Non-bonding orbitals in graphite, carbon tubules, toroids andfullerenes

It is shown that the non-bonding orbitals of many graphite-derived carbon frameworks can be understood in terms of the four non-bonding orbitals of the graphite sheet. Several infinite series of fullerenes with non-bonding orbitals are identified, and the frontier orbitals of icosahedral fullerenes rationalised, by considering fullerenes as cut and folded graphite. The leapfrog construction, which produces only closed-shells when acting on fullerenes, is shown in contrast to produce exactly the metallic tubules and the open-shell polyhex toroids when acting within these families.