Improved Rate Expression in the Quasi-Equilibrium Theory of Mass Spectra

Abstract

An improved continuous approximation to the number of states of a collection of harmonic oscillators of different frequencies has been developed and applied to the quasi-equilibrium theory of mass spectra. The classical approximation previously used in this theory has been shown to be invalid at low energies. The difficulties in the application of the quasi-equilibrium theory of mass spectra are to a great extent resolved by the use of this more reasonable approximation.

A numerical comparison of methhods for computing statistical complexions of harmonic oscillators

“…number of states, W(E), for a collection of harmonic oscillators is one of the most important prerequisites to the computation of the rate constant1,2 of an isolated system. A number of approaches to finding a continuous function for discrete energy level has been proposed in the past few years.1-8 Thiele's formulation has been shown1 23456 to correlate the first few terms with those given by Schlag and Sandsmark7 and by Whitten and Rabinovitch.8 In this study, a numerical comparison is made of exact counting with the classical and semiclassical methods and with the methods of Vestal, et al, 3 Lin, et al,* Haarhoff,6 and Thiele,6 as applied to the molecules of acetylene, cyclopropane, and ¿-butyl chloride.…”

Numbers and densities of vibrational states for the system represented by harmonic oscillators with a cutoff

“…Evaluation of vibrational-energy-level sums and densities is central to the statistical rate theory, and has received great attention in the literature [1][2][3][4][5][6][7][8]. Of course, these quantities are of considerable importance for other phenomena as well [9].…”

A mass spectroscopy experiment

“…A number of statistical or quasi-equilibrium models of the breakup of excited molecules have been proposed at many levels of sophistication (1)(2)(3)(4)(5); the following is based on the Rice-Ramsperger-Kassel theory (6).…”

“…The rate constant for unimolecular decomposition can be expressed as a frequency factor, on the order of vibrational frequencies, multiplied by the expression in eqn. (4).…”