Theoretical Study of the Stability of $\mathrm{Au_nGe_{m}}$ Clusters

We investigate the properties of clusters formed from two connected $\mathrm{Ge_{m}}$ cage-like clusters, such as experimentally synthesized $\mathrm{Au_3Ge_{18}^{5-}}$, using first-principles DFT methods. We focus particularly on $\mathrm{Au_nGe_{12}^{q-}}$ formed from $\mathrm{Ge_{6}}$, where $n=0-3$ and $q=0,2$. We examine the geometries, electronic structure, and thermal excitations of these clusters using the SIESTA code, where we test stability using short molecular dynamics simulations. Our examination of intercluster bridges between $\mathrm{Ge_{m}}$, formed of either Ge-Ge or Au-Ge bonds, indicates that the overlap of interacting molecular orbitals of $\mathrm{Ge_{m}}$~can either bind a cluster together or tear it apart depending on the orientation of the bridging atoms with respect to the cages. We characterize the properties of stable isomers of neutrally charged $\mathrm{AuGe_{12}}$ and $\mathrm{Au_2Ge_{12}}$, seeing that radially directed molecular orbitals stabilize $\mathrm{AuGe_{12}}$ while a geometric asymmetry stabilizes $\mathrm{Au_2Ge_{12}}$ and $\mathrm{Au_3Ge_{18}}$. We examine a two-dimensional $_2^\infty[\mathrm{Au_2Ge_{6}}]$ structure, finding it more stable than other periodic $[\mathrm{Au_nGe_{6}}]$ subunits. We observe no stable neutral isomers of $\mathrm{Au_3Ge_{12}}$, but see that additional charge supports isomers of both $\mathrm{Au_2Ge_{12}}$ and $\mathrm{Au_3Ge_{12}}$.