Mobius orbitals

The tangential pjp orbitals form a Hiickel system for even-membered rings but a Mobius system for odd-membered rings. However, this seems to be of little consequence because it has been shown that both Hiickel and Mobius orbital systems have always an aromatic... 

There is, however, an important difference between examples 27 and 41. The later compound forms a Huckel-aromatic orbital system in 41b while the former compound adopts a Mobius orbital system with 4q + 2 electrons, i.e. 27 is Mobius antiaromatic although six electrons participate in cyclic delocalization (see Section III. B). This is in line with a destabilizing resonance energy of 9.9 kcalmol"1 (Table 2) calculated with the MM2ERW method41-42. 

FIGURE 9. Huckel and Mobius orbital systems for homoconjugated molecules. In each case, the number of participating electrons (e) is given and classification according to aromatic or antiaromatic... 

If we now calculate the orbital energies for the Mobius orbitals, as was done for the normal Hiickel tt orbitals in Figure 21-13, we get the results shown... 

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 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... 

Htickel Orbital Array Mobius Orbital Array... 

The stereoselectivities of DPM rearrangement reactions involving acyclic substrates have been examined and clear outcomes observed. Thus, direct photolysis of the (E)-1,4-diene 88 affords the trans-configured cyclopropane 89 as the major product, while equivalent treatment of the (Z)-isomer 90 delivers the cis-configured cyclopropane 91. It has been suggested that the involvement of an excited singlet Mobius orbital array accounts for the observed selectivities. 

Huckel orbital aray Mobius orbital array... 

More recently Corminboeuf et al. [124] based on structural and NICS analysis provided striking insights into the magnetic criteria for aromaticity in the group 8 metal carbonyl [M3(CO)i2](M = Fe, Ru, Os) clusters. Typically [Fe3(CO)i2] (C2v) exhibits the same type of diatropic behavior as Dsh cyclopropane arising from one 3c-2e radial Hiickel orbital and the 3c-4e peripheral Mobius orbitals. The radial orbitals remain also diatropic in both [Ru3(CO)i2] (i>3h) and [Os3(CO)i2] ( 3h),... 

The electrocyclic ring closure of hexatriene (Eq. 5.13) can also be considered in terms of its transition state, shown in Figure 5.13a, where a complete loop of overlap is followed with a dashed line from atom to atom through all six. This as drawn with a minimum of nodal zones resembles the lowest molecular orbital of aromatic benzene since there are six electrons and no nodes. This transition state is favored by aromatic stabilization and is reached only by disrotation. Conrotation would have given a transition state with one nodal zone (Fig. 5.13b) that would be part of a Mobius orbital set, but six electrons do not give a closed shell in this set, and the transition state does not have aromatic stabilization and is not allowed. 

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