I have interest in this matter too.
I know the Pauli's exclusion principle, but I do not understand why.
I was taught about Hund's rule , but I do not know why it holds still now.
Methinks that the core problem lies in the mathematical content of the atomic orbital wave functions if they are valid assumption. I think that the 4S atomic orbital wave function for N protons nucleus must differ from the same 4S atomic orbital wave function for N+1 protons nucleus, and in the same way the energy levels that correspond to the p orbitals for N and N+1 protons nuclei are different.
First of all, I am suspicious about the current theory of atomic orbital.
I am waiting for someone to deliver the numerical or analytical solution of ab initio calculaiton for many electron atom.
June 18, 2013