The B3LYP, CAM-B3LYP, and RCCSD(T) theories have been used to calculate the ground state equilibrium geometries of the linear cationic chains NC 2 n +1 N + (n=1–6). Compared with the system NC 2 n N + , the odd-n cationic chains are more susceptible to fragmentation than the even-n cationic chains. The complete active space self-consistent-field method has been utilized to determine the stationary structure of the ground state (X 2 П g/u ) and first excited state (1 2 П u/g ). The complete active space second-order perturbation theory has been used to compute the vertical excitation energies for the dipole-allowed (1,2,3) 2 П u/g ←X 2 П g/u transitions as well as the dipole-forbidden 1 2 Φ u/g ←X 2 П g/u transitions. The calculated transition energies of 1 2 П u/g ←X 2 П g/u in the gas phase are 2.61, 2.37, 2.07, 1.88, 1.64, and 1.34eV, respectively, which accord well with the available experimental values. Moreover, the absorption spectra of 2 2 П u/g ←X 2 П g/u may be detected more easily among the selected four transitions.