{"id":"https://openalex.org/W2058730565","doi":"https://doi.org/10.1103/physrevb.57.3799","title":"Order- N method for a nonorthogonal tight-binding Hamiltonian","display_name":"Order- N method for a nonorthogonal tight-binding Hamiltonian","publication_year":1998,"publication_date":"1998-02-15","ids":{"openalex":"https://openalex.org/W2058730565","doi":"https://doi.org/10.1103/physrevb.57.3799","mag":"2058730565"},"language":"en","primary_location":{"id":"doi:10.1103/physrevb.57.3799","doi":"https://doi.org/10.1103/physrevb.57.3799","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.57.3799","pdf_url":null,"source":{"id":"https://openalex.org/S4210174675","display_name":"Physical review. B, Condensed matter","issn_l":"0163-1829","issn":["0163-1829","1095-3795"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","ki-jl-2"],"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"},"parent_works":[],"lineage":["https://openalex.org/W2058730565"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5109057803","display_name":"C. S. Jayanthi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. S. Jayanthi","raw_affiliation_strings":["Department of Physics, University of Louisville, Louisville, Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067088561","display_name":"Shiyu Wu","orcid":"https://orcid.org/0000-0002-8809-8326","observed_orcids":["https://orcid.org/0000-0002-8809-8326"]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Y. Wu","raw_affiliation_strings":["Department of Physics, University of Louisville, Louisville, Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026031830","display_name":"J. A. Cocks","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Cocks","raw_affiliation_strings":["Department of Physics, University of Louisville, Louisville, Kentucky 40292","Information Technology, University of Louisville, Louisville, Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]},{"raw_affiliation_string":"Information Technology, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108437317","display_name":"N. S. Luo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. S. Luo","raw_affiliation_strings":["Department of Physics, University of Louisville, Louisville, Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036727003","display_name":"Zun Xie","orcid":"https://orcid.org/0000-0001-6964-0661","observed_orcids":["https://orcid.org/0000-0001-6964-0661"]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Z. L. Xie","raw_affiliation_strings":["Department of Physics, University of Louisville, Louisville, Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048056000","display_name":"Madhu Menon","orcid":"https://orcid.org/0000-0002-8283-138X","observed_orcids":["https://orcid.org/0000-0002-8283-138X","https://orcid.org/0000-0003-4278-7588"]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]},{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Menon","raw_affiliation_strings":["Department of Physics, University of Louisville, Louisville, Kentucky 40292","Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky, 40506"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]},{"raw_affiliation_string":"Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky, 40506","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101488530","display_name":"Gang Yang","orcid":"https://orcid.org/0000-0003-2613-5387","observed_orcids":["https://orcid.org/0000-0003-2613-5387"]},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. Yang","raw_affiliation_strings":["Department of Physics, University of Louisville, Louisville, Kentucky 40292"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Louisville, Louisville, Kentucky 40292","institution_ids":["https://openalex.org/I142740786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2687,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.86918825,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"57","issue":"7","first_page":"3799","last_page":"3802"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9589999914169312,"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":0.9589999914169312,"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/T13531","display_name":"Surface and Thin Film Phenomena","score":0.005400000140070915,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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":0.00419999985024333,"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/total-energy-calculations","display_name":"total energy calculations","score":0.8360000252723694},{"id":"https://openalex.org/keywords/atomic-forces","display_name":"atomic forces","score":0.9660000205039978},{"id":"https://openalex.org/keywords/silicon-clusters","display_name":"silicon clusters","score":0.8029999732971191},{"id":"https://openalex.org/keywords/equilibrium-configurations","display_name":"equilibrium configurations","score":0.6629999876022339},{"id":"https://openalex.org/keywords/annealing-and-quenching","display_name":"quenching and annealing","score":0.8960000276565552},{"id":"https://openalex.org/keywords/molecular-dynamics","display_name":"molecular dynamics","score":0.7820000052452087},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.5299999713897705}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.7226474285125732},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.6130653023719788},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.43698850274086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39016062021255493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3521576523780823},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2484770119190216},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23813247680664062},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07910177111625671},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrevb.57.3799","doi":"https://doi.org/10.1103/physrevb.57.3799","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.57.3799","pdf_url":null,"source":{"id":"https://openalex.org/S4210174675","display_name":"Physical review. B, Condensed matter","issn_l":"0163-1829","issn":["0163-1829","1095-3795"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","ki-jl-2"],"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":23,"referenced_works":["https://openalex.org/W580971478","https://openalex.org/W1964357583","https://openalex.org/W1974792239","https://openalex.org/W1982961891","https://openalex.org/W1982991255","https://openalex.org/W1986751761","https://openalex.org/W1986827037","https://openalex.org/W1991050432","https://openalex.org/W2001762863","https://openalex.org/W2002796843","https://openalex.org/W2025652901","https://openalex.org/W2028090311","https://openalex.org/W2033429577","https://openalex.org/W2035721486","https://openalex.org/W2039214958","https://openalex.org/W2062120937","https://openalex.org/W2065742525","https://openalex.org/W2068725607","https://openalex.org/W2072258077","https://openalex.org/W2084990884","https://openalex.org/W2089405697","https://openalex.org/W2090628212","https://openalex.org/W2149751265"],"related_works":["https://openalex.org/W1964113030","https://openalex.org/W2075225978","https://openalex.org/W2082029872","https://openalex.org/W1974341315","https://openalex.org/W2062810454","https://openalex.org/W2069396629","https://openalex.org/W1995640797","https://openalex.org/W2146189340","https://openalex.org/W2995219767","https://openalex.org/W1977173487"],"abstract_inverted_index":{"We":[0,19],"have":[1,20],"developed":[2],"an":[3],"order-$N$":[4],"method":[5],"to":[6],"calculate":[7],"the":[8,23,33,54],"total":[9],"energy":[10],"and":[11,63],"atomic":[12],"forces":[13],"for":[14,36,46],"a":[15,37,47,58],"nonorthogonal":[16],"tight-binding":[17],"Hamiltonian.":[18],"first":[21],"confirmed":[22],"validity":[24],"of":[25,43,57],"our":[26,30,44],"approach":[27,45],"by":[28,52],"comparing":[29],"results":[31],"with":[32],"exact":[34],"calculation":[35],"small":[38],"silicon":[39],"cluster.":[40],"The":[41],"efficiency":[42],"large":[48],"system":[49],"is":[50],"demonstrated":[51],"determining":[53],"equilibrium":[55],"configuration":[56],"${\\mathrm{Si}}_{1000}$":[59],"cluster":[60],"using":[61],"quenching":[62],"annealing":[64],"techniques":[65],"based":[66],"on":[67],"molecular":[68],"dynamics.":[69]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}