CANONICAL FLEXIBLE TRANSITION-STATE THEORY FOR GENERALIZED REACTION PATHS

In previous work (J. Chem. Phys., 995, 103, 2917), simple yet exact fo rmulae for the canonical flexible transition-state theory expression f or 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 r eaction coordinate. In this paper, we derive the fundamental modificat ions required to generalize the reaction coordinate for all fragment-t ype pairings. That is, the hinge point about which each fragment rotat es is no longer constrained to be the centre of mass of the fragment, being in general arbitrarily displaced from the fragment centre of mas s. The generalized reaction coordinate is the line connecting the disp laced hinge points. It is shown that only the kinetic energy associate d with the internal relative motion of the two fragments is affected b y a generalized reaction coordinate. The correction to this kinetic en ergy has a simple functional form whose evaluation for a given fragmen t-type pairing is straightforward. The ensuing formulae for the canoni cal rate constant will not be as simple as for the centres-of-mass rea ction coordinate case, but are not more difficult to employ computatio nally. The new theory is applied to the simplest possible fragment-typ e pairing, atom-diatom, which serves to illustrate the essential featu res of the method and some of the implications of a generalized reacti on coordinate.