Organic π-conjugated solids are promising candidates for new optoelectronic materials. The large body of evidence points at their advantageous properties such as high charge-carrier mobility, large nonlinear polarizability, mechanical flexibility, simple and low cost fabrication and superior luminescence. They can be used as nonlinear optical (NLO) materials with large two-photon absorption (2PA) and as electronic components capable of generating nonlinear neutral (excitonic) and charged (polaronic) excitations. In this work, we investigate the appropriate theoretical methods used for the (a) prediction of 2PA properties for rational design of organic materials with improved NLO properties, and (b) understanding of the essential electronic excitations controlling the energy-transfer and charge-transport properties in organic optoelectronics. Accurate prediction of these electro-optical properties is helpful for structureactivity relationships useful for technological innovations. In Chapter 1 we emphasize on the potential use of the organic materials for these two applications. The 2PA process is advantageous over one-photon absorption for deep-tissue fluorescence microscopy, photodynamic therapy, microfabrication and optical data storage owing to the three-dimensional spatial selectivity and improved penetration depth in the absorbing or scattering media. The design of the NLO materials with large 2PA cross-sections may reduce the optical damage due to the use of the high intensity laser beams for excitation. The organic molecules also possess self-localized excited states which can decay radiatively or nonradiatively to form excitonic states. This suggests the use of these materials in the electroluminescent devices such as light-emitting diodes and photovoltaic cells through the processes of exciton formation or dissociation, respectively. It is therefore necessary to understand ultrafast relaxation processes required in understanding the interplay between the iv efficient radiative transfer between the excited states and exciton dissociation into polarons for improving the efficiency of these devices. In Chapter 2, we provide the detailed description of the various theoretical methods applied for the prediction as well as the interpretation of the optical properties of a special class of substituted PPV [poly (p-phenylene vinylene)] oligomers. In Chapter 3, we report the accuracy of different second and third order time dependent density functional theory (TD-DFT) formalisms in prediction of the 2PA spectra compared to the experimental measurements for donor-acceptor PPV derivatives. We recommend a posteriori Tamm-Dancoff approximation method for both qualitative and quantitative analysis of 2PA properties. Whereas, Agren's quadratic response methods lack the double excitations and are not suitable for the qualitative analysis of the state-specific contributions distorting the overall quality of the 2PA predictions. We trace the reasons to the artifactual excited states above the ionization threshold. We also study the effect of the basis set, geometrical constraints and the orbital exchange fraction on the 2PA excitation energies and cross-sections. Higher exchange (BMK and M05-2X) and range-separated (CAM-B3LYP) hybrid functionals are found to yield inaccurate predictions both quantitatively and qualitatively. The failure of the exchangecorrelation (XC) functionals with correct asymptotic is traced to the inaccurate transition dipoles between the valence states, where functionals with low HF exchange succeed. In Chapter 4, we test the performance of different semiempirical wavefunction theory methods for the prediction of 2PA properties compared to the DFT results for the same set of molecules. The spectroscopic parameterized (ZINDO/S) method is relatively better than the general purpose parameterized (PM6) method but the accuracy is trailing behind the DFT methods. The poor performances of PM6 and ZINDO/S methods are attributed to the incorrect description of excited-to-excited state transition and 2PA energies, respectively. The different v semiempirical parameterizations can at best be used for quantitative analysis of the 2PA properties. The ZINDO/S method combined with different orders of multi-reference configuration interactions provide an improved description of 2PA properties. However, the results are observed to be highly dependent on the specific choice for the active space, order of excitation and reference configurations. In Chapter 5, we present a linear response TD-DFT study to benchmark the ability of existing functional models to describe the extent of self-trapped neutral and charged excitations in PPV and its derivative MEH-PPV considered in their trans-isomeric forms. The electronic excitations in question include the lowest singlet (S1) and triplet (T1 † ) excitons, positive (P+ ) and negative (P- ) polarons and the lowest triplet (T1) states. Use of the long-range-corrected DFT functional, such as LC-wPBE, is found to be crucial in order to predict the physically correct spatial localization of all the electronic excitations in agreement with experiment. The inclusion of polarizable dielectric environment play an important role for the charged states. The particlehole symmetry is preserved for both the polymers in trans geometries. These studies indicate two distinct origins leading to self-localization of electronic excitations. Firstly, distortion of molecular geometry may create a spatially localized potential energy well where the state wavefunction self-traps. Secondly, even in the absence of geometric and vibrational dynamics, the excitation may become spatially confined due to energy stabilization caused by polarization effects from surrounding dielectric medium. In Chapter 6, we aim to separate these two fundamental sources of spatial localization. We observe the electronic localization of P + and Pis determined by the polarization effects of the surrounding media and the character of the DFT functional. In contrast, the self-trapping of the electronic wavefunctions of S1 and T1(T1 † ) mostly follows their lattice distortions. Geometry vi relaxation plays an important role in the localization of the S1 and T1 † excitons owing to the nonvariational construction of the excited state wavefunction. While, mean-field calculated P + , Pand T1 states are always spatially localized even in ground state S0 geometry. Polaron P+ and Pformation is signified by the presence of the localized states for the hole or the electron deep inside the HOMO-LUMO gap of the oligomer as a result of the orbital stabilization at the LCwPBE level. The broadening of the HOMO-LUMO band gap for the T1 exciton compared to the charged states is associated with the inverted bond length alternation observed at this level. The molecular orbital energetics are investigated to identify the relationships between state localization and the corresponding orbital structure. In Chapter 7, we investigate the effect of various conformational defects of trans and cis nature on the energetics and localization of the charged P + and Pexcitations in PPV and MEHPPV. We observe that the extent of self-trapping for P+ and Ppolarons is highly sensitive on molecular and structural conformations, and distribution of atomic charges within the polymers. The particle-hole symmetry is broken with the introduction of trans defects and inclusion of the polarizable environment in consistent with experiment. The differences in the behavior of PPV and MEH-PPV is rationalized based on their orbital energetics and atomic charge distributions. We show these isomeric defects influence the behavior and drift mobilities of the charge carriers in substituted PPVs.

Time Dependent Density Functional Theory offers a good accuracy/computational cost ratio among different methods used to predict the electronic structure for molecules of practical interest. The Coupled Electronic Oscillator (CEO) formalism was recently shown to accurately predict Nonlinear Optical (NLO) properties of organic chromophores when combined with Time Dependent Density Functional Theory. Unfortunately, CEO does not lend itself easily to interpretation of the structure activity relationships of chromophores. On the other hand, the Sum Over States formalism in combination with semiempirical wavefunction methods has been used in the past for the design of simplified essential states models. These models can be applied to optimization of NLO properties of interest for applications. Unfortunately, TD-DFT can not be combined directly with SOS because state-to-state transition dipoles are not defined in the linear response TD approach. In this work, a second order CEO approach to TD-DFT is simplified so that properties of double excited states and state-to-state transition dipoles may be expressed through the combination of linear response properties. This approach is termed the a posteriori Tamm-Dancoff approximation (ATDA), and validated against high-level wavefunction theory methods. Sum over States (SOS) and related Two-Photon Transition Matrix formalism are then used to predict Two-Photon Absorption (2PA) profiles and anisotropy, as well as Second Harmonic Generation (SHG) properties. Numerical results for several conjugated molecules are in excellent agreement with CEO and finite field calculations, and reproduce experimental measurements well.

High harmonic generation (HHG) is an extreme non-linear phenomenon where strong laser fields interact with a medium to produce coherent and high-frequency harmonics of the incident light. It has emerged as a rapidly growing research area in bulk materials since its first observation in ZnO crystals in 2011. Over the past decade, pioneering studies have already been made in understanding the details of the microscopic mechanism behind this phenomenon, like the role of intra- and inter-band transitions, the contribution of the modulus and the phase of the dipole moment to even and odd harmonic peaks, the role of the oscillating dipoles, effects of broken symmetry, etc. However, the role of electron-electron correlations in the HHG from strongly correlated materials is much less understood. In these materials the interactions between electrons play a significant role, leading to complex and intriguing physical behaviors. In this dissertation, on the example of ZnO, perovskites BaTiO3 and BiFeO3, and transition-metal oxide VO2 I will study the role of electron-electron interaction effects in the HH spectra by using the time-dependent density-functional theory (TDDFT) approach with the exchange-correlation kernel obtained with dynamical mean- field theory (DMFT). In DMFT, one takes into account time-resolved on-site electron-electron interactions (neglected in most of other approaches) that are crucial for a larger part of strongly correlated materials. As I demonstrate, correlation effects significantly modify the HH spectrum, e.g., through the ultrafast modification of the spectrum of the system, as it was found for ZnO. As the next step, I explored the effects of electron-electron correlations in the HH spectrum of BaTiO3 perturbed by intense, few-cycle mid-infrared laser excitations. The correlation effects in this system lead to the emergence of "super-harmonics" - periodic enhancements and suppressions of specific harmonic orders that depend on the correlation strength. I extended my analysis to the case of BiFeO3, where in addition to correlation effects the effects of memory in HHG were analyzed. I have found that both correlation effects and memory lead to an extension of the harmonic cutoff. In my final part, I explored the effect of electron correlations on the HH spectrum of VO2 and compared my findings with the experiment. The obtained results may shed light on the often important role of electron correlations in the HH spectra of solids, providing valuable insights into ultrafast dynamics in complex materials, and contributing to advancements in nonlinear optics and strong-field physics, with the potential for novel photonic devices and imaging techniques in the attosecond and femtosecond regimes.

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.

The non-adiabatic quantum molecular dynamics (NA-QMD) method couples self-consistently classical nuclear motion with time-dependent density functional theory (TDDFT) in basis expansion for the electron dynamics. It has become a versatile approach to study the dynamics of atoms, molecules and clusters in a wide range of scenarios. This work presents applications of the NA-QMD method to important benchmark systems and its systematic extension to include quantum effects in the nuclear motion. Regarding the first objective, a complete study of the strong-field ionization and dissociation dynamics of nature’s simplest molecule H2+ is performed. By including all electronic and nuclear degrees of freedom and all reaction channels, molecular rotation is shown to play an important role in the ionization process. In addition, strong orientation effects in the energy deposition process of the Buckminster fullerene C60 in short intense laser pulses are surprisingly found in full dimensional calculations. Their consequences on the subsequent nuclear relaxation dynamics shed new light on available experimental data and future experiments are proposed to confirm the detailed predictions. Regarding the second objective, the NA-QMD formalism is basically extended to take electron-nuclear correlations into account. This extension is achieved by means of a trajectory surface hopping scheme in the adiabatic Kohn-Sham framework. First studied examples from collision physics and photochemistry illustrate the relevance and importance of quantum effects in the nuclear dynamics.

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.

No description available.