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Insights from intracules and Coulomb holes

We point out that a typical two-electron distribution function in atoms and molecules often called the intracule depends sensitively on the electron-electron repulsion which leads to the so-called Coulomb correlation. The difference between the intracule densities computed by using the correlated and uncorrelated wave functions has been given the name Coulomb hole. Studies in intracule densities and Coulomb holes form a subject of considerable current interest. We make use of a three-parameter correlated wave function and its uncorrelated limit to study the properties of intracules and Coulomb holes in $He$, $Li^+$, $Be^{2+}$ and $Ne^{8+}$ and thus provide a transparent physical picture for the interplay between the electron-nucleus attraction and electron-electron repulsion in forming Coulomb holes around electrons in atoms of different $Z$ values.