Local mode behavior: The Morse oscillator model

Abstract

The bond-stretching vibrations of H 2O, NH 3 and SO 2 (also HDO and D 2O) are treated computationally according to a model in which the bond oscillators are Morse oscillators, coupled only through a mass and bond-angle dependent kinetic-energy term. Each calculation invokes only the two parameters which define a Morse potential, but the calculations extend to comparatively high quantum numbers (up to seven quanta) and in the high overtone region prove (as far as can be judged) to be reliably predictive of energy levels and of the general intensity patterns of absorption. By comparison, in the high-overtone region, the predictions of conventional theory, based on harmonic oscillators and normal modes, appear to be ineffective. For the hydride molecules, the calculations provide a simple quantitative description which illuminates the concept of ‘local modes’ of oscillation. For SO 2, in which the mass difference between the two bonded atoms is less pronounced, the coupled Morse oscillator model remains suitable, but it does not invite a local mode description of the vibrations, for reasons which are examined.