{"id":"https://openalex.org/W2073829819","doi":"https://doi.org/10.1137/130911032","title":"On the Convergence of the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory","display_name":"On the Convergence of the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2073829819","doi":"https://doi.org/10.1137/130911032","mag":"2073829819"},"language":"en","primary_location":{"id":"doi:10.1137/130911032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911032","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100352359","display_name":"Xin Liu","orcid":"https://orcid.org/0009-0005-5174-9446"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin Liu","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, CHINA"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, CHINA","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101991291","display_name":"Xiao Wang","orcid":"https://orcid.org/0000-0003-2898-3355"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, CHINA"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, CHINA","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006127137","display_name":"Zaiwen Wen","orcid":"https://orcid.org/0000-0003-1762-0671"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zaiwen Wen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5107835542","display_name":"Ya-xiang Yuan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaxiang Yuan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100352359"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":null,"apc_paid":null,"fwci":1.3776,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.81191927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"2","first_page":"546","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T11682","display_name":"Advanced Condensed Matter Physics","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T10607","display_name":"Magnetic and transport properties of perovskites and related materials","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8747588992118835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8014075756072998},{"id":"https://openalex.org/keywords/kohn\u2013sham-equations","display_name":"Kohn\u2013Sham equations","score":0.6444939374923706},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5851089954376221},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5729344487190247},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5238523483276367},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5060474276542664},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.44234758615493774},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.4298844039440155},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.41972461342811584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3536335229873657},{"id":"https://openalex.org/keywords/density-functional-theory","display_name":"Density functional theory","score":0.2836013734340668},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18280458450317383},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18071627616882324},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12149760127067566},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0947847068309784}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8747588992118835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8014075756072998},{"id":"https://openalex.org/C9059619","wikidata":"https://www.wikidata.org/wiki/Q3272140","display_name":"Kohn\u2013Sham equations","level":3,"score":0.6444939374923706},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5851089954376221},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5729344487190247},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5238523483276367},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5060474276542664},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.44234758615493774},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4298844039440155},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.41972461342811584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3536335229873657},{"id":"https://openalex.org/C152365726","wikidata":"https://www.wikidata.org/wiki/Q1048589","display_name":"Density functional theory","level":2,"score":0.2836013734340668},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18280458450317383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18071627616882324},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12149760127067566},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0947847068309784},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130911032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130911032","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8700000047683716}],"awards":[{"id":"https://openalex.org/G2776650721","display_name":null,"funder_award_id":"1133101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3549876584","display_name":null,"funder_award_id":"11322109","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G385937226","display_name":null,"funder_award_id":"11301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5653340087","display_name":null,"funder_award_id":"11301505","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5850044563","display_name":null,"funder_award_id":"91330202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G603791882","display_name":null,"funder_award_id":"11331012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6258415954","display_name":null,"funder_award_id":"Chinese","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7377904560","display_name":null,"funder_award_id":"Engin","funder_id":"https://openalex.org/F4320323383","funder_display_name":"Technische Universit\u00e4t M\u00fcnchen"},{"id":"https://openalex.org/G7876063575","display_name":null,"funder_award_id":"11331012","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"}],"funders":[{"id":"https://openalex.org/F4320314331","display_name":"Centre de Recherches Math\u00e9matiques","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"},{"id":"https://openalex.org/F4320324787","display_name":"Peking University","ror":"https://ror.org/02v51f717"},{"id":"https://openalex.org/F4320326970","display_name":"State Key Laboratory of Scientific and Engineering Computing","ror":null},{"id":"https://openalex.org/F4320326972","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57"},{"id":"https://openalex.org/F4320336876","display_name":"National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences","ror":"https://ror.org/00s97k668"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W946524491","https://openalex.org/W1459519259","https://openalex.org/W1544171083","https://openalex.org/W1585439088","https://openalex.org/W1645422644","https://openalex.org/W1969824929","https://openalex.org/W1974333117","https://openalex.org/W1992013802","https://openalex.org/W2007395042","https://openalex.org/W2013467868","https://openalex.org/W2014042806","https://openalex.org/W2025470258","https://openalex.org/W2045512849","https://openalex.org/W2046434053","https://openalex.org/W2057342157","https://openalex.org/W2065519604","https://openalex.org/W2066898005","https://openalex.org/W2092344142","https://openalex.org/W2108974381","https://openalex.org/W2144692620","https://openalex.org/W2169650761","https://openalex.org/W3147626731"],"related_works":["https://openalex.org/W2049211387","https://openalex.org/W2040131087","https://openalex.org/W1997143650","https://openalex.org/W2214322677","https://openalex.org/W3105317704","https://openalex.org/W3014969982","https://openalex.org/W2047887265","https://openalex.org/W2086725245","https://openalex.org/W2956460414","https://openalex.org/W2549759121"],"abstract_inverted_index":{"It":[0],"is":[1,22,71,120,152],"well":[2],"known":[3],"that":[4,110,157],"the":[5,12,31,35,39,47,52,59,62,65,68,75,101,104,108,111,114,124,128,155,164,167],"self-consistent":[6],"field":[7],"(SCF)":[8],"iteration":[9,33],"for":[10],"solving":[11],"Kohn--Sham":[13],"(KS)":[14],"equation":[15,106],"often":[16],"fails":[17],"to":[18,81,100],"converge,":[19],"yet":[20],"there":[21],"no":[23],"clear":[24],"explanation.":[25],"In":[26],"this":[27],"paper,":[28],"we":[29,78],"investigate":[30],"SCF":[32,76,168],"from":[34,85,94,135],"perspective":[36],"of":[37,51,67,103,127,163,166],"minimizing":[38],"corresponding":[40],"KS":[41,53,105],"total":[42,54],"energy":[43,55],"functional.":[44],"By":[45],"analyzing":[46],"second-order":[48,125],"Taylor":[49],"expansion":[50],"functional":[56,131],"and":[57,64,90,117,123,143],"estimating":[58],"relationship":[60],"between":[61,113],"Hamiltonian":[63],"part":[66],"Hessian":[69],"which":[70],"not":[72],"used":[73],"in":[74,148,154],"iteration,":[77],"are":[79,132,140,144],"able":[80],"prove":[82],"global":[83],"convergence":[84,93],"an":[86,95],"arbitrary":[87],"initial":[88,96],"point":[89,97],"local":[91],"linear":[92],"sufficiently":[98,121],"close":[99],"solution":[102],"under":[107],"assumptions":[109],"gap":[112],"occupied":[115],"states":[116,119],"unoccupied":[118],"large":[122],"derivatives":[126],"exchange":[129],"correlation":[130],"uniformly":[133],"bounded":[134],"above.":[136],"Although":[137],"these":[138],"conditions":[139],"very":[141],"stringent":[142],"almost":[145],"never":[146],"satisfied":[147],"reality,":[149],"our":[150],"analysis":[151],"interesting":[153],"sense":[156],"it":[158],"provides":[159],"a":[160],"qualitative":[161],"prediction":[162],"behavior":[165],"iteration.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}