Orbitals Mobius type

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

E. Heilbronner, Tetrahedron Lett. 5, 1923 (1964). Hiickel Molecular Orbitals of Mobius-Type Conformations of Annulenes. 

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. 

Heilbronner, E. Hiickel molecular orbitals of Mobius-type conformations of annulenes, Tetrahedron Lett. 1964, 5,1923-1928. 

The HMO-orbital energies for idealized Mobius-type (pd)n systems (9) may be given in closed form 1,6> (5). 

Now the pattern has changed drastically relative to Fig. 9. Practically all the systems containing one d-orbital center are below the limit of aromaticity except the Mobius-type eight- and twelve-membered ring compounds, for which no examples of chemical compounds are known (compare Fig. 1 the phos-phonitrilic compounds 16a and 16b are of the unfavourable Hiickel type and already ruled out by consideration of the idealized systems). 

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. 

The three possible topological interactions in [ 2 + 2] cyclo-addition reactions are shown in Fig. 5.2 again the basis molecular orbitals of the ethylene components are considered. In the supra-supra and i v antara-antara combinations there are no out of phase orbital overlaps (or two if the signs are reversed on one ethylene component). In the supra intara mode there is one out of phase overlap. Since there are four electrons involved, the Mobius type interaction (i.e. supra-antard) should be preferred the other combinations should therefore be possible under photochemical control. These results accord with the previous findings of orbital symmetry theory. 

The appropriate correlation diagrams can also be constructed for the Hiickel and Mobius closures in pericyclic processes where the system maintains some symmetry, and the method is capable of extension to include for unsymmetrical systems (Zimmerman, 1966, 1971). The molecular orbital energies of Hiickel- and Mobius-type cyclic polyenes are readily derived from the simple circle mnemonic discussed earlier (see pp. 43 and 55). 

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. 

Fig. 6. Bond Order Effects in the Type A Zwitterion Rearrangement. Note Basis orbitals are shown with arbitrary orientation, hence plus-minus overlaps do not imply antibonding between any particular orbital pair. However, with an odd number of such overlaps, the system is Mobius...

In a pericyclic reaction the array of basis orbitals of the reacting molecule is cyclic halfway along the reaction coordinate. The array will either be of the Mobius or the Hiickel type. Since the circle mnemonics give the distribution of MO energies... 

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... 

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