Atom localization energy

Table 1-4 gives some calculated reactivity indices free valence or Wheland atomic localization energies for radical, electrophilic, or nucleophilic substitution. For each set of data the order of decreasing reactivity is indicated. In practice this order is more reliable than the absolute values of the reactivity indices themselves. 

A second theoretical index, and one for which there appears to be more justification in its application to free-radical reactions, is the atom localization energy. This index is a measure of the energy required to localize one electron of the 7r-electron system in the aromatic molecule at the point of attack of the radical. The formation of the intermediate adduct in a free-radical aromatic substitution may be regarded as the sum of two processes one, the localization of an electron at the point of attack and the other, the pairing of this... 

It is of interest that both the methyl affinities and the reactivities of aromatic compounds toward the pheny radical are correlated both by Froax and by atom localization energies. Dewar has shown that the energy required to remove one atom from conjugation (in a hydrocarbon containing an even number of carbon atoms) is greater... 

Figure 2. Minimum atomic localization energy in benzenoid hydrocarbons plotted against energy of the highest occupied molecular orbital (HOMO).

A well understood case is that of quinoline reaction at position 2 is kinetically favored as compared with reaction at position 4, but the adduct from the latter is thermodynamically more stable. This situation, where the site of attack leading to the more stable adduct is the y position, is analogous with those regarding the formation of Meisenheimer adducts from benzene and pyridine derivatives and RCT nucleophiles. Presumably, with quinoline kinetic control favors the position that is more strongly influenced by the inductive effect of the heteroatom. The fact that position 2 of quinoline is the most reactive toward nucleophilic reagents is probably related to the lower 71-electron density at that position.123 However, the predominance of the C-4 adduct at equilibrium can be better justified by the atom localization energies for nucleophilic attachment at the different positions of quinoline. Moreover, both 7t-electron densities and atom localization energies indicate position 1 of isoquinoline to be the most favored one for nucleophilic addition. 

Somewhat more involved is the computation of further reactivity indices Wheland s atom localization energy, A6 exact super-delocalizability, S7 various polarizabilities, ir8 Brown s factor, Z° Dewar s reactivity number, Ap10 and the approximate superdelocali-zability, S 7... 

The letters A and B in parentheses indicate the empirical parameter used in the HMO calculation (A 8jr = 0.5 B 8k+ = 2.0). Af denotes the atom localization energy. c Correlation coefficient. d Number of data points. 

It was found years ago136 that atom localization energies are correlated with free valences and autopolarizabilities. 

Recently, a series of models of 16 polynuclear pyridine-like heterocycles (Fig. 9 shows formulas of eleven of these) were treated using the HMO approximation7 (SN = 0.6, inductive effect not allowed for) and the following reactivity indices calculated 77-electron densities (q), bond orders (p), free valences (F, N x = Wheland s atom localization energies (A(,Ar,An), and superdelocalizabilities, both exact (Se,Sr,Sn) and approximate (S e,S r,S n). Atom-atom polarizabilities150 (773) had been calculated earlier.151 Some of the indices calculated are presented in Section VI, B. 

Atom localization energy for the parent hydrocarbon in the position in which the heterocycle carries a nitrogen atom. Water, according to refs. 162 and 162a. 

The following quantities are presented in Table IX total 77-elec-tronic energy (W), its deviation from that of the parent hydrocarbon (AW), energies of the four frontier 7r-molecular orbitals (k2, klt and Jfc 2 k is the highest occupied orbital, HOMO is the lowest free orbital, LFMO), Fj transition energy [ (A - Ft)] and the atom localization energy for the parent hydrocarbon in the position in which the heterocycle has a nitrogen atom. 

B. Indices of Chemical Reactivity Table X presents the following data for models of molecules XV-XXV 7r-electron densities (q), atom-atom polarizabilities (77 ), free valences (F, Nmhx = /3), and exact superdelocalizabilities (Se,8r, and Sn). Table XI gives Wheland s atom-localization energies for a few molecules. Bond orders for molecules XV-XXV are compiled in Table XII. 

Atom-Localization Energies of Various Heterocyclic Compounds... 

Fig. 11. Plot of logiofo against atom localization energy [atom localization energy values taken from S. Sato and R. J. Cvetanovic, J. Am. Chem. Soc., 81, 3223 (1959) TetraME = tetramethylethylene].

The dimerization of butadiene, aryl olefins and ethyl vinyl ether is best rationalized by postulating a radical cation 89 (Eq. (174) ) as first intermediate. As the fi -carbon of 89 has the highest free valence, the highest positive charge density and the lowest atom localization energy radical or electrophilic reactions of 89... 

Pyridine A-oxide is considered to be a resonance hybrid of various canonical structures (la-e). Atom localization energies calculated... 

Since sulfonation of pyridine iV-oxide is about as difficult as is that of pyridine itself and takes place at the 3-position,17 it has been assumed18 that, in fuming sulfuric acid, pyridine iV-oxide reacts only in the salt form (3), when the prediction is that substitution at C-3 would take place. It is, however, difficult to account for the fact that bromination, even at 110° in the presence of iron powder, does not occur.17 Bromination in chloroform solution in the presence of acetic anhydride and sodium acetate (when the O-acetate is the the probable substrate) take place readily, however, to give 3,5-dibromopyridine JV-oxide.19 The predicted order of nucleophilic reactivity, on the basis of both atom localization energies and ground-state v-electron density calculations, is 4 > 2 > 3. The same order is predicted for the nucleophilic substitution reactions of the salts of pyridine JV-oxide. In actual practice, iV-alkoxypyridinium derivatives undergo nucleophilic attack preferentially at C-2.20-23 The reaction of some pyridine iV-oxides with phosphorus pentachloride may involve the formation... 

The free-radical arylation of pyridine N-oxides has not been studied systematically, alkylation not at all. When pyridine A-oxide was treated with benzene- and p-chlorobenzenediazonium salts only the 2-arylpyridine jV-oxides were isolated.393 No mention was made of the formation of the 3- and 4-aryl derivatives expected to be produced as well. The phenylation of pyridine N-oxide (diazoaminobenzene at 131° or 181° was found to be the most convenient source of phenyl radicals) was reinvestigated,394 and the reactivities of the nuclear positions found to be in the order 2 > 4 > 3, which is also that predicted6 on the basis of atom localization energy calculations. 2-Phenyl-pyridine N-oxide formed 71-81% of the total phenylation products, whereas the 3-isomer comprised only 5.6-9.6% of that total. The phenylpyridines were found among the by-products of the reaction. 

Another approach consists of the calculation of relative rates for substitution from the atom localization energies of Wheland. It gives a more qualitative insight. However in the instance of homolytic reactions at 80 C the relative reaction rates arc better approaching the experimental results (Fig. 14c). 

It is notable that pyridine is activated relative to benzene and quinoline is activated relative to naphthalene, but that the reactivities of anthracene, acridine, and phenazine decrease in that order. A small activation of pyridine and quinoline is reasonable on the basis of quantum-mechanical predictions of atom localization energies,107 whereas the unexpected decrease in reactivity from anthracene to phenazine can be best interpreted on the basis of a model for the transition state of methylation suggested by Szwarc and Binks.100 The coulombic repulsion between the -n-electrons of the aromatic nucleus and the p-electron of the radical should be smaller if the radical approaches the aromatic system along the nodal plane rather than perpendicular to it. This approach to a nitrogen center would be very unfavorable, however, since the lone pair of electrons of the nitrogen lies in the nodal plane and since the methyl radical is... 

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