Wavelets and wavelet optimized-finite differences for electronic structure calculations

To perform electronic structure calculations on inhomogenous systems, it is desirable to use methods which adapt to the problem by using a spatially-varying level of resolution. A wavelet basis can efficiently represent a function which is rapidly varying in certain regions of space. One-dimensional calculations using Daubechies wavelets as an adaptive basis have been performed, showing that a compressed wavelet basis can determine the eigenvalues of a system with high accuracy using relatively few functions. Using the Wavelet Optimized Finite Difference Method (WOFD) [1], wavelets can also be used to determine a grid for finite difference calculations. In one dimension, starting with a guess for the wavefunction on a coarse grid with few points, an accurate solution on a nouniform grid can be evolved. In three dimensions, self-consistent total energy calculations employing density functional theory using real-space grids have been performed on atomis, molecules, and quantum dots. Calculations employing WOFD grids are much more accurate than calculations using uniform grids of the same size. Comparisons are made with other adaptive methods.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Rao, Vivek

Contributors dc:contributor

• Martin, Richard M.

• wavelets
• Daubechies wavelets
• Wavelet Optimized Finite Difference Model

Statement dc:rights

• ©1998 Rao

Language dc:language

en

Identifier

4120443

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/30849