Cage connectivity and frontier π orbitals govern the relative stability of charged fullerene isomers.

Fullerene anions and cations have unique structural, electronic, magnetic and chemical properties that make them substantially different from neutral fullerenes. Although much theoretical effort has been devoted to characterizing and predicting their properties, this has been limited to a fraction of isomeric forms, mostly for fullerene anions, and has practically ignored fullerene cations. Here we show that the concepts of cage connectivity and frontier π orbitals allow one to understand the relative stability of charged fullerene isomers without performing elaborate quantum chemistry calculations. The latter is not a trivial matter, as the number of possible isomers for a medium-sized fullerene is many more than 100,000. The model correctly predicts the structures observed experimentally and explains why the isolated pentagon rule is often violated for fullerene anions, but the opposite is found for fullerene cations. These predictions are relevant in fields as diverse as astrophysics, electrochemistry and supramolecular chemistry.