[en] This work emphasizes the stability of C₆N linear carbon chains and carbon clusters containing three-body rings. C₆N possesses at least 44 neutral isomers and 38 and 35 isomers with a negative or a positive charge. The lowest-energy structures, which can be candidates for laboratory and astrophysical detection, were studied with RCCSD(T)-F12 and MRCI/CASSCF, specifying properties for various electronic states. Neutral C₆N displays two prominent equilibrium structures, a nitrogen-terminated linear form (X²Π) and a ${\mathrm{C}}_{2\mathrm{v}}$ form (X²B₂) containing a three-carbon ring. They are separated by 0.21 eV. For the linear one, Renner–Teller and spin–orbit effects are expected. Its equilibrium spin–orbit constant ∣ ${\mathrm{A}}_{\mathrm{s}\mathrm{o},\mathrm{e}}$ ∣was predicted to be 29.09 cm⁻¹, the dipole moment was computed to be 0.2059 D, and B_e was computed to be 868.20 MHz, very close to the experimental value (B₀(exp)-B_e(calc) ∼ 4.9 MHz). The anion presents two stable forms, a linear triplet (X³Σ⁻) and a ${\mathrm{C}}_{2\mathrm{v}}$(X¹A₁) isomer, whereas for the cation most stable structures are both linear. For the linear anion and the two linear cations B₀ was estimated to be 870.05 MHz, 875.72 MHz, and 917.36 MHz and μ was estimated to be 4.4200 D, 4.2013D, and 0.7828D. For the neutral ${\mathrm{C}}_{2\mathrm{V}}$ form, Ae = 45048.74 MHz, Be = 1062.78 MHz, Ce = 1038.30 MHz, and μ = 0.8840 D, whereas for the negative ${\mathrm{C}}_{2\mathrm{V}}$ form, Ae = 40087.48 MHz, Be = 1067.35 MHz, Ce = 1039.67 MHz, and μ = 6.2854 D. Below the electron affinity of the most stable isomer (EA = −3.42 eV), the linear anion displays three probably existing electronic states. Detectability is discussed in terms of the symmetry and spin multiplicity of the ground electronic states.