Electronic extracule moments of atoms in position and momentum spaces

Abstract

The electronic extracule density represents the probability density function for the center-of-mass motion of any pair of electrons. Two methods are presented for the calculation of electronic extracule moments 〈Rn〉 in position space and 〈Pn〉 in momentum space of atomic systems within the Hartree–Fock framework, where R and P are respectively the position and momentum distances between the center-of-mass of any pair of electrons and the coordinate origin. The methods are applied to the neutral atoms from He to Xe in their ground state, and the moments 〈Rn〉 with n=−2 to +4 and 〈Pn〉 with n=−2 to +3 are reported based on the numerical Hartree–Fock calculations. These extracule moments are pointed out to have intimate relations with their partner intracule moments. The present results, together with the previous ones for the electronic intracule moments [J. Chem. Phys., 107, 8510 (1997)], compile accurate Hartree–Fock electron-pair moments for all the 53 atoms He through Xe in both position and momentum spaces.