The potential energy surfaces of the initial reactions of ethylene insertion for the Ziegler-Natta catalysis with bridging groups of Cp ligands were studied by ab initio MO and density functional methods. Three metals (Ti, Zr, and Hf) in the Zeigler-Natta catalysis and eight bridging groups (BH, CH 2 , NH, O, AlH, SiH 2 , PH, and S) were treated. For the complex formation between ethylene and metallocenes, two type structures (vertical and horizon) were found. The vertical type structures are more stable in energy than the horizon types. The formation energy of the complex between ethylene and the metallocenes by incorporation of bridging atom or group is related to the geometrical hindrance and the bond interaction as shown in the case of boron bridging system.