A core level spectroscopy study of ice and water is presented in this thesis. Combining a number of experiments and spectrum calculations based on density functional theory, changes in the local valence electronic structure are shown to be sensitive to the local H-bonding configurations. Exploiting this sensitivity, we are able to approach important scientific problems for a number of aggregation states; liquid water, the water-metal interface, bulk and surface of hexagonal ice. For the H-bonded model system hexagonal ice, we have probed the occupied valence electronic structure by x-ray emission and x-ray photoelectron spectroscopy. Stepwise inclusion of different types of interactions within density functional theory, together with a local valence electron population analysis, show that it is essential to include intermolecular charge transfer together with internal s-p rehybridizations in order to describe the changes in electronic structure seen in the experiment. The attractive electrostatic interaction between water molecules is enhanced by a decrease in Pauli repulsion. A simple electrostatic model due to charge induction from the surrounding water is unable to explain the electronic structure changes. By varying the probing depth in x-ray absorption the structure of the bulk, subsurface and surface regions is probed in a thin ice film. A pronounced continuum for fully coordinated species in the bulk is in sharp contrast to the spectrum associated with a broken symmetry at the surface. In particular molecular arrangements of water with one uncoordinated OH group have unoccupied electronic states below the conduction band that are responsible for a strong anisotropic pre-edge intensity in the x-ray absorption spectrum. The topmost layer is dominated by an almost isotropic distribution of these species, which is inconsistent with an unrelaxed surface structure. For liquid water the x-ray absorption spectrum resembles that of the ice surface, indicating a domination of species with broken hydrogen bond configurations. The sensitivity to the local hydrogen bond configuration, in particular the sensitivity to broken bonds on the donor side, allows for a detailed analysis of the liquid water spectrum. Most molecules in liquid water are found in two-hydrogen-bonded configurations with one strong donor and one strong acceptor hydrogen bond. The results, consistent with diffraction data, imply that most molecules are arranged in strongly H-bonded chains or rings embedded in a disordered cluster network. Molecular dynamics simulations are unable to describe the experimental data. The water overlayer on the close-packed platinum surface is studied using a combination of core-level spectroscopy and density functional theory. A new structure for water adsorption on close-packed transition metal surfaces is found, where a weakly corrugated non-dissociated overlayer interacts via alternating oxygen-metal and hydrogen-metal bonds. The latter results from a balance between metal-hydrogen bond formation and OH bond weakening. The ultrashort core-hole lifetime of oxygen provides a powerful probe of excited state dynamics via studies of the non-radiative or radiative decay following x-ray absorption. Electrons excited into the pre-edge state for single donor species at the ice surface remain localized long enough for early time solvation dynamics to occur and these species are suggested as strong pre-existing traps to the hydrated electron. Fully coordinated molecules in the bulk contribute to a strong conduction band with electron transfer times below 0.5 femtoseconds. Upon core-ionization, both protons are found to migrate substantial distances on a femtosecond timescale. This unusually fast proton dynamics for non-resonant excitation is captured both by theory and experiment with a measurable isotope effect.

This thesis concerns methods of reduced complexity for electronic structure calculations.  When quantum chemistry methods are applied to large systems, it is important to optimally use computer resources and only store data and perform operations that contribute to the overall accuracy. At the same time, precarious approximations could jeopardize the reliability of the whole calculation.  In this thesis, the self-consistent field method is seen as a sequence of rotations of the occupied subspace. Errors coming from computational approximations are characterized as erroneous rotations of this subspace. This viewpoint is optimal in the sense that the occupied subspace uniquely defines the electron density. Errors should be measured by their impact on the overall accuracy instead of by their constituent parts. With this point of view, a mathematical framework for control of errors in Hartree-Fock/Kohn-Sham calculations is proposed.  A unifying framework is of particular importance when computational approximations are introduced to efficiently handle large systems. An important operation in Hartree-Fock/Kohn-Sham calculations is the calculation of the density matrix for a given Fock/Kohn-Sham matrix. In this thesis, density matrix purification is used to compute the density matrix with time and memory usage increasing only linearly with system size. The forward error of purification is analyzed and schemes to control the forward error are proposed. The presented purification methods are coupled with effective methods to compute interior eigenvalues of the Fock/Kohn-Sham matrix also proposed in this thesis.New methods for inverse factorizations of Hermitian positive definite matrices that can be used for congruence transformations of the Fock/Kohn-Sham and density matrices are suggested as well. Most of the methods above have been implemented in the Ergo quantum chemistry program. This program uses a hierarchic sparse matrix library, also presented in this thesis, which is parallelized for shared memory computer architectures. It is demonstrated that the Ergo program is able to perform linear scaling Hartree-Fock calculations. / QC 20100908

Transition metal oxides have proven to be a fertile research area for condensed matter physicists due to the fascinating array of superconducting, magnetic and electronic properties they exhibit. A particular resurgence of intense activity in investigating the properties of these systems followed the discovery of high temperature superconductivity in the cuprates, colossal magnetoresistance in the manganites, ferroelectricity in the cobaltites and simultaneous ferroelectric and ferromagnetic ordering in the manganites. These diverse properties of transition metal compounds arise due to the presence of strong electron-electron interactions within the transition element 3d states. Indeed, it is the competition between the localizing effects of such interactions and the comparable hopping strengths driving the system towards delocalization, that is responsible for these wide spectrum of interesting properties. In terms of theoretical and fundamental issues, electronic structure of transition metal oxides play a most important role, providing a testing ground for new many-body theoretical approaches treating the correlation problem at various levels of approximations. In addition to this rich spectrum of properties, metal-insulator transitions often occur and can even be coincident with structural or magnetic changes due to the strong coupling between charge, magnetic and lattice degrees of freedom. However, in spite of the immense activities in this area, the underlying phenomena is not yet completely understood. A careful investigation of the electronic structure of these systems will help in the microscopic understanding of these and photoelectron spectroscopy has been established as the most powerful tool for investigating the electronic structures of these systems. In this thesis we investigate the electronic structures of some of these transition metal oxides and the metal-insulator transition as a function of electron correlation strength and doping of charge carriers by means of photoelectron spectroscopy; we analyze the experimental results using various theoretical approaches, in order to obtain detailed and quantitative understandings. This thesis is organized into seven chapters. Chapter 1 is a general introduction to the various concepts discussed in this thesis. Here we briefly describe the various mechanisms and theoretical formalisms used for understanding the metal-insulator transitions in strongly correlated systems and the evolution of the electronic structure across the transition. The experimental and the calculational techniques used in this thesis is described in Chapter 2. This includes different sample synthesis techniques and the characterization tools used in the present study. Photoelectron spectroscopic techniques used for probing the electronic structure of various systems are also discussed in this chapter. In Chapter 3, we discuss the coexistence of ferromagnetism and superconductivity in ruthenocuprates by looking at the electronic structures of RuSr2Eu1.5Ce0.5Cu2O10 which is a ferromagnetic superconductor having the ferromagnetic TC ~ 100 K and a superconducting transition of ~ 30 K compared with RuSr2EuCeCu2O10 which is a ferromagnetic (TC ~ 150 K) insulator in conjunction with two reference systems, RuSr2GdO6and Sr2RuO4. The coexistence of ferromagnetic order with superconductivity below the superconducting temperature is an interesting issue since the pair-breaking due to magnetic interactions is not significant in these cases. Extensive photoelectron spectroscopic measurements were performed on these systems and our results show that Eu and Ce in both the ruthenocuprates exists in 3+ and 4+ states, respectively. Also the analysis of the Ru 3d and 3p core levels suggests that Ru remains in the pentavalent state in both the cases. The constancy of Ru valency with doping of charge carriers that bring about an insulator to metal transition and the superconducting state suggests that the electronic structure and transport properties of these compounds are not governed by the Ru-O plane, but by the Cu-O plane, much as in the case of other high TC cuprates. Analysis of the Cu 2p core level spectra in terms of a cluster model, including configuration interaction and multiplet interactions between Cu 3d and 2p as well as that within the Cu 3d states, establish a close similarity of the basic electronic structure of these ruthenocuprates to those of other high TC cuprates. Here the charge transfer energy, Δ << Udd,Cu 3d multiplet-averaged Coulomb repulsion energy, establishing the compounds to be deep in the charge transfer regime. Continuing with the ruthenocuprate systems in Chapter 4, we look at the electronic structure of hole doped La2CuRuO6systems using various photoemission techniques. It was expected that since the substitution of La3+by Sr2+changes the d electron count, the system will undergo a metal to insulator transition, but the transport properties show that all of them remain semiconducting through out the lowest temperature of measurement. A careful analysis of the Ru 3d and 3p core level spectra shows that Ru exists in Ru 4+state in La2CuRuO6and goes towards Ru 5+state with hole doping. This suggests that the doped holes affects the electronic structure of the Ru levels in these systems. A spectral decomposition of the Ru 3d core level suggests the existence of a spin orbit split doublet having two peaks, a main core level peak and a satellite peak at the higher binding energy side of the main peak and the intensity ratio of the satellite peak to the main peak increases with the insulating nature of the compounds as reported for other Ru 4d strongly correlated systems. This observation is also consistent with the transport properties. Cu 2p core level spectra also shows variations in the satellite-to-main peak Cu 2p intensities suggesting that the electronic structure of the Cu levels are also getting affected with Sr doping. Valence band spectral features near the Fermi level shows that the spectral weight is highest for La2CuRuO6and depletes slowly with Sr doping consistent with the expected d electron count as suggested by the Ru valencies. In Chapter 5 and Chapter 6 we discuss the electronic structure investigations of two early transition metal oxide series, namely Ca1−xSrxVO3and Ce1−xSrxTiO3. Surface sensitivity dependence of photoemission experiments has been explored to show that the surface and the bulk electronic structures of Ca1−xSrxVO3system is different. Photoemission spectra of this system using synchrotron radiation reveal a hither to unnoticed polarization dependence of the photoemission matrix elements for the surface component leading to substantial underestimation. Extracted bulk spectra from experimentally determined electron escape depth and underestimation of surface contributions resolve the puzzling issues that arose due to the recent diverse interpretations of the electronic structure in Ca1−xSrxVO3. Keeping in mind the above-mentioned caveat, the present results still clearly establish that the linear polarization of synchrotron radiation plays a key role in determining the spectral lineshape in these systems. The experimentally-determined bulk spectra provide an understanding of the electronic structure in Ca1−xSrxVO3, consistent with experimental γ values, calculated change in the d-bandwidth and the geometrical/structural trends across the series, thereby resolving the puzzle concerning the structure-property relationship in this interesting class of compounds. In Chapter 6 we discuss the issues of metal-insulator transition close to the d0limit as well as the evolution of the electronic structure of a strongly correlated system as a function of electron occupancy, by investigating the family of Ce1−xSrxTiO3compounds by recording core level as well as valence band photoemission spectra using lab source as well as synchrotron radiations. Core level Ce 3d spectra from Ce1−xSrxTiO3samples establish a trivalent state of Ce in these compounds for all values of x confirming that charge doping in the present system does not alter the electronic structure of Ce. Hence the change in valency due to Sr substitution and thus, the carrier number, takes place only in the Ti 3d-O 2p manifold. We also carried out extensive VUV photoemission experiments on these samples with the photon energy varying between 26-122 eV. From the difference spectrum obtained by subtracting the off-resonance spectrum from the on-resonance one, we obtain the Ce 4f spectral signature; thus obtained Ce 4f spectrum which has a peak at about 3 eV binding energy and shows no intensity at EF even for the metallic samples, consistent with a Ce3+state. In order to study the states near EF responsible for the metal-insulator transition in these compounds, we recorded the valence band spectra at the Ce 4f off-resonance condition so that the coherent and the incoherent spectral features arising from the Ti 3d states could be clearly resolved, allowing us to investigate the metal insulator transition in the Ce1−xSrxTiO3system as a function of Sr or hole doping. The experimental spectra of the metallic compounds exhibit an intensity of the incoherent feature considerably larger than that predicted by theory. This discrepancy is possibly due to a difference in the surface and the bulk electronic structures of these compounds. Chapter 7 is divided into two parts. In the first part we discuss the extended x-ray absorption fine structure (EXAFS) studies performed on two transition metal oxide series, La1−xSrxCoO3and La1−xSrxFeO3to look at the local structure distortions happening around the transition metal ions and its role in bringing out metal to insulator transitions in transition metal oxide systems. Here we chose to investigate these two systems since La1−xSrxCoO3undergoes an insulator to metal transition for x ∼ 0.15 and La1−xSrxFeO3remains insulating for the entire range of doping. The static mean square relative displacement, which we believe to be a representation of the disorder present in the system, extracted by fitting the experimental data by a correlated Einstein model, as a function of composition in La1−xSrxCoO3saturates beyond the critical composition where as the disorder parameter continues to increase through out the entire doping range in the case of La1−xSrxFeO3where metal-insulator transition is absent. In the second part of Chapter 7 we discuss the x-ray absorption near edge structure (XANES) studies performed on the above mentioned series of systems. Co K-edge XANES spectra of La1−xSrxCoO3show that there is a systematic shift of the main absorption peak with hole doping suggesting that the Co valency changes systematically with Sr doping. Also, the pre-edge feature of LaCoO3shows the transitions to t2g level clearly showing that Co3+in LaCoO3is not in a pure low spin (t6 2g) state. The Fe K-edge XANES spectra of La1−xSrxFeO3also exhibit a systematic shift to the higher energy side with increase in Sr content, indicating an increase in the Fe valence. Also from the La L3edge analysis, it can be concluded that the oxygen environment around La and the electronic configuration of La are systematically changing with Sr doping.

This work presents a joint theoretical and experimental investigation of the electronic structure of quasi one-dimensional cuprates and vanadates. Electron energy-loss spectroscopy in transmission was employed to measure the momentum-dependent loss function of Li2CuO2, CuGeO3, V2O5 and NaV2O5. The comparison between the experimental data and the results from bandstructure as well as cluster calculations allows an explanation of the mobility and correlations of the electrons in these systems. The investigation of the electronic structure of the structurally related cuprates Li2CuO2 and CuGeO3 is exemplary for the study of the transition from a quasi zero-dimensional to a quasi one-dimensional system. In contrast to Li2CuO2 where the electron transitions are strongly localized, the excited states in CuGeO3 can be assigned to the electron hopping to the nearest-neighboured CuO4 plaquettes. The shift of spectral weight from the high energy to the low energy region with increasing coupling between the plaquettes, observed in edge-sharing CuO2 chains, is confirmed by the applied cluster modell. The momentum dependent loss functions of NaV2O5 deliver information about the mobility and correlations of electrons in a quarter-filled ladder system which determine the transition from the charge ordered state into the unordered state at 34 K. Thcontributions of the 3d electrons to the EELS spectra of NaV2O5 are filtered by comparing these spectra with the loss functions of the structurally related V2O5 (d0 configuration). For NaV2O5 the picture of linear chains of V-O-V rungs containing a single d electron in a molecular orbital-like state is confirmed. The comparison of the experimentally determined optical conductivities and those derived from the bandstructrure calculations yield a good agreement upon adoption of an on-site Coulomb interaction U = 2-3 eV. In contrast to the strongly anisotropic hopping within the ladder plane the intersite Coulomb interactions V are about the same size. These interactions are the driving force for the transition from an unordered state at room temperature into a zigzag ordered state observed at low temperatures. / In einer Kombination aus experimentellen und theoretischen Methoden wurden in dieser Arbeit die Elektronenstrukturen von quasi-eindimensionalen Kupraten und Vanadaten untersucht. Dazu wurde die impulsabhängige Verlustfunktion mit Hilfe der Elektronen-Energieverlustspektroskopie in Transmission an Einkristallen von Li2CuO2, CuGeO3, V2O5 und NaV2O5 gemessen. Der Vergleich der experimentellen Daten mit Ergebnissen aus Bandstruktur- und Cluster-Rechnungen erlaubte Rückschlüsse auf die Beweglichkeit und Korrelationen der Elektronen in diesen Systemen. Die Untersuchung der elektronischen Anregungen in den strukturell sehr ähnlichen Kupraten Li2CuO2 und CuGeO3 ist beispielhaft für das Studium des Übergangs von einem quasi-nulldimensionalen zu einem quasi-eindimensionalen System. In Li2CuO2 finden die elektronischen Übergänge vorwiegend lokal auf der CuO4-Plakette statt. Dagegen findet man in CuGeO3 angeregte Zustände, die als das Hüpfen der Elektronen auf benachbarte Plaketten interpretiert werden können. Das angewandte Cluster-Modell bestätigt für eine zunehmende Kopplung zwischen den Plaketten die in eckenverbundenen Kupratketten beobachtete Verschiebung des spektralen Gewichts vom hoch- zum niederenergetischen Bereich. Die Verlustfunktionen von NaV2O5 liefern wertvolle Informationen über die Freiheitsgrade und Korrelationen der Elektronen in einem viertelgefüllten Leitersystem, die wesentlich den Phasenübergang zwischen geordneter und ungeordneter Ladung bei 34 K bestimmen. Die Beiträge der 3d-Elektronen von NaV2O5 zu den EELS-Spektren konnten durch eine vergleichende Studie der Verlustfunktionen des strukturell verwandten V2O5, das keine d-Elektronen besitzt, separiert werden. Die Beschreibbarkeit der Elektronenstruktur in NaV2O5 durch ein effektives Modell einfach besetzter, molekülähnlicher V-O-V-Sprossen wird bestätigt. Die Coulomb-Wechselwirkung U kann in diesem Modell auf den Wertebereich zwischen 2 und 3 eV eingeschränkt werden. Im Gegensatz zu den stark anisotropen Hüpfwahrscheinlichkeiten in der Leiterebene sind die Coulomb-Wechselwirkungen V zwischen Elektronen auf benachbarten Vanadiumplätzen nahezu von gleicher Größe. Diese Wechselwirkungen sind die treibende Kraft für den Übergang von einem ungeordneten Zustand bei Raumtemperatur in einen zickzackgeordneten Grundzustand bei tiefen Temperaturen.

Im Rahmen der vorliegenden Arbeit wird eine Tight-Binding-Formulierung der Korringa-Kohn-Rostoker-Greenschen-Funktionsmethode vorgestellt. Dabei werden mittels eines geeignet gewählten Referenzsystems abgeschirmte Strukturkonstanten konstruiert. Es werden die Vorteile und Grenzen dieser Transformation des Formalismus diskutiert. Es wird gezeigt, daß der numerische Aufwand zur erechnung der Elektronenstruktur von Systemen mit langgestreckter Elementarzelle linear mit der Systemgröße wächst. Damit ist eine Behandlung von Systemen mit 500 und mehr Atomen pro Elementarzelle möglich. Anhand von umfangreichen Testrechnungen kann demonstriert werden, daß das neue Verfahren bezüglich seiner Genauigkeit mit dem traditionellen KKR-Verfahren vergleichbar ist. Es werden Anwendungen zur Berechnung der Elektronenstruktur sowie zur Zwischenlagenaustauschkopplung von Co/Cu(100)-Vielfachschichten vorgestellt. / A newly developed ab initio tight-binding-formulation of the Korringa-Kohn-Rostoker-Green's function method for layered systems is presented. Screened structure constants are calculated by means of a repulsive reference system. Advantages and limits of this transformation of the formalism are discussed in detail. The numerical effort for self consistent electronic structure calculations of systems with a large prolonged supercell scales linearly with the system size. Systems with up to 500 atoms per unit cell can be treated easily. The accuracy of the new method is of the same order as the traditional KKR method. Applications to electronic structure calculations and magnetic interlayer exchange coupling in Co/Cu(100) multilayers are presented.

The search for alternate and renewable energy resources as well as the efficient use of energy and development of such systems that can help to save the energy consumption is needed because of exponential growth in world population, limited conventional fossil fuel resources, and to meet the increasing demand of clean and environment friendly substitutes. Hydrogen being the simplest, most abundant and clean energy carrier has the potential to fulfill some of these requirements provided the development of efficient, safe and durable systems for its production, storage and usage. Chemical hydrides, complex hydrides and nanomaterials, where the hydrogen is either chemically bonded to the metal ions or physiosorbed, are the possible means to overcome the difficulties associated with the storage and usage of hydrogen at favorable conditions. We have studied the structural and electronic properties of some of the chemical hydrides, complex hydrides and functionalized nanostructures to understand the kinetics and thermodynamics of these materials. Another active field relating to energy storage is rechargeable batteries. We have studied the detailed crystal and electronic structures of Li and Mg based cathode materials and calculated the average intercalation voltage of the corresponding batteries. We found that transition metal doped MgH2 nanocluster is a material to use efficiently not only in batteries but also in fuel-cell technologies. MAX phases can be used to develop the systems to save the energy consumption. We have chosen one compound from each of all known types of MAX phases and analyzed the structural, electronic, and mechanical properties using the hybrid functional. We suggest that the proper treatment of correlation effects is important for the correct description of Cr2AlC and Cr2GeC by the good choice of Hubbard 'U' in DFT+U method. Hydrogen is fascinating to physicists due to predicted possibility of metallization and high temperature superconductivity. On the basis of our ab initio molecular dynamics studies, we propose that the recent claim of conductive hydrogen by experiments might be explained by the diffusion of hydrogen at relevant pressure and temperature. In this thesis we also present the studies of phase change memory materials, oxides and amorphization of oxide materials, spintronics and sulfide materials.

Photoelectron spectroscopy is an experimental method to study the electronic structure in matter. In this thesis, a combination of soft and hard X-ray based photoelectron spectroscopy has been used to obtain atomic level understanding of electronic structures and energy level alignments in mesoscopic solar cells. The thesis describes how the method can be varied between being surface and bulk sensitive and how to follow the structure linked to particular elements. The results were discussed with respect to the material function in mesoscopic solar cell configurations. The heart of a solar cell is the charge separation of photoexcited electrons and holes, and in a mesoscopic solar cell, this occurs at interfaces between different materials. Understanding the energy level alignment between the materials is important for developing the function of the device. In this work, it is shown that photoelectron spectroscopy can be used to experimentally follow the energy level alignment at interfaces such as TiO2/metal sulfide/polymer, as well as TiO2/perovskite. The electronic structures of two perovskite materials, CH3NH3PbI3 and CH3NH3PbBr3 were characterized by photoelectron spectroscopy and the results were discussed with support from quantum chemical calculations. The outermost levels consisted mainly of lead and halide orbitals and due to a relatively higher cross section for heavier elements, hard X-ray excitation was shown useful to study the position as well as the orbital character of the valence band edge. Modifications of the energy level positions can be followed by core level shifts. Such studies showed that a commonly used additive in mesoscopic solar cells, Li-TFSI, affected molecular hole conductors in the same way as a p-dopant. A more controlled doping can also be achieved by redox active dopants such as Co(+III) complexes and can be studied quantitatively with photoelectron spectroscopy methods. Hard X-rays allow studies of hidden interfaces, which were used to follow the oxidation of Ti in stacks of thin films for conducting glass. By the use of soft X-rays, the interface structure and bonding of dye molecules to mesoporous TiO2 or ZnO could be studied in detail. A combination of the two methods can be used to obtain a depth profiling of the sample.

La présente thèse porte sur l'utilité de la théorie de la fonctionnelle de la densité dans le design de polymères pour applications photovoltaïques. L'étude porte d'abord sur le rôle des calculs théoriques pour la caractérisation des polymères dans le cadre de collaborations entre la théorie et l'expérience. La stabilité et les niveaux énergétiques de certaines molécules organiques sont étudiés avant et après la sulfuration de leurs groupements carbonyles, un procédé destiné à diminuer le band gap. Les propriétés de dynamique électronique, de séparation des porteurs de charges et de spectres de vibrations Raman sont également explorées dans un polymère à base de polycarbazole. Par la suite, l'utilité des calculs théoriques dans le design de polymères avant leurs synthèses est considérée. La théorie de la fonctionnelle de la densité est étudiée dans le cadre du modèle de Scharber afin de prédire l'efficacité des cellules solaires organiques. Une nouvelle méthode de design de polymères à faible band gaps, basée sur la forme structurale aromatique ou quinoide est également présentée, dont l'efficacité surpasse l'approche actuelle de donneur-accepteur. Ces études sont mises à profit dans l'exploration de l'espace moléculaire et plusieurs candidats de polymères aux propriétés électroniques intéressantes sont présentés. / This thesis focuses on the role of density functional theory in the design of polymers for photovoltaic applications. Theoretical calculations are first studied in the characterization of polymers in the context of collaborations between theory and experiment. The stability and the energy levels of some organic molecules are studied before and after a sulfurization of their carbonyl groups, a process destined to lower the band gaps. The dynamics of the electronic processes and the Raman vibration spectra are also explored in a polycarbazole-based polymer. From then, the usefulness of theoretical calculations in the design of polymers before their syntheses is explored. Density functional theory calculations are studied under the Scharber model in order to predict the efficiency of organic solar cells. Then, a new approach for the design of low band gap polymer based on the aromatic or quinoid structures is established, whose efficiency surpasses the actual donor-acceptor approach. These studies are used in the exploration of the chemical space and several candidate for polymers with interesting electronic properties are presented.

In der vorliegenden Diplomarbeit wurden sekundäre Isotopeneffekte auf NMR-chemische Verschiebungen mit ab-initio quantenchemischen Methoden bestimmt. Um die zu erwartenden Fehler verschiedener Methoden abschätzen zu können, wurden die sekundären Isotopeneffekte von Fluor(2-2H1)ethan auf HF, MP2 und CCSD(T)-Niveau mit tripel- und quadrupel-Zeta Basissätzen berechnet. Anhand der Ergebnisse dieser Rechnungen lässt sich zeigen, dass gauche und antiperiplanare Konformere bereits mithilfe von sekundären Isotopenverschiebungen unterschieden werden können, die auf HF/tz2p-Niveau berechnet wurden. Weiterhin wurde untersucht, ob es eine Abhängingkeit des Isotopeneffektes von den Diederwinkeln zwischen Deuterium- und Fluorsubstituenten gibt. Die sekundären Isotopeneffekte auf 19F-NMR-chemische Verschiebungen von exo- und endo-2-Fluornorbornanen mit Deuterium Substituenten in den endo-3, exo-3, syn-7 oder anti-7 Positionen wurden auf HF/tz2p-Niveau berechnet. Es wird gezeigt, dass die berechneten Isotopeneffekte an 2-Fluornorbornanen eine Identifizierung der verschiedenen Stereoisomere erlauben. / In the present Diploma thesis secondary isotope effects on NMR chemical shieldings were determined using ab-initio quantum chemical methods. In order to estimate errors of various methods, secondary isotope effects on fluoro(2-2H1)ethane were calculated at the HF, MP2 and CCSD(T) level of theory using triple- and quadruple zeta basis sets. On the basis of these calculations it can be shown that gauche and antiperiplanar conformers can already be distinguished by their secondary isotope shifts calculated at the HF/tz2p level of theory. Furthermore it was investigated, whether a dependency of the isotope effects on dihedral angles between the deuterium and the fluorine substituent exists. The secondary isotope effects on 19F chemical shifts of exo- and endo-2-fluoronorbornanes with deuterium subsituents in the endo-3, exo-3, syn-7 or anti-7 positions were calculated at the HF/tz2p level. It is shown that the calculated isotope effects of 2-fluoronorbornanes allow to identify various stereoisomers.

In this thesis the application of novel tensor decomposition and tensor representation techniques in highly accurate post Hartree-Fock methods is evaluated. These representation techniques can help to overcome the steep scaling behaviour of high level ab-initio calculations with increasing system size and therefore break the "curse of dimensionality". After a comparison of various tensor formats the application of the "canonical polyadic" format (CP) is described in detail. There, especially the casting of a normal, index based tensor into the CP format (tensor decomposition) and a method for a low rank approximation (rank reduction) of the two-electron integrals in the AO basis are investigated. The decisive quantity for the applicability of the CP format is the scaling of the rank with increasing system and basis set size. The memory requirements and the computational effort for tensor manipulations in the CP format are only linear in the number of dimensions but still depend on the expansion length (rank) of the approximation. Furthermore, the AO-MO transformation and a MP2 algorithm with decomposed tensors in the CP format is evaluated and the scaling with increasing system and basis set size is investigated. Finally, a Coupled-Cluster algorithm based only on low-rank CP representation of the MO integrals is developed. There, especially the successive tensor contraction during the iterative solution of the amplitude equations and the error propagation upon multiple application of the reduction procedure are discussed. In conclusion the overall complexity of a Coupled-Cluster procedure with tensors in CP format is evaluated and some possibilities for improvements of the rank reduction procedure tailored to the needs in electronic structure calculations are shown. / Die vorliegende Arbeit beschäftigt sich mit der Anwendung neuartiger Tensorzerlegungs- und Tensorrepesentationstechniken in hochgenauen post Hartree-Fock Methoden um das hohe Skalierungsverhalten dieser Verfahren mit steigender Systemgröße zu verringern und somit den "Fluch der Dimensionen" zu brechen. Nach einer vergleichenden Betrachtung verschiedener Representationsformate wird auf die Anwendung des "canonical polyadic" Formates (CP) detailliert eingegangen. Dabei stehen zunächst die Umwandlung eines normalen, indexbasierten Tensors in das CP Format (Tensorzerlegung) und eine Methode der Niedrigrang Approximation (Rangreduktion) für Zweielektronenintegrale in der AO Basis im Vordergrund. Die entscheidende Größe für die Anwendbarkeit ist dabei das Skalierungsverhalten das Ranges mit steigender System- und Basissatzgröße, da der Speicheraufwand und die Berechnungskosten für Tensormanipulationen im CP Format zwar nur noch linear von der Anzahl der Dimensionen des Tensors abhängen, allerdings auch mit der Expansionslänge (Rang) skalieren. Im Anschluss wird die AO-MO Transformation und der MP2 Algorithmus mit zerlegten Tensoren im CP Format diskutiert und erneut das Skalierungsverhalten mit steigender System- und Basissatzgröße untersucht. Abschließend wird ein Coupled-Cluster Algorithmus vorgestellt, welcher ausschließlich mit Tensoren in einer Niedrigrang CP Darstellung arbeitet. Dabei wird vor allem auf die sukzessive Tensorkontraktion während der iterativen Bestimmung der Amplituden eingegangen und die Fehlerfortpanzung durch Anwendung des Rangreduktions-Algorithmus analysiert. Abschließend wird die Komplexität des gesamten Verfahrens bewertet und Verbesserungsmöglichkeiten der Reduktionsprozedur aufgezeigt.