The potential energy surface for the reaction of doubler methylidyne with acetylene has been investigated in detail using the B3LYP-DFT/6-31G** quantum chemical method. Three barrierless entrance channels lead to the formation of initially highly excited C3H3 radicals, the most stable of which is the 2-propynyl radical (propargyl). Other C3H3 isomers characterized include 1-propynyl, as well as the cyclic structures cycloprop-2-enyl and cycloprop-1-enyl which were net considered in a previous theoretical study by Walch. All identified C3H3 isomers can interconvert via transition states lying well below the entrance and exit channels. The dissociation pathways of the C3H3 radicals leading to various C3H2 isomers+H have been identified. The energetically most favorable of these exit channels was found to be the formation of singlet cyclopropenylidene+H. Other favored routes are formation of tripler prop-2-ynylidene+H and of singlet propadienylidene+H. Also identified are pathways leading to linear-C3H+H-2. The transition paths of all barrierless reactions were characterized by calculating a large number of points along the reaction coordinate, allowing for a microvariational treatment of these reactions in later kinetic RRKM calculations. The kinetic and mechanistic aspects of the CH+C2H2 reaction are discussed qualitatively, based on the data obtained in this study and in the available experimental and theoretical literature.