Fakultät für Chemie und Pharmazie - Digitale Hochschulschriften der LMU - Teil 02/06 Archiv

An efficient computational LSDA+DMFT toolbox for the description of correlated materials has been established. The method developed in this work provides an appropriate description of 3d-transition metal correlated bulk systems, concerning their ground-state properties (magnetic moments, total energies) as well as the high- and low-energy spectroscopies (valence-band angular-resolved photoemission, Fano-effect, optical and magneto-optical properties). The incorporation of the perturbational impurity solvers within the spin-polarized relativistic Korringa-Kohn-Rostoker (SPR-KKR) Green’s function method gives rise to a fully self-consistent procedure with respect both to the DFT (charge) and the DMFT (localized dynamical self-energy) self-consistency requirements. Thus, the solution of the many-electron problem can be achieved with a high precision. In turn this opens a possibility to investigate very delicate properties, as the orbital magnetic moments of 3d-transition metals. To develop a relatively fast and accurate approach for the low-energy spectroscopies, the DMFT was implemented within the wave function formalism in the framework of the Linearized Muffin-Tin Orbitals method (LMTO). Calculations are performed in a one-shot run, that does not allow to get the charge-self-consistent solution. In such a way all effects of the localized correlations are encapsulated in the Green’s function constructed as a resolvent to the LMTO one-particle Hamiltonian and accounting for the corresponding self-energy via the Dyson equation. The LMTO+DMFT scheme gives in comparison to a plain LSDA a significantly improved description of the magneto-optics in the 3d-transition metals, half-metallic Heusler ferromagnet NiMnSb, as well as for the heavy-fermion US compound.

Die vorliegende Arbeit behandelt die experimentell umsetzbare Implementierung von Molekularem Quantencomputing, wie es in der Arbeitsgruppe um R. de Vivie-Riedle entwickelt wurde. Dieses Konzept beruht auf Laser-vermittelter Kontrolle intramolekularer Schwingungsdynamik. So fungieren ausgewählte Normalmoden eines polyatomaren Moleküls als Quanteninformationseinheiten (Qubits), wobei die Information in den Schwingungseigenzuständen kodiert wird. Diese lässt sich durch kurze geformte infrarote Lichtpulse, die als logische Gatter operieren, kontrolliert manipulieren. Für die Prozessoreinheit wird Mangan-pentacarbonyl-bromid (MnBr(CO)5) gewählt und ein Zwei-Qubit-System mit den beiden stärksten IR-aktiven CO-Streckschwingungen (2000 cm^{-1} bzw. 2050 cm^{-1}) definiert. In den quantenmechanischen Untersuchungen wird das System durch seine Schwingungseigenfunktionen repräsentiert. Das zugrunde liegende Modell ergibt sich durch sorgfältige Anpassung an neueste spektroskopische Daten des MnBr(CO)5. Ein dafür im Rahmen dieser Arbeit entwickeltes komplexes Optimierungsverfahren ermöglicht die effiziente Konstruktion des Modells. Einen Schwerpunkt bildet die Berechnung und Untersuchung eines universellen Satzes globaler Quantengatter bestehend aus den Operationen NOT, CNOT, Π und Hadamard. Diese werden mit einem "multi-target-Optimal-Control"-Algorithmus optimiert, der die simultane Optimierung der relevanten Übergänge des jeweiligen Gatters unter Berücksichtigung aller berechneten Eigenfunktionen erlaubt. Schalteffizienz und Struktur des resultierenden Laserfelds hängen dabei maßgeblich von der gewählten Pulsdauer ab. Durch die individuelle Wahl einer günstigen Dauer (5 ps - 11 ps), die sich nach den spektroskopischen Anforderungen der logischen Operationen richtet, ergeben sich erstmals für alle Gatter hocheffiziente und einfach strukturierte Pulse. Besondere Beachtung findet in dieser Arbeit die Gewährleistung experimenteller Umsetzbarkeit des Molekularen Quantencomputings. Untersuchungen zur Erzeugung der optimierten Pulse sind dabei von primärer Bedeutung. Pulszerlegung und die Berechnung von Maskenfunktionen zeigen, dass sich sowohl indirektes als auch direktes Pulsformen für die Generierung der Laserfelder eignen. Gegen dabei entstehende Abweichungen von der optimalen Pulsstruktur sind die Gatter robust. Um die Laser-Molekül-Wechselwirkung im Experiment zusätzlich zu steigern, können die Prozessoreinheiten fixiert und ausgerichtet werden. Dies lässt sich durch Immobilisierung in der Kristallstruktur eines Zeoliths erreichen, wie erste Rechnungen ergeben. Darüber hinaus wird die Relevanz potentieller Störungen des Qubitsystems wie Dissipation und interner Schwingungsumverteilung überprüft. Die Ergebnisse zeigen, dass das Qubitsystem einen nahezu dekohärenzfreien Raum für die Informationsverarbeitung bietet. Durch die sorgfältige Wahl einer geeigneten molekularen Spezies und die auf das Qubitsystem individuell abgestimmten Pulsdauern ist es gelungen, Molekulares Quantencomputing experimentell zugänglich mit hocheffizienten robusten Quantengattern zu implementieren.

One of the important transformations of alcohols to esters is the reaction with acetic anhydride catalysed by 4-(dimethylamino)pyridine (DMAP) in the presence of an auxiliary base like triethyl amine. Although this is a widely used reaction, several questions left unaddressed until now: the reaction mechanism of the latter transformation was not completely conceived. Since Steglich and Litvenencko found DMAP in 1969 independently as nucleophilic catalyst, there was hardly any effort to search for new nucleophilic catalysts of higher catalytic efficiency than DMAP or 4-(pyrrolidinyl)pyridine (PPY). All chiral nucleophilic catalysts are based on these structural motifs and due to their lack of catalytic efficiency, there are hitherto no examples for kinetic resolution experiments of tertiary alcohols described. In this dissertation, the following goals were achieved: With computational methods, the reaction pathway of tert-butanol with acetic anhydride in the presence of DMAP was explored. Based on these results a fast computational tool was developed to screen for more efficient nucleophilic catalysts. The best candidates were synthesised, the catalytic efficiency quantified and the best catalysts applied in the synthesis of esters. The reaction mechanism of the acetylation of tert-alcohols was explored by calculating the nucleophilic and base catalysed reaction pathway of tert-butanol with acetic anhydride in the presence of DMAP at B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level of theory. In the course of this study, a nucleophilic and base catalysed reaction pathway with DMAP as catalyst was found. The energetically lowest transition state of the base catalysed reaction pathway is 37.9 kJ mol-1 higher in energy then the energetically lowest transition state in the rate-determining step of the nucleophilic reaction path. The combination of kinetic measurements with the calculation of the nucleophilic reaction path reveals that no triethyl amine is involved in the rate-determining step of nucleophilic reaction pathway. This shows clearly that nucleophilic catalysis is the preferred and that the acetate anion is deprotonating the alcohol in the rate-determining step. Furthermore, the results of the recalculation of the nucleophilic reaction path with a different catalyst show that a higher stabilisation of the transient acylpyridinium cation has a pivotal influence on the overall reaction rate of the ester formation. Therefore, relative acetylation enthalpies (ΔH298) were calculated at B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level of theory by using an isodesmic reaction approach. In this way a large number of new nucleophilic catalysts were screened and numerous promising candidates were synthesised which have a larger negative ΔH298 value then DMAP (-82.1 kJ mol 1). The catalytic effiency of the new nucleophilic catalysts was quantified by a test reaction using 1 equiv. of 1-ethynylcyclohexanol, 2 equiv. of acetic or isobutyric anhydride and 3 equiv. triethyl amine. The conversion of 1-ethynylcyclohexyl acetate or -isobutyrate was monitored by 1H NMR spectroscopy. Pyrido[3,4-b]pyrazine- and pyrido[3,4 b]quinoxaline-derivatives show the best catalytic effiency. Especially (rac) 5,10-diethyl-5,5a,6,7,8,9a,10-octahydropyrido[3,4 b]-quinoxaline (DOPQ) shows equal to better catalytic efficiency then 6,6-tricyloaminopyridine (TCAP), which was hitherto the best nucleophilic catalyst. DOPQ can be synthesised very efficiently in a four step protocol starting from commercially available 3,4-diaminopyridine and cyclohexane-1,2-dione with an overall yield of 45 % while TCAP is only available in a five step synthesis with an overall yield of 8-13 %. The synthesis of DOPQ starts with the Schiff-base formation of 3,4-diaminopyridine and cyclohexane-1,2-dione. Reduction with LiAlH4 yields the cis-configured octahydro[3,4-b]quinoxaline, which can be alkylated without the use of any protecting group in the presence of acetic anhydride in pyridine and subsequent reduction with LiAlH4/AlCl3 to yield DOPQ. The structure of the latter compound was confirmed by X ray single crystal structure. The new catalysts were applied to an enhanced Gooßen esterification to transform sterically hindered acids to their tert-butyl esters. The reaction mechanism was explored by monitoring the substrate, intermediate and product conversions with 1H NMR spectroscopy. With this enhanced reaction protocol, it was possible to transform 1-phenylcyclohexane carboxylic acid into the tert-butyl ester under high concentration conditions at room temperature in the presence of 5 mol% DOPQ within 270 min while with the standard DCC/DMAP protocol only the anhydride of the carboxylic acid is formed. With this very mild method, it was possible to convert a variety of substrates into their tert-butyl- and benzyl esters, which are not accessible with any other method starting from the free carboxylic acid. In the case of chiral substrates no lose of stereochemical information was detected. Combination of high concentration conditions and new catalysts provide attractive reaction times of a few minutes instead of several hours with the Gooßen protocol.