Distributing Many Electrons on the Unit Sphere for Minimizing of the Potential Energy

The problem of distributing of points on a sphere has a long history. In fact, the problem is how should one place np electrons on a sphere so as to minimize the potential energy, i.e., given p n electrons, find the equilibrium state distribution of minimal Coulomb potential of the electrons positioned on a conducting sphere. This problem, known as the Thomson problem of finding the lowest energy configuration of np point charges on a conducting sphere, originated with Thomson’s plum pudding model of the atomic nucleus.