Ab initio calculations of the potential energy surface for the C-3((1)Sigma(+)(g)) + C2H2((1)Sigma(+)(g)) reaction have been performed at the RCCSD(T)/cc-pVQZ//B3LYP/6-311G(d,p) + ZPE[B3LYP/6-311G(d,p)] level with extrapolation to the complete basis set limit for key intermediates and products. These calculations have been followed by statistical calculations of reaction rate constants and product branching ratios. The results show the reaction to begin with the formation of the 3-(didehydrovinylidene)cyclopropene intermediate i1 or five-member ring isomer i7 with the entrance barriers of 7.6 and 13.8 kcal/mol, respectively. i1 rearranges to the other C5H2 isomers, including ethynylpropadienylidene i2, singlet pentadiynylidene i3, pentatetraenylidene i4, ethynylcyclopropenylidene i5, and four- and five-member ring structures i6, i7, and i8 by ring-closure and ring-opening processes and hydrogen migrations. i2, i3, and i4 lose a hydrogen atom to produce the most stable linear isomer of C5H with the overall reaction endothermicity of similar to 24 kcal/mol. H elimination from i5 leads to the formation of the cyclic C5H isomer, HC2C3, + H, 27 kcal/ mol above C-3 + C2H2. 1,1-H-2 loss from i4 results in the linear pentacarbon C-5 + H-2 products endothermic by 4 kcal/mol. The H elimination pathways occur without exit barriers, whereas the H-2 loss from i4 proceeds via a tight transition state 26.4 kcal/mol above the reactants. The characteristic energy threshold for the reaction under single collision conditions is predicted be in the range of similar to 24 kcal/mol. Product branching ratios obtained by solving kinetic equations with individual rate constants calculated using RRKM and VTST theories for collision energies between 25 and 35 kcal/mol show that l-C5H + H are the dominant reaction products, whereas HC2C3 + H and l-C-5 + H-2 are minor products with branching ratios not exceeding 2.5% and 0.7%, respectively. The ethynylcyclopropenylidene isomer i5 is calculated to be the most stable C5H2 species, more favorable than triplet pentadiynylidene i3t by similar to 2 kcal/mol.