Frontier electrons

Fig. 1. Frontier electron levels for polymethines containing the simplest end groups with low basicity (a, high basicity (P, 63°).

An alternative approach is in terms of frontier electron densities. In electrophilic substitution, the frontier electron density is taken as the electron density in the highest filled MO. In nucleophilic substitution the frontier orbital is taken as the lowest vacant MO the frontier electron density at a carbon atom is then the electron density that would be present in this MO if it were occupied by two electrons. Both electrophilic and nucleophilic substitution thus occur at the carbon atom with the greatest appropriate frontier electron density. 

The significance of frontier electron densities is limited to the orientation of substitution for a given aromatic system, but this approach has been developed to give two more complex reactivity indices termed superdelocalizabilities and Z values, which indicate the relative reactivities of different aromatic systems. 

Polarization and dipole moment studies for alkyl-, aryl-, carbonyl- hydroxy- (keto-) and amino-isoxazoles have been compiled and likewise support the low electron nature of the ring 63AHC(2)365, 62HC(l7)l,p. 177). More recent studies predict the order of electrophilic substitution to be 5>4> 3 on frontier electron density values of 0.7831, 0.3721 and 0.0659, respectively 7lPMH(4)237,pp.245,247). This contrasts with earlier reports of 4>5>3 on density values of —0.09, -t-0.14 and -t-0.18 in that order 63AHC(2 365). 

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... 

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". 

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 behaviour of the frontier electrons was also attributed to a certain type of electron delocalization between the reactant and the reagent 40). A concept of pseudo-n-orbital was introduced by setting up a simplified model, and the electron delocalization between the 71-electron system of aromatic nuclei and the pseudo-orbital was considered to be essential to aromatic substitutions. The pseudo-orbital was assumed to be built up out of the hydrogen atom AO attached to the carbon atom at the reaction center and the AO of the reagent species, and to be occupied by zero, one, and two electrons in electrophilic, radical, and nucleophilic reactions. A theoretical quantity called "superdelocalizability was derived from this model. This quantity will be discussed in detail later in Chap. 6. 

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). 

Hi) The principle of growing frontier-electron density along the reaction path... 

The importance of the frontier-orbital AO coefficient is evident from Eqs. (3.21) and (3.26). The problem is how this quantity changes along the reaction path. It can be shown by actual calculation that the frontier-electron density generally increases as the reaction proceeds. 

In order to understand qualitatively how the frontier-electron density, (cconjugated hydrocarbons, it is convenient to take account of Stage III. In this stage it is easily proved that... 

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 reactivity indices derived from the theory which has been developed in Chap. 3 are the frontier-electron density, the delocalizability, and the superdelocalizability, as has been mentioned in Chap. 2. These indices usually give predictions which are parallel with the general orientation rule mentioned in Chap. 5. The superdelocalizability is conventionally defined for the jr-electron systems on the basis of Eq. (3.21) and Eq. (3.24) as a dimensionless quantity of a positive value by the following equations 49> ... 

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 ... 

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. 

The reactivity of hydrogens in norbomane towards abstraction is of interest since the difference between two hydrogen atoms attached to the same carbon atom of position 2 can well be explained. The frontier electron density values 105> are in accord with the reactive exo hydrogen (Fig. 7.20). 

Figure 2. Frontier electron density distribution for the p-toluidinyl radical...

Probability of Finding the Frontier Electron at the Various Sites in the Arylaminyl Radicals... 

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. 

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. 

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