La réponse linéaire de la théorie de la fonctionnelle de la densité dépendante du temps est étudiée dans le cadre du formalisme d'ondelettes du code BigDFT, qui permet d'exprimer les fonctions d'onde électroniques sur une grille de simulation dans l'espace réel. L'objectif est de déterminer un spectre d'excitations de référence pour un système et un potentiel d'échange-corrélation donnés.Il apparaît que seule une partie du spectre, concernant les transitions entre orbitales liées, peut être facilement amenée à convergence par rapport aux paramètres d'entrée de BigDFT, que sont l'extension de la grille de simulation et le nombre d'orbitales du continuum qui sont considérées pour le calcul des spectres. L'énergie de la dernière orbitale inoccupée utilisée dans les calculs se révèle d'ailleurs être un paramètre plus important que ce nombre d'orbitales inoccupées. La justification vient de l'étude de la complétude des bases formées par les orbitales de l'état fondamental du système. Tout ceci permet de porter un regard neuf sur les résultats obtenus avec le formalisme à base gaussienne, tel qu'implémenté dans le code NWChem.En ce qui concerne la convergence du spectre de plus haute énergie, concernant des transitions entre orbitales occupées et orbitales inoccupées du continuum, l'espoir d'une convergence se heurte au problème du tassement du continuum. Il faut alors songer à une manière différente de capter l'information contenue dans ce continuum.Le formalisme des états résonants, dont les fondements ont été posés lors de la première moitié du XXème siècle, est une piste très encourageante pour cela. Une étude préliminaire dans le cas du puits de potentiel carré à une dimension est donc présentée. La première étape a consisté en la détermination de ces états résonants, dont les énergies et fonctions d'onde sont complexes. Une normalisation a notamment pu leur être attribuée. Il est ensuite montré, sous certaines conditions, que la base formée par les états propres de ce potentiel, dont une partie est constituée par les états du continuum, peut être efficacement remplacée par une base discrète et complète faite d'états résonants. Des applications numériques montreront qu'ils peuvent être avantageusement utilisés pour définir la fonction de Green ou encore calculer la propagation temporelle d'un paquet d'onde. / The linear response on the time-dependent density functional theory is studied in the wavelets formalism used in the BigDFT code, that allows the representations of electronic wave-functions on a simulation grid in real space. The goal of this study is to determine a reference excitation spectrum for a given system and exchange-correlation potential.It appears that only one part of the spectrum can be easily brought to convergence with respect to the input parameters of BigDFT, which are the simulation grid extension and the number of unoccupied continuum orbitals considered in the spectrum calculation. The energy of the last unoccupied orbital used actually proves to be more important as a parameter than this number of unoccupied orbitals. This is justified by the study of the completeness of the basis sets made of the ground state orbitals of the system. This gives another point of view regarding spectrum obtained by using the Gausian basis sets formalism, as the one implemented in the code NWChem.As to the convergence of the spectrum at higher energy, concerning transitions between occupied orbitals and unoccupied orbitals of the continuum, the hope for a convergence faces the problem of the continuum collapse. One therefore has to think of another way of retrieving the data contained in this continuum.The resonant states formalism, whose foundations were laid in the first half of the 20th century, is very encouraging in this regard. A preliminary study in the case of the one-dimension square well potential is therefore presented. The first step consisted in the determination of these resonant states, whose energies and wavefunctions are complex valued in general. Their normalization was also clearly defined. It is then shown, under certain conditions, that the basis set formed by the eigenstates of this potential, including the continuum states, can be efficiently replaced by a discrete and complete basis set made of resonant states. Numerical applications also show that these states can also be advantageously used to define the Green's function or even compute the time propagation of a wavepacket.

<p>Atomic physics plays an important role in determining the evolution stages in a wide range of laboratory and cosmic plasmas. Therefore, the main contribution to our ability to model, infer and control plasma sources is the knowledge of underlying atomic processes. Of particular importance are reliable low temperature dielectronic recombination (DR) rate coefficients.</p><p>This thesis provides systematically calculated DR rate coefficients of lithium-like beryllium and sodium ions via ∆n = 0 doubly excited resonant states. The calculations are based on complex-scaled relativistic many-body perturbation theory in an all-order formulation within the single- and double-excitation coupled-cluster scheme, including radiative corrections.</p><p>Comparison of DR resonance parameters (energy levels, autoionization widths, radiative transition probabilities and strengths) between our theoretical predictions and the heavy-ion storage rings experiments (CRYRING-Stockholm and TSRHeidelberg) shows good agreement.</p><p>The intruder state problem is a principal obstacle for general application of the coupled-cluster formalism on doubly excited states. Thus, we have developed a technique designed to avoid the intruder state problem. It is based on a convenient partitioning of the Hilbert space and reformulation of the conventional set of pairequations. The general aspects of this development are discussed, and the effectiveness of its numerical implementation (within the non-relativistic framework) is selectively illustrated on autoionizing doubly excited states of helium.</p>

Šis darbas yra skirtas šiuolaikinės atomo trikdžių teorijos matematinio aparato, paremto efektinių operatorių formalizmu, plėtojimui. Darbe nuosekliai ir sistemingai, pradedant nuo pačių bendriausių principų, nagrinėjami Foko erdvės apribojimo į redukavimo grupių neredukuotinus poerdvius metodai bei pateikiama neredukuotinų tenzorinių operatorių, charakterizuojančių fizikines ir efektines sąveikas, klasifikacija bendrais ir tam tikrais atskirais atvejais. Gautos išraiškos ir iš jų išplaukiančios išvados yra grindžiamos matematine kalba. Dauguma esminių rezultatų yra suformuluoti teoremų pavidalu. Disertaciją sudaro 101 puslapis, 5 skyriai, 4 priedai, 40 lentelių ir 9 paveikslėliai. Pagrindiniai rezultatai, pateikti disertacijoje, yra publikuoti fizikos ir matematikos mokslų žurnaluose. / The principal goals of the thesis are subjected to general methods and forms of effective operators by the nowadays demands of theoretical application of many-body perturbation theory to atomic physics. The present theoretical research follows up step by step by systematic observation of various possibilities to restrict the Fock space operators to their irreducible subspaces and the classification of irreducible tensor operators which represent the physical as well as the effective interactions. To ground the results of the thesis, the symbolic preparation of obtained expressions is strictly proved mathematically. Most of the main results are listed in theorems. The doctoral dissertation contains 101 pages, 5 sections, 4 appendices, 40 tables and 9 figures. The main results described in the present dissertation have been published in journals of physical and mathematical sciences.

The principal goals of the thesis are subjected to general methods and forms of effective operators by the nowadays demands of theoretical application of many-body perturbation theory to atomic physics. The present theoretical research follows up step by step by systematic observation of various possibilities to restrict the Fock space operators to their irreducible subspaces and the classification of irreducible tensor operators which represent the physical as well as the effective interactions. To ground the results of the thesis, the symbolic preparation of obtained expressions is strictly proved mathematically. Most of the main results are listed in theorems. The doctoral dissertation contains 101 pages, 5 sections, 4 appendices, 40 tables and 9 figures. The main results described in the present dissertation have been published in journals of physical and mathematical sciences. / Šis darbas yra skirtas šiuolaikinės atomo trikdžių teorijos matematinio aparato, paremto efektinių operatorių formalizmu, plėtojimui. Darbe nuosekliai ir sistemingai, pradedant nuo pačių bendriausių principų, nagrinėjami Foko erdvės apribojimo į redukavimo grupių neredukuotinus poerdvius metodai bei pateikiama neredukuotinų tenzorinių operatorių, charakterizuojančių fizikines ir efektines sąveikas, klasifikacija bendrais ir tam tikrais atskirais atvejais. Gautos išraiškos ir iš jų išplaukiančios išvados yra grindžiamos matematine kalba. Dauguma esminių rezultatų yra suformuluoti teoremų pavidalu. Disertaciją sudaro 101 puslapis, 5 skyriai, 4 priedai, 40 lentelių ir 9 paveikslėliai. Pagrindiniai rezultatai, pateikti disertacijoje, yra publikuoti fizikos ir matematikos mokslų žurnaluose.

Atomic physics plays an important role in determining the evolution stages in a wide range of laboratory and cosmic plasmas. Therefore, the main contribution to our ability to model, infer and control plasma sources is the knowledge of underlying atomic processes. Of particular importance are reliable low temperature dielectronic recombination (DR) rate coefficients. This thesis provides systematically calculated DR rate coefficients of lithium-like beryllium and sodium ions via ∆n = 0 doubly excited resonant states. The calculations are based on complex-scaled relativistic many-body perturbation theory in an all-order formulation within the single- and double-excitation coupled-cluster scheme, including radiative corrections. Comparison of DR resonance parameters (energy levels, autoionization widths, radiative transition probabilities and strengths) between our theoretical predictions and the heavy-ion storage rings experiments (CRYRING-Stockholm and TSRHeidelberg) shows good agreement. The intruder state problem is a principal obstacle for general application of the coupled-cluster formalism on doubly excited states. Thus, we have developed a technique designed to avoid the intruder state problem. It is based on a convenient partitioning of the Hilbert space and reformulation of the conventional set of pairequations. The general aspects of this development are discussed, and the effectiveness of its numerical implementation (within the non-relativistic framework) is selectively illustrated on autoionizing doubly excited states of helium.

Cette thèse se propose d'explorer les mérites d'une famille d'approches de simulation quantique ab initio, les théories de perturbation à N-corps, pour l'exploration des propriétés électroniques et optiques de systèmes organiques. Nous avons étudié en particulier l'approximation dite de GW et l'équation de Bethe-Salpeter, très largement utilisées dès les années soixante pour les semiconducteurs de volume, mais dont l'utilisation pour les systèmes organiques moléculaires est très limitée. L'étude de quelques cas d'intérêt pour le photovoltaïque organique, et en particulier de petites molécules pour lesquelles sont disponibles des données expérimentales ou des résultats issus d'approches de chimie quantique, nous ont permis de valider ces approches issues de la physique du solide.Ce doctorat s'inscrit dans le cadre du développement d'un outil de simulation quantique spécifique (le projet FIESTA) dont l'objectif est de combiner les formalismes GW et Bethe-Salpeter avec les techniques de la chimie quantique, c'est-à-dire en particulier l'utilisation de bases localisées analytiques (bases gaussiennes) et des approches de type «résolution de l'identité» pour le traitement des intégrales Coulombiennes. Ce code est aujourd'hui massivement parallélisé, permettant, au delà des études de validation présentées dans ce travail de thèse, l'étude de systèmes complexes comprenant plusieurs centaines d'atomes. En cours de développement, l'incorporation d'approches hybrides combinant mécanique quantique et écrantage à longue portée par des approches modèles de milieu polarisable m'a permis d'une part de me familiariser avec le code et le développement méthodologique, et permet d'autre part d'envisager l'étude de systèmes réalistes en couplage avec leur environnement.Le manuscrit s‘ouvre sur une introduction au photovoltaïque organique afin de mettre en lumière les questionnements spécifiques qui requièrent le développement de nouveaux outils théoriques à la fois fiables en terme de précision et suffisamment efficaces pour traiter des systèmes de grande taille. Le premier chapitre est d'ordre méthodologique et rappelle les fondements des techniques ab initio de type champ-moyen (Hartree, Hartree-Fock et théorie de la fonctionnelle de la densité). En partant des principes de la photoémission, les théories de perturbation à N-corps et la notion de quasi-particule sont ensuite introduites, conduisant aux équations de Hedin et aux approximations GW et COHSEX. De même, à partir de la compréhension d'une expérience d'optique, le traitement des interactions électron-trou est présenté, menant à l'équation de Bethe-Salpeter. Le chapitre 2 introduit brièvement les spécificités techniques liées à l'implémentation des formalismes GW et Bethe-Salpeter. Les propriétés analytiques des bases gaussiennes et les principes mathématiques derrière les techniques de type «résolution de l'identité» et «déformation de contour», sont brièvement décrites. Le troisième chapitre présente les résultats scientifiques obtenus durant cette thèse. Le cas paradigmatique d'un polypeptide model nous permettra de discuter des spécificités de l'approche GW appliquée à des systèmes moléculaires afin d'obtenir des énergies de quasiparticule de bonne qualité. De même, l'utilisation de l'équation de Bethe-Salpeter pour l'obtention du spectre optique de ce système sera présentée, ainsi que le cas d'une famille de colorants d'importance pour les cellules de Graetzel (les coumarines). Finalement, nous explorons dans le cas du fullerène C60 et du graphène le calcul des termes de couplage électron-phonon dans le cadre de l'approche GW, c'est-à-dire au delà des approches standards de type théorie de la fonctionnelle de la densité. Notre étude vise à vérifier si une approximation statique et à écrantage constant au premier ordre permet de garder la qualité des résultats GW pour un coût numérique réduit. Après la conclusion, les appendices donnent le détail de certaines dérivations. / The present thesis aims at exploring the properties and merits of the ab initio Green's function many-body perturbation theory (MBPT) GW and Bethe-Salpeter formalisms, in order to provide a well-grounded and accurate description of the electronic and optical properties of condensed matter systems. While these approaches have been developed for extended inorganic semiconductors and extensively tested on this class of systems since the 60 s, the present work wants to assess their quality for gas phase organic molecules, where systematic studies still remain scarce. By means of small isolated study case molecules, we want to progress in the development of a theoretical framework, allowing an accurate description of complex organic systems of interest for organic photovoltaic devices. This represents the main motivation of this scientific project and we profit here from the wealth of experimental or high-level quantum chemistry reference data, which is available for these small, but paradigmatic study cases.This doctoral thesis came along with the development of a specific tool, the FIESTA package, which is a Gaussian basis implementation of the GW and Bethe-Salpeter formalisms applying resolution of the identity techniques with auxiliary bases and a contour deformation approach to dynamical correlations. Initially conceived as a serial GW code, with limited basis sets and functionalities, the code is now massively parallel and includes the Bethe-Salpeter formalism. The capacity to perform calculations on several hundreds of atoms to moderate costs clearly paves the way to enlarge our studies from simple model molecules to more realistic organic systems. An ongoing project related to the development of discrete polarizable models accounting for the molecular environment allowed me further to become more familiar with the actual implementation and code structure.The manuscript at hand is organized as follows. In an introductory chapter, we briefly present the basic mechanisms characterizing organic solar cells, accentuating the properties which seek for an accurate theoretical description in order to provide some insight into the factors determining solar cell efficiencies. The first chapter of the main part is methodological, including a discussion of the principle features and approximations behind standard mean-field techniques (Hartree, Hartree-Fock, density functional theory). Starting from a description of photoemission experiments, the MBPT and quasiparticle ideas are introduced, leading to the so-called Hedin's equations, the GW method and the COHSEX approach. In order to properly describe optical experiments, electron-hole interactions are included on top of the description of inter-electronic correlations. In this context, the Bethe-Salpeter formalism is introduced, along with an excursus on time-dependent density functional theory. Chapter 2 briefly presents the technical specifications of the GW and Bethe-Salpeter implementation in the FIESTA package. The properties of Gaussian basis sets, the ideas behind the resolution of the identity techniques and finally the contour deformation approach to dynamical correlations are discussed. The third chapter deals with the results obtained during this doctoral thesis. On the electronic structure level, a recent study on a paradigmatic dipeptide molecule will be presented. Further, also its optical properties will be explored, together with an in-depth discussion of charge-transfer excitations in a family of coumarin molecules. Finally, by means of the Buckminster fullerene C60 and the two-dimensional semi-metal graphene, we will analyze the reliability of two many-body formalisms, the so-called static COHSEX and constant-screening approximation, for an efficient calculation of electron-phonon interactions in organic systems at the MBPT level. After a short conclusion, the Appendix containing details and derivations of the formalisms presented before closes this work.

In this thesis we describe the extension and implementation of the Sternheimer- GW method to a first-principles pseudopotential framework based on a planewaves basis. The Sternheimer-GW method consists of calculating the GW self-energy operator without resorting to the standard expansion over unoccupied Kohn- Sham electronic states. The Green's function is calculated by solving linear systems for frequencies along the real axis. The screened Coulomb interaction is calculated for frequencies along the imaginary axis using the Sternheimer equa- tion, and analytically continued to the real axis. We exploit novel techniques for generating the frequency dependence of these operators, and discuss the imple- mentation and efficiency of the methodology. We benchmark our implementation by performing quasiparticle calculations on common insulators and semiconductors, including Si, diamond, LiCl, and SiC. Our calculated quasiparticle energies are in good agreement with the results of fully-converged calculations based on the standard sum-over-states approach and experimental data. We exploit the methodology to calculate the spectral func- tions for silicon and diamond and discuss quasiparticle lifetimes and plasmaronic features in these materials. We also exploit the methodology to perform quasiparticle calculations on the 2-dimensional transition metal dichalcogenide system molybdenum disulfide (MoS₂). We compare the quasiparticle properties for bulk and monolayer MoS2 , and identify significant corrections at the GW level to the LDA bandstructure of these materials. We also discuss changes in the frequency dependence of the electronic screening in the bulk and monolayer systems and relate these changes to the quasiparticle lifetimes and spectral functions in the two limits.

Materialien formen die moderne Welt: Sie umgeben uns in unserem alltäglichen Leben. Unser Ziel ist die Materialeigenschaften nach unseren Bedürfnissen maßzuschneidern. Viele Materialeigenschaften wie Bandücken und Elektronendichteverteilung werden durch elektronische Zustände bestimmt. Die meisten Vorhersagen in Bezug auf Materialien entstammen der Dichtefunktionaltheorie (DFT). Diese Theorie ermittelt Grundzustandseigenschaften und kann jedoch keine Energien von angeregten Zuständen liefern. Um angeregte Zusände zu beschreiben, bedarf es daher einer höherstufigen Theorie: die Vielteilchen-Störungstheorie (MBPT) . Im Rahmen von MBPT ist das üblichste Verfahren die GW-Näherung (GWA), worin Elektronen als Quasiteilchen (QP) beschrieben werden. Der Energieunterschied zwischen einem nicht-wechselwirkenden Teilchen und einem QP ist die Selbstenergie. In GWA ergibt sich die Selbsenergie als Produkt aus die Einteilchen-Greenfunktion, G, und die abgeschirmte Coulomb-Wechselwirkung, W, und führt zu der wahren Anregungsenergie von QP. Diese Doktorarbeit beinhaltet die Implementierung von selbstkonsistentem Quasiteilchen-GW (QSGW) im exciting Code. Dieses Software-Paket benutzt die Linearized-Augmented-Plane-Wave-Methode (LAPW), welche alle Elektronen gleichberechtigt behandelt. Beginnend mit DFT optimiert die QSGW-Methode den Einteilchen-Hamiltonoperator durch eine selbstkonsistente Suche eines optimierten Austausch-Korrelationspotentials. Am Ende des iterativen Prozesses liefert die QSGW-Methode Eigenfunktionen und Eigenwerte der QP. Wir präsentieren mit QSGW ermittelte elektronische Strukturen von neun kristallinen Festkörpern. Wir präsentieren die zugehörigen Bandstrukturen und Zustandsdichtediagramme und vergleichen anhand dieser die QSGW-Ergebnisse mit Ergebnissen von DFT und G0W0. Zusätzlich untersuchen wir die elektronische Ladungsdichte und Wellenfunktion in ausgewählten Materialien. / Materials shape the modern world: they appear everywhere in our daily life. We investigate what governs the material's properties, in order to tailor them to meet our needs. Properties, e.g., bandgaps, and electronic density distribution are determined by the electronic structure. Most predictions on materials follow from computational physics, in particular density-functional theory (DFT). This scheme returns ground-state properties, but it fails to provide excited-state energies. To find the latter, we have to recourse to a higher degree of theory, namely many-body perturbation theory (MBPT). Within MBPT, the most popular framework is the GW approximation (GWA) which describes electrons as quasiparticles (QP). The difference in energy between a non-interacting particle and a QP is called the self-energy. In GWA, the product of the Green function G and W, the screened Coulomb interaction, returns the self-energy. GWA is in principle self-consistent, but is mostly implemented as a perturbative correction to DFT results, known as G0W0. Unfortunately, the electronic structure given by G0W0 depends on the initial DFT results. This PhD project consists in the implementation of the self-consistent quasiparticle GW (QSGW) in the exciting code. This software package uses the all-electron linearized augmented planewave (LAPW) method, treating every electron on equal footing. Starting from DFT, the QSGW method (based in the GWA) optimizes the one-particle Hamiltonian through a self-consistent search for an optimized exchange-correlation potential. At the end of the iterative process, the QSGW method provides eigenfunctions and eigenvalues of the QPs. Considering nine crystalline solids, we present their electronic structure by means of QSGW. We present the bandstructures and density of state diagrams, comparing QSGW results to DFT and G0W0 results. In addition, we study the electronic charge density and wavefunction in selected materials.

The binary neutron star merger of 2017 and its corresponding electromagnetic signature resembling that of a kilonova has been one of the most groundbreaking astrophysical occurrences in the last decade. Indications of r-process nucleosynthesis in this event presents new opportunities for learning about the astrophysical origin of heavy elements. This has been a long-standing mystery in our understanding of the chemical evolution of the universe. This leads to the requirement of developing more accurate calculations of the corresponding atomic properties. In this work, I have studied the potential of utilizing a combined configuration-interaction and many-body perturbation theory approach.The goal is to study if a generalized and computationally efficient method is possible with this approach, so that it can be used to develop accurate and complete atomic structures applicable to any ion of any element in the periodic table. Focusing on the lanthanide group of elements, and in Ce in particular, the method in this work builds on including the bulk of strong correlation contributions in the configuration-interaction model, complemented with perturbation theory corrections in subsequent many-body perturbation theory calculations. For all Ce ions, this was however not possible without having to compromise the completeness condition. In conclusion, in the scope of this project, we find that it is challenging to generalize a procedure for near-neutral systems due to the amount of correlation needed to be treated with configuration-interaction. / <p>Project made as part of the course: "Project in physics and astronomy - 1FA195, 15 ECTS" at Uppsala University</p>

Many-Body Perturbation Theory is put to test as a method for reliable calculations of the electron-electron interaction in two-dimensional quantum dots. We show that second order correlation gives qualitative agreement with experiments on a level which was not found within the Hartree-Fock description. For weaker confinements, the second order correction is shown to be insufficient and higher order contributions must be taken into account. We demonstrate that all order Many-Body Perturbation Theory in the form of the Coupled Cluster Singles and Doubles method yields very reliable results for confinements close to those estimated from experimental data. The possibility to use very large basis sets is shown to be a major advantage compared to Full Configuration Interaction approaches, especially for more than five confined electrons. Also, the possibility to utilize two-electron correlation in combination with tailor made potentials to achieve useful properties is explored. In the case of a two-dimensional quantum dot molecule we vary the interdot distance, and in the case of a two-dimensional quantum ring we vary the ring radius, in order to alter the spectra. In the latter case we demonstrate that correlation in combination with electromagnetic pulses can be used for the realization of quantum logical gates. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript.