Dynamics of the Quasi-Linear Molecule

Abstract

Calculations of energy levels, eigenfunctions, dipole transition moments, and other significant properties have been made for a phenomenological model of a two‐dimensional harmonic oscillator with a superposed barrier at the minimum of the harmonic potential. A high‐speed electronic digital computer was employed. The method of calculation does not involve perturbation theory and converges rapidly for all barrier heights. The problem concerns the behavior of the degenerate bending vibration of a linear triatomic molecule, for example, when a potential barrier is introduced at the linear configuration. In the limit of a high barrier, the motion is that of a ``bent'' molecule with rotational motion superposed on the bending vibration about the minimum of potential energy. Results for moderate to low barriers, and those for anharmonic vibration in a well with no barrier, show that the rigid classification of molecules as ``linear'' or ``bent'' is not possible in some cases and that the intermediate case of the ``quasi‐linear'' molecule must be considered. The dynamical behavior of such anharmonic motion and its interaction with other vibrations have been investigated, and the primary identifying characteristics of the quasi‐linear molecule delineated. The analytical method of solution used has also been applied successfully to the one‐dimensional barrier problem.