The distribution of intensities in a vibrational spectrum: a model computational study of the transition to classical chaos

A model Hamiltonian for two coupled oscillators is used to generate Franck-Condon factors corresponding to transitions between two displaced potential energy surfaces. The distribution of intensities is examined as a function of the energy of the initial state. The fluctuations in the intensities about their smooth envelope are found to diminish at higher initial energies when the corresponding classical motion is more chaotic. The fluctuations remain, however, even in the fully chaotic limit. The distribution in that regime is very closely fitted by one of maximum entropy subject only to a given oscillator strength.