Frontier electron population

Indole (2) undergoes electrophilic substitution preferentially at the b(C3)-position whereas pyrrole (1) reacts predominantly at the a(C2)-position [15]. The positional selectivity in these five-membered ring systems is well explained by the stability of the Wheland intermediates for electrophilic substitution. The intermediate cations from 3 (for indole, 2) and a (for pyrrole, 1) are the more stabilized. Pyrrole compounds can also participate in cycloaddition (Diels-Alder) reactions under certain conditions, such as Lewis acid catalysis, heating, or high pressure [15]. However, calculations of the frontier electron population for indole and pyrrole show that the HOMO of indole exhibits high electron density at the C3 while the HOMO of pyrrole is high at the C2 position [25-28] (Scheme 3). 

Fig. 4.6 Frontier electron populations and the sites (arrowed) of nitration...

According to the frontier orbital theory, the frontier electron populations of the parent benzo[3]furan 82 are represented as illustrated . It should be noted that the more positive the numerical values, the mote reactive is the corresponding carbon toward electrophiles. 

Figure 8. Frontier electron population of naphthalene (eV) - HOMO for Ca and CB - using AMI semi-empirical method. () According to ref. [18].

Fukui has explicitly examined this problem,45 stressing just the frontier electron population, which this time is defined to include orbitals just below the HOMO itself. The expression he uses (equation 3-2) defines a function (f) which is an estimate of the effective -electron population when both and ij/3 are... 

For a Z-substituted benzene ring, the total electron population is usually calculated to be higher on the ortho than on the para position (and much higher on the meta position, of course). The frontier electron population is probably... 

This trend is usually put down, without explanation, to the increasing electro-philicity of the radicals. Because the HOMO and LUMO energies of X-substituted benzenes will be raised, we can expect that the HOMO of the aromatic ring is the more important frontier orbital. We have already seen (p. 54) how the frontier electron population is effectively higher in the ortho and para positions for an X-substituted benzene. Thus, the lower the energy of the SOMO of the radical, the better the interaction with the HOMO of the benzene ring, as we have already seen in Fig. 5-7, and hence the more ortho and para attack there is. 

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