{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T18:41:47Z","timestamp":1783449707898,"version":"3.55.0"},"reference-count":81,"publisher":"AIP Publishing","issue":"1","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["396890929\/GRK 2482"],"award-info":[{"award-number":["396890929\/GRK 2482"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,7,7]]},"abstract":"<jats:p>We present an efficient implementation of nonadiabatic coupling matrix elements (NACMEs) for density functional theory\/multireference configuration interaction (DFT\/MRCI) wave functions of singlet and triplet multiplicity and an extension of the Vibes program that allows us to determine rate constants for internal conversion (IC) in addition to intersystem crossing (ISC) nonradiative transitions. Following the suggestion of Plasser et al. [J. Chem. Theory Comput. 12, 1207 (2016)], the derivative couplings are computed as finite differences of wave function overlaps. Several measures have been taken to speed up the calculation of the NACMEs. Schur\u2019s determinant complement is employed to build up the determinant of the full matrix of spin-blocked orbital overlaps from precomputed spin factors with fixed orbital occupation. Test calculations on formaldehyde, pyrazine, and xanthone show that the mutual excitation level of the configurations at the reference and displaced geometries can be restricted to 1. In combination with a cutoff parameter of tnorm = 10\u22128 for the DFT\/MRCI wave function expansion, this approximation leads to substantial savings of cpu time without essential loss of precision. With regard to applications, the photoexcitation decay kinetics of xanthone in apolar media and in aqueous solution is in the focus of the present work. The results of our computational study substantiate the conjecture that S1\u2008 T2 reverse ISC outcompetes the T2 \u219d T1 IC in aqueous solution, thus explaining the occurrence of delayed fluorescence in addition to prompt fluorescence.<\/jats:p>","DOI":"10.1063\/5.0056182","type":"journal-article","created":{"date-parts":[[2021,7,2]],"date-time":"2021-07-02T10:16:47Z","timestamp":1625221007000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":24,"title":["Internal conversion of singlet and triplet states employing numerical DFT\/MRCI derivative couplings: Implementation, tests, and application to xanthone"],"prefix":"10.1063","volume":"155","author":[{"given":"Mario","family":"Bracker","sequence":"first","affiliation":[{"name":"Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University D\u00fcsseldorf , Universit\u00e4tsstra\u00dfe 1, 40225 D\u00fcsseldorf, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7148-0900","authenticated-orcid":false,"given":"Christel M.","family":"Marian","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University D\u00fcsseldorf , Universit\u00e4tsstra\u00dfe 1, 40225 D\u00fcsseldorf, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7433-3938","authenticated-orcid":false,"given":"Martin","family":"Kleinschmidt","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University D\u00fcsseldorf , Universit\u00e4tsstra\u00dfe 1, 40225 D\u00fcsseldorf, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2021,7,2]]},"reference":[{"key":"2023070116384440800_c1","doi-asserted-by":"publisher","first-page":"5645","DOI":"10.1063\/1.479866","volume":"111","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c2","doi-asserted-by":"publisher","first-page":"044708","DOI":"10.1063\/1.3062842","volume":"130","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c3","doi-asserted-by":"publisher","first-page":"e1394","DOI":"10.1002\/wcms.1394","volume":"9","year":"2019","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023070116384440800_c4","doi-asserted-by":"publisher","first-page":"104103","DOI":"10.1063\/1.2973541","volume":"129","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c5","doi-asserted-by":"publisher","first-page":"1501","DOI":"10.1021\/ct8001738","volume":"4","year":"2008","journal-title":"J. Chem. Theory Comput."},{"key":"2023070116384440800_c6","doi-asserted-by":"publisher","first-page":"034104","DOI":"10.1063\/1.4940036","volume":"144","year":"2016","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c7","doi-asserted-by":"publisher","first-page":"164106","DOI":"10.1063\/1.5050476","volume":"149","year":"2018","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c8","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1002\/jcc.10064","volume":"23","year":"2002","journal-title":"J. Comput. Chem."},{"key":"2023070116384440800_c9","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.chemphys.2004.10.025","volume":"311","year":"2005","journal-title":"Chem. Phys."},{"key":"2023070116384440800_c10","doi-asserted-by":"publisher","first-page":"124101","DOI":"10.1063\/1.2173246","volume":"124","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c11","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1002\/wcms.83","volume":"2","year":"2012","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023070116384440800_c12","doi-asserted-by":"publisher","first-page":"3935","DOI":"10.1021\/jp401755j","volume":"117","year":"2013","journal-title":"J. Phys. Chem. A"},{"key":"2023070116384440800_c13","doi-asserted-by":"publisher","first-page":"114104","DOI":"10.1063\/1.4868484","volume":"140","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c14","doi-asserted-by":"publisher","first-page":"6975","DOI":"10.1021\/acs.chemrev.7b00617","volume":"118","year":"2018","journal-title":"Chem. Rev."},{"key":"2023070116384440800_c15","doi-asserted-by":"publisher","first-page":"044107","DOI":"10.1063\/1.3292571","volume":"132","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c16","doi-asserted-by":"publisher","first-page":"014110","DOI":"10.1063\/1.4885817","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c17","doi-asserted-by":"publisher","first-page":"024114","DOI":"10.1063\/1.4887256","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c18","doi-asserted-by":"publisher","first-page":"064109","DOI":"10.1063\/1.4907376","volume":"142","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c19","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1063\/1.478179","volume":"110","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c20","doi-asserted-by":"publisher","first-page":"124104","DOI":"10.1063\/1.3232011","volume":"131","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c21","doi-asserted-by":"publisher","first-page":"044103","DOI":"10.1063\/1.5009433","volume":"148","year":"2018","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c22","doi-asserted-by":"publisher","first-page":"4549","DOI":"10.1063\/1.447428","volume":"81","year":"1984","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c23","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/0009-2614(85)80935-0","volume":"113","year":"1984","journal-title":"Chem. Phys. Lett."},{"key":"2023070116384440800_c24","doi-asserted-by":"publisher","first-page":"7573","DOI":"10.1063\/1.463477","volume":"97","year":"1992","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c25","doi-asserted-by":"publisher","first-page":"154107","DOI":"10.1063\/1.4932613","volume":"143","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c26","doi-asserted-by":"publisher","first-page":"3636","DOI":"10.1021\/acs.jctc.6b00384","volume":"12","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"2023070116384440800_c27","doi-asserted-by":"publisher","first-page":"2561","DOI":"10.1021\/acs.jctc.7b00018","volume":"13","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"2023070116384440800_c28","doi-asserted-by":"publisher","first-page":"7322","DOI":"10.1063\/1.1668615","volume":"120","year":"2004","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c29","doi-asserted-by":"publisher","first-page":"7330","DOI":"10.1063\/1.1668631","volume":"120","year":"2004","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c30","doi-asserted-by":"publisher","first-page":"2703","DOI":"10.1080\/00268976.2010.521777","volume":"108","year":"2010","journal-title":"Mol. Phys."},{"key":"2023070116384440800_c31","doi-asserted-by":"publisher","first-page":"5532","DOI":"10.1063\/1.438971","volume":"72","year":"1980","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c32","doi-asserted-by":"publisher","first-page":"1132","DOI":"10.1021\/ct300798t","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023070116384440800_c33","doi-asserted-by":"publisher","first-page":"4657","DOI":"10.1063\/1.467455","volume":"101","year":"1994","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c34","doi-asserted-by":"publisher","first-page":"023001","DOI":"10.1103\/physrevlett.98.023001","volume":"98","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"2023070116384440800_c35","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.chemphys.2008.10.013","volume":"356","year":"2009","journal-title":"Chem. Phys."},{"key":"2023070116384440800_c36","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1002\/9780470142813.ch2","volume":"57","year":"1984","journal-title":"Adv. Chem. Phys."},{"key":"2023070116384440800_c37","doi-asserted-by":"publisher","first-page":"21145","DOI":"10.1021\/acs.jpcc.7b06187","volume":"121","year":"2017","journal-title":"J. Phys. Chem. C"},{"key":"2023070116384440800_c38","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1021\/acs.jctc.5b01148","volume":"12","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"2023070116384440800_c39","doi-asserted-by":"publisher","first-page":"114110","DOI":"10.1063\/1.5143126","volume":"152","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c40","doi-asserted-by":"publisher","first-page":"10072","DOI":"10.1021\/jp047583+","volume":"108","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"2023070116384440800_c41","doi-asserted-by":"publisher","first-page":"3432","DOI":"10.1039\/b603560d","volume":"8","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023070116384440800_c42","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1146\/annurev.pc.19.100168.001113","volume":"19","year":"1968","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2023070116384440800_c43","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1063\/1.1674940","volume":"54","year":"1971","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c44","first-page":"153","volume-title":"Organic Molecular Photophysics","author":"Birks","year":"1973"},{"key":"2023070116384440800_c45","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1002\/9780470125908","volume-title":"Reviews in Computational Chemistry","author":"Lipkowitz","year":"1999; 2001"},{"key":"2023070116384440800_c46","doi-asserted-by":"publisher","first-page":"5209","DOI":"10.1039\/b706410a","volume":"9","year":"2007","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023070116384440800_c47","doi-asserted-by":"publisher","first-page":"2133","DOI":"10.1039\/b518436c","volume":"8","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023070116384440800_c48","doi-asserted-by":"publisher","first-page":"154105","DOI":"10.1063\/1.3575582","volume":"134","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c49","doi-asserted-by":"publisher","first-page":"4740","DOI":"10.1039\/c3cp53247j","volume":"16","year":"2014","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023070116384440800_c50","volume-title":"Introduction to Quantum Mechanics: A Time-Dependent Perspective","year":"2006"},{"key":"2023070116384440800_c51","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1515\/crll.1866.66.161","volume":"66","year":"1866","journal-title":"J. Reine Angew. Math."},{"key":"2023070116384440800_c52","doi-asserted-by":"publisher","first-page":"956","DOI":"10.1103\/revmodphys.31.956","volume":"31","year":"1959","journal-title":"Rev. Mod. Phys."},{"key":"2023070116384440800_c53","doi-asserted-by":"publisher","first-page":"9454","DOI":"10.1021\/jp073280e","volume":"111","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"2023070116384440800_c54","doi-asserted-by":"publisher","first-page":"3461","DOI":"10.1021\/acs.jctc.9b00235","volume":"15","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"2023070116384440800_c55","volume-title":"Numerical Linear Algebra","year":"1997"},{"key":"2023070116384440800_c56","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1021\/acs.jctc.8b01049","volume":"15","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"2023070116384440800_c57","doi-asserted-by":"publisher","first-page":"e1370","DOI":"10.1002\/wcms.1400","volume":"8","year":"2018","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023070116384440800_c58","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1002\/wcms.25","volume":"1","year":"2011","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023070116384440800_c59","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1039\/b008063m","volume":"3","year":"2001","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023070116384440800_c60","article-title":"COLUMBUS, an ab initio electronic structure program, release 7.0","year":"2017"},{"key":"2023070116384440800_c61","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1016\/0009-2614(93)89151-7","volume":"213","year":"1993","journal-title":"Chem. Phys. Lett."},{"key":"2023070116384440800_c62","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/s0009-2614(98)00862-8","volume":"294","year":"1998","journal-title":"Chem. Phys. Lett."},{"key":"2023070116384440800_c63","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1016\/0022-2852(88)90343-8","volume":"132","year":"1988","journal-title":"J. Mol. Spectrosc."},{"key":"2023070116384440800_c64","doi-asserted-by":"publisher","first-page":"5298","DOI":"10.1063\/1.462715","volume":"96","year":"1992","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c65","doi-asserted-by":"publisher","first-page":"1400","DOI":"10.1063\/1.466618","volume":"100","year":"1994","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c66","doi-asserted-by":"publisher","first-page":"4412","DOI":"10.1063\/1.472327","volume":"105","year":"1996","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c67","doi-asserted-by":"publisher","first-page":"936","DOI":"10.1063\/1.478061","volume":"110","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c68","doi-asserted-by":"publisher","first-page":"7157","DOI":"10.1021\/jp981597w","volume":"102","year":"1998","journal-title":"J. Phys. Chem. A"},{"key":"2023070116384440800_c69","doi-asserted-by":"publisher","first-page":"819","DOI":"10.2298\/jsc190510048d","volume":"84","year":"2019","journal-title":"J. Serb. Chem. Soc."},{"key":"2023070116384440800_c70","doi-asserted-by":"publisher","first-page":"1537","DOI":"10.1139\/v93-193","volume":"71","year":"1993","journal-title":"Can. J. Chem."},{"key":"2023070116384440800_c71","unstructured":"TURBOMOLE, A Development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989\u20132007, TURBOMOLE GmbH, since 2007; available from http:\/\/www.turbomole.com."},{"key":"2023070116384440800_c72","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1016\/0009-2614(96)00782-8","volume":"259","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2023070116384440800_c73","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/s1010-6030(00)00374-9","volume":"137","year":"2000","journal-title":"J. Photochem. Photobiol., A"},{"key":"2023070116384440800_c74","doi-asserted-by":"publisher","first-page":"6429","DOI":"10.1021\/ja00753a016","volume":"93","year":"1971","journal-title":"J. Am. Chem. Soc."},{"key":"2023070116384440800_c75","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.1002\/jrs.4954","volume":"47","year":"2016","journal-title":"J. Raman Spectrosc."},{"key":"2023070116384440800_c76","doi-asserted-by":"publisher","first-page":"8410","DOI":"10.1021\/jp051510o","volume":"109","year":"2005","journal-title":"J. Phys. Chem. A"},{"key":"2023070116384440800_c77","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.jphotochem.2008.03.015","volume":"198","year":"2008","journal-title":"J. Photochem. Photobiol., A"},{"key":"2023070116384440800_c78","doi-asserted-by":"publisher","first-page":"9912","DOI":"10.1039\/c9cp00805e","volume":"21","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023070116384440800_c79","doi-asserted-by":"publisher","first-page":"7980","DOI":"10.1063\/1.476233","volume":"108","year":"1998","journal-title":"J. Chem. Phys."},{"key":"2023070116384440800_c80","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1016\/j.cplett.2010.08.051","volume":"498","year":"2010","journal-title":"Chem. Phys. Lett."},{"key":"2023070116384440800_c81","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1146\/annurev-physchem-061020-053433","volume":"72","year":"2021","journal-title":"Annu. Rev. Phys. Chem."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0056182\/13761799\/014102_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\/5.0056182\/13761799\/014102_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T16:38:53Z","timestamp":1688229533000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/155\/1\/014102\/313213\/Internal-conversion-of-singlet-and-triplet-states"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,2]]},"references-count":81,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,7,7]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0056182","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,7,7]]},"published":{"date-parts":[[2021,7,2]]},"article-number":"014102"}}