{"id":"https://openalex.org/W1967575228","doi":"https://doi.org/10.1002/jcc.540161103","title":"Analysis of the updated Hessian matrices for locating transition structures","display_name":"Analysis of the updated Hessian matrices for locating transition structures","publication_year":1995,"publication_date":"1995-11-01","ids":{"openalex":"https://openalex.org/W1967575228","doi":"https://doi.org/10.1002/jcc.540161103","mag":"1967575228"},"language":"en","primary_location":{"id":"doi:10.1002/jcc.540161103","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jcc.540161103","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/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"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Josep Maria Bofill","raw_affiliation_strings":["Departament de Quimica Orga\u0300nica, Universitat de Barcelona, Marti\u0301 i Franque\u0300s 1, E-08028 Barcelona, Catalunya, Spain","Departament de Qu\u00edmica Org\u00e0nica, Universitat de Barcelona, Mart\u00ed i Franqu\u00e8s 1, E\u201008028 Barcelona, Catalunya, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Quimica Orga\u0300nica, Universitat de Barcelona, Marti\u0301 i Franque\u0300s 1, E-08028 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I71999127"]},{"raw_affiliation_string":"Departament de Qu\u00edmica Org\u00e0nica, Universitat de Barcelona, Mart\u00ed i Franqu\u00e8s 1, E\u201008028 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I71999127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081285343","display_name":"M\u00f3anica Comajuan","orcid":null},"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"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M\u00f3anica Comajuan","raw_affiliation_strings":["Departament de Quimica Orga\u0300nica, Universitat de Barcelona, Marti\u0301 i Franque\u0300s 1, E-08028 Barcelona, Catalunya, Spain","Departament de Qu\u00edmica Org\u00e0nica, Universitat de Barcelona, Mart\u00ed i Franqu\u00e8s 1, E\u201008028 Barcelona, Catalunya, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Quimica Orga\u0300nica, Universitat de Barcelona, Marti\u0301 i Franque\u0300s 1, E-08028 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I71999127"]},{"raw_affiliation_string":"Departament de Qu\u00edmica Org\u00e0nica, Universitat de Barcelona, Mart\u00ed i Franqu\u00e8s 1, E\u201008028 Barcelona, Catalunya, Spain","institution_ids":["https://openalex.org/I71999127"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045879904"],"corresponding_institution_ids":["https://openalex.org/I71999127"],"apc_list":{"value":4520,"currency":"USD","value_usd":4520},"apc_paid":null,"fwci":2.655,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.88268685,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"11","first_page":"1326","last_page":"1338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9625999927520752,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9625999927520752,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.9841529130935669},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.6910159587860107},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6773466467857361},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5258857607841492},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5176830291748047},{"id":"https://openalex.org/keywords/perturbation-theory","display_name":"Perturbation theory (quantum mechanics)","score":0.4670711159706116},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.4512922763824463},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4386886656284332},{"id":"https://openalex.org/keywords/first-order","display_name":"First order","score":0.43529990315437317},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3843690752983093},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3385566473007202},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16805779933929443},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.14668607711791992},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14380058646202087},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12123394012451172},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06378427147865295},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.06277236342430115}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9841529130935669},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.6910159587860107},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6773466467857361},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5258857607841492},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5176830291748047},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.4670711159706116},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.4512922763824463},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4386886656284332},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.43529990315437317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3843690752983093},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3385566473007202},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16805779933929443},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.14668607711791992},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14380058646202087},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12123394012451172},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06378427147865295},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.06277236342430115},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jcc.540161103","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jcc.540161103","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W209493197","https://openalex.org/W1975319829","https://openalex.org/W1985001178","https://openalex.org/W1985864737","https://openalex.org/W1988675445","https://openalex.org/W2005724054","https://openalex.org/W2006041360","https://openalex.org/W2007663400","https://openalex.org/W2018624971","https://openalex.org/W2020109851","https://openalex.org/W2021350363","https://openalex.org/W2038210983","https://openalex.org/W2041792275","https://openalex.org/W2056673717","https://openalex.org/W2062920273","https://openalex.org/W2069828243","https://openalex.org/W2077658674","https://openalex.org/W2079473982","https://openalex.org/W2081159460","https://openalex.org/W2099428582","https://openalex.org/W2133524519","https://openalex.org/W4212997115","https://openalex.org/W4248247707"],"related_works":["https://openalex.org/W1991833659","https://openalex.org/W2023266244","https://openalex.org/W203338483","https://openalex.org/W19604512","https://openalex.org/W2015856668","https://openalex.org/W2033626567","https://openalex.org/W1977452077","https://openalex.org/W2089895988","https://openalex.org/W2083194257","https://openalex.org/W2082542187"],"abstract_inverted_index":{"Abstract":[0],"We":[1,71],"present":[2],"an":[3],"analysis":[4,26],"of":[5,8,22,32,36,50,58,61,77,85],"the":[6,18,30,34,37,65,74,83],"behavior":[7],"different":[9],"updating":[10],"Hessian":[11,51],"formulas":[12],"when":[13],"they":[14],"are":[15],"used":[16],"for":[17,82],"location":[19],"and":[20,42],"optimization":[21,84],"transition":[23,86],"structures.":[24,87],"The":[25],"is":[27,80],"based":[28],"on":[29],"number":[31],"iterations,":[33],"minimum":[35],"weighted":[38],"Euclidean":[39],"matrix":[40],"norm,":[41],"first\u2010order":[43],"perturbation":[44],"theory":[45],"applied":[46],"to":[47],"each":[48],"type":[49],"correction.":[52],"Finally,":[53],"we":[54],"give":[55],"a":[56,59],"derivation":[57],"family":[60,76],"updated":[62,78],"Hessians":[63,79],"from":[64],"variational":[66],"method":[67],"proposed":[68,75],"by":[69],"Greenstadt.":[70],"conclude":[72],"that":[73],"useful":[81],"\u00a9":[88],"1995":[89],"John":[90],"Wiley":[91],"&":[92],"Sons,":[93],"Inc.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}