M. S. Child, C. Cooper and M. P. Jacobson

Physical and Theoretical Chemistry Laboratory, Oxford University, UK

1. A variety of cases of Fermi resonance will be used to demonstrate how the energies of quantized periodic orbits of the system provide natural divisions between different regions of the quantum mechanical spectrum. The discussion will be set in the context of Kellman's catastrophe map, which will be extended to include physically important situations that have not hitherto been considered – notably by including higher terms in the coupling function and considering non-zero angular momentum.
2. The concept of quantum monodromy will be used to demonstrate certain generic vibrational-rotational energy level patterns around the energy thresholds at which a bent molecule becomes linear, or parts of a linear molecule begin to rotate around each other.
3. Applications to possible observables in the spectrum of HCP will be discussed.