Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 189-196).

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 64-67). Also available in print.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 64-67). Also available online.

Thesis (M. Sc.)--University of Alberta, 2009. / Title from pdf file main screen (viewed on Dec. 11, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Statistics, Department of Mathematical and Statistical Sciences, University of Alberta." Includes bibliographical references.

published_or_final_version / Physics / Master / Master of Philosophy

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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

The challenge of density functional theory is the useful approximation of the exchange - correlation energy. This energy can be approximated with the local electron density and the gradient of the density. Many different generalized gradient approximations (GGA) have been made recently and there is controversy over the best overall functional. Recent Monte Carlo simulations give evidence that the Laplacian of the density might be a better starting place than the gradient to correct the local density approximation. We have tested several Laplacian based GGA models for exchange for small atoms. We use known constraints on the exchange energy used in current GGA’s. In many models unphysical oscillations occur in the potential when using the Laplacian, and understanding and eliminating them is part of the focus of this research. We also find that mixing gradient and Laplacian seems to give a better result than only using one or the other. / Department of Physics and Astronomy