An analytic semiclassical model for local and normal stretching modes in AB2 molecules

James Muckerman, M. S. Child

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)477-482
Number of pages6
JournalChemical Physics Letters
Issue number6
Publication statusPublished - Dec 30 1988

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Spectroscopy
  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics
  • Surfaces and Interfaces

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