Representation in hyperspherical and related coordinates of the potential-energy surface for triatomic reactions

Abstract

Useful formulae for the treatment in hyperspherical and related coordinates of the elementary chemical reaction as a three-body problem are reported. In the kinetic plane (where one-dimensional potential-energy surfaces are represented) besides rotations describing all rearrangements, also those pertaining to the heliocentric Radau–Smith representation are exhibited. Explicit relations are given between physical quantities (distances, bond angles) and the two basic hyperspherical parametrisations. They are based on a formulation of internal coordinates which leads also to the systematic study of alternative ways for the graphical representation of three-dimensional potential-energy surfaces. The usefulness and some properties of kinetic paths (essentially two-dimensional plots of specific features of the potential-energy surface as a function of the hyperradius) are finally presented. Alternative notations employed in the recent literature on chemical kinetics are compared in an Appendix.