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Potential energy surface study of X@Si$_{32}$X$^-_{44}$(X=Cl, Br) clusters to decipher the stabilization process of Si$_{20}$ fullerene

Efforts toward stabilization of the Si$_{20}$ fullerene through different schemes have failed despite several theoretical predictions. However, recently Tillmann {\it et. al.} succeeded to stabilize the Si$_{20}$ fullerene through exohedral decoration with eight Cl substituents and twelve SiCl$_3$ groups on the surface and enclosing Cl$^-$ ion. A deeper understanding on what factors lead to stabilization will open the path for stabilizing other systems of interest. Here, we employ the minima hopping method within density functional theory to understand the potential energy surface. The study shows that the exo-endo halide decoration of the cage alters the glassy nature of the potential energy surface of pure cage to structure seeker. Further analysis of different properties of the global minima, reveal that the extra electron instead of residing on the central encapsulated atom in the cage, it is distributed on the cage and increases the encapsulation energy; thereby stabilizing the system. We also provide estimates of the stability for different kind of exo-endo halide decorations and their feasible realization in experiments.