Several functionals combined with different basis sets have been examined for the Sc2, Y2 and La2 dimer by using density functional theory. Compared with previous theoretical and experimental data of dimers, the BP86/CEP121G level for Scn and Yn clusters, the PBE1PBE/LANL2DZ level for Lan (n=2—10) clusters were selected to investigate the geometry, stability, electronic and magnetic properties of these clusters. The relative stability of these clusters of the same group have the same results, which can be explained by the model with geometry of dense packing. The highest occupied molecular orbital—lowest unoccupied molecular orbital gap of Lan clusters are bigger than those of Scn and Yn clusters, and a relative bigger energy gap are found for the magic clusters with n=4, 7 and 9. The vertical ionization energy VIP and electron affinity were calculated, and the VIP is in good agreement with experiments for yttrium clusters. The static polarizabilities can characterize the stability of these clusters. Big and anomalous magnetic moments are discovered and are in agreement with the experiments for Scn, Yn and Lan clusters, but they decrease with the increasing of cluster size and have local oscillatory character.