{"id":"https://openalex.org/W2056914158","doi":"https://doi.org/10.1002/(sici)1096-987x(199802)19:3<349::aid-jcc8>3.0.co;2-t","title":"How good is a Broyden-Fletcher-Goldfarb-Shanno-like update Hessian formula to locate transition structures? Specific reformulation of Broyden-Fletcher-Goldfarb-Shanno for optimizing saddle points","display_name":"How good is a Broyden-Fletcher-Goldfarb-Shanno-like update Hessian formula to locate transition structures? Specific reformulation of Broyden-Fletcher-Goldfarb-Shanno for optimizing saddle points","publication_year":1998,"publication_date":"1998-02-01","ids":{"openalex":"https://openalex.org/W2056914158","doi":"https://doi.org/10.1002/(sici)1096-987x(199802)19:3<349::aid-jcc8>3.0.co;2-t","mag":"2056914158"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1096-987x(199802)19:3<349::aid-jcc8>3.0.co;2-t","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(199802)19:3<349::aid-jcc8>3.0.co;2-t","pdf_url":null,"source":{"id":"https://openalex.org/S21117631","display_name":"Journal of Computational Chemistry","issn_l":"0192-8651","issn":["0192-8651","1096-987X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Chemistry","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/A5067761441","display_name":"Josep M. Anglada","orcid":"https://orcid.org/0000-0003-4526-3624"},"institutions":[{"id":"https://openalex.org/I4210099652","display_name":"Centro de Investigaci\u00f3n y Desarrollo","ror":"https://ror.org/01297db79","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210099652"]},{"id":"https://openalex.org/I4210165511","display_name":"Centre d\u2019Investigaci\u00f3 i Desenvolupament","ror":"https://ror.org/05s24hr53","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210165511"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Josep Maria Anglada","raw_affiliation_strings":["C.I.D\u2013C.S.I.C., Jordi Girona Salgado 18-26, E-08034 Barcelona, Catalunya, Spain","C.I.D\u2013C.S.I.C., Jordi Girona Salgado 18\u201026, E\u201008034 Barcelona, Catalunya, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"C.I.D\u2013C.S.I.C., Jordi Girona Salgado 18-26, E-08034 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I4210099652","https://openalex.org/I4210165511"]},{"raw_affiliation_string":"C.I.D\u2013C.S.I.C., Jordi Girona Salgado 18\u201026, E\u201008034 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I4210099652","https://openalex.org/I4210165511"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045879904","display_name":"Josep Mar\u00eda Bofill","orcid":"https://orcid.org/0000-0002-0974-4618"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]},{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Josep Maria Bofill","raw_affiliation_strings":["Departament de Qui\u0301mica Orga\u0300nica, Universitat de Barcelona, Marti\u0301 i Franque\u0300s 1-11, E-08028 Barcelona, Catalunya, Spain","Departament de Qu\u00edmica Org\u00e1nica, Universitat de Barcelona, Mart\u00ed i Franqu\u00e9s 1-11, E-08028 Barcelona, Catalunya, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Qui\u0301mica Orga\u0300nica, Universitat de Barcelona, Marti\u0301 i Franque\u0300s 1-11, E-08028 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I71999127"]},{"raw_affiliation_string":"Departament de Qu\u00edmica Org\u00e1nica, Universitat de Barcelona, Mart\u00ed i Franqu\u00e9s 1-11, E-08028 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I71999127","https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5045879904"],"corresponding_institution_ids":["https://openalex.org/I71999127","https://openalex.org/I9617848"],"apc_list":{"value":4520,"currency":"USD","value_usd":4520},"apc_paid":null,"fwci":0.9156,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.70960359,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"3","first_page":"349","last_page":"362"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9988999962806702,"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":0.9988999962806702,"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/T10683","display_name":"Mass Spectrometry Techniques and Applications","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10044","display_name":"Protein Structure and Dynamics","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.9596933126449585},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.9362388849258423},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7124203443527222},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.5432636737823486},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5172324776649475},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.5082821249961853},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49834227561950684},{"id":"https://openalex.org/keywords/hypersurface","display_name":"Hypersurface","score":0.46360480785369873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4350118041038513},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3503582179546356},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.19428566098213196},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1706923246383667},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16551750898361206},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1597541868686676},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14818820357322693},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05318203568458557}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9596933126449585},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.9362388849258423},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7124203443527222},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.5432636737823486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5172324776649475},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5082821249961853},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49834227561950684},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.46360480785369873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4350118041038513},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3503582179546356},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.19428566098213196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1706923246383667},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16551750898361206},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1597541868686676},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14818820357322693},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05318203568458557},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1096-987x(199802)19:3<349::aid-jcc8>3.0.co;2-t","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(199802)19:3<349::aid-jcc8>3.0.co;2-t","pdf_url":null,"source":{"id":"https://openalex.org/S21117631","display_name":"Journal of Computational Chemistry","issn_l":"0192-8651","issn":["0192-8651","1096-987X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Chemistry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8700000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1542136219","https://openalex.org/W1966221177","https://openalex.org/W1966539012","https://openalex.org/W1967575228","https://openalex.org/W1975319829","https://openalex.org/W1980918702","https://openalex.org/W1985001178","https://openalex.org/W1988675445","https://openalex.org/W1996802194","https://openalex.org/W2005136695","https://openalex.org/W2005724054","https://openalex.org/W2006041360","https://openalex.org/W2007663400","https://openalex.org/W2018624971","https://openalex.org/W2021350363","https://openalex.org/W2022950330","https://openalex.org/W2038210983","https://openalex.org/W2042803051","https://openalex.org/W2062920273","https://openalex.org/W2073318058","https://openalex.org/W2077658674","https://openalex.org/W2077973224","https://openalex.org/W2078409719","https://openalex.org/W2099428582","https://openalex.org/W2128417152","https://openalex.org/W2316769148","https://openalex.org/W2569942938","https://openalex.org/W4210949334","https://openalex.org/W4212997115","https://openalex.org/W4243168863"],"related_works":["https://openalex.org/W2026245502","https://openalex.org/W4318192194","https://openalex.org/W2070932288","https://openalex.org/W4221162014","https://openalex.org/W2937637171","https://openalex.org/W2572889128","https://openalex.org/W3091576739","https://openalex.org/W2892976100","https://openalex.org/W1964096161","https://openalex.org/W2958624776"],"abstract_inverted_index":{"Based":[0],"on":[1,14],"a":[2,15],"study":[3],"of":[4,31,42,51,92],"the":[5,39,43,58,65,73,84],"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno":[6],"(BFGS)":[7],"update":[8,45,75],"Hessian":[9,23,61],"formula":[10,24,54],"to":[11,25],"locate":[12,26],"minima":[13],"hypersurface":[16],"potential":[17],"energy,":[18],"we":[19],"present":[20],"an":[21],"updated":[22,60],"and":[27,49,67],"optimize":[28],"saddle":[29,93],"points":[30],"any":[32,90],"order":[33],"that":[34,72],"in":[35,89],"some":[36],"sense":[37],"preserves":[38],"initial":[40],"structure":[41],"BFGS":[44],"formula.":[46],"The":[47],"performance":[48],"efficiency":[50],"this":[52],"new":[53],"is":[55,76],"compared":[56],"with":[57],"previous":[59],"formulae":[62],"such":[63],"as":[64],"Powell":[66],"MSP":[68],"ones.":[69],"We":[70],"conclude":[71],"proposed":[74],"quite":[77],"competitive":[78],"but":[79],"no":[80],"more":[81],"efficient":[82],"than":[83],"normal":[85],"updates":[86],"normally":[87],"used":[88],"optimization":[91],"points.":[94],"\u00a9":[95],"1998":[96,107],"John":[97],"Wiley":[98],"&":[99],"Sons,":[100],"Inc.":[101],"J":[102],"Comput":[103],"Chem":[104],"19:":[105],"349\u2013362,":[106]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}