Hiickel system

A more general classification considers the phase of the total electronic wave function [13]. We have treated the case of cyclic polyenes in detail [28,48,49] and showed that for Hiickel systems the ground state may be considered as the combination of two Kekule structures. If the number of electron pairs in the system is odd, the ground state is the in-phase combination, and the system is aromatic. If the number of electron pairs is even (as in cyclobutadiene, pentalene, etc.), the ground state is the out-of-phase combination, and the system is antiaromatic. These ideas are in line with previous work on specific systems [40,50]. 

Here, with six electrons involved, it is the disrotatory mode (Hiickel system) in which the transition state is stabilized. There are numerous examples of interconversion of 1,3,5-... 

The thiirene oxide system is of particular interest due to it being simultaneously both a potentially nonbenzenoid aromatic (4n + 2)n and antiaromatic 4nn Hiickel system. 

The rule may then be stated A thermal pericyclic reaction involving a Hiickel system is allowed only if the total number of electrons is 4n + 2. A thermal pericyclic reaction involving a Mobius system is allowed only if the total number of electrons is 4n. For photochemical reactions these rules are reversed. Since both the 2 + 4 and 2 + 2 cycloadditions are Hiickel systems, the Mdbius-Hiickel method predicts that the 2 + 4 reaction, with 6 electrons, is thermally allowed, but the 2 + 2 reaction is not. One the other hand, the 2 + 2 reaction is allowed photochemically, while the 2 + 4 reaction is forbidden. 

Note that both the 2 + 2 and 2 + 4 transition states are Hiickel systems no matter what basis sets we chose. For example. Figure 15.8 shows other basis sets we might have chosen. In every case there will be zero or an even number of sign inversions. 

In the Mobius-Hiickel approach, diagrams similar to Figure 18.4 can be drawn for this case. Here too, the disrotatory pathway is a Hiickel system and the conrotatory pathway a Mobius system, but since six electrons are now involved, the thermal reaction follows the Hiickel pathway and the photochemical reaction the Mobius pathway. 

As expected, the Mobius-Hiickel method leads to the same predictions. Here we look at the basis set of orbitals shown in G and H for [1,3] and [1,5] rearrangements, respectively, A [1,3] shift involves four electrons, so an allowed thermal pericyclic reaction must be a Mobius system (p. 1070) with one or an odd number of sign inversions. As can be seen in G, only an antarafacial migration can achieve this. A [1,5] shift, with six electrons, is allowed thermally only when it is a Hiickel system with zero or an even number of sign inversions hence it requires a suprafacial migration. 

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 9.17. (a) Conrotatory, Mobius system, one sign inversion, (b) Disrotatory, Hiickel system, no sign inversions. 

The operation of (d) is seen in cyclopentadiene (14) which is found to have a pKa value of 16 compared with 37 for a simple alkene. This is due to the resultant carbanion, the cyclopentadienyl anion (15), being a 6n electron delocalised system, i.e. a 4n + 2 Hiickel system where n = 1 (cf. p. 18). The 6 electrons can be accommodated in three stabilised n molecular orbitals, like benzene, and the anion thus shows quasi-aromatic stabilisation it is stabilised by aromatisation ... 

Cyclooctatetraene (COT) —> Semibullvalene (SB) Photorearrangement. Irradiation of COT yields semibullvalene [97], in spite of the fact that this photochemical reaction is forbidden by orbital conservation mles. The Longuet-Higgins loop for this system actually predicts that this should happen, although the reaction is phase preserving. (Fig. 42). This is another example of type C loop (Fig. 11). Only six of the eight electrons re-pair as COT transforms to SB. The reaction is made possible by the fact that COT valence isomerization, a phase-inverting reaction (four electron-pair Hiickel system), takes place simultaneously. One expects to produce in the reaction a COT isomer, that can be detected solely by proper substitution. 

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... 

If you compare the orbital energies of the Hiickel and Mobius cyclic 7r systems (Figures 21-13 and 21-16), you will see that the Hiickel systems have only one lowest-energy MO, whereas the Mobius systems have two. Hiickel systems have an odd number of bonding orbitals (which, when full, accommodate 2, 6, 10, 14, or An + 2 electrons) and the Mobius systems have an even number of bonding orbitals (which, when full, accommodate 4, 8, 12, or An electrons). The Hiickel molecular orbitals have zero or an even number of nodes (see, for example, the benzene MOs, Figure 21-5) the Mobius molecular orbitals are not shown, but they have one or an odd number of nodes. 

Whereas in the Frost mnemonic for Hiickel systems the polygon is inscribed with a vertex down, in the Zimmerman mnemonic for Mobius systems the inscription is with the polygon side down. Three examples of each type are shown in Figure 9. Note that each intersection of the polygon with the inscribed circle corresponds to an MO and that the vertical positioning of the intersection gives the MO energy analytically. Thus, all of the Hiickel systems, with one vertex at the bottom, have in common one MO at —2 P. Also the odd-sized arrays have their Hiickel and Mobius relatives turned upside down from one another, while in the even series there is no such relationship. 

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. 

According to Zimmermann [101] and Dewar [102], the allowedness of a concerted pericyclic reaction can be predicted in the following way A cyclic array of orbitals belongs to the Hiickel system if it has zero or an even-number phase inversions. For such a system, a transition state with An+ 2 electrons will be thermally allowed due to aromaticity, while the transition state with An electrons will be thermally forbidden due to antiaromaticity. 

The first real Mobius systems ([16]annulenes) were only synthesized a few years ago [105], In these systems the authors achieved enough rigidity for the molecules so that they would not flip back to a Hiickel system. It was also determined that these Mobius-twisted annulenes are more aromatic in their character than the Hiickel-systems [106],... 

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