Dissertation/Thesis Abstract

Orbital-free density functional theory at the nanoscale and beyond: Algorithms and applications
by Hung, Linda, Ph.D., Princeton University, 2011, 232; 3445577
Abstract (Summary)

Orbital-free density functional theory (OFDFT) is a quantum mechanical theory where the total energy of a system depends only on the electron density and an external potential. While not as well-known as its relative, the wavefunction-based Kohn-Sham density functional theory (KSDFT), OFDFT has been established as a fast yet accurate theory for modeling materials – like aluminum – where the valence electron density is nearly homogeneous. In this thesis, we describe improvements to the implementation of OFDFT that allow the study of materials at the nanoscale and beyond. We approximate the structure factor that appears in ion-electron and ion-ion terms with B-splines, so that the scaling of their computations is reduced from quadratic to quasilinear ( O(N log(N)), where N is some measure of system size). We also review the treatment of optimization variables, implement a norm-conserving line search, and use preconditioners to improve optimization algorithms. These preconditioners have limited success for simulation cells with regions of low electron density, but can speed up optimization 3-4 times in other cells. Many of these improvements are included in a new version of the PRinceton Orbital-Free Electronic Structure Software (PROFESS). With all energy, potential, force, and stress computations now parallelized and scaling quasilinearly, more than a million Al atoms can be explicitly simulated on 192 cores. Using this PROFESS 2.0 code, we study Al crack tips using a quasi-two-dimensional setup with ~20 nm × 20 nm samples. Although both the embedded-atom method (EAM) and OFDFT can reproduce KSDFT material properties, the mechanism of plasticity at crack tips in simulation can occur through different slip planes, depending on the choice of OFDFT or the EAM. We also model [111]-oriented Al nanowires with 1-8 nm diameter and length up to ~20 nm. During tensile loading from equilibrium, the iv axial displacements of surface atoms (not noticed in past nanowire simulations) are a driving force for plasticity. Materials at the microscale cannot yet be explicitly modeled by OFDFT. However, they can be treated using multiscale models fully based on OFDFT, as demonstrated by an implementation of quasicontinuum density functional theory that can simulate the nanoindentation of a 2 μm × 1 μm × 4.9 Å Al thin film.

Indexing (document details)
Advisor: Carter, Emily
Commitee:
School: Princeton University
School Location: United States -- New Jersey
Source: DAI-B 72/04, Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Applied Mathematics, Nanoscience, Materials science
Keywords: Aluminum, Orbital free
Publication Number: 3445577
ISBN: 9781124491738
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