Dissertation/Thesis Abstract

Real-Space Localization Methods for Minimizing the Kohn-Sham Energy
by Millstone, Marc, Ph.D., New York University, 2011, 84; 3466938
Abstract (Summary)

The combination of ever increasing computational power and new mathematical models has fundamentally changed the field of computational chemistry. One example of this is the use of new algorithms for computing the charge density of a molecular system from which one can predict many physical properties of the system.

This thesis presents two new algorithms for minimizingthe Kohn-Sham energy, which is used to describe a system of non-interacting electrons through a set of single-particle wavefunctions. By exploiting a known localization region of the wavefunctions, each algorithm evaluates the Kohn-Sham energy function and gradient at a set of iterates that have a special sparsity structure. We have chosen to represent the problem in real-space using finite-differences, allowing us to efficiently evaluate the energy function and gradient using sparse linear algebra. Detailed numerical experiments are provided on a set of representative molecules demonstrating the performance and robustness of these methods.

Indexing (document details)
Advisor: Overton, Michael
Commitee: Meza, Juan, Ren, Weiqing, Widlund, Olof, Yang, Chao
School: New York University
Department: Computer Science
School Location: United States -- New York
Source: DAI-B 72/10, Dissertation Abstracts International
Subjects: Analytical chemistry, Computer science
Keywords: Computational chemistry, Density functional theory, Kohn-Sham energy, Optimization
Publication Number: 3466938
ISBN: 978-1-124-80845-1
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