Sensitivity of intramolecular vibrational energy relaxation to stretch–bend potential energy coupling and stability of periodic orbits

Stretch–bend coupling via 2:1 Fermi resonance is an important mechanism for rapid energy flow from overtone excited CH local mode states. To elucidate the role of potential energy coupling, we have studied the classical dynamics of a two-mode stretch–bend Hamiltonian for the benzene fragment C3 H. The effects of attenuation of the CCH bend force constant by stretching of the CH bond on the short time (up to 0.12 ps) probability decay dynamics of the model system are in good qualitative accord with trends found previously in full scale classical trajectory simulations on planar benzene by Lu, Hase, and Wolf. Surfaces of section are used to study the classical phase space structure of the stretch–bend Hamiltonian. A close correlation between instability of the CH periodic orbit and exponential decay of probability is found, and relaxation rates can be estimated to good accuracy by linear stability analysis of the periodic orbit. Increasing the strength of the potential coupling stabilizes the CH periodic orbit, thereby suppressing overtone relaxation. There is therefore an effective cancellation of kinetic and potential stretch–bend coupling terms.