Statistical approximations in the study of wave packet dynamics for non-adiabatic intramolecular processes induced by a coherent excitation

Publisher Website
Google Scholar
Abstract
The dynamics of wave packets prepared by a coherent process on a set of potential energy surfaces is studied with the help of three related functions: P(t), the probability of staying in the electronic state initially prepared, C(t)2, the square of the autocorrelation function which can be obtained by Fourier transformation of an electron spectrum, and the function ℋ(t) introduced by Boltzmann which can be shown to decrease spontaneously as time increases, at least if the interference terms vanish. The model considered here describes a predissociation process. Two levels of approximation are considered. The statistical approximation (SA) consists in retaining only the terms which involve probabilities. This is formally similar to the procedure which leads to the well-known Pauli master equation, but has to be rationalized in an entirely different way. A good description of the average behaviour of the system is obtained by this method. In a much cruder approximation (IR), all the resonances are supposed not to interfere. The latter is found to be successful only when the Mies and Krauss parameter R = Γ/ΔE is less than about 0.25.