The structures and energies of singlet and triplet neutral carbon linear chains up to 22 atoms - and frequencies of vibrations for chains up to 17 atoms - are obtained using density functional theory (B3LYP) with a polarized split-valence basis set (6-31G*). Analytical expressions for the dependence of the energy with the number of atoms in the chains are presented with an explicit identification of the electrostatic contribution. The addition reaction free energies of two linear chains allow to visualize the reaction pathways of formation of chains up to 17 carbon atoms and to establish their dissociation temperatures. Free energy calculations show that odd chains of more than 15 atoms have triplet ground states at experimental accessible temperatures. Cycling characteristics of linear chains are discussed.