Energetic and Kinetic Competition on the Stability of Pd 13 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 Pd 13 clusters, because of their observable magnetic moment in experiment. Energetically, the CALYPSO searching method and first-principles calculations find that Pd 13 (C 2 ) is the ground state at 0 K while the static frequency calculations demonstrate that the icosahedron Pd 13 (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 Pd 13 (C 3v ) (6 μ B ) has supreme isomerization temperature and the other 11 low-lying isomers transform to Pd 13 (C 3v ) directly or indirectly, demonstrating that Pd 13 (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 Pd 13 clusters) originates from the kinetic stability.