The unimolecular triplet potential energy surface was explored with the complete basis set method with the aim being to evaluate the possibility of the triplet oxygen atom assisted acetylene rearrangement into vinylidine. Various linear and cyclic oxygen-acetylene adducts and isomers are located, and their structures are optimized at the MP2/6-31G(d') level of theory, with the energy evaluation at the CBSQ ab initio level of theory. These stationary points are connected with 17 transition state structures. Their interconversion activation barriers were evaluated together with the enthalpies of the reactions, and for some C2H2O isomers, the selective bond dissociation energies were also estimated. The experimental feasibility of some of the reaction channels was discussed, and from all calculations presented in this paper it is a general conclusion that the oxygen assisted acetylene-vinylidene rearrangement is not possible through the unimolecular reactions of the C2H2O isomers in their triplet states. The possibility of the existence of the two-molecule hydrogen reactions was indicated, for which additional potential energy surface exploration is required.