Slater Theory

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. 

N. B. Slater, Theory of Vnimolecular Reactions, Methuen, London, 1959, p. 186. 

But it was not really until 1931, when Slater and Pauling independently developed methods to explain directed chemical valence by orbital orientation that it can truly be said that a chemical quantum mechanics, rather than an application of quantum mechanics to chemistry, had been created. In a study of Slater, S. S. Schweber notes the distinction between the Heitler-London-Pauling-Slater theory and the Heitler-London theory. Heitler and London successfully explained the electron-valence pair on the basis of the Goudsmit-Uhlenbeck theory of spin. Slater and Pauling explained the carbon tetrahedron. This second explanation distinguishes quantum chemistry from quantum physics.2... 

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. 

N.B. Slater, Theory of Unimolecular Reactions (Cornell University Press, Ithaca, NY 1959) K.J. Laidler, op. cit. 

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. 

Figure 5. Lindemann plot for the dissociation of cyclobutane at 722 K, compared with the predictions of RRK theory and Slater theory with strong collisions.

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. 

N. B. Slater, Proc. Cambridge Phil. Soc., 35 (1939) 56 and many subsequent papers for a general account see N. B. Slater, Theory of Unimolecular Reactions, Cornell Univ. Press, Ithaca, N. Y., 1959. 

Experimental studies have had an enormous impact on the development of unimolecular rate theory. A set of classical thermal unimolecular dissociation reactions by Rabinovitch and co-workers [6-10], and chemical activation experiments by Rabinovitch and others [11-14], illustrated that the separability and symmetry of normal modes assumed by Slater theory is inconsistent with experiments. Eor many molecules and experimental conditions, RRKM theory is a substantially more accurate model for the unimolecular rate constant. Chemical activation experiments at high pressures [15,16] also provided information regarding the rate of vibrational energy flow within molecules. Experiments [17,18] for which molecules are vibrationally excited by overtone excitation of a local mode (e.g. C-H or O-H bond) gave results consistent with the chemical activation experiments and in overall good agreement with RRKM theory [19]. 

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