Anti-Hiickel

The next step in the analysis is to provide an unambiguous method of recognizing systems of the Hiickel or anti-Hiickel type. We introduce first the idea of a phase inversion.3 In the orbital interaction diagram, each interaction joining lobes of opposite sign constitutes a phase inversion. A change of sign within an orbital does not constitute a phase inversion. In 42, for example, there... 

Anti-Hiickel systems. In 1964 E. Heilbronner considered an unusual type of cyclic jc-electron systems with polyene ribbon twisted an odd number of times. The topology of... 

Anti-Hiickel aromaticity. The aromaticity rules for anti-Hiickel systems are opposite to those for conventional (Hiickel) systems (Table 9). 

Zimmern)an s diagrams. For anti-Hiickel systems thee MO energies are defined by the following formula ... 

Evans-Dewar-Zimmerman criterion. In accordance with this criterion the pericyclic reactions proceed through the cyclic transition state of the Htickel topological type if it contains AN + 2) jt-electrons, and through the state with anti-Hiickel (Mobius) topology if it contains AN ji-electrons. 

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 PMO treatment of anti-Hiickel systems presents no problems. The distinction between Huckel and anti-Hiickel types applies only to cyclic conjugated systems, since in an open-chain system it is always possible to choose the phases of AOs so that there are no phase dislocations. The only problem then is that of aromaticity under what conditions are the cyclic anti-Hiickel systems more or less stable than the open-chain analogs ... 

This simple extension of the rules given above (p. 100) extends the PMO treatment to hydrocarbons of all types, both Hiickel and anti-Hiickel. The distinction between the aromaticity of Hiickel and anti-Hiickel systems is crucial to the understanding of the stereochemistry of pericyclic reactions (Sections 5.6 and 6.16) which prefer to proceed through o-n delocalized aromatic transition states. 

The treatment of heteroconjugated systems which follows can be applied to both Hiickel and anti-Hiickel systems in precisely the same way. 

Compare the relative stabilities of the following anti-Hiickel hydrocarbons. 

There is, however, one very important difference between the delocalized MOs in a pericyclic transition state and the delocalized n MOs in a cyclic polyene. In the latter, the phases of the 2p AOs can be chosen so that they always overlap in phase the resulting n systems are consequently of Hiickel type (p. 106). While it is possible to envisage anti-Hiickel n systems (p. 108), none has yet been prepared. Pericyclic transition states, on the other hand. 

We are dealing here with four-atom conjugated systems containing four electrons, i.e., the two pairs of electrons that form the C=C n bond and the CH2—CH2 (7 bond in (144). The disrotatory transition state (145), being of Huckel type, will then be isoconjugate with normal cyclobutadiene and so will be antiaromatic, whereas the conrotatory transition state will be isoconjugate with an anti-Hiickel analog of cyclobutadiene and so will be aromatic (see Table 4.2). 

This argument can obviously be extended to concerted pericyclic reactions of all kinds. The transition state for any such reaction will be isoconjugate with a normal Hiickel-type cyclic polyene or an anti-Hiickel analog of one. If the transition state is aromatic, the resulting stabilization will lower its energy and so accelerate the reaction. If it is antiaromatic, the converse will be true. Since, moreover, the rules for aromaticity in Huckel-type and anti-Huckel-type systems are diametrically opposite, in each case one will be aromatic and the other antiaromatic. If, then, a reaction can follow one of two alternative pericyclic paths, one involving a Hiickel-type transition state and the other an anti-Hiickel-type transition, the reaction will prefer to follow the path in which the transition state is aromatic. If, on the other hand, only one of the two alternatives is sterically possible, the reaction will take place relatively easily if the corresponding transition state is aromatic and with relative difficulty if it is antiaromatic. In the latter case, the antiaromatic transition state will, if possible, be bypassed by a two-step mechanism in which the transition state is linear instead of cyclic [e.g., equation (5.291)]. 

Is there an unavoidable phase dislocation (There cannot be more than one, see p. 106). If not, the transition state is of Hiickel type. If there is, it is of anti-Hiickel type. 

If a 7T cycloaddition takes place by cis addition to the n systems, the transition state is of Hiickel type. If, however, one of them adds trans, the transition state has a phase dislocation and so is anti-Hiickel. This is shown in (158) and... 

Even the concerted pericyclic dimerization of an olefin to a cyclobutane [equation (5.290)] can occur if the two double bonds are twisted sufficiently. It may then be possible for the top lobes of the 2p AOs in one olefin moiety to overlap with a top and a bottom lobe of the 2p AOs of the other (165). The transition state is then of anti-Hiickel type and so is aromatic, being an anti-Hiickel analog of cyclobutadiene. The arrows in (165) indicate the relative directions in which the terminal atoms of the C=C bonds are twisted. 

The transition state is precisely analogous to that in a ti cycloaddition, the only difference being that the reactants in the n cycloaddition are both even, while here R and S are both odd. We can therefore see at once that if the 71 systems in (176) both interact in cis fashion or both in trans fashion, the transition state will be of Huckel type, while a cis-trans interaction will lead to an anti-Hiickel transition state. 

The first step is a disrotatory chelotropic reaction, the transition state being isoconjugate with naphthalene (218). The second step is a conrotatory electrocyclization, the transition state being isoconjugate with an anti-Hiickel analog of (219). 

Six-Electron Anti-Htickel Systems. C/ -type photochemical reactions in six-electron systems involve anti-Hiickel transition states. Equations (6.58) and (6.59) show two typical examples ... 

It is rather difficult to see from two-dimensional drawings how the orbitals of the transition states overlap, so we will not try to illustrate them. Examination of models shows that the intermediates (75) and (78) are in fact of anti-Hiickel type. If the orbital phases are chosen so that the overlaps in (74) and (77) are all positive, the 1,6 overlaps in (75) and (78) are both negative, the rest positive. The transition states are isoconjugate with (80) and (81) but with one p inverted as indicated. 

Hexatrienes can also cyclize photochemically through anti-Hiickel... 

The cyclization of stilbene occurs through an anti-Hiickel transition state analogous to anti-Hiickel phenanthrene. Photodimerizations of polycyclic aromatic systems are also very common. The dimerization of anthracene derivatives is a classical example ... 

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. 

Antiaromatic ground states of nonalternant monocyclic hydrocarbons will be aromatic with reference to the excited singlet states of their open-chain analogs nonaromatic (radical), nonalternant systems will be nonaromatic with reference to the excited singlet states of their open-chain analogs. Complete the proof that the rules for aromaticity in anti-Hiickel systems hold for the excited states of monocyclic Hiickel systems. 

Prove that 4n — 1 Hiickel and 4 -I- 1 anti-Hiickel odd cyclopolyenemethylenes are aromatic with reference to open-chain radical ions. 

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