The geometries and energies of the isomers in alkyne complexes MCl(PH3)2(η2-C2H2), M=Rh and Ir, are theoretically investigated using ab initio methods at the Hartree-Fock and up to MP4 level of theory and relativistic effective core potentials for Rh and Ir metals. The optimized structures of Rh complexes, 1-3 at MP2/ECP1 level are in good agreement with the related experimental data. The binding energies of C2H2 to d8-metal fragments are computed to be ∼55 kcal/mol. The vinylidene complexes for Rh and Ir metals are calculated to be much lower in energy than the alkyne complexes. The alkyne-vinylidene rearrangement is possible to proceed exothermically through the intermediate hydrido-alkynyl complexes, 2 or 9. Detailed comparison is given about the geometries and relative energies on Rh and Ir isomers at the various level ab initio calculations with orbital analysis.