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What determines the smallest fullerene cage that can trap an atom inside it?

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The size of the smallest fullerene cage capable of trapping an atom inside it is determined by the size of the encapsulated atom itself.1

In these "endohedral" complexes, where an atom is physically enclosed within the carbon cage, the internal dimensions of the fullerene must be sufficient to accommodate the specific atom being trapped. Researchers have successfully studied various endohedral species, such as those involving alkali metals, alkaline earth metals, early lanthanoids, and helium, by matching the cage structure to the requirements of the guest atom.1