Using molecular graphics software, we designed numerous models of CnN3-(n=1-8). Geometry optimization and calculation on vibration frequency were carried out by the B3LYP density functional method. After comparison of structure stability, we found that the structures of ground-state CN3- and C2N3- are bent chains with a nitrogen atom at either end, whereas when n=3-8, the ground-state clusters show three branches, each with a nitrogen atom located at the end. When n=5-8, the longest branch of CnN3- is polyacetylenelike. When n=5 or 7, the longest branch is connected to the central sp(2) carbon in a nonlinear manner. The CnN3- (n=1-8) with an even number of carbon atoms are more stable than those with odd numbers, matching the peak pattern observed in laser-induced mass spectra of CnN3-. The trend of such odd/even alternation is explained based on concepts of bonding characteristics, electron affinities, and incremental binding energies. (C) 2004 American Institute of Physics.