Triplet vinylidene, first predicted to have a sizeable barrier to unimolecular rearrangement in 1978 by theory, has now been observed under three different sets of experimental conditions. In order to quantitatively characterize the potential energy hypersurface of triplet vinylidene and triplet acetylene, high-level ab initio quantum mechanical methods have been employed. Basis sets as large as triple zeta plus two sets of polarization functions augmented with higher angular momentum functions [TZ(2df,2pd)] have been utilized in conjunction with correlated methods as sophisticated as the coupled cluster approach including all single, double, and perturbative triple excitations [CCSD(T)]. Of particular interest are predictions of the zero-point vibrational energy corrected barriers for rearrangement of a3B2 vinylidene to b3B(u) trans-bent acetylene and of cis-bent a3B2 acetylene to trans-bent b3B(u) acetylene. At the highest level of theory used here, TZ(2df,2pd) CCSD(T), these are predicted to be 47.9 and 13.0 kcal/mol, respectively. The physical properties of a3B2 vinylidene, including the dipole moment, harmonic vibrational frequencies, and the infrared intensities, have also been reported.