Origin of kinetic instability of fullerenes that violate the isolated pentagon rule.

The isolated pentagon rule (IPR) holds without exceptions for neutral fullerene Molecules. Unlike those in non-IPR fullerenes, 5/5 bonds (i.e., pi-bonds shared by two pentagons) in many planar polycyclic pi-systems are kinetically rather stable with large positive bond resonance energies (BREs), where BRE is a graph-theoretically defined index of kinetic stability. Geometric conditions were explored for designing planar polycyclic pi-systems with unstable 5/5 bonds. We then found that the kinetic instability of non-IPR fullerenes stems from the coexistence of pentalene substructures and nearby disjoint pentagons. Proper arrangements of fused pentagons and disjoint pentagons make the 5/5 bonds highly reactive with large negative BREs.