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Density functional theory (using Becke's exchange and Lee-Yang-Parr's correlation functionals (BLYP)) and ab initio Hartree-Fock calculations were carried out in order to investigate the molecular structure and vibrational spectra of 9,10-anthraquinone and its perdeuterated analog. The calculated structural and spectral features are in good agreement with the available experimental results. Most of the BLYP/6-31G* non-CH(D) stretching frequencies are slightly lower than reliable experimental assignments; the mean absolute deviation is about 14 cm-1. On the basis of agreement between calculated and experimental results, assignments of the fundamental vibrational modes were examined and some reassignments were proposed. The calculated results can serve as a guide for a future experimental search for the missing fundamentals of the target molecules.

Thesis (Ph. D. (Physics)) -- University of Limpopo, 2020 / Titanium dioxide is among the most abundant materials and it has many of interesting physical and chemical properties (i.e., low density, high thermal and mechanical strength, insensitivity to corrosion) that make it a compound of choice for electrodes materials in energy storage. There are, however, limitations on the theoretical side to using the main electronic structure theories such as Hartree-Fock (HF) or density functional (DFT) especially for large periodic and molecular systems. The aim of the theses is to develop a new, widely transferable, self-consistent density functional tight binding SCC-DFTB data base of TiO2, which could be applied in energy storage anodes with a large number of atoms. The TiO2, LiTiO2 and NaTiO2 potentials were derived following the SCC-DFTB parameterization procedure; where the generalized gradient approximation (GGA) and local density approximation (LDA) exchange-correlation functional were employed yielding Slater-Koster DFTB parameters. The results of derived parameters were validated by being compared with those of the bulk rutile and brookite polymorphs. The structural lattice parameters and electronic properties, such as the bandgaps were well reproduced. Most mechanical properties were close to those in literature, except mainly for C33 which tended to be underestimated due to the choice of exchange-correlation functional. The variation of the bulk lattice parameter and volume with lithiation and sodiation were predicted and compared reasonably with those in literature. The newly derived DFTB parameters were further used to calculate bulk properties of the anatase, which is chemically more stable than other polymorphs. Generally, the accuracy of the lattice structural, electronic and mechanical properties of the bulk anantase were consistent with those of the rutile and brookite polymorphs. Furthermore, nanostructures consisting of a large number of atoms, which extend beyond the normal scope of the conventional DFT calculations, were modelled both structurally and electronically. Structural variations with lithiation was consistent with experimental and sodiation tends to enhance volume expansion than lithiation. Anatase TiO2 and LiTO2 nanotubes of various diameters were generated using NanoWrap builder within MedeA® software. Its outstanding resistance to expansion during lithium insertion and larger surface area make the TiO2 nanotube a promising candidate for rechargeable lithium ion batteries. The outcomes of this study will be beneficial to future development of TiO2 nanotube and other nanostructures. Lastly, our DFTB Slater-Koster potentials were applied to recently discovered trigonal bipyramid (TB), i.e. TiO2 (TB)-I and TiO2 (TB)-II polymorphs, which have enormous 1- D channels that provide suitable pathways for mobile ion transport. All structural, electronic properties were consistent with those in literature and all elastic properties agreed excellently with those that were calculated using DFT methods. Finally, the bulk structures of the two polymorphs, were lithiated and sodiated versions and electronic and structural properties were studied, together with the lithiated versions of associated nanostructures consisting of a large number of atoms. Generally, the TiO2 (TB)-I structure was found to be mechanically, energetically more stable and ductile than TiO2 (TB)-II. Hence, it will be beneficial to use TiO2 (TB)-I as an anode material for sodium ion batteries (SIB), due to its unique ductility and larger 1D channels. / National Research Fund (NRF), the Department of Science and Innovation (DSI) Energy Storage Research Development and Innovation initiative and Materials Modeling Centre

Melatonin (N-acetyl-5-methoxytryptamin, MLT) is a naturally occurring antioxidant which has shown some potential for use as a spin trap. Spin traps react with short lived hydroxyl radicals (HO·) to produce more stable products called spin adducts which may be characterized by electron paramagnetic resonance spectroscopy. However, the relative stability of hydroxyl spin adducts of melatonin derivatives (MLTD) compared to 2-hydroxymelatonin (HO-MLT) has not been examined computationally. Computational studies have been done on four selected MLTD; methylmelatonin (Me-MLT), chloromelatonin (Cl-MLT), cyanomelatonin (CN-MLT), and nitromelatonin (NO2-MLT). Geometry of the structures were optimized at the HF/6-31G(d), cc-pVXZ, (X=D and T) and DFT/B3LYP/6-31G(d), cc-pVDZ and cc-pVTZ levels of theory and extrapolated to the complete basis set limit using cc-pVXZ (X=D, T) basis sets. The lowest relative energy was found to be a mix of results for 2-OH-MLT-Me at HF and 2-OH-MLT-NO2 at DFT.

Scope and Contents: A generalized pairing theory has been developed which diagonalizes matrix elements of the effective nucleon-nucleon interaction in a space of one, two and three-pair excitations from a Skyrme Hartree-Fock solution for deformed rotational nuclei. The "pairing" excitation energy for the configurations of time-reversed pairs of particles is obtained from the Hartree-Fock approximation as opposed to the conventional (BCS) residual interaction point of view. The effects of the finite-range character of the effective nucleon-nucleon interaction are studied in the single-particle structure they induce in the pairing matrix elements. Microscopic form factors for (p,t) and (t, p) reactions between states of the rotational bands built on the K^π=0^+ pairing solution band-head states are constructed in the cylindrical Harmonic-Oscillator basis in which the Hartree-Fock solution is expanded. These form factors are used in DWBA calculations for the differential cross-sections. Preliminary calculations for (p,t) and (t,p) transitions between states in 172Yb and 174Yb were performed. The calculations emphasize the effects of structure in the pairing matrix elements, and the necessity for a self-consistent calculation of the diagonal pairing matrix elements sing the Hartree-Fock equations. / Thesis / Doctor of Philosophy (PhD)

In this dissertation, we solve multivariable Nevanlinna-Pick type interpolation problems. Particularly, we consider the left tangential interpolation problems on the commutative or noncommutative unit ball. For the commutative setting, we discuss left-tangential operator-argument interpolation problems for Schur-class multipliers on the Drury-Arveson space and for the noncommutative setting, we discuss interpolation problems for Schur-class multipliers on Fock space. We apply the Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the Krein-space geometry method is particularly simple in solving the interpolation problems when the Beurling-Lax representer is bounded. The Potapov approach applies equally well whether the representer is bounded or not. / Ph. D.

In dieser Arbeit werden verschiedene Ansätze untersucht, um Tensorzerlegungsmethoden auf die Full-Configuration-Interaction-Methode (FCI) anzuwenden. Das Ziel dieser Ansätze ist es, zuverlässig konvergierende Algorithmen zu erstellen, welche es erlauben, die Wellenfunktion effizient im Canonical-Product-Tensorformat (CP) zu approximieren. Hierzu werden drei Ansätze vorgestellt, um die FCI-Wellenfunktion zu repräsentieren und darauf basierend die benötigten Koeffizienten zu bestimmen. Der erste Ansatz beruht auf einer Entwicklung der Wellenfunktion als Linearkombination von Slaterdeterminanten, bei welcher in einer Hierarchie ausgehend von der Hartree-Fock-Slaterdeterminante sukzessive besetzte Orbitale durch virtuelle Orbitale ersetzt werden. Unter Nutzung von Tensorrepräsentationen im CP wird ein lineares Gleichungssystem gelöst, um die FCI-Koeffizienten zu bestimmen. Im darauf folgenden Ansatz, welcher an Direct-CI angelehnt ist, werden Tensorrepräsentationen der Hamiltonmatrix und des Koeffizientenvektors aufgestellt, welche zur Lösung des FCI-Eigenwertproblems erforderlich sind. Hier wird ein Algorithmus vorgestellt, mit welchem das Eigenwertproblem im CP gelöst wird. In einem weiteren Ansatz wird die Repräsentation der Hamiltonmatrix und des Koeffizientenvektors im Fockraum formuliert. Dieser Ansatz erlaubt die Lösung des FCI-Eigenwertproblems mit Hilfe verschiedener Algorithmen. Diese orientieren sich an den Rayleighquotienteniterationen oder dem Davidsonalgorithmus, wobei für den ersten Algorithmus eine zweite Version entwickelt wurde, wo die Rangreduktion teilweise durch Projektionen ersetzt wurde. Für den Davidsonalgorithmus ist ein breiteres Spektrum von Molekülen behandelbar und somit können erste Untersuchungen zur Skalierung und zu den zu erwartenden Fehlern vorgestellt werden. Schließlich wird ein Ausblick auf mögliche Weiterentwicklungen gegeben, welche eine effizientere Berechnung ermöglichen und somit FCI im CP auch für größere Moleküle zugänglich macht. / In this thesis, various approaches are investigated to apply tensor decomposition methods to the Full Configuration Interaction method (FCI). The aim of these approaches is the development of algorithms, which converge reliably and which permit to approximate the wave function efficiently in the Canonical Product format (CP). Three approaches are introduced to represent the FCI wave function and to obtain the corresponding coefficients. The first approach ist based on an expansion of the wave function as a linear combination of slater determinants. In this hierarchical expansion, starting from the Hartree Fock slater determinant, the occupied orbitals are substituted by virtual orbitals. Using tensor representations in the CP, a linear system of equations is solved to obtain the FCI coefficients. In a further approach, tensor representations of the Hamiltonian matrix and the coefficient vectors are set up, which are required to solve the FCI eigenvalue problem. The tensor contractions and an algorithm to solve the eigenvalue problem in the CP are explained her in detail. In the next approach, tensor representations of the Hamiltonian matrix and the coefficient vector are constructed in the Fock space. This approach allows the application of various algorithms. They are based on the Rayleight Quotient Algorithm and the Davidson algorithm and for the first one, there exists a second version, where the rank reduction algorithm is replaced by projections. The Davidson algorithm allows to treat a broader spectrum of molecules. First investigations regarding the scaling behaviour and the expectable errors can be shown for this approach. Finally, an outlook on the further development is given, that allows for more efficient calculations and makes FCI in the CP accessible for larger molecules.

Dans cette thèse, on étudie plusieurs modèles et problèmes issus de la mécanique quantique. Ces modèles interviennent naturellement en chimie quantique pour le calcul de la structure électronique de la matière. Ils présentent des difficultés théoriques liées aux problèmes d'existence de solutions et à leur calcul numérique. Cette thèse est une contribution à l'étude de ces problèmes. / This thesis is concerned with several mathematical problems in quantum mechanics. These problems arise naturally in quantum chemistry in connection with the electronic structure of matter. Of particular interest are the questions of existence of solutions and of ways to compute them effectively.

Dans une première partie, nous avons étudié quelques propriétés de molécules magnétiques impliquant des radicaux organiques (seuls ou conjointement avec des terres rares). Nous avons ainsi pu interpréter l'évolution de la susceptibilité magnétique et de l'aimantation en fonction de la température en évaluant par des approches ab initio fonctions d'onde les constantes d'échange ou le tenseur g au sein de ces matériaux. De plus, nous avons chercher à définir les conditions pour que des matériaux à base de radicaux organiques présentent simultanément des propriétés magnétiques et conductrices. Nous avons ainsi examiné différentes familles de composés et l'influence de la structure géométrique et chimique des radicaux organiques utilisés. Pour cette partie, nous avons extrait les intégrales physiques pertinentes par la méthode des Hamiltoniens effectifs.Dans une deuxième partie, nous avons utilisés ces quantités physiques (intégrale de saut, répulsion sur site, échange) pour décrire le phénomène de transport dans des jonctions pour lesquelles les effets de la corrélation électronique ne peuvent être écartés. Munis de ces paramètres ab initio, nous avons développé un modèle phénoménologique permettant de décrire la conduction moléculaire à l'aide d'un jeu d'équations maîtresses. Nous avons ainsi cherché à mettre en évidence l'intérêt des approches post Hartree-Fock empruntant une fonction d'onde corrélée et de spin adapté dans la description du transport électronique. Que ce soit dans le cas de transport polarisé en spin ou non, l'approche utilisée (mono ou multi-déterminentale) conditionne qualitativement et quantitativement la caractéristique courant/tension. / In a first part, we studied the magnetic properties of organic radicals (coupled with rare earth or between each other). We calculated the magnetic exchange and the g-tensor of these compounds to understand their magnetic susceptibility and thei magnetization curves via ab initio calculations based on the wave-function. We studied how the chemistry and the crystal stacking affect meaningful parameters linked to magnetism and conduction. Those parameters were extracted with the thory of effective Hamiltonians fo various families of organic radicals. From the observed trends for the different parameters, we predicted some ways to obtain multifunctional compounds. In a second part, we used the same parameters (hoping integral, coulombic repulsion, magnetic exchange) to describe transport properties through highly correlated molecular junctions. From the ab initio parameters, we developed a phenomenological model based on master equations to describe the electronic transport. We stressed the importance of a multiconfigurational description to reproduce properly the transport properties for spin unpolarized and spin polarized situations. In both cases, the mono- or multi-configurational description affects qualitatively and quantitatively the predicted conductance curve.

Les composés à commutation électronique constituent une large famille de systèmes particulièrement prometteuse, notamment pour le stockage de l’information à l’échelle moléculaire. Parmi ces composés, les analogues du bleu de Prusse cobalt-fer (ABP AxCoFe) sont des polymères inorganiques formés d’enchaînements Co-N≡C-Fe pouvant présenter deux états électroniques CoII(HS)-N≡C-FeIII(BS) et CoIII(BS)-N≡C-FeII(BS) (HS : haut spin ; BS : bas spin) aux propriétés structurales et électroniques bien distinctes. La transition électronique entre ces deux états peut être contrôlée de manière réversible par une grande variété de paramètres chimique (insertion de cations alcalins) et physiques (température, pression, irradiation). Ces propriétés de photo-commutation sont particulièrement intéressantes pour le développement de mémoires optiques à l’échelle moléculaire.Afin de comprendre les propriétés électroniques des ABP AxCoFe, nous nous sommes intéressés à l’interaction entre les centres métalliques via le pont cyanure dans l’enchaînement Co-N≡C-Fe, aussi bien sur un plan expérimental (mise en œuvre de techniques d’analyse reposant sur l’utilisation du rayonnement synchrotron) que théorique (modélisation ab initio de type post-Hartree-Fock). Nous avons également étudié la nature de l’interaction, démontrée expérimentalement, entre les cations alcalins et le réseau bimétallique formé par les enchaînements Co-N≡C-Fe. Finalement, la pertinence du modèle à deux états, habituellement utilisé pour rendre compte des propriétés électroniques des systèmes commutables, est discutée, avec la mise en évidence de multistabilités au sein des ABP AxCoFe. Ce travail propose ainsi une étude la plus complète possible des phénomènes électroniques rencontrés dans ces systèmes. / Electronically switchable compounds constitute a wide family of very promising systems, especially in the field of data storage at a molecular scale. Amongst these compounds, cobalt-iron Prussian blue analogues (AxCoFe PBAs) are inorganic polymers based on Co-N≡C-Fe linkages that may exhibit two CoII(HS)-N≡C-FeIII(LS) and CoIII(LS)-N≡C-FeII(LS) (HS: high spin; LS: low spin) electronic states with very different structural and electronic properties. Electronic transition in between these two states can be reversibly controlled by a large variety of both chemical (insertion of alkali cations) and physical (temperature, pressure, irradiation) parameters. These photo switching properties are extremely appealing for the development of optical memory devices at the molecular scale.In order to understand the electronic properties of AxCoFe PBAs, the interaction occurring between the metallic centres through the cyanide bridge in the Co-N≡C-Fe linkages was investigated both at an experimental (use of synchrotron-radiation-based analytic techniques) and a theoretical (post-Hartree-Fock ab initio modelling) levels. The nature of the experimentally-demonstrated interaction between the alkali cations and the bimetallic network, made of the Co-N≡C-Fe linkages, was also studied. Finally, the relevance of the two-state model, usually invoked to account for the electronic properties of switchable systems, is discussed, as multistabilities are evidenced in PBAs. This work therefore offers study of the electronic phenomena occurring in such systems as comprehensive as possible.