Size matching and electrostatic potential as complementary methods for understanding the metallic cluster configurations inside fullerenes

The size matching between the internal cluster and the outer cage is widely used to explain the former's configuration in endohedral clusterfullerenes (ECFs). For example, the trimetallic nitride (M₃N) clusters within smaller fullerenes are expected to become more relaxed in larger ones due to the weak cage confinement. However, recent single-crystal X-ray diffraction (SCXRD) experiments reveal that, although being planar in C₈₀, the Sc₃N cluster exhibits an abnormal pyramidal shape in <i>C</i>_s(51365)-C₈₄ and <i>D</i>₃(19)-C₈₆. This phenomenon can be explained by the "spider effect," which occurs when a small cluster meets a large cage. Herein, to further solve this puzzle and deeply understand the internal cluster configurations of ECFs, density functional theory calculations were conducted for nine SCXRD-characterized Sc₃N@C_2<i>n</i> (2<i>n</i> = 68, 70, 78-86) nitride clusterfullerenes. After successfully reproducing their structural characteristics, we found that all their cluster configurations can be rationalized by the electrostatic potentials (ESPs) inside the corresponding C_2<i>n</i>^6- anionic empty cages. These cage anions exhibit rather different ESP distributions, and the intramolecular host-guest electrostatic interactions drive the three Sc³⁺ cations toward the more negative region and the central N^3- anion toward the less negative one, thus resulting in a planar or slightly pyramidal shape of the whole (Sc₃N)⁶⁺ unit. Moreover, besides these nitride ECFs, ESPs can explain the internal cluster configurations of other types of ECFs as well. Different from the conventional viewpoint, which focuses only on the cluster and cage sizes, our work uncovers the overlooked role of ESPs in affecting the cluster configurations besides the most important metal-cage interactions. Based on this finding, we further demonstrated that one could easily regulate the internal cluster shape by changing the ESPs.