Nonlinear Vibrational Modes of Molecule with Octahedral Configuration

Nonlinear Vibrational Modes of Molecule with Octahedral Configuration | 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Article Nonlinear Vibrational Modes of Molecule with Octahedral Configuration Jingzhou Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7438523/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 17 You are reading this latest preprint version Abstract In this work, we investigate the nonlinear dynamics of molecules with an octahedral configuration, with particular focus on sulfur hexafluoride SF6. Under the assumption of isotypic nonresonance, we apply the method of equivariant gradient degree to prove the existence of branches of periodic solutions emerging from the critical orbit of equilibrium, corresponding toat least 16 distinct types of symmetries with maximal orbit kinds. Numerical animations arepresented to illustrate the detected vibrational modes. AMS subject classications: 37G40, 47J15, 47H11, 37G15, 37J46, 70H33 symmetric bifurcation nonlinear dynamics equivariant gradient degree octahedral molecule Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 08 Dec, 2025 Reviews received at journal 08 Dec, 2025 Reviews received at journal 05 Dec, 2025 Reviews received at journal 02 Dec, 2025 Reviews received at journal 20 Nov, 2025 Reviews received at journal 16 Nov, 2025 Reviews received at journal 03 Nov, 2025 Reviewers agreed at journal 28 Oct, 2025 Reviewers agreed at journal 21 Oct, 2025 Reviewers agreed at journal 19 Oct, 2025 Reviewers agreed at journal 17 Oct, 2025 Reviewers agreed at journal 17 Oct, 2025 Reviewers agreed at journal 05 Oct, 2025 Reviewers invited by journal 29 Sep, 2025 Editor assigned by journal 30 Aug, 2025 Submission checks completed at journal 30 Aug, 2025 First submitted to journal 23 Aug, 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. 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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-7438523","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":527316206,"identity":"4da7b5f6-0261-4419-a0cf-406897ad0187","order_by":0,"name":"Jingzhou Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIie3RvUpDMRTA8YRAupxr1yNK+wrJpEPxWVIKnVxcxMHhXC5cF9H1Ftp36COcS8Cp2PUWlz7AFQqCi1JNnRxqdHTIf0z4cfIhRCr1D5OkyL9fDc50h4QAcXr8tQxRInOGxXjUBZYEAuFXElDBWenlpHJ/JKoaEqNWyqzak3V7jdC9Z7l+LiMzbmtiA/rAPJ3bfPqAgI1TdhYjNzmxQ1A7UoAOB2uEPspipJDEbFDOV4tAtgj9JXfeoiRMqcmZcH2wRVYiGHZaRUm4ixfswiOPLyazOwTbDIvD6ePPxFYj/yK3H+Er/XzTvg56vaWvN+1lhNCeyXvWvtWP7qZSqVRq1yfsGVWikD1xBgAAAABJRU5ErkJggg==","orcid":"","institution":"The University of Texas at Dallas","correspondingAuthor":true,"prefix":"","firstName":"Jingzhou","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-08-23 04:38:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7438523/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7438523/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":93360046,"identity":"02e6cf96-5470-4e1d-9da9-5130594151ad","added_by":"auto","created_at":"2025-10-13 03:00:43","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2614,"visible":true,"origin":"","legend":"","description":"","filename":"4bced9056cf24618b2b5b4a165e84b4f.json","url":"https://assets-eu.researchsquare.com/files/rs-7438523/v1/f4e0a308ed4cf39eb9d0d579.json"},{"id":93360721,"identity":"0189ce94-da1e-47c7-ba8a-ce9943e61ab7","added_by":"auto","created_at":"2025-10-13 03:08:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":929846,"visible":true,"origin":"","legend":"","description":"","filename":"octahedralmolecule08282025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7438523/v1_covered_a0950af6-c830-432e-a0bb-346240ac1e3f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear Vibrational Modes of Molecule with Octahedral Configuration","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-nonlinear-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jnls","sideBox":"Learn more about [Journal of Nonlinear Science](http://link.springer.com/journal/332)","snPcode":"332","submissionUrl":"https://submission.nature.com/new-submission/332/3","title":"Journal of Nonlinear Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"symmetric bifurcation, nonlinear dynamics, equivariant gradient degree, octahedral molecule","lastPublishedDoi":"10.21203/rs.3.rs-7438523/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7438523/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this work, we investigate the nonlinear dynamics of molecules with an octahedral configuration, with particular focus on sulfur hexafluoride SF6. 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