{"title":"Variational determination of the two-electron reduced density matrix: A tutorial review","authors":"A. Eugene DePrince III","doi":"10.1002/wcms.1702","DOIUrl":null,"url":null,"abstract":"<p>The two-electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many-electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave function, by minimizing this energy with respect to variations in the elements of the 2RDM, while also enforcing known <i>N</i>-representability conditions. In this tutorial review, we provide an overview of the theoretical underpinnings of the v2RDM approach and the <i>N</i>-representability constraints that are typically applied to the 2RDM. We also discuss the semidefinite programming (SDP) techniques used in v2RDM computations and provide enough Python code to develop a working v2RDM code that interfaces to the <span>libSDP</span> library of SDP solvers.</p><p>This article is categorized under:\n </p>","PeriodicalId":236,"journal":{"name":"Wiley Interdisciplinary Reviews: Computational Molecular Science","volume":"14 1","pages":""},"PeriodicalIF":16.8000,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wiley Interdisciplinary Reviews: Computational Molecular Science","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/wcms.1702","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The two-electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many-electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave function, by minimizing this energy with respect to variations in the elements of the 2RDM, while also enforcing known N-representability conditions. In this tutorial review, we provide an overview of the theoretical underpinnings of the v2RDM approach and the N-representability constraints that are typically applied to the 2RDM. We also discuss the semidefinite programming (SDP) techniques used in v2RDM computations and provide enough Python code to develop a working v2RDM code that interfaces to the libSDP library of SDP solvers.
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Computational molecular sciences harness the power of rigorous chemical and physical theories, employing computer-based modeling, specialized hardware, software development, algorithm design, and database management to explore and illuminate every facet of molecular sciences. These interdisciplinary approaches form a bridge between chemistry, biology, and materials sciences, establishing connections with adjacent application-driven fields in both chemistry and biology. WIREs Computational Molecular Science stands as a platform to comprehensively review and spotlight research from these dynamic and interconnected fields.
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