The olefin polymerization reaction by silylene-bridged zirconocene catalysts has been investigated theoretically. With the ab initio molecular orbital (MO) method the structure and energetics of the reactants, the {pi}-complex, the transition state, and the product for insertion of ethylene into (SiH{sub 2}Cp{sub 2})ZrCH{sub 3}{sup +} have been determined. The nearly C{sub s}-symmetric transition state has a low activation barrier (about 6.0 kcal/mol from the {pi}-complex). The product shows a strong C{sup {beta}}-H agostic interaction. Based on the above transition state structure, molecular mechanics (MM) calculations have been carried out to investigate the effects of alkyl substituents on olefins and methyl groups and other substituents on the Cp rings as well as the effects of the alkyl group on Zr, a model polymer chain end. The regioselectivity in propylene polymerization, that the primary insertion is preferred to the secondary insertion, is reproduced well by the energy difference at the transition state but not by that of the {pi}-complex. As to the steroselectivity in isotactic polymerization of propylene by SiH{sub 2}(CpMe{sub n}){sub 2}ZrR{sup +}, the substituents on the Cp rings have been found to determine the conformation of the polymer chain end, and the fixed polymer chain end conformation in turn determinesmore » the sterochemistry of olefin insertion at the transition state. The direct steric effect of the Cp methyl groups on the olefin insertion sterochemistry is negligible small. The same direct control mechanism is operational also in syndiotactic polymerization of propylene and 4-methyl-1-pentene. 34 refs., 7 figs., 6 tabs.« less