Pauli Constraints and Aufbau Ordering in thePeriodic Table

Pauli Constraints and Aufbau Ordering in thePeriodic Table | 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Article Pauli Constraints and Aufbau Ordering in thePeriodic Table Cesar A. Cohen de Mello This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9141320/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Pauli constraints and Aufbau ordering are usually introduced in chemistry as empirical filling rules, even though both point toward a deeper operator-level structure. A spectral interpretation of the periodic table is developed within a Pauli-constrained variational occupation framework in which ground-state electronic configurations arise from occupation of the lowest admissible eigenvalues of an effective self-adjoint one-particle operator associated with a reduced description of the many-electron problem. In this setting, Aufbau ordering appears as a consequence of fermionic energy minimization rather than as an externally imposed mnemonic rule. The subshell capacities (2), (6), (10), and (14) follow from angular-momentum multiplicities, while the approximate ordering of orbitals is related to the radial spectral problem together with penetration, screening, and semiclassical effects. Local deviations from naive filling patterns are interpreted in terms of near-degeneracies and avoided spectral reordering, especially in transition metals, and relativistic corrections are described as deformations of the high-(Z) eigenvalue landscape. The analysis is structural rather than benchmark-driven: the aim is not an exact reconstruction of all atomic data, but a mathematically coherent account of block structure, orbital ordering, and localized anomalies within one spectral language. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 23 Apr, 2026 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 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-9141320","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":628572948,"identity":"7a7894d1-82aa-4114-b9d9-6cd9a1cfd467","order_by":0,"name":"Cesar A. 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A spectral interpretation of the periodic table is developed within a Pauli-constrained variational occupation framework in which ground-state electronic configurations arise from occupation of the lowest admissible eigenvalues of an effective self-adjoint one-particle operator associated with a reduced description of the many-electron problem. In this setting, Aufbau ordering appears as a consequence of fermionic energy minimization rather than as an externally imposed mnemonic rule. The subshell capacities \\(2\\), \\(6\\), \\(10\\), and \\(14\\) follow from angular-momentum multiplicities, while the approximate ordering of orbitals is related to the radial spectral problem together with penetration, screening, and semiclassical effects. Local deviations from naive filling patterns are interpreted in terms of near-degeneracies and avoided spectral reordering, especially in transition metals, and relativistic corrections are described as deformations of the high-\\(Z\\) eigenvalue landscape. 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