Huckel and Mobius systems

Finally, the distinction between Huckel and Mobius systems is considered. The above definitions are valid for Hiickel-type reactions. For aromatic Mobius-type reations, the reverse holds An ATS is formed when an even number of electron pairs is re-paired. 

The three stmctures in Figure 11.104 illustrate the contrasts between Huckel and Mobius systems. 

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... 

The tangential pjp orbitals form a Huckel 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 Huckel and Mobius orbital systems have always an aromatic... 

While all cyclic, conjugated six-membered phosphorus heterocycles with AV -phosphorus are clearly Hiickel-aromatic systems, the bonding situation in the cyclic conjugated six-membered systems containing AV -phosphorus has been discussed rather controversially. Schweig and coworkers, for example, discussed a mixture of Huckel and Mobius aromaticity and ylide character... 

The rule may then be stated A thermal pericyclic reaction involving a Huckel system is allowed only if the total number of electrons is4n + 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 Huckel systems, the Mobius-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. 

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

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. 

We note that it is the Htickel systems with 4N electrons and the Mobius systems with 4N + 2 electrons which have a nonbonding degenerate pair of MO s and thus a facile mode of converting starting excited state to ground state of product. Finally, it should be noted the the Mobius-Huckel method is fully consistent with the Woodward-Hoffmann treatment, both for ground state and for photochemical reactions 40). 

Figure 7.14 Reaction paths for 1 pericyclic reactions involving aromatic and non-aromatic numbers of electrons. Number of aromatic electrons is 4n + 2 for Huckel systems with no antara-facial components, or An electrons for Mobius systems with one antarafacial component...

As is often the case with simple HMO theory, it is the energy levels of the Mobius systems and not the MOs themselves that are of primary interest. Zimmerman developed a circle mnemonic, analogous to the circle mnemonic used with HMO theory in Chapter 4, which provides a shortcut to finding tt e Mobius energy levels. For Mobius MOs, the polygon corresponding to the cyclic molecule is inscribed in the circle of radius 26 with one side down (not with a comer down as was done for Huckel systems). This procedtue is illustrated in Figure 11.104 for both (a) Huckel MOs and (b) Mobius MOs for cyclopropenyl, cyclobutadiene, and benzene. 

NDO VB WAVEFUNCTIONS OF FOUR-ELECTRON-FOUR-ORBITAL HUCKEL (HAO) AND MOBIUS (MAO) AO SYSTEMS... 

In HMO theory, the cyclopropenyl cation is aromatic (i.e., it is a closed shell system with large delocalization energy), since both electrons are in the orbital with E = a -I- 26. The Huckel cyclopropenyl anion is antiaromatic because it is an open shell system (having one electron in each of the = a - 6 orbitals) with zero delocalization energy. In contrast, the Mobius cyclopropenyl anion is aromatic, since it is a closed shell system with all four electrons in bonding orbitals, and the Mobius cyclopropenyl cation is antiaromatic. 

In the PMO method, we analyze an electrocyclic reaction through the following steps (1) Define a basis set of 2p-atomic orbitals for all atoms involved (li for hydrogen atoms). (2) Then connect the orbital lobes that interact in the starting materials. (3) Now let the reaction start and then we identify the new interactions that are occurring at the transition state. (4) Depending upon the number of electrons in the cyclic array of orbitals and whether the orbital interaction topology corresponds to a Huckel-type system or Mobius-type system, we conclude about the feasibility of the reaction under thermal and photochemical conditions. 

In case of [tt s + tu s] cycloaddition (4n 7r-electron system), a supra—supra mode of addition leads to a Huckel array, which is antiaromatic with 4n 7u-electrons (Figure 4.7). Therefore, the supra—supra mode of reaction is thermally forbidden and photochemically allowed. However, a supra—antara mode of addition uses a Mobius array, which is aromatic with 4n 7t-electrons. Therefore, [rt s + rc a] cycloaddition reaction is thermally allowed and photochemically forbidden. Similarly, we can analyze the [tu" s + Tt s] cycloaddition having (4n + 2) 7t-electrons (Figure 4.7). In this case, a supra—supra mode of addition leads to a Huckel array, which is aromatic with (4n + 2) 7C-electrons. Therefore, [7t" s + tu s] cycloaddition reaction now becomes thermally allowed and photochemically forbidden. However, a Itch s + Tu a] cycloaddition uses a Mobius array, which is antiaromatic with (4n + 2) 7u-electrons. Therefore, the reaction is thermally forbidden and photochemically allowed in this mode. 

Three C - C bonds are primarily due to the double occupation of the bonding orbitals of P and R - S. Thus, the three C - C bonds constitute an "aromatic" system in the conventional sense because P is a Mobius and S - R a Huckel AO ring. 

A. A Huckel topology with no nodes, or an even number of nodes. B. A Mobius topology. The twist in the system alters the topology,. such that the top" of one i orbital must interact with the "bottom" of the other. Such a system must have at least one node (dotted line), and will always have an odd number of nodes. 

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