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Optical and magnetic excitations of metal-encapsulating Si cages: A systematic study by time-dependent density functional theory

Systematic study of the optical and magnetic excitations of twelve MSi$_{12}$ and four MSi$_{10}$ transition metal encapsulating Si cages has been carried out by employing real time time-dependent density functional theory. Criteria for the choice of transition metals (M) are clusters' stability, synthesizability, and diversity. It was found that both the optical absorption and the spin-susceptibility spectra are mainly determined by, in decreasing order of importance: 1) the cage shape, 2) the group in the Periodic Table M belongs to, and 3) the period of M in the Periodic Table. Cages with similar structures and metal species that are close to each other in the Periodic Table possess spectra sharing many similarities, e. g., the optical absorption spectra of the MSi$_{12}$ (M = V, Nb, Ta, Cr, Mo, and W), which are highly symmetric and belong to groups 4 and 5 of the Periodic Table, all share a very distinctive peak at around 4 eV. In all cases, although some of the observed transitions are located at the Si skeleton of the cages, the transition metal specie is always significant for the optical absorption and the spin-susceptibility spectra. Our results provide finger-print data for identification of gas-phase MSi$_{12}$ and MSi$_{10}$ by optical absorption spectroscopy.