No description available.

Warm dense matter (WDM) is an extreme state of matter induced by extreme conditions and characterized as an intermediary state between (high-pressure) condensed matter and plasma. It has sparked a lot of attention in recent years as a result of current innovations in experiments and theoretical methods for modeling such complex systems. Such conditions naturally occur in astrophysical objects such as the interiors of the planets, and in white and brown dwarfs. WDM can be created in the laboratory via various methods such as laser compression, Z-pinches and heated diamond anvil cells. This thesis describes the results obtained for many such systems across a range of conditions modeled using ab-initio simulation methods. The first testbed concerns the electronic structure and linear response of the carbon phases under high-pressure and warm dense matter conditions. The focus is on modeling inelastic x-ray scattering spectra across a range of conditions useful for the analysis and interpretation of x-ray Thomson scattering (XRTS) experiments. Another major goal is to improve the existing models to compute static properties such as the equation of state, density of states with the inclusion of highly accurate data from quantum Monte Carlo (QMC) simulations relevant at finite-temperatures. This approach improves the accuracy and is also computationally inexpensive compared to path integral Monte Carlo (PIMC) methods. Lastly, improvements in linear response theory relevant for XRTS are incorporated with the inclusion of local field corrections (LFC) and finite-temperature local field corrections (T-LFC) using data from QMC simulations.

Cette thèse présente différentes approches quantiques pour l'exploration de processus dynamiques dans des systèmes multiélectroniques, en particulier après une forte excitation qui peut aboutir à des effets dissipatifs. Les théories de champ moyen sont un outil utile à cet égard. Malgré l'existence de nombreux travaux réalisés ces deux dernières décennies, ces théories peinent à reproduire complètement la corrélation à deux corps. La thermalisation est un des effets des collisions électron-électron. Après un chapitre introductif, on présentera dans le chapitre 2 le formalisme de plusieurs méthodes étudiées dans cette thèse, ayant pour but la description de ces effets en ajoutant un terme de collision au champ moyen. Ces méthodes sont appelées Stochastic Time-Dependent Hartree Fock (STDHF), Extended TDHF (ETDHF) et Collisional TDHF (CTDHF). Cette dernière méthode représente d'une certaine façon le résultat principal de cette thèse. L'implémentation numérique de chacune de ces méthodes sera aussi examinée en détail. Dans les chapitres 3, 4 et 5, nous appliquerons à différents systèmes les méthodes présentées dans le chapitre 2. Dans le chapitre 3, nous étudions d'abord un canal de réaction rare, ici la probabilité d'un électron de s'attacher à un petit agrégat d'eau. Un bon accord avec les données expérimentales a été observé. Dans le chapitre 4, un modèle fréquemment utilisé en physique nucléaire est résolu exactement et comparé quantitativement à STDHF. L'évolution temporelle des observables à un corps s'accorde entre les deux méthodes, plus particulièrement en ce qui concerne le comportement thermique. Néanmoins, pour permettre une bonne description de la dynamique, il est nécessaire d'avoir une grande statistique, ce qui peut être un frein à l'utilisation de STDHF sur de larges systèmes. Pour surpasser cette difficulté, dans le chapitre 5 nous testons CTDHF, qui a été introduit dans le chapitre 2, sur un modèle à une dimension (et sans émission électronique). Le modèle se compose d'électrons dans un potentiel de type jellium avec une interaction auto-cohérente sous la forme d'une fonctionnelle de la densité. L'avantage de ce modèle à une dimension est que les calculs STDHF sont possibles numériquement, ce qui permet une comparaison directe aux calculs CTDHF. Dans cette étude de validité du concept, CTDHF s'accorde remarquablement bien avec STDHF. Cela pose les jalons pour une description efficace de la dissipation dans des systèmes réalistes en trois dimensions par CTDHF. / This thesis presents various quantal approaches for the exploration of dynamical processes in multielectronic systems, especially after an intense excitation which can possibly lead to dissipative effects. Mean field theories constitute useful tools in that respect. Despite the existence of numerous works during the past two decades, they have strong difficulties to capture full 2-body correlations. Thermalization is one of these effects that stems from electron-electron collisions. After an introductory chapter, we present in Chapter 2 the formalism of the various schemes studied in this thesis toward the description of such an effect by including collisional terms on top of a mean field theory. These schemes are called Stochastic Time-Dependent Hartree Fock (STDHF), Extended TDHF (ETDHF) and Collisional TDHF (CTDHF). The latter scheme constitutes in some sense the main achievement of this thesis. The numerical realizations of each scheme are also discussed in detail. In Chapters 3, 4 and 5, we apply the approaches discussed in Chapter 2 but in various systems. In Chapter 3, we first explore a rare reaction channel, that is the probability of an electron to attach on small water clusters. Good agreement with experimental data is achieved. In Chapter 4, a model widely used in nuclear physics is exactly solved and quantitatively compared to STDHF. The time evolution of 1-body observables agrees well in both schemes, especially what concerns thermal behavior. However, to allow a good description of the dynamics, one is bound to use a large statistics, which can constitute a hindrance of the use of STDHF in larger systems. To overcome this problem, in Chapter 5, we go for a testing of CTDHF developed in Chapter 2 in a one-dimensional system (and without electronic emission). This system consists in electrons in a jellium potential with a simplified self-consistent interaction expressed as a functional of the density. The advantage of this 1D model is that STDHF calculations are numerically manageable and therefore allows a direct comparison with CTDHF calculations. In this proof of concept study, CTDHF compares remarkably well with STDHF. This thus paves the road toward an efficient description of dissipation in realistic 3D systems by CTDHF.

No description available.

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