Antarafacial migration rearrangement

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. 

A similar analysis of [1,5] sigmatropic rearrangements shows that in this case the thermal reaction must be suprafacial and the photochemical process antarafacial. For the general case, with odd-numbered /, we can say that [1,/] suprafacial migrations are allowed thermally when j is of the form 4n + 1, and photochemically when j has the form An - 1 the opposite is true for antarafacial migrations. 

The degenerate rearrangement of methylenecyclobutane occurs with inversion at C2 and suprafacial migration across one side of the allylie unit. However, the rearrangement is 65% antarafacial with respect to the allylie component.82... 

The rules for [m,n -sigmatropic rearrangements, where m / 1 and n / I, are more complex still. The bond can migrate suprafacially or antarafacially on either component, with the great majority of known reactions being... 

Some other stepwise reactions seeming to disobey the rules, are the 1,2-shifts of ylids, like the Stevens rearrangement 6.107 >6.109. The symmetry-allowed reactions, suprafacial-with-inversion 6.74 or antarafacial-with-retention 6.75, are unreasonable—there is no flexibility for migration across only two atoms, and yet reactions like this take place easily. It is now clear that these reactions are stepwise, taking place by homolytic cleavage 6.107 —> 6.108, followed by rapid radical recombination 6.108 —> 6.109. 

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