Les travaux présentés dans ce manuscrit de thèse peuvent être divisés en deux parties. Dans une première partie, nous nous sommes intéressé à une extension multiconfigurationnelle de la théorie de la fonctionnelle de la densité (DFT) par l'intermédiaire d'une séparation de portée permettant un traitement hybride entre DFT et fonction d'onde multiconfigurationnelle « state-averaged ». Ainsi, nous récupérons en même temps la corrélation dynamique et la corrélation statique. De plus, cette étude est réalisée en considérant la DFT pour les ensembles afin de considérer une alternative à la méthode usuelle utilisée (DFT dépendante du temps) pour la détermination des états excités d'une molécule, évitant ainsi certains problèmes théoriques rencontrés avec cette approche. En particulier, les intersections coniques entre états excités nous intéressent particulièrement car il s'agit de cas pour lesquels une approche multiconfigurationnelle est primordiale. Dans une seconde partie, le développement de nouvelles fonctionnelles est réalisé sur le dimère de Hubbard asymétrique afin de tester de nouvelles approximations et d'étudier plus en détail les processus auto-cohérents. De plus, des couplages non-adiabatiques sont calculés en utilisant des énergies déterminées dans le cadre de la DFT pour les ensembles ayant la particularité de ne pas être dépendant du temps. / This thesis manuscript can be divided in two parts. In the first one, we are interested in a multiconfigurational extension for the density functional theory (DFT) including a range separation to deal with a hybrid theory between DFT and state-averaged wave function theory. In this case, we recover, at the same time, the dynamical correlation and the static correlation. Moreover, this study is performed considering the ensemble DFT to use an alternative to the usual method (time-dependent DFT) to describe the excited states of a molecule, avoiding some theoretical problems known with this approach. Particularly, conical intersections between excited states are interesting because a multiconfigurational approach is necessary. In the second part, new functionals development are performed and applied on the non-symmetric Hubbard dimer in order to test new approximations and to study more in detail self-consistency processes. In addition, non-adiabatic couplings are calculated using energies from ensemble DFT framework without time-dependence.

Jusqu’à son abolition en 1848, l’esclavage transatlantique a constitué un rôle fondamental dans la colonisation par la France de la Martinique. Cette étude examine la façon, dont les personnes, où les familles ont, dans le passé, été directement touché par l’esclavage perçoivent les politiques nationales relatives aux réparations. Les politiques concernant les esclaves et leurs descendants ont opéré en faveur des propriétaires d’esclaves (et leurs descendants), affirmant que l’avènement de la liberté a été une rémunération honorable et suffisante. Malgré une position politique antérieure de l’oubli, les descendants d’esclaves continuent d’agir pour la reconnaissance de l’esclavage dans l’histoire de la nation, et remettent en question la possibilité des réparations en matière de politiques publiques. Dans cette étude trois positions personnelles ont été observées : les sceptiques, les réparationistes et les indéterminés. L’étude révèle qu’une politique relative aux réparations est considérée comme acceptable si elle comprend une pleine reconnaissance et si elle est accompagnée d’une politique de compensation. Des politiques qui favorisent l’amnésie ou l’exaltation du passé sont perçues comme inacceptables. Les politiques de réparations sont envisagées comme plus acceptables dans les situations où l’intégration socioéconomique des descendants d’esclaves a été atteinte que dans les situations où elle ne l’a pas été. Comme en Martinique, le sujet des réparations gagne du terrain dans les arènes populaires, politiques et universitaires à l’échelle internationale : quels éléments sont considérés pour juger des positions politiques ? Quelles sont les opinions qui se révèlent ? / Until its abolition in 1848, transatlantic slavery constituted a fundamental role in France's colonization of Martinique. This study assesses the views regarding the possible national policies related to the slavery of people whose families have, in the past, been directly affected by slavery in Martinique. Policies regarding slaves and their descendants have operated in favor of slave owners (and their descendants), claiming that the advent of freedom was honorable and sufficient compensation. Despite instances of cultural amnesia in France, slave descendants continue to advocate for recognition of slavery in the nation’s history and they continue to question the possibility of reparations in public politics. Three qualitatively different personal positions were culled from this study’s participating slave descendants: Skeptics, Reparationists, and Undetermined. In addition to studying the factors that differentiate these groups, this study determines that a policy concerning reparations is acceptable if it includes the public recognition of historic prejudice and if it is accompanied by a policy for material compensation. Furthermore, the results indicate that policies which foster amnesia and an exaltation of a colonial past are perceived as unacceptable. In this study, reparations are considered more acceptable to slave descendants in policies where their socio-economic integration is directly addressed. As in Martinique, the subject of reparations is gaining traction in popular, political and academic arenas internationally: What factors should be examined to understand the opinions held by the descendants of slaves? What trends emerge from these ethical questions?

Des facteurs fondamentaux pour la performance de matériaux à haute permittivité basés sur des pérovskites sont étudiés par des techniques ab-initio. L’anomalie diélectrique géante à 0K des pérovskites est investiguée aux niveaux Hartree-Fock, Théorie de la Fonctionnelle de la Densité et méthodes hybrides, en termes de la stabilité thermodynamique des phases, des contributions structurales et vibrationnelles et des charges effectives de Born. Le mode mou actif en infra-rouge est responsable par l’anomalie et des méthodes hybrides sont nécessaires pour reproduire les données expérimentales. L’évolution de l’instabilité ferroélectrique dans les pérovskites ABO3 avec la substitution de l’ion A est reliée de façon systématique aux rayons ioniques ainsi qu’aux degrés d’hybridation dans les liaisons pour des tantalates, niobates et titanates. / Ab-initio techniques are used to investigate key factors influencing the dielectric performance of high permittivity materials based on perovskites. The pressure-induced giant dielectric anomaly at 0K of ABO3 perovskites is investigated at the Hartree-Fock, density-functional theory and hybrid levels. Its mechanism is analyzed in terms of thermodynamic phase stability, structural and phonon contributions and Born effective charges. It is shown that the IR-active soft phonon is responsible for the anomaly and the use of hybrid functionals is required for agreement with experimental data. The evolution of the ferroelectric instability in ABO3 perovskites with substitution of the ion in the A site is systematically investigated for tantalates, niobates and titanates and correlated with the ionic radii as well as the degree of hybridization in the bonds.

O iminente fim da \"era do Silício\" tem motivado a busca de novas tecnologias para utilização na indústria eletrônica. Dentre estas tecnologias, a eletrônica molecular explora o uso moléculas como elementos funcionais em dispositivos eletrônicos. Nesta Tese, realizamos cálculos de primeiros princípios baseados na teoria do funcional da densidade (DFT) para determinar as propriedades eletrônicas, estruturais e de transporte em sistemas com aplicação em eletrônica molecular. Para o benzeno-1,4-ditiol (BDT), considerado um sistema protótipo dentro da eletrônica molecular, correlacionamos a adsorção, em uma superfície de Au, com as propriedades de transporte. Na sequência, analisamos evolução estrutural e o efeito de átomos de Au adsorvidos na superfície de Au na transmitância do BDT entre eletrodos de Au. A importância da correção de auto-interação (SIC), nos cálculos de transporte da junção molecular (Au/BDT/Au), também foi discutida. Em seguida, determinamos as propriedades eletrônicas e estruturais da molécula y[(tpy SH)2]x, onde y representa os metais de transição Co, Fe e Ni e; x está associado aos estados de carga 0, +, 2+ e 3+. Verificamos que os metais de transição ficam em uma configuração de baixo spin e, dependendo do estado de carga do metal de transição uma distorção Jahn-Teller leva a uma redução na simetria local de D2d para C2v. Por fim, devido à possibilidade de aplicação em spintrônica, discutimos o efeito de uma impureza de Cobalto na evolução estrutural e transmitância de um nanofio de Au. / The possible end of the road for Silicon has motivated academic researchers and research laboratories to search for new technologies to be applied in the electronic industry. The molecular electronics, which studies the possibility of using molecules as active elements in a new generation of electronic devices, is among these new technologies. In this Thesis, we performed first principles calculations within the density functional theory (DFT) framework to determine the structural, electronic and transport properties of systems with strong application on molecular electronics. We analised the benzene-1,4-dithiol (BDT). For this prototypical system we coupled its adsorption on an Au(111) surface with its transport properties. After this, we investigated its structural evolution between gold leads and the effects of adsorded gold atoms on the Au(111) surface in the trasmitance. The effect of the self-interaction correction (SIC) in the transport calculations of the molecular junction (Au/BDT/Au) was discussed as well. Moreover, we determined the electronic and the structural properties of the molecule y[(tpySH)2]x, where y stands for the transition metals Co, Fe and Ni and; x is associated with the charge states 0, +, 2+ e 3+. We verified that the transition metals are more stable at the low spin configuration. Depending on the charge state a Jahn-Teller distortion leads to a local symmetry reduction: D2d to C2v. Finally, with a spintronic application in mind, we analised the effect of a Cobalt impurity on the structural evolution and transmitance of a gold nanowire.

La fonctionnalisation non covalente des nanotubes de carbone constitue une approche élégante pour moduler leurs propriétés physiques. Néanmoins, une compréhension profonde des interactions entre la matrice hôte et les substances ajoutés est nécessaire pour maîtriser les propriétés physiques des systèmes hybrides ainsi construits. Dans ce cadre, l'étude des propriétés vibrationnelles, par le biais de techniques spectroscopiques, est une étape indispensable. Cependant, la mise en jeu de plusieurs composantes en interaction au sein de ces systèmes hybrides rend difficile l'extraction de l'information pertinente de leur réponse spectrale. Ainsi, plusieurs approches doivent être considérées. Le présent travail de thèse combine une approche expérimentale et théorique, se basant sur la théorie de la fonctionnelle de la densité (DFT), pour l'étude de la réponse infrarouge d'un système modèle de nanotubes de carbone fonctionnalisés avec des diméthyl-quaterthiophènes. De plus, une étude énergétique DFT est réalisée pour un autre système modèle de nanotube de carbone fonctionnalisés avec des molécules de phthalocyanine. Cette étude est effectuée dans le but de déterminer la conformation structurale de ces molécules à l'intérieur et à l'extérieur des nanotubes. / Non covalent functionalization of carbon nanotubes is an elegant approach to modulate their physical properties. Yet, a deep understanding of the interactions between the host matrix and the added substances is necessary to master the physical properties of the constructed hybrid systems. In this context, the study of the vibrational properties, via spectroscopic techniques, is an essential step. However, the interactions between several components within these hybrid systems makes it difficult to extract the relevant information from their spectral response. Thus, several approaches need to be considered. The present work combine an experimental approach and a theoretical one, based on the density functional theory (DFT), to study the infrared response of a model system of carbon nanotubes functionalized with dimethyl-quaterthiophenes. Moreover, a DFT energetic study is realized for another model system of carbon nanotubes functionalized with phthalocyanine molecules. This study is performed to determine the structural conformation of these molecules inside and outside the nanotube

Orientador: Ronei Miotto. / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós Graduação em Nanociências e Materiais Avançados, 2010.

Orientadora: Paula Homem de Mello / Disseração (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Ciência eTecnologia/Química, 2012

Orientadora: Profa. Dra. Káthia Maria Honório / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Ciência & Tecnologia - Química, 2014. / Polimeros de impressao molecular (MIPs) sao materiais sinteticos que possuem sitios de reconhecimento molecular especificos para determinado analito de interesse (molecula molde), e tem sido empregados para a pre-concentracao e extracao em amostras complexas, considerando a maior seletividade em relacao aos sorventes convencionais empregados na extracao em fase solida. A escolha dos reagentes utilizados na sintese de um MIP deve ser criteriosa, a fim de que sejam criados sitios de ligacoes especificos. Metodos computacionais de Quimica Teorica podem ser empregados para racionalizar o planejamento de MIPs, por intermedio do estudo de parametros fisico-quimicos das moleculas envolvidas e as interacoes que ocorrem no sistema de pre-polimerizacao. Com a utilizacao de metodos de quimica quantica, foi objetivo desse trabalho o estudo previo das interacoes entre as moleculas moldes e os possiveis reagentes empregados na sintese de MIPs, como forma de predicao das melhores interacoes que promovam um MIP de desempenho ideal. O estudo teorico foi direcionado para a molecula de ¿¢9-tetrahidrocanabinol (¿¢9-THC), substancia presente na planta Cannabis sativa e que e a substancia ilicita mais produzida e consumida mundialmente, e seu principal metabolito de excrecao urinario, o 11-nor-9-carboxi-¿¢9-THC (THC-COOH). A simulacao computacional foi realizada utilizando a Teoria do Funcional da Densidade (DFT), e a metodologia envolveu a comparacao das energias de interacao (¿¢E) dos adutos de pre-polimerizacao entre a molecula molde e os reagentes de sintese. Com os resultados das simulacoes, verificou-se que as melhores interacoes ocorrem quando o monomero utilizado tem caracteristica acida, como o acido acrilico e o acido metacrilico; e que o solvente mais adequado para a sintese sao os que apresentam baixa constante dieletrica, como o cloroformio e o tolueno, por interferirem menos na formacao do complexo de interacao entre a molecula molde e o monomero na etapa de pre-polimerizacao. Detalhes das interacoes existentes entre as moleculas do meio reacional tambem foram analisadas e forneceram informacoes sobre a possivel competicao entre as moleculas no acesso aos sitios de interacao das moleculas moldes, informacao crucial para obtencao de MIPs seletivos e de grande afinidade a molecula molde desejada. A partir das predicoes do estudo computacional, os MIPs de THC-COOH foram sintetizados com os monomeros indicados, juntamente com o polimero nao impresso (NIP), em alguns dos solventes simulados (agua, acetonitrila, metanol e agua), para avaliacao da interferencia do solvente na eficiencia do MIP obtido. Foi realizada a analise dos MIPs por espectroscopia vibracional na regiao do infravermelho, e avaliada as bandas de absorcao nas regioes dos grupos C=O e O-H, para analise da formacao de interacoes por ligacao de hidrogenio. Concluiu-se, portanto, que sem substituir os ensaios experimentais, a abordagem computacional pode ser utilizada como uma ferramenta preliminar e complementar a selecao experimental. / Molecularly imprinted polymers (MIPs) are synthetic materials with specific sites of molecular recognition for a given analyte of interest (template molecule), and have been used for the extraction and pre-concentration in complex samples, considering the higher selectivity presented in relation to the sorbent employed in conventional solid phase extraction. The choice of the reagents used in the synthesis of a MIP must be chosen carefully, so that site-specific linkages are created. Computational methods in Theoretical Chemistry can be used to rationalize the planning of MIPs through the study of physico-chemical parameters of the molecules involved and the interactions that occur in the pre-polymerization system. Using quantum chemical methods, the aim of this study was a preliminary investigation of the interactions between the template molecules and the possible reagents used in the synthesis of MIPs, as a way to predict the best interactions that promote MIPs with optimal performance. The theoretical study was directed to the molecule of Ä9-tetrahydrocannabinol (Ä9-THC), present in the plant Cannabis sativa, and that is the illicit substance most widely produced and consumed globally, as well as its major metabolite urinary excretion, 11 -nor-9-carboxy-Ä9-THC (THC-COOH). The computational simulation was performed using the Density Functional Theory (DFT), and the methodology involved the comparison of the interaction energies (ÄE) of adducts in pre-polymerization between the template molecule and reagents for synthesis. From the results of the simulations, it was found that the best interactions occur when the monomer has acid characteristic, such as acrylic acid and methacrylic acid; and that the most suitable solvent for synthesis are those with low dielectric constant such as toluene and chloroform, by interfering less in the formation of complex interaction between the template molecule and monomer in the pre-polymerization step. Details of the existing interactions between the molecules of the reactional medium were analyzed and provided information about the possible competition between the molecules in the access to the interaction sites of the template molecules, which is a crucial information for obtaining selective MIPs and with high affinity to the template molecule desired. From the computational predictions obtainde in this study, the MIPs of THC-COOH was synthesized with the indicated monomers, and also a non-imprinted polymer (NIP), considering some of simulated solvents (water, acetonitrile, methanol and water) for evaluation of the interference of solvent in the efficiency of the MIP obtained. Analyses on the formed MIPs were performed by spectroscopy in the infrared region, and the absorption bands in the regions of the groups C=O and OH were evaluated with the aim of analysing the formation of hydrogen bond interactions. Therefore, it is possible to conclude that, without replacing the experimental trials, the computational approach can be used as a preliminary and complementary tool to experimental selection.

Nesta dissertação, estudamos cadeias unidimensionais antiferromagnéticas de spins 1/2 modeladas pelo Hamiltoniano de Heisenberg na presença de inomogeneidades causadas principalmente pela introdução de ligações substitucionais (defeitos nas ligações) e por efeitos de borda. Interessados então em determinar a energia do estado fundamental de sistemas com quaisquer distribuições das ligações, utilizamos o formalismo da Teoria do Funcional da Densidade (DFT) desenvolvido para o modelo de Heisenberg. O formalismo da DFT permite a estimativa da energia do estado fundamental de sistemas não-homogêneos conhecendo-se o sistema homogêneo. Construímos funcionais na aproximação da ligação local (LBA), proposta recentemente em analogia à já conhecida LSA (aproximação local para o spin). A obtenção dos funcionais se baseou no estudo do modelo de uma cadeia de spins em que as ligações são alternadas, isto é, a interação de troca se alterna em valor de sítio para sítio. Isso originou um funcional não-local na interação de troca da cadeia. Apesar disso, continuamos utilizando a nomenclatura LBA. Todos os resultados fornecidos pelos funcionais são comparados a dados provenientes de diagonalização numérica exata. / In this dissertation, we use the Heisenberg model to describe inhomogeneous antiferromagnetic spin 1/2 chains. The translational invariance is broken mainly due to the non-uniform distribution of bond interactions (defects) and the presence of boundaries. Interested in obtaining the ground-state energy of systems with any distribution of exchange couplings (Jij), we use the density-functional theory (DFT) formalism, developed for the Heisenberg model. The DFT formalism allows an estimate of the ground-state energy of inhomogeneous systems based on the homogeneous systems. We build functionals for the ground-state energy using a local bond approximation (LBA), recently proposed in analogy to the already known LSA (local spin approximation). To obtain the functionals we studied a model that describes an alternating chain, in which the exchange coupling alternates from site-to-site. This resulted in non-local functionals on the spin-spin exchange interaction. Nevertheless, we still call them LBA functionals. All the results from the functionals are compared with exact numerical data.

O efeito Hall quântico surge em gases de elétrons bidimensionais (2DEG) na presença de altos campos magnéticos B. O campo magnético quantiza o movimento planar dos elétrons em órbitas ciclotrônicas caracterizadas pelos níveis de Landau. Neste regime a resistividade transversal (ou Hall) ρxy em função de B exibe platôs em submúltiplos inteiros de e2/h, i.e., ρxy = ν-1 e2/h, sendo ν o fator de preenchimento dos níveis de Landau. Por sua vez, a resistividade longitudinal ρxx apresenta picos nas transições entre platôs de ρxy. Em primeira instância, ρxx é uma medida indireta da densidade de estados no nível de Fermi g(εF), e os picos dos mesmos indicam cruzamentos do nível de Fermi εF com niveis de Landau. Assim, o diagrama de densidade de elétrons n2D e B dos picos de ρxx ~ g(εF) fornece um mapa topológico da estrutura eletrônica do sistema. Em sistemas de duas subbandas, ρxx(n2D, B) exibe estruturas em forma de anel devido a cruzamentos de níveis de Landau de subbandas distintas [experimentos do grupo do Prof. Jiang (UCLA)]. Estes cruzamentos podem ainda levar a instabilidades ferromagnéticas. Investigamos estas instabilidades usando a teoria do funcional da densidade (DFT) para o cálculo da estrutura eletrônica, e o modelo de Ando (formalismo de Kubo) para o cálculo de ρxx e ρxy. Para temperaturas mais altas (340 mK) obtemos as estruturas em forma de anel em ρxx. Para temperaturas mais baixas (70 mK), observamos uma quebra dos anéis devido a transições de fase ferromagnéticas. Variando-se o ângulo θ de B com relação ao 2DEG observa-se o encolhimento do anel. Nossos resultados mostram que o ângulo de colapso total do anel depende de uma competição entre o termo de troca da interação de Coulomb (princípio de Pauli) e cruzamentos evitados devido ao ângulo θ finito. As transições de fase exibem ainda o fenômeno de histerese. Na região de instabilidade ferromagnética obtemos diferentes soluções variando B de forma crescente ou decrescente. Estas soluções possuem energias total diferentes, de forma que representam estados fundamental e excitado de muitos corpos. Esta observação, juntamente com resultados anteriores do grupo [Freire & Egues (2007)], representam as primeiras realizações teóricas da previsão da possibilidade de estados excitados como mínimos locais do funcional de energia do estado fundamental [Perdew & Levy (1985)]. O modelo aqui proposto fornece excelente acordo com os experimentos considerados. Adicionalmente, a observação sistemática e experimentalmente verificada dos estados excitados valida as previsões de Perdew & Levy. Aplicamos ainda estas mesmas ideias no cálculo da estrutura eletrônica e condutância de fios quânticos na presença de campos magnéticos, mostrando que cruzamentos de modos transversais também exibem instabilidades ferromagnéticas observadas em experimentos recentes [Dissertação de Mestrado de Filipe Sammarco, IFSC/USP], fortalecendo a validade do modelo apresentado nesta tese. / The quantum Hall effect arises in two dimensional electron gases (2DEG) under high magnetic fields B. The magnetic field quantizes the planar motion of the electrons into cyclotron orbits given by the Landau levels. In this regime the transversal (Hall) resistivity ρxy shows plateaus as a function of B at integer sub-multiples of e2/h, i.e., ρxy = ν-1 e2/h, where n is the filling factor of the Landau levels. The longitudinal resistivity ρxx shows peaks at the transition between the plateaus of ρxy. In principle, ρxx is an indirect measure of the density of states at the Fermi level g(εF), so that the peaks indicate when the Fermi level εF crosses a Landau level. Therefore, a density-B-field diagram n2D-B of the ρxx ~ g(εF) peaks shows a topological map of the electronic structure of the system. In two-subband systems, ρxx( n2D, B) shows ringlike structures due to crossings of spin-split Landau levels from distinct subbands [experiments from the group of Prof. Jiang (UCLA)] that could lead to ferromagnetic instabilities. We study these instabilities using the density functional theory (DFT) to calculate the electronic structure, and Ando\'s model (Kubo formalism) for ρxx and ρxy. At higher temperatures (340 mK) we also obtain the ringlike structures in ρxx. At lower temperatures (70 mK) we see broken rings due to quantum Hall ferromagnetic phase transitions. Tilting B by theta with respect to the 2DEG normal we find that the ring structure shrinks. Our results show that the angle of full collapse depends on a competition between the exchange term from the Coulomb interaction (Pauli principle) and the anticrossing of Landau levels due to the finite angle theta. Additionally, at the instabilities we observe hysteresis. Sweeping the B field up or down near these regions we obtain two different solutions with distinct total energies, corresponding to the ground state and an excited state of the many-body system. This result, together with previous results of our group [Freire & Egues (2007)], are the first realizations of the theoretical prediction of the possibility of excited states as local minima of the ground state energy functional [Perdew & Levy (1985)]. The model proposed here shows an excellent agreement with the experiments. Additionally, the systematic and experimentally verified observation of excited states corroborates the predictions of Perdew & Levy. Similar ideas as presented here when applied to the electronic structure and conductance of quantum wires with an in-plane magnetic field show ferromagnetic instabilities at crossings of the wire transverse modes [Master Thesis of Filipe Sammarco, IFSC/USP], also with excellent experimental agreement. This strengthen the range of validity of the model proposed in this Thesis.