Exploring the Nature of the Energy Barriers on the Mechanism of the Zirconocene-Catalyzed Ethylene Polymerization: A Quantitative Study from Reaction Force Analysis

Abstract

Ethylene polymerization mediated by methyl-bis(cyclopentadienyl)-zirconium or zirconocene catalyst, [ZrCp₂CH₃]⁺, is one of the most popular catalytic reaction for polyethylene production. Rationalizing the major effects that control the polymer growth result in a challenge for computational studies. Through quantum chemical calculations, we characterized the zirconocene ethylene polymerization reaction mechanism: chain initiation (I; first ethylene insertion) [ZrCp₂CH₂CH₂CH₃]⁺, chain propagation (P; from second (P₁) to ninth (P₉) ethylene insertion) [ZrCp₂ (CH₂)₂₀CH₃]⁺, and chain termination processes (T; β-hydrogen elimination from P₅ or P₉) [ZrHCp₂ (H₂C═CH(CH₂)₁₈CH₃]⁺ are analyzed through the potential energy surface (PES) and reaction force analysis (RFA). The RFA approach involves pulling out the portion of an activation barrier that corresponds to distorting reactants into the geometries they adopt in a transition state structure until it reaches the structural relaxation toward the equilibrium geometry of the product. Because the interactions between the zirconocene and the ethylene molecule are influenced by a combination of several kinds of steric and electronic effects, it is indispensable to understanding these interactions in order to rationalize and predict in a quantitative manner the reaction barrier heights and the concomitant polymer growth. In the present work, we employ a simple procedure within the framework of the RFA and the density functional steric energy decomposition analysis (EDA) approach to quantitatively separate the different types of interactions; steric (ΔE_s), electrostatic (ΔE_e), and quantum (ΔE_q) effects in order to predict the impact of each factor on the course of the polymerization process as well as for the polymer control and design.