Localization energies for

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. 

The localization energies for electrophilic substitution in benzimidazole predict that all three reactive forms should undergo substitution in the 4-position. This does not explain the formation of the 5-nitro compound or that of the 2-deutero compound. It is doubtful whether any electrophilic substitution occurs preferentially in the 4-position. 

CNDO calculations provide estimates of the localization energies. For benzene, naphthalene, and anthracene, these are, respectively, 36.3, 15.4, and 8.3 kcal/mol. ... 

It is difficult to treat the effect of a heteroatom on the localization energies of aromatic systems, but Brown has derived molecular orbital parameters from which he has shown that the rates of attack of the phenyl radical at the three positions of pyridine relatively to benzene agree within 10% with the experimental results. He and his co-workers have shown that the formation of 1-bromoisoquinoline on free-radical bromination of isoquinoline is in agreement with predictions from localization energies for physically reasonable values of the Coulomb parameters, but the observed orientation of the phcnylation of quinoline cannot be correlated with localization ener-... 

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. 

A systematic and intensive theoretical study of reactivity has been reported by Brown and his colleagues,8,115,139-142 who discussed the reactivity of pyridine, quinoline, and isoquinoline in terms of localization energies. They investigated the values of these indices, first of all for electrophilic substitution, with regard to the value of the Coulomb integral of the heteroatom orbital and the orbitals adjacent to it (auxiliary inductive parameters). They demonstrated that the course of electrophilic substitution can be estimated from theoretical reactivity indices if 77-electron densities are used for reactions that occur readily and localization energies for those occurring only reluctantly. 

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. 

Localization energies for electrophilic substitution were also calculated for a number of systems and were found to be in accord with experimental data. In these calculations a model was used with a core charge of 1 on both nitrogen and boron. In (3) the 3-position was predicted to be the most reactive to electrophilic substitution, in (17) the 2-position and in (16) the 3-position. These predictions were also made by Carbo using Fukui s superdelocalizability. 

Scheme 2. Calculation of the reactivity number (localization energy) for the 1-position of naphthalene according to the PMO and PMO-F method. (The denominator follows from the normalization condition, i.e. the normalized NBMO coefficients are inversely proportional to the root of the sum of squares of the unnormalized coefficients)...

As the values of the minimum Dewar reactivity number can obviously be connected only with the initial step of the thermal chemistry of benzenoid hydrocarbons it was concluded that the initial step is rate-determining. However, it is also possible that some other factor, connected with the Dewar localization energies for topological reasons, determines the rates of reaction. 

MO studies of aromatic nitration cast doubt on the existence of jt-complexes and electron-transfer complexes in liquid-phase nitrations.14 The enthalpy of protonation of aromatic substrates provides a very good index of substrate reactivity to nitration. Coulomb interaction between electrophile and substituent can be a special factor influencing regioselectivity. A detailed DFT study of the reaction of toluene with the nitronium ion has been reported.15 Calculated IR spectra for the Wheland intermediates suggest a classical SE2 mechanism. MO calculations of cationic localization energies for the interaction of monosubstituted benzenes with the nitronium ion correlate with observed product yields.16... 

Fig. 9.2. Plot of

By applying this calculation to the system which remains after localization, it is possible to calculate also the localization energy (p. 258) even for complicated molecules, or, better, differences in localization energy for various positions. 

These results have made possible a comparison of the reactivities of the chlorine atoms in 3-phenyl-5-chlororl,2,4-thiadiazole, 2-phenyl-5-chloro-l,3,4-thiadiazole, and 3-chloro-5-phenyl-l,2,4-thia-diazole. The reaction of the first and last compound with piperidine in ethanol has been investigated by Goerdeler and Hellerand the rate constants of the three compounds at 30° decrease in the ratio 7000 64 1. This order is the same as has been predicted by Zahradnfk and Koutecky on the basis of localization energies for the nucleophilic reactivity of the simple ring systems. 

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