The geometries, electronic structures of pure carbon clusters were investigated in the range of C3 to C6 size. To obtain accurate results, the STO double-zeta basis sets with a polarization function are selected. The main focuses are on the new geometry, electronic structures of carbon clusters, such as the three-dimensional structure for C4, Cs and so on. The clusters are found to have more isomers corresponding to different geometries and spin multiplicities close to their ground states. We find that the spin multiplicity of the ground state or close to ground state of odd-numbered linear chain is 1. But in even-numbered linear chains, the spin multiplicity is 3. In odd-numbered cyclic structure without branch chain, the spin multiplicity of the ground state or close ground state is 3, and that of even-numbered is 1. But the three-dimensional structure disagree those principles.