We present a simple, analytic model for the normal and local mode behavior of the stretching vibrations in AB2 molecules. Starting with a zeroth-order description of degenerate, harmonic normal modes, we introduce a quartic perturbation and employ first-order secular perturbation theory to obtain a closed-form expression for the Poincaré surface of section for the action-angle variable pair corresponding to the vibrational angular momentum. Local modes correspond to pairs of levels trapped below a dynamical barrier along this angle variable; normal modes, to levels above the barrier. Uniform semiclassical quantization completely lifts the degeneracy of the zeroth-order states, and predicts the appropriate trends in the ordering of the various modes and the splitting between local mode pairs.
ASJC Scopus subject areas
- Physical and Theoretical Chemistry
- Condensed Matter Physics
- Atomic and Molecular Physics, and Optics
- Surfaces and Interfaces