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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 favorable 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.<\/jats:p>","DOI":"10.1063\/5.0355867","type":"journal-article","created":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T10:50:31Z","timestamp":1792666231000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Efficient searches for low-energy structures in clusters with thousands of particles: Application to the Thomson problem"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1321-9437","authenticated-orcid":false,"given":"Paolo","family":"Amore","sequence":"first","affiliation":[{"name":"Facultad de Ciencias, CUICBAS, Universidad de Colima 1 , Bernal D\u00edaz del Castillo 340, Colima,","place":["Mexico"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3555-6645","authenticated-orcid":false,"given":"David J.","family":"Wales","sequence":"additional","affiliation":[{"name":"Yusuf Hamied Department of Chemistry, University of Cambridge 2 , Lensfield Road, Cambridge CB2 1EW,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,22]]},"reference":[{"key":"2026102206502752300_c1","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1080\/14786440409463107","article-title":"XXIV. 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