Electrophilic aromatic frontier orbital theory

The frontier orbital theory was developed for electrophilic aromatic substitution (Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). Application is successful to the ortho-para orientation (Scheme 23a) for the benzenes substituted with electron donating groups. The ortho and para positions have larger HOMO amplitudes. The meta orientation (Scheme 23b) for the electron accepting groups is under control of both HOMO and the next HOMO [25]. 

The ortho-para- versus meta-directing and activating versus deactivating effects of substituents can also be described in terms of PMO theory. The discussion can focus either on the structure of the cr complex or on the aromatic substrate. According to the Hammond postulate, it would be most appropriate to focus on the intermediate in the case of reactions which are relatively endothermic. The transition state should then resemble the a complex in reactions when the initial step has an appreciable activation energy. For more highly reactive electrophiles the transition state may be more reactant-like, in which case consideration of the reactant and application of frontier orbital theory would be more appropriate. Let us examine the effect of substituents from both perspectives. 

The first paper of the frontier-electron theory pointed out that the electrophilic aromatic substitution in aromatic hydrocarbons should take place at the position of the greatest density of electrons in the highest occupied (HO) molecular orbital (MO). The second paper disclosed that the nucleophilic replacement should occur at the carbon atom where the lowest unoccupied (LU) MO exhibited the maximum density of extension. These particular MO s were called "frontier MO s . In homolytic replacements, both HO and LU.were shown to serve as the frontier MO s. In these papers the "partial" density of 2 pn electron, in the HO (or LU) MO, at a certain carbon atom was simply interpreted by the square of the atomic orbital (AO) coefficient in these particular MO s which were represented by a linear combination (LC) of 2 pn AO s in the frame of the Huckel approximation. These partial densities were named frontier-electron densities . 

None of the above results addresses the question of the position of reaction in the aromatic molecule. In DFT this is done by considering the Fukui function,/. It is interesting that this orientation problem was also the topic of the first paper on frontier orbital theoryReaction was predicted to occur at the position of highest frontier orbital (FO) electron density. The frontier orbital in electrophilic substitution would be the HOMO. If this orbital were written as the usual linear combination of atomic orbitals, then the density at each atom would simply be the square of the coefficient in the LCAO, or c where i indicates the atom. Since this is also one of the ways of approximating / the success of the FO method may also be claimed for DFT. However, the details of the Fukui function application will be postponed briefly to look at a method unique to density functional theory, and using the concept of hardness. ... 

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