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Some fundamental aspects of sigmatropic shifts a re discussed with the help of INDO calculations and perturbation theory. In cyclic systems the degeneracy of the highest occupied molecular orbital is lifted in the transition state. A suprafacial H shift is determined by a combination of the Is orbital of the migrating hydrogen with the symmetric MO’s of the system and an antarafacial shift by a combination with the antisymmetric MO’s. The used perturbation model offers the possibility to reconcile somewhat the concepts of “allowed” and “forbidden”. Formally forbidden reactions which, however, have been found experimentally can be explained with this model. Many “forbidden” reactions are in fact “allowed”, but they proceed with a higher activation enthalpy. Some transition state geometries have been calculated and the occurring charge transfer is explained in terms of aromaticity. In 1965 Woodward and Hoffmann postulated their concept of orbital symmetry rules governing pericyclic reactions.’ In the particular case of sigmatropic reactions, the transition state is thought to be determined by the migrating group and the HOMO or LUMO of the radical-like species left behind, after splitting off the migrating group in thermal and photochemical rearrangements, respectively. In principle, the symmetry properties of the HOMO or LUMO were considered for acyclic polyenes. The major part of the experimental work reported in the last ten years is in agreement with the predictions. Curiously enough, this applied also to a host of cyclic systems. Whereas the description of acyclic systems is relatively straightforward, cyclic systems have, so far, defied a truly general explanation. The major problem has been the fact that in these systems all but the lowest molecular orbitals are doubly degenerate in the transition state. In 1968 Anastassiou tried to work out the degeneracy problem in C,H,+, monocycles.* It was postulated that the presence of the migrating group will disturb the symmetry of the radical, thereby lifting the degeneracy. It was then concluded that the migrating group will combine with the “genuine” HOMO again. In our opinion, however, the real perturbation is formed by a hydrogen nucleus in the transition state in contrast with Anastassiou’s approach in which the perturbation was applied to the reactant. This leads to an entirely different result (see also next section). There are no compelling reasons to confine the discussion to the HOMO, as already suggested by Berson3 and, in a more elaborate way, by Anh4 and F u k ~ i , ~ who worked out the application of perturbation theory to pericyclic rearrangements. The implications of this method have, so far, not been discussed in detail for sigmatropic rearrangements. In general, the nomenclature and selection rules derived for acyclic systems are used without modifications for cyclic polyenes as well. Here we wish to present evidence that simple perturbation theory allows one to predict several aspects of [ l j ] rearrangements in simple systems in a relatively simple fashion. The results are substantiated by INDO calculations. Before specific examples are discussed, it should be realized that a migrating hydrogen, involved in a suprafacial shift, will have to interact with symmetric molecular orbitals. On the other hand, in antarafacial rearrangements the interaction necessarily originates from combination with asymmetric orbitals. Journal of the American Chemical Society / 99.2 / January 19, 1977

Thermal sigmatropic [1,j] shifts in cyclic systems. A perturbation approach and INDO calculations