Shull and Löwdin [3] represented the total wavefunction in the form

,

where is the angle between and , while is the Legendre polynomial of degree . Note that the functions contain internal angular dependence but can still represent atomic states, such as and , with . In the computations presented in this Demonstration, we consider only the , , and contributions to CI. The contribution is taken as the HF function , which can be very closely approximated using double-zeta orbitals

.

The contribution is represented by the orthogonalized Slater-type function

.

Together, these two contributions can closely approximate the -limit to the CI function, as defined by Shull and Löwdin. The and contributions are represented using simple Slater-type orbitals:

and

,

with

for and

for .

All the relevant matrix elements of the Hamiltonian are then computed; for example,

,

,

and so forth. All energies are expressed in Hartree atomic units: .

Plots of the radial distribution function for each component configuration are also shown on the left. The relative magnitudes are not to scale.