Static and ab initio molecular dynamics study of the titanium(IV)-constrained geometry catalyst (CpSiH2NH)Ti-R+ .2. Chain termination and long chain branching

We present a comprehensive survey of chain termination and long chain branching processes for the ''constrained-geometry'' olefin polymerization catalyst (CpSiH2NH)Ti-R+ (R = ethyl, propyl) based on static and dynamic density functional theory. Car-Parrinello molecular dynamics calculations are used to locate reaction pathways and estimate free energies of activation, and conventional static calculations are used to ascertain stationary points and relative energies. We have examined three distinct chain termination processes: (a) beta-hydrogen transfer to the monomer, (b) beta-hydrogen transfer to the metal, and (c) olefin C-H sigma-bond metathesis. We find alternative (a) to be the most viable one [Delta H-el(double dagger)(R = ethyl) = 32 kJ/mol; Delta F-double dagger(R = ethyl) = 40.1; Delta F-double dagger(R = propyl) = 43 +/- 8 kJ/mol at 300 K], whereas pathways (b) [Delta H-el(double dagger)(R = propyl) = 67; Delta F-double dagger(R = propyl) = 57 +/- 3 at 300 K] and (c) [Delta H-el(double dagger)(R = ethyl) = 93; Delta F-double dagger(R = ethyl) = 91.7 kJ/mol; Delta F-double dagger(R = propyl)= 87 +/- 5 at 300 K] have much higher activation barriers. In addition, we investigated an unconventional long chain branching mechanism (d), where a polymer chain binds to the metal center in apt eta(2)-agostic fashion via aliphatic hydrogens, followed by activation of one aliphatic C-H bond and transfer of the hydrogen to the a-carbon to-bond metathesis). For this process we have found a large electronic barrier of Delta H-el(double dagger)(R = ethyl) = 77 kJ/mol and a free energy barrier of Delta F-double dagger(R = ethyl) = 72.3 kJ/mol; Delta F-double dagger (R = propyl) = 70 +/- 3 kJ/mol at 300 K. On the basis of our data, we favor the conventional long chain branching mechanism consisting of chain termination via mechanism (a) to produce a vinyl-terminated chain and reincorporation of the terminated chain into the polymer. In this study we have calculated free energy barriers for each of the aforementioned processes by a conventional static calculations and by a Car-Parrinello ''first principles'' molecular dynamics simulations. The agreement of the two methods is exceptional, demonstrating utility of first principles molecular dynamics to determine free energy barriers.