Currently, there are two main methodologies for the calculation of the electronic structure and properties of crystalline solids. Known as the Hartree-Fock Method (HF) and the Density Functional Theory (DFT) methods, they are based on two different theories for the numerical solution of the many electron Schrödinger equation. Unfortunately, in highly correlated electron systems like transition metal complexes, both the HF and DFT methods have severe shortcomings. In some cases they fail to provide the correct description of the electronic structure. <p>In general, the HF method overestimates the energy band gap due to the neglect of electron correlation effects and the incorrect description of electron interactions in the unoccupied orbitals. In contrast, even though electron correlation effects are implicitly included in the density functional, DFT often underestimates the band gap due to the improper treatment of the electron self-interaction. <p> To amend these problems, two approaches have been proposed. The deficiency in the HF scheme can be corrected using a hybrid method which adds exchange correlation energy borrowed from DFT to help reduce the band gap energy and bring the predictions in better agreement with experiment. To improve DFT, the LDA+U approach, which uses a model Hubbard-like Hamiltonian including an on-site repulsion parameter U, can be employed. This method is a convenient semi-quantitative way to efficiently calculate the band gap of insulators and semiconductors.<p> In this thesis, the electronic structure of YTiO₃ under pressure is investigated using the aforementioned approaches. The performance and reliability of these methods will be examined, compared and discussed.

Currently, there are two main methodologies for the calculation of the electronic structure and properties of crystalline solids. Known as the Hartree-Fock Method (HF) and the Density Functional Theory (DFT) methods, they are based on two different theories for the numerical solution of the many electron Schrödinger equation. Unfortunately, in highly correlated electron systems like transition metal complexes, both the HF and DFT methods have severe shortcomings. In some cases they fail to provide the correct description of the electronic structure. <p>In general, the HF method overestimates the energy band gap due to the neglect of electron correlation effects and the incorrect description of electron interactions in the unoccupied orbitals. In contrast, even though electron correlation effects are implicitly included in the density functional, DFT often underestimates the band gap due to the improper treatment of the electron self-interaction. <p> To amend these problems, two approaches have been proposed. The deficiency in the HF scheme can be corrected using a hybrid method which adds exchange correlation energy borrowed from DFT to help reduce the band gap energy and bring the predictions in better agreement with experiment. To improve DFT, the LDA+U approach, which uses a model Hubbard-like Hamiltonian including an on-site repulsion parameter U, can be employed. This method is a convenient semi-quantitative way to efficiently calculate the band gap of insulators and semiconductors.<p> In this thesis, the electronic structure of YTiO₃ under pressure is investigated using the aforementioned approaches. The performance and reliability of these methods will be examined, compared and discussed.

La présente thèse traite de la description de systèmes complexes, notamment des polymères et des cuprates, par la théorie de la fonctionnelle de la densité. En premier lieu, la théorie de la fonctionnelle de la densité ainsi que différentes fonctionnelles utilisées pour simuler les matériaux à l’étude sont présentées. Plus spécifiquement, les fonctionnelles LDA et GGA sont décrites et leurs limites sont exposées. De plus, le modèle de Hubbard ainsi que la fonctionnelle LDA+U qui en découle sont abordés dans ce chapitre afin de permettre la simulation des propriétés de matériaux à forte corrélation électronique. Par la suite, les résultats obtenus sur les polymères sont résumés par deux articles. Le premier traite de la variation de la bande interdite entre les polymères pontés et leurs homologues non pontés. Le second se penche sur l’étude de polymères à faible largeur de bande interdite. Dans ce dernier, il sera démontré qu’une fonctionnelle hybride, contenant de l’échange exact, est nécessaire afin de décrire les propriétés électroniques des systèmes à l’étude. Finalement, le dernier chapitre est consacré à l’étude des cuprates supraconducteurs. La LDA+U pouvant rendre compte de la forte localisation dans les orbitales 3d des atomes de cuivre, une étude de l’impact de cette fonctionnelle sur les propriétés électroniques est effectuée. Un dernier article investiguant différents ordres magnétiques dans le La2CuO4 dopé termine le dernier chapitre. On trouve aussi, en annexe, un complément d’information pour le second article et une description de la théorie de la supraconductivité de Bardeen, Cooper et Schrieffer. / Description of complex systems by Density functional theory is treated in this thesis. First, the Density functional theory and a few functionals used to simulate cristals are presented. Specifically, the LDA and GGA functionnals are described and their limits are exposed. Furthermore, the Hubbard model as well as the LDA+U functionnal are addressed in this chapter. These methods enable the study of highly correlated materials. Then, results obtained on polymers are summarized in two articles. The first one treats the band gap variation of ladder-type polymers compared to non ladder type ones. The second article considers small band gap polymers. In this case, it will be shown that an hybrid functional, which contains exact exchange, is required to describe the electronic properties of the polymers under study. Finally, the last chapter address the study of cuprates superconductors. The LDA+U can account for the localization of electrons in copper orbitals. Consequently, a study of the impact of this functionnal on electronic properties of cuprates is conducted. The chapter is ended by an article treating magnetic orders in doped La2CuO4. Supplementary materials of the second article and a description of the theory of superconductivity of Bardeen, Cooper and Schrieffer are put in annex.

La présente thèse traite de la description de systèmes complexes, notamment des polymères et des cuprates, par la théorie de la fonctionnelle de la densité. En premier lieu, la théorie de la fonctionnelle de la densité ainsi que différentes fonctionnelles utilisées pour simuler les matériaux à l’étude sont présentées. Plus spécifiquement, les fonctionnelles LDA et GGA sont décrites et leurs limites sont exposées. De plus, le modèle de Hubbard ainsi que la fonctionnelle LDA+U qui en découle sont abordés dans ce chapitre afin de permettre la simulation des propriétés de matériaux à forte corrélation électronique. Par la suite, les résultats obtenus sur les polymères sont résumés par deux articles. Le premier traite de la variation de la bande interdite entre les polymères pontés et leurs homologues non pontés. Le second se penche sur l’étude de polymères à faible largeur de bande interdite. Dans ce dernier, il sera démontré qu’une fonctionnelle hybride, contenant de l’échange exact, est nécessaire afin de décrire les propriétés électroniques des systèmes à l’étude. Finalement, le dernier chapitre est consacré à l’étude des cuprates supraconducteurs. La LDA+U pouvant rendre compte de la forte localisation dans les orbitales 3d des atomes de cuivre, une étude de l’impact de cette fonctionnelle sur les propriétés électroniques est effectuée. Un dernier article investiguant différents ordres magnétiques dans le La2CuO4 dopé termine le dernier chapitre. On trouve aussi, en annexe, un complément d’information pour le second article et une description de la théorie de la supraconductivité de Bardeen, Cooper et Schrieffer. / Description of complex systems by Density functional theory is treated in this thesis. First, the Density functional theory and a few functionals used to simulate cristals are presented. Specifically, the LDA and GGA functionnals are described and their limits are exposed. Furthermore, the Hubbard model as well as the LDA+U functionnal are addressed in this chapter. These methods enable the study of highly correlated materials. Then, results obtained on polymers are summarized in two articles. The first one treats the band gap variation of ladder-type polymers compared to non ladder type ones. The second article considers small band gap polymers. In this case, it will be shown that an hybrid functional, which contains exact exchange, is required to describe the electronic properties of the polymers under study. Finally, the last chapter address the study of cuprates superconductors. The LDA+U can account for the localization of electrons in copper orbitals. Consequently, a study of the impact of this functionnal on electronic properties of cuprates is conducted. The chapter is ended by an article treating magnetic orders in doped La2CuO4. Supplementary materials of the second article and a description of the theory of superconductivity of Bardeen, Cooper and Schrieffer are put in annex.

<p>The solid oxide fuel cell (SOFC) technology has been under research since thelate 1950s, and most of the research has been on designs utilizing yttria stabilized zirconia (YSZ) as the electrolyte of choice. However, the SOFC technology has the major drawback of requiring high operation temperatures (up to 1000 degrees Celcius), so research of alternative materials have come into interest that would possibly require a lower working temperature without any significant loss of conductivity.One such material of interest for the electrolyte is compounds of ceriumdioxide (ceria). Ceria is well known for its ability to release oxygen by formingoxygen vacancies under oxygen-poor conditions, which increases its oxygen ionconductivity, and works at a lower temperature than the YSZ compounds whenproperly doped. Conversely, ceria is also able to absorb oxygen under oxygen-rich conditions, and those two abilities make it a very good material to use in catalytic converters for reduction of carbon monoxide and nitrogen oxide emission. The ability for the oxygen ions to easily relocate inbetween the different lattice sites is likely the key property of oxygen ion transportation in ceria. Also, in oxygen-rich conditions, the absorbed oxygen atom is assumed to join the structure at either the roomy octrahedral sites, or the vacant tetrahedral sites. Following that, the oxygen atom may relocate to other vacant locations, given it can overcome a possible potential barrier.</p><p>This thesis studies how those interstitial oxygen vacancies (defects) affect theenergy profile of ceria-based supercells by first principles calculations. The system is modeled within the density functional theory (DFT) with aid of (extended) local density approximation (LDA+U) using the software VASP. Furthermore, it is studied how those vacancies affect neighbouring oxygen atoms, and wether or not it is energetically benificial for the neighbouring atoms to readjust their positions closer or further away from the vacancy. The purpose of this thesis is to analyze wether or not it is theoretically possible that interstitial oxygen vacancies may cause neighbouring oxygen atoms to naturally relocate to the octahedral site in ceria, and how this affects the overall energy profile of the material.</p>

The solid oxide fuel cell (SOFC) technology has been under research since thelate 1950s, and most of the research has been on designs utilizing yttria stabilized zirconia (YSZ) as the electrolyte of choice. However, the SOFC technology has the major drawback of requiring high operation temperatures (up to 1000 degrees Celcius), so research of alternative materials have come into interest that would possibly require a lower working temperature without any significant loss of conductivity.One such material of interest for the electrolyte is compounds of ceriumdioxide (ceria). Ceria is well known for its ability to release oxygen by formingoxygen vacancies under oxygen-poor conditions, which increases its oxygen ionconductivity, and works at a lower temperature than the YSZ compounds whenproperly doped. Conversely, ceria is also able to absorb oxygen under oxygen-rich conditions, and those two abilities make it a very good material to use in catalytic converters for reduction of carbon monoxide and nitrogen oxide emission. The ability for the oxygen ions to easily relocate inbetween the different lattice sites is likely the key property of oxygen ion transportation in ceria. Also, in oxygen-rich conditions, the absorbed oxygen atom is assumed to join the structure at either the roomy octrahedral sites, or the vacant tetrahedral sites. Following that, the oxygen atom may relocate to other vacant locations, given it can overcome a possible potential barrier. This thesis studies how those interstitial oxygen vacancies (defects) affect theenergy profile of ceria-based supercells by first principles calculations. The system is modeled within the density functional theory (DFT) with aid of (extended) local density approximation (LDA+U) using the software VASP. Furthermore, it is studied how those vacancies affect neighbouring oxygen atoms, and wether or not it is energetically benificial for the neighbouring atoms to readjust their positions closer or further away from the vacancy. The purpose of this thesis is to analyze wether or not it is theoretically possible that interstitial oxygen vacancies may cause neighbouring oxygen atoms to naturally relocate to the octahedral site in ceria, and how this affects the overall energy profile of the material.