Hiickel-Mobius concept

Huckel s rule [7-47], if such a system has 4n -I- 2 electrons, the molecule will be aromatic and stable. On the other hand, a Hiickel ring with An electrons will be antiaromatic. 

According to Zimmermann [7-44] and Dewar [7-45], 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 of phase inversions. For such a system, a transition state with 4n -t- 2 electrons will be thermally allowed due to aromaticity, while the transition state with An electrons will be thermally forbidden due to antiaromaticity. 

Both the Woodward-Hoffmann approach and the Hiickel-Mobius concept are useful for predicting the course of concerted reactions. They both have their limitations as well. The application of the Hiickel-Mobius concept is probably preferable for systems with low symmetry. On the other hand, this 

The potential of a unified treatment of organic and inorganic systems has been expressed eloquently in Roald Hoffmann s Nobel lecture [7-11], entitled Building Bridges between Inorganic and Organic Chemistry.  

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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. 

The rules based on the Hiickel-Mobius concept have their counterpart among the Woodward-Hoffmann selection rules. There was a marked difference between the suprafacial and antarafacial arrangements in the application of the Woodward-Hoffmann treatment of cycloadditions. The disrotatory and conrotatory processes in elec-trocyclic reactions presented similar differences. The suprafacial arrangement in both of the reacting molecules in the cycloaddition as well as the disrotatory ring closure in Figure 7-25 correspond to... 

The Hiickel-Mobius concept may also be applied to the allene problem we described earlier. Reference 40 shows the walks or orbital overlap pathways which distinguish the two isomers. 

The Mobius-Hiickel Concept and Photochemistry 3.1 Application to Correlation Diagrams... 

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. 

Mobius aromaticity A monocyclic array of orbitals in which a single out-of-phase overlap (or, more generally, an odd number of out-of-phase overlaps) reveals the opposite pattern of aromatic character to Hiickel systems with 4n electrons it is stabilized (aromatic), whereas with 4n + 2 it is destabilized (antiaromatic). In the excited state 4n + 2, Mobius pi-electron systems are stabilized, and 4n systems are destabilized. No examples of ground-state Mobius pi systems are known, but the concept has been applied to transition states of PERI-CYCLIC REACTIONS (see AROMATIC [3]). 

The Woochvard-Huflimnn rules are a general expression of this. A pericyclic reaction which is entirely suprafacial is allowed thermally if 4n + 2 electrons are involved (Hiickel transition state), but forbidden for 4n electrons. If there is one antarafacial component, the reaction will be allowed thermally if 4n electrons are involved (Mobius transition state), but forbidden for 4n + 2 electrons. For photochemical reactions, these rules are reversed. Roald Hoffmann shared the Nobel prize for Chemistry with Kenichi Fukui in 1981 for his contribution to this concept Robert Burns Woodward had already won the prize in 1965. 

The concepts of frontier orbital HOMO LUMO interactions, the idea of an aromatic transition state, and the alternative concept of conservation of orbital symmetry (not developed in this chapter) all lead to the same result for pericyclic reactions which involve a cyclic overlap of orbitals in the transition slate, thermal reactions are allowed for reactions involving 4n + 2 electrons in Hiickel systems (no change in phase between overlapped orbitals in the cyclic transition state) or for 4/j electrons in Mobius systems (phase between overlapped orbitals in the cyclic transition state changes once on going round the ring). For photochemical systems, these rules are reversed. 

The [nlannulenes may be defined as cyclic polyaUcenes possessing a closed circuit of n Ti-conjugated pz-orbitals. The first three small annulenes are shown in Fig. 1 and include [4]annulene (cyclobutadiene), [6]annulene (benzene), and [8]annulene (cyclooctatetraene). The bracketed number, n, can be classified as either a 4n+2 (Hiickel aromatic/Mobous antiasomatic) or 4n (Huckel antiaromatic/ Mobius aromatic) delocalized n-electron species. That said, it is not surprising that the concept of aromaticity is closely associated with the annulenes. Indeed, the first three annulenes listed cover the concepts of Hiickel aromatic, antiaromatic, and nonaromatic properties (see Fig. 1). 

The concept of Mobius aromaticity has been extended from transition structures to discussions of the stability of organic molecules. Extensive reviews of Mobius aromaticity and of Mobius structures were provided by Rzepa and by Herges. A computational study of the (CH)i2, (CH)i6, and (CH)2o annulenes found twisted Mobius structures to be energy minima, but in each case steric strain caused such structures to be higher in energy than their nontwisted Hiickel coimterparts. Similar results from another study are shown in Table 11.7. In order to test the stabilizing effect of Mobius... 

H. E. Zimmerman, The Mobius-Hiickel concept in organic chemistry Application to organic molecules and reactions, Acc. Chem, Res. 4, 272 (1971). 

The concept of the Mobius strip was explained earlier (see p. 55). The basis of the Zimmerman analysis is an extension of this idea. A cyclic polyene is defined as a Hiickel system if its basis molecular orbital (i.e. the lowest filled TT-level as in the case of benzene, for example) contains zero or an even number of phase dislocations. Mbbius systems possess an odd number of phase dislocations in the basis molecular orbitals. In accordance with the rules predicting aromaticity for these systems, which results from the application of the Hiickel molecular orbital theory, it may be inferred that since cyclic conjugation also arises in the transition states of pericyclic reactions, the foDowing conclusions apply ... 

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