Assigning vibrational spectra of highly excited molecules: classical and quantum vibrational dynamics of the H2O molecule

We study the classical and quantum mechanics of the 3-mode Baggot vibrational Hamiltonian for H2O. Chirikov resonance analysis gives an approximate view of the classical phase space structure. Computation of periodic orbits and families of resonant 2-tori provides a more rigorous basis for the use of the Chirikov picture. Examination of classical surfaces of section together with quantum mechanical Husimi phase space distribution functions leads to a dynamical assignment of almost all 45 states considered. The most extensive mixing occurs via a 2-state avoided crossing.