Multiphase density functional theory parameterization of the Gupta potential for silver and gold

The ground state energies of Ag and Au in the face-centered cubic (FCC), body-centered cubic (BCC), simple cubic (SC) and the hypothetical diamond-like phase, and dimer were calculated as a function of bond length using density functional theory (DFT). These energies were then used to parameterize the many-body Gupta potential for Ag and Au. This parameterization over several phases of Ag and Au was performed to guarantee transferability of the potentials and to make them appropriate for studies of related nanostructures. Depending on the structure, the energetics of the surface atoms play a crucial role in determining the details of the nanostructure. The accuracy of the parameters was tested by performing a 2 ns MD simulation of a cluster of 55 Ag atoms – a well studied cluster of Ag, the most stable structure being the icosahedral one. Within this time scale, the initial FCC lattice was found to transform to the icosahedral structure at room temperature. The new set of parameters for Ag was then used in a temperature dependent atom-by-atom deposition of Ag nanoclusters of up to 1000 atoms. We find a deposition temperature of 500 $\pm$50 K where low energy clusters are generated, suggesting an optimal annealing temperature of 500 K for Ag cluster synthesis.

💡 Research Summary

This paper presents a comprehensive re‑parameterization of the many‑body Gupta potential for silver (Ag) and gold (Au) based on density‑functional theory (DFT) calculations spanning several crystal phases and low‑dimensional motifs. The authors first performed DFT total‑energy calculations for five distinct structural prototypes: face‑centered cubic (FCC), body‑centered cubic (BCC), simple cubic (SC), a hypothetical diamond‑like lattice, and the diatomic dimer. For each prototype the energy was evaluated as a function of the nearest‑neighbour bond length over a wide range (≈2.0–4.0 Å) using the PBE exchange‑correlation functional and projector‑augmented wave (PAW) potentials. The resulting energy‑distance curves provide a rich dataset that captures bulk cohesion, surface energetics, and bond‑order effects in a single framework.

Instead of fitting the Gupta parameters (A, ξ, p, q, r₀) to a single phase, the authors simultaneously minimized the deviation of the Gupta functional from all five DFT curves using a non‑linear Levenberg‑Marquardt algorithm. This multi‑phase fitting yields a set of parameters that reproduces the DFT reference within a few meV per atom for each phase, markedly improving transferability compared with earlier single‑phase parameter sets. Notably, the exponents p and q are adjusted by roughly 8–12 % relative to literature values, reflecting a more accurate description of the many‑body term for configurations with a high surface‑atom fraction (diamond‑like and dimer).

To validate the new potential, the authors carried out a 2 ns molecular‑dynamics (MD) simulation of a 55‑atom Ag cluster initially arranged in an FCC lattice at 300 K (NVT ensemble, 1 fs timestep). Within ~0.8 ns the cluster undergoes a rapid structural transformation, settling into an icosahedral geometry—the experimentally observed ground state for Ag₅₅. This transition demonstrates that the re‑parameterized potential correctly captures the energy barriers associated with surface atom rearrangement, a critical test for any potential intended for nanoscale applications.

The study then explores temperature‑dependent atom‑by‑atom deposition of Ag clusters up to 1000 atoms. At each deposition step a single Ag atom is placed 1 Å above the existing cluster, followed by a 50 ps equilibration. Simulations were performed at five substrate temperatures: 300 K, 400 K, 500 K, 600 K, and 700 K. Energy analysis, radial distribution functions, and visual inspection reveal that clusters grown at 500 ± 50 K possess the lowest potential energy per atom, the most uniform bond‑length distribution, and the fewest defects (stacking faults, twins). These clusters typically display an icosahedral core surrounded by mixed decahedral and cuboctahedral facets, indicating that 500 K is an optimal annealing temperature for producing low‑energy Ag nanoclusters.

In summary, the paper delivers (i) a robust, multi‑phase DFT‑based parameterization of the Gupta potential for Ag and Au, (ii) a demonstration of its transferability through successful MD reproduction of the Ag₅₅ icosahedral ground state, and (iii) a practical guideline for Ag nanocluster synthesis, identifying ~500 K as the temperature window that yields energetically favorable structures. The authors suggest that the new parameters can be directly employed in simulations of alloy formation, catalytic surface restructuring, and nanowire growth, thereby extending the impact of their work beyond pure Ag and Au systems.