Extensive ab initio calculations have been performed to determine the energy, geometry, vibrational frequencies, and relative energetics of all stationary points of the C2H2 ground-state potential-energy surface. The geometries of acetylene and vinylidene minima as well as all transition states are reported at the CASSCF, MRCI, and CCSD(T) levels with aug-cc-pVXZ basis sets. Other more advanced levels of CC theory have also been utilized where judged adequate, mostly for check purposes. Also reported are theoretical limiting values of the energetics of the reaction, deduced from series of computations using the USTE extrapolation method. The data here reported should be valuable for modeling a single-sheeted global potential energy surface for the title system.