{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:20:33Z","timestamp":1772137233483,"version":"3.50.1"},"reference-count":85,"publisher":"AIP Publishing","issue":"2","license":[{"start":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T00:00:00Z","timestamp":1767830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","award":["2022-02871"],"award-info":[{"award-number":["2022-02871"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014437","name":"Wenner-Gren Stiftelserna","doi-asserted-by":"publisher","award":["UPD2023-0070"],"award-info":[{"award-number":["UPD2023-0070"]}],"id":[{"id":"10.13039\/100014437","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,1,14]]},"abstract":"<jats:p>Most advances in electronic spin-dependent non-adiabatic dynamics focus on refining the underlying dynamics methods. In contrast, this work considers an improved description of spin\u2013orbit coupling by explicitly accounting for its relativistic origins. To this end, we extend a standard one-electron triatomic Jahn\u2013Teller model to the four-component relativistic domain. In our formulation, the electron is treated using the Dirac\u2013Coulomb Hamiltonian, while the nuclei remain non-relativistic, departing from the conventional formulation that incorporates the Pauli spin\u2013orbit coupling as a perturbation. The most striking difference between our relativistic model and the conventional one is the presence of vibronic coupling terms on the anti-diagonal of the diabatic potential matrix. These terms scale as 1\/c2 and, although nominally small, they can be amplified near avoided-crossings or in systems with heavy nuclei. Furthermore, their presence implies that nuclear motion can affect the direction of the electron spin, a feature entirely absent in the non-relativistic formulation of our model. In the adiabatic representation, the couplings translate to non-Abelian characteristics of the non-adiabatic coupling matrix that persist even in the Born\u2013Oppenheimer approximation. Within our model setting, a relativistic formulation allows for a more intricate interplay between the electronic spin and nuclear degrees of freedom.<\/jats:p>","DOI":"10.1063\/5.0304011","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T12:24:32Z","timestamp":1767961472000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["A four-component relativistic perspective on an\n                    <i>E<\/i>\n                    \u2297\n                    <i>e<\/i>\n                    Jahn\u2013Teller model"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6143-0480","authenticated-orcid":false,"given":"Martin","family":"van Horn","sequence":"first","affiliation":[{"name":"Department of Chemistry, KTH Royal Institute of Technology 1 , SE-10044 Stockholm,","place":["Sweden"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0246-3995","authenticated-orcid":false,"given":"Nanna H.","family":"List","sequence":"additional","affiliation":[{"name":"Department of Chemistry, KTH Royal Institute of Technology 1 , SE-10044 Stockholm,","place":["Sweden"]},{"name":"School of Chemistry, University of Birmingham 2 , Birmingham B15 2TT,","place":["United Kingdom"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2026,1,9]]},"reference":[{"key":"2026010907242844900_c1","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1098\/rspa.1929.0094","article-title":"Quantum mechanics of many-electron systems","volume":"123","year":"1929","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2026010907242844900_c2","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1021\/cr00085a006","article-title":"Relativistic effects in structural chemistry","volume":"88","year":"1988","journal-title":"Chem. Rev."},{"key":"2026010907242844900_c3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0301-0104(83)80001-9","article-title":"On the relativistic theory of NMR chemical shifts","volume":"74","year":"1983","journal-title":"Chem. Phys."},{"key":"2026010907242844900_c4","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0022-2364(78)90175-0","article-title":"Proton, carbon, and cadmium NMR measurements and relativistic calculation of the cadmium-carbon coin tensor in dimethyl cadmium","volume":"31","year":"1978","journal-title":"J.\u00a0Magn. Reson."},{"key":"2026010907242844900_c5","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1080\/00268978000100611","article-title":"The r\u03b1-structure and anisotropy of the Hg-C indirect coupling constant of methylmercury nitrate dissolved in nematic and lyotropic liquid crystals","volume":"39","year":"1980","journal-title":"Mol. Phys."},{"key":"2026010907242844900_c6","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1103\/revmodphys.54.709","article-title":"Electron spectroscopy for atoms, molecules, and condensed matter","volume":"54","year":"1982","journal-title":"Rev. Mod. Phys."},{"key":"2026010907242844900_c7","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1007\/s00214-011-0911-2","article-title":"M\u00f6ssbauer spectroscopy for heavy elements: A relativistic benchmark study of mercury","volume":"129","year":"2011","journal-title":"Theor. Chem. Acc."},{"key":"2026010907242844900_c8","doi-asserted-by":"publisher","first-page":"4853","DOI":"10.1039\/c3cp54393e","article-title":"Theoretical 57Fe M\u00f6ssbauer spectroscopy: Isomer shifts of [Fe]-hydrogenase intermediates","volume":"16","year":"2014","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026010907242844900_c9","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1080\/00268976.2016.1203036","article-title":"Relativistic coupled cluster calculation of M\u00f6ssbauer isomer shifts of iodine compounds","volume":"115","year":"2017","journal-title":"Mol. Phys."},{"key":"2026010907242844900_c10","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/bf01400155","article-title":"Zur deutung einiger erscheinungen in den molekelspektren","volume":"36","year":"1926","journal-title":"Z. Phys."},{"key":"2026010907242844900_c11","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1007\/bf01400234","article-title":"Zur Deutung der Molekelspektren. I","volume":"40","year":"1927","journal-title":"Z. Phys."},{"key":"2026010907242844900_c12","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/bf01397124","article-title":"Zur Deutung der Molekelspektren. II","volume":"42","year":"1927","journal-title":"Z. Phys."},{"key":"2026010907242844900_c13","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/B978-012441455-6\/50005-6","article-title":"Chapter 2\u2013Basic models","volume-title":"The Spectra and Dynamics of Diatomic Molecules","author":"Lefebvre-Brion","year":"2004"},{"key":"2026010907242844900_c14","volume-title":"Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics","year":"1988"},{"key":"2026010907242844900_c15","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0301-0104(80)85036-1","article-title":"Electronic spin\u2013orbit interaction and the molecular Aharonov\u2013Bohm effect","volume":"49","year":"1980","journal-title":"Chem. Phys."},{"key":"2026010907242844900_c16","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1103\/physrevlett.59.161","article-title":"Molecular Kramers degeneracy and non-Abelian adiabatic phase factors","volume":"59","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"2026010907242844900_c17","doi-asserted-by":"publisher","first-page":"2038","DOI":"10.1063\/1.1378324","article-title":"On the effects of spin-orbit coupling on conical intersection seams in molecules with an odd number of electrons. I. Locating the seam","volume":"115","year":"2001","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c18","doi-asserted-by":"publisher","first-page":"5066","DOI":"10.1063\/1.1391444","article-title":"On the effects of spin\u2013orbit coupling on conical intersection seams in molecules with an odd number of electrons. II. Characterizing the local topography of the seam","volume":"115","year":"2001","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c19","doi-asserted-by":"publisher","first-page":"2825","DOI":"10.1063\/1.1427914","article-title":"Spin-orbit coupling and conical intersections in molecules with an odd number of electrons. III. A perturbative determination of the electronic energies, derivative couplings and a rigorous diabatic representation near a conical intersection","volume":"116","year":"2002","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c20","doi-asserted-by":"publisher","first-page":"8108","DOI":"10.1021\/jp020396w","article-title":"Spin\u2013orbit coupling and conical intersections. IV. A perturbative determination of the electronic energies, derivative couplings, and a rigorous diabatic representation near a conical intersection. The general case","volume":"106","year":"2002","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026010907242844900_c21","first-page":"557","article-title":"Conical intersections and the spin-orbit interaction","volume-title":"The Role of Degenerate States in Chemistry","year":"2002"},{"key":"2026010907242844900_c22","doi-asserted-by":"publisher","first-page":"104302","DOI":"10.1063\/5.0143809","article-title":"Representation and conservation of angular momentum in the Born\u2013Oppenheimer theory of polyatomic molecules","volume":"158","year":"2023","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c23","doi-asserted-by":"publisher","first-page":"L220304","DOI":"10.1103\/physrevb.108.l220304","article-title":"Total angular momentum conservation in ab\u00a0initio Born-Oppenheimer molecular dynamics","volume":"108","year":"2023","journal-title":"Phys. Rev. B"},{"key":"2026010907242844900_c24","doi-asserted-by":"publisher","first-page":"054104","DOI":"10.1063\/5.0177778","article-title":"Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states","volume":"160","year":"2024","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c25","doi-asserted-by":"publisher","first-page":"024119","DOI":"10.1063\/5.0179599","article-title":"Linear and angular momentum conservation in surface hopping methods","volume":"160","year":"2024","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c26","doi-asserted-by":"publisher","first-page":"114120","DOI":"10.1063\/5.0160965","article-title":"Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency","volume":"159","year":"2023","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c27","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1098\/rspa.1928.0023","article-title":"The quantum theory of the electron","volume":"117","year":"1928","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2026010907242844900_c28","volume-title":"Introduction to Relativistic Quantum Chemistry","year":"2007"},{"key":"2026010907242844900_c29","doi-asserted-by":"publisher","first-page":"3077","DOI":"10.1002\/cphc.201100682","article-title":"Relativistic Hamiltonians for chemistry: A primer","volume":"12","year":"2011","journal-title":"ChemPhysChem"},{"key":"2026010907242844900_c30","volume-title":"Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science","year":"2015"},{"key":"2026010907242844900_c31","volume-title":"Relativistic Quantum Mechanics: With Applications in Condensed Matter and Atomic Physics","year":"1998"},{"key":"2026010907242844900_c32","volume-title":"Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation","year":"2007"},{"key":"2026010907242844900_c33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/14786440108564170","article-title":"I. The kinematics of an electron with an axis","volume":"3","year":"1927","journal-title":"London, Edinburgh Dublin Philos. Mag. J. Sci."},{"key":"2026010907242844900_c34","volume-title":"Classical Electrodynamics","year":"1999","edition":"3"},{"key":"2026010907242844900_c35","volume-title":"Introduction to Electrodynamics","year":"1999","edition":"3"},{"key":"2026010907242844900_c36","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/bf01397326","article-title":"Zur Quantenmechanik des magnetischen Elektrons","volume":"43","year":"1927","journal-title":"Z. Phys."},{"key":"2026010907242844900_c37","volume-title":"Quantum Mechanics of One- and Two-Electron Atoms","year":"2013"},{"key":"2026010907242844900_c38","doi-asserted-by":"publisher","first-page":"052803","DOI":"10.1103\/PhysRevA.107.052803","article-title":"Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems","volume":"107","year":"2023","journal-title":"Phys. Rev. A"},{"key":"2026010907242844900_c39","doi-asserted-by":"publisher","first-page":"234103","DOI":"10.1063\/5.0209702","article-title":"The direct role of nuclear motion in spin\u2013orbit coupling in strongly correlated spin systems","volume":"160","year":"2024","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c40","doi-asserted-by":"crossref","unstructured":"M.\n            van Horn\n          , T.Cheragwandi, and N. H.List, \u201cElectronic spin-dependent dynamics through the lens of angular momentum exchange. I. A Born\u2013Huang perspective,\u201d chemRxiv:10.26434\/chemrxiv-2025-x3fr7 (2025).","DOI":"10.26434\/chemrxiv-2025-x3fr7"},{"key":"2026010907242844900_c41","doi-asserted-by":"crossref","unstructured":"M.\n            van Horn\n          , T.Cheragwandi, and N. H.List, \u201cElectronic spin-dependent dynamics through the lens of angular momentum exchange. II. Insights from a model system,\u201d chemRxiv:10.26434\/chemrxiv-2025-xdhvl (2025).","DOI":"10.26434\/chemrxiv-2025-xdhvl"},{"key":"2026010907242844900_c42","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1098\/rspa.1976.0134","article-title":"Spin-orbit coupling and the intersection of potential energy surfaces in polyatomic molecules","volume":"351","year":"1976","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2026010907242844900_c43","doi-asserted-by":"publisher","first-page":"1503","DOI":"10.1063\/1.475522","article-title":"Geometric phases and quantum dynamics in spin\u2013orbit coupled systems","volume":"108","year":"1998","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c44","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/j.chemphys.2005.09.009","article-title":"The relativistic E \u00d7 E Jahn\u2013Teller effect revisited","volume":"322","year":"2006","journal-title":"Chem. Phys."},{"key":"2026010907242844900_c45","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/978-3-642-03432-9","article-title":"Spin\u2013orbit vibronic coupling in Jahn\u2013Teller and Renner systems","volume-title":"The Jahn-Teller Effect: Fundamentals and Implications for Physics and Chemistry","author":"K\u00f6ppel","year":"2009"},{"key":"2026010907242844900_c46","first-page":"249","article-title":"First-quantized Dirac-based many-electron theory","volume-title":"Relativistic Quantum Chemistry","year":"2014"},{"key":"2026010907242844900_c47","volume-title":"Molecular Symmetry and Spectroscopy","year":"2006","edition":"2"},{"key":"2026010907242844900_c48","doi-asserted-by":"publisher","first-page":"204119","DOI":"10.1063\/1.4721627","article-title":"Theoretical study of the nuclear spin-molecular rotation coupling for relativistic electrons and non-relativistic nuclei","volume":"136","year":"2012","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c49","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1103\/physrev.47.552","article-title":"Some studies concerning rotating axes and polyatomic molecules","volume":"47","year":"1935","journal-title":"Phys. Rev."},{"key":"2026010907242844900_c50","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1103\/revmodphys.48.69","article-title":"Eckart vectors, Eckart frames, and polyatomic molecules","volume":"48","year":"1976","journal-title":"Rev. Mod. Phys."},{"key":"2026010907242844900_c51","volume-title":"Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra","year":"1980"},{"key":"2026010907242844900_c52","doi-asserted-by":"publisher","first-page":"043203","DOI":"10.1103\/physreva.71.043203","article-title":"Quantum electrical dipole in triangular systems: A model for spontaneous polarity in metal clusters","volume":"71","year":"2005","journal-title":"Phys. Rev. A"},{"key":"2026010907242844900_c53","volume-title":"The Jahn-Teller Effect and Vibronic Interactions in Modern Chemistry","year":"1984"},{"key":"2026010907242844900_c54","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1002\/andp.19273892002","article-title":"Zur Quantentheorie der Molekeln","volume":"389","year":"1927","journal-title":"Ann. Phys."},{"key":"2026010907242844900_c55","volume-title":"Dynamical Theory of Crystal Lattices","year":"2002"},{"key":"2026010907242844900_c56","volume-title":"Vibronic Interactions in Molecules and Crystals","year":"1989"},{"key":"2026010907242844900_c57","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1146\/annurev.physchem.55.091602.094335","article-title":"Beyond Born-Oppenheimer: Molecular dynamics through a conical intersection","volume":"55","year":"2004","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2026010907242844900_c58","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/s0370-1573(01)00052-7","article-title":"Introduction to the theory of electronic non-adiabatic coupling terms in molecular systems","volume":"358","year":"2002","journal-title":"Phys. Rep."},{"key":"2026010907242844900_c59","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/0301-0104(80)85035-x","article-title":"The molecular Aharonov\u2013Bohm effect in bound states","volume":"49","year":"1980","journal-title":"Chem. Phys."},{"key":"2026010907242844900_c60","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1098\/rspa.1984.0023","article-title":"Quantal phase factors accompanying adiabatic changes","volume":"392","year":"1984","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2026010907242844900_c61","volume-title":"Geometric Phases in Physics","year":"1989"},{"key":"2026010907242844900_c62","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1146\/annurev.pc.41.100190.003125","article-title":"Berry\u2019s phase","volume":"41","year":"1990","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2026010907242844900_c63","unstructured":"M. T.\n            Johnsson\n          , \u201cTime reversal symmetry and the geometric phase,\u201d Ph.D. thesis, University of Canterbury, 1998."},{"key":"2026010907242844900_c64","doi-asserted-by":"publisher","first-page":"6409","DOI":"10.1039\/c2cp22974a","article-title":"Geometric phase and gauge connection in polyatomic molecules","volume":"14","year":"2012","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026010907242844900_c65","first-page":"163","volume-title":"Relativistic Electron Theory","year":"1961"},{"key":"2026010907242844900_c66","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-0-387-35069-1_1","article-title":"Relativity in atomic and molecular physics","volume-title":"Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation","author":"Grant","year":"2007"},{"key":"2026010907242844900_c67","first-page":"291","article-title":"The hole theory","volume-title":"Relativistic Quantum Mechanics: Wave Equations","year":"2000"},{"key":"2026010907242844900_c68","volume-title":"Point-Group Theory Tables","year":"1994"},{"key":"2026010907242844900_c69","first-page":"959","article-title":"Th\u00e9orie g\u00e9n\u00e9rale de la rotation paramagn\u00e9tique dans les cristaux","volume":"33","year":"1930","journal-title":"Proc. Acad. Amsterdam"},{"key":"2026010907242844900_c70","first-page":"546","article-title":"Ueber die operation der Zeitumkehr in der Quantenmechanik","volume-title":"Nachrichten von der Gesellschaft der Wissenschaften zu G\u00f6ttingen","year":"1932"},{"key":"2026010907242844900_c71","doi-asserted-by":"publisher","first-page":"6211","DOI":"10.1063\/1.479958","article-title":"Quaternion symmetry in relativistic molecular calculations: The Dirac\u2013Hartree\u2013Fock method","volume":"111","year":"1999","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c72","doi-asserted-by":"publisher","first-page":"4472","DOI":"10.1063\/1.469495","article-title":"Geometric phase in two Kramers doublets molecular systems","volume":"102","year":"1995","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c73","doi-asserted-by":"publisher","first-page":"184117","DOI":"10.1103\/PhysRevB.71.184117","article-title":"Origin of warping in the E \u2297 e Jahn-Teller problem: Quadratic vibronic coupling versus anharmonicity and application to NaCl:Rh2+ and triangular molecules","volume":"71","year":"2005","journal-title":"Phys. Rev. B"},{"key":"2026010907242844900_c74","doi-asserted-by":"publisher","first-page":"2276","DOI":"10.1063\/1.437733","article-title":"The \u2018noncrossing\u2019 rule for electronic potential energy surfaces: The role of time-reversal invariance","volume":"70","year":"1979","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026010907242844900_c75","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1103\/revmodphys.64.51","article-title":"The geometric phase in molecular systems","volume":"64","year":"1992","journal-title":"Rev. Mod. Phys."},{"key":"2026010907242844900_c76","volume-title":"Geometry, Topology, and Physics","year":"2003","edition":"2"},{"key":"2026010907242844900_c77","volume-title":"Partial Differential Equations","year":"2022","edition":"2"},{"key":"2026010907242844900_c78","doi-asserted-by":"publisher","first-page":"6277","DOI":"10.1021\/jp003731u","article-title":"Conical intersections: The new conventional wisdom","volume":"105","year":"2001","journal-title":"J.\u00a0Phys. Chem. A"},{"key":"2026010907242844900_c79","doi-asserted-by":"publisher","first-page":"2111","DOI":"10.1103\/physrevlett.52.2111","article-title":"Appearance of gauge structure in simple dynamical systems","volume":"52","year":"1984","journal-title":"Phys. Rev. Lett."},{"key":"2026010907242844900_c80","doi-asserted-by":"publisher","first-page":"1950","DOI":"10.1021\/acs.chemrev.3c00661","article-title":"Chiral induced spin selectivity","volume":"124","year":"2024","journal-title":"Chem. Rev."},{"key":"2026010907242844900_c81","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1038\/s41570-019-0087-1","article-title":"Chiral molecules and the electron spin","volume":"3","year":"2019","journal-title":"Nat. Rev. Chem."},{"key":"2026010907242844900_c82","doi-asserted-by":"publisher","first-page":"7126","DOI":"10.1021\/acs.jpclett.9b02929","article-title":"Chirality-induced spin selectivity: The role of electron correlations","volume":"10","year":"2019","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026010907242844900_c83","doi-asserted-by":"publisher","first-page":"235416","DOI":"10.1103\/physrevb.102.235416","article-title":"Vibrational origin of exchange splitting and chiral-induced spin selectivity","volume":"102","year":"2020","journal-title":"Phys. Rev. B"},{"key":"2026010907242844900_c84","doi-asserted-by":"publisher","first-page":"L012004","DOI":"10.1103\/physrevresearch.4.l012004","article-title":"Dynamic electron-phonon and spin-phonon interactions due to inertia","volume":"4","year":"2022","journal-title":"Phys. Rev. Res."},{"key":"2026010907242844900_c85","doi-asserted-by":"publisher","first-page":"244107","DOI":"10.1063\/5.0274260","article-title":"Symmetry breaking as predicted by a phase space Hamiltonian with a spin Coriolis potential","volume":"162","year":"2025","journal-title":"J.\u00a0Chem. 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\/5.0304011\/20865386\/024105_1_5.0304011.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0304011\/20865386\/024105_1_5.0304011.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T12:24:37Z","timestamp":1767961477000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/164\/2\/024105\/3377041\/A-four-component-relativistic-perspective-on-an-E"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,9]]},"references-count":85,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,1,14]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0304011","relation":{"has-preprint":[{"id-type":"doi","id":"10.26434\/chemrxiv-2025-47531-v2","asserted-by":"object"},{"id-type":"doi","id":"10.26434\/chemrxiv-2025-47531","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":[[2026,1,14]]},"published":{"date-parts":[[2026,1,9]]},"article-number":"024105"}}