The structure and stabilities of linear and cyclic isomers of Ce-6(-) and N2C4+ were investigated by DFT, MP2, CISD, and CCSD methods. The linear isomers of C-6(-) and NC4N+ are predicted to be the most stable forms. Multireference configuration interaction methodology was used for the calculation of the doublet and quartet excited states. Assignments to observed transitions in matrix spectroscopy of these species are made. The first X (2)Pi --> (2)Pi transitions for C-6(-), NC4N+, and CNC3N+ occur at 1.98, 2.14, and 2.65 eV, respectively, showing similar features with large oscillator strengths. On the other hand, a significant difference exists in the X (2)Pi (u) --> 1 (2)Sigma (+)(g) band system between the C-6(-) and NC4N+. Correlation between the relative molecular orbital energy and spectroscopic properties is discussed. The predicted electronic spectra agree well with available experimental data.