Freedom and constraints of a metal atom encapsulated in fullerene cages

Fullerenes are a beautiful example of hollow structures that give rise to endohedral host--guest complexes with a wide range of potential applications. Only very recently was the first solid metallofullerene characterized \cite{shino}, but key long-standing questions concerning metallofullerenes remain unanswered. ``Are there general rules for metal-cage chemistry? At room temperature, does the metal atom move? If so, how and on which time scale?'' We present {\it ab-initio} molecular dynamics simulations of La- and Y-fullerenes, which reveal how the fullerene structure determines the chemisorption sites, and to what extent chemical constraints limit the freedom of the metal atom. In C$_{60}$, high symmetry and low barriers allow it to diffuse and make a round trip in $\sim$1 psec. C$_{82}$ offers only few and unforeseen attractive nests to the metal atom. Trapped there, it moves with characteristic times of $\sim$0.1 psec. Our results shed light on the strikingly higher stability of the C$_{82}$ system, and suggest its ability to be used as an electronic switch.