Die vorliegende Promotionsarbeit “Density functional study of the electronic and magnetic properties of selected transition metal complexes” beschäftigt sich mit dem Zusammenhang zwischen strukturellen Merkmalen sowie elektronischen und magnetischen Eigenschaften von Einzelmolekül-Magneten. Im Wesentlichen konnte dabei gezeigt werden, dass die magnetischen Eigenschaften sowohl von strukturellen Merkmalen als auch von den elektronischen Eigenschaften bestimmt werden. Des Weiteren ergab sich, dass verschiedene Kenngrößen der magnetischen Eigenschaften (im speziellen der magnetische Grundzustand S sowie die magnetische Anisotropie D) miteinander korreliert sind. Dies ist im Besonderen für eine mögliche Anwendung von Einzelmolekül-Magneten im Bereich der Datenspeicherung von Bedeutung.

The physics of cuprates is strongly influenced by the dimension of the cooper-oxygen network in the considered crystals. Due to the rich manifoldness of different network geometries realized by nature, cuprates are ideal model systems for experimental and theoretical studies of low-dimensional, strongly correlated systems. The dimensionality of the considered model compounds varies between zero and three with a focus on one- and two-dimensional compounds. Starting from LDA band structure calculations, the relevant orbitals for the low-energy physics have been characterized together with a discussion of the chemical bonding in the investigated compounds. By means of a systematic approach for various compounds, the influence of particular structural components on the electronic structure could be concluded. For the undoped cuprate compounds, paramagnetic LDA band structure calculations yield a metallic groundstate instead of the experimentally observed insulating behavoir. The strong correlations were taken into account using Hubbard- or Heisenberg-like models for the investigation of the magnetic couplings in cuprates. The necessary parameters were obtained from tight-binding parameterizations of LDA band structures. Finallly, several ARPES as well as XAS measurements were interpreted. The present work shows, that the combination of experiment, LDA, and model calculations is a powerful tool for the investigation of the electronic structure of strongly correlated systems.

Uwe Stephan Dissertation This work is concerned with methods and results for the calculation of electronic properties of amorphous carbon models (a-C). These investigations are based upon a very efficient non-selfconsistent ab-initio procedure for the evaluation of electronic states of extended systems using modified self- consistent DFT-LDA states and potentials of neutral atoms. Starting from the LCAO matrices constructed in this method, the electronic densities of states (DOS) of model systems are calculated by diagonalization or with use of the recursion method. Both techniques and, in particular, several versions of the recursion method will be investigated and compared with respect to their numerical efficiency and practical applicability. For DOS calculations in carbon systems a modification of the atomic SCF routine will be proposed and tested in application to the crystalline carbon allotropes diamond and graphite. In this work, the investigation of a-C structures is based on various structural models which have been generated in the author's research group by means of molecular-dynamics simulations using the empirical Tersoff potential as well as the just mentioned DFT-LDA approach. The total energy in this latter procedure is calculated as the sum of the band-structure energy and an empirical repulsive pair potential; contrary to the purely empirical approach, this scheme therefore includes pi-bonding effects and gives rise to a superior description of defect states in these models. As suggested by an analysis of the localization properties of the eigenstates, the defect structure in a-C models depends primarily on the ability of pi- and weak-sigma-bonded undercoordinated atoms to cluster. To investigate these clustering effects, a pi-bonding analysis will be proposed which enables the quantification and classification of the defect states and the estimation of gaps between pi bands. This procedure, which will be justified by local DOS calculations, provides essential structure-property correlations in dependence on the mass densities of the models. Within predominantly fourfold-coordinated models, the occurrence of a certain fraction of threefold-coordinated atoms turns out to stabilize the network by achieving optimum stress and defect minimization due to the preferred formation of pi-bonded atom pairs. Such models exhibit mass densities and pi gaps of about 3.0 g/cm^3 and 2.4 eV, respectively, in close agreement with recent experimental results.

Die vorliegende Promotionsarbeit “Density functional study of the electronic and magnetic properties of selected transition metal complexes” beschäftigt sich mit dem Zusammenhang zwischen strukturellen Merkmalen sowie elektronischen und magnetischen Eigenschaften von Einzelmolekül-Magneten. Im Wesentlichen konnte dabei gezeigt werden, dass die magnetischen Eigenschaften sowohl von strukturellen Merkmalen als auch von den elektronischen Eigenschaften bestimmt werden. Des Weiteren ergab sich, dass verschiedene Kenngrößen der magnetischen Eigenschaften (im speziellen der magnetische Grundzustand S sowie die magnetische Anisotropie D) miteinander korreliert sind. Dies ist im Besonderen für eine mögliche Anwendung von Einzelmolekül-Magneten im Bereich der Datenspeicherung von Bedeutung.

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.

In the first two chapters we presented the basics of density functional theory and semiempirical LSD+U approximation, which was implemented in the full-potential local-orbital (FPLO) minimal-basis calculation scheme. In the third chapter we tested the implemented version of LSDA+U on 3d transitional metal monoxides. Essential improvement of the spectroscopic properties was obtained. A simple model describing the value and direction of the magnetic moment of a transition metal ion was presented. The model visualizes the interplay of the spin-orbit coupling and crystal field splitting. In the fourth chapter we calculated the electronic spectrum of the single Zn impurity in CuO2 plane considered as a vacancy in Cu 3d states. The analytic solution for the states of different symmetry was obtained. Depending on the strength of perturbation induced by the impurity on the neighboring Cu ions, the states are either resonant or localized. The critical values of the perturbation were computed. In the fifth chapter we presented the calculations for three novel vanadates: MgVO3, Sb2O2VO3 and VOMoO4. The tight-binding parameters and the exchange integrals were computed. The magnesium and antimony vanadates appeared to be spin-½ one-dimensional systems, the latter having much stronger one-dimensional character and being probably the best realization of inorganic spin-Peierls system. The molybdenum vanadate was found to be two-dimensional spin-½ system. The Mo 4d orbitals play an important role in the electronic transfer.

Solid state physics comprises many interesting physical phenomena driven by the complex interplay of the crystal structure, magnetic and orbital degrees of freedom, quantum fluctuations and correlation. The discovery of materials which exhibit exotic phenomena like low dimensional magnetism, superconductivity, thermoelectricity or multiferroic behavior leads to various applications which even directly influence our daily live. For such technical applications and the purposive modification of materials, the understanding of the underlying mechanisms in solids is a precondition. Nowadays DFT based band structure programs become broadly available with the possibility to calculate systems with several hundreds of atoms in reasonable time scales and high accuracy using standard computers due to the rapid technical and conceptional development in the last decades. These improvements allow to study physical properties of solids from their crystal structure and support the search for underlying mechanisms of different phenomena from microscopic grounds. This thesis focuses on the theoretical description of low dimensional magnets and intermetallic compounds. We combine DFT based electronic structure and model calculations to develop the magnetic properties of the compounds from microscopic grounds. The developed, intuitive pictures were challenged by model simulations with various experiments, probing microscopic and macroscopic properties, such as thermodynamic measurements, high field magnetization, nuclear magnetic resonance or electron spin resonance experiments. This combined approach allows to investigate the close interplay of the crystal structure and the magnetic properties of complex materials in close collaboration with experimentalists. In turn, the systematic variation of intrinsic parameters by substitution or of extrinsic factors, like magnetic field, temperature or pressure is an efficient way to probe the derived models. Especially pressure allows a continuous change of the crystal structure on a rather large energy scale without the chemical complexity of substitution, thus being an ideal tool to consistently alter the electronic structure in a controlled way. Our theoretical results not only provide reliable descriptions of real materials, exhibiting disorder, partial site occupation and/or strong correlations, but also predict fascinating phenomena upon extreme conditions. In parts this theoretical predictions were already confirmed by own experiments on large scale facilities. Whereas in the first part of this work the main purpose was to develop reliable magnetic models of low dimensional magnets, in the second part we unraveled the underlying mechanism for different phase transitions upon pressure. In more detail, the first part of this thesis is focused on the magnetic ground states of spin 1/2 transition metal compounds which show fascinating phase diagrams with many unusual ground states, including various types of magnetic order, like helical states exhibiting different pitch angles, driven by the intimate interplay of structural details and quantum fluctuations. The exact arrangement and the connection of the magnetically active building blocks within these materials determine the hybridization, orbital occupation, and orbital orientation, this way altering the exchange paths and strengths of magnetic interaction within the system and consequently being crucial for the formation of the respective ground states. The spin 1/2 transition metal compounds, which have been investigated in this work, illustrate the great variety of exciting phenomena fueling the huge interest in this class of materials. We focused on cuprates with magnetically active CuO4 plaquettes, mainly arranged into edge sharing geometries. The influence of structural peculiarities, as distortion, folding, changed bonding angles, substitution or exchanged ligands has been studied with respect to their relevance for the magnetic ground state. Besides the detailed description of the magnetic ground states of selected compounds, we attempted to unravel the origin for the formation of a particular magnetic ground state by deriving general trends and relations for this class of compounds. The details of the treatment of the correlation and influence of structural peculiarities like distortion or the bond angles are evaluated carefully. In the second part of this work we presented the results of joint theoretical and experimental studies for intermetallic compounds, all exhibiting an isostructural phase transition upon pressure. Many different driving forces for such phase transitions are known like quantum fluctuations, valence instabilities or magnetic ordering. The combination of extensive computational studies and high pressure XRD, XAS and XMCD experiments using synchrotron radiation reveals completely different underlying mechanism for the onset of the phase transitions in YCo5, SrFe2As2 and EuPd3Bx. This thesis demonstrates on a series of complex compounds that the combination of ab-initio electronic structure calculations with numerical simulations and with various experimental techniques is an extremely powerful tool for a successful description of the intriguing quantum phenomena in solids. This approach is able to reduce the complex behavior of real materials to simple but appropriate models, this way providing a deep understanding for the underlying mechanisms and an intuitive picture for many phenomena. In addition, the close interaction of theory and experiment stimulates the improvement and refinement of the methods in both areas, pioneering the grounds for more and more precise descriptions. Further pushing the limits of these mighty techniques will not only be a precondition for the success of fundamental research at the frontier between physics and chemistry, but also enables an advanced material design on computational grounds.

Solid state physics comprises many interesting physical phenomena driven by the complex interplay of the crystal structure, magnetic and orbital degrees of freedom, quantum fluctuations and correlation. The discovery of materials which exhibit exotic phenomena like low dimensional magnetism, superconductivity, thermoelectricity or multiferroic behavior leads to various applications which even directly influence our daily live. For such technical applications and the purposive modification of materials, the understanding of the underlying mechanisms in solids is a precondition. Nowadays DFT based band structure programs become broadly available with the possibility to calculate systems with several hundreds of atoms in reasonable time scales and high accuracy using standard computers due to the rapid technical and conceptional development in the last decades. These improvements allow to study physical properties of solids from their crystal structure and support the search for underlying mechanisms of different phenomena from microscopic grounds. This thesis focuses on the theoretical description of low dimensional magnets and intermetallic compounds. We combine DFT based electronic structure and model calculations to develop the magnetic properties of the compounds from microscopic grounds. The developed, intuitive pictures were challenged by model simulations with various experiments, probing microscopic and macroscopic properties, such as thermodynamic measurements, high field magnetization, nuclear magnetic resonance or electron spin resonance experiments. This combined approach allows to investigate the close interplay of the crystal structure and the magnetic properties of complex materials in close collaboration with experimentalists. In turn, the systematic variation of intrinsic parameters by substitution or of extrinsic factors, like magnetic field, temperature or pressure is an efficient way to probe the derived models. Especially pressure allows a continuous change of the crystal structure on a rather large energy scale without the chemical complexity of substitution, thus being an ideal tool to consistently alter the electronic structure in a controlled way. Our theoretical results not only provide reliable descriptions of real materials, exhibiting disorder, partial site occupation and/or strong correlations, but also predict fascinating phenomena upon extreme conditions. In parts this theoretical predictions were already confirmed by own experiments on large scale facilities. Whereas in the first part of this work the main purpose was to develop reliable magnetic models of low dimensional magnets, in the second part we unraveled the underlying mechanism for different phase transitions upon pressure. In more detail, the first part of this thesis is focused on the magnetic ground states of spin 1/2 transition metal compounds which show fascinating phase diagrams with many unusual ground states, including various types of magnetic order, like helical states exhibiting different pitch angles, driven by the intimate interplay of structural details and quantum fluctuations. The exact arrangement and the connection of the magnetically active building blocks within these materials determine the hybridization, orbital occupation, and orbital orientation, this way altering the exchange paths and strengths of magnetic interaction within the system and consequently being crucial for the formation of the respective ground states. The spin 1/2 transition metal compounds, which have been investigated in this work, illustrate the great variety of exciting phenomena fueling the huge interest in this class of materials. We focused on cuprates with magnetically active CuO4 plaquettes, mainly arranged into edge sharing geometries. The influence of structural peculiarities, as distortion, folding, changed bonding angles, substitution or exchanged ligands has been studied with respect to their relevance for the magnetic ground state. Besides the detailed description of the magnetic ground states of selected compounds, we attempted to unravel the origin for the formation of a particular magnetic ground state by deriving general trends and relations for this class of compounds. The details of the treatment of the correlation and influence of structural peculiarities like distortion or the bond angles are evaluated carefully. In the second part of this work we presented the results of joint theoretical and experimental studies for intermetallic compounds, all exhibiting an isostructural phase transition upon pressure. Many different driving forces for such phase transitions are known like quantum fluctuations, valence instabilities or magnetic ordering. The combination of extensive computational studies and high pressure XRD, XAS and XMCD experiments using synchrotron radiation reveals completely different underlying mechanism for the onset of the phase transitions in YCo5, SrFe2As2 and EuPd3Bx. This thesis demonstrates on a series of complex compounds that the combination of ab-initio electronic structure calculations with numerical simulations and with various experimental techniques is an extremely powerful tool for a successful description of the intriguing quantum phenomena in solids. This approach is able to reduce the complex behavior of real materials to simple but appropriate models, this way providing a deep understanding for the underlying mechanisms and an intuitive picture for many phenomena. In addition, the close interaction of theory and experiment stimulates the improvement and refinement of the methods in both areas, pioneering the grounds for more and more precise descriptions. Further pushing the limits of these mighty techniques will not only be a precondition for the success of fundamental research at the frontier between physics and chemistry, but also enables an advanced material design on computational grounds.:Contents List of abbreviations 1. Introduction 2. Methods 2.1. Electronic structure and magnetic models for real compounds 2.1.1. Describing a solid 2.1.2. Basic exchange and correlation functionals 2.1.3. Strong correlations 2.1.4. Band structure codes 2.1.5. Disorder and vacancies 2.1.6. Models on top of DFT 2.2. X-ray diffraction and x-ray absorption at extreme conditions 2.2.1. Diamond anvil cells 2.2.2. ID09 - XRD under pressure 2.2.3. ID24 - XAS and XMCD under pressure 3. Low dimensional magnets 3.1. Materials 3.1.1 AgCuVO4 - a model compound between two archetypes of Cu-O chains 3.1.2 Li2ZrCuO4 - in close vicinity to a quantum critical point 3.1.3 PbCuSO4(OH)2 -magnetic exchange ruled by H 3.1.4 CuCl2 and CuBr2 - flipping magnetic orbitals by crystal water 3.1.5 Na3Cu2SbO6 and Na2Cu2TeO6 - alternating chain systems 3.1.6 Cu2(PO3)2CH2 - magnetic vs. structural dimers 3.1.7 Cu2PO4OH - orbital order between dimers and chains 3.1.8 A2CuEO6 - an new family of spin 1/2 square lattice compounds 3.2. General trends and relations 3.2.1. Approximation for the treatment of strong correlation 3.2.2. Structural elements 4. Magnetic intermetallic compounds under extreme conditions 115 4.1. Itinerant magnets 4.1.1. YCo5 - a direct proof for a magneto elastic transition by XMCD 4.1.2. SrFe2As2 - symmetry-preserving lattice collapse 4.2. Localized magnets 4.2.1. EuPd3Bx - valence transition under doping and pressure 5. Summary and outlook A. Technical details B. Crystal Structures C. Supporting Material Bibliography List of Publications Acknowledgments

In this work, the structural, electronic, and optical properties of CdS nanoparticles with sizes up to 4nm have been calculated using density-functional theory (DFT). Inaccuracies in the description of the unoccupied states of the applied density-functional based tight-binding method (DFTB) are overcome by a new SCF-DFTB method. Density-functional-based calculations employing linear-response theory have been performed on cadmium sulfide nanoparticles considering different stoichiometries, underlying crystal structures (zincblende, wurtzite, rocksalt), particle shapes (spherical, cuboctahedral, tetrahedral), and saturations (unsaturated, partly saturated, completely saturated). For saturated particles, the calculated onset excitations are strong excitonic. The quantum-confinement effect in the lowest excitation is visible as the excitation energy decreases towards the bulk band gap with increasing particle size. Dangling bonds at unsaturated surface atoms introduce trapped surface states which lie below the lowest excitations of the completely saturated particles. The molecular orbitals (MOs), that are participating in the excitonic excitations, show the shape of the angular momenta of a hydrogen atom (s, p). Zincblende- and wurtzite-derived particles show very similar spectra, whereas the spectra of rocksalt-derived particles are rather featureless. Particle shapes that confine the orbital wavefunctions strongly (tetrahedron) give rise to less pronounced spectra with lower oscillator strengths. Finally, a very good agreement of the calculated data to experimentally available spectra and excitation energies is found.

Thema der vorliegenden Arbeit ist die Untersuchung ausgewählter niederdimensionaler Schichtgittersysteme, wobei das Hauptinteresse in der Erforschung der elektronischen Struktur im Zusammenhang mit Interkalationsexperimenten liegt. Einkristalline Graphit-, TiSe2- und TaSe2-Proben wurden vor und nach der Interkalation mit winkelaufgelöster Photoemission, Fermi- und Isoenergieflächenmessungen und Elektronenbeugung (LEED) analysiert. Als Interkalationsmaterialien wurden U, Eu, Gd und Cs verwendet. Die experimentellen Daten wurden mit Ergebnissen von LDA-LCAO-Bandstrukturrechnungen und Simulationen im Rahmen eines Single-Impurity-Anderson-Modells verglichen. Neben dem Einfluß unterschiedlicher Valenzelektronen der interkalierten Atome auf den Einlagerungsprozeß werden Fragen zum Lokalisierungsverhalten von 4f- und 5f-Zuständen und zu den Veränderungen in der Dimensionalität der Verbindungen durch die Einlagerung diskutiert. Ein weiterer Schwerpunkt dieser Arbeit befaßt sich mit Untersuchungen zur temperaturabhängigen Ausbildung von Ladungsdichtewellen in 1T-TaSe2. / Subject of the present thesis are investigations of selected low-dimensional layered lattice systems, with the principal goal to study the electronic structure in relation to intercalation experiments. Single-crystalline graphite-, TiSe2 - and TaSe2- samples were analyzed by angle-resolved photoemission, Fermi- and isoenergy-surface measurements, and low energy electron diffraction experiments before and after intercalation. U, Eu, Gd, and Cs were used as materials for the intercalation process. The experimental results were compared with theoretical LDA-LCAO band-structure calculations and with simulations in the framework of a single-impurity Anderson model. In addition to the influence of different numbers of valence electrons from intercalated atoms, questions concerning the localization of 4f and 5f states and changes in the dimensionality of the compounds due to the intercalation process are discussed. Investigations of the temperature dependent formation of charge density waves in 1T-TaSe2 complete this work.