The importance and promise that topological materials hold has been recently underscored by the award of the Nobel Prize in Physics in 2016 ``for theoretical discoveries of topological phase transitions and topological phases of matter." This dissertation explores the novel qualities and useful topologically protected surface states of topological insulators and semimetals. Topological materials have protected qualities which are not removed by weak perturbations. The manifestations of these qualities in topological insulators are spin-momentum-locked surface states, and in Weyl and Dirac semimetals they are unconventional open surface states (Fermi arcs) with anomalous electrical transport properties. There is great promise in utilizing the topologically protected surface states in electronics of the future, including spintronics, quantum computers, and highly sensitive devices. Physicists and chemists are also interested in the fundamental physics and exotic fermions exhibited in topological materials and in heterostructures including them. Chapter 1 provides an introduction to the concepts and methods of topological band theory. Chapter 2 investigates the spin and spin-orbital texture and electronic structures of the surface states at side surfaces of a topological insulator, Bi2Se3, by using slab models within density functional theory. Two representative, experimentally achieved surfaces are examined, and it is shown that careful consideration of the crystal symmetry is necessary to understand the physics of the surface state Dirac cones at these surfaces. This advances the existing literature by properly taking into account surface relaxation and symmetry beyond what is contained in effective bulk model Hamiltonians. Chapter 3 examines the Fermi arcs of a topological Dirac semimetal (DSM) in the presence of asymmetric charge transfer, of the kind which would be present in heterostructures. Asymmetric charge transfer allows one to accurately identify the projections of Dirac nodes despite the existence of a band gap and to engineer the properties of the Fermi arcs, including spin texture. Chapter 4 investigates the effect of an external magnetic field applied to a DSM. The breaking of time reversal symmetry splits the Dirac nodes into topologically charged Weyl nodes which exhibit Fermi arcs as well as conventionally-closed surface states as one varies the chemical potential. / Ph. D. / The importance and promise that topological materials hold has been recently underscored by the award of the Nobel Prize in Physics in 2016 “for theoretical discoveries of topological phase transitions and topological phases of matter.” This dissertation explores the novel qualities and useful topologically protected surface states of topological insulators and semimetals. Topological materials have protected qualities which are not removed by weak perturbations to the system. The manifestations of these qualities in topological insulators are spin-momentum-locked surface states which can be used to develop spin-polarized currents in electronics. Further, these states have linear dispersion at a special momentum point, called the Dirac cone. Conventionally these surface states form closed loops in momentum space. But in two other species of topological materials, Weyl and Dirac semimetals, the surface states form open arcs (called Fermi arcs) and these cause anomalous electrical transport properties including Hall conductivity and Nernst effect. Weyl and Dirac semimetals also have special momentum points (nodes) at which the bulk conduction and valence bands touch with linear dispersion. There is great promise in utilizing the topologically protected surface states in the electronics of the future, including spintronics, quantum computers, and highly sensitive devices. Physicists and chemists are also interested in the fundamental physics and exotic fermions exhibited in topological materials and in heterostructures including them. Chapter 1 provides an introduction to the concepts and methods of topological band theory. Chapter 2 investigates the spin and spin-orbital texture and electronic structures of the surface states of a topological insulator, Bi₂Se₃, at its side surfaces (beyond the familiar cleaving surface). We use slab models within density functional theory (DFT) to investigate two representative, experimentally achieved surfaces, and it is shown that careful consideration of the threefold rotational crystal symmetry is necessary to understand the physics of the surface state Dirac cones at these surfaces. The differing atomic orbital and cationic/anionic characters of the topological states are examined. This advances the existing literature by properly taking into account how the atoms at the surface relax at the interface with the vacuum and the full symmetry beyond what is contained in effective bulk model Hamiltonians. Chapter 3 examines the Fermi arcs of a topological Dirac semimetal (DSM) in the presence of asymmetric charge transfer at only one surface, of the kind which would be present in heterostructures comprised of DSMs and topologically-trivial materials. We use a thin slab model within DFT to calculate the electronic structure of the DSM. Asymmetric charge transfer allows one to accurately identify the projections of the linearly dispersing Dirac nodes despite the existence of a bulk band gap and to engineer the properties of the surface Fermi arcs, including their spin texture. Chapter 4 investigates the effect of an external magnetic field applied to a DSM. The breaking of time reversal symmetry splits the Dirac nodes into topologically charged Weyl nodes which exhibit Fermi arcs as well as conventionally-closed surface states as one varies the chemical potential. The topological charge of the Weyl nodes is what makes them, and their Fermi arcs, robust against weak perturbations such as strain. Meticulously determining the topological index, or Chern number, of Fermi surface sheets demonstrates the bulk-boundary correspondence between the Weyl nodes and their Fermi arcs, and provides evidence for the existence of multiple-charge double Weyl nodes which, until now, have only been discussed sparingly in the literature on topological DSMs.

Since its inception, nuclear magnetic resonance (NMR) has been a valuable tool for determining chemical structure. In recent years, the field of NMR has been advanced forward by the ability to calculate theoretical parameters with increasing accuracy and efficiency. These calculations are compared to experimental data to produce high resolution structures. The progression of these applications has been made possible by improved instrumentation, data processing methods, probe and experiment design, better quality functionals and basis sets, as well as increased computational power. This research is especially relevant with the emergence of artificial intelligence, which has great potential to expedite steps of the process. Combining experimental NMR with theoretical calculations has applications in both solid state and solution NMR and has several advantages that are discussed herein. One advantage is to simplify the process of structure elucidation, illustrated in chapter three in which a single experiment yields the complete characterization of a structure, including connectivity, conformation, tautomeric form and dynamics. These parameters are provided unambiguously, simplifying the process leading from data to structure. In solid state NMR these techniques provide unusually high resolution and accuracy and provide a tool capable of both assisting traditional diffraction methods for crystallography, as well as independently solving crystal structures. This is particularly useful in cases where traditional diffraction methods fall short. Examples of such include cases in material sciences in which crystallite sizes are too small for conventional single crystal diffraction, disorder that disrupts the conversion from diffraction pattern to structure, inadequate placement of weakly diffracting hydrogen atoms, and isoelectric systems such as aluminosilicates often seen in material sciences. The application of these techniques with solid state NMR is discussed in chapter five.

Yes / The density functional theory (DFT) based a unique model has been developed to predict the toxicity of ionic liquids using structural-feature based quantum chemical reactivity descriptors. Electrophilic indices (ω), the energy of highest occupied (EHOMO) and lowest unoccupied molecular orbital, (ELUMO) and energy gap (∆ E) were selected as the best toxicity descriptors of ILs via Pearson correlation and multiple linear regression analyses. The principle components analysis (PCA) demonstrated the distribution and inter-relation of descriptors of the model. A multiple linear regression (MLR) analysis on selected descriptors derived the model equation for toxicity prediction of ionic liquids. The model predicted toxicity values and mechanism are very consistent with observed toxicity. Cationic and side chains length effect are pronounced to the toxicity of ILs. The model will provide an economic screening method to predict the toxicity of a wide range of ionic liquids and their toxicity mechanism.

La présente thèse porte sur les calculs utilisant la théorie de la fonctionnelle de la densité (DFT) pour simuler des systèmes dans lesquels les effets à longue portée sont importants. Une emphase particulière est mise sur les calculs des énergies d’excitations, tout particulièrement dans le cadre des applications photovoltaïques. Cette thèse aborde ces calculs sous deux angles. Tout d’abord, des outils DFT déjà bien établis seront utilisés pour simuler des systèmes d’intérêt expérimental. Par la suite, la théorie sous-jacente à la DFT sera explorée, ses limites seront identifiées et de nouveaux développements théoriques remédiant à ceux-ci seront proposés. Ainsi, dans la première partie de cette thèse, des calculs numériques utilisant la DFT et la théorie de la fonctionnelle de la densité dépendante du temps (TDDFT) telles qu’implémentées dans le logiciel Gaussian [1] sont faits avec des fonctionnelles courantes sur des molécules et des polymères d’intérêt expérimental. En particulier, le projet présenté dans le chapitre 2 explore l’utilisation de chaînes latérales pour optimiser les propriétés électroniques de polymères déjà couramment utilisés en photovoltaïque organique. Les résultats obtenus montrent qu’un choix judicieux de chaînes latérales permet de contrôler les propriétés électroniques de ces polymères et d’augmenter l’efficacité des cellules photovoltaïques les utilisant. Par la suite, le projet présenté dans le chapitre 3 utilise la TDDFT pour explorer les propriétés optiques de deux polymères, le poly-3-hexyl-thiophène (P3HT) et le poly-3-hexyl- sélénophène (P3HS), ainsi que leur mélange, dans le but d’appuyer les observations expérimentales indiquant la formation d’exciplexe dans ces derniers. Les calculs numériques effectués dans la première partie de cette thèse permettent de tirer plusieurs conclusions intéressantes, mais mettent également en évidence certaines limites de la DFT et de la TDDFT pour le traitement des états excités, dues au traitement approximatif de l’interaction coulombienne à longue portée. Ainsi, la deuxième partie de cette thèse revient aux fondements théoriques de la DFT. Plus précisément, dans le chapitre 4, une série de fonctionnelles modélisant plus précisément l’interaction coulombienne à longue portée grâce à une approche non-locale est élaborée. Ces fonctionnelles sont basées sur la WDA (weighted density approximation), qui est modifiée afin d’imposer plusieurs conditions exactes qui devraient être satisfaites par le trou d’échange. Ces fonctionnelles sont ensuite implémentées dans le logiciel Gaussian [1] et leurs performances sont évaluées grâce à des tests effectués sur une série de molécules et d’atomes. Les résultats obtenus indiquent que plusieurs de ces fonctionnelles donnent de meilleurs résultats que la WDA. De plus, ils permettrent de discuter de l’importance relative de satisfaire chacune des conditions exactes. / This thesis is about calculations using density functional theory (DFT) in order to simulate systems in which long range peoperties are important. Particular emphasis is put on excitation energies, especially in the context of applications in photovoltaics. These effects are adressed in two different ways. In the first place, well-established DFT tools are used to simulate systems of experimental interest. Secondly, DFT’s underlying theory will be explored, its limits will be identified and new theoretical developments will be suggested in reponse to them. For the first part of this thesis, numerical calculations using DFT and time- dependent density functional theory (TDDFT) as implemented in the Gaussian software system [1] are done with known functionals on molecules and polymers of experimental interest. In particular, the project presented in chapter 2 explores the use of lateral chains in order to optimize electronic properties of polymers which are already widely used in organic photovoltaics. The results obtained show that a judicious choice of lateral chains can allow good control of the electronic properties of these polymers and can make photovoltaic cells using these polymers more efficient. The project presented in chapter 3 uses TDDFT in order to explore the optical properties of two polymers, poly-3-hexyl-thiophene (P3HT) and poly- 3-hexyl-selenophene (P3HS) as well as a blend of these two polymers, in order to support experimental observations indicating an exciplex formation in the blend. The numerical calculations in the first part of this thesis allow us to make a few very interesting conclusions, however they also emphasize certain limitations of DFT and TDDFT when treating excited states, due to the approximate treatment of long-range Coulombic interactions. So, the second part of this thesis comes back to the theoretical foundations of DFT. To be more precise, in chapter 4, a series of functionals better modelizing long-range Coulombic interactions based on a non-local approach is elaborated. The functionals expand upon the weighted density approximation (WDA) and impose several exact conditions which should be satisfied by the exchange hole. These functionals are implemented in the Gaussian [1] software system and their performances are evaluated with tests on a series of atoms and molecules. The results obtained show that many of these functionals improve upon the WDA and they also provide some insight on the relative importance of satisfying each of the exact conditions.

Cette thèse fait partie d’un projet franco-keyan dénommé ELEPHOX (ELEctrochemical and PHOto Properties of Some Remarkable Ruthenium and Iron CompleXes). En particulier, notre focus est la continuation du travail de C. Muhavini Wawire, Damien Jouvenot, Fréd erique Loiseau, Pablo Baudin, Sébastien Liatard, Lydia Njenga, Geoffrey Kamau, et Mark E. Casida, “Density-Functional Study of Lumininescence in Polypyridine Ruthenium Complexes,” J. Photochem. and Photobiol. A 276, 8 (2014). Cet article a proposé une indice orbitalaire de temps de luminescence pour les complexesde ruthénium. Cependant cet article n’était limité qu’à quelques mnolecules. Afin d’avoir une théorie plus fiable et donc potentiellement plus utile, il faudra tester l’indice de luminescence sur beaucoup plus de molécules. Ayant établi le protocol, il était “évident” mais toujours un défi de le tester sur encore une centaine de molécules pour démonter ou infirmer l’indice proposée. Pour ce faire, j’ai examainé les 98 pages de la Table I de A. Juris, V. Balzani, F. Bargelleti, S. Campagna, P. Belser, et A.V. Zelewsky, “Ru(II) polypyridine complexes: Photophysics, photochemistry, electrochemistry, and chemiluminescence,” Chem. Rev. 84, 85 (1988) et j’ai extrait un nombre important de données susceptibles à comparaison avec les résultats des calculs de la théorie de la fonctionelle de la densité (DFT) et la DFT dépendante du temps (TD-DFT). Comme les résultats étaient suffisament encourageant, le modèle DFT était examiné de plus près avec la méthode d’une théorie de champs de ligands (LFT) à la base de la densité des états partielle (PDOS). Ainsi j’ai pu tester l’indice de luminescence proposée précédement par laméthode PDOS-LFT et j’ai trouvé des difficultés avec l’indice initialement proposée. Par contre, nous avons pu proposer une nouvelle indice de luminescence qui, à quelques exceptions près, a une corrélation linéaire avec une barrière énergétique moyenne pour l’état triplet excité dérivée à partir des données experimentales. À l’avenir nous pouvons proposer une investigation plus directe de la barrière sur la surface triplet excité pour remplacer la valeur approximative déduite de l’expérience. Puis nous voulons voir sinotre indice de luminescence s’appliquent aux cas des complexes d’iridium. / This thesis is part of the Franco-Kenyan project ELEPHOX (ELEctrochemicaland PHOto Properties of Some Remarkable Ruthenium and Iron CompleXes)project. In particular, it focused on the continuation of the work ofC. Muhavini Wawire, Damien Jouvenot, Fréd erique Loiseau, Pablo Baudin,Sébastien Liatard, Lydia Njenga, Geoffrey Kamau, and Mark E. Casida,“Density-Functional Study of Lumininescence in Polypyridine RutheniumComplexes,” J. Photochem. and Photobiol. A 276, 8 (2014). That paperproposed a luminescence index for estimating whether a ruthenium complexwill luminesce or not. However that paper only tested the theory ona few molecules. In order for the theory to have a significant impact, itmust be tested on many more molecules. Now that the protocol has beenworked out, it was a straightforward but still quite challenging matter todo another 100 or so molecules to prove or disprove the theory. In order todo so, I went through the 98 pages of Table I of A. Juris, V. Balzani, F.Bargelleti, S. Campagna, P. Belser, and A.V. Zelewsky, “Ru(II) polypyridinecomplexes: Photophysics, photochemistry, electrochemistry, and chemiluminescence,”Chem. Rev. 84, 85 (1988) and extracted data suitable for comparingagainst density-functional theory (DFT) and time-dependent (TD-)DFT.Since the results were sufficiently encouraging, the DFT model was examinedin the light of partial density of states ligand field theory (PDOS-LFT) andthe previously proposed luminescence indices were tested. In fact, the originallyproposed indices were not found to be very reliable but we were able topropose a new luminescence index based upon much more data and in analogywith frontier-molecular orbital ideas. Except for a few compounds, this index provides a luminescence index with a good linear correlation with anexperimentally-derived average excited-state activation energy barrier. Futurework should be aimed at both explicit theoretical calculations of thisbarrier for ruthenium complexes and extension of the luminescence indexidea to iridium complexes.

Ces dernières années, un nouveau type de polymère donneur d’électron pour des applications photovoltaïques a été étudié de manière intensive, les copolymères à faible bande interdite. Ils sont constitués d’un groupement riche en électron (ER) et d’un groupement pauvre (EP) permettant de contrôler les orbitales frontières et d’induire une délocalisation de l’exciton généré lors du processus de photo-excitation. Une large variété de dispositifs est basée sur ces copolymères avec des rendements d’environ 10% et, pour accroitre leur efficacité, il est nécessaire d’avoir une meilleure compréhension de ces polymères pendant le phénomène de photo-absorption. La chimie théorique apparait comme un outil permettant de prédire différentes propriétés optoélectroniques. Au cours de ce travail, nous avons utilisé la théorie de la fonctionnelle de la densité indépendante (DFT) et dépendante du temps (TD DFT) pour simuler les propriétés optiques d’oligomères de taille croissante avec différents groupements ER et EP. Les propriétés optiques des polymères correspondant ont été extrapolées à l’aide du modèle de Kuhn. Ce criblage théorique nous a permis de sélectionner des systèmes prometteurs à base de benzodithiophène, de benzothiadiazole et de benzofurazane qui ont ensuite été synthétisés par couplage de Stille. Les polymères et oligomères obtenus ont été caractérisés par spectroscopie UV-visible et de fluorescence, chromatographie d’exclusion stérique et par RMN dans le but d’observer des relations structure-propriétés et de faire des corrélations entre résultats expérimentaux et théoriques. / During the last decade, a new kind of donor polymers for photovoltaic application have been intensively studied, the low band-gap polymers. They are based on repeating units associating two different moieties, one electron-rich (ER) and one electron-poor (EP), which allow to finely tune the molecular orbitals and to induce a delocalization of the exciton generated upon the photo-excitation process. A large variety of devices are based on such low band-gap polymers, with a power conversion efficiency record around 10%, and, to increase the efficiency, it is necessary to have a better understanding of these polymers during the photo-absorption phenomenon. Computational chemistry isa powerful tool that permits to predict different opto-electronic properties. For this work, we used Density Functional Theory and Time-Dependent Density Functional Theory to compute the optical properties of increasingly large oligomers involving various ER and EP subunits. The optical properties in the polymer limit were then estimated for the different systems by using an extrapolation scheme based on the Kuhn equation. This theoretical screening allowed us to select promising candidates based on benzodithiophene, benzothiadiazole and benzofurazan for syntheses, which were performed by a Stille coupling. The obtained polymers and size-controlled oligomers were further characterized by UV visible spectroscopy, fluorescence, size exclusion chromatography and NMR, in order to extractstructure-properties relationships and correlate experimental results to theoretical data.

Le but de cette thèse est la compréhension de pourquoi certains complexes de ruthénium sont soit pasluminescents soit avec un temps de vie très courte de l’état excité. Des calculs de type théorie de lafonctionnelle de la densité (DFT) ou DFT dépendante du temps (TD-DFT) étaient effectués pour cinqcomplexes existants et aussi pour un complexe hypothétique. Selon la théorie de champs de ligand (LFT),la plus proche sont les énergies des états de type transfert de charge métal-ligand (MLCT) à un état de typemétal centré (MC), alors le plus facile est-ce à peupler l’état MC ainsi menant à une dèsexcitation nonradiative de l’état MLCT. Les calculs DFT/TD-DFT s’avéraient suffisants pour reproduire les géométrieset spectres d’absorption expérimentales. Ceci, ensemble avec la technique de densité d’états partielle,permettaient une validation de l’idée fondamentale issue du modèle LFT en confrontant les résultats denos calculs avec les temps de vie mesurés. / Density-functional theory (DFT) and time-dependent DFT (TD-DFT) were carried out for 5 rutheniumcomplexes and one hypothetical one. The goal was to understand the lack of luminescence or very shortexcited state lifetimes at room temperature in some of them. According to ligand-field theory (LFT), thecloser the energies of the metal-to-ligand charge transfer (MLCT ) and the metal-centred (MC) states,the easier it is to populate the MC state, leading to radiationless disactivation of the luminescent MLCT.DFT/TD-DFT calculations proved adequate in reproducing experimental geometries and absorption spectra.Verification of LFT explanation was done by use of partial density of states whose results agreedreasonably well with the usual hypothesis.

Neste trabalho utilizamos sistemas modelos no desenvolvimento, implementação e análise de funcionais orbitais da densidade, focando, em particular, nas correções de autointeração de Perdew-Zunger (PZSIC) e Lundin-Eriksson (LESIC). Aplicamos as correções de auto-interação ao funcional local (LDA) do modelo de Hubbard e de poços quânticos semicondutores, ambos unidimensionais, no caso estático e dependente do tempo, respectivamente. Para o modelo de Hubbard unidimensional, comparamos a LDA, LDA+PZSIC e LDA+LESIC, identificando o desempenho para energias e densidades do estado fundamental, com e sem impurezas locais, além do gap fundamental de energia. Em adição, averiguamos o desempenho diante de cargas fracionárias, estabelecendo conexões com o erro de delocalização da LDA. Mostramos a possibilidade da correta descrição das freqüências das oscilações de Friedel no modelo de Hubbard, além de investigar como a falha da LDA em reproduzir esse aspecto pode estar relacionada com os erros de auto-interação e delocalização. Investigamos ainda as diferentes possibilidades de implementação autoconsistente de qualquer funcional orbital da densidade, analisando a relação entre funcionais aproximados e suas implementações aproximadas. Nos poços quânticos, sob o enfoque dependente do tempo, analisamos a descontinuidade do potencial de troca e correlação ao variarmos o número de partículas, em dois processos distintos: a ionização eletrônica em um poço simples e dissociação de um poço duplo assimétrico. No último caso, avaliamos os efeitos da descontinuidade no número total de partículas em cada poço, revelando os mecanismos que resgatam a neutralidade elétrica durante processos de dissociação, com a correta carga final inteira. / In this work we use model systems to develop, implement and analyse orbital-dependent density functionals, focusing, specifically, on the self-interaction corrections (SICs) of Perdew and Zunger (PZSIC) and of Lundin and Eriksson (LESIC). These self-interaction corrections are applied to the local-density approximation (LDA) for the one-dimensional Hubbard model and for semiconductor quantum wells, in one-dimensional static and time-dependent situations. For the one-dimensional Hubbard model we compare LDA, LDA+PZSIC and LDA+LESIC, and investigate the performance of these approaches for ground-state energies, densities and energy gaps, with and without impurities in the system. We also consider the case of fractional charges, where a connection to the delocalization error of the LDA can be made. We show that in principle a correct description of the frequences of Friedel oscillations in the Hubbard model can be obtained from DFT, and investigate how the failure of the LDA in reproducing this is related to the selfinteraction and delocalization errors. Moreover, we investigate different procedures for the selfconsistent implementation of any orbital-dependent functional, and analyse the question of the interplay between an approximate functional and its approximate implementation. For quantum wells sytems we analyse, in a time-dependent framework, the discontinuity of the exchange-correlation potential under variation of the particle number in two different processes: the ionization of a simple quantum well and the dissociation of an asymmetric double well. In the latter case, we also consider the effect of changes in the particle number in each subwell, thus revealing the mechanism that restores electric neutrality during dissociation, with correct final charge.

Neste trabalho utilizamos sistemas modelos no desenvolvimento, implementação e análise de funcionais orbitais da densidade, focando, em particular, nas correções de autointeração de Perdew-Zunger (PZSIC) e Lundin-Eriksson (LESIC). Aplicamos as correções de auto-interação ao funcional local (LDA) do modelo de Hubbard e de poços quânticos semicondutores, ambos unidimensionais, no caso estático e dependente do tempo, respectivamente. Para o modelo de Hubbard unidimensional, comparamos a LDA, LDA+PZSIC e LDA+LESIC, identificando o desempenho para energias e densidades do estado fundamental, com e sem impurezas locais, além do gap fundamental de energia. Em adição, averiguamos o desempenho diante de cargas fracionárias, estabelecendo conexões com o erro de delocalização da LDA. Mostramos a possibilidade da correta descrição das freqüências das oscilações de Friedel no modelo de Hubbard, além de investigar como a falha da LDA em reproduzir esse aspecto pode estar relacionada com os erros de auto-interação e delocalização. Investigamos ainda as diferentes possibilidades de implementação autoconsistente de qualquer funcional orbital da densidade, analisando a relação entre funcionais aproximados e suas implementações aproximadas. Nos poços quânticos, sob o enfoque dependente do tempo, analisamos a descontinuidade do potencial de troca e correlação ao variarmos o número de partículas, em dois processos distintos: a ionização eletrônica em um poço simples e dissociação de um poço duplo assimétrico. No último caso, avaliamos os efeitos da descontinuidade no número total de partículas em cada poço, revelando os mecanismos que resgatam a neutralidade elétrica durante processos de dissociação, com a correta carga final inteira. / In this work we use model systems to develop, implement and analyse orbital-dependent density functionals, focusing, specifically, on the self-interaction corrections (SICs) of Perdew and Zunger (PZSIC) and of Lundin and Eriksson (LESIC). These self-interaction corrections are applied to the local-density approximation (LDA) for the one-dimensional Hubbard model and for semiconductor quantum wells, in one-dimensional static and time-dependent situations. For the one-dimensional Hubbard model we compare LDA, LDA+PZSIC and LDA+LESIC, and investigate the performance of these approaches for ground-state energies, densities and energy gaps, with and without impurities in the system. We also consider the case of fractional charges, where a connection to the delocalization error of the LDA can be made. We show that in principle a correct description of the frequences of Friedel oscillations in the Hubbard model can be obtained from DFT, and investigate how the failure of the LDA in reproducing this is related to the selfinteraction and delocalization errors. Moreover, we investigate different procedures for the selfconsistent implementation of any orbital-dependent functional, and analyse the question of the interplay between an approximate functional and its approximate implementation. For quantum wells sytems we analyse, in a time-dependent framework, the discontinuity of the exchange-correlation potential under variation of the particle number in two different processes: the ionization of a simple quantum well and the dissociation of an asymmetric double well. In the latter case, we also consider the effect of changes in the particle number in each subwell, thus revealing the mechanism that restores electric neutrality during dissociation, with correct final charge.

Computational methodologies were employed to study a supramolecular micellar structure and its application, nanoreactor. This task was done through rigorous scale-up procedure using both atomistic and mesoscopic simulations. Primarily, density functional theory (DFT) calculation was used to characterize the smallest unit of complex molecules in the multicomponent mixture system. The following step involved transferring the information achieved by DFT calculation to larger scale simulation, such as molecular dynamics (MD) simulation. Lastly, based on the atomistic simulation results, we performed a series of dissipative particle dynamics (DPD) simulations to study a full body of polymeric multicompartment micelle. In the course of research, we built a systematic procedure to minimize the complexity of computation and efficiently characterize macromolecular structures and its application.