The evaluation of electronic extracule and intracule densities and related probability functions in terms of Gaussian basis functions

The evaluation of the basic two-electron integrals involved in the calculation of extracule and intracule densities is described. Expressions are given for the evaluation of the related spherically averaged, longitudinal, and transverse probability functions from wave functions constructed from Gaussian basis sets. All results are expressed in closed analytical forms which are suited to efficient coding. Given that certain pair densities can be related to experimental scattering cross sections, the formulae reported herein will facilitate further comparison between experiment and theory and lead to a more comprehensive understanding of the electronic structures of molecules.