Wavefunction parameterizations using the atomic cluster expansion
department or school: Science, Faculty of
department or school: Chemistry, Department of
data provider: DSpace
degree campus: UBCV
creator: Hsu, Bernie (Po Cheng)
issued: 2024-01-05T17:32:32Z
issued: 2023
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: 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.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/87132
note: Wavefunction Parameterizations Using The Atomic Cluster ExpansionbyBernie (Po Cheng) HsuHBSc, The University of Toronto, 2021A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Chemistry)The University of British Columbia(Vancouver)December 2023© Bernie (Po Cheng) Hsu, 2023The following individuals certify that they have read, and recommend to the Faculty of Graduate and Post-doctoral Studies for acceptance, the thesis entitled:Wavefunction Parameterizations Using The Atomic Cluster Expansionsubmitted by Bernie (Po Cheng) Hsu in partial fulfillment of the requirements for the degree of Master ofScience in Chemistry.Examining Committee:Christoph Ortner, Professor, Mathematics, UBCCo-SupervisorYan Alexander Wang, Associate Professor, Chemistry, UBCCo-SupervisorRoman Krems, Professor, Chemistry, UBCSupervisory Committee MemberAlireza Nojeh, Professor, Electrical and Computer Engineering, UBCSupervisory Committee MemberiiAbstractIn recent decades, Ab initio quantum chemistry methods have played a crucial role in elucidating theelectronic structures of molecules and materials. Despite their widespread application, the constant emer-gence 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 mathematicallens, leveraging existing numerical analysis results to address the electronic structure problem.Focusing on wavefunction methods, specifically Variational Monte Carlo, our investigation delves intothe distinctive features of the Schro¨dinger equation across different chemical systems, encompassing vari-ations between molecules and materials. We conduct a numerical analysis to derive the convergence of theEwald Summation of the simulated potential. Subsequently, we employ the Atomic Cluster Expansion toparameterize the trial wavefunction, demonst…
has type: Thesis/Dissertation
date issued: 2024-05
is shown at: 10.14288/1.0438554
language: eng
degree discipline: Chemistry
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Ortner, Christoph
contributor: Wang, Yan Alexander
type: Text
identifier URI: http://hdl.handle.net/2429/87132