DFT calculations were performed with the Vienna ab initio Simulation Package (43, 44). The exchange-correlation interaction was described by optPBE functional with van der Waals correction (4547). The Kohn-Sham equations were solved in a plane wave basis set with a kinetic energy cutoff of 400 eV. To model Pd(111) and Pd(211) surfaces, the four-layer slab models were used with (4 by 4) and (2 by 4) unit cells, respectively. The freestanding Pd55, Pd147, and Pd309 clusters were modeled using the cubeoctahedral structure based on the literature (11, 38). A (3 by 3 by 1) k-point mesh and Γ-point were used to sample the surface Brillouin zone for the surface and cluster, respectively. A 12-Å vacuum was introduced with correction of dipole moment between the repeated slabs/clusters. During optimization, the bottom two layers of the slab were fixed, while the remaining atoms of the slab, all the atoms of the clusters and the adsorbates were relaxed until the residual force was less than 0.02 eV/Å. The barriers of the elementary steps were calculated by the climbing image nudged elastic band (CI-NEB) method (48), and the transition states were confirmed by single imaginary frequency.

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