Novel organometallic complexes of fullerene C₈₀ and aryl ligands were simulated. The nature and characteristics of this family of complexes involving π coordination between the fullerene and a metal centre have been studied from a theoretical point of view. We are particularly interested in complexes where η⁶ coordination is present, this being the strangest manifestation of known coordinations, and thus we have studied several known and simulated compounds of this kind in order to understand the lack of examples. The presence of other η⁶ or η⁵ ligands on the opposite side seems to be an important element aiding the stabilization of these complexes, also inducing the conductive and semiconductive behaviour of the studied species.