ABSTRACT
A crude, but nevertheless very successful description of the electronic system of a metal is the free-electron model, which assumes that the valence electrons move through the in nite metal lattice like free particles. In this model, the electronic wavefunctions are just plane waves; any wavelength is allowed. is changes dramatically if the metal is shrunk down to nanoscopic dimensions. Now, the wavefunctions form standing waves between the surfaces of the particle, which is possible only for certain wavelengths. A direct consequence is the discretization of the electronic density of states: the continuous valence band breaks up into a nite number of states. is is the so-called quantum size e ect, which can lead to signi cant changes of the metal particle properties. One can expect that such e ects can be most clearly seen for a metal that comes close to ideal freeelectron behavior. e alkali metal sodium is a very promising candidate: it exhibits a band structure with a dispersion very close to that of free electrons (Figure 6.1); its Fermi surface deviates from a sphere only by less than 0.1% (Ashcro and Mermin, 1976). It is therefore not surprising that the rst observation of a quantum size e ect in free metal particles was made on sodium clusters.
