The electric field in a hydrogen molecule

The electric field in a hydrogen molecule | 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Download PDF Research Article The electric field in a hydrogen molecule Valentin Kochnev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7403238/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 electric field is addressed for the charge density based on the Fermi-Dirac function in the presence of two protons at points $A$ and $B$ at low temperature. The Poisson equation is solved for the electrostatic potential $\varphi$ with two asymptotic boundary conditions: $\varphi \sim \frac{1}{r_A}$ as $r_A \rightarrow 0$ for a point $A$, and $\varphi \sim \frac{1}{r_B}$ as $r_B \rightarrow 0$ for a point $B$. The energy of the field is computed relying on the value of the chemical potential for electrons as defined by the Fermi-Dirac function itself. chemical bond Fermi-Dirac function Poisson equation the direct method Full Text Additional Declarations No competing interests reported. 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-7403238","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":514993073,"identity":"903d2c73-e0de-478a-97ed-4f51856599d1","order_by":0,"name":"Valentin 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molecule\u003c/p\u003e","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":"chemical bond, Fermi-Dirac function, Poisson equation, the direct method","lastPublishedDoi":"10.21203/rs.3.rs-7403238/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7403238/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The electric field is addressed for the charge density based on the Fermi-Dirac function in the presence of two protons at points $A$ and $B$ at low temperature. The Poisson equation is solved for the electrostatic potential $\\varphi$ with two asymptotic boundary conditions: $\\varphi \\sim \\frac{1}{r_A}$ as $r_A \\rightarrow 0$ for a point $A$, and $\\varphi \\sim \\frac{1}{r_B}$ as $r_B \\rightarrow 0$ for a point $B$. 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