Core Polarization in the Optical Response of Metal Clusters: Generalized Time-Dependent Density-Functional Theory

We present a generalized time-dependent density-functional theory (TDDFT) for the optical response of metal clusters where both core polarization and valence responses are treated microscopically. It is shown that the valence electrons response is described by an effective external field and residual interaction that are those of the standard TDDFT modified by the self-consistent contributions of the array of polarizable ionic cores. As an application the equations are solved within the adiabatic local-density approximation for silver clusters, where core $4d$ electrons greatly influence the optical response. The experimental data are well reproduced by the present theory.