{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T13:01:31Z","timestamp":1770555691786,"version":"3.49.0"},"reference-count":58,"publisher":"IOP Publishing","issue":"21","license":[{"start":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T00:00:00Z","timestamp":1552953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T00:00:00Z","timestamp":1552953600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["SFRH\/BPD\/78610\/2011"],"award-info":[{"award-number":["SFRH\/BPD\/78610\/2011"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Phys.: Condens. Matter"],"published-print":{"date-parts":[[2019,5,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We present a scheme that interpolates the energy bands of a crystal with a modified tight-binding Hamiltonian. We start from a pseudopotential plane-wave calculation of the eigenvalues in a three-dimensional coarse uniform grid of k-points in the Brillouin zone and from the evaluation of the single particle Hamiltonian and overlap matrix elements for a small localised basis set of atomic orbitals in the same k-point grid. A simple matrix manipulation procedure that replaces the eigenvalues obtained from the atomic orbital method by the eigenvalues of the plane-wave method generates the modified tight-binding Hamiltonian on the coarse grid. A subsequent three-dimensional Fourier interpolation of the modified tight-binding Hamiltonian and overlap matrices leads to a fast, yet accurate, determination of interpolated Hamiltonians and overlap matrices at an arbitrary k-point, or in a denser grid of k-points. We present examples of the application of the scheme to density functional calculations of germanium, graphite, graphene, copper and a SiGe superlattice.<\/jats:p>","DOI":"10.1088\/1361-648x\/ab0932","type":"journal-article","created":{"date-parts":[[2019,2,21]],"date-time":"2019-02-21T17:45:54Z","timestamp":1550771154000},"page":"215501","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Practical band interpolation with a modified tight-binding method"],"prefix":"10.1088","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8193-6964","authenticated-orcid":false,"given":"Carlos L","family":"Reis","sequence":"first","affiliation":[]},{"given":"Jos\u00e9 Lu\u00eds","family":"Martins","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2019,3,19]]},"reference":[{"key":"cmab0932bib001","doi-asserted-by":"publisher","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","type":"journal-article","volume":"136","author":"Hohenberg","year":"1964","journal-title":"Phys. Rev."},{"key":"cmab0932bib002","doi-asserted-by":"publisher","first-page":"A1133","DOI":"10.1103\/PhysRev.140.A1133","type":"journal-article","volume":"140","author":"Kohn","year":"1965","journal-title":"Phys. Rev."},{"key":"cmab0932bib003","doi-asserted-by":"publisher","first-page":"4409","DOI":"10.1088\/0022-3719\/12\/21\/009","type":"journal-article","volume":"12","author":"Ihm","year":"1979","journal-title":"J. Phys. C: Solid State Phys."},{"key":"cmab0932bib004","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/0167-7977(89)90002-6","type":"journal-article","volume":"9","author":"Pickett","year":"1989","journal-title":"Comput. Phys. Rep."},{"key":"cmab0932bib005","doi-asserted-by":"publisher","author":"Martin","year":"2004","DOI":"10.1017\/CBO9780511805769","type":"book"},{"key":"cmab0932bib006","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/BF02959829","type":"journal-article","volume":"11","author":"Fermi","year":"1934","journal-title":"Nuovo Cimento"},{"key":"cmab0932bib007","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1103\/PhysRev.116.287","type":"journal-article","volume":"116","author":"Phillips","year":"1959","journal-title":"Phys. Rev."},{"key":"cmab0932bib008","doi-asserted-by":"publisher","first-page":"1498","DOI":"10.1103\/PhysRev.94.1498","type":"journal-article","volume":"94","author":"Slater","year":"1954","journal-title":"Phys. Rev."},{"key":"cmab0932bib009","doi-asserted-by":"publisher","first-page":"4745","DOI":"10.1103\/PhysRevB.24.4745","type":"journal-article","volume":"24","author":"Bachelet","year":"1981","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib010","doi-asserted-by":"publisher","first-page":"3470","DOI":"10.1103\/PhysRevB.29.3470","type":"journal-article","volume":"29","author":"Chelikowsky","year":"1984","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib011","doi-asserted-by":"publisher","first-page":"3979","DOI":"10.1103\/PhysRevB.40.3979","type":"journal-article","volume":"40","author":"Sankey","year":"1989","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib012","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.cpc.2006.03.007","type":"journal-article","volume":"175","author":"Madsen","year":"2006","journal-title":"Comput. Phys. Commun."},{"key":"cmab0932bib013","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1016\/j.commatsci.2017.11.034","type":"journal-article","volume":"143","author":"Nardelli","year":"2018","journal-title":"Comput. Mater. Sci."},{"key":"cmab0932bib014","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1016\/j.cpc.2013.09.015","type":"journal-article","volume":"185","author":"Pizzi","year":"2014","journal-title":"Comput. Phys. Commun."},{"key":"cmab0932bib015","doi-asserted-by":"publisher","first-page":"869","DOI":"10.1103\/PhysRev.97.869","type":"journal-article","volume":"97","author":"Luttinger","year":"1955","journal-title":"Phys. Rev."},{"key":"cmab0932bib016","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1103\/PhysRev.98.368","type":"journal-article","volume":"98","author":"Dresselhaus","year":"1955","journal-title":"Phys. Rev."},{"key":"cmab0932bib017","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/0022-3697(56)90014-2","type":"journal-article","volume":"1","author":"Kane","year":"1956","journal-title":"J. Phys. Chem. Solids"},{"key":"cmab0932bib018","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1103\/PhysRev.142.530","type":"journal-article","volume":"142","author":"Cardona","year":"1966","journal-title":"Phys. Rev."},{"key":"cmab0932bib019","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1103\/PhysRev.178.1419","type":"journal-article","volume":"178","author":"Euwema","year":"1969","journal-title":"Phys. Rev."},{"key":"cmab0932bib020","doi-asserted-by":"publisher","first-page":"2721","DOI":"10.1103\/PhysRevB.38.2721","type":"journal-article","volume":"38","author":"Pickett","year":"1988","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib021","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1007\/BF01339455","type":"journal-article","volume":"52","author":"Bloch","year":"1929","journal-title":"Z. Phys."},{"key":"cmab0932bib022","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1088\/0034-4885\/60\/12\/001","type":"journal-article","volume":"60","author":"Goringe","year":"1997","journal-title":"Rep. Prog. Phys."},{"key":"cmab0932bib023","doi-asserted-by":"publisher","first-page":"12520","DOI":"10.1103\/PhysRevB.39.12520","type":"journal-article","volume":"39","author":"Foulkes","year":"1989","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib024","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1103\/RevModPhys.84.1419","type":"journal-article","volume":"84","author":"Marzari","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"cmab0932bib025","doi-asserted-by":"publisher","first-page":"2745","DOI":"10.1088\/0953-8984\/14\/11\/302","type":"journal-article","volume":"14","author":"Soler","year":"2002","journal-title":"J. Phys.: Condens. Matter"},{"key":"cmab0932bib026","doi-asserted-by":"publisher","first-page":"12947","DOI":"10.1103\/PhysRevB.51.12947","type":"journal-article","volume":"51","author":"Porezag","year":"1995","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib027","doi-asserted-by":"publisher","first-page":"12847","DOI":"10.1103\/PhysRevB.56.12847","type":"journal-article","volume":"56","author":"Marzari","year":"1997","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib028","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.65.035109","type":"journal-article","volume":"65","author":"Souza","year":"2001","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib029","doi-asserted-by":"publisher","first-page":"A685","DOI":"10.1103\/PhysRev.135.A685","type":"journal-article","volume":"135","author":"Cloizeaux","year":"1964","journal-title":"Phys. Rev."},{"key":"cmab0932bib030","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.88.165127","type":"journal-article","volume":"88","author":"Agapito","year":"2013","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib031","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.93.035104","type":"journal-article","volume":"93","author":"Agapito","year":"2016","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib032","doi-asserted-by":"publisher","first-page":"2571","DOI":"10.1103\/PhysRevLett.53.2571","type":"journal-article","volume":"53","author":"Andersen","year":"1984","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib033","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.70.041101","type":"journal-article","volume":"70","author":"Lu","year":"2004","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib034","doi-asserted-by":"publisher","first-page":"1425","DOI":"10.1103\/PhysRevLett.48.1425","type":"journal-article","volume":"48","author":"Kleinman","year":"1982","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib035","doi-asserted-by":"publisher","first-page":"2471","DOI":"10.1103\/PhysRevLett.55.2471","type":"journal-article","volume":"55","author":"Car","year":"1985","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib036","doi-asserted-by":"publisher","first-page":"6134","DOI":"10.1103\/PhysRevB.37.6134","type":"journal-article","volume":"37","author":"Martins","year":"1988","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib037","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.89.165102","type":"journal-article","volume":"89","author":"Reis","year":"2014","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib038","doi-asserted-by":"publisher","first-page":"5188","DOI":"10.1103\/PhysRevB.13.5188","type":"journal-article","volume":"13","author":"Monkhorst","year":"1976","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib039","volume":"vol 1","author":"Press","year":"1992","type":"book"},{"key":"cmab0932bib040","doi-asserted-by":"publisher","first-page":"1993","DOI":"10.1103\/PhysRevB.43.1993","type":"journal-article","volume":"43","author":"Troullier","year":"1991","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib041","doi-asserted-by":"publisher","first-page":"5048","DOI":"10.1103\/PhysRevB.23.5048","type":"journal-article","volume":"23","author":"Perdew","year":"1981","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib042","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1103\/PhysRevLett.45.566","type":"journal-article","volume":"45","author":"Ceperley","year":"1980","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib043","doi-asserted-by":"publisher","DOI":"10.1063\/1.2213970","type":"journal-article","volume":"124","author":"Becke","year":"2006","journal-title":"J. Chem. Phys."},{"key":"cmab0932bib044","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1039\/9781849734790-00168","type":"book","volume":"vol 9","author":"Civalleri","year":"2012"},{"key":"cmab0932bib045","doi-asserted-by":"publisher","first-page":"4165","DOI":"10.1021\/acs.jpclett.6b01807","type":"journal-article","volume":"7","author":"Garza","year":"2016","journal-title":"J. Phys. Chem. Lett."},{"key":"cmab0932bib046","doi-asserted-by":"publisher","first-page":"5288","DOI":"10.1021\/jp509980w","type":"journal-article","volume":"119","author":"Pernot","year":"2015","journal-title":"J. Phys. Chem. A"},{"key":"cmab0932bib047","doi-asserted-by":"publisher","first-page":"2272","DOI":"10.1016\/j.cpc.2012.05.007","type":"journal-article","volume":"183","author":"Marques","year":"2012","journal-title":"Comput. Phys. Commun."},{"key":"cmab0932bib048","doi-asserted-by":"publisher","first-page":"7185","DOI":"10.1103\/PhysRevB.46.7185","type":"journal-article","volume":"46","author":"Schabel","year":"1992","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib049","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1103\/PhysRevLett.65.84","type":"journal-article","volume":"65","author":"Baroni","year":"1990","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib050","doi-asserted-by":"publisher","first-page":"9625","DOI":"10.1103\/PhysRevB.56.9625","type":"journal-article","volume":"56","author":"Dargam","year":"1997","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib051","doi-asserted-by":"publisher","first-page":"4725","DOI":"10.1103\/PhysRevLett.80.4725","type":"journal-article","volume":"80","author":"Wang","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib052","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.71.115215","type":"journal-article","volume":"71","author":"Boykin","year":"2005","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib053","doi-asserted-by":"publisher","DOI":"10.1088\/0953-8984\/19\/3\/036203","type":"journal-article","volume":"19","author":"Boykin","year":"2007","journal-title":"J. Phys.: Condens. Matter"},{"key":"cmab0932bib054","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.236403","type":"journal-article","volume":"104","author":"Popescu","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib055","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.85.085201","type":"journal-article","volume":"85","author":"Popescu","year":"2012","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib056","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.216401","type":"journal-article","volume":"104","author":"Ku","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"cmab0932bib057","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.87.085322","type":"journal-article","volume":"87","author":"Allen","year":"2013","journal-title":"Phys. Rev. B"},{"key":"cmab0932bib058","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/16\/3\/033034","type":"journal-article","volume":"16","author":"Huang","year":"2014","journal-title":"New J. Phys."}],"container-title":["Journal of Physics: Condensed Matter"],"original-title":[],"link":[{"URL":"http:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"http:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"http:\/\/stacks.iop.org\/0953-8984\/31\/i=21\/a=215501\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/stacks.iop.org\/0953-8984\/31\/i=21\/a=215501?key=crossref.ba66d09c1697e9ab50941be767479a8f","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"http:\/\/stacks.iop.org\/0953-8984\/31\/i=21\/a=215501\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/stacks.iop.org\/0953-8984\/31\/i=21\/a=215501?key=crossref.ba66d09c1697e9ab50941be767479a8f","content-type":"text\/html","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T13:23:48Z","timestamp":1770470628000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/ab0932"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,19]]},"references-count":58,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2019,3,19]]},"published-print":{"date-parts":[[2019,5,29]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-648x\/ab0932","relation":{},"ISSN":["0953-8984","1361-648X"],"issn-type":[{"value":"0953-8984","type":"print"},{"value":"1361-648X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,19]]},"assertion":[{"value":"Practical band interpolation with a modified tight-binding method","name":"article_title","label":"Article Title"},{"value":"Journal of Physics: Condensed Matter","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2019 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2018-12-18","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-02-21","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2019-03-19","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}