The Slater Theory

The average number of times per unit time that the combination of sine waves, calculated for the summed normal modes, exceeds the critical extension can be found, and this gives a value for the first order high pressure rate constant. 

Slater s theory assumes that the normal modes behave as harmonic oscillators, which requires that there be no flow of energy between the normal modes once the molecule is suitably activated, and so the energy distribution remains fixed between collisions. But spectroscopy shows that energy can flow around a molecule, and allowing for such a flow between collisions vastly improves the theory. Like Kassel s theory a fully quantum theory would be superior. 

The equation for the high pressure rate constant predicts strict Arrhenius behaviour, and also a non-linear plot for l/kobs versus 1/[A], both in agreement with experiment. 

However, the beauty of Slater s theory is that it gives a very clear description of the process of reaction, which is easy to visualize that is, the molecule splits up if some bond(s), bond angle(s) or a combination of both is extended too far . 

Laidler K.J. and Meiser J.H., Physical Chemistry, 3rd edn, Houghton Mifflin, New York, 1999. 

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For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. 

The Slater theory starts initially from the earlier treatments of Hinshel-wood and Lindemann. It provides a d5Tiamic representation of how a molecule with sufficient energy reaches the configuration of the activated complex. The model treats all oscillators as simple harmonic. 

Elements of classical dynamics of unimolecular reactions in particular, the Slater theory for indirect reactions, where the molecule is modeled as a set of uncoupled harmonic oscillators. Reaction is defined to occur when a particular bond length attains a critical value, and the rate constant is given as the frequency with which this occurs. 

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... 

In the case of dimethyl malcate the rate was observed to fall off with pressures near 100 mm Hg, and a side reaction in which CO2 was evolved also took place. The region of pressure fall-off together with the low frocpiency factor is in dirc( t contradiction to the Slater theory or any reasonable variant. It is the feeling of the author that these are chain sensitized reactions. 

The fall-off in k could be fitted to the rrk equation with s = 23, and it was again concluded that the results were inconsistent with the Slater theory. 

For a decade, a rival theory due to Slater (1955, 1959) provided considerable motivation for more detailed experimental as well as theoretical investigations. This, very interesting and elegant theory, which is discussed in more detail by Robinson and Holbrook (1972) and Nikitin (1974), as well as in chapter 8, is more akin to a dynamical than a statistical theory. Because the Slater theory treats the vibrations classically, it also requires the use of fewer oscillators to fit the experiment (sec fig. 1.1). Its flawed fundamental hypothesis that the molecule s modes were strictly harmonic, thereby preventing energy flow among them, and its failure to account quantitatively for the experimentally measured rates led to its being quickly overshadowed by the successes of the RRKM/QET theory. 

By the end of 1972, a second cornerstone of the transition state approach was beginning to crumble significantly, for it was now quite evident that widely different transition states could be assumed for a given reaction, but the Rice-Ramsperger-Kassel-Marcus (RRKM) procedure would give the same result for the shape of the fall-off curve [72.N 72.R 74.F 79.A1]. This, as is now well known, arises through the adjustment of the model after the transition state has been chosen so as to force it to be consistent with the observed high pressure rate constant [72.R 80.P1], Perhaps it should have sounded the knell for the RRKM theory, much as the unsymmetric isotopic replacement experiments did for the Slater theory a decade earlier, but there was no other substitute available. 

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