Periodic Orbits and Bifurcations of the Vibrational Modes of the Ozone Molecule at High Energies

The study of quantum states near the dissociation threshold is necessary both to understand the formation of molecules and to explore accurately chemical reactions. Quantum calculations of highly excited states can be complemented by methods of nonlinear classical mechanics that help revealing the stable modes of molecular vibrations and their transformations (bifurcations) during excitation of a molecule. The classical approach is particularly efficient at high energies where due to their high density, strong state mixing could occur, and simple assignment in terms of the standard normal modes becomes impossible. In this work we present first results for periodic orbits of the main isotopologue of the ozone molecule (O-16(3)) using recent accurate ab initio potential energy surface. Along with the principle families of the periodic orbits corresponding to the symmetric, antisymmetric, and bending types of molecular vibrations, we have located bifurcations corresponding to the transition to local modes as well as resonance orbits that are responsible for new types of vibrational motions in the high energy range. The classical trajectories of nuclei and their correspondence to the wave functions of the quantum states are also discussed.