Frontier Orbital and Charge Transfer Theories

The frontier orbital approach (Fukui et al., 1962, 1954b) has met with considerable success in so far as frontier orbital charges correlate well with experimental data. The performance of these indices is often superior to that of others, with the possible exception of localization energies. It is, however, difficult to give meaning to the correlation since physical interpretations of the role of the frontier electrons in reaction mechanisms are often obscure, and attempts to give substance to Fukui s hypothesis have frequently embodied questionable procedures or models. 

A roughly symmetrical disposition of the centres X and H about the plane of the molecule is assumed, and the pseudo (or group ) orbital has the form j % where 

The coulomb integral associated with f is a and the resonance integral between f % and f r is jS. The secular determinant defining the augmented system takes the form 

Fukui used perturbation methods, assuming j8 to he small, to derive an approximate expression for the change 8 due to hyperconjugation, or augmentation of the tt electron system  

The index j is taken over all MO s of the molecule under attack, and Vj is the occupancy v is 0, 1 or 2 according as the reagent is electrophilic, radical or nucleophilic. The coefficient of j8 in (70) is itself independent of p, and is thus merely an expansion coefficient, analogous to those of 

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B. Analytical Properties of Exaet Methods Relationship between the Indices Frontier Orbital and Charge Transfer Theories The Physical Basis of Reactivity Indices... 

Charge-transfer interactions between frontier molecular orbitals are clearly not the only factors which determine the relative stabilities of various transition states, in spite of the fact that frontier orbital theory has been remarkably successful in accounting for relative reactivities and regioselectivities in various reactions. For example, frontier molecular orbital theory is based on orbital shapes and energies present in the isolated molecules, and these are expected to change upon the approach of one molecule to another. 

In order to understand the importance of frontier orbitals in chemical reactivity, Berkowitz [213] studied the frontier-controlled reactions within the purview of density functional theory. It is evident that the directional characteristics of frontier orbitals determine the extent of charge transfer, and soft-soft interactions are frontier-con-trolled. A somewhat similar analysis showed that charge transfer would be facilitated at a place where the difference in local softness of two partners is large [87], It may be noted that Fukui function is obtainable from local softness but the reverse is not true. On the other hand, local hardness suffers from the drawback of ambiguity [87], which allows one to even consider it to be equal to global hardness without disturbing their... 

These reactivity trends clearly show that polar effects are involved in these radical substitution reactions. The transition state is thought to include a charge transfer 9) from the radical (electron donor) to the pyridinium ion (electron acceptor) [13], Frontier Molecular Orbital Theory (FMO) [14] has been applied to explain the reactivity differences which have been observed upon varying the substituents at the pyridinium ion and upon altering the nucleophilicity of the attacking radical. Moreover, FMO can be used to explain the regioselectivities obtained in these homolytic aromatic substitutions. The LUMO of the substituted pyridinium cation... 

Longuet-Higgins and Salem [1,8] proposed a molecular force field for localized a- electrons and delocalized 77 electrons. Their scheme has become attractive for conjugated polymers [25,26], now in conjunction with semiempirical rather than simple Hiickel calculations. Warshel and Karplus [27] and Hemley et al. [28] combine all-electron calculations of geometry with PPP models for 77 electrons (see also Ref. 21). We will focus exclusively on delocalization or 77-electron contributions using linear response (LR) theory, as illustrated by the AM formalism. LR has been widely applied to vibrational spectra of charge transfer and ion-radical organic crystals [29-32]. The idea is to model shifts due to delocalization relative to some localized reference. The concomitant problem of localized or other contributions is the choice of a reference force field discussed in Section II.B. The solid-state perspective of LR theory is quite compatible with 77-electron or other models based on frontier orbitals. 

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