47r-electron system

The 47r-electron system of nitrile oxides can also participate in 1,3-dipolar cycloaddition with 2H-azirines (71TL4831). For example. 

In the following reaction, the 47r-electron system of the nitrile oxide reacts with the 27t system of one of the acetylenic bonds. 

Here r o = e2/47r t me2 is the classical electron radius and S(q, u) is the scattering function which reflects the properties of the unperturbed scattering system. S(q, to), which is also called the dynamic structure factor, can be expressed [van Hove 1954] by 

We consider systems consisting of two electrons and an infinitely massive nucleus of charge Z, moving subject to the nonrelativistic Hamiltonian (in hartree atomic units, me = it = c = 47r o= 1) 

Classically, cation (3) might be anticipated to be considerably stabilized by the neighboring oxygen atom and double bond on the other hand, its 47r-electron system would suggest anti-aromaticity. The isodesmic calculations showed it to be about 200 kJ mol-1 less stable than the model cation (19b) and about 40 kJ mol-1 less stable than the allyl cation. Thus it appears that it would have an anti-aromatic electronic structure, if it was formed (80TL1807). 

If R1 and R2 are a tri- or tetra-methylene bridge then the products (127) are heterocyclic propellanes (78CI(L)95>. Photolysis of the sulfone (128) eliminates sulfur dioxide to give a 47r-electron system which can be trapped by N- phenylmaleimide (Scheme 41) (78JOC3374). 

Due to their strain and putative electronic destabilization, such three-membered heterocycles possessing a cyclic array of 47r-electrons offer a considerable challenge to synthesis. Such molecules are expected to be both unimolecularly and bimolecularly reactive, if they exist at all as energy minima. Since no isolable tellurirenes have been reported, only some reactions of selenirenes are described in this section. Selenirene and its kindred systems, oxirene, azirine, and thiirene, are of interest because of their theoretical significance as prototypes of antiaromatic species. 

In fact we shall always work in a system of atomic units which is described in Appendix l.Ato this chapter. Roughly speaking, choice of Planck s constant divided by (ft), the charge on the proton (to avoid sign absurdities), and the mass of the electron as units fixes all mechanical quantities. More controversially, perhaps, choosing 47r o (the permittivity of the vacuum) as unity simplifies our Hamiltonian since we are always concerned with electrostatic interactions. 

An extensively investigated and useful hetero-2-azadiene system capable of 4it participation in Diels-Alder reactions is the vinylnitroso compounds.75-78 The complementary addition of electron-withdrawing substituents to the 3 position of the vinylnitroso system enhances the rate of diene participation in inverse electron demand Diels-Alder reactions with electron-rich or neutral dienophiles (simple olefins).75,76 Table 9-IV summarizes a series of representative examples of the 47r participation of vinylnitroso compounds in Diels-Alder reactions, and an extensive review has summarized much of this work.5,75 

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