Abstract: All geometry structures of Con(n=2～10) clusters have been optimized, and the energy, frequency and magnetism of Con(n=2～10) clusters were calculated using the local spin density approximation and generalized gradient approximation of density functional theory. We found the same ground state structures in the two methods, and discussed theoretically the influence of the average coordination number, average bond length and symmetry on clusters magnetism. For Con(n=2～4) clusters, the magnetism of ground states strongly depends on average bond length, for Con(n=5～9),it strongly depend on average coordination number, for Co10,the factors of interatomic distance and average coordination number together lead to the same magnetism as Co8 cluster. Average moments of Co5 and Co9 present magnetic magic number.

Key words: Clusters, Structure of ground state, Magnetic moment, Average bond length, Average coordination number, Symmetry