C₃₂: Computations of Low-Energy Cages with Four-Membered Rings

Abstract

C₃₂ cages built from four-, five-, six-, and seven-membered rings are computed. The computations are primarily performed with semiempirical quantum-chemical methods (AM1, PM3, SAM1), and altogether 199 cages are optimized. The energetics is further checked through ab initio HF SCF computations with the standard 3-21G basis set, and also by density functional theory at the B3LYP level in the standard 6-31G∗ basis set. All five levels of theory suggest a D_4d cage (two four-membered rings, eight pentagons, eight hexagons) as the lowest-energy structure. Temperature effects are treated in the terms of partition functions so that the entropy contributions are considered accordingly. The thermodynamic treatment points out five cages significantly populated at high temperatures. At very high temperatures the structure lowest in energy is not the most abundant isomer. There are just six conventional fullerenes C₃₂, built exclusively from pentagons and hexagons, however, only two of them show significant populations at high temperatures. The remaining three relatively stable cages contain at least one four-membered ring. No structure with a heptagon shows a non-negligible concentration at high temperatures. The study suggests that in the non-IPR region the quasi-fullerene cages with four-membered rings can in some cases be more important than the conventional fullerenes built from pentagons and hexagons only.