Ultrafast Pinpointing the Global‐Minimum Structures of Fullerenes C n ( n  = 20–10 260)

ABSTRACT Identifying the global‐minimum (GM) structure of fullerenes is crucial for understanding their chemical and physical properties, yet it remains a significant challenge due to the exponential growth of isomers with increasing carbon atom count in O ( N 9 ). In this study, we systematically searched for the GM structures of all fullerenes spanning from C 20 to C 10260 using the TGMin‐3 program. This integrated approach ensures remarkable efficiency and accuracy in locating the most stable configurations. Comprehensive analyses of the structures, symmetries, relative energies, Schlegel diagrams, and topologies were conducted, leading to the discovery of several previously unreported fullerene structures. Key findings include: high‐symmetry small fullerenes such as C 20 ( I h ), C 24 ( D 6 d ), C 36 ( D 2 d ), C 50 ( D 5 h ), C 60 ( I h ), C 70 ( D 5 h ), C 80 ( D 5 d ), C 90 ( D 5 h ), C 100 ( D 5 d ); large fullerenes C 720 , C 10220 and C 10260 exhibiting pseudo‐ I h symmetry; and giant fullerenes C 60 n 2 ( n = 1–13) forming the perfect I h ‐symmetric icosahedral structures that satisfy the isolated pentagon rule (IPR). Notably, as the number of carbon atoms increases, fullerenes prefer spherical structures with I h or I symmetry, attributed to enhanced electron delocalization on the spherical surface. Additionally, the nonclassical fullerene C 22 was confirmed to have a GM structure with C 2 symmetry, containing 1 four‐membered ring, 10 pentagons, and 2 hexagons. This systematic work provides a complete set of stable structures for both small and large fullerenes, filling critical gaps in the current understanding of fullerene configurations.