Electron-pair relative-motion densities of atoms in position and momentum spaces

Abstract

Spherically averaged electron-pair relative-motion (intracule) densities $h(u)$ in position space and $\overline{h}(v)$ in momentum space represent probability densities of finding interelectronic position and momentum distances, $|{\mathbf{r}}_{j}\ensuremath{-}{\mathbf{r}}_{k}|$ and $|{\mathbf{p}}_{j}\ensuremath{-}{\mathbf{p}}_{k}|,$ of any pair of electrons $j$ and $k$ to be $u$ and $v,$ respectively. Using the numerical Hartree-Fock method, these electron-pair densities $h(u)$ and $\overline{h}(v)$ are constructed and examined systematically for the atoms from He to Xe in their ground state. In position space, the intracule density $h(u)$ is a monotonically decreasing function for all the atoms. In momentum space, however, the intracule densities $\overline{h}(v)$ are found to be classified into three types according to the number of local maxima and their locations. These different behaviors of the densities $h(u)$ and $\overline{h}(v)$ are studied in detail based on the contributions of electrons in a pair of atomic spinorbitals and subshells.