| Izvleček: | <p>Full-dimensional quantum reactive scattering (QRS) calculations provide the most accurate dynamical results which include the rate constants for a chemical reaction. However, the computational costs involved in the calculations scale significantly with the size of the reacting system. Transition State Theory with Multi-Dimensional Tunnelling (TST/MT) and Reduced Dimensionality (RD) methods are two methods that are more efficient in computing reaction rate constants for general polyatomic reacting systems. In RD methods, only a subset of degrees of freedom are treated explicitly in calculations. In TST/MT, reaction rate constants are obtained by multiplying the TST reaction rate constants with a transmission coefficient, calculated based on the adiabatic ground state potential energy and other relevant properties obtained along the minimum energy path.</p> <p>In this thesis, TST with zero-, small-, and large-curvature tunnelling approximations (abbreviated as TST/ZCT, TST/SCT and TST/LCT respectively) were applied to previously constructed RD potential energy surfaces (RD PES) with and without a mapped interpolation (MI) procedure. They were applied to the reactions CH<sub>4</sub> +H, C<sub>2</sub>H<sub>6</sub> +H, cyc-C<sub>3</sub>H<sub>6</sub> +H, CH<sub>4</sub> +CH<sub>3</sub>, CH<sub>3</sub>D+CH<sub>3</sub> and CD<sub>4</sub> +CD<sub>3</sub> to test the TST/MT methods against accurate QRS calculations on the same PESs on these reactions. The use of MI improved the results by correcting the shape of the adiabatic ground state potential energy curves and the threshold energies of the reactions. TST/ZCT (MI) shows poor agreement with QRS results due to the lack of accounting for reaction path curvature, and TST/LCT (MI) shows moderate agreement for CH<sub>4</sub> +CH<sub>3</sub> with large reaction path curvature. For all reactions, TST/SCT (MI) shows the best agreement to QRS results and experimental data. Such agreement suggests the potential applicability of the TST/MT methods to larger polyatomic systems under the RD framework.</p> <p>Primary kinetic isotope effects (KIE) for CH<sub>4</sub>+CH<sub>3</sub> are shown to be significant due to the substitution of the exchanged hydrogen atom with a much heavier deuterium isotope. Secondary KIE for CH<sub>3</sub>D+CH<sub>3</sub> are shown to be less significant and do not contribute much to the reaction rate constants in the case of CD<sub>4</sub>+CD<sub>3</sub>.</p>
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