Auxiliary inductive parameters

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. 

In view of the highly reactive character of pyrrole, the controlling factor for electrophilic substitution is considered to be the v-electron densities. To obtain an agreement between Hiickel MO calculations and experimental observations of chemical reactivity, recourse has to be made to the use of the auxiliary inductive parameter. Satisfactory results are obtained when h = 2 and = 0.25. 

The somewhat arbitrary use of the auxiliary inductive parameter in the Hiickel MO calculations has been questioned and the effect of the nonuniform distribution of a-electron densities, particularly in the CN bond,90 upon the 77-electron distribution has been discussed.65 Variable electronegativity self-consistent field (VESCF) molecular orbital calculations, which are an elaboration of the conventional SCF method and allow for the variation in electronegativity of an... 

Additional problems in theoretical calculations are (1) selection of the coulomb and resonance integral parameters (2) whether an auxiliary inductive parameter be used for the a-carbons (3) whether d orbitals, etc., be taken into account for S, Se, and Te and (4) what type of calculations to use. 

Quinazoline (11.16) nitrates in the 6-position, and because theoretical calculations predict 8- > 6-substitution (the 5- and 7-positions are each conjugatively deactivated by both nitrogens), it has been assumed that reaction must involve the hydrated quinazolinium cation (11.93) (47JOC405 49JCS1367). However, these calculations may not take sufficient account of inductive deactivation of the 8-position the deficiency of the calculations in this respect will be particularly marked if no auxiliary inductive parameter is used for the bridgehead carbon between the 1- and 8-positions. 

The precise values of the -it densities will vary according to the values chosen for the coulomb and resonance integrals however, there seems to be general agreement that aN = ac + 0.5p, and that pCN = (3CC (i.e., h = 0.5, k = 1.0). For more meaningful results an auxiliary inductive parameter (h1) for carbon adjacent to nitrogen is necessary. 

Some -it densities for a representative set of azaphenanthrenes and which demonstrate some of the general points are shown in Scheme 11.7 these were calculated with an extended set of auxiliary inductive parameters of 0.17, 0.055, and 0.002 for carbons a, p, and 7 to nitrogen (62T507). The following main features are evident. 

As stated already, the observed orientations of electrophilic substitution can be accounted for, in the pyrrole molecule, in terms of electrophilic localization energies, without invoking an auxiliary inductive parameter, for positive values of A. However, pyrrole is very reactive, and for this reason orientation would be expected to follow 7r-electron densities. These fall into line (when the acceptable value A = + 2 is used) if A >0 19. The orientation of electrophilic substitution is satisfactorily accounted foi s when A = 2 and A = 0 25. 

Numerous computations of the various reactivity indices of molecular orbital theory have been made. As regards 7r-electron densities, a number of results have been summarized already in Table 3.1. Generally, the Hiickel method gives 7r-electron densities in the order 3 > 2,4 when the auxiliary inductive parameter is small or zero, and to that extent the results correctly... 

---