The super-atom model: link between the metal atom and the infinite metal

Abstract

Prompted by the analysis of experimental absorption spectra of small Ag clusters, embedded in rare-gas matrices at low temperatures, the size dependence of the electronic properties of metal clusters is studied within the socalled super-atom model. It is found that the electronic properties do not change monotonously from the atom to the bulk, but show - in agreement with the experimental findings - a pronounced oscillatory behaviour. In analogy to similar phenomena in nuclear physics, there are mass numbers of strongly enhanced stability (the so-called magic numbers), which are genuine properties of the jellium model used here. Both the ionization potential and the electron affinity show sharp discontinuities at these magic numbers. All these effects can be shown to be caused by so-called Quantum Size Effects (QSE) in the electronic orbitals, which originate from surface quantization conditions, and NOT from bulk quantization conditions. In agreement with experimental findings, QSE determine the electronic properties of alkali metal clusters Me ^N, with N < 1500. The generation of size-dependent collective excitations is studied within the time-dependent local-density approximation (TDLDA). In agreement with experimental data, surface plasmons show a pronounced red shift from the classical Mie value, The oscillator strengths of both volume plasmons, at frequency, and individual particle-hole pairs are smaller by at least three orders of magnitude.