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In this thesis, the low-temperature regime of replica symmetry breaking in the SK-model has been thoroughly investigated. In order to access this regime and to perform self-consistence calculations with high accuracy at high orders of replica symmetry breaking, a formalism has been developed which reduces the numerical effort to the absolute minimum. The central idea of its derivation is the identification of asymptotic regions in which the recursion relations can be solved analytically. The new object in the numerical treatment is then the correction to this asymptotic regime, represented by a sequence of so-called kernel correction functions. This method increased the effciency of the numerics considerably so that up to 200 orders of RSB could be calculated at zero temperature and zero external field, and up to 60 (65) orders of RSB for finite temperature (external field). The remarkable high precision of these calculations allowed the extraction of several quantities with accuracy exceeding the literature values by several orders of magnitude. The results of the numerical calculations have been analyzed in great detail. Especially the convergence behavior of various observables and of the order function with respect to the RSB order has been investigated since the high but finite RSB regime has been addressed in the present work for the first time. Several unexpected features of finite order replica symmetry breaking have been observed. / In der vorliegenden Dissertation wurden die Eigenschaften der Replikasymmetriebrechung (RSB) im Sherrington-Kirkpatrick-Modell bei tiefen Temperaturen gründlich untersucht. Um entsprechend tiefe Temperaturen und sogar T = 0 zu erreichen und gleichzeitig die Selbstkonsistenzrechnungen mit hoher numerischer Genauigkeit und bei hohen RSB Ordnungen durchzuführen, wurde ein Formalismus entwickelt, welcher den numerischen Aufwand auf ein absolutes Minimum reduziert. Das zentrale Konzept der Ableitung dieser Formulierung ist die Identifikation asymptotischer Bereiche, in denen die Rekursionsgleichungen der Replikasymmetriebrechung bei endlichen Ordnungen analytisch gelöst werden können. Das neue Objekt, welches numerisch behandelt werden muss, ist die Korrektur zu diesen asymptotischen Bereichen, welche durch eine Reihe von Funktionen, den sogenannten kernel correction functions beschrieben wird. Diese Methode hat die Effizienz der numerischen Behandlung erheblich verbessert, so dass bis zu 200 RSB Ordnungen bei verschwindender Temperatur und bei verschwindendem Magnetfeld und bis zu 60 (65) RSB Ordnungen bei endlichen Temperaturen (Magnetfeldern) berechnet werden konnten. Die ungewöhnlich hohe Genauigkeit dieser Rechnungen erlaubte die Bestimmung vieler Observablen mit einer Genauigkeit, die mehrere Größenordnungen über den Literaturwerten liegt. Die Ergebnisse der numerischen Rechnungen wurden im Detail analysiert. Speziell das Konvergenzverhalten der Ordnungsfunktion und der interessanten Observablen als Funktionen der RSB Ordnung wurde untersucht. Dieser Bereich hoher, aber endlicher RSB Ordnungen wurde in der vorliegenden Arbeit das erste Mal analysiert und viele unerwartete Eigenschaften wurden gefunden.

Stoffe mit schnell zerfallendem Magnetresonanz (MR)-Signal sind mit herkömmlichen MR- Sequenzen nicht darstellbar. Solche Stoffe haben meist starke Bindungen, wie im menschlichen Körper beispielsweise Sehnen, Bänder, Knochen oder Zähne. In den letzten Dekaden wurden spezielle Sequenzen mit ultrakurzer Echozeit entwickelt, die Signale von diesen Stoffen messen können. Messungen mit ultrakurzen Echozeiten eröffnen der Kernspintomographie neue Anwendungsgebiete. In dieser Doktorarbeit werden die in der Literatur bekannten Methoden zur Messung mit ultrakurzen Echozeiten untersucht und evaluiert. Es werden zwei neue, in dieser Arbeit entwickelte Ansätze vorgestellt, die es zum Ziel haben, bestehende Probleme der vorhandenen Methoden bei robuster Bildqualität zu lösen, ohne auf Hardwareänderungen am Kernspintomographen angewiesen zu sein. Die ’Gradient Optimized Single Point imaging with Echo time Leveraging’ (GOSPEL) Sequenz ist eine Single-Point-Sequenz, die im Vergleich zu den bekannten Single-Point-Sequenzen eine stark reduzierte Echozeit ermöglicht. Es wird gezeigt, dass dadurch ein deutlich besseres Signalzu-Rausch-Verhältnis (SNR) von Stoffen mit schnell zerfallendem Signal erreicht wird. Das Problem der sehr langen Messzeit bei Single-Point-Verfahren wird mit der ’Pointwise Encoding Time reduction with Radial Acquisition’ (PETRA) Sequenz gelöst. Bei diesem Ansatz wird der k-Raum-Außenbereich radial und das k-Raum-Zentrum single-point-artig abgetastet. Durch die Kombination beider Akquisitionsstrategien ist eine schnelle und robuste Bildgebung mit ultrakurzer Echozeit und ohne Hardwareänderungen möglich. Wie bei anderen Ansätzen sind bei der PETRA-Sequenz die Bildgebungsgradienten zum Anregungszeitpunkt bereites angeschaltet. Es wird untersucht, welchen Einfluss ungewollte Schichtselektionen auf die Bildgebung haben können und ein Korrekturalgorithmus entwickelt, mit dem sich dadurch entstehende Artefakte im Bild beheben lassen. Die Limitationen des Korrekturalgorithmus sowie mögliche Artefakte der PETRA-Sequenz werden untersucht und diskutiert. Erste Anwendungsbeispiele der PETRA-Sequenz bei verschiedenen Feldstärken und Applikationen werden demonstriert. Wie bei anderen Sequenzen mit ultrakurzen Echozeiten sind die Gradientenaktivitäten bei der PETRA- und GOSPEL-Sequenz gering, wodurch die Messung sehr leise sein kann. Lautstärkemessungen zeigen, dass bei Messungen mit der PETRA-Sequenz der Geräuschpegel um nur ein bis fünf dB(A) im Vergleich zum Hintergrundgeräuschpegel steigt. Es wird demonstriert, dass sich dadurch neue Anwendungsgebiete eröffnen könnten. Vergleichsmessungen zwischen einer T1-gewichteten PETRA- und einer MPRAGE-Messung weisen Bilder auf, die in Kontrast, Auflösung, SNR und Messzeit vergleichbar sind. Mit den in dieser Arbeit entwickelten Methoden konnten Probleme bestehender Ansätze gelöst und offene Fragen beantwortet werden. Die Ergebnisse können helfen, Applikationen von Sequenzen mit ultrakurzen Echozeiten in der klinischen Routine weiter zu etablieren. / Tissues with fast decaying magnetic resonance (MR) signal are not measureable with conventional MR sequences. These tissues mostly have strong covalent bondings, like in the human body tendons, ligaments, bones and teeth. In the last decade, special MR sequences with ultrashort echo times have been developed that are able to depict signal from those tissues. Ultrashort echo time imaging opens new application fields for magnetic resonance imaging. In this thesis, the known methods for imaging with ultrashort echo times are investigated and evaluated. Two new approaches that were developed in this work are presented. They aim to solve the problems of the previous methods and to allow for robust image quality. No hardware changes should be required for the MR scanner. The ’Gradient Optimized Single Point imaging with Echo time Leveraging’ (GOSPEL) sequence is a single-point sequence. Compared to the known single-point sequences, GOSPEL enables a reduced echo time. It is demonstrated that this allows for an enhanced SNR for tissues with fast decaying signal. The problem of very long measurement times with single point sequences is solved with the ’Pointwise Encoding Time reduction with Radial Acquisition’ (PETRA) sequence. In this approach, outer k-space is acquired with radial half-projections while the k-space center is acquired single-pointwise. The combination of these two acquisition strategies allows for fast and robust ultrashort echo time imaging without the need for hardware changes. Comparable to other approaches, the imaging gradients at the PETRA sequence are already switched on during the excitation pulse. The influence of unwanted slice-selectivity of the pulse is investigated. A newly developed correction algorithm is presented that eliminates artefacts due to unwanted slice-selectivity. The limitations of the correction approach are presented and discussed. A number of application examples of the PETRA sequence at different field strengths is demonstrated. The PETRA and GOSPEL sequence, and other ultrashort echo time sequences, have very limited gradient activities. Due to this, the measurements can be kept very silent. Acoustic noise measurements show that the acoustic noise level during PETRA examinations is only raised by one to five dB(A). It is demonstrated, that this might enable new applications. Comparing measurements between T1-weighted PETRA images and MPRAGE images lead to images with comparable contrast, resolution, SNR and measurement times. With the methods developed in this thesis, issues of existing ultrashort echo time approaches can be solved and answers to open questions are given. The outcomes could help to further establish the use of ultrashort echo time sequences in clinical routine applications.

<p>The spin of an electron often misleadingly interpreted as the classical rotationof a particle. The quantum spin distinguishes itself from classicalrotation by possessing quantized states and can be detected by its magneticmoment. The properties of spin and its collective behavior with otherfundamental properties are fascinating in basic sciences. In many aspectsit offers scope for designing new materials by manipulating the ensemblesof spin. In recent years attention towards high density storage devices hasdriven the attention to the fundamental level were quantum physics rules.To understand better design of molecule based storage materials, studies onspin degrees of freedom and their coupling properties can not be neglected.</p><p>To account for many body effect of two or more electrons consistent withrelativity, an approximation like the Breit Hamiltonian(BH) is used in modernquantum chemical calculations, which is successful in explaining the splitin the spectra and corresponding properties associated with it. Often differenttactics are involved for a specific level of computations. For example themulti-configurational practice is different from the functional based calculations,and it depends on the size of the system to choose between resourcesand accuracy. As the coupling terms offers extra burden of calculating theintegrals it is literally challenging.</p><p>One can readily employ approximations as it suits best for the applicationoriented device computations. The possible methods available in the literatureare presented in chapter 2. The theoretical implementations of couplingfor the multi-reference and density functional method are discussed in detail.The multi-reference method precedes the density functional methodin terms of accuracy and generalizations, however it is inefficient in dealingvery large systems involving many transition elements, which is vital formolecule based magnets as they often possess open shell manifolds. On theother hand existing density functional method exercise perturbations techniqueswhich is extremely specialized for a specific system - highly coupledspins.</p><p>The importance of spin-spin coupling(SSC) in organic radical-Oxyallyl(OXA)was systematically studied with different basis sets and compared with asimilar isoelectronic radical(TMM). The method of spin-spin coupling implementationsare also emphasized. Similar coupling studies were carriedivout for the species HCP and NCN along with spin-orbit coupling(SOC).The splitting of the triplet states are in good agreement with experiments</p>

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Molecules with unusual steric crowding are always interesting in chemistry. They give the opportunity to explore the limits of stable molecular structures and the synthesis of unnatural products. They also provide points of calibration for modern computational methods. This dissertation describes the design, synthesis and characterization of two types of crowded complex aromatic compounds. The goal of the first project was to synthesize in-keto cyclophanes, that is, molecules with ketone oxygens pressed toward the centers of benzene rings. Several likely precursors were synthesized and fully characterized, but attempts to make the in-keto cyclophanes themselves were unsuccessful. The nonbonded interaction between the ketone oxygen and basal benzene ring may be so close in the target structures as to prevent the formation of an in-keto cyclophane. The second project describes the design, synthesis and characterization of several macrobicyclic, bis(triarylelement)-containing cyclophanes with various bridgehead heteroatoms. Computational studies accurately predicted that when the bridgehead substituents are small (lone pairs or protons), an in,in bridgehead stereochemistry is strongly favored, but larger bridgehead substituents favor the formation of in,out stereoisomers. The NMR spectra of several of these compounds show unusual through-space spin-spin coupling between atoms along the central axis. Most importantly, one of these compounds, an in,in-bis(hydrosilane), possesses a hydrogen-hydrogen nonbonded contact distance of approximately 1.56 Å, a new “world record” for such a contact in any crystallographically characterized compound. / 1 / Jie Zong

NMR spectroscopy has evolved into one of the most important characterization techniques in chemistry with which it is possible to obtain valuable structural, dynamical, and mechanistic information. Most applications of NMR have however been limited to the use of nuclei having spin quantum numbers of 1/2. This thesis discusses the developments that have been advanced in order to extract quantitative structural information from the NMR spectroscopy of quadrupolar nuclei (spin, I>1/2) which account for the vast majority of the NMR-active nuclei. In a first part of the thesis, a NMR crystallographic method is developed which uses the electric field gradient tensor measured at the nuclear sites as an experimental constraint in DFT-based crystal structure refinements. This inclusion of experimental data into crystal structure refinements enables the determination of higher quality, and experimentally-relevant, structures. We apply this new methodology in order to determine higher quality crystal structures for the non-linear optical material Na2B2Al2O7, sodium pyrophosphates, and the near-zero thermal expansion material ZrMgMo3O12. In a second part of this thesis, experimental techniques are developed for the measurement of spin-spin coupling between pairs of quadrupolar nuclei; the measurement of spin-spin coupling carries with it extremely valuable distance and connectivity information. Using DOR NMR, heteronuclear residual dipolar coupling as well as homonuclear J coupling multiplets can be observed. Notably, the J coupling between quadrupolar nuclei can still be measured in A2 spin systems, unlike in the case of pairs of spin-1/2 nuclei. The theory that was developed for the characterization of these multiplets was extended for the general simulation of exact NMR spectra of quadrupolar. This program, known as QUEST, is now free to use by anyone in the scientific community. Pulsed J-resolved NMR experiments are then described which enable the facile measurement of J and dipolar coupling in homonuclear pairs of quadrupolar nuclei. Notably, the J splitting is greatly amplified in A2 spin systems which provides strong structural information and enables the precise detection of smaller J coupling constants. These techniques are applied towards directly studying gallium metal-metal bonding interactions as well as boron-boron bonds in diboron compounds of importance in β-boration chemistry.

The spin of an electron often misleadingly interpreted as the classical rotationof a particle. The quantum spin distinguishes itself from classicalrotation by possessing quantized states and can be detected by its magneticmoment. The properties of spin and its collective behavior with otherfundamental properties are fascinating in basic sciences. In many aspectsit offers scope for designing new materials by manipulating the ensemblesof spin. In recent years attention towards high density storage devices hasdriven the attention to the fundamental level were quantum physics rules.To understand better design of molecule based storage materials, studies onspin degrees of freedom and their coupling properties can not be neglected. To account for many body effect of two or more electrons consistent withrelativity, an approximation like the Breit Hamiltonian(BH) is used in modernquantum chemical calculations, which is successful in explaining the splitin the spectra and corresponding properties associated with it. Often differenttactics are involved for a specific level of computations. For example themulti-configurational practice is different from the functional based calculations,and it depends on the size of the system to choose between resourcesand accuracy. As the coupling terms offers extra burden of calculating theintegrals it is literally challenging. One can readily employ approximations as it suits best for the applicationoriented device computations. The possible methods available in the literatureare presented in chapter 2. The theoretical implementations of couplingfor the multi-reference and density functional method are discussed in detail.The multi-reference method precedes the density functional methodin terms of accuracy and generalizations, however it is inefficient in dealingvery large systems involving many transition elements, which is vital formolecule based magnets as they often possess open shell manifolds. On theother hand existing density functional method exercise perturbations techniqueswhich is extremely specialized for a specific system - highly coupledspins. The importance of spin-spin coupling(SSC) in organic radical-Oxyallyl(OXA)was systematically studied with different basis sets and compared with asimilar isoelectronic radical(TMM). The method of spin-spin coupling implementationsare also emphasized. Similar coupling studies were carriedivout for the species HCP and NCN along with spin-orbit coupling(SOC).The splitting of the triplet states are in good agreement with experiments / QC 20110210

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