{"id":"https://openalex.org/W2091842285","doi":"https://doi.org/10.1002/(sici)1096-987x(199608)17:11<1287::aid-jcc1>3.0.co;2-i","title":"Simultaneous integration of mixed quantum-classical systems by density matrix evolution equations using interaction representation and adaptive time step integrator","display_name":"Simultaneous integration of mixed quantum-classical systems by density matrix evolution equations using interaction representation and adaptive time step integrator","publication_year":1996,"publication_date":"1996-08-01","ids":{"openalex":"https://openalex.org/W2091842285","doi":"https://doi.org/10.1002/(sici)1096-987x(199608)17:11<1287::aid-jcc1>3.0.co;2-i","mag":"2091842285","pmid":"https://pubmed.ncbi.nlm.nih.gov/25400147"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1096-987x(199608)17:11<1287::aid-jcc1>3.0.co;2-i","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(199608)17:11<1287::aid-jcc1>3.0.co;2-i","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/A5054179571","display_name":"Marc F. Lensink","orcid":"https://orcid.org/0000-0003-3957-9470"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Marc F. Lensink","raw_affiliation_strings":["BIOSON Research Institute, Department of Biophysical Chemistry, the University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands","BIOSON Research Institute, Department of Biophysical Chemistry, The University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"BIOSON Research Institute, Department of Biophysical Chemistry, the University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"BIOSON Research Institute, Department of Biophysical Chemistry, The University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081106233","display_name":"Janez Mavri","orcid":"https://orcid.org/0000-0002-0767-6367"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Janez Mavri","raw_affiliation_strings":["BIOSON Research Institute, Department of Biophysical Chemistry, the University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands","BIOSON Research Institute, Department of Biophysical Chemistry, The University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"BIOSON Research Institute, Department of Biophysical Chemistry, the University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"BIOSON Research Institute, Department of Biophysical Chemistry, The University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083564020","display_name":"Herman J. C. Berendsen","orcid":null},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Herman J. C. Berendsen","raw_affiliation_strings":["BIOSON Research Institute, Department of Biophysical Chemistry, the University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands","Faculty of Science and Engineering"],"affiliations":[{"raw_affiliation_string":"BIOSON Research Institute, Department of Biophysical Chemistry, the University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"Faculty of Science and Engineering","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083564020"],"corresponding_institution_ids":["https://openalex.org/I169381384"],"apc_list":{"value":4840,"currency":"USD","value_usd":4840},"apc_paid":null,"fwci":0.5175,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.64820468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"17","issue":"11","first_page":"1287","last_page":"1295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11177","display_name":"Spectroscopy and Quantum Chemical Studies","score":0.998199999332428,"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/T11177","display_name":"Spectroscopy and Quantum Chemical Studies","score":0.998199999332428,"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/T11416","display_name":"Numerical methods for differential equations","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9923999905586243,"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/integrator","display_name":"Integrator","score":0.7762719988822937},{"id":"https://openalex.org/keywords/density-matrix","display_name":"Density matrix","score":0.660892128944397},{"id":"https://openalex.org/keywords/harmonic-oscillator","display_name":"Harmonic oscillator","score":0.6538559198379517},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5848168134689331},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.5643226504325867},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5336559414863586},{"id":"https://openalex.org/keywords/time-evolution","display_name":"Time evolution","score":0.46745190024375916},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.4575464129447937},{"id":"https://openalex.org/keywords/quantum-harmonic-oscillator","display_name":"Quantum harmonic oscillator","score":0.4227152466773987},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4203074872493744},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40211328864097595},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3823970556259155},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.37186744809150696},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3617328405380249},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2880319654941559},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2832604646682739},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.22476553916931152},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09699246287345886},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07827463746070862}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.7762719988822937},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.660892128944397},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.6538559198379517},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5848168134689331},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.5643226504325867},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5336559414863586},{"id":"https://openalex.org/C106553664","wikidata":"https://www.wikidata.org/wiki/Q1156744","display_name":"Time evolution","level":2,"score":0.46745190024375916},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.4575464129447937},{"id":"https://openalex.org/C122332657","wikidata":"https://www.wikidata.org/wiki/Q677864","display_name":"Quantum harmonic oscillator","level":3,"score":0.4227152466773987},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4203074872493744},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40211328864097595},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3823970556259155},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.37186744809150696},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3617328405380249},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2880319654941559},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2832604646682739},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.22476553916931152},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09699246287345886},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07827463746070862},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/(sici)1096-987x(199608)17:11<1287::aid-jcc1>3.0.co;2-i","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-987x(199608)17:11<1287::aid-jcc1>3.0.co;2-i","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:25400147","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25400147","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},{"id":"pmh:oai:dipot.ulb.ac.be:2013/234229","is_oa":false,"landing_page_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/234229/3/Lensink1996.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of computational chemistry, 17 (11","raw_type":"info:ulb-repo/semantics/openurl/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W616844775","https://openalex.org/W1619326219","https://openalex.org/W1969728895","https://openalex.org/W1971346858","https://openalex.org/W1973805557","https://openalex.org/W1975223395","https://openalex.org/W1978997652","https://openalex.org/W1987598922","https://openalex.org/W1995412269","https://openalex.org/W1999354240","https://openalex.org/W2006019045","https://openalex.org/W2007274640","https://openalex.org/W2012549881","https://openalex.org/W2015876808","https://openalex.org/W2017192136","https://openalex.org/W2018687780","https://openalex.org/W2025514257","https://openalex.org/W2032238232","https://openalex.org/W2036167508","https://openalex.org/W2046001409","https://openalex.org/W2046300008","https://openalex.org/W2051320909","https://openalex.org/W2060565668","https://openalex.org/W2074674667","https://openalex.org/W2079823795","https://openalex.org/W2089128598","https://openalex.org/W2089258537","https://openalex.org/W2092144432","https://openalex.org/W2093136987","https://openalex.org/W2103734924","https://openalex.org/W2104099426","https://openalex.org/W2106140689","https://openalex.org/W2111267460","https://openalex.org/W2123300247","https://openalex.org/W2746718465","https://openalex.org/W4251744914"],"related_works":["https://openalex.org/W2035711260","https://openalex.org/W2955062048","https://openalex.org/W2299929204","https://openalex.org/W2058138583","https://openalex.org/W4237937763","https://openalex.org/W3016716526","https://openalex.org/W2085454897","https://openalex.org/W3105018232","https://openalex.org/W2127766232","https://openalex.org/W1977730396"],"abstract_inverted_index":{"A":[0],"density":[1],"matrix":[2],"evolution":[3],"method":[4],"[H.":[5],"J.":[6,10,12],"C.":[7],"Berendsen":[8],"and":[9,62],"Mavri,":[11],"Phys.":[13],"Chem.,":[14],"97,":[15],"13464":[16],"(1993)]":[17],"to":[18,32],"simulate":[19],"the":[20,34,49,54,59,65,68,74,96],"dynamics":[21],"of":[22,37,67,73],"quantum":[23,44],"systems":[24],"embedded":[25],"in":[26,58,90],"a":[27,38,42],"classical":[28,39],"environment":[29],"is":[30],"applied":[31],"study":[33],"inelastic":[35],"collisions":[36],"particle":[40],"with":[41,81],"five-level":[43],"harmonic":[45],"oscillator.":[46,70],"We":[47],"improved":[48],"numerical":[50],"performance":[51],"by":[52,102],"rewriting":[53],"Liouville-von":[55],"Neumann":[56],"equation":[57],"interaction":[60],"representation":[61],"so":[63],"eliminated":[64],"frequencies":[66],"unperturbed":[69],"Furthermore,":[71],"replacement":[72],"fixed":[75],"time":[76],"step":[77,84],"fourth-order":[78,87],"Runge-Kutta":[79,88],"integrator":[80],"an":[82],"adaptive":[83],"size":[85],"control":[86],"resulted":[89],"significantly":[91],"lower":[92],"computational":[93],"effort":[94],"at":[95],"same":[97],"desired":[98],"accuracy.":[99],"\u00a9":[100],"1996":[101],"John":[103],"Wiley":[104],"&":[105],"Sons,":[106],"Inc.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
