All-electron DFT (B3LYP) calculations with a split-valence basis set of double- and triple-xi quality have been used to study the reaction paths of the first and second step insertion as well as of the sigma-bond metathesis for the reaction of Geometry optimizations of the reactants, intermediates, transition states and products were acetylene with (C2H5)(2)ZrCH3+ carried out without symmetry constraints. The nature of the particular points on the potential energy surfaces was verified by the analytical calculation of the Hessian matrices. The relative electronic energies are corrected for ZPVE, entropic and thermal contributions, and correspond to the Gibbs free energies (Delta Delta G(298)). It is, shown that the propagation step of acetylene polymerization is a facile process from kinetic and thermodynamic point of view, and that the investigated insertion reactions are kinetically and thermodynamically favoured over the sigma-bond metathesis reaction. The calculated energetics and structures of either reaction are compared with available theoretical and experimental data of relevant complexes of group III and IV transition metals.