Determination of the integrated x-ray scattering intensities through the electron-pair relative-motion density at the origin

A relation connecting the integrated total x-ray scattering intensity and the electron-pair relative-motion density at the origin or electron-electron coalescence density, I(0), is put forward. This link shows that the electron-electron coalescence density can be deter-mined by the experiment. In addition, the proposed relation opens the possibility for assessing the quality of the theoretical calculations of the electron-electron coalescence density against experimental data. A series of atomic and molecular integrated x-ray scattering intensities are reported from the theoretically determined electron-electron coalescence data. Additionally, the integrated elastic and inelastic components are determined and their importance in describing the charge concentration and the exchange and correlation effects in molecular systems is discussed.