Topological Electronic Sensitivity Index (TESI): Weighted Graph Spectral Analysis of Molecular Systems with Electron Delocalization Indices

Topological Electronic Sensitivity Index (TESI): Weighted Graph Spectral Analysis of Molecular Systems with Electron Delocalization Indices | 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 Topological Electronic Sensitivity Index (TESI): Weighted Graph Spectral Analysis of Molecular Systems with Electron Delocalization Indices Samir Kenouche, Jorge Ignacio Martínez-Araya This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8905580/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This work introduces the Topological Electronic Sensitivity Index (TESI), a response-based descriptor that combines quantum chemical topology with molecular spectral graph theory to characterize global electronic redistribution in extended pi-systems. TESI is constructed from a Laplacian matrix derived from atomic delocalization indices and augmented by Non-local Second-order Fukui Indices (NSFI), enabling identification of the dominant connectivity channels governing changes in the molecular charge state. The findings reveal that TESI goes beyond the limitations of static bonding descriptors by identifying how the global molecular architecture constrains or facilitates electronic connectivity. This approach demonstrates that algebraic connectivity, as captured by the Fiedler eigenvalue and vector, provides a robust descriptor of the electronic sensitivity of the molecular skeleton. It reveals preferential connectivity pathways and channels of electronic redistribution that are not necessarily apparent from conventional delocalization indices alone. Within this framework, charge-redistribution channels in complex pi-networks can be systematically characterized, offering a quantitative and formal link between QCT theory and molecular spectral graph theory Quantum Chemical Topology Molecular Spectral Graph Theory Delocalization Indices Non-local Second-order Fukui Indices (NSFI) Topological Electronic Sensitivity Index (TESI) Full Text Additional Declarations No competing interests reported. Supplementary Files TESIpaperSI.pdf Cite Share Download PDF Status: Posted Version 1 posted 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. We do this by developing innovative software and high quality services for the global research community. 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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-8905580","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":593525190,"identity":"d9ed9802-ae81-44c4-af81-b5ce05e3a596","order_by":0,"name":"Samir Kenouche","email":"","orcid":"","institution":"University of Biskra","correspondingAuthor":false,"prefix":"","firstName":"Samir","middleName":"","lastName":"Kenouche","suffix":""},{"id":593525191,"identity":"1f7e340a-be4f-4fd9-8c26-1b2129f206eb","order_by":1,"name":"Jorge Ignacio Martínez-Araya","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYBACxgZUpg0Q8wBxATFa2MDMNKgWA2LsYwOThwlrYW7vffziA8M2efP5zW0PPvw5n7id/ewBhh94tDD2HDeznMFw23DOMcZ2wxk8txN39uQlMPbg0zIjjc2Yh+E24ww2xjZpHonbiRsO5Bgw43MYWMsfhtv2YC1/DM4lbjj/hqAW5scMDLcTwVoYEg4kbrhByJaeY2xAl99OnsGW2CbZcyDZeMONdwkH8fnFsL2N+cOPitu2M5iPP5P48cdOdsP53IMPflTg0dLAwCaB4YwDuDUwMMgDo+YDPgWjYBSMglEwChgATIBR3W/k4LoAAAAASUVORK5CYII=","orcid":"","institution":"Universidad Andres Bello (UNAB)","correspondingAuthor":true,"prefix":"","firstName":"Jorge","middleName":"Ignacio","lastName":"Martínez-Araya","suffix":""}],"badges":[],"createdAt":"2026-02-18 04:23:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8905580/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8905580/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103326672,"identity":"4bec4216-882e-4e4e-a360-84a265bc5a0b","added_by":"auto","created_at":"2026-02-24 12:57:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":956566,"visible":true,"origin":"","legend":"","description":"","filename":"TESIPAPER.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8905580/v1_covered_8cd1920d-2bfd-4727-8785-8effd4d6b270.pdf"},{"id":103238963,"identity":"a4c07fab-4e2c-4cd7-8de2-622d5d034855","added_by":"auto","created_at":"2026-02-23 13:42:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":494944,"visible":true,"origin":"","legend":"","description":"","filename":"TESIpaperSI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8905580/v1/4bdf51bd72fb8c89a581be62.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Topological Electronic Sensitivity Index (TESI): Weighted Graph Spectral Analysis of Molecular Systems with Electron Delocalization Indices","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Quantum Chemical Topology, Molecular Spectral Graph Theory, Delocalization Indices, Non-local Second-order Fukui Indices (NSFI),Topological Electronic Sensitivity Index (TESI)","lastPublishedDoi":"10.21203/rs.3.rs-8905580/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8905580/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This work introduces the Topological Electronic Sensitivity Index (TESI), a response-based descriptor that combines quantum chemical topology with molecular spectral graph theory to characterize global electronic redistribution in extended pi-systems. 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