Periodic orbit assignment for spectra of highly excited molecular systems

Recent experiments in high-energy molecular spectroscopy have shown that coarse grained molecular spectra are often very simple, characterized by a few frequencies or correlation times. Experiments in molecular scattering such as the hydrogen exchange reactions have demonstrated the existence of short-lived resonances. I show that these seemingly differing experiments may be interpreted and assigned in terms of the normal modes of periodic orbits, which are determined by a linear stability analysis. Specific examples include three-dimensional resonances of the hydrogen exchange reaction as well as three-dimensional high-energy bound states of the Hg molecular ion. A new semiclassical quantization method based on unstable periodic orbits is presented and used to explain the observed scarring of high-energy quantum states.