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

✍ Scribed by J.T. Muckerman; M.S. Child

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 466 KB
• Volume: 153
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(88)85246-1

✦ Synopsis

We present a simple, analytic model for the normal and local mode behavior of the stretching vibrations in AB, molecules.

Starting with a zeroth-order description ofdegenerate, harmonic normal modes, we introduce a quartic perturbation and employ first-order secular perturbation theory to obtain a closed-form expression for the Poincare 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 com- pletely lifts the degeneracy ofthe zeroth-order states, and predicts the appropriate trends in the ordering of the various modes and the splitting between local mode pairs