{"id":"https://openalex.org/W1966298537","doi":"https://doi.org/10.1002/(sici)1096-987x(199605)17:7<851::aid-jcc9>3.0.co;2-r","title":"Molecular symmetry andab initio calculations. II. Symmetry-matrix and symmetry-supermatrix in the Dirac-Fock method","display_name":"Molecular symmetry andab initio calculations. II. Symmetry-matrix and symmetry-supermatrix in the Dirac-Fock method","publication_year":1996,"publication_date":"1996-05-01","ids":{"openalex":"https://openalex.org/W1966298537","doi":"https://doi.org/10.1002/(sici)1096-987x(199605)17:7<851::aid-jcc9>3.0.co;2-r","mag":"1966298537"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1096-987x(199605)17:7<851::aid-jcc9>3.0.co;2-r","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(199605)17:7<851::aid-jcc9>3.0.co;2-r","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/A5009070444","display_name":"Xiao\u2010Ping Cao","orcid":"https://orcid.org/0000-0001-8340-1122"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoping Cao","raw_affiliation_strings":["Department of Chemistry, Tsinghua University, Beijing 100084, P.R. China","Department of Chemistry, Tsinghua University, Bejing 100084, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Tsinghua University, Beijing 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Chemistry, Tsinghua University, Bejing 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109094626","display_name":"Muzhen Liao","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Muzhen Liao","raw_affiliation_strings":["Department of Chemistry, Tsinghua University, Beijing 100084, P.R. China","Department of chemistry, Tsinghua University, Beijing 100084, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Tsinghua University, Beijing 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of chemistry, Tsinghua University, Beijing 100084, P.R. China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101478358","display_name":"Xuejun Chen","orcid":"https://orcid.org/0000-0002-7650-5756"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuejun Chen","raw_affiliation_strings":["Department of Physics, Tsinghua University, Beijing 100084, P.R. China","Dept. of Physics, Tsinghua University, Beijing, 100084, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Tsinghua University, Beijing 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Physics, Tsinghua University, Beijing, 100084, P. R. China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100374376","display_name":"Bo Li","orcid":"https://orcid.org/0000-0001-8895-2054"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Li","raw_affiliation_strings":["Department of Physics, Tsinghua University, Beijing 100084, P.R. China","Dept. of Physics, Tsinghua University, Beijing, 100084, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Tsinghua University, Beijing 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Physics, Tsinghua University, Beijing, 100084, P. R. China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009070444"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":{"value":4840,"currency":"USD","value_usd":4840},"apc_paid":null,"fwci":0.2566,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.47831667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"7","first_page":"851","last_page":"863"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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/T10523","display_name":"Atomic and Molecular Physics","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fock-space","display_name":"Fock space","score":0.7620659470558167},{"id":"https://openalex.org/keywords/supermatrix","display_name":"Supermatrix","score":0.655011773109436},{"id":"https://openalex.org/keywords/fock-matrix","display_name":"Fock matrix","score":0.6000137329101562},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5583469867706299},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.531130313873291},{"id":"https://openalex.org/keywords/irreducible-representation","display_name":"Irreducible representation","score":0.5022709369659424},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.4924543797969818},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.485664963722229},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.47430184483528137},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4739668071269989},{"id":"https://openalex.org/keywords/molecular-symmetry","display_name":"Molecular symmetry","score":0.4415321350097656},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.4305155873298645},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.42652127146720886},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3974651098251343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2890779972076416},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2522268295288086},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22022941708564758},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.1453675627708435},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12271249294281006}],"concepts":[{"id":"https://openalex.org/C114852677","wikidata":"https://www.wikidata.org/wiki/Q899044","display_name":"Fock space","level":2,"score":0.7620659470558167},{"id":"https://openalex.org/C123439655","wikidata":"https://www.wikidata.org/wiki/Q3977978","display_name":"Supermatrix","level":5,"score":0.655011773109436},{"id":"https://openalex.org/C207113745","wikidata":"https://www.wikidata.org/wiki/Q2526030","display_name":"Fock matrix","level":3,"score":0.6000137329101562},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5583469867706299},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.531130313873291},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.5022709369659424},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4924543797969818},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.485664963722229},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.47430184483528137},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4739668071269989},{"id":"https://openalex.org/C37197862","wikidata":"https://www.wikidata.org/wiki/Q2066775","display_name":"Molecular symmetry","level":3,"score":0.4415321350097656},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.4305155873298645},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.42652127146720886},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3974651098251343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2890779972076416},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2522268295288086},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22022941708564758},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.1453675627708435},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12271249294281006},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.0},{"id":"https://openalex.org/C5475112","wikidata":"https://www.wikidata.org/wiki/Q632521","display_name":"Affine Lie algebra","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1096-987x(199605)17:7<851::aid-jcc9>3.0.co;2-r","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(199605)17:7<851::aid-jcc9>3.0.co;2-r","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":[{"id":"https://openalex.org/F4320322392","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W569717857","https://openalex.org/W1491547160","https://openalex.org/W1557916006","https://openalex.org/W1981262887","https://openalex.org/W1990343077","https://openalex.org/W1990896036","https://openalex.org/W2005695312","https://openalex.org/W2011876515","https://openalex.org/W2012130532","https://openalex.org/W2015265547","https://openalex.org/W2020382253","https://openalex.org/W2022950330","https://openalex.org/W2024029329","https://openalex.org/W2025061081","https://openalex.org/W2026364647","https://openalex.org/W2028022118","https://openalex.org/W2029668617","https://openalex.org/W2032650366","https://openalex.org/W2037724617","https://openalex.org/W2046013326","https://openalex.org/W2060133498","https://openalex.org/W2067127621","https://openalex.org/W2070045737","https://openalex.org/W2072012006","https://openalex.org/W2086262708","https://openalex.org/W2087838447","https://openalex.org/W2090133662","https://openalex.org/W2096197682","https://openalex.org/W2109211139","https://openalex.org/W2115088436","https://openalex.org/W2118018703","https://openalex.org/W2124434871","https://openalex.org/W2141201350","https://openalex.org/W2143517266","https://openalex.org/W2563484724","https://openalex.org/W4239375047"],"related_works":["https://openalex.org/W2008427452","https://openalex.org/W179746446","https://openalex.org/W1977432091","https://openalex.org/W2086179685","https://openalex.org/W2096197682","https://openalex.org/W4240877239","https://openalex.org/W603358221","https://openalex.org/W1996591382","https://openalex.org/W1980415582","https://openalex.org/W1966298537"],"abstract_inverted_index":{"The":[0],"concepts":[1],"of":[2,29,41,70,85,89,132,138,146,153],"symmetry-matrix":[3,117],"and":[4,31,104,118,136],"symmetry-supermatrix":[5,119],"introduced":[6],"in":[7,55,72,93,113,124],"article":[8],"I":[9],"[J.":[10],"Comput.":[11],"Chem.,":[12],"10,":[13],"957":[14],"(1989)]":[15],"can":[16,51,97,105,120],"be":[17,52,98,106,122],"generalized":[18],"to":[19,65,128,162],"the":[20,25,32,37,56,67,73,80,87,94,111,116,125,130,151,154,165],"Dirac-Fock":[21,95,126],"method.":[22],"By":[23],"using":[24],"semidirect":[26],"product":[27],"decomposition":[28],"Oh":[30,42],"linear":[33],"vector":[34],"space":[35,167],"theory,":[36],"irreducible":[38,82],"representation":[39,83],"basis":[40,84],"for":[43],"any":[44],"molecular":[45,155],"system":[46],"(Oh":[47],"or":[48],"its":[49],"subgroups)":[50],"deduced":[53],"analytically":[54],"nonorthonormal":[57,166],"Cartesian":[58,75],"Gaussian":[59,76],"basis.":[60,78],"This":[61],"method":[62,127,161],"is":[63,150,168],"extended":[64],"discuss":[66],"double-valued":[68,81],"representations":[69],"Oh*":[71],"complex":[74],"spinor":[77],"In":[79,158],"D2*,":[86],"matrix":[88,140],"kinetic":[90],"operator":[91],"c(OVERLINE)\u03c3(/OVERLINE)\u00b7(OVERLINE)p(/OVELINE)":[92],"equation":[96],"reduced":[99],"into":[100,108],"a":[101,144,160],"real":[102],"symmetric":[103],"grouped":[107],"classes":[109],"under":[110],"operations":[112],"D3d.":[114],"Therefore,":[115],"also":[121],"used":[123],"reduce":[129],"storage":[131],"two":[133],"electron":[134],"integrals":[135],"calculations":[137],"Fock":[139],"during":[141],"iterations":[142],"by":[143,172],"factor":[145],"ca.":[147],"g2":[148],"(g":[149],"order":[152],"symmetry":[156],"group).":[157],"addition,":[159],"deal":[163],"with":[164],"presented.":[169],"\u00a9":[170],"1996":[171],"John":[173],"Wiley":[174],"&":[175],"Sons,":[176],"Inc.":[177]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
