The development of efficient catalyst for water oxidation is of paramount importance to artificial photosynthesis, but before this can be achieved a deeper understanding of this reaction is essential. In nature this reaction occurs in a tetranuclear Mn-cluster which serves as the work-horse of oxygenic photosynthesis. This thesis summarises my efforts at developing molecular systems capable of mimicking this complex employing a biomimetic approach. Three different approaches towards this goal are described here-in. The first section describes a screening study, in which a number of manganese complexes were tested to see whether or not they were capable of catalysing the formation of dioxygen when treated with different oxidants (Papers I). For those reactions in which dioxygen formation was observed the reactions were repeated in labelled water and the incorporation of labelled O-atoms was studied by mass spectrometry. This allowed us to determine to what extent water was the source of the evolved dioxygen (Papers II-III). In Chapter three a reported catalyst and a derivative thereof is studied in depth. The influence of changes to the ligand on the oxygen–oxygen bond forming reaction could unfortunately not be reliably addressed, because of the instability of the complexes under “catalytic” conditions. Nevertheless, the study allowed us to revise the “carboxylate shift”-mechanism suggested in the literature (Papers IV-V). Chapter four describes the continuation of my work on ligands featuring the carboxylate ligand motif first introduced in Chapter three. In this study ligands containing multiple binding pockets were designed and synthesised (Paper VI). A better understanding of the mechanism in the natural water oxidising enzyme will facilitate the design of biomimetic complexes, this is discussed in Chapter five. In this work model complexes (Paper VII) are used to study the mechanism by which natures own water oxidising catalyst performs this reaction.

Esta tesis está dedicada al desarrollo, aplicación y test de métodos para la simulación numérica de problemas procedentes de la física y de la ingeniería electrónica. La principal herramienta aplicada a lo largo de todo el trabajo es la ecuación de Vlasov (transporte) en la forma de la Boltzmann Transport Equation (BTE) para la descripción del transporte de partículas cargadas en plasmas y dispositivos electrónicos: las cargas se mueven bajo el efecto de un campo de fuerza y sufren scattering debido a otras cargas o fonones (pseudo-partículas que describen de manera efectiva las vibraciones de los iones del retículo cristalino).La BTE ha de ser acoplada con una ecuación o sistema de ecuaciones para calcular el campo de fuerza: para estructuras simples se usa la ecuación de Poisson; para plasmas, donde los efectos magnéticos no se pueden despreciar debido a las altas velocidades de las partículas, se usa la fuerza de Lorentz, por lo cual se han de resolver las ecuaciones de Maxwell; en nanoestructuras, por ejemplo transistores con dimensiones confinadas, la ecuación de Poisson necesita ser acoplada con la ecuación de Schrödinger para la descripción de las dimensiones cuánticas y para la descomposición en sub-bandas, o niveles de energía.Las colisiones son el scattering que las cargas padecen debido a las interacciones con otras cargas o con el retículo cristalino fijo, representado en forma de fonones. En la tesis se emplean diversos operadores de scattering: los más simples son operadores lineales de relajación; se estudia un modelo para la simulación de semiconductores donde se tienen en cuenta colisiones con fonones acústicos, en aproximación elástica, y fonones ópticos.Tras la introducción, en el primer capítulo se desarrollan los métodos numéricos más importantes: primero un método de interpolación no oscilante (PWENO), necesario para evitar las oscilaciones producidas por la reconstrucción por polinomios de Lagrange, que incrementa la variación total cuando aparecen choques: las oscilaciones en el espacio de fases son características del problema, pero si el método añade oscilaciones espúreas (es decir, debidas al método en sí), entonces el resultado numérico no tiene sentido, o simplemente explota. El segundo método numérico fundamental es la técnica de splitting: cuando se resuelve un problema complicado, si se puede dividir en sub-problemas y resolverlos por separado, entonces se puede reconstruir una aproximación para el problema completo; esta técnica se usa para el time splitting (separación de la parte de transporte y de colisión) y el splitting dimensional (dividir el espacio de fases en posición y velocidad). La tercera herramienta fundamental es un sólver para advección lineal: se usan dos métodos, uno basado en trazar hacia atrás las características a nivel puntual y otro basado en reconstruir valores integrales en segmentos en lugar de puntos; el primero controla mejor las oscilaciones, el segundo fuerza la conservación de masa.En el capítulo 2 estos métodos se aplican a algunos tests conocidos para averiguar su solidez.En el capítulo 3 estos métodos se aplican a la simulación de un diodo, y los resultados se comparan con resultados anteriores obtenidos por esquemas Runge-Kutta basados en diferencias finitas para aproximar las derivadas parciales.El capítulo 4 está dedicado a la construcción y simulación de modelos intermedios entre una ecuación cinética, con operador de colisión de tipo relajación, y su aproximación más grosera, ésta última siendo la ecuación del calor. Para obtener modelos intermedios, se busca un cierre de las ecuaciones de los momentos de orden cero y uno. Se proponen esquemas "asymptotic-preserving" para la ecuación cinética, que evitan la stiffness de la parte de advección a través de una descomposición de la función de distribución en su media más fluctuaciones. En cuanto a las clausuras de las ecuaciones de los momentos, se proponen esquemas de relajación para aislar las no-linealidades. Estos métodos son aplicados a un test conocido, el Su-Olson test.El último capítulo está dedicado a la simulación de un MOSFET (Metal Oxide Semiconductor Field Effect Transistor) 2D de dimensión nanométrica en el que los electrones se comportan como partículas en una dimensión y como ondas en las dimensiones confinadas. La descomposición en sub-bandas se realiza a través de una ecuación de Schrödinger 1D en estado estacionario. Las dimensiones, así como las sub-bandas, están acopladas por la ecuación de Poisson en la expresión de la densidad, y por el operador de colisión. Se propone un sólver microscópico para estados transitorios, basado en técnicas de splitting para las BTEs (una para cada nivel de energía), métodos de características para el transporte y una iteración de tipo Newton para resolver el problema acoplado Schrödinger-Poisson para el cálculo del campo de fuerza. / This thesis is dedicated to the development, application and test of numerical methods for the numerical simulation of problems arising from physics and electronic engineering. The main tool which is used all along the work is the Vlasov (transport) equation in the form of the Boltzmann Transport Equation (BTE) for the description of the transport and collisions of charged particles in plasmas and electronic devices: charge carriers are driven by a force field and scattered by other carriers or phonons (pseudo-particles giving an effective representation of the oscillating field produced by the vibrating ions).The BTE must be coupled to an equation or a system of equations for the computation of the force field: for simple structures the Poisson equation is used; for plasmas, where the magnetic phenomena cannot be neglected due to the high velocities of the particles, the Lorentz force is used, so the Maxwell equations have to be solved; for nanostructures, e.g. transistors with confined dimensions, the Poisson equation needs coupling with Schrödinger equation for the description of the quantum dimensions and the decomposition into subbands, or energy levels.Collisions mean the scattering the carriers suffer due to the interactions with other carriers or the fixed lattice, in form of phonons. All along the thesis several scattering operator are used: the simplest ones are linear relaxation-time operators; a model for the simulation of a semiconductor is studied in which collisions are taken into account with acoustic phonons, in the elastic approximation, and optical phonons.After the introduction, in the first chapter the most important numerical methods are developed: first of all a pointwise non-oscillatory interpolation method (PWENO) needed to avoid the simple Lagrange polynomial reconstruction, which increases the total variation when shocks appear: oscillations are part of the physics of the problem, but if the method adds spurious, non-physical oscillations, then the numerical result is meaningless, or it simply blows up. The second fundamental numerical method is the splitting technique: when solving a complicated problem, if we are able to subdivide it into sub-problem and solve them for separate, then we can reconstruct an approximation for the complete problem; this technique is used for both time splitting (separate transport from collisions) and dimensional splitting (split the phase space into either dimensions). The third fundamental instrument is the solver for linear advections: two methods are used, one based on pointwise following backwards the characteristics and another one based on reconstructing integral values along segments instead of point values; the first one controls better oscillations, the second one forces mass conservation.These methods are applied in chapter 2 to some well-known benchmark tests to control their robustness.In chapter 3 these methods are applied to the simulation of a diode, and the results compared to previous results obtained by Runge-Kutta schemes based on finite differences schemes for the approximation of the partial derivatives.Chapter 4 is dedicated to the construction and simulation of intermediate models between a kinetic equation, with relaxation-time collision operator, and its coarsest approximation, this one being the heat equations. In order to obtain intermediate models, the moment equations are closed at zeroth and first order. Asymptotic-preserving schemes are proposed for the kinetic equation, which avoid the stiffness of the advection part by decomposing the distribution function into its average plus fluctuations. As for the moment closures, relaxation schemes are proposed in order to confine the non-linearities in the right hand side. These methods are then applied to a known benchmark, the Su-Olson test.The last chapter is dedicated to the simulation of a nanoscaled 2D MOSFET (Metal Oxide Field Effect Transistor) in which electrons behave as particles in one dimension and as waves in the confined dimensions. The subband decomposition is realized through a stationary-state 1D Schrödinger equation. The dimensions as well as the subbands are coupled by the Poisson equation in the expression of the density and by the collision operator. A transient-state microscopic solver is proposed, based on splitting techniques for the BTE's (one for each energy level), characteristics methods for the transport and a Newton iteration for the solution of the coupled Schrödinger-Poisson system for computing the force field.

Hydrogen production by water-splitting using solar energy and nanostructure photocatalysts is very promising as a renewable, efficient, environmentally clean technology. The key is to reduce the cost of hydrogen production as well as increase the solar-to-hydrogen conversion efficiency by searching for cost-effective photocatalytic materials. In this dissertation, energy efficiency calculation was carried out based on hydrogen production observation to evaluate the nanomaterials activity. The results are important to gain better understanding of water-splitting reaction mechanism. Design, synthesis, characterization/properties and application of these nanomaterials was the road-map to achieve the research objectives. The design of TiO2 is selected based on unique photocatalytic and photovoltaic properties and high stability in aqueous solution. Various structures of nanocomposites TiO2 were designed according to their characteristics and potential activity. TiO2 with quantum dots, nanocomposites thin film, nanofibers, nanorods, nanowires (core/shell), nanotubes, nanopowders, nanoparticles, and nanosphere decorated with low cost metals, sensitized with dye, and doped with nitrogen are designed. Green physical and chemical synthesis methods such as sol-gel techniques, autoclave, microwave, electrospinning, wet impregnation, hydrothermal, chemical vapor deposition, template-based fabrication (porous anodic aluminium oxide membrane), drop casting, dip coating, wet coating were used to synthesize and fabricate the nanomaterials and quantum dots.Both bottom-up and top-down synthesis techniques were used. The ability to control and manipulate the size, shape/geometry, crystal structure, chemical compositions, interaction and interface properties of these materials at nano-scale during the synthesis enable to enhance their thermal, optical, chemical, electrical, …etc properties. Several characterization techniques such as XRD, XPS, EDS, SEM, UV-visible spectra, and optical microscopic and digital camera were also obtained to characterize the properties and confirm to achieve the desired design. The application or processing to test the activity of these nanomaterials for hydrogen production by water-splitting was conducted through extensive experimental program. It was carried out in a one photo-single column experimental set-up to detect hydrogen evolution. A high throughput screening process to evaluate single photo reduction catalysts was established here for simplicity, safety, cost-effective and flexibility of testing nanomaterials for water photoreduction reactivity and hydrogen generation. Therefore, methanol as electron donor or oxidation agent was mixed with water in equal volume ratio in order to prevent the oxygen evolution and only measured the time course of hydrogen production. The primary objectives of this study is to investigate the following (1) The structure-properties relationship through testing quantum dots, nanocomposites thin film, nanofibers, nanorods, nanowires (core/shell), nanotubes, nanopowders, nanoparticles, nanospheres of TiO2 decorated with metals, dye sensitization, and nitrogen-doping. (2) The role of adding electron donors/relays to solution and their effect on semiconductor surface-electrolyte interface under constant conditions such as KI, Mv 2, NaCl, NaHCO3, sea and pure water. (3) Band gap and defect engineering by cation and anion doping. (4) Quantum dots and dye sensitization effect. The nanomaterials activity evaluated based on observed hydrogen production rate (μmol/h/g) experimentally and based on the energy efficiency (percent) calculation. Major findings in this dissertation are (1) A high throughput screening process to evaluate single photoreduction catalysts for solar-hydrogen production by water-splitting was established. (2) nanofibers structure of TiO2 doped with nitrogen, sensitized with dye (Rose Bengal Sodium) and quantum dots (CuInS2), and decorated with metals (Ag) showed the high solar-to-hydrogen conversion efficiency and high hydrogen production rate (3) Simple, safe, inexpensive, robust, efficient and green physical and chemical synthesis methods were used to prepare the nanomaterials and quantum dots. (4) Gaining insight and better understanding of water-splitting reaction mechanism by (a) Studying the structure-properties relationship of nanomaterials (b) Studying the role of additives on surface-interface chemistry of semiconductor and electrolyte (c) Knowing how to reduce the electron-hole recombination reactions to enhance quantum efficiency (d) Extending the absorption of nanomaterials to harness the visible light of solar spectrum radiation by doping and defect chemistry.

Veeco Applied EPI 930 molecular beam epitaxy system equipped with a radio frequency plasma assisted nitrogen source has been introduced and the growth procedure and some specialized measurements are also described. The GaN thin films grown by RF-MBE have been talked about nitridation, low temperature GaN buffer layer, and GaN epilayer. The nitridation is a necessary for grown GaN on c-sapphire. From the result of the HRXRD symmetric (002) rocking curve, the magnitude of the FWHM of the GaN films without nitridation was larger than the films with nitridation. The growth temperature of the LT GaN buffer layer was the major factor on the quality of GaN epilayer which grown on the almost without nitridated sapphire substrate. The growth condition of high growth temperature, thin, low growth rate, and low N/Ga ratio of the LT GaN buffer layer can improve the sequent GaN epilayer quality. On the other hand, in the N/Ga flux ratio of GaN epitaxy layer experiment, we have found three interesting results. First, the narrowest peak width of PL spectrum appeared in a slight Ga-rich condition. Second, the smallest of HRXRD FWHM appeared in the nearly stoichiometry condition. Third, the highest electron mobility and less overall dislocations appeared in a slight N-rich condition. Finally, we report the results about AlGaN/GaN heterostructure grown by metalorganic chemical vapor deposition. The piezoelectric effect on the Alx-£_In£_Ga1-xN/GaN heterostructures was investigated and we found that a little In atom in the spacer (£_< 0.01 %) will substantially reduce the strain at interface due to the much larger size of the In atom in comparison to Al and Ga atoms. The electric field at the interface is reduced one order of magnitude smaller than that of the heterostructure without In atom. Two SdH oscillations beat each other due to the population of the lowest two subbands was been seen. Another two SdH oscillations beating have been observed in modulation-doped AlxGa1-xN/GaN heterostructures caused by the finite zero-filed spin splitting due to the inversion-asymmetry-induced bulk k3 term.

Since the plus fraction of reservoir fluids has some uncertainty in its molecular weight and critical properties, equation-of-state, EOS, are generally not predictive without tuning its parameters to match experimental data. Tuning of the EOS is found to be the best method for improving the predictions of compositional reservoir simulators. The proposed strategy for tuning EOS consists of seven steps: (1) split the laboratory plus fraction to single carbon number groups, SCN, usually up to SCN 44; the last component will be C45+, (2) use set of correlations to calculate the critical properties and acentric factor for each SCN group, (3) match the saturation pressure at reservoir temperature by altering the measured value of the molecular weight of the plus fraction using the extended composition, (4) group SCN groups to multiple carbon number groups, MCN, (5) assign critical properties and acentric factor for each MCN group, (6) rematch the saturation pressure at reservoir temperature using the grouped composition, and (7) match the volumetric data by regressing on volume shift parameters of all components in grouped composition. This research shows an accurate method to split the plus fraction to SCN groups. The most accurate set of correlations to calculate the critical properties and acentric factor for each SCN group that will result in a small adjustment for the molecular weight of the plus fraction when saturation pressure is matched using the extended composition. The proposed strategy groups the extended composition to eight pseudocomponents. The binary interaction coefficients between hydrocarbons and between hydrocarbons and non-hydrocarbons are set to zero which dramatically reduces the simulation time. The strategy proposed in this research for tuning EOS to match experimental data has been tested for a wide range of C7+ mole% (4 – 25) which covers gas condensate and volatile oil samples. Also, using this strategy to tune EOS at reservoir temperature will accurately predict the fluid properties at separator conditions and saturation pressures at different temperatures. The scope of this research is to come up with an accurate and systematic technique for tuning an EOS for use in compositional simulation.

The energy requirements of our planet will continue to grow with increasing world population and the modernization of currently underdeveloped countries. This will force us to search for environmental friendly alternative energy resources. Solar energy by far provides the largest of all renewable energy resources with an average power of 120 000 TW irradiated from the sun which can be exploited through solar electricity, solar fuel, and biomass. Nanostructured materials have been the subject of extensive research as the building block for construction of solar energy conversion devices for the past decades. The nanostructured materials sometimes have peculiar electrical and optical properties that are often shape and size dependent and are not expected in the bulk phase. Recent research has focused on new strategies to control nanostructured morphologies and compositions of semiconductor materials to optimize their solar conversion efficiency. In this dissertation, we discuss the synthesis and characterizations of one dimensional nanostructured TiO₂ based materials and their solar energy conversion applications. We have developed a solvothermal synthesis method for growing densely packed, vertical, single crystalline TiO₂ rutile nanowire arrays with unprecedented small feature sizes of 5 nm and lengths up to 4.4 [mu]m. Because of TiO₂'s large band gap, the working spectrum of TiO₂ is limited to the ultra violet region with photons shorter than 420 nm. We demonstrate that the active spectrum of TiO₂ can be shifted to ~ 520 nm with incorporation of N via nitridation of TiO₂ nanowires in NH₃ flow. In addition, we demonstrate a synergistic effect involving hydrogenation and nitridation cotreatment of TiO₂ nanowires that further redshift the active spectrum of TiO₂ to 570 nm. The Ta and N co-incorporated TiO₂ nanowires were also prepared and showed significant enhancement in photoelectrochemical performance compared to mono-incorporation of Ta or N. This enhancement is due to fewer recombination centers from charge compensation effects and suppression of the formation of an amorphous layer on the nanowires during the nitridation process. Finally, we have developed hydrothermal synthesis of single crystalline TiO₂ nanoplatelet arrays on virtually all substrates and demonstrated their applications in water photo-oxidation and dye sensitized solar cells. / text

The sun is a vast source of renewable energy, which can potentially be used to satisfy the world's increasing energy demand. Yet many material challenges need to be overcome before solar energy conversion can be implemented on a larger scale. This dissertation focuses on materials used for solar energy conversion through photo-electrochemical (PEC) processes. It discusses methods for improving PEC materials, namely mixed metal oxide semiconductors, by nanostructuring, incorporation of additional elements, and application surface electrocatalysts. In this dissertation several material synthesis techniques are detailed. A high vacuum synthesis process known as reactive ballistic deposition (RBD) is used to synthesize nanostructured bismuth vanadate (BiVO₄), which is studied for PEC water oxidation. Additionally, ballistic deposition (BD) is used to incorporate Mo and W into nanostructured BiVO₄ to improve the PEC activity. An array dispenser and scanner system is used to incorporate metals into copper oxide (CuO) and copper bismuth oxide (CuBi₂O₄) and over 3,000 unique material compositions are tested for cathodic photoactivity. The system is also used to test 35 elements as single component metal oxides, mixed metal oxides, and dopants for titanium dioxide (TiO₂) for use in dye-sensitized solar cells (DSCs). Lastly, RBD is used to deposit tungsten semicarbide (W₂C) onto p-type silicon (p-type) substrates as an electrocatalyst for PEC proton reduction. In many cases, the synthesis techniques and new material combinations presented in this dissertation result in improved PEC performance. The materials are thoroughly assessed and characterized to gain insights into their nanostructure, chemical composition, light absorption, charge transport properties, catalytic activity, and stability. / text

The properties of free-standing cubic silicon carbide for optoelectronic applications are explored in this work. The main focus of the work is on boron doped cubic silicon carbide, which is proposed as a highly useful material in several optoelectronic applications. The material is grown using sublimation epitaxy and the doped material is grown homoepitaxially on nominally undoped seeds. It is characterized using the experimental setups of photoluminescence spectroscopy, Nomarski interference spectroscopy and absorption spectroscopy. I have studied seed growth of nominally undoped cubic material on hexagonal (4H) substrates, and the influence on the grown material from the different faces of the substrate. It is found that it is not possible under the explored conditions to completely cover the growth area with the cubic polytype on the carbon face, but it can be done reproducibly on the silicon face. Reasons for this are discussed. Different doping setups are also explored. The influence on the material properties from growth conditions is explored. It is shown from absorption measurements that it is possible to grow boron doped cubic silicon carbide using this growth method, whereas optical microscopy studies show that the sample quality degrades with high doping concentrations. I have explored the luminescence properties of the material. No boron related emission is found with either room temperature or low temperature photoluminescence spectroscopy. Reasons for this are discussed using results from absorption measurements and optical microscopy.

Photosynthesis is the unique biological process that converts carbon dioxide into organic compounds, for example sugars, using the energy of sunlight. Thereby solar energy is converted into chemical energy. Nearly all life depends on this reaction, either directly, or indirectly as the ultimate source of their food. Oxygenic photosynthesis occurs in plants, algae and cyanobacteria. This process created the present level of oxygen in the atmosphere, which allowed the formation of higher life, since respiration allows extracting up to 15-times more energy from organic matter than anaerobic fermentation. Oxygenic photosynthesis uses as substrate for the ubiquitous water. The light-induced oxidation of water to molecular oxygen (O2), catalyzed by the Mn4CaO5 cluster associated with the photosystem II (PS II) complex, is thus one of the most important and wide spread chemical processes occurring in the biosphere. Understanding the mechanism of water-oxidation by the Mn4CaO5 cluster is one of today’s great challenges in science. It is believed that one can extract basic principles of catalyst design from the natural system that than can be applied to artificial systems. Such systems can be used in the future for the generation of fuel from sunlight. In this thesis the light-induced production of molecular oxygen and carbon dioxide (CO2) by PSII was observed by membrane-inlet mass spectrometry. By analyzing this observation is shown that CO2 not only is the substrate in photosynthesis for the production of sugars, but that it also regulates the efficiency of the initial steps of the electron transport chain of oxygenic photosynthesis by acting, in form of HCO3-, as acceptor for protons produced during water-splitting. This finding concludes the 50-years old search for the function of CO2/HCO3− in photosynthetic water oxidation. For understanding the mechanism of water oxidation it is crucial to resolve the structures of all oxidation states, including transient once, of the Mn4CaO5 cluster. With this application in mind a new illumination setup was developed and characterized that allowed to bring the Mn4CaO5 cluster of PSII microcrystals into known oxidation states while they flow through a narrow capillary. The optimized illumination conditions were employed at the X-ray free electron laser at the Linac Coherent Light Source (LCLS) to obtain simultaneous x-ray diffraction (XRD) and x-ray emission spectroscopy (XES) at room temperature. This two methods probe the overall protein structure and the electronic structure of the Mn4CaO5 cluster, respectively. Data are presented from both the dark state (S1) and the first illuminated state (S2) of PS II. This approach opens new directions for studying structural changes during the catalytic cycle of the Mn4CaO5 cluster, and for resolving the mechanism of O-O bond formation. In two other projects the mechanism of molecular oxygen formation by artificial water oxidation catalysts containing inexpensive and abundant elements were studied. Oxygen evolution catalyzed by calcium manganese and manganese only oxides was studied in 18O-enriched water. It was concluded that molecular oxygen is formed by entirely different pathways depending on what chemical oxidant was used.  Only strong non-oxygen donating oxidants were found to support ‘true’ water-oxidation. For cobalt oxides a study was designed to understand the mechanistic details of how the O-O bond forms. The data demonstrate that O-O bond formation occurs by direct coupling between two terminal water-derived ligands. Moreover, by detailed theoretical modelling of the data the number of cobalt atoms per catalytic site was derived.

We study the conjectured equivalence between the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under a naive application of the bosonization rules. We start with a review of the equivalence between sine-Gordon model and the massive Thirring model. We study the models by perturbation theory and then determine the equivalence. We find that the dependence of the identifications on the couplings can change according to the definition of the vector current. With the operator identifications of the special case corresponding to a free fermionic theory, known as the bosonization rules, we describe the equivalence between the massless Thirring model and the model of a compactified free boson field. For the massless Thirring model, or equivalently the O(2) Gross-Neveu model, we study the conservation laws for the vector current and the axial current by employing a generalized point-splitting method which allows a one-parameter family of definitions of the vector current. With this parameter, we can make contact with different approaches that can be found in the literature; these approaches differ mainly because of the specific definition of the current that was used. We also find the Sugawara form of the stress-energy tensor and its commutation relations. Further, we rewrite the identifications between sine-Gordon and Thirring models in our generalized framework. For the O(3) Gross-Neveu model, we extend our point-splitting method to determine the exact expression for the supercurrent. Using this current, we compute the superalgebra which determines three quantum components of the stress-energy tensor. With an Ansatz for the undetermined component, we find the trace anomaly and the first beta-function coefficient. The central charge which can be computed without using our point-splitting method is independent of the coupling constant, in fact, it is always zero. For the supersymmetric sine-Gordon model, we review its supersymmetry in the context of models derived from a scalar multiplet in two dimensions. We then obtain the central charge and discover an extra term that was missing in the original derivation. We also analyze how normal ordering modifies the central charge. Finally, we discuss the conjectured equivalence of the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under the naive application of the bosonization rules. Comparing our results of the central charges and the supercurrents for these models, we find that they disagree; consequently the models should be generically inequivalent. We also conclude that the naive application of the bosonization rules at the Lagrangian level does not always lead to an equivalent theory.