Structures and stabilities of linear carbon chains C2n+1S and C2n+1Cl+ (n = 0-4) in their ground states have been investigated by the CCSD and B3LYP approaches. The CASSCF calculations have been used to determine geometries of selected excited states of both isoelectronic series. Linear C2n+1S cluster has a cumulenic carbon framework, whereas its isoelectronic C2n+1Cl+ has a dominant character of acetylenic structure in the vicinity of terminal Cl. The vertical excitation energies of low-lying excited states have been calculated by the CASPT2 method. Calculations show that the excitation energies have nonlinear size dependence. The 2(1)Sigma(+)<- X-1 Sigma(+) transition energy in C2n+1S has a limit of 1.78 eV, as the chain size is long enough. The predicted vertical excitation energies for relatively strong 1(1)Pi <- X-1 Sigma(+) and 2(1)Sigma(+)<- X-1 Sigma(+) transitions are in reasonable agreement with available experimental values. The spin-orbit effect on the spin-forbidden transition in both series is generally small, and the enhancement of the spin-forbidden transition by spin-orbit coupling exhibits geometrical and electronic structural dependence.