Electronic Theses and Dissertations

Sarah Pak

Date

2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Chemistry

Committee Chair

Daniel Nascimento

Committee Member

Nathan DeYonker

Committee Member

Qianyi Cheng

Committee Member

Xiao Shen

Committee Member

Yongmei Wang

Abstract

This dissertation addresses the challenges in simulating the core-level spectra of transition metal complexes, focusing on validating simplified methods that are both efficient and sufficiently accurate. Proper simulation requires incorporating relativistic effects, such as spin-orbit coupling, which significantly increases computational demands. To address these difficulties, this work provides an overview of the theoretical foundations behind the employed methodologies, including linear-response time-dependent density functional theory (LR-TD-DFT) and the zeroth-order regular approximation (ZORA) Hamiltonian, and the state-interaction framework. Key findings demonstrate that simplified state-interaction-based approaches produce near-edge X-ray absorption spectra (XAS) that are nearly indistinguishable from those obtained using more rigorous methods, ensuring reliable analysis at a fraction of the computational cost. Further optimization can be achieved by applying approximations to the $\sigma$ vectors in the Davidson algorithm, which are constructed from the Fock matrix, Coulomb and exchange-like terms, and the exchange-correlation kernel. Our studies have revealed that the exchange-correlation kernel has a negligible impact on the qualitative features of the spectra, whereas the Hartree-Fock exchange term is crucial. These results establish the validity of the simplified approaches, highlighting their potential to reduce computational overhead without compromising accuracy.

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Data is provided by the student.

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Open access.

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