Electrons of l shells of free atoms as a regular system of points on a sphere: I. Modeling by polyhedra

Abstract

Electron l shells of free atoms have been modeled on the basis of regular and semiregular polyhedra by determining stable systems of identical Coulomb particles with an increase in their number. It is shown that such stable systems correspond to the location of the maxima of electron density at the vertices of inversion-center polyhedra forming a sequence in which the first polyhedron has two vertices and the number of vertices in each subsequent polyhedron exceeds the number of vertices in the previous one by four. The electron s, p, d, and f shells are modeled by a dumbbell and trigonal, pentagonal, and heptagonal antiprisms, respectively. Thus, in addition to the quantum-mechanical properties, l shells should have the symmetry properties of these antiprisms. It is believed that consideration of the noncrystallographic (for the three-dimensional Euclidean space) fivefold and seven-fold symmetries of d and f shells of free atoms will make it possible to obtain a unified explanation for a number of phenomena in crystal structures and other ordered media.