All-electron calculations were performed for Ni-2, Ni-3, and Ni-4 clusters and their respective anions and cations using density functional theory techniques as implemented in the DGauss code. Both local and generalized gradient-corrected functionals were employed. Three different multiplicities were examined for each cluster (M = 3, 5, and 7). The calculated ground states were found to have multiplicities of M = 3 for Ni-2: and Ni-3 and M = 5 for Ni-4 with associated magnetic moments per atom of 1.0 mu(B) for Ni-2 and Ni-4, while Ni-3 shows an isotropic magnetic distribution. The cluster magnetization is enhanced relative to that of the bulk, which is in qualitative agreement with experimental data for clusters larger than 50 atoms. For these smallest Ni, clusters, there is a mixture of 3d and 4s bonding. The 3d(4s) contribution to the bonding decreases (increases) going from n = 2 to n = 4, which is reflected by the larger equilibrium bond lengths of Ni-4, as compared to that of Ni-2. The frontier molecular orbitals, the so-called HOMO and LUMO, were studied; they provide insight into the reactivity of these small particles. We also determined the lowest-energy states of anions, Ni-n(-), and cations, Ni-n(+). The calculated ionization potentials and electron affinities are in reasonable agreement with experimental observations as well as with other reported theoretical results. (C) 1999 John Wiley & Sons, Inc.