{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T05:54:26Z","timestamp":1781589266987,"version":"3.54.5"},"reference-count":40,"publisher":"AIP Publishing","issue":"23","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2020-06420"],"award-info":[{"award-number":["RGPIN-2020-06420"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004489","name":"Mitacs","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004489","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,6,21]]},"abstract":"<jats:p>Basis sets consisting of functions that form linearly independent products (LIPs) have remarkable applications in quantum chemistry but are scarce because of mathematical limitations. We show how to linearly transform a given set of basis functions to maximize the linear independence of their products by maximizing the determinant of the appropriate Gram matrix. The proposed method enhances the utility of the LIP basis set technology and clarifies why canonical molecular orbitals form LIPs more readily than atomic orbitals. The same approach can also be used to orthogonalize basis functions themselves, which means that various orthogonalization techniques may be viewed as special cases of a certain nonlinear optimization problem.<\/jats:p>","DOI":"10.1063\/5.0210971","type":"journal-article","created":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T09:39:25Z","timestamp":1718703565000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Maximization of linear independence of basis function products"],"prefix":"10.1063","volume":"160","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1021-4401","authenticated-orcid":false,"given":"Georgii N.","family":"Sizov","sequence":"first","affiliation":[{"name":"Department of Chemistry, The University of Western Ontario , London Ontario N6A 5B7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-8208-4793","authenticated-orcid":false,"given":"Vincent","family":"Lazeran","sequence":"additional","affiliation":[{"name":"Department of Chemistry, The University of Western Ontario , London Ontario N6A 5B7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-3930-3457","authenticated-orcid":false,"given":"Lloren\u00e7","family":"Balada Gaggioli","sequence":"additional","affiliation":[{"name":"Department of Chemistry, The University of Western Ontario , London Ontario N6A 5B7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6828-3815","authenticated-orcid":false,"given":"Viktor N.","family":"Staroverov","sequence":"additional","affiliation":[{"name":"Department of Chemistry, The University of Western Ontario , London Ontario N6A 5B7, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"key":"2024061809392225200_c1","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1103\/physreva.27.632","article-title":"Geometry of density matrices. 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