Search for lowest-energy fullerenes 2: C ₃₈ to C ₈₀ and C ₁₁₂ to C ₁₂₀

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 C ₁₁₀ to C ₁₂₀. In addition, a systematic study of low-lying structures of lower fullerenes C ₃₈ to C ₈₀ 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 C ₇₂ but are gradually phased out of the low-lying population when the fullerene size increases toward C ₈₀. 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 C ₃₈ - C ₇₀) have the same number of adjacent pentagons. For higher fullerenes C ¹¹² to C ₁₂₀, 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 C ₁₁₂, C ₁₁₈, and C ₁₂₀. Among them, C ₁₁₂:3299 and C ₁₁₈:7308 exhibit a large HOMO-LUMO gap. For C ₁₁₆, a sole candidate for the lowest-energy structure was identified, namely, C ₁₁₆:6061 which has a high T _h symmetry and a large HOMO-LUMO gap and is 12.5 kcal/mol lower in energy than the second lowest-energy isomer. Thus, C ₁₁₆: 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 C ₁₁₂ to C ₁₂₀ were calculated for comparison with the experiment.