Exploration of the eigenvectors of the Localization Delocalization Matrices for TiO2 Finite Cells and Solids: from resonance to QTAIM

Exploration of the eigenvectors of the Localization Delocalization Matrices for TiO2 Finite Cells and Solids: from resonance to QTAIM | 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 Exploration of the eigenvectors of the Localization Delocalization Matrices for TiO2 Finite Cells and Solids: from resonance to QTAIM Guadalupe Ureiro-Cueto, James S. M. Anderson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8253125/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Mar, 2026 Read the published version in Structural Chemistry → Version 1 posted 7 You are reading this latest preprint version Abstract The newly introduced eigenvectors of the localization-delocalization matrices (LDM) is used to characterize the distinct functional groups in the TiO 2 rutile solid material. A 1X1X1 unit and the 1X1X1 unit cell with atoms on the next cell included (edge and corner atoms) as well as the infinite material. The same LDM is used in both cases (for the infinite cases the other atoms are neglected). The eigenvectors and the corresponding localization/delocalization modes are used to indicate the functional groups and the resonance structures. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 27 Mar, 2026 Read the published version in Structural Chemistry → Version 1 posted Editorial decision: Revision requested 18 Dec, 2025 Reviews received at journal 17 Dec, 2025 Reviewers agreed at journal 17 Dec, 2025 Reviewers invited by journal 17 Dec, 2025 Editor assigned by journal 16 Dec, 2025 Submission checks completed at journal 15 Dec, 2025 First submitted to journal 01 Dec, 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. 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-8253125","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":562299973,"identity":"3a59ee46-51fd-46a4-a8ec-08c785f4f4b1","order_by":0,"name":"Guadalupe Ureiro-Cueto","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIie3PPQrCMBTA8SeB5xLsGkE8Q6Aggm5eRJe4xL2D+EGhm3oDvYKTsyXYKToLjgUHJ0VwFFMnpzZugvkPSYb3IwmAy/WjbQHadfRCswOr2RLhV1jSzQi1vUj1liB5diom/KRiFQSqFIG+X47DJoWy2q1zyUF0Y637BMls05KJeRgV4phLNOXxNGohwn7jSzSE0UYB8a6GEIogz758WhEKhnSYISQdRBakqpHHEy04sqRBBnNGsegvFU3S2yRoj1eLML3Lx6julVWSSz5D9l5tx7PI9Ztpl8vl+p9eTihHz/Kw9OQAAAAASUVORK5CYII=","orcid":"","institution":"Universidad Nacional Autónoma de México","correspondingAuthor":true,"prefix":"","firstName":"Guadalupe","middleName":"","lastName":"Ureiro-Cueto","suffix":""},{"id":562299976,"identity":"a4ea91a5-bf20-4bd9-84fd-0d19919c9ddb","order_by":1,"name":"James S. 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