Algebraic resonance dynamics of the normal/local transition from experimental spectra of ABA triatomics

Abstract

An algebraic transformation is used to demonstrate the exact equivalence of the local and normal mode Hamiltonians for coupled anharmonic stretches. This SU(2) model is then interpreted semiclassically to extract quantitative information about nonlinear resonances in ABA triatomics from the Darling–Dennison spectral fit. A ‘‘glossary’’ is presented which makes it very easy to translate between the SU(2) language and standard spectroscopic terminology. In spectra predicted from the Darling–Dennison fit, transitions from a normal to local mode level pattern in molecules such as O3 are easily interpreted semiclassically in terms of trajectories in action/angle space and dynamical barriers. Although the local and normal algebraic Hamiltonians are equivalent for spectral fitting, local modes have the desirable property that they admit a simple representation in the coordinate picture. Local modes such as Morse oscillators therefore are the preferred physical starting point for stretching vibrations of general ABA triatomics.