{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:45:17Z","timestamp":1792784717321,"version":"4.5.0"},"reference-count":68,"publisher":"American Chemical Society (ACS)","issue":"38","license":[{"start":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T00:00:00Z","timestamp":1789171200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T00:00:00Z","timestamp":1789171200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T00:00:00Z","timestamp":1789171200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People's Republic of China","doi-asserted-by":"publisher","award":["JYB2025XDXIM414"],"award-info":[{"award-number":["JYB2025XDXIM414"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017683","name":"Dalian Science and Technology Innovation Fund","doi-asserted-by":"publisher","award":["2025JJ12GX012"],"award-info":[{"award-number":["2025JJ12GX012"]}],"id":[{"id":"10.13039\/501100017683","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Basic Research Program of China (973 Program)","award":["2024YFA1409600"],"award-info":[{"award-number":["2024YFA1409600"]}]},{"name":"National Basic Research Program of China (973 Program)","award":["2024YFE0213500"],"award-info":[{"award-number":["2024YFE0213500"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["12374174"],"award-info":[{"award-number":["12374174"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["12374253"],"award-info":[{"award-number":["12374253"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"name":"R&D project of Joint Funds of Liaoning Province","award":["2023JH2\/101800038"],"award-info":[{"award-number":["2023JH2\/101800038"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The evolution of cluster structure with size and the critical size for the transition from cluster to nanocrystal have long been fundamental problems in nanoscience. Solving this problem is still a big challenge due to limitations of experimental technology and computational methods. Here, we proposed a machine learning force field (MLFF) that can generalize well to various copper systems ranging from small clusters to large clusters and bulk. The continuous evolution of copper clusters CuN towards nanocrystal was revealed by investigating clusters in a wide size range (7 \u2264 N \u2264 17885) based on MLFF simulated annealing (SA). For small CuN (N &amp;lt; 40), electron counting rule and geometric symmetry play a major role in stability. For large CuN (N &amp;gt; 80), geometric magic number rule plays a dominant role and the evolution of clusters is based on the formation of more and more icosahedral shells. For medium size CuN (40 \u2264 N \u2264 80), both electron counting rule and geometric magic number rule contribute. The critical size from cluster to nanocrystal was calculated to be around 8200 atoms (about 6 nm in diameter). Our results shed light on the structural evolution of copper clusters and lay the methodological foundation for subsequent research on other cluster systems.<\/jats:p>","DOI":"10.1021\/acs.jpclett.6c02146","type":"journal-article","created":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T16:02:25Z","timestamp":1789228945000},"page":"10820-10828","source":"Crossref","is-referenced-by-count":0,"title":["From Clusters\nto Nanocrystals: The Continuous Evolution\nof Copper Clusters Revealed by Machine Learning"],"prefix":"10.1021","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5883-0862","authenticated-orcid":true,"given":"Hongsheng","family":"Liu","sequence":"first","affiliation":[{"name":"Ministry of Education, School of Physics , , ,","place":["Dalian, China, 116024"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luneng","family":"Zhao","sequence":"additional","affiliation":[{"name":"Ministry of Education, School of Physics , , ,","place":["Dalian, China, 116024"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaning","family":"Li","sequence":"additional","affiliation":[{"name":"Ministry of Education, School of Physics , , ,","place":["Dalian, China, 116024"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Chang","sequence":"additional","affiliation":[{"name":"Ministry of Education, School of Physics , , ,","place":["Dalian, China, 116024"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shi","family":"Qiu","sequence":"additional","affiliation":[{"name":"Ministry of Education, School of Physics , , ,","place":["Dalian, China, 116024"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Ding","sequence":"additional","affiliation":[{"name":"Suzhou Laboratory , ,","place":["Suzhou, China, 215123"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5732-9905","authenticated-orcid":true,"given":"Junfeng","family":"Gao","sequence":"additional","affiliation":[{"name":"Ministry of Education, School of Physics , , ,","place":["Dalian, China, 116024"]},{"name":"Suzhou Laboratory , ,","place":["Suzhou, China, 215123"]},{"name":"Dalian University of Technology , , ,","place":["Dalian, China, 116024"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,12]]},"reference":[{"key":"2026092408415997900_cit1","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1126\/science.271.5251.889","article-title":"Clusters","volume":"271","author":"Brauman","year":"1996","journal-title":"Science"},{"key":"2026092408415997900_cit2","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1126\/science.1093902","article-title":"Formation\nof Al13I\u2013: Evidence for the Superhalogen\nCharacter\nof Al13","volume":"304","author":"Bergeron","year":"2004","journal-title":"Science"},{"key":"2026092408415997900_cit3","doi-asserted-by":"publisher","first-page":"4981","DOI":"10.1021\/acs.chemrev.7b00776","article-title":"Metal Catalysts for\nHeterogeneous Catalysis: From Single Atoms to\nNanoclusters and Nanoparticles","volume":"118","author":"Liu","year":"2018","journal-title":"Chem. Rev."},{"key":"2026092408415997900_cit4","doi-asserted-by":"publisher","first-page":"9144","DOI":"10.1038\/s41467-025-64187-3","article-title":"Collectivity effect\nin cluster catalysis\nunder operational conditions","volume":"16","author":"Chen","year":"2025","journal-title":"Nat. Commun."},{"key":"2026092408415997900_cit5","doi-asserted-by":"publisher","first-page":"4000","DOI":"10.1038\/s41467-025-58590-z","article-title":"Nickel Ion Induced Multistage Assembly\nof Th13 Cluster","volume":"16","author":"Hu","year":"2025","journal-title":"Nat. Commun."},{"key":"2026092408415997900_cit6","doi-asserted-by":"publisher","first-page":"7030","DOI":"10.1038\/s41467-025-62192-0","article-title":"Fully exposed Ptn cluster\ncatalysts enable cascade oxidation of polyol to dicarboxylic acid","volume":"16","author":"Yan","year":"2025","journal-title":"Nat. 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Energy Mater."},{"key":"2026092408415997900_cit10","doi-asserted-by":"publisher","first-page":"1692","DOI":"10.1039\/C7SC05295B","article-title":"Polyoxovanadate-alkoxide\nclusters as multi-electron charge carriers for symmetric non-aqueous\nredox flow batteries","volume":"9","author":"VanGelder","year":"2018","journal-title":"Chem. Sci."},{"key":"2026092408415997900_cit11","doi-asserted-by":"publisher","first-page":"2107425","DOI":"10.1002\/adma.202107425","article-title":"POM Anolyte\nfor All-Anion Redox Flow Batteries with High Capacity Retention and\nCoulombic Efficiency at Mild pH","volume":"34","author":"Yang","year":"2022","journal-title":"Adv. Mater."},{"key":"2026092408415997900_cit12","doi-asserted-by":"publisher","DOI":"10.1002\/agt2.266","article-title":"Atomically precise\ncopper nanoclusters as ultrasmall\nmolecular aggregates: Appealing compositions, structures, properties,\nand applications","volume":"4","author":"Zhang","year":"2023","journal-title":"Aggregate"},{"key":"2026092408415997900_cit13","doi-asserted-by":"publisher","DOI":"10.1002\/anie.202317597","article-title":"Electroluminescent\nClusters","volume":"63","author":"Zhang","year":"2024","journal-title":"Angew. Chem. Int.\nEd."},{"key":"2026092408415997900_cit14","doi-asserted-by":"publisher","first-page":"9639","DOI":"10.1038\/s41467-025-64637-y","article-title":"Dual-band\nhigh-dissymmetry circularly polarized luminescence from cholesteric\nliquid crystals overlaid a gold cluster film","volume":"16","author":"Hao","year":"2025","journal-title":"Nat. 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Syst."},{"key":"2026092408415997900_cit24","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1080\/08927022.2015.1121386","article-title":"Comprehensive genetic\nalgorithm for ab initio global optimisation of clusters","volume":"42","author":"Zhao","year":"2016","journal-title":"Mol. Simul."},{"key":"2026092408415997900_cit25","doi-asserted-by":"publisher","first-page":"5111","DOI":"10.1021\/jp970984n","article-title":"Global Optimization by Basin-Hopping\nand the Lowest\nEnergy Structures of Lennard-Jones Clusters Containing up to 110 Atoms","volume":"101","author":"Wales","year":"1997","journal-title":"J. Phys. Chem. A"},{"key":"2026092408415997900_cit26","doi-asserted-by":"publisher","first-page":"1136","DOI":"10.1021\/ct9005147","article-title":"Constrained Broyden Minimization Combined with the\nDimer Method for Locating Transition State of Complex Reactions","volume":"6","author":"Shang","year":"2010","journal-title":"J. Chem. Theory Comput."},{"key":"2026092408415997900_cit27","doi-asserted-by":"publisher","first-page":"17845","DOI":"10.1039\/C4CP01485E","article-title":"Stochastic surface walking method\nfor crystal structure and phase transition pathway prediction","volume":"16","author":"Shang","year":"2014","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026092408415997900_cit28","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1016\/j.commatsci.2015.09.037","article-title":"CALYPSO structure prediction method and its wide application","volume":"112","author":"Wang","year":"2016","journal-title":"Comput. Mater. Sci."},{"key":"2026092408415997900_cit29","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1038\/s41524-022-00856-x","article-title":"Accelerated\nprediction of atomically\nprecise cluster structures using on-the-fly machine learning","volume":"8","author":"Wang","year":"2022","journal-title":"npj Comput. Mater."},{"key":"2026092408415997900_cit30","doi-asserted-by":"publisher","first-page":"094106","DOI":"10.1063\/5.0180529","article-title":"Machine-learning accelerated\nstructure search for ligand-protected clusters","volume":"160","author":"Fang","year":"2024","journal-title":"J. Chem. Phys."},{"key":"2026092408415997900_cit31","doi-asserted-by":"publisher","first-page":"074304","DOI":"10.1063\/5.0100505","article-title":"Structural and electrocatalytic\nproperties of copper clusters: A study via deep learning and first\nprinciples","volume":"157","author":"Wang","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2026092408415997900_cit32","doi-asserted-by":"publisher","first-page":"9160","DOI":"10.1021\/acs.jpclett.4c01953","article-title":"Accelerating Global Search of Large-Sized\nSilver Clusters Using Cluster Graph Attention Network","volume":"15","author":"Fu","year":"2024","journal-title":"J. Phys. Chem. Lett."},{"key":"2026092408415997900_cit33","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.ccr.2018.01.001","article-title":"Atomically precise copper nanoclusters and their applications","volume":"359","author":"Liu","year":"2018","journal-title":"Coord. Chem. Rev."},{"key":"2026092408415997900_cit34","doi-asserted-by":"publisher","first-page":"6283","DOI":"10.1039\/D0NR08489A","article-title":"Copper nanoclusters: designed synthesis,\nstructural\ndiversity, and multiplatform applications","volume":"13","author":"Baghdasaryan","year":"2021","journal-title":"Nanoscale"},{"key":"2026092408415997900_cit35","doi-asserted-by":"publisher","DOI":"10.1002\/anie.202205626","article-title":"Mediating CO2\nElectroreduction Activity and Selectivity\nover Atomically Precise Copper Clusters","volume":"61","author":"Liu","year":"2022","journal-title":"Angew.\nChem. Int. Ed."},{"key":"2026092408415997900_cit36","doi-asserted-by":"publisher","first-page":"1906872","DOI":"10.1002\/adma.201906872","article-title":"Development of Copper Nanoclusters\nfor In Vitro and In Vivo Theranostic Applications","volume":"32","author":"Lai","year":"2020","journal-title":"Adv. Mater."},{"key":"2026092408415997900_cit37","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1007\/s00604-021-05011-9","article-title":"Copper nanocluster\ncomposites for analytical (bio)-sensing and imaging: a review","volume":"188","author":"Mu","year":"2021","journal-title":"Microchim. Acta"},{"key":"2026092408415997900_cit38","doi-asserted-by":"publisher","first-page":"106632","DOI":"10.1016\/j.phrs.2022.106632","article-title":"A copper nanocluster-based multifunctional nanoplatform for augmented\nchemo\/chemodynamic\/photodynamic combination therapy of breast cancer","volume":"187","author":"Zhang","year":"2023","journal-title":"Pharmacol. Res."},{"key":"2026092408415997900_cit39","doi-asserted-by":"publisher","first-page":"35128","DOI":"10.1021\/jacs.5c13006","article-title":"Ultrastable\nCopper Cluster Enables Highly Site-Selective and Chemoselective Carbocation\nC(sp3)-H and C(sp2)-H Bonds Functionalization","volume":"147","author":"Jia","year":"2025","journal-title":"J. Am. Chem. Soc."},{"key":"2026092408415997900_cit40","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1016\/j.jcis.2024.08.236","article-title":"Copper cluster regulated by N, B atoms for enhanced\nCO2 electroreduction to formate","volume":"678","author":"Zhao","year":"2025","journal-title":"J. Colloid\nInterface Sci."},{"key":"2026092408415997900_cit41","doi-asserted-by":"publisher","first-page":"2417747","DOI":"10.1002\/adma.202417747","article-title":"Accurate Thermal\nResection of Atomically Precise Copper Clusters to Achieve Near-IR\nLight-Driven CO2 Reduction","volume":"37","author":"Dong","year":"2025","journal-title":"Adv. Mater."},{"key":"2026092408415997900_cit42","doi-asserted-by":"publisher","first-page":"6877","DOI":"10.1038\/s41467-023-42688-3","article-title":"Atomically\nprecise ultrasmall copper cluster for room-temperature\nhighly regioselective dehydrogenative coupling","volume":"14","author":"Jia","year":"2023","journal-title":"Nat. Commun."},{"key":"2026092408415997900_cit43","doi-asserted-by":"publisher","first-page":"12652","DOI":"10.1021\/jacs.5c00340","article-title":"Few-Atom Copper Cluster Facilitates\nH2O2 Activation to Promote Selective Oxidation of Benzene to Phenol","volume":"147","author":"Zhang","year":"2025","journal-title":"J. Am. Chem. Soc."},{"key":"2026092408415997900_cit44","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1016\/j.ijhydene.2024.06.382","article-title":"Effect of copper cluster\non reaction pathways of carbon dioxide hydrogenation on magnesium\nhydride surface","volume":"78","author":"Yao","year":"2024","journal-title":"Int. J. Hydrog. Energy"},{"key":"2026092408415997900_cit45","doi-asserted-by":"publisher","first-page":"9551","DOI":"10.1038\/s41467-024-53950-7","article-title":"Atomically precise\ncopper clusters with dual sites\nfor highly chemoselective and efficient hydroboration","volume":"15","author":"Jia","year":"2024","journal-title":"Nat. Commun."},{"key":"2026092408415997900_cit46","doi-asserted-by":"publisher","first-page":"38922","DOI":"10.1021\/jacs.5c15400","article-title":"Atomically Precise\nCopper Cluster for Highly Chemoselective Carbenoid Insertion into\nthe N-H Bond of Aliphatic Amine","volume":"147","author":"Jia","year":"2025","journal-title":"J. Am. Chem.\nSoc."},{"key":"2026092408415997900_cit47","doi-asserted-by":"publisher","first-page":"4497","DOI":"10.1063\/1.1436465","article-title":"Structure\nand stability of small copper clusters","volume":"116","author":"Jug","year":"2002","journal-title":"J. Chem.\nPhys."},{"key":"2026092408415997900_cit48","doi-asserted-by":"publisher","first-page":"043203","DOI":"10.1103\/PhysRevA.69.043203","article-title":"Structure and stability of copper\nclusters: A tight-binding molecular dynamics study","volume":"69","author":"Kabir","year":"2004","journal-title":"Phys. Rev. A"},{"key":"2026092408415997900_cit49","doi-asserted-by":"publisher","first-page":"165403","DOI":"10.1103\/PhysRevB.70.165403","article-title":"Trends\nin the structure and bonding of noble metal clusters","volume":"70","author":"Ferna\u0301ndez","year":"2004","journal-title":"Phys. Rev. B"},{"key":"2026092408415997900_cit50","doi-asserted-by":"publisher","first-page":"026103","DOI":"10.1103\/PhysRevLett.94.026103","article-title":"Evolution of Small\nCopper Clusters and Dissociative Chemisorption of Hydrogen","volume":"94","author":"Guvelioglu","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"2026092408415997900_cit51","doi-asserted-by":"publisher","first-page":"024308","DOI":"10.1063\/1.2150439","article-title":"Structure and shape variations in intermediate-size\ncopper clusters","volume":"124","author":"Yang","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2026092408415997900_cit52","doi-asserted-by":"publisher","first-page":"245402","DOI":"10.1103\/PhysRevB.83.245402","article-title":"First-principles absorption\nspectra\nof Cun (n=2-20) clusters","volume":"83","author":"Baishya","year":"2011","journal-title":"Phys. Rev.\nB"},{"key":"2026092408415997900_cit53","doi-asserted-by":"publisher","first-page":"245401","DOI":"10.1103\/PhysRevB.79.245401","article-title":"Quantum Monte Carlo\nstudies of covalent and metallic clusters: Accuracy of density functional\napproximations","volume":"79","author":"Hsing","year":"2009","journal-title":"Phys. Rev. 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Rep"},{"key":"2026092408415997900_cit56","doi-asserted-by":"publisher","first-page":"15484","DOI":"10.1039\/C7CP02240A","article-title":"Evolution of the structural, energetic,\nand electronic properties of the 3d, 4d, and 5d transition-metal clusters\n(30 TMn systems for n = 2-15): a density functional theory investigation","volume":"19","author":"Chaves","year":"2017","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026092408415997900_cit57","doi-asserted-by":"publisher","first-page":"174510","DOI":"10.1063\/1.3187934","article-title":"Comprehensive study\nof sodium, copper, and silver clusters over a wide range of sizes\n2\u2264N\u226475","volume":"131","author":"Itoh","year":"2009","journal-title":"J. Chem. 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