Geometries and electronic structures of ZrnCu (n = 2–12) clusters: A joint machine-learning potential density functional theory investigation

Figure 1. The evolution of the RMSE for the energy (eV⋅atom⁻¹), force (eV⋅Å⁻¹), and stress (GPa) tested on different testing sets.

Figure 2. Ground state structure of the Zr_nCu_13−n (n = 3–10) clusters searched by MLP (green balls represent Zr atoms, cyan balls represent Cu atoms).

Figure 3. The geometry of the three lowest energy isomers of the Zr_nCu (n = 2–12) nanoclusters searched by MLP, and the energy difference in electronvolts from the lowest energy isomer at the same size (green balls represent Zr atoms, cyan balls represent Cu atoms).

Figure 4. Size dependence of (a) the averaged binding energy (E_b), (b) the second-order energy difference (Δ₂E), and (c) the dissociation energy (E_d) for the lowest energy Zr_nCu (n = 2–12) clusters.

Figure 5. The two-dimensional ELF of the (a) Zr₅Cu, (b) Zr₇Cu, (c) Zr₉Cu, and (d) Zr₁₂Cu clusters.

Figure 6. The PDOS of the Cu and Zr atoms in (a) the lowest-energy Zr₅Cu cluster, (b) the lowest-energy Zr₇Cu cluster, (c) the lowest-energy Zr₉Cu cluster, and (d) the lowest-energy Zr₁₂Cu cluster.

Figure 7. MOs and corresponding energy levels of the 12B cluster.

Figure 8. The 6c–1e chemical bond analyzed by the AdNDP method. ON means the occupancy number.