Search for Lowest-Energy Fullerenes 2: C38 to C80 and C112 to C120

Abstract

An efficient computational approach that combines semiempirical density-functional based tight-binding method (DFTB) for geometry optimization and density-functional theory for single-point energy calculation is employed to search for the lowest-energy structures of higher fullerenes C110 to C120. In addition, a systematic study of low-lying structures of lower fullerenes C38 to C80 is undertaken. For the latter study, the targeted isomers amount to 131 164, including 17 IPR (isolated pentagon rule) isomers and all non-IPR isomers. Non-IPR isomers dominate the low-lying population of C72 but are gradually phased out of the low-lying population when the fullerene size increases toward C80. An unexpected manner of pentagonal adjacency was observed, that is, for fullerenes containing an adjacent-pentagon chain with less than five pentagons, the longer chain incurs less energy penalty than the shorter chain when the top-two lowest-energy fullerene cages (for all C38− C70) have the same number of adjacent pentagons. For higher fullerenes C112 to C120, a full set of total 32 795 IPR isomers were optimized using the DFTB method. An energy cutoff value of 6.3 kcal/mol was used to collect low-lying candidate isomers for the second-stage single-point energy calculation at the DFT level. Multiple candidates for the lowest-energy structure were identified for C112, C118, and C120. Among them, C112:3299 and C118:7308 exhibit a large HOMO−LUMO gap. For C116, a sole candidate for the lowest-energy structure was identified, namely, C116:6061 which has a high Th symmetry and a large HOMO−LUMO gap and is 12.5 kcal/mol lower in energy than the second lowest-energy isomer. Thus, C116: 6061 is most likely to be isolated first in the laboratory among the five large fullerenes. 13C NMR spectra of the ten lowest-energy isomers of C112 to C120 were calculated for comparison with the experiment.