The Asymmetric Source Field Model (ASFM) for Atomic Valence A Deterministic Residual-Field Formalism for Valence Pattern Formation

The Asymmetric Source Field Model (ASFM) for Atomic Valence A Deterministic Residual-Field Formalism for Valence Pattern Formation | 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 Asymmetric Source Field Model (ASFM) for Atomic Valence A Deterministic Residual-Field Formalism for Valence Pattern Formation Andreas Pernt This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9148867/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract We present the Asymmetric Source Field Model (ASFM) as a deterministic residual-field formalism for the reconstruction of atomic valence patterns in real space. In this approach, outer-shell structure is described through the interference topology of harmonically scaled spherical source fields generated by nucleonic emitters. A residual field is defined from a constructive component and a phase-shifted conjugate component with radial damping and controlled phase asymmetry. Stable outer-shell nodes are then identified on a three-dimensional voxel grid by a sweep-and-detect procedure over phase offset, damping, and node-selection parameters. For the light-element domain Z = 1–20, the number of stable residual nodes recovered in the outer-shell region reproduces the chemically expected valence organization, including single-valence cases, progressive p-shell filling, and noble-gas closure. In addition, a secondary comparison shows a strong correlation between simulated node amplitude and experimental first ionization energy, indicating that the residual-node topology is not only structurally informative but also linked to energetic trends. The formalism is intended as a real-space mathematical framework for valence pattern formation and residual-field organization, rather than as a reformulation of orbital quantum mechanics. In this sense, ASFM provides a deterministic structural model for analyzing chemically relevant outer-shell regularities and their relation to residual coherence geometry. Asymmetric Source Field Model atomic valence residual-field topology deterministic formalism coherence nodes ionization energy Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 21 Apr, 2026 Editor assigned by journal 19 Mar, 2026 Submission checks completed at journal 19 Mar, 2026 First submitted to journal 17 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. 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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-9148867","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627153747,"identity":"2af32580-fdea-4838-ad0a-1a03ba941515","order_by":0,"name":"Andreas Pernt","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIie3RvQrCMBDA8QsHugS6VvDjFVIcFZ+lIugiqJtjpOAkzkJfwk3cUgLd1LVgB8UXEFyKOHjF1da6CeY/ZAj8uBwBMJl+tzYAspOCMVbBLiTcPhEUCgTyokTTgQIKEcv3wtskOXQ3ZWTqKlrc8iW7TO/ZxI7Dnr9yj92thxCsxIDbsUJnt8wZEw2byImstaU0F5pD5JYqs0W2aESjG5E9EQT9INL4REQ0RCLqRYCISIlMsokTh/Swfq+ZkmBBuzhx4DkzmU3qR++CvN2prQ8ar8m0Vaeb4CwfOeu/+QUmgc2/I2l5U0wmk+nfegJHilPnLhOUlQAAAABJRU5ErkJggg==","orcid":"","institution":"UnifiedLab Research","correspondingAuthor":true,"prefix":"","firstName":"Andreas","middleName":"","lastName":"Pernt","suffix":""}],"badges":[],"createdAt":"2026-03-17 12:48:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9148867/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9148867/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108144346,"identity":"01574da8-e476-4733-ae25-0c4e0cb190e5","added_by":"auto","created_at":"2026-04-29 20:37:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":523562,"visible":true,"origin":"","legend":"","description":"","filename":"ASFMJMC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9148867/v1_covered_f0cb2607-a142-4176-8212-279b9ac1ee62.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Asymmetric Source Field Model (ASFM) for Atomic Valence A Deterministic Residual-Field Formalism for Valence Pattern Formation","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":"journal-of-mathematical-chemistry","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jomc","sideBox":"Learn more about [Journal of Mathematical Chemistry](http://link.springer.com/journal/10910)","snPcode":"10910","submissionUrl":"https://submission.nature.com/new-submission/10910/3","title":"Journal of Mathematical Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Asymmetric Source Field Model, atomic valence, residual-field topology, deterministic formalism, coherence nodes, ionization energy","lastPublishedDoi":"10.21203/rs.3.rs-9148867/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9148867/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present the Asymmetric Source Field Model (ASFM) as a deterministic residual-field formalism for the reconstruction of atomic valence patterns in real space. In this approach, outer-shell structure is described through the interference topology of harmonically scaled spherical source fields generated by nucleonic emitters. A residual field is defined from a constructive component and a phase-shifted conjugate component with radial damping and controlled phase asymmetry. Stable outer-shell nodes are then identified on a three-dimensional voxel grid by a sweep-and-detect procedure over phase offset, damping, and node-selection parameters.\u003c/p\u003e \u003cp\u003eFor the light-element domain Z\u0026thinsp;=\u0026thinsp;1\u0026ndash;20, the number of stable residual nodes recovered in the outer-shell region reproduces the chemically expected valence organization, including single-valence cases, progressive p-shell filling, and noble-gas closure. In addition, a secondary comparison shows a strong correlation between simulated node amplitude and experimental first ionization energy, indicating that the residual-node topology is not only structurally informative but also linked to energetic trends.\u003c/p\u003e \u003cp\u003eThe formalism is intended as a real-space mathematical framework for valence pattern formation and residual-field organization, rather than as a reformulation of orbital quantum mechanics. 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