Interelectronic angle densities of atoms

In many-electron systems, the interelectronic angle density A(θ_12) represents the probability density function for the interelectronic angle θ_ij spanned by position vectors r_i and r_j of any two electrons to be θ_12. It is shown that in general the interelectronic angle density A(θ_12) is expressed by a linear combination of Legendre polynomials P_n(cos θ_12). Explicit formulas for the expansion coefficients are presented for atoms described by determinantal wave functions. The results are applied to the 102 atoms He through Lr in their ground states within the Hartree–Fock framework, and the expansion coefficients as well as the average interelectronic angles 〈θ_12〉 are reported