Interelectronic angles: Rounding out a geometric picture of the helium atom

Multi-configuration Hartree–Fock expectation values of the inner 〈r<〉 and outer 〈r>〉 electron radii and the interelectronic angle 〈θ12〉 are reported for the ground and 54 singly-excited states of helium. These mean values can be visualized as defining a nearly right-angled triangle. Expressions connecting these expectation values with the mean value of the interelectronic distance 〈r12〉 are found to be quite accurate. Some observations are made on singlet–triplet differences of 〈θ12〉.