Local and normal vibrational states: a harmonically coupled anharmonic-oscillator model

Abstract

Analysis of previous calculations indicates that the observations of an irregular overtone/combination spectrum implies increasingly close local-mode near-degeneracies in the higher overtone states. This behaviour is accurately reproduced by a model of two harmonically coupled anharmonic oscillators, when the anharmonicity parameter exceeds the coupling strength, the effect being independent of the momentum or potential origin of the coupling. The same model reproduces familiar normal mode behaviour in the opposite limit. Applications of the model indicate local-mode behaviour for H₂O and C₂H₂ and normal mode features for C₂D₂ and SO₂, the dominant inter-bond coupling in all cases except H₂O being due to cross-terms in the kinetic-energy operator. In H₂O such momentum coupling is combined with an approximately equal potential coupling contribution.