Unimolecular reactions Slater theory

Slater N B 1959 Theory of Unimolecular Reactions (Wnaca, NY Cornell University Press)... 

Slater, N. B. Theory of Unimolecular Reactions Cornell University Press Ithaca, NY, 1973. 

Pritchard et al. (1953), using an improved analjdiical technique, were able to study the reaction down to a pressure of less than 0-1 mm (where the rate constant is only 10 % of the high-pressure value). Their results indicated quite clearly that the reaction was unimolecular, and in the pressure region, where the rate constant had decreased appreciably addition of inert gases did lead to an increase in rate. At the same time. Slater (1953) applied his theory of unimolecular reactions to this isomerization. 

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... 

As early as 1939 Slater proposed an alternative approach that related the rate of a unimolecular reaction to the vibrations of the reacting molecule [55]. This theory was developed over the succeeding years, and is explained in Slater s famous 1959 book [56]. The theory is based on the familiar description of molecular vibrations in terms of normal modes [57]. If the vibrations of a molecule are assumed to be harmonic, they can be reduced to a set of independent harmonic... 

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. 

It seems worthwhile to examine critically this transcription of the Slater method into the standard absolute reaction rate theory. In the simple unimolecular bond break, it does appear reasonable that the coordinate q between the tvfo atoms A and B must reach and go beyond a critical extension q0 in order that decomposition takes place. In Slater s calculations account is taken of the different energies involved in stretching q to q0. In regarding q as the mode of decomposition in the transition state method, one must, however, first look at the potential energy surface. The decomposition path involves passage over the lowest possible barrier between reactants and products. It does not seem reasonable to assume that this path necessarily only involves motion of the atoms A and B at the activated complex. Possibly, a more reasonable a priori formulation in a simple decomposition process would be to choose q as the coordinate which tears the two decomposition fragments apart. Such a coordinate would lead roughly to the relation... 

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]. 

An early paper by Sun and Rice considered the relaxation rate of a diatomic molecule in a one-dimensional monatomic chain. An analysis similar to the Slater theoiy of unimolecular reaction was used to obtain the frequency of hard repulsive core-core collisions, and then (in the spirit of the IBC model) this was multiplied by the transition probability per collision from perturbation theory and averaged over the velocity distribution to obtain the population relaxation rate. This was apparently the first prediction that condensed-phase relaxation could occur on a time scale as long as seconds. 

Slater [13] has criticized the RRKM theory, mainly on the grounds that the proposed model assumes that the intramolecular transfer of energy between vibrational degrees of freedom is very rapid compared to the rate of reaction. In fact, all theories of unimolecular reactions, aside from Slater s, involve this particular assumption. Slater assumes that the rate of intramolecular vibrational-energy transfer is very slow. He then performs a normal-mode analysis of the reacting molecule, assuming that reaction occurs when the bond to be broken reaches a certain critical length. A formally correct expression for is obtained, namely. 

Several theories have been developed for the unimolecular reactions. The earliest, proposed by KASSEL, HINSHELWOOD, RICE, and RAMSPERGER /136/, as well as the later theory of SLATER /137/, are based on classical models. The most recent and important theory of MARCUS ans RICE /138/ rests on the semiclassical activated complex theory which makes use of potential energy surfaces. 

N. B.SLATER, "Theory of Unimolecular Reactions",Methuen,London,... 

This paper is widely regarded as the origin of Slater s theory of unimolecular reactions, it seems to me ironic that Polanyi Wigner were so close to a successful formulation of unimolecular reactions, but lacking the necessary theoretical apparatus at that time, they were forced to resort to a mechanical analogy one stage too soon the end result, despite valiant efforts by Noel Slater, is a morass. 

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