Mathematical Crystal Chemistry

Mathematical Crystal Chemistry | 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Cite Share Download PDF Research Article Mathematical Crystal Chemistry Ryotaro, Taisuke This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4345319/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 Efficient heuristics have predicted many functional materials such as high-temperature superconducting hydrides, while inorganic structural chemistry explains why and how the crystal structures are stabilized. Here we develop the paired mathematical programming formalism for searching and systematizing the structural prototypes of crystals. The first is the minimization of the volume of the unit cell under the constraints of only the minimum and maximum distances between pairs of atoms. We show the capabilities of linear relaxations of inequality constraints to optimize structures by the steepest-descent method, which is computationally very efficient. The second is the discrete optimization to assign five kinds of geometrical constraints including chemical bonds for pairs of atoms. Under the constraints, the two object functions, formulated as mathematical programming, are alternately optimized to realize the given coordination numbers of atoms. This approach successfully generates a wide variety of crystal structures of oxides such as spinel, pyrochlore-α, and K 2 NiF 4 structures. Inorganic Chemistry inorganic structural chemistry Full Text Additional Declarations The authors declare no competing interests. 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-4345319","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":296952503,"identity":"ca8ddf66-3052-4236-a765-61ec09564abb","order_by":0,"name":"Ryotaro","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIie3PMWrDMBiG4S8IpEVOV5kUegWVDFmMcxUFgbJk6BEEBWUpZM45smRUECRLDxFT6Nxu9haZ1KvtboXqXSSEHvELSKX+ZBSYWBDKLPzPkRpJuI9E/YIAQo243LawdFU1x4JN84/q1NQod8DntY88ehrm2bshdGZk4Ap6b7GWfUSAudnEhUiUDHEwLT2MGCJ505L88nWqxxF6FllLBJc+DlYOE0L1PHPxL3zzErgRKn8d+gtzz1XjCv20vRy+66JYPrA3c+0jIPdFd0+sLOGmV3SV3WYJsPMokkqlUv+mG01LP8HlY3nWAAAAAElFTkSuQmCC","orcid":"","institution":"Koshoji","correspondingAuthor":true,"prefix":"","firstName":"","middleName":"","lastName":"Ryotaro","suffix":""},{"id":296952504,"identity":"7dc5879a-da7b-4e93-805a-5c28bb43ed33","order_by":1,"name":"Taisuke","email":"","orcid":"","institution":"Ozaki","correspondingAuthor":false,"prefix":"","firstName":"","middleName":"","lastName":"Taisuke","suffix":""}],"badges":[],"createdAt":"2024-04-29 23:54:56","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4345319/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4345319/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55761074,"identity":"8aba5a66-9510-4d17-bb90-c2a29147ef1b","added_by":"auto","created_at":"2024-05-02 19:00:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1385394,"visible":true,"origin":"","legend":"","description":"","filename":"2404.14181v2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4345319/v1_covered_628634e3-f07b-4a08-a417-13475e0a9146.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eMathematical Crystal Chemistry\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"National Institute of Advanced Industrial Science and Technology","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":"inorganic structural chemistry","lastPublishedDoi":"10.21203/rs.3.rs-4345319/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4345319/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEfficient heuristics have predicted many functional materials such as high-temperature superconducting hydrides, while inorganic structural chemistry explains why and how the crystal structures are stabilized. Here we develop the paired mathematical programming formalism for searching and systematizing the structural prototypes of crystals. The first is the minimization of the volume of the unit cell under the constraints of only the minimum and maximum distances between pairs of atoms. We show the capabilities of linear relaxations of inequality constraints to optimize structures by the steepest-descent method, which is computationally very efficient. The second is the discrete optimization to assign five kinds of geometrical constraints including chemical bonds for pairs of atoms. Under the constraints, the two object functions, formulated as mathematical programming, are alternately optimized to realize the given coordination numbers of atoms. This approach successfully generates a wide variety of crystal structures of oxides such as spinel, pyrochlore-α, and K\u003csub\u003e2\u003c/sub\u003eNiF\u003csub\u003e4\u003c/sub\u003e structures.\u003c/p\u003e","manuscriptTitle":"Mathematical Crystal Chemistry","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-02 18:52:14","doi":"10.21203/rs.3.rs-4345319/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"22253b0b-4fa0-4b8e-9489-0b81d5382728","owner":[],"postedDate":"May 2nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":31322608,"name":"Inorganic Chemistry"}],"tags":[],"updatedAt":"2024-05-02T18:52:14+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-02 18:52:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4345319","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4345319","identity":"rs-4345319","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}