Date of Award

2026-08-01

Degree Name

Master of Science

Department

Physics

Advisor(s)

Tunna Baruah

Abstract

Density Functional Theory (DFT) is a widely used approach for studying the electronic and vibrational properties of atomic and molecular systems. It provides a practical balance between accuracy and computational cost, making it suitable for a broad range of applications in quantum chemistry and materials science. The primary focus of this thesis is the electronic structure of lanthanide atoms, where strongly localized 4f electrons give rise to significant self-interaction errors in conventional density functional approximations. The performance of the Perdew-Zunger self-interaction correction (PZSIC) and the locally scaled self-interaction correction (LSIC) approach developed by Zope et al. is investigated using both conventional Kohn-Sham approaches and the Fermi-Löwdin orbital self-interaction correction (FLOSIC) framework across the lanthanide series. Particular attention is given to the optimization of Fermi Orbital Descriptors (FODs), which define the localized orbitals in the Fermi-Löwdin approach, and their influence on orbital localization and electronic structure. Electronic properties, including ionization energies, orbital eigenvalues, and shell structure, are analyzed to assess the effects of self-interaction correction. The results obtained within the Kohn-Sham formalism using optimized effective potential schemes within the Krieger-Li-Iafrate (KLI) approximation show that, although total-energy ionization energies differ only modestly from conventional DFT due to error cancellation, self-interaction correction leads to improved 4f orbital localization and a more physically meaningful description of the electronic potential. These effects are observed through changes in orbital expectation values, including ⟨r⟩ and ⟨r²⟩, orbital eigenvalues, and radial distributions, which provide insight into the influence of self-interaction correction on the underlying electronic structure. These results establish a systematic benchmark for applying parameter-free self-interaction correction methods to localized 4f-electron systems and provide a foundation for extending FLOSIC to lanthanide-containing molecules and materials.

The second study examines the vibrational properties of octanoic acid using DFT-based calculations. Harmonic and anharmonic frequency analyses are performed to characterize the vibrational spectrum, and Einstein frequency analysis is used to understand atom-specific vibrational behavior. The results provide insight into local atomic motion and serve as a model for understanding related molecular systems. Together, these studies demonstrate the versatility of DFT-based methods in addressing different types of quantum mechanical problems. The lanthanide study focuses on improving the treatment of localized electronic states, while the octanoic acid study explores molecular vibrational dynamics. Both contribute to a broader understanding of how first principles methods can be used to describe electronic structure and nuclear motion in complex systems.

Language

en

Provenance

Received from ProQuest

File Size

107 p.

File Format

application/pdf

Rights Holder

Sonam Choki Lhamo

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Physics Commons

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