Thesis is aimed at studying of magnetic iron oxide particles of submicron and nanoscale dimensions by means of nuclear magnetic resonance (NMR). 57 Fe NMR inves- tigations were carried out in composite bentonite/maghemite with respect to tempera- ture of calcination (Tcalc) during the sample preparation and in magnetite submicron powders with respect to various range of the particles size. One of the main findings is that increasing Tcalc improves resolution in the NMR spectra, which is most likely connected with higher degree of atomic ordering in the spinel structure. Evaluating the integral intensities of NMR spectra allowed us to determine the relative content of maghemite phase in particular samples of the series: the content rapidly grows for Tcalc up to ∼420 deg. An approach to distinguish signal from tetrahedral and octahedral irons was developed and tested on pure maghemite sample. Analysis based on vacancy- distribution models was performed in the spinel structure and the results were compared to the experiment. 57 Fe NMR spectra in submicron magnetite samples were found to differ markedly from spectrum of a single crystal. It was concluded that the investigated powders possess high amount of defects in the crystal structure or contain additional phase (probably closely related to the maghemite phase).

In this thesis, we summarize the material-specific theories of strongly correlated systems and apply them to selected materials. We describe and apply the corre- lated band theory methods: the local density approximation plus Coulomb U, and the density functional theory plus exact diagonalization of single impurity An- derson model. First, we investigate the systems containing impurity atoms: cobalt impurity located in the bulk copper and samarium, and neodymium adatoms on the surface of graphene. We present the spectral densities and study the magnetism of those compounds. Afterwards, we analyze three Np-based compounds: NpPt2In7, Np2Ni17 and NpBC. For all three compounds we analyze the spin, orbital and to- tal magnetic moments and the total density of states, as well as its projections for selected orbitals and spins. Moreover, for NpPt2In7 and NpBC we perform the to- tal energy analysis between different magnetic moment arrangements on the Np atoms.

In dieser Doktorarbeit wurde die elektronische Struktur von konventionellen und unkonventionellen Supraleitern untersucht. Das Ziel dieser Arbeit war es, die dHvA Parameter zu berechnen und mit experimentellen Daten zu vergleichen. Mit Hilfe des Bandstrukturprogrammes FPLO, welches auf der DFT basiert, untersuchten wir Diboride (MgB$_2$ und TaB$_2$) und schwere Fermionenverbindungen (CeMIn$_5$ und PuMGa$_5$, M=Co, Rh, und Ir) innerhalb der LSD-Näherung. / In this thesis theoretical study of the electronic structure of conventional and unconventional superconductor compounds was carried out. The goal was to calculate the dHvA parameters in comparison with available experimental data. By means of FPLO band structure code based on DFT within LSDA we investigated diborides (MgB$_2$ and TaB$_2$) and heavy fermion compounds (CeMIn$_5$ and PuMGa$_5$, M=Co, Rh, and Ir).

Accurate energetic modeling of large molecular systems is always desired by chemists. For example, ligand-protein binding simulations and enzymatic catalysis studies all involve with a small energy difference. The energetic accuracy depends largely on a proper handling of electronic correlations. Molecular mechanics (MM) methods deliver a parameterized Newtonian treatment to these problems. They show great capability in handling large calculations but give only qualitatively good results. Quantum mechanics (QM) methods solve Schrödinger equations and exhibit much better energy accuracy, though the computational cost can be prohibitive if directly applied to very large systems. Fragment-based methods have been developed to decompose large QM calculations into fragment calculations. However, most current schemes use a self- consistent field (SCF) method on fragments, in which no electronic correlation is accounted for. The super-system energy is computed as a sum of fragment energies plus two-body corrections and, possibly, three-body corrections (a "body" is a fragment). Higher order corrections can be added. Nevertheless, many problems require the treatment of high order electronic correlations. The coupled-cluster (CC) theory is the state-of-the-art QM method for handling electronic correlations. The CC wavefunction contains correlated excitations up to a given truncated level and coincidental excitations for all possible electronic excitations. It is a brilliant way of including more electronic correlations while maintaining a low-order scaling. In the proposed excitonic coupled-cluster (X-CC) theory, substantial modifications have been made to allow CC algorithms to act on the collective coordinates of fragment fluctuations to obtain super-system energy. The X-CC theory is designed to achieve accurate energetic modeling results for large chemical systems with much improved affordability and systematic improvability. The test system used in this work is a chain of beryllium atoms. A 30-fragment X-CCSD(2) calculation delivered matching accuracy with traditional CCSD method. An X-CCSD(2) calculation on a chain of 100 bonded fragments finished in 7 hours on a single 2.2 GHz CPU core. The X-CC scheme also demonstrates the ability in handling charge transfer problems. Due to the use of fluctuation basis in the test cases, the excitonic algorithms can be easily generalized to inhomogeneous systems. This will be investigated in future work.

No description available.

This thesis describes an accurate and scalable computational method designed to perform nanoelectronic structure calculations. Built around the FEAST framework, this method directly addresses the nonlinear eigenvalue problem. The new approach allows us to bypass traditional approximation techniques typically used for first-principle calculations. As a result, this method is able to take advantage of standard muffin-tin type domain decomposition techniques without being hindered by their perceived limitations. In addition to increased accuracy, this method also has the potential to take advantage of parallel processing for increased scalability. The Introduction presents the motivation behind the proposed method and gives an overview of what will be presented for this thesis. Chapter 1 explains how electronic structure calculations are currently performed, including an overview of Density Functional Theory and the advantages and disadvantages of various numerical techniques. Chapter 2 describes, in detail, the method proposed for this thesis, including mathematical justification, a matrix-level example, and a description of implementing the FEAST algorithm. Chapter 3 presents and discusses results from numerical experiments for Hydrogen and various Hydrogen molecules, Methane, Ethane, and Benzene. Chapter 4 concludes with a summary of the presented work and its impact in the field.

No description available.

<p> Working within the framework of the linearized Boltzmann equation for the conduction electrons the existing theoretical treatments of ultrasonic attenuation in metals are extended to include realistic descriptions of the electronic structure and electron-lattice interaction. A variational solution of the Boltzmann equation which allows the inclusion of phonon drag effects is derived. An anisotropic scattering time solution is also presented. Both of these solutions are applied to calculation of the attenuation coefficient in pure metals and dilute alloys. </p> <p> The theory of the effects of electron-electron collisions on the ultrasonic attenuation in metals is also examined. </p> / Thesis / Doctor of Philosophy (PhD)

This dissertation focuses on computational study of the geometry and energetics small molecules and nanoclusters involving transition metals (TM). These clusters may be used for various industrial applications including catalysis and photonics. Specifically, in this work we have studied hydrides and carbides of 3d-transition metal systems (Sc through Cu), small nickel and gold clusters. Qualitatively correct description of the bond dissociation is ensured by allowing the spatial and spin symmetry to break. We have tested applicability of new exchange-correlation functional and alternative theoretical descriptions (spin-contamination correction in broken symmetry DFT and ensemble Kohn-Sham (EKS)) as well. We studies TM hydrides and carbides systems to understand the importance of underlying phenomenon of bond breaking in catalytic processes. We have tested several exchange-correlation functionals including explicit dependence on kinetic energy density for the description of hydrides (both neutral and cationic) and carbides formed by 3d-transition metals. We find M05-2x and BMK dissociation energies are in better agreement with experiment (where available) than those obtained with high level wavefunction theory methods, published previously. This agreement with experiment deteriorates quickly for other functionals when the fraction of the Hartree-Fock exchange in DFT functional is decreased. Higher fraction of HF exchange is also essential in EKS formalism, but it does not help when spin-adapted unrestricted approach is employed. We analyze the electron spin densities using Natural Bond Orbital population analysis and find that simple description of 3d electrons as non-bonding in character is rarely correct. Unrestricted formalism results in appreciable spin-contamination for some of the systems at equilibrium, which motivated us to investigate it further in details. In order to correct the spin contamination effect on the energies, we propose a new scheme to correct for spin contamination arising in broken-symmetry DFT approach. Unlike conventional schemes, our spin correction is introduced for each spin-polarized electron pair individually and therefore is expected to yield more accurate energy values. We derive an expression to extract the energy of the pure singlet state from the energy of the broken-symmetry DFT description of the low spin state and the energies of the high spin states (pentuplet and two spin-contaminated triplets in the case of two spin-polarized electron pairs). We validate our spin-contamination correction approach by a simple example of H2 and applied to more complex MnH system. Ensemble KS formalism is also applied to investigate the dissociation of C2 molecule. We find that high fraction of HF exchange is essential to reproduce the results of EKS treatment with exact exchange-correlation functional. We analyze the geometry and energetics of small nickel clusters (Ni2-Ni5) for several lowest energy isomers. We also study all possible spin states of small nickel cluster isomers and report observed trends in energetics. Finally we determine the geometry and energetics of ten lowest energy isomers of four small gold clusters (Au2, Au4, Au6, and Au8). We have also investigated the influence of cluster geometry, ligation, solvation and relativistic effects on electronic structure of these gold clusters. The effect of one-by-one ligand attachment in vacuum and solvent environment is also studied. Performance of five DFT functionals are tested as well; Local Spin Density Approximation (SVWN5), Generalized Gradient Approximation (PBE), kinetic energy density-dependent functional (TPSS), hybrid DFT (B3LYP), and CAM-B3LYP which accounts for long-range exchange effects believed to be important in the analysis of metal bonding in gold complexes and clusters. Our results exhibit the ligand induced stability enhancement of otherwise less stable isomers of Au4, Au6 and Au8. Ligands are found to play a crucial role in determining the 2D to 3D transition realized in small gold clusters. In order to select an appropriate theory level to use in this study, we investigate the effect of attachment of four different ligands (NH3, NMe3, PH3, PMe3) on cluster geometry and energetics of Au2 and Au4 in vacuum and in solution. Our results benchmark the applicability of DFT functional model and polarization functions in the basis set for calculations of ligated gold cluster systems. We employ five different basis sets with increasing amount of polarization and diffuse functions; LANL2DZ, LANL2DZ-P, def2-SVP, def2-TZVP, and def2-QZVP. We obtain NMe3 = NH3 > PH3 > PMe3 order of ligand binding energies and observe shallow potential energy surfaces in all molecules. Our results suggest appropriate quantum-chemical methodologies to model small noble metal clusters in realistic ligand environment to provide reliable theoretical analysis in order to complement experiments.

Transition-metal-centered monocyclic boron wheels are important candidates in the family of planar hypercoordinate species that show intriguing structure, stability and bonding situation. Through the detailed potential energy surface explorations of MB9 − (M Fe, Ru, Os) clusters, we introduce herein OsB9 − to be a new member in the transition-metalcentered borometallic molecular wheel gallery. Previously, FeB9 − and RuB9 − clusters were detected by photoelectron spectroscopy and the structures were reported to have singlet D9h symmetry. Our present results show that the global minimum for FeB9 − has a molecular wheel-like structure in triplet spin state with Cs symmetry, whereas its heavier homologues are singlet molecular wheels with D9h symmetry. Chemical bonding analyses show that RuB9 − and OsB9 − display a similar type of electronic structure, where the dual σ + π aromaticity, originated from three delocalized σ bonds and three delocalized π bonds, accounts for highly stable borometallic molecular wheels.