Flexible transition state theory for a variable reaction coordinate: Derivation of canonical and microcanonical forms

Abstract

A completely general canonical and microcanonical (energy-resolved) flexible transition state theory (FTST) expression for the rate constant is derived for an arbitrary choice of reaction coordinate. The derivation is thorough and rigorous within the framework of FTST and replaces our previous treatments [Robertson et al., J. Chem. Phys. 103, 2917 (1995); Robertson et al., Faraday Discuss. Chem. Soc. 102, 65 (1995)] which implicitly involved some significant assumptions. The canonical rate expressions obtained here agree with our earlier results. The corresponding microcanonical results are new. The rate expressions apply to any definition of the separation distance between fragments in a barrierless recombination (or dissociation) that is held fixed during hindered rotations at the transition state, and to any combination of fragment structure (atom, linear top, nonlinear top). The minimization of the rate constant with respect to this definition can be regarded as optimizing the reaction coordinate within a canonical or microcanonical framework. The expression is analytic except for a configuration integral whose evaluation generally requires numerical integration over internal angles (from one to five depending on the fragment structures). The form of the integrand in this integral has important conceptual and computational implications. The primary component of the integrand is the determinant of the inverse G-matrix associated with the external rotations and the relative internal motion of the fragments.