The Theory of Unimolecular Reactions

Collisional energy transfer in molecules is a field in itself and is of relevance for kinetic theory (chapter A3.1). gas phase kmetics (chapter A3.4). RRKM theory (chapter A3.12). the theory of unimolecular reactions in general,... 

The theory of unimolecular reactions is that the specific rate, k, depends on the pressure as... 

The quasi-equilibrium theory (QET) of mass spectra is a theoretical approach to describe the unimolecular decompositions of ions and hence their mass spectra. [12-14,14] QET has been developed as an adaptation of Rice-Ramsperger-Marcus-Kassel (RRKM) theory to fit the conditions of mass spectrometry and it represents a landmark in the theory of mass spectra. [11] In the mass spectrometer almost all processes occur under high vacuum conditions, i.e., in the highly diluted gas phase, and one has to become aware of the differences to chemical reactions in the condensed phase as they are usually carried out in the laboratory. [15,16] Consequently, bimolecular reactions are rare and the chemistry in a mass spectrometer is rather the chemistry of isolated ions in the gas phase. Isolated ions are not in thermal equilibrium with their surroundings as assumed by RRKM theory. Instead, to be isolated in the gas phase means for an ion that it may only internally redistribute energy and that it may only undergo unimolecular reactions such as isomerization or dissociation. This is why the theory of unimolecular reactions plays an important role in mass spectrometry. 

Thus transition-state theory provides a relatively straightforward way of estimating Aoo if it is unavailable from experiment. The next section treats the theory of unimolecular reactions, and in particular, their pressure dependence, much more rigorously. 

Rice, Ramsperger, and Kassel [206,333,334] developed further refinements in the theory of unimolecular reactions in what is known as RRK theory. Kassel extended the model to account for quantum effects [207] this treatment is known as QRRK theory. 

The theory of unimolecular reactions was at first based upon very scanty data and, until more experimental evidence was forthcoming, discussion of the mechanism tended to be a little unsatisfactory and inconclusive. The great theoretical interest of these changes will be made evident if we consider in turn the various theories about them which have been current. 

It is the existence of this time lag between activation by collision and reaction which is basic and crucial to the theory of unimolecular reactions, and this assumption leads inevitably to first order kinetics at high pressures, and second order kinetics at low pressures. 

Note The Lindemann mechanism was also suggested independently by Christiansen. Hence, it is also sometimes referred to as the Lindemann-Christiansen mechanism. The theory of unimolecular reactions was further developed by Hinshelwood and refined by Rice, Rampsberger, Kassel and Marcus. 

W. Forst, The Theory of Unimolecular Reactions, Academic, New York, 1973. 

This reaction almost certainly occurs in an elementary manner, and it therefore represents one of the simplest of all unimolecular reactions. As will be discussed later, it has been carefully studied over a wide range of temperatures and pressures, and has played an important part in the testing of the theories of unimolecular reactions. 

Role of computational chemistry in the theory of unimolecular reaction rates... 

Chapter 15 - Role of computational chemistry in the theory of unimolecular reaction rates. Pages 397-423, William L. Hase and Reinhard Schinke... 

This paper deals with some aspects of the theory of photochemical reactions, and necessarily makes contact with the theory of unimolecular reactions and the theory of energy transfer. The indirect influence of Henry Eyring s work is manifest in much of what follows since, in part, we are concerned with the validity of the usual concepts of unimolecular reaction rate theory. 

These high collision efficiencies have some interesting consequences for the theory of unimolecular reactions. In particular, they imply that the preferred path for fission reactions involve appreciable storage of internal energy in two rotational modes (5). For pyrolysis reactions, they suggest that atom-atom recombination will usually contribute very little to over-all recombination relative to atom-radical or radical-radical reactions. The reason is that the atom-atom recombination is third order. 

Almost as old as quantitative, gas-phase kinetics is the appreciation of the fact that not all rate constants are well behaved. From the theory of unimolecular reactions it is possible to conclude that at sufficiently high temperatures, all gas-phase, unimolecular rate constants tend to depart from Arrhenius-like behavior and become pressure dependent. If these reactions correspond to fission into two fragments, there is a corollary of this high temperature behavior for the reverse, association reaction of these two fragments. The second-order association reaction also becomes pressure dependent (Le., the association tend towards third order) and can have an appreciable negative activation energy. 

As will be discussed in chapter 6, of fundamental importance in the theory of unimolecular reactions is the concept of a microcanonical ensemble, for which every zero-order state within an energy interval AE is populated with an equal probability. Thus, it is relevant to know the time required for an initially prepared zero-order state j) to relax to a microcanonical ensemble. Because of low resolution and/or a large number of states coupled to i), an experimental absorption spectrum may have a Lorentzian-like band envelope. However, as discussed in the preceding sections, this does not necessarily mean that all zero-order states are coupled to r) within the time scale given by the line width. Thus, it is somewhat unfortunate that the observation of a Lorentzian band envelope is called the statistical limit. In general, one expects a hierarchy of couplings between the zero-order states and it may be exceedingly difficult to identify from an absorption spectrum the time required for IVR to form a micro-canonical ensemble. 

The partition function and the sum or density of states are functions which are to statistical mechanics what the wave function is to quantum mechanics. Once they are known, all of the thermodynamic quantities of interest can be calculated. It is instructive to compare these two functions because they are closely related. Both provide a measure of the number of states in a system. The partition function is a quantity that is appropriate for thermal systems at a given temperature (canonical ensemble), whereas the sum and density of states are equivalent functions for systems at constant energy (microcanonical ensemble). In order to lay the groundwork for an understanding of these two functions as well as a number of other topics in the theory of unimolecular reactions, it is essential to review some basic ideas from classical and quantum statistical mechanics. 

CH3NC — CH3CN has also been carried out, the principal object being the interpretation of the transition state. This particular tautomerism has also been the subject of an investigation in which experiments have been made to assess the importance of radical chain effects in the thermally induced reaction. It is concluded that there is no reason to doubt the fact that the isomerization of methyl isocyanide is an excellent test for the theory of unimolecular reactions. 

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