Matter on a length scale comparable to that of a chemical bond is governed by the theory of quantum mechanics, but quantum mechanics is a many body theory, hence for the sake of chemistry or solid state physics, finding solutions to the governing equation, Schrodinger's equation, is hopeless for all but the smallest of systems. As the number of electrons increases, the complexity of solving the equations grows rapidly without bound. One way to make progress is to treat the electrons in a system as independent particles and to attempt to capture the many-body effects in a functional of the electrons' density distribution. When this approximation is made, the resulting equation is called the Kohn-Sham equation, and instead of requiring solving for one function of many variables, it requires solving for many functions of the three spatial variables. This problem turns out to be easier than the many body problem, but it still scales cubically in the number of electrons. In this work we will explore ways of obtaining the solutions to the Kohn-Sham equation in the framework of real-space pseudopotential density functional theory. The Kohn-Sham equation itself is an eigenvalue problem, just as Schrodinger's equation. For each electron in the system, there is a corresponding eigenvector. So the task of solving the equation is to compute many eigenpairs of a large Hermitian matrix. In order to mitigate the problem of cubic scaling, we develop an algorithm to slice the spectrum into disjoint segments. This allows a smaller eigenproblem to be solved in each segment where a post-processing step combines the results from each segment and prevents double counting of the eigenpairs. The efficacy of this method depends on the use of high order polynomial filters that enhance only a segment of the spectrum. The order of the filter is the number of matrix-vector multiplication operations that must be done with the Hamiltonian. Therefore the performance of these operations is critical. We develop a scalable algorithm for computing these multiplications and introduce a new density functional theory code implementing the algorithm. / text

Através de cálculos de pseudopotenciais ab initio, dentro do esquema de Car-Parrinello, investigamos diferentes defeitos no GAAS dopado com elementos do grupo IV da tabela periódica. Estudamos a formação dos níveis doadores profundos relacionados ao SI e ao GE substitucionais no Arseneto de Gálio. Esse defeito, conhecido como centro DX, de acordo com nossos cálculos de energia total, possui configurações estruturais que dependem do elemento doador (grupo IV), na formação do nível profundo. Para a impureza de GE, encontramos uma estrutura microscópica para o DX diferente dos modelos propostos até hoje, não havendo grandes relaxações da rede. Com o objetivo de esclarecer os efeitos de compensação em altas concentrações de C no GAAS, verificamos que o C prefere o sítio do AS, com o conhecido caráter aceitador para essa impureza. Entretanto se o C\' ocupar o sítio do GA, como um possível fator de redução de portadores, o nível de impureza torna-se extremamente profundo, um comportamento muito diferente comparado aos outros elementos com 4 elétrons de valência, ou seja, a impureza de C mantém características sempre aceitadoras. Também investigamos super-redes-delta formadas por GAAS dopado com SI, ou seja, defeitos planares. Esse sistema, até então só estudado via teoria da massa efetiva, aqui é abordado através de um cálculo ab initio, onde a dimensionalidade é definida \"per si\" sem nenhuma imposição na equação de Schrõdinger. Esta abordagem é direcionada a sistemas altamente dopados, onde estudamos as possíveis causas da saturação de portadores nesse limite. / We investigate the electronic and structural properties of defects in GAAS originated by dopants of the fourth group elements of the periodic table. Our calculations were obtained by using an ab initio non local pseudopotential method, within the local density approximation. The Kohn-Sham equations are solved in the Car-Parrinello scheme. Our results indicate that all impurities studied (O, SI and GE) present different behaviors in GAAS. The DX-center introduced by substitutional GE IND. GA impurity can be well described by a relaxation in T IND. D symmetry along the breathing mode, whereas in the SI IND. GA defect, a distortion in direction is involved. For the GE impurity there is a qualitative difference from that of SI, even though the electronic structure behaves similarly. For the C IND. AS impurity we find a shallow-level acceptor defect, as expected. However, for the C IND. GA as a possible compensation factor, we find a very deep amphoteric impurity level. Also we present, for the first time to our knowledge, a microscopic model based on an ab initio calculation of a periodically SI-delta doping in GAAS. In the high donor concentration regime, our results show that the subband-delta presents a small dispersion like 2D-system, even for small doping period.

Através de cálculos de pseudopotenciais ab initio, dentro do esquema de Car-Parrinello, investigamos diferentes defeitos no GAAS dopado com elementos do grupo IV da tabela periódica. Estudamos a formação dos níveis doadores profundos relacionados ao SI e ao GE substitucionais no Arseneto de Gálio. Esse defeito, conhecido como centro DX, de acordo com nossos cálculos de energia total, possui configurações estruturais que dependem do elemento doador (grupo IV), na formação do nível profundo. Para a impureza de GE, encontramos uma estrutura microscópica para o DX diferente dos modelos propostos até hoje, não havendo grandes relaxações da rede. Com o objetivo de esclarecer os efeitos de compensação em altas concentrações de C no GAAS, verificamos que o C prefere o sítio do AS, com o conhecido caráter aceitador para essa impureza. Entretanto se o C\' ocupar o sítio do GA, como um possível fator de redução de portadores, o nível de impureza torna-se extremamente profundo, um comportamento muito diferente comparado aos outros elementos com 4 elétrons de valência, ou seja, a impureza de C mantém características sempre aceitadoras. Também investigamos super-redes-delta formadas por GAAS dopado com SI, ou seja, defeitos planares. Esse sistema, até então só estudado via teoria da massa efetiva, aqui é abordado através de um cálculo ab initio, onde a dimensionalidade é definida \"per si\" sem nenhuma imposição na equação de Schrõdinger. Esta abordagem é direcionada a sistemas altamente dopados, onde estudamos as possíveis causas da saturação de portadores nesse limite. / We investigate the electronic and structural properties of defects in GAAS originated by dopants of the fourth group elements of the periodic table. Our calculations were obtained by using an ab initio non local pseudopotential method, within the local density approximation. The Kohn-Sham equations are solved in the Car-Parrinello scheme. Our results indicate that all impurities studied (O, SI and GE) present different behaviors in GAAS. The DX-center introduced by substitutional GE IND. GA impurity can be well described by a relaxation in T IND. D symmetry along the breathing mode, whereas in the SI IND. GA defect, a distortion in direction is involved. For the GE impurity there is a qualitative difference from that of SI, even though the electronic structure behaves similarly. For the C IND. AS impurity we find a shallow-level acceptor defect, as expected. However, for the C IND. GA as a possible compensation factor, we find a very deep amphoteric impurity level. Also we present, for the first time to our knowledge, a microscopic model based on an ab initio calculation of a periodically SI-delta doping in GAAS. In the high donor concentration regime, our results show that the subband-delta presents a small dispersion like 2D-system, even for small doping period.

The quantum simulation of large molecular systems is a formidable task. We explore the use of effective potentials based on the Feynman path centroid variable in order to simulate large quantum clusters at a reduced computational cost. This centroid can be viewed as the “most” classical variable of a quantum system. Earlier work has shown that one can use a pairwise centroid pseudo-potential to simulate the quantum dynamics of hydrogen in the bulk phase at 25 K and 14 K [Chem. Phys. Lett. 249, 231, (1996)]. Bulk hydrogen, however, freezes below 14 K, so we focus on hydrogen clusters and nanodroplets in the very low temperature regime in order to study their structural behaviours. The calculation of the effective centroid potential is addressed along with its use in the context of molecular dynamics simulations. The effective pseudo-potential of a cluster is temperature dependent and shares similar behaviour as that in the bulk phase. Centroid structural properties in three dimensional space are presented and compared to the results of reference path-integral Monte Carlo simulations. The centroid pseudo-potential approach yields a great reduction in computation cost. With large cluster sizes, the approximate pseudo-potential results are in agreement with the exact reference calculations. An approach to deconvolute centroid structural properties in order to obtain real space results for hydrogen clusters of a wide range of sizes is also presented. The extension of the approach to the treatment of confined hydrogen is discussed, and concluding remarks are presented.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 86-90).

Το οξείδιο του ψευδαργύρου είναι ένας ημιαγωγός της ομάδας II-VI και έχει μεγάλη ποικιλία σε τεχνολογικές εφαρμογές όπως οι αισθητήρες διαφόρων χημικών αερίων, τα lasers, οι δίοδοι εκπομπής φωτός, οι νανο-γεννήτριες, τα ηλιακά κύτταρα και πολλές άλλες. Το ευρύ του ενεργειακό κενό (3.445 eV) το καθιστά ένα πολλά υποσχόμενο υλικό για φωτονικές εφαρμογές στην περιοχή του UV ή του ιώδους, ενώ ταυτόχρονα η υψηλή ενέργεια συνοχής του εξιτονίου που το χαρακτηρίζει (περίπου στα 60 meV) επιτρέπει την αποτελεσματική εξιτονική εκπομπή σε θερμοκρασία δωματίου. Οι πιο πρόσφατες εξελίξεις στον τομέα του νανοδομημένου ZnO είναι οι νανοδρόμοι, οι νανογέφυρες, οι νανοπροπέλες, οι νανοδακτύλιοι, τα νανονήματα κ.α. Στην παρούσα διπλωματική εργασία μελετώνται οι ηλεκτρονιακές και οπτικές ιδιότητες νανονημάτων οξειδίου του ψευδαργύρου (ZnO) για ένα εύρος διαμέτρων από 2 έως 6 nm και με την βοήθεια της εμπειρικής μεθόδου των ψευδοδυναμικών και της Configuration Interaction (CI). Μια ανασκόπηση των ιδιοτήτων και χαρακτηριστικών του bulk ZnO, όπως η κρυσταλλική και η ενεργειακή του δομή, κάποιες τεχνολογικές εφαρμογές και μέθοδοι ανάπτυξης δίνονται στο πρώτο κεφάλαιο. Το δεύτερο κεφάλαιο περιέχει την περιγραφή διαφόρων υπολογιστικών μεθόδων όπως της προσέγγισης ενεργούς μάζας ( Effective Mass Approximation), της θεωρίας του συναρτησιακού της πυκνότητας (Density Functional Theory) και τέλος, της εμπειρικής μεθόδου των ψευδοδυναμικών που χρησιμοποιείται στους υπολογισμούς των ηλεκτρονιακών και οπτικών ιδιοτήτων των νανοδομών που μελετάμε. Στο τρίτο και τελευταίο κεφάλαιο, παρατίθενται τα αριθμητικά αποτελέσματα . Αυτά, αφορούν στο εξαρτώμενο από το μέγεθος, οπτικό ενεργειακό κενό, το Stokes shift, και το φάσμα φωτοφωταύγειας. Στο τέλος του κεφαλαίου περιγράφονται τα συμπεράσματα. / Zinc oxide (ZnO), a typical group II-VI compound, has a great variety of device applications, such as chemical sensors, lasers, light-emitting diodes, nanogenerators, solar cells and so forth. The wide band gap (3.445 eV) makes it a promising material for photonic applications in the UV or the blue range, while the high exciton binding energy (around 60 meV at room temperature) allows efficient excitonic emission at room temperature. The most recent developments are towards the nanostructured ZnO, such as nanorods, nanobridges, nanopropellers, nanorings, nanowires, et al. In the present master thesis, the electronic and optical properties of ZnO nanowires within the range of 2-6 nm in diameter are studied by means of atomistic empirical pseudopotential method and configuration interaction. A review of the bulk ZnO, such as the crystal and band structures, technological applications and synthesis methods, is presented in chapter one. The second chapter is devoted to the discussion of various types of methods, e.g., effective-mass approximation, density-functional theory (DFT), and especially the empirical pseudopotential method used herein, for the calculations of the electronic and optical properties of nanostructured ZnO. The numerical results, based on the empirical pseudopotential methods and configuration interaction approach, are present in the following chapter. These results cover the size-dependent optical band gap, Stokes shift and photoluminescence spectrum. A summarization of the results is given in the last chapter.

The quantum simulation of large molecular systems is a formidable task. We explore the use of effective potentials based on the Feynman path centroid variable in order to simulate large quantum clusters at a reduced computational cost. This centroid can be viewed as the “most” classical variable of a quantum system. Earlier work has shown that one can use a pairwise centroid pseudo-potential to simulate the quantum dynamics of hydrogen in the bulk phase at 25 K and 14 K [Chem. Phys. Lett. 249, 231, (1996)]. Bulk hydrogen, however, freezes below 14 K, so we focus on hydrogen clusters and nanodroplets in the very low temperature regime in order to study their structural behaviours. The calculation of the effective centroid potential is addressed along with its use in the context of molecular dynamics simulations. The effective pseudo-potential of a cluster is temperature dependent and shares similar behaviour as that in the bulk phase. Centroid structural properties in three dimensional space are presented and compared to the results of reference path-integral Monte Carlo simulations. The centroid pseudo-potential approach yields a great reduction in computation cost. With large cluster sizes, the approximate pseudo-potential results are in agreement with the exact reference calculations. An approach to deconvolute centroid structural properties in order to obtain real space results for hydrogen clusters of a wide range of sizes is also presented. The extension of the approach to the treatment of confined hydrogen is discussed, and concluding remarks are presented.

Transition metal oxides constitute a large class of materials with variety of very interesting properties and important technological utility. A subset with perovskite structure has been the subject matter of the current theoretical investigation with an emphasis on their electronic and structural behavior. An analytical and a computational method are used to calculate physical entities like lattice parameters, bulk moduli, band structures, density of electronic states and charge density distributions for various topologies. Results are discussed and compared with the available experimental findings.

Orientador: Nelson Henrique Morgon / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-18T09:48:03Z (GMT). No. of bitstreams: 1 Silva_MauricioChagasda_D.pdf: 1640271 bytes, checksum: 4dc0aa6f7b350fe3e8808a9095aba5fe (MD5) Previous issue date: 2011 / Resumo: Utilizando a implementação do método da coordenada geradora discretizada nos orbitais atômicos, conjuntos de bases adaptados ao pseudopotencial de caroço SBKJC (conjuntos GBSMCS) foram desenvolvidos, validados e utilizados no estudo de possíveis efeitos de solvatação do tetraidrofurano sobre um mecanismo modelo de Suzuki-Miyaura. As metodologias de validação adotadas para os conjuntos GBSMCS foram os cálculos teóricos da afinidade por próton de sistemas atômicos e moleculares, iônicos e neutros, das entalpias de liquefação de alguns solventes orgânicos rotineiros e das entalpias de hidratação de 29 compostos orgânicos diversos. Nas etapas de validação, observou-se de uma maneira geral, uma boa relação entre custo e benefício na utilização dos conjuntos de bases GBSMCS, obteveram-se desvios médios por volta de 0 até 20 kJ.mol, nas propriedades estudadas. Com as metodologias propostas neste trabalho e com a utilização dos conjuntos GBSMCS, determinou-se o perfil potencial da reação modelo de Suzuki-Miyaura tanto em fase gasosa como em fase solvatada de tetraidrofurano. Não se observou efeitos significativos nas estruturas dos estados estacionários caracterizados e nem nas DrG para as etapas de adição-oxidativa, transmetalação, eliminação-redutiva e isomerização. Contudo, observou-se que há efeitos consideráveis de solvatação para as espécies individuais. As etapas de adição-oxidativa e de eliminação-redutiva apresentaram-se como sendo etapas exergônicas e a etapa de transmetalação como sendo uma etapa endergônica tanto em fase gasosa como em tetraidrofurano. Abordou-se um mecanismo associativo em todas as etapas principais reacionais, contudo inferiu-se que a etapa de transmetalação tenha possíveis rotas mecanísticas dissociativas iônicas que serão estudadas em trabalhos futuros / Abstract: Using the implementation of the discretized generator coordinate method in atomic orbitals, atomic basis sets adapted to the pseudopotential core SBKJC were developed ( GBSMCS ), validated and used to study possible effects of tetrahydrofuran¿s solvation over a model Suzuki-Miyaura¿s mechanism. The methodologies adopted for the validation of GBSMCS basis sets were the theoretical calculations of proton affinities of atomic and molecular, ionic and neutral, systems, the liquefaction enthalpies of some common organic solvents and the hydration enthalpies of 29 organic compounds. In the validation steps a good relationship was abserved between cost and benefit in the use of GBSMCS basis set, average deviations around 0 to 20 kJ.mol for the properties studied. Applying the methodologies proposed in this research and using the GBSMCS atomic basis sets, the potential profile of the Suzuki- Miyaura¿s model mechanism was determinated in the gas and tetrahydrofuran phases. No significant tetrahydronfuran¿s solvation effects were observed for molecular stationarys state structures, neither for DrG for oxidative- addition, transmetallation, reductive-elimination and isomerization reaction steps. However, some strong solvation effects were observed for individual species. The oxidative-addition and reductive-elimination reaction steps were characterized as exergonic steps, but transmetallation reaction step was presented as an endergonic step, both in the gas and tetrahydrofuran phases. This work approaches an associative mechanism for all main reaction steps; however, we inferred that the transmetallation reaction step could have some ionic pathways and should be studied in future works / Doutorado / Físico-Química / Doutor em Ciências

Orientador: Nelson Henrique Morgon / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-07T03:03:20Z (GMT). No. of bitstreams: 1 Sanvido_CibelledeSouza_M.pdf: 3049772 bytes, checksum: 93473c5a86f022408435d3d8d4bfadd4 (MD5) Previous issue date: 2006 / Mestrado / Físico-Química / Mestre em Química