Growth Patterns\nof Carbon Clusters C<i><sub>n</sub></i> (<i>n</i> = 2–60) Identified via ABCluster\nSearching and DFT Benchmarking

Recently, novel algorithms and enhanced\ncomputational\ncapabilities\nhave created unprecedented opportunities to precisely determine the\ngeometric structures of clusters through theoretical calculations.\nIn this study, we extensively investigated and characterized the geometric\narrangements of the carbon clusters C<i><sub>n</sub></i> (<i>n</i> = 2–60), employing the efficient ABCluster\nalgorithm in conjunction with the gradient-corrected PBE and higher-accuracy\nB3LYP hybrid functional in density functional theory (DFT). New structures\nand a discernible structural growth pattern have been discovered.\nWe observed a distinct preference in carbon clusters that transform\nfrom the linear chains (<i>n</i> = 2–9) to closed\nsingle-ring and planar structures (<i>n</i> = 10–27)\nand finally evolve to carbon cages (<i>n</i> = 28–60).\nA shortcut to construct the cage clusters was unveiled by inserting\nor rotating specific atoms within a distinct structural unit. The\nresearch results obtained from combining ABCluster with DFT calculations\noffer valuable new insights into the growth mechanisms and evolutionary\ntrajectories of carbon clusters, providing a crucial theoretical framework\nfor the development of innovative carbon-based materials and their\npotential applications.