.

A THEORY OF LUMINESCENCE OF LIGHT-COLLECTING MOLECULAR SYSTEMS *

Expressions are obtained for the intensity and the quantum yield of the sensitized luminescence of the chromophore that plays the role of a reaction center in the simplest model trichromophore molecular [light‐collecting] antenna which is so constructed and so oriented in space that the irradiation photons coherently excite its other two chromophores‐pigments. The quantum electrodynamics formalism which takes into account the radiative dissipative interaction between the pigments and the reaction center of the antenna was used. The comparative analysis of the obtained expressions with the corresponding expressions for the luminescence of a bichromophore molecular system, differing from the trichromophore antenna by the absence of one of the pigments, has shown that the collective dissipative interaction of the pigments with the reaction center of the antenna can be considered as a highly efficient mechanism of [light collection] in molecular antennas.