Energetic and Kinetic Competition on the Stability\nof Pd<sub>13</sub> Clusters: Ab Initio Molecular Dynamics Simulations

Material\nstability is the focus on both experiments and calculations,\nwhich includes the energetic stability at the static state and the\nthermodynamic stability at the kinetic state. To show whether energetics\nor kinetics dominates on material stability, this study focuses on\nthe Pd<sub>13</sub> clusters, because of their observable magnetic\nmoment in experiment. Energetically, the CALYPSO searching method\nand first-principles calculations find that Pd<sub>13</sub>(C<sub>2</sub>) is the ground state at 0 K while the static frequency calculations\ndemonstrate that the icosahedron Pd<sub>13</sub>(I<sub>h</sub>) becomes\nmore favorable on free energy as temperature increases. However, their\nmagnetic moments (8 μ<sub>B</sub>) are not in agreement with\nthe experimental value (<5.2 μ<sub>B</sub>). Kinetically,\nab initio molecular dynamics simulations reveal that Pd<sub>13</sub>(C<sub>3v</sub>) (6 μ<sub>B</sub>) has supreme isomerization\ntemperature and the other 11 low-lying isomers transform to Pd<sub>13</sub>(C<sub>3v</sub>) directly or indirectly, demonstrating that\nPd<sub>13</sub>(C<sub>3v</sub>) has the maximum probability to be\nobserved in experiment. The magnetic moment difference between experiment\n(<5.2 μ<sub>B</sub>) and this calculation (6 μ<sub>B</sub>) may be due to the spin multiplicities. Our result suggests\nthat the magnetic moment disparity between theory and experiment (in\nPd<sub>13</sub> clusters) originates from the kinetic stability.