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Spin-orbit coupling (SOC) is a relativistic effect whose origin lies in the Dirac’s equation – a relativistic analogue of Schrödinger’s equation. SOC corrects the electronic states of a quantum mechanical system up to ~1 eV in case of semiconductors and ~ 2 – 3.6 eV in case of actinides and heavy elements by considering not only the coordinates but also the spin of the electrons in the system. Most of the applications of the present day technology are based on manipulating the electronic structure of a system with very high accuracy and precision. This demands availability of correct electronic structure of a material or molecule within a feasible computational time. Some direct consequences of SOC in materials can be noticed in analyzing the charge-transport properties of a semiconductor, evaluating the candidature of transition metal dichalcogenides (TMDCs) for spintronic, twistronic and valleytronic applications, and in the origin of topological properties of a material. Not only in materials but also in molecules the SOC effects can be observed. Fine-structure of atomic spectra was explained on the account of SOC. Several additional peaks and wavelength shift in UV-vis spectroscopy of Gold Superatoms can only be explained by correctly considering the energy level splittings caused by SOC. SOC allows intersystem and reverse intersystem crossing by mixing the spin states, ultimately opening various chemical reaction pathways which were spin forbidden before. Current advancements in computational power enrich us to work shoulder to shoulder with experiments where one can simulate the synthesized structures containing thousands of atoms using semi-empirical methods as in DFTB, GFN-XTB. These methods so far considered SOC effects but only as case studies in testing the implementation of SOC Hamiltonian rather than a systemic extension of SOC parameters to most part of the periodic table and studying SOC effects for different categories of materials and molecules. This motivated us to implement the SOC either in the form of highly accurate parameters throughout the periodic table or as addition in hamiltonian in such methods. Twisted van der Waals 2D materials as in twisted TMDC bilayers shows exciting electronic and optoelectronic properties and depending on the twist angle and chemical composition they can have thousands of atoms in their superlattices. A correct electronic analysis of such structures with SOC corrected DFT is computationally very expensive but is feasible at semi-empirical level. Here, we have applied our implementation on TMDC homo and heterobilayer twisted superlattices and studied the effect of SOC on the excitonic properties of the system. Therefore, this work opens the way for realizing various exotic applications of present day materials as well as molecules.:Table of Contents Abstract 4 1 Introduction 8 1.1 Quantum Chemistry: 8 1.2 HF based Semi-Empirical Methods 9 1.3 DFT based Semi-Empirical Methods 11 1.3.1 Density Functional based Tight-Binding Method (DFTB) 11 1.3.2 Geometry, Frequency, Non-Covalent, extended Tight Binding (GFN-xTB) 12 1.4 Spin-Orbit Coupling (SOC) 14 1.4.1 SOC in Materials 18 1.4.2 SOC in Molecular Structures 22 1.5 Theoretical Models for Accounting SOC 24 1.6 Motivation, Objective and Outline of thesis 26 2 Methodology 29 2.1 Quantum Chemistry 30 2.1.1 Schrödinger equation 30 2.2 Density Functional Theory 33 2.2.1 Generalized Gradient Approximations 39 2.3 Spin-orbit Coupling (SOC) 41 2.3.1 Classical Picture of SOC in LS model 42 2.3.2 Quantum Picture of SOC in LS model: 43 2.3.3 Calculation of SOC Paramentes 45 2.4 Density Functional Based Semi-empirical Quantum Mechanical Methods 48 2.4.1 Self-Consistent Charge Density Functional Based Tight Binding Method (SCC-DFTB) 48 2.4.2 Extended Tight-Binding (GFN1-xTB) 51 2.4.3 Addition of Spin-Orbit Coupling Hamiltonian in DFTB and GFN-xTB 54 3 Benchmarking Spin-Orbit Coupling Parameters for DFTB 56 3.1 Introduction 58 3.2 Computational Details of the DFT benchmark calculations 60 3.3 Benchmarking Spin-Orbit Coupling Parameters 60 3.3.1 III-V Bulk Semiconductor 61 3.3.2 Transition Metal Dichalcogenide 2D Crystals 65 3.3.3 Topological Insulators 68 3.4 Conclusions 70 4 Spin-Orbit Coupling Corrections for the GFN-xTB method 71 4.1.1 Introduction 73 4.2 Computational Details of The Benchmark Calculations 75 4.3 Results & Discussion 76 4.3.1 Geometries 76 4.3.2 Effect of SOC on Charge Transport Properties of Chromophores in MOFs 77 4.3.3 Superatoms 82 4.3.4 Effect of SOC on Binding of O2 on Ferrous Deoxyheme 85 4.4 Conclusions 86 5 Spin Orbit Coupling Effects on The Excitonic Properties of Twisted Moiré Transition Metal Dichalcogenides 88 5.1 Introduction 90 5.2 Computational Details 92 5.3 Results & Discussions 93 5.4 Excitons in Twisted Moiré Homobilayers 93 5.5 Excitons in Twisted Moiré Heterobilayers 102 5.6 Conclusions 109 6 Summary 112 A. Acronym 116 B. Appendices 120 SOC Parameters 120 7 References 147 C. Acknowledgement 173

Ce travail est une contribution ab initio à la caractérisation d'halogénures diatomiques de métaux de transition. Nous avons choisi de caractériser la structure électronique des chlorures de métaux de transition du groupe Vb (NbCl et TaCl) et du fluorure de nickel car une série de spectres les concernant ont été enregistrés mais aucune donnée théorique fiable n'était disponible dans la littérature. Pour étudier ces molécules, nous avons appliqué une procédure de calcul à deux étapes qui permet de tenir compte des effets de corrélation électronique et des effets relativistes. Dans la première étape, nous avons réalisé des calculs CASSCF/ICMRCI+Q de grande taille qui tiennent compte de l'énergie de corrélation et introduisent des effets relativistes scalaires. Dans la deuxième étape, le couplage spin-orbite est traité par la "state interacting method" implémentée dans le logiciel MOLPRO. Nous avons développé des stratégies de calcul basées sur ces méthodes de calcul et adaptées aux différentes molécules ciblées. Ainsi, pour les molécules NbCl et TaCl, nous avons utilisé des pseudopotentiels relativistes scalaires et spin-orbite, tandis que pour la molécule NiF, nous avons réalisé des calculs tous électrons. Nous avons d'abord testé la stratégie de calcul sur les cations Nb+ et Ta+. Ensuite, nous avons calculé pour la première fois les structures électroniques relativiste scalaire et spin-orbite des molécules NbCl (de 0 à 17000 cm-1) et TaCl (de 0 à 23000 cm-1). A l'aide de ces données théoriques, nous avons interprété les spectres expérimentaux en collaboration avec Bernath et al. Nous avons proposé plusieurs attributions de transitions électroniques en accord avec l'expérience mais nos résultats théoriques ne nous ont pas permis de les attribuer toutes. Néanmoins, nous avons mis en évidence une série d'autres transitions électroniques probables qui pourraient, à l'avenir, servir à l'interprétation de nouveaux spectres mieux résolus. Outre son intérêt expérimental, cette étude a permis de comparer les structures électroniques des molécules isovalencielles VCl, NbCl et TaCl, mettant en évidence des différences importantes. L'élaboration d'une nouvelle stratégie de calcul pour décrire les systèmes contenant l'atome de nickel représentait un véritable défi en raison de la complexité des effets de corrélation électronique. Notre stratégie de calcul a consisté à introduire ces effets en veillant à réduire au maximum la taille des calculs qui devenait considérable. Nous l'avons testée sur l'atome Ni et appliquée ensuite au calcul des structures électroniques relativiste scalaire et spin-orbite de la molécule NiF entre 0 à 2500 cm-1. Nous avons obtenus des résultats qui corroborent l'expérience.

Au cours de cette thèse, on étudie les systèmes différents : graphène (une monocouche de carbone), graphène fonctionnalisé et les nanofils de Bismuth en induisant la supraconductivité par l’effet proximité. On montre que l’effet proximité fonctionne comme un probe sensible pour les effets des interactions, de couplage spin-orbite, etc.La structure de band de graphène a une relation dispersion linéaire au niveau de Fermi, et le band de conductance et le band de valence est lié aux six points dans l’espace réciproque, appelé le point Dirac. Autour du point Dirac, graphène occupe d’une densité d’état faible (par rapport aux métaux). Alors le niveau de Fermi dans graphene est modulable. On fabrique les jonctions S/Graphene/S avec les contacts de matériaux différents (Al, ReW, Nb). En comparant avec la théorie, on a complété le diagramme du produit R_N I_c (R_N la résistance d’état normal, I_c le courant critique dans une jonction) vs l’énergie Thouless E_Th (une énergie caractéristique intervient dans la jonction SNS longue et dépend la partie normale). Une réduction de R_N I_c globale de la jonction courte à la jonction longue, surtout dans la limite de la jonction longue, la réduction est 10 fois plus grande que celle de la jonction courte. On l’explique par une réduction d’une énergie Thouless effective à cause l’interface S/G imparfaite. Une suppression du supercourant près du point Dirac dans les jonctions longues est considérée comme une signature de la réflexion Andreev spéculaire sur les « puddles » dans le graphène. Aussi, l’injection des paires de Cooper dans les états de bord de l’effet Hall quantique du graphène est étudiée dans cette thèse.L’interaction du couplage spin-orbite et l’effet proximité peut produire les physiques très intéressantes comme le supra de triplet, jonction π, et récemment la formation des Fermions majoranas. Motivé par ces possibilités d’explorer les nouvelles physiques, on a essayé d’induire le couplage spin-orbite dans graphène dans lequel ce couplage est initialement très faible. En greffant les molécules de Pt-porphyrines, qui tiennent un atome de Pt au milieu, on espère que le couplage spin-orbite fort dans l’atome de Pt peut « diffuser » dans le graphène. Au lieu d’avoir vu le couplage spin-orbite, on a plutôt découvert un magnétisme qui dépend la grille dans le graphène induit par les molécules. Plusieurs échantillons avec les contacts normaux ou supraconducteurs sont mesurés avant et après mettant les molécules. Un transfert de charge dans deux sens (électron ou trou) est observé à la température ambiante. Il est lié à l’alignement des niveaux de Fermi des molécules et le graphène. A basse température (~70mK), les hystérésis dans la magnétorésistance (MR) et une asymétrie en B_(//) et B_⊥ impliquent un magnétisme dans graphène. Plus spectaculaire, une asymétrie en la dépendance de la grille du supercurrent est détectée. Bismuth est un élément très lourd et un matériau avec le couplage Rashba spin-orbite fort. On a connecté les nanofils de Bismuth avec tungstène (H_c∼12T) électrodes par FIB (Focused Ions Beam) et induit l’effet proximité dans les fils. Les résultats les plus étonnants sont : (1) le supercourant se tient au champ magnétique jusqu’à 11 Tesla. (2) Il y a des oscillations dans le courant critique en fonction du champ avec une période de centaine gauss qui ressemble à celui d’une structure de SQUID (composé des deux jonctions Josephson en parallèles. (3) Sur ces oscillations, nous trouvons aussi une modulation quasi-périodique lente de quelque milles gauss. Pour expliquer tous ces phénomènes, nous proposons qu’il y a quelques canaux étroites balistiques 1D se forment aux bords des certaines surfaces qui se tiennent au champ jusqu’à 11T et se construisent une interférence entre eux. L’effet Zeeman cause une modulation de phase entre les quasi-particules dans une paire d’Andreev qui module donc le supercourant en échelle de quelques milles gauss. / In this thesis we investigated graphene and Bi nanowire systems by inducing superconducting proximity effect in them. Typically the samples are realized in the form of S/N/S junction. The special properties of these systems are revealed by observing some unusual proximity effect in them. The interplay of the superconducting proximity effect and other effects (spin-orbit coupling, Zeeman effect, quantum Hall effect, impurities, etc...) at the mesoscopic scale gives rise to new physics. Some of our main results are listed below.GrapheneWe succeeded to induce superconducting proximity effect in the very long junction limit, thus completing the diagram of the superconducting proximity effect in graphene. Since by changing the gate voltage, one changes the carrier density in graphene and eventually the transport characteristic quantities (l_e, E_Th etc...). We could scan a whole range of Thouless energy. We present a diagram of eR_N I_c vs Thouless energy compared to theoretical prediction. The Thouless energy dependence of the eR_N I_c products varies from the long junction limit to the short junction limit. The discrepancy (mainly due to the imperfect S/G interface) between theory and experiment is also limit dependent: in the short junction limit, the eR_N I_c products are smaller than the theoretical prediction (with a perfect interface) by a factor of about 3-4; in the long junction limit, however, the disagreement is increased to about 100. We show that the factor deduced from the junctions in different limits is length dependent. This can be explained by the effect of finite transmission at the S/G interface in both the critical current I_c and the induced mini-gap in the graphene. In another hand, a suppression of supercurrent near the Dirac point is observed in long junctions which is attributed to the indication of the specular Andreev reflection upon the puddles in graphene. Also the injection of the Cooper pairs into the QHE edge states is investigated in this thesis.Graphene grafted with Pt-porphyrinsBy grafting the Pt-porphyrins onto graphene, we observed a charge transfer between molecules and the graphene both for electrons and holes. One of the important consequences of the charge transfer is that when the molecules are ionized, a collective magnetic order can be formed by the long range RKKY interaction: the magnetic moments interact via the carrier in graphene. This effect is detected by a hysteretic magnetoresistance of the graphene in a perpendicular field and the asymmetric magnetoresistance in parallel field. Even more striking, the observation of a unipolar supercurrent in S/G/S junction implies that this magnetism induced by porphyrins is gate dependent. The theoretical calculations by Uchoa et al. using the Anderson model indeed find that the gate voltage should tune the impurities in graphene between non-magnetic state and magnetic state.Bi nanowireThe observation of a SQUID-like oscillations persisting up to 10 T and thousands Gauss range modulation in I_c hints to a complex physic in the W-Bi nanowire-W junctions. The results are consistent with a SQUID structure consisting of 2 edges channels which could have an I_c oscillation with period defined by the area between the two edges, typically the size of the nanowire. The origin of the edge states formation is attributed to the strong spin-orbit coupling in Bi that leads to the quantum spin Hall (QSH) state. The thousands Gauss range modulation is the consequence of the interplay between the Zeeman effect and the proximity effect. The phase accumulation in an Andreev quasiparticle pair is Δϕ=g_eff⋅μ_B⋅B_(//) (ℏv_F/L) which is of the order of few thousands Gauss. In one particular sample, a full modulation of the critical current with about 1 T range is observed. This is similar to the proximity effect in S/F/S junctions which suggests a 0-π junction transition.

Neste trabalho foram estudadas as fases topológicas não triviais presentes em sistemas formados pela deposição de átomos de grafeno. Encontramos que quando um átomo hibridiza fortemente com o grafeno, apresenta um momento magnético e um forte spin-órbirta é possível a formação de uma rede hexagonal de baricentros que efetivamente gera uma estrutura de bandas característica de um efeito hall quântico anômalo. Especificamente, determinamos que o Ru satisfaz estas características. Quando este metal é depositado em uma configuração triangular no grafeno ocorrem picos na densidade de estados localizados no centro geométrico (baricentro) dos triângulos formados pelos Ru. Estes picos estão distribuídos de forma hexagonal e efetivamente geram uma estrutura de bandas que nas proximidades do nível de Fermi apresenta uma configuração de spin característica do efeito Hall quântico anômalo. Adicionalmente, encontramos que o sistema composto pela absorção de Ba ou Sr no grafeno favorece a formação do efeito Hall quântico de spin. Neste sistema, o acoplamento spin-órbita (SOC) gera um gap mais de 1000 vezes maior ao período no grafeno prístino. Para o estudo destes sistemas, implementamos no código SIESTA a aproximação on-site do acoplamento spin-órbita via o formalismo dos pseudopotenciais relativísticos de norma conservada. Nossa implementação foi testada a partir do estudo de fenômenos já conhecidos: i) o strong spin-splitting gerado no grafeno pela adsorção de Au, ii) o efeito hall quântico de spin no poço quântico de HgTe/CdTe e, iii) a formação de estados topológicos na superfície do Bi2Se3 e as fases magnéticas deste material com átomos de Mn adsorvidos. / In this work, were studied the non-trivial topological phases present in systems formed by deposition of atoms in graphene. We found that when an atom hybridizes strongly with grapheme, has a magnetic moment and a strong spin-orbit it is possible the formation of a hexagonal network of barycentres that effectively generates a structure band characteristic of a quantum anomalous Hall effect. Specifically, we determined that Ru satisfies these characteristics. When this metal is deposited in a triangular configuration in grapheme, peaks occur in the density of localized states in the geometric center (centroid) of the triangles formed by Ru. These peaks are distributed in a hexagonal structure and effectively generates a band structure that near the Fermi level has a spin configuration characteristic of the spin quantum Hall effect anomalous. Additionally, we found that the system composed by the adsorption of Ba or Sr in grapheme, promotes the formation of spin quantum Hall effect. In this system, the spin-orbit coupling (SOC) generates a gap more than 1000 times grater that predicted in pristine praphene. To study these systems, wu implemented in the code SIESTA the on-site approach of the spin-orbit coupling throught the formalism of norm conserved relativistic pseudo potentials. Our implementation was tested from the study of phenomena already known: i) the strong spin-splitting generated in graphene by adsorption of Au, ii) the quantum spin Hall effect in quantum well of HgTe / CdTe and, iii) formation of topological states in the surface of Bi2Se3 and the magnetic of this material with Mn atoms adsorved.

<p>The main focus of this thesis is the investigation of the dissociation dynamics of aryl halides using femtosecond pump-probe spectroscopy. In the monohalogenated aryl halides, iodo-, bromo- and chlorobenzene, the rate of dissociation following excitation at 266 nm in the gas phase increased with increasing mass of the halogen atom. This process was assigned to predissociation of the initially excited singlet (π, π*) state via a repulsive triplet (n, σ*) state due to spin-orbit interaction. In addition to the predissociative mechanism, a direct dissociation channel was observed in iodobenzene. The rate of the predissociation in bromobenzene was found to be faster in the condensed phase than in the gas phase, which can be explained by solvent-induced symmetry perturbations. <i>Ab initio</i> calculations of the potential energy surfaces of the ground state and several low lying excited states in bromobenzene have been performed in order to verify the suggested mechanism. Substituting one of the hydrogen atoms in bromobenzene affected the predissociation rate significantly. In o-, m- and p-dibromobenzene the predissociation rate increased with decreasing distance between the bromine atoms in accordance with an increased spin-orbit interaction introduced by the bromine substituent. The fastest predissociation rate was observed in 1,3,5-tribromobenzene. With chlorine and fluorine substitution, inductive and conjugative effects were found to be of importance. In the o- and m-isomers of the dihalogenated aryl halides, an additional faster dissociation channel was observed. Guided by <i>ab initio</i> calculations of the potential energy surfaces in the dibromobenzene isomers, we ascribed the fast dissociation pathway to predissociation of an initially excited triplet state. Upon methyl group substitution in bromobenzene, the decreased lifetime of the initially excited state was attributed to an incresaed density of coupled states.</p><p>Another system which has been studied in the condensed phase is diiodomethane. Using Car-Parrinello molecular dynamics simulations we observed a prompt dissociation and subsequent recombination to the isomer, iso-diiodomethane, in acetonitrile solution.</p><p>Vibrational wavepacket dynamics in the C (¹Σ⁺) state of NaK were studied using a direct ionization probing scheme. A simple analytical expression for the pump-probe signal was developed in order to see what factors that govern direct ionization of the vibrational wavepacket. Our experimental data was consistent with a photoionization transition dipole moment that varies with internuclear distance.</p>

The main focus of this thesis is the investigation of the dissociation dynamics of aryl halides using femtosecond pump-probe spectroscopy. In the monohalogenated aryl halides, iodo-, bromo- and chlorobenzene, the rate of dissociation following excitation at 266 nm in the gas phase increased with increasing mass of the halogen atom. This process was assigned to predissociation of the initially excited singlet (π, π*) state via a repulsive triplet (n, σ*) state due to spin-orbit interaction. In addition to the predissociative mechanism, a direct dissociation channel was observed in iodobenzene. The rate of the predissociation in bromobenzene was found to be faster in the condensed phase than in the gas phase, which can be explained by solvent-induced symmetry perturbations. Ab initio calculations of the potential energy surfaces of the ground state and several low lying excited states in bromobenzene have been performed in order to verify the suggested mechanism. Substituting one of the hydrogen atoms in bromobenzene affected the predissociation rate significantly. In o-, m- and p-dibromobenzene the predissociation rate increased with decreasing distance between the bromine atoms in accordance with an increased spin-orbit interaction introduced by the bromine substituent. The fastest predissociation rate was observed in 1,3,5-tribromobenzene. With chlorine and fluorine substitution, inductive and conjugative effects were found to be of importance. In the o- and m-isomers of the dihalogenated aryl halides, an additional faster dissociation channel was observed. Guided by ab initio calculations of the potential energy surfaces in the dibromobenzene isomers, we ascribed the fast dissociation pathway to predissociation of an initially excited triplet state. Upon methyl group substitution in bromobenzene, the decreased lifetime of the initially excited state was attributed to an incresaed density of coupled states. Another system which has been studied in the condensed phase is diiodomethane. Using Car-Parrinello molecular dynamics simulations we observed a prompt dissociation and subsequent recombination to the isomer, iso-diiodomethane, in acetonitrile solution. Vibrational wavepacket dynamics in the C (1Σ+) state of NaK were studied using a direct ionization probing scheme. A simple analytical expression for the pump-probe signal was developed in order to see what factors that govern direct ionization of the vibrational wavepacket. Our experimental data was consistent with a photoionization transition dipole moment that varies with internuclear distance.

This work comprises two main parts. The first part outlines our efforts to expand on the recent work of Gütlich et.al. by synthesizing Co(II) based spin crossover systems within a dendritic framework. We wanted to investigate the possibility of synthesizing different first generation, triazole containing dendrimers using “click” type reactions and their coordination ability with Co(II) ions. To this end we have had limited success mainly due to the numerous challenges in synthesizing a pure dendrimer product. The second part details our efforts in the synthesis of a mononuclear Co(II) based single molecule magnet. This comes as an extension to recent reports by Chang and Long where they have successfully obtained mononuclear Fe(II) single molecule magnets by inducing structural distortions within the complexes to amplify the spin-orbit coupling. We postulated that the use of Co(II) in conjunction with a bulky ligand framework would lead to desirable magnetic properties. We chose the known bis(imino)pyridine ligand scaffold due to its rich chemistry and its interesting and unexpected coordination behaviour, as we have seen in previous research efforts by our lab. To this end we were successful in isolating and characterizing 4 compounds, and we have carried out detailed magnetic measurements on the two most magnetically interesting species.

This work comprises two main parts. The first part outlines our efforts to expand on the recent work of Gütlich et.al. by synthesizing Co(II) based spin crossover systems within a dendritic framework. We wanted to investigate the possibility of synthesizing different first generation, triazole containing dendrimers using “click” type reactions and their coordination ability with Co(II) ions. To this end we have had limited success mainly due to the numerous challenges in synthesizing a pure dendrimer product. The second part details our efforts in the synthesis of a mononuclear Co(II) based single molecule magnet. This comes as an extension to recent reports by Chang and Long where they have successfully obtained mononuclear Fe(II) single molecule magnets by inducing structural distortions within the complexes to amplify the spin-orbit coupling. We postulated that the use of Co(II) in conjunction with a bulky ligand framework would lead to desirable magnetic properties. We chose the known bis(imino)pyridine ligand scaffold due to its rich chemistry and its interesting and unexpected coordination behaviour, as we have seen in previous research efforts by our lab. To this end we were successful in isolating and characterizing 4 compounds, and we have carried out detailed magnetic measurements on the two most magnetically interesting species.