Frontier electron theory

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 . 

The explanation of these findings was at that time never self-evident. In contrast to the other reactivity theories, which then existed and had already been well-established theoretically, the infant frontier-electron theory was short of solid physical ground, having suggested a possibility of the involvement of a new principle relating to the nature of chemical reactions. 

In the same year as that of the proposal of the frontier-electron theory, the theory of charge-transfer force was developed by Mulliken with regard to the molecular complex formation between an electron donor and an acceptor 47>. In this connection he proposed the "overlap and orientation principle 48> in which only the overlap interaction between the HO MO of the donor and the LU MO of the acceptor is considered. 

The frontier-electron density was used for discussing the reactivity within a molecule, while the superdelocalizability was employed in comparing the reactivity of different molecules 44>. Afterwards, the applicability of the frontier-electron theory was extended to saturated compounds 50>. The new theoretical quantity "delocalizability was introduced for discussing the reactivity of saturated molecules 60>. These indices satisfactorily reflected experimental results of various chemical reactions. In addition to this, the conspicuous behavior of HO and LU in determining the steric course of organic reactions was disclosed 44.51). 

The reactivity index is the conventional theoretical quantity which is used as a measure of the relative rate of reactions of similar sort occurring in different positions in a molecule or in different molecules. As has already been mentioned in Chap. 2, most reactivity indices have been derived from LCAO MO calculations for unicentric reactions of planar n electron systems as). The theoretical indices for saturated molecules have also been put to use B0>. In the present section the discussion is limited to the indices derived from the theory developed in the preceding sections, since the other reactivity indices are presented in more detail than the frontier-electron theory in the usual textbooks 65,86) jn this field. 

The contribution of the frontier orbitals would be maximized in certain special donor-acceptor reactions. The stabilization energy is represented by Eqs. (3.25) and (3.26). Even in a less extreme case, the frontier orbital contribution maybe much more than in the expression of the superdelocalizability. If we adopt the approximation of Eq. (6.3), the intramolecular comparison of reactivity can be made only by the numerator value. In this way, it is understood that the frontier electron density, /r, is qualified to be an intramolecular reactivity index. The finding of the parallelism between fr and the experimental results has thus become the origin of the frontier-electron theory. The definition of fr is hence as follows ... 

Parr, R. G., and W. Yang. 1984. Density Functional Approach to the Frontier-Electron Theory of Chemical Reactivity. J. Chem. Soc. 106, 4049. 

Parr, R.G. and Yang, W. 1984. Density functional approach to the frontier-electron theory of chemical reactivity. J. Am. Chem. Soc. 106 4049-4050. 

Scheme 3-5). Ohya-Nishiguchi et al. (1980) noted that such a large localized spin density is very rare in a ir-electron system of purine s size and should have important application to its chemical reactivity. Reactions such as protonation should take place preferentially at position 6. This was deduced from the result of molecular orbital calculations (Nakajima Pullman 1959). According to Fukui s frontier electron theory (Fukui et al. 1952), such areaction should take place at the position where the frontier electron density is the largest. The calculations clearly indicate that the large electron density is at position 6. Scheme 3-5 describes the protonation of the purine anion radical (Yao Musha 1974). Protonation indeed takes place at position 6. After that, the radical center appears at the cyclic nitrogen in the vicinal 1 position.

In the HMO if> of styrene, the coefficients at the a and / carbon atoms are ca. 0-4 and 0-6 respectively. In the HMO ifi7 of acenaphthylene, the coefficients at carbon atoms 1 and 2 are ca. — 032 and 0-32. Therefore, the directive effect for addition is syn in styrene and anti in acenaphthylene Second, MO calculations may be helpful in new or different systems. With respect to eliminations, Fukui and Fujimoto (1965) used frontier electron theory to provide reactivity indices for two model... 

The reactivity indices of amine derivatives based on the frontier electron theory show that there are maximum activities at 0.25 and 0.4... 

Theoretical studies are also done to interpret the synthesis reactions and mechanism of reactions. The regioselectivity of 1,3-dipolar cycloaddition reaction between substituted trimethylstannyl-ethynes and nitrile oxides yielding isoxazoles, was interpreted by the application of frontier electron theory <93CPB478>. By the combination of experimental and molecular orbital (ab initio) studies, a multistep mechanism is proposed for unimolecular radical chemistry of isoxazoles in the gas phase <920MS(27)317>. 

In DFT the frontier electron theory has also been given a more rigorous foundation in terms of the new reactivity index for open molecular systems, called the electronic FF [3-5,84,92,118-122], the CS measuring a response in the local electron density per unit displacement in the system global number of electrons N ... 

Frontier orbital Frontier electron theory is based on the idea that a reaction should occur at the position of largest electron density in the frontier orbitals. In the case of an electrophilic reaction, the frontier orbital is the HOMO, and the LUMO in the case of a nucleophilic reaction. 

The applications of local quantities start with the use of the Fukui function in the frontier-electron theory of chemical reactivity within a density functional framework [19]. In this approach there are three different types of Fukui functions, viz.,... 

Tehan et al. employed AMI calculations [211] to calculate descriptors from frontier electron theory and applied these to estimating the pK, s ol phenols, benzoic acids, and aliphatic acids [212]. Among the descriptors examined the electrophilic delocalizability generally provided the best models for the pK, s of these compounds. 

In 2002 Tehan et al. [213] used semiempirical AMI [211] computations and descriptors from the frontier electron theory [214] to analyze the pK s of nitrogen acids. For a set of 77 aliphatic amines they found... 

Although the title paper from 1952 was only for electrophilic substitution reactions. Fukui et al. [5] further developed the frontier electron theory to be applicable to nucleophilic and radical reagents. In the case of reactions with a nucleophilic reagent, they postulated that the more susceptible position to attack has the higher density of the two electrons assumed to occupy the lowest unoccupied (LU) MO, while the position with the higher density of the two electrons, one occupying the HOMO and the other the LUMO, is more reactive with a radical reagent. With this extension of the theory, they reached the concept of frontier orbitals, i.e. 

Perspective on Density functional approach to the frontier-electron theory of chemical reactivity ... 

Approach to the Frontier-Electron Theory of Chemical Rectivity. 

If this condition is regarded inversely, so to speak when A/ is non-zero, the binding process is promoted, i.e., the Principle of Frontier Electron Theory follows (Parr Yang, 1984, 1989 Yang et al., 1984 Berkowitz, 1987) ... 

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