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.
Extensive experimental and theoretical studies show that small gold clusters exhibit a preference for planar (2D) geometries up to a critical size, beyond which three-dimensional (3D) compact structures, (i.e structures which can not host an extra endohedral atom), become energetically favorable [1][2][3][4] . For anionic clusters, photoelectron spectroscopy, ion mobility measurements and Density Functional Theory (DFT) calculations consistently show that clusters remain planar up to Au 11 , with a structural transition occurring at Au 12 where planar and 3D isomers coexist and clusters of Au n≥13 are 3D geometries 1,3,5,6 . DFT predictions for the 2D to 3D crossover in neutral clusters are strongly method-dependent: Local Density Approximation (LDA) favors a transition at Au 7 , whereas Generalized Gradient Approximation (GGA) with scalarrelativistic can stabilize planar motifs up to Au 11 7 . Cage motifs emerge for Au 10 -Au 14 , followed by a transition to compact structures at Au 15 4 . Finite-temperature free-energy calculations using van der Waals-corrected DFT predict that Au 9,10 remain planar at 100 K, whereas Au 11 adopts a nonplanar capped trigonal prism with D 3h symmetry; increasing temperature generally shifts populations toward nonplanar structures for Au 8 -Au 13 , with Au 11 being a notable exception due to many accessible near-degenerate planar isomers 8 . A recent machine-learning-based global search has further refined this picture by systematically investigating Au 2 -Au 55 clusters, identifying the planar to 3D transition at Au 14 already reveal an extremely shallow Potential Energy Surface (PES) with many quasi-degenerate compact and non-compact isomers and a strong XC functional dependence of the predicted ground state 14 . For Au 32 , a cage with icosahedral symmetry satisfying the 2(N + 1) 2 spherical aromaticity rule 15 and exhibiting a large HOMO-LUMO gap is proposed as a "golden fullerene" 16 . Stability, arising from aromaticity and a large HOMO-LUMO gap, was also found for Au 50 , where a DFT-based comparison of cage and compact structures found that a cage with D 6d was the global minimum 17,18 . Au 42 with icosahedral and Au 60 with chiral icosahedral symmetry cages are typically slightly higher in energy than compacts, remain structurally robust local minima and can act as components in nested or multi-shell clusters 19,20 . A study based on icosahedral-inspired templates showed that large quasiicosahedral cages such as Au 92 and Au 122 , although not global minima, are low-lying energy metastable structures with high symmetry and strong metallicity 21 . Clusters in the Au n∼100 size range are compact, and entirely different structural motifs-such as icosahedral, decahedral, or octahedral-can be nearly degenerate in energy. As a consequence, the ground-state structural motif can change upon the addition of a single atom, and the groundstate structure oscillates among these motifs with increasing cluster size 22 .
While early studies primarily focused on small clusters and their transition from planar to compact geometries, recent experimental studies have demonstrated that atomically thin, freestanding gold monolayers can be synthesized using ligandassisted self-assembly 23 , intercalation beneath graphene 24 , exfoliation from layered precursors 25 and in-situ dealloying inside electron microscopes 26,27 . These monolayers exhibit remarkable thermal stability, metallic conductivity, and even magnetic edge states in nanoribbons. Moreover, studies based on DFT predicted that hexagonally close-packed 2D gold is dynamically 28 and thermodynamically 29 stable. Systematic DFT calculations indicate that graphene pores can stabilize free-standing 2D metal patches up to ∼ 8 nm 2 , and identify Au as one of the most promising elemental metals for forming stable pore-confined 2D phases 30 . Complementary computational simulations using abinitio and molecular dynamics methods further reveal unique behaviors such as 2D liquid phases 31 , strain-induced electronic transitions 24 , and strong environment-dependent catalytic activity [32][33][34] . These findings establish that planar gold structures are not restricted to small clusters but constitute a broader and experimentally realizable class of 2D materials.
These results collectively suggest that planar and cage motifs represent an important class of stable and potentially synthesizable configurations for medium-sized and large gold clusters. We therefore explored whether positive ionization, hereafter referred to simply as ionization, of electron-rich gold clusters provides a route to stabilizing planar or cage motifs. The rationale is based on the assumption that the positive charge is distributed over all atoms, leading to a repulsion between the ionic nuclei. Hence, the electrostatic energy will be smaller in a planar or cage structure, where the number of nearest neighbors is smaller than in compact structures. To test this h
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