Energetic and Kinetic Competition on the Stability of Pd₁₃ Clusters: Ab Initio Molecular Dynamics Simulations

Material stability is the focus on both experiments and calculations, which includes the energetic stability at the static state and the thermodynamic stability at the kinetic state. To show whether energetics or kinetics dominates on material stability, this study focuses on the Pd₁₃ clusters, because of their observable magnetic moment in experiment. Energetically, the CALYPSO searching method and first-principles calculations find that Pd₁₃(C₂) is the ground state at 0 K while the static frequency calculations demonstrate that the icosahedron Pd₁₃(I_h) becomes more favorable on free energy as temperature increases. However, their magnetic moments (8 μ_B) are not in agreement with the experimental value (<5.2 μ_B). Kinetically, ab initio molecular dynamics simulations reveal that Pd₁₃(C_3v) (6 μ_B) has supreme isomerization temperature and the other 11 low-lying isomers transform to Pd₁₃(C_3v) directly or indirectly, demonstrating that Pd₁₃(C_3v) has the maximum probability to be observed in experiment. The magnetic moment difference between experiment (<5.2 μ_B) and this calculation (6 μ_B) may be due to the spin multiplicities. Our result suggests that the magnetic moment disparity between theory and experiment (in Pd₁₃ clusters) originates from the kinetic stability.