Frontier orbital correlation diagrams

Figure 7. Frontier orbital correlation diagram for the Mn + Oj --> MnO + O2 reaction. Adapted from Ref. [40].

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

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. 

Most of the theoretical methods used to correlate chemical reactivity trends implicitly (or in some cases explicitly) use a model of interacting diabatic surfaces in which the transition structure is associated with an avoided crossing of a reactant-like or a product-like diabatic surface. In the molecular-orbital correlation diagram approach of Woodward and Hoffmann or the frontier orbital method of Fukui, the molecular orbitals of the fragments are first mixed to form the MO of the supermolecule and then the electrons are assigned to various configurations of these supermolecule MO. We shall refer... 

The Woodward-Hoffmann mles for cycloaddition reactions can be explained from frontier orbital interactions, orbital correlation diagram and aromatic transition... 

A more complete analysis of interacting molecules would examine all of the involved MOs in a similar wty. A correlation diagram would be constructed to determine which reactant orbital is transformed into wfiich product orbital. Reactions which permit smooth transformation of the reactant orbitals to product orbitals without intervention of high-energy transition states or intermediates can be identified in this way. If no such transformation is possible, a much higher activation energy is likely since the absence of a smooth transformation implies that bonds must be broken before they can be reformed. This treatment is more complete than the frontier orbital treatment because it focuses attention not only on the reactants but also on the products. We will describe this method of analysis in more detail in Chapter 11. The qualitative approach that has been described here is a useful and simple wty to apply MO theory to reactivity problems, and we will employ it in subsequent chapters to problems in reactivity that are best described in MO terms. I... 

Application to the Construction of Frontier Orbitals and to Correlation Diagrams... 

Thus, the frontier-orbital and Hiickel-Mobius methods (and the correlation-diagram method as well) lead to the same conclusions thermal 2 + 4 cycloadditions and photochemical 2 + 2 cycloadditions (and the reverse ring openings) are allowed, while photochemical 2 + 4 and thermal 2 + 2 ring closings (and openings) are forbidden. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

Three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

The Woodward-Hoffmann rules arise fundamentally from the conservation of orbital symmetry seen in the correlation diagrams. These powerful constraints govern which pericyclic reactions can take place and with what stereochemistry. As we have seen, frontier orbital interactions are consistent with these features,... 

The frontier orbital approach leads to the same predictions as those based on an analysis of correlation diagrams, but instead of considering all of the orbitals of the tt system, only the frontier orbitals, the HOMOs and LUMOs are considered. A general discussion of frontier orbital theory is given in Fukui, K. Acc. Chem. Res. 1971, 57-64. The choice of which HOMOs and LUMOs to combine requires an analysis that we will not undertake here. We will simply show that when these orbitals are combined, we can rationalize reactions observed experimentally in terms of the orbitals derived from this type of analysis. 

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