ABSTRACT
Jellium is a quantum mechanical model which describes electrons interacting in a potential created by a uniform positive background charge. The advantage of this model is that it retains much of the simplicity of the harmonic oscillator description, while being numerically adjustable to account for different electron densities. In the most general terms, variational methods are simply ways of finding the functions which maximise or minimise the value of a quantity that depends upon those functions. The use of a spherical jellium model can be used to produce effective potentials and corresponding electronic energies for different metals, based on the Wigner Seitz radius – the volume of each atom. Before continuing to a discussion of the detailed differences between different types of superatomic clusters, one need to extend their discussion of the jellium model to the most frequent tool used for atomistic calculation of their properties: that is Density Functional Theory.
