Geodesic costs on a scalar field over the periodic table predict diatomic bond dissociation energies

Geodesic costs on a scalar field over the periodic table predict diatomic bond dissociation energies | 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 Geodesic costs on a scalar field over the periodic table predict diatomic bond dissociation energies Anderson Rodriguez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9133045/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract We construct a scalar configuration field Φ on the periodic table lattice from z-score-normalized first ionization energy and covalent radius, with a single cou- pling parameter λ fixed a priori. Geodesic costs computed on this field via Dijkstra’s algorithm predict experimental diatomic bond dissociation energies D0 for 201 diatomics at Spearman ρ = −0.325 (95% CI: [−0.462, −0.180], p < 10−5), outperforming both Manhattan and Euclidean distance baselines without molecular orbital theory, fitted regression, or element-pair-specific parameters. On the sparser gradient-magnitude cost field, the correlation strengthens to ρ = −0.633 (p < 10−7, N = 60). The field’s curvature (second differ- ence along atomic number) also correlates with Pearson–Parr chemical hardness at r = −0.830 (95% CI: [−0.947, −0.604], p < 10−9, N = 35). A 16-configuration ablation study confirms robustness across λ ∈ [0.5, 2.0], connectivity, and cost-field choices. We do not propose this framework as a com- petitor to quantum chemical calculations of bond energies; rather, we present it as evidence that the periodic table possesses intrinsic differential-geometric structure from which chemical observables can be recovered without reference to electronic wavefunctions. periodic table scalar field differential geometry bond dissociation energy geodesic cost chemical hardness Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 26 Mar, 2026 Reviewers agreed at journal 26 Mar, 2026 Reviewers invited by journal 24 Mar, 2026 Editor invited by journal 24 Mar, 2026 Editor assigned by journal 20 Mar, 2026 Submission checks completed at journal 20 Mar, 2026 First submitted to journal 16 Mar, 2026 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-9133045","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":611194713,"identity":"106cca35-ac91-409a-bfe2-962a20921976","order_by":0,"name":"Anderson Rodriguez","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYHACxgcfKmzs+CEcZqK0MBvOOJOWLNlAghY2ad6Ww4wbDhCrhX/a2QeSMxsOMxvfSL/4gaHCOrGBkBaJ2+kGBh93pPOZ3cgplmA4k05YC8PtNIbEmWesmYFaEiQY2w4T1iIP1HKYt42ZcfOMnOQfjP+I0GJwO42xmbfNmXGDRPoxCcYGIrQY3k5jZgQFssSZN2wWCcfSjQlqkbudxv4DHJXt6Y9vfKixliWoBQnwGDAkkKAcBNgfkKhhFIyCUTAKRgoAAL9VQz0qJ3RpAAAAAElFTkSuQmCC","orcid":"","institution":"Independent Researcher","correspondingAuthor":true,"prefix":"","firstName":"Anderson","middleName":"","lastName":"Rodriguez","suffix":""}],"badges":[],"createdAt":"2026-03-16 04:53:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9133045/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9133045/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105566887,"identity":"013c05c0-5678-40d1-9034-47c54e6b3220","added_by":"auto","created_at":"2026-03-27 12:57:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":369597,"visible":true,"origin":"","legend":"","description":"","filename":"RodriguezDiscoverChemsubmitted.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9133045/v1_covered_ba17cc34-db4f-41e8-974a-7c326cf3c028.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Geodesic costs on a scalar field over the periodic table predict diatomic bond dissociation energies","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":"discover-chemistry","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Chemistry](https://link.springer.com/journal/44371)","snPcode":"44371","submissionUrl":"https://submission.nature.com/new-submission/44371/3","title":"Discover Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"periodic table, scalar field, differential geometry, bond dissociation energy, geodesic cost, chemical hardness","lastPublishedDoi":"10.21203/rs.3.rs-9133045/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9133045/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We construct a scalar configuration field Φ on the periodic table lattice from z-score-normalized first ionization energy and covalent radius, with a single cou- pling parameter λ fixed a priori. 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