[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125371-en":3,"doc-seo-125371-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125371,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Spectroscopic constants from atomic properties - a machine learning approach","A machine-learning framework predicts molecular spectroscopic constants directly from atomic properties. An extensive database is constructed from spectroscopic information on diatomic molecules, then Gaussian process regression is used to select efficient molecular characterization for equilibrium distance, vibrational harmonic frequency, and dissociation energy. Equilibrium distance reaches an absolute error of 0.04 Å and vibrational harmonic frequency 36 cm−1 using atomic properties alone. Incorporating prior molecular-property information improves errors to 0.02 Å and 28 cm−1, respectively, while dissociation energy is also benchmarked and additional generalization and classification insights are provided.","Digital  \nDiscovery  \n[rsc.li/digitaldiscovery](rsc.li/digitaldiscovery)  \nVolume 3 Number 1 January 2024 Pages 1-222  \nISSN 2635-098X  \nPAPER  \nJ. Pérez-Ríos et al.  \nSpectroscopic constants from atomic properties: a machine learning approach  \nOpen Access Article . Pu on 06 Novem 2023. Down on 1/30/2024blished ber loaded 3: 18: 15 PM .  \nhicle is licensed under a Creative C mmons A 3 0 U d[ttr .](ttr .)ibution npor e nce.  \nDigital  \nDiscovery  \nPAPER  \nView Article Online View Journal | View Issue  \nCite this: Digital Discovery, 2024, 3, 34  \nReceived 14th August 2023  \nAccepted 31st October 2023  \nDOI: 10.1039/d3dd00152k[rsc.li/digitaldiscovery](rsc.li/digitaldiscovery)  \nSpectroscopic constants from atomic properties: a machine learning approach  \nMahmoud A. E. Ibrahim,abc X. Liu d and J. Prez-R os  *ab  \nWe present a machine-learning approach toward predicting spectroscopic constants based on atomic properties. After collecting spectroscopic information on diatomics and generating an extensive database, we employ Gaussian process regression to identify the most efficient characterization of molecules to predict the equilibrium distance, vibrational harmonic frequency, and dissociation energy. As a result, we show that it is possible to predict the equilibrium distance with an absolute error of 0.04 Å and vibrational harmonic frequency with an absolute error of 36 cm −1, including only atomic properties. These results can be improved by including prior information on molecular properties leading to an absolute error of 0 . 02 Å and 28 cm −1 for the equilibrium distance and vibrational harmonic frequency, respectively. In contrast, the dissociation energy is predicted with an absolute error (0 .4 eV. Alongside these results, we prove that it is possible to predict spectroscopic constants of homonuclear molecules from the atomic and molecular properties of heteronuclears. Finally, based on our results, we present a new way to classify diatomic molecules beyond chemical bond properties.  \n1 Introduction  \nSince the beginning of molecular spectroscopy in the 1920s, the relationship between spectroscopic constants of diatomic molecules has been an intriguing and captivating matter in chemical physics. Following early attempts by Kratzer, Birge and Mecke,1–3 Morse proposed a relationship between the equilibrium distance, Re, and the harmonic vibrational frequency, ue, as Rue = g, where g is a constant, a􀀁er analyzing the spectral properties of 16 diatomic molecules.4 However, as more spectroscopic data became available, further examination of the Morse relation revealed its applicability to only a tiny number of diatomic molecules.5 Next, in a series of papers, Clark et al. generalized Morse's idea via the concept of a periodic table of diatomic molecules. Eventually, Clark's efforts translated into several relations, each limited to speci􀀁c classes of molecules.5–8 Simultaneously, Badger proposed a more neat relationship, including atomic properties of the atoms constituting the molecule.9 Following Badger's proposal, multiple authors have found new relations, which have seen some utility even for polyatomic molecules.10–12 Nevertheless, Badger's relations are not generalizable to all diatomic molecules.13–15 In general, several empirical relationships between Re and ue were proposed in the 1930s and the 1940s.7,8,16–25 In summary, from  \naDepartment of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, [USA. E-mail: jesus.perezrios@stonybrook.edu](USA. E-mail: jesus.perezrios@stonybrook.edu)  \nbInstitute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794, USA  \ncDepartment of Physics, Faculty of Science, Assiut University, Assiut, 71515, Egypt dFritz-Haber-Institut der Max-Planck-Gesellscha􀀁, D-14195 Berlin, Germany  \n1920 till now, the number of empirical relations published is around 70 collected by Kraka et al.10 Most of these empirical relations were tested by sev","cbCaiaLdnnpsq8JJ","https://ap.wps.com/l/cbCaiaLdnnpsq8JJ","pdf",2354876,1,18,"English","en",105,"# Introduction\n## Empirical relationships for diatomic spectroscopic constants\n## Theoretical justifications and virial-theorem connections\n## Electron-density based developments and parameterized relations","[{\"question\":\"How does the document predict spectroscopic constants from atomic properties?\",\"answer\":\"It builds a database of spectroscopic data for diatomic molecules and applies Gaussian process regression to learn efficient molecular characterizations from atomic properties.\"},{\"question\":\"What prediction accuracy is achieved for equilibrium distance and vibrational harmonic frequency?\",\"answer\":\"Using only atomic properties, the equilibrium distance has an absolute error of 0.04 Å and the vibrational harmonic frequency has an absolute error of 36 cm−1.\"},{\"question\":\"How can the model performance be improved according to the paper?\",\"answer\":\"The results improve by including prior information on molecular properties, reducing errors to 0.02 Å for equilibrium distance and 28 cm−1 for vibrational harmonic frequency.\"}]","Spectroscopic constants from atomic properties - a machine learning approach | PDF",1785898518,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"spectroscopic-constants-from-atomic-properties-a-machine-learning-approach","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/spectroscopic-constants-from-atomic-properties-a-machine-learning-approach/125371/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the document predict spectroscopic constants from atomic properties?","Question",{"text":75,"@type":76},"It builds a database of spectroscopic data for diatomic molecules and applies Gaussian process regression to learn efficient molecular characterizations from atomic properties.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What prediction accuracy is achieved for equilibrium distance and vibrational harmonic frequency?",{"text":80,"@type":76},"Using only atomic properties, the equilibrium distance has an absolute error of 0.04 Å and the vibrational harmonic frequency has an absolute error of 36 cm−1.",{"name":82,"@type":73,"acceptedAnswer":83},"How can the model performance be improved according to the paper?",{"text":84,"@type":76},"The results improve by including prior information on molecular properties, reducing errors to 0.02 Å for equilibrium distance and 28 cm−1 for vibrational harmonic frequency.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]