Mobius systems, allowed

Conrotatory gives a 4-electron Mobius system allowed... 

The rule may then be stated A thermal pericyclic reaction involving a Hiickel system is allowed only if the total number of electrons is 4n + 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 Hiickel systems, the Mdbius-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. 

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 alternate approach of Dewar and Zimmerman can be illustrated by an examination of the 1,3,5-hexatriene system.<81,92> The disrotatory closure has no sign discontinuity (Hiickel system) and has 4n + 2 (where n = 1) ir electrons, so that the transition state for the thermal reaction is aromatic and the reaction is thermally allowed. For the conrotatory closure there is one sign discontinuity (Mobius system) and there are 4u + 2 (n = 1) ir electrons, so that the transition state for the thermal reaction is antiaromatic and forbidden but the transition state for the photochemical reaction is aromatic or allowed (see Chapter 8 and Table 9.8). If we reexamine the butadiene... 

A cyclic array of orbitals is a Mobius system if it has an odd number of phase inversions. For a Mobius system, a transition state with An electrons will be aromatic and thermally allowed, while that with An+ 2 electrons will be antiaromatic and thermally forbidden. For a concerted photochemical reaction, the rules are exactly the opposite to those for the corresponding thermal process. 

Sigmatropic shifts represent another important class of pericyclic reactions to which the Woodward-Hoffmann rules apply. The selection rules for these reactions are best discussed by means of the Dewar-Evans-Zimmerman rules. It is then easy to see that a suprafacial [1,3]-hydrogen shift is forbidden in the ground state but allowed in the excited state, since the transition state is isoelectronic with an antiaromatic 4N-HQckel system (with n = 1), in which the signs of the 4N AOs can be chosen such that all overlaps are positive. The antarafacial reaction, on the other hand, is thermally allowed, inasmuch as the transition state may be considered as a Mobius system with just one change in phase. 

The concepts of frontier orbital HOMO LUMO interactions, the idea of an aromatic transition state, and the alternative concept of conservation of orbital symmetry (not developed in this chapter) all lead to the same result for pericyclic reactions which involve a cyclic overlap of orbitals in the transition slate, thermal reactions are allowed for reactions involving 4n + 2 electrons in Hiickel systems (no change in phase between overlapped orbitals in the cyclic transition state) or for 4/j electrons in Mobius systems (phase between overlapped orbitals in the cyclic transition state changes once on going round the ring). For photochemical systems, these rules are reversed. 

T. S. for [ji4s + jt a] cycloaddition, Mobius system, node, 6 electrons, antiaromatic, bv allowed... 

The FMO analysis is as shown in Figure 15.10 C. The HOMO-LUMO interaction is now favorable and leads naturally to the formation of the two new bonds. Figure 15.10 D shows the aromatic transition state analysis. Using the looped lines, we have designated the full cyclic array of interactions. As shown, there is one node in the system, so this is a Mobius system. Since there are four electrons in the cyclic array, the reaction is allowed. By the generalized orbital symmetry rule, this approach trajectory ([ 2s + is thermally allowed [only the component fits the 4q + 2)s and (4r)a formulas]. In summary, it is incorrect to say that... 

The conventional analysis of carbene additions emphasizes the interaction of the filled carbene orbital with the olefin tt system. This makes the system a four-electron system, and so a non-linear approach should be preferred. The drawings in Figure 15.29 show why this should be so. A linear approach creates a four-electron Hiickel system that is antiaromatic. A non-linear approach creates a four-electron Mobius system, and so it is allowed. 

In the butadiene example, the conrotatory transition state has a Mobius topology, and will be aromatic four electrons are present). Thus, the conrotatory process is allowed. The disrotatory transition state is a Hiickel system, and will require two or six electrons for aromaticity. Since in butadiene only four electrons are present, the disrotation pathway will be forbidden. 

Similarly, for hexatriene, the Mobius and Hiickel topologies are shown in Fig. 8.50. It is clear that in a [b-rr]-electrons system, the Hiickel topology is aromatic and the reaction is symmetry allowed by disrotation cyclization. 

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