Orbital Treatment of the Isolated Molecule Method

The work of Wheland and Pauling may be outlined as follows. The TT- electron density at atom r in the aromatic structure is given by 

It is useful to digress slightly at this point to notice some relationships which justify the importance attached to the quantities qr and the bond order, prsi already seen to be of great value in discussing aromatic structure. From the expression for Ej (p. 23), the energy of the jth molecular orbital, we have, by normalizing and neglecting overlap  

These expressions show that qr and prs are indeed basically important to the properties of the system. 

Evaluation of the coefficients c r makes possible a more complete description of the isolated aromatic molecule than is provided merely by the 77-electron densities and the bond orders, prs- A quantity related to prsy the free valency at the rth atom, FV, is useful in considerations of reactivity. Coulson24 defined this quantity as 

The numerical factor in this equation refers to the a bonds in which atom r is engaged. iVmax is the maximum degree of bonding of which atom r is capable. Since Nr measures the extent to which the atom is already committed to bond formation, it is not unreasonable to regard Fr as a measure of its residual valency, and thus, of its reactivity towards attack by free radicals. Various values have been used for that used by a particular 

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