Kassels theory

The simple model outlined in the previous section would require that be a linear function of [M] . In fact, such plots of experimental data show marked curvature. The simple scheme fails because the mean time for decomposition of X decreases with its energy. In Kassel s theory [3], the Lindemann scheme is taken to be valid for a small energy range and ft, and fe3 are evaluated as a function of energy. 

Kassel treats a system of s coupled, classical harmonic oscillators. For a non-linear molecule, s = 3n — 6, where n is the number of atoms. 

Consider isomerisation of X to a transition complex X+, which has achieved the critical configuration and is at the point of decomposition. 

When the states are populated statistically, the ratio of the concentrations is just the ratio of the density of states, which may be written down using eqn.(3) 

C 0 is the difference of zero point energy between the transition complex and the reactant molecule X, and e is the excitation energy of X. The reaction coordinate is given no special consideration, remaining as a classical oscillator in the transition complex. However, the energy probability function of a single oscillator is the same as for one-dimensional translation, provided the latter is suitably velocity weighted as it has to be in a rate expression. Therefore, a theory which treats the reaction coordinate as a translational motion yields essentially the same result, as will be seen later. 

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Fig. 9. Log-log plot of the homogeneous unimolecular rate constant vs. pressure in the decomposition of C2F40 at 126°C. The solid lines represent theoretical curves from Kassel theory with 8 and 9 effective oscillators. From Lenzi and Mele106 with permission of the American Institute of Physics.

Rabinovitch et al. (85) studied the reaction of H atoms with trans-ethylene-d2 as a function of ethylene pressure in the temperature range — 78 to 160°C. They were able to account for all secondary reactions of the hot ethyl radicals and to determine the rates of their decomposition (relative to stablization). Simultaneously they calculated the theoretical rates on the basis of the Rice-Ramsperger-Kassel theory of uni-molecular reactions, using expressions derived by Marcus (71), and found a reasonable agreement with the experimental values. Similar satisfactory agreements had been found previously by Rabinovitch and Die-sen (84) for hot sec-butyl radicals. Extensive studies of hot radicals produced by H or D atom additions to various olefins have been carried... 

In the Hinshelwood theory the time lag corresponds to the time taken for the activated molecule to rearrange configuration into the critical configuration of the activated complex. The Kassel theory deals explicitly with this process, and imposes a much more severe restriction than does Hinshelwood. Before an activated molecule can react there must be a flow of energy at least 0 into a... 

The RRK (after Rice, Ramsperger, and Kassel) theory is, like the Slater theory, a model for a unimolecular reaction rather than a faithful representation. The molecule is again represented by a collection of s uncoupled harmonic oscillators, which is an exact representation close to a stationary point on the potential energy surface. One of these... 

When the system is not in thermal equilibrium, the use of thermodynamic relationships like equations (5) and (6) would not be rigorous. However, it has been shown that these equations can be derived from RRK (Rice-Ramsperger-Kassel) theory without assuming thermal equilibrium for the system. Furthermore,... 

The Kassel theory is of course quantized and in essential agreement with the classical model. N. B. Slater, Proc. Roy. Soc. Edinburgh 64, 161 (1955), has given a quantum version with results somewhat different from his classical model. 

The lower activation energy found at these high temperatures was explained by Schott and Davidson in terms of the Rice-Ramsperger-Kassel theory. 

The strong collision correction factor Fsc is a function of two further parameters that arise in Kassel theory (see Section 3). These are the number of effective oscillators, S, and B = Eg/kT, a measure of the relative magnitudes of the threshold energy and thermal energy. Troe used an energy criterion to obtain the number of effective oscillators. 

Rice-Ramsperger-Kassel) theory/ giving activation energies of 1.0-1.5 eV, but entropic effects were not considered in this analysis. 

This chapter is devoted to the presentation of the computational methods used for the determination of the thermodynamic and the kinetic data of the compound considered in this work. We give in a first part a theoretical background of the methods used in the present work Electronic Structure Theory (ah initio, and Density Functional Theory), Statistical Mechanics theory. Group Additivity method, and multifrequency Quantum Rice-Ramsperger-Kassel theory (QRRK). 

RRK theory, also referred as quantum Kassel theory. 

Is best used for representing the pressure dependence of the termolecular reaction rate constant. This equation is based on the curve fitting to the pressure dependence of the unimolecular decomposition rate by the Kassel theory. In Eq. (2.54), is called a broadening factor, and it is a good experimental fitting for many termolecular reactions in atmospheric chemistry has been obtained by taking e.g. Fp = 0.6. The curve (b) in Fig. 2.9 shows the schematic pressure dependence... 

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