Insight into group 4 metallocenium-mediated olefin polymerization reaction coordinates using a metadynamics approach

We report here the first application of the computationally efficient metadynamics approach for analyzing single-site olefin polymerization mechanisms. The mechanism of group 4 metallocenium catalysis for ethylene homopolymerization is investigated by modeling the ethylene insertion step at the cationic (η⁵-C₅H₅)Zr(CH ₃)₂⁺ center using molecular dynamics simulations within the Density Functional Theory (DFT) framework. In particular, the metadynamics formalism is adopted to enable theoretical characterization of covalent bond forming/breaking processes using molecular dynamics ab initio tools. Analysis of the ethylene insertion step free energy surface indicates a slightly exoergic process (-3.2 kcal/mol) with a barrier of 8.6 kcal/mol, in good agreement with conventional ab initio static calculations. Analysis of the structural and dynamic aspects of the simulated reaction coordinate reveals a preferred olefin configuration which aligns parallel to the Zr-CH₃ vector in concert with insertion and a slightly bent conformation of the product n-propyl chain to avoid nonbonded repulsion between methylene groups. It is found that the unsaturated/electrophilic CpZr(CH₃)₂ ⁺ center drives the insertion step, thus promoting the formation of the Zr-alkyl bond. The metadynamics analysis uniquely encompasses all energetically possible reaction coordinates, thus providing a more detailed mechanistic picture. These results demonstrate the potential of metadynamics in the conformational and geometrical analysis of transition metal-centered homogeneous catalytic processes.