Highly correlated ab initio calculations are employed for the structural and spectroscopic characterization of small odd chains of type C 2n+1 H, considering neutral forms, cations, and giving special attention to the anions. This work confirms the stability of the linear carbon chains and carbon clusters containing three-body rings. The smallest species, C 3 H, displays three stable structures, whereas C 5 H possesses at least 8 neutral isomers and 11 and 10 isomers with a negative or a positive charge. The equilibrium geometries, which can be candidates for laboratory and astrophysical detection, are studied using the RCCSD(T)-F12 and MRCI/CASSCF levels of theory, specifying properties for various electronic states. Four different stable isomers are confirmed for the C 5 H − anion. They are two rings and two chains, all showing singlet ground electronic states. The viability of the triplet linear form of C 5 H − (¥ C v (X 3 Σ −)) postulated in previous works, is not confirmed because it appears to be really dependent on the electron correlation energy denoting instability. A quasi-linear singlet (C s (X 1 A′)) represents a secondary minimum. Electronic state crossing occurs close to the linear structure where spin-orbit effects are negligible. The most stable structure of C 5 H − is a three-carbon cycle in which rotational constants have been determined to be A 0 =35479.86 MHz, B 0 =3618.29 MHz, and C 0 =3280.10 MHz. Its dipole moment is relatively large (6.4086 D).