Das Ziel dieser Doktorarbeit ist die Berechnung, aus ersten Prinzipien, von Niedrigenenergiekonstanten (NEK), welche die chirale Störungsheorie (ChST) parametrisieren, durch Simulationen auf dem Gitter. Diese Arbeit ist eine Pilotstudie und will deshalb nicht zu definitiven und präzisen quantitativen Vorhersagen führen, sondern wir möchten qualitative Leitlinien für zukünftige genauere Erforschungen der epsilon-Entwicklung der ChST geben. Letztere ist ein Gebiet in dem die chirale Symmetrie wiederhergestellt ist und wo die Compton-Wellenlänge der leichtesten Mesonen grösser als die lineare Dimension des endlichen Volumens ist. Die epsilon-Region ist weiterhin durch die wichtige Rolle der topologischen Ladung, nu, charakterisiert, so dass die Untersuchung der mesonischen Zweipunkt-Korrelationsfunktionen in definierten topologischen Sektoren vorzunehmen ist. Aus diesem Grunde haben wir chirale Fermionen auf dem Gitter simuliert, wobei der overlap Formalismus für den Dirac Operator, mit dem gewöhnliches Wilson Dirac Operator als Kern, in der quenched Approximation genommen wurde. Wir demonstrieren dass der Sektor mit neutraler topologischer Ladung, nu = 0, numerisch sehr schwierig zu untersuchen ist, weil die Daten von erheblichen Spitzen beeinflusst werden, die aufgrund sehr kleiner, nicht verschwindender Eigenwerte herrühren. Diese Beobachtung findet eine Übereinstimmung in einer Studie der Random Matrix Theory (RMT), die besagt, dass man eine Statistik von mehr als 10000 Konfigurationen benötigt, falls man auf kleine Eigenwerte empfindlich reagierende physikalische Grössen, im triviale topologische Sektoren simulieren möchte. Weniger Probleme ergeben sich in dem nicht-trivialen Sektoren |nu| > 0: wir präsentieren deshalb unsere Ergebnisse aus dem topologisches Sektor nu = 1 und den Daten aus das Sektor mit nu = 2 nur als Gegenprobe. Wir zeigen die Existenz einer unteren Schranke für das physikalisches Volumen bei V > 1 fm zur vierten Potenz für die Gültigkeit der ChST, übereinstimmend mit einer vorherigen Beobachtung aus der RMT. Wir beschränken deshalb unsere Untersuchung auf ein grösseres Gitter, wo wir die Daten des axialen Korrelators mit den Vorhersagen der ChST in der Valenzquark-Approximation fitten und eine stabile Bestimmung der gequenchten Pionen-Zerfallskonstante, F, erhalten. Die skalaren und pseudoskalaren Korrelationsfunktionen sind durch mehrere NEK parametrisiert. Dadurch ist der Vergleich mit den Vorhersagen der ChST schwieriger, und deshalb präsentieren wir nur einige Abschätzungen, die mit der entsprechenden Literatur verglichen werden. Zum Schluss präsentieren wir mögliche Implementierungen von verbesserten Algorithmen für die Inversion des overlap Operators, die die Simulationkosten reduzieren. / The aim of this thesis is the computation of Low Energy Constants (LEC) which parameterise Chiral Perturbation Theory (ChPT) from a first principles analysis via lattice simulations. The thesis provides a pilot study and will not give definitive and precise quantitative predictions, but rather our aim is to provide qualitative hints for future accurate investigations of the epsilon-expansion of ChPT, where chiral symmetry is restored and the Compton wavelength of the lightest meson is larger than the linear size of the finite volume. One of the property characterising the epsilon-regime is the important role played by the topological charge, nu, leading to the investigation of the two-point meson correlation functions in distinct topological sectors. To this end, we simulate chiral fermions on the lattice adopting the overlap formalism for the Dirac operator in the quenched approximation, with the kernel provided by the usual Wilson Dirac operator. We demonstrate that the neutral topological sector, nu = 0, is very difficult to explore numerically, as the data are affected by large spikes due to the presence of very small, non-zero eigenvalues. This observation is in agreement with a study of Random Matrix Theory (RMT), which indicates that a statistic of more than 10000 configurations is required when physical quantities sensitive to small eigenvalues are investigated in the neutral topological sector. Therefore, we present our results corresponding to the topological sector nu = 1. Due to the modest statistic, we only use the nu = 2 data as a crosscheck. We find a lower bound on the physical volume V > 1 fm to the four for ChPT to be used, in agreement with a previous observation using RMT. Restricting our attention to a larger lattice, we fit the data of the axial correlation function with the predictions of quenched ChPT, obtaining a stable determination of the quenched pion decay constant, F. The scalar and pseudoscalar correlation functions are parameterised by a larger number of LEC, rendering the comparison with ChPT predictions much more difficult and hence we present only some estimates that are compared with other determinations in the literature. Finally, we present possible implementations of improved algorithms used in the ``inversion'''' of the overlap operator, whose aim is to reduce the computational cost of the simulations.

L’ionomycine est un ionophore produit par la bactérie gram-positive streptomyces conglobatus. Sa synthèse représente un défi, car il possède plusieurs centres chiraux dans un motif polypropylène. De plus, la grande densité d’oxygène sur celui-ci oblige l’utilisation de plusieurs protections orthogonales. Notre stratégie divise l’ionomycine en quatre fragments, trois possédant le motif polypropylène, ainsi qu’un quatrième, bis-tétrahydrofuranne. Les trois premiers sont synthétisés en utilisant une méthodologie puissante développée dans le laboratoire du Pr Spino, qui utilise l’addition d’alkylcyanocuprates sur les carbonates allyliques dérivés de la menthone. Celle-ci permet l’introduction d’une unité propylène, avec un excellent contrôle du centre chiral introduit. Cette méthode est utilisée de manière itérative, afin d’introduire plusieurs unités propylènes. De plus, notre stratégie est hautement convergente, puisque des intermédiaires des fragments plus courts servent de produit de départ pour la synthèse des fragments plus longs. Le dernier fragment, bis-tétrahydrofuranne, a été fabriqué à partir de l’acétate de géranyle, par une polycyclisation d’un diépoxyde chiral, les époxydes ayant été introduits par une époxydation de Shi. Cette synthèse, si complétée, serait la plus courte publiée, avec 24 étapes pour la séquence linéaire la plus longue (51 au total).

Achiral wide bite angle ligands have been shown to be highly active and to induce excellent chemo- and regioselectivities in many homogeneously catalyzed reactions. However, only a few examples of chiral wide bite angle ligands are known so far. A diphenyl ether backbone was selected to allow maximum synthetic versatility and potential for a modular approach to design and synthesize such chiral diphosphorus ligands. Three synthetic strategies have been explored in this thesis: i) introduction of chiral substituents in the ligand backbone, ii) the use of P-stereogenic donor atoms and iii) the synthesis of chiral mixed-donor ligands bearing chiral auxiliary groups on the phosphorus atoms. Functionalization of the 3,3'-positions of 2,2'-bis(diphenylphosphino)diphenyl ether by carboxylic acid or ether auxiliaries was achieved via straightforward four-step routes to generate a library of ligands that were tested in various catalytic reactions. In the Pd-catalyzed asymmetric allylic alkylation of l,3-diphenyl-2-propenyl acetate and cyclohexyl-2-enyl acetate with dimethyl malonate the enantioselectivity was found to depend on the size of the chiral auxiliary introduced within the diphenyl ether backbone and its proximity to the phosphorus donor groups and hence to the active metal centre. Two types of mixed donor bidentate diphosphorus ligands based on the diphenylether backbone have been established, i.e. phosphine-phosphite and phosphine-phosphonite derivatives. A small ligand library bearing different chiral auxiliaries was accomplished via straightforward syntheses that enable derivatization of the respective phosphite and phosphonite moieties in the final step. In the Rh-catalysed hydrogenation of several benchmark substrates high conversion and moderate to high enantioselectivities (up to 97% for dimethyl itaconate) were obtained. The enantioselectivity was influenced by the size of the ortho-substituent on the chiral auxiliary group of the phosphite or phosphonite fragment. Two modular synthetic approaches for the preparation of novel wide bite angle diphosphine ligands containing stereogenic P-atoms have been developed. Both protocols involved diphenylether as backbone and the chiral ephedrine based precursor (2R[subscript(P)],4S[subscript(C)],5R[subscript(C)])-oxazaphospholidine borane as initial auxiliary to induce chirality at phosphorus. Various novel diphosphines were isolated as highly enantioenriched compounds with dr-ratios up to 95:5.

Aiming at a systematic inclusion of pseudoscalar and vector mesons as active degrees of freedom in an effective Lagrangian, studies have been performed in this thesis concerning the foundations of such an effective Lagrangian as well as tree-level and beyond-tree-level calculations. Hereby, vector mesons are described by antisymmetric tensor fields. First, an existing power counting scheme for both pseudoscalar and vector mesons is extended to include the pseudoscalar-meson singlet in a systematic way. Based on this, tree-level calculations are carried out which are in good agreement with the available experimental data and several processes are predicted. In particular, the ω-π0 transition form factor is in better agreement with experimental data than the prediction done in the vector-meson-dominance model. Furthermore, a Lagrangian with vector mesons is used together with the leading contributions of chiral perturbation theory in order to calculate tree-level reactions in the sector of odd intrinsic parity. It turns out that both the Lagrangian with vector mesons and the Lagrangian of chiral perturbation theory are needed to describe experimental data. Additionally, a feasibility check for one-loop calculations with pseudoscalar and vector mesons in the loop is performed. Thereby, only a limited number of interaction terms in the Lagrangian with vector mesons is used. The results are used to both renormalise the low-energy constants of chiral perturbation theory up to chiral order Q4 and to determine the influence of loops with vector mesons on masses and decay constants of pseudoscalar mesons.

Thesis (PhD)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Benzoxazoles are an important class of π-electron-excessive, benzene-fused heterocyclic compounds found in natural products and display a wide range of pharmacological applications. It is therefore a widely used starting scaffold for drug and agrochemical discovery programs. Other applications include: chiral auxiliaries in asymmetric reactions, chiral receptors for the resolution of racemic mixtures, fluorescent whitening dyes, various photochromic materials and as ligands for a wide range of catalytic reactions. Due to our interests in resorcinarenes, we came across 4-hydroxybenzoxazoles, a structural motif that has not been explored as potential asymmetric ligands. In this thesis it was attempted to investigate the synthesis, functionalisation and coordination chemistry of these compound class and finally look at a method of synthesising chiral 4-hydroxybenzoxazoles from amino acids. A small library of achiral 4-hydroxybenzoxazoles were synthesised in good yields. These compounds were then reacted with various transition metals, of which only the Pd-salts proved to return any usable compounds. The first structural evidence of the bonding of 4- hydroxybenzoxazoles was recorded from single crystal X-ray diffraction analysis of the coordination compounds that formed. Different coordination modes were recorded, depending on the ligand and the Pd-salt used. The PdCl2 compounds were also tested for catalytic activity with a Heck reaction, showing good conversions for the reaction between iodobenzene and styrene to form stilbene. Further examination pointed to the ligands playing an insignificant role in the reaction and the products possibly due to only the PdCl2’s reactivity. During this period it was also attempted to functionalise the phenol group with P(III) groups and repeat the coordination and catalytic studies. Efforts to synthesise these compounds were not successful, with oxidation of the P(III) to P(V) groups or degradation of these compounds. Efforts to synthesise these via phosphorous protection, utilising BH3 or the in situ trapping of the compounds with transition metals, were also not successful. During the trapping experiments the phosphinite and Pd-salt formed a re-arranged product that is a known and useful catalyst on its own. Finally a small library of chiral benzoxazoles and 4-hydroxybenzoxazoles were synthesised, starting from amino acids and utilising a Mitsunobu reaction to perform the ring closing. Antimicrobial tests with these compounds did not return any appreciable results. / AFRIKAANSE OPSOMMING: Bensoksasool is 'n belangrike klas van π-elektron-ryk, benseen-saamgesmelte heterosikliese verbindings wat in natuurlike produkte voorkom en 'n wye verskeidenheid van farmakologiese funksies vertoon. Dit is dus 'n baie algemene basis struktuur vir dwelm- en landbouchemiese ontdekkings programme. Ander gebruike sluit in: chirale ligande in asimmetriese reaksies, chirale reseptore vir die resolusie van rasemiese mengsels, fluoresserende verwittings kleurstowwe, verskeie fotochromiese materiaal en as ligande vir 'n wye verskeidenheid van katalitiese reaksies. As gevolg van ons belangstelling in resorsinarene, het ons op 'n strukturele motief afgekom wat nog nie ondersoek is as potensiële asimmetriese ligande nie, die 4- hidroksiebensoksasole. In hierdie tesis is gepoog om die sintese, funksionalisering en koördinasie chemie van hierdie klas verbindings te ondersoek en uiteindelik 'n metode te ontwikkel om die sintese van chirale 4-hidroksiebensoksasole vanaf aminosure te bewerkstellig. 'n Klein biblioteek van achirale 4-hidroksiebensoksasole was gesintetiseer in goeie opbrengste. Hierdie verbindings was toe behandel met verskeie oorgangsmetale, waarvan slegs die Pdsoute enige bruikbare verbindings gevorm het. Die eerste strukturele bewyse van die binding van die 4-hidroksiebensoksasole is aangeteken met behulp van enkelkristal X-straaldiffraksie ontleding van die koördinasieverbindings wat gevorm is. Verskillende koördinasie mode is aangeteken, afhangende van die ligand en die Pd-sout wat gebruik was. Die PdCl2 verbindings is ook vir katalitiese aktiwiteit met 'n Heck reaksie getoets. Die reaksie het baie goeie omskakeling gewys vir die reaksie tussen iodobenseen en stireen na stilbeen. Verdere ondersoeke het getoon dat die ligande nie ‘n beduidende rol in die reaksie speel nie en die produkte moontlik slegs as gevolg van die PdCl2 se reaktiwiteit is. Gedurende hierdie tydperk was daar ook probeer om die fenol groep met P(III) groepe te funksionaliseer. Met die uitgangstowwe sou die koördinering en katalitiese studies herhaal word. Pogings om hierdie verbindings te sintetiseer was nie suksesvol nie, met oksidasie van die P(III) na P(V) groepe of afbreking van hierdie verbindings. Pogings om dit te sintetiseer via fosfor beskermingstegnieke, deur gebruik te maak van BH3 of die in situ vasvang van die verbindings met oorgangsmetale, was ook nie suksesvol nie. Gedurende die vasvang eksperimente het die fosfien en PdCl2 ‘n herrangskikkings-produk gevorm wat op sy eie ‘n bekende en nuttige katalisator is. Ten slotte was 'n klein biblioteek van chirale bensoksasole en 4-hidroksiebensoksasole gesintetiseer, vanaf aminosure. Om die ringsluiting te bewerkstellig was ‘n Mitsunobu reaksie gebruik. Antimikrobiese toetse met hierdie verbindings het nie enige noemenswaardige resultate opgelewer nie.

The use of ionic liquids (ILs) as both reagents and solvents is widely recognised. ILs offer a number of advantages compared to regular molecular solvents. These advantages include: chemical and thermal stability, no measurable vapour pressure, no or lower toxicity, non-flammability, catalytic ability, high polarity and they can be recycled. There are a number of research groups investigating the various applications of this reaction medium and most studies have focused on solvents derived from the imidazolium cation. The use of the imidazolium-based ILs in the Diels-Alder reaction has been studied in detail and higher yields compared to conventional methods have been reported. The IL affects the rate and interesting selectivities have been observed. However, not much attention has been paid to the scope and limitations of phosphonium ILs (PILs). Therefore the focus of this thesis is the synthesis and application of novel chiral PILs as environmentally benign, task-specific solvents for the Diels-Alder reaction. In addition, this research seeks alternative ways to eliminate the use of toxic heavy metal catalysts and to exploit methodologies which reduce the energy consumption of the Diels-Alder reaction. A series of CILs were synthesised from the chiral pool and they were characterised by thermogravimetric analysis, differential scanning calorimetry and spectroscopy. They were then investigated as solvents and catalysts in the Diels-Alder reactions of a series of dienes (cyclopentadiene, isoprene, 2,3-dimethylbuta-1,3-diene, furan, pyrrole, N-methyl pyrrole) and dienophiles (methyl acrylate, methyl vinyl ketone, acrylonitrile, dimethyl maleate, acrolein, dimethylacetylene dicarboxylate, maleic anhydride and maleimide). Investigation of the effect of PILs in the presence of three heterogeneous catalysts Al2O3, SiO2 and K-10 montmorillonite were studied. Ultrasound and microwave-assisted Diels-Alder reactions in the PILs, in the absence and presence of the catalysts, were also studied. The reactions of these prototypical substrates illustrated that the solvents are indeed task-specific.

Vertex algebras and strongly homotopy Lie algebras (SHLA) are extensively used in qunatum field theory and string theory. Recently, it was shown that a Courant algebroid can be naturally lifted to a SHLA. The 0-product in the de Rham chiral algebra has an identical formula to the Courant bracket of vector fields and 1-forms. We show that in general, a vertex algebra has an SHLA structure and that the de Rham chiral algebra has a non-zero l4 homotopy.

<p>This thesis describes the use of 2H-azirines as reactivesubstrates in Lewis acid catalysed nucleophilic additions andin the Diels-Alder reaction.A number of carbon nucleophiles have been added to aseries of 2H-azirines in the presence and absence ofBF3·Et2O. 3-(2-Naphthyl)-2H-azirine has been used as amodel substrate in the enantioselective addition oforganolithium reagents to an 2H-azirine.A selection of Lewis acids has been screened for theirpossible use in the normal electron demand Diels-Alder reactionbetween 3-alkyl-, 3-aryl-, and 3- carboxyl-2H-azirines and avariety of dienes. Lewis acid activation was found to shortenreaction times and facilitate lower reaction temperatures.These cycloadditions proceeded with endo selectivity providinga single diastereoisomeric product.DFT calculations of Lewis acid activated 2H-azirineshave been carried out.</p><p><b>Keywords:</b>2H-azirines, Lewis acid activation, chiralligands, organolithium reagents, Diels-Alder reactions,DFT-calculations</p>

<p>This thesis deals with the synthesis and characterization ofnovel polyhydroxyl surfactants. The first part describes thesynthesis of a number of stereoisomers of a polyhydroxylsurfactant, and the second part concerns surface chemicalcharacterization.</p><p>A stereodivergent route for preparation of the hydrophilichead group was developed, featuring consecutive stereoselectivedihydroxylations of a diene. This afforded in total fourdifferent polyhydroxyl head groups. These surfactant headgroups were natural and unnatural sugar analogues, and wereused for the coupling with two different hydrophobic tailgroups.</p><p>Three of these surfactants were used to investigate thechiral discrimination in Langmuir monolayers at an air-waterinterface. The isotherms showed a remarkable difference incompressibility between surfactants of diastereomericrelationship and also a pronounced chiral discriminationbetween racemic and enantiomerically pure surfactants favoringheterochiral discrimination.</p>

This thesis describes the preparation and characterisation of a number of homochiral coordination and metallosupramolecular assemblies. These species were formed from the reaction of chiral pyridine and quinoline containing ligands and metal ions. The combination of traditional coordination chemistry and supramolecular interactions led to a range of polymeric and network structures being formed. The ligands used in this thesis can be divided into two broad categories: alkaloids and ligands derived from them, and amino acid-based ligands. In the first category three new ligands were synthesized, and a variety of routes towards alkaloid-based homochiral ligands were investigated. The second category focused on three ligand motifs, and resulted in the preparation of 16 ligands. These two categories of ligands were reacted with a range of metal salts to investigate their coordination and supramolecular chemistry. The structure of twenty complexes was determined by single crystal X-ray crystallography. The complexes had a range of structures, with discrete and polymeric species being formed. Hydrogen bonding was an important feature in the supramolecular chemistry of the complexes, playing a different role in different series of complexes. Two chiral coordination polymers and one chiral coordination network were synthesized. All three of these structures possessed directionality to some degree: in the coordination network and one of the polymers the directionality is counterbalanced by the opposite directionality being present in the crystal, while the second coordination polymer is generated by the screw axis present and has a high degree of overall directionality.