Qualitative study of a model three-level Hamiltonian with SU(3) dynamical symmetry

Assigning vibrational polyads using relative equilibria: application to ozone

We demonstrate how relative equilibria of a vibrating molecule, which are families of principal periodic orbits otherwise known as nonlinear normal modes, can be used to describe the global polyad structure of vibrational energy levels. The classical action integral n(E) computed along these orbits at different energies E corresponds to the polyad quantum number n so that the energy En of different relative equilibria describes the splitting of n-polyads. Further information on the internal polyad structure can be driven from the stability analysis of relative equilibria. We use the ozone molecule as a concrete example where n-polyads or "hyperpolyads" should be distinguished from the well-known polyads of the 1:1 stretching mode resonance; the stretching polyads are structural elements of hyperpolyads. We give dynamical interpretation of the relation between relative equilibria and n-polyads based on the normal form reduction in the limit of small vibrations near the equilibrium.

Analysis of the "Unusual" Vibrational Components of Triply Degenerate Vibrational Mode nu(6) of Mo(CO)(6) Based on the Classical Interpretation of the Effective Rotation-Vibration Hamiltonian

Rotational structure of the triply degenerate vibrational state nu(6)(F(1u)) of the octahedral molecule Mo(CO)(6) is analyzed qualitatively on the basis of classical mechanics. We show that the energy level redistribution between the vibrational components of nu(6)(F(1u)) occurs due to rotational excitation and is related to the formation of singular points of classical rotational energy surfaces. The singularity is stable under small variations of parameters of the effective rovibrational Hamiltonian. Parameters responsible for the persistence of this phenomenon are specified. Comparison with quantum calculations demonstrates the high qualitative and quantitative accuracy of our classical analysis. Copyright 2000 Academic Press.