Impact of the Kohn-Sham Delocalization Error on Organic Conjugated π Systems

Impact of the Kohn-Sham Delocalization Error on Organic Conjugated π Systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Impact of the Kohn-Sham Delocalization Error on Organic Conjugated π Systems Dong Le, Mia Yang, Jochen Autschbach This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7171990/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Sep, 2025 Read the published version in Structural Chemistry → Version 1 posted 9 You are reading this latest preprint version Abstract This study investigates the extent of π-orbital delocalization in Kohn-Sham (KS) density functional calculations in relation to the KS delocalization error (DE) for different classes of π-conjugated organic molecules. The set of molecules includes conjugated polyenes,Hückel aromatic cyclic polyenes, cyanines, and merocyanines. The DE as probed by the curvature of the energy E(N) as a function of the electron number N in fractional-electron calculations causes corresponding trends in the extent of the delocalization of the π-orbitals when the latter are chosen to be localized. The DE is assessed in comparison with calculations based on 'optimally tuned' functionals with range-separated exchange (OT-RSH) and varying fractions of exact exchange in the short-range limit of the interelectronic separation. The OT-RSH calculations produce negligible E(N) curvature for all tested systems. An interpolation for E(N) proposed in the literature gives, which only requires integer-N calculations, gives excellent agreement with the fractional-N KS data, with the exception of the longer-chain merocyanines in conjunction with Hartree-Fock calculations. The breakdown of the fractional-electron calculations for the latter cases goes along with a triplet instability of the closed-shell singlet electronic structures. Density functional theory Molecular orbitals Orbital delocalization Conjugated bonds Delocalization error Full Text Additional Declarations No competing interests reported. Supplementary Files supportinginfoleyangautschbach.pdf Cite Share Download PDF Status: Published Journal Publication published 27 Sep, 2025 Read the published version in Structural Chemistry → Version 1 posted Editorial decision: Revision requested 25 Aug, 2025 Reviews received at journal 24 Aug, 2025 Reviews received at journal 15 Aug, 2025 Reviewers agreed at journal 31 Jul, 2025 Reviewers agreed at journal 29 Jul, 2025 Reviewers invited by journal 28 Jul, 2025 Editor assigned by journal 23 Jul, 2025 Submission checks completed at journal 22 Jul, 2025 First submitted to journal 20 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7171990","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":492460516,"identity":"bde49621-d579-4d0d-91f8-2fb28d412f06","order_by":0,"name":"Dong Le","email":"","orcid":"","institution":"University at Buffalo, State University of New York","correspondingAuthor":false,"prefix":"","firstName":"Dong","middleName":"","lastName":"Le","suffix":""},{"id":492460517,"identity":"dca39eec-1c5a-4b2a-a058-a1c83df7e858","order_by":1,"name":"Mia Yang","email":"","orcid":"","institution":"University at Buffalo, State University of New York","correspondingAuthor":false,"prefix":"","firstName":"Mia","middleName":"","lastName":"Yang","suffix":""},{"id":492460518,"identity":"6e52106d-05cb-425c-aa82-6e2f0573344a","order_by":2,"name":"Jochen Autschbach","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYBACxgYGNhAtZ8DA+OADQwGInUCcFmMDBmbDGQwGRGgBArCWxA1Ea2Fub3724OMOu/TtEsmMDT8MbBj42XMM8Dus55i54cwzybk7ZyQzNvYYpDFI9rwhoGVGDps0bxtz7oYb+ccf8BgcZjC4QcgWkJa/bfXpBjeAtvwBarEnSgtj2+EEkJZmsC0ShP1iJtnbdtxwZ89jxmYZgzQeiTPPCvBqMQSGmMTPtmp5c3agw95U2MjxtydvwK+lAU2AB69yEJAnqGIUjIJRMApGAQDogUVWXhFE0gAAAABJRU5ErkJggg==","orcid":"","institution":"University at Buffalo, State University of New York","correspondingAuthor":true,"prefix":"","firstName":"Jochen","middleName":"","lastName":"Autschbach","suffix":""}],"badges":[],"createdAt":"2025-07-20 23:38:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7171990/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7171990/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11224-025-02622-3","type":"published","date":"2025-09-27T15:57:01+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92430419,"identity":"f900ae29-c731-4d37-8733-870228ff37fc","added_by":"auto","created_at":"2025-09-29 16:02:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1317832,"visible":true,"origin":"","legend":"","description":"","filename":"esub.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7171990/v1_covered_1274fda2-33c2-413d-8e72-1dad67cd6567.pdf"},{"id":87940862,"identity":"ba507d55-238c-4189-b262-a69640aed494","added_by":"auto","created_at":"2025-07-30 15:15:57","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1173645,"visible":true,"origin":"","legend":"","description":"","filename":"supportinginfoleyangautschbach.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7171990/v1/0d9afddcf78b6110ad890720.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Impact of the Kohn-Sham Delocalization Error on Organic Conjugated π Systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"structural-chemistry","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stuc","sideBox":"Learn more about [Structural Chemistry](https://www.springer.com/journal/11224)","snPcode":"11224","submissionUrl":"https://submission.nature.com/new-submission/11224/3","title":"Structural Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Density functional theory, Molecular orbitals, Orbital delocalization, Conjugated bonds, Delocalization error","lastPublishedDoi":"10.21203/rs.3.rs-7171990/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7171990/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study investigates the extent of π-orbital delocalization in Kohn-Sham (KS) density functional calculations in relation to the KS delocalization error (DE) for different classes of π-conjugated organic molecules. 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