Cette thèse traite du développement et de l’implémentation de nouvelles méthodes visant à décrire la corrélation électronique forte dans les molécules et les solides. Après avoir introduit l’état de l’art des méthodes utilisées en chimie quantique et en physique de la matière condensée, une nouvelle méthode hybride combinant théorie de la fonction d’onde et théorie de la fonctionnelle de la densité (DFT) est présentée et s’intitule “site-occupation embedding theory” (SOET). Celle-ci est appliquée au modèle de Hubbard à une dimension. Ensuite, le problème du gap fondamental est revisité en DFT pour les ensembles, où la dérivée discontinue est réécrite comme une fonctionnelle de la densité de l'état fondamental. Enfin, une extension à la chimie quantique est proposée, basée sur une fonction d’onde de séniorité zéro complémentée par une fonctionnelle de la matrice densité, et exprimée dans la base des orbitales naturelles. / The thesis deals with the development and implementation of new methods for the description of strong electron correlation effects in molecules and solids. After introducing the state of the art in quantum chemistry and in condensed matter physics, a new hybrid method so-called ``site-occupation embedding theory'' (SOET) is presented and is based on the merging of wavefunction theory and density functional theory (DFT). Different formulations of this theory are described and applied to the one-dimensional Hubbard model. In addition, a novel ensemble density functional theory approach has been derived to extract the fundamental gap exactly. In the latter approach, the infamous derivative discontinuity is reformulated as a derivative of a weight-dependent exchange-correlation functional. Finally, a quantum chemical extension of SOET is proposed and based on a seniority-zero wavefunction, completed by a functional of the density matrix and expressed in the natural orbital basis.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T11:49:17Z No. of bitstreams: 1 arquivototal.pdf: 2571485 bytes, checksum: 176b4eb5f639864aaef387d41330b286 (MD5) / Made available in DSpace on 2017-09-18T11:49:17Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2571485 bytes, checksum: 176b4eb5f639864aaef387d41330b286 (MD5) Previous issue date: 2016-03-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / After the formulation of general relativity differential geometry has become an increasing important tool in theoretical physics. This is even more clear in the investigation of the so-called embedding space-time theories. In this work we focus our attention in the Cauchy problem. These have played a crucial role in our understanding of the mathematical struc­ture of general relativity and embedding theories. We investigate the similarities and diffe­rences between the two approaches. We also study an extension of the Campbell-Magaard theorem and give two examples of both formalisms. / A geometria diferencial passou a ser uma ferramenta fundamental na fisica com o surgi­mento da relatividade geral. Em particular, destacamos sua importância na investigado das chamadas teorias de imersdo do espaco-tempo. Neste trabalho analisamos dois grandes for­malismos fundamentados de forma direta ou indireta na teoria de imersões: o teorema de Campbell-Magaard e o problema de Cauchy para a relatividade geral. Tendo como princi­pal objetivo tracar um paralelo entre esses dois formalismos, estudamos, nesta dissertacdo, o problema de valor inicial (pvi) para a relatividade geral mostrando que alem de admitir a formulae-do de pvi, a mesma é bem posta. Ademais, aplicamos este formalismo para o caso de uma metrica do tipo Friedmann-Robertson-Walker em (3+1). Estudamos tambem o teorema de Campbell-Magaard e sua extensdo para o espaco-tempo de Einstein e aplicamos este teorema para uma metrica do tipo de Sitter em (2+1).