Electrons of l shells of free atoms as a regular system of points on a sphere: III. Factors of self-organization of electrons in the periodic table

The factors determining the self-organization of the electron system of an atom at different levels of the periodic table are considered. Specifically, these factors are the isotropy and three-dimensional nature of space and the indistinguishability of electrons. The concept of a simplex is used, whose vertices correspond to a regular system of particles (minimum in number for a given space) in the state of the global minimum of the system’s potential. These factors implement the principle of simplicity (small number of particles) and hierarchy in the periodic table of elements. The global minimum of the potential of s, p, d, and f shells is reached in odd-dimensional spaces. In a three-dimensional space, such a minimum is reached for d and f shells, in contrast to s and p shells, through shell mixing.