Mobius cyclobutadiene

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)...

The energy levels of Hiickel and Mobius orbital arrays are easily generated. (In Ref. 14 we show in detail how the orbital energies of Mobius cyclobutadiene are obtained... 

Figure 7.12 Molecular orbitals for the (hypothetical) Mobius cyclobutadiene...

Mobius cyclobutadiene has four electrons in the two lowest energy levels (E = a + 1.4146), as shown in Figure 11.103. Mobius cyclobutadiene should therefore be a closed shell system with some delo-... 

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... 

The [nlannulenes may be defined as cyclic polyaUcenes possessing a closed circuit of n Ti-conjugated pz-orbitals. The first three small annulenes are shown in Fig. 1 and include [4]annulene (cyclobutadiene), [6]annulene (benzene), and [8]annulene (cyclooctatetraene). The bracketed number, n, can be classified as either a 4n+2 (Hiickel aromatic/Mobous antiasomatic) or 4n (Huckel antiaromatic/ Mobius aromatic) delocalized n-electron species. That said, it is not surprising that the concept of aromaticity is closely associated with the annulenes. Indeed, the first three annulenes listed cover the concepts of Hiickel aromatic, antiaromatic, and nonaromatic properties (see Fig. 1). 

As is often the case with simple HMO theory, it is the energy levels of the Mobius systems and not the MOs themselves that are of primary interest. Zimmerman developed a circle mnemonic, analogous to the circle mnemonic used with HMO theory in Chapter 4, which provides a shortcut to finding tt e Mobius energy levels. For Mobius MOs, the polygon corresponding to the cyclic molecule is inscribed in the circle of radius 26 with one side down (not with a comer down as was done for Huckel systems). This procedtue is illustrated in Figure 11.104 for both (a) Huckel MOs and (b) Mobius MOs for cyclopropenyl, cyclobutadiene, and benzene. 

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