This thesis presents quantum chemical calculations, applications of the response function formalism recently implemented within the framework of density functional theory (DFT) by our research group. The purpose of the calculations is to assess the performance of this perturbative approach to determining heavy atom effects on magnetic resonance parameters. Relativistic corrections can be generated by spin-orbit interactions or by scalar relativistic effects due to high velocity electrons in the atomic core region of heavy atoms. In this work, the evaluation of nuclear magnetic resonance (NMR) parameters is considered, the nuclear shielding tensor and the indirect nuclear spin-spin coupling tensor. For series of homologous compounds, it is found that both types of corrections to these parameters are increasing in size upon substitution of a constituent atom by a heavier element, but that their relative importance is system dependent. The obtained results are compatible with the ones provided by electron correlated ab initio methods, and a qualitative agreement with experimentally determined parameters is overall achieved. The methodology presented in this thesis aims to be a practical approach which can be applied in the study of molecular properties of large systems. This thesis also addresses the calculation of hyperfine coupling constants, and evaluates a novel approach to the treatment of spin-polarization in spin restricted calculations without the spin contamination associated with spin unrestricted calculations. / QC 20101122

Diese Dissertation besteht aus zwei Teilen von Studien. Der erste Teil demonstriert die Steuerung der Elektron-Kern-Spin-Systems in II-VI Halbleiter Quantum Dots (QDs) durch elektrische Ströme über Mikrospulen. Mikrometer-große Leiterschleifen sind auf der Oberseite von Heterostrukturen mit geladenen CdSe/ZnS QDs hergestellt worden. Eine Strominjektion erzeugt magnetische Felder im Bereich von einige 10 mT, welche stark genug sind, um die Hyperfeinwechselwirkung in CdSe QDs modulieren zu können. Der Durchmesser des Spulen im Mikrometer-Bereich ermöglicht die Generation von schnellen Feld transienten im Bereich von wenigen ns. Mit diesen Vorteilen der Mikrospulen werden die Steuerungs des Spins der residenten Elektronen sowie das Auslesen des Kernspinzustandes durch elektrische Impulse nachgewiesen. Der zweite Teil befasst sich mit der Ladungsträger-Spindynamik in ZnO Quantum Well (QW) Strukturen und Epitaxieschichten, die mittels des optischen Übergang von negativ geladenen Exzitonen X− beziehungsweise des am neutralen Donator gebunden Exziton D0X untersucht werden. Der Loch-Spin kann direkt über die zirkular polarisierten Photolumineszenz der beiden Komplexe zurückverfolgt werde. Die Spin-Relaxationszeit von QW und Epiplyer verfolgt werden. Der Spin des Donatorelektronens wird über die Ausbleichung des Spin-selektive Anregungprozesses nachgewiesen. Es werden longitudinale Loch-Spinrelaxationszeiten von 80 bis 140 ps für D0X und X− gefunden. Deutlich längere longitudinalen Elektronen-Spin-Relaxationszeiten in Bereich von mehreren 100 ns werden gefunden, wenn die Hyperfeinwechselwirkung durch ein geeignetes externes Magnetfeld unterdrückt wird. Eine Feldstärke von 2 mT ist groß genug. Dies zeigt den extrem kleinen Wert des Overhauser-Feldes in ZnO auf, der durch die sehr begrenzte Anzahl von magnetischen Kernen in Wechselwirkung mit dem Elektronen innerhalb des Volumens des Donators verursacht wird. / This work is composed of two parts of studies. The first part represents an electron-nuclear spin control in II-VI semiconductor quantum dots (QDs) by electrical currents via micro coils. Micrometer single turn coils are fabricated on top of heterostructures with charged CdSe/ZnSe QDs. Current injection creates magnetic fields in the range of some 10 mT which is strong enough to modulate the hyperfine interaction in CdSe. The micrometer-range diameter of coil allows for generation of fast field transient in the range of few ns. Using these advantages of micro coils, local control of the resident electron spin as well as read out of the nuclear spin state are demonstrated by electrical pulses. The second part presents charged carrier spin dynamics in ZnO quantum wells and epilayers using the optical transition of the negatively charged exciton X− and the neutral donor bound exciton D0X, respectively. The hole spin can be directly traced by the circular polarized photoluminescence of both complexes. The spin relaxation of the resident electrons and donor electrons is accessed via the bleaching of the spin selective excitation process. Longitudinal hole spin relaxation times of 80 and 140 ps are found for D0X and X−, respectively. Much longer longitudinal electron spin relaxation times in the several 100 ns range are uncovered if the hyperfine interaction is suppressed by a proper external magnetic field. A field strength of 2 mT is large enough proving that the extremely small value of the Overhauser field in ZnO caused by the very restricted number of magnetic nuclei interacting with the electron inside the donor volume.

Dipolar couplings are one of the major source of structural information. Due to their dependence on the distance between the nuclei and the angle of orientation of the dipolar vector with respect to the magnetic field, they provide significant insight into the geometry and topology of molecules. As the dipolar interactions are in general present in the solid phase of the compounds, solid state NMR experiments have gained significant popularity and is widely used. Separated Local Field NMR spectroscopy based on cross-polarization technique has been used to measure the heteronuclear dipolar couplings in solid state. However, the technique undergoes many experimental challenges and requires further development. This thesis is concerned mainly with the development of techniques to measure the dipolar couplings accurately in oriented molecules. In this regard, a method for fast data acquisition is also proposed. The first chapter briefly introduces the basics of NMR spectroscopy, methodologies applied for obtaining a high resolution NMR spectrum in the solid state. An introduction to liquid crystals is presented and the nature of NMR interaction in the liquid crystalline phases is described. In chapter-2, a new pulse scheme has been proposed that includes the X-nucleus polarization in the SLF experiments and is shown to provide better sensitivity and resolution. A quantitative analysis with simulation and experimental results are also presented. In chapter-3, the performance of various homonuclear decoupling pulse schemes incorporated into SLF experiments tested on oriented systems are compared. The proposed pulse schemes are shown to provide high resolution spectrum with accurate dipolar coupling measurement for natural abundant samples and for uniformly labeled compounds as well. Theoretical description with simulation and experimental results shown here are found to provide optimum results under several technical complications seen with respect to the conventional methods used for SLF experiments. Chapter-4, an attempt is made to reconstruct 2D J-resolved and 2D- SLF spectra from several 1D experimental data. This is achieved with the help of projection reconstruction method and is shown to provide high resolution 2D spectrum with saving of experimental time by an order of two. Chapter-5, high resolution spectra from SLF experiments under phase alternating pulses and using amplitude and time averaged nutation techniques are shown for accurate dipolar coupling measurement with a dramatic reduction in rf power. This is important as the use of low rf power leads to low sample heating and can be applied suitably for the study of liquid crystals and salty biomolecules. Chapter-6, attempts are made to characterize two novel thiophene based liquid crystals using both solution and solid state NMR spectroscopy. C-H dipolar couplings measured from SLF experiments are mainly used to find the order parameters and geometry of the molecules.

The study of quadrupolar nuclei using NMR spectroscopy in the solid state significantly increased in popularity from the end of the 20th century, with the introduction of specific methods to acquire spectra free from the effects of the quadrupolar interaction, that results in broadened lineshapes that cannot be completely removed by spinning the sample at the magic angle (MAS), unlike most of the other interactions present in the solid state. The first technique which allows, without any specific hardware, the removal of this broadening has been the Multiple-Quantum MQMAS experiment. The method quickly gained a popularity within the NMR community, with numerous successful applications published. However, the multiple-quantum filtration step in this experiment relies on severely limits sensitivity, restricting application to the most sensitive nuclei. Extending the applicability of MQMAS to less receptive nuclei requires the use of signal improvement techniques. There are multiple examples of such approaches in the literature, but most of these require additional optimisation that may be time-consuming, or simply impossible, on less receptive nuclei. This work introduces a novel signal improvement technique for MQMAS, called FAM-N. Its optimisation is solely based on density matrix simulations using SIMPSON, implying no additional experimental optimisation is required, while improving the signal in MQMAS spectra by equivalent or higher amounts than other common methods. In order to prove the applicability of this method on virtually any system, FAM-N has been investigated by simulation, and tested experimentally using a number of model samples, as well as samples known to be challenging to study by NMR. This work also explores other aspects of NMR spectroscopy on quadrupolar nuclei. Adiabatic inversion of the satellite populations can be performed to improve the central transition signal in static or MAS spectra. A range of methods has been tested and compared, with particular attention given to hyperbolic secant-shaped pulses, for which its performance have been described. Finally, cross-polarisation from a spin I = 1/2 nucleus to a quadrupolar nucleus has been investigated. After reviewing the theory for the static case, simulations have been performed under MAS in order to identify the conditions for efficient magnetisation transfer, with applications in spectral editing or for the combination with MQMAS.

Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital quantum simulation of the mirror inversion propagator corresponding to the time evolution of an XY spin chain. This simulation has been used to experimentally demonstrate the mirror inversion of quantum states, proposed by Albanese et al.[Phys.Rev.Lett.93,230502(2004)], by which entangled states can be transferred from one end of the chain to the other end. The experiments have been performed in a 5-qubit dipolar coupled nuclear spin system. For simulation, we make use of the recently proposed unitary operator decomposition algorithm along with the numerical pulse optimization techniques, which assisted in achieving high experimental fidelities. Chapter 5 contains a digital quantum simulation of the unitary propagator of a transverse Ising spin chain, which has been used to experimentally demonstrate the perfect state transfer protocol of Di Franco et al. [Phys.Rev.Lett.101,230502(2008)]. The importance of this protocol arises due to the fact that it achieves perfect state transfer from one end of the chain to the other end without the necessity of initializing the intermediate spins of the chain, whereas most of the previously proposed protocols require initialization. The experiments have been performed in a 3-spin nuclear spin system. The simulation has also been used to demonstrate the generation of a GHZ state.

Conventional computing faces a huge technical challenge as traditional transistors will soon reach their size limitations. This will halt progress in reaching faster processing speeds and to overcome this problem, require an entirely new approach. Quantum computing (QC) is a natural solution offering a route to miniaturisation by, for example, storing information in electron or nuclear spin states, whilst harnessing the power of quantum physics to perform certain calculations exponentially faster than its classical counterpart. However, QCs face many difficulties, such as, protecting the quantum-bit (qubit) from the environment and its irreversible loss through the process of decoherence. Hybrid systems provide a route to harnessing the benefits of multiple degrees of freedom through the coherent transfer of quantum information between them. In this thesis I show coherent qubit transfer between electron and nuclear spin states in a ¹⁵N@C₆₀ molecular system (comprising a nitrogen atom encapsulated in a carbon cage) and a solid state system, using phosphorous donors in silicon (Si:P). The propagation uses a series of resonant mi- crowave and radiofrequency pulses and is shown with a two-way fidelity of around 90% for an arbitrary qubit state. The transfer allows quantum information to be held in the nuclear spin for up to 3 orders of magnitude longer than in the electron spin, producing a ¹⁵N@C₆₀ and Si:P ‘quantum memory’ of up to 130 ms and 1.75 s, respectively. I show electron and nuclear spin relaxation (T₁), in both systems, is dominated by a two-phonon process resonant with an excited state, with a constant electron/nuclear T₁ ratio. The thesis further investigates the decoherence and relaxation properties of metal atoms encapsulated in a carbon cage, termed metallofullerenes, discovering that exceptionally long electron spin decoherence times are possible, such that these can be considered a viable QC candidate.

The work presented in this thesis has two parts. The first part deals with methodological developments in the area of solid-state NMR, relevant to the study of partially ordered systems. Liquid crystals are best examples of such partially ordered systems and they are easily oriented by the magnetic field used for the NMR study. They provide spectra rich in information useful for the study of structure and dynamic s of the oriented molecule. Dipolar couplings and anisotropic chemical shifts are relatively easy to obtain for these systems. However, the methodologies used for extracting the required information are constantly undergoing change, with newer ideas being used for optimal use of the technique and increasing the sensitivity of the methodology. In this thesis, existing methods used for obtaining dipolar couplings from oriented liquid crystalline samples are examined in detail and conditions for optimal use of the methods are investigated. Different approaches for enhancing the sensitivity of the techniques are also proposed. Estimation of chemical shift anisotropy of carbons for a molecule that is used as a building block for several mesogens has been obtained and its utility for estimating the order parameters of the system have been examined. The second part of the thesis deals with the application of solid state NMR methods to the study of a number of novel liquid crystalline systems and for the estimation of dynamics, order and orientation of the mesogenic molecules in the magnetic field. Chapter-2 deals with a detailed and systematic study to improve the sensitivity of cross-polarization based separated local field (SLF) NMR spectroscopy techniques such as PISEMA(Polarization Inversion Spin Exchange at the Magic Angle) and PDLF(Pro-ton Detected Local Field). The chapter has been further divided into three sections. Section-A describes the optimization procedure for cross-polarization period for reducing zero-frequency peaks in SLF experiments. Polarization Inversion(PI) is one of the important components of PISEMA and plays a crucial role in enhancing the dipolar cross-peaks and suppressing the axial-peaks. Shortening this period has the advantage of less r.f. power input into the system, thus less susceptibility to sample heating. Therefore it is crucial to arrive at the optimum condition for which maximum sensitivity and resolution are obtained. A detailed experimental investigation of the role of the initial po1arization period has been carried out for two different samples of static oriented liquid crystalline material at two different temperatures and a contact time of 2ms has been found to be optimal for such samples. Insection-B of this chapter, the initial preparation period of the experiment is considered as a possible means of increasing the sensitivity of the experiment. Thus the use of cross-polarization via the dipolar bath by the use of a diabatic demagnetization in the rotating frame(ADRF-CP) has been proposed to be incorporated into PISEMA. To understand the CP dynamics, magnetization in double-and zero-quantum reservoirs of an ensemble of spin-1/2 nuclei and their role in determining the sensitivity the experiments have been theoretically examined. Experimentally, a modification incorporating ADRF-CP is shown to result in enhancement of signal-to-noise by as much as 90% in the case of rigid single crystals of a model peptide and up to 50% in non-rigid, partially ordered liquid crystalline systems. In section-C another useful SLF technique known as PDLF spectroscopy has also been examined. In this case a sweep of one of the r.f. amplitudes(RAMP-CP),rather than ADRF is found to work well. The reason for the different behaviours has been discussed. Chapter-3 highlights two experimental approaches used to extract the chemical shift anisotropy(CSA) tensor information from rotating solids. Section-A is devoted to the measurement of the CSA values of thiophene by using MAS side band analysis, by extracting the principal values from the intensities of just a few spinning side bands. Experiments have been performed on thiophene-2 carboxylic acid and thiophene-3 carboxylic acid samples and the carbon CSA values have been obtained. In section-B, CSA values of carbons of the core unit of the liquid crystal4- hexyloxybenzoic acid (HBA) have been obtained by using the recoupling pulse sequence SUPER(Separation of Undistorted Powder patterns by Effortless Recoupling).HBA belongs to an important class of thermotropic liquid crystals which are structurally simple and often used as starting materials for many novel mesogens. As this molecule could serve as an ideal model compound, high resolution13C NMR studies of HBA in solution, solid and liquid crystalline phases have been also undertaken. The CSA values obtained from the 2D SUPER experiment showed good agreement to those computed by DFT calculations. The CSA values were used for obtaining the order parameter of the system at different temperatures. These matched well the order parameter obtained from the 13C-1 H dipolar couplings in the nematic phase determined by SLF spectroscopy at various temperatures. A knowledge of the CSA of the carbons is thus very useful, as they can be used for gaining knowledge about the system from the chemical shifts obtained from a simple 1D spectrum. In chapter-4, 1-and 2-dimensional13CNMR techniques have been utilized to obtain extensive information about some novel mesogenic molecules. Four molecules of different structure and topology have been taken up for study. These molecules have the following features. Mesogen-1 has a terminal hydroxyl group. Such systems with further modification can result in mesogenic monomers for side chain liquid crystalline polymers. Mesogen-2 has a dimethyl amino group at one end and has three phenyl groups connected by appropriate linking units that form the core. In the third case, mesogen-3, the terminal hydroxyl group of mesogen-1 is replaced with a hydrogen such that13C-1 H dipolar couplings provide directly information on molecular ordering and orientation. In the fourth case, mesogen-4, the core is built with four phenyl rings. Here the fourth ring is linked to other three rings via a flexible chain unit. In each of these cases the 2DSLFNMR experiments have been carried out where13C-1 H dipolar couplings as well as13C chemical shifts were used for obtaining the order parameters of various segments of the molecule. The data provide useful insight into the phase behaviour, ordering and orientation of the molecules. Chapter-5 discusses the applications of the natural abundance 13CNMR techniques to thiophene based mesogens, that have the potential for use in molecular electronics material. Typically, these molecules consist of phenyl rings appropriately connected by linking units with thiophene. Different core units as well as different linking units to thiophene have been considered. The six mesogens thus obtained have been investigated in detail using 1D and 2D NMR methods.13C-1 H dipolar couplings have been used to obtain ordering information, that show interesting correlation to the molecular orientation and dynamics.