We present a first principles study of the Ziegler-Natta MgCl2-supported polymerization of ethylene in the framework of the Car-Parrinello approach. In particular we investigate the titanium active sites on the (110) surface of the support focusing on Corradini＇s model and the possible alternative configurations. We find that different catalyst sites are allowed and that the relevant energetics as well as the reactivity in the alkyl chain formation process strongly depend on the local geometry. During deposition of TiCl4 and complex formation, which are energetically downhill, the dynamical approach allows us to follow the reaction pathway in an unbiased way. By means of Car-Parrinello constrained molecular dynamics we then determine the free energy profiles and estimate activation barriers in the alkene insertion processes. Furthermore a dynamical study of the insertion of a second ethylene molecule offers an interesting insight into the chain growth process and the stereochemical character of the polymer, providing a complete picture of the reaction mechanism.