Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 63-66).

In this thesis, a wide breadth of topics related to the field of surface science are addressed using density functional theory (DFT). Specifically, five studies with relevance to molecular electronics and heterogeneous catalysis are presented, with a particular focus on interadsorbate interactions, reactivity and characterisation of molecules on transition metal surfaces. The first part of this work focuses on giving strong theoretical underpinning to the atomic-scale observations provided by scanning tunnelling microscopy (STM) experiments conducted by my group colleagues. The theoretical calculations presented here provide support to the experimental evidences but also serve to unravel information that is inaccessible from the experiments. On the one hand, the variety of results obtained in this thesis using standard DFT methods serve to highlight the capabilities of the computationally low-demanding methods for modelling processes occurring on metal surfaces. On the other hand, we notice that these workhorse methods in DFT have inherent limitations for providing an accurate description of some properties, in particular binding energies. This, further improvements in the level of theory are necessary for advancing the computational accuracy of standard DFT methods in materials science. The second part of this thesis is devoted to highlight the high level of accuracy obtained by the new theoretical approaches in the field of materials science. Due to the recent implementation of new algorithms combined with the increasing computer power that is available to the scientific community, these sophisticated methods are becoming more accessible for modelling solid-state systems. Here, the recent implementation of the random-phase approximation (RPA) for solids is employed to perform to benchmark study on the adsorption of benzene on different close-packed transition metal surfaces. The development of new theoretical tools is also essential to improve our predictive capabilities in surface science. A novel approach to correct vibrational intensities by including anharmonicities using density functional perturbation theory (DFPT) is proposed. The new method is tested for the adsorption of different organic molecules on various transition metal surfaces. The results obtained by this implementation demonstrate excellent improvements for predicting accurate spectra of molecules on surfaces.

The purpose of this paper is to explore certain properties of Banach spaces. The first chapter begins with basic definitions, includes examples of Banach spaces, and concludes with some properties of continuous linear functionals. In the second chapter, dimension is discussed; then one version of the Hahn-Banach Theorem is presented. The third chapter focuses on dual spaces and includes an example using co, RI, and e'. The role of locally convex spaces is also explored in this chapter. In the fourth chapter, several more theorems concerning dual spaces and related topologies are presented. The final chapter focuses on reflexive spaces. In the main theorem, the relation between compactness and reflexivity is examined. The paper concludes with an example of a non-reflexive space.

In this study, attention has been given to the design and synthesis of novel multidentate ligands for use in the construction of ruthenium-based metathesis catalysts, and their chelating potential has been explored by computer modelling at the Density Functional Theory (DFT) level. Both Kemp’s triacid (1,3,5-trimethyl-1,3,5-cyclohexanetricarboxylic acid) and D-(+)-camphor have been investigated as molecular scaffolds for the development of such ligands. However selective elaboration of the functional groups in Kemp’s triacid proved difficult to achieve, and the research has focused on the development of camphor derivatives. The synthesis of the camphor-based ligands has involved C-8 functionalisation and ring-opening of the bicyclic system to afford tridentate products. The formation of 9-iodocamphorquinone bis(ethylene ketal) together with the desired product, the 8-iodo isomer, has been confirmed by single crystal X-ray analysis of both compounds. Formation of the 9-iodo analogue has provided new insights into the intramolecular rearrangement of camphor skeleton, and the mechanistic implications have been assessed by coset analysis. Attempts to effect nucleophilic displacement of the 8-halogeno groups by nucleophilic donor moieties proved unexpectedly difficult and, coupled with the susceptibility of the carbonyl groups to nucleophilic attack, has led to the formation of novel tricyclic products, viz., 1,6-dimethyl-3-(2-pyridylamino)-4-oxatricyclo[4.3.0.0[superscript 3,7]]-2-nonanone and 6,7-dimethyl-3-(2-pyridylamino)-4-oxatricyclo -[4.3.0.0[superscript 3,7]]-2-nonanone. However the diphenylphosphine group was successfully introduced at C-8 and oxidative ring-opening of the camphor skeleton has afforded the tridentate ligands, 2-(diphenylphosphinoylmethyl)-1,2-dimethyl-1,3-cyclopentanedicarboxylic acid and 2-(diphenylphosphinoylmethyl)-1,3-bis(hydroxymethyl)1,2-dimethylcyclopentane. One- and two-dimensional NMR and, where appropriate, high-resolution MS methods have been used to characterise the products. Three [superscript 13]C NMR chemical shift prediction programmes, viz., ChemWindow and the MODGRAPH neural network and HOSE (Hierachially Ordered Spherical description of Environment), have been applied to representative compounds to assess their efficacy. While the predicted shifts correlated reasonably well with the experimental data, they proved to be insufficiently accurate to differentiate the isomeric systems examined.

Density functional theory (DFT) provides an affordable computational tool to understand electronic structure of various molecules and solids. However, the use of DFT is still challenging to investigate nanomaterials of intermediate size that are too small to assume translational symmetry and too large to be considered as molecules. This thesis focuses on developing cost-effective but accurate computational methods for nanomaterials and using the methods to rationalize and predict experimental behaviors. A notable difference of a nanomaterial from its bulk counterpart is that its properties are exceptionally sensitive to the dielectric environment, requiring a proper treatment of the surrounding dielectrics for an accurate understanding. The consequences of heterogeneous dielectric screening on transition metal dichalcogenides are studied by developing a new theory based on classical electrostatics, which closely reproduced the band gaps and optical gaps calculated by the ab initio GW approximation and the Bethe-Salpeter equation (BSE). The relative insensitivity of the first optical transition energy observed by experiments was explained for the first time in terms of the cancellation effect of changes of the band gap and the exciton binding energy. The theory of heterogeneous dielectric environments is further developed to be used in an atomistic calculation of layered hybrid organic-inorganic lead halide perovskites via a tight-binding GW-BSE method. The binding energies of trions and biexcitons were also calculated using the stochastic variational method to give spectrum peak energies that show a good agreement with reported experimental measurements. Lastly, the tight-binding GW-BSE method is generalized into an atomistic, semiempirical approach to calculate the electronic structure and optical spectra of arbitrary nanomaterials, termed semiempirical GW (sGW) and BSE (sBSE).

No description available.

This bachelor's thesis discusses from an ergodic-theoretical perspective the "metric functional analysis" that Anders Karlsson and others have developed in the recent years. We introduce a new symbolic calculus for metric functionals which includes a notion of the adjoint of a nonexpansive map. Using these tools we revisit many central results, including Karlsson's spectral principle and its stronger form for star-shaped spaces due to Gaubert and Vigeral, as well as the multiplicative ergodic theorem of Karlsson-Ledrappier.

No description available.

We use a combination of Density Functional Theory and Dynamical Mean Field Theory (DFT+DMFT) to study electronic correlations in unconventional superconductors, with a focus on nickelate analogs of cuprate superconductors. We study the infinite layer nickelate superconductor NdNiO₂ in parallel with the isostructural CaCuO₂. Our results point to superconductivity in the nickelate being cupratelike, with correlations dominated by a hybrid Ni-𝑑_{𝑥²-𝑦²} and O-𝑝 band, and with the extra bands not contributing substantially to the superconducting state. We find that the infinite layer nickelate NdNiO₂ and the trilayer nickelate Pr₄Ni₃O₈ are virtually identical in terms of correlation physics when compared at the same chemical doping, despite the differences in Fermiology, indicating that the number of layers can stand in for chemical doping for some properties related to electronic correlations. We find that as opposed to in narrow window DFT+DMFT, in wide window DFT+DMFT the choice of downfolding procedure leads to very different results. This is an important ambiguity in the method that must be resolved or the method is incomplete by itself. We also study Sr₂MoO₄ in parallel with the Hund's superconductor Sr₂RuO₄, and find that Sr₂MoO₄ is a particle-hole dual of Sr₂RuO₄ but without the van Hove singularity at the Fermi level, which disentangles the influence of the van Hove singularity from Hund's physics. We show that Sr₂MoO₄ has a characteristic Hund's peak on the occupied of the spectral function, indicating that the peak should be observable by photoemission experiments.

<p> This thesis is concerned with a necessary and sufficient condition for the existence of non-zero linear continuous functionals on Fréchet or more general topological vector spaces. The main idea is based on the famous Hahn-Banach theorem. Since the connection between Hahn-Banach theorem and separation theorems is well known, here we study some separation theorems as well.</p> / Thesis / Master of Science (MSc)