Mobius orbital systems

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... 

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. 

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 factors that control if and how these cyclization and rearrangement reactions occur in a concerted manner can be understood from the aromaticity or lack of aromaticity achieved in their cyclic transition states. For a concerted pericyclic reaction to be thermally favorable, the transition state must involve An + 2 participating electrons if it is a Hiickel orbital system, or 4 electrons if it is a Mobius orbital system. A Hiickel transition state is one in which the cyclic array of participating orbitals has no nodes (or an even number) and a Mobius transition state has an odd number of nodes. 

This is an example of a Mobius reaction system—a node along the reaction coordinate is introduced by the placement of a phase inverting orbital. As in the H - - H2 system, a single spin-pair exchange takes place. Thus, the reaction is phase preserving. Mobius reaction systems are quite common when p orbitals (or hybrid orbitals containing p orbitals) participate in the reaction, as further discussed in Section ni.B.2. 

In the potentially homoantiaromatic molecules of Figure 11, electron delocalization occurs along the periphery of a bicyclic system, involving in this way Aq + 2 rather than 4 q electrons. Since, however, the corresponding orbital system is of Mobius rather than Hiickel type (Figure 9), delocalization of 4q + 2 electrons leads to overall destabilization rather than stabilization. 

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]). 

If the orbital is directed tangentially, all MO s of the it system contain an additional node which is caused by the symmetry behaviour of the tangential d orbital. But, as this additional node is not located at a fixed position, one obtains a delocalized (pd)n system showing the same properties as a Mobius it system 34 which may be obtained by gradually twisting all p orbitals of a tt system through a small angle in the same direction 1161. 

A hypothetical array of twisted p orbitals leading to a Mobius n system. 

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. 

Mobius jr-systems are those in which, along a cycle of overlapping p-orbitals, by gradual twisting, eventually we have overlap of p-orbitals of opposite sign, for the pattern of /r-orbital levels. 

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. 

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