{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T22:04:15Z","timestamp":1786399455529,"version":"build-2736575974"},"reference-count":89,"publisher":"AIP Publishing","issue":"14","funder":[{"DOI":"10.13039\/501100006595","name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","doi-asserted-by":"publisher","award":["PN-IV- P8-8.3-PM-RO-FR-2024-00-22"],"award-info":[{"award-number":["PN-IV- P8-8.3-PM-RO-FR-2024-00-22"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"publisher"}]},{"name":"French Ministry for Europe and Foreign Affairs, the French Ministry for Higher Education and Research and the Ministry of Research, Inovation and Digitalization","award":["51686YA"],"award-info":[{"award-number":["51686YA"]}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"crossref","award":["ANR-23-PETQ-0007"],"award-info":[{"award-number":["ANR-23-PETQ-0007"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,4,14]]},"abstract":"<jats:p>The crystal field theory as explained by Abragam and Bleaney in their landmark 1970 book on transition-ion electron paramagnetic resonance remains a cornerstone in the development of luminescence applications and molecular magnets based on the f-elements. The modern numerical derivation of the 27 Bkq Stevens crystal field parameters (CFPs), which describe the splitting of the energy levels of a central ion, is traditionally achieved through the effective Hamiltonian theory and multiconfiguration wave function theory calculations, insofar as the lowest J level fully captures the targeted low-energy physics. In this study, we present a novel theoretical approach for determining the CFPs. The procedure resembles the traditional extraction path but crucially accounts for the full |J, MJ\u27e9 space of an ion configuration with L = 3 and S = 1\/2. By demonstrating the extraction procedure using the simplest case of a CeIII 4f1 ion with a crystal-field split J \u2208 {5\/2, 7\/2} manifold, it is shown for the first time that a unique set of CFPs describes the splitting and mixing of both the J manifolds. In fact, this J\/J\u2032 mixing is analogous to the \u201cspin mixing\u201d in binuclear transition metal complexes. At the employed level of calculation, we demonstrate that there is no spin\u2013orbit coupling influence on the CFP values. Moreover, for the 4f1 case, the present extraction yields crystal-field and spin\u2013orbit parameters similar to those obtained from ab\u00a0initio ligand field theory. This study represents the first step of a larger effort in reviewing the theory and extraction procedures of CFPs in f-element complexes.<\/jats:p>","DOI":"10.1063\/5.0313869","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:38:07Z","timestamp":1775644687000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["<i>Ab initio<\/i>\n                    derivation of the crystal field parameters for lanthanide ions: The f1 case"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6570-5245","authenticated-orcid":false,"given":"Dumitru-Claudiu","family":"Sergentu","sequence":"first","affiliation":[{"name":"Faculty of Chemistry, \u201cAlexandru Ioan Cuza\u201d University of Ia\u015fi 1 , Ia\u015fi,","place":["Romania"]},{"name":"ICI-RECENT AIR (RA03), \u201cAlexandru Ioan Cuza\u201d University of Ia\u015fi 2 , Ia\u015fi,","place":["Romania"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8393-0494","authenticated-orcid":false,"given":"Gwenha\u00ebl","family":"Duplaix-Rata","sequence":"additional","affiliation":[{"name":"Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)\u2013UMR 6226 3 , F-35000 Rennes,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2253-0531","authenticated-orcid":false,"given":"Ionel","family":"Humelnicu","sequence":"additional","affiliation":[{"name":"Faculty of Chemistry, \u201cAlexandru Ioan Cuza\u201d University of Ia\u015fi 1 , Ia\u015fi,","place":["Romania"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3013-0546","authenticated-orcid":false,"given":"Boris","family":"Le Guennic","sequence":"additional","affiliation":[{"name":"Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)\u2013UMR 6226 3 , F-35000 Rennes,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2889-6518","authenticated-orcid":false,"given":"R\u00e9mi","family":"Maurice","sequence":"additional","affiliation":[{"name":"Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)\u2013UMR 6226 3 , F-35000 Rennes,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"2026040806380149600_c1","volume-title":"Electron Paramagnetic Resonance of Transition Ions","year":"1970"},{"key":"2026040806380149600_c2","doi-asserted-by":"publisher","first-page":"1583","DOI":"10.1016\/j.ccr.2012.03.029","article-title":"Developments in the photophysics and photochemistry of actinide ions and their coordination compounds","volume":"256","year":"2012","journal-title":"Coord. Chem. Rev."},{"key":"2026040806380149600_c3","doi-asserted-by":"publisher","first-page":"17787","DOI":"10.1039\/d3ra00991b","article-title":"The role of lanthanide luminescence in advancing technology","volume":"13","year":"2023","journal-title":"RSC Adv."},{"key":"2026040806380149600_c4","doi-asserted-by":"publisher","first-page":"2078","DOI":"10.1039\/c1sc00513h","article-title":"Exploiting single-ion anisotropy in the design of f-element single-molecule magnets","volume":"2","year":"2011","journal-title":"Chem. Sci."},{"key":"2026040806380149600_c5","doi-asserted-by":"publisher","first-page":"6655","DOI":"10.1039\/c5cs00222b","article-title":"Improving f-element single molecule magnets","volume":"44","year":"2015","journal-title":"Chem. Soc. Rev."},{"key":"2026040806380149600_c6","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1038\/s41578-019-0146-8","article-title":"Molecular magnetism: From chemical design to spin control in molecules, materials and devices","volume":"5","year":"2019","journal-title":"Nat. Rev. Mater."},{"key":"2026040806380149600_c7","doi-asserted-by":"publisher","first-page":"e202300336","DOI":"10.1002\/ejic.202300336","article-title":"Get under the umbrella: A comprehensive gateway for researchers on lanthanide-based single-molecule magnets","volume":"26","year":"2023","journal-title":"Eur. J. Inorg. Chem."},{"key":"2026040806380149600_c8","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.ccr.2017.03.015","article-title":"Molecular single-ion magnets based on lanthanides and actinides: Design considerations and new advances in the context of quantum technologies","volume":"346","year":"2017","journal-title":"Coord. Chem. Rev."},{"key":"2026040806380149600_c9","doi-asserted-by":"publisher","first-page":"2300367","DOI":"10.1002\/qute.202300367","article-title":"Magnetic molecules as building blocks for quantum technologies","volume":"8","year":"2025","journal-title":"Adv. Quantum Technol."},{"key":"2026040806380149600_c10","doi-asserted-by":"publisher","first-page":"5110","DOI":"10.1021\/cr400018q","article-title":"Lanthanide single-molecule magnets","volume":"113","year":"2013","journal-title":"Chem. Rev."},{"key":"2026040806380149600_c11","volume-title":"Lanthanides and Actinides in Molecular Magnetism","year":"2015"},{"key":"2026040806380149600_c12","doi-asserted-by":"publisher","first-page":"11883","DOI":"10.1021\/acs.inorgchem.9b01610","article-title":"Exploring the high-temperature Frontier in molecular nanomagnets: From lanthanides to actinides","volume":"58","year":"2019","journal-title":"Inorg. Chem."},{"key":"2026040806380149600_c13","doi-asserted-by":"publisher","first-page":"1349","DOI":"10.1039\/d4qi02326a","article-title":"Recent advances in computational modelling of mononuclear actinide single molecule magnets","volume":"12","year":"2025","journal-title":"Inorg. Chem. Front."},{"key":"2026040806380149600_c14","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.ccr.2016.12.017","article-title":"Uncommon lanthanide ions in purely 4f single molecule magnets","volume":"346","year":"2017","journal-title":"Coord. Chem. Rev."},{"key":"2026040806380149600_c15","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1038\/s41570-024-00641-y","article-title":"Understanding covalency in molecular f-block compounds from the synergy of spectroscopy and quantum chemistry","volume":"8","year":"2024","journal-title":"Nat. Rev. Chem."},{"key":"2026040806380149600_c16","doi-asserted-by":"publisher","first-page":"11445","DOI":"10.1002\/anie.201705426","article-title":"A dysprosium metallocene single-molecule magnet functioning at the axial limit","volume":"56","year":"2017","journal-title":"Angew. Chem., Int. Ed."},{"key":"2026040806380149600_c17","doi-asserted-by":"publisher","first-page":"1400","DOI":"10.1126\/science.aav0652","article-title":"Magnetic hysteresis up to 80 kelvin in a dysprosium metallocene single-molecule magnet","volume":"362","year":"2018","journal-title":"Science"},{"key":"2026040806380149600_c18","doi-asserted-by":"publisher","first-page":"6017","DOI":"10.1021\/acs.inorgchem.1c03980","article-title":"Discovery of a dysprosium metallocene single-molecule magnet with two high-temperature orbach processes","volume":"61","year":"2022","journal-title":"Inorg. Chem."},{"key":"2026040806380149600_c19","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1126\/science.abl5470","article-title":"Ultrahard magnetism from mixed-valence dilanthanide complexes with metal-metal bonding","volume":"375","year":"2022","journal-title":"Science"},{"key":"2026040806380149600_c20","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1038\/nature23447","article-title":"Molecular magnetic hysteresis at 60 kelvin in dysprosocenium","volume":"548","year":"2017","journal-title":"Nature"},{"key":"2026040806380149600_c21","doi-asserted-by":"publisher","first-page":"8694","DOI":"10.1021\/ja029629n","article-title":"Lanthanide double-decker complexes functioning as magnets at the single-molecular level","volume":"125","year":"2003","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026040806380149600_c22","doi-asserted-by":"publisher","first-page":"11265","DOI":"10.1021\/jp0376065","article-title":"Mononuclear lanthanide complexes with a long magnetization relaxation time at high temperatures: A new category of magnets at the single-molecular level","volume":"108","year":"2004","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026040806380149600_c23","doi-asserted-by":"publisher","first-page":"6055","DOI":"10.1021\/jp1015214","article-title":"What use are crystal field parameters? A chemist\u2019s viewpoint","volume":"114","year":"2010","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2026040806380149600_c24","doi-asserted-by":"publisher","first-page":"1164","DOI":"10.1002\/jcc.23234","article-title":"Phi: A powerful new program for the analysis of anisotropic monomeric and exchange-coupled polynuclear d-and f-block complexes","volume":"34","year":"2013","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026040806380149600_c25","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.jmmm.2004.03.041","article-title":"Computerized magnetic studies on d, f, d\u2013d, f\u2013f, and d\u2013s, f\u2013s systems under varying ligand and magnetic fields","volume":"281","year":"2004","journal-title":"J.\u00a0Magn. Magn. Mater."},{"key":"2026040806380149600_c26","doi-asserted-by":"publisher","first-page":"1961","DOI":"10.1002\/jcc.23341","article-title":"SIMPRE: A software package to calculate crystal field parameters, energy levels, and magnetic properties on mononuclear lanthanoid complexes based on charge distributions","volume":"34","year":"2013","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026040806380149600_c27","doi-asserted-by":"publisher","first-page":"1930","DOI":"10.1002\/jcc.23699","article-title":"An updated version of the computational package SIMPRE that uses the standard conventions for Stevens crystal field parameters","volume":"35","year":"2014","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026040806380149600_c28","doi-asserted-by":"publisher","first-page":"985","DOI":"10.1002\/jcc.1059","article-title":"Magpack1 a package to calculate the energy levels, bulk magnetic properties, and inelastic neutron scattering spectra of high nuclearity spin clusters","volume":"22","year":"2001","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026040806380149600_c29","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1107\/s160057672001554x","article-title":"Pycrystalfield: Software for calculation, analysis and fitting of crystal electric field Hamiltonians","volume":"54","year":"2021","journal-title":"J.\u00a0Appl. Crystallogr."},{"key":"2026040806380149600_c30","doi-asserted-by":"publisher","first-page":"e70063","DOI":"10.1002\/jcc.70063","article-title":"Not just another crystal field software","volume":"46","year":"2025","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026040806380149600_c31","doi-asserted-by":"publisher","first-page":"033003","DOI":"10.1103\/physrevlett.101.033003","article-title":"Unique definition of the Zeeman-splitting g tensor of a kramers doublet","volume":"101","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"2026040806380149600_c32","doi-asserted-by":"publisher","first-page":"064112","DOI":"10.1063\/1.4739763","article-title":"Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation","volume":"137","year":"2012","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026040806380149600_c33","doi-asserted-by":"publisher","first-page":"7994","DOI":"10.1002\/chem.201305039","article-title":"Magnetic properties and electronic structure of neptunyl(VI) complexes: Wavefunctions, orbitals, and crystal-field models","volume":"20","year":"2014","journal-title":"Chem. Eur. J."},{"key":"2026040806380149600_c34","doi-asserted-by":"publisher","first-page":"19886","DOI":"10.1039\/c5dt02858b","article-title":"Single-ion 4f element magnetism: An ab-initio look at Ln(COT)2\u2212","volume":"44","year":"2015","journal-title":"Dalton Trans."},{"key":"2026040806380149600_c35","doi-asserted-by":"publisher","first-page":"3708","DOI":"10.1002\/chem.201605102","article-title":"Ab initio crystal field for lanthanides","volume":"23","year":"2017","journal-title":"Chem. - Eur. J."},{"key":"2026040806380149600_c36","doi-asserted-by":"publisher","first-page":"5538","DOI":"10.1002\/chem.201705748","article-title":"Crystal field in rare-earth complexes: From electrostatics to bonding","volume":"24","year":"2018","journal-title":"Chem. - Eur. J."},{"key":"2026040806380149600_c37","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/978-3-031-31038-6","article-title":"Modeling magnetic properties of actinide complexes","volume-title":"Computational Modelling of Molecular Nanomagnets","author":"Rajaraman","year":"2023"},{"key":"2026040806380149600_c38","doi-asserted-by":"publisher","first-page":"17254","DOI":"10.1021\/acs.inorgchem.3c02482","article-title":"Bonding and magnetic trends in the [AnIII (DPA)3]3\u2212 series compared to the Ln(III) and An(IV) analogues","volume":"62","year":"2023","journal-title":"Inorg. Chem."},{"key":"2026040806380149600_c39","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/0301-0104(80)80045-0","article-title":"A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach","volume":"48","year":"1980","journal-title":"Chem. Phys."},{"key":"2026040806380149600_c40","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1002\/qua.560180822","article-title":"The complete active space SCF method in a fock-matrix-based super-CI formulation","volume":"18","year":"2009","journal-title":"Int. J. Quantum Chem."},{"key":"2026040806380149600_c41","doi-asserted-by":"publisher","first-page":"5483","DOI":"10.1021\/j100377a012","article-title":"Second-order perturbation theory with a CASSCF reference function","volume":"94","year":"1990","journal-title":"J.\u00a0Phys. Chem."},{"key":"2026040806380149600_c42","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1063\/1.462209","article-title":"Second-order perturbation theory with a complete active space self-consistent field reference function","volume":"96","year":"1992","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026040806380149600_c43","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/s0009-2614(98)00252-8","article-title":"The multi-state CASPT2 method","volume":"288","year":"1998","journal-title":"Chem. Phys. Lett."},{"key":"2026040806380149600_c44","doi-asserted-by":"publisher","first-page":"10252","DOI":"10.1063\/1.1361246","article-title":"Introduction of n-electron valence states for multireference perturbation theory","volume":"114","year":"2001","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026040806380149600_c45","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/s0009-2614(02)00498-0","article-title":"The restricted active space (RAS) state interaction approach with spin\u2013orbit coupling","volume":"357","year":"2002","journal-title":"Chem. Phys. Lett."},{"key":"2026040806380149600_c46","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1002\/wcms.81","article-title":"The ORCA program system","volume":"2","year":"2012","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026040806380149600_c47","doi-asserted-by":"publisher","first-page":"e1606","DOI":"10.1002\/wcms.1606","article-title":"Software update: The ORCA program system-version 5.0","volume":"12","year":"2022","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026040806380149600_c48","doi-asserted-by":"publisher","first-page":"6933","DOI":"10.1021\/acs.jctc.3c00182","article-title":"The Openmolcas Web: A community-driven approach to advancing computational chemistry","volume":"19","year":"2023","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026040806380149600_c49","doi-asserted-by":"publisher","first-page":"18899","DOI":"10.1021\/jacs.4c07412","article-title":"Record quantum tunneling time in an air-stable exchange-bias dysprosium macrocycle","volume":"146","year":"2024","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026040806380149600_c50","doi-asserted-by":"publisher","first-page":"e202300598","DOI":"10.1002\/ejic.202300598","article-title":"Dysprosium-radical based single-molecule magnet containing a seven coordinate Dy(III) ion: A system for ab\u00a0initio study","volume":"27","year":"2024","journal-title":"Eur. J. Inorg. Chem."},{"key":"2026040806380149600_c51","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1039\/d4sc06661h","article-title":"A fluorobenzene-bound dysprosium half-sandwich dication single-molecule magnet","volume":"16","year":"2025","journal-title":"Chem. Sci."},{"key":"2026040806380149600_c52","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.ccr.2014.10.015","article-title":"First principles approach to the electronic structure, magnetic anisotropy and spin relaxation in mononuclear 3d-transition metal single molecule magnets","volume":"289\u2013290","year":"2015","journal-title":"Coord. Chem. Rev."},{"key":"2026040806380149600_c53","doi-asserted-by":"publisher","first-page":"4457","DOI":"10.1021\/acs.inorgchem.6b00244","article-title":"Periodic trends in lanthanide compounds through the eyes of multireference ab\u00a0initio theory","volume":"55","year":"2016","journal-title":"Inorg. Chem."},{"key":"2026040806380149600_c54","doi-asserted-by":"publisher","first-page":"8802","DOI":"10.1021\/acs.inorgchem.7b00642","article-title":"Ab initio ligand-field theory analysis and covalency trends in actinide and lanthanide free ions and octahedral complexes","volume":"56","year":"2017","journal-title":"Inorg. Chem."},{"key":"2026040806380149600_c55","doi-asserted-by":"publisher","first-page":"15112","DOI":"10.1002\/chem.201903141","article-title":"Derivation of lanthanide series crystal field parameters from first principles","volume":"25","year":"2019","journal-title":"Chem. - Eur. J."},{"key":"2026040806380149600_c56","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1021\/acs.jpca.9b11227","article-title":"Improvement of ab\u00a0initio ligand field theory by means of multistate perturbation theory","volume":"124","year":"2020","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2026040806380149600_c57","doi-asserted-by":"publisher","first-page":"12969","DOI":"10.1021\/acs.inorgchem.4c01694","article-title":"Paramagnetic properties of [AnIV (NO3)6]2\u2212 complexes (An = U, Np, Pu) probed by NMR spectroscopy and quantum chemical calculations","volume":"63","year":"2024","journal-title":"Inorg. Chem."},{"key":"2026040806380149600_c58","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1088\/0370-1298\/65\/3\/308","article-title":"Matrix elements and operator equivalents connected with the magnetic properties of rare earth ions","volume":"65","year":"1952","journal-title":"Proc. Phys. Soc. A"},{"key":"2026040806380149600_c59","first-page":"665","article-title":"Elementary theory of the crystal field","volume-title":"Electron Paramagnetic Resonance of Transition Ions","year":"1970"},{"key":"2026040806380149600_c60","doi-asserted-by":"publisher","first-page":"5825","DOI":"10.1088\/0953-8984\/16\/32\/018","article-title":"The generalization of the extended Stevens operators to higher ranks and spins, and a systematic review of the tables of the tensor operators and their matrixelements","volume":"16","year":"2004","journal-title":"J.\u00a0Phys.: Condens. Matter"},{"key":"2026040806380149600_c61","doi-asserted-by":"publisher","first-page":"025207","DOI":"10.1088\/1751-8121\/ad96fc","article-title":"General expressions for Stevens and Racah operator equivalents","volume":"58","year":"2024","journal-title":"J.\u00a0Phys. A: Math. Theor."},{"key":"2026040806380149600_c62","doi-asserted-by":"publisher","first-page":"8734","DOI":"10.1039\/d4cp00281d","article-title":"Geometry and electronic structure of Yb(III)[CH(SiMe3)2]3 from EPR and solid-state NMR augmented by computations","volume":"26","year":"2024","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026040806380149600_c63","doi-asserted-by":"publisher","first-page":"14293","DOI":"10.1039\/d0cp02137g","article-title":"Crystallographic structure and crystal field parameters in the [AnIV (DPA)3]2\u2212 series, An = Th, U, Np, Pu","volume":"22","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026040806380149600_c64","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1021\/om7012327","article-title":"Cerocene revisited: The electronic structure of and interconversion between Ce2(C8H8)3 and Ce(C8H8)2","volume":"28","year":"2009","journal-title":"Organometallics"},{"key":"2026040806380149600_c65","doi-asserted-by":"publisher","first-page":"e70019","DOI":"10.1002\/wcms.70019","article-title":"Software update: The ORCA program system\u2014Version 6.0","volume":"15","year":"2025","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026040806380149600_c66","doi-asserted-by":"publisher","first-page":"1148","DOI":"10.1021\/acs.jctc.5b01048","article-title":"Improved segmented all-electron relativistically contracted basis sets for the lanthanides","volume":"12","year":"2016","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026040806380149600_c67","doi-asserted-by":"publisher","first-page":"C15","DOI":"10.1016\/0022-328X(94)80091-X","article-title":"Cyclooctatetraenyl-komplexe der fr\u00fchen \u00fcbergangsmetalle und lanthanoide: IV. Strukturchemie des anionisichen sandwich-komplexes [Ce(COT)2]\u2212","volume":"469","year":"1994","journal-title":"J.\u00a0Organomet. Chem."},{"key":"2026040806380149600_c68","doi-asserted-by":"publisher","first-page":"2229","DOI":"10.1021\/ct900090f","article-title":"All-electron scalar relativistic basis sets for the lanthanides","volume":"5","year":"2009","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026040806380149600_c69","doi-asserted-by":"publisher","first-page":"3297","DOI":"10.1039\/b508541a","article-title":"Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy","volume":"7","year":"2005","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026040806380149600_c70","doi-asserted-by":"publisher","first-page":"104109","DOI":"10.1063\/5.0058766","article-title":"An improved chain of spheres for exchange algorithm","volume":"155","year":"2021","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026040806380149600_c71","doi-asserted-by":"publisher","first-page":"1740","DOI":"10.1002\/jcc.10318","article-title":"An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix","volume":"24","year":"2003","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026040806380149600_c72","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1021\/acs.jctc.6b01041","article-title":"Automatic generation of auxiliary basis sets","volume":"13","year":"2017","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026040806380149600_c73","doi-asserted-by":"publisher","first-page":"10945","DOI":"10.1063\/1.1818681","article-title":"Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas\u2013Kroll\u2013Hess transformation up to arbitrary order","volume":"121","year":"2004","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026040806380149600_c74","doi-asserted-by":"publisher","first-page":"034107","DOI":"10.1063\/1.1829047","article-title":"Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations","volume":"122","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026040806380149600_c75","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1063\/1.1747632","article-title":"On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals","volume":"18","year":"1950","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026040806380149600_c76","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0029-5582(60)90177-2","article-title":"Extension d\u2019une formule de lagrange \u00e0 des probl\u00e8mes de valeurs propres","volume":"20","year":"1960","journal-title":"Nucl. Phys."},{"key":"2026040806380149600_c77","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0166-1280(97)00185-1","article-title":"Evaluation of the rotation matrices in the basis of real spherical harmonics","volume":"419","year":"1997","journal-title":"J.\u00a0Mol. Struct.: THEOCHEM"},{"key":"2026040806380149600_c78","volume-title":"Spectroscopic Properties of Rare Earths","year":"1965"},{"key":"2026040806380149600_c79","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1364\/josa.66.000599","article-title":"The sixth spectrum of uranium (U VI)","volume":"66","year":"1976","journal-title":"J.\u00a0Opt. Soc. Am."},{"key":"2026040806380149600_c80","doi-asserted-by":"publisher","first-page":"6084","DOI":"10.1021\/ja9740172","article-title":"EPR and angle-selected ENDOR study of 5f-ligand interactions in the [U(\u03b77-C7H7)2]\u2212 anion, an f1 analogue of uranocene","volume":"120","year":"1998","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026040806380149600_c81","first-page":"149","article-title":"Molecular electronic structures of transition metal complexes II","volume-title":"Structure and Bonding","author":"Mingos","year":"2011"},{"key":"2026040806380149600_c82","doi-asserted-by":"publisher","first-page":"1993","DOI":"10.1021\/ja512232f","article-title":"The ligand field of the azido ligand: Insights into bonding parameters and magnetic anisotropy in a Co(II)\u2013azido complex","volume":"137","year":"2015","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026040806380149600_c83","doi-asserted-by":"publisher","first-page":"14130","DOI":"10.1039\/d1dt02346b","article-title":"Assessment of minimal active space CASSCF-SO methods for calculation of atomic Slater\u2013Condon and spin\u2013orbit coupling parameters in d\u2013 and f\u2013block ions","volume":"50","year":"2021","journal-title":"Dalton Trans."},{"key":"2026040806380149600_c84","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1021\/ct900473u","article-title":"Rigorous extraction of the anisotropic multispin Hamiltonian in bimetallic complexes from the exact electronic Hamiltonian","volume":"6","year":"2010","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026040806380149600_c85","doi-asserted-by":"publisher","first-page":"214427","DOI":"10.1103\/physrevb.81.214427","article-title":"Magnetic anisotropy in binuclear complexes in the weak-exchange limit: From the multispin to the giant-spin Hamiltonian","volume":"81","year":"2010","journal-title":"Phys. Rev. B"},{"key":"2026040806380149600_c86","doi-asserted-by":"publisher","first-page":"6844","DOI":"10.1039\/d3cp04943d","article-title":"The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes","volume":"26","year":"2024","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026040806380149600_c87","doi-asserted-by":"publisher","first-page":"4834","DOI":"10.1039\/C7DT00111H","article-title":"Modeling the electronic states and magnetic properties derived from the f1 configuration in lanthanocene and actinocene compounds","volume":"46","year":"2017","journal-title":"Dalton Trans."},{"key":"2026040806380149600_c88","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1021\/acs.inorgchem.8b02771","article-title":"Magnetic coupling in the Ce(III) dimer Ce2(COT)3","volume":"58","year":"2019","journal-title":"Inorg. Chem."},{"key":"2026040806380149600_c89","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1002\/qua.20376","article-title":"Calculation of spin-orbit coupling within the LFDFT: Applications to [NiX4]2\u2212 (X = F\u2212, Cl\u2212, Br\u2212, I\u2212)","volume":"102","year":"2005","journal-title":"Int. J. Quantum 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\/5.0313869\/20968884\/144304_1_5.0313869.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0313869\/20968884\/144304_1_5.0313869.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T10:38:09Z","timestamp":1775644689000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/164\/14\/144304\/3386469\/Ab-initio-derivation-of-the-crystal-field"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,8]]},"references-count":89,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0313869","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,4,14]]},"published":{"date-parts":[[2026,4,8]]},"article-number":"144304"}}