Geometric Structure, Magic Numbers and Coordination Numbers of Small Clusters

Abstract

Packing structures of spherical particles are determined by the range of interatomic or intermolecular interactions. The most stable structures are normally those with the highest average coordination number of nearest neighbours. Except for gold where relativistic effects play a more important role this leads to near spherical cluster shapes, and closed geometric shells are the most stable. This extra stability leads to a dominance of closed shell structures in atomic or small molecule molecular beams, and the numbers of atoms in such stable clusters are called magic numbers. Apart from magic numbers formed by geometric shells closing, there is a second set of magic numbers which are due to electronic shells closing. These are essentially noble gas configurations of clusters with delocalised electrons. As in atoms, this leads to odd–even effects due to single or double occupation of orbitals with electrons. Small clusters are often icosahedral, a symmetry that is not compatible with crystalline structures in the bulk. When clusters grow, more atoms are found in the long-range part of the potential curve, which contributes to tipping the structure towards the one found in the bulk.