TY - JOUR T1 - Assigning vibrational polyads using relative equilibria: application to ozone JO - Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy VL - 61 IS - 13-14 SP - 2867 EP - 2885 PY - 2005/10// T2 - AU - Kozin, I.N. AU - Sadovskií, D.A. AU - Zhilinskií, B.I. SN - 1386-1425 M3 - doi: DOI: 10.1016/j.saa.2004.10.039 UR - http://www.sciencedirect.com/science/article/B6VNG-4F1GW80-1/2/b5a10b9a7ecd95e0e927d502561756e0 KW - Relative equilibrium KW - Normal form KW - Periodic orbit KW - Vibrational polyad KW - Dynamical symmetry KW - Local mode AB - 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 E (n) 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. ER -