Collective excitations in open-shell metal clusters: The time-dependent local-density approximation applied to the self-consistent spheroidal jellium particle

The self-consistent and microscopic time-dependent local-density-approximation (TDLDA) formalism for the calculation of the dynamical electronic response properties of open-shell, axially deformed small metal clusters is presented in detail. The model is based on the self-consistent ground-state calculation of the spheroidal jellium model, giving the optimized cluster shape, driven by its open-valence-shell electronic structure. First results on the static and dynamical electronic polarizability of the strongly axially deformed ${\mathrm{Na}}_{10}$ cluster are reported and compared with the experimental polarizability and photoabsorption cross-section results. The variety of the future applications of the model is outlined, as well as the possible improvement of the formalism.