Semiconductor quantum dot systems offer a promising platform for quantum computation. And these quantum computation candidates are normally based on spin or charge properties of electrons. In these systems, we focus on quantum computation based on electron spins since these systems has good scalability, long coherence times, and rapid gate operations. And this thesis focuses on building a theoretical description of quantum dot systems and the link between theory and experiments. In many quantum dot systems, exchange interactions are the primary mechanism used to control spins and generate entanglement. And exchange energies are normally positive, which limits control flexibility. However, recent experiments show that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet-like rather than singlet-like ground state. Here we show using a microscopic model based on the configuration interaction (CI) method that both triplet-like and singlet-like ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet-like ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons. Recent experiments also show the potential to utilize large quantum dots to mediate superexchange interaction and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use CI calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays. / Doctor of Philosophy / Semiconductor quantum dot systems offer a promising platform for quantum computation. And these quantum computation candidates are normally based on spin or charge properties of electrons. In these systems, we focus on quantum computation based on electron spins since these systems has good scalability, long coherence times, and rapid gate operations. And this thesis focuses on building a theoretical description of quantum dot systems and the link between theory and experiments. A key requirement for quantum computation is the ability to control individual qubits and couple them together to create entanglement. In quantum dot spin qubit systems, the exchange interaction is the primary mechanism used to accomplish these tasks. This thesis is about attaining a better understanding of exchange interactions in quantum dot spin qubit systems and how they can be manipulated by changing the configuration of the system and the number of electrons. In this thesis, we show negative exchange energy can arise in large size quantum dots. This result holds for symmetric and asymmetric shape of the large dots. And we also provide a quantitative analysis of how large quantum dots can be used to create long-distance spin-spin interactions. This capability would greatly increase the flexibility in designing quantum processors built by quantum dot spins. The interplay of these systems with different geometry can serve as a guide to assist further experiments and may hopefully be the basis to build two-dimensional quantum dot arrays.

Estudamos neste trabalho o comportamento da impureza oxigênio em rede cristalina de silício, usando primeiramente o método INDO (lntermediate Neglect of Differential Overlap) com parametrização espectroscópica e incluímos os efeitos de muitos elétrons via Método CI-(Interacão de Configuração). Fazemos uma análise sobre as possíveis origens do posicionamento não-central (off-center) dessa impureza, - se decorrente de uma distorsão Pseudo Jahn-Teller: - se originária de um CR Reconstrução Química. Quando o átomo de Oxigênio é deslocado ao longo da direção [100] ocupa um sitio de mínimo absoluto. O oxigênio introduz no gap de banda um orbital anti-ligante de simetria a1 totalmente ocupado, situação semelhante à dos anti-sitios em materiais semi-condutores III-V. Estudamos também o comportamento dessa impureza quando a mesma é deslocada ao longo da direção [111], verificando que é criada uma posição de Instabilidade mas, os auto-valores têm comportamento não esperado para orbitais anti-ligantes. / In this work we studied the Oxygen impurity in Silicon. The calculations were performed using a semi-empirical method (INDO/S) with Configuration Interaction to account for many-electron effects. We analyse the origin of the off-center position for substitutional oxygen. Pseudo Jahn-Teller distortion or Chemical Rebonding effects. The oxygen introduces an a1 anti-bonding state in the forbidden band-gap similar to anti-site defects in III-V materials. To answer the question about distortion, we also studied oxygen dislocation in the (111) direction and we obtained a metastable state but his eigen-value has a non-expected behavior for anti-bonding orbitals.

Estudamos neste trabalho o comportamento da impureza oxigênio em rede cristalina de silício, usando primeiramente o método INDO (lntermediate Neglect of Differential Overlap) com parametrização espectroscópica e incluímos os efeitos de muitos elétrons via Método CI-(Interacão de Configuração). Fazemos uma análise sobre as possíveis origens do posicionamento não-central (off-center) dessa impureza, - se decorrente de uma distorsão Pseudo Jahn-Teller: - se originária de um CR Reconstrução Química. Quando o átomo de Oxigênio é deslocado ao longo da direção [100] ocupa um sitio de mínimo absoluto. O oxigênio introduz no gap de banda um orbital anti-ligante de simetria a1 totalmente ocupado, situação semelhante à dos anti-sitios em materiais semi-condutores III-V. Estudamos também o comportamento dessa impureza quando a mesma é deslocada ao longo da direção [111], verificando que é criada uma posição de Instabilidade mas, os auto-valores têm comportamento não esperado para orbitais anti-ligantes. / In this work we studied the Oxygen impurity in Silicon. The calculations were performed using a semi-empirical method (INDO/S) with Configuration Interaction to account for many-electron effects. We analyse the origin of the off-center position for substitutional oxygen. Pseudo Jahn-Teller distortion or Chemical Rebonding effects. The oxygen introduces an a1 anti-bonding state in the forbidden band-gap similar to anti-site defects in III-V materials. To answer the question about distortion, we also studied oxygen dislocation in the (111) direction and we obtained a metastable state but his eigen-value has a non-expected behavior for anti-bonding orbitals.

Dans cette thèse ont été développés de nouveaux outils de calcul théorique de spectres moléculaires rovibrationnels qui permettent de mieux traiter les états vibrationnels très excités ainsi que les mouvements de grandes amplitudes avec la méthode d’interactions de configurations en champ moyen. Dans un premier temps, nous avons discuté la question du choix des bases modales et les différents compromis à trouver afin de pallier aux défauts possibles des surfaces d'énergie potentielle. Dans ce cadre nous avons également développé un critère de sélection visant à améliorer la qualité des fonctions d'ondes rovibrationnelles de base. Ces approches ont été appliquées avec succès à la molécule de méthane CH4.Dans un second temps, nous avons implémenté un algorithme de calcul formel des opérateurs d'énergie cinétique en coordonnées quelconques qui permet d'avoir des expressions exactes ainsi que leurs développements en série de Taylor ou Fourier, qui exploite au mieux les potentialités du logiciel MATHEMATICA et a permis d'obtenir des hamiltoniens rovibrationnels en coordonnées de valence de façon particulièrement efficace. Enfin, nous avons généralisé la méthode d’interactions de configurations en champ moyen en ajoutant de façon perturbative un champ effectif d'ordre deux. Nous avons appliqué cette généralisation à la molécule de péroxyde d'hydrogène HOOH, ce qui a permis de montrer son intérêt tant pour l'amélioration des niveaux d'énergie que des fonctions d'onde associées, lorsqu'on a affaire à des groupes de degrés de liberté bien séparés énergétiquement. / In this thesis we developed new theoretical tools for molecular rovibrational spectra for a better description of the excited vibrational states and movements with large amplitudes using mean field configuration interaction method. First, we discussed the choice of modal basis and different trade-off to overcome the possible shortcomings of potential energy surfaces. In this context we have also developed selection criteria to improve the quality of rovibrational wave functions. These approaches have been successfully applied to the methane molecule (CH4). Secondly, we have implemented a formal algorithm for calculating the kinetic energy operators in arbitrary coordinates that allows the derivation of exact expressions and their Taylor and Fourier series, using, in a very efficient way, the capabilities of the software MATHEMATICA which yield to the derivation of rovibrational Hamiltonians in valence coordinated. Finally, we have generalized the mean-field configuration interaction method by adding perturbatively a second order effective field. We applied this generalization to the hydrogen peroxide molecule (HOOH), which has shown an improvement for both energy levels and the associated wave functions, when dealing with groups of degrees of freedom that are energetically well separated.

Une étude théorique ab initio des structures électroniques des molécules Diatomiques polaires BN, SiN et LaH dans la représentation 2s+1Λ(+/-)Ont été effectués par la méthode du champ auto-cohérent de l'espace Actif complet (CASSCF), suivie par l'interaction de la configuration multiréférence (MRSDCI). La correction de Davidson, notée (MRSDCI+ Q), a ensuite été appliquée pour rendre compte de clusters ou agrégats quadruples non liés. L'ensemble de l'espace de configuration de CASSCF a été utilisé comme référence dans le calcul MRCI, qui a été effectués en utilisant le programme de calcul de chimie physique MOLPRO et en tirant parti de l'interface graphique Gabedit. Quarante-deux de plus bas états électroniques dans la représentation 2s+1Λ(+/-)au-dessous de 95000 cm-1 ont été étudiés de la molécule BN. Alors que vingt-huit états électroniques dans les représentations 2s+1Λ(+/-) jusqu'à 70000 cm-1 de la molécule de SiN ont été étudiés. D'autre part, les vingt-quatre bas états électroniques de LaH dans les représentations 2s+1Λ(+/-) au-dessous de 70000 cm-1 ont été étudiées par deux méthodes différentes et en prenant en considération l'effet des spin-orbite de la molécule LaH et nous avons observé la division énergétique des huit états électroniques. Les courbes d'énergie potentielle ont été construites avec la fréquence co-harmonique ωe, la distance internucléaire de l'équilibre re, les constantes de rotation Be. L'énergie électronique par rapport à l'état fondamentale Te a été calculé pour les états électroniques considérés comme des BN, SiN et la molécule LaH respectivement. En utilisant l'approche des fonctions canoniques, les valeurs propres Ev, les constantes rotationnelles Bv, la constante de distorsion centrifuge Dv et les abscisses des points de retournement Rmin and Rmax ont été calculés pour les états électroniques au niveau de vibration v=51 pour LaH molécule. Dix-huit et neuf états électroniques ont été étudiées pour la molécule BN et SiN respectivement. Pour LaH, vingt-trois états électroniques de la molécule LaH et l'effet de spin-orbite de molécule LaH sont donnés ici pour la première fois. La comparaison avec les données expérimentales et théoriques pour la plupart des constantes calculées démontre une très bonne précision. Enfin, ces résultats devraient ainsi mener à des études expérimentales plus poussées pour ces molécules. Nos résultats ont été publiés dans le Canadian Journal of Chemistry, Journal of Quantitative Spectroscopy and Radiative Transfer, nous avons deux autres articles en préparation à soumettre. / In the present work a theoretical investigation of the lowest molecular states of BN, SiN and LaH molecule, in the representation 2s+1Λ(+/-), has been performed via complete active space self-consistent field method (CASSCF) followed by multireference single and double configuration interaction method (MRSDCI). The Davidson correction noted as (MRSDCI+Q) was then invoked in order to account for unlinked quadruple clusters. The entire CASSCF configuration space was used as a reference in the MRCI calculation which has been performed via the computational chemistry program MOLPRO and by taking advantage of the graphical user interface Gabedit. Forty-two singlet, triplet, and quintet lowest electronic states in the 2s+1Λ(+/-) representation below 95000 cm-1 have been investigated of the molecule BN. While twenty-eight electronic states in the representation2s+1Λ(+/-)up to 70000 cm-1 of the SiN molecule have been investigated.On the other hand the Twenty four low-lying electronic states of LaH in the representation 2s+1Λ(+/-) below 35000 cm-1 have been studied by two different methods and by taking into consideration the spin orbit effect of the molecule LaH we give in the energy splitting of the eight electronic states. The potential energy curves (PECs) together with the harmonic frequency ωe, the equilibrium internuclear distance re, the rotational constants Be and the electronic energy with respect to the ground state Te have been calculated for the considered electronic states of BN, SiN and LaH molecule respectively. Using the canonical functions approach, the eigenvalues Ev, the rotational constants Bv ,the centrifugal distortion constants Dv and the abscissas of the turning points Rmin and Rmax have been calculated for electronic states up to the vibrational level v =51 for LaH molecule.Eighteen and Nine electronic states have been investigated here for the first time for the molecules of BN and SiN respectively, while for LaH, news results are performed for twenty three electronic states of LaH molecule and the spin-orbit effect of LaH molecule is given here for the first time. A comparison with experimental and theoretical data for most of the calculated constants demonstrated a very good accuracy. Finally, we expect that the results of our work should invoke further experimental investigations for these molecules. Our results have been published in Canadian journal of chemistry, Journal of Quantitative Spectroscopy and Radiative Transfer and we have two other papers in preparation to submit.

Cette thèse, ayant pour thème les algorithmes de la chimie quantique, s'inscrit dans le cade du changement de paradigme observé depuis une douzaines d'années, dans lequel les méthodes de calcul séquentielles se doivent d'être progressivement remplacées par des méthodes parallèles. En effet, l'augmentation de la fréquences des processeurs se heurtant à des barrières physiques difficilement franchissables, l'augmentation de la puissance de calcul se fait par l'augmentation du nombre d'unités de calcul. Toutefois, là où une augmentation de la fréquence conduisait mécaniquement à une exécution plus rapide d'un code, l'augmentation du nombre de cœurs peut se heurter à des barrières algorithmiques, qui peuvent nécessiter une adaptation ou un changement d'algorithme. Parmi les méthodes développées afin de contourner ce problème, on trouve en particulier celles de type Monte-Carlo (stochastiques), qui sont intrinsèquement "embarrassingly parallel", c'est à dire qu'elles sont par construction constituées d'une multitudes de tâches indépendantes, et de ce fait particulièrement adaptées aux architectures massivement parallèles. Elles ont également l'avantage, dans de nombreux cas, d'être capables de produire un résultat approché pour une fraction du coût calculatoire de l'équivalent déterministe exacte. Lors de cette thèse, des implémentations massivement parallèles de certains algorithmes déterministes de chimie quantique ont été réalisées. Il s'agit des algorithmes suivants : CIPSI, diagonalisation de Davidson, calcul de la perturbation au second ordre, shifted-Bk, et Coupled Cluster Multi Références. Pour certains, une composante stochastique a été introduite en vue d'améliorer leur efficacité. Toutes ces méthodes ont été implémentées sur un modèle de tâches distribuées en TCP, où un processus central distribue des tâches par le réseau et collecte les résultats. En d'autres termes, des nœuds esclaves peuvent être ajoutés au cours du calcul depuis n'importe quelle machine accessible depuis internet. L'efficacité parallèle des algorithmes implémentés dans cette thèse a été étudiée, et le programme a pu donner lieu à de nombreuses applications, notamment pour permettre d'obtenir des énergies de références pour des systèmes moléculaires difficiles. / This thesis, whose topic is quantum chemistry algorithms, is made in the context of the change in paradigm that has been going on for the last decade, in which the usual sequential algorithms are progressively replaced by parallel equivalents. Indeed, the increase in processors' frequency is challenged by physical barriers, so increase in computational power is achieved through increasing the number of cores. However, where an increase of frequency mechanically leads to a faster execution of a code, an increase in number of cores may be challenged by algorithmic barriers, which may require adapting of even changing the algorithm. Among methods developed to circumvent this issue, we find in particular Monte-Carlo methods (stochastic methods), which are intrinsically "embarrassingly parallel", meaning they are by design composed of a large number of independent tasks, and thus, particularly well-adapted to massively parallel architectures. In addition, they often are able to yield an approximate result for just a fraction of the cost of the equivalent deterministic, exact computation. During this thesis, massively parallel implementations of some deterministic quantum chemistry algorithms were realized. Those methods are: CIPSI, Davidson diagonalization, computation of second-order perturbation, shifted-Bk, Multi-Reference Coupled-Cluster. For some of these, a stochastic aspect was introduced in order to improve their efficiency. All of them were implemented on a distributed task model, with a central process distributing tasks and collecting results. In other words, slave nodes can be added during the computation from any location reachable through Internet. The efficiency for the implemented algorithms has been studied, and the code could give way to numerous applications, in particular to obtain reference energies for difficult molecular systems.

Many-body perturbation theory and coupled-cluster theory, combined with carefully constructed basis sets, can be used to accurately compute the properties of small molecules. We applied a series of methods and basis sets aimed at reaching the ab initio limit to determine the barrier to planarity for ethylene cation. For potential energy surfaces corresponding to bond dissociation, a single Slater determinant is no longer an appropriate reference, and the single-reference hierarchy breaks down. We computed full configuration interaction benchmark data for calibrating new and existing quantum chemical methods for the accurate description of potential energy surfaces. We used the data to calibrate single-reference configuration interaction, perturbation theory, and coupled-cluster theory and multi-reference configuration interaction and perturbation theory, using various types of molecular orbitals, for breaking single and multiple bonds on ground-state and excited-state surfaces. We developed a determinant-based method which generalizes the formulation of many-body wave functions and energy expectation values. We used the method to calibrate single-reference and multi-reference configuration interaction and coupled-cluster theories, using different types of molecular orbitals, for the symmetric dissociation of water. We extended the determinant-based method to work with general configuration lists, enabling us to study, for the first time, arbitrarily truncated coupled-cluster wave functions. We used this new capability to study the importance of configurations in configuration interaction and coupled-cluster wave functions at different regions of a potential energy surface.

Orientador: Roy Edward Bruns / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-15T20:17:10Z (GMT). No. of bitstreams: 1 Meneses_HelenGraciCoelhode_M.pdf: 636858 bytes, checksum: 800e3602970307826daad0f0170d7220 (MD5) Previous issue date: 2010 / Resumo: Neste trabalho investigamos se o método QCISD e o conjunto de base de cc-pVTZ apresentariam resultados mais próximos das intensidades experimentais no infravermelho do que as obtidas dos cálculos usando o método MP2 e a função de base 6-311++G(3d,3p) para os hidrocarbonetos. Nos níveis com o método QCISD o erro rms foi de 4,7 km/mol para as duas bases enquanto que no nível MP2/6-311++G(3d,3p) foi de 7,6 km/mol e para o nível MP2/cc-pVTZ 9,0 km/mol. Foi observado que para as intensidades o efeito do método é maior que o efeito da base e que o efeito de interação método base, em geral, é muito pequeno. Também foi avaliado, através de um planejamento fatorial, se os parâmetros CCFDF (Charge-Charge Flux-Dipole Flux) dependem sensivelmente do método e da base utilizados no cálculo. Para as contribuições de carga, fluxo de carga e fluxo de dipolo para as derivadas médias do momento dipolar em termos de coordenadas cartesianas, de um modo geral, a base tem efeitos maiores do que o método e o efeito de interação entre método e base é muito pequeno. Entretanto, para a derivada total o efeito do método é maior do que o da base, o que é consistente com os resultados para as intensidades. Os cálculos foram feitos para moléculas de metano (CH4), etano (C2H6), eteno (C2H4), etino (C2H2), aleno (C3H4), propino (C3H4) e ciclo-propano (C3H6) / Abstract: The QCISD quantum method and cc-pVTZ basis set were investigated relative to the second order Möller-Plesset level and 6-311G++(3d,3p) basis set for calculating accurate infrared vibrational intensities of fundamental bands of the hydrocarbons. The QCISD results for both basis sets had root mean square errors of 4.7 km mol whereas at the Möller-Plesset level, the 6-311++G(3d,3p) basis set provided a 7.6 km mol error and the cc-pVTZ basis, a 9.0 km mol error. The effects of changing the quantum method on the intensities were larger than the effects of changing basis sets. Furthermore their interaction effects were small. Also by means of a factorial design, the sensitivities of charge - charge flux ¿ dipole flux (CCFDF) parameters to quantum level and basis set changes were evaluated. The basis set change provoked a larger effect on the charge, charge flux and dipole flux contributions to the mean dipole moment derivative than did the change in quantum level. On the other hand, the total mean dipole moment derivative is more sensitive to changes in the quantum method than the basis set, consistent with the finding for the intensities. Calculations were carried out on methane (CH4), ethane (C2H6), ethylene (C2H4), acetylene (C2H2), allene (C3H4), propene (C3H4 ) and cyclkopropane (C3H6) / Mestrado / Físico-Química / Mestre em Química

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