Determining Molecular Structure, Coordination Geometry, and Molecular Symmetry

Determining Molecular Structure, Coordination Geometry, and Molecular Symmetry | 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 Determining Molecular Structure, Coordination Geometry, and Molecular Symmetry Thomas Just Sørensen, Villads Nielsen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6860832/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Nov, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Chemists have a strong language describing and defining idealized polyhedra P and symmetry point groups G , but no efficient measure to correlate these to real molecular structures Q . Symmetry and structure have been ascribed through experience, but this approach is error-prone and provides no measure that can correlate molecular structure to molecular properties. Quantification of molecular structure and symmetry is crucial, and this requires two tools: a tool that orients a molecular structure to a symmetry axis, and a tool that measures the deviation of the molecular structure from symmetry. The first approach developed was the Continuous Symmetry Measure (CSM), which does both tasks and is exact across all symmetries as well as mathematically elegant. Unfortunately as a tool the CSM is close to impossible to implement. This led to the development of the Continuous Shape Measure (CShM) that measures how close a molecular structure Q is to a set of selected structures P ’. The CShM tool have severe limitations, and we suggest that the Continuous Symmetry operation Measure (CSoM) should be the preferred tool. The CSoM tool can quantify the symmetry of any structure that can be described as a list of points in space. Here, we describe the CSM, CShM, and CSoM approaches and demonstrate how these can be used as tools to determine molecular structure, coordination geometry, and symmetry of water, organic molecules, transition metal complexes, and lanthanide compounds. Physical sciences/Chemistry/Inorganic chemistry/Group theory Physical sciences/Chemistry/Organic chemistry/Structure elucidation Physical sciences/Materials science/Theory and computation/Electronic structure Physical sciences/Chemistry/Theoretical chemistry/Structure prediction Physical sciences/Chemistry/Inorganic chemistry/Crystal field theory Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Published Journal Publication published 21 Nov, 2025 Read the published version in Nature Communications → 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-6860832","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":472138059,"identity":"6bba0e08-a84e-4a6e-88b4-6fa6a60d55b3","order_by":0,"name":"Thomas Just Sørensen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAApElEQVRIiWNgGAWjYBAC+8PHHz5gbACyeED4ABFa2BjOGBuQrIVNgnQtFT932EQz8JwxYHhzhigtx5/d7D2TltvA22PAOOcGUVoOmN1mbDuc28DPY8DM84FILcWMbf9J0cJxwIyZse0A2GHMPEQ5jLfHWLK3LTm3jedYwcE5RHmfnf3hh59tdrn9PMkbH7w5RoQWhF4gPkCKhlEwCkbBKBgFeAAALgU2zax9/jwAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-1491-5116","institution":"University of Copenhagen","correspondingAuthor":true,"prefix":"","firstName":"Thomas","middleName":"Just","lastName":"Sørensen","suffix":""},{"id":472138060,"identity":"83682a60-75ed-4222-8f3a-81ad5e672828","order_by":1,"name":"Villads Nielsen","email":"","orcid":"https://orcid.org/0000-0002-5808-4433","institution":"University of Copenhagen","correspondingAuthor":false,"prefix":"","firstName":"Villads","middleName":"","lastName":"Nielsen","suffix":""}],"badges":[],"createdAt":"2025-06-10 08:25:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6860832/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6860832/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-66054-7","type":"published","date":"2025-11-21T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98289987,"identity":"7a1130c7-395a-4396-bb1d-402f215aab17","added_by":"auto","created_at":"2025-12-16 08:07:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1796069,"visible":true,"origin":"","legend":"","description":"","filename":"DeterminingMolecularStructureNatChemRevsubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6860832/v1_covered_eb55cdaa-cf98-456e-9c41-3a0839c9918e.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Determining Molecular Structure, Coordination Geometry, and Molecular Symmetry","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6860832/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6860832/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eChemists have a strong language describing and defining idealized polyhedra \u003cb\u003eP\u003c/b\u003e and symmetry point groups \u003cb\u003eG\u003c/b\u003e, but no efficient measure to correlate these to real molecular structures \u003cb\u003eQ\u003c/b\u003e. Symmetry and structure have been ascribed through experience, but this approach is error-prone and provides no measure that can correlate molecular structure to molecular properties. Quantification of molecular structure and symmetry is crucial, and this requires two tools: a tool that orients a molecular structure to a symmetry axis, and a tool that measures the deviation of the molecular structure from symmetry. The first approach developed was the Continuous Symmetry Measure (CSM), which does both tasks and is exact across all symmetries as well as mathematically elegant. Unfortunately as a tool the CSM is close to impossible to implement. This led to the development of the Continuous Shape Measure (CShM) that measures how close a molecular structure \u003cb\u003eQ\u003c/b\u003e is to a set of selected structures \u003cb\u003eP\u003c/b\u003e\u0026rsquo;. The CShM tool have severe limitations, and we suggest that the Continuous Symmetry operation Measure (CSoM) should be the preferred tool. The CSoM tool can quantify the symmetry of any structure that can be described as a list of points in space. Here, we describe the CSM, CShM, and CSoM approaches and demonstrate how these can be used as tools to determine molecular structure, coordination geometry, and symmetry of water, organic molecules, transition metal complexes, and lanthanide compounds.\u003c/p\u003e","manuscriptTitle":"Determining Molecular Structure, Coordination Geometry, and Molecular Symmetry","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-19 04:42:43","doi":"10.21203/rs.3.rs-6860832/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"eb4f8ff8-01e4-4103-8a73-54ef97e7004e","owner":[],"postedDate":"June 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":50140410,"name":"Physical sciences/Chemistry/Inorganic chemistry/Group theory"},{"id":50140411,"name":"Physical sciences/Chemistry/Organic chemistry/Structure elucidation"},{"id":50140412,"name":"Physical sciences/Materials science/Theory and computation/Electronic structure"},{"id":50140413,"name":"Physical sciences/Chemistry/Theoretical chemistry/Structure prediction"},{"id":50140414,"name":"Physical sciences/Chemistry/Inorganic chemistry/Crystal field theory"}],"tags":[],"updatedAt":"2025-12-16T08:07:19+00:00","versionOfRecord":{"articleIdentity":"rs-6860832","link":"https://doi.org/10.1038/s41467-025-66054-7","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-11-21 05:00:00","publishedOnDateReadable":"November 21st, 2025"},"versionCreatedAt":"2025-06-19 04:42:43","video":"","vorDoi":"10.1038/s41467-025-66054-7","vorDoiUrl":"https://doi.org/10.1038/s41467-025-66054-7","workflowStages":[]},"version":"v1","identity":"rs-6860832","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6860832","identity":"rs-6860832","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}