Temperature and size dependence of the optical response of small Ag

The absorption spectra of small Ag+_n clusters are calculated at finite vibrational temperature by using a microscopic tight-binding RPA method. We consider free clusters with sizes between n = 3 and n=13 and take into account explicitly the degrees of freedom corresponding to the 4d-electrons. We analyze the optical absorption as a function of the cluster size. We show that the contribution of the d-electrons has an important influence on the size dependence of the energy of the Mie plasmon. We also perform ensemble averages to obtain the absorption spectra for different vibrational temperatures. We obtain relatively good agreement with experiment for a temperature $T\sim 500\;{\rm K}$. The dynamics of the 4d-electrons, which shows in small clusters an incipient delocalized character for n>7, yields an important contribution to the absorption spectrum already for n=13. We find that the strength of this contribution can be controlled by varying the vibrational temperature