An analysis of normal and local mode dynamics based on periodic orbits. I. Symmetric ABA triatomic molecules

Abstract

This paper shows how to quantize Hamiltonians of symmetric ABA molecules using energies and stability frequencies of simple normal and local mode periodic orbits. It is shown that the quantization can be based either on the idea of adiabatic dynamical potentials or on the hindered rotor representation. In the former case, the stable periodic orbits correspond to the wells and the unstable ones to the barriers of the adiabatic potentials. In the latter case the normal mode periodic orbits correspond to the equilibria of the hindered rotor Hamiltonian, and the local mode periodic orbits correspond to the rotor’s orbits with the maximal allowed ‘‘angular momentum.’’ Results of extensive numerical testing of both approaches are presented for the H2O model Hamiltonian used by Sibert et al., and for the Davis–Heller potential.