C-32: Computations of low-energy cages with four-membered rings

C-32 cages built from four-, five-, six-, and seven-membered rings are comp uted. The computations are primarily performed with semiempirical quantum-c hemical methods (AM1, PM3, SAM1), and altogether 199 cages are optimized. T he 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 su ggest a D-4d cage (two four-membered rings, eight pentagons, eight hexagons ) as the lowest-energy structure. Temperature effects are treated in the te rms of partition functions so that the entropy contributions are considered accordingly. The thermodynamic treatment points out five cages significant ly populated at high temperatures. At very high temperatures the structure lowest in energy is not the most abundant isomer. There are just six conven tional fullerenes C-32, built exclusively from pentagons and hexagons, howe ver, only two of them show significant populations at high temperatures. Th e remaining three relatively stable cages contain at least one four-membere d ring. No structure with a heptagon shows a nonnegligible 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 importa nt than the conventional fullerenes built from pentagons and hexagons only.