The Molecular Orbital Account of Polarizability

Some quantities related to the self-polarizability, 7Tr, r are of practical utility in connection with heteroaromatic molecules. They are the mutual polarizabilities of atoms r and s and the polarizability of atom r by the bond s-t defined, respectively, as 

The point of practical importance is that, in certain important cases, namely when the parent hydrocarbon is an alternant hydrocarbon (see below), this equation can be greatly simplified. Then, is always unity (i.e. the TT-electron distribution is always uniform), and thus TTr tu is zero . Therefore, for heteroaromatic systems which are isoconjugate with, alternant hydrocarbons, 

Calculations for quinoline to these degrees of approximation have been compared with values obtained by direct solution of the secular equations Longuet-Higgins and Coulson have used the method to deduce charge distributions for mono- and di-aza-derivatives of naphthalene, anthracene and phenanthrene. Some of the values are included in Table 3,1, others are referred to elsewhere. 

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