Frontier-electron method

From 1933 85>, several theoretical approaches to the problem of the chemical reactivity of planar conjugated molecules began to appear, mainly by the Huckel molecular orbital theory. These were roughly divided into two groups 36>. The one was called the "static approach 35,37-40)j and the other, the "localization approach 41,42). in 1952, another method which was referred to as the "frontier-electron method was proposed 43> and was conventionally grouped 44> together with other related methods 45 48> as the "delocalization approach". 

One example showing a serious discrepancy of the frontier electron method was reported by Dewar H8,ii9). This is 10,9-borazaphenanthrene, and the value of / -B) was reported to have been calculated by the Pople method, but the parameters usyd were not indicated. Fujimoto s calculation by the Pariser-Parr-Pople method 120>, in perfect disagreement with Dewar s, gives the most reactive position as 8, which parallels experiment. The ambiguity involved in the integral values adopted seems to be serious, so that the establishment of parametrization for boron heterocycles is desirable. 

One example showing a serious discrepancy of the frontier electron method was reported by Dewar This is 10j9-borazaphenanthrene,... 

Several calculations of the electronic structure of isoindoles have Ijeen published, and the distribution of charge density around the isoindole nucleus calculated by these methods is summarized in X able I. A common prediction of the calculations, which are based on tlie LCAO-MO method or the frontier electron concept, is the relatively high electron density to bo found at position 1, and the expectation, thei efore, i.s that electrophilic substitution on carbon... 

Calculations predict the most reactive sites in thieno[2,3-b]quinoline (8.132) to be the expected 2- or 3-positions [77ZN(B)1331], but there is little agreement on the positional reactivity order in 6-methylindolo-[2,3-6]quinoxaline (8.133) (84CHE687). tt Densities predict the order 7 > 9 > 1 (Huckel) or 7 > 9 > 3,4 (CNDO/2), localization energies (Huckel) predict 4 > 7 > 1, superdelocalizabilities predict 4 > 1 > 7, and frontier electron densities predict 1 > 4 > 3 (Huckel) or 4 > 1 > 2 (CNDO/2). The observed nitration and bromination at the 9-position serve to underline the inadequacy of all these theoretical methods. Localization energies predict that pyrrolo[l,2-[Pg.251]

In all of the above discussion we have assumed that a given molecule forms both the new ct bonds from the same face of the n system. This manner of bond formation, called suprafacial, is certainly most reasonable and almost always takes place. The subscript s is used to designate this geometry, and a normal Diels-Alder reaction would be called a [ 2s + 4J-cycloaddition (the subscript 71 indicates that n electrons are involved in the cycloaddition). However, we can conceive of another approach in which the newly forming bonds of the diene lie on opposite faces of the n system, that is, they point in opposite directions. This type of orientation of the newly formed bonds is called antarafacial, and the reaction would be a [ 2 + 4a]-cycloaddition (a stands for antarafacial). We can easily show by the frontier-orbital method that this reaction (and consequently the reverse ring-opening reactions) are thermally forbidden and photoche-mically allowed. Thus in order for a [fZs + -reaction to proceed, overlap between the highest occupied n orbital of the alkene and the lowest unoccupied 71 orbital of the diene would have to occur as shown in Fig. 15.10, with a + lobe... 

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

The reactivity indices method is based on the assumption of a direct correlation between the activation free energy of a process and some intrinsic parameters, called reactivity indices, related to the electronic properties of the heteroaromatic species involved in the process itself. Some indices, such as charge density, frontier electron density, polarizability, or free valence, pertain to electronic properties of the unperturbed neutral substrate, which is considered in an isolated state. Other indices, such as the localization energy, are related to the stability of the transitional or intermediate state of the substitution process, e.g., the n or a complex in electrophilic substitution reactions (Fig. 1). 

Professors Kenichi Fukui (Kyoto University) and Roald Hoffmann (Cornell University) received the 1981 Nobel Prize in Chemistry for their quantum mechanical studies of chemical reactivity. Their applied theoretical chemistry research is certainly at the core of computational chemistry by today s yardstick. Professor Fukui s name is associated with frontier electrons, which govern the transition states in reactions, while that of Hoffmann is often hyphenated to R. B. Woodward s name in regard to their orbital symmetry rules. In addition, Professor Hoffmann s name is strongly identified with the extended Hiickel molecular orbital method. Not only was he a pioneer in the development of the method, he has continued to use it in almost all of his over 300 papers. 

Several sets of theoretical calculations have been performed on the parent ring system. HMO calculations of total rr-electron densities and frontier electron densities successfully predicted that the nucleus would undergo electrophilic substitution at the 6- and 8-positions. Two groups, " have compared the electronic structure of indolizine and various aza derivatives using the SCF or semiempirical antisymmetric configuration interaction method. The results allowed interpretations of the electronic spectrum to be made which were in good agreement with experiment. 

Tehan et al. [213] used the AMI [211] semiempirical method and parameters from frontier electron theory [214] to model the pK s of 55 anilines, Using the electrophilic superdelocalizability SE, of the nitrogen atom they obtained the relation... 

Most of the theoretical methods used to correlate chemical reactivity trends implicitly (or in some cases explicitly) use a model of interacting diabatic surfaces in which the transition structure is associated with an avoided crossing of a reactant-like or a product-like diabatic surface. In the molecular-orbital correlation diagram approach of Woodward and Hoffmann or the frontier orbital method of Fukui, the molecular orbitals of the fragments are first mixed to form the MO of the supermolecule and then the electrons are assigned to various configurations of these supermolecule MO. We shall refer... 

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