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Regression analyses indicate that hybrid functionals (B3LYP, O3LYP, and PBE0) rank among the best ones with a slope of typically 0.5, i.e., 100% overestimation with a standard error of about 50\u2002cm\u22121. The efficiency of the highly ranked functionals for predicting the correct \u201cexact states\u201d (after diagonalization of the Heisenberg Hamiltonian) is validated, and a statistical standard error is assigned for each functional. The singular value decomposition approach is used for treating the overdetermination of the system of equations when the number of magnetic centers is greater than 3. Further discussions particularly about the fortuitous success of the Becke00-x-only functional for treating hydrogenic models are presented.<\/jats:p>","DOI":"10.1063\/1.3264570","type":"journal-article","created":{"date-parts":[[2009,12,11]],"date-time":"2009-12-11T23:36:39Z","timestamp":1260574599000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":19,"title":["Density functional estimations of Heisenberg exchange constants in oligonuclear magnetic compounds: Assessment of density functional theory versus <i>ab initio<\/i>"],"prefix":"10.1063","volume":"131","author":[{"given":"Samir","family":"Zein","sequence":"first","affiliation":[{"name":"Katholieke Universiteit Leuven 1 Afdeling Kwantumchemie en Fysicochemie, , Celestijnenlaan 200 F-bus 2404, B-3001 Heverlee, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mahboubeh","family":"Poor Kalhor","sequence":"additional","affiliation":[{"name":"Universit\u00e9 De Lyon 2 Laboratoire de Chimie Physique Th\u00e9orique, Universit\u00e9 Lyon 1 et CNRS UMR 5180 Sciences Analytiques, , b\u00e2t Dirac, 43 Bd. du 11 Novembre 1918, 69622 Villeurbanne Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liviu F.","family":"Chibotaru","sequence":"additional","affiliation":[{"name":"Katholieke Universiteit Leuven 1 Afdeling Kwantumchemie en Fysicochemie, , Celestijnenlaan 200 F-bus 2404, B-3001 Heverlee, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Henry","family":"Chermette","sequence":"additional","affiliation":[{"name":"Universit\u00e9 De Lyon 2 Laboratoire de Chimie Physique Th\u00e9orique, Universit\u00e9 Lyon 1 et CNRS UMR 5180 Sciences Analytiques, , b\u00e2t Dirac, 43 Bd. du 11 Novembre 1918, 69622 Villeurbanne Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2009,12,11]]},"reference":[{"key":"2023080221080006200_c1a","doi-asserted-by":"crossref","first-page":"4414","DOI":"10.1021\/cr050185y","volume":"107","year":"2007","journal-title":"Chem. 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