{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T13:13:47Z","timestamp":1788354827406,"version":"build-2803163510"},"reference-count":199,"publisher":"AIP Publishing","issue":"19","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["CRC 1573"],"award-info":[{"award-number":["CRC 1573"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["471424360"],"award-info":[{"award-number":["471424360"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["Project Q"],"award-info":[{"award-number":["Project Q"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100021104","name":"TURBOMOLE","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100021104","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001663","name":"Volkswagen Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,11,21]]},"abstract":"<jats:p>An efficient implementation of zero-field splitting parameters based on the work of Schmitt et al. [J. Chem. Phys. 134, 194113 (2011)] is presented. Seminumerical integration techniques are used for the two-electron spin\u2013dipole contribution and the response equations of the spin\u2013orbit perturbation. The original formulation is further generalized. First, it is extended to meta-generalized gradient approximations and local hybrid functionals. For these functional classes, the response of the paramagnetic current density is considered in the coupled-perturbed Kohn\u2013Sham equations for the spin\u2013orbit perturbation term. Second, the spin\u2013orbit perturbation is formulated within relativistic exact two-component theory and the screened nuclear spin\u2013orbit (SNSO) approximation. The accuracy of the implementation is demonstrated for transition-metal and diatomic main-group compounds. The efficiency is assessed for Mn and Mo complexes. Here, it is found that coarse integration grids for the seminumerical schemes lead to drastic speedups while introducing clearly negligible errors. In addition, the SNSO approximation substantially reduces the computational demands and leads to very similar results as the spin\u2013orbit mean field Ansatz.<\/jats:p>","DOI":"10.1063\/5.0175758","type":"journal-article","created":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T05:58:44Z","timestamp":1700546324000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":10,"title":["Zero-field splitting parameters within exact two-component theory and modern density functional theory using seminumerical integration"],"prefix":"10.1063","volume":"159","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-8368-081X","authenticated-orcid":false,"given":"Florian","family":"Bruder","sequence":"first","affiliation":[{"name":"Fachbereich Chemie, Philipps-Universit\u00e4t Marburg 1 , Hans-Meerwein-Stra\u00dfe 4, 35032 Marburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8344-113X","authenticated-orcid":false,"given":"Yannick J.","family":"Franzke","sequence":"additional","affiliation":[{"name":"Fachbereich Chemie, Philipps-Universit\u00e4t Marburg 1 , Hans-Meerwein-Stra\u00dfe 4, 35032 Marburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8234-260X","authenticated-orcid":false,"given":"Christof","family":"Holzer","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT) 2 , Wolfgang-Gaede-Stra\u00dfe 1, 76131 Karlsruhe, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5060-1689","authenticated-orcid":false,"given":"Florian","family":"Weigend","sequence":"additional","affiliation":[{"name":"Fachbereich Chemie, Philipps-Universit\u00e4t Marburg 1 , Hans-Meerwein-Stra\u00dfe 4, 35032 Marburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2023,11,21]]},"reference":[{"key":"2023112110571831500_c1","doi-asserted-by":"publisher","first-page":"9566","DOI":"10.1103\/physrevb.60.9566","volume":"60","year":"1999","journal-title":"Phys. Rev. B"},{"key":"2023112110571831500_c2","doi-asserted-by":"publisher","first-page":"4699","DOI":"10.1103\/physrevb.59.4699","volume":"59","year":"1999","journal-title":"Phys. Rev. B"},{"key":"2023112110571831500_c3","doi-asserted-by":"publisher","first-page":"12267","DOI":"10.1021\/jp0643303","volume":"110","year":"2006","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c4","doi-asserted-by":"publisher","first-page":"10213","DOI":"10.1021\/ja061798a","volume":"128","year":"2006","journal-title":"J. Am. Chem. Soc."},{"key":"2023112110571831500_c5","doi-asserted-by":"publisher","first-page":"164112","DOI":"10.1063\/1.2772857","volume":"127","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c6","doi-asserted-by":"publisher","first-page":"2238","DOI":"10.1016\/j.poly.2005.03.087","volume":"24","year":"2005","journal-title":"Polyhedron"},{"key":"2023112110571831500_c7","doi-asserted-by":"publisher","first-page":"054110","DOI":"10.1063\/1.2227382","volume":"125","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c8","doi-asserted-by":"publisher","first-page":"194109","DOI":"10.1063\/1.3134430","volume":"130","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c9","doi-asserted-by":"publisher","first-page":"194113","DOI":"10.1063\/1.3590362","volume":"134","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c10","doi-asserted-by":"publisher","first-page":"184110","DOI":"10.1063\/1.4828727","volume":"139","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c11","doi-asserted-by":"publisher","first-page":"9857","DOI":"10.1021\/acs.jpca.6b10253","volume":"120","year":"2016","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c12","doi-asserted-by":"publisher","first-page":"2199","DOI":"10.1021\/acs.jctc.1c01115","volume":"18","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c13","doi-asserted-by":"publisher","first-page":"6568","DOI":"10.1021\/ic980948i","volume":"37","year":"1998","journal-title":"Inorg. Chem."},{"key":"2023112110571831500_c14","doi-asserted-by":"publisher","first-page":"2299","DOI":"10.1039\/a906648i","volume":"1999","journal-title":"J. Chem. Soc., Perkin Trans. 2"},{"key":"2023112110571831500_c15","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/s0301-0104(02)00451-2","volume":"279","year":"2002","journal-title":"Chem. Phys."},{"key":"2023112110571831500_c16","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/s0301-0104(02)00914-x","volume":"286","year":"2003","journal-title":"Chem. Phys."},{"key":"2023112110571831500_c17","doi-asserted-by":"publisher","first-page":"2470","DOI":"10.1002\/qua.21042","volume":"106","year":"2006","journal-title":"Int. J. Quantum Chem."},{"key":"2023112110571831500_c18","doi-asserted-by":"publisher","first-page":"024103","DOI":"10.1063\/1.2213976","volume":"125","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c19","doi-asserted-by":"publisher","first-page":"6021","DOI":"10.1039\/b902743b","volume":"2009","journal-title":"Dalton Trans."},{"key":"2023112110571831500_c20","doi-asserted-by":"publisher","first-page":"144111","DOI":"10.1063\/1.3367718","volume":"132","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c21","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/j.cplett.2009.07.007","volume":"477","year":"2009","journal-title":"Chem. Phys. Lett."},{"key":"2023112110571831500_c22","doi-asserted-by":"publisher","first-page":"3146","DOI":"10.1002\/cphc.201000492","volume":"11","year":"2010","journal-title":"ChemPhysChem"},{"key":"2023112110571831500_c23","doi-asserted-by":"publisher","first-page":"30128","DOI":"10.1039\/c7cp05533a","volume":"19","year":"2017","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c24","doi-asserted-by":"publisher","first-page":"e202100648","DOI":"10.1002\/cphc.202100648","volume":"23","year":"2022","journal-title":"ChemPhysChem"},{"key":"2023112110571831500_c25","doi-asserted-by":"publisher","first-page":"054113","DOI":"10.1063\/1.4789398","volume":"138","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c26","doi-asserted-by":"publisher","first-page":"4840","DOI":"10.1021\/acs.jctc.5b00656","volume":"11","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c27","doi-asserted-by":"publisher","first-page":"054108","DOI":"10.1063\/1.4906318","volume":"142","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c28","doi-asserted-by":"publisher","first-page":"21051","DOI":"10.1039\/c5cp07667f","volume":"18","year":"2016","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c29","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1002\/3527601678","volume-title":"Calculation of NMR and EPR Parameters: Theory and Applications","author":"Kaupp","year":"2004"},{"key":"2023112110571831500_c30","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1098\/rspa.1961.0008","volume":"259","year":"1961","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2023112110571831500_c31","volume-title":"Quantum Mechanics of One- and Two-Electron Atoms","year":"1957"},{"key":"2023112110571831500_c32","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1063\/1.449486","volume":"83","year":"1985","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c33","year":"2023"},{"key":"2023112110571831500_c34","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/0009-2614(85)80121-4","volume":"116","year":"1985","journal-title":"Chem. Phys. Lett."},{"key":"2023112110571831500_c35","doi-asserted-by":"publisher","first-page":"1462","DOI":"10.1063\/1.451237","volume":"85","year":"1986","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c36","doi-asserted-by":"publisher","first-page":"3522","DOI":"10.1063\/1.451955","volume":"86","year":"1987","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c37","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.chemphys.2008.10.036","volume":"356","year":"2009","journal-title":"Chem. Phys."},{"key":"2023112110571831500_c38","doi-asserted-by":"publisher","first-page":"144105","DOI":"10.1063\/1.3646921","volume":"135","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c39","doi-asserted-by":"publisher","first-page":"094111","DOI":"10.1063\/1.4819264","volume":"139","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c40","doi-asserted-by":"publisher","first-page":"104109","DOI":"10.1063\/5.0058766","volume":"155","year":"2021","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c41","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1002\/jcc.22901","volume":"33","year":"2012","journal-title":"J. Comput. Chem."},{"key":"2023112110571831500_c42","doi-asserted-by":"publisher","first-page":"184115","DOI":"10.1063\/5.0022755","volume":"153","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c43","doi-asserted-by":"publisher","first-page":"1456","DOI":"10.1021\/acs.jctc.9b00860","volume":"16","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c44","first-page":"1132","article-title":"Pseudospectral methods applied to the electron correlation problem","volume-title":"Modern Electronic Structure Theory: Part II","author":"Yarkony","year":"1995"},{"key":"2023112110571831500_c45","doi-asserted-by":"publisher","first-page":"1068","DOI":"10.1063\/1.1528936","volume":"118","year":"2003","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c46","doi-asserted-by":"publisher","first-page":"8870","DOI":"10.1063\/1.464444","volume":"98","year":"1993","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c47","doi-asserted-by":"publisher","first-page":"6935","DOI":"10.1063\/1.1503772","volume":"117","year":"2002","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c48","doi-asserted-by":"publisher","first-page":"205107","DOI":"10.1103\/physrevb.71.205107","volume":"71","year":"2005","journal-title":"Phys. Rev. B"},{"key":"2023112110571831500_c49","doi-asserted-by":"publisher","first-page":"164105","DOI":"10.1063\/1.4759080","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c50","doi-asserted-by":"publisher","first-page":"2928","DOI":"10.1021\/acs.jctc.1c00203","volume":"17","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c51","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1021\/acs.jctc.1c00999","volume":"18","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c52","doi-asserted-by":"publisher","first-page":"031102","DOI":"10.1063\/5.0103898","volume":"157","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c53","doi-asserted-by":"publisher","first-page":"5050","DOI":"10.1021\/acs.jpca.2c03579","volume":"126","year":"2022","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c54","doi-asserted-by":"publisher","first-page":"204102","DOI":"10.1063\/5.0122394","volume":"157","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c55","doi-asserted-by":"publisher","first-page":"1469","DOI":"10.1021\/acs.jctc.0c01223","volume":"17","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c56","doi-asserted-by":"publisher","first-page":"111102","DOI":"10.1063\/5.0113083","volume":"157","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c57","doi-asserted-by":"publisher","first-page":"4335","DOI":"10.1021\/acs.jpclett.2c01082","volume":"13","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"2023112110571831500_c58","doi-asserted-by":"publisher","first-page":"194101","DOI":"10.1063\/1.2370993","volume":"125","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c59","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s00214-007-0310-x","volume":"120","year":"2008","journal-title":"Theor. Chem. Acc."},{"key":"2023112110571831500_c60","doi-asserted-by":"publisher","first-page":"036402","DOI":"10.1103\/physrevlett.115.036402","volume":"115","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"2023112110571831500_c61","doi-asserted-by":"publisher","first-page":"8208","DOI":"10.1021\/acs.jpclett.0c02405","volume":"11","year":"2020","journal-title":"J. Phys. Chem. Lett."},{"key":"2023112110571831500_c62","doi-asserted-by":"publisher","first-page":"9248","DOI":"10.1021\/acs.jpclett.0c03077","volume":"11","year":"2020","journal-title":"J. Phys. Chem. Lett."},{"key":"2023112110571831500_c63","doi-asserted-by":"publisher","first-page":"134105","DOI":"10.1063\/5.0086040","volume":"156","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c64","doi-asserted-by":"publisher","first-page":"241102","DOI":"10.1063\/1.2137315","volume":"123","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c65","doi-asserted-by":"publisher","first-page":"114107","DOI":"10.1063\/1.2710258","volume":"126","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c66","doi-asserted-by":"publisher","first-page":"044102","DOI":"10.1063\/1.2222365","volume":"125","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c67","doi-asserted-by":"publisher","first-page":"149901","DOI":"10.1063\/1.2348637","volume":"125","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c68","doi-asserted-by":"publisher","first-page":"064102","DOI":"10.1063\/1.2436882","volume":"126","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c69","doi-asserted-by":"publisher","first-page":"031104","DOI":"10.1063\/1.3159445","volume":"131","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c70","doi-asserted-by":"publisher","first-page":"104106","DOI":"10.1063\/1.2772856","volume":"127","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c71","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1146\/annurev-physchem-032511-143755","volume":"63","year":"2012","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2023112110571831500_c72","doi-asserted-by":"publisher","first-page":"3077","DOI":"10.1002\/cphc.201100682","volume":"12","year":"2011","journal-title":"ChemPhysChem"},{"key":"2023112110571831500_c73","doi-asserted-by":"publisher","first-page":"150902","DOI":"10.1063\/1.3702628","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c74","doi-asserted-by":"publisher","first-page":"180901","DOI":"10.1063\/5.0008432","volume":"152","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c75","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1007\/s00214-011-1081-y","volume":"131","year":"2012","journal-title":"Theor. Chem. Acc."},{"key":"2023112110571831500_c76","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/978-1-4020-9975-5","article-title":"Relativistic effects on magnetic resonance parameters and other properties of inorganic molecules and metal complexes","volume-title":"Relativistic Methods for Chemists","author":"Barysz","year":"2010"},{"key":"2023112110571831500_c77","doi-asserted-by":"publisher","first-page":"20120489","DOI":"10.1098\/rsta.2012.0489","volume":"372","year":"2014","journal-title":"Philos. Trans. R. Soc., A"},{"key":"2023112110571831500_c78","volume-title":"Introduction to Relativistic Quantum Chemistry","year":"2007"},{"key":"2023112110571831500_c79","volume-title":"Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science","year":"2015","edition":"2nd ed."},{"key":"2023112110571831500_c80","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-40766-6","volume-title":"Handbook of Relativistic Quantum Chemistry","author":"Liu","year":"2017"},{"key":"2023112110571831500_c81","doi-asserted-by":"publisher","first-page":"2534","DOI":"10.1039\/c6cs00565a","volume":"47","year":"2018","journal-title":"Chem. Soc. Rev."},{"key":"2023112110571831500_c82","doi-asserted-by":"crossref","DOI":"10.1002\/3527601678","volume-title":"Calculation of NMR and EPR Parameters: Theory and Applications","author":"Kaupp","year":"2004"},{"key":"2023112110571831500_c83","first-page":"1","article-title":"Quantum chemistry and EPR parameters","volume-title":"eMagRes","author":"Harris","year":"2017"},{"key":"2023112110571831500_c84","volume-title":"EPR Spectroscopy: Fundamentals and Methods","author":"Goldfarb","year":"2018"},{"key":"2023112110571831500_c85","doi-asserted-by":"publisher","first-page":"244103","DOI":"10.1063\/1.2135290","volume":"123","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c86","doi-asserted-by":"publisher","first-page":"12892","DOI":"10.1021\/acs.jpca.5b10996","volume":"119","year":"2015","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c87","doi-asserted-by":"publisher","first-page":"1932","DOI":"10.1021\/ct301114z","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c88","doi-asserted-by":"publisher","first-page":"1052","DOI":"10.1021\/ct3009864","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c89","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1021\/acs.jctc.1c01027","volume":"18","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c90","doi-asserted-by":"publisher","first-page":"2246","DOI":"10.1021\/acs.jctc.1c01175","volume":"18","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c91","doi-asserted-by":"publisher","first-page":"5497","DOI":"10.1063\/1.471789","volume":"104","year":"1996","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c92","doi-asserted-by":"publisher","first-page":"2175","DOI":"10.1021\/ct200143w","volume":"7","year":"2011","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c93","doi-asserted-by":"publisher","first-page":"2360","DOI":"10.1103\/physrevlett.59.2360","volume":"59","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"2023112110571831500_c94","doi-asserted-by":"publisher","first-page":"124120","DOI":"10.1063\/1.4896302","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c95","doi-asserted-by":"publisher","first-page":"034108","DOI":"10.1063\/5.0100439","volume":"157","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c96","doi-asserted-by":"publisher","first-page":"e1378","DOI":"10.1002\/wcms.1378","volume":"9","year":"2018","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023112110571831500_c97","doi-asserted-by":"publisher","first-page":"014111","DOI":"10.1063\/1.3672080","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c98","doi-asserted-by":"publisher","first-page":"012509","DOI":"10.1103\/physreva.77.012509","volume":"77","year":"2008","journal-title":"Phys. Rev. A"},{"key":"2023112110571831500_c99","doi-asserted-by":"publisher","first-page":"204101","DOI":"10.1063\/1.4901238","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c100","doi-asserted-by":"publisher","first-page":"21133","DOI":"10.1039\/c6cp00990e","volume":"18","year":"2016","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c101","doi-asserted-by":"publisher","first-page":"1540","DOI":"10.1021\/ct501137x","volume":"11","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c102","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1021\/acs.jctc.9b00944","volume":"16","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c103","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/BF01113068","volume":"83","year":"1992","journal-title":"Theor. Chim. Acta"},{"key":"2023112110571831500_c104","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1021\/acs.jctc.7b01115","volume":"14","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c105","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.1021\/acs.jctc.8b01084","volume":"15","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c106","doi-asserted-by":"publisher","first-page":"9707","DOI":"10.1021\/acs.jpca.1c07793","volume":"125","year":"2021","journal-title":"J. Phys. Chem. A"},{"key":"#cr-split#-2023112110571831500_c107.1","doi-asserted-by":"crossref","unstructured":"Y. J.  Franzke  and C.Holzer, J. Chem. Phys.159, 184102 (2023)","DOI":"10.1063\/5.0171509"},{"key":"#cr-split#-2023112110571831500_c107.2","unstructured":"chemRxiv:10.26434 (2023).10.26434\/chemrxiv-2023-k8jwn-v3"},{"key":"2023112110571831500_c108","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/0009-2614(89)85118-8","volume":"162","year":"1989","journal-title":"Chem. Phys. Lett."},{"key":"2023112110571831500_c109","doi-asserted-by":"publisher","first-page":"184107","DOI":"10.1063\/5.0004635","volume":"152","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c110","doi-asserted-by":"publisher","first-page":"6859","DOI":"10.1021\/acs.jctc.3c00347","volume":"19","year":"2023","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c111","unstructured":"TURBOMOLE GmbH (2023), developers\u2019 version of TURBOMOLE V7.7.1, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989\u20132007, TURBOMOLE GmbH, since 2007; available from https:\/\/www.turbomole.org (retrieved July 26, 2023)."},{"key":"2023112110571831500_c112","doi-asserted-by":"publisher","first-page":"8529","DOI":"10.1021\/acs.jpca.0c06897","volume":"124","year":"2020","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c113","unstructured":"O.\n            Treutler\n          , \u201cEntwicklung und Anwendung von Dichtefunktionalmethoden,\u201d Dr. rer. nat. dissertation [University of Karlsruhe (TH), Germany, 1995]."},{"key":"2023112110571831500_c114","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1063\/1.469408","volume":"102","year":"1995","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c115","doi-asserted-by":"publisher","first-page":"16658","DOI":"10.1039\/c9cp02382h","volume":"21","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c116","doi-asserted-by":"publisher","first-page":"10768","DOI":"10.1021\/j100205a033","volume":"96","year":"1992","journal-title":"J. Phys. Chem."},{"key":"2023112110571831500_c117","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1016\/j.cpc.2013.10.014","volume":"185","year":"2014","journal-title":"Comput. Phys. Commun."},{"key":"2023112110571831500_c118","doi-asserted-by":"publisher","first-page":"7809","DOI":"10.1103\/physrevb.62.7809","volume":"62","year":"2000","journal-title":"Phys. Rev. B"},{"key":"2023112110571831500_c119","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/0009-2614(96)00119-4","volume":"251","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2023112110571831500_c120","doi-asserted-by":"publisher","first-page":"1892","DOI":"10.1021\/acs.jctc.5b01197","volume":"12","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c121","doi-asserted-by":"publisher","first-page":"244108","DOI":"10.1063\/1.4729788","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c122","doi-asserted-by":"publisher","first-page":"184105","DOI":"10.1063\/1.4803693","volume":"138","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c123","doi-asserted-by":"publisher","first-page":"014106","DOI":"10.1063\/1.4811776","volume":"139","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c124","doi-asserted-by":"publisher","first-page":"214106","DOI":"10.1063\/1.4921915","volume":"142","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c125","doi-asserted-by":"publisher","first-page":"184104","DOI":"10.1063\/1.4964765","volume":"145","year":"2016","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c126","doi-asserted-by":"publisher","first-page":"e1755064","DOI":"10.1080\/00268976.2020.1755064","volume":"118","year":"2020","journal-title":"Mol. Phys."},{"key":"2023112110571831500_c127","doi-asserted-by":"publisher","first-page":"104110","DOI":"10.1063\/1.5022153","volume":"148","year":"2018","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c128","doi-asserted-by":"publisher","first-page":"3974","DOI":"10.1021\/acs.jctc.1c00167","volume":"17","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c129","doi-asserted-by":"publisher","first-page":"2010","DOI":"10.1021\/acs.jctc.2c01248","volume":"19","year":"2023","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c130","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1002\/chem.201905061","volume":"26","year":"2020","journal-title":"Chem. Eur. J."},{"key":"2023112110571831500_c131","doi-asserted-by":"publisher","first-page":"4226","DOI":"10.1021\/acs.jctc.5b00624","volume":"11","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c132","doi-asserted-by":"publisher","first-page":"1971","DOI":"10.1021\/ct100117s","volume":"6","year":"2010","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c133","doi-asserted-by":"publisher","first-page":"2272","DOI":"10.1016\/j.cpc.2012.05.007","volume":"183","year":"2012","journal-title":"Comput. Phys. Commun."},{"key":"2023112110571831500_c134","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.softx.2017.11.002","volume":"7","year":"2018","journal-title":"SoftwareX"},{"key":"2023112110571831500_c135","unstructured":"Libxc, Version 6.2.2, available from https:\/\/www.tddft.org\/programs\/libxc\/ (retrieved July 26, 2023)."},{"key":"2023112110571831500_c136","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1039\/p29930000799","volume":"1993","journal-title":"J. Chem. Soc., Perkin Trans. 2"},{"key":"2023112110571831500_c137","doi-asserted-by":"publisher","first-page":"2187","DOI":"10.1039\/b000184h","volume":"2","year":"2000","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c138","unstructured":"OpenMP Architecture Review Boards, OpenMP API shared-memory parallel programming, https:\/\/www.openmp.org (retrieved August 15, 2023)."},{"key":"2023112110571831500_c139","unstructured":"C.\n            Holzer\n           and Y. J.Franzke, OpenMP version of ridft, rdgrad, and egrad with contributions to mpshift, dscf, and grad; improved OpenMP version of aoforce and escf, released with TURBOMOLE V7.4 and further improved in TURBOMOLE V7.5, see https:\/\/www.turbomole.org\/turbomole\/release-notes-turbomole-7-5\/ (retrieved July 31, 2023)."},{"key":"2023112110571831500_c140","volume-title":"Constants of Diatomic Molecules","year":"1979"},{"key":"2023112110571831500_c141","doi-asserted-by":"publisher","first-page":"e1606","DOI":"10.1002\/wcms.1606","volume":"12","year":"2022","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023112110571831500_c142","year":"2023"},{"key":"2023112110571831500_c143","doi-asserted-by":"publisher","first-page":"3098","DOI":"10.1103\/physreva.38.3098","volume":"38","year":"1988","journal-title":"Phys. Rev. A"},{"key":"2023112110571831500_c144","doi-asserted-by":"publisher","first-page":"8822","DOI":"10.1103\/physrevb.33.8822","volume":"33","year":"1986","journal-title":"Phys. Rev. B"},{"key":"2023112110571831500_c145","doi-asserted-by":"publisher","first-page":"3865","DOI":"10.1103\/physrevlett.77.3865","volume":"77","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"2023112110571831500_c146","doi-asserted-by":"publisher","first-page":"6158","DOI":"10.1063\/1.478522","volume":"110","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c147","doi-asserted-by":"publisher","first-page":"3297","DOI":"10.1039\/b508541a","volume":"7","year":"2005","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c148","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1039\/b515623h","volume":"8","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c149","doi-asserted-by":"publisher","first-page":"1169","DOI":"10.1002\/chem.200701243","volume":"14","year":"2008","journal-title":"Chem. Eur. J."},{"key":"2023112110571831500_c150","doi-asserted-by":"publisher","first-page":"977","DOI":"10.1021\/ic9017745","volume":"49","year":"2010","journal-title":"Inorg. Chem."},{"key":"2023112110571831500_c151","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1103\/physrevb.37.785","volume":"37","year":"1988","journal-title":"Phys. Rev. B"},{"key":"2023112110571831500_c152","doi-asserted-by":"publisher","first-page":"1372","DOI":"10.1063\/1.464304","volume":"98","year":"1993","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c153","doi-asserted-by":"publisher","first-page":"6615","DOI":"10.1039\/b810189b","volume":"10","year":"2008","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c154","doi-asserted-by":"publisher","first-page":"074111","DOI":"10.1063\/1.4907719","volume":"142","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c155","doi-asserted-by":"publisher","first-page":"214110","DOI":"10.1063\/1.4952647","volume":"144","year":"2016","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c156","doi-asserted-by":"publisher","first-page":"146401","DOI":"10.1103\/physrevlett.91.146401","volume":"91","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"2023112110571831500_c157","doi-asserted-by":"publisher","first-page":"12129","DOI":"10.1063\/1.1626543","volume":"119","year":"2003","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c158","doi-asserted-by":"publisher","first-page":"3067","DOI":"10.1021\/jp050036j","volume":"109","year":"2005","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c159","doi-asserted-by":"publisher","first-page":"5645","DOI":"10.1021\/acs.jctc.0c00498","volume":"16","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c160","doi-asserted-by":"publisher","first-page":"3696","DOI":"10.1021\/acs.jctc.7b00593","volume":"13","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c161","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1039\/a908859h","volume":"2","year":"2000","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023112110571831500_c162","doi-asserted-by":"publisher","first-page":"5658","DOI":"10.1021\/acs.jctc.0c00546","volume":"16","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c163","doi-asserted-by":"publisher","first-page":"14083","DOI":"10.1039\/c7dt02912h","volume":"46","year":"2017","journal-title":"Dalton Trans."},{"key":"2023112110571831500_c164","doi-asserted-by":"publisher","first-page":"11368","DOI":"10.1002\/anie.201602949","volume":"55","year":"2016","journal-title":"Angew. Chem., Int. Ed."},{"key":"2023112110571831500_c165","doi-asserted-by":"publisher","first-page":"1351","DOI":"10.1002\/anie.201309981","volume":"53","year":"2014","journal-title":"Angew. Chem., Int. Ed."},{"key":"2023112110571831500_c166","doi-asserted-by":"publisher","first-page":"3980","DOI":"10.1021\/ja910963x","volume":"132","year":"2010","journal-title":"J. Am. Chem. Soc."},{"key":"2023112110571831500_c167","doi-asserted-by":"publisher","first-page":"13737","DOI":"10.1021\/ja403154z","volume":"135","year":"2013","journal-title":"J. Am. Chem. Soc."},{"key":"2023112110571831500_c168","doi-asserted-by":"publisher","first-page":"154122","DOI":"10.1063\/1.5090222","volume":"150","year":"2019","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c169","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/bf01114537","volume":"77","year":"1990","journal-title":"Theor. Chim. Acta"},{"key":"2023112110571831500_c170","unstructured":"TURBOMOLE GmbH (2023), manual of TURBOMOLE V7.7.1, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989\u20132007, TURBOMOLE GmbH, since 2007; available from https:\/\/www.turbomole.org\/turbomole\/turbomole-documentation\/ (retrieved July 26, 2023)."},{"key":"2023112110571831500_c171","doi-asserted-by":"publisher","first-page":"1457","DOI":"10.1021\/acs.jctc.0c01190","volume":"17","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c172","doi-asserted-by":"publisher","first-page":"4629","DOI":"10.1021\/acs.jctc.1c00466","volume":"17","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c173","doi-asserted-by":"publisher","first-page":"174114","DOI":"10.1063\/5.0121187","volume":"157","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c174","doi-asserted-by":"publisher","first-page":"4180","DOI":"10.1021\/acs.jpca.3c00729","volume":"127","year":"2023","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c175","doi-asserted-by":"publisher","first-page":"2502","DOI":"10.1021\/acs.jctc.3c00183","volume":"19","year":"2023","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c176","doi-asserted-by":"publisher","first-page":"064304","DOI":"10.1063\/1.4790167","volume":"138","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c177","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.ccr.2014.10.015","volume":"289\u2013290","year":"2015","journal-title":"Coord. Chem. Rev."},{"key":"2023112110571831500_c178","doi-asserted-by":"publisher","first-page":"8721","DOI":"10.1021\/jp202278f","volume":"115","year":"2011","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c179","doi-asserted-by":"publisher","first-page":"174301","DOI":"10.1063\/1.4996712","volume":"147","year":"2017","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c180","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/s0022-2860(01)00551-8","volume":"595","year":"2001","journal-title":"J. Mol. Struct."},{"key":"2023112110571831500_c181","doi-asserted-by":"publisher","first-page":"5660","DOI":"10.1021\/acs.jpca.9b03979","volume":"123","year":"2019","journal-title":"J. Phys. Chem. A"},{"key":"2023112110571831500_c182","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/0003-4916(74)90333-9","volume":"82","year":"1974","journal-title":"Ann. Phys."},{"key":"2023112110571831500_c183","doi-asserted-by":"publisher","first-page":"3742","DOI":"10.1103\/physreva.33.3742","volume":"33","year":"1986","journal-title":"Phys. Rev. A"},{"key":"2023112110571831500_c184","doi-asserted-by":"publisher","first-page":"6016","DOI":"10.1103\/physreva.39.6016","volume":"39","year":"1989","journal-title":"Phys. Rev. A"},{"key":"2023112110571831500_c185","doi-asserted-by":"publisher","first-page":"204113","DOI":"10.1063\/1.2133731","volume":"123","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c186","doi-asserted-by":"publisher","first-page":"034107","DOI":"10.1063\/1.1829047","volume":"122","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c187","doi-asserted-by":"publisher","first-page":"9618","DOI":"10.1063\/1.473860","volume":"106","year":"1997","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c188","doi-asserted-by":"publisher","first-page":"4201","DOI":"10.1063\/1.477026","volume":"109","year":"1998","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c189","doi-asserted-by":"publisher","first-page":"10000","DOI":"10.1063\/1.480353","volume":"111","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c190","doi-asserted-by":"publisher","first-page":"9136","DOI":"10.1063\/1.1413512","volume":"115","year":"2001","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c191","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1002\/wcms.1181","volume":"4","year":"2014","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023112110571831500_c192","doi-asserted-by":"publisher","first-page":"134109","DOI":"10.1063\/1.4979499","volume":"146","year":"2017","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c193","doi-asserted-by":"publisher","first-page":"154114","DOI":"10.1063\/1.4758987","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c194","doi-asserted-by":"publisher","first-page":"054111","DOI":"10.1063\/1.4891567","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c195","doi-asserted-by":"publisher","first-page":"164107","DOI":"10.1063\/1.4897254","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c196","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1021\/acs.jctc.7b01019","volume":"14","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"2023112110571831500_c197","doi-asserted-by":"publisher","first-page":"044108","DOI":"10.1063\/1.5012041","volume":"148","year":"2018","journal-title":"J. Chem. Phys."},{"key":"2023112110571831500_c198","doi-asserted-by":"publisher","first-page":"e1768313","DOI":"10.1080\/00268976.2020.1768313","volume":"118","year":"2020","journal-title":"Mol. Phys."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0175758\/18219377\/194117_1_5.0175758.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0175758\/18219377\/194117_1_5.0175758.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T05:58:58Z","timestamp":1700546338000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/159\/19\/194117\/2922422\/Zero-field-splitting-parameters-within-exact-two"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,21]]},"references-count":199,"journal-issue":{"issue":"19","published-print":{"date-parts":[[2023,11,21]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0175758","relation":{"has-preprint":[{"id-type":"doi","id":"10.26434\/chemrxiv-2023-2kh59-v2","asserted-by":"object"},{"id-type":"doi","id":"10.26434\/chemrxiv-2023-2kh59","asserted-by":"object"}]},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,11,21]]},"published":{"date-parts":[[2023,11,21]]},"article-number":"194117"}}