Equivalence of charged and neutral density functional formulations for correcting the many-body self-interaction of polarons

Equivalence of charged and neutral density functional formulations for correcting the many-body self-interaction of polarons | 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 Article Equivalence of charged and neutral density functional formulations for correcting the many-body self-interaction of polarons Stefano Falletta, Jennifer Coulter, Joel B. Varley, Daniel Åberg, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8160837/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 The electron self-interaction problem in density functional theory affects the accurate modeling of polarons, particularly their localization and formation energy. Charged and neutral density functional formulations have been developed to address this issue, yet their relationship remains unclear. Here, we demonstrate their equivalence in treating the many-body self-interaction of the polaron state. In particular, we connect with each other piecewise-linear functionals based on adding an extra charge to the supercell, the pSIC approach derived from the energetics of the neutral defect with polaronic distortions in a supercell, and the unit-cell method for polarons based on electron–phonon couplings. We show that that these approaches lead to the same formal expression of the self-interaction corrected energy, which is fully defined by the energetics of the neutral charge state of the charged polaronic structure. Residual differences between these methods solely arise from the achieved polaronic structure, which is affected by different treatments of electron-screening and finite-size effects. We apply these methods to a set of prototypical small hole and electron polarons, including the hole polaron in MgO, the hole polaron in β-Ga2O3, the Vk center in NaI, the electron polaron in BiVO4, and the electron polaron in TiO2. We show that the ground-state properties of polarons obtained using charged and neutral density functional formulations are in excellent agreement. Physical sciences/Materials science Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files SI.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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8160837","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":553576489,"identity":"8608cc3d-9981-4896-9b56-eeb8b05dcf15","order_by":0,"name":"Stefano Falletta","email":"data:image/png;base64,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","orcid":"","institution":"Harvard University","correspondingAuthor":true,"prefix":"","firstName":"Stefano","middleName":"","lastName":"Falletta","suffix":""},{"id":553576490,"identity":"4b57e4dd-8753-4b3f-ac0c-7d01723fe0ee","order_by":1,"name":"Jennifer Coulter","email":"","orcid":"","institution":"Harvard University","correspondingAuthor":false,"prefix":"","firstName":"Jennifer","middleName":"","lastName":"Coulter","suffix":""},{"id":553576492,"identity":"fe5e7995-36e9-452c-afbd-aa5f306a4c02","order_by":2,"name":"Joel B. 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Charged and neutral density functional formulations have been developed to address this issue, yet their relationship remains unclear. Here, we demonstrate their equivalence in treating the many-body self-interaction of the polaron state. In particular, we connect with each other piecewise-linear functionals based on adding an extra charge to the supercell, the pSIC approach derived from the energetics of the neutral defect with polaronic distortions in a supercell, and the unit-cell method for polarons based on electron–phonon couplings. We show that that these approaches lead to the same formal expression of the self-interaction corrected energy, which is fully defined by the energetics of the neutral charge state of the charged polaronic structure. Residual differences between these methods solely arise from the achieved polaronic structure, which is affected by different treatments of electron-screening and finite-size effects. We apply these methods to a set of prototypical small hole and electron polarons, including the hole polaron in MgO, the hole polaron in β-Ga2O3, the Vk center in NaI, the electron polaron in BiVO4, and the electron polaron in TiO2. We show that the ground-state properties of polarons obtained using charged and neutral density functional formulations are in excellent agreement. 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