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Density Functional Theory Transformed Into a One-Electron Reduced Density Matrix Functional Theory for the Description of Static Correlation
Density Functional Theory Transformed Into a One-Electron Reduced Density Matrix Functional Theory for the Description of Static Correlation
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152811
- ISBN
- 9798384012405
- DDC
- 542
- 서명/저자
- Density Functional Theory Transformed Into a One-Electron Reduced Density Matrix Functional Theory for the Description of Static Correlation
- 발행사항
- [Sl] : The University of Chicago, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 165 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-02, Section: B.
- 주기사항
- Advisor: Mazziotti, David.
- 학위논문주기
- Thesis (Ph.D.)--The University of Chicago, 2024.
- 초록/해제
- 요약Kohn-Sham Density Functional Theory (KS-DFT or just DFT) has become a go-to method for electronic structure calculations due to its low computational scaling, allowing it to treat large systems, while still being relatively accurate. However, DFT still struggles in strongly correlated systems due to its inability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. This error is primarily driven by the single Slater determinant representation of the Kohn-Sham non-interacting auxiliary wave function, which leads to integer occupations of the electronic orbitals. In this thesis, we address this shortcoming by combining DFT with Semi-Definite Programming (SDP) and a 1-Electron Reduced Density Matrix Functional (RDMF) to capture static electron correlation through fractional orbital occupations. We derive our method termed Reduced Density Matrix Functional Theory (RDMFT) from a unitary decomposition of the 2-electron reduced density matrix's cumulant to obtain a system-specific dependence on the electron repulsion integrals. This methodology retains DFT's \uD835\uDCDE(N3 ) computational scaling while describing static correlation through fractional occupation. We apply this approach to a series of small molecules such as the benzynes and find noticeable improvements over DFT in each system tested. We've also modified the dependence of our method on the 2-electron integrals using the Cauchy-Schwarz inequalities to prevent the RDMF term from decaying to zero with growing system sizes, leading to size extensivity issues. We apply this modification to a series of linear hydrogen chains and find it remedies the size extensive issues of the original derivation. We further apply the modification to the singlet-triplet gaps of the acenes from pentacene to dodecacene and find excellent agreement with variational 2-RDM calculations.
- 일반주제명
- Computational chemistry
- 일반주제명
- Physical chemistry
- 일반주제명
- Inorganic chemistry
- 일반주제명
- Computer science
- 기타저자
- The University of Chicago Chemistry
- 기본자료저록
- Dissertations Abstracts International. 86-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211152811
■006m o d
■007cr#unu||||||||
■020 ▼a9798384012405
■035 ▼a(MiAaPQ)AAI31557967
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a542
■1001 ▼aGibney, Daniel Patrick.▼0(orcid)0000-0002-4915-3900
■24510▼aDensity Functional Theory Transformed Into a One-Electron Reduced Density Matrix Functional Theory for the Description of Static Correlation
■260 ▼a[Sl]▼bThe University of Chicago▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a165 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-02, Section: B.
■500 ▼aAdvisor: Mazziotti, David.
■5021 ▼aThesis (Ph.D.)--The University of Chicago, 2024.
■520 ▼aKohn-Sham Density Functional Theory (KS-DFT or just DFT) has become a go-to method for electronic structure calculations due to its low computational scaling, allowing it to treat large systems, while still being relatively accurate. However, DFT still struggles in strongly correlated systems due to its inability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. This error is primarily driven by the single Slater determinant representation of the Kohn-Sham non-interacting auxiliary wave function, which leads to integer occupations of the electronic orbitals. In this thesis, we address this shortcoming by combining DFT with Semi-Definite Programming (SDP) and a 1-Electron Reduced Density Matrix Functional (RDMF) to capture static electron correlation through fractional orbital occupations. We derive our method termed Reduced Density Matrix Functional Theory (RDMFT) from a unitary decomposition of the 2-electron reduced density matrix's cumulant to obtain a system-specific dependence on the electron repulsion integrals. This methodology retains DFT's \uD835\uDCDE(N3 ) computational scaling while describing static correlation through fractional occupation. We apply this approach to a series of small molecules such as the benzynes and find noticeable improvements over DFT in each system tested. We've also modified the dependence of our method on the 2-electron integrals using the Cauchy-Schwarz inequalities to prevent the RDMF term from decaying to zero with growing system sizes, leading to size extensivity issues. We apply this modification to a series of linear hydrogen chains and find it remedies the size extensive issues of the original derivation. We further apply the modification to the singlet-triplet gaps of the acenes from pentacene to dodecacene and find excellent agreement with variational 2-RDM calculations.
■590 ▼aSchool code: 0330.
■650 4▼aComputational chemistry
■650 4▼aPhysical chemistry
■650 4▼aInorganic chemistry
■650 4▼aComputer science
■653 ▼aKohn-Sham Density Functional Theory
■653 ▼aSemi-Definite Programming
■653 ▼aReduced Density Matrix Functional
■653 ▼aElectron repulsion integrals
■653 ▼aLinear hydrogen chains
■690 ▼a0219
■690 ▼a0488
■690 ▼a0984
■690 ▼a0494
■71020▼aThe University of Chicago▼bChemistry.
■7730 ▼tDissertations Abstracts International▼g86-02B.
■790 ▼a0330
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163936▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
