{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T04:40:25Z","timestamp":1770957625571,"version":"3.50.1"},"reference-count":96,"publisher":"AIP Publishing","issue":"22","funder":[{"DOI":"10.13039\/100006151","name":"Basic Energy Sciences","doi-asserted-by":"publisher","award":["E-SC0018326"],"award-info":[{"award-number":["E-SC0018326"]}],"id":[{"id":"10.13039\/100006151","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,6,14]]},"abstract":"<jats:p>A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas\u2013Kroll\u2013Hess (DKH) theory up to the second order is implemented within the ab\u00a0initio multireference methods, including spin\u2013orbit coupling in the Molcas\/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin\u2013orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s\/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).<\/jats:p>","DOI":"10.1063\/5.0208851","type":"journal-article","created":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T10:53:28Z","timestamp":1718016808000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Relativistic Douglas\u2013Kroll\u2013Hess calculations of hyperfine interactions within first-principles multireference methods"],"prefix":"10.1063","volume":"160","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8557-8527","authenticated-orcid":false,"given":"Aleksander L.","family":"Wysocki","sequence":"first","affiliation":[{"name":"Department of Physics, Virginia Tech , Blacksburg, Virginia 24061, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0597-204X","authenticated-orcid":false,"given":"Kyungwha","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Physics, Virginia Tech , Blacksburg, Virginia 24061, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2024,6,10]]},"reference":[{"key":"2024061010532331400_c1","volume-title":"Electron Paramagnetic Resonance of Transition Ions","year":"1970"},{"key":"2024061010532331400_c2","volume-title":"Principles of Electron Spin Resonance","year":"1993"},{"key":"2024061010532331400_c3","volume-title":"Solution NMR of Paramagnetic Molecules","year":"2001"},{"key":"2024061010532331400_c4","doi-asserted-by":"publisher","first-page":"130501","DOI":"10.1103\/physrevlett.93.130501","article-title":"Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate","volume":"93","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"2024061010532331400_c5","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1103\/revmodphys.76.1037","article-title":"NMR techniques for quantum control and computation","volume":"76","year":"2005","journal-title":"Rev. Mod. Phys."},{"key":"2024061010532331400_c6","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1038\/nature10900","article-title":"Decoherence-protected quantum gates for a hybrid solid-state spin register","volume":"484","year":"2012","journal-title":"Nature"},{"key":"2024061010532331400_c7","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1038\/nnano.2013.117","article-title":"Atomic clock transitions in silicon-based spin qubits","volume":"8","year":"2013","journal-title":"Nat. Nanotechnol."},{"key":"2024061010532331400_c8","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1126\/science.1249802","article-title":"Electrically driven nuclear spin resonance in single-molecule magnets","volume":"344","year":"2014","journal-title":"Science"},{"key":"2024061010532331400_c9","doi-asserted-by":"publisher","first-page":"6183","DOI":"10.1039\/c8sc01695j","article-title":"A two-qubit molecular architecture for electron-mediated nuclear quantum simulation","volume":"9","year":"2018","journal-title":"Chem. Sci."},{"key":"2024061010532331400_c10","doi-asserted-by":"publisher","first-page":"187702","DOI":"10.1103\/physrevlett.119.187702","article-title":"Operating quantum states in single magnetic molecules: Implementation of Grover\u2019s quantum algorithm","volume":"119","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"2024061010532331400_c11","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1038\/s41563-020-00802-6","article-title":"Entanglement and control of single nuclear spins in isotopically engineered silicon carbide","volume":"19","year":"2020","journal-title":"Nat. Mater."},{"key":"2024061010532331400_c12","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1038\/s41586-020-2057-7","article-title":"Coherent electrical control of a single high-spin nucleus in silicon","volume":"579","year":"2020","journal-title":"Nature"},{"key":"2024061010532331400_c13","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1038\/s41557-022-00894-4","article-title":"A 9.2-GHz clock transition in a Lu(II) molecular spin qubit arising from a 3,467-MHz hyperfine interaction","volume":"14","year":"2022","journal-title":"Nat. Chem."},{"key":"2024061010532331400_c14","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1038\/s41586-021-04293-6","article-title":"Nuclear spin-wave quantum register for a solid-state qubit","volume":"602","year":"2022","journal-title":"Nature"},{"key":"2024061010532331400_c15","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1038\/nature10314","article-title":"Decoherence in crystals of quantum molecular magnets","volume":"476","year":"2011","journal-title":"Nature"},{"key":"2024061010532331400_c16","doi-asserted-by":"publisher","first-page":"016001","DOI":"10.1088\/0034-4885\/80\/1\/016001","article-title":"Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths","volume":"80","year":"2016","journal-title":"Rep. Prog. Phys."},{"key":"2024061010532331400_c17","doi-asserted-by":"publisher","first-page":"3196","DOI":"10.1021\/jacs.6b13030","article-title":"Synthetic approach to determine the effect of nuclear spin distance on electronic spin decoherence","volume":"139","year":"2017","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2024061010532331400_c18","doi-asserted-by":"publisher","first-page":"010311","DOI":"10.1103\/prxquantum.2.010311","article-title":"Probing the coherence of solid-state qubits at avoided crossings","volume":"2","year":"2021","journal-title":"PRX Quantum"},{"key":"2024061010532331400_c19","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1007\/bf01339933","article-title":"\u00dcber die magnetischen Momente der Atomkerne","volume":"60","year":"1930","journal-title":"Z. Phys."},{"key":"2024061010532331400_c20","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1007\/978-3-642-40766-6","article-title":"Relativistic methods for calculating electron paramagnetic resonance (EPR) parameters","volume-title":"Handbook of Relativistic Quantum Chemistry","author":"Liu","year":"2017"},{"key":"2024061010532331400_c21","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1103\/physrev.176.10","article-title":"Theoretical analysis of the hyperfine structure of alkali atoms","volume":"176","year":"1968","journal-title":"Phys. Rev."},{"key":"2024061010532331400_c22","doi-asserted-by":"publisher","first-page":"2771","DOI":"10.1021\/acs.inorgchem.9b03136","article-title":"Nature of hyperfine interactions in TbPc2 single-molecule magnets: Multiconfigurational ab\u00a0initio study","volume":"59","year":"2020","journal-title":"Inorg. Chem."},{"key":"2024061010532331400_c23","doi-asserted-by":"publisher","first-page":"274002","DOI":"10.1088\/1361-648x\/ab757b","article-title":"Hyperfine and quadrupole interactions for Dy isotopes in DyPc2 molecules","volume":"32","year":"2020","journal-title":"J.\u00a0Phys.: Condens. Matter"},{"key":"2024061010532331400_c24","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1021\/ct500988h","article-title":"Effects from spin\u2013orbit coupling on electron\u2013nucleus hyperfine coupling calculated at the restricted active space level for Kramers doublets","volume":"11","year":"2015","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c25","doi-asserted-by":"publisher","first-page":"4783","DOI":"10.1063\/1.475889","article-title":"Density functional calculations of molecular hyperfine interactions in the zero order regular approximation for relativistic effects","volume":"108","year":"1998","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c26","doi-asserted-by":"publisher","first-page":"4421","DOI":"10.1063\/1.1345509","article-title":"An evaluation of the density functional approach in the zero order regular approximation for relativistic effects: Magnetic interactions in small metal compounds","volume":"114","year":"2001","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c27","doi-asserted-by":"publisher","first-page":"2175","DOI":"10.1021\/ct200143w","article-title":"Calculation of hyperfine tensors and paramagnetic NMR shifts using the relativistic zeroth-order regular approximation and density functional theory","volume":"7","year":"2011","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c28","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1021\/acs.jctc.1c01027","article-title":"Hyperfine coupling constants in local exact two-component theory","volume":"18","year":"2022","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c29","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/j.cplett.2004.08.037","article-title":"Scalar relativistic calculations of hyperfine coupling tensors using the Douglas\u2013Kroll\u2013Hess method","volume":"396","year":"2004","journal-title":"Chem. Phys. Lett."},{"key":"2024061010532331400_c30","doi-asserted-by":"publisher","first-page":"710","DOI":"10.1021\/acs.jctc.6b01014","article-title":"Relativistic effects on electron\u2013nucleus hyperfine coupling studied with an exact 2-component (X2C) Hamiltonian","volume":"13","year":"2017","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c31","doi-asserted-by":"publisher","first-page":"044111","DOI":"10.1063\/1.3526263","article-title":"Effects of finite size nuclei in relativistic four-component calculations of hyperfine structure","volume":"134","year":"2011","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c32","doi-asserted-by":"publisher","first-page":"598","DOI":"10.1021\/ct2008507","article-title":"Scalar relativistic computations and localized orbital analyses of nuclear hyperfine coupling and paramagnetic NMR chemical shifts","volume":"8","year":"2012","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c33","doi-asserted-by":"publisher","first-page":"4079","DOI":"10.1039\/b607044b","article-title":"Scalar relativistic calculations of hyperfine coupling tensors using the Douglas\u2013Kroll\u2013Hess method with a finite-size nucleus model","volume":"8","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2024061010532331400_c34","doi-asserted-by":"publisher","first-page":"104102","DOI":"10.1063\/1.4792362","article-title":"Derivation and assessment of relativistic hyperfine-coupling tensors on the basis of orbital-optimized second-order M\u00f8ller\u2013Plesset perturbation theory and the second-order Douglas\u2013Kroll\u2013Hess transformation","volume":"138","year":"2013","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c35","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1088\/0953-4075\/35\/4\/315","article-title":"Hyperfine structure in the 4d states of Rb-like Sr","volume":"35","year":"2002","journal-title":"J.\u00a0Phys. B: At., Mol. Opt. Phys."},{"key":"2024061010532331400_c36","doi-asserted-by":"publisher","first-page":"1899","DOI":"10.1088\/0953-4075\/36\/10\/301","article-title":"Influence of correlation effects on the magnetic dipole hyperfine interaction in the low-lying states of Ca+","volume":"36","year":"2003","journal-title":"J.\u00a0Phys. B: At., Mol. Opt. Phys."},{"key":"2024061010532331400_c37","doi-asserted-by":"publisher","first-page":"022512","DOI":"10.1103\/physreva.91.022512","article-title":"Relativistic extended-coupled-cluster method for the magnetic hyperfine structure constant","volume":"91","year":"2015","journal-title":"Phys. Rev. A"},{"key":"2024061010532331400_c38","doi-asserted-by":"publisher","first-page":"3157","DOI":"10.1021\/acs.jpca.0c00877","article-title":"Hyperfine structure constants on the relativistic coupled cluster level with associated uncertainties","volume":"124","year":"2020","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2024061010532331400_c39","doi-asserted-by":"publisher","first-page":"3412","DOI":"10.1063\/1.462977","article-title":"Spin polarization in restricted electronic structure theory: Multiconfiguration self-consistent-field calculations of hyperfine coupling constants","volume":"97","year":"1992","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c40","doi-asserted-by":"publisher","first-page":"012011","DOI":"10.1088\/1742-6596\/72\/1\/012011","article-title":"Theoretical studies of hyperfine effects","volume":"72","year":"2007","journal-title":"J.\u00a0Phys.: Conf. Ser."},{"key":"2024061010532331400_c41","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1088\/0953-4075\/40\/3\/003","article-title":"Multi-configuration Dirac\u2013Fock calculations of the hyperfine structure constants A and B of neutral Cu, Ag and Au","volume":"40","year":"2007","journal-title":"J.\u00a0Phys. B: At., Mol. Opt. Phys."},{"key":"2024061010532331400_c42","doi-asserted-by":"publisher","first-page":"052502","DOI":"10.1103\/physreva.79.052502","article-title":"Complete-active-space multiconfiguration Dirac\u2013Hartree\u2013Fock calculations of hyperfine-structure constants of the gold atom","volume":"79","year":"2009","journal-title":"Phys. Rev. A"},{"key":"2024061010532331400_c43","doi-asserted-by":"publisher","first-page":"1953","DOI":"10.1021\/ct400978j","article-title":"Toward reliable prediction of hyperfine coupling constants using ab\u00a0initio density matrix renormalization group method: Diatomic 2\u03c3 and vinyl radicals as test cases","volume":"10","year":"2014","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c44","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1021\/ct5007778","article-title":"Scalar relativistic calculations of hyperfine coupling constants using ab\u00a0initio density matrix renormalization group method in combination with third-order Douglas\u2013Kroll\u2013Hess transformation: Case studies on 4d transition metals","volume":"11","year":"2015","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c45","doi-asserted-by":"publisher","first-page":"4347","DOI":"10.1021\/acs.jctc.6b00646","article-title":"Hyperfine coupling constants from internally contracted multireference perturbation theory","volume":"12","year":"2016","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c46","doi-asserted-by":"publisher","first-page":"064101","DOI":"10.1063\/1.5040587","article-title":"First-order properties from internally contracted multireference coupled-cluster theory with particular focus on hyperfine coupling tensors","volume":"149","year":"2018","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c47","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1021\/acs.jctc.0c01005","article-title":"Electron\u2013nucleus hyperfine coupling calculated from restricted active space wavefunctions and an exact two-component Hamiltonian","volume":"17","year":"2021","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c48","doi-asserted-by":"publisher","first-page":"4719","DOI":"10.1021\/acs.jctc.2c00257","article-title":"Hyperion: A new computational tool for relativistic ab\u00a0initio hyperfine coupling","volume":"18","year":"2022","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c49","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1002\/jcc.24221","article-title":"Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table","volume":"37","year":"2016","journal-title":"J.\u00a0Comput. Chem."},{"key":"2024061010532331400_c50","doi-asserted-by":"publisher","first-page":"5925","DOI":"10.1021\/acs.jctc.9b00532","article-title":"OpenMolcas: From source code to insight","volume":"15","year":"2019","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c51","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1002\/(sici)1097-461x(2000)78:6&lt;412::aid-qua2&gt;3.3.co;2-l","article-title":"Relativistic electric and magnetic property operators for two-component transformed Hamiltonians","volume":"78","year":"2000","journal-title":"Int. J. Quantum Chem."},{"key":"2024061010532331400_c52","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1063\/1.1528933","article-title":"Quasirelativistic theory for the magnetic shielding constant. I. Formulation of Douglas\u2013Kroll\u2013Hess transformation for the magnetic field and its application to atomic systems","volume":"118","year":"2003","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c53","doi-asserted-by":"publisher","first-page":"204112","DOI":"10.1063\/1.2133730","article-title":"Relativistic calculation of indirect NMR spin\u2013spin couplings using the Douglas\u2013Kroll\u2013Hess approximation","volume":"123","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c54","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":"2024061010532331400_c55","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1103\/physrev.78.699","article-title":"Magnetic shielding of nuclei in molecules","volume":"78","year":"1950","journal-title":"Phys. Rev."},{"key":"2024061010532331400_c56","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/0003-4916(74)90333-9","article-title":"Quantum electrodynamical corrections to the fine structure of helium","volume":"82","year":"1974","journal-title":"Ann. Phys."},{"key":"2024061010532331400_c57","doi-asserted-by":"publisher","first-page":"3742","DOI":"10.1103\/physreva.33.3742","article-title":"Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators","volume":"33","year":"1986","journal-title":"Phys. Rev. A"},{"key":"2024061010532331400_c58","doi-asserted-by":"publisher","first-page":"9215","DOI":"10.1063\/1.1515314","article-title":"The generalized Douglas\u2013Kroll transformation","volume":"117","year":"2002","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c59","doi-asserted-by":"publisher","first-page":"2037","DOI":"10.1063\/1.1768160","article-title":"Exact decoupling of the Dirac Hamiltonian. I. General theory","volume":"121","year":"2004","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c60","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1103\/physrev.78.29","article-title":"On the Dirac theory of spin 1\/2 particles and its non-relativistic limit","volume":"78","year":"1950","journal-title":"Phys. Rev."},{"key":"2024061010532331400_c61","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1002\/qua.560290414","article-title":"Toward the variational treatment of spin\u2013orbit and other relativistic effects for heavy atoms and molecules","volume":"29","year":"1986","journal-title":"Int. J. Quantum Chem."},{"key":"2024061010532331400_c62","doi-asserted-by":"publisher","first-page":"5889","DOI":"10.1063\/1.461610","article-title":"The reduced multiplication scheme of the Rys quadrature and new recurrence relations for auxiliary function based two-electron integral evaluation","volume":"95","year":"1991","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c63","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/bf01120130","article-title":"Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions","volume":"77","year":"1990","journal-title":"Theor. Chim. Acta"},{"key":"2024061010532331400_c64","doi-asserted-by":"publisher","first-page":"2851","DOI":"10.1021\/jp031064+","article-title":"Main group atoms and dimers studied with a new relativistic ANO basis set","volume":"108","year":"2004","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2024061010532331400_c65","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":"2024061010532331400_c66","doi-asserted-by":"publisher","first-page":"2384","DOI":"10.1063\/1.441359","article-title":"The complete active space SCF (CASSCF) method in a Newton\u2013Raphson formulation with application to the HNO molecule","volume":"74","year":"1981","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c67","doi-asserted-by":"publisher","first-page":"5477","DOI":"10.1021\/j100377a011","article-title":"The restricted active space self-consistent-field method, implemented with a split graph unitary group approach","volume":"94","year":"1990","journal-title":"J.\u00a0Phys. Chem."},{"key":"2024061010532331400_c68","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/0009-2614(96)00119-4","article-title":"A mean-field spin\u2013orbit method applicable to correlated wavefunctions","volume":"251","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2024061010532331400_c69","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":"2024061010532331400_c70","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/bf01113132","article-title":"The spin polarization model for hyperfine coupling constants","volume":"82","year":"1992","journal-title":"Theor. Chim. Acta"},{"key":"2024061010532331400_c71","doi-asserted-by":"publisher","first-page":"3060","DOI":"10.1021\/ct9003299","article-title":"Assessment of orbital-optimized, spin-component scaled second-order many-body perturbation theory for thermochemistry and kinetics","volume":"5","year":"2009","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2024061010532331400_c72","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1098\/rspa.1955.0120","article-title":"On the hyperfine structure of paramagnetic resonance: The s-electron effect","volume":"230","year":"1955","journal-title":"Proc. R. Soc. A"},{"key":"2024061010532331400_c73","doi-asserted-by":"publisher","first-page":"2027","DOI":"10.1103\/physrev.123.2027","article-title":"Origin of effective fields in magnetic materials","volume":"123","year":"1961","journal-title":"Phys. Rev."},{"key":"2024061010532331400_c74","doi-asserted-by":"publisher","first-page":"5618","DOI":"10.1063\/1.1785772","article-title":"Relativistically corrected hyperfine structure constants calculated with the regular approximation applied to correlation corrected ab\u00a0initio theory","volume":"121","year":"2004","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c75","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1140\/epjd\/e2004-00176-1","article-title":"Comparative studies of the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of 25Mg+","volume":"32","year":"2005","journal-title":"Eur. Phys. J. D"},{"key":"2024061010532331400_c76","doi-asserted-by":"publisher","first-page":"040501","DOI":"10.1103\/physreva.68.040501","article-title":"Magnetic dipole hyperfine interactions in 137Ba+ and the accuracies of the neutral weak interaction matrix elements","volume":"68","year":"2003","journal-title":"Phys. Rev. A"},{"key":"2024061010532331400_c77","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1103\/physreva.24.1364","article-title":"Precision measurement of the ground-state hyperfine constant of 25Mg+","volume":"24","year":"1981","journal-title":"Phys. Rev. A"},{"key":"2024061010532331400_c78","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/bf01426573","article-title":"Precise determination of the ground state hyperfine structure splitting of 43Ca II","volume":"31","year":"1994","journal-title":"Z. Phys. D"},{"key":"2024061010532331400_c79","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/bf00568145","article-title":"A precision measurement of the hyperfine structure of 87Sr+","volume":"78","year":"1993","journal-title":"Hyperfine Interact."},{"key":"2024061010532331400_c80","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/BF01415749","article-title":"Precision ground state Hfs-separation of 137Ba","volume":"299","year":"1981","journal-title":"Z. Phys. A"},{"key":"2024061010532331400_c81","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1103\/physrev.105.581","article-title":"Hyperfine structure of Cu63 and Cu65","volume":"105","year":"1957","journal-title":"Phys. Rev."},{"key":"2024061010532331400_c82","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1103\/physrev.92.641","article-title":"Hyperfine structures of silver and gold by the atomic beam magnetic resonance method","volume":"92","year":"1953","journal-title":"Phys. Rev."},{"key":"2024061010532331400_c83","doi-asserted-by":"publisher","first-page":"150902","DOI":"10.1063\/1.3702628","article-title":"Perspective: Relativistic effects","volume":"136","year":"2012","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c84","volume-title":"Reference Data on Atoms, Molecules, and Ions","year":"1985"},{"key":"2024061010532331400_c85","doi-asserted-by":"publisher","first-page":"69","DOI":"10.3390\/magnetochemistry5040069","article-title":"First-principles calculation of transition metal hyperfine coupling constants with the strongly constrained and appropriately normed (SCAN) density functional and its hybrid variants","volume":"5","year":"2019","journal-title":"Magnetochemistry"},{"key":"2024061010532331400_c86","doi-asserted-by":"publisher","first-page":"5658","DOI":"10.1063\/1.478464","article-title":"Electron spin resonance studies of 45Sc17O,89Y17O, and 139La17O in rare gas matrices: Comparison with ab\u00a0initio electronic structure and nuclear hyperfine calculations","volume":"110","year":"1999","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c87","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0022-2852(71)90157-3","article-title":"Hyperfine interaction and chemical bonding in the PdH molecule","volume":"40","year":"1971","journal-title":"J.\u00a0Mol. Spectrosc."},{"key":"2024061010532331400_c88","doi-asserted-by":"publisher","first-page":"6009","DOI":"10.1063\/1.441040","article-title":"Photolytic codeposition generation of the HgF radical in an argon matrix at 12\u00a0K: an ESR investigation","volume":"74","year":"1981","journal-title":"J.\u00a0Chem. Phys."},{"key":"2024061010532331400_c89","doi-asserted-by":"publisher","first-page":"4387","DOI":"10.1021\/ja808649g","article-title":"Spin dynamics in the negatively charged terbium (III) bis-phthalocyaninato complex","volume":"131","year":"2009","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2024061010532331400_c90","doi-asserted-by":"publisher","first-page":"12967","DOI":"10.1021\/jacs.9b05816","article-title":"Synthesis and magnetism of neutral, linear metallocene complexes of terbium(II) and dysprosium(II)","volume":"141","year":"2019","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2024061010532331400_c91","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":"2024061010532331400_c92","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":"2024061010532331400_c93","doi-asserted-by":"publisher","first-page":"5498","DOI":"10.1021\/ic049348b","article-title":"Upward temperature shift of the intrinsic phase lag of the magnetization of bis(phthalocyaninato)terbium by ligand oxidation creating an S = 1\/2 spin","volume":"43","year":"2004","journal-title":"Inorg. Chem."},{"key":"2024061010532331400_c94","doi-asserted-by":"publisher","first-page":"6996","DOI":"10.1021\/acs.jpca.9b03708","article-title":"Multireference ab\u00a0initio studies of magnetic properties of terbium-based single-molecule magnets","volume":"123","year":"2019","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2024061010532331400_c95","doi-asserted-by":"publisher","first-page":"024405","DOI":"10.1103\/physrevmaterials.2.024405","article-title":"Radical-lanthanide ferromagnetic interaction in a TbIII bis-phthalocyaninato complex","volume":"2","year":"2018","journal-title":"Phys. Rev. Mater."},{"key":"2024061010532331400_c96","doi-asserted-by":"publisher","first-page":"21793","DOI":"10.1039\/d0cp04056h","article-title":"Electrically tuned hyperfine spectrum in neutral Tb(II)(CpiPr5)2 single-molecule magnet","volume":"22","year":"2020","journal-title":"Phys. Chem. Chem. 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\/5.0208851\/19985896\/224102_1_5.0208851.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0208851\/19985896\/224102_1_5.0208851.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T10:53:38Z","timestamp":1718016818000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/160\/22\/224102\/3297299\/Relativistic-Douglas-Kroll-Hess-calculations-of"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,10]]},"references-count":96,"journal-issue":{"issue":"22","published-print":{"date-parts":[[2024,6,14]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0208851","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,6,14]]},"published":{"date-parts":[[2024,6,10]]},"article-number":"224102"}}