Electron-pair density relaxation holes

The electron-pair density relaxation hole has been defined as the electron-pair density of the real molecule minus the electron-pair density of a reference system consisting of overlapping, spherically averaged, undeformed atoms, positioned at the molecular nuclear coordinates. We have shown how it can be calculated from one- and two-electron reduced density matrices expanded in a Gaussian type basis set. Analysis of the calculated radial electron-pair density holes, from full configuration interaction one- and two-electron reduce density matrices, for the ground states of the hydrogen molecule, the helium dimer and the lithium and beryllium hydrides reveal that the different types of bonding interactions yield distinctively visually recognizable different topological patterns of the electron-pair density relaxation hole.