{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T10:11:07Z","timestamp":1788603067288,"version":"build-2803163510"},"reference-count":36,"publisher":"AIP Publishing","issue":"19","funder":[{"name":"Fondet til professor Leif Trondstads minne"},{"DOI":"10.13039\/501100004209","name":"Otto M\u00f8nsteds Fond","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004209","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["263110"],"award-info":[{"award-number":["263110"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["765739"],"award-info":[{"award-number":["765739"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2019,5,21]]},"abstract":"<jats:p>Approximating the electron repulsion integrals using inner projections is a well-established approach to reduce the computational demands of electronic structure calculations. Here, we present a two-step Cholesky decomposition algorithm where only the elements of the Cholesky basis (the pivots) are determined in the pivoting procedure. This allows for improved screening, significantly reducing memory usage and computational cost. After the pivots have been determined, the Cholesky vectors are constructed using the inner projection formulation. We also propose a partitioned decomposition approach where the Cholesky basis is chosen from a reduced set generated by decomposing diagonal blocks of the matrix. The algorithm extends the application range of the methodology and is well suited for multilevel methods. We apply the algorithm to systems with up to 80 000 atomic orbitals. The accuracy of the integral approximations is demonstrated for a formaldehyde-water system using a new Cholesky-based CCSD implementation.<\/jats:p>","DOI":"10.1063\/1.5083802","type":"journal-article","created":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T13:51:36Z","timestamp":1558360296000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":76,"title":["An efficient algorithm for Cholesky decomposition of electron repulsion integrals"],"prefix":"10.1063","volume":"150","author":[{"given":"Sarai D.","family":"Folkestad","sequence":"first","affiliation":[{"name":"Department of Chemistry, Norwegian University of Science and Technology 1 , N-7491 Trondheim, Norway"},{"name":"Scuola Normale Superiore 2 , Piazza dei Cavaleri 7, 56126 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eirik F.","family":"Kj\u00f8nstad","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Norwegian University of Science and Technology 1 , N-7491 Trondheim, Norway"},{"name":"Scuola Normale Superiore 2 , Piazza dei Cavaleri 7, 56126 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8367-8727","authenticated-orcid":false,"given":"Henrik","family":"Koch","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Norwegian University of Science and Technology 1 , N-7491 Trondheim, Norway"},{"name":"Scuola Normale Superiore 2 , Piazza dei Cavaleri 7, 56126 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2019,5,20]]},"reference":[{"key":"2023062522053526800_c1","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1002\/qua.560120408","volume":"12","year":"1977","journal-title":"Int. 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