Theoretical Studies on the Smallest Fullerene: From Monomer to Oligomers and Solid States

Hybrid B3LYP and density-functional-based tight-binding (DFTB) computations on the solid-state structures and electronic properties of the C₂₀ fullerene monomer and oligomers are reported. C₂₀ cages with C₂, C_2h, C_i, D_3d, and D_2h symmetries have similar energies and geometries. Release of the very high C₂₀ strain is, in theory, responsible for the ready oligomerization and the formation of different solid phases. Open [2+2] bonding is preferred both in the oligomers and in the infinite one-dimensional solids; the latter may exhibit metallic character. Two types of three-dimensional solids, the open [2+2] simple cubic and the body-centered cubic (bcc) forms, are proposed. The energy of the latter is lower due to the better oligomer bonding. The open [2+2] simple cubic solid should be a conductor, whereas the bcc solids are insulators. The most stable three-dimensional solid-state structure, an anisotropically compressed form of the bcc solid, has a HOMO-LUMO gap of approximately 2 eV and a larger binding energy than that of the proposed C₃₆ solid.