Resonant Scattering Theory of Association Reactions and Unimolecular Decomposition. II. Comparison of the Collision Theory and the Absolute Rate Theory

Abstract

The rate expressions derived in the preceding paper using a resonant scattering theory (RST) to describe recombination and unimolecular decomposition are compared with the absolute rate theory (ART). A one-to-one correspondence exists between the resonance states in RST and the activated states in ART. The “states of the activated complex” are shown to be the channel states in RST, and using the adiabatic approximation to describe the continuum states it is shown that ART does give a proper upper bound to the rate even when nonadiabatic effects are included in RST, i.e., the mean transmission coefficient κ is equal to or less than one. The collision theory gives explicit expressions for κ(kT,P) which is a function of temperature and includes the dependence on pressure. Specific expressions are given for the “tight complex,” where the “activated complex” occurs at some distorted region in configuration space, and for the “loose complex,” where the activated complex is the rotational barrier in the asymptotic channel states. Particular attention is given to the high-pressure rate constant where the specific transmission coefficient can be simply related to the ratio of the mean widths to the mean spacings of the activated states. Criteria are given for the validity of ART, and it is shown that Light's statistical theory of reaction rates is a special microcanonical version of the ART for the “loose complex.”