Atomic clusters, covering the size range from a few to several
hundred thousand atoms, represent an intermediate stage in the
transition from small molecules to solids (for an overview see ).
For the theoretical description of clusters a variety of concepts,
reflecting the interdisciplinary nature of this research area, has
In microscopic approaches to small clusters the atoms are usually
decomposed into ionic cores, represented by suitable
pseudo-potentials, and the chemically active
The structure of the cluster is determined by searching for the
ionic configuration, which minimizes the total energy.
The absolute energy minimum corresponds to the ground state
configuration, local minima represent isomers of the cluster.
The search for energy minima is combined with the solution of the
electronic many-particle problem via density
functional methods in a particularly efficient way by the
Car-Parrinello technique [2,3] (also called quantum molecular
Based on the structures obtained in this way, the dynamical
properties of clusters can be investigated by means of linear
response and/or time-dependent density
In our group the structure of small
phosphorus clusters and the fusion of two Na_8 clusters
 have been studied on the basis of this microscopic approach
(see also ).
With increasing cluster size, however, the Car-Parrinello
scheme sooner or later becomes intractable with the available
computational resources, the critical size depending on the
system under consideration and the computer technology at hand.
In order to calculate properties of larger clusters additional
approximations are necessary.
A prominent approach to medium size and large metal clusters
is the so-called jellium model .
Here the ionic structure is smeared out to a uniform positive
background of bulk density, which binds a delocalized valence
The jellium model thus emphasizes collective electronic effects
over the detailed ionic structure, which is only reflected by the
shape of the jellium background.
This approach is thus particularly suitable for systems with
rather delocalized valence electrons.
A large variety of properties of metal clusters, such as static
polarizabilities, collective electronic excitations, ionization
potentials as well as the so-called 'magic numbers' [6-10], can be
explained in terms of the jellium model.
Our research aims at a deeper understanding of the role of
collective electronic effects in the fission and fusion of
metal clusters [11,12], their magnetic  and optical 
properties as well as cluster-cluster collisions 
(utilizing density functional methods).
In addition, a liquid drop model has been developed for the description
of very large metal clusters [16,17].