Frontier orbital interactions between cation

Fig. 2. Frontier orbital interactions between 16e-L5M and a diaminophosphenium cation.

We have now seen how the attraction of charges and the interaction of frontier orbitals combine to make a reaction between two such species as the allyl anion and allyl cation both fast and highly regioselective. We should remind ourselves that this is not the whole story another reason for both observations is that the reaction is very exothermic the energy of a full a bond is released with cancellation of charge, which would not be the case if reaction took place at C-2 on either component. Thus we are in the situation of Fig. 3.1a—the Coulombic forces and the frontier orbital interaction on one side, and the stability of the product on the other, combine to lower the energy of the transition structure. 

Frontier orbital theory also provides the basic framework for analysis of the effect that the symmetiy of orbitals has upon reactivity. One of the basic tenets of MO theory is that the symmetries of two orbitals must match to permit a strong interaction between them. This symmetry requirement, when used in the context of frontier orbital theory, can be a very powerful tool for predicting reactivity. As an example, let us examine the approach of an allyl cation and an ethylene molecule and ask whether the following reaction is likely to occur. 

The positively charged allyl cation would be expected to be the electron acceptor in any initial interaction with ethylene. Therefore, to consider this reaction in terms of frontier orbital theory, the question we need to answer is, do the ethylene HOMO and allyl cation LUMO interact favorably as the reactants approach one another The orbitals that are involved are shown in Fig. 1.27. If we analyze a symmetrical approach, which would be necessary for the simultaneous formation of the two new bonds, we see that the symmetries of the two orbitals do not match. Any bonding interaction developing at one end would be canceled by an antibonding interaction at the other end. The conclusion that is drawn from this analysis is that this particular reaction process is not favorable. We would need to consider other modes of approach to analyze the problem more thoroughly, but this analysis indicates that simultaneous (concerted) bond formation between ethylene and an allyl cation to form a cyclopentyl cation is not possible. 

Alston36,170 has pointed out that the regi selectivity in this and some other reactions may be better attributed, not to the primary interactions of the frontier orbitals that we have been using so far, but to the secondary interactions. 1 -substituted dienes often show very small differences in the coefficients on C-l and C-4 in the HOMO. (We have already seen, on p. 124, how some calculations make them come out the other way round from that shown on Fig. 4-38.) On the other hand, 1-substituted dienes regularly show a much larger difference between the coefficients on C-2 and C-3. The crude way we have handled the problem does not immediately demonstrate this thus we can see in the example in Fig. 4-50 how the contribution of the triene-like character and the pentadienyl-cation-like... 

The frontier orbital treatment for vinyl cation cycloadditions, such as those of ketenes, has some merits. It satisfyingly shows that the bond forming between C-l and C-l develops mainly from the interaction of the LUMO of the ketene (n of the C=0 group) and the HOMO of the alkene 6.178, and that the bond between C-2 and C-2 develops mainly from the interaction of the HOMO of the ketene (i/j2 of the 3-atom linear set of orbitals analogous to the allyl anion) and the LUMO of the alkene 6.179. 

In order to explain this fact we use the frontier orbital theory [7]. First of all we examine the probability of interaction between the methyl cation and hexamethyldisilazane in the condensation... 

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