Dissertations / Theses on the topic 'Ketone system'

Diacetyl (2,3-butanedione) is an important flavour active, oxidative compound that has significant impact on cellular health as well as financial impact in industrial fermentations. The presence of diacetyl in certain fermented beverages, such as beer, results in an unpleasant butterscotch-like flavour and its concentration needs to be reduced by yeast to below the taste threshold prior to filtration and packaging. This results in significant process inefficiency. Furthermore, diacetyl negatively impacts cellular health and has been associated with neurodegenerative diseases and general cell aging amongst others. The reduction of this compound is therefore essential for cellular health.<br>Several yeast cell enzymatic mechanisms responsible for diacetyl reduction were identified and characterised, including Old Yellow Enzyme (OYE) isoforms and D-Arabinose Dehydrogenase (ARA1). OYE isoforms displayed different micromolar affinities and catalytic turnover rates for diacetyl and catalysed diacetyl reduction in a biphasic manner. ARA1 catalysed diacetyl reduction in a monophasic manner with a millimolar Michaelis constant.<br>Knowledge gained in these studies was applied in investigations of diacetyl production and reduction in industrial brewing operations and the enzymatic systems further exploited for the development of a novel enzyme based assay to determine diacetyl concentrations in beer samples. Concentrations as low as 0.2 muM were detectable with high repeatability.

This thesis deals with different optimization problems encountered in organic synthesis. The use of response surface, sequential simplex and PLS techniques, for simultanious optimization of yield and suppression of side reactions is investigated. This is illustrated by an example of enamine synthesis, were a side reaction was a serious problem. The problem of efficient screening to find suitable catalysts and solvents in new reactions is also investigated. Here, the use of principal properties as selection criterion, is demonstrated with a new process for the silylation of a,ß-unsaturated ketones. The extension of the new method to bis silylation of 1,2- and 1,3-diketones is demonstrated. The total synthesis of (±)-geosmin is investigated by an approach aimed to reduce the number of necessary steps involved. The suggested strategy, is to find compatible solvents through several transformations in the sequence to accomplish one-pot multistep reactions. In this context an improved method for the preparation of 1,10-dimethyl-l(9)-octalone-2 was established. Comparison with previously reported total syntheses of (±)-geosmin was done.<br>digitalisering@umu

Reliability of low-level operating-system (OS) code is an indispensable requirement. This includes functional properties from the safety-liveness spectrum, but also quantitative properties stating, e.g., that the average waiting time on locks is sufficiently small or that the energy requirement of a certain system call is below a given threshold with a high probability. This paper reports on our experiences made in a running project where the goal is to apply probabilistic model checking techniques and to align the results of the model checker with measurements to predict quantitative properties of low-level OS code.

Reliability of low-level operating-system (OS) code is an indispensable requirement. This includes functional properties from the safety-liveness spectrum, but also quantitative properties stating, e.g., that the average waiting time on locks is sufficiently small or that the energy requirement of a certain system call is below a given threshold with a high probability. This paper reports on our experiences made in a running project where the goal is to apply probabilistic model checking techniques and to align the results of the model checker with measurements to predict quantitative properties of low-level OS code.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2012.<br>In title on title-page, "[gamma]" appears as the lower-case Greek letter. Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 170-192).<br>This thesis explores the use of ensemble, free energy models in the study and design of molecular, biochemical systems. We use physics based computational models to analyze the molecular basis of binding affinity in the context of protein-protein and protein-ligand binding as well as reaction rate enhancement in enzyme catalysis. First, we evaluate the solvent screened energetics of immunoglobulin G (IgG):Fc[gamma] receptor binding using molecular mechanics, Poisson-Boltzmann surface area (MMPBSA) models. We assess the role IgG1 linked glycans play in binding to human Fc[gamma]-III and computationally evaluate experimentally designed Fe mutations that recover binding affinity in the absence of glycosylation. Using the insight gained from this study, we developed novel murine IgG variants with engineered Fc[gamma] receptor binding patterns via the computational design and experimental validation of Fc mutations that are predicted to knock out binding to Fc[gamma]R-IV. Our design and analysis highlight the importance of solvent screened electrostatic interactions and electrostatic complementarity in protein-protein binding. Second, we develop novel, ensemble methods to measure configurational free energy and entropy changes in protein-ligand binding and use it to predict the relative binding affinity of a series of previously designed HIV-1 protease inhibitors. We find that using configurational free energies to evaluate inhibitor efficacy significantly improves relative ranking of inhibitors over traditional, single-point energy metrics, but that only a relatively small number of low energy configurations are necessary to capture the ensemble effect. Finally, we present a joint study of the redesign and dynamic analysis of ketol-acid isomeroreductase (KARI). We first develop and apply a novel, end-point method to rationally design enzyme variants that reduce the free energy of activation, and present the computational and experimental analysis of a series of designed KARI mutants. Our analysis reveals that this transition-state theory based approach is effective at reducing the enthalpy of activation, but also increases entropic activation penalties that ultimately overpower the enthalpic gains. A dynamic analysis of these KARI variants is also presented, in which the transition path ensemble is explored using transition path sampling. We find that this ensemble approach is better able to predict relative enzyme activities and suggests a conserved, dynamic mechanism for catalysis. The results and analysis presented herein demonstrate novel, computational approaches to account for ensemble effects in the study and design of effective biomolecules.<br>by Nathaniel White Silver.<br>Ph.D.

Diabetic ketoacidosis (DKA) is a life-threatening condition that can appear in patients with diabetes. High ketones in the blood lead to acidity of the blood. For DKA diagnosis and management, ketones such as hydroxybutyrate (HB) can be used to quantify the severity of the disease. The fabrication of electrochemical biosensors for the detection of HB is attractive since their capability to deliver fast response, high sensitivity, good selectivity and potential for miniaturisation. In this thesis, an integrated electrode system was prepared for the detection of HB. Laser-induced graphene (LIG) with a 3D porous structure was used as the flexible platform. Poly (toluidine blue O) (PTB) was electro-deposited on LIG (PTB/LIG) under the optimised conduction (pH of 9.7 and from 0.4 to an upper cyclic potential of 0.8 V). The single PTB/LIG working electrode demonstrated excellent performance towards the detection of NADH with a linear range of 6.7 M to 3 mM using chronoamperometry, high sensitivity of detecting NADH and excellent anti-fouling ability (94 % response current retained after 1500 s). Further integration of the 3-electrode system realised the static amperometric detection of NADH over the range of 78 M to 10 mM. Based on the excellent performance of PTB/LIG to NADH sensing, hydroxybutyrate dehydrogenase was immobilised via encapsulation with chitosan and polyvinyl butyral (PVB) which was used for HB biosensing over the linear range of 0.5 M to 1 mM with NAD+ dissolved in solution. In addition, the co-immobilisation of NAD+ and HBD on PTB/LIG was conducted by optimisation of enzyme and NAD+ amount per electrode, which shows excellent reproducibility and satisfactory HB biosensing performance. Further experiments to improve the long-term stability of the enzyme electrode is expected in the future. The proposed integrated electrode system also possesses the potential to extend to a multichannel sensor array for the detection of multiple biomarkers (e.g. pH and glucose) for diagnosis and management of DKA.

In the vast realm of inorganic materials, the Cu2+-containing cuprates form one of the richest classes. Due to the combined effect of crystal-field, covalency and strong correlations, all undoped cuprates are magnetic insulators with well-localized spins S=1/2, whereas the charge and orbital degrees of freedom are frozen out. The combination of the spin-only nature of their magnetism with the unique structural diversity renders cuprates as excellent model systems. The experimental studies, boosted by the discovery of high-temperature superconductivity in doped La2CuO4, revealed a fascinating variety of magnetic behaviors observed in cuprates. A digest of prominent examples should include the spin-Peierls transition in CuGeO3, the Bose-Einstein condensation of magnons in BaCuSi2O6, and the quantum critical behavior of Li2ZrCuO4. The magnetism of cuprates originates from short-range (typically, well below 1 nm) exchange interactions between pairs of spins Si and Sj, localized on Cu atoms i and j. Especially in low-dimensional compounds, these interactions are strongly anisotropic: even for similar interatomic distances |Rij|, the respective magnetic couplings Jij can vary by several orders of magnitude. On the other hand, there is an empirical evidence for the isotropic nature of this interaction in the spin space: different components of Si are coupled equally strong. Thus, the magnetism of cuprates is mostly described by a Heisenberg model, comprised of Jij(Si*Sj) terms. Although the applicability of this approach to cuprates is settled, the model parameters Jij are specific to a certain material, or more precisely, to a particular arrangement of the constituent atoms, i.e. the crystal structure. Typically, among the infinite number of Jij terms, only several are physically relevant. These leading exchange couplings constitute the (minimal) microscopic magnetic model. Already at the early stages of real material studies, it became gradually evident that the assignment of model parameters is a highly nontrivial task. In general, the problem can be solved experimentally, using elaborate measurements, such as inelastic neutron scattering on large single crystals, yielding the magnetic excitation spectrum. The measured dispersion is fitted using theoretical models, and in this way, the model parameters are refined. Despite excellent accuracy of this method, the measurements require high-quality samples and can be carried out only at special large-scale facilities. Therefore, less demanding (especially, regarding the sample requirements), yet reliable and accurate procedures are desirable. An alternative way to conjecture a magnetic model is the empirical approach, which typically relies on the Goodenough-Kanamori rules. This approach links the magnetic exchange couplings to the relevant structural parameters, such as bond angles. Despite the unbeatable performance of this approach, it is not universally applicable. Moreover, in certain cases the resulting tentative models are erroneous. The recent developments of computational facilities and techniques, especially for strongly correlated systems, turned density-functional theory (DFT) band structure calculations into an appealing alternative, complementary to the experiment. At present, the state-of-the-art computational methods yield accurate numerical estimates for the leading microscopic exchange couplings Jij (error bars typically do not exceed 10-15%). Although this computational approach is often regarded as ab initio, the actual procedure is not parameter-free. Moreover, the numerical results are dependent on the parameterization of the exchange and correlation potential, the type of the double-counting correction, the Hubbard repulsion U etc., thus an accurate choice of these crucial parameters is a prerequisite. In this work, the optimal parameters for cuprates are carefully evaluated based on extensive band structure calculations and subsequent model simulations. Considering the diversity of crystal structures, and consequently, magnetic behaviors, the evaluation of a microscopic model should be carried out in a systematic way. To this end, a multi-step computational approach is developed. The starting point of this procedure is a consideration of the experimental structural data, used as an input for DFT calculations. Next, a minimal DFT-based microscopic magnetic model is evaluated. This part of the study comprises band structure calculations, the analysis of the relevant bands, supercell calculations, and finally, the evaluation of a microscopic magnetic model. The ground state and the magnetic excitation spectrum of the evaluated model are analyzed using various simulation techniques, such as quantum Monte Carlo, exact diagonalization and density-matrix renormalization groups, while the choice of a particular technique is governed by the dimensionality of the model, and the presence or absence of magnetic frustration. To illustrate the performance of the approach and tune the free parameters, the computational scheme is applied to cuprates featuring rather simple, yet diverse magnetic behaviors: spin chains in CuSe2O5, [NO]Cu(NO3)3, and CaCu2(SeO3)2Cl2; quasi-two-dimensional lattices with dimer-like couplings in alpha-Cu2P2O7 and CdCu2(BO3)2, as well as the 3D magnetic model with pronounced 1D correlations in Cu6Si6O18*6H2O. Finally, the approach is applied to spin liquid candidates --- intricate materials featuring kagome-lattice arrangement of the constituent spins. Based on the DFT calculations, microscopic magnetic models are evaluated for herbertsmithite Cu3(Zn0.85Cu0.15)(OH)6Cl2, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, as well as for volborthite Cu3[V2O7](OH)2*2H2O. The results of the DFT calculations and model simulations are compared to and challenged with the available experimental data. The advantages of the developed approach should be briefly discussed. First, it allows to distinguish between different microscopic models that yield similar macroscopic behavior. One of the most remarkable example is volborthite Cu3[V2O7](OH)2*2H2O, initially described as an anisotropic kagome lattice. The DFT calculations reveal that this compound features strongly coupled frustrated spin chains, thus a completely different type of magnetic frustration is realized. Second, the developed approach is capable of providing accurate estimates for the leading magnetic couplings, and consequently, reliably parameterize the microscopic Hamiltonian. Dioptase Cu6Si6O18*6H2O is an instructive example showing that the microscopic theoretical approach eliminates possible ambiguity and reliably yields the correct parameterization. Third, DFT calculations yield even better accuracy for the ratios of magnetic exchange couplings. This holds also for small interchain or interplane couplings that can be substantially smaller than the leading exchange. Hence, band structure calculations provide a unique possibility to address the interchain or interplane coupling regime, essential for the magnetic ground state, but hardly perceptible in the experiment due to the different energy scales. Finally, an important advantage specific to magnetically frustrated systems should be mentioned. Numerous theoretical and numerical studies evidence that low-dimensionality and frustration effects are typically entwined, and their disentanglement in the experiment is at best challenging. In contrast, the computational procedure allows to distinguish between these two effects, as demonstrated by studying the long-range magnetic ordering transition in quasi-1D spin chain systems. The computational approach presented in the thesis is a powerful tool that can be directly applied to numerous S=1/2 Heisenberg materials. Moreover, with minor modifications, it can be largely extended to other metallates with higher value of spin. Besides the excellent performance of the computational approach, its relevance should be underscored: for all the systems investigated in this work, the DFT-based studies not only reproduced the experimental data, but instead delivered new valuable information on the magnetic properties for each particular compound. Beyond any doubt, further computational studies will yield new surprising results for known as well as for new, yet unexplored compounds. Such "surprising" outcomes can involve the ferromagnetic nature of the couplings that were previously considered antiferromagnetic, unexpected long-range couplings, or the subtle balance of antiferromagnetic and ferromagnetic contributions that "switches off" the respective magnetic exchange. In this way, dozens of potentially interesting systems can acquire quantitative microscopic magnetic models. The results of this work evidence that elaborate experimental methods and the DFT-based modeling are of comparable reliability and complement each other. In this way, the advantageous combination of theory and experiment can largely advance the research in the field of low-dimensional quantum magnetism. For practical applications, the excellent predictive power of the computational approach can largely alleviate designing materials with specific properties.

Die Arbeit beschäftigt sich mit der Untersuchung der Beanspruchungen von Staurollenketten. Zunächst wurde in den Grundlagen der Aufbau von unterschiedlichen Staurollenkettenarten dargestellt, die Eigenschaften miteinander verglichen und kategorisiert. Aufbauend auf dem anschließend geschaffenen Verständnis der wirkenden Reibpaarungen bzw. -arten wurden FEM-Analysen durchgeführt, um dadurch auftretende Spannungen zu detektieren und das thermische Verhalten der unterschiedlichen Werkstoffpaarungen zu ermitteln. Innerhalb der praktischen Versuche der Arbeit kam es zur Ermittlung der Bruch- und Dauerfestigkeiten nach ISO15654 [DIN04]. Zur Untersuchung der Eigenschaften der Ketten unter praxisnahen Randbedingungen wurde ein Versuchsstand konzipiert, welcher die Ermittlung von Kennwerten zwei unterschiedlicher Kettengrößen unter härtesten Bedingungen ermöglicht. Durch diesen Versuchsstand wurden die Staukraft, die Kettenzugkraft durch das Drehmoment am Antrieb, die Kettengeschwindigkeit, die Kettenlängung und das Temperaturverhalten dauerhaft überwacht. Im letzten Kapitel der Arbeit wurde eine Überwachungsstation für unterschiedliche Baugrößen von Staurollenketten entwickelt und die Funktionsweise durch Versuche nachgewiesen<br>This dissertation is dealing with the investigation of the load behaviour of accumulation roller chains. Initially, the structures of different types of accumulation roller chains are described, properties are compared and categorised. Based on the created understanding of acting tribological pairing and friction mechanisms, FEM analysis have been performed to evaluate occurring stresses and determine the thermal behaviour of the various material combinations. Within the testing procedures, breaking strength and fatigue strength have been investigated in accordance with DIN ISO 15654 [cf. DIN04]. A test bench has been developed for practically relevant testing of the chains, where determination of characteristic values can be done under hard testing conditions for two different chain types. The test bench ensures measurement and survey of accumulation forces, tensile chain forces (by torque moment at drive), chain speed, chain elongation and chain temperature during whole testing time. The last chapter of the dissertation deals with the development of a 'control and monitoring unit' for accumulation roller chains with various dimensions including proof of function by trials

In der vorliegenden Arbeit werden mithilfe von Methoden zur numerischen Behandlung schwach besetzter Matrizen O(n³)- und O(n)-Berechnungsalgorithmen für Mehrkörpersysteme aus deren Bewegungsgleichungen abgeleitet. Durch Verwendung von Dualen Basen kann gezeigt werden, dass sich die bezüglich der Berechnungszeit effizienten Algorithmen sowohl auf Systeme mit explizit als auch implizit formulierten Bindungsgleichungen anwenden lassen. Mit diesen gewonnen Erkenntnissen wird die derzeitige Implementierung der vorgestellten Algorithmen im Sprachstandard Modelica untersucht. Es werden Ansatzmöglichkeiten aufgezeigt, mit denen ausgewählte Modelica Compiler große Mehrkörpersysteme effizienter lösen können. Zum einen wird durch eine graphentheoretische Verallgemeinerung des O(n)-Algorithmus dieser direkt in dem freien Modelica Werkzeug OpenModelica umgesetzt. Zum anderen wird die Methode der Subsysteme für den O(n)-Algorithmus vorgestellt. Sie ermöglicht es, beliebig komplexe Teilsysteme als eigenständige Modellelemente zu erstellen. Die Berechnung von kinematischen Schleifen kann auf diese Weise wesentlich beschleunigt werden. Ferner wird gezeigt, dass sich mit der Methode der Subsysteme Modellgleichungen eines idealen homokinetischen Gelenks ableiten lassen, die frei von Zwangsbedingungen sind. Dies führt ebenfalls zu einer schnelleren und robusteren Berechnung<br>Using methods from sparse matrice theory, O(n³)- and O(n)-algorithms for multibody systems are derived from the equations of motion. The concept of Dual Bases reveals that efficient algorithms for explicit joint descriptions, regarding calculation time, may also be applied to systems which use implicit joint constraints. Consequently, the feasibility of implementing these results in Modelica is examined. This leads to new approaches which enable selected Modelica compilers to solve large multibody systems more efficiently. On the one hand side a graph-theoretic generalization of the O(n)-algorithm has been implemented into the OpenModelica compiler. On the other hand, a method of subsystems for the O(n)-algorithm has been devised. It allows to derive the model equations for arbitrary complex sub-systems which can be implemented as new model elements for an O(n)-algorithm library. This has been carried out for recurring kinematic loops of Mobile Machinery improving simulation speed considerably. Furthermore, it is shown that a fast and robust model of an ideal constant velocity joint can be derived that way

碩士<br>中原大學<br>化學研究所<br>91<br>A shaker-flask type reduction of phenyl n-propyl ketone with yeast Saccharomyces cerevisiae or Candida utilis are performed in seven different kinds of volume ratio n-hexane/water biphasic solution. A commercialized Chiralcel OB column and a mobile phase of n-hexane/isopropanol/acetic acid (99.2/0.7/0.1, v/v/v) has been used for the separation and analysis of chiral products R- and S-1-phenyl- 1-butanol. In the biphasic culture with a low volume percentage of n-hexane, the product is S-1-phenyl-1-butanol enantiomeric excess. In the biphasic cultures of moderate to high volume percentage of n-hexane, the product is exclusive R-1-phenyl-1-butanol. In S. cerevisiae or C. utilis mediated biphasic culture reduction with a 2 L bench scale fermentor, the matrix interference subjected in the analysis of R- and S-1-phenyl-1-butanol cannot be eliminated by the chiral high-performance liquid chromatography with a single column of either the Chiralcel OB column or the Chiralpak AD column. The analysis of the chiral products in the fermentation system with single column also exhibits a long analysis time. However, the application of column switching technique can hyphenate the Chiralcel OB column and the Chiralpak AD column together to resolve not only the matrix interference but a reduction of the analysis time. This coupled column system for the chiral products analysis possesses high accuracy (a recovery rate > 98.6%) and high precision (RSD > 1.6%). The limits of detection of phenyl n-propyl ketone, R- and S-1-phenyl-1-butanol determined by the coupled column system for the UV detector are 9 ppb, 48 ppb and 84 ppb, respectively. This technique for the on-line sample clean-up and analysis of phenyl n-propyl ketone, R- and S-1-phenyl-1-butanol in the biphasic culture is successful. This technique is also helpful in the development of an analytical technique with liquid chromatography-mass spectrometry for chiral compounds. There are many factors affect the yeast mediated enantioselective prochiral ketone reduction with a 2 L bench scale fermentor such as that the yeast mediated reduction performed with the biphasic n-hexane/water culture of different volume ratio produces different enantiomeric excess chiral products, the addition of zinc ions in the aqueous medium can raise not only the enantiomeric excess value but the reaction yield, the change of pH for the reaction culture also influences the growth of yeast and the reduction of phenyl n-propyl ketone. We found that the yeast can be grown best at pH 7.0 and the reaction has a best enantiomeric excess value and a best yield at pH 5.0. The effect of pH is the same for both the reactions in single phase aqueous culture or the n-hexane/water biphasic culture of volume ratio 40/60. The S. cerevisiae mediated estrone reduction has been successfully proceeded to produce estradiol, however, the yield and the enantioselectivity of the reaction should be surveyed further.

碩士<br>國立清華大學<br>化學系<br>87<br>This thesis describes a modified Robinson annelation process, which facilitates the preparation of a,a-disubstituted b,g-unsaturated ketones of general type 19 with complete regiocontrol, and the application of this modification to the synthesis of the marine natural product nanaimoal (33). The modified Robinson annelation makes use of the lithium naphthalenide induced reductive alkylation of g-cyano a,b-unsaturated ketones 18 as the key step. This type of cyano enones can be readily prepared from the corresponding a-cyano ketones 17 using the conventional Robinson annelation procedure (i.e. Michael addition followed by aldol condensation). Treatment of cyano enones 18 with lithium naphthalenide followed by trapping of the ensuing enolates with a suitable alkylating agent gave rise to the corresponding enones 19, which can not be easily prepared by the conventional Robinson annelation reaction. Towards the synthesis of nanaimoal (33), the known dicyano aldehyde 58 was subjected to treatment with methylenetriphenyl-phosphorane to give cyano ketone 59 as a result of concomitant Wittig reaction and Thorpe-Ziegler cyclization. This compound was then converted to ketone 61, using the newly developed modification of the Robinson annelation reaction. Wolff-Kishner reduction of 61 gave the known diene 57, which had previously been converted to nanaimoal (33) in two steps. Thus, a formal total synthesis of the marine natural product has been achieved.

A tall tower flux measurement setup was established in metropolitan Houston, Texas, to measure trace gas fluxes from both anthropogenic and biogenic emission sources in the urban surface layer. We describe a new relaxed eddy accumulation system combined with a dual-channel gas chromatography - flame ionization detection used for volatile organic compound (VOC) flux measurements in the urban area, focusing on the results of selected anthropogenic VOCs, including benzene, toluene, ethylbenzene and xylenes (BTEX), and biogenic VOCs including isoprene and its oxidation products, methacrolein (MACR) and methyl vinyl ketone (MVK). We present diurnal variations of concentrations and fluxes of BTEX, and isoprene and its oxidation products during summer time (May 22 - July 22, 2008) and winter time (January 1 - February 28). The measured BTEX values exhibited diurnal cycles with a morning peak during weekdays related to rush-hour traffic and additional workday daytime flux maxima for toluene and xylenes in summer time. However, in winter time there was no additional workday daytime peaks due mainly to the different flux footprints between the two seasons. A comparison with different EPA National Emission Inventories (NEI) with our summer time flux data suggests potential underestimates in the NEI by a factor of 3 to 5. The mixing ratios and fluxes of isoprene, MACR and MVK were measured during the same time period in summer 2008. The presented results show that the isoprene was affected by both tail-pipe emission sources during the morning rush hours and biogenic emission sources in daytime. The observed daytime mixing ratios of isoprene were much lower than over forested areas, caused by a comparatively low density of isoprene emitters in the tower's footprint area. The average daytime isoprene flux agreed well with emission rates predicted by a temperature and light only emission model (Guenther et al., 1993). Our investigation of isoprene's oxidation products MACR and MVK showed that both anthropogenic and biogenic emission sources exist for MACR, while MVK was strongly dominated by a biogenic source, likely the isoprene oxidation between the emission and sampling points.

Benzophenone (BP) and substituted BPs constitute a major class of aromatic ketones and are of potential interest in various areas of excited state solution phase photochemistry and photobiology. High triplet state energy, faster rate of intersystem crossing (ISC) and higher triplet state quantum yield enables BP systems as potential photosensitizers via triplet energy transfer mechanism. The short lived triplet state of BP systems are highly reactive and acts as potential electron acceptor and interesting photochemical behavior have been observed for photoinduced electron transfer reactions in various solvent media, in particular for donor-bridgeacceptor (D-B-A) family. Though detailed spectroscopic studies of BP and substituted BP are documented, not much attention are given to its heterocyclic analogue. Substitution of aromatic ring carbon with one or more heteroatom (N and S) results in drastical change in photochemical properties and excited state reactivity. In solution phase and in nanosecond time domain heteroaromatic ketones form the triplet excited state that upon subsequent photoreactions, leads to formation of short lived species viz. radicals, ions and radical ions. Therefore exploring the trends in excited state reactivity with the variation with functional group and ring substitution and solvent medium is of considerable interest. The complete reaction mechanism of a photoreaction can be understood by studying reactivity of various short lived intermediates formed. In solution phase, the reactivity of a certain species or rate of a chemical reaction can be well understood by correlating to its structure. This approach requires accurate reproducible techniques for the excited state structural determination. Wide range of time resolved (TR) spectroscopies spanning over whole electromagnetic spectrum have been developed over decades and successfully applied to study excited state phenomena. In a typical two beam experiment, the pump pulse excites the molecular system to higher electronic state and the probe pulse records the spectrum of intermediate species at variable delay time with respect to the pump. The data from different TR techniques used to be complementary in nature and the combination helps in a deeper understanding of excited state reaction mechanism. Though time resolved absorption (TRA) is the most popular and oldest technique to study the excited state photoreactions, no structural information and the poor spectral resolution of the broad and overlapping absorption bands are the limitations towards predicting the reactive intermediates with accuracy. However time resolved resonance Raman (TR3) spectroscopy is a very sensitive technique to obtain vibrational structural information of short lived intermediates. The position and intensity of highly resolved Raman bands provide information about the structural and kinetics parameters respectively. From a set of Raman spectra along various delay time, structure of multiple intermediates evolved for parallel photoreactions can be predicted accurately. We have employed TRA, TR3 and density functional theoretical (DFT) calculation to address few fundamental questions about effect of solvent and ring substitution on the excited state structure and energetics of heterocyclic ketones, hence the reactivity. Comparing the experimental findings with the theoretical output not only makes the data more accurate but also several additional conclusions can be drawn that could not be performed only with the experimental modality. In chapter 1 of the thesis, we have presented a general summary of photophysical phenomena and measured properties and parameters of heterocyclic ketones. Typical photoreactions involving various related aromatic ketones obtained from literature are discussed. This is followed by a brief account of theory of resonance Raman spectroscopy and density functional theoretical calculation. The objectives of the present investigation are highlighted. The detailed assembly of experimental techniques employed for present investigation is discussed in chapter 2. The lasers, spectrometers, collection optics, detection systems and data collection and analysis procedures are briefly illustrated for individual set up. The theory of methods of DFT calculations is also discussed. The effect of substitution of N atom in the aromatic rings on excited state structure and reactivity (hydrogen abstraction reaction) for isomeric (2, 3, 4) benzoylpyridines (BzPy) in various solvents is studied using the above experimental and theoretical methodologies and is presented in Chapter 3. In neutral solvents viz. acetonitrile and carbon tetrachloride the photogenerated lowest triplet state (T1) is observed to be formed that follow monoexponetial decay. In the presence of hydrogen donating solvents like methanol and isopropanol the triplet state is found to undergo hydrogen abstraction reaction to form a ketyl radical and solvent radical. The lifetime and absorption and Raman features of triplet state and ketyl radicals are entirely different from each other and lack any overlapping characteristics. The observed enhanced reactivity of BzPy in comparison to BP is believed to be because of the introduction of the N hetero atom in one of the phenyl ring. From the theoretical data, it was clear that more planarity is attained in case of BzPy as compared to BP and contributes to the enhanced reactivity. The spin density calculation shows that one third of the spin is localized in the phenyl ring in case of BP. The total spin density on Phenyl ring is 0.62 and on carbonyl group is 1.45. In case of BzPy the spin density on phenyl ring is 0.45 and on carbonyl group is 1.59. This indicates that in the excited state the spin is localized more on the carbonyl group. Also from charge density calculation using DFT it is clear that in the triplet state of BzPy the oxygen atom of C=O group is more positive than in case of BP which makes it more electrophilic. Among the three isomeric BzPy the trend in charge density is dependent on the position of nitrogen and found to be in the order of 2-BzPy>3-BzPy>4-BzPy. This can be explained on the basis of -I and –M effect of N atom and the extent depends on its position. So the trend for case of photoreduction follows the order 2-BzPy>3-BzPy>4-BzPy. The hydrogen abstraction reaction used to be considerably fast that produces a substrate ketyl radical and solvent radical (donor radical). These radicals further can dimerise to form various photoproducts viz. Pinacols or can form a stable complex between them. The fate of the radicals formed as a result of hydrogen abstraction of 4-BzPy and the accurate characterization of the adduct is explained in Chapter 4. In the present case the cross coupling reaction of the radicals is observed at longer delay time to form a light absorbing transient (LAT) which is the dominant pathway over other parallel reactions. The exact position of the donor radical in the complex is predicted by correlating the experimental Raman bands and theoretically obtained structural parameters and vibrational frequency. The adduct formed as a result of cross coupling reaction was identified as p-LAT, 2-[4-(hydroxylpyridylmethylene)cyclohexa-2,5dienyl]propan-2-ol. In case of benzoylthiophenes (BzTh), the effect of substitution of S atom on the excited state structure and reactivity towards various hydrogen donors viz. phenol and indole in different solvents are presented in Chapter 5. The difference in rate and mechanism of photoreaction for both the hydrogen donors are compared. For TPK the T1 state is of ππ* character and the T2 state is of nπ* character as is confirmed by flash photolysis and low temperature phosphorescence spectra in EPA matrix. The CO bond length for the triplet state species is more than that of ground state. In case of the ππ* triplet prominent structural changes in thienyl ring are observed and the phenyl ring remains much unaltered. The reaction of the triplet state species with phenol in two different solvents shows a relatively faster rate of reaction. If only ππ* triplet has been taking part in reaction, it might have resulted in slow reaction rate. Because the reaction rate is fairly high, It is concluded that not only ππ* triplet is involved in reaction but there is a contribution from the little higher energy T2 state having nπ* character. The reactivity trends towards hydrogen transfer reaction for three isomeric dithienyl ketones with respect to the position of heteroatoms in the ring are presented in Chapter 6. Energetically close lying (ππ* and nπ*) triplet states are observed to undergo state switching with the change in position of heteroatom in the ring and thus define the characteristics of the triplet state and plays important role in predicting the reactivity trend. Brief summary of the present investigation along with important possible extensions of the present work in described in Chapter 7.

Benzophenone (BP) and substituted BPs constitute a major class of aromatic ketones and are of potential interest in various areas of excited state solution phase photochemistry and photobiology. High triplet state energy, faster rate of intersystem crossing (ISC) and higher triplet state quantum yield enables BP systems as potential photosensitizers via triplet energy transfer mechanism. The short lived triplet state of BP systems are highly reactive and acts as potential electron acceptor and interesting photochemical behavior have been observed for photoinduced electron transfer reactions in various solvent media, in particular for donor-bridgeacceptor (D-B-A) family. Though detailed spectroscopic studies of BP and substituted BP are documented, not much attention are given to its heterocyclic analogue. Substitution of aromatic ring carbon with one or more heteroatom (N and S) results in drastical change in photochemical properties and excited state reactivity. In solution phase and in nanosecond time domain heteroaromatic ketones form the triplet excited state that upon subsequent photoreactions, leads to formation of short lived species viz. radicals, ions and radical ions. Therefore exploring the trends in excited state reactivity with the variation with functional group and ring substitution and solvent medium is of considerable interest. The complete reaction mechanism of a photoreaction can be understood by studying reactivity of various short lived intermediates formed. In solution phase, the reactivity of a certain species or rate of a chemical reaction can be well understood by correlating to its structure. This approach requires accurate reproducible techniques for the excited state structural determination. Wide range of time resolved (TR) spectroscopies spanning over whole electromagnetic spectrum have been developed over decades and successfully applied to study excited state phenomena. In a typical two beam experiment, the pump pulse excites the molecular system to higher electronic state and the probe pulse records the spectrum of intermediate species at variable delay time with respect to the pump. The data from different TR techniques used to be complementary in nature and the combination helps in a deeper understanding of excited state reaction mechanism. Though time resolved absorption (TRA) is the most popular and oldest technique to study the excited state photoreactions, no structural information and the poor spectral resolution of the broad and overlapping absorption bands are the limitations towards predicting the reactive intermediates with accuracy. However time resolved resonance Raman (TR3) spectroscopy is a very sensitive technique to obtain vibrational structural information of short lived intermediates. The position and intensity of highly resolved Raman bands provide information about the structural and kinetics parameters respectively. From a set of Raman spectra along various delay time, structure of multiple intermediates evolved for parallel photoreactions can be predicted accurately. We have employed TRA, TR3 and density functional theoretical (DFT) calculation to address few fundamental questions about effect of solvent and ring substitution on the excited state structure and energetics of heterocyclic ketones, hence the reactivity. Comparing the experimental findings with the theoretical output not only makes the data more accurate but also several additional conclusions can be drawn that could not be performed only with the experimental modality. In chapter 1 of the thesis, we have presented a general summary of photophysical phenomena and measured properties and parameters of heterocyclic ketones. Typical photoreactions involving various related aromatic ketones obtained from literature are discussed. This is followed by a brief account of theory of resonance Raman spectroscopy and density functional theoretical calculation. The objectives of the present investigation are highlighted. The detailed assembly of experimental techniques employed for present investigation is discussed in chapter 2. The lasers, spectrometers, collection optics, detection systems and data collection and analysis procedures are briefly illustrated for individual set up. The theory of methods of DFT calculations is also discussed. The effect of substitution of N atom in the aromatic rings on excited state structure and reactivity (hydrogen abstraction reaction) for isomeric (2, 3, 4) benzoylpyridines (BzPy) in various solvents is studied using the above experimental and theoretical methodologies and is presented in Chapter 3. In neutral solvents viz. acetonitrile and carbon tetrachloride the photogenerated lowest triplet state (T1) is observed to be formed that follow monoexponetial decay. In the presence of hydrogen donating solvents like methanol and isopropanol the triplet state is found to undergo hydrogen abstraction reaction to form a ketyl radical and solvent radical. The lifetime and absorption and Raman features of triplet state and ketyl radicals are entirely different from each other and lack any overlapping characteristics. The observed enhanced reactivity of BzPy in comparison to BP is believed to be because of the introduction of the N hetero atom in one of the phenyl ring. From the theoretical data, it was clear that more planarity is attained in case of BzPy as compared to BP and contributes to the enhanced reactivity. The spin density calculation shows that one third of the spin is localized in the phenyl ring in case of BP. The total spin density on Phenyl ring is 0.62 and on carbonyl group is 1.45. In case of BzPy the spin density on phenyl ring is 0.45 and on carbonyl group is 1.59. This indicates that in the excited state the spin is localized more on the carbonyl group. Also from charge density calculation using DFT it is clear that in the triplet state of BzPy the oxygen atom of C=O group is more positive than in case of BP which makes it more electrophilic. Among the three isomeric BzPy the trend in charge density is dependent on the position of nitrogen and found to be in the order of 2-BzPy>3-BzPy>4-BzPy. This can be explained on the basis of -I and –M effect of N atom and the extent depends on its position. So the trend for case of photoreduction follows the order 2-BzPy>3-BzPy>4-BzPy. The hydrogen abstraction reaction used to be considerably fast that produces a substrate ketyl radical and solvent radical (donor radical). These radicals further can dimerise to form various photoproducts viz. Pinacols or can form a stable complex between them. The fate of the radicals formed as a result of hydrogen abstraction of 4-BzPy and the accurate characterization of the adduct is explained in Chapter 4. In the present case the cross coupling reaction of the radicals is observed at longer delay time to form a light absorbing transient (LAT) which is the dominant pathway over other parallel reactions. The exact position of the donor radical in the complex is predicted by correlating the experimental Raman bands and theoretically obtained structural parameters and vibrational frequency. The adduct formed as a result of cross coupling reaction was identified as p-LAT, 2-[4-(hydroxylpyridylmethylene)cyclohexa-2,5dienyl]propan-2-ol. In case of benzoylthiophenes (BzTh), the effect of substitution of S atom on the excited state structure and reactivity towards various hydrogen donors viz. phenol and indole in different solvents are presented in Chapter 5. The difference in rate and mechanism of photoreaction for both the hydrogen donors are compared. For TPK the T1 state is of ππ* character and the T2 state is of nπ* character as is confirmed by flash photolysis and low temperature phosphorescence spectra in EPA matrix. The CO bond length for the triplet state species is more than that of ground state. In case of the ππ* triplet prominent structural changes in thienyl ring are observed and the phenyl ring remains much unaltered. The reaction of the triplet state species with phenol in two different solvents shows a relatively faster rate of reaction. If only ππ* triplet has been taking part in reaction, it might have resulted in slow reaction rate. Because the reaction rate is fairly high, It is concluded that not only ππ* triplet is involved in reaction but there is a contribution from the little higher energy T2 state having nπ* character. The reactivity trends towards hydrogen transfer reaction for three isomeric dithienyl ketones with respect to the position of heteroatoms in the ring are presented in Chapter 6. Energetically close lying (ππ* and nπ*) triplet states are observed to undergo state switching with the change in position of heteroatom in the ring and thus define the characteristics of the triplet state and plays important role in predicting the reactivity trend. Brief summary of the present investigation along with important possible extensions of the present work in described in Chapter 7.

Transfer hydrogenation has been recognized to be an important synthetic method in both academic and industrial research to obtain valuable products including alcohols. Transition metal catalysts based on precious metals, such as Ru, Rh and Ir, are typically employed for this process. In recent years, iron-based catalysts have attracted considerable attention as a greener and more sustainable alternative since iron is earth abundant, inexpensive and non-toxic. In this work, a combination of iron disulfide with chelating bipyridine ligand was found to be effective for the transfer hydrogenation of a variety of ketones to the corresponding alcohols in the presence of a simple base. It provided a convenient and economical way to conduct transfer hydrogenation. A plausible role of sulfide next to the metal center in facilitating the catalytic reaction is demonstrated.

Acetylpropionyl (2,3-pentanedione) and diacetyl (2,3-butanedione) are by-products of sugar manufacture. Both diketones have many uses, mainly food related. Vapour-liquid equilibrium data and infinite dilution activity coefficients are required to design purification processes for these chemicals. A review of available experimental methods revealed that the vapour and liquid recirculating still is most appropriate when both isobaric and isothermal VLE are required. The low-pressure dynamic still of Raal and Muhlbauer (1998) used in this study incorporates many features to ensure that measurements are of excellent quality (as demonstrated by Joseph et al., 2001). VLE measurements were made for the following systems: • Acetone with diacetyl at 30 C, 40 C, 50 C and 40 kPa • Methanol with diacetyl at 40 C, 50 C, 60 C and 40 kPa • Diacetyl with 2,3-pentanedione at 60 C, 70 C, 80 C and 40 kPa • Acetone with 2,3-pentanedione at 50 C, 30 kPa and 40 kPa. All the systems, except for methanol with diacetyl, displayed close to ideal behaviour. This was expected as they are mixtures of ketones. Solution thermodynamics allows one to perform data reduction of the measured VLE data to ensure accurate extrapolation and interpolation of the measurements. Furthermore, the quality of the data can be judged using thermodynamic consistency tests. The data were represented by the Gamma-Phi approach to VLE (the preferred method for low-pressure VLE computations). The two-term virial equation of state was used to account for vapour phase non-ideality. Second virial coefficients were calculated by the method of Hayden and 0'Connell (1975). The liquid phase non-ideality was accounted for by the Wilson, NRTL or UNIQUAC models. The best fit models are proposed for each system, as are parameters as functions of temperature for the isobaric data. The data were judged to be of high thermodynamic consistency by the stringent point test (Van Ness and Abbott, 1982) and the direct test (Van Ness, 1995) for thermodynamic consistency. The data sets were rated, at worst, "3" on the consistency index proposed by Van Ness (1995). A rating of "I" is given for a perfectly consistent data set and "10" for an unacceptable data set. For the system acetone with 2,3-pentanedione, isobars at 30 kPa and 40 kPa were measured. The results from the reduction of the 30 kPa set were used to accurately predict the 40 kPa data set. Infinite dilution activity coefficients were measured by the inert gas stripping method (based on the principle of exponential dilution). In order to specify the appropriate dilutor flask height (to ensure equilibrium is achieved), mass transfer considerations were made. These computations ensured that the gas phase was in equilibrium with the liquid phase at the gas exit point. The following infinite dilution activity coefficients were measured: • Acetone in diacetyl at 30 C • Methanol in diacetyl at 40 C • Diacetyl in 2,3-pentanedione at 60°C • Acetone in 2,3-pentanedione at 50 C. The ketone mixtures, once again, displayed close to ideal behaviour.<br>Thesis (M.Sc.)-University of Natal, Durban, 2003.

The molecular identity of the green emission of polyfluorene is investigated in the view point of the molecular interactions between modeled segments. The semi-empirical quantum methods, ZINDO/S and AM1 (AM1-CIS), are used in combination to provide reasonable explanations for experimental spectroscopic properties of monodisperse fluorene oligomers and fluorene oligomers with a central keto defect in dilute solutions. Applying the same method, the molecular interactions between model segments are found to exist and are significant. However, the spectroscopic property change from the molecular interactions is negligible. In addition, the effects of mechanical stress and multi-defects on fluorene oligomers are investigated. On the other hand, the redox mechanisms proposed for the oxidation of an amphiphilic cyanine (C8S3) J-aggregates immobilized at ITO electrode and the subsequent dehydrogenated dimmer formation during cyclic voltammetry based on analysis of absorption spectra during the process are verified with the combined semi-empirical quantum methods similar to the previous methods. The absorption spectra assigned by experiment for electrochemical species involved in the proposed mechanism show reasonable match to the theoretically estimated absorption energies of the corresponding simplified model systems. In addition, the standard reduction potentials of the fairly large molecules, C8S3 monomer and its dehydrogenated dimer, are pursued with quantum mechanical calculations. The free energy difference between the oxidized and reduced states of the target systems is decomposed to electronic energy, solvation energy and temperature-dependent free energies terms. Based on AM1 ground state geometries and with the corresponding temperature dependent free energies, the electronic energies and the solvation energies are each evaluated by two different methods. The electronic energies are calculated with AM1 method and DFT calculation and, also, the solvation energies are obtained based on the atomic partial charges from AM1 and DFT wavefunctions with continuum dielectric solvent approximation. The four calculation schemes from the combinations of the electronic and solvation energy estimation methods are tested with the redox compounds with various molecular weights and the estimations are compared with the corresponding experimental redox potentials. The relative redox potentials between two different redox systems are found to be reasonably estimated with the four calculation schemes.<br>text

碩士<br>國立清華大學<br>化學系<br>91<br>This thesis describes the application of a palladium(II) acetate mediated annulation reaction recently discovered in our laboratories toward the construction of bridged systems bearing an exocyclic carbon-carbon double. A series of cyclic α-cyano ketones bearing a suitably positioned tethered terminal carbon-carbon double bond (i.e. 86, 88, and 97) were readily synthesized from commercially available starting materials and, upon treatment with palladium(II) acetate, gave the bridged bicyclic products 120, 122, and 124, respectively. Interestingly, α-cynoketone 114, upon exposure to the same reaction conditions, did not give the expected bridged bicyclic product but dihydrofuranyl compound 126.

The development of the interrupted Nazarov cyclization of allenyl vinyl ketones is presented. The intermediate oxyallyl cation, derived from an allenyl vinyl ketone, may be trapped efficiently by a divergent array of nucleophilic species generating functionalized cyclopent-2-enone products. Allenyl vinyl ketones are also a versatile source of cyclic molecules via a tandem reaction sequence terminated via reaction with acyclic dienes, cyclic dienes, aza-heterocycles, electron-rich alkenes, or styrenes by the formation of an additional ring by a [4 + 3] and/or [3 + 2] cyclization or by the formation of one additional carbon-carbon bond. The bicyclic compounds generated by these processes are densely substituted, and would be difficult to access as succinctly in other ways. The products of these interrupted Nazarov reactions generally reflect excellent regio- and stereoselectivity in the trapping reaction. In some instances, equilibrating conditions were shown to enhance the proportion of one product at the expense of another or to provide a different carbon skeleton. This process appears fairly general, and can be conducted with unsubstituted or alkyl, aromatic, or heteroaromatic allenyl vinyl ketones. The exceptional affinity of allenyl vinyl ketones to undergo interrupted Nazarov reactions is likely a result of the increased longevity of the intermediate oxyallyl cation, due in part to the increased resonance stabilization provided by the allene unit. The high regioselectivity noted in the trapping process was computationally and experimentally confirmed to be a result of a localization of the positive charge in the intermediate oxyallyl cation. The application of this recently developed methodology towards the synthesis of the natural product (+)-roseadione is also described. The tandem Nazarov/[4 + 3] cascade of allenyl vinyl ketones provides a unique manner in which to access the tricyclic core of this cyclooctanoid natural product, a molecule which, to date, has never been synthesized.

博士<br>國立臺灣科技大學<br>化學工程系<br>98<br>Abstract In this study, an isothermal titration type calorimeter was installed to measure excess enthalpies(HE) for eighteen pairs of binary systems. The operating condition was fixed at 298.15 K (25℃) / 1.013 bar (1 atm). The binary systems contain 2-octanone, 3-octanone, 2-decanone, valeric anhydride, hexanoic anhydride or dipentyl ether + n-alkanes, where the alkanes include one of following three long chain paraffins: n-dodecane, n-tetradecane and n-hexadecane. The excess enthalpies are all positive, indicating that the mixing processes are all endothermic. The excess enthalpies vary symmetrically with the mole fraction of constituent components. The experimental values of the systems containing dipentyl ether are apparently greater than those of other systems. The correlated results of the modified Redlich-Kister equation are satisfactorily well with the average deviation to be about within the experimental uncertainty. In addition to the modified Redlich-Kister equation, three equations of state: Peng-Robinson (PR), Patel-Teja (PT) and Cubic Chain-of-Rotators (CCOR), and two solution theory models: Wilson and NRTL models were used to correlate excess enthalpy data. The correlated results from the PR and the PT equations of state are not adequate, except for the dipentyl ether-containing systems. The CCOR2, which adopted two binary interaction parameters in the mixing rules, improved the correlated results from the CCOR1. The Wilson model has an inherent upper limit, 800 (J．mol-1), for HE. It can only be applicable to the systems containing dipentyl ether whose values of HE are sufficient small . Among all the studied models, the NRTL gave the best results, except for the anhydride-containing systems; where the correlated results were better than other equations of state and solution theory models.

碩士<br>國立中興大學<br>化學系所<br>106<br>The novel bis-N-heterocyclic carbene salt 27 used in this study was easy to prepare. The bis-NHC–Pd catalytic system derived from the salt 27 with Pd(OAc)2 in situ can catalyze the reaction in the air and the aqueous phase. In this study, the transfer hydrogenation of aldehydes and ketones was performed in the presence of 5.0 mol% of salt 27 and Pd(OAc)2 when potassium formate (4.0 equiv.) was used as the hydrogen source and EtOH or DMF as a solvent at 80 °C. The corresponding primary or secondary alcohols were obtained in good yields. In addition, the aldehydes reacted with alcohols to obtain the corresponding esters when potassium formate (1.2 equiv.) was used in moderate yield. However, the oxidation of aldehydes raised to form the corresponding carboxylic acid in the presence of 1.0 mol% bis-NHC–Pd catalytic system in good yields. It is worth noting that the oxidation of 4-(trifluoromethyl)-benzaldehyde still gave in good yield when the loading of the catalytic system was reduced to 0.001 mol% from 1.0 mol%. The turnover number (TON) is up to 34000 and the turnover frequency (TOF) is 1417 h-1. In this study, the reduction and oxidation of aldehydes can be successfully catalyzed by the bis-NHC–Pd catalytic system at 80 °C. When a polar organic solvent such as dimethylformamide or ethanol is used, the aldehydes can be reduced to alcohols. The aldehydes can be oxided to carboxylic acid when water is used as the solvent. In addition, these catalytic reactions are completely operated in air. The aldehydes or ketones containing various functional groups, such as olefins, halogen, methoxy, cyano, ketones, are tolerated in the presence of bis-NHC–Pd catalytic system. The oxidations of aldehydes occur at mild temperature and can be carried out with 0.01 mol% loading of the bis-NHC–Pd catalytic system, even on a gram scale. The generality of these methodologies gives it operational simplicity and the potential for use on an industrial scale.

The thesis entitled "Structure and reactivity in bridged polycyclic systems: cis-trans enantiomerism, fulvene cycloadditions and crystallographic studies of bridgehead β-ketoacids " consists of two parts. Part I contains 3 chapters, and deals with cycloaddition reactions of 6-arylfulvenes with maleic anhydride and nitrones (The products in the case of maleic anhydride display cis-trans enantiomerism). Part II contains 2 chapters, and deals with resolution of racemic primary amines, racemic amino acids and the relative decarboxylation propensities of bicyclic β-ketoacids in solid state. Part I Chapter 1: A new case of the uncommon cis-trans enantiomerism is presented in the Diels-Alder cycloadducts (3 & 4) of 6-arylfulvenes (1) with maleic anhydride (2).1 The resolution of the cis-trans enantiomers were accomplished via the formation of diastereomeric imides 6 and 7 with (1S)-(naphth-1-yl)ethylamine (5), and their subsequent hydrolysis and recyclisation (Scheme 1). The enantiomers 3 and 4 were characterized spectrally, polarimetrically (including CD) and by chiral HPLC. The chiral anhydrides were also stereospecifically converted to the corresponding imides by treatment with aq. ammonia in excellent yields. The crystal structure of one of the diastereomeric imides (derived from 6-phenylfulvene) was determined, and based on the known S configuration of the naphthylethylamine moiety, the configurations of the original anhydride adducts could be assigned.2 Scheme 1 Chapter 2: In this chapter tricyclic imides (8a-c) were prepared by Diels-Alder reaction of 6-arylfulvenes (1a-c) and maleic anhydride (2),2 followed by treatment with aq. NH3. The exo isomers were found to exist as conglomerates when the aryl group was p-tolyl or p-anisyl (although not phenyl). Triage of the p-tolyl racemate (Scheme 2), followed by reaction with p-toluenesulphonyl chloride in CH2Cl2/Et3N, led to the crystalline enantiopure N-tosylimides 9 (These were also found to be conglomerates). X-ray diffraction analysis of the N-tosylimides (9) via the anomalous dispersion technique led to the assignment of the absolute configurations (as either E or Z).3, 4 The original p-tolyl imide enantiomers were found to racemise upon UV irradiation in CHCl3. Based on this, a possible second order asymmetric transformation under photochemical conditions was attempted, and indeed led to the isolation of crystalline imide with a small ee (~15%).5 Scheme 2 Chapter 3: This chapter deals with the fulvene-nitrone cycloadditions. The possibility of discovering examples of the rare (6π + 4π) cycloaddition prompted an exploration of the reaction between electron-rich nitrones and pentafulvenes. In previous reports of such cycloadditions, diazomethane or benzonitrile oxide was used as 4π component.6 Building on previous work from this laboratory,7 the reaction between a set of substituted fulvenes and electron rich nitrones were studied. Theoretical calculations indicate that the (6π + 4π) mode would be favored when the fulvene-nitrone cycloaddition is controlled by the LUMO (fulvene) – HOMO (nitrones) interaction.8 Electron withdrawing groups on the fulvene would lower the LUMO and facilitate the above orbital interaction. Therefore the reaction between electron poor fulvenes and nitrones was taken up for further study. In particular, fulvene (10) was reacted with nitrones (11). However, only a (2π + 4π) mode was observed, involving one of the endocyclic double bond of the fulvene, in moderate yields (Scheme 3). Structures of these adducts were assigned based on NMR and X-ray crystal structure determination. The failure to observe the (6π + 4π) mode (14) is intriguing, and it is not clear whether this is due to electronic or steric reason. Scheme 3 Part II Chapter 1 describes the resolution of racemic primary amines and racemic amino acids (16) via the formation of diastereomeric imides. For this purpose D-camphoric anhydride (15) was chosen as the chiral auxiliary for the following reasons: it is of low-molecular weight with a rigid backbone, and is also easily prepared and purified.9 Primary amine (16) was treated with D-camphoric anhydride (15) in presence of CHCl3/DCC to form the corresponding diastereomeric imides 17 and 18. (In the case of amino acids, the corresponding methyl esters were treated with D-camphoric anhydride (15) in presence of triethylamine in chloroform). The resulting diastereomeric imides 17 and 18 were separated by silica gel column chromatography (Scheme 4), and hydrolyzed to the chiral amines (or amino acids). (The by-produced camphoric acid could be reconverted to D-camphoric anhydride (15). Scheme 4 Chapter 2: The relative ease with which β-ketoacids tend to lose CO2 is intriguing and has been the focus of numerous mechanistic studies.10-12 It is generally believed that the decarboxylation of β-ketoacids occurs via a six-centered hydrogen bonded transition state (19), which leads to the formation of the enol tautomer (20) of the final ketone product (Scheme 5). Scheme 5 Scheme 6 The initial formation of the enol is apparently supported by the high thermal stability of bicyclic β-ketoacids, in which the carboxylic acid functionality is at bridgehead. In these the formation of the enol would be disfavored by Bredt’s rule, which forbids the formation of a double bond at the bridgehead (particularly in the smaller bicyclic compounds). Also, it may be expected that these trends would be manifested in the ground state. This is because there would be a stereoelectronic requirement for the decarboxylation reaction, by which the bond to the carboxylic group would need to be parallel to the C=O π bond of the keto group. Therefore, it was of interest to study the crystal structures of suitable β-ketoacids in the hope of evidencing the above structural trends (Structure for the analogs 21-23 have been reported previously (Scheme 6)).13-15 In fact, the approach pioneered by Dunitz was of particular interest in this regard. 16 In this approach crystal structures of a series of analogs were studied; these analogs possess varying degrees of strain that could be considered as leading to the transition state of a certain reaction. The bond length and related data are then employed to ‘map’ the reaction dynamics. Compound Bond* lengths (Å) Increase in the bond length compared to ketopinic acid (%) Decarboxylation temp.17 * fine bond at the bridgehead to the COOH group. In the case of the decarboxylation of β-ketoacids, a correlation between the lengthening of the bond to the COOH group and the ease of decarboxylation was sought. Therefore the set of analogs 24-26 were prepared (Scheme 6) and their crystal structures determined by X-ray diffraction (at 100K). In the case of 26, an increase of 2.47% relative to 21 in the Cα-COOH bond length was observed. However, no evidence for an intramolecular O=C-O-H…O=C H-bonding, was observed in the crystal structures of 24-26. Instead, the COOH moieties were seen to participate in intermolecular O-H…O hydrogen bonding via the well known carboxylic acid dimer motif. The β-ketoacids were also converted into their corresponding S-benzylisothiouronium salts (Scheme 6), to study the effect of destroying the COOH dimer motif. The salts 27 and 28 could be obtained in a form suitable for single crystal X-ray diffraction. The crystal structures revealed an increase in the Cα-COO- bond length to an extent of 1.97% in case of 28 relative to 27. Also, there is an increase in the relevant bond length of ~0.8% on going from 24 (m.p. 145 °C) to 26 (m.p. 132 °C). Note also that these compounds melts with decompositions. Therefore, it appears that the ease of decarboxylation of these analogs is reflected in the relative lengthening of the bond to the COOH group. Thus, this study represents an application of the Dunitz crystallographic approach to reaction dynamics,16 to the case of the decarboxylation of β-ketoacids.(For structural formula pl see the pdf file)

The thesis entitled "Structure and reactivity in bridged polycyclic systems: cis-trans enantiomerism, fulvene cycloadditions and crystallographic studies of bridgehead β-ketoacids " consists of two parts. Part I contains 3 chapters, and deals with cycloaddition reactions of 6-arylfulvenes with maleic anhydride and nitrones (The products in the case of maleic anhydride display cis-trans enantiomerism). Part II contains 2 chapters, and deals with resolution of racemic primary amines, racemic amino acids and the relative decarboxylation propensities of bicyclic β-ketoacids in solid state. Part I Chapter 1: A new case of the uncommon cis-trans enantiomerism is presented in the Diels-Alder cycloadducts (3 & 4) of 6-arylfulvenes (1) with maleic anhydride (2).1 The resolution of the cis-trans enantiomers were accomplished via the formation of diastereomeric imides 6 and 7 with (1S)-(naphth-1-yl)ethylamine (5), and their subsequent hydrolysis and recyclisation (Scheme 1). The enantiomers 3 and 4 were characterized spectrally, polarimetrically (including CD) and by chiral HPLC. The chiral anhydrides were also stereospecifically converted to the corresponding imides by treatment with aq. ammonia in excellent yields. The crystal structure of one of the diastereomeric imides (derived from 6-phenylfulvene) was determined, and based on the known S configuration of the naphthylethylamine moiety, the configurations of the original anhydride adducts could be assigned.2 Scheme 1 Chapter 2: In this chapter tricyclic imides (8a-c) were prepared by Diels-Alder reaction of 6-arylfulvenes (1a-c) and maleic anhydride (2),2 followed by treatment with aq. NH3. The exo isomers were found to exist as conglomerates when the aryl group was p-tolyl or p-anisyl (although not phenyl). Triage of the p-tolyl racemate (Scheme 2), followed by reaction with p-toluenesulphonyl chloride in CH2Cl2/Et3N, led to the crystalline enantiopure N-tosylimides 9 (These were also found to be conglomerates). X-ray diffraction analysis of the N-tosylimides (9) via the anomalous dispersion technique led to the assignment of the absolute configurations (as either E or Z).3, 4 The original p-tolyl imide enantiomers were found to racemise upon UV irradiation in CHCl3. Based on this, a possible second order asymmetric transformation under photochemical conditions was attempted, and indeed led to the isolation of crystalline imide with a small ee (~15%).5 Scheme 2 Chapter 3: This chapter deals with the fulvene-nitrone cycloadditions. The possibility of discovering examples of the rare (6π + 4π) cycloaddition prompted an exploration of the reaction between electron-rich nitrones and pentafulvenes. In previous reports of such cycloadditions, diazomethane or benzonitrile oxide was used as 4π component.6 Building on previous work from this laboratory,7 the reaction between a set of substituted fulvenes and electron rich nitrones were studied. Theoretical calculations indicate that the (6π + 4π) mode would be favored when the fulvene-nitrone cycloaddition is controlled by the LUMO (fulvene) – HOMO (nitrones) interaction.8 Electron withdrawing groups on the fulvene would lower the LUMO and facilitate the above orbital interaction. Therefore the reaction between electron poor fulvenes and nitrones was taken up for further study. In particular, fulvene (10) was reacted with nitrones (11). However, only a (2π + 4π) mode was observed, involving one of the endocyclic double bond of the fulvene, in moderate yields (Scheme 3). Structures of these adducts were assigned based on NMR and X-ray crystal structure determination. The failure to observe the (6π + 4π) mode (14) is intriguing, and it is not clear whether this is due to electronic or steric reason. Scheme 3 Part II Chapter 1 describes the resolution of racemic primary amines and racemic amino acids (16) via the formation of diastereomeric imides. For this purpose D-camphoric anhydride (15) was chosen as the chiral auxiliary for the following reasons: it is of low-molecular weight with a rigid backbone, and is also easily prepared and purified.9 Primary amine (16) was treated with D-camphoric anhydride (15) in presence of CHCl3/DCC to form the corresponding diastereomeric imides 17 and 18. (In the case of amino acids, the corresponding methyl esters were treated with D-camphoric anhydride (15) in presence of triethylamine in chloroform). The resulting diastereomeric imides 17 and 18 were separated by silica gel column chromatography (Scheme 4), and hydrolyzed to the chiral amines (or amino acids). (The by-produced camphoric acid could be reconverted to D-camphoric anhydride (15). Scheme 4 Chapter 2: The relative ease with which β-ketoacids tend to lose CO2 is intriguing and has been the focus of numerous mechanistic studies.10-12 It is generally believed that the decarboxylation of β-ketoacids occurs via a six-centered hydrogen bonded transition state (19), which leads to the formation of the enol tautomer (20) of the final ketone product (Scheme 5). Scheme 5 Scheme 6 The initial formation of the enol is apparently supported by the high thermal stability of bicyclic β-ketoacids, in which the carboxylic acid functionality is at bridgehead. In these the formation of the enol would be disfavored by Bredt’s rule, which forbids the formation of a double bond at the bridgehead (particularly in the smaller bicyclic compounds). Also, it may be expected that these trends would be manifested in the ground state. This is because there would be a stereoelectronic requirement for the decarboxylation reaction, by which the bond to the carboxylic group would need to be parallel to the C=O π bond of the keto group. Therefore, it was of interest to study the crystal structures of suitable β-ketoacids in the hope of evidencing the above structural trends (Structure for the analogs 21-23 have been reported previously (Scheme 6)).13-15 In fact, the approach pioneered by Dunitz was of particular interest in this regard. 16 In this approach crystal structures of a series of analogs were studied; these analogs possess varying degrees of strain that could be considered as leading to the transition state of a certain reaction. The bond length and related data are then employed to ‘map’ the reaction dynamics. Compound Bond* lengths (Å) Increase in the bond length compared to ketopinic acid (%) Decarboxylation temp.17 * fine bond at the bridgehead to the COOH group. In the case of the decarboxylation of β-ketoacids, a correlation between the lengthening of the bond to the COOH group and the ease of decarboxylation was sought. Therefore the set of analogs 24-26 were prepared (Scheme 6) and their crystal structures determined by X-ray diffraction (at 100K). In the case of 26, an increase of 2.47% relative to 21 in the Cα-COOH bond length was observed. However, no evidence for an intramolecular O=C-O-H…O=C H-bonding, was observed in the crystal structures of 24-26. Instead, the COOH moieties were seen to participate in intermolecular O-H…O hydrogen bonding via the well known carboxylic acid dimer motif. The β-ketoacids were also converted into their corresponding S-benzylisothiouronium salts (Scheme 6), to study the effect of destroying the COOH dimer motif. The salts 27 and 28 could be obtained in a form suitable for single crystal X-ray diffraction. The crystal structures revealed an increase in the Cα-COO- bond length to an extent of 1.97% in case of 28 relative to 27. Also, there is an increase in the relevant bond length of ~0.8% on going from 24 (m.p. 145 °C) to 26 (m.p. 132 °C). Note also that these compounds melts with decompositions. Therefore, it appears that the ease of decarboxylation of these analogs is reflected in the relative lengthening of the bond to the COOH group. Thus, this study represents an application of the Dunitz crystallographic approach to reaction dynamics,16 to the case of the decarboxylation of β-ketoacids.(For structural formula pl see the pdf file)

First section of chapter 1 deals with gold catalyzed synthesis of ring fused furo[3,2,b]pyrans and furo[3,2,b]furans. Furo[3,2,b]pyrans and furo[3,2,b]furans are ubiquitous structural segments found in a number of natural products including polyether containing marine toxins. Synthesis of furo[3,2,b]pyrans 2a was accomplished from the bis-propargyl ethers 1a, while the synthesis of furo[3,2,b]furans 2b was accomplished from the prenyl propargyl ethers 1b. Scheme 1: Synthesis of furo[3,2,b]pyrans and furo[3,2,b]furans Second section of chapter 1 describes an unusual ring-contraction rearrangement route to functionalized 2,8-oxymethano-bridged di and triquinane. During the course of investigations concerning the total synthesis of 6-oxabicyclo[3.2.1]octane framework containing natural products, an unusual ring-contraction rearrangement sequence was observed in the reaction of 5-substituted 1-methyl-4-isopropenyl-6-oxabicyclo[3.2.1]octan-8-ones 4 to the 2,8-oxymethano-bridged diquinanes 5. The reaction was further demonstrated in the synthesis of triquinane 7 framework. Scheme 2: Synthesis of functionalized di and triquinane In third section of chapter 1 gold catalyzed synthesis of isochromanones and isoquinolones from suitable substituted allyl propargyl ethers was discussed. Synthesis of isochromanones and isoquinolones comprising a quaternary center with high diastereoselectivity was realized via AuCl3 catalyzed tandem intramolecular exo-dig heterocyclization/enol isomerization/Claisen rearrangement sequence in excellent yields. The reaction was general and amenable for the synthesis of structurally diverse analogues. Scheme 3: Synthesis of isochromanones and isoquinolones Forth section of chapter 1 consists of gold catalyzed intramolecular hydroalkoxylation assisted ring opening of furans to the corresponding saturated -keto esters. During the course investigations concerning gold catalyzed intramolecular enyne cyclization reactions, an interesting ring opening of furans in furyl propargyl alcohols to the corresponding tetrahydrofuran appended saturated -keto esters exclusively driven by intramolecular hydroalkoxylation of the alkyne was observed. Reaction of furyl propargyl alcohols without free hydroxyl group, under similar conditions afforded the conjugated enynes involving dehydration/ketalization. Scheme 4: Synthesis of saturated -keto esters and enynes Chapter 2 delineates the enantiospecific synthesis of bicyclo[4.2.2]decadienes 15 via gold catalyzed tandem enyne cyclization, semipinacol rearrangement reaction. Bicyclodecadienes are key structural units of natural products nakafuran-8 and pallescensin B. Scheme 5: Synthesis of bicyclo[4.2.2]decadienes

First section of chapter 1 deals with gold catalyzed synthesis of ring fused furo[3,2,b]pyrans and furo[3,2,b]furans. Furo[3,2,b]pyrans and furo[3,2,b]furans are ubiquitous structural segments found in a number of natural products including polyether containing marine toxins. Synthesis of furo[3,2,b]pyrans 2a was accomplished from the bis-propargyl ethers 1a, while the synthesis of furo[3,2,b]furans 2b was accomplished from the prenyl propargyl ethers 1b. Scheme 1: Synthesis of furo[3,2,b]pyrans and furo[3,2,b]furans Second section of chapter 1 describes an unusual ring-contraction rearrangement route to functionalized 2,8-oxymethano-bridged di and triquinane. During the course of investigations concerning the total synthesis of 6-oxabicyclo[3.2.1]octane framework containing natural products, an unusual ring-contraction rearrangement sequence was observed in the reaction of 5-substituted 1-methyl-4-isopropenyl-6-oxabicyclo[3.2.1]octan-8-ones 4 to the 2,8-oxymethano-bridged diquinanes 5. The reaction was further demonstrated in the synthesis of triquinane 7 framework. Scheme 2: Synthesis of functionalized di and triquinane In third section of chapter 1 gold catalyzed synthesis of isochromanones and isoquinolones from suitable substituted allyl propargyl ethers was discussed. Synthesis of isochromanones and isoquinolones comprising a quaternary center with high diastereoselectivity was realized via AuCl3 catalyzed tandem intramolecular exo-dig heterocyclization/enol isomerization/Claisen rearrangement sequence in excellent yields. The reaction was general and amenable for the synthesis of structurally diverse analogues. Scheme 3: Synthesis of isochromanones and isoquinolones Forth section of chapter 1 consists of gold catalyzed intramolecular hydroalkoxylation assisted ring opening of furans to the corresponding saturated -keto esters. During the course investigations concerning gold catalyzed intramolecular enyne cyclization reactions, an interesting ring opening of furans in furyl propargyl alcohols to the corresponding tetrahydrofuran appended saturated -keto esters exclusively driven by intramolecular hydroalkoxylation of the alkyne was observed. Reaction of furyl propargyl alcohols without free hydroxyl group, under similar conditions afforded the conjugated enynes involving dehydration/ketalization. Scheme 4: Synthesis of saturated -keto esters and enynes Chapter 2 delineates the enantiospecific synthesis of bicyclo[4.2.2]decadienes 15 via gold catalyzed tandem enyne cyclization, semipinacol rearrangement reaction. Bicyclodecadienes are key structural units of natural products nakafuran-8 and pallescensin B. Scheme 5: Synthesis of bicyclo[4.2.2]decadienes

Thesis (M.S.)--University of Wisconsin--Madison, 2000.<br>Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 52-55).

Time-delayed actions appear as an essential component of numerous systems especially in evolution processes, natural phenomena, and particular technical applications and are associated with the existence of a memory. Under common conditions, external forces or state dependent parameters modify the length of the delay with time. Consequently, an altered dynamical behavior emerges, whose characterization is compulsory for a deeper understanding of these processes. In this thesis, the well-investigated class of time-homogeneous finite-state Markov processes is utilized to establish a variation of memory length by combining a first-order Markov chain with a memoryless Markov chain of order zero. The fluctuations induce a non-stationary process, which is accomplished for two special cases: a periodic and a random selection of the available Markov chains. For both cases, the Kolmogorov-Sinai entropy as a characteristic property is deduced analytically and compared to numerical approximations to the entropy rate of related symbolic dynamics. The convergences of per-symbol and conditional entropies are examined in order to recognize their behavior when identifying unknown processes. Additionally, the connection from Markov processes with varying memory length to hidden Markov models is illustrated enabling further analysis. Hence, the Kolmogorov-Sinai entropy of hidden Markov chains is calculated by means of Blackwell’s entropy rate involving Blackwell’s measure. These results are used to verify the previous computations.

In der vorliegenden Arbeit werden mithilfe von Methoden zur numerischen Behandlung schwach besetzter Matrizen O(n³)- und O(n)-Berechnungsalgorithmen für Mehrkörpersysteme aus deren Bewegungsgleichungen abgeleitet. Durch Verwendung von Dualen Basen kann gezeigt werden, dass sich die bezüglich der Berechnungszeit effizienten Algorithmen sowohl auf Systeme mit explizit als auch implizit formulierten Bindungsgleichungen anwenden lassen. Mit diesen gewonnen Erkenntnissen wird die derzeitige Implementierung der vorgestellten Algorithmen im Sprachstandard Modelica untersucht. Es werden Ansatzmöglichkeiten aufgezeigt, mit denen ausgewählte Modelica Compiler große Mehrkörpersysteme effizienter lösen können. Zum einen wird durch eine graphentheoretische Verallgemeinerung des O(n)-Algorithmus dieser direkt in dem freien Modelica Werkzeug OpenModelica umgesetzt. Zum anderen wird die Methode der Subsysteme für den O(n)-Algorithmus vorgestellt. Sie ermöglicht es, beliebig komplexe Teilsysteme als eigenständige Modellelemente zu erstellen. Die Berechnung von kinematischen Schleifen kann auf diese Weise wesentlich beschleunigt werden. Ferner wird gezeigt, dass sich mit der Methode der Subsysteme Modellgleichungen eines idealen homokinetischen Gelenks ableiten lassen, die frei von Zwangsbedingungen sind. Dies führt ebenfalls zu einer schnelleren und robusteren Berechnung.:1. Einleitung 1.1. Motivation 1.2. Präzisierung der Aufgabe 1.3. Aufbau der Arbeit 2. Mechanik der Mehrkörpersysteme 2.1. Bewegungsgleichung des starren Körpers 2.2. Beschreibung einer Bindung 2.3. Bewegungsgleichung eines Mehrkörpersystems 2.4. Zusammenfassung zur Mechanik der Mehrkörpersysteme 3. Lösungsalgorithmen für Mehrkörpersysteme 3.1. Die Graphen eines Mehrkörpersystems 3.2. Lösungsalgorithmen für Systeme mit Baumstruktur 3.3. Lösungsalgorithmen am Beispiel einer ebenen Pendelkette 3.4. Berücksichtigung kinematischer Schleifen 3.5. Zusammenfassung der Lösungsalgorithmen eines Mehrkörpersystems 4. Effiziente Berechnung von Mehrkörpersystemen 4.1. Berechnung von Mehrkörpersystemen basierend auf Modelica 4.2. O(n)-Algorithmus für Modelica Compiler 4.3. O(n)-Algorithmus für Bibliothekselemente 5. Zusammenfassung und Ausblick A. Anhang A.1. Grundlagen der Tensorrechnung A.2. Duale Basis einer Bindung A.3. Herleitung des Subsystems des Viergelenks A.4. Homokinetisches Gelenk als Subsystem<br>Using methods from sparse matrice theory, O(n³)- and O(n)-algorithms for multibody systems are derived from the equations of motion. The concept of Dual Bases reveals that efficient algorithms for explicit joint descriptions, regarding calculation time, may also be applied to systems which use implicit joint constraints. Consequently, the feasibility of implementing these results in Modelica is examined. This leads to new approaches which enable selected Modelica compilers to solve large multibody systems more efficiently. On the one hand side a graph-theoretic generalization of the O(n)-algorithm has been implemented into the OpenModelica compiler. On the other hand, a method of subsystems for the O(n)-algorithm has been devised. It allows to derive the model equations for arbitrary complex sub-systems which can be implemented as new model elements for an O(n)-algorithm library. This has been carried out for recurring kinematic loops of Mobile Machinery improving simulation speed considerably. Furthermore, it is shown that a fast and robust model of an ideal constant velocity joint can be derived that way.:1. Einleitung 1.1. Motivation 1.2. Präzisierung der Aufgabe 1.3. Aufbau der Arbeit 2. Mechanik der Mehrkörpersysteme 2.1. Bewegungsgleichung des starren Körpers 2.2. Beschreibung einer Bindung 2.3. Bewegungsgleichung eines Mehrkörpersystems 2.4. Zusammenfassung zur Mechanik der Mehrkörpersysteme 3. Lösungsalgorithmen für Mehrkörpersysteme 3.1. Die Graphen eines Mehrkörpersystems 3.2. Lösungsalgorithmen für Systeme mit Baumstruktur 3.3. Lösungsalgorithmen am Beispiel einer ebenen Pendelkette 3.4. Berücksichtigung kinematischer Schleifen 3.5. Zusammenfassung der Lösungsalgorithmen eines Mehrkörpersystems 4. Effiziente Berechnung von Mehrkörpersystemen 4.1. Berechnung von Mehrkörpersystemen basierend auf Modelica 4.2. O(n)-Algorithmus für Modelica Compiler 4.3. O(n)-Algorithmus für Bibliothekselemente 5. Zusammenfassung und Ausblick A. Anhang A.1. Grundlagen der Tensorrechnung A.2. Duale Basis einer Bindung A.3. Herleitung des Subsystems des Viergelenks A.4. Homokinetisches Gelenk als Subsystem