Nanotube junctions and the genus of multi-tori

Abstract

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.