{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T12:12:40Z","timestamp":1783944760795,"version":"3.55.0"},"reference-count":32,"publisher":"AIP Publishing","issue":"2","license":[{"start":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T00:00:00Z","timestamp":1783728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["536826332"],"award-info":[{"award-number":["536826332"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,7,14]]},"abstract":"<jats:p>We extend our recent work on the cavity-modified spin Zeeman effect of an effective spin-1\/2-system [E. W. Fischer and M. Roemelt, J. Chem. Phys. 163, 174307 (2025)] to a relativistic Jahn\u2013Teller scenario under strong light\u2013matter coupling. Here, the effective spin-1\/2-system is realized via a single electron or a single hole in a doubly degenerate molecular orbital system of trigonal symmetric transition metal complexes. Single-particle and single-hole systems are subject to both vibronic and spin\u2013orbit coupling (SOC) augmented by interactions with a quantized cavity field via the cavity\u2013Zeeman interaction. Methodologically, we combine the relativistic E \u00d7 e-Jahn\u2013Teller model with a recently introduced effective Hamiltonian formalism based on quasi-degenerate perturbation theory, which treats the cavity\u2013spin interaction in leading order beyond the dipole approximation. We derive analytic expressions for Kramers pair energies in weak and strong SOC regimes, as well as related cavity-modified effective electronic g-factors. We find cavity-induced modifications of the electronic g-factor to become relevant in the weak SOC regime for both single-particle and single-hole systems while being effectively quenched under strong SOC. Alternating signs of the cavity\u2013Zeeman correction render single-particle and single-hole scenarios distinct in their response to the cavity field from a g-factor perspective.<\/jats:p>","DOI":"10.1063\/5.0339669","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T11:46:28Z","timestamp":1783943188000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Spin\u2013cavity interactions in relativistic Jahn\u2013Teller systems under strong light\u2013matter coupling"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4786-4012","authenticated-orcid":false,"given":"Eric W.","family":"Fischer","sequence":"first","affiliation":[{"name":"Humboldt-Universit\u00e4t zu Berlin, Institut f\u00fcr Chemie , Brook-Taylor-Stra\u00dfe 2, D-12489 Berlin,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4780-5354","authenticated-orcid":false,"given":"Michael","family":"Roemelt","sequence":"additional","affiliation":[{"name":"Humboldt-Universit\u00e4t zu Berlin, Institut f\u00fcr Chemie , Brook-Taylor-Stra\u00dfe 2, D-12489 Berlin,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,7,13]]},"reference":[{"key":"2026071307462229200_c1","doi-asserted-by":"publisher","first-page":"2403","DOI":"10.1021\/acs.accounts.6b00295","article-title":"Hybrid light-matter states in a molecular and material science perspective","volume":"49","year":"2016","journal-title":"Acc. Chem. Res."},{"key":"2026071307462229200_c2","doi-asserted-by":"publisher","first-page":"eabd0336","DOI":"10.1126\/science.abd0336","article-title":"Manipulating matter by strong coupling to vacuum fields","volume":"373","year":"2021","journal-title":"Science"},{"key":"2026071307462229200_c3","doi-asserted-by":"publisher","first-page":"1592","DOI":"10.1002\/anie.201107033","article-title":"Modifying chemical landscapes by coupling to vacuum fields","volume":"51","year":"2012","journal-title":"Angew. Chem., Int. Ed."},{"key":"2026071307462229200_c4","doi-asserted-by":"publisher","first-page":"11462","DOI":"10.1002\/anie.201605504","article-title":"Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field","volume":"55","year":"2016","journal-title":"Angew. Chem., Int. Ed."},{"key":"2026071307462229200_c5","doi-asserted-by":"publisher","first-page":"e202401368","DOI":"10.1002\/ange.202401368","article-title":"Direct observation of polaritonic chemistry by nuclear magnetic resonance spectroscopy","volume":"136","year":"2024","journal-title":"Angew. Chem."},{"key":"2026071307462229200_c6","doi-asserted-by":"publisher","first-page":"120501","DOI":"10.1103\/physrevlett.112.120501","article-title":"Collective coupling of a macroscopic number of single-molecule magnets with a microwave cavity mode","volume":"112","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"2026071307462229200_c7","doi-asserted-by":"publisher","first-page":"16682","DOI":"10.1039\/c6dt02664h","article-title":"A scalable architecture for quantum computation with molecular nanomagnets","volume":"45","year":"2016","journal-title":"Dalton Trans."},{"key":"2026071307462229200_c8","doi-asserted-by":"publisher","first-page":"13096","DOI":"10.1038\/s41598-017-13271-w","article-title":"Coherent coupling between vanadyl phthalocyanine spin ensemble and microwave photons: Towards integration of molecular spin qubits into quantum circuits","volume":"7","year":"2017","journal-title":"Sci. Rep."},{"key":"2026071307462229200_c9","doi-asserted-by":"publisher","first-page":"041043","DOI":"10.1103\/physrevx.10.041043","article-title":"Coupled cluster theory for molecular polaritons: Changing ground and excited states","volume":"10","year":"2020","journal-title":"Phys. Rev. X"},{"key":"2026071307462229200_c10","doi-asserted-by":"publisher","first-page":"1368","DOI":"10.1038\/s41467-022-29003-2","article-title":"Molecular orbital theory in cavity QED environments","volume":"13","year":"2022","journal-title":"Nat. Commun."},{"key":"2026071307462229200_c11","doi-asserted-by":"publisher","first-page":"233001","DOI":"10.1103\/physrevlett.110.233001","article-title":"Time-dependent density functional theory for many-electron systems interacting with cavity photons","volume":"110","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"2026071307462229200_c12","doi-asserted-by":"publisher","first-page":"012508","DOI":"10.1103\/physreva.90.012508","article-title":"Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic structure theory","volume":"90","year":"2014","journal-title":"Phys. Rev. A"},{"key":"2026071307462229200_c13","doi-asserted-by":"publisher","first-page":"8024","DOI":"10.1021\/acs.jpclett.3c01842","article-title":"Cavity Born\u2013Oppenheimer Hartree\u2013Fock ansatz: Light-matter properties of strongly coupled molecular ensembles","volume":"14","year":"2023","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026071307462229200_c14","doi-asserted-by":"publisher","first-page":"164112","DOI":"10.1063\/5.0231528","article-title":"Cavity-modified local and non-local electronic interactions in molecular ensembles under vibrational strong coupling","volume":"161","year":"2024","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026071307462229200_c15","doi-asserted-by":"publisher","first-page":"12081","DOI":"10.1021\/acs.jctc.5c01604","article-title":"Cavity Born\u2013Oppenheimer coupled cluster theory: Toward electron correlation in the vibrational strong light-matter coupling regime","volume":"21","year":"2025","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026071307462229200_c16","doi-asserted-by":"publisher","first-page":"047202","DOI":"10.1103\/physrevlett.123.047202","article-title":"Quantum electrodynamical Bloch theory with homogeneous magnetic fields","volume":"123","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"2026071307462229200_c17","doi-asserted-by":"publisher","first-page":"205424","DOI":"10.1103\/physrevb.105.205424","article-title":"Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance","volume":"105","year":"2022","journal-title":"Phys. Rev. B"},{"key":"2026071307462229200_c18","doi-asserted-by":"publisher","first-page":"7841","DOI":"10.1021\/acs.jctc.4c00195","article-title":"Theory of magnetic properties in quantum electrodynamics environments: Application to molecular aromaticity","volume":"20","year":"2024","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026071307462229200_c19","doi-asserted-by":"publisher","first-page":"174307","DOI":"10.1063\/5.0303448","article-title":"Cavity-modified Zeeman effect via spin-polariton formation","volume":"163","year":"2025","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026071307462229200_c20","doi-asserted-by":"publisher","first-page":"031052","DOI":"10.1103\/ttc3-867m","article-title":"Relativistic linear response in quantum-electrodynamical density functional theory","volume":"15","year":"2025","journal-title":"Phys. Rev. X"},{"key":"2026071307462229200_c21","doi-asserted-by":"publisher","first-page":"026102","DOI":"10.1063\/5.0289813","article-title":"Linear-response quantum-electrodynamical density functional theory based on two-component X2C Hamiltonians","volume":"1","year":"2025","journal-title":"APL Comput. Phys."},{"key":"2026071307462229200_c22","doi-asserted-by":"publisher","first-page":"3775","DOI":"10.1021\/jacsau.5c00233","article-title":"A comprehensive theory for relativistic polaritonic chemistry: A four-component ab\u00a0initio treatment of molecular systems coupled to quantum fields","volume":"5","year":"2025","journal-title":"JACS Au"},{"key":"2026071307462229200_c23","volume-title":"The Jahn\u2013Teller Effect","year":"2006","edition":"1"},{"key":"2026071307462229200_c24","doi-asserted-by":"publisher","first-page":"253001","DOI":"10.1103\/physrevlett.121.253001","article-title":"Collective Jahn\u2013Teller interactions through light-matter coupling in a cavity","volume":"121","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"2026071307462229200_c25","doi-asserted-by":"publisher","first-page":"L061101","DOI":"10.1103\/physreva.107.l061101","article-title":"Cavity Jahn\u2013Teller polaritons in molecules","volume":"107","year":"2023","journal-title":"Phys. Rev. A"},{"key":"2026071307462229200_c26","doi-asserted-by":"publisher","first-page":"6906","DOI":"10.1021\/acs.inorgchem.7b00364","article-title":"Experimental and theoretical EPR study of Jahn\u2013Teller-active [HIPTN3N]MoL complexes (L = N2, CO, NH3)","volume":"56","year":"2017","journal-title":"Inorg. Chem."},{"issue":"25","key":"2026071307462229200_c27","doi-asserted-by":"publisher","first-page":"8645","DOI":"10.1021\/ja1004619","article-title":"Experimental and theoretical EPR study of Jahn\u2013Teller-active [HIPTN3N]MoL complexes (L = N2, CO, NH3)","volume":"132","year":"2010","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026071307462229200_c28","doi-asserted-by":"publisher","first-page":"1717","DOI":"10.1063\/1.1696183","article-title":"On the origin of spin-Hamiltonian parameters","volume":"42","year":"1965","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026071307462229200_c29","doi-asserted-by":"publisher","first-page":"6568","DOI":"10.1021\/ic980948i","article-title":"Calculation of zero-field splittings, g-values, and the relativistic nephelauxetic effect in transition metal complexes. Application to high-spin ferric complexes","volume":"37","year":"1998","journal-title":"Inorg.Chem."},{"key":"2026071307462229200_c30","article-title":"Quantum chemistry and EPR parameters","volume-title":"EPR Spectroscopy - Fundamentals and Methods","author":"Goldfarb","year":"2018"},{"key":"2026071307462229200_c31","doi-asserted-by":"publisher","first-page":"4662","DOI":"10.1021\/acs.jctc.8b00513","article-title":"Challenges in multireference perturbation theory for the calculations of the g-tensor of first-row transition-metal complexes","volume":"14","year":"2018","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026071307462229200_c32","doi-asserted-by":"publisher","first-page":"2262","DOI":"10.1021\/acs.jpclett.4c00105","article-title":"Quantum chemistry approach to linear vibro-polaritonic infrared spectra with perturbative electron-photon correlation","volume":"15","year":"2024","journal-title":"J.\u00a0Phys. Chem. Lett."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0339669\/21072270\/024310_1_5.0339669.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0339669\/21072270\/024310_1_5.0339669.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T11:46:30Z","timestamp":1783943190000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/165\/2\/024310\/3398195\/Spin-cavity-interactions-in-relativistic-Jahn"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,13]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,7,14]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0339669","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,7,14]]},"published":{"date-parts":[[2026,7,13]]},"article-number":"024310"}}