Pericyclic reaction general selection rule

Having described by means of correlation diagrams the nature of forbidden and allowed reactions of two particular pericyclic types, we wish to develop a notation that will permit us to state a generalized selection rule summarizing the conclusions of the pericyclic theory. 

The application of the general selection rule does not require analyzing a concerted reaction in any particular way. All descriptions of a pericyclic reaction that predict the same stereochemistry in the product will lead to the same conclusion. For example, three descriptions of the Diels-Alder reaction are given in Figure 11.88. In Figure 11.88(a), the reaction is described as a [ 2j + 4J cycloaddition. In this process there is one (4n - - 2)g component and no (4r)a component, so the total (1) is an odd number, and the reaction is allowed. In Figure 11.88(b), each double bond of the diene is considered to be a separate unit, so the reaction is described as a - - 2 -I- 2j process. 

The so-called aromaticity rules are chosen for comparison, as they provide a beautiful correspondence with the symmetry-based Woodward-Hoffmann rules. A detailed analysis [92] showed the equivalence of the generalized Woodward-Hoffmann selection rules and the aromaticity-based selection rules for pericyclic reactions. Zimmermann [93] and Dewar [94] have made especially important contributions in this field. 

The selection rules for cycloadditions (Table 11.1) apply to pericyclic reactions described as cycloadditions, but the rules may be generalized concise form as follows " ... 

It should be noted that the avoided crossing depicted in Fig. 1.23c does not do away with the crossing of the frontier orbitals (Fig. 1.23a). In general, all the foregoing discussion of nonadiabatic transitions concerns the electron states (terms) rather than the orbitals. Fruitfulness of an analysis of the correspondence between the electron states of the reactants and the products was vividly demonstrated by Longuet-Higgins and Abrahamson [129] who developed the most general rules of selection of symmetry-allowed pericyclic reactions. Furthermore, this correspondence served as the basis for a new quite rational classification of the photochemical reactions [127]. 

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