Nonradiative transitions in a molecule during vibrational-frequency relaxation

Abstract

In [4, 5], an attempt was made to obtain formulas for the transition probability in a relaxing molecule, in conditions where it is impossible to take account parametrically of the change in state of the system (nonadiabatic behavior of the system). A phenomenological description of the relaxation process was used here. In the general case, the formulas of [4, 5] are very unwieldy and their analysis in specific situations is difficult. It is desirable to simplify the formulas and their analysis in the cases (not considered in [5]) with relaxation of the vibration frequencies of the nuc!ei in the molecule. In general form, the problem with frequency relaxation is not solvable since it involves solving an equation coinciding in form with the equation of harmonic vibration but with a time-dependent frequency (the known particular solutions show that the behavior of this system may not be vibrational or monotonic [6]). At the same time, even in the case of molecular systems, without clearly expressed relaxation of the electronic state [7], experimental data and calculations indicate the presence of significant change in frequency with change in electronic state and the importance of taking this into account in considering processes occurring in a molecule. The problem of taking frequency relaxation into account is interesting from the viewpoint of application to systems with a four-level electron-state scheme [8-10], which in the cases that have been investigated are sufficiently complex molecules, whether isolated or in liquid solution. Note here that, with the development of lasers, one more field of application of the results of analyzing the probability properties of nonradiative transitions in systems with relaxation of the state after excitation has emerged. This field is the investigation of the laws governing the interaction of laser radiation with a condensed transparent medium in the case of radiant heating of the ]~r to pronounced temperatures. According to existing concepts, what is responsible for the heating of the medium is a different kind of inhomogeneity of the medium, which, in particular, may be an admixture of different absorbing molecules. Since at high radiation intensity the absorption capability of the molecule depends on the state of the molecule and whether deactivation of the molecule after excitation is possible the rate of nonradiative transitions is an important question. In this case, the molecule in the radiation zone is in conditions that change at a rate comparable with the length of the pulse, which is currently a time of the order of i0-~2-i0 -9 sec, i.e., a time comparable with the characteristic relaxation times in a sufficiently complex isolated molecule [ii) 8]. Consider a molecular system with two electron states (and a set of vibrational modes) capable of relaxing at the aoment of transition. The bulk of the normal vibrations in the two states are common, and described as in [4]. The presence of relaxation of the upper state is described by introducing one more vibration mode of the excited state which is not intrinsic to the lower state; the relaxational change in the parameters of this vibration reduces to decrease in vibration frequency. The physical situation assumed here is such that the appearance of the given additional vibration is associated with increase in effective dimensions of