Structures and energies of Pd, clusters, with n ranging from 2 to 7, were determined through density functional theory. The calculations were performed adopting the B3LYP functionals to calculate the exchange and correlation energy, the effective core potential basis set of Hay and Wadt for the core electrons of palladium (double-zeta on the valence electrons), and the Dunning/Huzinaga full double-zeta basis set for the other atoms. It was found that Pd-n optimized structures are almost regular polyhedrons, all stable as triplets. The calculated geometries were an isosceles triangle for Pd-3, a distorted tetrahedron for Pd-4, a bipyramid with triangular base for Pd-5, a distorted octahedron for Pd-6, and a bipyramid with pentagonal base for Pd-7. The interaction of these clusters with atomic hydrogen in terms of structure and energy was also considered. All structures are stable with the hydrogen lying outside of the cluster, preferably 3-fold coordinated. A maximum of the hydrogen bond energy was found for a cluster containing three palladium atoms. Increasing the number of palladium atoms diminishes the bond energy until a value near the experimentally measured adsorption energy for atomic hydrogen on a palladium surface is reached. Similarly Pd-n-CHx species, with x being between 0 and 3, were studied: all hydrogenated fragments are located outside the metal cluster, with coordination depending on the number of hydrogens, whereas the carbon atom is included in the cluster thus modifying its structure. If the influence of the support on reactivity can be neglected, palladium clusters can be viewed as a model of a supported catalyst with extremely dispersed particles, and some considerations about the coke formation process can be made. In particular this analysis shows that coking is favored by increasing cluster size.