This study uses computational chemistry and statistical reaction rate theory to investigate the chemically activated reaction of diacetylene (butadiyne, C4H2) with the propargyl radical (C˙H2CCH) and the reaction of acetylene (C2H2) with the i-C5H3 (CH2CCCC˙H) and n-C5H3 (CHCC˙HCCH) radicals. A detailed G3SX-level C7H5 energy surface demonstrates that the C3H3 + C4H2 and C5H3 + C2H2 addition reactions proceed with moderate barriers, on the order of 10 to 15 kcal mol−1, and form activated open-chain C7H5 species that can isomerize to the fulvenallenyl radical with the highest barrier still significantly below the entrance channel energy. Higher-energy pathways are available leading to other C7H5 isomers and to a number of C7H4 species + H. Rate constants in the large multiple-well (15) multiple-channel (30) chemically activated system are obtained from a stochastic solution of the one-dimensional master equation, with RRKM theory for microcanonical rate constants. The dominant products of the C4H2 + C3H3 reaction at combustion-relevant temperatures and pressures are i-C5H3 + C2H2 and CH2CCHCCCCH + H, along with several quenched C7H5 intermediate species below 1500 K. The major products in the n-C5H3 + C2H2 reaction are i-C5H3 + C2H2 and a number of C7H4 species + H, with C7H5 radical stabilization at lower temperatures. The i-C5H3 + C2H2 reaction predominantly leads to C7H4 + H and to stabilized C7H5 products. The title reactions may play an important role in polycyclic aromatic hydrocarbon (PAH) formation in combustion systems. The C7H5 potential energy surface developed here also provides insight into several other important reacting gas-phase systems relevant to combustion and astrochemistry, including C2H + the C3H4 isomers propyne and allene, benzyne + CH, benzene + C(3P), and C7H5 radical decomposition, for which some preliminary analysis is presented.