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Die Habilitationsschrift beinhaltet die Vorstellung eines neuen mathematischen Formalismus zur Erstellung approximativer Funktionale in der Dichtefunktionaltheorie. Im Gegensatz zu Dichtefunktionalen hängen Bifunktionale von zwei Variablen ab, nämlich der Dichte und des Potentials, welches als formale Funktionalableitung behandelt wird und somit nicht als Funktional der Dichte bekannt ist. Neben der Vorstellung des mathematischen Formalismus werden zwei Anwendungsgebiete vorgestellt: orbitalfreie Dichtefunktionaltheorie und die Entwicklung neuer Austauschkorrelationsfunktionale für konventionelle Kohn-Sham-Dichtefunktionaltheorie.

<p><strong>ABSTRACT </strong> Approximating the kinetic energy as a functional of the electron density is a daunting, but important, task. For molecules in equilibrium geometries, the kinetic energy is equal in magnitude to the total electronic energy, so achieving the exquisite accuracy in the total energy that is needed for chemical applications requires similar accuracy for the kinetic energy functional. For this reason, most density functional theory (DFT) calculations use the Kohn-Sham method, which provides a good estimate for the kinetic energy. But the computational cost of Kohn-Sham DFT calculations has a direct dependence on the total number of electrons because the Kohn-Sham method is based on the orbital picture, with one orbital per electron. Explicit density functionals, where the kinetic energy is written explicitly in terms of the density, and not in terms of orbitals, are much faster to compute. Unfortunately, the explicit density functionals in the literature had disappointing accuracy. This dissertation introduces several new approaches for orbital-free density functional methods. One can try to include information about the Pauli principle using the exchange hole. In the weighted density approximation (WDA), a model for the exchange hole is used to approximate the one-electron density matrix, which is then used to compute the kinetic energy. This thesis introduces a symmetric, normalized, weighted density approximation using the exchange hole of the uniform electron gas. Though the key results on kinetic energy are not accurate enough, an efficient algorithm is introduced which, with a more sophisticated hole model, might give better results. The effects of electron correlation on the kinetic energy can be modeled by moving beyond the one-electron distribution function (the electron density) to higherorder electron distributions (k-electron DFT). For example, one can model electron correlation directly using the pair electron density. In this thesis, we investigated two different functionals of the pair density, the Weizsäcker functional and the March-Santamaria functional. The Weizsäcker functional badly fails to describe the accurate kinetic energy due to the N-representability problem. The March-Santamaria functional is exact for a single Slater determinant, but fails to adequately model the effects of electron correlation on the kinetic energy. Finally, we established a relation between Fisher information and Weizsäcker kinetic energy functional. This allowed us to propose generalisations of the Weizsäcker kinetic energy density functional. It is hoped that the link between information theory and kinetic energy might provide a new approach to deriving improved kinetic energy functionals. <strong> Keywords: </strong><em>Kinetic energy functional, Density functional theory (DFT), von-Weizsäcker</em> <em> functional, March-Santamaria functional, Thomas-Fermi model, density matrix, Twopoint normalization, Pair-density functional theory (PDFT). </em></p> / Doctor of Science (PhD)

The purpose of the research contained in this thesis is to allow for the prediction of new structures and properties of crystalline structures due to the application of external pressure by using first-principles numerical computations. The body of the thesis is separated into two primary research projects. The properties of cupric oxide (CuO) have been studied at pressures below 70 GPa, and it has been suggested that it may show room-temperature multiferroics at pressure of 20 to 40 GPa. However, at pressures above these ranges, the properties of CuO have yet to be examined thoroughly. The changes in crystal structure of CuO were examined in these high-pressure ranges. It was predicted that the ambient pressure monoclinic structure changes to a rocksalt structure and CsCl structure at high pressure. Changes in the magnetic ordering were also suggested to occur due to superexchange interactions and Jahn-Teller instabilities arising from the d-orbital electrons. Barium chloride (BaCl) has also been observed, which undergoes a similar structural change due to an s – d transition, and whose structural changes can offer further insight into the transitions observed in CuO. Ammonia borane (NH3BH3) is known to have a crystal structure which contains the molecules in staggered conformation at low pressure. The crystalline structure of NH3BH3 was examined at high pressure, which revealed that the staggered configuration transforms to an eclipsed conformation stabilized by homopolar B–Hδ-∙∙∙ δ-H–B dihydrogen bonds. These bonds are shown to be covalent in nature, comparable in bond strength to conventional hydrogen bonds, and may allow for easier molecular hydrogen formation in hydrogen fuel storage.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: 2,7-dimethylocta-3,5-diyne-2,7-diol forms inclusion complexes with various guests molecules, where the guest molecules are polar-ordered. A Cambridge Structural Database (CSD) search revealed ten inclusion complexes where the guest molecules were polar-ordered. Using Density Functional Theory (DFT) computational methods (in the absence of the host), we evaluated the intra-channel and lateral guest-guest interactions between the guest molecules. Two polar-ordered inclusion complexes ((1,4,7-cyclohexane-1,2,4,5,7,8-hexaoxonane)·CHCl3 and (2,4,6-(endolongifolyl)-1,3,5-trioxane)·CDCl3) were singled out in the CSD search for further studies along with 2,7-dimethylocta-3,5-diyne-2,7-diol. Synthesis of any 1,2,4,5,7,8-hexaoxonane and 1,3,5-trioxane derivatives was attempted to establish whether the polar-ordering ability extends into the family of compounds. We managed to produce three new polar-ordered inclusion complexes with 2,7-dimethylocta-3,5-diyne-2,7-diol (ClC(CH3)3, BrC(CH3)3 and IC(CH3)3), thus extending the series to six guest polar-ordered systems. We were only able to synthesise 1,4,7-cyclohexane-1,2,4,5,7,8-hexaoxonane and produce the CHCl3 inclusion complex and one new polar-ordered inclusion complex (CHBr3). Three 1,3,5-trioxanes was synthesised (the cyclohexyl, cyclohex-3-en-1-yl and cyclopentyl derivatives), which did not include any solvents. However, these 1,3,5-trioxanes also form polar-ordered crystals. These compounds and inclusion complexes were analysed by means of single crystal X-ray diffraction to determine their crystal structures. All the crystal structures could be solved and refined to adequate accuracy (except for 2,4,6-tri(cyclopentyl)-1,3,5-trioxane) with no disorder of the guest molecules (where applicable) and their polar-ordering property investigated. Due to their vast molecular differences, these compounds were studied separately by means of visual crystal structure analysis and computational modelling techniques (Density functional theory, molecular mechanics, molecular dynamics and molecular quench dynamics). / AFRIKAANSE OPSOMMING: 2,7-dimetielokta-3,5-diyn-2,7-diol vorm insluitingskomplekse met verskeie molekules as gaste, waar die gas-molekules polêr georden is. 'n Cambridge Struktuur Databasis (CSD) soektog lewer tien insluitings komplekse waarvan die gas-molekules polêr georden is. Deur gebruik te maak van Digtheidsfunksionele teorie (DFT) berekeninge (in die afwesigheid van die gasheer) het ons die inter-kanaal en wedersydse gas-gas interaksies tussen die gas molekules geëvalueer. Twee polêr geordende insluitingskomplekse ((1,4,7-sikloheksaan-1,2,4,5,7,8-heksaoksonaan)·CHCl3 en (2,4,6-(endolongifolyl)-1,3,5-trioksaan)·CDCl3) is uitgesonder uit die CSD soektog vir verdere studies saam met 2,7-dimetielokta-3,5-diyn-2,7-diol. Aanslag was gemaak om enige 1,2,4,5,7,8-heksaoksonaan en 1,3,5-trioksaan derivate te sintetiseer en vas te stel of die polêre ordensvermoë oor die familie van verbindings strek. Ons het daarin geslaag om drie nuwe polêr geordende insluitingskomplekse op te lewer met 2,7-dimetielokta-3,5-diyn-2,7-diol (Cl(CH3)3, BrC(CH3)3 en I(CH3)3), en sodoende die reeks uitgebrei na ses gaste wat polêr geordende insluitingskomplekse vorm. Net 1,4,7-sikloheksaan-1,2,4,5,7,8-heksaoksonaan kon gesintetiseer word en dit lewer twee polêr geordende insluitingskomplekse (CHCl3 en CHBr3 (nuut)). Drie 1,3,5-trioksane is gesintetiseer (die sikloheksiel, sikloheks-3-een-1-iel en siklopentiel derivate) en het nie enige oplosmiddels (gaste) ingesluit nie. Nietemin vorm hiedie 1,3,5-trioksane ook polêr geordende kristalle. Hierdie verbindings en insluitingskomplekse is geanaliseer deur middel van enkelkristal X-straal diffraksie om hul kristalstrukture te bepaal. Alle kristalstrukture was opgelos en verwerk tot voldoende akkuraatheid (behalwe vir 2,4,6-tri(siklopentiel)-1,3,5-trioxane) met geen wanorde in die gas molekuul posisies nie (waar van toepassing) en hul polêre ordensvermoë is ondersoek. As gevolg van groot verskille in hul molekulêre strukture, is hierdie verbindings afsonderlik bestudeer deur middel van molekulêre modellerings metodes (Digtheidsfunksionele teorie, molekulêre meganika, molekulêre dinamika en molekulêre stakings dinamika).

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Please refer to full text for abstract / AFRIKAANSE OPSOMMING: Sien asb volteks vir opsomming

Matter on a length scale comparable to that of a chemical bond is governed by the theory of quantum mechanics, but quantum mechanics is a many body theory, hence for the sake of chemistry or solid state physics, finding solutions to the governing equation, Schrodinger's equation, is hopeless for all but the smallest of systems. As the number of electrons increases, the complexity of solving the equations grows rapidly without bound. One way to make progress is to treat the electrons in a system as independent particles and to attempt to capture the many-body effects in a functional of the electrons' density distribution. When this approximation is made, the resulting equation is called the Kohn-Sham equation, and instead of requiring solving for one function of many variables, it requires solving for many functions of the three spatial variables. This problem turns out to be easier than the many body problem, but it still scales cubically in the number of electrons. In this work we will explore ways of obtaining the solutions to the Kohn-Sham equation in the framework of real-space pseudopotential density functional theory. The Kohn-Sham equation itself is an eigenvalue problem, just as Schrodinger's equation. For each electron in the system, there is a corresponding eigenvector. So the task of solving the equation is to compute many eigenpairs of a large Hermitian matrix. In order to mitigate the problem of cubic scaling, we develop an algorithm to slice the spectrum into disjoint segments. This allows a smaller eigenproblem to be solved in each segment where a post-processing step combines the results from each segment and prevents double counting of the eigenpairs. The efficacy of this method depends on the use of high order polynomial filters that enhance only a segment of the spectrum. The order of the filter is the number of matrix-vector multiplication operations that must be done with the Hamiltonian. Therefore the performance of these operations is critical. We develop a scalable algorithm for computing these multiplications and introduce a new density functional theory code implementing the algorithm. / text

<p>Hydrogen is abundant, uniformly distributed throughout the Earth's surface and its oxidation product (water) is environmentally benign. Owing to these features, it is considered as an ideal synthetic fuel for a new world energetic matrix (renewable, secure and environmentally friendly) that could allow a sustainable future development. However, for this prospect to become a reality, efficient ways to produce, transport and store hydrogen still need to be developed. In the present thesis, theoretical studies of a number of potential hydrogen storage materials have been performed using density functional theory. In NaAlH₄ doped with 3d transition metals (TM), the hypothesis of the formation of Ti-Al intermetallic alloy as the main catalytic mechanism for the hydrogen sorption reaction is supported. The gateway hypothesis for the catalysis mechanism in TM-doped MgH₂ is confirmed through the investigation of MgH₂ nano-clusters. Thermodynamics of Li-Mg-N-H systems are analyzed with good agreement between theory and experiments. Besides chemical hydrides, the metal-organic frameworks (MOFs) have also been investigated. Li-decorated MOF-5 is demonstrated to possess enhanced hydrogen gas uptake properties with a theoretically predicted storage capacity of 2 wt% at 300 K and low pressure.</p><p>The metal-hydrogen systems undergo many structural and electronic phase transitions induced by changes in pressure and/or temperature and/or H-concentration. It is important both from a fundamental and applied viewpoint to understand the underlying physics of these phenomena. Here, the pressure-induced structural phase transformations of NaBH₄ and ErH₃ were investigated. In the latter, an electronic transition is shown to accompany the structural modification. The electronic and optical properties of the low and high-pressure phases of crystalline MgH₂ were calculated. The temperature-induced order-disorder transition in Li₂NH is demonstrated to be triggered by Li sub-lattice melting. This result may contribute to a better understanding of the important solid-solid hydrogen storage reactions that involve this compound. </p>

Several electrochemical processes are modeled at process levels and atomic scales. Processes are presented for acid generation and ion exchange media regeneration, along with corresponding process models. Transport and reaction processes in individual ion exchange beads are also modeled. Acids of mild strength (pH = ~1-2) are generated from electrolyte solutions and their strength is effectively modeled as a function of time. The regeneration of ion exchange media is also modeled, to close agreement with measurements, and the process model is reconciled with a model for solute flux from an individual ion exchange bead. Together, the models show that the "gentle" regeneration process is controlled by the plating rate. Processes interior to the particle are controlled by diffusion, but all processes are faster than the characteristic time for plating. In a separate process, an electrochemical method is used to produce hypochlorite for disinfection. The process generates perchlorate as a toxic byproduct. Density function theory is used to construct an atomic-scale model of the mechanism for producing perchlorate, as well as the aging of the boron-doped diamond anode used in the process. The mechanism shows that the boron-doped diamond surface plays an important role in chemisorbing and stabilizing radicals of oxychlorine anions, allowing the radicals to live long enough to react and form higher ions like perchlorate. Wear mechanisms that occur on the anode are shown to oxidize and etch the surface, changing its chemical functionality over time. As the surface ages, the overpotential for water oxidation is decreased, decreasing the efficiency of the electrode.

In this thesis, a combination of density functional theory (DFT) based calculations and nonequilibrium Green’s functions are employed to investigate electron transport in molecular switches, molecular cords and nanoscale devices.   Molecular electronic devices have been proposed as an approach to complement today’s silicon based electronic devices. However, engineering of such miniature devices and design of functional molecular components still present significant challenges.   First, the way to connect a molecule to conductive electrodes has to be controlled. We study, in a nanoelectrode-nanoparticle platform, how structural changes affect the measured conductance and how current fluctuations due to these structural changes can be decreased. We find that, for reproducible measurements, it is important to have the molecules chemically bonded to the surfaces of adjacent nanoparticles. Furthermore, we show by a combination of DFT and theoretical modeling that we can identify signals from single-molecules in inelastic electron spectroscopy measurements on these devices.   Second, active elements based on molecules, some examples being switches, rectifiers or memory devices, have to be designed. We study molecular conductance switches that can be operated by light and/or temperature. By tuning the substituents on the molecules, we can optimize the shift of the most conducting molecular orbital and increase the effective coupling between the molecule and the electrodes when going from the OFF to the ON-state of the switches, giving high switching ratio (up to three orders of magnitude). We also study so called mechanoswitches that are activated by a mechanical force elongating the molecules, which means that these switches could operate as sensors.   Furthermore, we have studied two different classes of compounds that may function either as rigid molecular spacers with a well-defined conductance or as molecular cords. In both cases, we find that it is of great importance to match the conjugation of the anchoring groups with the molecular backbone for high conductance.   The last part of the thesis is devoted to another interesting semiconductor material, diamond. We have accurately calculated the band structure and effective masses for this material. Furthermore, these results have been used to calculate the Hall coefficient, the resistivity and the Seebeck coefficient.