Variational optimizations in the Rice–Ramsperger–Kassel–Marcus theory calculations for unimolecular dissociations with no reverse barrier

A method is described for variationally optimizing not only the value of the reaction coordinate but also its definition in transition state theory calculations for reactions without a barrier. In this method the reaction coordinate is assumed to be described by the distance from a point fixed in one of the fragments to another point fixed in the other fragment. For linear fragments the fixed points are chosen along the fragment axes whereas for nonlinear fragments each fixed point may be chosen anywhere within a three-dimensional fragment-fixed coordinate system. Results of the variational optimization of the distance and the choices for the fixed points are reported for the dissociation of NCNO into CN and NO. The optimized reaction coordinate is seen in this case to correspond to each of the fixed points being outside of the actual fragment towards the overall center-of-mass. Comparison is made with previous calculations based on bond length and center-of-mass separation distance reaction coordinates, these latter two reaction coordinates being specific cases of the present general reaction coordinate.