La théorie de la fonctionnelle de la densité dépendante du temps (TDDFT) est une méthode basée sur la densité pour calculer les états excités. Bien que la TDDFT soit une théorie exacte, on doit en pratique partir d'une approximation de la fonctionnelle d'échange-corrélation, qui reste inconnue. L'approximation adiabatique est l'approximation de la fonctionnelle la plus courante. Cette approximation donne de très bons résultats pour les propriétés spectroscopiques, mais elle est inexacte pour les simulations en photochimie. Dans cette thèse, on montre que l'origine du problème réside dans l'approximation de la fonctionnelle de corrélation. Le résultat principal de la thèse consiste en un noyau de corrélation, qui peut être utilisé dans la formulation de la réponse linéaire, noyau dérivée à partir de la théorie des perturbations à plusieurs corps. Le noyau inclut de façon générale les excitations doubles qui donnent l'effet principal à la corrélation dans les états excités. La comparaison de ce noyau avec la fonctionnelle adiabatique nous a permis d'identifier les termes manquants à ce dernier. Nous avons testé la possibilité d'ajouter ces termes comme une correction à l'approximation adiabatique. Le noyau pourrait potentiellement être appliqué à des systèmes de grosse taille. / Time-dependent density-functional theory (TDDFT) is a density-functional method for calculating excited states. TDDFT is formally exact, though in practice one has to approximate the unknown exchange-correlation functional, which contains all the unknown many-body effects. The adiabatic functionals are the most commonly used. Although they are very successful for spectroscopy, the adiabatic functionals are too inaccurate to be applied to photochemistry. In this thesis, we show that the main problem is due to the approximations in the correlation functional. The main result of the thesis is a correlation kernel for linear-response TDDFT, derived using many-body perturbation theory techniques, which generally includes double excitations, thus introducing the leading correlation effects in the excited states. The comparison of this kernel with the adiabatic functionals allowed us to identify which correlation effects are missing in these approximation. We tested the possibility of improving the description of correlation by adding the missing terms from many-body theory to the adiabatic functionals. This mixed kernel is more efficient than the full many-body kernel, and can potentially be applied to systems of medium to large size.

Cette thèse présente des travaux dans 5 domaines où nous cherchons à améliorer ou étendre vers des cas dissipatifs la méthode TDLDA (Time Dependent Local Density Approximation). - La propagation en base naturelle permet avant tout de formaliser des techniques indispensables à la mise en oeuvre des méthodes prenant en compte les collisions. - La méthode SIC (Self Interaction Correction) dynamique améliore l'efficacité de la mise en oeuvre de la correction d'auto-interaction complète. Elle permet l'utilisation efficace de cette méthode dans des conditions compliquées comme les systèmes mixtes de molécules métalliques et covalentes. - La méthode TDCDFT (Time Dependent Current and Density Functional Theory) prend en compte un effet retard par l'introduction d'une fonctionnelle de la densité et du courant. Elle a pu être mise en oeuvre en 3 dimensions sur des petits atomes ou clusters. Les résultats ont confirmé l'amortissement déjà constaté dans des études existantes, mais la TDCDFT ne prédit pas correctement la dépendance non-linéaire de l'amortissement en fonction de l'intensité de l'excitation. - La méthode STDHF (Stochastic Time-Dependent Hartree Fock) introduit la corrélation par une méthode de sauts stochastiques, dans des parcours temporels successifs. Cette méthode a été modifiée (sous le nom Average Stochastic TDHF) pour n'utiliser qu'un seul champ moyen, les sauts étant alors introduits sous la forme de probabilités de transition, qui permettent de modifier les nombres d'occupation. Sous cette forme elle ne peut fonctionner que dans une boite de calcul fermée. Nous montrons ici son adaptation à une boite de calcul ouverte. - La méthode RTA (Relaxation Time Approximation) a été développée dans un modèle à deux dimensions. On montre ici son extension à 3 dimensions. L'ampleur de l'effort numérique impose l'introduction de nouvelles méthodes d'optimisation. Par contre les résultats confirment les tendances observée en 2D. Cette méthode permet aussi de calculer de nouvelles molécules. / This thesis presents works in 5 areas where we aim at improving or extending toward dissipative cases the TDLDA (Time Dependent Local Density Approximation) method. - The propagation in a natural basis allows first to formalize technics which are a prerequisite to the operation of methods accounting for collisions. - The SIC (Self Interaction Correction) method improves the efficiency of the full Self Interaction Correction. It allows to use efficiently this method in complex conditions such as mixed systems of metallic and covalent molecules. - The TDCDFT (Time Dependent Current and Density Functional Theory) allows to consider some time delay effects by introducing a functional of time and current. It was extended to a 3 dimensional case on little atoms and clusters. The results confirm the damping already evidenced in previous works, but TDCDFT does not predict correctly the non-linear dependence of the damping versus the excitation energy. - The TDHF((Stochastic Time-Dependent Hartree Fock) method introduces correlation by a method of stochastics jumps, in separate time-histories. This method has been modified (Average Stochastic TDHF) to use only one mean field, the jumps are then accounted for by transition probabilities, which allow to modify the occupation numbers. In this form it can work only in a closed box. We show here its extension to an open calculation space. - The RTA (Relaxation Time Approximation) was developed in a 2 dimension model. We show here the extension of this method to 3 dimensions. The amplitude of the numerical method leads to the introduction of new optimization methods. But the results do confirm the tendencies observed in the 2 dimensional case. This method also allows calculation on new molecules.

First-principles electronic structure theory explains properties of atoms, molecules and solids from underlying physical principles without input from empirical parameters. Time-dependent density functional theory (TDDFT) has emerged as arguably the most widely used first-principles method for describing the time-dependent quantum mechanics of many-electron systems. In this thesis, we will show how the fundamental principles of TDDFT can be extended and applied in two novel directions: The theory of open quantum systems (OQS) and quantum computation (QC). In the first part of this thesis, we prove theorems that establish the foundations of TDDFT for open quantum systems (OQS-TDDFT). OQS-TDDFT allows for a first principles description of non-equilibrium systems, in which the electronic degrees of freedom undergo relaxation and decoherence due to coupling with a thermal environment, such as a vibrational or photon bath. We then discuss properties of functionals in OQS-TDDFT and investigate how these differ from functionals in conventional TDDFT using an exactly solvable model system. Next, we formulate OQS-TDDFT in the linear-response regime, which gives access to environmentally broadened excitation spectra. Lastly, we present a hybrid approach in which TDDFT can be used to construct master equations from first-principles for describing energy transfer in condensed phase systems. In the second part of this thesis, we prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. TDDFT applied to universal Hamiltonians implies that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. This offers the possibility of simplifying computations by using the principles of TDDFT similar to how it is applied in electronic structure theory. Lastly, we discuss a related result; the computational complexity of TDDFT. / Physics

We demonstrate the ability to simulate targeted excitation of atomistic systems using our real-time TDDFT-based simulation framework NESSIE. Traditional ap- proaches for extracting spectra through real-time TDDFT involves excitation of all frequencies via impulse requiring long simulation times and yielding poor resolution. By exciting the system with a modulated sinc pulse between the frequencies of inter- est we are able to obtain a spectral response with far more precision in a significantly shorter time frame than competing implementations.

Les hydrogénases FeFe sont des métalloenzymes qui catalysent l'oxydation et la production de H$_2$. Le cycle catalytique et de nombreux aspects de la réactivité de ces enzymes, y compris l'inactivation aérobie et anaérobie, ne sont toujours pas complètement compris. J'ai développé une nouvelle technique appelée photo-électrochimie directe et je l'ai utilisée pour étudier l'effet de l'irradiation sur la cinétique d'inhibition par le CO de trois hydrogénases FeFe distinctes. J'ai déterminé le spectre d'action de la photo-dissociation de l'inhibiteur CO et j'ai décrit le processus au niveau QM pour la première fois, en obtenant un bon accord entre les expériences et la théorie.J'ai également étudié la photoinhibition de l'enzyme. J'ai effectué des expériences de photoélectrochimiques en irradiant la protéine avec des diodes laser monochromatiques dans le domaine de la lumière visible, une lampe halogène ou une lampe au xénon et j'ai observé que les hydrogénases FeFe de C. reinhardtii et C. acetobutylicum sont irréversiblement inactivées par la lumière UVB. En utilisant la DFT et la TDDFT, j'ai conclu que les étapes initiales de la photoinhibition consistent en la photodissociation d'un ligand carbonyle intrinsèque du site actif, suivie de la formation d'une espèce inactive stable.J'ai aussi effectué des expériences préliminaires pour examiner l'effet de la lumière sur l'activité de deux autres métalloenzymes: la CO déshydrogénase et la hydrogénase NiFe.Mes résultats illustrent la force de l'approche méthodologique qui combine électrochimie directe et TDDFT, et apportent de nouvelles connaissances sur les propriétés chimiques et photochimiques de plusieurs métalloenzymes. / FeFe hydrogenases are metalloenzymes that catalyze the oxidation and production of H$_2$. The catalytic cycle and many aspects of the reactivity of these enzymes, including their aerobic and anaerobic inactivation, are still the subjects of intense investigations. I developed a new technique called direct photo-electrochemistry and I used it to study the effect of monochromatic irradiation in the visible range on the kinetics of inhibition by CO of three distinct FeFe hydrogenases. I determined the action spectrum of the photo-dissociation of the inhibitor CO and I described the process at the QM level for the first time, obtaining good agreement between experiments and theory.I also studied the photoinhibition of the enzyme. I carried out photoelectrochemistry experiments irradiating the protein with monochromatic visible light laser diodes, a halogen lamp or a xenon lamp, and I observed that the FeFe hydrogenases from C. reinhardtii and C. acetobutylicum are irreversibly inactivated by UVB light. Using DFT and TDDFT, I concluded that the initial steps of photoinhibition consist in the photodissociation of one carbonyl intrinsic ligand of the active site, followed by the formation of a stable inactive species.I also performed preliminary experiments to examine the effect of light on the activity of two other metalloenzymes: Carbon monoxide dehydrogenase (CODH) and NiFe-hydrogenase.My results illustrate the strength of the methodological approach that combines direct electrochemistry and TDDFT, and reveal new insights in the chemical and photochemical properties of several metalloenzymes.

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Neste trabalho foram estudados os complexos de transferência de carga resultantes da interação entre as espécies aceptoras de elétrons tetracianoetileno (TCNE) e 7,7,8,8-tetracianoquinodimetano (TCNQ), com aminas mono, bi e tri aromáticas, como espécies doadoras de elétrons, em solução. Também foram estudadas as reações de substituição eletrofílica aromática que ocorre entre o TCNE e aminas. Para tal estudo, foram utilizadas as técnicas espectroscópicas de absorção UV-VIS e Raman, o que permitiu a caracterização dos complexos de transferência de carga, assim como das espécies participantes da reação de tricianovinilação que ocorre entre aminas e TCNE. Para dar suporte aos dados experimentais, cálculos DFT (Teoria do Funcional da Densidade) e TDDFT (Teoria do Funcional da Densidade dependente do tempo) foram realizados, o que permitiu a obtenção das geometrias otimizadas, valores de frequência Raman e energias de transição dessas espécies. Os espectros eletrônicos dos complexos formados entre TCNE e aminas monoaromáticas mostraram que suas energias de transição são proporcionais à capacidade de doação de elétrons da amina. De fato, as energias de transição puderam ser correlacionadas com os valores de potencial de ionização das aminas, apresentando uma correlação linear de acordo com a regra Mulliken. Os espectros Raman permitiram verificar que os modos vibracionais do TCNE envolvidos no processo de transferência de carga apresentam deslocamento para menores números de onda com a diminuição do potencial de ionização da amina, e analogamente, pôde-se obter uma correlação linear entre esses dois parâmetros. No caso das aminas bi e tri aromáticas, a tendência linear entre energia de transição e potencial de ionização foi observada, mas não para os deslocamentos Raman das bandas do TCNE. Na reação de tricianovinilação, os espectros eletrônicos possibilitaram a identificação das espécies participantes da reação, assim como sua caracterização vibracional por espectroscopia Raman ressonante. Através da espectroscopia Raman ressonante, pôde-se, pela primeira vez, caracterizar as espécies intermediárias da reação de tricianovinilação entre TCNE e aminas aromáticas. Os complexos envolvendo TCNQ e aminas monoaromáticas apresentou tendência semelhante à observada em complexos com o TCNE. As energias de transição desses complexos diminuem linearmente, assim como, os modos vibracionais do TCNQ, que apresentam deslocamentos para menores frequências Raman com a diminuição do potencial de ionização da amina. Por outro lado, complexos formados pelo TCNQ e aminas com mais de um anel aromático em sua estrutura, não apresentam correlação entre potencial de ionização do doador e energia de transição e deslocamentos Raman. Os cálculos dos espectros eletrônicos e vibracionais apresentaram boa concordância com os obtidos experimentalmente, porém algumas limitações ficam evidentes na descrição das interações π nesses sistemas modelo. / In this work the charge transfer complexes resulting from the interaction between tetracyanoethylene (TCNE) and 7,7,8,8-tetracyanoquinodimethane (TCNQ), as electron accepting species and mono, bi and tri aromatic amines, as electron donating species, were studied in solution. Also the electrophilic aromatic substitution that occurs between the TCNE and amines has been studied. For this study, the spectroscopic techniques of UV-VIS absorption and Raman were used, which allowed the characterization of the charge transfer complexes, as well as of the species involved in the reaction of tricianovinylation that occurs between amines and TCNE. In order to support the experimental data, DFT (Density Functional Theory) and TDDFT (Time-dependent Density Functional Theory) calculations were performed, to obtain the optimized geometries, Raman frequency values and theoretical transition energies of such species. The electronic spectra of the complexes formed between TCNE and monoaromatic amines showed that their transition energies are proportional to the amine electron donation capacity. In fact it could be linearly correlated with the ionization potential values of the amines, following the Mullikens rule. The Raman spectra allowed to verify that the vibrational modes of the TCNE involved in the process of charge transfer, were displaced to lower wavenumbers with the reduction of the ionization potential of the amine, and analogously, a linear correlation between these two parameters could be obtained. In the case of bi and tri aromatic amines, the linear trend between transition energy and ionization potential was observed, but not for the Raman shifts of the TCNE bands. In the reaction of tricianovinylation, the electronic spectra enabled the identification of the participating species in the reaction, and their vibrational characterization by resonance Raman. Using resonance Raman spectroscopy, it was possible to characterize the intermediate species of the tricianovinylation reaction between TCNE and aromatic amines for the first time. The complexes involving TCNQ and monoaromatic amines showed a similar trend to that observed in complexes with TCNE. The transition energies of these complexes decrease linearly, as well as the vibrational modes of the TCNQ, which present shifts to lower Raman frequencies with the decrease of the ionization potential of the amine. On the other hand, complexes formed by TCNQ and amines with more than one aromatic ring in their structure do not present correlation between donor ionization potential and transition energy and Raman displacements. The calculations of the electronic and vibrational spectra presented good agreement with those obtained experimentally, however some limitations were evidenced in the description of the π interactions in these model systems.

Neste trabalho foram estudados os complexos de transferência (CTC) de carga formados por iodeto com os derivados piridínicos C4(4CP)+ e C3bis(4CP)2+ em solução. A formação de um CTC é caracterizada pelo surgimento de uma nova banda no espectro eletrônico de absorção, em solventes orgânicos como acetonitrila. Este tipo de sistema tem recebido muito interesse em diversos campos como, por exemplo, eletrônica orgânica, espectroscopia não linear, bioquímica, no ramo farmacêutico, etc. O complexo C4(4CP)+I- é caracterizado por uma banda de transferência de carga com máximo em 421 nm em acetonitrila. Cálculos das propriedades eletrônicas e das energias de excitação do complexo foram realizados usando a teoria do funcional da densidade e a teoria do funcional da densidade dependente do tempo. O emprego de funcionais de troca e correlação com correções de longo alcance foi essencial para a obtenção de resultados acurados para as energias de excitação. Usando os funcionais CAM-B3LYP e B97X-D, associados ao modelo contínuo PCM, foi possível descrever muito bem o máximo da banda experimental. No caso do C3bis(4CP)2+ foram encontradas diferentes estruturas possíveis para o complexo, que podem ser formadas pela associação de um ou dois I-. Em todos os casos apenas um dos I- participa da excitação, o que explica a estequiometria 1:1 observada experimentalmente. Uma visão mais aprofunda do comportamento do complexo em solução foi obtida usando a dinâmica molecular clássica. O campo de força foi ajustado para reproduzir os resultados de uma dinâmica por primeiros princípios de vácuo. A dinâmica clássica mostrou não haver dissociação em acetonitrila no complexo formado com o C3bis(4CP)2+. A banda calculada a partir das configurações amostradas da dinâmica está em excelente acordo com o resultado experimental. / In this work, we have studied theoretically charge-transfer complexes (CTC) formed by pyridinium derivatives with iodide. The formation of a CTC is characterized by the appearance of a new absorption band on the electronic spectra, in organic polar solvents like acetonitrile. These type of systems have recently received much interest in a broad variety of fields, for example, organic electronics, nonlinear spectroscopy, medical biochemistry, pharmaceutical industry, etc. The C4(4CP)+I- complex is characterized by the charge-transfer band with a maximum at 421 nm in acetonitrile. We have used density functional theory (DFT) and time dependent density functional theory (TDDFT) to calculate electronic properties and the excitation energies of the complex. Functionals with long-range corrections were essential in describing the charge-transfer excitations. CAM-B3LYP and wB97X-D associated with the polarizable continuum model predicts CT excitations in good agreement with experiment. Our results also indicates the existence of different conformations for the complex formed by the C3bis(4CP)2+ with iodide. Complexes were formed by the association of one or two I- to C3bbis(4CP)2+, but the charge transfer excitations were calculated from only one iodide to the aromatic ring, what explain why the stoichiometry 1:1 was observed. A better description of the complex in solution was obtained using classical molecular dynamics. The OPLS-AA force field was fine-tuned to reproduce the results of a first principle molecular dynamics for the complex. No dissociation were observed. The calculated charge-transfer band using configurations sampled from molecular dynamics is in excellent agreement with experiment.

Neste trabalho foram estudados os complexos de transferência de carga resultantes da interação entre as espécies aceptoras de elétrons tetracianoetileno (TCNE) e 7,7,8,8-tetracianoquinodimetano (TCNQ), com aminas mono, bi e tri aromáticas, como espécies doadoras de elétrons, em solução. Também foram estudadas as reações de substituição eletrofílica aromática que ocorre entre o TCNE e aminas. Para tal estudo, foram utilizadas as técnicas espectroscópicas de absorção UV-VIS e Raman, o que permitiu a caracterização dos complexos de transferência de carga, assim como das espécies participantes da reação de tricianovinilação que ocorre entre aminas e TCNE. Para dar suporte aos dados experimentais, cálculos DFT (Teoria do Funcional da Densidade) e TDDFT (Teoria do Funcional da Densidade dependente do tempo) foram realizados, o que permitiu a obtenção das geometrias otimizadas, valores de frequência Raman e energias de transição dessas espécies. Os espectros eletrônicos dos complexos formados entre TCNE e aminas monoaromáticas mostraram que suas energias de transição são proporcionais à capacidade de doação de elétrons da amina. De fato, as energias de transição puderam ser correlacionadas com os valores de potencial de ionização das aminas, apresentando uma correlação linear de acordo com a regra Mulliken. Os espectros Raman permitiram verificar que os modos vibracionais do TCNE envolvidos no processo de transferência de carga apresentam deslocamento para menores números de onda com a diminuição do potencial de ionização da amina, e analogamente, pôde-se obter uma correlação linear entre esses dois parâmetros. No caso das aminas bi e tri aromáticas, a tendência linear entre energia de transição e potencial de ionização foi observada, mas não para os deslocamentos Raman das bandas do TCNE. Na reação de tricianovinilação, os espectros eletrônicos possibilitaram a identificação das espécies participantes da reação, assim como sua caracterização vibracional por espectroscopia Raman ressonante. Através da espectroscopia Raman ressonante, pôde-se, pela primeira vez, caracterizar as espécies intermediárias da reação de tricianovinilação entre TCNE e aminas aromáticas. Os complexos envolvendo TCNQ e aminas monoaromáticas apresentou tendência semelhante à observada em complexos com o TCNE. As energias de transição desses complexos diminuem linearmente, assim como, os modos vibracionais do TCNQ, que apresentam deslocamentos para menores frequências Raman com a diminuição do potencial de ionização da amina. Por outro lado, complexos formados pelo TCNQ e aminas com mais de um anel aromático em sua estrutura, não apresentam correlação entre potencial de ionização do doador e energia de transição e deslocamentos Raman. Os cálculos dos espectros eletrônicos e vibracionais apresentaram boa concordância com os obtidos experimentalmente, porém algumas limitações ficam evidentes na descrição das interações π nesses sistemas modelo. / In this work the charge transfer complexes resulting from the interaction between tetracyanoethylene (TCNE) and 7,7,8,8-tetracyanoquinodimethane (TCNQ), as electron accepting species and mono, bi and tri aromatic amines, as electron donating species, were studied in solution. Also the electrophilic aromatic substitution that occurs between the TCNE and amines has been studied. For this study, the spectroscopic techniques of UV-VIS absorption and Raman were used, which allowed the characterization of the charge transfer complexes, as well as of the species involved in the reaction of tricianovinylation that occurs between amines and TCNE. In order to support the experimental data, DFT (Density Functional Theory) and TDDFT (Time-dependent Density Functional Theory) calculations were performed, to obtain the optimized geometries, Raman frequency values and theoretical transition energies of such species. The electronic spectra of the complexes formed between TCNE and monoaromatic amines showed that their transition energies are proportional to the amine electron donation capacity. In fact it could be linearly correlated with the ionization potential values of the amines, following the Mullikens rule. The Raman spectra allowed to verify that the vibrational modes of the TCNE involved in the process of charge transfer, were displaced to lower wavenumbers with the reduction of the ionization potential of the amine, and analogously, a linear correlation between these two parameters could be obtained. In the case of bi and tri aromatic amines, the linear trend between transition energy and ionization potential was observed, but not for the Raman shifts of the TCNE bands. In the reaction of tricianovinylation, the electronic spectra enabled the identification of the participating species in the reaction, and their vibrational characterization by resonance Raman. Using resonance Raman spectroscopy, it was possible to characterize the intermediate species of the tricianovinylation reaction between TCNE and aromatic amines for the first time. The complexes involving TCNQ and monoaromatic amines showed a similar trend to that observed in complexes with TCNE. The transition energies of these complexes decrease linearly, as well as the vibrational modes of the TCNQ, which present shifts to lower Raman frequencies with the decrease of the ionization potential of the amine. On the other hand, complexes formed by TCNQ and amines with more than one aromatic ring in their structure do not present correlation between donor ionization potential and transition energy and Raman displacements. The calculations of the electronic and vibrational spectra presented good agreement with those obtained experimentally, however some limitations were evidenced in the description of the π interactions in these model systems.