Anti-Hiickel ring

If the Hiickel ring is twisted once, as shown in Figure 7-24a, the situation is reversed [7-48]. Therefore, Dewar [7-45] referred to this twisted ring as an anti-Hiickel system. It is also called a Mobius system [7-44, 7-49], an appropriate name indeed. A Mobius strip is a continuous, one-sided surface which is formed by twisting the strip by 180° around its own axis and then joining its two ends. There is a phase inversion at the point where the two ends meet, as seen in Figures 7-24a and b. Figure 7-24c and d depict yet other Mobius strips. 

The transition state for this reaction is a superantiaromatic (anti-Hiickel-dibenzo)-normal-Huckel-cyclooctatetraene. If the phase relationships in these reactions are examined, it is clear that there will be a phase inversion at both ring junctions. By proper choice of the basis set of AOs, these phase inversions can be eliminated, so the transition state is of Hiickel type. 

When a cyclic polyene is large enough, it can exist in both cis- and iraws-forms. Our approach to polyene cyclization has tacitly assumed an all cis -n chain in the form of a band or ribbon that would slip smoothly on to the surface of a cylinder of appropriate diameter. Should the orbitals of the two polyenes in (36) have a mismatch in their orbital symmetries, a single twist in the tt band of one of them could remedy this (Fig. 10c). Cycloaddition would now be allowed and the reaction would proceed, provided other factors were favorable. Such cases of Mobius (Zimmerman, 1966), anti (Fukui and Fujimoto, 1966b) or axisymmetric (Lemal and McGregor, 1966), as opposed to Hiickel, syn, or sigma-symmetric ring closure are unknown (or, at least, rare). A Mobius form has, however, been proposed as the key intermediate in the photochemical transformations of benzene (Farenhorst, 1966) in (48) in place of the disrotatory cyclization proposed by van Tamelen (1965). 

Several qualitative models, e.g. Platt s ring perimeter model [88], Clar s model [89] and Randic s conjugated circuits model [90-92] have either been or are frequently used for the rationalisation of their properties. All these qualitative models rationalise the properties of aromatic and anti-aromatic hydrocarbons in terms of the Hiickel [4n+2] and [4n] rules. The extra stability of a PAH, due to 7t-electron delocalisation, can also be determined, computationally or experimentally, by either considering homodesmotic relationships [36] or by the reaction enthalpy of the reaction of the PAH towards suitable chosen reference compounds [93],... 

Anti-aromaticity was predicted by the Hiickel approach for conjugated cyclic planar structures with 4n 7i electrons due to the presence of two electrons in antibonding orbitals, such as in the cydopropenyl anion, cydobutadiene, and the cydopentadienyl cation (n = 1), and in the cydoheptatrienyl anion and cydooctatetraene (n = 2). It has been argued that a simple definition of an anti-aromatic molecule is one for which the 1H NMR shifts reveal a paramagnetic ring current, but the subject is controversial. The power of the Hiickel theory indeed resides not only in the aromatic stabilization of cydic 4n + 2 electron systems, but also in the destabilization of those with An electrons [22, 27, 42]. 

In [m] circulenes, a family of polyaromatic hydrocarbons so named in 1975 by Wynsberg, in which m refers to the number of aromatic rings arranged in a circle, the total number of n electrons does not indicate aromaticity or anti-aromaticity according to the Hiickel rule. This rule is strictly only applicable to monocyclic systems. It is adequate, however, to consider the inner and the outer n electrons separately whose numbers obey the An + 2 Hiickel criterion for aromaticity, since both these circuits are monocyclic [49]. Coronene, a flat graphite frag-... 

It should be remembered that the Hiickel rule involving 4m- -2 7t-electrons (with n — 0, 1, 2,...) is necessary but insufficient, because other factors may interfere with the extent of delocalization. The most obvious ones are the existence of a closed shell of filled bonding electrons, the absence of occupied anti-bonding levels and the absence of non-bonding levels. As a consequence, no classically aromatic three-membered ring with a re-electron sextet is possible. As will be discussed in the section devoted to four-membered rings, steric strain is an important factor. 

Hiickel s rule Electron rings that have (4n+2)% electrons are aromatic, while those that have 4n % electrons are anti-aromatic. 

We therefore conclude that n.m.r. will differentiate between the [4 ]- and [4n + 2]-annulenes, for it is quite apparent that proton chemical shifts are sensitive to the magnetic properties of the tr-electrons therein. Insofar as this property parallels the Hiickel predictions regarding aromatic and anti-aromatic character (which we now identify with diamagnetic and paramagnetic ring currents) then n.m.r. is a qualitative8) criterion of aromatic character in the annulenes. 

Thus, from a consideration of both bridged and unbridged annulenes ranging from 6 to 36 peripheral iv-electrons, it has been seen that, in planar systems, n.m.r. spectroscopy can distinguish clearly between those aromatic (4n +2) it systems and the anti-aromatic Ann cases, until, at very larger ring size where Hiickel s rule becomes invalid, both series merge into non-aromatic behaviour. 

The directly bonded C—coupling constants have been used to give a measure of aromaticity in mono- and polycyclic hydrocarbon ring systems.Cyclo-octatetraene reacts with methylene dichloride and methyl-lithium to afford a mixture of syn and anti-9-chlorobicyclo[6,l,0]nona-2,4,6-triene (40 and 41) which, on treatment with a 30% lithium dispersion in tetrahydrofuran, gives cyclonona-tetraenide, which is isolated as the tetraethylammonium salt. The chemical shift and the coupling constant (7i3c-ih = 137 c./sec.) observed for the lithio-salt (42) are indicative of the aromatic character of the ring, in accord with the predictions of Hiickel s Aromaticity rule. 

So far we have considered only reactions in which the pericyclic ring contains an even number of atoms. Reactions of this kind are, however, known in which an odd-numbered ring is involved. A simple example is the Diels-Alder-like addition of 2-methylallyl cation (148) to cyclopentadiene (149) to form the methylbicyclooctyl cation (150). The transition state for this reaction is easily seen to be of Hiickel type (151) and so isoconjugate with tropylium. Since the allyl cation contains only two n electrons, we are dealing here with a six-electron system isoconjugate with the tropylium cation (147) and hence aromatic. In reactions of this kind, both the reactants and the transition state are odd. The reactions are therefore of 001 type. Since, moreover, the aromaticity or antiaromaticity of the transition state is again unrelated to the structures of the reactants or products, the reactions are of anti-BEP type and are consequently classed as 00 J. 

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