The sequential exploration of phase space in selectively excited polyatomic molecules

The squared Fourier transform of the optical absorption spectrum provides a very useful characterization of the intramolecular dynamics. In practice, most of the information content is in that portion of the transform whose magnitude is of the order of (1/N) of its value for time=0, where N is the number of eigenstates in the zero order nonstationary bright state which is optically accessed. If the highly resolved spectrum manifests inherent structures ("clumps") at lower levels of resolution then each clump can be regarded, for the purpose of the analysis, as a bright state with its own survival probability. This offers a significant advantage. We discuss theoretically and provide computational examples how this can be implemented within a maximum entropy formalism. We determine both the density of the region in phase space sampled up to time t and its entropy. Analytically and computationally it is shown that the evolution in phase space is sequential. Also discussed is the structure of the Hamiltonian matrix which can give rise to a nested inherent spectra. It is argued that each time scale is characterized by its set of good constants of motion which decrease in number upon the transition to the next time regime.