Theoretical Study of Small-Sized Carbon Clusters and the Formation of Fullerene Cages

Abstract

Systematical DFT study on small-sized carbon chains, rings, bowls and cages are performed. For carbon chains, the results show that the end bond will shorten compared with its nearest adjacent bond; the bond lengths are not alternated but symmetrically distributed based on the central atom (odd-number chains) and the middle point (even-number chains). Odd-number carbon chains are singlet and even-number chains are triplet. The diffidence in lengths of adjacent two bonds is slightly and much smaller than the length difference between triple and single bond in C2H2 and C2H6. All theoretical evidences here show that linear chains of carbon are polyene not polyalkyne. For carbon rings, their highest symmetrical (Dnh) isomers of Cn are not lowest energy ring isomers except for C25-Ring. For carbon cages, the interesting findings include (1) a new non-classical isomer of C24 is found to be more favored than the classical one which was reported to be most favored; (b) a new non-classical isomer of C26 is found to be more favored than the classical one which was reported to be the 2nd favored; (c) Small cages welcome strained square(s); and (d) The favored cages of them are structurally related to direct C2 insertion/extrusion. Comprehensive comparison show that carbon chains are more favored than rings and cages when n≤9,however, rings are more favored than chains when 10≤n≤20; Bowls/sheets are more favored than cages energetically for clusters of Cn with 18≤n≤24; The cages are increasing favorable and become dominant species when n≥26. These results clearly suggest the structural evolution from chains to rings or bowls and cages in turn.