Values and Positions of the Charges

The values of the various charges i and their positions (X(, yt, Zi) must satisfy the following relationships  

qiXiyt = Sgxydv. JjqtytZi = fgyzdv. qiZiXt = Igzxdv 

In any case the problem of molecular charges includes many special constraints, for in the mind of the chemist the charges are viewed as located near if not on the nuclei. Therefore, their number is limited and fixed in advance as being the same as the number of nuclei in the molecule. Of course, this restriction will have a great impact on the quality of the description, for it vrill be possible to equate only a small number of multipole terms. The increase in the number of point charges introduced will improve the description. For instance, for the molecule H2O, with 13 charges, one obtains a potential which practically coincides with the exact potential 

However, such a model does not interest the chemist. Therefore in the following, we shall alwa3re assume that the number of charges is the same as that of the nuclei. 

Let us examine, first the case of a diatomic molecule AB. Let qx and q be the charges. For S3mimetry reasons we shall place them on the nuclear axis. Let Zx and z-a be their non-vanishing coordinates. Then  

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