  Recently,a noticeable progress had been achieved in the area of high
temperature superconductors. The maximum temperature of 250K for LaH(10) and
288K for CSH(8) were reported at the megabar pressures. The highest possible
temperatures were achieved by employing hydrides of chemical elements.
Empirically, many of these are made of Madelung-exceptional atoms. Here the
theoretical background is provided explaining this observation. The, thus far
empirical, Madelung rule is controlling Mendeleev's law of periodicity.
Although the majority of elements do obey this rule, there are some exceptions.
Thus, it is of interest to derive it and its exceptions theoretically in view
of experimental findings. As a by product, such a study yields some plausible
explanation of the role of Madelung-exceptional atoms in the design of
hightemperature superconductors. Thus far the atoms obeying the Madelung rule
and its exceptions were studied with help of the relativistic Hartree-Fock
calculations. In this work we reobtain both the rule and the exceptions
analytically. The newly developed methods are expected to be of value in
quantum many-body theory and, in particular, in the theory of high temperature
superconductivity. Ultimately, new methods involve some uses of the
Seiberg-Witten (S-W) theory known as the extended Ginzburg-Landau theory of
superconductivity. Using results of the S-W theory the difference between the
Madelung-regular and Madelung-exceptional atoms is explained in terms of the
topological transition. Extension of this, single atom, result to solids of
respective elements is also discussed
