Aplicamos a técnica da função de Green em conjunto com o modelo de força de valência para estudar algumas propriedades vibracionais de redes perturbadas. Apresentamos uma descrição teórica dos modos locais de vibração de vacâncias e anti-sítios em GaAs. Incluímos efeitos de relaxação simétrica para as vacâncias. Baseados em nossos resultados, podemos concluir que o modo vibracional respiratório medido em 227 cm-1 não é devido a vacância de arsênio, conforme fora anteriormente sugerido. Aplicamos o mesmo método para o estudo da variação de densidade de estados vibracionais da vacância em silício. Efeitos de relaxação simétrica e distorção tetragonal são incluídos. Tais resultados são aplicados ao cálculo da entropia de formação deste defeito em Si. A partir destes cálculos verificamos que a vacância pode ser o defeito nativo responsável pela alta entropia de auto-difusão obtida experimentalmente. Finalmente, empregamos o modelo de aglomerado molecular e o método de Hartree-Fock para estudar a estrutura eletrônica da vacância neutra em Si. Calculamos a energia total destes sistemas quando submetidos aos efeitos simultâneos de relaxação e distorção. Verificamos que este modelo fornece resultados equivalentes aos obtidos por métodos de função de Green autoconsistente para a relaxação e apresenta a vantagem adicional de conseguir calcular a energia de distorção. Discutimos as consequências destes resultados sobre a entropia de formação de vacância. / The Green\'s-function technique within the framework of a valence-force field Hamiltonian has been used to study vibrational properties of intrinsic defects in gallium arsenide and silicon. This theoretical approach has been employed to predict the local vibrational modes for vacancies and antisites in GaAs. Symmetrical relaxation was included for vacancies. Our results indicate that the arsenjc vacancy can not explain the breathing mode recently found in 227 cm -1 by Raman studies. The same procedure has been applied to study the changes induced by an isolated vacancy to the local vibrational density of states in silicon. In order to treat the dangling bonds reconstruction, relaxation and tetragonal distortion effects have been included. These calculations have led to the formation entropy of a single vacancy in Si. It has been found that the single vacancy may play an important role in self-diffusion at high temperatures for this material. We also have performed cluster total-energy calculations to study relaxation and distortion around a silicon vacancy. These calculations were carried out under the Hartree-Fock approximation. Our results show that the cluster model, besides providing relaxation energies with the same accuracy of self consistent Green\'s-function method, has the additional advantage of calculating distortion energies. Consequences of these total-energy calculations on formation entropy of this defect have also discussed.

Neste trabalho apresentamos um estudo teórico sistemático de propriedades eletrônicas e estruturais de compostos intermetálicos que cristalizam na mesma estrutura Cllb. Realizamos este estudo utilizando o método \"Full-Potential-Linearized-Augmented Plane-Wave\"(FP-LAPW) na versão computacional do código Wien97 para a obtenção da estrutura eletrônica e do Gradiente de Campo Elétrico no núcleo (GCE). Nossos resultados teóricos de GCE são comparados com medidas efetuadas através da técnica Time differential Perturbed Angular Correlation (TDPAC), realizadas com a impureza de Ta em compostos com Zr e Hf Através da comparação de resultados teóricos e experimentais investigamos a influência da impureza no GCE. As estruturas perfeitas aqui estudadas são também otimizadas através da variação de seus parâmetros de rede e internos. / Here we present the theoretical study of structural and electronic properties of some intermetallic compounds, belonging to the common crystallographic structure of C11b type. We have performed self-consistent electronic structure calculations using the full potential linearized-augmented-plane-wave (FP-LAPW) method as embodied in the Wien97 code and determined also the electric field gradient (EFG) values for the nonequivalent sites in these systems. The applied approach is currently one of the most accurate schemes to determine the electronic structure in ordered metallic solids. By comparison of the EFG inferred from measurements at the 181Ta probe with EFG calculations without probe, we investigate the influence of the probe in compounds with Hf and Zr. Here we also study the influence of the precise knowledge of the internal structural parameters on the EFG at both metals in the pure compounds.

Neste trabalho nós propomos uma extensão da teoria Hadrodinâmica Quântica (QHD) para o estudo do emparelhamento nucleônico na matéria nuclear. O trabalho segue a formulação usual da QHD, descrevendo a interação-NN em termos de campos médios, tanto para a auto-energia usual, E, como para a energia de emparelhamento, A. As equações dos campos são obtidas em termos dos propagadores nucleônicos exatos, os quais são expandidos até a primeira ordem na interação-NN, definindo a aproxirnação auto-consistente Hartree-Fock-Bogoliubov (HFB) para E e A. Esta abordagem representa um avanço sobre as tradicionais formulações não-relativísticas, no sentido de que ela permite uma descrição simultânea de muitas propriedades da matéria nuclear como o ponto de saturação, a massa efetiva do nucleon, o gap de energia no espectro de partícula única, etc., de uma maneira consistente considerando apenas os graus de liberdade hadrônicos, ou seja, os nucleons interagindo na matéria nuclear através da troca de mésons. Os campos médios resultantes E e A, tem grandes componentes no espaço de Lorentz, que adequadamente se cancelam nas expressões tanto da energia de ligação por nucleon como no parâmetro de gap\", de forma que os valores resultantes dessas quantidades concordam com os resultados experimentais. Embora o parâmetro de gap possa ser adequadamente estimado com modelos não-relativísticos, em termos de interações de dois nucleons, o ponto de saturação da matéria nuclear não pode. O aspecto atraente do presente modelo é sua formulação fundamental bastante simples em termos de graus de liberdade hadrônicos e da aproximação HFB usual à teoria de muitos corpos, o que aponta para avanços futuros como poderiam ser obtidos com a aproximação Brueckner-HF auto-consistente. / In this work we propose an extension of the relativistic Quantum Hadrodynamic theory (QHD) to the study of nucleonic pairing in nuclear matter. The work follows the usual formulation of QHD by describing the NN-interaction in terms of mean fields either for the usual self-energy, E, or the pairing energy, A. The equations of the fields are obtained in terms of the exact nucleon propagators which are expanded up to the first order in the NN-interaction, defining the self-consistent Hartree-Fock-Bogoliubov (HPB) approximation E for A and .This approach represents an improvement over the old non-relativistic formulations in the sense that it allows for a simultaneous description of many nuclear matter properties as the saturation point, the effective mass or the nucleon, the energy gap in the sp-spectrum, etc., in a consistent fashion, by considering only the hadronic degrees of freedom, that is, the nucleons interacting in nuclear matter through the exchange of mesons. The resulting mean field energies, E and A, have large components in the Lorentz space, which adequately cancel each other in the expressions of either the energy per nucleon or the gap parameter\", so that the resulting values of these quantities agree with the experimental data. Although the gap parameter can be adequately estimated with non-relativistic models, in terms of two nucleon interactions, the saturation point of nuclear matter cannot be. The appealing feature of the present model is its rather simple fundamental formulation in terms of hadronic degrees of freedom and the usual HFB approximation to the many-body field theory, which points toward future improvements as would be obtained with a self-consistent Brueckner-HF approximation.

No description available.

by Chi Ching Mak. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 122-130). / Contents --- p.i / Acknowledgments --- p.iii / Abstract --- p.iv / Abbreviations --- p.v / List of publications originated from this thesis --- p.vi / Chapter I --- Introduction to Dendrimer Chemistry / Chapter I-1 --- Background --- p.1 / Chapter I-2 --- Comparison of Dendrimer and Linear Polymer --- p.6 / Chapter I-3 --- Synthesis --- p.8 / Chapter I-3-1 --- Divergent-growth Approach --- p.8 / Chapter I-3-2 --- Convergent-growth Approach --- p.10 / Chapter I-3-3 --- Accelerated Approach --- p.11 / Chapter II --- Functional Dendrimers --- p.14 / Chapter III --- Optically Active Dendrimers / Chapter III-1 --- Background --- p.18 / Chapter III-2 --- Architecture of Tartaric Acid-based Optically Active Dendrimers --- p.23 / Chapter III-3 --- Results and Discussion --- p.24 / Chapter III-3-1 --- Syntheses and Structure Elucidations of all (L)-Tartaric Acid-based Dendrimers 41 and 42 --- p.24 / Chapter III-3-2 --- Syntheses and Structure Elucidations of Optically Active Layer-block Dendrimers 43 and 44 --- p.29 / Chapter III-3-3 --- Structure-Optical Rotation Relationships --- p.33 / Chapter III-3-4 --- "Syntheses and Characterization of Higher Generation, Optically Active Dendritic Fragments" --- p.37 / Chapter III-3-5 --- Conclusions --- p.43 / Chapter IV --- Catalytic Dendrimers / Chapter IV-1 --- Background --- p.44 / Chapter IV-2 --- Syntheses and Characterization of Dendritic Bis(oxazoline) Copper(II) Catalyst --- p.47 / Chapter IV-2-1 --- Architecture --- p.47 / Chapter IV-2-2 --- Syntheses of the Bis(oxazoline) Core Precursors --- p.49 / Chapter IV-2-3 --- Syntheses of the Achiral Dendritic Sectors --- p.51 / Chapter IV-2-4 --- Syntheses of Dendritic Ligands --- p.52 / Chapter IV-3 --- Kinetics and Selectivity of Dendritic Bis(oxazoline)-Copper(II) Complex Catalyzed Diels-Alder Reaction --- p.55 / Chapter IV-3-1 --- Introduction --- p.55 / Chapter IV-3-2 --- Reaction Mechanism and Reactivity Kinetics --- p.56 / Chapter IV-3-3 --- Substrate Selectivity --- p.63 / Chapter IV-4 --- Syntheses and Properties of Optically Active Dendritic Bis(oxazoline) Ligands and Their Copper(II) Complexes Catalysts --- p.65 / Chapter IV-4-1 --- Background --- p.65 / Chapter IV-4-2 --- Syntheses and Characterization of Chiral Dendritic Bis(oxazoline) Ligands 109-112 --- p.67 / Chapter IV-4-3 --- Chiroptical Properties --- p.72 / Chapter IV-4-4 --- Enantioselectivity of the Metal-catalyzed Diels-Alder Reaction --- p.73 / Chapter IV-4-5 --- Conclusions --- p.74 / Chapter V --- Summary --- p.75 / Chapter VI --- Experimental --- p.77 / References --- p.122 / Spectra --- p.131

Aplicamos a técnica da função de Green em conjunto com o modelo de força de valência para estudar algumas propriedades vibracionais de redes perturbadas. Apresentamos uma descrição teórica dos modos locais de vibração de vacâncias e anti-sítios em GaAs. Incluímos efeitos de relaxação simétrica para as vacâncias. Baseados em nossos resultados, podemos concluir que o modo vibracional respiratório medido em 227 cm-1 não é devido a vacância de arsênio, conforme fora anteriormente sugerido. Aplicamos o mesmo método para o estudo da variação de densidade de estados vibracionais da vacância em silício. Efeitos de relaxação simétrica e distorção tetragonal são incluídos. Tais resultados são aplicados ao cálculo da entropia de formação deste defeito em Si. A partir destes cálculos verificamos que a vacância pode ser o defeito nativo responsável pela alta entropia de auto-difusão obtida experimentalmente. Finalmente, empregamos o modelo de aglomerado molecular e o método de Hartree-Fock para estudar a estrutura eletrônica da vacância neutra em Si. Calculamos a energia total destes sistemas quando submetidos aos efeitos simultâneos de relaxação e distorção. Verificamos que este modelo fornece resultados equivalentes aos obtidos por métodos de função de Green autoconsistente para a relaxação e apresenta a vantagem adicional de conseguir calcular a energia de distorção. Discutimos as consequências destes resultados sobre a entropia de formação de vacância. / The Green\'s-function technique within the framework of a valence-force field Hamiltonian has been used to study vibrational properties of intrinsic defects in gallium arsenide and silicon. This theoretical approach has been employed to predict the local vibrational modes for vacancies and antisites in GaAs. Symmetrical relaxation was included for vacancies. Our results indicate that the arsenjc vacancy can not explain the breathing mode recently found in 227 cm -1 by Raman studies. The same procedure has been applied to study the changes induced by an isolated vacancy to the local vibrational density of states in silicon. In order to treat the dangling bonds reconstruction, relaxation and tetragonal distortion effects have been included. These calculations have led to the formation entropy of a single vacancy in Si. It has been found that the single vacancy may play an important role in self-diffusion at high temperatures for this material. We also have performed cluster total-energy calculations to study relaxation and distortion around a silicon vacancy. These calculations were carried out under the Hartree-Fock approximation. Our results show that the cluster model, besides providing relaxation energies with the same accuracy of self consistent Green\'s-function method, has the additional advantage of calculating distortion energies. Consequences of these total-energy calculations on formation entropy of this defect have also discussed.

Estudamos neste trabalho a estrutura eletrônica de defeitos localizados em silício, responsáveis pela introdução de níveis profundos na faixa proibida do semicondutor. Utilizamos para tanto modelos de aglomerados moleculares dentro do formalismo do Espalhamento Múltiplo com aproximação local X para o potencial de troca (MS-X). Um tratamento adequado para os orbitais de superfície foi usado. Os defeitos estudados foram de dois tipos: defeitos simples (monovacância Si:V e oxigênio substitucional Si:O) e pares de defeitos vizinhos na rede (divacância Si : V IND 2) e par de átomos de fósforo Si: P IND 2). Os defeitos foram estudados em diferentes estados de carga (Si:O e Si : O POT -\', Si: P IND 2 e Si: P IND 2 POT + Si: V POT 0 IND 2, Si: V IND 2 POT + e Si: V POT IND 2) e no caso da divacância e do centro P IND 2 POT + foram incluídos efeitos de polarização de spin. Encontramos para todos os defeitos estudados indícios da ocorrência de efeitos Jahn-Teller. Incluímos análises das distorções dos primeiros vizinhos ao defeito nos sistemas Si: O POT , P IND 2 POT + e V POT IND 2. O modelo adotado mostrou-se capaz de descrever satisfatoriamente a estrutura eletrônica dos defeitos estudados, fornecendo resultados quantitativos que podem ser comparados diretamente com a experiência. / In this work we studied the electronic structure of deep-level defects in silicon. To do this we use molecular cluster models within the formalism of the Multiple Scattering method, in the local density functional approximation (X). The surface orbitals of the cluster are treated in a convenient way. The defects studied here were of two kinds: simple defects (single vacancy Si:V and oxygen substitutional Si:0), and pairs of defects occupying neighbouring sites in the lattice (divacancy Si :V2 and the pair of phosphoru- atoms Si :P2 ). The defects were studied in different charge states (Si:O and Si:O-, Si:P2 and Si:P+, Si:V20, SI:V2-) and for the divacancy and the center Si:P2+ the calculations were carried out to the spin-polarized limit. For all defects studied we found evidence as to the possible occurrence of Jahn-Teller effects. Analysis of nearest-neighbours distortions were included for the systems Si:O- , Si:V2+ and Si:V2-. The electronic structure of the defects studied here was satisfactorily described by the model we adopted, and quantitative results are given, that can be compared straightforwardly with experimental results.

Desenvolveu-se um processo para cálculo de faixas de energia aliando a aproximação de Células Unitárias Gigantes (LUC) e o método da Onda Plana Aumentada (APW) não muffin-tin. Os cálculos foram realizados para o diamante (2 átomos por célula) e silício (com 2 e 16 átomos por célula), usando a teoria de grupos para resolver o problema nos pontos de alta simetria da zona de Brillouin. Para o silício, com 16 átomos por célula primitiva, resultados satisfatórios foram obtidos a partir da utilização de 48 SAPWs na expansão da função de onda, o que representa um número bastante razoável neste tipo de cálculo. Nos estágios finais de desenvolvimento, o processo encontra-se em condições de ser aplicado no estudo de semi-condutores com impurezas (ou defeitos), sem a necessidade de grandes adaptações. / A procedure to calculate energy bands, using the Large Unit Cells approximation (LUC) by non muffin-tin Augmented Plane Waves (APW), was developed. The calculations were performed for the diamond (with 2 atoms in the primitive cell) and the silicon (with 2 and 16 atoms in the cell). The group theory was used on the high symmetry points of the Brillouin zone. With only 48 symmetrized APWs, good results were obtained for silicon with 16 atoms in the primitive cell. This is a reasonable basis set for this sort of calculations. This procedure may be readily applied to study semiconductors with impurities or defects.

Desenvolveu-se um processo para cálculo de faixas de energia aliando a aproximação de Células Unitárias Gigantes (LUC) e o método da Onda Plana Aumentada (APW) não muffin-tin. Os cálculos foram realizados para o diamante (2 átomos por célula) e silício (com 2 e 16 átomos por célula), usando a teoria de grupos para resolver o problema nos pontos de alta simetria da zona de Brillouin. Para o silício, com 16 átomos por célula primitiva, resultados satisfatórios foram obtidos a partir da utilização de 48 SAPWs na expansão da função de onda, o que representa um número bastante razoável neste tipo de cálculo. Nos estágios finais de desenvolvimento, o processo encontra-se em condições de ser aplicado no estudo de semi-condutores com impurezas (ou defeitos), sem a necessidade de grandes adaptações. / A procedure to calculate energy bands, using the Large Unit Cells approximation (LUC) by non muffin-tin Augmented Plane Waves (APW), was developed. The calculations were performed for the diamond (with 2 atoms in the primitive cell) and the silicon (with 2 and 16 atoms in the cell). The group theory was used on the high symmetry points of the Brillouin zone. With only 48 symmetrized APWs, good results were obtained for silicon with 16 atoms in the primitive cell. This is a reasonable basis set for this sort of calculations. This procedure may be readily applied to study semiconductors with impurities or defects.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. December 2015. / It is well-established that there is electronic communication between the equatorial and axial ligands in the cobalt corrins. It can therefore be anticipated that the electronic structure of the corrin ligand will affect the chemistry of the axial coordination sites of Co(III) in these complexes. To probe this cis-influence the electronic structure of the corrin was perturbed by substituting the H atom at C10 by Br (which is π electron-donating towards the corrin) in aquacobalamin ([H2OCbl]+), and by NO2 (which is strongly electron-withdrawing) and NH2 (which is strongly electron-donating) in aquacyanocobester ([ACCbs]+). The first part of this study was dedicated to aqua-10-bromocobalamin ([H2O-(10-Br)Cbl]+) and the second part to aquacyano-10-nitrocobester ([AC-(10-NO2)Cbs]+) and aquacyano-10-aminocobester ([AC-(10-NH2)Cbs]+). The successful synthesis of [H2O-(10-Br)Cbl]+, was verified by ESI-MS, 1H and 13C NMR, uv-vis spectroscopy and XRD. The stability constants for the substitution of coordinated H2O by a series of anionic (N3 –, NO2 –, SCN–, SO3 2–) and neutral N-donor ligands (imidazole, DMAP) were obtained for [H2OCbl]+, [H2O-(10-Br)Cbl]+ and [H2O-(10-Cl)Cbl]+ under the same conditions. Substitution of the C10 H by Cl or Br favours the coordination of anionic ligands, but discriminates against the binding of neutral N-donor ligands. The anionic ligands bind more strongly to [H2O-(10-Br)Cbl]+ than to [H2OCbl]+ with log K values between 0.05 and 0.62 (average 0.33) larger. Conversely, neutral ligands bind less strongly to [H2O-(10-Br)Cbl]+ than to [H2OCbl]+ with log K values between 0.29 and 0.36 (average 0.33) smaller. DFT (BP83/TZVP) calculations were used to rationalise these observations. When H is changed to Cl or Br, the metal ion becomes less positive. When the β ligand changes from a neutral to an anionic ligand, the partial charge on the C10 substituent becomes more negative. Replacing C10 H by Cl or Br discriminates against a neutral ligand because of the greater electron richness of the metal. If the ligand is an anion, however, the charge donation can be accepted by delocalisation onto the C10 substituent. The reaction kinetics of the substitution of H2O in [H2O-(10-Br)Cbl]+ were determined for the ligands N3 – and imidazole and were compared with values available for [H2OCbl]+ and [H2O-(10- Cl)Cbl]+. The results showed that both N3 – and imidazole react more slowly with [H2O-(10- Br)Cbl]+ than with [H2OCbl]+, consonant with the previous observations for [H2O-(10-Cl)Cbl]+. Although ΔH‡ values are smaller, they do not compensate for significantly more negative values of ΔS‡, indicative of a transition state that occurs earlier along the reaction coordinate in [H2O- (10-Br)Cbl]+ and [H2O-(10-Cl)Cbl]+ whereas the transition state occurs later along the reaction coordinate with [H2OCbl]+. It is argued that this is a consequence of the lower charge density on the metal, making it a better electrophile both towards the incoming and the departing ligand. Dicyano-10-nitrocobester ([DC-(10-NO2)Cbs]) and dicyano-10-aminocobester ([DC-(10- NH2)Cbs]) were synthesised from dicyanocobester [DCCbs] by established methods and converted to the aquacyano form so that the thermodynamics and kinetics of the substitution of coordinated H2O by a variety of ligands could be investigated. The stability constants for the substitution of coordinated H2O by a number of neutral (imidazole, DMAP, methylamine) and anionic (N3 –, NO2 –, SCN–, SO3 2–, CN–) ligands were determined for [ACCbs]+, [AC-(10-NO2)Cbs]+ and [AC-(10-NH2)Cbs]+ in 50% isopropanol. The soft anions (SO3 2– and CN–) bind better to the softer Co(III) metal centre in [AC-(10-NH2)Cbs]+ and [ACCbs]+ than in [AC-(10-NO2)Cbs]+ and the converse is true for the hard anions (N3 –, NO2 – and SCN–). The case is less clear for the N-donor ligands; DMAP clearly has a higher affinity for [AC-(10- NH2)Cbs]+ and [ACCbs]+ than for [AC-(10-NO2)Cbs]+, but there is little discrimination in the case of imidazole and methylamine. This implies that the affinity of the metal for an exogenous ligand depends on the electron density at the metal centre. DFT calculations showed that as the C10 substituent is changed from NH2 to H to NO2, the charge density on the metal centre decreases and the metal becomes harder. The kinetics of the substitution of H2O by CN– in [ACCbs]+, [AC-(10-NO2)Cbs]+ and[AC-(10- NH2)Cbs]+ in 50% isopropanol were determined. The results showed that the substitution of coordinated H2O proceeded with biphasic kinetics and through a dissociative interchange (Id) mechanism where there is nucleophilic participation of the entering ligand in the transition state. The slower phase corresponds to the substitution of coordinated H2O trans to OH– in the aqua hydroxo species, which, together with the dicyano species, is inevitably present in solutions of [ACCbs]+, and the faster phase corresponds to the substitution of the coordinated H2O trans to CN– in the aquacyano species. The difference in rate of the reaction of the [AC-(10-Z)Cbs] (Z = H, NH2 and NO2) was not very large, the ratio between the largest (for Z = H) and the smallest (for Z = NO2) is just over 40, and does not follow the electron donor properties of Z. This is misleading, however, because of a compensation effect between ΔH‡ and ΔS‡. As values of ΔH‡ become smaller, which causes an increase in the reaction rate, ΔS‡ becomes less positive (or more negative), which causes a decrease in the reaction rate. Hence, comparing rate constants at any particular temperature is not very informative and the compensation effect masks the very significant differences in the reactivity of the metal ion towards the entering CN– ligand. The compensation effect is attributed to the position of the transition state along the reaction coordinate, which depends on the charge density on the metal ion. Indeed, if all three reactions had the same value of ΔS‡ then the values of the rate constant would be in the approximate ratio 109:106:1 for Z = NH2, H and NO2, respectively. This study shows that how profoundly the perturbation of the electronic structure of the corrin affects the thermodynamic and kinetic properties of the Co(III) ion, and provides further evidence that the unusual chemistry of Co(III) in the cobalt corrins is a consequence of the cis-influence of the equatorial macrocyclic ligand. / LG2017