Ab initio modified Gaussian-2 G2M(RCC,MP2) calculations have been performed for various isomers and transition states on the singlet C4H4 potential energy surface. The computed relative energies and molecular parameters have then been used to calculate energy-dependent rate constants for different isomerization and dissociation processes in the C4H4 system employing Rice-Ramsperger-Kassel-Marcus theory and to predict branching ratios of possible products of the C2(1Sigmag+)+C2H4, C(1D)+H2CCCH2, and C(1D)+H3CCCH reactions under single-collision conditions. The results show that C2 adds to the double C=C bond of ethylene without a barrier to form carbenecyclopropane, which then isomerizes to butatriene by a formal C2 "insertion" into the C-C bond of the C2H4 fragment. Butatriene can rearrange to the other isomers of C4H4, including allenylcarbene, methylenecyclopropene, vinylacetylene, methylpropargylene, cyclobutadiene, tetrahedrane, methylcyclopropenylidene, and bicyclobutene. The major decomposition products of the chemically activated C4H4 molecule formed in the C2(1Sigmag+)+C2H4 reaction are calculated to be acetylene+vinylidene (48.6% at Ecol = 0) and 1-buten-3-yne-2-yl radical [i-C4H3(X2A'), H2C=C=C=CH*]+H (41.3%). As the collision energy increases from 0 to 10 kcal/mol, the relative yield of i-C4H3+H grows to 52.6% and that of C2H2+CCH2 decreases to 35.5%. For the C(1D)+allene reaction, the most important products are also i-C4H3+H (55.2%) and C2H2+CCH2 (30.1%), but for C(1D)+methylacetylene, which accesses a different region of the C4H4 singlet potential energy surface, the calculated product branching ratios differ significantly: 65%-69% for i-C4H3+H, 18%-14% for C2H2+CCH2, and approximately 8% for diacetylene+H2.