Planar Structures of Medium-Sized Gold Clusters Become Ground States upon Ionization

Abstract

This study investigates the structural stability of ionized gold clusters of sizes ranging from 22 to 100 atoms, contrasting compact, cage and planar structures. While it is well known that neutral clusters in the upper part of this size range predominantly favor compact structures, our results reveal that positively ionized gold clusters exhibit structural transitions in which planar structures become energetically preferred once the charge is sufficiently large. In addition, we study the finite-temperature stability of the structures and find that thermodynamic effects further stabilize planar configurations relative to their compact counterparts. To explore the potential energy surface, we use the Minima Hopping algorithm combined with a machine-learned potential. Since the machine-learned potential does not apply to ionized clusters, we introduce a charge-correction term to incorporate Coulomb interactions and charge screening.

Figures (12)

• Figure 1: Total PBE energies for the smallest ionization level that gives a cage or flake as its ground state for the PBE XC functional.
• Figure 2: Total PBEsol+MBD energies for the investigated neutral and ionized gold clusters. Shown is always the smallest ionization level that gives a cage or flake as its ground state. In contrast to experimental evidence, cages are never lower in energy than planar structures with this XC functional.
• Figure 3: Total r$^2$SCAN energies for the investigated neutral and ionized gold clusters. Shown is always the smallest ionization level that gives a cage or flake as its ground state. Shown are also the vibrational free energy differences at 300 K with respect to the free energies of the lowest compact structure. Downward arrows indicate that entropy effects stabilize planar structures.
• Figure 4: Planar configurations of minimally ionized gold clusters for all investigated sizes. The atoms are always arranged in a regular hexagonal close-packed pattern. The progression from one size to the next is obtained by adding to the atoms shown in gold the atoms highlighted in red, then blue and finally green.
• Figure 5: Subfigure (a)-(h) show the highly symmetric cage structures for $Au_{27}$, $Au_{29}$, $Au_{32}$, $Au_{37}$, $Au_{42}$, $Au_{50}$, $Au_{62}$ and $Au_{78}$ respectively.