Microcanonical variational theory of radical recombination by inversion of interpolated partition function, with examples: methyl + hydrogen atom, methyl + methyl

Abstract

A simple interpolation scheme involving the logarithms of partition functions for initial and final states in a bond-fission reaction is used to represent, as a function of distance along the reaction coordinate, the total partition function for the transition state. The inverse Laplace transform of this partition function yields a distance-dependent state count for the transition state that serves as input for a variational routine incorporated into a standard RRKM calculation. In this way, the number of states of so-called transitional modes, in particular, is made to connect smoothly with the proper number of states of fragment rotations. The interpolation makes use of simple Morse potential for the breaking bond and one of two similar S-type switching functions: a one-parameter Gaussian and a two-parameter hyperbolic tangent, either of which gave similar results for the title recombinations, in essential agreement with experiment. It is shown that the negative temperature coefficient of a radical recombination arises primarily from the above types of switching functions, which cause a late switch (i.e., at large interfragment distance) to product configuration.