Mobius systems, allowed reactions

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. 

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... 

How do we rationalize this allowed reaction Both FMO and aromatic transition state theory are easy to apply. As shown below, the extra node in the d orbital used in the alkylidene it bond allows the HOMO of the M=Cbond to interact with the UJMOoftheC=C bond constructively. Similarly, the extra node in the d orbital makes the four-electron system Mobius (remember we do not count nodes in the atomic orbitals themselves), and therefore allowed. 

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. 

An alternative analysis of sigmatropic reactions involves drawing the basis set atomic orbitals and classifying the resulting system as Htickel or Mobius in character. When this classification has been done, the electrons involved in the process are counted to determine if the TS is aromatic or antiaromatic. The conclusions reached are the same as for the frontier orbital approach. The suprafacial 1,3-shift of hydrogen is forbidden but the suprafacial 1,5-shift is allowed. Analysis of a 1,7-shift of hydrogen shows that the antarafacial shift is allowed. This analysis is illustrated in Figure 10.31. These conclusions based on orbital symmetry considerations are supported by HF/6-31G calculations, which conclude that 1,5-shifts should be suprafacial, whereas... 

Similarly, we can analyze the hexatriene-cyclohexadiene system having (4n + 2) 7T-electrons (Figure 2.10). In this case, a disrotatory mode of ring closure leads to a Hiickel array, which is aromatic with (4n + 2) rr-electrons. Therefore, the disrotatory mode of reaction now becomes thermally allowed. However, a conrotatory mode of ring closure uses a Mobius array, which is antiaromatic with (4n + 2) 7r-electrons. Therefore, the reaction is thermally forbidden in this mode. 

In case of [tt s + tu s] cycloaddition (4n 7r-electron system), a supra—supra mode of addition leads to a Huckel array, which is antiaromatic with 4n 7u-electrons (Figure 4.7). Therefore, the supra—supra mode of reaction is thermally forbidden and photochemically allowed. However, a supra—antara mode of addition uses a Mobius array, which is aromatic with 4n 7t-electrons. Therefore, [rt s + rc a] cycloaddition reaction is thermally allowed and photochemically forbidden. Similarly, we can analyze the [tu" s + Tt s] cycloaddition having (4n + 2) 7t-electrons (Figure 4.7). In this case, a supra—supra mode of addition leads to a Huckel array, which is aromatic with (4n + 2) 7C-electrons. Therefore, [7t" s + tu s] cycloaddition reaction now becomes thermally allowed and photochemically forbidden. However, a Itch s + Tu a] cycloaddition uses a Mobius array, which is antiaromatic with (4n + 2) 7u-electrons. Therefore, the reaction is thermally forbidden and photochemically allowed in this mode. 

The idea that transition states can be of Mobius type, in which the relative stability of AN- and 4A- -2-electron systems is reversed, was developed and systematized by Zimmerman [33], who derived the Woodward-Hoffmann Rules for the various thermo-rearrangements in terms of the Hiickel or Mobius nature of their transition states. As shown in (a) and (b) of Fig. 1.4, a cycloaddition in which one of the reaction partners reacts suprafacially and the other antarafacially mimics a Mobius surface, so [t 2s +7r2a]-cycloaddition is allowed whereas reaction along the [ Aa pathway is forbidden, as is the... 

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