Calculations are presented for the molecule HC2N and its geometrical isomers. The structures, harmonic frequencies and dipole moments are reported. The potential energy surface of the [H,C,C,N] system is investigated in detail, and the transition states, intermediate complexes, and the energies of barrier for the isomerization and dissociation reactions are computed in order to determine the reaction paths and to estimate the stability of the isomers. The barriers of isomerization among HCCN, HCNC and HNCC are computed to be rather large and dissociations of these molecules are highly endothermic, indicating that these molecules are kinetically stable. The association reactions HC + CN→HCCN, HC + NC→HCNC, and HN + CC →HNCC are barrierless and very exothermic, suggesting that they may be considered as efficient means of producing the HCCN and the isomers in the laboratory and in interstellar space.