Structural and Optical Properties of Sodium Clusters studied in Density Functional Theory

Clusters are aggregates of matter that contain between two and several thousand atoms. On the lower end of this size range, the field of cluster physics overlaps with molecular physics, whereas on the higher end, it touches the realm of solid state physics. Therefore, it is a matter of system size and partially also of personal taste whether a system is called a molecule, a cluster, or a mesoscopic particle. However, it helps to explicitly say what a cluster is not: A cluster is neither a single atom nor a small piece of bulk material. This means that a cluster always consists of several atoms, but that these atoms are not arranged according to the same rules as in the bulk material, e.g., in a crystal lattice. Besides the interest in cluster physics which is fueled by the technological opportunities that these particles offer, e.g., in catalysis, chemisorption and microelectronics, the question why small particles can behave very different from the bulk is one of the driving forces for cluster research. Questions like ``How many atoms does it take to build a piece of bulk metal? In which way does matter grow from the atom to the bulk? Which effects govern the structural and optical properties at different stages of this growing process?'' touch the basis of solid state and molecular physics and are of fundamental interest. It is the aim of this thesis to contribute to answering some of these questions. To this end

  • a local pseudopotential that compensates the LDA bond length underestimation and allows to extend the range of structure calculations is developed,
  • the ionic and electronic structure of sodium clusters with 2 to 58 electrons is calculated in density functional theory combined with Monte-Carlo simulated annealing,
  • a local current aproximation for the computation of excited states within density functional theory is introduced and applied to calculate static electric polarizabilities and photoabsorption spectra.

    Using these methods,

  • an icosahedral growth pattern is identified for sodium clusters,
  • the experimentally observed photoabsorption spectra are explained in terms of the local current approximation,
  • finite size effects in the thermal expansion coefficient of small metal particles are investigated,
  • and the close connection between electric polarizabilities and thermal expansion is demonstrated.

    Further information