Theoretical Study of the Stability of $\mathrm{A}{\mathrm{u}}_{\mathrm{n}}\mathrm{G}{\mathrm{e}}_{\mathrm{m}}$ Clusters

Abstract

We investigate the properties of clusters formed from two connected $\mathrm{G}{\mathrm{e}}_{\mathrm{m}}$ cage-like clusters, such as experimentally synthesized $\mathrm{A}{\mathrm{u}}_3\mathrm{G}{\mathrm{e}}_{18}^{5-}$, using first-principles DFT methods. We focus particularly on $\mathrm{A}{\mathrm{u}}_{\mathrm{n}}\mathrm{G}{\mathrm{e}}_{12}^{\mathrm{q}-}$ formed from $\mathrm{G}{\mathrm{e}}_6$, 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 $\mathrm{G}{\mathrm{e}}_{\mathrm{m}}$, formed of either Ge-Ge or Au-Ge bonds, indicates that the overlap of interacting molecular orbitals of $\mathrm{G}{\mathrm{e}}_{\mathrm{m}}$~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 $\mathrm{AuG}{\mathrm{e}}_{12}$ and $\mathrm{A}{\mathrm{u}}_2\mathrm{G}{\mathrm{e}}_{12}$, seeing that radially directed molecular orbitals stabilize $\mathrm{AuG}{\mathrm{e}}_{12}$ while a geometric asymmetry stabilizes $\mathrm{A}{\mathrm{u}}_2\mathrm{G}{\mathrm{e}}_{12}$ and $\mathrm{A}{\mathrm{u}}_3\mathrm{G}{\mathrm{e}}_{18}$. We examine a two-dimensional ${}_2^{\infty }[\mathrm{A}{\mathrm{u}}_2\mathrm{G}{\mathrm{e}}_6]$ structure, finding it more stable than other periodic $[\mathrm{A}{\mathrm{u}}_{\mathrm{n}}\mathrm{G}{\mathrm{e}}_6]$ subunits. We observe no stable neutral isomers of $\mathrm{A}{\mathrm{u}}_3\mathrm{G}{\mathrm{e}}_{12}$, but see that additional charge supports isomers of both $\mathrm{A}{\mathrm{u}}_2\mathrm{G}{\mathrm{e}}_{12}$ and $\mathrm{A}{\mathrm{u}}_3\mathrm{G}{\mathrm{e}}_{12}$.

arXiv comment19 pages, 16 figures + 7 supplemental figures