Genetic-algorithm energy minimization for point charges on a sphere
- 15 January 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 53 (4) , R1740-R1743
- https://doi.org/10.1103/physrevb.53.r1740
Abstract
We demonstrate that a recently developed approach for optimizing atomic structures is very effective for attacking the Thomson problem of finding the lowest-energy configuration of point charges on a unit sphere. Our approach uses a genetic algorithm, combined with a "cut and paste" scheme of mating, that efficiently explores the different low-energy structures. Not only have we reproduced the known results for , this approach has allowed us to extend the calculation for all . This has allowed us to identify series of "magic" numbers, where the lowest-energy structures are particularly stable. Most of these structures are icosahedral, but we also find low-energy structures that deviate from icosahedral symmetry.
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