Statistical angular correlation coefficients of atomic Hartree–Fock orbitals

Abstract

When the probe function f(r) is chosen to be f(r)=r, the statistical correlation coefficient τ[f] reduces to the angular correlation coefficient τ[r], which provides an overall measure of the difference between the electron-pair density and the product of single-electron densities. For a pair of atomic Hartree–Fock spin–orbitals i and j, the characteristics of the angular correlation coefficient τij[r] are studied. The coefficient τij[r] is found to be negative for two spin–orbitals with the same spin and with azimuthal quantum numbers different by unity and zero for other cases. It is shown that τij[r] is expressible in terms of the generalized electron-pair moments 〈q2〉(a,b)ij relevant to the spin–orbitals i and j. Especially, the relation for a=b=1 means that τij[r] is nothing but the difference between the center-of-mass motion and relative motion contributions of two electrons in those spin–orbitals. A numerical examination of 102 neutral atoms shows that the angular correlation is generally largest between the outermost s and p subshells.