Mobius array

What is noted is that in Mechanism A, the vertical excited state is bom in an energy well and unlikely to react. Indeed, it was Mechanism A which is the simplest and was initially favored on the basis of Occam s Razor type arguments. In retrospect it may be shown that this mechanism involves a Mobius array of 8 orbitals with 8 electrons, and is excited state forbidden. A variation in this mechanism (i.e. A ) in which the first two bridging steps are separated in time, clearly has improved matters so that... 

T electrons with one si inversion (Mdbius-like). A Mobius array in the ground state is antiaromatic with six electrons but is aromatic and stable in the excited state. °> Thus the di-ir-methane rearrangement via transition state (3) is photoallowed. The orbital scheme (4) involves a cyclic array of four 17- electrons with no sign inversions (Hiickel-like). Again the ground state is antiaromatic but it is aromatic in the excited state and the reaction is photochemically allowed. 

Similarly, we can analyze the hexatriene-cyclohexadiene system having (4n + 2) 7T-electrons (Figure 2.10). In this case, a disrotatory mode of ring closure leads to a Hiickel array, which is aromatic with (4n + 2) rr-electrons. Therefore, the disrotatory mode of reaction now becomes thermally allowed. However, a conrotatory mode of ring closure uses a Mobius array, which is antiaromatic with (4n + 2) 7r-electrons. Therefore, the reaction is thermally forbidden in this mode. 

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. 

Zimmerman has chosen to describe the di-n-methane rearrangement as in Mobius array which corresponds to a delocalised transition structure for an allowed photochenucal reaction, but not for ground state reaction. 

---