We analyze the electronic and optical excitations in silver clusters (${\text{Ag}}_n$, $n=1–8$) using density-functional and many-body theories within an ab initio pseudopotential framework. Vertical ionization potentials and electron affinities are calculated within the so-called $\Delta \text{SCF}$ and $GW$ approximations. Results are compared with experimental data. For molecular orbitals of predominantly $sp$ character, the $GW$ results are found to be in good agreement with experiment. For orbitals of mainly $d$ character, good agreement with experiment can be achieved only via the use of semicore pseudopotentials, due to strong correlations among $4s$, $4p$, and $4d$ electrons. Optical excitations are computed within the time-dependent local-density approximation (TDLDA) and by solving the Bethe-Salpeter equation (BSE) for electrons and holes. For most clusters, the TDLDA spectra are in reasonable agreement with experimental data. The optical excitations computed with the BSE method, on the other hand, are generally in poor agreement with experiment, especially as size increases. This finding is explained in terms of the nonlocality of the BSE kernel and correlations involving $4d$ electrons. We also discuss the roles played by self-consistency, vertex corrections, and satellite structures in the $GW$ results of these confined systems with $d$ valence electrons.

• Received 17 December 2008

DOI:https://doi.org/10.1103/PhysRevB.79.155419