Orientador: Rogério Custodio / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-18T08:56:05Z (GMT). No. of bitstreams: 1 Abreu_Leandrode_M.pdf: 3333566 bytes, checksum: 9df2fe3268e83e70fae31b792fc76513 (MD5) Previous issue date: 2011 / Resumo: Este trabalho avaliou o cálculo de energias de ionização verticais e as possibilidades de construção e interpretação de diagramas de correlação através do uso dos métodos Monte Carlo Quântico (MCQ) e Outer Valence Green¿s Function (OVGF). O trabalho foi dividido em quatro partes: Energias de ionização simples: Avaliou-se a capacidade dos métodos MCQ e OVGF em descrever os valores de energia de ionização de valência e de caroço e testou-se o uso de funções de onda relaxadas. A faixa dos desvios observados obtidas com o método Monte Carlo Quântico de Difusão (MCQD), em relação aos valores experimentais, é comparável a de outros métodos, como DFT (Teoria do Funcional de Densidade - Density Functional Theory) e CCGF (Funções de Green com Pares Acoplados - Coupled-Cluster Green¿s Function), 0,01 a 2 eV, e verificou-se que uso das funções de onda relaxadas é importante na descrição das ionizações de caroço. Energias de ionização sucessivas: Estimou-se as energias de ionização sucessivas dos elementos do 2º período a partir das energias orbitais do sistema neutro e comparou-se com resultados obtidos através dos métodos MCQ utilizando-se a função de onda do sistema não-ionizado. Pode-se demonstrar a falha das energias orbitais em descrever as energias de ionização sucessivas e obter correções com o uso dos métodos MCQ. Diagramas de correlação: Construíram-se diagramas de energia eletrônica total e de correlação quantitativos utilizando energia de ionização como binding energy para moléculas do tipo BAB (H2O e Li2O) através do uso dos métodos MCQ. Foram construídos diagramas de cargas parciais de Bader através das distribuições discretas de carga obtidas com os métodos MCQ para tentar interpretar os diagramas de correlação, porém a interpretação por comparação direta não foi possível, contudo foram obtidas informações importantes através dos diagramas de cargas parciais. Energias de dupla ionização: Foram calculadas energias de dupla ionização de sistemas atômicos e moleculares através do método OVGF e compararam-se os resultados obtidos com a Teoria do Funcional de Densidade (DFT). O método OVGF mostrou-se tão preciso quanto a teoria DFT na descrição das energias de dupla ionização / Abstract: The study was divided into 4 parts: Simple Ionization Energies: We evaluated the ability of MQC and OVGF methods in describing the values of the ionization energy of valence and core and tested the use of relaxed wave functions. The range of deviations obtained with the method of diffusion quantum Monte Carlo (MCQD), in relation to the experimental values, is comparable to other methods such as DFT (Density Functional Theory) and CCGF (Coupled-Cluster Green's Function), from 0.01 to 2 eV, and it was found that the use of the relaxed wave functions is important in the description of core ionizations. Successive Ionization Energies: We estimated the successive ionization energies of successive elements of the 2nd period from the orbital energies of the neutral system and compared with results obtained using the methods MCQ with the wave function of nonionized system. It can be shown the failure of the orbital energies to describe the successive ionization energies and to obtain corrections with the use of MCQ methods. Correlation Diagrams: Diagrams of total electronic energy and quantitative correlation diagrams were constructed using the ionization energy as binding energy for molecules of the type BAB (Li2O and H2O) through the use of MCQ methods. We constructed Bader¿s partial charges diagrams with the discrete charge distributions obtained with MCQ methods to try to interpret the correlation diagrams, but the interpretation by direct comparison was not possible, however, important information was obtained through diagrams of partial charges. Double Ionization Energies: We calculated double ionization energies of atomic and molecular systems by the OVGF method and compared the results obtained with the Density Functional Theory (DFT). The OVGF method proved to be as accurate as the DFT theory in describing the double ionization energies / Mestrado / Físico-Química / Mestre em Química

Orientador: Rogério Custodio / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-21T05:01:18Z (GMT). No. of bitstreams: 1 Streit_Livia_D.pdf: 1852639 bytes, checksum: 1d6bd6190d21b329d992dfe5f74f8993 (MD5) Previous issue date: 2012 / Resumo: O estudo de processos fotoeletrônicos, como energias de dupla ionização é de grante interesse teórico e experimental na área da física molecular. Cálculos e medidas experimentais de energias de dupla ionização e de energias de ligação de elétron envolvem o entendimento de correlação e relaxação eletrônica. A consideração de tais efeitos é indispensável para a obtenção de resultados precisos. No presente trabalho, tais processos fotoeletrônicos são estudados com métodos Pós-Hartree-Fock e Monte Carlo Quântico (MCQ). No último caso, o método foi adaptado de maneira a utilizar um tipo diferente de função de onda. A primeira parte desta tese envolve o estudo de energias de dupla ionização. O objetivo prinicipal é a análise do tipo de função de onda tentativa no método MCQ. Três diferentes formas foram estudadas: Uma função Hartree-Fock monodeterminante com uma função de correlação eletrônica explícita de Boys-Handy otimizada para a molécula; uma função CI multideterminante; e ainda, uma função de onda multideterminante construída a partir de orbitais de Dyson. Para obter a função de onda de Dyson, um extenso trabalho envolvendo estudo e programação do programa de cálculo de estrutura eletrônica Gaussian 09 foi necessário. A primeira parte da tese ainda envolve o estudo de energias de dupla ionização por métodos Interação de Configurações Multireferência MRCI e Gaussian-3 G3. Os resultados obtidos são comparados aos resultados obtidos por MCQ. A segunda parte da tese compreende o estudo de energias de ligação de elétron de complexos de gases nobres com o ânion Uracila. A coexistência de ânions em que o orbital singularmente ocupado apresenta características de um orbital de valência e de um orbital muito difuso é investigada através de análise de geometria e do cálculo de energias de afinidade eletrônica e de ligação de elétron dos complexos neutros e aniônicos / Abstract: The study of photoelectron processes such as double ionization energies has become a very interesting field in experimental and theoretical molecular physics. Calculation and experimental measure of double ionization energies and electron binding energies involve understanding of electron correlation and relaxation energies. Consideration of those effects are a requisite in order to predict precise values. In this work, those photoelectron processes are studied with post-Hartree-Fock and Quantum Monte Carlo (QMC) methods. In the latter case, the method was also modified to take in account a different type of wavefunction. The first part of this thesis is concerned with the study of double ionization energies. The main objective of this work is the analysis of the type of trial wavefunction in QMC method. Three different forms were studied: A single determinant Hartree-Fock function, with the Boys-Handy explicit electron correlation function optimized for the molecule; a multi-determinant CI wavefunction; and finally, a multi-determinant wavefunction built from Dyson orbitals. In order to obtain the Dyson wavefunction, an extensive work on studying and programming the electron structure package Gaussian 09 was necessary. The first part still comprises the study of double ionization energies with MRCI and G3 methods. The results thus obtained were compared to the QMC results. The second part of this thesis embraces the study of electron binding energies of uracil¿noble-gas complexes. The coexistence of valence and diffuse¿bound anions of U(Xe), suggested by experimental studies is investigated with geometry analysis and calculation of adiabatic electron affinities and vertical electron detachment energies of the neutral an anionic complexes / Doutorado / Físico-Química / Doutor em Ciências

Dans cette thèse nous présentons des progrès algorithmiques ainsi que plusieurs applications des méthodes de Monte Carlo quantique (QMC) pour simulations à partir des premiers principes. Les améliorations que nous proposons permettent d'étudier par QMC des systèmes de plus grosse taille voire périodiques, avec l'ambition de faire du QMC une alternative valable à la théorie de la fonctionnelle de la densité (DFT). Tous les résultats ont été obtenus par le logiciel TurboRVB. D'abord, nous présentons une implémentation du QMC basée sur la fonction d'onde Jastrow-Geminale qui combine une grande flexibilité avec un traitement précis des corrélations électroniques. On a appliqué une technique originale de plongement pour réduire la taille de la base atomique à la molécule d'eau ainsi qu'à un modèle simplifié du transfert de protons (TP) dans l'eau. Nos résultats ouvrent la voie à l'étude des phénomènes microscopiques tels que le TP directement par QMC. Ensuite, on a amélioré notre méthode afin de simuler les solides cristallins. Grâce à une nouvelle procédure pour choisir de manière appropriée les conditions aux limites, nous avons pu réduire les erreurs de taille finie qui affectent les simulations QMC des solides. Sur la base des techniques développées, nous étudions enfin le supraconducteur FeSe. Le QMC fournit le meilleur résultat concernant sa structure cristalline; via une étude systématique du paysage énergétique à différentes configurations magnétiques, nous montrons un lien fort entre la structure, le magnétisme et les mouvements de charge dans ce matériau, prélude à une compréhension quantitative de la supraconductivité à haute température des premiers principes. / In this thesis we present algorithmic progresses as well as applications of continuum quantum Monte Carlo (QMC) methods for electronic structure calculations by first principles. The improvements we propose allow to tackle much larger molecular as well as extended systems by QMC, with the ultimate goal of making QMC a valid alternative to density functional theory (DFT). All results have been obtained with the TurboRVB software, which we contributed to develop. At first, we present a QMC framework based on the Jastrow-Geminal wavefunction which combines great flexibility with a compact analytical form, while providing at the same time an accurate treatment of electron correlations. We apply an original atomic embedding scheme for reducing the basis set size to the water molecule and to a simple model of proton transfer (PT) in aqueous systems. Our results pave the way to the study of microscopic phenomena such as PT directly by QMC. Afterwards, we extend our QMC framework in order to simulate crystalline solids. We propose a novel procedure to find special values of the boundary conditions which allow to greatly reduce the finite-size errors affecting solid state QMC simulations. Using the techniques previously developed, we study the iron-based superconductor FeSe. We show that QMC provides the best crystal structure predictions on this compound; by means of a systematic study of the energy landscape at different magnetic orderings, we show a strong link between structural, magnetic and charge degrees of freedom in FeSe. Our results represent an important step towards a quantitative understanding of high-temperature superconductivity by first-principles.

De nos jours, il n'existe encore aucune théorie capable de proposer une description précise et quantitative du transfert de proton en solution. En effet, ce problème est complexe du fait de la grande diversité des interactions existant dans l'eau liquide, à savoir: des interactions non liantes de type Van der Waals, des liaisons faiblement covalentes et des liaisons hydrogènes remarquablement fortes. Ces dernières sont d'ailleurs à l'origine des nombreuses propriétés fascinantes de l'eau à l'échelle macroscopique. À cela s'ajoutent les effets quantiques nucléaires dus à la faible masse de l'hydrogène, qui modifient profondément la nature de la surface d'énergie potentielle décrivant le transfert de proton le long de sa coordonnée de réaction. Nous proposons dans cette thèse une approche tout quantique basée sur une description quasi exacte de la fonction d'onde du système par l'utilisation de méthodes stochastiques de type Monte Carlo Quantique. Cette technique, combinée avec le formalisme des équations de Langevin et des intégrales de chemin de Feynman, permet de simuler à un niveau de précision inédit, n'importe quel système chimique en phase gaz ou en solution. Nous appliquons cette méthodologie à des agrégats d'eau neutres ou protonés pour apporter de nouveaux éclaircissements sur les phénomènes microscopiques régissant la diffusion du proton hydraté dans de tels systèmes. Il est mis en évidence que la mobilité du proton est optimale pour des températures proches des conditions ambiantes, du fait de la compétition subtile entre les effets thermiques et quantiques nucléaires. / There is no theory up to now able to provide an accurate and quantitative description of the proton transfer (PT) yet. Indeed, the complexity of the problem stems from the large diversity of the existing interactions in liquid water, namely: non bonding Van der Waals interactions, weakly covalent bonds and remarkably strong H-bonds. The latter ones are at the origin of the numerous fascinating properties of water at the macroscopic scale. In addition to such interactions, the nuclear quantum effects arising from the hydrogen light mass deeply modify the potential energy surface, and must be taken into account. In this thesis, we propose a fully quantum approach based on an almost exact description of the electronic wave function by means of Quantum Monte Carlo (QMC) methods. Our novel technique combines QMC with a Langevin-based Molecular Dynamics and the Feynman's path integral formalism. This allows one to perform fully quantum simulations of systems in gas or condensed phase, at an unprecedented level of accuracy,. We apply our approach to neutral or charged protonated water clusters to shed light on the microscopic phenomena driving the proton diffusion in such systems. We discovered that the proton hopping is optimal for temperatures close to ambient conditions, due to the subtle competition between thermal and nuclear quantum effects. This is highly suggestive of the importance of quantum nuclear effects to make PT processes - relevant for life - most efficient at room temperature.

By numerical methods, two models of anisotropic mixed quantum spin chains, consisting of spins of two different sizes, Sa = 1/2 and Sb = 1 as well as Sb = 3/2, are studied with respect to their critical properties at quantum phase transitions in a selected region of parameter space. The quantum spin chains are made up of basecells of four spins, according to the structure Sa − Sa − Sb − Sb. They are described by the XXZ Hamiltonian, that extends the quantum Heisenberg model by a variable anisotropic exchange interaction. As additional control parameter, an alternating exchange constant between nearest-neighbour spins is introduced. Insight gained by complementary application of exact diagonalization and quantum Monte Carlo simulations, as well as appropriate methods of analysis, is embedded in the broad existing knowledge on homogeneous quantum spin chains. In anisotropic homogeneous quantum spin chains, there exist phase boundaries with continuously varying critical exponents, the Gaussian critical lines, along which, in addition to standard scaling relations, further extended scaling relations hold. Reweighting methods, also applied to improved quantum Monte Carlo estimators, and finite-size scaling analysis of simulation data deliver a wealth of numerical results confirming the existence of a Gaussian critical line also in the mixed spin models considered. Extrapolation of exact data offers, apart from confirmation of simulation data, furthermore, insight into the conformal operator content of the model with Sb = 1. / Mittels numerischer Methoden werden zwei Modelle anisotroper gemischter Quantenspinketten, bestehend aus Spins zweier unterschiedlicher Größen, Sa = 1/2 und Sb = 1 sowie Sb = 3/2, hinsichtlich ihrer kritischen Eigenschaften an Quanten-Phasenübergängen in einem ausgewählten Parameterbereich untersucht. Die Quantenspinketten sind aus Basiszellen zu vier Spins, gemäß der Struktur Sa − Sa − Sb − Sb, aufgebaut. Sie werden durch den XXZ Hamiltonoperator beschrieben, der das isotrope Quanten-Heisenberg Modell um eine variable anistrope Austauschwechselwirkung erweitert. Als zusätzlicher Kontrollparameter wird eine alterniernde Kopplungskonstante zwischen unmittelbar benachbarten Spins eingeführt. Die durch komplementäre Anwendung exakter Diagonalisierung und Quanten-Monte-Carlo Simulationen, sowie entsprechender Analyseverfahren, gewonnenen Erkenntnisse werden in das umfangreiche existierende Wissen über homogene Quantenspinketten eingebettet. Im Speziellen treten in anisotropen homogenen Quantenspinketten Phasengrenzen mit kontinuierlich variierenden kritischen Exponenten auf, die Gaußschen kritischen Linien, auf denen neben den herkömmlichen auch erweiterte Skalenrelationen Gültigkeit besitzen. Umgewichtungsmethoden, speziell auch angewandt auf verbesserte Quanten-Monte-Carlo Schätzer, und Endlichkeitsskalenanalyse von Simulationsdaten liefern eine Fülle von numerischen Ergebnissen, die das Auftreten der Gaußschen kritischen Linie auch in den untersuchten gemischten Quantenspinketten bestätigen. Die Extrapolation exakter Daten bietet, neben der Bestätigung der Simulationsdaten, darüber hinaus Einblick in einen Teil des konformen Operatorinhalts des Modells mit Sb = 1.

La recherche de phases magnétiques exotiques de la matière qui fondent même à T=0 uniquement sous l'action des fluctuations quantiques a été long et ardu, à la fois théoriquement et expérimentalement. La percée est venue récemment avec la découverte de l'Herbertsmithite, un composé formant un réseau kagome parfait avec des moments magnétiques de spin-1/2. Des expériences pionnières, mêlant des mesures de NMR, µSR et de diffusion de neutrons, ont montré une absence totale de gel ou d'ordre des moments magnétiques de spin, fournissant ainsi une forte signature d'une phase paramgnétique quantique. Théoriquement, l'Herbertsmithite est extrêmement bien modélisé par le modèle de Heisenberg quantique antiferromagnétique pour des spins-1/2 sur le réseau kagome, problème qui n'a pas été résolu jusqu'à présent. Plusieurs méthodes approximatives numériques et analytiques ont donné différents états fondamentaux, allant des liquides de spins Z2 gappés et un liquide de spins exotique algébrique U(1) de Dirac aux liquides de spins chiraux et les cristaux à liaisons de valence. Dans cette thèse, le problème est traité dans le cadre d'une approche particule-esclave fermionique, à savoir le formalisme des fermions de Schwinger SU(2). Il est conclu qu'un liquide de spins sans gap algébrique de Dirac a l'énergie variationnelle la plus basse et peut en fait constituer un vrai état fondamental physique de liquide de spins. Une implémentation sophistiquée de méthodes numériques de pointes comme le Monte-Carlo variationnel, le Monte-Carlo fonctions de Green et l'application de pas Lanczos dans un schéma variationnel ont été utilisés. Il est montré que contrairement à la croyance habituelle, le liquide de spins de Dirac U(1) projeté en "2+1" dimensions est remarquablement robuste par rapport à une large classe de perturbations, incluant les liquides de spins topologiques Z2 et les cristaux à liaisons de valence. De plus, l'application de deux pas Lanczos sur la fonction d'onde du liquide de spins de Dirac U(1) montre que son énergie est compétitive avec celles proposées pour les liquides de spins topologiques Z2. Ce résultat, combiné avec les indications expérimentales qui pointent vers un liquide de spins sans gap pour l'Herbertsmithite, appuie l'affirmation que le vrai état fondamental de ce modèle est en fait un liquide de spins algébrique de Dirac.

The advancement in the eld of cold-atoms has generated a lot of interest in the condensed matter community. Cold-atom experiments can simulate clean, disor-der/impurity free systems very easily. In these systems, we have a control over various parameters like tuning the interaction between particles by the Feshbach resonance, tuning the hopping between lattice sites by laser intensity and so on. As a result, these systems can be used to mimic various theoretical models, which was hindered because of various experimental limitations. Thus, we have an ex-perimental tool in which we can start with a simple theoretical model and later tune the model experimentally and theoretically to simulate the real materials. This will be helpful in studying the physics of the real materials as we can control interactions as well as the impurities can also be taken care of. But the advance-ment in the eld of cold atoms has seen a roadblock for the fermions in optical lattices. The super uid and anti-ferromagnetic phases has not been achieved for fermions in optical lattices due to the \cooling problem" (entropy issues). In this thesis, we have addressed the issue of the \cooling problem" for fermions in optical lattice systems and studied the system with determinant quantum Monte Carlo technique. We start by giving a general idea of cold-atoms and optical lat-tice potentials, and a brief review of the experimental work going on in the cold-atomic systems. Experimental limitations like \fermionic cooling problem" have been discussed in some detail. Then we proposed a bilayer band-insulator model to circumvent the \entropy problem" and simultaneously increasing the transi-tion temperature for fermions in optical lattices. We have studied the attractive Hubbard model, which is the minimal model for fermions in optical lattices. The techniques that we have used to study the model are mean- eld theory, Gaussian uctuation theory and determinant quantum Monte Carlo numerical technique. . Chapter-1 : provides a general introduction to the ultra-cold atoms, optical lattice and Feshbach resonance. In this chapter we have discussed about cold-atom experiments in optical lattice systems. Here, we have brie y discussed the control over various parameters in the experiments. The goal of these experiments is to realize or mimic many many-body Hamiltonians in experiments, which until now was just a theoretical tool to describe various many-body physics. In the end we give a brief idea for introducing disorder in the cold-atom experiments discuss the limitations of these experiments in realizing the \interesting" super uid and anti-ferromagnetic phases of fermionic Hubbard model in optical lattices. Chapter-2 : gives a brief idea of \Determinant Quantum Monte-Carlo" (DQM C) technique that has been used to study these systems. In this chapter we will discuss the DQM C algorithm and the observables that can be calculated. We will discuss certain limitation of the DQM C algorithm like numerical instability and sign problem. We will brie y discuss how sign problem doesn't occur in the model we studied. Chapter-3 : discusses the way by which we can bypass the \cooling problem" (high entropy state) to get a fermionic super uid state in the cold atom experi-ments. In this chapter we propose a model whose idea hinges on a low-entropy band-insulator state, which can be tuned to super uid state by tuning the on-site attractive interaction by Feshbach resonance. We show through Gaussian uctua-tion theory that the critical temperature achieved is much higher in our model as compared to the single-band Hubbard model. Through detailed variational Monte Carlo calculations, we have shown that the super uid state is indeed the most stable ground state and there is no other competing order. In the end we give a proposal for its realization in the ultra-cold atom optical lattice systems. Chapter-4 : discusses the DQM C study of the model proposed in chapter- 3. Here we have studied the various single-particle properties like momentum distribution, double occupancies which can be easily measured in cold-atom ex-periments. We also studied the pair-pair and the density-density correlations in detail through DQM C algorithm and mapped out the full T U phase diagram. We show that the proposed model doesn't favor the charge density wave for the interaction strengths we are interested in. Chapter-5 : gives a brief idea of the e ect of adding an on-site random disorder in our proposed bilayer-Hubbard model. We study the e ect of random disorder on various single-particle properties which can be easily veri ed in cold-atom ex-periments. We studied the suppression of the pair-pair correlations as we increase the disorder strength in our proposed model. We nd that the critical value of the interaction doesn't change in the weak-disorder limit. We estimated the critical disorder strength needed to destroy the super uid state and argued that the tran-sition from the super uid to Bose-glass phase in presence of disorder lies in the universality class of (d + 1) XY model. In the end, we give a schematic U V phase diagram for our system. Chapter-6 : We studied the bilayer attractive Hubbard model in different lattice geometry, the bilayer honeycomb lattice, both in presence and in absence of the on-site random disorder. We discussed how the pair-pair and density-density cor-relations behave in the presence and absence of disorder. Through the finite-size scaling analysis we see the co-existence of the super fluid and the charge density wave order at half- lling. An in nitesimal disorder destroys the CDW order com-pletely while the super uid phase found to be robust against weak-disorder. We estimated the critical interaction strength, the critical temperature and the critical disorder strength through nite-size scaling, and provide a putative phase diagram for the system considered.

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-29T18:35:28Z No. of bitstreams: 2 Tese - Jose Higino Damasceno Junior - 2015.pdf: 2058291 bytes, checksum: ed4c947cd5e0f908dddc93570ac84dbb (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-11-03T14:21:33Z (GMT) No. of bitstreams: 2 Tese - Jose Higino Damasceno Junior - 2015.pdf: 2058291 bytes, checksum: ed4c947cd5e0f908dddc93570ac84dbb (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-11-03T14:21:33Z (GMT). No. of bitstreams: 2 Tese - Jose Higino Damasceno Junior - 2015.pdf: 2058291 bytes, checksum: ed4c947cd5e0f908dddc93570ac84dbb (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-09-25 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / Clusters systems are very different from molecules or their bulk materials, since they exhibit many specific properties. As example, the bond in metallic clusters of metallic atoms is intermediate between metallic and covalent bonding. In general, the structural and electronic properties of these systems are very difficult to measure experimentally, and therefore theoretical modeling is very important in characterizing them. In this thesis, we employed ab initio methods to study metallic clusters such as the aluminum hydride clusters as well as a few aromatic metal clusters. The optimized geometries of the studied clusters have been determined using DFT. The electronic structures of these systems were investigated using the QMC methods. The calculations were carried out within the Variational (VMC) and fixed-node diffusion (DMC) quantum Monte Carlo methods. The calculations are also performed in the Hartree-Fock (HF) approximation in order to analyze the impact of electron correlation. With regards the aluminum hydride clusters, the total atomic binding energy impact varies from ~20% up to about ~50%, whereas for the electron binding energy it ranges from ~1% up to ~73%. The decomposition of the electron binding energies clearly shows that both charge redistribution and electron correlation are important in determining the detachment energies, whereas electrostatic and exchange interactions are responsible for the ionization potential. For the aromatic metal clusters, the presence of a dopant plays important role in their electronic properties enhancing their binding energy, electron affinity, hardness and resonance energy. / Clusters são sistemas bastante diferentes de moléculas e sólidos, pois exibem propriedades bastante peculiares. Por exemplo, a ligação em um cluster metálico tem intensidade intermediária entre as ligações covalentes e metálicas. Em geral, as propriedades eletrônicas e estruturais desses sistemas são bastante difíceis de serem medidas experimentalmente e, portanto, uma modelagem teórica é muito importante na caracterização desses. Nesta Tese, utilizamos métodos ab initio para estudar clusters metálicos, tal como clusters de hidretos de alumínio assim como também alguns clusters metálicos aromáticos. As estruturas geométricas dos clusters estudados foram otimizadas via DFT. A estrutura eletrônica desses clusters foi investigada usando o método de Monte Carlo Quântico Variacional (MCQD) e de difusão (MCQD) com aproximação de nós fixos. Os cálculos também foram realizados a partir da aproximação de Hartree-Fock, afim de se analisar o impacto da energia de correlação eletrônica. Para os hidretos de alumínio, a energia de correlação eletrônica tem impacto na energia total de ligação variando de 20% a 50%. Da mesma maneira, a energia de ligação de um elétron ao cluster tem grande contribuição da energia de correlação eletrônica, variando de 1% a 73%. A decomposição da energia de ligação mostra claramente que a relaxação e a correlação eletrônica são importantes na determinação da afinidade eletrônica, enquanto que a interação de troca eletrostática é responsável pelo potencial de ionização. Para os clusters aromáticos, a presença do dopante desempenha um importante papel nas propriedades desses clusters, uma vez que otimiza a energia de ligação, a afinidade eletrônica, a dureza e a energia de ressonância.

This thesis analyzes charge properties of (undoped) cuprate compounds from a theoretical point of view. The central question considered here is: How does the dimensionality of the CU-O sub-structure influence its charge degrees of freedom? The model used to describe the Cu-O sub-structure is the three- (or multi-) band Hubbard model. Analytical approaches are employed (ground-state formalism for strongly correlated systems, Mori-Zwanzig projection technique) as well as numerical simulations (Projector Quantum Monte Carlo, exact diagonalization). Several results are compared to experimental data. The following materials have been chosen as candidates to represent different Cu-O sub-structures: Bi2CuO4 (isolated CuO4 plaquettes), Li2CuO2 (chains of edge-sharing plaquettes), Sr2CuO3 (chains of corner-sharing plaquettes), and Sr2CuO2Cl2 (planes of plaquettes). Several results presented in this thesis are valid for other cuprates as well. Two different aspects of charge properties are analyzed: 1) Charge properties of the ground state 2) Charge excitations. (gekürzte Fassung)

By numerical methods, two models of anisotropic mixed quantum spin chains, consisting of spins of two different sizes, Sa = 1/2 and Sb = 1 as well as Sb = 3/2, are studied with respect to their critical properties at quantum phase transitions in a selected region of parameter space. The quantum spin chains are made up of basecells of four spins, according to the structure Sa − Sa − Sb − Sb. They are described by the XXZ Hamiltonian, that extends the quantum Heisenberg model by a variable anisotropic exchange interaction. As additional control parameter, an alternating exchange constant between nearest-neighbour spins is introduced. Insight gained by complementary application of exact diagonalization and quantum Monte Carlo simulations, as well as appropriate methods of analysis, is embedded in the broad existing knowledge on homogeneous quantum spin chains. In anisotropic homogeneous quantum spin chains, there exist phase boundaries with continuously varying critical exponents, the Gaussian critical lines, along which, in addition to standard scaling relations, further extended scaling relations hold. Reweighting methods, also applied to improved quantum Monte Carlo estimators, and finite-size scaling analysis of simulation data deliver a wealth of numerical results confirming the existence of a Gaussian critical line also in the mixed spin models considered. Extrapolation of exact data offers, apart from confirmation of simulation data, furthermore, insight into the conformal operator content of the model with Sb = 1. / Mittels numerischer Methoden werden zwei Modelle anisotroper gemischter Quantenspinketten, bestehend aus Spins zweier unterschiedlicher Größen, Sa = 1/2 und Sb = 1 sowie Sb = 3/2, hinsichtlich ihrer kritischen Eigenschaften an Quanten-Phasenübergängen in einem ausgewählten Parameterbereich untersucht. Die Quantenspinketten sind aus Basiszellen zu vier Spins, gemäß der Struktur Sa − Sa − Sb − Sb, aufgebaut. Sie werden durch den XXZ Hamiltonoperator beschrieben, der das isotrope Quanten-Heisenberg Modell um eine variable anistrope Austauschwechselwirkung erweitert. Als zusätzlicher Kontrollparameter wird eine alterniernde Kopplungskonstante zwischen unmittelbar benachbarten Spins eingeführt. Die durch komplementäre Anwendung exakter Diagonalisierung und Quanten-Monte-Carlo Simulationen, sowie entsprechender Analyseverfahren, gewonnenen Erkenntnisse werden in das umfangreiche existierende Wissen über homogene Quantenspinketten eingebettet. Im Speziellen treten in anisotropen homogenen Quantenspinketten Phasengrenzen mit kontinuierlich variierenden kritischen Exponenten auf, die Gaußschen kritischen Linien, auf denen neben den herkömmlichen auch erweiterte Skalenrelationen Gültigkeit besitzen. Umgewichtungsmethoden, speziell auch angewandt auf verbesserte Quanten-Monte-Carlo Schätzer, und Endlichkeitsskalenanalyse von Simulationsdaten liefern eine Fülle von numerischen Ergebnissen, die das Auftreten der Gaußschen kritischen Linie auch in den untersuchten gemischten Quantenspinketten bestätigen. Die Extrapolation exakter Daten bietet, neben der Bestätigung der Simulationsdaten, darüber hinaus Einblick in einen Teil des konformen Operatorinhalts des Modells mit Sb = 1.