Exchange-overlap charges

Coulomb integrals Jij describe the coulombic interaction of one charge density (( )i2 above) with another charge density (c )j2 above) exchange integrals Kij describe the interaction of an overlap charge density (i.e., a density of the form ( )i( )j) with itself ((l)i(l)j with ( )i( )j in the above). 

On grouping functions of the same variable again, as in Eq. (8.12), we find A"(l,2) to describe something like the repulsion between overlap charge clouds . This has no classical parallel and the integral is simply called the exchange integral, for that is how it arose quantum mechanically. 

These integrals are clearly of the exchange type because they involve the coulombic interaction of the 2s 2px y or z overlap charge density with itself. 

The exchange-repulsion energy is approximately proportional to the overlap of the charge densities of the interacting molecules [71, 72 and 73]... 

If the ion exchange column is loaded with several ions of similar charge, B, C, etc., elution curves may be obtained for each ion by the use of appropriate eluants. If the elution curves are sufficiently far apart, as in Fig. 7.2, a quantitative separation is possible only an incomplete separation is obtained if the elution curves overlap. Ideally the curves should approach a Gaussian (normal) distribution (Section 4.9) and excessive departure from this distribution may indicate faulty technique and/or column operating conditions. 

If the charge distributions of the D and A overlap than a new class of interactions has to be considered, namely the exchange interaction between the electrons on D and on A. This type of energy transfer is called Dexter transfer [80, 96,98], Here we briefly outline the physical principles involved. 

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