Mobius topology

Notice that the orbital array is of the Mobius topology with a phase change depicted between the C-1 and C-2 positions. This corresponds to an allowed photochemical process since there are six electrons involved in bonding changes. 

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. 

Transition state aromaticity (Huckel and Mobius topologies)... 

A thermally activated pericyclic reaction will proceed via a Mobius topology containing one antarafacial component if the cyclically conjugated TT-electrons equal [4n] (n = 0, 1,2,...). 

Thermally, it will proceed via a Mobius topology involving one antarafacial component. Both methyl groups will rotate in the same direction conrotation) leaving one endocyclic and one exocyclic. However, under photochemical conditions, a [4n] ir-reaction is predicted to proceed via a Hiickel topology with suprafacial (disrotation) bond formation. 

Conrotation allowed Mobius topology (aromatic) 4n = [47c]-electrons... 

In the butadiene example, the conrotatory transition state has a Mobius topology, and will be aromatic four electrons are present). Thus, the conrotatory process is allowed. The disrotatory transition state is a Hiickel system, and will require two or six electrons for aromaticity. Since in butadiene only four electrons are present, the disrotation pathway will be forbidden. 

There is another aspect of cycloaddition TS structure that must be considered. It is conceivable that some systems might react through an arrangement with Mobius rather than Hiickel topology (see p. 716). Mobius systems can also be achieved by addition to opposite faces of the tt system. This mode of addition is called antarafacial and the face-to-face addition is called suprafacial. In order to specify the topology of cycloaddition reactions, subscripts s and aare added to the numerical classification. For systems of Mobius topology, as for aromaticity, 4n combinations are favored and 4n- -2 combinations are unfavorable... 

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. 

Figure 15.17 B shows the aromatic transition state analysis of these reactions. We draw a picture of an opening pathway with the minimum number of phase changes and examine the number of nodes. The four-electron butadiene-cyclobutene system should follow the Mobius/conrotatory path, and the six-electron hexatriene-cyclohexadiene system should follow the Hiickel/disrotatory path. As such, aromatic transition state theory provides a simple analysis of electrocyclic reactions. The disrotatory motion is always of Hiickel topology, and the conrotatory motion is always of Mobius topology.

Fig. 12 Isotropic NICS (NICS given in parentheses) contributions at the ring center for the 3c-2e radial orbitals with Hiickel topology and the 3c-4e peripheral orbitals with Mobius topology in a) cyclopropane andb) [Fe3(CO)i2], Z>3h [Ru3(CO)i2], and >3h [Os3(CO)i2]. Values...

Finally, a new class of DBA 14 with a triply twisted Mobius topology of the % electrons, consisting of three 2,2 -binaphthylene units connected by (4.4.4)... 

Synthesis has enabled chemists to explore new topological space, as represented in Figure 5 by the catenanes 49), rotaxanes (50), and molecules with a Mobius topology 51). 

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