Solvent dynamics: Modified Rice–Ramsperger–Kassel–Marcus theory. II. Vibrationally assisted case

Abstract

Expressions are given for a solvent dynamics-modified Rice–Ramsperger–Kassel–Marcus (RRKM) theory for clusters. The role of vibrational assistance across the transition state region is included. The usual differential equation for motion along the slow coordinate X in constant temperature systems is modified so as to apply to microcanonical systems. A negative entropy term, –Sv(X), replaces the (1/T)∂U/∂X or (1/T)∂G/∂X which appears in canonical systems. Expressions are obtained for the RRKM-type rate constant k(X) and for the Sv(X) which appear in the differential equation. An approximate solution for steady-state conditions is given for the case that the "reaction window" is narrow. The solution then takes on a simple functional form. The validity of the assumption can be checked a posteriori. Recrossings of the transition state are included and the condition under which the treatment approaches that in Part I is described.