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

A completely general canonical and microcanonical (energy-resolved) flexibl e transition state theory (FTST) expression for the rate constant is derive d for an arbitrary choice of reaction coordinate. The derivation is thoroug h and rigorous within the framework of FTST and replaces our previous treat ments [Robertson , J. Chem. Phys. 103, 2917 (1995); Robertson , Faraday Dis cuss. Chem. Soc. 102, 65 (1995)] which implicitly involved some significant assumptions. The canonical rate expressions obtained here agree with our e arlier results. The corresponding microcanonical results are new. The rate expressions apply to any definition of the separation distance between frag ments in a barrierless recombination (or dissociation) that is held fixed d uring 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 optimi zing the reaction coordinate within a canonical or microcanonical framework . The expression is analytic except for a configuration integral whose eval uation generally requires numerical integration over internal angles (from one to five depending on the fragment structures). The form of the integran d 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 mo tion of the fragments. (C) 2000 American Institute of Physics. [S0021-9606( 00)00531-6].