The gradient term
The term corresponds to the first isoelectronic series firstly and secondly: This term describes the Schrödinger solution for all similar to hydrogen one-electron-systems, thus for H, He +, Li + +, .. etc.
Regarding the isoelectronic series, this term is the first of each series. The term describes the slope and herewith the assignment of the element is into the corresponding period. All polynomials with the same n are summed upto one period.
The Schrödinger solution confirms the first isolectronic row, but calculates different principal quantum numbers regarding other elements.
By interchange of the elements between the sub shells s and d these elements get wrong quantum numbersBut the quantum numbers influence the fixing of the ionization energy.
How can it be that the Schrödinger solution is able to calculate the correct energies for those elements although their calculation bases on wrong quantum numbers? This is a deciding question and the quantum mechanics does not respond to this problem.