{"id":"https://openalex.org/W2011837589","doi":"https://doi.org/10.1103/physrevb.69.037103","title":"Comment on \u201cBreakdown of the Hellmann-Feynman theorem: Degeneracy is the key\u201d","display_name":"Comment on \u201cBreakdown of the Hellmann-Feynman theorem: Degeneracy is the key\u201d","publication_year":2004,"publication_date":"2004-01-14","ids":{"openalex":"https://openalex.org/W2011837589","doi":"https://doi.org/10.1103/physrevb.69.037103","mag":"2011837589"},"language":"en","primary_location":{"id":"doi:10.1103/physrevb.69.037103","doi":"https://doi.org/10.1103/physrevb.69.037103","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.69.037103","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},"volume":null,"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/A5003378724","display_name":"Robert Balawender","orcid":"https://orcid.org/0000-0002-4216-5255","observed_orcids":["https://orcid.org/0000-0002-4216-5255"]},"institutions":[{"id":"https://openalex.org/I4210157029","display_name":"Institute of Physical Chemistry","ror":"https://ror.org/05e830h62","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210157029","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"R. Balawender","raw_affiliation_strings":["Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw, Poland","institution_ids":["https://openalex.org/I4210157029","https://openalex.org/I99542240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021497314","display_name":"A. Holas","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210157029","display_name":"Institute of Physical Chemistry","ror":"https://ror.org/05e830h62","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210157029","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"A. Holas","raw_affiliation_strings":["Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw, Poland","institution_ids":["https://openalex.org/I4210157029","https://openalex.org/I99542240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003286982","display_name":"Norman Henry March","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I149213910","display_name":"University of Antwerp","ror":"https://ror.org/008x57b05","country_code":"BE","type":"education","lineage":["https://openalex.org/I149213910"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210157029","display_name":"Institute of Physical Chemistry","ror":"https://ror.org/05e830h62","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210157029","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["BE","GB","PL"],"is_corresponding":false,"raw_author_name":"N. H. March","raw_affiliation_strings":["Department of Physics, University of Antwerp (RUCA), Groenenborgerlaan 171, B-2020 Antwerp, Belgium","Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw, Poland","University of Oxford, Oxford, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Antwerp (RUCA), Groenenborgerlaan 171, B-2020 Antwerp, Belgium","institution_ids":["https://openalex.org/I149213910"]},{"raw_affiliation_string":"Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw, Poland","institution_ids":["https://openalex.org/I4210157029","https://openalex.org/I99542240"]},{"raw_affiliation_string":"University of Oxford, Oxford, England","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":null,"fwci":0.4094,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.5830862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"69","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.823199987411499,"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":0.823199987411499,"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/T12044","display_name":"Advanced Physical and Chemical Molecular Interactions","score":0.03779999911785126,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.02930000051856041,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/hellmann-feynman-theorem","display_name":"Hellmann-Feynman theorem","score":0.9950000047683716},{"id":"https://openalex.org/keywords/degeneracy","display_name":"degeneracy","score":0.8320000171661377},{"id":"https://openalex.org/keywords/degenerate-perturbation-theory","display_name":"degenerate perturbation theory","score":0.9240000247955322},{"id":"https://openalex.org/keywords/force-calculation","display_name":"force calculation","score":0.42100000381469727},{"id":"https://openalex.org/keywords/average-force","display_name":"average force","score":0.46399998664855957},{"id":"https://openalex.org/keywords/anisotropic-confinement","display_name":"anisotropic confinement","score":0.6660000085830688},{"id":"https://openalex.org/keywords/harmonic-confinement","display_name":"harmonic confinement","score":0.7950000166893005}],"concepts":[{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.8543878793716431},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7161498069763184},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.6366977691650391},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5656675696372986},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.48172929883003235},{"id":"https://openalex.org/C65574998","wikidata":"https://www.wikidata.org/wiki/Q386272","display_name":"Feynman diagram","level":2,"score":0.43582791090011597},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.40545541048049927},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3994283974170685},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrevb.69.037103","doi":"https://doi.org/10.1103/physrevb.69.037103","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.69.037103","pdf_url":null,"source":{"id":"https://openalex.org/S6791298","display_name":"Physical Review B","issn_l":"1098-0121","issn":["1098-0121","1538-4489","1550-235X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1479923323","https://openalex.org/W1980508183","https://openalex.org/W1990079924","https://openalex.org/W2010785223","https://openalex.org/W2045506155","https://openalex.org/W2065103077"],"related_works":["https://openalex.org/W2090685516","https://openalex.org/W2045506155","https://openalex.org/W2039120648","https://openalex.org/W4287996000","https://openalex.org/W775737003","https://openalex.org/W2002277176","https://openalex.org/W320886262","https://openalex.org/W168460013","https://openalex.org/W2087116106","https://openalex.org/W1977360531"],"abstract_inverted_index":{"In":[0],"a":[1,56,60,68,89,115,145,151],"recent":[2],"paper,":[3],"Zhang":[4],"and":[5],"George":[6],"[Phys.":[7],"Rev.":[8],"B":[9],"66,":[10],"033110":[11],"(2002)]":[12],"have":[13],"made":[14],"an":[15,27,162],"application":[16,109],"of":[17,29,62,84,94,105,118,129,161],"the":[18,30,77,82,106,119,130],"Hellmann-Feynman":[19],"theorem":[20],"(HFT)":[21],"to":[22,35,55,80,103,110],"calculate":[23],"forces":[24,50,66,86,124,155],"acting":[25],"on":[26,98],"atom":[28],"buckyball":[31],"${\\mathrm{C}}_{60}$":[32],"when":[33],"subjected":[34],"small":[36],"displacement.":[37],"They":[38],"noticed":[39],"inconsistent":[40],"results":[41],"(as":[42],"compared":[43],"with":[44,52,88,158],"that":[45],"by":[46,144],"other":[47],"method)":[48],"for":[49,67],"connected":[51,87,157],"states":[53,138],"belonging":[54],"degenerate-energy":[57],"level.":[58,91],"However":[59],"sum":[61],"all":[63,85],"such":[64],"HFT":[65,107],"given":[69],"level":[70,131],"was":[71],"found":[72],"consistent.":[73],"Therefore":[74],"they":[75],"proposed":[76],"average":[78],"force":[79],"be":[81],"representative":[83],"degenerate":[90,99],"Our":[92,140],"analysis":[93],"these":[95],"difficulties,":[96],"based":[97],"perturbation":[100],"theory,":[101],"leads":[102],"modification":[104],"in":[108,150],"degenerate-level":[111],"states.":[112],"By":[113],"solving":[114],"matrix":[116,135],"eigenequation":[117],"extended":[120],"HFT,":[121],"as":[122,127],"many":[123],"are":[125,142,156],"obtained":[126],"degeneracy":[128],"amounts.":[132],"The":[133],"diagonalized":[134],"involves":[136],"unperturbed":[137],"only.":[139],"considerations":[141],"illustrated":[143],"simple":[146],"system---a":[147],"particle":[148],"moving":[149],"harmonic":[152],"confinement,":[153],"where":[154],"anisotropic":[159],"deformation":[160],"isotropic":[163],"confinement.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2016-06-24T00:00:00"}
