{"id":"https://openalex.org/W2112305226","doi":"https://doi.org/10.1002/jcc.10016","title":"Accompanying coordinate expansion formulas derived with the solid harmonic gradient","display_name":"Accompanying coordinate expansion formulas derived with the solid harmonic gradient","publication_year":2001,"publication_date":"2001-12-26","ids":{"openalex":"https://openalex.org/W2112305226","doi":"https://doi.org/10.1002/jcc.10016","mag":"2112305226","pmid":"https://pubmed.ncbi.nlm.nih.gov/11908501"},"language":"en","primary_location":{"id":"doi:10.1002/jcc.10016","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jcc.10016","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","pubmed"],"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/A5108252601","display_name":"Kazuhiro Ishida","orcid":null},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazuhiro Ishida","raw_affiliation_strings":["Department of Chemistry and Frontier Research Center for Computational Science, Faculty of Science, Science University of Tokyo, Japan. k-ishida@fancy.ocn.ne.jp","Department of Chemistry and Frontier Research Center for Computational Science, Faculty of Science, Science University of Tokyo, Shinjuku\u2010ku, Tokyo 162\u20108601, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemistry and Frontier Research Center for Computational Science, Faculty of Science, Science University of Tokyo, Japan. k-ishida@fancy.ocn.ne.jp","institution_ids":["https://openalex.org/I161296585"]},{"raw_affiliation_string":"Department of Chemistry and Frontier Research Center for Computational Science, Faculty of Science, Science University of Tokyo, Shinjuku\u2010ku, Tokyo 162\u20108601, Japan","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108252601"],"corresponding_institution_ids":["https://openalex.org/I161296585","https://openalex.org/I74801974"],"apc_list":{"value":4840,"currency":"USD","value_usd":4840},"apc_paid":null,"fwci":0.7536,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.71548431,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"3","first_page":"378","last_page":"393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9997000098228455,"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":0.9997000098228455,"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/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"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":0.9970999956130981,"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/harmonics","display_name":"Harmonics","score":0.6594545841217041},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.6499928832054138},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5289331078529358},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.489876925945282},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.4320046603679657},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.4287107586860657},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4281000792980194},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41569316387176514},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3929029107093811},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3582730293273926},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.3403487801551819},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33929574489593506},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3312676250934601},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2713684141635895},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2588222026824951},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15313377976417542}],"concepts":[{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.6594545841217041},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.6499928832054138},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5289331078529358},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.489876925945282},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.4320046603679657},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.4287107586860657},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4281000792980194},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41569316387176514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3929029107093811},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3582730293273926},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.3403487801551819},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33929574489593506},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3312676250934601},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2713684141635895},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2588222026824951},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15313377976417542},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"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":2,"locations":[{"id":"doi:10.1002/jcc.10016","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jcc.10016","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":"pmid:11908501","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/11908501","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,"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":"Journal of computational chemistry","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322832","display_name":"University of Tokyo","ror":"https://ror.org/057zh3y96"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1977646543","https://openalex.org/W1978664561","https://openalex.org/W1981655171","https://openalex.org/W1984549626","https://openalex.org/W1987752850","https://openalex.org/W1990626714","https://openalex.org/W2003050169","https://openalex.org/W2014611981","https://openalex.org/W2016293616","https://openalex.org/W2031324175","https://openalex.org/W2044682544","https://openalex.org/W2054510591","https://openalex.org/W2055316829","https://openalex.org/W2057061175","https://openalex.org/W2061038638","https://openalex.org/W2073972481","https://openalex.org/W2078177861","https://openalex.org/W2087394433","https://openalex.org/W2089442143","https://openalex.org/W2091485425","https://openalex.org/W2095126010","https://openalex.org/W2095999364","https://openalex.org/W2161637189","https://openalex.org/W4251375550"],"related_works":["https://openalex.org/W2370517014","https://openalex.org/W2039242888","https://openalex.org/W2515867587","https://openalex.org/W1838021708","https://openalex.org/W1579696083","https://openalex.org/W94697941","https://openalex.org/W2131300395","https://openalex.org/W2367352519","https://openalex.org/W4206226528","https://openalex.org/W2004163324"],"abstract_inverted_index":{"A":[0],"series":[1,104],"of":[2,33,42,47,140,158,168],"accompanying":[3],"coordinate":[4],"expansion":[5],"(ACE)":[6],"formulas":[7,62],"for":[8,164],"calculating":[9,134],"the":[10,31,34,43,50,64,83,103,119,127,147,156,159,165,184,189,196],"electron":[11],"repulsion":[12],"integral":[13],"(ERI)":[14],"over":[15,170],"both":[16,171],"generally":[17,172],"and":[18,49,82,131,173],"segmentally":[19,174],"contracted":[20,175],"solid":[21,38,52,67,87],"harmonic":[22,39,53],"(SH)":[23],"Gaussian-type":[24],"orbitals":[25],"(GTOs)":[26],"can":[27,114],"be":[28,115],"rederived":[29],"by":[30,155],"use":[32,157],"modified":[35],"operator":[36],"(called":[37],"gradient":[40,46,54],"here)":[41],"spherical":[44],"tensor":[45],"Bayman":[48],"reducing":[51,65,84],"defined":[55,69,89],"in":[56,70,102,124,195],"this":[57],"article.":[58],"The":[59],"final":[60],"general":[61,100,112,120],"contain":[63],"mixed":[66,86],"harmonics":[68,88],"a":[71],"previous":[72],"article":[73],"[Ishida,":[74,91],"K.":[75,92],"J":[76,93],"Chem":[77,94],"Phys":[78,95],"1999,":[79],"111,":[80],"4913]":[81],"triply":[85],"previously":[90,128],"2000,":[96],"113,":[97],"7818].":[98],"Each":[99],"formula":[101,121],"is":[105,162,181,187],"named":[106,122],"ACEb1k1,":[107],"ACEb2k3,":[108,123],"or":[109],"ACEb3k3.":[110,132],"New":[111],"algorithm":[113],"obtained":[116],"inductively":[117],"from":[118],"addition":[125],"to":[126],"developed":[129],"ACEb1k1":[130],"For":[133],"ERI":[135],"practically,":[136],"we":[137],"select":[138],"one":[139],"these":[141],"ACE":[142,186],"algorithms,":[143],"as":[144],"it":[145],"gives":[146],"minimum":[148],"floating-point":[149],"operation":[150],"(FLOP)":[151],"count.":[152],"Theoretical":[153],"assessment":[154],"FLOP":[160],"count":[161],"performed":[163],"(LL/LL)":[166],"class":[167],"ERIs":[169],"SH-GTOs":[176],"(L":[177],"=":[178],"1-3).":[179],"It":[180],"found":[182],"that":[183],"present":[185],"theoretically":[188],"fastest":[190],"among":[191],"all":[192],"rigorous":[193],"methods":[194],"literature.":[197]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
