Interelectronic angles of atoms in position and momentum spaces

For wave functions of atoms expressed by linear combinations of Slater determinants, a general formalism is presented to evaluate the angular expectation values 〈cosθ12〉 and 〈cosθ̄12〉 where θ12 and θ̄12 are the angles subtended, respectively, by the position and momentum vectors of two electrons. The results are applied to the 102 atoms He through Lr in their ground states within the Hartree–Fock framework. It is found that both 〈cosθ12〉 and 〈cosθ̄12〉 are non-positive for all the atoms, implying that the interelectronic angles θ12 and θ̄12 are never smaller than 90° in an average sense.