Violating the isolated pentagon rule (IPR): Endohedral Non-IPR C ₉₈ Cages of Gd ₂@C ₉₈

The geometric, electronic structure, and thermodynamic stability of large gadolinium-containing endohedral metallofullerenes, Gd ₂@ C ₉₈, have been systematically investigated by comprehensive density functional theory calculations combined with statistical mechanics treatments. The Gd ₂@C ₂(230924)-C ₉₈ structure, which satisfies the isolated-pentagon rule (IPR), is determined to possess the lowest energy followed with some stable non-IPR isomers. In order to clarify the relative stabilities at elevated temperatures, entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP level for the first time. Interestingly, a novel non- IPR Gd ₂@C ₁(168785)- C ₉₈ isomer which has one pair of pentagon adjacency is more thermodynamically stable than the lowest energy IPR species within a wide temperature interval related to fullerene formation. Therefore, the Gd ₂@ C ₁(168785)-C ₉₈ is predicted to be the most proper isomer obtained experimentally, which is the largest non-IPR carbon cage found so far. Our findings demonstrate that interaction between metals and carbon cages could stabilize the fused pentagons effectively, and thus, the non-IPR isomers should not be ignored in some cases of endohedral metallofullerenes. The IR features of Gd ₂@C ₉₈ are simulated to assist its future experimental characterization.