{"title":"Reconstruction of the On-Top Two-Electron Density from Natural Orbitals and Their Occupation Numbers.","authors":"Jerzy Cioslowski, Krzysztof Strasburger","doi":"10.1021/acs.jctc.5c00024","DOIUrl":null,"url":null,"abstract":"<p><p>Spatial derivatives of the natural orbitals (NOs) at their nodal surfaces are shown to encode information about the on-top two-electron density Φ<sub>2</sub>(<i>r⃗</i>) in an approximate manner. This encoding, which becomes exact at the limit of an infinite number of nodal surfaces, allows the reconstruction of Φ<sub>2</sub>(<i>r⃗</i>) up to a multiplicative constant that can be retrieved from an identity involving the NO in question and its occupation number. This reconstruction provides a new consistency check for electronic structure formalisms, such as the one-electron reduced density matrix theory, that employ NOs as primary quantities.</p>","PeriodicalId":45,"journal":{"name":"Journal of Chemical Theory and Computation","volume":" ","pages":"3945-3952"},"PeriodicalIF":5.5000,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12020370/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Chemical Theory and Computation","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1021/acs.jctc.5c00024","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/8 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Spatial derivatives of the natural orbitals (NOs) at their nodal surfaces are shown to encode information about the on-top two-electron density Φ2(r⃗) in an approximate manner. This encoding, which becomes exact at the limit of an infinite number of nodal surfaces, allows the reconstruction of Φ2(r⃗) up to a multiplicative constant that can be retrieved from an identity involving the NO in question and its occupation number. This reconstruction provides a new consistency check for electronic structure formalisms, such as the one-electron reduced density matrix theory, that employ NOs as primary quantities.
自然轨道（NOs）在其节点表面的空间导数以近似的方式编码有关上双电子密度Φ2（r - l - l）的信息。这种编码在无限个节点表面的极限处变得精确，允许重建Φ2（r - l - l）直到一个乘法常数，该常数可以从涉及所讨论的NO及其占用号的恒等式中检索到。这种重构为电子结构形式提供了一种新的一致性检验，例如单电子简化密度矩阵理论，这些电子结构形式使用NOs作为主要量。
期刊介绍：
The Journal of Chemical Theory and Computation invites new and original contributions with the understanding that, if accepted, they will not be published elsewhere. Papers reporting new theories, methodology, and/or important applications in quantum electronic structure, molecular dynamics, and statistical mechanics are appropriate for submission to this Journal. Specific topics include advances in or applications of ab initio quantum mechanics, density functional theory, design and properties of new materials, surface science, Monte Carlo simulations, solvation models, QM/MM calculations, biomolecular structure prediction, and molecular dynamics in the broadest sense including gas-phase dynamics, ab initio dynamics, biomolecular dynamics, and protein folding. The Journal does not consider papers that are straightforward applications of known methods including DFT and molecular dynamics. The Journal favors submissions that include advances in theory or methodology with applications to compelling problems.
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