This thesis concerns quadratic response properties and their application to properties in Jablonski diagrams such as resonant two-photon absorption and excited state absorption. Our main interest lies in optical power limiting applications, and in this context, molecules containing heavy metal atoms prove superior. Therefore, we are interested in how relativity affects these properties, and in order to assess this, a four-component relativistic framework is adopted. To properly address the molecular properties of interest, both relativistic effects and electron correlation need to be accounted for. These two properties are not additive, and, therefore, correlation needs to be incorporated into the four-component framework. We present the implementation of quadratic response properties at the four-component density functional level of theory. For second-harmonic generation, we have, with numerical examples, demonstrated that correlation and relativity are indeed not additive and that the inclusion of noncollinear magnetization is of little importance. We report that both electron correlation as well as relativity strongly affect results for second-harmonic generation. For example, relativity alone reduces the µβ-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. In the four-component framework, we present the implementations of single and double residues of the quadratic response function, which allows for the evaluation of resonant two-photon absorption cross sections and excited state properties. Using these tools, we discuss different levels of approximation to the relativistic Hamiltonian and we demonstrate that for two-photon absorption, a proper treatment of relativistic effects qualitatively alters the spectrum. For example, already for an element as light as neon, significant differences are seen between the relativistic and nonrelativistic spectra as triplet transitions acquire substantial absorption cross sections in the former case. Finally, quantum mechanics in conjunction with electrodynamics is applied to determine clamping levels in macroscopic samples. The microscopic properties of the optically active chromophores are determined by response theory, and then, electrodynamics is used to describe the interactions between the chromophores and incident laser pulses. Using this approach a series of molecules have been investigated and their performances have been compared and ranked in order to find novel materials for optical power limiting applications.

This thesis concerns methods of reduced complexity for electronic structure calculations.  When quantum chemistry methods are applied to large systems, it is important to optimally use computer resources and only store data and perform operations that contribute to the overall accuracy. At the same time, precarious approximations could jeopardize the reliability of the whole calculation.  In this thesis, the self-consistent field method is seen as a sequence of rotations of the occupied subspace. Errors coming from computational approximations are characterized as erroneous rotations of this subspace. This viewpoint is optimal in the sense that the occupied subspace uniquely defines the electron density. Errors should be measured by their impact on the overall accuracy instead of by their constituent parts. With this point of view, a mathematical framework for control of errors in Hartree-Fock/Kohn-Sham calculations is proposed.  A unifying framework is of particular importance when computational approximations are introduced to efficiently handle large systems. An important operation in Hartree-Fock/Kohn-Sham calculations is the calculation of the density matrix for a given Fock/Kohn-Sham matrix. In this thesis, density matrix purification is used to compute the density matrix with time and memory usage increasing only linearly with system size. The forward error of purification is analyzed and schemes to control the forward error are proposed. The presented purification methods are coupled with effective methods to compute interior eigenvalues of the Fock/Kohn-Sham matrix also proposed in this thesis.New methods for inverse factorizations of Hermitian positive definite matrices that can be used for congruence transformations of the Fock/Kohn-Sham and density matrices are suggested as well. Most of the methods above have been implemented in the Ergo quantum chemistry program. This program uses a hierarchic sparse matrix library, also presented in this thesis, which is parallelized for shared memory computer architectures. It is demonstrated that the Ergo program is able to perform linear scaling Hartree-Fock calculations. / QC 20100908

We consider a system of few electrons trapped in a two-dimensional circularquantum dot with harmonic confinement and in the presence of ahomogeneous magnetic field, with focus on the role of e-e interaction. Byperforming the exact diagonalization of the Hamiltonian in second quantization,the low-lying energy levels for spin polarized system are obtained. The singlet-triplet oscillation in the ground state of the two-electron system showing up inthe result is explained due to the role of Coulomb interaction. The splitting ofthe lowest Landau level is another effect of the e-e interaction, which is alsoobserved in the results.

L'appariement est une composante indispensable à la description des noyaux atomiques. Ses effets sur les propriétés statiques du noyau sont à présent bien connus. Dans ce mémoire, l'effet de l'appariement sur la dynamique nucléaire est étudié. Différentes théories qui incluent l'appariement sont comparées dans un cas modèle. La théorie TDHF+BCS qui apparaît comme un bon compromis entre la richesse de la physique qu'elle contient et son coût numérique est retenue pour les applications aux noyaux. L'introduction de l'appariement dans cette approximation pose de nouveaux problémes liés à (1) la brisure de la symétrie associée au nombre de particules, (2) la non-conservation de l'équation de continuité. Ces difficultés sont analysées en détail et des solutions pratiques sont proposées. Dans cette thèse, un programme TDHF+BCS en 3 dimensions permettant de simuler la dynamique des noyaux a été d'eveloppé. L'application de cette théorie aux résonances géantes a montré que l'appariement n'affecte que les états excités de basse énergie. La composante collective de haute énergie n'étant modifiée que par les conditions initiales. Une étude complète des résonances géantes quadrupolaires a été réalisée pour plus de 700 noyaux sphériques ou déformés. Un bon accord est alors trouvé avec les données expérimentales pour l'énergie collective de la résonance. Cette théorie a ensuite été appliquée à l'étude des réactions de transfert de nucléons lors des collisions noyau-noyau. Une nouvelle méthode de détermination des probabilités de transfert est proposée. Il est montré que l'appariement augmente de manière significative les probabilités de transférer deux nucléons.

Grâce à l'amélioration des performances des outils expérimentaux et numériques, la mécanique des matériaux peut explorer des échelles de plus en plus fines. Une meilleure compréhension, voire une prédiction, des phénomènes locaux mis en jeu est alors espérée. Cette thèse s'intéresse à la plus petite échelle impliquée dans le comportement mécanique des matériaux, c.-à-d. les interactions entre noyaux dues au comportement des électrons, et notamment des électrons de valence. L'originalité de ce travail est dans la mise en place des éléments finis comme outil numérique de résolution de ce problème. Cette approche largement utilisée dans le domaine de la mécanique des structures fournit de puissants outils numériques permettant de résoudre le problème électronique. Des modèles de Hartree-Fock et post-Hatree-Fock sont implémentés, et les caractéristiques mécaniques des structures électroniques sont estimées. Ces résultats reposent sur de nombreuses approximations dues aussi bien à la modélisation qu'aux approximations numériques. Des estimateurs d'erreur sont développés pour analyser les résultats.

The multiconfiguration time-dependent Hartree-Fock (MCTDHF) and multiconfiguration time-dependent Hartree (MCTDH) methods are employed to investigate nonperturbative multielectron dynamics in finite quantum systems. MCTDHF is a powerful tool that allows for the investigation of multielectron dynamics in strongly perturbed quantum systems. We have developed an MCTDHF code that is capable of treating problems involving three dimensional (3D) atoms and molecules exposed to strong laser fields. This code will allow for the theoretical treatment of multielectron phenomena in attosecond science that were previously inaccessible. These problems include complex ionization processes in pump-probe experiments on noble gas atoms, the nonlinear effects that have been observed in Ne atoms in the presence of an x-ray free-electron laser (XFEL) and the molecular rearrangement of cations after ionization. An implementation of MCTDH that is optimized for two electrons, each moving in two dimensions (2D), is also presented. This implementation of MCTDH allows for the efficient treatment of 2D spin-free systems involving two electrons; however, it does not scale well to 3D or to systems containing more that two electrons. Both MCTDHF and MCTDH were used to treat 2D problems in nanophysics and attosecond science. MCTDHF is used to investigate plasmon dynamics and the quantum breathing mode for several electrons in finite lateral quantum dots. MCTDHF is also used to study the effects of manipulating the potential of a double lateral quantum dot containing two electrons; applications to quantum computing are discussed. MCTDH is used to examine a diatomic model molecular system exposed to a strong laser field; nonsequential double ionization and high harmonic generation are studied and new processes identified and explained. An implementation of MCTDHF is developed for nonuniform tensor product grids; this will allow for the full 3D implementation of MCTDHF and will provide a means to investigate a wide variety of problems that cannot be currently treated by any other method. Finally, the time it takes for an electron to tunnel from a bound state is investigated; a definition of the tunnel time is established and the Keldysh time is connected to the wavefunction dynamics.

Understanding the complexities of the interior of planets and stars requires the help of analyzing the effects of high pressures on certain elements believed to be found within. The Hartree-Fock method uses the Schr¨odinger equation, Kummer’s differential equations and a confinement potential to simulate an atom being squeezed to high pressures. The Hartree-Fock method was used to calculate the total energies of atoms. After being compared to Gaussian03 and VASP, the results were deemed accurate. It was also observed that the pressure versus density data closely approximated those pairs found in outer space in the interiors of, for example, Jupiter.

Quand les effets de la masse finie du noyau et de la distribution de charge spatiale sont pris en compte dans l’Hamiltonien décrivant un système atomique, les isotopes d’un élément, caractérisés par le même nombre de protons mais un nombre différent de neutrons, ont des niveaux d’énergie électronique différents. Le déplacement entre les niveaux d’énergie (pour un même état quantique) de deux isotopes différents est appelé le déplacement isotopique de niveau. De manière générale, on peut distinguer les déplacements isotopiques de champ (field shift) et les déplacements isotopiques de masse (mass shift). Pour les systèmes à plus d’un électron, le specific mass shift (SMS) apparaît. Grâce à sa faible pondération, le paramètre SMS peut être traité comme une perturbation de l’Hamiltonien ;son estimation fait appel aux intégrales de Vinti [5].<p>Dans un contexte relativiste, les programmes grasp2K [2] et mcdf-gme [1] permettent de résoudre les équations de Dirac-Fock associées à un état multiconfigurationnel et d’en fournir l’énergie ainsi que la représentation numérique des orbitales monoélectroniques. Nous avons créé et introduit dans le programme mcdf-gme une sous-routine capable d’estimer les paramètres de masse et de champ à partir des fonctions d’onde multiconfigurationnelles. Pour le programme GRASP2K, un module indépendant à été créé. <p>Par ailleurs, un opérateur plus complet impliquant des corrections en αZ, a été dérivé par Shabaev [4] et, de manière indépendante, par Palmer [3]. Nous avons déduit la forme tensorielle de cet opérateur et avons également implémenté dans les programmes cités ci-dessus le calcul de ses éléments de matrice.<p>Grâce à ces outils nous avons pu étudier la détérioration de l’opérateur d’énergie cinétique pour estimer le normal mass shift et travailler divers systèmes comme le lithium neutre et sa séquence isoélectronique. Par la suite nous avons également travaillé sur les séquences isoélectroniques du bore, du béryllium, du carbone et de l’azote. Enfin, certains effets isotopiques ont été étudiés pour plusieurs transitions dans le baryum neutre.<p>Bibliographie<p>[1] J. P. Desclaux. A relativistic multiconfiguration Dirac-Fock package. In E. Clementi, editor, Methods and Techniques in Computational Chemistry - vol. A :Small Systems of METTEC, page 253. STEF, Cagliari, 1993.<p>[2] P. Jönsson, X. He, C. Froese Fischer and I. P. Grant. The GRASP2K relativistic atomic structure package. Comput. Phys. Commun. 177 :597–622, 2007.<p>[3] C. W. P. Palmer. Reformulation of the theory of the mass shift. J. Phys. B :At. Mol. Phys. 20 :5987–5996, 1987.<p>[4] V. M. Shabaev and A. N. Artemyev. Relativistic nuclear recoil corrections to the energy levels of multicharged ions. J. Phys. B :At. Mol. Phys. 27 :1307–1314, 1994.<p>[5] J. P. Vinti. Isotope shift in magnesium. Phys. Rev. 56 :1120–1132, 1939. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

The multiconfiguration time-dependent Hartree-Fock (MCTDHF) and multiconfiguration time-dependent Hartree (MCTDH) methods are employed to investigate nonperturbative multielectron dynamics in finite quantum systems. MCTDHF is a powerful tool that allows for the investigation of multielectron dynamics in strongly perturbed quantum systems. We have developed an MCTDHF code that is capable of treating problems involving three dimensional (3D) atoms and molecules exposed to strong laser fields. This code will allow for the theoretical treatment of multielectron phenomena in attosecond science that were previously inaccessible. These problems include complex ionization processes in pump-probe experiments on noble gas atoms, the nonlinear effects that have been observed in Ne atoms in the presence of an x-ray free-electron laser (XFEL) and the molecular rearrangement of cations after ionization. An implementation of MCTDH that is optimized for two electrons, each moving in two dimensions (2D), is also presented. This implementation of MCTDH allows for the efficient treatment of 2D spin-free systems involving two electrons; however, it does not scale well to 3D or to systems containing more that two electrons. Both MCTDHF and MCTDH were used to treat 2D problems in nanophysics and attosecond science. MCTDHF is used to investigate plasmon dynamics and the quantum breathing mode for several electrons in finite lateral quantum dots. MCTDHF is also used to study the effects of manipulating the potential of a double lateral quantum dot containing two electrons; applications to quantum computing are discussed. MCTDH is used to examine a diatomic model molecular system exposed to a strong laser field; nonsequential double ionization and high harmonic generation are studied and new processes identified and explained. An implementation of MCTDHF is developed for nonuniform tensor product grids; this will allow for the full 3D implementation of MCTDHF and will provide a means to investigate a wide variety of problems that cannot be currently treated by any other method. Finally, the time it takes for an electron to tunnel from a bound state is investigated; a definition of the tunnel time is established and the Keldysh time is connected to the wavefunction dynamics.

V této práci je prezentována studie fragmentačního procesu zvolené molekuly a jeho vztah ke složení fragmentačních produktů. Práce je zaměřená na výpočet fragmentační energie molekuly pomocí ab initio kvantově chemických metod, metodou „density functional theory (DFT)“ a také srovnáním s experimentem. Je prezentován vliv výpočetní metody, bázového setu, a geometrie molekuly na simulaci. Byla porovnána fragmentace methylfenylsilanu (MPS), dimethylfenylsilanu (DMPS), a trimetylfenylsilanu (TMPS). Fragmentace byla iniciována monochromatickým elektronovým svazkem (EII). Hmotnostní spektrometrie byla využita ke studiu složení fragmentačních produktů MPS a TMPS. Fragmentační produkty MPS a TMPS měřené v rámci této práce byly doplněny o experimentální studii DMPS, která byla prezentována v literatuře. Takto byla získána řada molekul, které jsou strukturně podobné, ale mají výrazně rozdílné chování během fragmentace. Pomocí měření účinného průřezu byly měřeny disociační energie vazeb a tyto disociační energie byly vypočteny pomocí metody DFT. Kombinací teoretického výpočtu metodou DFT a experimentálního měření jsme poukázali na společné rysy a na rozdíly ve fragmentačním schématu všech tří molekul. Navrhli jsme odštěpení dvou vodíkových atomů během plazmově indukovaného fragmentačního procesu. Vodíky mohou být odštěpeny pomocí dvou mechanismů: i. odštěpení dvou vodíků jeden po druhém a ii. odštěpení molekuly H2 v jednom kroku. Z profilů energie dokážeme určit, který mechanismus bude v tom konkrétním případě pravděpodobnější. Předpokládaný mechanismus je v korelaci s experimentálními výsledky fragmentace zjištěnými z hmotnostních spekter.