Nanotube junctions and the genus of multi-tori

Carbon nanotube junctions can be modeled by fullerene spanning or by using some operations on map. They can self-assemble into more complex structures, such as finite or infinite high genera multi-tori. Four junctions of tetrahedral and octahedral symmetry, covered by patches consisting only of hexagons, were designed. Their stability is discussed in terms of total energy, evaluated at Hartree-Fock (HF) level of theory, HOMO-LUMO gap, strain energy, HOMA index of aromaticity and the Kekulé structure count. Vibrational spectra of these junctions are given as well. A new multi-toroidal structure, of octahedral symmetry, is presented for the first time. The study on topology of the multi-tori herein designed revealed the relation of these structures with the genus of their embedding surface.