{"id":"https://openalex.org/W2135173718","doi":"https://doi.org/10.1002/(sici)1096-987x(19980715)19:9<1087::aid-jcc9>3.0.co;2-m","title":"Searching for saddle points of potential energy surfaces by following a reduced gradient","display_name":"Searching for saddle points of potential energy surfaces by following a reduced gradient","publication_year":1998,"publication_date":"1998-07-15","ids":{"openalex":"https://openalex.org/W2135173718","doi":"https://doi.org/10.1002/(sici)1096-987x(19980715)19:9<1087::aid-jcc9>3.0.co;2-m","mag":"2135173718"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1096-987x(19980715)19:9<1087::aid-jcc9>3.0.co;2-m","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(19980715)19:9<1087::aid-jcc9>3.0.co;2-m","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/A5059932944","display_name":"Wolfgang Quapp","orcid":"https://orcid.org/0000-0002-0366-1408"},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Wolfgang Quapp","raw_affiliation_strings":["Mathematisches Institut, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","Mathematisches Institut, Universit\u00e4t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]},{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067089721","display_name":"Michael Hirsch","orcid":"https://orcid.org/0000-0001-6183-6256"},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Hirsch","raw_affiliation_strings":["Mathematisches Institut, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","Mathematisches Institut, Universit\u00e4t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]},{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043845063","display_name":"Olaf Imig","orcid":null},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Olaf Imig","raw_affiliation_strings":["Institut fu\u0308r Physikalische und Theoretische Chemie, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","Institut f\u00fcr Physikalische und Theoretische Chemie, Universit\u00e4t Leipzig, Augustus\u2010Platz, D\u201004109 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Institut fu\u0308r Physikalische und Theoretische Chemie, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]},{"raw_affiliation_string":"Institut f\u00fcr Physikalische und Theoretische Chemie, Universit\u00e4t Leipzig, Augustus\u2010Platz, D\u201004109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039238459","display_name":"Dietmar Heidrich","orcid":null},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dietmar Heidrich","raw_affiliation_strings":["Institut fu\u0308r Physikalische und Theoretische Chemie, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","Institut f\u00fcr Physikalische und Theoretische Chemie, Universit\u00e4t Leipzig, Augustus\u2010Platz, D\u201004109 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Institut fu\u0308r Physikalische und Theoretische Chemie, Universita\u0308t Leipzig, Augustus-Platz, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]},{"raw_affiliation_string":"Institut f\u00fcr Physikalische und Theoretische Chemie, Universit\u00e4t Leipzig, Augustus\u2010Platz, D\u201004109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059932944"],"corresponding_institution_ids":["https://openalex.org/I926574661"],"apc_list":{"value":4840,"currency":"USD","value_usd":4840},"apc_paid":null,"fwci":3.3153,"has_fulltext":false,"cited_by_count":189,"citation_normalized_percentile":{"value":0.92788621,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"19","issue":"9","first_page":"1087","last_page":"1100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.9970999956130981,"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"}},{"id":"https://openalex.org/T12893","display_name":"Organic Chemistry Cycloaddition Reactions","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"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/T12327","display_name":"Various Chemistry Research Topics","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8186819553375244},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.740351676940918},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.6356908082962036},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.6348394155502319},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5748991966247559},{"id":"https://openalex.org/keywords/energy-profile","display_name":"Energy profile","score":0.42426103353500366},{"id":"https://openalex.org/keywords/potential-energy","display_name":"Potential energy","score":0.42240110039711},{"id":"https://openalex.org/keywords/potential-energy-surface","display_name":"Potential energy surface","score":0.4180436432361603},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3850817382335663},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3756970763206482},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.3487601578235626},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.3480664789676666},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.30671706795692444},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2301485240459442},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.18577778339385986},{"id":"https://openalex.org/keywords/ab-initio","display_name":"Ab initio","score":0.16471806168556213},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15512919425964355}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8186819553375244},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.740351676940918},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.6356908082962036},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.6348394155502319},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5748991966247559},{"id":"https://openalex.org/C82160515","wikidata":"https://www.wikidata.org/wiki/Q5377201","display_name":"Energy profile","level":3,"score":0.42426103353500366},{"id":"https://openalex.org/C84551667","wikidata":"https://www.wikidata.org/wiki/Q155640","display_name":"Potential energy","level":2,"score":0.42240110039711},{"id":"https://openalex.org/C125277925","wikidata":"https://www.wikidata.org/wiki/Q2572687","display_name":"Potential energy surface","level":3,"score":0.4180436432361603},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3850817382335663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3756970763206482},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3487601578235626},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.3480664789676666},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30671706795692444},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2301485240459442},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.18577778339385986},{"id":"https://openalex.org/C2781442258","wikidata":"https://www.wikidata.org/wiki/Q46310","display_name":"Ab initio","level":2,"score":0.16471806168556213},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15512919425964355},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/(sici)1096-987x(19980715)19:9<1087::aid-jcc9>3.0.co;2-m","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(19980715)19:9<1087::aid-jcc9>3.0.co;2-m","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.9914","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.9914","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-leipzig.de/~quapp/JCCqhih.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":89,"referenced_works":["https://openalex.org/W25631744","https://openalex.org/W66206807","https://openalex.org/W97737013","https://openalex.org/W658638790","https://openalex.org/W987012670","https://openalex.org/W1558320072","https://openalex.org/W1601682635","https://openalex.org/W1642314829","https://openalex.org/W1965087316","https://openalex.org/W1969382351","https://openalex.org/W1971247409","https://openalex.org/W1975319829","https://openalex.org/W1978235668","https://openalex.org/W1979332585","https://openalex.org/W1980918702","https://openalex.org/W1982200843","https://openalex.org/W1984540707","https://openalex.org/W1987203045","https://openalex.org/W1988260109","https://openalex.org/W1988800957","https://openalex.org/W1989240462","https://openalex.org/W1996098619","https://openalex.org/W1996802194","https://openalex.org/W1997054314","https://openalex.org/W1998206772","https://openalex.org/W2005461875","https://openalex.org/W2006134762","https://openalex.org/W2008082462","https://openalex.org/W2011153362","https://openalex.org/W2012712437","https://openalex.org/W2013671650","https://openalex.org/W2020484023","https://openalex.org/W2021599769","https://openalex.org/W2022772618","https://openalex.org/W2022950330","https://openalex.org/W2026750696","https://openalex.org/W2027060437","https://openalex.org/W2027801610","https://openalex.org/W2028702957","https://openalex.org/W2029421131","https://openalex.org/W2032380345","https://openalex.org/W2032898330","https://openalex.org/W2034382532","https://openalex.org/W2035184441","https://openalex.org/W2039948490","https://openalex.org/W2041748729","https://openalex.org/W2042880975","https://openalex.org/W2044940020","https://openalex.org/W2047529218","https://openalex.org/W2054085358","https://openalex.org/W2054754597","https://openalex.org/W2055468061","https://openalex.org/W2057099891","https://openalex.org/W2059473243","https://openalex.org/W2063214713","https://openalex.org/W2067090808","https://openalex.org/W2067558303","https://openalex.org/W2072176109","https://openalex.org/W2073974904","https://openalex.org/W2078136230","https://openalex.org/W2080183275","https://openalex.org/W2081071108","https://openalex.org/W2083089432","https://openalex.org/W2083881957","https://openalex.org/W2084252775","https://openalex.org/W2087630594","https://openalex.org/W2088673416","https://openalex.org/W2088986191","https://openalex.org/W2089398223","https://openalex.org/W2089759714","https://openalex.org/W2095260255","https://openalex.org/W2105350306","https://openalex.org/W2109200759","https://openalex.org/W2109928268","https://openalex.org/W2110043143","https://openalex.org/W2113261321","https://openalex.org/W2114278710","https://openalex.org/W2135098885","https://openalex.org/W2167496439","https://openalex.org/W2186590998","https://openalex.org/W2188432502","https://openalex.org/W2263329696","https://openalex.org/W2485476539","https://openalex.org/W2506567672","https://openalex.org/W3106395562","https://openalex.org/W4234129564","https://openalex.org/W4243372013","https://openalex.org/W4243600950","https://openalex.org/W4378373542"],"related_works":["https://openalex.org/W1989888202","https://openalex.org/W1978576933","https://openalex.org/W3125203780","https://openalex.org/W2324822375","https://openalex.org/W2006550696","https://openalex.org/W2058033289","https://openalex.org/W2036365018","https://openalex.org/W2081567253","https://openalex.org/W2009937900","https://openalex.org/W4296467167"],"abstract_inverted_index":{"The":[0,14,83,211],"old":[1],"coordinate":[2,63,75],"driving":[3],"procedure":[4],"to":[5,36,64,79,173,209,224,228],"find":[6],"transition":[7],"structures":[8,168],"in":[9,171,232],"chemical":[10],"systems":[11],"is":[12,30],"revisited.":[13],"well-known":[15],"gradient":[16,87,108,218],"criterion,":[17],"\u2207E(x)=0,":[18],"which":[19],"defines":[20],"the":[21,25,52,66,80,107,110,116,123,130,141,147,181,189,192,195,204,216],"stationary":[22,49,164],"points":[23,50,155,165,231],"of":[24,51,68,115,125,133,156,184,191,207],"potential":[26],"energy":[27],"surface":[28],"(PES),":[29],"reduced":[31,86,217],"by":[32,138],"one":[33,37,59],"equation":[34],"corresponding":[35],"search":[38,178],"direction.":[39],"In":[40],"this":[41,74],"manner,":[42],"abstract":[43],"curves":[44],"can":[45],"be":[46,77],"defined":[47],"connecting":[48],"PES.":[53],"Starting":[54],"at":[55,118],"a":[56,61,98,127,221],"given":[57],"minimum,":[58],"follows":[60],"well-selected":[62],"reach":[65],"saddle":[67,154,193,230],"interest.":[69],"Usually,":[70],"but":[71],"not":[72],"necessarily,":[73],"will":[76],"related":[78],"reaction":[81],"progress.":[82],"method,":[84],"called":[85],"following":[88,215],"(RGF),":[89],"locally":[90],"has":[91],"an":[92],"explicit":[93],"analytical":[94],"definition.":[95],"We":[96],"present":[97],"predictor\u2013corrector":[99],"method":[100,145],"for":[101,194,199,203],"tracing":[102],"such":[103],"curves.":[104],"RGF":[105,139],"uses":[106],"and":[109,146,153,202],"Hessian":[111],"matrix":[112],"or":[113],"updates":[114],"latter":[117],"every":[119],"curve":[120],"point.":[121],"For":[122],"purpose":[124],"testing":[126],"whole":[128],"surface,":[129],"six-dimensional":[131],"PES":[132],"formaldehyde,":[134],"H2CO,":[135],"was":[136],"explored":[137],"using":[140,176],"restricted":[142],"Hartree\u2013Fock":[143],"(RHF)":[144],"STO-3G":[148],"basis":[149],"set.":[150],"Forty-nine":[151],"minima":[152],"different":[157],"indices":[158],"were":[159,169],"found.":[160],"At":[161],"least":[162],"seven":[163],"representing":[166],"bonded":[167],"detected":[170],"addition":[172],"those":[174],"located":[175],"another":[177],"algorithm":[179],"on":[180],"same":[182],"level":[183],"theory.":[185],"Further":[186],"examples":[187],"are":[188],"localization":[190],"HCN\u21ccCNH":[196],"isomerization":[197],"(used":[198],"steplength":[200],"tests)":[201],"ring":[205],"closure":[206],"azidoazomethine":[208],"1H-tetrazole.":[210],"results":[212],"show":[213],"that":[214],"may":[219],"represent":[220],"serious":[222],"alternative":[223],"other":[225],"methods":[226],"used":[227],"locate":[229],"quantum":[233],"chemistry.":[234],"\u00a9":[235],"1998":[236,247],"John":[237],"Wiley":[238],"&":[239],"Sons,":[240],"Inc.":[241],"J":[242],"Comput":[243],"Chem":[244],"19:":[245],"1087\u20131100,":[246]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}