Correlation diagrams, pericyclic reaction analysis

The following sections present an empirical approach to applying the selection rules. The chapter continues with a basic introduction to the analysis of symmetry properties of orbitals and the application of orbital correlation diagrams to the relatively simply cyclobutene-butadiene interconversion it concludes with some examples of the frontier orbital approach to pericyclic reactions. 

The photochemistry of alkenes, dienes, and conjugated polyenes in relation to orbital symmetry relationships has been the subject of extensive experimental and theoretical studyThe analysis of concerted pericyclic reactions by the principles of orbital symmetry leads to a complementary relationship between photochemical and thermal reactions. A process that is forbidden thermally is allowed photochemically and vice versa. The complementary relationship between thermal and photochemical reactions can be illustrated by considering some of the reaction types discussed in Chapter 10 and applying orbital symmetry considerations to the photochemical mode of reaction. The case of [2Tr- -2Tr] cycloaddition of two alkenes, which was classified as a forbidden thermal reaction (see Section 10.1), can serve as an example. The correlation diagram (Figure 12.17) shows that the ground state molecules would lead to a doubly excited state of cyclobutane, and would therefore involve a prohibitive thermal activation energy. 

Although it is more fruitful to construct a correlation diagram for the detailed analysis of a pericyclic reaction, there is, nevertheless, an altemative method that also enables us to reach similar conclusions. It is an easy and extremely simple approach that is based on the interaction of the frontier orbitals, i.e., the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the components that are involved in a pericyclic reaction. 

This is a very powerful rule, and it is especially useful when there are several components to a pericyclic reaction. With several components it is often difficult to identify the appropriate HOMOs and LUMOs for an FMO analysis, and difficult to quickly write an orbital or state correlation diagram. In such cases, aromatic transition state theory, or the generalized orbital symmetry rule, are the easiest approaches for analyzing the reaction. It is your decision as to which works best for you. 

While photocycloadditions are typically not concerted, pericyclic processes, our analysis of the thermal [2+2] reaction from Chapter 15 is instructive. Recall that suprafacial-suprafacial [2+2] cycloaddition reactions are thermally forbidden. Such reactions typically lead to an avoided crossing in the state correlation diagram, and that presents a perfect situation for funnel formation. This can be seen in Figure 16.17, where a portion of Figure 15.4 is reproduced using the symmetry and state definitions explained in detail in Section 15.2.2. The barrier to the thermal process is substantial, but the first excited state has a surface that comes close to the thermal barrier. At this point a funnel will form allowing the photochemical process to proceed. It is for this reason that reactions that are thermally forbidden are often efficient photochemical processes. It is debatable, however, whether to consider the [2+2] photochemical reactions orbital symmetry "allowed". Rather, the thermal forbiddenness tends to produce energy surface features that are conducive to efficient photochemical processes. As we will see below, even systems that could react via a photochemically "allowed" concerted pathway, often choose a stepwise mechanism instead. 

From the foregoing discussion it appears that the frontier orbital method is at once a simple, concise, and accurate method for assessing the stereochemical outcome of pericyclic reactions. Furthermore, it is a method that is equally applicable to symmetrical and to unsymmetrical systems. There are some disadvantages in the theory, however. Firstly, it is necessary to derive the general phase characteristics of the HOMO and LUMO levels. Hiickel molecular calculations can be used for tliis purpose, but there are available a number of approximate methods, for example the electron-in-a-box model, which are usually satisfactory even if they are more difficult to apply to more complex systems. Nevertheless, frontier orbital analysis is quicker and more simple than the formalized correlation diagram approach, and with a little practice one can intuitively arrive at the correct relative phase relationsliips in the HOMO and LUMO levels. 

In summary, the PMO method when extended to photochemical reactions of the G-type predicts a reversal of aromatic properties from ground state to excited state. This justifies the set of rules for photochemical pericyclic reactions given above. Dougherty s analysis also reveals dangers in the use of orbital and state correlation diagrams for assessing photo-pericyclic reactions because the breakdown in the BO approximation leads to a destruction of symmetry. 

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