The rule of four: anomalous stoichiometries of inorganic compounds

The rule of four: anomalous stoichiometries of inorganic compounds | 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 The rule of four: anomalous stoichiometries of inorganic compounds Elena Gazzarrini, Rose Cersonsky, Marnik Bercx, Simon Adorf, Nicola Marzari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3206854/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 Apr, 2024 Read the published version in npj Computational Materials → Version 1 posted 11 You are reading this latest preprint version Abstract Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence - named here the rule of four - has to our knowledge not previously been reported or studied. Here, we first highlight the rule's existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method. Physical sciences/Physics/Condensed-matter physics Physical sciences/Materials science/Condensed-matter physics Full Text Additional Declarations (Not answered) Supplementary Files TheruleoffourSI.pdf Cite Share Download PDF Status: Published Journal Publication published 12 Apr, 2024 Read the published version in npj Computational Materials → Version 1 posted Editorial decision: revise 20 Sep, 2023 Review # 1 received at journal 07 Sep, 2023 Review # 3 received at journal 05 Sep, 2023 Reviewer # 3 agreed at journal 05 Sep, 2023 Review # 2 received at journal 05 Sep, 2023 Reviewer # 2 agreed at journal 05 Sep, 2023 Reviewer # 1 agreed at journal 15 Aug, 2023 Reviewers invited by journal 14 Aug, 2023 Submission checks completed at journal 27 Jul, 2023 First submitted to journal 26 Jul, 2023 Editor assigned by journal 26 Jul, 2023 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-3206854","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":226375941,"identity":"99272fd7-a727-4425-af97-3d001d98a5f0","order_by":0,"name":"Elena Gazzarrini","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIiWNgGAWjYBADHgZmIPkAiPlB3IQCYrUkALFkA4hhQKxdIC0GB0AsPFrk3Y8//vBzzz0Zc3YGxgcJFXfkjc+vTvzwwIBBnl/sAFYthmcSEgx7nhXzWDYzMBsknHlmuO3G280SQIcZzpydgF1LQ8KBBB4gMjjMwCaR2HaYcduNsxtAWhIMbuPQ0v+w4eAfiBb2H4n/DttvnnF28w98WuQlkhmbYbYwJDYcTtzA37sNry0GEs+YmWXAWhibJRKOHU6ecYN3m0WCgQROv8j3pz/++OZAgr3B+cMHP3yoOWzb3392880fFTby/NI4bDkAZzI2QGgJsEoJrMrBtjRgCPEfwBAaBaNgFIyCkQ0AQB5jqkJA3OAAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-5772-5166","institution":"École Polytechnique Fédérale de Lausanne (EPFL)","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Elena","middleName":"","lastName":"Gazzarrini","suffix":""},{"id":226375942,"identity":"b26b1c17-5d42-4d65-bc94-78fa5b4c92c8","order_by":1,"name":"Rose Cersonsky","email":"","orcid":"https://orcid.org/0000-0003-4515-3441","institution":"University of Wisconsin - 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