Is the Isolated Pentagon Rule Always Satisfied for Metallic Carbide Endohedral Fullerenes?

Quantum-chemical calculations reveal that metallic carbide endohedral fullerene Y₂C₂@C₈₄ possesses a novel fullerene cage, C₁(51383)-C₈₄, with one pair of pentagon adjacencies. One of the encapsulated yttrium atoms is located on the adjacent pentagons, while the other stays on a hexagonal ring in the fullerene cage. As one of numerous metallic carbide endohedral fullerenes, Y₂C₂@C₁(51383)-C₈₄ is the first example that violates the well-known isolated pentagon rule (IPR). More interestingly, compared with the fact that Sc₂C₂@C₈₄ has a conventional IPR-satisfying cage, D_2d(51591)-C₈₄, Y₂C₂@C₈₄ utilizes the novel fullerene cage C₁(51383)-C₈₄ with one pair of pentagon adjacencies.