Frontier-orbital method

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

This type of orientation of the newly formed bonds is called antarafacial, and the reaction would be a [ 2s + 4a] cycloaddition (a stands for antarafacial). We can easily show by the frontier-orbital method that this reaction (and consequently the reverse ring-opening reactions) are thermally forbidden and photochemically allowed. Thus in order for a reaction to proceed,... 

As applied to these reactions, the frontier-orbital method may be expressed A... 

The highest-energy occupied molecular orbital (HOMO) and the lowest-energy unoccupied molecular orbital (LUMO) of a particular molecular entity. The HOMO can be completely or partially filled whereas the LUMO can be completely or partially vacant. The frontier orbital method allows one to interpret reaction behavior by studying HOMO and LUMO overlaps between reacting entities. 

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. 

As applied to these reactions, the frontier-orbital method may be expressed A cr bond will open in such a way that the resulting p orbitals will have die symmetry of the highest occupied -it orbital of the product. In the case of cyclobutenes, the HOMO of the product in the thermal reaction is the X2 orbital (Figure 18.1). Therefore, in a thermal process, the cyclo-... 

The problem can be resolved by using PMO or frontier orbital methods. In the PMO approach, we compare Reaction (4.1) with three other reactions, Reactions (4.2)-(4.4). 

Kenichi Fukui and Roald Hoffmann won the Nobel prize in 1981 (Woodward died in 1979 and so couldn t share this prize he had already won the Nobel prize in 1965 for his work on synthesis) for the application of orbital symmetry to pericyclic reactions. Theirs is an alternative description to the frontier orbital method we have used and you need to know a little about it. They considered a more fundamental correlation between the symmetry of all the orbitals in the starting materials and all the orbitals in the products. This is rather too complex for our consideration here, and we shall concentrate only on a summary of the conclusions—the Woodward-Hoffmann rules. The most important of these states ... 

In most cases, dienophile addition occurs across the 3- and 6-positions of the 1,2,4-triazine ring as shown in Scheme 56, but acetylenes can also add across the 2- and 5-positions (Scheme 57). The orientations can be explained using the frontier orbital method, or through secondary orbital interactions. 

In all of the above discussion we have assumed that a given molecule forms both the new ct bonds from the same face of the n system. This manner of bond formation, called suprafacial, is certainly most reasonable and almost always takes place. The subscript s is used to designate this geometry, and a normal Diels-Alder reaction would be called a [ 2s + 4J-cycloaddition (the subscript 71 indicates that n electrons are involved in the cycloaddition). However, we can conceive of another approach in which the newly forming bonds of the diene lie on opposite faces of the n system, that is, they point in opposite directions. This type of orientation of the newly formed bonds is called antarafacial, and the reaction would be a [ 2 + 4a]-cycloaddition (a stands for antarafacial). We can easily show by the frontier-orbital method that this reaction (and consequently the reverse ring-opening reactions) are thermally forbidden and photoche-mically allowed. Thus in order for a [fZs + -reaction to proceed, overlap between the highest occupied n orbital of the alkene and the lowest unoccupied 71 orbital of the diene would have to occur as shown in Fig. 15.10, with a + lobe... 

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