Correlations hole density with

In this chapter we make first contact with the electron density. We will discuss some of its properties and then extend our discussion to the closely related concept of the pair density. We will recognize that the latter contains all information needed to describe the exchange and correlation effects in atoms and molecules. An appealing avenue to visualize and understand these effects is provided by the concept of the exchange-correlation hole which emerges naturally from the pair density. This important concept, which will be of great use in later parts of this book, will finally be used to discuss from a different point of view why the restricted Hartree-Fock approach so badly fails to correctly describe the dissociation of the hydrogen molecule. 

We found that our method results in electron densities nx(r) which deviate from the reference density by less than 1%. This is shown in figure 1(a) where the density is plotted as a function of A along a line parallel to the direction in which the external potential varies (we call this the ( direction). While the density is fixed, all other physical quantities vary smoothly and monotically with A. As an example we consider the spherically-averaged exchange-correlation hole... 

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