And the Mobius-Hiickel method

Both the frontier-orbital and the Mobius-Hiickel methods can also be applied to the cyclohexadiene 1,3,5-triene reaction in either case the predicted result is that for the thermal process, only the disrotatory pathway is allowed, and for the... 

As expected, the Mobius-Hiickel method leads to the same predictions. Here we look at the basis set of orbitals shown in G and H for [1,3] and [1,5] rearrangements, respectively, A [1,3] shift involves four electrons, so an allowed thermal pericyclic reaction must be a Mobius system (p. 1070) with one or an odd number of sign inversions. As can be seen in G, only an antarafacial migration can achieve this. A [1,5] shift, with six electrons, is allowed thermally only when it is a Hiickel system with zero or an even number of sign inversions hence it requires a suprafacial migration. 

The rule may then be stated A thermal pericyclic reaction involving a Huckel system is allowed only if the total number of electrons is4n + 2. A thermal pericyclic reaction involving a Mobius system is allowed only if the total number of electrons is 4n. For photochemical reactions these rules are reversed. Since both the 2 + 4 and 2 + 2 cycloadditions are Huckel systems, the Mobius-Hiickel method predicts that the 2 +4 reaction, with 6 electrons, is thermally allowed, but the 2 + 2 reaction is not. One the other hand, the 2 + 2 reaction is allowed photochemically, while the 2 + 4 reaction is forbidden. 

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. 

Another explanation has been proposed by K. Fukuii on the basis of frontier molecular orbitals (HOMO—LUMO) of the substrates this method is known as the frontier molecular orbitals (FMO) method. Alternatively, the PMO theory based on the Woodward—Hoffmann rule and Hiickel-Mobius method is also used to explain the results of pericyclic reactions. 

Analysis of electrocyclic reactions using a variety of methods and the various conclusions that are drawn. A. FMO theory for ring-opening. The LUMOs of the ir systems are compared to the HOMO of the C-C o bond in cyclobutene and 1,3-cyclohexadiene. B. The Hiickel/Mobius approach. C. Using the generalized orbital symmetry rule. Note, as always, that all the methods predict the same outcome. 

The appropriate correlation diagrams can also be constructed for the Hiickel and Mobius closures in pericyclic processes where the system maintains some symmetry, and the method is capable of extension to include for unsymmetrical systems (Zimmerman, 1966, 1971). The molecular orbital energies of Hiickel- and Mobius-type cyclic polyenes are readily derived from the simple circle mnemonic discussed earlier (see pp. 43 and 55). 

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