Omni-conducting fullerenes

Within the graph-theoretical SPP (Source-and-Sink Potential) model, a strong omni-conductor can be defined as a molecular graph that is predicted to conduct at the Fermi level, no matter how it is connected by single-atom contacts to the wires. Exhaustive search ( n ⩽ 70 for general isomers; n ⩽ 140 for isolated-pentagon isomers) shows that nearly all fullerene isomers Cn in the chemical size range are strong omni-conductors. The isolated-pentagon isomer of C60 is a strong omniconductor, whereas the isolated-pentagon isomer of C70, which has a non-bonding LUMO, has some insulating pairs of connections.