  Correspondences between the Thomson Problem and atomic electron shell-filling
patterns are observed as systematic non-uniformities in the distribution of
potential energy necessary to change configurations of $N\le 100$ electrons
into discrete geometries of neighboring $N-1$ systems. These non-uniformities
yield electron energy pairs, intra-subshell pattern similarities with empirical
ionization energy, and a salient pattern that coincides with size-normalized
empirical ionization energies. Spatial symmetry limitations on discrete charges
constrained to a spherical volume are conjectured as underlying physical
mechanisms responsible for shell-filling patterns in atomic electronic
structure and the Periodic Law.

Classical Physics