Ab initio and density functional RCCSD(T)/cc-pVQZ//B3LYP/6-311G** calculations of various stationary points on the C(4)H(5) global potential energy surface have been performed to resolve the C(2)H + C(2)H(4) and C(2)H(3) + C(2)H(2) reaction mechanisms under single-collision conditions. The results show vinylacetylene + H as the nearly exclusive products for both reactions, with exothermicities of 26.5 and 4.3 kcal/mol, respectively. For C(2)H + C(2)H(4), the most important mechanisms include a barrierless formation of the CH(2)CH(2)CCH adduct c6 (56.9 kcal/mol below the reactants) in the entrance channel followed either by H loss from the vicinal CH(2) group via a barrier of 35.7 kcal/mol or by 1,2-H migration to form CH(3)CHCCH c3 (69.8 kcal/mol lower in energy than C(2)H + C(2)H(4)) via a 33.8 kcal/mol barrier and H elimination from the terminal CH(3) group occurring with a barrier of 49.4 kcal/mol. RRKM calculations of energy-dependent rate constants for individual reaction steps and branching ratios for various channels indicate that 77-78% of vinylacetylene is formed from the initial adduct, whereas 22-21% is produced via the two-step mechanism involving the 1,2-H shift c6-c3, with alternative channels contributing less than 1%. The theoretical results support the experimental crossed molecular beams observations of vinylacetylene being the major product of the C(2)H + C(2)H(4) reaction and the fact that CH(2)CHCCH is formed via a tight transition state with an exit barrier of 5-6 kcal/mol and also confirm that vinylacetylene can be produced from C(2)H + C(2)H(4) under low temperature conditions of Titan's atmosphere. The prevailing mechanism for the C(2)H(3) + C(2)H(2) reaction starts from the initial formation of different n-C(4)H(5) conformers occurring with significant entrance barriers of approximately 6 kcal/mol. The n-C(4)H(5) isomers reside 35-38 kcal/mol lower in energy than C(2)H(3) + C(2)H(2) and can rapidly rearrange to one another overcoming relatively low barriers of 3-5 kcal/mol. H loss from the n-C(4)H(5) species then gives the vinylacetylene product via exit barriers of approximately 6 kcal/mol with the corresponding transition states lying 1.2-1.6 kcal/mol above the C(2)H(3) + C(2)H(2) reactants. Since the C(2)H(3) + C(2)H(2) reaction is hindered by relatively high entrance barriers, it is not expected to be important in Titan's atmospheric environments but can produce n-C(4)H(5) or vinylacetylene under high temperature and pressure combustion conditions.