A systematic investigation of palladium nanoparticles of up to 55 atoms (1.4 nm) has been conducted using density functional theory with a plane wave basis set. The stability of these nanoparticles increases with cluster size and dimensionality. It also depends strongly on the cluster structures through two factors, the coordination numbers of atoms and the strength of the single bonds. Both the energy gap between the highest occupied and the lowest unoccupied molecular orbitals and the magnetic moment change oscillatorily with cluster size. Furthermore, highly magnetic clusters tend to have large energy gaps. Analysis of the atom-resolved magnetic moment reveals that the local magnetism of a cluster depends mainly on the atomic bonding environments. A simple approach is proposed to predict relative stabilities of various structures for larger clusters. In addition, a structure factor is defined to correlate quantitatively various properties of the Pd clusters with their structures. (C) 2003 American Institute of Physics.