{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:08:15Z","timestamp":1753870095862,"version":"3.41.2"},"reference-count":39,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T00:00:00Z","timestamp":1603929600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/05367\/2020"],"award-info":[{"award-number":["UID\/05367\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Physica Status Solidi (b)"],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:sec><jats:label\/><jats:p>Herein, an interpolation scheme for energy and wave functions of a crystal using a generalization of Luttinger\u2013Kohn functions is presented. For each <jats:bold>k<\/jats:bold>\u2010point where the interpolated bands are desired, a variational orthogonal basis is constructed using a singular value decomposition (SVD) where the Luttinger\u2013Kohn functions are derived from reference <jats:bold>k<\/jats:bold>\u2010points. A crucial step of the scheme is that before the SVD, the Luttinger\u2013Kohn functions are multiplied by weights that depend on the distance between the reference <jats:bold>k<\/jats:bold>\u2010points and the <jats:bold>k<\/jats:bold>\u2010point to be interpolated. After the SVD, the less relevant orthogonal functions may be discarded. In contrast with some other methods, it is a true interpolation and it is continuous, it does not require a starting localized basis set or band disentanglement or any specific information from the user. The procedure should be straightforward to implement in most electronic\u2010structure codes. Examples of the application of the scheme to density functional calculations of silicon, copper, and rhombohedral graphite are presented.<\/jats:p><\/jats:sec>","DOI":"10.1002\/pssb.202000260","type":"journal-article","created":{"date-parts":[[2020,10,14]],"date-time":"2020-10-14T19:29:12Z","timestamp":1602703752000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Practical Band Interpolation with a Generalized Luttinger\u2013Kohn Method"],"prefix":"10.1002","volume":"258","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8193-6964","authenticated-orcid":false,"given":"Carlos L.","family":"Reis","sequence":"first","affiliation":[{"name":"Materials Simulation Group INESC-MN  Rua Alves Redol 9 1000-029 Lisboa Portugal"}]},{"given":"Jos\u00e9 Lu\u00eds","family":"Martins","sequence":"additional","affiliation":[{"name":"Materials Simulation Group INESC-MN  Rua Alves Redol 9 1000-029 Lisboa Portugal"},{"name":"Departamento de Fsica Instituto Superior T\u00e9cnico Universidade de Lisboa  Av. Rovisco Pais 1049-001 Lisboa Portugal"}]}],"member":"311","published-online":{"date-parts":[[2020,10,29]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.94.1498"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.97.869"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.98.368"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-3697(56)90014-2"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.84.1419"},{"volume-title":"The Art of Parallel Scientific Computing","year":"1996","author":"Press W. 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If we do a Fourier interpolation and then we discard small components the function will pass close but strictly not through the reference points and no cost function is minimized. By strict interpolation we mean that the interpolating function passes through the interpolated points."},{"key":"e_1_2_7_28_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.37.6134"},{"key":"e_1_2_7_29_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.55.2471"},{"key":"e_1_2_7_30_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.43.1993"},{"key":"e_1_2_7_31_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.48.1425"},{"key":"e_1_2_7_32_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.13.5188"},{"key":"e_1_2_7_33_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.23.5048"},{"key":"e_1_2_7_34_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.45.566"},{"key":"e_1_2_7_35_1","doi-asserted-by":"publisher","DOI":"10.1139\/p58-036"},{"key":"e_1_2_7_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/0008-6223(94)90192-9"},{"key":"e_1_2_7_37_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.84.165404"},{"key":"e_1_2_7_38_1","unstructured":"In Bernal (hexagonal) graphite \u03c0 bands cross at a high symmetry point that is degenerate by symmetry. By choosing multiples of 3 for the number of BZ sampling points in the layer plane a zero shift and the conventional lattice vectors the points where bands cross near the Fermi level are included in the coarse reference grid. In rhombohedral graphite there is no such trick as the degeneracy of the \u03c0 bands occurs on a symmetry line not at symmetry point."},{"key":"e_1_2_7_39_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1129696"},{"key":"e_1_2_7_40_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-648X\/ab51ff"}],"container-title":["physica status solidi (b)"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pssb.202000260","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/pssb.202000260","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pssb.202000260","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T09:19:44Z","timestamp":1693646384000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/pssb.202000260"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,29]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1002\/pssb.202000260"],"URL":"https:\/\/doi.org\/10.1002\/pssb.202000260","archive":["Portico"],"relation":{},"ISSN":["0370-1972","1521-3951"],"issn-type":[{"type":"print","value":"0370-1972"},{"type":"electronic","value":"1521-3951"}],"subject":[],"published":{"date-parts":[[2020,10,29]]},"assertion":[{"value":"2020-05-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-10-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"2000260"}}