{"id":"https://openalex.org/W2151698022","doi":"https://doi.org/10.1137/080729050","title":"Explicit Large Nuclear Charge Limit of Electronic Ground States for Li, Be, B, C, N, O, F, Ne and Basic Aspects of the Periodic Table","display_name":"Explicit Large Nuclear Charge Limit of Electronic Ground States for Li, Be, B, C, N, O, F, Ne and Basic Aspects of the Periodic Table","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2151698022","doi":"https://doi.org/10.1137/080729050","mag":"2151698022"},"language":"en","primary_location":{"id":"doi:10.1137/080729050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080729050","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/en/publications/d8448def-650e-45ca-bf1c-b0a698ff1b3a","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044120743","display_name":"Gero Friesecke","orcid":"https://orcid.org/0000-0003-0066-3966"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gero Friesecke","raw_affiliation_strings":["Center for Mathematics, TU Munich, Munich, Germany"],"affiliations":[{"raw_affiliation_string":"Center for Mathematics, TU Munich, Munich, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071177310","display_name":"Benjamin D. Goddard","orcid":"https://orcid.org/0000-0002-8781-014X"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Benjamin D. Goddard","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry, UK"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071177310"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":1.3838,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.81641322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"41","issue":"2","first_page":"631","last_page":"664"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10523","display_name":"Atomic and Molecular Physics","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10093","display_name":"Nuclear physics research studies","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/wave-function","display_name":"Wave function","score":0.6833686828613281},{"id":"https://openalex.org/keywords/angular-momentum","display_name":"Angular momentum","score":0.6376843452453613},{"id":"https://openalex.org/keywords/atomic-physics","display_name":"Atomic physics","score":0.611747145652771},{"id":"https://openalex.org/keywords/quantum-number","display_name":"Quantum number","score":0.5963025093078613},{"id":"https://openalex.org/keywords/ground-state","display_name":"Ground state","score":0.5962244868278503},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5892937779426575},{"id":"https://openalex.org/keywords/electron","display_name":"Electron","score":0.5715358853340149},{"id":"https://openalex.org/keywords/charge","display_name":"Charge (physics)","score":0.5490347743034363},{"id":"https://openalex.org/keywords/effective-nuclear-charge","display_name":"Effective nuclear charge","score":0.5477275252342224},{"id":"https://openalex.org/keywords/bohr-model","display_name":"Bohr model","score":0.5354272127151489},{"id":"https://openalex.org/keywords/total-angular-momentum-quantum-number","display_name":"Total angular momentum quantum number","score":0.5235331058502197},{"id":"https://openalex.org/keywords/spin","display_name":"Spin (aerodynamics)","score":0.5153231024742126},{"id":"https://openalex.org/keywords/ion","display_name":"Ion","score":0.500244140625},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.47772619128227234},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.4428797960281372},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4306378662586212},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.43060699105262756},{"id":"https://openalex.org/keywords/principal-quantum-number","display_name":"Principal quantum number","score":0.4239114224910736},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.30852097272872925}],"concepts":[{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.6833686828613281},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.6376843452453613},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.611747145652771},{"id":"https://openalex.org/C174038435","wikidata":"https://www.wikidata.org/wiki/Q232431","display_name":"Quantum number","level":2,"score":0.5963025093078613},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.5962244868278503},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5892937779426575},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.5715358853340149},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.5490347743034363},{"id":"https://openalex.org/C138775182","wikidata":"https://www.wikidata.org/wiki/Q909960","display_name":"Effective nuclear charge","level":3,"score":0.5477275252342224},{"id":"https://openalex.org/C68030841","wikidata":"https://www.wikidata.org/wiki/Q172948","display_name":"Bohr model","level":2,"score":0.5354272127151489},{"id":"https://openalex.org/C45193367","wikidata":"https://www.wikidata.org/wiki/Q1141095","display_name":"Total angular momentum quantum number","level":3,"score":0.5235331058502197},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.5153231024742126},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.500244140625},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.47772619128227234},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4428797960281372},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4306378662586212},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.43060699105262756},{"id":"https://openalex.org/C104240894","wikidata":"https://www.wikidata.org/wiki/Q867448","display_name":"Principal quantum number","level":4,"score":0.4239114224910736},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.30852097272872925},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C194975256","wikidata":"https://www.wikidata.org/wiki/Q7269039","display_name":"Quantum dissipation","level":3,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/080729050","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080729050","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/d8448def-650e-45ca-bf1c-b0a698ff1b3a","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/d8448def-650e-45ca-bf1c-b0a698ff1b3a","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Friesecke, G & Goddard, B D 2009, 'Explicit large nuclear charge limit of electronic ground states for Li, Be, B, C, N, O, F, Ne and basic aspects of the periodic table', SIAM Journal on Mathematical Analysis, vol. 41, no. 2, pp. 631-664. https://doi.org/10.1137/080729050","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:wrap.warwick.ac.uk:2209","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/d8448def-650e-45ca-bf1c-b0a698ff1b3a","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11820/d8448def-650e-45ca-bf1c-b0a698ff1b3a","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/10461","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/10461","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"664","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/d8448def-650e-45ca-bf1c-b0a698ff1b3a","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/d8448def-650e-45ca-bf1c-b0a698ff1b3a","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Friesecke, G & Goddard, B D 2009, 'Explicit large nuclear charge limit of electronic ground states for Li, Be, B, C, N, O, F, Ne and basic aspects of the periodic table', SIAM Journal on Mathematical Analysis, vol. 41, no. 2, pp. 631-664. https://doi.org/10.1137/080729050","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"score":0.6899999976158142,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W120113281","https://openalex.org/W577312108","https://openalex.org/W1525296983","https://openalex.org/W1538202910","https://openalex.org/W1578501920","https://openalex.org/W1595263782","https://openalex.org/W1647151594","https://openalex.org/W1967825690","https://openalex.org/W1968570399","https://openalex.org/W1969087239","https://openalex.org/W1980619662","https://openalex.org/W1987150718","https://openalex.org/W1996160600","https://openalex.org/W1996978411","https://openalex.org/W1998411741","https://openalex.org/W1999626677","https://openalex.org/W2019598322","https://openalex.org/W2022308475","https://openalex.org/W2032098987","https://openalex.org/W2033824900","https://openalex.org/W2034362549","https://openalex.org/W2035000332","https://openalex.org/W2036524141","https://openalex.org/W2036595722","https://openalex.org/W2046030515","https://openalex.org/W2054597929","https://openalex.org/W2056370537","https://openalex.org/W2060501150","https://openalex.org/W2062057620","https://openalex.org/W2081658913","https://openalex.org/W2084238650","https://openalex.org/W2092952049","https://openalex.org/W2154558448","https://openalex.org/W2595512009","https://openalex.org/W2796714365","https://openalex.org/W2798456356","https://openalex.org/W2801179766","https://openalex.org/W2953991578","https://openalex.org/W2999526552","https://openalex.org/W4231247751","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3172815739","https://openalex.org/W148068826","https://openalex.org/W2004212904","https://openalex.org/W2013400606","https://openalex.org/W2063935509","https://openalex.org/W3194865051","https://openalex.org/W1994197447","https://openalex.org/W2078210200","https://openalex.org/W4248926469","https://openalex.org/W2075209062"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"concerned":[3],"with":[4,12,45,98,113],"the":[5,18,29,63,114,127,142,145,152],"Schr\u00f6dinger":[6,105],"equation":[7],"for":[8,48,57,74,79,84,87,93],"atoms":[9,59],"and":[10,33,38,51,68,81,89,91,95,123,148,160],"ions":[11],"$N=1$":[13],"to":[14,110,125],"10":[15],"electrons.":[16],"In":[17,61,130],"asymptotic":[19,36,104],"limit":[20],"of":[21,144,151],"large":[22],"nuclear":[23],"charge":[24],"Z,":[25],"we":[26],"determine":[27],"explicitly":[28],"low-lying":[30],"energy":[31],"levels":[32],"eigenstates.":[34],"The":[35,103],"energies":[37],"wavefunctions":[39],"are":[40],"in":[41,52,100],"good":[42],"quantitative":[43],"agreement":[44,55],"experimental":[46],"data":[47],"positive":[49],"ions,":[50],"excellent":[53],"qualitative":[54],"even":[56],"neutral":[58],"($Z=N$).":[60],"particular,":[62],"predicted":[64],"ground":[65,106],"state":[66],"spin":[67],"angular":[69],"momentum":[70],"quantum":[71],"numbers":[72],"($^1S$":[73],"He,":[75],"Be,":[76],"Ne,":[77],"$^2S$":[78],"H":[80],"Li,":[82],"$^4S$":[83],"N,":[85],"$^2P$":[86],"B":[88],"F,":[90],"$^3P$":[92],"C":[94],"O)":[96],"agree":[97],"experiment":[99,156],"every":[101],"case.":[102],"states":[107,150],"agree,":[108],"up":[109],"small":[111],"corrections,":[112],"semiempirical":[115],"hydrogen":[116],"orbital":[117],"configurations":[118],"developed":[119],"by":[120],"Bohr,":[121],"Hund,":[122],"Slater":[124],"explain":[126],"periodic":[128],"table.":[129],"rare":[131],"cases":[132],"where":[133],"our":[134,158],"results":[135],"deviate":[136],"from":[137],"this":[138],"picture,":[139],"such":[140],"as":[141],"ordering":[143],"lowest":[146],"$^1D^o$":[147],"$^3S^o$":[149],"carbon":[153],"isoelectronic":[154],"sequence,":[155],"confirms":[157],"predictions":[159],"not":[161],"Hund's.":[162]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}