Date of Award

2020-01-01

Degree Name

Master of Science

Department

Computational Science

Advisor(s)

Rajendra R. Zope

Second Advisor

Tunna Baruah

Abstract

The Hohenberg-Kohn-Sham (HKS) density functional theory (DFT) is widely used to compute electronic structures of atoms, molecules, and solids. It is an exact theory in which ground state electron density plays the role of basic variable, same as the wavefunction does in quantum mechanics. The total ground state energy is a functional of electron density. The practical application of HKS DFT require approximation to the exchange-correlation energy functional. Many density functional approximations (DFAs) with various degree of sophistication and complexities have been developed. Depending on the complexity, these functionals include electron density, density gradients, density Laplacian, kinetic energy densities, Hartree-Fock exchange etc. Some examples of widely used non-empirical functionals are local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), and strongly constrained and appropriately normalized (SCAN) meta-GGA.

Practically all DFAs suffer from a systematic error known as self-interaction error (SIE) where an electron incorrectly interacts with itself. These DFAs can fail dramatically for cases such as systems with a stretched bond where SIE is pronounced. The SIE arises from an improper cancellation of the self-Coulomb energy with the approximated self-exchange-correlation energy for the one-electron limit. Perdew and Zunger self-interaction correction (PZSIC) provides the exact cancellation for one- and two-electron self-interaction, but it does not necessarily eliminate many-electron self-interaction. The present work uses Fermi-Lowdin orbitals (FLOS) which are Fermi orbitals orthogonalized via Löwdin scheme. FLOs are localized orbitals through Fermi orbital descriptors (FODs) which are special positions to capture the electronic density of a system. The PZSIC implementation using FLOs, called FLOSIC, results in size-extensive implementation of the PZSIC. The PZSIC calculations provide more accurate results for stretched bond and anionic states but worsen properties where DFA performs well, this is known as the PZSIC paradox.

The present Thesis deals with development and assessments of methods to overcome the paradoxical behavior of PZSIC. We compare PZSIC against the new local scaling SIC (LSIC) with two different approaches. The first approach uses ratio of kinetic energy densities referred to as LSIC(z) hereafter. It showed impressive results by keeping the correct behavior PZSIC and improving it where PZSIC fails. LSIC(w), the second method that uses orbital and total densities as scaling factor is proposed in this work. We compare the methods against orbital scaling SIC (OSIC). The comparison is done with an extensive test of different properties such as total energies, ionization potentials and electron affinities for atoms, atomization energies, dissociation and reaction energies, and reaction barrier heights of molecules. We also show that unlike LSIZ(z) the simple scaling factor in LSIC(w) can describe binding of hydrogen bonded water well. This work also presents an extensive study of OSIC applied to SCAN functional for different forms of scaling factors to identify one-electron regions, OSIC-SCAN provides better results than the previously reported OSIC-LSDA, -PBE and -TPSS results. Furthermore, we propose a new method of selective scaling of OSIC to remove the major shortcoming of OSIC that destroys the -1/r asymptotic behavior of the potential shape. The SOSIC gives the HOMO eigenvalues practically identical to PZSIC, unlikely to OSIC. Overall, the Thesis presents new methods for self-interaction free density functional calculations.

Language

en

Provenance

Received from ProQuest

File Size

105 pages

File Format

application/pdf

Rights Holder

Selim Romero

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