Metal Clusters, Quantum Dots, and Trapped Atoms

In this chapter, we discuss the electronic structure of finite quantal systems on the nanoscale. After a few general remarks on the many-particle physics of the harmonic oscillator, likely being the most studied example for the many-body systems of finite quantal systems, we turn to the electronic structure of metal clusters. We discuss Jahn–Teller deformations for the so-called “ultimate” jellium model which assumes a complete cancelation of the electronic charge with the ionic background. Within this model, we are also able to understand the stable electronic shell structure of tetrahedral (three-dimensional) or triangular (two-dimensional [2D]) cluster geometries, resembling closed shell…