On the separation of time scales in the exploration of phase space of an isolated molecule

The rate of exploration of phase space can be usefully probed in terms of the Fourier time transform of the experimental frequency spectrum. If the internal energy is not too large (i.e. if one deals with a case that is closer to the regular, separable modes limit), the spacings between optically bright states can be expected to be significantly larger than the strength of their coupling to the background "dark" states. This results from the different magnitudes of the zero-order frequencies (ω_e) and anharmonicities (ω_eχ_e). As a consequence, the relaxation takes place on two different time scales. The earliest stage corresponds to a rapid sampling of that part of phase space spanned by the subset of optically directly accessed states (belonging to the totally symmetric representation). For a medium-sized molecule at lower energies, this stage is over by a time which is below 0.2 ps. The second time regime is controlled by the interstate couplings (i.e. the Fermi and Darling-Dennison resonances), which allow the participation of optically inactive modes. A third time scale can be defined if the molecule dissociates. The stronger the coupling with the continuum, the lesser is the number of phase-space cells sampled by the system before dissociation.