Transition Mobius

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

FIGURE 15.6 Transition states illustrating Huckel-Mobius rules for cycloaddition reactions. 

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... 

Using the nomenclature of Dewar and Zimmerman, the transition state for the 2, + 2S cycloaddition is a 4n Hiickel system (zero nodes) and is antiaromatic in the ground state and aromatic in the excited state. The transition state for the 2S + 20 cycloaddition is a 4n Mobius system (one node) and is aromatic in the ground state and antiaromatic in the excited state (see Chapter 8). The general cycloaddition rules are given in Table 9.5. 

The transition state in suprafacial attack is designated as of Huckel type in which no sign inversion of the cycle has taken place. The other type of migration involves one sign inversion. This is called mobius type inversion. The Huckel type of inversion occurs when the total number of electrons is 2, 6,. .., (4n + 2). This is also called aromatic transition state. In mobius type the participating electrons is 4, 8,. .. i.e. An. 

While the initial formulation of homoaromaticity pre-dated the introduction of orbital symmetry by some eight years33, the two concepts are inextricably linked34. This is most evident when pericyclic reactions are considered from the perspective of aromatic or antiaromatic transitions states35 and the Huckel/Mobius concept31. The inter-relationship can be demonstrated by the electrocyclic reaction shown in Scheme 136. 

The closed and open forms, 4 and 5, respectively, represent the formal starting and end points of an electrocyclic reaction. In terms of this pericyclic reaction, the transition state 6 can be analysed with respect to its configurational and electronic properties as either a stabilized or destabilized Huckel or Mobius transition state. Where 4 and 5 are linked by a thermally allowed disrotatory process, then 6 will have a Hiickel-type configuration. Where the process involves (4q + 2) electrons, the electrocyclic reaction is thermally allowed and 6 can be considered to be homoaromatic. In those instances where the 4/5 interconversion is a 4q process, then 6 is formally an homoantiaromatic molecule or ion. 

The relevance of all this may seem tenuous, especially because no example of a simple cyclic polyene with a Mobius 7r system is known. However, the Mobius arrangement is relevant to cycloaddition because we can conceive of alkenes, alkadienes, and so on approaching each other to produce Mobius transition states when An electrons are involved. 

For example, consider two molecules of ethene, which we showed previously would violate the An + 2 rule by undergoing cycloaddition through a transition state represented by 37. There is an alternative transition state, 38, in which the four p orbitals come together in the Mobius arrangement (with one node for minimum energy). 

A much less strained Mobius [4 + 4] transition state can be formed from two s-cis molecules of 1,3-butadiene. When 1,3-butadiene is heated by itself, a few percent of 1,5-cyclooctadiene is formed, but it is not known for sure whether the mechanism is that shown ... 

How can we account for the stereoselectivity of thermal electrocyclic reactions Our problem is to understand why it is that concerted 4n electro-cyclic rearrangements are conrotatory, whereas the corresponding 4n + 2 processes are disrotatory. From what has been said previously, we can expect that the conrotatory processes are related to the Mobius molecular orbitals and the disrotatory processes are related to Hiickel molecular orbitals. Let us see why this is so. Consider the electrocyclic interconversion of a 1,3-diene and a cyclobutene. In this case, the Hiickel transition state one having an... 

In contrast, the Mobius transition state (one having an odd number of nodes) is formed by conrotation and is favorable with four An) electrons ... 

The factors that control if and how these cyclization and rearrangement reactions occur in a concerted manner can be understood from the aromaticity or lack of aromaticity achieved in their cyclic transition states. For a concerted pericyclic reaction to be thermally favorable, the transition state must involve An + 2 participating electrons if it is a Hiickel orbital system, or 4 electrons if it is a Mobius orbital system. A Hiickel transition state is one in which the cyclic array of participating orbitals has no nodes (or an even number) and a Mobius transition state has an odd number of nodes. 

The second step is to determine whether the transition states are Hiickel or Mobius from the number of nodes. This is readily done by assigning signs to the lobes of the orbitals corresponding to their phases and counting the number of nodes that develop in the circle of overlapping orbitals. An odd number denotes a Mobius transition state, whereas an even number, including zero, denotes a Hiickel transition state. 

We have not given you much evidence to decide why it is that some thermal [2 + 2] cycloadditions occur but not others. What is special about fluoroalkenes, allenes, and ketenes in these reactions One possibility is that Mobius rather than the Hiickel transition states are involved, but the Mobius transition states are expected to suffer from steric hindrance (Section 21-10B). It is also possible that [2 + 2] cycloadditions, unlike the Diels-Alder additions, proceed by stepwise mechanisms. This possibility is strongly supported by the fact that these reactions generally are not stereospecific. Thus with tetrafluoroethene and trans,trans-2,5-bexadiene two products are formed, which differ in that the 1-propenyl group is trans to the methyl group in one adduct, 45, and cis in the other, 46 ... 

Use the procedure of Section 21-1 OF to set up transition-state orbitals and determine whether these lead to a favored Huckel or a favored Mobius transition state for the following processes ... 

Mobius transition state (achieved by conrotation), whereas the photochemical reaction is most favorable with a Hiickel transition state (achieved by disrotation). 

Figure 7 Orbital correlation diagram for the antarafacial [1,3] shift of a proton in propene. The transition-state orbitals are based on the orbitals of Mobius cyclobutadiene (see text)...

Day21 has given a careful account of the relationship between the Woodward-Hoffmann rules and Mobius/Hiickel aromaticity, and has defined the terms supra-facial and antarafacial in terms of the nodal structure of the atomic basis functions. His approach makes quite explicit the assumption that the transition state involves a cyclic array of basis functions. Thus the interconversion of prismane (10) and benzene, apparently an allowed (n2s+ 2S+ 2S) process, is in fact forbidden because there are additional unfavourable overlaps across the ring.2... 

DFT investigation of the eight-electron electrocyclization reactions of 1,8-disubsti-tuted (3Z,5Z)-octa-l,3,5,7-tetraenes has found that these reactions proceed via a Mobius helical aromatic transition state. It was also found that outward substituents were preferred to inward ones, regardless of the electronic nature of the substituents, and that torquoelectronic effects are overridden by secondary orbital, electrostatic,... 

Independent interpretation of mass spectroscopic data by Wolovsky 66> and Ben-Efraim, Batich, and Wasserman 6 ) indicate that cyclic olefins subjected to disproportionation conditions form interlocking rings (catenanes) as well as cyclopolyolefins. The proposed scheme involves four-center transition state and Mobius-Strip approach... 

Overbeck, G. A. Honig, D. Mobius, D. Visualization of first and second order phase transitions m eicosanol monolayers using Brewster angle microscopy. Langmuir 1993, 9, 555. 

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. 

To explain the increase in the rate of the cyclobutene opening 6.292 —> 6.293, we need to remember that the conrotatory pathway will have a Mobius-like aromatic transition structure, not the anti-aromatic Hiickel cyclobutadiene that we saw in Fig. 1.38. We have not seen the energies for this system expressed in 8 terms, nor can we do it easily here, but the numbers are in Fig. 6.42, where we can see that a... 

Evans-Dewar-Zimmerman criterion. In accordance with this criterion the pericyclic reactions proceed through the cyclic transition state of the Htickel topological type if it contains AN + 2) jt-electrons, and through the state with anti-Hiickel (Mobius) topology if it contains AN ji-electrons. 

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