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Geometry optimization is a fundamental step in the numerical modelling of chemical reactions. Many thermodynamic and kinetic properties are closely related to the structure of the reactant, product, and the transition states connecting them. Different from the reaction and product, which are local minima on the potential energy surface, a transition state is the first-order saddle point with only one negative curvature. Over years, many methods have been devised to tackle the problem. Locating stable structures is relatively easy with a reliable algorithm and high accuracy. One can follow the gradient descent direction to pursuit the local minimum until convergence is reached. But for the transition state, the determination is more challenging as either the up-hill or down-hill direction is allowed in the process. Motivated by the difficulty, many well-designed optimization algorithms are elaborated specifically to stress the problem. The performance of geometry optimization is affected by various aspects: the initial guess structure, the coordinate system representing the molecule, the accuracy of the initial Hessian matrix, the Hessian update schemes, and the step-size control of each iteration. In this thesis, we propose a new geometry optimization algorithm considering all the important components. More specifically, in Chapter 2, a new set of robust dihedral and redundant internal coordinates is introduced to effectively represent the molecular structures, as well as a computational efficient transformation method to generate a guess structure. In Chapter 3 and 5, a sophisticated robust algorithm is presented and tested to solve intricate transition state optimization problems. In Chapter 4, a new algorithm to exploring reaction pathways based on redundant internal coordinates is illustrated with real chemical reactions. Last but not least, in Chapter 6, a systematic test to explore the optimal methods in each procedure is presented. A well-performed combination of optimization methods is drawn for generic optimization purposes. All the methods and algorithms introduced in this thesis is included in our forth-coming open-source Python package named GOpt. It's a general-purpose library that can work in conjunction with major quantum chemistry software including Gaussian. More features are under development and await to be released in the coming update. / Thesis / Doctor of Science (PhD)

A fundamental understanding of the process of devolatilization requires extensive knowledge of not only the intrinsic properties of the parent coal and its subsequent formed products (tars, gases and chars), but also its characteristic reaction rate behaviour. Devolatilization behaviour has been extensively addressed in literature with the use of powdered coal samples, which normally do not adhere to particle size constraints of coal conversion processes utilizing lump coal. The aim of this investigation was therefore to assess the devolatilization behaviour (with respect to product yield and -quality; and reaction rate modelling) of four typical South African coals (UMZ, INY, G#5 and TSH) confined to the large particle regime. All four coals were found to be bituminous in rank, with vitrinite contents ranging between 24.4 vol.% and 69.2 vol.% (mineral matter free basis). Two were inertinite-rich coals (UMZ and INY) and the other two were vitrinite-rich coals (G#5 and TSH). From thermoplasticity measurements it was evident that only coal TSH displayed extensive thermoplastic behaviour, while a comparison between molecular properties confirmed the higher abundance of poly-condensed aromatic structures (aromaticity of 81%) present in this coal. Product evolution was evaluated under atmospheric conditions in a self-constructed, large particle, fixed-bed reactor, on two particle sizes (5 mm and 20 mm) at two isothermal reactor temperatures (450°C and 750°C) using a combination of both GC and MS techniques for gas species measurement, while standard gravimetric methods were used to quantify tar- and char yield respectively. Elucidation of tar- and char structural features involved the use of both conventional- and advanced analytical techniques. From the results it could be concluded that temperature was the dominating factor controlling product yield- and quality, with significant increases in both volatile- and gas yield observed for an increase in temperature. Tar yields ranged between 3.6 wt.% and 10.1 wt.% and increased in the order UMZ < INY < TSH < G#5, with higher tar yields obtained for coal G#5, being ascribed to larger abundances of vitrinite and liptinite present in this coal. For coal TSH, lower tar yields could mainly be attributed to the higher aromaticity and extensive swelling nature of this coal. Evolved gases were found to be mainly composed of H2, CH4, CO and CO2, low molecular weight olefins and paraffins; and some C4 homologues. Advanced analytical techniques (NMR, SEC, GC-MS, XRD, etc.) revealed the progressive increase of the aromatic nature of both tars and chars with increasing temperature; as well as subsequent differences in tar composition between the different parent coals. In all cases, an increase in devolatilization temperature led to the evolution of larger amounts of aromatic compounds such as alkyl-naphthalenes and PAHs, while significant decreases in the amount of aliphatics and mixed compounds could be observed. From 13C NMR, HRTEM and XRD carbon crystallite results it was clear that an increase in temperature led to the formation of progressively larger, more aromatic and structurally orientated polycondensed carbon structures. Reaction rate studies involved the use of non-isothermal (5-40 K/min) and isothermal (350- 900°C) thermogravimetry of both powdered (-200 μm) and large particle samples (20 mm) in order to assess intrinsic kinetics and large particle rate behaviour, respectively. Evaluation of the intrinsic kinetic parameters of each coal involved the numerical regression of non-isothermal rate data in MATLAB® 7.1.1 according to a pseudo-component modelling philosophy. Modelling results indicated that the intrinsic devolatilization behaviour of each coal could be adequately described by using a total number of eight pseudo-components, while reported activation energies were found to range between 22.3 kJ/mol and 244.3 kJ/mol. Description of the rate of large particle devolatilization involved the evaluation of a novel, comprehensive rate model accounting for derived kinetics, heat and mass transport effects, as well as physical changes due to particle swelling/shrinkage. Evaluation of the proposed model with the aid of the COMSOL Multiphysics 4.3 simulation software provided a suitable fit to the experimental data of all four coals, while simulation studies highlighted the relevant importance of not only the effect of particle size, but also the importance of including terms affecting for heat losses due to particle swelling/shrinkage, transport of volatile products through the porous char structure, heat of reaction and heat of vaporization of water. / Thesis (PhD (Chemical Engineering))--North-West University, Potchefstroom Campus, 2013

A fundamental understanding of the process of devolatilization requires extensive knowledge of not only the intrinsic properties of the parent coal and its subsequent formed products (tars, gases and chars), but also its characteristic reaction rate behaviour. Devolatilization behaviour has been extensively addressed in literature with the use of powdered coal samples, which normally do not adhere to particle size constraints of coal conversion processes utilizing lump coal. The aim of this investigation was therefore to assess the devolatilization behaviour (with respect to product yield and -quality; and reaction rate modelling) of four typical South African coals (UMZ, INY, G#5 and TSH) confined to the large particle regime. All four coals were found to be bituminous in rank, with vitrinite contents ranging between 24.4 vol.% and 69.2 vol.% (mineral matter free basis). Two were inertinite-rich coals (UMZ and INY) and the other two were vitrinite-rich coals (G#5 and TSH). From thermoplasticity measurements it was evident that only coal TSH displayed extensive thermoplastic behaviour, while a comparison between molecular properties confirmed the higher abundance of poly-condensed aromatic structures (aromaticity of 81%) present in this coal. Product evolution was evaluated under atmospheric conditions in a self-constructed, large particle, fixed-bed reactor, on two particle sizes (5 mm and 20 mm) at two isothermal reactor temperatures (450°C and 750°C) using a combination of both GC and MS techniques for gas species measurement, while standard gravimetric methods were used to quantify tar- and char yield respectively. Elucidation of tar- and char structural features involved the use of both conventional- and advanced analytical techniques. From the results it could be concluded that temperature was the dominating factor controlling product yield- and quality, with significant increases in both volatile- and gas yield observed for an increase in temperature. Tar yields ranged between 3.6 wt.% and 10.1 wt.% and increased in the order UMZ < INY < TSH < G#5, with higher tar yields obtained for coal G#5, being ascribed to larger abundances of vitrinite and liptinite present in this coal. For coal TSH, lower tar yields could mainly be attributed to the higher aromaticity and extensive swelling nature of this coal. Evolved gases were found to be mainly composed of H2, CH4, CO and CO2, low molecular weight olefins and paraffins; and some C4 homologues. Advanced analytical techniques (NMR, SEC, GC-MS, XRD, etc.) revealed the progressive increase of the aromatic nature of both tars and chars with increasing temperature; as well as subsequent differences in tar composition between the different parent coals. In all cases, an increase in devolatilization temperature led to the evolution of larger amounts of aromatic compounds such as alkyl-naphthalenes and PAHs, while significant decreases in the amount of aliphatics and mixed compounds could be observed. From 13C NMR, HRTEM and XRD carbon crystallite results it was clear that an increase in temperature led to the formation of progressively larger, more aromatic and structurally orientated polycondensed carbon structures. Reaction rate studies involved the use of non-isothermal (5-40 K/min) and isothermal (350- 900°C) thermogravimetry of both powdered (-200 μm) and large particle samples (20 mm) in order to assess intrinsic kinetics and large particle rate behaviour, respectively. Evaluation of the intrinsic kinetic parameters of each coal involved the numerical regression of non-isothermal rate data in MATLAB® 7.1.1 according to a pseudo-component modelling philosophy. Modelling results indicated that the intrinsic devolatilization behaviour of each coal could be adequately described by using a total number of eight pseudo-components, while reported activation energies were found to range between 22.3 kJ/mol and 244.3 kJ/mol. Description of the rate of large particle devolatilization involved the evaluation of a novel, comprehensive rate model accounting for derived kinetics, heat and mass transport effects, as well as physical changes due to particle swelling/shrinkage. Evaluation of the proposed model with the aid of the COMSOL Multiphysics 4.3 simulation software provided a suitable fit to the experimental data of all four coals, while simulation studies highlighted the relevant importance of not only the effect of particle size, but also the importance of including terms affecting for heat losses due to particle swelling/shrinkage, transport of volatile products through the porous char structure, heat of reaction and heat of vaporization of water. / Thesis (PhD (Chemical Engineering))--North-West University, Potchefstroom Campus, 2013