An approach to describing the topology of polynuclear clusters

The literature on metal clusters reveals numerous examples of polynuclear clusters made up of ions with open shells displaying interesting structural, chemical and physical properties. For example, such clusters are found in biology and are modeled in bioinorganic, biomimetic chemistry. Another area of current intense research activity looks at open shell clusters, which behave as nanoscale magnetic materials, which on a molecular level are denoted as Single-Molecule Magnets or SMMs. In contrast to most closed shell clusters many of these clusters possess topologies which are difficult to describe in terms of familiar polyhedra. The central idea of this tutorial is to extend the accepted and useful topological description according to Schläfli symbols applied to networks in order to introduce a new and convenient approach to describing the topology of polynuclear clusters.