Mobius orbital array

The energy levels of Hiickel and Mobius orbital arrays are easily generated. (In Ref. 14 we show in detail how the orbital energies of Mobius cyclobutadiene are obtained... 

Htickel Orbital Array Mobius Orbital Array... 

The stereoselectivities of DPM rearrangement reactions involving acyclic substrates have been examined and clear outcomes observed. Thus, direct photolysis of the (E)-1,4-diene 88 affords the trans-configured cyclopropane 89 as the major product, while equivalent treatment of the (Z)-isomer 90 delivers the cis-configured cyclopropane 91. It has been suggested that the involvement of an excited singlet Mobius orbital array accounts for the observed selectivities. 

Huckel orbital aray Mobius orbital array... 

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. 

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. 

Valence electron rules have been theoretically proposed for three- and four-membered atomic rings [7], The p, p and p orbital arrays are of the Hiickel or Mobius conjugation (Scheme 2) [9, 10], The splitting patterns of the energy levels are well known... 

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. 

An approach very closely related to that of Woodward and Hoffmann is the so-called Hiickel-Mobius approach 35> based on the rule An +2 electron systems prefer Hiickel geometries and An electron systems prefer Mobius geometries 36>. When no symmetry exists and there is no cyclic orbital array the allowedness or forbiddenness of a reaction can be determined by following the form of the MO s during the reaction 37>. A detailed quantum mechanical study of the stereochemistry of thermal and photo cyclo-addition reactions has been reported38), and a quantum mechanical discussion of the applicability of the Woodward-Hoffmann rules can be found in a paper by George and Ross 39>. 

It has been pointed out that a different array of atomic orbitals might be conceived of in large conjugated rings. The array, called a Mobius twist, results in there being one point in the ring at which the atomic orbitals would show a phase discontinuity. ... 

Scheme 2 Htickel or Mobius conjugation of the arrays of i-orbitals and radial (p ), tangential (p ), and perpendicular (pj p-orbitals...

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. 

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... 

A cyclic array of orbitals is a Mobius system if it has an odd number of phase inversions. For a Mobius system, a transition state with An electrons will be aromatic and thermally allowed, while that with An+ 2 electrons will be antiaromatic and thermally forbidden. For a concerted photochemical reaction, the rules are exactly the opposite to those for the corresponding thermal process. 

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 concept can only be applied when there is a cyclic array of orbitals. The conservation of orbital symmetry approach does not have this limitation. 

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