Ab initio CCSD(T)cc-pVTZ//B3LYP6-311G(**) and CCSD(T)/complete basis set (CBS) calculations of stationary points on the C(6)H(3) potential energy surface have been performed to investigate the reaction mechanism of C(2)H with diacetylene and C(4)H with acetylene. Totally, 25 different C(6)H(3) isomers and 40 transition states are located and all possible bimolecular decomposition products are also characterized. 1,2,3- and 1,2,4-tridehydrobenzene and H(2)CCCCCCH isomers are found to be the most stable thermodynamically residing 77.2, 75.1, and 75.7 kcal/mol lower in energy than C(2)H + C(4)H(2), respectively, at the CCSD(T)/CBS level of theory. The results show that the most favorable C(2)H + C(4)H(2) entrance channel is C(2)H addition to a terminal carbon of C(4)H(2) producing HCCCHCCCH, 70.2 kcal/mol below the reactants. This adduct loses a hydrogen atom from the nonterminal position to give the HCCCCCCH (triacetylene) product exothermic by 29.7 kcal/mol via an exit barrier of 5.3 kcal/mol. Based on Rice-Ramsperger-Kassel-Marcus calculations under single-collision conditions, triacetylene+H are concluded to be the only reaction products, with more than 98% of them formed directly from HCCCHCCCH. The C(2)H + C(4)H(2) reaction rate constants calculated by employing canonical variational transition state theory are found to be similar to those for the related C(2)H + C(2)H(2) reaction in the order of magnitude of 10(-10) cm(3) molecule(-1) s(-1) for T = 298-63 K, and to show a negative temperature dependence at low T. A general mechanism for the growth of polyyne chains involving C(2)H + H(C[triple bond]C)(n)H --> H(C[triple bond]C)(n+1)H + H reactions has been suggested based on a comparison of the reactions of ethynyl radical with acetylene and diacetylene. The C(4)H + C(2)H(2) reaction is also predicted to readily produce triacetylene + H via barrierless C(4)H addition to acetylene, followed by H elimination.