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 C-20 fullerene monomer and oligomers are reported. C-20 cages with C-2, C-2h, C-i, D-3d, and D-2h symmetries have similar energies and geometries. Release of the very high C-20 strain is, in theory, responsible for the ready oligomerization and the formation of different solid phases. Open [2+2] bonding is prefer-red 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 C-36 solid.