{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T05:17:58Z","timestamp":1772687878472,"version":"3.50.1"},"reference-count":60,"publisher":"AIP Publishing","issue":"11","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2010,9,21]]},"abstract":"<jats:p>A linear least-squares methodology was used to determine the vibrational scaling factors for the X3LYP density functional. Uncertainties for these scaling factors were calculated according to the method devised by Irikura et al. [J. Phys. Chem. A\u2008109, 8430 (2005)]. The calibration set was systematically partitioned according to several of its descriptors and the scaling factors for X3LYP were recalculated for each subset. The results show that the scaling factors are only significant up to the second digit, irrespective of the calibration set used. Furthermore, multivariate statistical analysis allowed us to conclude that the scaling factors and the associated uncertainties are independent of the size of the calibration set and strongly suggest the practical impossibility of obtaining vibrational scaling factors with more than two significant digits.<\/jats:p>","DOI":"10.1063\/1.3493630","type":"journal-article","created":{"date-parts":[[2010,9,20]],"date-time":"2010-09-20T22:10:01Z","timestamp":1285020601000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":35,"title":["Calibration sets and the accuracy of vibrational scaling factors: A case study with the X3LYP hybrid functional"],"prefix":"10.1063","volume":"133","author":[{"given":"Filipe","family":"Teixeira","sequence":"first","affiliation":[{"name":"Universidade do Porto 1 Departamento de Qu\u00edmica e Bioqu\u00edmica, REQUIMTE, Faculdade de Ci\u00eancias, , Rua do Campo Alegre, 687, 4169-007 Porto, Portugal"}]},{"given":"Andr\u00e9","family":"Melo","sequence":"additional","affiliation":[{"name":"Universidade do Porto 1 Departamento de Qu\u00edmica e Bioqu\u00edmica, REQUIMTE, Faculdade de Ci\u00eancias, , Rua do Campo Alegre, 687, 4169-007 Porto, Portugal"}]},{"given":"M. Nat\u00e1lia D. S.","family":"Cordeiro","sequence":"additional","affiliation":[{"name":"Universidade de Vigo 2 Departamento de Qu\u00edmica F\u00edsica, , Campus Universitario Lagoas-Marcosende, 36310 Vigo, Spain"}]}],"member":"317","published-online":{"date-parts":[[2010,9,20]]},"reference":[{"key":"2023062605021464700_c1","doi-asserted-by":"publisher","first-page":"3949","DOI":"10.1039\/b005091l","volume":"2","year":"2000","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023062605021464700_c2","doi-asserted-by":"publisher","first-page":"2121","DOI":"10.1016\/j.saa.2004.06.059","volume":"61","year":"2005","journal-title":"Spectrochim. Acta, Part A"},{"key":"2023062605021464700_c3","doi-asserted-by":"publisher","first-page":"11897","DOI":"10.1021\/jp021357n","volume":"106","year":"2002","journal-title":"J. Phys. Chem. A"},{"key":"2023062605021464700_c4","doi-asserted-by":"publisher","first-page":"608","DOI":"10.1002\/poc.652","volume":"16","year":"2003","journal-title":"J. Phys. Org. Chem."},{"key":"2023062605021464700_c5","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1063\/1.1723744","volume":"10","year":"1942","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c6","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1007\/s00214-007-0376-5","volume":"118","year":"2007","journal-title":"Theor. Chem. Acc."},{"key":"2023062605021464700_c7","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1002\/qua.560200829","volume":"20","year":"1981","journal-title":"Int. J. Quantum Chem., Quantum Chem. Symp."},{"key":"2023062605021464700_c8","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1063\/1.448805","volume":"82","year":"1985","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c9","doi-asserted-by":"publisher","first-page":"14689","DOI":"10.1021\/j100040a017","volume":"99","year":"1995","journal-title":"J. Phys. Chem."},{"key":"2023062605021464700_c10","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/0166-1280(95)04333-8","volume":"357","year":"1995","journal-title":"THEOCHEM"},{"key":"2023062605021464700_c11","doi-asserted-by":"publisher","first-page":"3093","DOI":"10.1021\/j100010a019","volume":"99","year":"1995","journal-title":"J. Phys. Chem."},{"key":"2023062605021464700_c12","doi-asserted-by":"publisher","first-page":"5927","DOI":"10.1021\/j100016a030","volume":"99","year":"1995","journal-title":"J. Phys. Chem."},{"key":"2023062605021464700_c13","doi-asserted-by":"publisher","first-page":"16502","DOI":"10.1021\/jp960976r","volume":"100","year":"1996","journal-title":"J. Phys. Chem."},{"key":"2023062605021464700_c14","doi-asserted-by":"publisher","first-page":"9213","DOI":"10.1021\/jp048233q","volume":"108","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"2023062605021464700_c15","doi-asserted-by":"publisher","first-page":"2937","DOI":"10.1021\/jp045733a","volume":"109","year":"2005","journal-title":"J. Phys. Chem. A"},{"key":"2023062605021464700_c16","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.theochem.2005.12.007","volume":"760","year":"2006","journal-title":"THEOCHEM"},{"key":"2023062605021464700_c17","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/s002140000204","volume":"105","year":"2001","journal-title":"Theor. Chem. Acc."},{"key":"2023062605021464700_c18","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1134\/1.1563679","volume":"94","year":"2003","journal-title":"Opt. Spectrosc."},{"key":"2023062605021464700_c19","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/0009-2614(96)00483-6","volume":"256","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2023062605021464700_c20","doi-asserted-by":"publisher","first-page":"8430","DOI":"10.1021\/jp052793n","volume":"109","year":"2005","journal-title":"J. Phys. Chem. A"},{"key":"2023062605021464700_c21","doi-asserted-by":"publisher","first-page":"114102","DOI":"10.1063\/1.3086931","volume":"130","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c22","volume-title":"Guide to the Expression of Uncertainty in Measurement","year":"1995","edition":"2nd ed."},{"key":"2023062605021464700_c23","author":"Linstrom","year":"2009"},{"key":"2023062605021464700_c24","volume-title":"Tables of Molecular Vibrational Frequencies Consolidated","year":"1972"},{"key":"2023062605021464700_c25","doi-asserted-by":"publisher","first-page":"3411","DOI":"10.1063\/1.461942","volume":"96","year":"1992","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c26","doi-asserted-by":"publisher","first-page":"2438","DOI":"10.1063\/1.453135","volume":"87","year":"1987","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c27","doi-asserted-by":"publisher","first-page":"6566","DOI":"10.1063\/1.457375","volume":"91","year":"1989","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c28","doi-asserted-by":"publisher","first-page":"5469","DOI":"10.1063\/1.464896","volume":"98","year":"1993","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c29","doi-asserted-by":"publisher","first-page":"014306","DOI":"10.1063\/1.1812755","volume":"122","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c30","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/0009-2614(96)00411-3","volume":"256","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2023062605021464700_c31","doi-asserted-by":"publisher","first-page":"8955","DOI":"10.1063\/1.474028","volume":"106","year":"1997","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c32","doi-asserted-by":"publisher","first-page":"1504","DOI":"10.1063\/1.457110","volume":"91","year":"1989","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c33","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1006\/jmsp.1999.7807","volume":"195","year":"1999","journal-title":"J. Mol. Spectrosc."},{"key":"2023062605021464700_c34","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/S0009-2614(99)00756-3","volume":"311","year":"1999","journal-title":"Chem. Phys. Lett."},{"key":"2023062605021464700_c35","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1006\/jmsp.1994.1102","volume":"164","year":"1994","journal-title":"J. Mol. Spectrosc."},{"key":"2023062605021464700_c36","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0022-2852(86)90010-X","volume":"120","year":"1986","journal-title":"J. Mol. Spectrosc."},{"key":"2023062605021464700_c37","doi-asserted-by":"publisher","first-page":"3837","DOI":"10.1039\/ft9908603837","volume":"86","year":"1990","journal-title":"J. Chem. Soc., Faraday Trans."},{"key":"2023062605021464700_c38","doi-asserted-by":"publisher","first-page":"7601","DOI":"10.1063\/1.459391","volume":"93","year":"1990","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c39","doi-asserted-by":"publisher","first-page":"5805","DOI":"10.1063\/1.473246","volume":"106","year":"1996","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c40","doi-asserted-by":"publisher","first-page":"9764","DOI":"10.1063\/1.475274","volume":"107","year":"1997","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c41","doi-asserted-by":"publisher","first-page":"1544","DOI":"10.1063\/1.1747538","volume":"18","year":"1950","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c42","doi-asserted-by":"publisher","first-page":"9154","DOI":"10.1021\/jp992224d","volume":"103","year":"1999","journal-title":"J. Phys. Chem. A"},{"key":"2023062605021464700_c43","doi-asserted-by":"publisher","first-page":"2457","DOI":"10.1063\/1.1725546","volume":"40","year":"1964","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c44","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1016\/0022-2852(89)90003-9","volume":"138","year":"1989","journal-title":"J. Mol. Spectrosc."},{"key":"2023062605021464700_c45","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1016\/0022-2852(88)90224-X","volume":"128","year":"1988","journal-title":"J. Mol. Spectrosc."},{"key":"2023062605021464700_c46","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1063\/1.2436891","volume":"36","year":"2007","journal-title":"J. Phys. Chem. Ref. Data"},{"key":"2023062605021464700_c47","doi-asserted-by":"publisher","first-page":"9173","DOI":"10.1063\/1.463343","volume":"97","year":"1992","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c48","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1103\/PhysRevB.37.785","volume":"37","year":"1988","journal-title":"Phys. Rev. B"},{"key":"2023062605021464700_c49","doi-asserted-by":"publisher","first-page":"014105","DOI":"10.1063\/1.1812257","volume":"122","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c50","doi-asserted-by":"publisher","first-page":"2673","DOI":"10.1073\/pnas.0308730100","volume":"101","year":"2004","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2023062605021464700_c51","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.1002\/jcc.540141112","volume":"14","year":"1993","journal-title":"J. Comput. Chem."},{"key":"2023062605021464700_c52","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1002\/(SICI)1096-987X(199610)17:13<1571::AID-JCC9>3.0.CO;2-P","volume":"17","year":"1996","journal-title":"J. Comput. Chem."},{"key":"2023062605021464700_c53","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1021\/ci600510j","volume":"47","year":"2007","journal-title":"J. Chem. Inf. Model."},{"key":"2023062605021464700_c54","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/S1093-3263(99)00002-9","volume":"16","year":"1998","journal-title":"J. Mol. Graphics Modell."},{"key":"2023062605021464700_c55","author":"R Development Core Team","year":"2009"},{"key":"2023062605021464700_c56","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1360\/jos180001","volume":"18","year":"2007","journal-title":"J. Stat. Software"},{"key":"2023062605021464700_c57","unstructured":"See supplementary material at http:\/\/dx.doi.org\/10.1063\/1.3493630 for the molecular set and scaling factors determined using all calibration sets at all levels of theory."},{"key":"2023062605021464700_c58","doi-asserted-by":"publisher","first-page":"2118","DOI":"10.1063\/1.1670373","volume":"49","year":"1968","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c59","doi-asserted-by":"publisher","first-page":"2342","DOI":"10.1063\/1.1682312","volume":"61","year":"1974","journal-title":"J. Chem. Phys."},{"key":"2023062605021464700_c60","doi-asserted-by":"publisher","first-page":"1913","DOI":"10.1016\/S0584-8539(09)91006-6","volume":"49","year":"1993","journal-title":"Spectrochim. Acta, Part A"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/1.3493630\/15430239\/114109_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/1.3493630\/15430239\/114109_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T05:02:22Z","timestamp":1687755742000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/133\/11\/114109\/189125\/Calibration-sets-and-the-accuracy-of-vibrational"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,20]]},"references-count":60,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2010,9,21]]}},"URL":"https:\/\/doi.org\/10.1063\/1.3493630","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2010,9,21]]},"published":{"date-parts":[[2010,9,20]]},"article-number":"114109"}}