Interelectronic angle densities of atoms

In many-electron systems, the interelectronic angle density $A(θ12)$ represents the probability density function for the interelectronic angle $θij$ spanned by position vectors $ri$ and $rj$ of any two electrons to be $θ12.$ It is shown that in general the interelectronic angle density $A(θ12)$ is expressed by a linear combination of Legendre polynomials $Pn(cos θ12).$ 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 $〈θ12〉$ are reported.