Degenerate reactions

In this article we consider problems concerning the interpretation of unsaturated, steady-state NMR spectra of spin systems which are in a state of dynamic equilibrium. Spin exchange processes may occur with frequencies between a few sec-1 and several thousand sec-1 and thus modify the spectral lineshapes. In this case we use the terms dynamic NMR and dynamic spectra. The analysis of dynamic NMR lineshapes constitutes an important, and often unique, source of information about intra- and inter-molecular reaction rates. This is especially true for degenerate reactions where the products are chemically identical with the substrates. For this and similar reasons, dynamic NMR analysis has attracted considerable attention for about twenty years. 

Let us consider a system of substances Ai i = 1, 2,..., S, which undergo fi different reactions. A reaction will be understood here as a one-way process for the formation of certain products and the disappearance of certain substrates. We take into account also degenerate reactions, e.g. intramolecular rearrangements which preserve the chemical identity of the reagents involved. The reactions are numbered by subscripts a, belonging to the set 1, 2,..., Q. For any reaction a, there is exactly one opposite reaction, that denoted by the subscript co(cr), where the co function has the property ... 

Most systematic studies on gas-phase SN2 reactions have been carried out with methyl halides, substrates which are free of complications due to competing elimination. Application of the Marcus rate-equilibrium formalism to the double-minimum potential energy surface led to the development of a model for intrinsic nucleophilicity in S 2 reactions233. The key quantities in this model are the central energy barriers, Eq, to degenerate reactions, like the one of equation 22, which are free of a thermodynamic driving force. 

Carbon shifts 228 U-, 1,3-, 1,4- and 1,5-Hydride shifts 229 Homoallylic-, cyclopropylcarbinyl- and homocyclopropylcarbinyl rearrangements 230 Other degenerate reactions 231... 

Degenerate reactions regarded as a series of irreversible processes 242... 

Carbon scrambling has also been observed in the cyclopentyl cation and a possible intermediate or transition state in this degenerate reaction is [22],... 

DEGENERATE REACTIONS REGARDED AS A SERIES OF IRREVERSIBLE PROCESSES... 

A degenerate reaction is a special case of a reversible reaction (A B) in... 

This way of regarding reversible processes has been used to improve the theory of chromatography (Gut and Ahlberg, 1981) and should be particularly useful in the study of degenerate reactions on the ordinary time scale rather than on the nmr time scale by e.g. using multiply-labelled compounds (Rappoport, private communication). 

In the present review only some of the more recent results on the 2-nor-bornyl cation will be treated and examples of the different types of degenerate reactions will be given. 

So far, only degenerate reaction networks have been considered, where reactants of, say, type A, react irreversibly (or, within rather strict specifications, re-... 

Decarboxylation of p-lactones described above may be considered a degenerate reaction of this type. Another example is the loss of CO from certain ketones ... 

A table was prepared to confirm above theory or to foresee the directions of degeneration reactions (Table 1). In the table, materials are arranged in the order of their solubilities. 

Table 1. Table for foreseeing degeneration reaction at 30°C with two materials in a solid mixture... 

A few examples of foreseeing the degeneration reactions are presented from Table 1. 

In this case the reaction proceeds in the same way as the reaction (1) This is an ordinary reaction which follows the minimum solubility law. (In this reaction the volume of the right side mixture increases five percent from the left. Therefore, it is better to use the ammonium dichromate in place of the potassium dichromate to avoid cracking of stars during the store.) However, when using dichromates, they often create acid. The values of solubility of materials in acid are not always clear. In such cases, the direction of degeneration reaction must be experimentally confirmed. Examples are shown as follows (... 

In contrast, for the case of a non-degenerate reaction where A represents the dominant form and B the dominant intermediate it has been shown [19b] that... 

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