| Summary: | Accurate studies of catalytic reaction mechanisms require high-level methods such as coupled-cluster theory. Approximations must be made to incorporate this level of theory, either for benchmarking of lower-level methods such as density functional theory, or for the direct application of high-level methods. One approach to this is in using symmetry to reduce the computational cost of coupled-cluster theory. This approach is used to study the mechanism of the aqueous Fenton reaction, which has been the subject of much debate. The most thorough experimental evidence appears to support a hydroxyl radical mechanism, whereas theoretical studies using density functional theory predict that a mechanism involving a ferryl-oxo species should occur. The coupled-cluster results reported here show that exact exchange plays a key role in describing the system accurately. Calculations with a hybrid functional show support for the radical mechanism, suggesting that the choice of pure functionals in previous theoretical studies was the cause for disagreement with experiment. A second approach involves the simplification of a large transition-metal complex to produce a small model system. A study of the methane activation mechanism in particulate methane methoxygenase enzymes is performed using this approach, where large histidine ligands are replaced by ammonia ligands. Coupled-cluster theory calculations on this model provide a benchmark for a density functional theory study, leading to the suggestion of a new radical rebound mechanism via a crossing from the singlet to the triplet potential energy surface. The model approach is again used to provide a benchmark for the study of the hydrogen evolution mechanism of a molecular MoS2 species. In this study, errors associated with the model are observed to be larger, though density functional theory results for the full system show good agreement with experimental observations for the suggested mechanism. In both cases, the MoS2 species is predicted to undergo a total of three reductions and two protonations before release of molecular hydrogen. A Tafel mechanism is ruled out for hydrogen evolution due to a high barrier, leading to the suggestion that a Heyrovsky mechanism is likely. An alternative mechanistic pathway is considered where the loss of hydrogen sulfide occurs as a precatalytic step, though a high barrier to this process makes it unlikely. A third approach is to use multi scale modelling, which doesn't require model systems. The projector-based embedding technique described here can produce results of a coupled-cluster level, regardless of the low-level subsystem method. The technique is shown to be effective even when the high-level subsystem is small, and it is invariant to basis set. Large errors are observed in some open-shell systems due to an inaccurate self-consistent density; these are avoided through the use of density-corrected calculations in which the Hartree-Fock density is used. An application of the embedding method is described where a molecular mechanics subsystem is added. This three-tiered multiscale procedure is found to produce extremely accurate energies for the enolization step in the mechanism of citrate synthase enzymes. The method is also observed to show a favourable scaling of computational cost with the size of the quantum mechanics region.
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