Distributions of r1·r2 and p1·p2 in Atoms.

We consider the two-electron position and momentum dot products, α = r1·r2 and β = p1·p2, and present a method for extracting their distributions, A(α) and B(β), from molecular wave functions built on Gaussian basis functions. The characteristics of the Hartree-Fock AHF(α) and BHF(β) for He and the first-row atoms are investigated, with particular attention to the effects of Pauli exchange. The effects of electron correlation are studied via the holes, ΔA(α) ≡ A(α) - AHF(α) and ΔB(β) ≡ B(β) - BHF(β), and the hole structures are rationalized in terms of radial and angular correlation effects. Correlation effects are also examined through an analysis of the first moments of A(α), AHF(α), B(β), and BHF(β).