Allylic systems, orbital diagram

The energy level diagram including electron populations for the allyl radical, cation, and anion can be shown as illustrated in Figure 5.16. The orbital diagram and energy levels for the allyl system is shown in Figure 5.17. 

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 1.18 The tt MO s of the allyl system. The basis orbitals from which the tt MO s are constructed are shown at the top of the figure, and below are the molecular orbitals in an energy-level diagram.

The essential features of the Diels-Alder reaction are a four-electron n system and a two-electron it system which interact by a HOMO-LUMO interaction. The Diels-Alder reaction uses a conjugated diene as the four-electron n system and a it bond between two elements as the two-electron component. However, other four-electron it systems could potentially interact widi olefins in a similar fashion to give cycloaddition products. For example, an allyl anion is a four-electron it system whose orbital diagram is shown below. The symmetry of the allyl anion nonbonding HOMO matches that of the olefin LUMO (as does the olefin HOMO and the allyl anion LUMO) thus effective overlap is possible and cycloaddition is allowed. The HOMO-LUMO energy gap determines the rate of reaction, which happens to be relatively slow in this case. 

The molecular orbital energy diagram for the carboxylate anion is the very similar to that of the allyl system. There are just two main differences. 

Just to reiterate, the same molecular orbital energy diagram can be used for the allyl systems and the carboxylate and nitro groups. Only the absolute energies of the molecular orbitals are different since different elements with different electronegativities are used in each. 

Why would the following molecular orbital diagram for the allyl system be incorrect ... 

We can summarize all this information in a molecular orbital energy level diagram, the n molecular orbitals of the allyl system the allyl cation... 

Fig. 6a and b. Correlation diagram for the orbitals in the cyclopropyl-allyl systems a) conrotatory motion b) disrotatory motion... 

The n molecular orbital energy level diagram sketched, for the allyl system under Huckel approximation and computed the delocalization energy of allyl cation ... 

This diagram shows only the 7C orbitals of the allyl system. 

The most common and also most effective mechanism of radical stabilization involves the resonant delocalization of the unpaired spin into an adjacent 7r system, the allyl radical being the prototype case. A minimal orbital interaction diagram describing this type of stabilization mechanism involves the unpaired electron located in a 7r-type orbital at the formal radical center and the 7r- and tt -orbitals of the n system (Scheme 1). 

So once again we have three p orbitals to combine. This is the same situation as before. We have the same atoms, the same orbitals, and so the same energy levels. In fact, the molecular orbital energy level diagram for this compound is almost the same as the one for the allyl cation the only difference is the number of electrons in the it system. Whereas in the allyl cation Jt system we only had two electrons, here we have three (two from the 7t bond plus the single one). Where does this extra election go Answer in tire next lowest molecular orbital—the nonbonding molecular orbital,... 

Frontier orbitals can help to explain the results seen when a sigmatropic shift involves migration of carbon rather than hydrogen. A [1,3] migration of carbon involves Att electrons. We can think of the reaction as migration of a carbon radical across the tt system of an allylic radical. In this case, overlap of the p orbital of the carbon radical with the allylic v system can be visualized as shown in the following diagram. 

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