Frontier orbitals of trivalent cages: (3,6) cages and (4,6) cages.

A qualitative molecular-orbital treatment and group-theoretical analysis reveals the nature of the frontier orbitals of (3,6) and (4,6) polyhedral cages, consisting of a hexagonal network with triangular and square defects, respectively. Leapfrog (3,6) cages have two nonbonding filled orbitals. Leapfrog (4,6) cages have a high HOMO-LUMO gap, while nonleapfrog (4,6) cages with octahedral symmetry have a very small HOMO-LUMO gap. The symmetry of the frontier orbitals is determined.