This thesis presents a means of enhancing the iterative calculation techniques used in electronic structure calculations, particularly Kohn-Sham DFT. Based on the subspace iteration method of the FEAST eigenvalue solving algorithm, this nonlinear FEAST algorithm (NLFEAST) improves the convergence rate of traditional iterative methods and dramatically improves their robustness. A description of the algorithm is given, along with the results of numerical experiments that demonstrate its effectiveness and offer insight into the factors that determine how well it performs.

The phase behavior of chiral block copolymers (BCPs*), namely, BCPs with at least one of the constituent block is formed by chiral monomers, is studied both experimentally and theoretically. Specifically, the formation of a unique morphology with helical sense, the H* phase, where the chiral block forms nanohelices hexagonally embedded in the matrix of achiral block, is investigated. Such unique morphology was first observed in the cast film of polystyrene-b-poly(L-lactide) (PS-b-PLLA) from a neutral solvent dichloromethane at room temperature with all the nanohelices being left-handed, which would switch to right-handed if the PLLA block changes to PDLA. Further studies revealed that such morphology only forms when the chiral PLLA block possesses certain volume fraction (from 0.32 to 0.36), and the molecular weight exceeds certain critical value (around 20,000 to 25,000 g/mol). Achiral phases such as lamellae, gyroid, cylinder, and sphere will form if the above criteria are not satisfied. Even though the unique H* phase has been extensively studied and utilized for many applications, many fundamental and important questions remain unanswered for such BCP* system. Specifically, how does the molecular level chirality transfer from the several-angstrom scale of the lactide monomer to the tens-of-nanometer size scale of the H* domain morphology? Why is the chirality transfer not automatic for this BCP* system? Is H* phase a thermodynamic stable or metastable phase? Are there other novel phases other than the H* phase that could form within the BCP* system? We aimed at providing answers to the abovementioned questions regarding the formation of chiral H* phase, which is no longer limited to the PS-b-PLLA/PDLA system. We divided our studies into both experimental and theoretical parts. In the experiments, we studied the effect of solvent casting conditions, including solvent removal rate and polymer-solvent interactions, on the formation of the H* phase in PS-b-PLLA/PDLA BCPs*. In addition, we monitored the morphological evolution during solvent casting using time-resolved x-ray scattering technique. We found that good solubility towards both PS and PLLA/PDLA blocks are required for the formation of the H* phase, and microphase separation has to happen prior to crystallization of chiral block. Most importantly, we found that crystalline ordering is not necessary for the H* phase formation. This result led us to propose melt-state twisted molecular packing as the underlying driving force for such helical phase to form, and began our work on the theory for BCPs*. First we built the theoretical tool by incorporating the orientational segmental interactions into the self-consistent field theory (SCFT) for BCPs. As a demonstration, we constructed the phase diagrams for one-dimensional (1D) and two-dimensional (2D) phases, for achiral BCPs with different orientational stiffness. We found that orientational stiffness could serve as another parameter to introduce asymmetry into BCP systems, in addition to conformational and architectural asymmetry. This model was further applied to study the phase behavior of BCPs*, and two phase diagrams were constructed. Another chiral phase, wavy lamellae (L* phase), was observed for BCPs*. The H* phase was found to be a thermodynamic stable phase, as long as the segregation strength ����and chiral strength ��! exceed certain critical values. Energetically favorable cholesteric texture was observed for the chiral segment packing inside the H* phase, which is believed to drive such unusual morphology to form. A simple geometrical argument based on bending of cylindrical microdomain and twisted packing of the bended microdomain can be given to explain the nonlinear chiral sensitivity of BCP* morphology, which further explains the non-automatic feature of chirality transfer in such system.

<p>The phase behavior of AB diblock copolymers mixed with C homopolymers (AB/C), in which A and C are capable of forming hydrogen-bonds, is examined using self-consistent field theory. The study focuses on the modeling of hydrogen-bonding in polymers. Specifically, we examine two models for the formation of hydrogen-bonds between polymer chains. The first commonly used model assumes a large attractive interaction parameter between the A/C monomers. This model reproduces correct phase transition sequences as compared with experiments, but it fails to correctly describe the change of lamellar spacing induced by the addition of the C homopolymers. The second model is based on the fact that hydrogen-bonding leads to A/C complexation. We show that the interpolymer complexation model predicts correctly the order-order phase transition sequences and the decrease of lamellar spacing for strong hydrogen-bonding. Our analysis demonstrates that hydrogen-bonding of polymers should be modeled by interpolymer complexation.</p> / Master of Science (MSc)

Die Ladungsinjektion (-extraktion) an einer Schnittstelle spielt in der organischen Elektronik eine entscheidende Rolle, da sie die Leistung des Bauelements stark beeinflusst. Eine der effizientesten Methoden zur Optimierung der Energiebarrieren für die Injektion ist die Modifikation der Austrittsarbeit der Elektroden. In dieser Dissertation untersuchen wir die Modifikation der Austrittsarbeit von Au(111) durch dithiol-terminiertes Polyethylenglykol (PEG(thiol)) sowie deren Abhängigkeit von der Anzahl der PEG-Wiederholungseinheiten. In beiden Fällen beobachten wir, dass die Austrittsarbeit des Au(111) durch eine Monoschicht PEG(thiol)-Moleküle reduziert wird. Unsere Berechnungen zeigen, dass diese Änderung der Austrittsarbeit hauptsächlich durch (i) die Ladungsumlagerung aufgrund der Chemisorption und (ii) das intrinsische Dipolmoment der PEG(thiol)-Monoschicht verursacht wird. Die Größe des letzteren Beitrags hängt spürbar von der Anzahl der Wiederholungseinheiten ab und bewirkt somit eine Variation in der Reduktion der Austrittsarbeit. Das oszillatorische Verhalten spiegelt einen ausgeprägten Odd-Even-Effekt wider. Dadurch kann die Austrittsarbeit der Metallelektrode unter Berücksichtigung des Odd-Even-Effekts gesteuert werden. Die Konvergenz der selbstkonsistenten Felditeration für unsere Systeme ist nicht garantiert. Um die Konvergenz zu verbessern, schlagen wir die Verwendung eines speziell auf die FP-LAPW-Methode zugeschnittenen Mischalgorithmus vor. In einem auf Ag(111) basierenden System zeigt sich, dass eine Struktur mit drei Leerstellen in der Substratschicht besonders stabil ist. Dabei ist eine kontinuierliche Abnahme der Austrittsarbeit des Ag(111) feststellbar. Ähnlich wie beim Au(111) manifestiert sich der Odd-Even-Effekt, der auf das Dipolmoment der Molekularschicht zurückzuführen ist. / Charge injection (extraction) at an interface plays a crucial role to organic electronics because this injection (extraction) heavily affects the device performance. One of the most efficient way to optimize energy barriers of the injection (extraction) is modifying the work function of electrodes. In this dissertation, we investigate the modification of work function of Au(111) and Ag(111) induced by the dithiol-terminated polyethylene glycol (PEG(thiol)) as well as a dependence of the work function change on different numbers of PEG repeat units. We find that the work function of the Au(111) is reduced by a monolayer of PEG(thiol) molecules. Overall, our calculations indicate that the work function change is mainly induced by (i) the charge rearrangement due to chemisorption and (ii) the intrinsic dipole moment of the PEG(thiol) monolayer. The magnitude of the latter contribution noticeably depends on the number of repeat units and, thus, causes a variation in the reduction of the work function. The oscillatory behavior reflects a pronounced odd-even effect. As a result, the work function of the metal electrode would be controlled by considering the odd-even effect. Unfortunately, the convergence of the self-consistent field iteration is not guaranteed for our investigated systems. To make the smooth convergence, a mixing algorithm, which is applicable to FP-LAPW method, is devised. We add the Kerker preconditioner as well as further improvements to Pulay’s direct inversion in the iterative subspace. Using this method, one can avoid charge sloshing and noise in the exchange-correlation potential. This method is also implemented in the exciting code. We find the decrease of the work function of the Ag(111) surface is always presented. Similar to the Au(111) case, the odd-even effect is revealed, arising from the dipole moment of the molecular layer.

Dans la modélisation de la matière dense, et partiellement ionisée, une question importante concerne le traitement des électrons libres. Vis-à-vis des électrons liés, la nature délocalisée et non discrète de ces électrons est responsable d’une différence de traitement, qui est souvent effectuée dans les modélisations des propriétés radiatives des plasmas. Cependant, afin d’éviter les incohérences dans le calcul des spectres d’absorption, tous les électrons devraient, en principe, être décrits dans un même formalisme.Nous utilisons deux modèles variationnels d’atome-moyen : un modèle semi-classique, et un modèle quantique, qui permettent cette égalité de traitement pour tous les électrons. Nous calculons la section-efficace de photo-extinction, en appliquant le cadre de la théorie de la réponse linéaire dynamique à chacun de ces modèles d’atome dans un plasma. Pour cette étude, nous développons et utilisons une approche auto-cohérente, de type random-phase-approximation (RPA), qui, en allant au-delà de la réponse des électrons indépendants, permet d’évaluer les effets collectifs, par l’introduction de la polarisation dynamique. Cette approche s’inscrit dans le formalisme de la théorie de la fonctionnelle de la densité dépendant du temps (TDDFT), appliquée au cas d’un système atomique immergé dans un plasma.Pour les deux modèles, semi-classique et quantique, nous dérivons, et vérifions dans nos calculs, une nouvelle règle de somme, qui permet d’évaluer le dipôle atomique à partir d’un volume fini dans le plasma. Cette règle de somme s’avère être un outil de premier ordre pour le calcul des propriétés radiatives des atomes dans les plasmas denses. / In modeling dense and partially ionized matter, the treatment of the free electrons remains an important issue. Compared to bound electrons, the delocalized and non-discrete nature of these electrons is responsible to treat them differently, which is usually adopted in the modelings of radiative properties of plasmas. However, in order to avoid inconsistencies in the calculation of absorption spectra, all the electrons should be described in the same formalism.We use two variational average-atom models: a semi-classical and a quantum model, which allow this common treatment for all the electrons. We calculate the photo-extinction cross-section, by applying the framework of the linear dynamical response theory to each of these models of an atom in a plasma. For this study, we develop and use a self-consistent approach, of random-phase-approximation (RPA) type, which, while going beyond the independent electron response, permits to evaluate the collective effects by the introduction of the dynamical polarization. This approach uses the formalism of the time dependent density functional theory (TDDFT), applied in the case of an atomic system immersed in a plasma.For both models, semi-classical and quantum, we derive and verify in our calculations, a new sum rule, which allows the evaluation of the atomic dipole from a finite volume in the plasma. This sum rule turns out to be a crucial device in the calculation of radiative properties of atoms in dense plasmas.

L’auto-assemblage de macromolécules amphiphiles dans des solutions aqueuses est un mécanisme important sous-jacent à de nombreux processus présents dans les organismes vivants. La formation spontanée de structures auto-organisées de phospholipides et de biomacromolécules se produit en raison d'un équilibre délicat entre les forces d'attraction et de répulsion. Ces forces comprennent l'attraction hydrophobe, la liaison hydrogène, les forces de coordination des métaux et la répulsion stérique ou électrostatique. En outre, l'auto-assemblage de molécules amphiphiles synthétiques est largement utilisé dans divers domaines technologiques. Un exemple frappant est celui des surfactants de faible poids moléculaire qui peuvent modifier de manière significative les propriétés des systèmes. Les autres domaines importants dans lesquels les tensioactifs et les macromolécules amphiphiles sont activement utilisés sont la cosmétologie et l'hygiène. Cependant, l'utilisation de structures auto-organisatrices de macromolécules amphiphiles nécessite une étude approfondie et soulève quelques questions pour les chercheurs concernant leur structure, leur comportement sous l'influence de facteurs externes et leur stabilité. L'objectif principal de la thèse était de développer une théorie de champ analytique auto-cohérente de l'auto-organisation dans des solutions de copolymères de déblocage non ioniques linéaires dendritiques et dendritiques doubles dans des solvants sélectifs. Cette théorie nous permet de prédire comment la dendronisation d'un ou des deux blocs affecte les propriétés structurelles et thermodynamiques d'assemblages auto-organisés formés par des copolymères. Il a été démontré que la dendronisation des corona bloc permet d’obtenir les micelles stables de taille relativement petite, mais avec de nombreux groupes terminaux. Cette dernière caractéristique est particulièrement intéressante dans le contexte de la liberation contrôlée, puisque les groupes terminaux exposés à l'environnement peuvent être facilement fonctionnalisés par des groupes de ligands pouvant être ciblés. Ces deux caractéristiques peuvent être obtenues simultanément car la dendronisation des corona bloc réduit le nombre d'agrégation à l'équilibre et les dimensions globales des micelles par rapport aux micelles formées par des molécules de copolymères diblocs linéaires homologues tout en conservant un grand nombre de groupes terminaux par micelle. La dendronisation du bloc insoluble peut être utilisée pour augmenter le nombre d'unités monomères terminales dans le core. Nous avons également démontré que la dendronisation des blocs solubles favorise la formation de micelles sphériques, alors que les gammes de stabilité thermodynamique des micelles cylindriques et des dendrimersomes sont déplacées vers un degré plus élevé de polymérisation des séquences insolubles. Au contraire, la dendronisation du bloc insoluble a l'effet inverse et conduit à un élargissement des gammes de stabilité des polymeres et des micelles cylindriques.Nous avons étudié les effets de l'extensibilité finie dans les brosses polyélectrolytes à chaîne linéaire et à dendron contenant des groupes ioniques. Nous avons développé la théorie analytique des brosses polyélectrolytiques dans l'approximation de Poisson-Boltzmann qui explique explicitement l'extensibilité finie des chaînes de polyélectrolytes formant des brosses. Il a été montré que pour la même série de paramètres de la brosse, la théorie basée sur l’élasticité non linéaire des polyions prédit une épaisseur de la brosse plus faible et une plus grande amplitude du saut de la densité du polymère au bord du pinceau. Les connaissances obtenues fourniront une base rationnelle pour la conception moléculaire de nouveaux copolymères à blocs complexes sur le plan architectural, y compris ceux destinés à des applications médicales. / An important mechanism underlying many processes occurring in living organisms is self-assembly of amphiphilic (macro)molecules in aqueous solutions. Spontaneous formation of self-organized structures of phospholipids and biomacromolecules occurs because of a delicate balance between attraction and repulsion forces. Such forces include hydrophobic attraction, hydrogen bonding, metal coordination forces and steric or electrostatic repulsion.In addition, self-assembly of synthetic amphiphilic molecules is widely used in various technical fields. A striking example are low molecular weight surfactants (small amphiphilic molecules) that can significantly change the properties of systems. Other important areas in which surfactants and amphiphilic macromolecules are actively used are cosmetology and hygiene. However, the use of self-organizing structures of amphiphilic macromolecules requires detailed study and raises a few questions for researchers regarding their structure, behavior under the influence of external factors and their stability.The main goal of the present work was development of the theory of self-assembly of diblock copolymers where one or both of blocks (soluble or/and insoluble) exhibit dendritic branching and established relations between degree of branching of the block(s) and structural properties (size, shape, aggregation number) of the self-assembled aggregates.The major focus of the thesis was on developing an analytical self-consistent field theory of self-organization in solutions of non-ionic linear-dendritic and double-dendritic deblock copolymers in selective solvents. This theory enables us to predict how dendronization of one or both blocks affects structural and thermodynamic properties of self-organized assemblies formed by copolymers. It was demonstrated that dendronisation of the corona blocks allows obtaining the stable micelles of relatively small size, but with many terminal groups.The latter feature is most attractive in the context of controlled delivery, since the exposed to the environment terminal groups can be readily functionalized by targetable ligand groups. Both these features can simultaneously be achieved because dendronization of the corona blocks reduces the equilibrium aggregation number and overall dimensions of micelles compared to micelles formed by homologous linear-linear diblock copolymer molecules while keeping large number of terminal groups per micelle. Dendronization of the insoluble block may be used for increasing of the number of terminal monomer units in the core. Such terminal groups can be further functionalized to be able to interact with active drugs, thereby increasing the loading capacity of the micelle.We have also demonstrated that dendronization of the soluble blocks favors formation of spherical micelles, whereas the ranges of thermodynamic stability of cylindrical wormlike micelles and dendrimersomes are shifted to larger degree of polymerisation of the insoluble blocks. On the contrary, dendronization of the insoluble block has the opposite effect and leads to widening of the stability ranges of polymersomes and cylindrical micelles.We investigated effects of finite extensibility (non-linear elasticity) in linear chain and dendron polyelectrolyte brushes containing ionic groups. We developed the analytical theory of polyelectrolyte brushes within the Poisson-Boltzmann approximation which explicitly accounts for finite extensibility of the brush-forming polyelectrolyte chains. It was shown that for the same set of the brush parameters the theory based on non-linear elasticity of the polyions predicts smaller thickness of the brush and larger magnitude of the jump in polymer density at the edge of the brush.The obtained knowledge will provide a rational background for molecular design of novel architecturally complex block copolymers, including those for medical applications.

Cette thèse est consacrée à l'étude ab initio des structures électroniques des molécules diatomiques polaires YN, YS, ZrN, et ZrS. Cette étude est motivé par le manque d’informations dans la littérature sur la structure électronique de ces molécules, alors qu’elles ont clairement été identifiées dans le spectre de certaines étoiles. Des calculs théoriques sont ainsi nécessaire puisqu’ils peuvent fournir d'importantes informations quant aux propriétés des états électroniques fondamentaux et excités qui ne sont pas accessibles expérimentalement. Dans ce travail les calculs ab initio ont été effectués par la méthode du champ auto-cohérent de l'espace actif complet (CASSCF), suivie par l'interaction de configuration multiréférence (MRSDCI). La correction de Davidson, notée (MRSDCI+ Q), a ensuite été appliquée pour rendre compte de clusters ou agrégats quadruples non liés. Les calculs ont été effectués selon deux schémas. Dans le premier les effets spin-orbite ont été négligés alors que dans le second les effets spin orbite ont été inclus par la méthode des potentiels de noyau efficaces. Tous les calculs ont été effectués en utilisant le programme de calcul de chimie physique MOLPRO et en tirant parti de l’interface graphique Gabedit. Les courbes d'énergie potentielle ont été construites et des constantes spectroscopiques calculées, ainsi que les moments dipolaires électriques permanent, les champs électriques moléculaires intenses et les structures énergétiques de vibration-rotation. Nous avons détecté dans la molécule ZrS plusieurs niveaux vibrationnels dégénérés ceux-ci peuvent être utilisés pour rechercher les variantes possibles de la constante de structure fine α etdu rapport de masse μ de l’electron par rapport au proton dans trois étoiles de type S, du nomde Rand, les RCas, et χCyg. La comparaison des données expérimentales et théoriques pour la plupart des constantes calculées a montré une bonne précision pour nos prédictions avec une différence relative (en pourcentage) qui varie entre 0,1% et 10%. Ces résultats devraient ainsi mener à des études expérimentales plus poussées pour ces molécules. / This dissertation is dedicated to the ab initio study of the electronic structures of the polardiatomic molecules YN, YS, ZrN, and ZrS. The identification of these molecules in the spectraof stars as well as the lack in literature on the electronic structures of these molecules motivatedthe present study. Theoretical calculations are useful in this respect since they can provideimportant data for the properties of the ground and excited electronic states that are not availablefrom experimental means. In the present work the ab initio calculations were performed at thecomplete active space self-consistent field method (CASSCF) followed by multireference singleand double configuration interaction method (MRSDCI). The Davidson correction noted as(MRSDCI+Q) was then invoked in order to account for unlinked quadruple clusters. Thecalculations were performed on two stages in the first spin orbit effects were neglected while inthe second type of calculations spin orbit effects were included by the method of effective corepotentials. All of the calculations were done by using the computational physical chemistryprogram MOLPRO and by taking advantage of the graphical user interface Gabedit. In thepresent work potential energy curves were constructed and spectroscopic constants computed,along with permanent electric dipole moments, internal molecular electric fields, and vibrationalrotationalenergy structures. We detected in the ZrS molecule several degenerate vibrationalenergy levels which can be used to search for possible variations of the fine structure constant αand the electron to proton mass ratio μ in three S-type stars, named Rand, RCas, and χCyg. Acomparison with experimental and theoretical data for most of the calculated constantsdemonstrated a good accuracy for our predictions giving a percentage relative difference thatranged between 0.1% and 10%. Finally, we expect that the results of the present work shouldinvoke further experimental investigations for these molecules.

This work describes theoretical studies on molecular and electronic structures of lanthanide-based single-molecule magnets focusing on their magnetic properties. In this work, two main problems are covered: the structural ordering of endohedral fullerenes in different supramolecular arrangements, and the magnetic anisotropy of lanthanides in different charge coordinations. The basic methodes used in this work are density functional theory and multiconfigurational self-consistent field.:CHAPTER 1. THEORETICAL FOUNDATIONS OF RARE-EARTH MAGNETISM 12 1.1. Single-molecule magnetism and 4f-elements 14 1.1.1. Electronic structure of 4f-elements 16 1.1.2. LS-coupling scheme 19 1.1.3. Parameterization of the Crystal-Field splitting effect. 20 1.1.4. Zeeman splitting for a free ion 24 1.1.5. Spin Hamiltonian and pseudospin approximation 24 1.1.6. Kramers theorem 25 1.1.7. Weak and strong molecular interactions. 26 1.2. Computational methods in application to Ln-based SMMs 27 1.2.1. Density functional theory (DFT). 28 1.2.2. Multiconfigurational methods in quantum chemistry 33 1.3. Role of molecular structure in single-molecular magnetism 41 1.3.1. Complexes of SMMs with organic molecules 45 1.3.2. SMMs deposited on surfaces 46 CHAPTER 2. STRUCTURAL ORDERING IN COCRYSTALS OF EMFs AND Ni(OEP) 49 2.1. Ordering in endohedral metallofullerenes 49 2.2. Modeling details 51 2.3. Conformer analysis 54 2.4. Electrostatic potential 58 CHAPTER 3. ISOMERISM OF Dy2ScN@C80 DEPOSITED ON SURFACES 61 3.1. Modeling details 62 3.2. Cluster conformation analysis 69 3.3. Charge density analysis 75 CHAPTER 4. Ho|MgO AS A SINGLE-ATOMIC MAGNET. FV-MAGNETISM. 80 4.1. DFT description of Ln|MgO 85 4.2. Ho|MgO system: ab initio calculations 92 4.3. Magnetic properties of lanthanides with FV magnetism 99 4.4. Generalized ligand field and spin Hamiltonians for FV systems. 101 CHAPTER 5. FV-MAGNETISM IN [Ln2+] METALLOCENE COMPLEXES 107 5.1. TbII(CpiPr5)2 DFT-model 108 5.2. FV-interaction in terms of ab initio multiconfigurational approach 113 5.3. Point-charge model 115

Unravelling details of charge, structure and molecular interactions of functional polymer coatings defines an important analytical challenge that requires the extension of current methodologies. In this article we demonstrate how streaming current measurements interpreted with combined self consistent field (SCF) and soft surface electrokinetic theories allow the evaluation of the segment distribution within poly(ethylene oxide) (PEO) brushes beyond the resolution limits of neutron reflectivity technique.