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Although band theory is about a century old, it remains relevant today as a tool for the treatment of electrons in solids. The confluence of mathematical ideas like geometry and topology with band theory has proven to be a ripe avenue for research in the past few decades. The importance of Fermi surface geometry, especially in conjunction with electronic correlation, has been well recognized. One particular thread in this direction is probing the occurrence of non-trivial Fermi surface geometry, and its influence on macroscopic properties of materials. A notable example of exotic Fermi surface geometry arises from singular points of the dispersion, and these have been known since 1953. The investigation into these was reignited recently, culminating in the work presented in this thesis. In this dissertation, I investigate two broad categories of singular points in bands. At a singular point, either the dispersion or the Fermi surface fail to be smooth. This may cause distinct signatures in transport and spectroscopic properties when the singular point occurs close to the Fermi level. In the two dimensional setting, I classify using catastrophe theory, the point singularities arising from higher order saddles of the dispersion. These are the more exclusive cousins of the regular van Hove saddle that cause, among other things, a power law divergence in the density of states. The role of lattice symmetries in aiding or preventing the occurrence of these singularities is also carefully explored. In the case of three dimensional bands, I investigate the spectroscopic properties of the nodal point singularity, arising from a linear band crossing. In particular, I determine the distinct signature of nodal points in the analytic, momentum resolved, joint density of states (JDOS) and the numerically calculated resonant inelastic x-ray scattering (RIXS) spectrum, within the fast collision approximation that ignores core hole effects. The results presented here will be the stepping stone towards a careful future calculation, incorporating the potential edge singularity effects through core hole potential. Such a calculation may be directly comparable with ongoing experiments.

In this dissertation, investigations regarding magnetism within metal-organic frameworks (MOFs) based on calculations in the framework of density functional theory (DFT) were carried out. On the one hand, the intrinsic magnetic properties within the MOF DUT-8(Ni) were studied (DUT -- Dresden University of Technology). This MOF is flexible, thus it can exist in two crystal structures named DUT-8(Ni)ppen and DUT-8(Ni)closed. A transition from one structure to the other can be achieved via e.g. gas adsorption, leading to a volume increase of approximately 260 %. The magnetic properties originate from spin-spin interactions between the unpaired electrons at the Ni centers. The magnetic coupling between the Ni ions was found to be low-spin (antiferromagnetic). Considering that MOFs tend to have rather large unit cells (> 100 atoms), model systems (< 30 atoms) were generated. Such models can qualitatively as well as quantitatively describe the coupling inside the crystal structure while drastically reducing computational time. Furthermore, the model systems can be easily altered e.g. to introduce defects. The influence of these alterations on the magnetic coupling was studied. In addition, the metal centers have been exchanged by other 3d-metals to analyze the coupling constant with respect to different magnetic centers. On the other hand, the magnetic shielding of Xe adsorbed into the MOFs UiO-66 and UiO-67 was investigated (UiO -- University of Oslo). Based on high-pressure nuclear magnetic resonance (NMR) measurements, which showed a decrease of the total chemical shift when going from the smaller MOF (UiO-66) to the larger one (UiO-67), a thorough theoretical analysis was carried out. For this purpose the ansatz of Ito and Fraissard, i.e. the chemical shift of Xe being a sum of different contributions, was employed. Accordingly, model systems which describe the influences of the MOFs and adjacent Xe atoms on the magnetic shielding were contructed. After equilibrating the Xe positions using molecular dynamics simulations, these model systems were taken to study the chemical shift of all Xe atoms individually. Thus, an analysis of the chemical shift inside each pore of the MOFs was carried out. This allows a description of different influences (Xe-surface, Xe-Xe) on the chemical shift, explaining the experimental behavior at an atomistic level.

Tesis por compendio / [EN] The dimensionality of the system plays a decisive role in the behavior of the electronic dynamics of interacting electrons. In particular, the quasi-2D dimensionality is responsible for the unusual behavior observed in graphene-like materials and layered van-der-Waal systems. Moreover, such effects are also observed for superconducting materials of high critical temperature, even in the normal state, due to their low-dimensionality. The experimental study of graphene triggered a growing attention to respective electronic properties, because the honeycomb lattice defines a band structure with two nodal points in the Brillouin zone which determines a relativistic Dirac-type electronic dynamics. Within a theoretical framework, many properties of single-layer graphene have been studied to allow further characterization of this material. These properties are unconventional due to the unique band structure of graphene, which is described in terms of Dirac fermions, creating links with certain theories of particle physics. In fact, several theoretical groups have employed phenomenological models inspired in quantum cromodynamics (i.e. Nambu-Jona Lassino and Gross-Neveu models) applied to the study of graphene properties. These properties are responsible for the unusual phenomena, such as the fractional Hall effect, which allows the possibility for magnetic catalysis of an excitonic gap, ferromagnetism and superconductivity. The research of high critical temperature superconductors with impurity centers is significant for understanding the underlying physics of such disordered systems. While the cuprate family present insulating properties in the pristine state, the undoped iron pnictides (i.e. LaOFeAs) show a semi-metallic behavior. Inspite these diferences, both compounds are layered structures, where the superconducting state is supported by a quasi-2D square lattice. While for iron pnictides this state is formed by the FeAs layer, the cuprate superconducting state is formed by the CuO layer. The current work focuses on the theoretical study of the structural, electronic and optical properties of graphene-type materials, such as bilayer graphene; and also of s- and d-wave superconductors, more specifically iron pnictides and cuprates, respectively. Furthermore, disordered systems will be focused upon since these (quasi-)2D systems are quite sensitive to disorder. Such properties have major importance for technological device applications, as can be observed in the increasing technological fields of high temperature superconductores and electronic devices. The type of perturbations applied to the systems of interest are chemical impurities and/or external electric bias, and these show variations of the electronic and optical properties when compared to the pristine systems. / [ES] La dimensionalidad de un sistema juega un papel fundamental en la conducta de la dinámica de los electrones que interactúan. En particular, la dimensionalidad cuasi-2D es responsable del comportamiento inusual observado en materiales de tipo grafeno y sistemas laminares basados en enlaces de tipo van der Waals. Además, estos efectos también se observan en materiales superconductores de alta temperatura crítica, incluso en el estado normal, debido a su baja dimensionalidad. El estudio experimental del grafeno provocó una atención creciente a sus propie-dades electrónicas, porque su estructura en forma de panal de abejas da lugar a una estructura de bandas con dos puntos nodales en la zona de Brillouin que determina una dinámica electrónica relativista de tipo Dirac. En el plano teórico, muchas propiedades del grafeno de una sola capa se han estudiado para permitir una mayor caracterización de este material. Estas propiedades son poco convencionales debido a la singular estructura de bandas del grafeno, que se describe en términos de fermiones de Dirac, lo que crea vínculos con ciertas teorías de la física de partículas. De hecho, varios grupos teóricos han empleado modelos fenomenológicos inspirados en la cromodinámica cuántica (es decir, los modelos Nambu-Jona Lassino y Gross-Neveu) aplicados al estudio de las propiedades del grafeno. Estas propiedades son responsables de inusuales fenómenos, como el efecto Hall fraccionario, que permite la posibilidad de catálisis magnética de un gap excitónico, ferromagnetismo y superconductividad. La investigación de superconductores de alta temperatura crítica con centros de impurezas es importante para comprender la física subyacente de tales sistemas desordenados. Mientras que la familia de los cupratos presenta propiedades aislantes en estado prístino, los pnictogenuros de hierro sin dopar (es decir, LaOFeAs) muestran un comportamiento semimetálico. A pesar de estas diferencias, ambos compuestos son estructuras en capas, donde el estado superconductor está respaldado por una red cuadrada cuasi-2D. Mientras que para los pnictogenuros de hierro este estado está formado por la capa de FeAs, el estado superconductor de cuprato está formado por la capa de CuO. El presente trabajo se centra en el estudio teórico de las propiedades estructurales, electrónicas y ópticas de los materiales de tipo grafeno, como el grafeno bicapa; y también de superconductores de ondas s y d, más específicamente pnictogenuros y cupratos de hierro, respectivamente. Además, se hace hincapié en sistemas desordenados ya que estos sistemas (cuasi-)2D son bastante sensibles al desorden. Tales propiedades tienen gran importancia para aplicaciones de dispositivos tecnológicos, como se puede observar en la creciente tecnología campos de tensiotrónica y espintrónica. El tipo de perturbaciones aplicadas a los sistemas de interés son las impurezas químicas y campos eléctricos externos. Estas perturbaciones producen variaciones de las propiedades electrónicas y ópticas cuando se comparan con los sistemas prístinos. / [CAT] La dimensionalitat d'un sistema juga un paper fonamental en la conducta de la dinámica dels electrons que interactúen. En particular, la dimensionalitat cuasi-2D és responsable del comportament inusual observat a materials de tipus grafè i sistemes laminars basats en enllaços de tipus van der Waals. A més a més, aquestos efectes també s'observen a materials superconductors d'alta temperatura crítica, inclús al seu estat normal, degut a la seua baixa dimensionalitat. L'estudi experimental del grafè va produir una atenció creixent a les seues propietats electròniques, perque la seua estructura en forma de panal d'abelles dona lloc a una estructura de bandes amb dos punts nodals a la zona de Brillouin que determinen una dinámica electrónica relativista de tipus Dirac. Al planol teòric, moltes propietats del grafè d'una sola capa s'han estudiat per a permetre una major caracterizació d'aquest material. Aquestes propietat són poc convencionals degut a la singular estructura de bandes del grafè, que es descriu mitjançant fermions de Dirac. Aquestos fermions permeten establir víncles amb certes teories de la física de particles. De fet, alguns grups teòrics han empleat models fenomenològics inspirats a la cromodinàmica quàntica (es a dir, els models Nambu-Jona Lassino i Gross-Neveu) aplicats a l'estudi de les propietats del grafè. Aquestes propietats són responsables d'inusuals fenómens, com l'efecte Hall fraccionari, que permet la possibilitat de catálisi magnètica d'un gap excitònic, ferromagnetisme i superconductivitat. La investigació de superconductors d'alta temperatura crítica amb centres d'impureses és important per a comprendre la física subjacent de tals sistemes desordenats. Mentre que la família dels cuprats presenta propietats aïllants en estat pristí, els pnictogenurs de ferro sense dopar (és a dir, LaOFeAs) mostren un comportament semimetálico. Malgrat aquestes diferències, tots dos compostos són estructures en capes, on l'estat superconductor està recolzat per una xarxa quadrada quasi-2D. Mentre que per als pnictogenurs de ferro aquest estat està format per la capa de FeAs, l'estat superconductor dels cuprats està format per la capa de CuO. El present treball es centra en l'estudi teòric de les propietats estructurals, electròniques i òptiques dels materials de tipus grafè, com el grafè bicapa; i també de superconductors d'ones s i d, més específicament pnictogenurs i cuprats de ferro, respectivament. A més a més, es fa emfasi en sistemes desordenats ja que aquestos sistemes (cuasi-)2D són prou sensibles al desordre. Aquestes propietats tenen gran importància per a aplicacions de dispositius tecnològics, com es pot observar a la creixent tecnologia dels camps de la tensiotrònica i l'espintrònica. El tipus de pertorbacions aplicades als sistemes d'interés són les impureses químiques i els camps elèctrics externs. Aquestes pertorbacions produeixen variacions de les propietats electròniques i òptiques quan es comparen amb els sistemes pristins. / César Dos Santos, MJ. (2021). Effects of symmetry breaking in low dimensional materials [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176058 / TESIS / Compendio

Orientador: Augusto Batagin Neto / Resumo: Polímeros orgânicos conjugados são considerados materiais de grande relevância para aplicações tecnológicas variadas, principalmente devido às suas propriedades optoeletrônicas únicas e métodos utilizados em sua síntese. Nesse contexto, os derivados de polipirrol (PPy) têm sido amplamente empregados. A grande variabilidade de síntese desse material permite a produção de uma série de derivados com propriedades distintas, permitindo sua aplicação em diversas áreas. Neste trabalho, cálculos de estrutura eletrônica foram realizados para avaliar a influência de grupos laterais nas propriedades estruturais, ópticas, eletrônicas e de reatividade de derivados de PPy, em especial para aplicações como sensores químicos. Os cálculos foram feitos para sistemas oligoméricos aplicando a teoria do funcional da densidade. Estudos de preliminares foram conduzidos utilizando dois funcionais distintos para otimização de geometria e avaliação de propriedades optoeletrônicas. Estudos comparativos da alternância de comprimento de ligação, distribuição espacial e energética dos orbitais de fronteira, gaps eletrônicos, energias de ligação de éxcitons, espectros de absorção óptica, densidade eletrônica de estados e reatividade local foram conduzidos para cada derivado e a influência dos grupos laterais foi discutida em termos de suas propriedades de inserção/retirada de elétrons. Um conjunto de regras simples (equações lineares) foi proposto para a predição de propriedades optoeletrônicas de derivado... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Conjugated organic polymers have been considered interesting materials for varied technological applications, mainly due to their unique optoelectronic properties and variety of methods employed in their synthesis. In this context, polypyrrole (PPy) derivatives have been widely employed. The great versatility of synthesis of this material allows the production of a number of derivatives with distinct properties, allowing their application in several areas. In this report, aiming to guide the design of compounds with specific features, electronic structure calculations were conducted to evaluate the influence of side groups in the structural, optical and electronic properties of PPy derivatives, specially for application in chemical sensors. The calculations were carried out for oligomeric systems in the framework of the density functional theory. Preliminary benchmark studies were conducted by employing two distinct functionals for geometry optimization and evaluation of optoelectronic properties. Comparative studies of the bond length alternation, spatial and energetic distribution of the frontier orbitals, electronic gaps, exciton binding energies, optical absorption spectra, electronic density of states and local reactivity were conducted for each derivative and the influence of the side groups was discussed in terms of their electron donation/withdrawing properties. A set of simple rules (linear equations) was proposed for the prediction of optoelectronic properties of PP... (Complete abstract click electronic access below) / Mestre

<p>Climate change and the energy crisis are substantial challenges facing the human species, and they are projected to threaten life on our planet. For millions of years, the sun has been the main source of energy for life on Earth; this inspires ongoing research efforts focusing on a “sunlight to fuel” energy solution. Photosynthesis is nature’s tool to derive energy from the sun. Hence, scientists focus on the biochemistry of this phenomenon to employ photosynthesis in a man-made device. Such a device is able to convert solar energy to chemical energy through a light-driven cycle of the chemical reactions which produce hydrogen gas, later used as fuel. This process, often called “artificial photosynthesis,” needs efficient catalysts which can be incorporated into a molecular assembly and other microscopic structures or immobilized on an electrode surface. </p><p>Additionally, evolution, in the course of billions of years, chose manganese as an abundant and effective metal to facilitate the process of photosynthesis. These manganese atoms formed a cluster and an optimized ligand field to maximize efficiency. The photochemistry and photo-physics process behind photosynthesis is yet to be fully understood and implemented in a man-made apparatus with comparable efficiency and durability. </p><p>Photosynthesis requires a source of electrons. Water is an abundant molecule on earth that can provide the electrons needed for the photosynthesis. Although water is ubiquitous, it is one of the most stable molecules; hence, splitting it demands a well-designed system with strong oxidizing capability. Because a single atom of oxygen is highly reactive, there should be at least four oxidation states in the system to remove four electrons and release molecular oxygen: O2. The O-O bond formation is one of the most important steps in photosynthesis to fully understand. Lacking a thorough knowledge of this step prevents design and fabrication of robust and active water oxidizing catalysts. To fully understand O-O formation, one should perform a comprehensive study of each of the intermediates of the system. In other words, we need an understanding of the structure and electronic configuration of the system (natural or artificial) from the moment that a water molecule attaches to the catalyst (usually a metal core, central in the complex), until the moment that oxygen released as an O2 molecule. </p><p>There are multiple possible mechanisms to explain O-O formation. Two mechanisms that were extensively studied in this thesis are water nucleophilic attack and radical coupling. The prevailing view about oxygen formation in the catalysts that we study here explains the O-O bond formation by nucleophilic attack of a water molecule to a highly oxidized ruthenium (RuV=O) species. In this hypothesis, all polypyridine ligands that are coordinated to ruthenium remain neutral during the water oxidation process, while the formation of RuV=O (the key intermediate) would require a relatively high free energy (about 1.8 to 2 eV); use of computational (numerical) calculations determine this to be thermodynamically inaccessible. Furthermore, the failure of spectroscopic techniques to confirm the presence of RuV=O calls the validity of this model into question.)</p><p>Alternatively, radical coupling hypothesis considers another pathway to oxygen bond formation. Here, one of the nitrogen atoms coordinated to ruthenium in polypyridine plays a crucial role. We hypothesize that after formation of RuIV=O (which is spectroscopically observed), one nitrogen decoordinates from the metallic core (ruthenium) and oxidizes to form Ru-ON species. This N-oxide ligand can be further oxidized to form a ligand cation radical. It has been shown that [ligand-NO]+• can have almost no energy barrier for O-O bond formation via spin alignment. The study of the role of N-oxide is one of the main focuses of this work. Since this hypothesis does not require RuV=O nor water nucleophilic attack, it explains the process of water oxidation and opens further avenues for the design of future catalysts.</p><p>To confirm our hypothesis, I employed several spectroscopic methods and computational calculations. This new pathway predicts new intermediates exclusive to this model. Our objective is to prove their presence by in situ spectroscopy and test the possibility of formation of each intermediate computationally, to see if their formation is thermodynamically feasible. </p><div><br></div>

Recent research has shown that small hydrogen bonding catalysts can catalyze the hetero Diels-Alder reaction. In this thesis such hydrogen bonding catalysts in conjunction with varying functional groups and their effect on the hetero Diels-Alder reaction have been investigated. The influence of the different solvents has been investigated as well. The activation barriers for the different region- and stereo isomeric pathways have been compared in order to determine the stereo specificity of the reactions. These calculations have been done using the B3LYP functional for the geometry optimizations and then M06-2X for single point calculations. For the solvated cases the cPCM model and the M06-2X functional were used. It was shown that for the catalyzed systems bulkier groups in the endo position tend to have a lower activation barrier, allowing for control over the stereoselectivity. Electron withdrawing groups have an activating effect and are also synergistic with the hydrogen bonding catalysts. The solvent with the lowest dielectric constant gave the lowest activation barrier.

Predicting new materials through virtually screening a large number of hypothetical materials using supercomputers has enabled materials discovery at an accelerated pace. However, the innumerable number of possible hypothetical materials necessitates the development of faster computational methods for speedier screening of materials reducing the time of discovery. In this thesis, I aim to understand and apply two computational methods for materials prediction. The first method deals with a computational high-throughput study of superalloys. Superalloys are materials which exhibit high-temperature strength. A combinatorial high-throughput search across 2224 ternary alloy systems revealed 102 potential superalloys of which 37 are brand new, all of which we patented. The second computational method deals with a machine-learning (ML) approach and aims at understanding the consistency among five different state-of-the-art machine-learning models in predicting the formation enthalpy of 10 different binary alloys. The study revealed that although the five different ML models approach the problem uniquely, their predictions are consistent with each other and that they are all capable of predicting multiple materials simultaneously.My contribution to both the projects included conceiving the idea, performing calculations, interpreting the results, and writing significant portions of the two journal articles published related to each project. A follow-up work of both computational approaches, their impact, and future outlook of materials prediction are also presented.

In the exploration of chemical systems through quantum mechanics, accurate treatment of the electron wavefunction, and the related electron density, is fundamental to extracting information concerning properties of a system. This work examines challenges in achieving accurate chemical information through manipulation of the one-electron basis set.