Geometry and Stability of Small Gold Cluster Ions by Graph Theory and Hückel model

Structure and stability of the gold cluster ions of which skeleton are synthesized as a complex were analyzed using the Hückel method based on graph theory. Hückel Energy (HE) and Topological Resonance Energy (TRE) were determined for neutral, positive ion, and negative ion clusters, where all the isomers of the gold cluster up to octamer were considered. Since some graphically designed isomers include bonds that cannot be realized in three- dimensional space, the screening was carried out by a molecular force field calculation with LAMMPS (lammps.sandia.gov/.). Among the isomers thus obtained, both HE and TRE were most stable when the tetramer was Au₄ ^{2 +} with a tetrahedral structure, and with the hexamer, Au₆ ²⁺ with two tetrahedrons sharing one side. The complexes with these structures have actually been synthesized. On the other hand, the synthesis example of the most stable cluster for octamer Au₈ has not been reported.