The magnetic properties of some rare earth based Heusler alloys have been investigated. Rare earth Heusler alloys of the form Pd2Reln exhibit magnetic behaviour characterised by magnetic moments localised on the rare earth atoms. X-ray and neutron diffraction investigation show that all alloys crystallise in the cubic L21 Heusler structure with space group Fm3m.

This thesis describes the synthesis of ruthenium based molecular clusters and their characterisation. Chapter 2 introduces the concept that the very large zero-field splitting (D = 2.9 cm–1) in the S = 5/2 ground state of [Ru2Mn(μ3-O)(tBuCO2)6(py)3] can be modelled by antisymmetric exchange effects. This is supported by measurement of the single ion D values from the Fe2Mn analogue. The same model is applied to the Ru2Ni analogue to describe the zero-field splitting in the S = 1 ground state, (DGS = +8.0 cm–1 from DNi = -4.0 cm–1) in Chapter 3.Chapters 3 and 4 give the full characterisation of each of the two families, [MIII2MII(μ3-O)(tBuCO2)6(py)3] (MIII = Ru or Fe, MII = Mn, Co, Ni or Zn), through IR, electronic absorption and NMR spectroscopy and are structurally characterised by X-ray diffraction. The total spin ground states and zero-field splitting of those ground states have been ascertained by SQUID magnetometry and EPR spectroscopy. Due to the redox activity of the Ru2M complexes chemical oxidations led to the isolation of [RuIII2CoIIIO(tBuCO2)6(py)3]+ (5) and [RuIIIRuIVNiIIO(tBuCO2)6(py)3]+ (6); the locus of their oxidation was determined with the aid of X-ray absorption spectroscopy (XAS).Chapter 5 shows that due to the ease of the substitution of the terminal ligand in Ru2M they can be linked to other molecular clusters with N-donor ligands, in this case [Cr7NiF8(tBuCO2)15(O2CC5H4N)][NH2Pr2] in order to synthesise [Ru2NiO(tBuCO2)6(py)(Cr7NiF8(tBuCO2)15(O2CC5H4N))2][NH2Pr2]2. In situ oxidation experiments have also been carried out to assess the switchabilty of the redox active linker. Chapter 6 demonstrates a new structural archetype for tetranuclear ruthenium mixed-metal complexes, with the formula, [Ru2M2(µ3-OH)2(tBuCO2)7(py)4], where M is either Co (1) or Ni (2). SQUID magnetometry and EPR spectroscopy have determined the spin ground states as, Seff = 1/2 in 1 and S = 3/2 in 2. The magnetic anisotropy in 2 has been determined as +2.02 cm–1 for the S = 3/2 ground state.

The Multiplicative Schwarz Preconditioned Inexact Newton (MSPIN) algorithm is presented as a complement to Additive Schwarz Preconditioned Inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. The ASPIN framework, as an option for the outermost solver, successfully handles strong nonlinearities in computational fluid dynamics, but is barely explored for the highly nonlinear models of complex multiphase flow with capillarity, heterogeneity, and complex geometry. In this dissertation, the fully implicit ASPIN method is demonstrated for a finite volume discretization based on incompressible two-phase reservoir simulators in the presence of capillary forces and gravity. Numerical experiments show that the number of global nonlinear iterations is not only scalable with respect to the number of processors, but also significantly reduced compared with the standard inexact Newton method with a backtracking technique. Moreover, the ASPIN method, in contrast with the IMPES method, saves overall execution time because of the savings in timestep size. We consider the additive and multiplicative types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Moreover, we provide the convergence analysis of the MSPIN algorithm. Under suitable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN, and maintain fast convergence even for challenging problems, such as high-Reynolds number Navier-Stokes equations.

The prime objectives of contrast agents in Magnetic Resonance Imaging(MRI) is to accelerate the relaxation rate of the solvent water protons in the surrounding tissue. Paramagnetic relaxation originates from dipole-dipole interactions between the nuclear spins and the fluctuating magnetic field induced by unpaired electrons. Currently Gadolinium(III) chelates are the most widely used contrast agents in MRI, and therefore it is incumbent to extend the fundamental theoretical understanding of parameters that drive the relaxation mechanism in these complexes. Traditionally the Solomon-Bloembergen-Morgan equations have been utilized to describe relaxation times in terms, primarily of the Zeeman interaction, which is the splitting of degenerate energy levels due to an applied magnetic field. However, in compounds such as Gadolinium(III) complexes with total electron spins higher than 1 (in this case S=7/2) other interactions such as the Zero-Field Splitting(ZFS) play a significant role. ZFS is the splitting of degenerate energy levels in the absence of an external magnetic field. For this purpose, the current research delves into an understanding of the relaxation process, focusing on ZFS in various complexes of interest, using quantum chemical methods as well as molecular dynamic simulations.

Lors d'examens IRM des agents de contraste sont utilisés afin d'affiner les diagnostics. Ces agents sont constitués d'un ion paramagnétique, la plupart du temps le gadolinium, chélaté par un ligand linéaire ou macrocyclique afin d'éviter tout relargage et donc toute toxicité. Dans cette thèse, nous étudions les propriétés magnétiques de complexes de gadolinium. Ces propriétés magnétiques influencent la relaxation d'une molécule d'eau coordinée à l'ion central, relaxation à l'origine des contrastes visibles sur les images IRM. Nous nous sommes intéressés à l'agent de contraste commercial ProHance ainsi qu'à des systèmes dérivés. Après avoir réalisé des simulations de dynamique moléculaire ab initio des espèces à étudier, et les avoir analysées, nous avons sur ces systèmes des calculs de structure électronique explicitant les interactions hyperfines en jeu au sein du système, ainsi que le Zero-Field Splitting. Il a ainsi été possible de définir un tenseur hyperfin moyen pour chacun des systèmes étudiés. De plus, une décomposition du terme en fonction de variables collectives géométriques a permis d'expliciter l'origine des fluctuations rapides du tenseur hyperfin dans le cas du ProHance. Enfin, le ZFS a été décomposé en un terme dit transitoire et un terme dit statique. Ceci permettra par la suite de modéliser la relaxation électronique des systèmes étudiés et la relaxation du proton de la molécule d'eau coordinée.

Comme nous le savons, les applications sont déterminées par des propriétés, qui sont essentiellement déterminées par la structure. L’interaction entre la forme (structure moléculaire) et la fonction (propriétés physiques) peut être exploitée par le ligand, l’ion métallique, l'approche métallacrown et ainsi de suite. Les travaux portent sur la synthèse et l’étude du comportement magnétique de complexes mononucléaires cobalt(II) de géométrie bipyramide trigonale et sur l’étude de complexes mononucléaires de lanthanides possédant une structure de type métallacrown.Pour les complexes de cobalt(II), l’objectif a été de modifier l’anisotropie magnétique en modifiant la nature du ligand organique tétradenté et du ligand terminal en gardant, autant que faire se peut, la géométrie et même la symétrie des complexes. Presque tous ces complexes se comportent comme des molécules-aimants avec une barrière énergétique à l’inversion de l’aimantation qui peut être liée à leur anisotropie magnétique et donc à la nature des ligands. Et les complexes métallacrown à base de lanthanides étant hautement symétriques, permet de les utiliser comme modèles pour effectuer une corrélation entre la nature de l’ion lanthanide et leurs propriétés d’aimants.La thèse est composée de 6 chapitres. Le chapitre 1 présente l’état de l’art du magnétisme, des molécules-aimants (SMMs et SIMs), et quelques exemples importants. Le chapitre 2 se concentre sur une famille de complexes de géométriebipyramide trigonale de formule générale [Co(Me6tren)X]Y avec le ligand axial (X) et le contre-ion (Y) induisant le comportement SMM.Dans cette série de composés, j’ai étudié l’influence du ligand axial X sur la nature et l’amplitude de l’anisotropie magnétique. J’ai montré que la série des halogénures, l’anisotropie la plus forte est obtenue pour le ligand axial fluorure (F–). J’ai aussi étudié l’effet du cation Y qui influence l’interaction entre les molécules qui affectent le comportement d’aimant moléculaire. Au chapitre 3, on étudie l’influence du changement du ligand tétradenté. Le remplacement des trois atomes d’azote qui se trouvent en position équatoriale dans la sphère de coordination de cobalt(II) par des atomes de soufre induit une augmentation des distances Co–L dans le plan équatorial qui conduit à une plus forte anisotropie. Les calculs théoriques effectués sur ces complexes permettent de rationaliser les résultats expérimentaux et surtout de prévoir les propriétés de nouveaux complexes. Les chapitres 4 et 5 concernent deux séries de SMM 12-MC-4 basées sur LnGa4 (Ln = TbIII, DyIII, HoIII, ErIII, YbIII) avec les ligands basés sur l’acide salicylhydroxamique (H3shi) et l’acide 3-hydroxy-2-naphtohydroxamique (H3nha). J’ai préparé plusieurs complexes et étudié leurs propriétés magnétiques. Les calculs théoriques permettent de rationaliser la différence entre les propriétés des magnétiques dues aux différents ions lanthanide. Enfin, une conclusion générale avec des perspectives sont récapitulées au chapitre 6. / As we know, the applications are determined by properties, which are essentially determined by structure. The interplay between form (molecular structure) and function (physical properties) can be exploited engineering by the ligand, the metal ion, the metallacrown approach and so on. The work focuses on the synthesis and the study of the magnetic behavior of mononuclear cobalt(II) complexes with trigonal geometry and on the study of mononuclear lanthanide complexes that possess a metallacrown structure.For the cobalt(II) complexes, the aim was to tune the magnetic anisotropy by changing the nature of the tetradentate organic ligand and the terminal ligand. Almost all these complexes behave as Single Molecule Magnets with an energy barrier to the reversal of the magnetization that can be linked to their magnetic anisotropy and thus to the nature of the organic ligands. The lanthanide containing metallacrown complexes are highly symmetric, which allows performing a correlation between the nature of the lanthanide ion and their Single Molecule Magnet properties.The dissertation will be composed of 6 chapters. Chapter 1 introduces the background of the magnetism, Single Molecule Magnets, Single Ion Magnets, and some important SIMs. Chapter 2 focuses on a family of trigonal bipyramidal complexes [Co(Me6tren)X]Y. We show that the axial ligand affects the SMM behavior allowing us to prepare a complex with a magnetic bistability at T = 2 K. In Chapter 3, we examine the effect of changing the coordinated atoms (sulfur instead of nitrogen) in the equatorial coordination sphere of cobalt(II). We demonstrate that this slight change improves the SMM behavior. Chapter 4 and 5, which concern two series of 12-MC-4 SMMs based on LnGa4 (Ln = TbIII, DyIII, HoIII, ErIII, YbIII) with the ligands salicylhydroxamic acid (H3shi) and 3-hydroxy-2-naphthohydroxamic acid (H3nha), respectively, where we correlate the nature of the lanthanide ion to its magnetic behavior using ab initio calculations. At last, the understanding gained from this dissertation research, along with future research directions will be recapitulated in Chapter 6.

Ideal magnetohydrodynamics (MHD) simulations are known to have problems in satisfying the solenoidal constraint (i.e. the divergence of magnetic field should be equal to zero, $ ablacdotvec{B} = 0$). The simulations become unstable unless specific measures have been taken. In this thesis, a solenoidal constraint satisfying technique that allows discrete satisfaction of the solenoidal constraint up to the machine accuracy is presented and validated with a variety of test cases. Due to its inspiration from Chorin's artificial compressibility method developed for incompressible CFD applications, the technique was named as extit{artificial compressibility analogy (ACA)} approach. It is demonstrated that ACA is a purely hyperbolic, stable and consistent technique, which is moreover easy to implement. Unlike some other techniques, it does not pose any problems of the sort that $ ablacdotvec{B}$ errors accumulate in the vicinity of the stagnant regions of flow. With these crucial properties, ACA is thought to be a remedy to the drawbacks of the most commonly used solenoidal constraint satisfying techniques in the literature namely: Incorrect shock capturing and poor performance of the convective stabilization mechanism in regions of stagnant flow for Powell's source term method; exceedingly complex implementation for constrained transport technique due to the staggered grid representation; computationally expensive nature due to the necessity of a Poisson solver combined with hyperbolic/elliptic numerical methods for classical projection schemes. In the first chapter of the thesis, general background knowledge is given about plasmas, MHD and its history, a certain class of upwind finite volume methods, namely Riemann solvers, and their applications in MHD, the definition, constituents, formation mechanisms and effects of space weather and some of the space missions that are and will be performed in its prediction. Secondly, detailed analysis of the compressible ideal MHD equations is given in the form of the derivation of the equations, their dimensionless numbers which will be of use to specify the flows in the following chapters, and finally, the presentation of the MHD waves and discontinuities, which indicates the complexity of the system of ideal MHD equations and therefore their further numerical analysis. The next discussion is about the main subject of the thesis, namely the solenoidal constraint satisfying techniques. First of all, the definition and significance of the solenoidal constraint is given. Afterwards, the most common solenoidal constraint satisfying techniques in the literature are reviewed along with their abovementioned drawbacks. Moreover, particular emphasis is given to the Powell's source term approach which was also implemented in the upwind finite volume MHD solver developed. In addition, the hyperbolic divergence cleaning technique is presented in detail together with the resemblance and differences between it and ACA. Some other solenoidal constraint satisfying techniques are briefly mentioned at this stage. After these, ACA is presented in the following way: The point of inspiration, which is the analogy made with Chorin's artificial compressibility method developed for incompressible CFD, the introduction of the modified system of ideal MHD equations due to ACA, the derivation of the wave equation governing the propagation of $ ablacdotvec{B}$ errors and the analytical consistency proof. Having finished the core discussion of the thesis, the solver developed and its constituents are given in the fourth chapter. Furthermore, a brief overview of the platform into which this solver was implemented, namely COOLFluiD, is also given at this point. Afterwards, a thorough numerical verification of the ACA approach has been made on an increasingly complex suite of test cases. The results obtained with ACA and Powell's source term implementations are given in order to numerically analyse and verify ACA and compare the two methods and validate them with the results from literature. The sixth chapter is devoted to further validation of ACA performed with a variety of more advanced space weather-related simulations. In this chapter, also the $vec{B}_{ extrm{0}} + vec{B}_{ extrm{1}}$ splitting technique used to treat planetary magnetosphere is presented along with its application to ACA and Powell's source term approaches. This technique is utilized in obtaining the solar wind/Earth's magnetosphere interaction results and is based on suppressing the direct inclusion of the Earth's magnetic field, which is a dipole field, in the solution variables. In this way, problems are avoided with the energy equation that could arise from the drastic change of the ratio of the dipole field and the variable field computed by the solver (i.e. $frac{lvertvec{B}_{ extrm{0}}lvert}{lvertvec{B}_{ extrm{1}}lvert}$) in the computational domain. Finally, conclusions and future perspectives related to the material presented in the thesis are put forward.

Nous avons étudié, par RPE impulsionnelle, la cohérence quantique et des spins électroniques des ions de transition Mn2+, Co2+, Fe3+, et des complexes Fe3+/Cs+ et Fe3+/Na+, tous présents dans le ZnO monocristallin. Nous avons trouvé que l’anisotropie magnétique peut altérer la cohérence de la phase dynamique des qubits des spins électroniques. Nous avons mesuré une faible décohérence pour les spins d’ions Mn2+et Fe3+ dans ZnO, qui ont tous deux une faible anisotropie magnétique uniaxiale, tandis que les ions Co2+ isolés avec une très forte anisotropie magnétique uniaxiale, une décohérence rapide a été mis en évidence. Nous avons trouvé que les spins électroniques des complexes de type Fe3+/Cs+, ayant un tenseur d’anisotropie magnétique plus complexe que la simple anisotropie uniaxiale des ions Fe3+ isolés, possèdent presque le même temps de décohérence. Par la méthode des perturbations, nous avons mis en évidence théoriquement un terme supplémentaire à la phase habituelle de Berry, dû à l’anisotropie magnétique et qui existe dans tout système ayant un spin S>1/2. / We studied by pulsed EPR (p-EPR), the quantum coherence of electronic spins qubits of isolated transition metal ions of Mn2+, Co2+, Fe3+ and Fe3+/Cs+ as well as Fe3+/Na+ complexes, all found as traces in mono-crystalline ZnO. Indeed, we experimentally demonstrated that the magnetic anisotropy can alter the coherence of the dynamic phase of electronic spins qubits. We found a small decoherence for Mn2+ and Fe3+, spins having a small uniaxial magnetic anisotropy, and on the contrary, we found a very strong decoherence for Co2+ spins having a very strong uniaxial magnetic anisotropy. We found that the electronic spins of the Fe3+/Cs+ complex, having a more complex tensor magnetic anisotropy compared to the simplest uniaxial one of isolated Fe3+ spins in ZnO, have almost the same coherence time. By the perturbation method, we have found theoretically an additional term to the usual geometric Berry phase, due to the magnetic anisotropy which exists in any system having a spin S>1/2.

<p>In this thesis we have performed core-electron spectroscopy studies of gas phase molecular systems starting with smaller diatomic, continuing with triatomic and extending our research to more complex polyatomic ones. We can subdivide the results presented here into two categories: the first one focusing on electronic fine structure and effect of the chemical bonds on molecular core-levels and the other one dealing with nuclear dynamics induced by creation of a core hole. In our research we have mostly used synchrotron radiation based techniques such as X-ray Photoelectron (XPS), X-ray Absorption (XAS), normal and Resonant Auger (AES and RAS, respectively) and Energy-Selected Auger Electron PhotoIon COincidence (ES-AEPICO) spectroscopies.</p><p>We have demonstrated that resonant Auger spectroscopy can be used to aid interpretation of the features observed in XAS for Rydberg structures in the case of Cl₂ and C1s⁻¹π*¹ states of allene molecules. The combined use of high-resolution spectroscopy with <i>ab initio</i> calculations can help the interpretation of strongly overlapped spectral features and disentangle their complex profiles. This approach enabled us to determine the differences in the lifetimes for core-hole 2p sublevels of Cl₂ which are caused by the presence of the chemical bond. We have shown that contribution in terms of the Mulliken population of valence molecular orbitals is a determining factor for resonant enhancement of different final states and fragmentation patterns reached after resonant Auger decays in N₂O.</p><p>We have also performed a systematic study of the dependence of the C1s resonant Auger kinetic energies on the presence of different substituents in CH₃X compounds. For the first time we have studied possible isomerization reaction induced by core excitation of acetylacetone. We could observe a new spectral feature in the resonant Auger decay spectra which we interpreted as a signature of core-excitation-induced keto-enol tautomerism.</p>

<p>Atoms, molecules and clusters all constitute building blocks of macroscopic matter. Therefore, understanding the electronic and geometrical properties of such systems is the key to understanding the properties of solid state objects.</p><p>In this thesis, some atomic, molecular and cluster systems (clusters of O₂, CH₃Br, Ar/O₂, Ar/Xe and Ar/Kr; dimers of Na; Na and K atoms) have been investigated using synchrotron radiation, and in the two last instances, laser light. We have performed x-ray photoelectron spectroscopy (XPS) on all of these systems. We have also applied ultraviolet photoelectron spectroscopy (UPS), resonant Auger spectroscopy (RAS) and near-edge x-ray absorption spectroscopy (NEXAFS) to study many of the systems. Calculations using <i>ab initio</i> methods, namely density functional theory (DFT) and Møller-Plesset perturbation theory (MP), were employed for electronic structure calculations. The geometrical structure was studied using a combination of <i>ab initio</i> and molecular dynamics (MD) methods.</p><p>Results on the dissociation behavior of CH₃Br and O₂ molecules in clusters are presented. The dissociation of the Na₂ molecule has been characterized and the molecular field splitting of the Na 2<i>p</i> level in the dimer has been measured. The molecular field splitting of the CH₃Br 3<i>d</i> level has been measured and the structure of CH₃Br clusters has been determined to be similar to the structure of the bulk solid. The diffusion behavior of O₂, Kr and Xe on large Ar clusters, as a function of doping rate, has been investigated. The shake-down process has been observed from excited states of Na and K. Laser excited Na atoms have been shown to be magnetically aligned. The shake-down process was used to characterize the origin of various final states that can be observed in the spectrum of ground-state K.</p>