As the technology underlying modern electronics advances, it is unlikely that previous rates of power use and computational speed improvement can be maintained. Devices using the spin of an electron or hole, "spintronic" systems, can begin to address these problems, creating new devices which can be used as a continuation and augmentation of existing electronic systems. In addition, spintronic devices could make special use of coherent quantum states, making it feasible to address certain problems which are computationally intractable using classical electronic components. Unlike higher-dimensional nanostructures such as quantum wires and wells, quantum dots allow a single electron or hole to be confined to the dot. Through the spin-orbit effect, the electron and hole g-tensor can be influenced by quantum dot shape and applied electric fields, leading to the possibility of gating a single quantum dot and using a single electron or hole spin for quantum information storage or manipulation. In this thesis, the spin of electrons and holes in isolated semiconductor quantum dots are investigated in the presence of electric and magnetic fields using realspace numerical 8-band strain-dependent k · p theory. The calculations of electron and hole g-tensors are then used to predict excitonic g-tensors as a function of electric field. These excitonic g-factors are then compared against existing experimental work, and show that in-plane excitonic g-factor dependence on electric field is dominated by the hole g-factor. The dependence of the electron and hole g-tensors on the applied electric field are then used to propose a class of novel quantum dot devices which manipulate the electron or hole spins in either a resonant or a non-resonant mode. Because of the highly parabolic dependence of some components of the hole g-tensor on the applied electric field, a shift in the Larmor frequency and an additional resonance are predicted, with additional shifts and resonances occurring for higher-order dependencies. Spin manipulation times down to 3.9ns for electrons and 180ps for holes are reported using these methods.

Relativistic effects are extremely important for heavy atoms and heavy atom containing molecules. Therefore, a relativistic treatment is needed when calculating molecular properties of these species. The fully- relativistic Dirac treatment involves electronic and positronic wavefunctions and a very large basis set is required. This leads to calculations that are too costly and time-consuming for larger molecules. The Zeroth-Order Regular Approximation (ZORA) is an approximation to the Dirac approach, which only deals with the electronic wavefunction. However, unfortunately this method is plagued by the gauge-dependence problem. The gauge-independent ZORA (ZORA-GI) and strictly atomic ZORA approaches provide solutions to this problem.In this work, the ZORA-GI and strictly atomic ZORA codes have been successfully implemented into the Gaussian 09 program. They have been used to calculate the bond lengths, harmonic vibrational frequencies and dissociation energies of the I2, Au2 and Pt2 diatomic molecules. The results show good agreement with experiment and previous theoretical studies. The non-relativistic, ZORA-GI, strictly atomic ZORA and pseudopotential approximations have been used to investigate the electronic structure of the actinide monoxides, AnO, and actinide monoxide cations, AnO+ (An = Th – Cm). It was found that the ground state configurations were dependent on the relativistic approximation chosen. The bond lengths, harmonic vibrational frequencies and dissociation energies were also calculated, with the ZORA methods generally outperforming the pseudopotential approximation. The first theoretical g-tensor study of the organouranium(V) complexes [U(C7H7)2]-, [U(η8-C8H8)(NEt2)(THF)]+, [U(η5-C5H5)(NMe2)3(THF)]+, [U(η8-C8H8)(NEt2)3], [U(η5-C5H5)2(NEt2)2]+ and [U(η8-C8H8)(η5-C5H5)(NEt2)2] has been carried out. It was demonstrated that the choice of density functional affects the way in which the g-tensor axes are assigned. The ground state spin density and SOMO are also sensitive to the choice of density functional. It is these factors that determine the value of the g-tensor.

In dieser Arbeit wird eine unrestricted Coupled-Cluster CC2 Response-Methode für die Berechnung von Eigenschaften erster und zweiter Ordnung, mit dem elektronischen g-Tensor als Schwerpunkt, präsentiert. Lokale Korrelations- und Dichtefittingnäherungen wurden verwendet. Die fundamentalen Konzepte notwendig für das Verständnis von Coupled-Cluster-Theorie, Dichtefitting, lokaler Korrelation, allgemeinen Coupled-Cluster Eigenschaften und dem elektronischen g-Tensor werden diskutiert. Die berechneten g-Tensoren werden mit denen durch Coupled-Cluster Singles and Doubles, Dichtefunktionaltheorie und Experiment erhaltenen verglichen. Effizienz und Genauigkeit der Näherung wird untersucht. Ein detailierter Anhang beschreibt die diagrammatische Coupled-Cluster-Theorie sowie ihre Anwendung zur Herleitung der verwendeten Arbeitsgleichungen. Die in dieser Arbeit entwickelte Methode ermöglicht es, den elektronischen g-Tensor von ausgedehnten Systemen mit einer Methode, die nicht auf Dichtefunktionaltheorie basiert, quantitativ vorherzusagen. Damit ist sie ein wichtiger Schritt hin zur Entwicklung von niedrig skalierenden Coupled-Cluster-Methoden höherer Ordnung für diese Art von Problem. / This work presents an unrestricted coupled-cluster CC2 response method using local correlation and density fitting approximations for the calculation of first and second order properties with particular focus on the electronic g-tensor. The fundamental concepts related to coupled-cluster theory, density fitting, local correlation, general coupled-cluster properties and the electronic g-tensor are discussed. The calculated g-tensors are benchmarked against those obtained from coupled-cluster singles and doubles, density functional theory and experiment. Efficiency and accuracy of the approximations is investigated. A detailed appendix covers the fundamentals of diagrammatic coupled-cluster and its application to the derivation of the working equations. The method presented in this thesis enables the quantitative prediction of the electronic g-tensor of extended systems with a method other than density functional theory. It represents an important step towards the development of low-scaling higher order coupled-cluster methods for this type of problem.

<p>The recent state of art in the magnetic resonance area putsforward the electron paramagnetic resonance, EPR, and nuclearmagnetic resonance, NMR, experiments on prominent positions forinvestigations of molecular and electronic structure. A mostdifficult aspect of such experiments is usually the properinterpretation of data obtained from high-resolution spectra,that, however, at the same time opens a great challenge forpure theoretical methods to interpret the spectral features.This thesis constitutes an effort in this respect, as itpresents and discusses calculations of EPR and NMR parametersof paramagnetic molecules. The calculations are based on newmethodology for determination of properties of paramagneticmolecules in the framework of the density functional theory,which has been developed in our laboratory.</p><p>Paramagnetic molecules are, in some sense, very special. Thepresence of unpaired electrons essentially modifies theirspectra. The experimental determination of the magneticresonance parameters of such molecules is, especially in theNMR case, quite complicated and requires special techniques ofspectral detection. The significant efforts put into suchexperiments are completely justi fied though by the importantroles of paramagnetic species playing in many areas, such as,for example, molecular magnets, active centers in biologicalsystems, and defects in inorganic conductive materials.</p><p>The first two papers of this thesis deal with thetheoretical determination of NMR parameters, such as thenuclear shielding tensors and the chemical shifts, inparamagnetic nitroxides that form core units in molecularmagnets. The developed methodology aimed to realize highaccuracy in the calculations in order to achieve successfulapplications for the mentioned systems. Theeffects of hydrogenbonding are also described in that context. Our theory forevaluation of nuclear shielding tensors in paramagneticmolecules is consistent up to the second order in the finestructure constant and considers orbital, fully isotropicdipolar, and isotropic contact contributions to the shieldingtensor.</p><p>The next three projects concern electron paramagneticresonance. The wellknown EPR parameters, such as the g-tensorsand the hyperfine coupling constants are explored. Calculationsof electronic g-tensors were carried out in the framework of aspin-restricted open-shell Kohn-Sham method combined with thelinear response theory recently developed in our laboratory.The spincontamination problem is then automatically avoided.The solvent effects, described by the polarizable continuummodel, are also considered. For calculations of the hyperfinecoupling constants a so-called restricted-unrestricted approachhas been developed in the context of density functional theory.Comparison of experimentally and theoretically determinedparameters shows that qualitative mutual agreement of the twosets of data can be easily achieved by employing the proposedformalisms.</p>

The recent state of art in the magnetic resonance area putsforward the electron paramagnetic resonance, EPR, and nuclearmagnetic resonance, NMR, experiments on prominent positions forinvestigations of molecular and electronic structure. A mostdifficult aspect of such experiments is usually the properinterpretation of data obtained from high-resolution spectra,that, however, at the same time opens a great challenge forpure theoretical methods to interpret the spectral features.This thesis constitutes an effort in this respect, as itpresents and discusses calculations of EPR and NMR parametersof paramagnetic molecules. The calculations are based on newmethodology for determination of properties of paramagneticmolecules in the framework of the density functional theory,which has been developed in our laboratory. Paramagnetic molecules are, in some sense, very special. Thepresence of unpaired electrons essentially modifies theirspectra. The experimental determination of the magneticresonance parameters of such molecules is, especially in theNMR case, quite complicated and requires special techniques ofspectral detection. The significant efforts put into suchexperiments are completely justi fied though by the importantroles of paramagnetic species playing in many areas, such as,for example, molecular magnets, active centers in biologicalsystems, and defects in inorganic conductive materials. The first two papers of this thesis deal with thetheoretical determination of NMR parameters, such as thenuclear shielding tensors and the chemical shifts, inparamagnetic nitroxides that form core units in molecularmagnets. The developed methodology aimed to realize highaccuracy in the calculations in order to achieve successfulapplications for the mentioned systems. Theeffects of hydrogenbonding are also described in that context. Our theory forevaluation of nuclear shielding tensors in paramagneticmolecules is consistent up to the second order in the finestructure constant and considers orbital, fully isotropicdipolar, and isotropic contact contributions to the shieldingtensor. The next three projects concern electron paramagneticresonance. The wellknown EPR parameters, such as the g-tensorsand the hyperfine coupling constants are explored. Calculationsof electronic g-tensors were carried out in the framework of aspin-restricted open-shell Kohn-Sham method combined with thelinear response theory recently developed in our laboratory.The spincontamination problem is then automatically avoided.The solvent effects, described by the polarizable continuummodel, are also considered. For calculations of the hyperfinecoupling constants a so-called restricted-unrestricted approachhas been developed in the context of density functional theory.Comparison of experimentally and theoretically determinedparameters shows that qualitative mutual agreement of the twosets of data can be easily achieved by employing the proposedformalisms.

In dieser Arbeit wird eine unrestricted Coupled-Cluster CC2 Response-Methode für die Berechnung von Eigenschaften erster und zweiter Ordnung, mit dem elektronischen g-Tensor als Schwerpunkt, präsentiert. Lokale Korrelations- und Dichtefittingnäherungen wurden verwendet. Die fundamentalen Konzepte notwendig für das Verständnis von Coupled-Cluster-Theorie, Dichtefitting, lokaler Korrelation, allgemeinen Coupled-Cluster Eigenschaften und dem elektronischen g-Tensor werden diskutiert. Die berechneten g-Tensoren werden mit denen durch Coupled-Cluster Singles and Doubles, Dichtefunktionaltheorie und Experiment erhaltenen verglichen. Effizienz und Genauigkeit der Näherung wird untersucht. Ein detailierter Anhang beschreibt die diagrammatische Coupled-Cluster-Theorie sowie ihre Anwendung zur Herleitung der verwendeten Arbeitsgleichungen. Die in dieser Arbeit entwickelte Methode ermöglicht es, den elektronischen g-Tensor von ausgedehnten Systemen mit einer Methode, die nicht auf Dichtefunktionaltheorie basiert, quantitativ vorherzusagen. Damit ist sie ein wichtiger Schritt hin zur Entwicklung von niedrig skalierenden Coupled-Cluster-Methoden höherer Ordnung für diese Art von Problem. / This work presents an unrestricted coupled-cluster CC2 response method using local correlation and density fitting approximations for the calculation of first and second order properties with particular focus on the electronic g-tensor. The fundamental concepts related to coupled-cluster theory, density fitting, local correlation, general coupled-cluster properties and the electronic g-tensor are discussed. The calculated g-tensors are benchmarked against those obtained from coupled-cluster singles and doubles, density functional theory and experiment. Efficiency and accuracy of the approximations is investigated. A detailed appendix covers the fundamentals of diagrammatic coupled-cluster and its application to the derivation of the working equations. The method presented in this thesis enables the quantitative prediction of the electronic g-tensor of extended systems with a method other than density functional theory. It represents an important step towards the development of low-scaling higher order coupled-cluster methods for this type of problem.

Os radicais nitróxidos tem sido muito utilizados em estudos de sistemas biológicos através do método de marcagem de spin. Apesar do grande número de publicações sobre aplicações, o número de estudos das propriedades intrínsecas dos nitróxidos ê bem reduzido. A importância de tais estudos é grande uma vez que o estudo de um sistema simples permite avaliar e interpretar os resultados dos sistemas biológicos, geralmente mais complicados Assim no presente trabalho estudou-se o espectro do RPE do 4-hidroxi-2,2,6,6-tetrametil piperidina-1 oxil (I) introduzido como impureza na sua matriz diamagnética 4-hidroxi-2,2,6,6-tetrametilpiperidina (II). Este processo de dopagem muito utilizado em física do estado sólido permitiu a determinação dos tensores g e A. Os valores obtidos gxx = 2.0098, gyy = 2.0061, gzz = 2.0024, e A xx = 5.3 G, Ayy = 7.0 G, Azz = 35.0 G, encontram-se dentro do esperado sendo que o valor de go = 2.0061 e Ao = 15.8 G evidencia a interação do fragmento N-O com ponte de hidrogênio (de hidroxila na posição 4 de uma molécula vizinha). A existência de dois centros paramagnéticos inequivalentes é interpretada corno devido a presença de duas possíveis conformações do fragmento N-O. As larguras das linhas de RPE observadas são grandes e em certas orientações do campo magnético ocorre o desdobramento da transição eletrônica num dubleto devido a interação com o hidrogênio da hidroxiIa que faz ponte com o N-O. A temperatura de cerca de -140&#176C e observada uma mudança sensível nos espectros de RPE evidenciando a desaparição da estrutura hiperfina na região de Axx e Ayy. Esta mudança está relacionada com o congelamento da rotação dos grupos metila afetando assim a interação dos prótons destes grupos com o elétron do fragmento N-O. O sistema estudado parece ser extremamente interessante do ponto de vista do estudo de influência de prótons na relaxação eletrônica do radical nitroxido. É evidenciada a forte dependência das propriedades paramagnéticas do nitróxido em relação à estrutura da vizinhança do fragmento N-O. / Nitroxide radicals are being used in many studies of biological systems through the spin label method. Despite the great number of publications involving the application of nitroxides only a reduced number of work s about nitroxides themselves is known. These studies are important because the knowledge of the properties of simple systems could be used in the interpretation of results in biological systems, normally mare complicated. In the present work the EPR spectra of 4-hydraxy-2,2,6,6-tetramethyl piperidine-l oxyl (I) introduced as impurity in the diamagnetic matrix of 4-hidraxy-2,2,6,6-tetramethyl piperidine (II) were studied. This process commonly used in solid state physics made it possible the determination of the g and A tensors. The values obtained : gxx = 2.0098, gyy = 2.0061, gzz = 2.0024, and A xx = 5.3 G, Ayy = 7.0 G, Azz = 35.0 G are typical for nitroxides. The mean values go = 2.0061 and Ao 15.8G are consistent with the presence af hydrogen bond to the N-O fragment (this bond is made with the proton of a hydroxyl in position 4 of a neighbour molecule). The existence of two magnetically inequivalent centers is interpreted so that two different conformations for the N-O fragment are possible. The line widths of the EPR lines are quite great and for some orientations of the magnetic field a splitting of the electronic transition in to a dublet occur. This splitting is due to the interaction of the electron in the N-Q fragment with the hydroxyl hydrogen which is bonded to the nitroxide group. At a temperature around -140&#176C a change in the EPR spectra is observed, when the hyperfine nitrogen structure in the region of A and A disappear. This change x y is related to the freezing of the rotation of the methyl groups affecting the interaction of the protons of these groups with the electron in the N-O. The system studied in the present work seems to be very interesting from the point of view of the influence of the protons in the electronic relaxation in the nitroxide radical. ln this context the strong dependency of the properties of the nitroxide relative to the structure of the neighbouring of the N-O fragment become evident.

Os radicais nitróxidos tem sido muito utilizados em estudos de sistemas biológicos através do método de marcagem de spin. Apesar do grande número de publicações sobre aplicações, o número de estudos das propriedades intrínsecas dos nitróxidos ê bem reduzido. A importância de tais estudos é grande uma vez que o estudo de um sistema simples permite avaliar e interpretar os resultados dos sistemas biológicos, geralmente mais complicados Assim no presente trabalho estudou-se o espectro do RPE do 4-hidroxi-2,2,6,6-tetrametil piperidina-1 oxil (I) introduzido como impureza na sua matriz diamagnética 4-hidroxi-2,2,6,6-tetrametilpiperidina (II). Este processo de dopagem muito utilizado em física do estado sólido permitiu a determinação dos tensores g e A. Os valores obtidos gxx = 2.0098, gyy = 2.0061, gzz = 2.0024, e A xx = 5.3 G, Ayy = 7.0 G, Azz = 35.0 G, encontram-se dentro do esperado sendo que o valor de go = 2.0061 e Ao = 15.8 G evidencia a interação do fragmento N-O com ponte de hidrogênio (de hidroxila na posição 4 de uma molécula vizinha). A existência de dois centros paramagnéticos inequivalentes é interpretada corno devido a presença de duas possíveis conformações do fragmento N-O. As larguras das linhas de RPE observadas são grandes e em certas orientações do campo magnético ocorre o desdobramento da transição eletrônica num dubleto devido a interação com o hidrogênio da hidroxiIa que faz ponte com o N-O. A temperatura de cerca de -140&#176C e observada uma mudança sensível nos espectros de RPE evidenciando a desaparição da estrutura hiperfina na região de Axx e Ayy. Esta mudança está relacionada com o congelamento da rotação dos grupos metila afetando assim a interação dos prótons destes grupos com o elétron do fragmento N-O. O sistema estudado parece ser extremamente interessante do ponto de vista do estudo de influência de prótons na relaxação eletrônica do radical nitroxido. É evidenciada a forte dependência das propriedades paramagnéticas do nitróxido em relação à estrutura da vizinhança do fragmento N-O. / Nitroxide radicals are being used in many studies of biological systems through the spin label method. Despite the great number of publications involving the application of nitroxides only a reduced number of work s about nitroxides themselves is known. These studies are important because the knowledge of the properties of simple systems could be used in the interpretation of results in biological systems, normally mare complicated. In the present work the EPR spectra of 4-hydraxy-2,2,6,6-tetramethyl piperidine-l oxyl (I) introduced as impurity in the diamagnetic matrix of 4-hidraxy-2,2,6,6-tetramethyl piperidine (II) were studied. This process commonly used in solid state physics made it possible the determination of the g and A tensors. The values obtained : gxx = 2.0098, gyy = 2.0061, gzz = 2.0024, and A xx = 5.3 G, Ayy = 7.0 G, Azz = 35.0 G are typical for nitroxides. The mean values go = 2.0061 and Ao 15.8G are consistent with the presence af hydrogen bond to the N-O fragment (this bond is made with the proton of a hydroxyl in position 4 of a neighbour molecule). The existence of two magnetically inequivalent centers is interpreted so that two different conformations for the N-O fragment are possible. The line widths of the EPR lines are quite great and for some orientations of the magnetic field a splitting of the electronic transition in to a dublet occur. This splitting is due to the interaction of the electron in the N-Q fragment with the hydroxyl hydrogen which is bonded to the nitroxide group. At a temperature around -140&#176C a change in the EPR spectra is observed, when the hyperfine nitrogen structure in the region of A and A disappear. This change x y is related to the freezing of the rotation of the methyl groups affecting the interaction of the protons of these groups with the electron in the N-O. The system studied in the present work seems to be very interesting from the point of view of the influence of the protons in the electronic relaxation in the nitroxide radical. ln this context the strong dependency of the properties of the nitroxide relative to the structure of the neighbouring of the N-O fragment become evident.

Abstract In this thesis, the theory of static magnetic resonance spectral parameters of nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy is investigated in terms of the molecular Breit-Pauli Hamiltonian, which is obtained from the relativistic Dirac equation via the Foldy-Wouthuysen transformation. A leading-order perturbational relativistic theory of NMR nuclear shielding and spin-spin coupling tensors, and ESR electronic g-tensor, is presented. In addition, the possibility of external magnetic-field dependency of NMR parameters is discussed. Various first-principles methods of electronic structure theory and the role of one-electron basis sets and their performance in magnetic resonance properties in terms of their completeness profiles are discussed. The presented leading-order perturbational relativistic theories of NMR nuclear shielding tensors and ESR electronic g-tensors, as well as the theory of the magnetic-field dependent NMR shielding and quadrupole coupling are evaluated using first-principles wave function and density-functional theories.

Dans une première partie, nous avons étudié quelques propriétés de molécules magnétiques impliquant des radicaux organiques (seuls ou conjointement avec des terres rares). Nous avons ainsi pu interpréter l'évolution de la susceptibilité magnétique et de l'aimantation en fonction de la température en évaluant par des approches ab initio fonctions d'onde les constantes d'échange ou le tenseur g au sein de ces matériaux. De plus, nous avons chercher à définir les conditions pour que des matériaux à base de radicaux organiques présentent simultanément des propriétés magnétiques et conductrices. Nous avons ainsi examiné différentes familles de composés et l'influence de la structure géométrique et chimique des radicaux organiques utilisés. Pour cette partie, nous avons extrait les intégrales physiques pertinentes par la méthode des Hamiltoniens effectifs.Dans une deuxième partie, nous avons utilisés ces quantités physiques (intégrale de saut, répulsion sur site, échange) pour décrire le phénomène de transport dans des jonctions pour lesquelles les effets de la corrélation électronique ne peuvent être écartés. Munis de ces paramètres ab initio, nous avons développé un modèle phénoménologique permettant de décrire la conduction moléculaire à l'aide d'un jeu d'équations maîtresses. Nous avons ainsi cherché à mettre en évidence l'intérêt des approches post Hartree-Fock empruntant une fonction d'onde corrélée et de spin adapté dans la description du transport électronique. Que ce soit dans le cas de transport polarisé en spin ou non, l'approche utilisée (mono ou multi-déterminentale) conditionne qualitativement et quantitativement la caractéristique courant/tension. / In a first part, we studied the magnetic properties of organic radicals (coupled with rare earth or between each other). We calculated the magnetic exchange and the g-tensor of these compounds to understand their magnetic susceptibility and thei magnetization curves via ab initio calculations based on the wave-function. We studied how the chemistry and the crystal stacking affect meaningful parameters linked to magnetism and conduction. Those parameters were extracted with the thory of effective Hamiltonians fo various families of organic radicals. From the observed trends for the different parameters, we predicted some ways to obtain multifunctional compounds. In a second part, we used the same parameters (hoping integral, coulombic repulsion, magnetic exchange) to describe transport properties through highly correlated molecular junctions. From the ab initio parameters, we developed a phenomenological model based on master equations to describe the electronic transport. We stressed the importance of a multiconfigurational description to reproduce properly the transport properties for spin unpolarized and spin polarized situations. In both cases, the mono- or multi-configurational description affects qualitatively and quantitatively the predicted conductance curve.