Mobius system

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 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. 

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 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. 

Propadiene is represented in Figure 13-4 as if it were two isolated Huckel ring systems. This molecule also may be represented as a stable Mobius system of Att electrons. Draw an orbital diagram of 1,2-propadiene to indicate this relationship. If 1,2-propadiene twisted so that the hydrogens on the ends all were in the same plane, 57, would it be a Huckel or a Mobius polyene, or neither ... 

H. E. Zimmerman, /. Am. Chem. Soc., 88, 1566 (1966). Molecular Orbital Correlation Diagrams, Mobius Systems, and Factors Controlling Ground- and Excited-State Reactions. II. 

On molecular orbital correlation diagrams, the occurrence of Mobius systems in cyclization reactions, and factors controlling ground- and excited- state reactions. I. J. Amer. chem. Soc. 88, 1564 (1966),... 

The Mobius-Huckel concept was introduced by Zimmerman in 1966 35). It was suggested that each cyclic array of orbitals in a reacting system may be categorized as a Hiickel type or a Mobius type , depending on the number of plus-minus overlaps between adjacent orbitals. With zero or an even number of such sign inversions, the system is a Hiickel variety array while with one or some other odd number the system is a Mobius system. 

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. 

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). 

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. 

Even though the stability of Mobius systems was predicted over 40 years ago [103], for a long time no such systems were synthesized. One possible reason for this is the expected strain in the twisted structure. Based on quantum chemical calculations, different groups suggested the stability of [4 ]annulenes [(CH) , with n = 3-5], but it was also shown that there are many possible isomers of this system that are close in energy and thus the Mobius system might easily flip back to the less strained Hiickel structures [104],... 

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],... 

Edgar Heilbronner in 1964 worked out that such a twisted system (Mobius system) would be aromatic if it contained 4n conjugated tr-electrons. Curiously, no actual examples were identified until relatively recently, when it was proposed that [12], [16] and [20] annulenes have several higher energy conformations which adopt this mode. In 2003, the first crystal structure of a true stable Mobius [16] annulene was completed, and various heteroannulenes were identified as existing in Mobius form. 

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