Density functional study of palladium clusters

Neutral, ligand-free Pdn clusters, n = 2–309, are investigated using density functional calculations. We treat numerous clusters not considered before, always optimize all structural parameters within a given symmetry, and investigate Jahn–Teller distortions for n up to about 100. For n = 4–7,9 and 13 the most stable structures found correspond to the global minima of the Lennard-Jones potential, although some show Jahn–Teller distortions. These small clusters prefer high-spin states, have small HOMO–LUMO gaps, below 0.1 eV, and appear very floppy with various structures very close in energy. For n = 16–59 structures are analyzed that are found as icosahedral cores of ligand-stabilized clusters (N. T. Tran, M. Kawano and L. F. Dahl, J. Chem. Soc., Dalton Trans., 2001, 19, 2731). The intermediates in the growth pathways proposed for these systems are often appreciably less stable than the alternative structures with fcc, hcp, and decahedral packing. Ligand and kinetic effects thus may play an important role in driving the formation of ligand-stabilized clusters. For n > 100 the fcc structures have consistently higher cohesive energy than icosahedra and decahedra, which suggests an early preference for the packing found in the bulk phase. From a regression analysis for structures with n ≥ 38 we extrapolate a bulk distance of 2.816 Å and cohesive energy of 3.59 eV, in good agreement with experimental values of 2.748 Å and 3.9 eV.