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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 focusparticularly 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, andthermal excitations of these clusters using the SIESTA code, where we teststability using short molecular dynamics simulations. Our examination ofintercluster bridges between $\mathrm{Ge_{m}}$, formed of either Ge-Ge or Au-Gebonds, indicates that the overlap of interacting molecular orbitals of$\mathrm{Ge_{m}}$~can either bind a cluster together or tear it apart dependingon the orientation of the bridging atoms with respect to the cages. Wecharacterize the properties of stable isomers of neutrally charged$\mathrm{AuGe_{12}}$ and $\mathrm{Au_2Ge_{12}}$, seeing that radially directedmolecular orbitals stabilize $\mathrm{AuGe_{12}}$ while a geometric asymmetrystabilizes $\mathrm{Au_2Ge_{12}}$ and $\mathrm{Au_3Ge_{18}}$. We examine atwo-dimensional $_2^\infty[\mathrm{Au_2Ge_{6}}]$ structure, finding it morestable than other periodic $[\mathrm{Au_nGe_{6}}]$ subunits. We observe nostable neutral isomers of $\mathrm{Au_3Ge_{12}}$, but see that additionalcharge supports isomers of both $\mathrm{Au_2Ge_{12}}$ and$\mathrm{Au_3Ge_{12}}$.

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