Transition path sampling in organometallic catalysis: Overcoming the rare event problem in ab initio molecular dynamics

Since the advent of density functional theory (DFT), computational modelling has become a widely-used tool in organometallic chemistry. This modelling is typically limited to identifying the minima and transition states on the potential energy surface (PES) of a reaction and calculating free energies using the harmonic approximation. Ab initio molecular dynamics (AIMD) is an obvious strategy to address these issues. Within these simulations, the full range of thermally accessible structures is explored and anharmonicity is expressed intrinsically. As AIMD simulations are computationally demanding, the maximum length of a simulation is on the order of 100 ps. It is exceedingly rare for a chemical reaction to occur within this time scale, which precludes the use of straightforward AIMD simulations to study organometallic reaction dynamics or to calculate free energy barriers. We attempt to resolve this time scale limitation by adapting Transition Path Sampling (TPS) for use in organometallic chemistry. TPS is a novel Monte Carlo technique to focus an MD simulation on a reactive event. We present new algorithms to generate initial reactive trajectories for TPS and a novel trajectory generation algorithm which uses a variable perturbation size to improve the sampling efficiency. Our first path sampling study investigated the Ru---hydride catalyzed H2hydrogenation of olefins We identified non-RRKM behaviour of the elimination step of a critical reaction intermediate of the hydrogenation catalytic cycle. Through a spectral decomposition of the vibrational energy, we determined the non-RRKM behaviour results from a localization of vibrational energy in the reactive modes of this intermediate following the rate-limiting insertion step. Our second TPS study modelled the beta-hydrogen transfer chain termination reaction of a zirconocene polymerization catalyst. The reaction dynamics showed that the barder of the e-hydrogen transfer is atypically flat due to a Zr---H interaction in the transition state. We subsequently used AIMD to study the equilibrium structure and beta-hydrogen transfer free energy profile of this system with and without a counteranion present. These simulations showed that the counteranion-dipole interactions have a significant impact on the preferred configuration of the catalyst and the free energy profile of the transfer.