We present a study of the optical response of compact and hollow icosahedral clusters containing up to 868 silver atoms by means of time-dependent density functional theory. We have studied the dependence on size and morphology of both the sharp plasmonic resonance at 3-4 eV (originated mainly from $sp$-electrons), and the less studied broader feature appearing in the 6-7 eV range (interband transitions). An analysis of the effect of structural relaxations, as well as the choice of exchange correlation functional (local density versus generalized gradient approximations) both in the ground state and optical response calculations is also presented. We have further analysed the role of the different atom layers (surface versus inner layers) and the different orbital symmetries on the absorption cross-section for energies up to 8 eV. We have also studied the dependence on the number of atom layers in hollow structures. Shells formed by a single layer of atoms show a pronounced red shift of the main plasmon resonances that, however, rapidly converge to those of the compact structures as the number of layers is increased. The methods used to obtain these results are also carefully discussed. Our methodology is based on the use of localized basis (atomic orbitals, and atom-centered- and dominant- product functions), which bring several computational advantages related to their relatively small size and the sparsity of the resulting matrices. Furthermore, the use of basis sets of atomic orbitals also brings the possibility to extend some of the standard population analysis tools (e.g., Mulliken population analysis) to the realm of optical excitations. Some examples of these analyses are described in the present work.
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