Efficient Searches for Low-Energy Structures in Clusters with Thousands of Particles: Application to the Thomson Problem

Abstract: We propose an algorithm for identifying low-energy minima in systems containing thousands of particles, at moderate computational cost. We focus on spherical crystals, in which particles form ordered structures on the surface of a sphere. Our method uses symmetric seed configurations, or known structures, to initialize searches across contiguous ranges of system sizes. Newly identified minima are then used to guide searches at neighbouring sizes, allowing information to propagate efficiently through configuration space. We have tested this approach on the Thomson problem, one of the few interacting-particle systems for which global optimization has been considered for systems of this size. We substantially improve on many previous solutions, particularly at larger system sizes, where systematic global optimization is computationally expensive. Since favourable packings for the Thomson problem are reflected in systems spanning atomistic to mesoscopic length scales, the newly characterized defect patterns may inform structure prediction for a broad range of problems with spherical topology.