Theoretical Central Field Calculation of Madelung Rule
Many of the most important quantum mechanical systems involve atoms or
molecules which must be solved numerically since there is no analytical
solution with many body interactions. As can be pointed out with many
authors [9, 13] these problems involve a number of electrons
around a number of atomic nuclei (only for one nuclei for atoms).
Unfortunately, a full quantum solution of such a system of any
nontrivial size is very difficult [14]. As discussed with T.
Kago et al in order to find any correlation with the spectroscopic
results, some approximation can be made. One of such approximation is
the Hartree Fock approximation. We are not going to discuss the way of
calculation but a good review of how to apply Hartree Fock approximation
is given by [15]. By using gaussian type molecular orbital we have
calculated the energies of two different configurations. It is quite
clear that our results are in good agreement with the literature which
is displayed in table 1.
Table1: \(E\ \)is the deviation from the Madelung rule (energies are in
a.u.)