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Russian Journal of Physical Chemistry B

Mathematical modeling of photoisomerization with intramolecular proton transfer

V. A. Morozov

Published Feb 1, 2011• 3 citations
Publisher

Abstract

A system of equations describing time changes in the matrix elements of the density operator of a seven-level model of a molecule interacting with a light pulse taking into account spontaneous (including collective) decays of molecule excited states is suggested. Model parameters were selected to allow us to perform modeling of the photoisomerization of a molecule with two isomeric states with different stable proton positions on an intramolecular H-bond by numerically solving the suggested system of equations for density operator matrix elements. An analysis of the characteristic time dependences of the population of states of the model under consideration showed that proton phototransfer in the collective decay of various isomeric states of a molecule in an excited electronic state can be one of effective mechanisms of the photoisomerization of molecules whose structure is described by the model.

DOI
10.1134/s1990793111020084

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A system of equations describing time changes in the matrix elements of the density operator of a seven-level model of a molecule interacting with a light pulse taking into account spontaneous (including collective) decays of molecule excited states is suggested. Model parameters were selected to allow us to perform modeling of the photoisomerization of a molecule with two isomeric states with different stable proton positions on an intramolecular H-bond by numerically solving the suggested system of equations for density operator matrix elements. An analysis of the characteristic time dependences of the population of states of the model under consideration showed that proton phototransfer in the collective decay of various isomeric states of a molecule in an excited electronic state can be one of effective mechanisms of the photoisomerization of molecules whose structure is described by the model.
The dynamics of transformation of a light pulse by a five-level model molecule whose secondary emission spectrum can contain two fluorescence bands is simulated. The system of equations that determine the time behavior of the matrix elements of the statistical operator of the molecule interacting with the light pulse is numerically solved. From this solution, the time dependences of the populations of the molecular states are determined for different values of the parameters of the irradiation pulse, which is described in terms of the classical theory, and of the parameters that characterize the rates of radiative and nonradiative spontaneous transitions of the molecule. Based on particular examples of the choice of these parameters, it is demonstrated that the mechanism by which dual fluorescence occurs in molecules with intramolecular hydrogen bonds can be efficiently established from the numerically simulated intramolecular dynamics.
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.
Abstract Mathematical modeling of the excitation dynamics of an isolated two-level particle under bichromatic irradiation is carried out on basis of solutions of the Schrödinger equation for the probability amplitudes of the states of the composite system of the particle and an interaction two-mode quantized radiation field, with the photons for each of which in a superposition state at the initial time. An analytical expression describing the change in the time of the population of the excited state of a particle in the adsorption of one of the irradiation photons in the simplest case when the irradiation is a sequence of identical pulses of a sinusoidal form is obtained. The obtained time dependence is compared with the time dependence of the diagonal matrix element of the statistical operator of the particle in the excited state found on the basis of the numerical solution of the system of the optical Bloch equations, with the corresponding irradiation described by the classical theory. Examples of significant differences in the type of these compared time dependences for a number of characteristic cases of irradiation are given.
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.
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.
Abstract A system of equations is obtained for describing the dynamics of the secondary photoreaction of two-level molecules emitting spontaneous fluorescence at initial excitation of one of them. The system is derived using the Schrödinger equation for the compound system of a reagent molecule, a reaction product molecule, and a quantized radiation field. Unlike those commonly used in similar modeling, optical Bloch equations describing the dynamics of a non-selective (collective) population of the ground states of two molecules (i.e., the total number of molecules of a pair in their ground states), the system of equations (and its generalization allowing for the longitudinal and transverse relaxation of excited states of molecules) allows estimates of the relative number of reagent molecules and the product in their ground states, the use of which provides a complete idea of the effectiveness of the reaction.