Growth Patterns of Carbon Clusters C (n = 2-60) Identified via ABCluster Searching and DFT Benchmarking

Recently, novel algorithms and enhanced computational capabilities have created unprecedented opportunities to precisely determine the geometric structures of clusters through theoretical calculations. In this study, we extensively investigated and characterized the geometric arrangements of the carbon clusters C (n = 2-60), employing the efficient ABCluster algorithm in conjunction with the gradient-corrected PBE and higher-accuracy B3LYP hybrid functional in density functional theory (DFT). New structures and a discernible structural growth pattern have been discovered. We observed a distinct preference in carbon clusters that transform from the linear chains (n = 2-9) to closed single-ring and planar structures (n = 10-27) and finally evolve to carbon cages (n = 28-60). A shortcut to construct the cage clusters was unveiled by inserting or rotating specific atoms within a distinct structural unit. The research results obtained from combining ABCluster with DFT calculations offer valuable new insights into the growth mechanisms and evolutionary trajectories of carbon clusters, providing a crucial theoretical framework for the development of innovative carbon-based materials and their potential applications.