The ability to model ground-state properties in density function theory (DFT) is a ected by the theoretical treatment of the electrons and the numerical approach to the theory. The electron-electron interaction energy is approximated by exchange- correlation (XC) functionals which are functions of the electron density. Popular functionals include the localized density approximation (LDA) or one of many gen- eralized gradient approximations (GGA). The numerical approaches used are the core-electron approximating pseudopotential (PsP) or the more accurate all-electron (AE) method. We test whether PsP calculations for some new GGA's can accurately reproduce AE values for cohesive energy, lattice constant, and bulk modulus for six- teen solids. We compare our PsP results to AE results for several XC functionals and gauge the quality of functionals by comparison to experiment. This allows us to determine which errors are caused by functionals and which are caused by PsP's.

Density functional theory is a successful theory used in physics, chemistry and nanoscience to describe the ground state properties of solids and molecules. It calculates ground state energies and related properties by using the density of the valence electrons as a fundamental variable. In a system of interacting electrons, the electrons will correlate due to the Pauli exclusion principle, as well as their coulomb repulsion. This interaction energy is known as the exchange-correlation energy and is approximated in density functional theory because it is the only unknown in the energy as a functional of density. The simplest model to approximate this exchangecorrelation energy is the local density approximation, which only relies on the local density of the valence electrons at every point. Generalized gradient approximations are approximations which build upon the local density approximation by also using the gradient of the local density. Recently, many new versions of the generalized gradient approximation have been developed to attempt to obtain better energetic and structural properties either at the same time, or at the expense of the other. In this study, we examine the performance of these models by calculating the atomization energy of the AE6 test set. The cohesive energy, lattice constant and bulk modulus of a four solid test set was also calculated. These calculations were done using ABINIT, a density functional theory code that uses a pseudopotential model with plane waves to examine molecules and solids. One of the more recently developed generalized gradient approximation models, the SOGGA, is tested to compare with the standard models. The accuracy of using a pseudopotential model is also tested. It was found that by using a generalized gradient approximation that was better for energy calculations, the structural property calculations would not be as accurate. The SOGGA is a functional that approximates structural properties of solids accurately but does not calculate energies as well. It was also found that using a pseudopotential model resulted in a 1% difference from the all electron calculations. / Density functional theory -- Molecular data -- Solids -- Second order GGA -- Discussions and conclusions. / Department of Physics and Astronomy

Orientador: Maria Aparecida Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-07-28T22:58:14Z (GMT). No. of bitstreams: 1 Souza_FabianodoValede_M.pdf: 3561550 bytes, checksum: f3b4f61836648dece8c995dd128d26c3 (MD5) Previous issue date: 2001 / Resumo: O conhecimento das propriedades fisicas dos materiais é de fundamental importância na caracterização de sólidos e de misturas de sólidos. As misturas de sólidos têm sido utilizadas cada dia mais em processos industriais, visando aprimorar as propriedades de interesse relativas a um material, como capacidade de adsorção e tempo de secagem. Este trabalho visa determinar varias propriedades físicas de dois sólidos, o Caulim e a Zeólita NaY, bem como a mistura destes dois sólidos, caracterizando estes materiais para que eles possam ser aplicados em processos industriais de uma forma mais eficiente. O objetivo do trabalho é apresentar equações que relacionem as propriedades dos materiais puros com as propriedades de suas respectivas misturas através das frações mássica e volumétrica das amostras. Desta forma, apenas a caracterização dos materiais puros seria suficiente para predizer as propriedades físicas de uma mistura binária ou de um sólido composto por três ou mais componentes. Outro objetivo do trabalho é apresentar valores confiáveis para que estes possam ser utilizados no estudo do transporte de massa no interior dos poros do material. Os aparelhos picnômetro de Hélio e porosímetro de Mercúrio foram utilizados na determinação das densidades real e bulk, e também na determinação da porosidade dos sólidos utilizados neste trabalho. A partir dos dados obtidos na porosimetria de Mercúrio e da equação de Wasburn, também foi possível a determinação das permeabilidades intrínseca e relativa das amostras. O método clássico de obtenção das isotermas de dessorção foi utilizado, onde os resultados foram aplicados nas equações de Kelvin e BET para a determinação da área superficial e da fração de microporos presente nas amostras. Finalmente, a distribuição de tamanho de partícula foi realizada para o Caulim e para a Zeólita Na Y através do Contador Coulter, para uma análise de como as partículas destes dois materiais se arranjam entre si. As equações propostas produziram curvas que estão de acordo com os resultados experimentais obtidos neste trabalho. Todas as propriedades fisicas puderam ser reproduzi das com as equações propostas, especialmente a área superficial especifica das partículas e a fração de microporos, onde a concordância com os resultados experimentais foi praticamente total / Abstract: The knowledge of the materials physical properties is specially important in the characterization of pure solids and mixtures. The solids mixtures have been used frequent1y in industriaI processes to improve the properties of interest of a material, as capacity of adsorption and drying time. This work aims to determine some physical properties of two solids, Kaolin and Zeolite Na Y, as well as of mixtures of these two solids. With this characterization, these materials wiIl be able to be applied in industrial processes with a better efficiency. The objective of the work is also to present equations that relate the properties of the pure materiais with the properties of their respective mixtures through the mass and volumetric fractions of the samples. In this way, only the characterization of the pure materials would be enough to predict the physical properties of a binary mixture or of a solid hold for three or more components. Another objective is to present reliable results so that these results can be used in the study of mass transport in the pores of materiais. The picnometer and mercury porosimeter had been used to determine the real and bulk densities, and also to determine the porosity of solids used in this work. From the data gotten in the porosimeter and using the equation of Washburn, the determination of the intrinsic and relative permeabilities of the samples was possible. The classic method to draw the desorption isotherms was used, where the results had been applied in the Kelvin and BET equations to determine the specific surface area and the fraction of micropores in the samples. Finally the particle size distribution was determined for the Kaolin and Zeolite Na Y with a Coulter Counter, for an analysis of how the particles of these two materials could be arranged between themselves. The derived equations had drawn curves that are in agreement with the experimental data gotten in this work. AlI the physical properties could be reproduced with the derived equations, especially the solid specific surface area and the fraction of micropores, where the agreement with the experimental results was practically total / Mestrado / Engenharia de Processos / Mestre em Engenharia Química