# Application of a dynamical S matrix method to the three-dimensional H+H_{2} exchange reaction

## Abstract

A quantum dynamical S matrix formalism which enables population distributions to be computed as a function of a reaction coordinate μ is described and applied to the three-dimensional H+H2 exchange reaction. Quantum dynamical R matrix methods and programs of Stechel, Walker, and Light have been adapted for this purpose. The method has been applied to examine the suitability of the simple surprisal formula [pj∝ oc pj0exp(λkj)] describing rotational product state population distributions [Pj]. Previous results on the semiempirical Porter-Kaplus (PK) potential energy surface for total angular momentum J=0 showed that the computed quantum dynamical population distributions can be fitted accurately by the surprisal formula for all values of u. The microcanonical prior distribution function, pj0 ∝ kj(2j+1)final product states was found to be appropriate, even though the statistical justification of this function fails because of angular momentum conservation. In the present work this surprisal theory study has been extended and a comparison has been made between the population distributions computed using the PK potential and the potential of Truhlar and Horowitz derived from the ab initio CI study of Siegbahn and Liu (THSL). Although the surprisal formula is curate for all values of u for the PK potential and for small values of u for the THSL potential, it does not give such a good fit for larger values of u for the THSL potential. This result is linked directly with the fact that for the THSL potential the H3 conformation of minimum potential energy is nonlinear for relatively large values of u. These results strongly suggest that a justification for the successes of surprisal theory must result from a detailed examination of the collision dynamics, rather than from statistical considerations. The dynamical S matrix method is also used to explain an approximate reactive flux rule for the H + H2 reaction: the sum of unnormalized reaction probabilities into product states with even rotational quantum numbers is approximately equal to the sum of reaction probabilities into odd product states. © 1979 American Institute of Physics.