Molecular-orbital calculations allyl systems

Of all these (c) is much less likely to be formed because it involves twisting of the allyl system while (a) and (b) are strain free. Again of these (a) is more favoured because the six p lobes are in a quasi planar arrangement. Moreover the molecular orbital calculations made by Dewar have shown that the central p lobes of the two allyl systems in the boat form appear to have a slight destabilizing effect and this has also been confirmed by Woodward and Hoffmann with the aid of correlation diagrams. But both the chair and boat forms have been found in practice. 

Figure 13.3 The n molecular orbitals of the allyl cation. The allyl cation, like the allyl radical, is a conjugated unsaturated system. The shapes of molecular orbitals for the allyl cation calculated using quantum mechanical principles are shown alongside the schematic orbitals. 

Calculate DE py, 9 and for the allyl radical, carbonium ion, and carbanion. Sketch out the molecular orbitals for the allyl system. 

Now let us determine the HMOs of an allyl system by considering the combination of three parallel p orbitals (Figure 4.3). It does not matter whether we are interested in the allyl cation or the radical or the anion. In HMO theory the molecular orbitals are calculated on the basis of the number of p orbitals in the n system, not the number of electrons. We presume that we can determine the HMOs for the assembled nuclei and then add the electrons later. 

FIGURE 3.34 Calculated molecular orbitals of the allyl system. 

A 1,3-dipole as shown in Schemes 6-5 and 6-6 corresponds to a system with three parallel atomic p-orbitals, i.e., to an allyl anion, but without net charge. It is, therefore, called an allyl-type 1,3-dipole. The system may contain, however, an additional 7i-bond in the plane perpendicular to the allyl anion type molecular oribtal, and then belongs to the propargyl - allenyl type. Normally, 1,3-dipoles of this type are linear, whereas those of the allyl type are bent. The term 1,3 relates to the reactivity in these positions, not to formal charges. A series of theoretical studies (e. g., by Hiberty and Leforestier, 1978 Yamaguchi et al., 1980 see review of Houk and Yamaguchi, 1984) clearly show, however, that some of these 1,3-dipoles have considerable biradical character (e.g., O3 53% and CH2N2 28% in ab initio calculations at the 4-3IG level). We will return to biradicals in the mechanistic discussion of Sect. 6.3. 

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