Heteronuclear recoupling methods in solid-state NMR

This thesis is focused on the development of heteronuclear correlation methods in solid-state NMR spectroscopy, where the spatial dependence of the dipolar coupling is exploited to obtain structural and dynamical information in solids. Quantitative results on dipolar coupling constants are extracted by means of spinning sideband analysis in the indirect dimension of the two-dimensional experiments. The principles of sideband analysis were established and are currently widely used in the group of Prof. Spiess for the special case of homonuclear 1H double-quantum spectroscopy. The generalization of these principles to the heteronuclear case is presented, with special emphasis on naturally abundant 13C-1H systems. For proton spectroscopy in the solid state, line-narrowing is of particular importance, and is here achieved by very-fast sample rotation at the magic angle (MAS), with frequencies up to 35 kHz. Therefore, the heteronuclear dipolar couplings are suppressed and have to be recoupled in order to achieve an efficient excitation of the observed multiple-quantum modes. Heteronuclear recoupling is most straightforwardly accomplished by performing the known REDOR experiment, where pi-pulses are applied every half rotor period. This experiment was modified by the insertion of an additional spectroscopic dimension, such that heteronuclear multiple-quantum experiments can be carried out, which, as shown experimentally and theoretically, closely resemble homonuclear double-quantum experiments. Variants are presented which are well-suited for the recording of high-resolution 13C-1H shift correlation and spinning-sideband spectra, by means of which spatial proximities and quantitative dipolar coupling constants, respectively, of heteronuclear spin pairs can be determined. Spectral editing of 13C spectra is shown to be feasible with these techniques. Moreover, order phenomena and dynamics in columnar mesophases with 13C in natural abundance were investigated. Two further modifications of the REDOR concept allow the correlation of 13C with quadrupolar nuclei, such as 2H. The spectroscopic handling of these nuclei is challenging in that they cover large frequency ranges, and with the new experiments it is shown how the excitation problem can be tackled or circumvented altogether, respectively. As an example, one of the techniques is used for the identification of a yet unknown motional process of the H-bonded protons in the crystalline parts of poly(vinyl alcohol).

Characterisation of supramolecular structures by novel recoupling methods in solid-state NMR

In this work, solid-state NMR methods suitable for the investigation of supramolecular systems were developed and improved. In this context, special interest was focussed on non-covalent interactions responsible for the formation of supramolecular structures, such as pi-pi interacions and hydrogen-bonds. In the first part of this work, solid-state NMR methods were presented that provide information on molecular structure and motion via the investigation of anisotropic interactions, namely quadrupole and dipole-dipole couplings, under magic-angle spinning conditions. A two-dimensional 2H double quantum experiment was developed, which is performed under off magic-angle conditions and correlates 2H isotropic chemical shifts with quasistatic DQ-filtered line shapes. From the latter, the quadrupole coupling parameters of samples deuterated at multiple sites can be extracted in a site-selective fashion. Furthermore, 7Li quadrupole parameters of lithium intercalated into TiO2 were determined by NMR experiments performed under static and MAS conditions, and could provide information on the crystal geometry. For the determination of 7Li-7Li dipole-dipole couplings, multiple-quantum NMR experiments were performed. The 1H-13C REREDOR experiment was found to be capable of determining strong proton-carbon dipole-dipole couplings with an accuracy of 500~Hz, corresponding to a determination of proton-carbon chemical-bond lengths with picometer accuracy In the second part of this work, solid-state NMR experiments were combined with quantum-chemical calculations in order to aid and optimise the interpretation of experimental results. The investigations on Calix[4]hydroquinone nanotubes have shown that this combined approach can provide information on the presence of disordered and/or mobile species in supramolecular structures. As a second example, C3-symmetric discs arranging in helical columnar stacks were investigated. In these systems, 1H chemical shifts experience large pi-shifts due to packing effects, which were found to be long-ranged. Moreover, quantum-chemical calculations revealed that helicity in these systems is induced by the propeller-like conformation of the core of the molecules.

Helicity methods in LO and NLO QCD calculations

The goal of this thesis is the acceleration of numerical calculations of QCD observables, both at leading order and next–to–leading order in the coupling constant. In particular, the optimization of helicity and spin summation in the context of VEGAS Monte Carlo algorithms is investigated. In the literature, two such methods are mentioned but without detailed analyses. Only one of these methods can be used at next–to–leading order. This work presents a total of five different methods that replace the helicity sums with a Monte Carlo integration. This integration can be combined with the existing phase space integral, in the hope that this causes less overhead than the complete summation. For three of these methods, an extension to existing subtraction terms is developed which is required to enable next–to–leading order calculations. All methods are analyzed with respect to efficiency, accuracy, and ease of implementation before they are compared with each other. In this process, one method shows clear advantages in relation to all others.

Higher-order molecular properties and excitation energies in single-reference and multireference coupled-cluster theory

Coupled-cluster (CC) theory is one of the most successful approaches in high-accuracy quantum chemistry. The present thesis makes a number of contributions to the determination of molecular properties and excitation energies within the CC framework. The multireference CC (MRCC) method proposed by Mukherjee and coworkers (Mk-MRCC) has been benchmarked within the singles and doubles approximation (Mk-MRCCSD) for molecular equilibrium structures. It is demonstrated that Mk-MRCCSD yields reliable results for multireference cases where single-reference CC methods fail. At the same time, the present work also illustrates that Mk-MRCC still suffers from a number of theoretical problems and sometimes gives rise to results of unsatisfactory accuracy. To determine polarizability tensors and excitation spectra in the MRCC framework, the Mk-MRCC linear-response function has been derived together with the corresponding linear-response equations. Pilot applications show that Mk-MRCC linear-response theory suffers from a severe problem when applied to the calculation of dynamic properties and excitation energies: The Mk-MRCC sufficiency conditions give rise to a redundancy in the Mk-MRCC Jacobian matrix, which entails an artificial splitting of certain excited states. This finding has established a new paradigm in MRCC theory, namely that a convincing method should not only yield accurate energies, but ought to allow for the reliable calculation of dynamic properties as well. In the context of single-reference CC theory, an analytic expression for the dipole Hessian matrix, a third-order quantity relevant to infrared spectroscopy, has been derived and implemented within the CC singles and doubles approximation. The advantages of analytic derivatives over numerical differentiation schemes are demonstrated in some pilot applications.