Aspects of a theory of unimolecular reaction rates

Abstract

A uniform gas of polyatomic molecules is treated as an assembly of classical vibrating systems, which dissociate when one internal co-ordinate q reaches a critically high value q o which is related to the dissociation energy E 0 . The unimolecular velocity constant at temperature T is found to be K = v exp (— EJkT), where the ‘frequency factor’ v lies in the range of molecular vibration frequencies. The factor v may be interpreted (i) as a weighted average of the noi nal vibration frequencies, or (ii) as the ratio of the product of the normal frequencies to the product of the frequencies with q fixed, or (iii) in the case where dissociation is due to the rupture of an isolated bond, as the vibration frequency of an imaginary diatomic molecule consisting merely of the two bonded atoms connected by the original bond-force. The dissociation rate is formulated in several ways, which represent different aspects of the physical picture. The main contrast is between (a) the rate as the average frequency with which the normal-mode vibrations come sufficiently into phase to carry q to the critical value q0, and (b) ‘transition state’ formulations, giving the rate as the product of the relative concentration of activated complexes (molecules with q near q 0 ) and the mean transition frequency. The mathematical equivalence of these methods is shown by a study of the asymptotic distribution of values of sums of harmonic vibrations. The present model is used to illustrate some concepts of transition state or activated complex theory, such as the ‘effective mass’ in the reaction co-ordinate, and the partition function of the activated complex. The relation of the model to Kassel’s theory is shown by calculating the dissociation rates of molecules of specified total energy.