{"id":"https://openalex.org/W1089797291","doi":"https://doi.org/10.1137/14098973x","title":"A Proximal Gradient Method for Ensemble Density Functional Theory","display_name":"A Proximal Gradient Method for Ensemble Density Functional Theory","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1089797291","doi":"https://doi.org/10.1137/14098973x","mag":"1089797291"},"language":"en","primary_location":{"id":"doi:10.1137/14098973x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14098973x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5014423708","display_name":"Michael Ulbrich","orcid":"https://orcid.org/0000-0002-4320-8616"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Ulbrich","raw_affiliation_strings":["Technical University of Munich"],"affiliations":[{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006127137","display_name":"Zaiwen Wen","orcid":"https://orcid.org/0000-0003-1762-0671"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zaiwen Wen","raw_affiliation_strings":["Peking University"],"affiliations":[{"raw_affiliation_string":"Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077547409","display_name":"Chao Yang","orcid":"https://orcid.org/0000-0001-7172-7539"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chao Yang","raw_affiliation_strings":["Lawrence Berkeley National Laboratory"],"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005904781","display_name":"Dennis Kl\u00f6ckner","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dennis Kl\u00f6ckner","raw_affiliation_strings":["Technical University of Munich"],"affiliations":[{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000609407","display_name":"Zhaosong Lu","orcid":"https://orcid.org/0000-0003-3277-7853"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhaosong Lu","raw_affiliation_strings":["Simon Fraser University"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5014423708"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":1.0847,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.76961363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"4","first_page":"A1975","last_page":"A2002"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9991999864578247,"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":0.9991999864578247,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9990000128746033,"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/T10440","display_name":"Advanced Thermoelectric Materials and Devices","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"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/mathematics","display_name":"Mathematics","score":0.6941534280776978},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5022175312042236},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.4800166189670563},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.468642920255661},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46347272396087646},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4297504723072052},{"id":"https://openalex.org/keywords/density-functional-theory","display_name":"Density functional theory","score":0.41308704018592834},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.326811283826828},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2597687840461731},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.10742127895355225},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09096509218215942}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6941534280776978},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5022175312042236},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.4800166189670563},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.468642920255661},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46347272396087646},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4297504723072052},{"id":"https://openalex.org/C152365726","wikidata":"https://www.wikidata.org/wiki/Q1048589","display_name":"Density functional theory","level":2,"score":0.41308704018592834},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.326811283826828},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2597687840461731},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.10742127895355225},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09096509218215942},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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:10.1137/14098973x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/14098973x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8999999761581421,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W946524491","https://openalex.org/W1560925248","https://openalex.org/W1715013119","https://openalex.org/W1852068959","https://openalex.org/W1966406013","https://openalex.org/W1969824929","https://openalex.org/W1981078764","https://openalex.org/W1988809402","https://openalex.org/W1992013802","https://openalex.org/W1996728110","https://openalex.org/W1998134546","https://openalex.org/W2007395042","https://openalex.org/W2009702064","https://openalex.org/W2015600650","https://openalex.org/W2020428152","https://openalex.org/W2021326308","https://openalex.org/W2022611944","https://openalex.org/W2025470258","https://openalex.org/W2030976617","https://openalex.org/W2046434053","https://openalex.org/W2048633871","https://openalex.org/W2050729144","https://openalex.org/W2051142108","https://openalex.org/W2051906496","https://openalex.org/W2052171888","https://openalex.org/W2057342157","https://openalex.org/W2063209308","https://openalex.org/W2066898005","https://openalex.org/W2068300001","https://openalex.org/W2076605490","https://openalex.org/W2078223384","https://openalex.org/W2080654525","https://openalex.org/W2086953401","https://openalex.org/W2089859140","https://openalex.org/W2092344142","https://openalex.org/W2092718912","https://openalex.org/W2094849288","https://openalex.org/W2098432400","https://openalex.org/W2138522514","https://openalex.org/W2144692620","https://openalex.org/W2160632209","https://openalex.org/W2162349032","https://openalex.org/W2163052154","https://openalex.org/W2166742209","https://openalex.org/W2167137033","https://openalex.org/W2182110422","https://openalex.org/W2230728100","https://openalex.org/W2963649064","https://openalex.org/W3099787153"],"related_works":["https://openalex.org/W2013110429","https://openalex.org/W4378191142","https://openalex.org/W4297729575","https://openalex.org/W2963802160","https://openalex.org/W4292316381","https://openalex.org/W2139060521","https://openalex.org/W2214322677","https://openalex.org/W103696570","https://openalex.org/W3093006204","https://openalex.org/W3104010593"],"abstract_inverted_index":{"The":[0],"ensemble":[1],"density":[2],"functional":[3,47],"theory":[4],"(E-DFT)":[5],"is":[6,54,93,115],"valuable":[7],"for":[8],"simulations":[9],"of":[10,17,23,43,61],"metallic":[11,130],"systems":[12],"due":[13],"to":[14,39,50,111],"the":[15,21,24,28,41,44,59,83,86,97,106,112,120],"absence":[16],"a":[18,73,77],"gap":[19],"in":[20,105],"spectrum":[22],"Hamiltonian":[25],"matrices.":[26],"Although":[27],"widely":[29],"used":[30],"self-consistent":[31],"field":[32],"(SCF)":[33],"iteration":[34],"method":[35,92],"can":[36,124],"be":[37],"extended":[38],"solve":[40],"minimization":[42],"total":[45,107],"energy":[46,108],"with":[48,72],"respect":[49],"orthogonality":[51],"constraints,":[52],"there":[53],"no":[55],"theoretical":[56],"guarantee":[57],"on":[58,85,128],"convergence":[60],"these":[62],"algorithms.":[63],"In":[64],"this":[65],"paper,":[66],"we":[67],"consider":[68],"an":[69],"equivalent":[70],"model":[71],"single":[74,78],"variable":[75],"and":[76],"spherical":[79],"constraint":[80],"by":[81,95],"eliminating":[82],"dependence":[84],"fractional":[87],"occupancies.":[88],"A":[89],"proximal":[90],"gradient":[91],"developed":[94],"keeping":[96],"entropy":[98],"term":[99],"but":[100],"linearizing":[101],"all":[102],"other":[103],"terms":[104],"functional.":[109],"Convergence":[110],"stationary":[113],"point":[114],"established.":[116],"Numerical":[117],"results":[118],"using":[119],"MATLAB":[121],"toolbox":[122],"KSSOLV":[123],"outperform":[125],"SCF":[126],"consistently":[127],"many":[129],"systems.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}