We present abinitio calculations of geometries, energies, and normal mode frequencies for complexes and saddle points along the minimum energy reaction path for the reaction C + HCCH --> C3H2 --> C3H + H. We also present ab initio calculations along the minimum energy reaction path in the entrance channel for the reactions C + HCCH, CH + BCCH, and (CH2)-C-1 + HCCH. These results and those presented earlier by Walch(1) are used to calculate rate constants for the reactions of C, CH, and (CH2)-C-1 with acetylene, using variational RRKM theory. The rate constants obtained agree well with experimental results for all three reactions. Unimolecular lifetimes for intermediate complexes associated with each reaction path are also presented. Among the more stable C-3 isomers are propargyl and propargylene, which have lifetimes of 25 and 1900 ps, respectively, under thermal reaction conditions.