Fig. \[fig:systems\]) which is a medium size alkaline cluster. It contains 40 valence electrons forming an electronic shell closure. This leads to a particularly abundant/stable species. The s.p. energies span an energy range of order 2.6 eV and the Ionization Potential (IP) is of order 5.3 eV. Such values are typical of alkaline clusters. The optical response displays a pronounced collective, essentially single, peak around 2.6 eV. This is called the Mie surface plasmon and it is a typical mode for simple metal clusters. In larger clusters, the density of s.p. states grows, which leads to more Landau fragmentation and somewhat broadens the plasmon peak. The Mie plasmon frequency is related to a typical time scale of order 1.5 fs, again a characteristic time scale for simple metals. Ionic time scales (not shown in Fig. \[fig:systems\]) are more sensitive to the actual material due to the largely differing atomic weight. In Na clusters, vibrational modes typically lie in the 10 meV range and are associated to ionic motion in the 100 fs range.

The second example is C$_{60}$ (upper right block) with 240 valence electrons (4 per C atom). The s.p. energies now ranges in a span of about 17.3 