Charge-cloud notation

There are a variety of notations for the repulsion integrals either singly or in standard combinations , each has its own logic and there is no overwhelming reason to choose one or the other. It is sometimes more intuitively acceptable to use the physical interpretation of these integrals as the net repulsion between a charge distribution Xi(Ti)Xfe( i) and Xj 2)xi 2) as a justification for the charge-cloud notation ... 

The notation indieates that the summation runs over all distinct pairs i and j or triplets i,j and k, without counting any pair or triplet twice. Ineq. [8.86], the first term represents the effect of an external field on the system, while the remaining terms represent interactions between the particles of the system. Among them, the second one, the pair potential, is the most important. As said in the previous section, in the case of molecular systems the interaction between nuclei and electronic charge clouds of a pair of molecules i and j is generally a complicated function of the relative positions r and rj, and orientations Q and Oj (for atomic systems this term depends only on the pair separation, so that it may written as V2(rij)). 

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