Mobius antiaromaticity

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. 

For a homoantiaromatic system, surface delocalization in the cyclopropyl ring is parallel to the bridging bond, thus forming a Mobius antiaromatic electron ensemble delocalized along the periphery of the bi(poly)cyclic ring system. 

Castro and Kamey conjectured that the bond shift that takes 47 into 58 should proceed through a Mobius antiaromatic transition state. They located a Mbbius TS 57, shown in Figure 3.13. The value of NICS(O) is +19.0 and the computed chemical shifts of the inner hydrogens are 26.4 and 26.7 ppm, all indicative of its Mobius antiaromatic nature. 

Generalizing the results from these three examples leads to the conclusion that a system with in electrons in a cyclic array of orbitals having one (- -)-(—) overlap is Mobius aromatic, while a similar system witti in + 2 electrons is Mobius antiaromatic. 

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. 

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... 

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 word aromaticity usually implies that a given molecule is stable, compared to the corresponding open chain hydrocarbon. For a detailed account on aromaticity, see, e.g., Reference [95], The aromaticity rules are based on the Hiickel-Mobius concept. A cyclic polyene is called a Hiickel system if its constituent p orbitals overlap everywhere in phase, i.e., the p orbitals all have the same sign above and below the nodal plane (Figure 7-23). According to HiickeTs rule [96], if such a system has 4n + 2 electrons, the molecule will be aromatic and stable. On the other hand, a Hiickel ring with 4n electrons will be antiaromatic. 

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. 

The common Mobius strip has a single half twist. Ribbons can be even more twisted and so higher order annulenes might be possible, expressing potential aromatic or antiaromatic properties. Rzepa et al. have found examples of these higher order twisted annulenes, such as Ci4Hx4 (63) with one full twist, Ci Hj ... 

Rzepa, H. S. Lemniscular hexaphyrins as examples of aromatic and antiaromatic double-twist Mobius molecules, Org. Lett. 2008,10, 949-952. 

The antiaromatic geometry found along the concerted path of ground-state-forbidden pericyclic reactions, which is topologically equivalent to an antiaromatic Hiickel [4n]annulene or MObius [An + 2]annulene, is a particularly interesting type of biradicaloid geometry. (Cf. Section 4.4.) Other biradicaloid geometries and combinations of those mentioned are equally possible. 

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. 

Mobius aromaticity A monocyclic array of orbitals in which a single out-of-phase overlap (or, more generally, an odd number of out-of-phase overlaps) reveals the opposite pattern of aromatic character to Hiickel systems with 4n electrons it is stabilized (aromatic), whereas with 4n + 2 it is destabilized (antiaromatic). In the excited state 4n + 2, Mobius pi-electron systems are stabilized, and 4n systems are destabilized. No examples of ground-state Mobius pi systems are known, but the concept has been applied to transition states of PERI-CYCLIC REACTIONS (see AROMATIC [3]). 

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