This dissertation deals with the calculation of the mechanical properties, electronic structure, electronic transport, and optical properties of strained carbon nanotubes (CNTs). CNTs are discussed for straintronics as their electronic bands show a strong strain-sensitivity. Further, CNTs are stiff, possess a large rupture strain and they are chemically inert, which make them a suitable material in terms of reliability and functionality for straintronic devices. Therefore, this work aims to explore the potential of strain-dependent CNT devices with regard to their mechanical, electronic, and optical properties from a first-principles point of view. There is no work so far that systematically compares these strain-dependent, physical properties from ab initio calculations, which are suitable for small CNTs only, to tight-binding calculations, which are suitable to model large CNTs. First, the structural and mechanical properties of CNTs are investigated: Structural properties are obtained by geometry optimization of many CNTs using density functional theory (DFT). The mechanical properties of CNTs are calculated in the same way. The resulting stress-strain relations are investigated and their key parameters are systematically displayed with respect to the CNT chirality and radius. The ground state electronic properties are calculated using tight-binding models and DFT. Both methods are compared systematically and it is explored where the tight-binding approximation can be applied in order to obtain meaningful results. On top of the electronic structure, a transport model is used to calculate the current through strained CNTs. The model includes the effect of ballistic conductance, parametrized electron-phonon scattering and the influence of an applied gate voltage. Finally, a computationally efficient model is described, which is able to predict the current through strained CNT transistors and enables to find optimal operation regimes for single-chirality devices and devices containing CNT mixtures. Optical properties of strained CNTs are explored by calculating quasiparticle excitations by the means of the GW approximation and the solution of the Bethe-Salpeter equation for CNT excitons. Due to the numerical effort of these approaches, the data for just one CNT is obtained. Still, it is explored how the above-mentioned many-body properties can be related to the ground state results for this CNT. This finally leads to empirical approaches that approximately describe the many-body results from the ground state properties. It is elucidated how such a model can be generalized to other CNTs in order to describe the strain dependence of their optical transitions. / Diese Dissertation befasst sich mit der Berechnung der mechanischen Eigenschaften, der elektronischen Struktur, der Transport- und der optischen Eigenschaften von verspannten Kohlenstoffnanoröhrchen (engl. carbon nanotubes, CNTs). CNTs werden für die Straintronik diskutiert, da ihre elektronischen Bänder eine starke Dehnungsempfindlichkeit aufweisen. Weiterhin sind CNTs steif, besitzen eine hohe Zugfestigkeit und sind chemisch inert, weshalb sie in Bezug auf Zuverlässigkeit und Funktionalität ein geeignetes Material für straintronische Bauelemente sind. Ziel dieser Arbeit ist es daher, das Potenzial von dehnungsabhängigen CNT-Bauteilen hinsichtlich ihrer mechanischen, elektronischen und optischen Eigenschaften aus der Perspektive von first principles-Methoden zu untersuchen. Es gibt bisher keine Arbeit, in der die Ergebnisse verschiedener Methoden – ab initio-basierte Berechnungen für kleine CNTs und tight-binding Berechnungen, die näherungsweise die elektronische Struktur großer CNTs beschreiben – miteinander systematisch vergleicht. Einführend werden die strukturellen und mechanischen Eigenschaften von CNTs untersucht: Strukturelle Eigenschaften ergeben sich durch Geometrieoptimierung vieler CNTs mittels Dichtefunktionaltheorie (DFT). Die mechanischen Eigenschaften von CNTs werden in gleicher Weise berechnet. Die daraus resultierenden Spannungs-Dehnungs-Beziehungen werden untersucht und deren relevante Parameter systematisch in Abhängigkeit von CNT-Chiralität und CNT-Radius dargestellt. Die Eigenschaften des CNT-Grundzustands werden unter Verwendung von tight-binding-Modellen und DFT berechnet. Beide Methoden werden systematisch verglichen und es wird untersucht, wo die tight-binding-Näherung angewendet werden kann, um aussagekräftige Ergebnisse zu erzielen. Basierend auf der elektronischen Struktur der CNTs wird ein Transportmodell aufgesetzt, durch das der Strom durch verspannte CNTs berechnet werden kann. Dieses Modell beinhaltet den Einfluss der ballistischen Leitfähigkeit, Elektron-Phonon-Streuung in parametrisierter Form und den Einfluss eines Gates. Damit wird ein numerisch effizientes Modell beschrieben, das in der Lage ist, den Strom durch verspannte CNT-Transistoren vorherzusagen. Auf dessen Basis wird es möglich, optimale Arbeitsbereiche für reine CNT-Bauelemente und Bauelemente mit CNT-Mischungen zu berechnen. Die optischen Eigenschaften verspannter CNTs werden durch die Berechnung von Quasiteilchenanregungen mittels der GW-Approximation und der Lösung der Bethe-Salpeter-Gleichung für CNT-Exzitonen untersucht. Aufgrund des numerischen Aufwandes dieser Ansätze werden diese Daten für nur ein CNT erhalten. Daran wird der Zusammenhang zwischen den oben genannten Vielteilchen-Eigenschaften und den Grundzustandseigenschaften für dieses CNT demonstriert. Daraus ergeben sich empirische Ansätze, die es gestatten, die Vielteilchen-Ergebnisse näherungsweise auf die elektronischen Grundzustandseigenschaften zurückzuführen. Es wird dargestellt, wie ein solches Modell für andere CNTs verallgemeinert werden kann, um die Verspannungsabhängigkeit ihrer optischen Übergänge zu beschreiben.

This work presents applications of an ab-initio molecular dynamics method, the so-called nonadiabatic quantum molecular dynamics (NA-QMD), for various molecular systems with many electronic and nuclear degrees of freedom. Thereby, the nuclei will be treated classically and the electrons with time-dependent density functional theory (TD-DFT) in basis expansion. Depending on the actual system and physical process, well suited basis sets for the Kohn-Sham orbitals has to be chosen. For the ionization process a novel absorber acting in the energy space as well as additional basis functions will be used depending on the laser frequency. In the first part of the applications, a large variety of different laser-induced molecular processes will be investigated. This concerns, the orientation dependence of the ionization of multielectronic diatomics (N2, O2), the isomerization of organic molecules (N2H2) and the giant excitation of the breathing mode in fullerenes (C60). In the second part, fullerene-fullerene collisions are investigated, for the first time in the whole range of relevant impact velocities concerning the vibrational and electronic energy transfer (\"stopping~power\"). For low energetic (adiabatic) collisions, it is surprisingly found, that a two-dimensional, phenomenological collision model can reproduce (even quantitatively) the basic features of fusion and scattering observed in the fully microscopic calculations as well as in the experiment. For high energetic (nonadiabatic) collisions, the electronic and vibrational excitation regimes are predicted, leading to multifragmentation up to complete atomization.

In our pursuit of ever smaller transistors, with greater computational throughput, many questions arise about how material properties change with size, and how these properties may be modelled more accurately. Metallic nanocontacts, especially those for which magnetic properties are important, are of great interest due to their potential spintronic applications. Yet, serious challenges remain from the standpoint of theoretical and computational modelling, particularly with respect to the coupling of the spin and lattice degrees of freedom in ferromagnetic nanocontacts in emerging spintronic technologies. In this thesis, an extended method is developed, and applied for the first time, to model the interplay between magnetism and atomic structure in transition metal nanocontacts. The dynamic evolution of the model contacts emulates the experimental approaches used in scanning tunnelling microscopy and mechanically controllable break junctions, and is realised in this work by classical molecular dynamics and, for the first time, spin-lattice dynamics. The electronic structure of the model contacts is calculated via plane-wave and local-atomic orbital density functional theory, at the scalar- and vector-relativistic level of sophistication. The effects of scalar-relativistic and/or spin-orbit coupling on a number of emergent properties exhibited by transition metal nanocontacts, in experimental measurements of conductance, are elucidated by non-equilibrium Green’s Function quantum transport calculations. The impact of relativistic effects during contact formation in non-magnetic gold is quantified, and it is found that scalar-relativistic effects enhance the force of attraction between gold atoms much more than between between atoms which do not have significant relativistic effects, such as silver atoms. The role of non-collinear magnetism in the electronic transport of iron and nickel nanocontacts is clarified, and it is found that the most-likely conductance values reported for these metals, at first- and lastcontact, are determined by geometrical factors, such as the degree of covalent bonding in iron, and the preference of a certain crystallographic orientation in nickel. / Physics / Ph. D. (Physics)

Die fortschreitenden Entwicklungen in der Mikro- und Nanotechnologie erfordern eine solide Unterstützung durch Simulationen. Numerische Bauelementesimulationen waren und sind dabei unerlässliche Werkzeuge, die jedoch zunehmend an ihre Grenzen kommen. So basieren sie auf Parametern, die für beliebige Atomanordnungen nicht verfügbar sind, und scheitern für stark verkleinerte Strukturen infolge zunehmender Relevanz von Quanteneffekten. Diese Arbeit behandelt den Transport in Siliziumnanodrähten sowie durch NiSi2-Si-Grenzflächen. Dichtefunktionaltheorie wird dabei verwendet, um die stabile Atomanordnung und alle für den elektronischen Transport relevanten quantenmechanischen Effekte zu beschreiben. Bei der Untersuchung der Nanodrähte liegt das Hauptaugenmerk auf der radialen Abhängigkeit der elektronischen Struktur sowie deren Änderung bei Variation des Durchmessers. Dabei zeigt sich, dass der Kern der Nanodrähte für den Ladungstransport bestimmend ist. Weiterhin kann ein Durchmesser von ungefähr 5 nm identifiziert werden, oberhalb dessen die Zustandsdichte im Nanodraht große Ähnlichkeiten mit jener des Silizium-Volumenkristalls aufweist und der Draht somit zunehmend mit Näherungen für den perfekt periodischen Kristall beschrieben werden kann. Der Fokus bei der Untersuchung der NiSi2-Si-Grenzflächen liegt auf der Symmetrie von Elektron- und Lochströmen im Tunnelregime, welche für die Entwicklung von rekonfigurierbaren Feldeffekttransistoren besondere Relevanz hat. Verschiedene NiSi2-Si-Grenzflächen und Verzerrungszustände werden dabei systematisch untersucht. Je nach Grenzfläche ist die Symmetrie dabei sehr unterschiedlich und zeigt auch ein sehr unterschiedliches Verhalten bei externer Verzerrung. Weiterhin werden grundlegende physikalische Größen mit Bezug zu NiSi2-Si-Grenzflächen betrachtet. So wird beispielsweise die Stabilität anhand von Grenzflächen-Energien ermittelt. Am stabilsten sind {111}-Grenzflächen, was deren bevorzugtes Auftreten in Experimenten erklärt. Weitere wichtige Größen, deren Verzerrungsabhängigkeit untersucht wird, sind die Schottky-Barrierenhöhe, die effektive Masse der Ladungsträger sowie die Austrittsarbeiten von NiSi2- und Si-Oberflächen. Ein Beitrag zur Modellentwicklung numerischer Bauelementesimulationen wird durch einen Vergleich zwischen den Ergebnissen von Dichtefunktionaltheorie-basierten Transportrechnungen und denen eines vereinfachten Models basierend auf der Wentzel-Kramers-Brillouin-Näherung geliefert. Diese Näherung ist Teil vieler numerischer Bauelementesimulatoren und erlaubt die Berechnung des Tunnelstroms basierend auf grundlegenden physikalischen Größen. Der Vergleich ermöglicht eine Evaluierung des vereinfachten Models, welches anschließend genutzt wird, um den Einfluss der grundlegenden physikalischen Größen auf den Tunneltransport zu untersuchen.:Index of Abbreviations 1. Introduction 2. Silicon Based Devices and Silicon Nanowires 2.1. Introduction 2.2. The Reconfigurable Field-effect Transistor 2.2.1. Design and Functionality 2.2.2. Fabrication 2.3. Overview Over Silicon Nanowires 2.3.1. Geometric Structure 2.3.2. Fabrication Techniques 2.3.3. Electronic Properties 3. Simulation Tools 3.1. Introduction 3.2. Electronic Structure Calculations 3.2.1. Introduction and Basis Functions 3.2.2. Density Functional Theory 3.2.3. Description of Exchange and Correlation Effects 3.2.4. Practical Aspects of Density Functional Theory 3.3. Electron Transport 3.3.1. Introduction 3.3.2. Scattering Theory 3.3.3. Wentzel-Kramers-Brillouin Approximation for a Triangular Barrier 3.3.4. Non-equilibrium Green’s Function Formalism A. Radially Resolved Electronic Structure and Charge Carrier Transport in Silicon Nanowires A.1. Introduction A.2. Model System A.3. Results and Discussion A.4. Summary and Conclusions A.5. Appendix A: Computational Details A.6. Appendix B: Supplementary Material A.6.1. Comparison of the Band Gap Between Relaxed and Unrelaxed SiNWs A.6.2. Band Structures for Some of the Calculated SiNWs A.6.3. Radially Resolved Density of States for Some of the Calculated SiNWs B. Electron Transport Through NiSi2-Si Contacts and Their Role in Reconfigurable Field-effect Transistors B.1. Introduction B.2. Model for Reconfigurable Field-effect Transistors B.2.1. Atomistic Quantum Transport Model to Describe Transport Across the Contact Interface B.2.2. Simplified Compact Model to Calculate the Device Characteristics B.3. Results and Discussion B.3.1. Characteristics of a Reconfigurable Field-effect Transistor B.3.2. Variation of the Crystal Orientations and Influence of the Schottky Barrier B.3.3. Comparison to Fabricated Reconfigurable Field-effect Transistors B.4. Summary and Conclusions B.5. Appendix: Supplementary Material B.5.1. Band Structure and Density of States of the Contact Metal B.5.2. Relaxation Procedure B.5.3. Total Transmission Through Multiple Barriers C. Formation and Crystallographic Orientation of NiSi2-Si Interfaces C.1. Introduction C.2. Fabrication and characterization methods C.3. Model System and Simulation Details C.4. Results and discussion C.4.1. Atomic structure of the interface C.4.2. Discussion of ways to modify the interface orientation C.5. Summary C.6. Appendix: Supplementary Material D. NiSi2-Si Interfaces Under Strain: From Bulk and Interface Properties to Tunneling Transport D.1. Introduction D.2. Model System and Simulation Approach D.3. Computational Details D.3.1. Electronic Structure Calculations (Geometry Relaxations) D.3.2. Electronic Structure Calculations (Electronic Structure) D.3.3. Device Calculations D.4. Tunneling Transport From First-principles Calculations D.4.1. Evaluation of the Current D.4.2. Isotropic Strain D.4.3. Anisotropic Strain D.5. Transport Related Properties and Effective Modeling Schemes D.5.1. Schottky Barrier Height D.5.2. Simplified Transport Model D.5.3. Models for the Schottky Barrier Height D.6. Summary and Conclusions D.7. Appendix: Supplementary Material D.7.1. Schottky Barriers of the {110} Interface Under Anisotropic Strain D.7.2. Silicon Band Structure, Electric Field, and Number of Transmission Channels D.7.3. k∥-resolved Material Properties D.7.4. Evaluation of the Work Functions and Electron Affinities D.7.5. Verification of the Work Function Calculation 4. Discussion 5. Ongoing Work and Possible Extensions 6. Summary Bibliography List of Figures List of Tables Acknowledgements Selbstständigkeitserklärung Curriculum Vitae Scientific Contributions / The ongoing developments in micro- and nanotechnologies require a profound support from simulations. Numerical device simulations were and still are essential tools to support the device development. However, they gradually reach their limits as they rely on parameters, which are not always available, and neglect quantum effects for small structures. This work addresses the transport in silicon nanowires and through NiSi2-Si interfaces. By using density functional theory, the atomic structure is considered, and all electron transport related quantum effects are taken into account. Silicon nanowires are investigated with special attention to their radially resolved electronic structure and the corresponding modifications when the silicon diameter is reduced. The charge transport occurs mostly in the nanowire core. A diameter of around 5 nm can be identified, above which the nanowire core exhibits a similar density of states as bulk silicon. Thus, bulk approximations become increasingly valid above this diameter. NiSi2-Si interfaces are studied with focus on the symmetry between electron and hole currents in the tunneling regime. The symmetry is especially relevant for the development of reconfigurable field-effect transistors. Different NiSi2-Si interfaces and strain states are studied systematically. The symmetry is found to be different between the interfaces. Changes of the symmetry upon external strain are also very interface dependent. Furthermore, fundamental physical properties related to NiSi2-Si interfaces are evaluated. The stability of the different interfaces is compared in terms of interface energies. {111} interfaces are most stable, which explains their preferred occurrence in experiments. Other properties, whose strain dependence is studied, include the Schottky barrier height, the effective mass of the carriers, and work functions. A contribution to the development of numerical device simulators will be given by comparing the results from density functional theory based transport calculations and a model based on the Wentzel-Kramers-Brillouin approximation. This approximation, which is often employed in numerical device simulators, offers a relation between interface properties and the tunneling transport. The comparison allows an evaluation of the simplified model, which is then used to investigate the relation between the fundamental physical properties and the tunneling transport.:Index of Abbreviations 1. Introduction 2. Silicon Based Devices and Silicon Nanowires 2.1. Introduction 2.2. The Reconfigurable Field-effect Transistor 2.2.1. Design and Functionality 2.2.2. Fabrication 2.3. Overview Over Silicon Nanowires 2.3.1. Geometric Structure 2.3.2. Fabrication Techniques 2.3.3. Electronic Properties 3. Simulation Tools 3.1. Introduction 3.2. Electronic Structure Calculations 3.2.1. Introduction and Basis Functions 3.2.2. Density Functional Theory 3.2.3. Description of Exchange and Correlation Effects 3.2.4. Practical Aspects of Density Functional Theory 3.3. Electron Transport 3.3.1. Introduction 3.3.2. Scattering Theory 3.3.3. Wentzel-Kramers-Brillouin Approximation for a Triangular Barrier 3.3.4. Non-equilibrium Green’s Function Formalism A. Radially Resolved Electronic Structure and Charge Carrier Transport in Silicon Nanowires A.1. Introduction A.2. Model System A.3. Results and Discussion A.4. Summary and Conclusions A.5. Appendix A: Computational Details A.6. Appendix B: Supplementary Material A.6.1. Comparison of the Band Gap Between Relaxed and Unrelaxed SiNWs A.6.2. Band Structures for Some of the Calculated SiNWs A.6.3. Radially Resolved Density of States for Some of the Calculated SiNWs B. Electron Transport Through NiSi2-Si Contacts and Their Role in Reconfigurable Field-effect Transistors B.1. Introduction B.2. Model for Reconfigurable Field-effect Transistors B.2.1. Atomistic Quantum Transport Model to Describe Transport Across the Contact Interface B.2.2. Simplified Compact Model to Calculate the Device Characteristics B.3. Results and Discussion B.3.1. Characteristics of a Reconfigurable Field-effect Transistor B.3.2. Variation of the Crystal Orientations and Influence of the Schottky Barrier B.3.3. Comparison to Fabricated Reconfigurable Field-effect Transistors B.4. Summary and Conclusions B.5. Appendix: Supplementary Material B.5.1. Band Structure and Density of States of the Contact Metal B.5.2. Relaxation Procedure B.5.3. Total Transmission Through Multiple Barriers C. Formation and Crystallographic Orientation of NiSi2-Si Interfaces C.1. Introduction C.2. Fabrication and characterization methods C.3. Model System and Simulation Details C.4. Results and discussion C.4.1. Atomic structure of the interface C.4.2. Discussion of ways to modify the interface orientation C.5. Summary C.6. Appendix: Supplementary Material D. NiSi2-Si Interfaces Under Strain: From Bulk and Interface Properties to Tunneling Transport D.1. Introduction D.2. Model System and Simulation Approach D.3. Computational Details D.3.1. Electronic Structure Calculations (Geometry Relaxations) D.3.2. Electronic Structure Calculations (Electronic Structure) D.3.3. Device Calculations D.4. Tunneling Transport From First-principles Calculations D.4.1. Evaluation of the Current D.4.2. Isotropic Strain D.4.3. Anisotropic Strain D.5. Transport Related Properties and Effective Modeling Schemes D.5.1. Schottky Barrier Height D.5.2. Simplified Transport Model D.5.3. Models for the Schottky Barrier Height D.6. Summary and Conclusions D.7. Appendix: Supplementary Material D.7.1. Schottky Barriers of the {110} Interface Under Anisotropic Strain D.7.2. Silicon Band Structure, Electric Field, and Number of Transmission Channels D.7.3. k∥-resolved Material Properties D.7.4. Evaluation of the Work Functions and Electron Affinities D.7.5. Verification of the Work Function Calculation 4. Discussion 5. Ongoing Work and Possible Extensions 6. Summary Bibliography List of Figures List of Tables Acknowledgements Selbstständigkeitserklärung Curriculum Vitae Scientific Contributions

I present and discuss the results of calculations ofelectronic structures of perfect and defective CaF2 and BaF2 crystals. These are based on the ab initio Hartree-Fock method with electron correlation corrections and ondensity-functional theory calculations with different exchange-correlation functionals, including hybrid exchange techniques.The defective systems include F centers, M centers, O-V dipoles, Hydrogen impurities and H centers.

The presented thesis includes investigations to fully characterize the electronic structure and magnetic properties ofselected manganese containing high-spin molecules by means of various X-ray spectroscopic, magnetic and theoretical methods. The investigations on the Mn4 star-shaped molecule havelead to a number of interesting results. Magneto-chemical studies exhibit very weak exchange coupling constantsbetween the four Mn(II) ions, leading to complicated low lying states in which the ground state is not well separated, resulting from a dominant weak ferromagnetic coupling and a giant moment of up to 20 µB/f.u. XMCD measurements revealed that almost the completemagnetic moment is located around the Mn(II) ions.This is in agreement with only a few charge transfer states foundwithin the detailed X-ray absorption spectroscopic study. The electronic structure and detailed magnetic properties of the star-shaped heteronuclear CrIIIMnII3 complex have been precisely investigated.With XPS the homovalency of Mn and Cr have been verified. The XA-spectra of the manganese and chromium L edges were measured and compared to earlier investigated Mn4 spectra.The combination high-magnetic field magnetic measurements and element selective XMCD of Mn and Cr L edges and quantum model calculations lead to a complete analysis of the magnetic structure of the CrMn3 magnetic core. The III valence state of the manganese ions in MnIII6O2Salox has been verified. From X-ray diffraction, typical Jahn-Teller distorted oxygen octahedra have been found for Mn(III) ions. Comparisons of XPS and XAS spectra of the complex to corresponding spectraof maganite and tetranuclear manganese(II) cluster it was definitely possible to identify MnIII6O2Salox as a pure Mn(III) compound.

<p>A wide range of optoelectronic applications demand semiconductors optimized for purpose.</p> <p>My research focused on data-driven identification of ABX3 Halide perovskite compositions for optimum photovoltaic absorption in solar cells.</p> <p>I trained machine learning models on previously reported datasets of halide perovskite band gaps based on first principles computations performed at different fidelities.</p> <p>Using these, I identified mixtures of candidate constituents at the A, B or X sites of the perovskite supercell which leveraged how mixed perovskite band gaps deviate from the linear interpolations predicted by Vegard's law of mixing to obtain a selection of stable perovskites with band gaps in the ideal range of 1 to 2 eV for visible light spectrum absorption.</p> <p>These models predict the perovskite band gap using the composition and inherent elemental properties as descriptors.</p> <p>This enables accurate, high fidelity prediction and screening of the much larger chemical space from which the data samples were drawn.</p> <p><br></p> <p>I utilized a recently published density functional theory (DFT) dataset of more than 1300 perovskite band gaps from four different levels of theory, added to an experimental perovskite band gap dataset of \textasciitilde{}100 points, to train random forest regression (RFR), Gaussian process regression (GPR), and Sure Independence Screening and Sparsifying Operator (SISSO) regression models, with data fidelity added as one-hot encoded features.</p> <p>I found that RFR yields the best model with a band gap root mean square error of 0.12 eV on the total dataset and 0.15 eV on the experimental points.</p> <p>SISSO provided compound features and functions for direct prediction of band gap, but errors were larger than from RFR and GPR.</p> <p>Additional insights gained from Pearson correlation and Shapley additive explanation (SHAP) analysis of learned descriptors suggest the RFR models performed best because of (a) their focus on identifying and capturing relevant feature interactions and (b) their flexibility to represent nonlinear relationships between such interactions and the band gap.</p> <p>The best model was deployed for predicting experimental band gap of 37785 hypothetical compounds.</p> <p>Based on this, we identified 1251 stable compounds with band gap predicted to be between 1 and 2 eV at experimental accuracy, successfully narrowing the candidates to about 3% of the screened compositions.</p>

Le présent travail concerne l’avancement des approximations de l’énergie d’échange- corrélation (XC) de la théorie fonctionnelle de la densité (DFT) de Kohn-Sham (KS) basée sur l’approche du facteur de corrélation (CF). Le travail est organisé en trois parties où chaque partie est construite sur des modèles et méthodes précédents. La première partie du travail introduit une nouvelle condition physique à travers la déri- vation du développement en série du quatrième ordre du trou d’échange exact. La dérivation détaillée des formules requises est suivie d’une analyse approfondie qui montre que le terme de quatrième ordre peut ajouter des informations supplémentaires importantes qui sont par- ticulièrement pertinentes pour les molécules par rapport aux atomes. Sur la base de ces résultats, nous explorons les fonctionnelles d’échange qui dépendent du terme de quatrième ordre de l’expansion du trou d’échange. Nous constatons également que les développements d’ensembles de base gaussiens, fréquemment utilisés dans les codes de structure électronique, donnent des représentations insatisfaisantes du terme de quatrième ordre. La deuxième partie de ce travail porte sur la mise en œuvre de nouvelles versions du modèle CF initial [J. P. Precechtelova, H. Bahmann, M. Kaupp et M. Ernzerhof, J. Chem. Phys. 143, 144102 (2015)] dans lequel le trou XC est approximé. Étant donné que diverses contraintes satisfaites par le trou XC sont connues, des approximations peuvent être conçues pour éviter en grande partie des ajustements empiriques. Dans l’approche CF, le trou XC est écrit comme le produit d’un trou d’échange multiplié par un facteur de corrélation. Une contrainte importante satisfaite par le modèle CF est qu’il reproduit correctement l’éner- gie d’échange exacte dans la limite de haute densité. Ceci est réalisé en utilisant l’énergie d’échange exacte par particule comme variable d’entrée, c’est-à-dire que le modèle CF s’ap- puie sur l’échange exact. Des variations du modèle CF initial sont proposées qui assurent que la réponse exacte est obtenue dans la limite homogène. De plus, nous appliquons une correction à la profondeur du trou XC qui est conçue pour capturer une forte corrélation. Les fonctions d’échange-corrélation qui s’appuient sur un échange exact, comme les hybrides, échouent souvent pour les systèmes qui présentent une corrélation électronique importante. Malgré ce fait et malgré la réduction de l’empirisme à un seul paramètre dans CF, des énergies d’atomisation précises sont obtenues pour des composés de métaux de transition fortement corrélés. Le modèle CF montre des résultats significativement supérieurs aux fonctionnelles populaires comme Perdew-Burke-Ernzerhof (PBE), PBE hybride et Tao-Perdew-Staroverov- Scuseria (TPSS). La troisième partie du travail s’appuie sur les modèles CF précédents développés dans notre groupe et aborde l’erreur d’auto-interaction à un électron et introduit un modèle de facteur de corrélation modifié où f C (r, u) est construit tel qu’il se réduit à un dans les régions à un électron d’un système à plusieurs électrons. Ce trou XC avec une correction d’auto- interaction est ensuite utilisé pour générer la fonctionnelle énergie XC correspondante. La nouvelle fonctionnelle est évaluée en l’implémentant dans un programme KS et en calculant diverses propriétés moléculaires. Nous constatons que, dans l’ensemble, une amélioration significative est obtenue par rapport aux versions précédentes du modèle de facteur de cor- rélation. / The present work is concerned with the advancement of approximations to the exchangecorrelation (XC) energy of Kohn-Sham (KS) density functional theory (DFT) based on the correlation factor (CF) approach. The work is organized in three parts where each part is build upon previous models and methods. The first part of the work introduces a new physical condition through the derivation of the fourth-order series expansion of the exact exchange hole. The detailed derivation of the required formulas is followed by a thorough analysis that shows that the fourth-order term can add important additional information that is particularly relevant for molecules compared to atoms. Drawing on these findings, we explore exchange functionals that depend on the fourth-order term of the expansion of the exchange hole. We also find that Gaussian basis set expansions, frequently used in electronic structure codes, result in unsatisfactory representations of the fourth-order term. The second part of this work addresses the implementation of new versions of the initial CF model [J. P. Precechtelova, H. Bahmann, M. Kaupp, and M. Ernzerhof, J. Chem. Phys. 143, 144102 (2015)] in which the XC hole is approximated. Since various constraints satisfied by the XC hole are known, approximations to it can be designed which largely avoid empirical adjustments. In the CF approach, the XC-hole is written as a product of an exchange hole times a correlation factor. An important constraint satisfied by the CF model is that it correctly reproduces the exact exchange energy in the high density limit. This is achieved by employing the exact exchange-energy per particle as an input variable, i.e., the CF model builds on exact exchange. Variations of the initial CF model are proposed which ensure that the exact answer is obtained in the homogeneous limit. Furthermore, we apply a correction to the depth of the XC-hole that is designed to capture strong correlation. Exchangecorrelation functionals that build on exact exchange, such as hybrids, often fail for systems that exhibit sizeable electron correlation. Despite this fact and despite the reduction of empiricism to a single parameter within CF, accurate atomization energies are obtained for strongly-correlated transition metal compounds. The CF model significantly improves upon widely used functionals such as Perdew-Burke-Ernzerhof (PBE), PBE hybrid, and Tao-Perdew-Staroverov-Scuseria (TPSS) density functionals. The third part of the work builds on the previous CF models developed in our group and addresses the one-electron, self-interaction error and introduces a modified correlation factor model where fC(r, u) is constructed such that it reduces identically to one in oneelectron regions of a many-electron system. This self-interaction corrected XC-hole is then used to generate the corresponding XC-energy functional. The new functional is assessed by implementing it into a KS program and by calculating various molecular properties. We find that, overall, a significant improvement is obtained compared to previous versions of the correlation factor model.

Le progrès technologique de nos sociétés est intimement lié aux matériaux. La physique de la matière condensée cherche à expliquer, décrire et prédire leurs propriétés à partir de lois fondamentales. Bien que l’on connaisse assez bien les axiomes qui régissent notre univers, la combinaison d’un grand nombre de petits systèmes compris individuellement mais interagissants ensemble mène à des propriétés émergentes qui peuvent être complexes et difficilement prévisibles. Dans cette thèse, nous étudions la supraconductivité non-conventionnelle dans les matériaux corrélés, un phénomène émergent des fortes interactions électroniques qui possède un immense potentiel technologique. Pour ce faire, nous réalisons des simulations numériques sur un matériau bien spécifique: le ruthénate de strontium. Dans un premier temps, nous discutons des états normaux des matériaux corrélés devenant supraconducteurs. Alors que la théorie des bandes permet de décrire le continuum entre un isolant électrique et un métal, elle n’arrive pas à décrire les phénomènes émergeant des interactions à plusieurs électrons. Nous expliquons comment la théorie de la fonctionnelle de la densité permet d’obtenir la densité du niveau fondamental d’un système interagissant en le transformant vers un problème non-interagissant effectif. Elle peut également être employée pour les systèmes possédant un important couplage spin-orbite. Cependant, les fonctionnelles disponibles n’arrivent pas à bien incorporer les fortes corrélations électroniques. Une manière de corriger ce manque est d’employer la théorie du champ moyen dynamique. Cette dernière permet de capturer la dépendance en temps des interactions locales à un corps. Toutefois, la supraconductivité impliquant des paires d’électrons, il faut plutôt étudier des objets à deux corps afin de la caractériser. Nous discutons des critères nécessaires à la provocation de transitions supraconductrices, exprimés en termes de corrections du vertex. Également, nous présentons les paramètres d’ordre pour caractériser une phase supraconductrice. La seconde partie se concentre sur la supraconductivité. D’abord, nous faisons un survol son historique, depuis sa découverte en 1911 jusqu’à celle de l’état supraconducteur du ruthénate de strontium. Ensuite, nous décrivons la supraconductivité conventionnelle, une classe particulière pour laquelle l’état ordonné est attribué à l’interaction entre les électrons et les vibrations du réseau cristallin. Puis, nous introduisons un autre mécanisme d’appariement: l’échange de fluctuations de spin et de charge. Finalement, nous présentons l’état des connaissances collectives modernes en ce qui a trait au ruthénate de strontium. Nos articles proposent de nouvelles avenues impliquant le couplage spin-orbite et les corrélations impaires en fréquences. Nous terminons en introduisant différentes perspectives de recherche dans le domaine de la supraconductivité. / The technological progress of our societies is intimately linked with materials. Condensed matter physics tries to explain, describe and predict their properties from fundamental laws. Although we are quite familiar with the axioms that govern our universe, the combination of a large number of small systems understood individually but interacting together leads to emerging properties that can be complex and difficult to predict. In this thesis, we study unconventional superconductivity in correlated materials, a phenomenon emerging from strong electronic interactions that has immense technological potential. To do this, we carry out numerical simulations on a very specific material: strontium ruthenate. First, we discuss the normal states of correlated materials becoming superconducting. While band theory can describe the continuum between an electrical insulator and a metal, it cannot describe the phenomena emerging from interactions with several electrons. We explain how density functional theory makes it possible to obtain the density of the fundamental level of an interacting system by mapping it into an effective non-interacting problem. It can also be used for systems with a large spin-orbit coupling. However, the available functionals do not manage to incorporate strong electronic correlations well. One way to correct this deficiency is to employ dynamical mean field theory. The latter makes it possible to capture the time dependence of interactions at the one body level. However, since superconductivity involves pairs of electrons, it is rather necessary to study two body objects in order to characterize it. We discuss the criteria necessary for inducing superconducting transitions, expressed in terms of vertex corrections. Also, we present the order parameters to characterize a superconducting phase. The second part focuses on superconductivity. First, we review its history, from its discovery in 1911 to that of the superconducting state of strontium ruthenate. Next, we describe conventional superconductivity, a particular class for which the ordered state is attributed to the interaction between electrons and the vibrations of the crystal lattice. Then, we introduce another pairing mechanism: the exchange of spin and charge fluctuations. Finally, we present the state of modern collective knowledge about strontium ruthenate. Our articles propose new avenues involving spin-orbit coupling and odd frequency correlations. We end by introducing different research perspectives in the field of superconductivity.

This master thesis presents a theoretical investigation of the energy and stability of interfaces in iron-carbide compounds, specifically focusing on the α-Fe/Cr7C3 system. The study aims to fill the gap in knowledge regarding the surface energetics of these interfaces using Density Functional Theory (DFT). Six different α-Fe/Cr7C3 interfaceswere constructed α-Fe(001)/Cr7C3(024), α-Fe(001)/Cr7C3(202), α-Fe(001)/Cr7C3(040),α-Fe(110)/Cr7C3(024), α-Fe(110)/Cr7C3(202) and α-Fe(110)/Cr7C3(040). Due to limited computational resources, only one of them was computationally analyzed to determine its interfacial energy value. The results revealed that the interfacial energy of the α-Fe(001)/Cr7C3(040) interface falls within the range of incoherent interfaces, indicating its stability. The computed interfacial energy values ranged from 0.94 to 3.39 J/m2, consistent with similar studies on other iron interfaces. The simulations also identified minimum and local minimum points in the interface energy curve, representing stable configurations at specific interface separation distances. The presence of a minimum point at an interface separation value of d = 1.3551 Å with an interfacial energy of 0.94 J/m2 indicates the most stable configuration, while a local minimum point at d = 2.27 Å with an interfacial energy of 2.12 J/m2 suggests another stable configuration for the interface. The conclusion that the computations were correctly performed with an interfacial energy value of 0.94 J/m2 for the most stable configuration at a supercell length (aSupercell ) of 22.23 Å is drawn. The findings of this research have significant implications for future investigations and applications. Firstly, this study fills the gap of the unresearched ferrite-carbide interfaces with theoretical data. Secondly, the knowledge gained from studying these interfaces contributes to understanding hydrogen interactions, which is fundamental for the transition towards a hydrogen economy. Additionally, the incoherent nature of the interface introduces challenges in understanding material behavior and properties, necessitating further investigations for designing efficient systems. Future work includes experimental validation of the α-Fe/Cr7C3 interface to compare the theoretical and experimental energies and stability. Investigating the remaining interfaces and examining the effects of introducing hydrogen atoms in these interfaces, along with calculating the corresponding hydrogen trapping energies, are important research areas. Further advancements in understanding these interfaces can be achieved through interface engineering, multiscale modeling, and studying other iron-carbide systems. / Detta examensarbete presenterar en teoretisk undersökning av energin och stabiliteten hos gränssnitt i järnkarbidföreningar och fokuserar specifikt på α-Fe/Cr7C3-systemet. Studien syftar till att fylla kunskaps tomrummet gällande ytegenskaperna hos dessa gränssnitt genom användning av densitetsfunktionalteori (DFT). Sex olika α-Fe/Cr7C3-gränssnitt konstruerades α-Fe(001)/Cr7C3(024), α-Fe(001)/Cr7C3(202), α-Fe(001)/Cr7C3(040), α-Fe(110)/Cr7C3(024), α-Fe(110)/Cr7C3(202) och α-Fe(110)/Cr7C3(040). På grund av begränsade beräkningsresurser analyserades endast ett av dem för att bestämma dess gränssnittsenergivärde. Resultaten visade att gränssnittsenergin för α-Fe(001)/Cr7C3(040)- gränssnittet ligger inom intervallet för inkoherenta gränssnitt, vilket indikerar dess stabilitet. De beräknade gränssnittsenergivärdena varierade mellan 0,94 och 3,39 J/m2 , vilket är i linje med liknande studier där järngränssnitt studeras. Minimi och lokala minimipunkter i gränssnittets energikurva, vilket representerar stabila konfigurationer vid specifika avstånd mellan gränssnittet. Förekomsten av en minimipunkt vid ett gränssnittsavstånd på d = 1,35 Å med en gränssnittsenergi på 0,94 J/m2 indikerar den mest stabila konfigurationen, medan en lokal minimipunkt vid d = 2,27 Å med en gränssnittsenergi på 2,12 J/m2 antyder en annan stabil konfiguration för gränssnittet. Slutsatsen dras att beräkningarna utfördes korrekt med ett gränssnittsenergivärde på 0,94 J/m2 för den mest stabila konfigurationen vid en supercellslängd (aSupercell) på 22,23 Å. Fynden från denna forskning har betydande implikationer för framtida undersökningar och tillämpningar. För det första fyller denna studie kunskapsgapet gällande de otillräckligt utforskade ferrit-karbidgränssnitten med teoretisk data. För det andra bidrar den erhållna kunskapen från studiet av dessa gränssnitt till förståelsen av väteinteraktioner, vilket är grundläggande för övergången till en väteekonomi. Dessutom innebär gränssnittets inkoherenta natur utmaningar när det gäller att förstå materialbeteende och egenskaper, vilket kräver ytterligare undersökningar för att utforma effektiva system. Framtida arbete inkluderar experimentell validering av gränssnittet mellan α-Fe/Cr7C3 för att jämföra teoretiska och experimentella energier och stabilitet. Att undersöka återstående gränssnitt och undersöka effekterna av att introducera väteatomer i dessa gränssnitt och beräkna motsvarande vätefällningsenergier är viktiga forskningsområden. Gränssnittsdesign, flerskalig modellering och studier av andra järnkarbid-system kan ytterligare främja förståelsen av dessa gränssnitt.