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

TL;DR

This study uses first-principles DFT calculations to analyze the stability, electronic structure, and geometries of gold-germanium clusters, revealing how orbital interactions and charge states influence their stability and structure.

Contribution

It provides a detailed theoretical investigation of Au-Ge clusters, including stability analysis, geometric and electronic characterization, and the effects of charge and bonding configurations.

Findings

Stable isomers of AuGe12 and Au2Ge12 identified

Orbital overlap influences cluster stability and bonding

Charge state affects isomer stability and structure

Abstract

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 $\mathrm{Au_3Ge_{12}}$.