  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.
