Canonical flexible transition-state theory for generalized reaction paths

Abstract

In previous work (J. Chem. Phys., 995, 103, 2917), simple yet exact formulae for the canonical flexible transition-state theory expression for the thermal reaction-rate constant were derived for all pairings of atomic, linear rigid top, and non-linear rigid top fragments when the distance between the centres of mass of the fragments serves as the reaction coordinate. In this paper, we derive the fundamental modifications required to generalize the reaction coordinate for all fragment-type pairings. That is, the hinge point about which each fragment rotates is no longer constrained to be the centre of mass of the fragment, being in general arbitrarily displaced from the fragment centre of mass. The generalized reaction coordinate is the line connecting the displaced hinge points. It is shown that only the kinetic energy associated with the internal relative motion of the two fragments is affected by a generalized reaction coordinate. The correction to this kinetic energy has a simple functional form whose evaluation for a given fragment-type pairing is straightforward. The ensuing formulae for the canonical rate constant will not be as simple as for the centres-of-mass reaction coordinate case, but are not more difficult to employ computationally. The new theory is applied to the simplest possible fragment-type pairing, atom–diatom, which serves to illustrate the essential features of the method and some of the implications of a generalized reaction coordinate.