Orbital Mobius aromaticity

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]). 

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). 

Mobius Aromaticity An aromatic annulene composed of a continuous array of p -orbitals containing a 4n... 

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 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. 

It is established that in addition to Huckel aromaticity which is an extra stabilization of a molecule due to delocalized bonding involving 4N + 2 electrons, there is also Mobius aromaticity [69,70]. The latter is associated with 4N electrons involved in delocalized bonding in molecules that exhibit similarity between the nodal structure of their molecular orbitals and orbitals of Heilbronner s polyenes... 

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. 

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. 

Hehre66 69 and independently Jorgensen72,73 pointed out that the Mobius and Hiickel description of homoconjugated molecules (Figure 9) is consistent with the assumed homoaromtic and homoantiaromatic character of these compounds. However, it was also realized that in the general case such a classification might not be sufficient to describe subtle differences in orbital interactions, which determine the homo(anti)aromatic character of a molecule. 

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 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. 

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,... 

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. 

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