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 ͑RRKM͒ 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, ϪS v (X), replaces the (1/T)‫ץ‬U/‫ץ‬X or (1/T)‫ץ‬G/‫ץ‬X which appears in canonical systems. Expressions are obtained for the RRKM-type rate constant k(X) and for the S v (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.

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