On the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics: Application to O + CS₂ → SO + CS

We explore the use of mass scaled cluster coordinates to describe polyatomic molecule reaction dynamics. These coordinates provide the natural extension to polyatomic systems of the familiar atom-diatom model of "rolling a marble" on a skewed and scaled potential surface in that they reduce the kinetic energy of an arbitrary system to one equivalent to that of a single mass point moving in 3N - 3 dimensions. For any given number of atoms, usually several distinct types of mass scaled cluster coordinates can be introduced, all of which are interrelated by orthogonal transformations, and many of which are convenient for describing trajectory motion in one or more arrangement channels. We illustrate these points by an application to the collinear O + CS₂ → SO + CS reaction. For this system, the reagent to product coordinate transformation is conveniently described in terms of two Euler angles α and β, for which β is analogous to the atom-diatom skew angle, and α determines how the reagent vibrational normal modes relate to the product degrees of freedom. Examination of trajectory behavior indicates that the rather small value of π - α (21.7°) leads to a rather clean correlation between CS₂ asymmetric stretch motion and product CS vibrational motion, and between CS₂ symmetric stretch and a combination of SO stretch and product translation. This explains why symmetric stretch mode excitation enhances the O + CS₂ reaction rate more efficiently than asymmetric stretch mode excitation. We also find for O + CS₂ (and many other reactions for which the unbroken bond does not significantly change its length during the reaction) that the reagent and product segments of the minimum energy path are coplanar. This means that a natural partitioning of the reaction dynamics exists in which motions parallel to this plane tend to be active in promoting the reaction whereas motions perpendicular tend to be inactive. A study of trajectory motions and product state energy partitioning for O + CS₂ confirms this.