{"id":"https://openalex.org/W7124178798","doi":"https://doi.org/10.1063/5.0312045","title":"Definitions of atoms in molecules with the modified Dirac equations","display_name":"Definitions of atoms in molecules with the modified Dirac equations","publication_year":2026,"publication_date":"2026-01-14","ids":{"openalex":"https://openalex.org/W7124178798","doi":"https://doi.org/10.1063/5.0312045","pmid":"https://pubmed.ncbi.nlm.nih.gov/41532737"},"language":"en","primary_location":{"id":"doi:10.1063/5.0312045","doi":"https://doi.org/10.1063/5.0312045","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0312045","pdf_url":null,"source":{"id":"https://openalex.org/S77047749","display_name":"The Journal of Chemical Physics","issn_l":"0021-9606","issn":["0021-9606","1089-7690","1520-9032"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","medline","norway-1"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Chemical Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11336/285576","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021765371","display_name":"Andy D. Zapata\u2013Escobar","orcid":"https://orcid.org/0000-0001-6096-2074","observed_orcids":["https://orcid.org/0000-0001-6096-2074"]},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Andy D. Zapata\u2013Escobar","raw_affiliation_strings":["Instituto de Modelado e Innovaci\u00f3n Tecnol\u00f3gica, IMIT (CONICET-UNNE) , Avda Libertad 5460, W3404AAS Corrientes,"],"raw_orcid":"https://orcid.org/0000-0001-6096-2074","affiliations":[{"raw_affiliation_string":"Instituto de Modelado e Innovaci\u00f3n Tecnol\u00f3gica, IMIT (CONICET-UNNE) , Avda Libertad 5460, W3404AAS Corrientes,","institution_ids":["https://openalex.org/I151201029"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032788720","display_name":"Alejandro F. Maldonado","orcid":"https://orcid.org/0000-0003-3587-3736","observed_orcids":["https://orcid.org/0000-0003-3587-3736"]},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Alejandro F. Maldonado","raw_affiliation_strings":["Instituto de Modelado e Innovaci\u00f3n Tecnol\u00f3gica, IMIT (CONICET-UNNE) , Avda Libertad 5460, W3404AAS Corrientes,"],"raw_orcid":"https://orcid.org/0000-0003-3587-3736","affiliations":[{"raw_affiliation_string":"Instituto de Modelado e Innovaci\u00f3n Tecnol\u00f3gica, IMIT (CONICET-UNNE) , Avda Libertad 5460, W3404AAS Corrientes,","institution_ids":["https://openalex.org/I151201029"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I151201029"],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":2.8439,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.83752569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"164","issue":"2","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":0.9926999807357788,"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":0.9926999807357788,"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/T10523","display_name":"Atomic and Molecular Physics","score":0.002400000113993883,"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":0.0017999999690800905,"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/quantum-theory-of-atoms-in-molecules","display_name":"quantum theory of atoms in molecules","score":0.8610000014305115},{"id":"https://openalex.org/keywords/relativistic-effects","display_name":"relativistic effects","score":0.8230000138282776},{"id":"https://openalex.org/keywords/basins-of-attraction","display_name":"basins of attraction","score":0.6010000109672546},{"id":"https://openalex.org/keywords/lagrangian-density","display_name":"Lagrangian density","score":0.8320000171661377},{"id":"https://openalex.org/keywords/continuity-equation","display_name":"continuity equation","score":0.8230000138282776},{"id":"https://openalex.org/keywords/hydrogen-halides","display_name":"hydrogen halides","score":0.7200000286102295},{"id":"https://openalex.org/keywords/snh4","display_name":"SnH4","score":0.859000027179718},{"id":"https://openalex.org/keywords/dipole-moment","display_name":"dipole moment","score":0.8399999737739563}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6868000030517578},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.671500027179718},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.516700029373169},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.47519999742507935},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.4632999897003174},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C81263218","wikidata":"https://www.wikidata.org/wiki/Q7330289","display_name":"Relativistic quantum chemistry","level":2,"score":0.4253000020980835},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4066999852657318},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.4041000008583069},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.40220001339912415},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.3912999927997589},{"id":"https://openalex.org/C164866673","wikidata":"https://www.wikidata.org/wiki/Q304054","display_name":"Charge conservation","level":3,"score":0.37709999084472656},{"id":"https://openalex.org/C63385615","wikidata":"https://www.wikidata.org/wiki/Q2869600","display_name":"Atoms in molecules","level":3,"score":0.3718000054359436},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3449000120162964},{"id":"https://openalex.org/C140673361","wikidata":"https://www.wikidata.org/wiki/Q7310838","display_name":"Relativistic wave equations","level":3,"score":0.34369999170303345},{"id":"https://openalex.org/C86025842","wikidata":"https://www.wikidata.org/wiki/Q5358432","display_name":"Electronic structure","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C30005106","wikidata":"https://www.wikidata.org/wiki/Q7858689","display_name":"Two-body Dirac equations","level":3,"score":0.3314000070095062},{"id":"https://openalex.org/C125485243","wikidata":"https://www.wikidata.org/wiki/Q905186","display_name":"Electron density","level":3,"score":0.3203999996185303},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.30390000343322754},{"id":"https://openalex.org/C31836371","wikidata":"https://www.wikidata.org/wiki/Q1856609","display_name":"Scalar potential","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C57476683","wikidata":"https://www.wikidata.org/wiki/Q3332147","display_name":"Relativistic quantum mechanics","level":4,"score":0.296099990606308},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2775000035762787},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C175749648","wikidata":"https://www.wikidata.org/wiki/Q1068091","display_name":"Point particle","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C168997771","wikidata":"https://www.wikidata.org/wiki/Q2022629","display_name":"Relativistic particle","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C92915299","wikidata":"https://www.wikidata.org/wiki/Q905186","display_name":"Electronic density","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.25769999623298645},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C7214806","wikidata":"https://www.wikidata.org/wiki/Q2957735","display_name":"Mulliken population analysis","level":3,"score":0.2531999945640564}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1063/5.0312045","doi":"https://doi.org/10.1063/5.0312045","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0312045","pdf_url":null,"source":{"id":"https://openalex.org/S77047749","display_name":"The Journal of Chemical Physics","issn_l":"0021-9606","issn":["0021-9606","1089-7690","1520-9032"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","ki-jl-1","medline","norway-1"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Chemical Physics","raw_type":"journal-article"},{"id":"pmid:41532737","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41532737","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of chemical physics","raw_type":"Journal Article"},{"id":"pmh:oai:ri.conicet.gov.ar:11336/285576","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/285576","pdf_url":null,"source":{"id":"https://openalex.org/S4306401400","display_name":"Conicet","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210104196","host_organization_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Nordeste","host_organization_lineage":["https://openalex.org/I4210104196"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ri.conicet.gov.ar:11336/285576","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/285576","pdf_url":null,"source":{"id":"https://openalex.org/S4306401400","display_name":"Conicet","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210104196","host_organization_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Nordeste","host_organization_lineage":["https://openalex.org/I4210104196"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G505980809","display_name":null,"funder_award_id":"PIP 112202101 00483","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G837265393","display_name":null,"funder_award_id":"PICT-2021-I-A-00933","funder_id":"https://openalex.org/F4320337954","funder_display_name":"Fondo para la Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"}],"funders":[{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F4320337954","display_name":"Fondo para la Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/03stxzb56"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W431748896","https://openalex.org/W1653050201","https://openalex.org/W1978683587","https://openalex.org/W1979069170","https://openalex.org/W1982809301","https://openalex.org/W1992262155","https://openalex.org/W1994253622","https://openalex.org/W1996700831","https://openalex.org/W2007110112","https://openalex.org/W2011301426","https://openalex.org/W2012986644","https://openalex.org/W2013711359","https://openalex.org/W2022085321","https://openalex.org/W2022917232","https://openalex.org/W2023814380","https://openalex.org/W2029667189","https://openalex.org/W2032440360","https://openalex.org/W2035395141","https://openalex.org/W2049058194","https://openalex.org/W2049452744","https://openalex.org/W2050889869","https://openalex.org/W2055403740","https://openalex.org/W2056474482","https://openalex.org/W2060274246","https://openalex.org/W2092532828","https://openalex.org/W2117546220","https://openalex.org/W2119607070","https://openalex.org/W2127865535","https://openalex.org/W2132525235","https://openalex.org/W2134769107","https://openalex.org/W2150687058","https://openalex.org/W2168299072","https://openalex.org/W2312655509","https://openalex.org/W2315360863","https://openalex.org/W2438334672","https://openalex.org/W2549826563","https://openalex.org/W2739477519","https://openalex.org/W2756519801","https://openalex.org/W2783551376","https://openalex.org/W2899875406","https://openalex.org/W3007178273","https://openalex.org/W4248710233","https://openalex.org/W4401916766","https://openalex.org/W4412111181"],"related_works":[],"abstract_inverted_index":{"In":[0,133],"this":[1,158],"work,":[2],"we":[3,135,163],"present":[4,136],"calculations":[5,68],"of":[6,51,58,79,105,112,160,197],"the":[7,13,26,48,52,55,59,80,84,99,106,110,113,118,121,130,137,141,149,155,171,184,189,194,204],"basins":[8,53],"and":[9,31,54,65,74,93],"electronic":[10,60,66,122],"population":[11,67,123],"at":[12],"relativistic":[14,73,100,205],"level,":[15],"with":[16,25,157,170],"expressions":[17],"derived":[18],"from":[19,140,174,203],"a":[20,44,103,127,165,209],"total":[21,81],"Lagrangian":[22,167],"density":[23,108,168],"associated":[24,169],"modified":[27,142],"Dirac":[28,143,172],"Hamiltonian":[29,144],"[Zapata-Escobar":[30],"Maldonado,":[32],"J.":[33],"Chem.":[34],"Phys.":[35],"163,":[36],"024310":[37],"(2025)].":[38],"Calculations":[39],"were":[40,69],"carried":[41],"out":[42],"using":[43],"local":[45],"implementation":[46],"for":[47,117,183],"numerical":[49],"construction":[50],"corresponding":[56],"integrations":[57],"population.":[61],"The":[62],"basins'":[63],"evaluation":[64],"obtained":[70],"on":[71],"both":[72],"nonrelativistic":[75,190],"expressions,":[76],"reproducing":[77],"99.9%":[78],"charge":[82],"in":[83,129,145,199],"HX":[85],"(X":[86],"=":[87],"F,":[88],"Cl,":[89],"Br,":[90],"I,":[91],"At)":[92],"SnH4":[94],"molecules.":[95],"We":[96],"found":[97],"that":[98],"effects":[101],"cause":[102],"contraction":[104],"electron":[107],"around":[109],"nuclei":[111],"heavy":[114],"atoms,":[115],"while":[116],"hydrogen":[119],"atom,":[120],"decreases,":[124],"leading":[125],"to":[126,147,153,179],"decrease":[128],"dipole":[131],"moment.":[132],"addition,":[134],"continuity":[138],"equation":[139],"order":[146],"interpret":[148],"scalar":[150],"field":[151],"used":[152],"obtain":[154,180],"basin":[156,191],"scheme":[159],"calculation.":[161],"Finally,":[162],"propose":[164],"new":[166],"Hamiltonian,":[173],"which":[175],"it":[176],"is":[177],"possible":[178],"an":[181],"expression":[182,192],"zero-flux":[185],"condition,":[186],"thereby":[187],"recovering":[188],"within":[193],"quantum":[195],"theory":[196],"atoms":[198],"molecules":[200],"approach":[201],"directly":[202],"formulation":[206],"without":[207],"adding":[208],"heuristic":[210],"term.":[211]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2026-01-15T00:00:00"}