The main steps in the reaction of an ethylene molecule with a Ti catalytic center. The ethylene approaches the catalyst (the ball at the center in the left image) from the empty side, thus forming a complex. Then an energy barrier of about 6 kcal/mol is overcome, represented by the central image (transition state) and eventually (right image) the old Ti-carbon bond breaks and the molecule is fully inserted in the chain. This is the common reaction used in industry to produce polyethylene and polypropylene.
Data simulation by Mauro Boero, Joint Research Center for Atom Technology (Japan)