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

This thesis begins with a review on the topic of molecular electronics. The purpose of this review is to motivate the need for good theory to understand and predict molecular electronics behaviour. At present the most promising theoretical formalism for dealing with this problem is a combination of density functional theory and nonequilibrium Green's functions (NEGF-DFT). This formalism is especially attractive because it is an ab-initio technique, meaning that it is completely from first principles and does not require any empirical parameters. An implementation of this formalism has been developed by the research group of Hong Guo and is presented and explained here. A few other implementations which are similar but differ in some ways are also discussed briefly to highlight their various advantages and disadvantages. / One of the difficulties of ab-initio calculations is that they can be extremely costly in terms of the computing time and memory that they require. For this reason, in addition to using appropriate approximations, sophisticated numerical analysis tech niques need to be used. One of the bottlenecks in the NEGF-DFT method is solving the Poisson equation on a large real space grid. For studying systems incorporating a gate voltage it is required to be able to solve this problem with nonperiodic boundary conditions. In order to do this a technique called multigrid is used. This thesis examines the multigrid technique and develops an efficient implementation for the purpose of use in the NEGF-DFT formalism. For large systems, where it is necessary to use especially large real space grids, it is desirable to run simulations on parallel computing clusters to handle the memory requirements and make the code run faster. For this reason a parallel implementation of multigrid is developed and tested for performance. The multigrid tool is incorporated into the NEGF-DFT formalism and tested to ensure that it is properly implemented. A few calculations are made on a benzenedithiol system with gold leads to show the effect of an applied gate voltage.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 415-446).

Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 102-114).

Thesis (Ph. D.)--University of Hong Kong, 2009. / Includes bibliographical references (leave 94-102). Also available in print.

Thesis (Ph.D.)--Texas Christian University, 2009. / Title from dissertation title page (viewed Oct. 30, 2009). Includes abstract. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 121-127).

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Leaves 14 and 46 are blank. Typescript. Vita. Includes bibliographical references (leaves 96-100). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Leaves 14 and 46 are blank. Typescript. Vita. Includes bibliographical references (leaves 96-100). Also available on the Internet.