Optical response of small silver clusters

The time-dependent local-density approximation is applied to the optical response of the silver clusters, Ag₂, Ag₃, Ag₈, and Ag₉⁺. The calculation includes all the electrons beyond the closed-shell Ag¹¹⁺ ionic core, thus including explicitly the filled d shell in the response. The excitation energy of the strong surface plasmon near 4 eV agrees well with experiment. The theoretical transition strength is quenched by a factor of 4 with respect to the pure s-electron sum rule in Ag₈ due to the d electrons. Also, in this system the theoretical integrated strength function is remarkably well described by the Mie theory using the bulk dielectric constant. However, the strength is somewhat less than reported experimentally.