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.)