Reaction pathways are identified for Na-, Al-, and Y-induced acetylene (HCCH)-vinylidene (CCH2) rearrangements in the gas phase. Density functional and coupled cluster calculations are performed with basis set extrapolations. The rearrangement barriers decrease from 44.0 kcal/mol in the metal-free reaction to 41.3 (Na), 19.1 (Al), and 16.1 (Y) kcal/mol in the metal-induced reactions. This decrease results from the strengthening of the M-C bonds (Na-C < Al-C < Y-C) in the M(HCCH) and M(CCH2) complexes. Natural bond orbital analysis reveals the metallacyclopropene and metallaallene character of several of the M(HCCH) and M(CCH2) complexes. In addition, analysis of the transition states provides a detailed picture of the redistribution of bonding and nonbonding electrons along the reaction pathway. The metal-free and Na-induced rearrangements proceed via 1,2-hydride shifts, whereas the Al- and Y-induced reactions proceed via 1,2-hydrogen shifts. The latter reactions involve homolytic bond cleavage and formation, with the alpha and beta electron densities undergoing redistribution in opposing directions.