Density functional theory (DFT) is a popular approach to solving the many-electron Schrödinger equation, in order to investigate the properties of matter from first principles. While DFT can give the exact ground state electronic density of a system, in practice, an approximation is required for the many-body effects contained in the exchange-correlation functional. The accuracy of calculations performed using DFT is strongly related to the choice of approximation. In this thesis we will investigate and build upon a fully non-local approach to modeling exchange-correlation in the form of the weighted density approximation (WDA). Central to the WDA is the model function chosen for the coupling-constant averaged pair-correlation function (PCF). We show that a model PCF can be selected from a set to give excellent bulk properties for a particular system. However, this model is not necessarily transferable to other systems and there is no method of selecting an appropriate model from this set a priori. We suggest that the model PCF can be improved systematically by satisfying known physical constraints. One such constraint is the Kimball cusp condition, which we include in our model and implement. We demonstrate that surfaces are systems that require a non-local treatment of exchange-correlation by applying the WDA to metal surfaces and investigate the dissociative adsorption of H2 on the Cu(100) surface. A new framework for a model PCF with spin resolution is developed, providing a route for more physical constraints to be satisfied within a weighted spin density approximation (WSDA). A simple model is suggested and implemented and comparisons are made to the coupling-constant averaged PCF in the homogeneous electron gas. We then apply a selection of our new models to a number of materials and show that our model for the WSDA gives improved band gaps over the local density approximation. Application of the WSDA to spin polarised materials reveals shortcomings in our simple model. We then suggest further refinements to our implementation of the WSDA. It is expected that the inclusion of additional physical constraints will systematically improve results given in a weighted-density based approximation to exchange-correlation.

abstract: In software testing, components are tested individually to make sure each performs as expected. The next step is to confirm that two or more components are able to work together. This stage of testing is often difficult because there can be numerous configurations between just two components. Covering arrays are one way to ensure a set of tests will cover every possible configuration at least once. However, on systems with many settings, it is computationally intensive to run every possible test. Test prioritization methods can identify tests of greater importance. This concept of test prioritization can help determine which tests can be removed with minimal impact to the overall testing of the system. This thesis presents three algorithms that generate covering arrays that test the interaction of every two components at least twice. These algorithms extend the functionality of an established greedy test prioritization method to ensure important components are selected in earlier tests. The algorithms are tested on various inputs and the results reveal that on average, the resulting covering arrays are two-fifths to one-half times smaller than a covering array generated through brute force. / Dissertation/Thesis / Masters Thesis Computer Science 2015

<p>Approximating the exchange-correlation energy in density functional theory (DFT) is a crucial task. As the only missing element in the Kohn-Sham DFT, the search for better exchange-correlation functionals has been an active field of research for fifty years. Many models and approximations are known and they can be summarized in what is known as the Jacob’s ladder. All the functionals in that ladder are local in the sense that they rely on the information of only one electronic coordinate. That is, even though the exchange-correlation hole, the cornerstone in density functional theory, is a two-electron coordinate quantity, one of the coordinates is averaged over in “Jacob’s ladder functionals.” This makes the calculations considerably more efficient. On the other hand, some of the important constraints on the form of the exchange-correlation functional become inaccessible in the one-point forms. The violation of these constraints leads to functionals plagued by systematic errors, leading to qualitatively incorrect descriptions of some chemical and physical processes.</p> <p>In this thesis the idea of a weighted density approximation (WDA) is explored. More specifically, a symmetric and normalized two-point functional is proposed for the exchange-correlation energy functional. The functional is based entirely on the hole for the uniform electron gas. By construction, these functionals fulfill two of the most important constraints: the normalization of the exchange-correlation hole and the uniform electron gas limit. The findings suggest that we should pursue a whole new generation of “new Jacob’s ladder” functionals.</p> <p>A further step was considered. Given the relevance of the long-range behavior of the exchange-correlation hole, a study of the electronic direct correlation function was performed. The idea was to build up the long-range character of the hole as convoluted pieces of the simple and short-ranged direct correlation function. This direct correlation function provides better results, at least for the correlation energy in the spin-polarized uniform electron gas.</p> <p>The advantage of one-point functionals is their computational efficiency. We therefore attempted to develop new methods that mitigate the relative computational inefficiency of two-point functionals. This led to new methods for evaluating the six-dimensional integrals that are inherent to the exchange-correlation energy.</p> / Doctor of Philosophy (PhD)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The imminence of Panambi s dam construction, in the municipality of Alecrim, Rio Grande do Sul, affecting the municipality of Porto Mauá, which will overflow thousands of hectares of rainforest, Macluratinctoria s habitat and, the great exploitation of the specie in the region led to the initiation of this research work. The specie is commonly known as Tajuva, presents arboreal sized, and belongs to the botanical family Moraceae, native of Rio Grande do Sul. It is a semideciduous specie, with heights between 10 to 30 meters and, up to 100 cm of diameter; short trunk, with a smooth bark, grayish green with many yellowed lenticels, many times, with the presence of branched thorns. The study aimed to the realization of anatomical description, the chemical characterization and the basic and weighted densities of Maclura tinctoria(L) D. Don Ex Steud wood. The five studied exemplars were obtained through environmental license, in accordance with current legislation. Three wood samples, taken from BHD were used for the manufacture of histological slides and for the fibers quantification. To the determination of wood density and the chemical analysis of wood, disks were removed from the trunk and divided into opposing wedges. It were used opposing wedges removed from six pre-established heights (base, DAP, 25%, 50%, 75% and 100% of commercial height). It was used the ASTM standards to determinate the density, and from TAPPI to the chemical analysis of wood. The wood was anatomically described and illustrated with photomicrographs. The woody tissue consist mainly of fibers (60 ± 3,4%) and rays (20 ± 2,3%), totaling approximately 80%. The remaining, in other words, 20% are divided into vessels (12 ± 4%) and axial parenchyma (8 ± 3%). The mean values, to the basic density (pb) and weighted density (ppond), were 0,539 and 0,555 g/cm³, respectively. The macromolecular constituents of heartwood and sapwood were determinate separately. The average content found for extractives (18,92; 6,32%); Klason lignin (17,58; 17,55%); holocellulose (63,45; 78,59%); alpha-cellulose ( 35,44; 44,38%); hemicelluloses (28,01; 34,21%) and ashes (1,08; 1,35%), to the heartwood and sapwood, respectively, totaling 102,42 ± 3,1%. The Tajuva s wood brings together the anatomical characteristics prevalent in Moraceae, framing the specie in their respective botanical family. It is considered an evolved specie anatomically. The density presents a decrease in the values in relation to the axial position of the plant. The heartwood is constituted of phenolic compounds and acids in a higher proportion relative to the sapwood, which presents higher starch contents. Studies about the natural durability and the wood quality are fundamental to indicate the best application of wood. / A eminência da construção da barragem Panambi, no município de Alecrim, Rio Grande do Sul, afetando o município de Porto Mauá, a qual alagará milhares de hectares de mata atlântica, habitat da Maclura tinctoria e, a grande exploração da espécie na região motivaram o início desse trabalho de pesquisa. Popularmente, a espécie é conhecida como Tajuva, apresenta porte arbóreo, e pertence à família botânica Moraceae, nativa do Rio Grande do Sul. É uma espécie semicaducifólia, com altura entre 10 a 30 metros e, com até 100 cm de diâmetro; fuste curto, com casca lisa, verde acinzentada com numerosas lenticelas amareladas, muitas vezes, com presença de espinhos ramificados. O estudo teve como objetivo a descrição anatômica, a caracterização química e a determinação das densidades básica e ponderada da madeira de Maclura tinctoria (L) D. Don ex Steud. As cinco árvores estudadas foram obtidas através de licenciamento ambiental, de acordo com a legislação vigente. Três amostras do lenho, retiradas do DAP foram utilizadas para a confecção de lâminas histológicas e para a quantificação das fibras. Para a determinação da densidade da madeira e para as análises químicas da madeira, foram retirados discos do tronco e divididos em cunhas. Foram utilizadas cunhas opostas retiradas de seis alturas pré-estabelecidas (base, DAP, 25, 50, 75 e 100% da altura comercial). Utilizou-se as normas da ASTM para determinação da densidade, e da TAPPI para as análises químicas da madeira. O lenho foi anatomicamente descrito e ilustrado com fotomicrografias. O tecido lenhoso é constituído principalmente por fibras (60 ± 3,4%) e raios (20 ± 2,3%), totalizando aproximadamente 80%. O restante, ou seja, 20 % estão divididos entre vasos (12 ± 4%) e parênquima axial (8 ± 3%). Os valores médios, para a densidade básica média (ρb) e ponderada (ρpond), foram de 0,539 e 0,555 g/cm³, respectivamente. Os constituintes macromoleculares da madeira de cerne e alburno foram determinados separadamente. Os teores médios encontrados para extrativos totais (18,92; 6,32%); lignina Klason (17,58; 17,55%); holocelulose (63,45; 78,59%); alfa celulose (35,44; 44,38%); hemiceluloses (28,01; 34,21%) e cinzas (1,08; 1,35%), para cerne e alburno, respectivamente, totalizando 102,42 ± 3,1%. O lenho da Tajuva reúne as características anatômicas predominantes em Moraceae, enquadrando a espécie em sua respectiva família botânica. É considerada uma espécie evoluída anatomicamente. A densidade apresenta decréscimo de valores em relação à posição axial da planta. O cerne é constituído por compostos fenólicos e ácidos em maior proporção em relação ao alburno, que apresenta maiores teores de amido. Estudos sobre a durabilidade natural e a qualidade da madeira são fundamentais para indicar a melhor aplicação da madeira.