Possible Global Minimum Lattice Configurations for Thomson`s Problem of Charges on a Sphere

What configuration of N point charges on a conducting sphere minimizes the Coulombic energy? J.J. Thomson posed this question in 1904. For N{le}112, numerical methods have found apparent global minimum-energy configurations; but the number of local minima appears to grow exponentially with N, making many such methods impractical. Here we describe a topological/numerical procedure that we believe gives the global energy minimum lattice configuration for N of the form N=10(m{sup 2}+n{sup 2}+mn)+2 (m, n positive integers). For those N with more than one lattice, we give a rule to choose the minimum one. {copyright} {ital 1997} {ital The American Physical Society}