what is disclosed is a method for preparing a catalyst system and a catalyst system for polymerizing or copolymerizing an α - olefin . catalyst component is obtained by a process of reacting a magnesium complex containing acid salts of group ib - viiib elements formed by contacting a magnesium halide with an acid salt solution of group ib - viiib metals or spherical particles adducts , an internal electron donor of diester or diether or composite compounds , and a titanium compound . the catalyst compound is contacted with a silicon compound and an organoaluminium compound to complete the catalyst system providing a good balance of catalyst performance in terms of activity and stereo - specificity .