Induction energy non-additivity

The non-additivity of the intermolecular interaction results mainly from the non-additivity of the induction contribution. 

How do we convince ourselves about the non-additiviiy This is very easy. It will be sufficient to write the expression for the induetion energy for the case of three molecules and to see whether it gives the sum of the pairwise induction interactions. Before we do this, let us write the formula for the total second order energy correction (similar to the case of two molecules on p. 694)  

For the time being let us consider the induction energy EindiABC). WWting V as the sum of the Coulomb interactions of the pairs of molecules we have 

Look at the product in the nominator. The induction non-additivity arises just because of this product. If the product (being the square of the absolute value of nA B VAB A B) + nA c VAC A c)) were equal to the square of the absolute values of the first and second component, the total expression shown expHdtly would be equal to the induction energy corresponding to the polarization of A by the frozen charge distribution of B plus a similar term corresponding to the polarization of A by C, i.e. the polarization occurring separately. Together with the other terms in i ind( B— - C)-l- ind( C B) we would obtain the additivity of the 

we obtain the following expression for the induction non-additivity ia fABCy. 

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