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Hsu, Bernie (Po Cheng)

University of British Columbia

In recent decades, Ab initio quantum chemistry methods have played a crucial role in elucidating the electronic structures of molecules and materials. Despite their widespread application, the constant emergence of new methods lacking rigorous mathematical foundations raises concerns about their reliability. This thesis seeks to bridge this gap by addressing the electronic structure problem through a mathematical lens, leveraging existing numerical analysis results to address the electronic structure problem. Focusing on wavefunction methods, specifically Variational Monte Carlo, our investigation delves into the distinctive features of the Schrodinger equation across different chemical systems, encompassing variations between molecules and materials. We conduct a numerical analysis to derive the convergence of the Ewald Summation of the simulated potential. Subsequently, we employ the Atomic Cluster Expansion to parameterize the trial wavefunction, demonstrating its adaptability to different chemical systems. Building upon existing numerical analyses of the Atomic Cluster Expansion, we argue that our methodology not only provides superior parameterization flexibility compared to existing methods but also ensures a systematic and mathematically sound process for deriving the parameterizations. Finally, we implement simulations to assess the effectiveness of our proposed wavefunction architectures in the 1D uniform electron gas, a system allowing us to probe electronic correlation effects. Through this comprehensive approach, our research aspires to contribute to the development of more robust and mathematically justified methods in the field of Ab initio quantum chemistry.

Text

2024-01-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/87132

Chemistry

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/