Coulomb clusters on a sphere: topological classification

The symmetry, energy, dipole and quadrupole moments of the ground states in `Thomsonʹs problemʹ of point Coulomb charges on a sphere are found and analized for the number of charges N=2–100. The equilibrium configurations are considered as closed quasi-2D triangular lattices with topological defects (disclinations of various charge). An appropriate classification of the structures is proposed. The approach is compared with the description of the configurations in terms of `ring structures on sphereʹ. The problem has a number of physical and chemical realizations.