| Summary: | This study on Lu<sub>2</sub>@C<sub>60</sub> isomers provides insights into the metal–metal bond through the confinement effect of fullerene cages. Density functional theory calculations were used to study the nature of the Lu-Lu bond in two stable endohedral metallofullerenes (EMFs), Lu<sub>2</sub>@<i>C</i><sub>2<i>v</i></sub>_C<sub>60</sub> and Lu<sub>2</sub>@<i>I<sub>h</sub></i>_C<sub>60</sub>, both with negative endohedral energy. These two isomers are geometrically connected through a simple Stone–Wales (SW) transformation. The electronic configuration of (Lu<sub>2</sub>)<sup>4+</sup>@C<sub>60</sub><sup>4−</sup> was also confirmed, leading to the formation of a two-center two-electron (2c–2e) Lu-Lu σ single bond. By comparing the Lu-Lu bonds in Lu<sub>2</sub>@C<sub>60</sub> with those in acknowledged Lu<sub>2</sub>@C<sub>2<i>n</i></sub>, the smaller C<sub>60</sub> fullerene compressed the geometry of Lu<sub>2</sub> resulting in a much shorter Lu-Lu bond length. However, the Lu-Lu bond strength is slightly weaker in Lu<sub>2</sub>@C<sub>60</sub> than that in large fullerenes, as the Lu-Lu bond in C<sub>60</sub> is likely a p-p σ bond with an above the 40% contribution of p orbital and a strong metal–cage interaction. Additionally, the vis-NIR spectra of Lu<sub>2</sub>@<i>C</i><sub>2<i>v</i></sub>_C<sub>60</sub> and Lu<sub>2</sub>@<i>I<sub>h</sub></i>_C<sub>60</sub> were simulated, which could provide valuable information for future experimental studies on Lu-based EMFs.
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