The average bond length in Pd clusters Pdn, n=4–309: A density-functional case study on the scaling of cluster properties

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Abstract
For a series of clusters Pd n (n=4–309) the average metal–metal bond distance has been determined with an accurate all-electron density functional approach. In contrast to experimental data on supported or ligand stabilized palladium clusters, bond lengths of gas-phase Pd clusters are calculated to increase with size, exhibiting remarkably linear scaling with the average coordination number. To achieve good agreement of extrapolated nearest-neighbor distances with EXAFS data and the experimental bulk value, relativistic effects have to be taken into account in the electronic structure calculations. For the example of Pd 55 O 20 , the effect of surface oxidation has been examined, indicating a strong increase of the nearest-neighbor distance.