Migration, antarafacial

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. 

In structure (a) the hydrogen orbital overlaps suprafacially with the terminal p orbitals of the n system while in structure (b) the overlap is antarafacially. Therefore the geometry of the two transition systems becomes different. While the suprafacial overlap has a plane of symmetry, the antarafacial migration has two fold axis. 

In acyclic dienes [1, 5] suprafacial nature of hydrogen shift has also been demonstrated. In acyclic 1, 3 diene with a chiral group at one terminal gave two isomers expected from a suprafacial [1, 5] shift but gave neither of isomers that would result from an antarafacial migration. In this reaction chirality is first transferred from one terminal to the other. 

If j is of the form 4n 1, suprafacial migrations are photochemically allowed. For antarafacial migrations, the restrictions are reversed. See also Antarafacial Suprafacial Reactions... 

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. 

More generally, we can say that suprafacial [1J] migrations of carbon in systems where j = An - 1 proceed with inversion thermally and retention photochemically, while systems where j = An + 1 show the opposite behavior. Where antarafacial migrations take place, all these predictions are of course reversed. 

It should be clear that the selection rules apply to concerted processes between spatially accessible parts of a molecule. Antarafacial [1,3], [1,5], or [3,3] reactions involving u-orbital transfers between carbon atoms are not possible. Antarafacial migrations do become feasible when the transition state forms a cycle of at least 7 or 8 atoms Woodward and Hoffmann (1965b) cite the [1,7] example (76). 

The hydrogen atom leaves the top side of the triene and adds back in on the bottom side. Antarafacial migration is allowed and possible. 

For [1,3] and [1,5] shifts, the geometry pretty effectively prevents antarafacial migration. Limiting ourselves, then, to suprafacial migrations, we make these predictions [1,3] migration with inversion [1,5] migration with retention. These predictions have been borne out by experiment. 

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