Thesis (MSc (Physics))--University of Stellenbosch, 2007. / A relativistic plane wave model is developed for electromagnetic production of unbound hyperons with free kaons from nuclei. The differential cross section is expressed as a contraction of leptonic and hadronic tensors. The leptonic tensor is constructed by using the helicity representation of a free Dirac spinor. A model for the corresponding elementary process is used to calculate the hadronic tensor, in which the hadronic current operator Jˆμ is written as a linear combination of six invariant amplitudes and six Lorentz and gauge invariant quantities. The kinematics for this process is assumed to be a quasi-free process i.e., the electron interacts with only one bound nucleon inside the nucleus. The bound state wavefunction of the bound nucleon is calculated within the framework of the relativistic mean-field approximation. The unpolarized differential cross section for the K+ electroproduction process, e + A −→ e + K+ + A + Aresidual is calculated as a function of the hyperon scattering angle.

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The work presented in this thesis is dedicated to developing inexpensive quantum-chemical models that are able to produce smooth and physically correct potential energy curves for the dissociation of single covalent bonds. It is well known that the energies produced by many ab initio theories scaling as the fifth order with the system size (for instance, second-order Moller-Plesset (MP2) and Epstein-Nesbet perturbation theories) diverge at large interatomic separations. We show that the divergent behavior of such perturbation schemes is due to a small number of terms in the energy expressions. Then, we demonstrate that the self-consistent replacement of these terms by their analogs from the coupled cluster theory (such as CCSD) allows one to redress the erroneous behavior of the perturbation theories without the damage to the overall scaling. We also investigate the accuracy of these hybrid perturbation theory-coupled cluster theories near equilibrium geometry. Judging from the computed spectroscopic constants and shapes of the potential energy curves, one such model, denoted MP2-CCSD(II) in this work, performs consistently better than the MP2 theory at essentially the same computational cost.

Ab initio molecular orbital theory has been successful in predicting the stabilities of many weak complexes; typical of these are the complexes formed between water and various small molecules. To account for the correlation effect, Moller-Plesset perturbation theory truncated at the second order level was employed. In order to account for the hydrogen bonding, the 6-3lG** basis set was used. The geometry optimisations of the complexes were carried out using the Gaussian-92 suite of programs installed on a Hewlett-Packard 720 computer operating under UNIX. The interaction energies of the complexes were subjected to further analysis by applying the Morokuma decomposition scheme. The electrostatic interaction component accounts for over 40% of the total stabilisation energy in all the typical hydrogen bonded complexes. Gas phase enthalpies were computed and compared with the experimental values of similar systems. For the systems studied here, the prediction is that all complexes are stable at 25° C. A second program, Vibra, was used for carrying out a normal coordinate analysis. A third computer program for the graphical representation of molecular and crystallographic models, Schakal-92, was employed to illustrate the predicted equilibrium geometries and the fundamental vibrational modes. The predicted geometries, interaction energies, charge redistributions, vibrational wave numbers, infrared intensities and force constants are listed and compared with those in the literature, where applicable. Correlations between the various predicted properties show some interesting chemistry. / Thesis (Ph.D.)-University of Natal, Durban, 1996.

Les composés en couches avec des ions métaux de transition ont leur bande de conduction dans les orbitales d. On se concentrera dans cette thèse sur les systèmes où le champs cristallin sépare les orbitales en deux sets dégénérés, t2g et eg, où les électrons de conduction sont sur les orbitales eg. C'est le cas pour les dichalcogénures en couches à métaux de transitions et 2H-AgNiO2 qui sont connus pour présenter des ordres de charge, un arrangement périodique des électrons sur le réseau. Les dichalcogénures en couches à métaux de transitions ont divers motifs, des ordres des charge commensurables et incommensurables, parmi eux, des ordres de charge à grande maille unité,comme le motif √13x√13 en étoile de David. 2H-AgNiO2 a un ordre de charge triple mais reste métallique.Dans le but de comprendre leurs ordres de charge, nous avons établi un modèle de Hubbard étendu multibandes et nous avons recentré notre intérêt sur les orbitales eg avec fortes interactions coulombiennes locales. À l'aide d'une approche en liaison forte et de considérations électrostatiques, puis grâce à la méthode de Hartree-Fock non restreinte, nous avons construit le diagramme de phases en fonction de la force des interactions coulombiennes, aussi bien locale qu'à courte portée, et nous avons fait évoluer la structure de bande en utilisant le ratio libre t'/t qui décrit la structure de bande dans les matériaux ayant des orbitales eg. Nous avons révélé un diagramme de phase riche avec plus de dix phases où certaines transitions peuvent être contrôlées par la structure de bande. En particulier, nous avons trouvé des phases pinball liquid, un ordre de charge métallique à trois sites par maille unité, où des charges localisées (pins) sont entourées de charges itinérantes (balls) sur un réseau hexagonal. Des ordres de charges à grande maille unité sont aussi stabilisés, tels que des ordres de charge et d'orbitale incommensurables et un ordre de charge √12x√12, qui rappelle le motif √13x√13 en étoile de David présent dans 1T-TaS2. Ces états électroniques s'avèrent génériques pour le réseau triangulaire demi rempli et sont aussi trouvés dans le cas isotrope, qui correspond au modèle de Hubbard étendu à une bande.Cependant, la méthode de Hartree-Fock non restreinte est problématique pou saisir les propriétés des phases lors d'une forte anisotropie de la structure de bande pour les états de Mott. Pour résoudre ce problème, nous avons établi un hamiltonien type Heisenberg à partir d'une théorie de perturbation. Ensuite, nous avons établit le diagramme de phases de ce nouvel hamiltonien en utilisant une approche classique et la diagonalisation exacte avec une analyse de symétries et l'algorithme de Lanczos pour un système de 24 sites. Mis à part les phases connues du modèle de Heisenberg en présence d'un champ magnétique, les configuration Y et V, le plateau 1/3, la phase ferro-orbitale, l'anisotropie de la structure de bande des orbitales eg conduit à d'autres ordres avec une composante τy ou τx et τz finies, différents ordres en bande et des ondes de densité d'orbitales. / Layered compounds are materials which exhibit charge order and novel phase of matter. This is the case in layered transition metal compounds, which have their band conduction on d-orbitals, a key ingredient to understand their electronic properties. We will focus in this dissertation on systems where the crystal-field splits orbitals into two degenerate subsets, t2g and eg, and where conduction electrons are on eg-orbitals. It is the case for layered transition-metal dichalcogenides and 2H-AgNiO2, which are known to exhibit charge orders, a periodic arrangement of electrons on the lattice. Layered transition-metal dichalcogenides have various pattern, incommensurate or commensurate insulating charge orders, among them large-unit cells charge orders. 2H-AgNiO2 have a charge order but is yet metallic.In order to investigate their charge orders, we derive a generic multiorbital extended Hubbard model and we refine our interest to eg-orbital with strong local Coulomb interactions. With a tight binding approach and electrostatic considerations, then the unrestricted Hartree-Fock method, we build the phase diagrams as a function of the strength of the Coulomb interactions, local and short-range, and we tun the band structure using the ratio $t'/t$ of the $e_g$-orbitals. We unravel a rich phase diagram with more than ten phases where some transitions can be controlled by the band structure. In particular, we found pinball liquid phases, metallic threefold charge orders where localized charges (pins) are surrounded by itinerant charges (balls) on a honeycomb lattice. Phases with large unit-cells are also stabilized, such as incommensurate charge and orbital orders and a √12x√12 charge order. These electronic states are generic for the half-filled triangular lattice and are also found in the isotropic limit, which corresponds to the single-band spinful extended Hubbard model.To capture the properties of phases with strong band structure anisotropy in the Mott state, that unrestricted Hartree-Fock fails to capture, we derived a Heisenberg-like Hamiltonian from perturbation theory. Then, we build the phase diagram of this new effective Hamiltonian using a classical approach and exact diagonalization with a symmetry analysis and Lanczos algorithm for a 24-site cluster. Apart from the known phases of the Heisenberg model in presence of a field, the Y and V configuration, the 1/3 plateau, the ferro-orbital phase, the anisotropy of the band structure of eg-orbitals leads to other ordering with finite τy or τx and τz components, different stripe orders and orbital density waves. We build a rich phase diagram from this new Hamiltonian.

A scheme, analogous to the linear combination of atomic orbitals (LCAO), is used to calculate rates of reactions for the fusion of nuclei con¯ned in molecules. As an example, the possibility of nuclear fusion in rotationally excited H2O molecules of angular momentum 1¡ is estimated for the p + p + 16O ! 18Ne¤(4:522; 1¡) nuclear transition. Due to a practically exact agreement of the energy of the Ne resonance and of the p + p + 16O threshold, the possibility of an enhanced transition probability is investigated. / Physics / M.Sc.

<p>A systematic study of trends in band gap and lattice energies for bare zinc oxide nanoparticles were performed by means of quantum chemical density functional theory (DFT) calculations and density of states (DOS) calculations. The geometry of the optimized structures and the appearance of their frontier orbitals were also studied. The particles studied varied in sizes from (ZnO)₆ up to (ZnO)₁₉₂.The functionalization of bare and hydroxylated ZnO surfaces with MPTMS was studied with emphasis on the adsorption energies for adsorption to different surfaces and the effects on the band gap for such adsorptions.</p>

The experimental section in this thesis was based on the work of Kanan, M.W, et al reported in Science in December of 2008. A catalyst containing cobalt and phosphate was synthesized and used to decompose water into oxygen and hydrogen. This was done at nearly neutral pH. Cyclic voltammetry was performed to analyze the catalyst’s efficiency. Some surfaces were analyzed in a scanning electron microscope and the elemental composition was determined using energy-dispersive X-ray spectroscopy. A catalytic effect was observed at a potential of about 1,3 V. EDX showed Co at some of the surfaces. Quantum calculations were used to develop a model for the catalyst material. Molecular orbitals, interaction energies and vibrational frequencies were calculated for two different complexes of Co and phosphate. Patrik Larses was responsible for the electrochemical evaluation and synthesis in the experimental section of this thesis and Lina Tegesjö for the computational part.

A systematic study of trends in band gap and lattice energies for bare zinc oxide nanoparticles were performed by means of quantum chemical density functional theory (DFT) calculations and density of states (DOS) calculations. The geometry of the optimized structures and the appearance of their frontier orbitals were also studied. The particles studied varied in sizes from (ZnO)6 up to (ZnO)192.The functionalization of bare and hydroxylated ZnO surfaces with MPTMS was studied with emphasis on the adsorption energies for adsorption to different surfaces and the effects on the band gap for such adsorptions.

Diese Arbeit beschäftigt sich mit den besonderen elektronischen Eigenschaften der Übergangsmetall-Aluminide. In Anlehnung an die Quasikristalle und ihre Approximanten zeigt sich, dass selbst Materialien mit kleinen Einheitszellen die gleichen überraschenden Effekte aufweisen. So gibt es unter den Übergangsmetall-Aluminiden auch semimetallische und halbleitende Verbindungen, auch wenn sie aus klassisch-metallischen Komponenten wie Fe, Al oder Cr bestehen. Diese Eigenschaften sind außerdem mit einem tiefen Pseudogap bzw. Gap in der Zustandsdichte und starken kovalenten Bindungen gekoppelt. Bindungen werden im Rahmen dieser Arbeit durch zwei wesentliche Eigenschaften beschrieben. Erstens durch die Bindungsladung und zweitens durch die energetische Auswirkung der Bindung. Es ergibt sich, dass im Fall halbleitender Übergangsmetall-Aluminide zum einen eine Sättigung von bestimmten Bindungen, wie auch ein bindungs-antibindungs-Wechsel bei der Fermi-Energie vorliegt. Mit der Analyse der Nahordnung in Form der sogenannten lokalen Koordinationspolyeder ist es gelungen, eine einfache Regel für Halbleiter aufzustellen, die Fünffachkoordination für Al. Diese Regel besagt, dass Aluminium-Atome mit ihren drei Valenzelektronen nicht in der Lage sind, mehr als fünf gesättigte Bindungen zu ihren nächsten Übergangsmetall-Nachbarn aufzubauen. In exzellenter Übereinstimmung mit den in Annahme gleichartiger Bindungen theoretisch vorhergesagten Bindungswinkel ergibt sich, dass alle binären Übergangs-Aluminid-Halbleiter für die Al-Atome die gleiche Nahordnung aufweisen. Typische Werte für spezifische Widerstände der untersuchten Materialien bei Raumtemperatur liegen im Bereich von einigen 100µOhm cm, was weit größer ist als einige 10µOhm cm wie im Fall der unlegierten Metalle. Überraschend ist außerdem eine hohe Transportanisotropie mit einem Verhältnis der spezifischen Widerstände bis zu 3.0. Eine wesentliche Errungenschaft der Arbeit kann in der Verknüpfung der Eigenschaft des elektronischen Transports und der Bindungseigenschaften gesehen werden. Die geringen Leitfähigkeiten konnten durch geringe Werte in der Zustandsdichte (DOS) und einem bei gleicher Energie stattfindenden bindungs-antibindungs-Wechsel erklärt werden.