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This paper introduces an efficient algorithm for finding low-energy minima in large-scale (thousands of particles) spherical crystal systems, specifically applied to the Thomson problem. By leveraging symmetric seed configurations and propagating information across contiguous system sizes, the method significantly improves upon previous solutions, especially for larger particle counts where global optimization is computationally prohibitive. The identified defect patterns offer insights into structure prediction for diverse problems with spherical topology.
Discovering thousands of new low-energy structures for the Thomson problem reveals defect patterns crucial for spherical topology problems from atomistic to mesoscopic scales.
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.