Topological rotational strengths as chirality descriptors for fullerenes

A graph-theoretical procedure is proposed for assigning a chirality descriptor (the topological sign tau(+) or tau(-)) to each enantiomer of a chiral polyhedron, polyhedral molecule or graph, independently of any vertex labelling scheme. Model Cartesian coordinates and rotational strengths are obtained using only adjacency information; a generalised HOMO-LUMO rotational strength is used to associate a sign with a Schlegel diagram and the corresponding three-dimensional structure, polyhedron or molecule. The topological sign gives an unambiguous way of communicating the identity of an enantiomer. The mean-square topological rotational strength is a possible measure of the chirality content of a polyhedral graph or structure.