CANONICAL FLEXIBLE TRANSITION-STATE THEORY REVISITED

A simple formula for the canonical flexible transition state theory ex pression for the thermal reaction rate Constant is derived that is exa ct in the limit of the reaction path being well approximated by the di stance between the centers of mass of the reactants. This formula eval uates classically the contribution to the rate constant from transitio nal degrees of freedom (those that evolve from free rotations in the l imit of infinite separation of the reactants). As a result of this tre atment, the formula contains the product of two factors: one that excl usively depends on the collision kinematics and one that exclusively d epends on the potential energy surface that controls the transitional degrees of freedom. This second factor smoothly varies, in the classic al limit, from harmonic oscillator to hindered rotor to free rotor par tition functions as the potential energy surface varies from quadratic to sinusoidal to a constant in its dependence on the relative orienta tion angles of the fragments. An application to the recombination of C H3+H essentially demonstrates exact agreement with a previous flexible transition state theory study in which all integrals are carried out numerically. The simple formulas presented in this paper allow the cla ssical inclusion of large amplitude motion of arbitrary complexity in the determination of the canonical rate constant for reactions whose r eaction path is dominated by the distance between the centers of mass of the reactants. (C) 1995 American Institute of Physics.