Hole, correlation

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. 

The concept of the exchange-correlation hole is widely used in density functional theory and its most relevant properties are the subject of the following section. 

The exchange-correlation hole can formally be split into the Fermi hole, hx =°2 (r, r2)... 

Figure 2-2. Fermi, Coulomb and the resulting total exchange-correlation holes for H2 at three different intemuclear distances the position of the probe electron is marked with an arrow (adapted from Baerends and Gritsenko, J. Phys. Chem. A, 101, 5390 (1997), with permission by the American Chemical Society).

Exchange-Correlation Energy and Exchange-Correlation Hole.87... 

EXCHANGE-CORRELATION ENERGY AND EXCHANGE-CORRELATION HOLE... 

This function also gives an accurate description of the behavior of a linear chain in a good solvent (the expansion of the chain size is scaled by the x variable) except for very high values of x, corresponding to short distances between units. These short distances are dominated by the correlation hole effect due to EV [16,26]. 

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