Separation and semiclassical quantization of bending motion near linear geometries of a triatom

Abstract

It is shown that separation of internal bending motion from other degrees of freedom in the vicinity of linear configurations of a triatom leads to the one-dimensional Schrödinger equation for the centrifugal oscillator for a very broad family of coordinate transformations. This feature makes the approach especially attractive for semiclassical quantization of bending motion, compared with the alternative, broadly used approach treating bending motion as two mutually perpendicular bending modes. Significant errors due to the neglect of the quartic potential term coupling the mutually perpendicular bending modes are demonstrated using bending resonances in partial cross sections for the H+H2 exchange reaction as an example. Another important issue addressed in the paper is how the choice of rotating axes affects the rotational energy. It is shown that the correct expression for the rotational energy is obtained only if the body-fixed axes are directed along the principal inertia axes of the triatom in its accessible nearly linear configurations.