{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T13:04:53Z","timestamp":1789391093201,"version":"build-2803163510"},"reference-count":54,"publisher":"American Chemical Society (ACS)","issue":"36","license":[{"start":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T00:00:00Z","timestamp":1788134400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T00:00:00Z","timestamp":1788134400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T00:00:00Z","timestamp":1788134400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100017596","name":"Natural Science Basic Research Program of Shaanxi Province","doi-asserted-by":"publisher","award":["2021JM-005"],"award-info":[{"award-number":["2021JM-005"]}],"id":[{"id":"10.13039\/501100017596","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["21773181"],"award-info":[{"award-number":["21773181"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U2241207"],"award-info":[{"award-number":["U2241207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The unique two-center-one-electron (2c-1e) metal\u2013metal bond exhibits unique electronic structure and magnetic properties, giving birth to various candidates in the field of molecular spin devices (MSDs). Experimental characterization, theoretical researches, and device developments for these paramagnetic molecules highly rely on the key parameter of anisotropic Lande\u0301 g-factor, while the relevance of geometric or electronic structure to g-factor anisotropy has remained unclear yet for species encapsulating such 2c-1e bond (denoted by the symbol {2c-1e}). To remove the barrier to in-depth study and further applications, here we develop a theoretical framework describing the g-factor anisotropy in S = 1\/2 {2c-1e} systems. Taking the anion Y2@C80\u2013 as exemplar, we integrate theoretical derivations with ab initio computations to elucidate how point group symmetry determines the spin\u2013orbit coupling interactions between electronic states in a {2c-1e} system, thereby consequently governing the anisotropy of the g-factor. On such basis, explicit formulations describing the g-factor anisotropy are derived, on which we conduct mathematical analyses, identifying and summarizing several general rules about the variation patterns of g-tensor. The analytical methodology and the resulting conclusions in this work are universally applicable for various {2c-1e} systems, offering direct guidance for the spectroscopic analysis and supports future development of related MSDs.<\/jats:p>","DOI":"10.1021\/acs.inorgchem.6c02404","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T02:30:44Z","timestamp":1788402644000},"page":"20934-20943","source":"Crossref","is-referenced-by-count":0,"title":["Key Role of\nPoint Group Symmetry:\n                    <i>g<\/i>\n                    -Factor Anisotropy\nin the Paramagnetic Two-Center-One-Electron\nMolecular System"],"prefix":"10.1021","volume":"65","author":[{"given":"Yi","family":"Zhou","sequence":"first","affiliation":[{"name":"Xi\u2019an Jiaotong University , , ,","place":["Xi\u2019an, China, 710049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenke","family":"Wang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jiaotong University , , ,","place":["Xi\u2019an, China, 710049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruiyu","family":"Liu","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jiaotong University , , ,","place":["Xi\u2019an, China, 710049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yajie","family":"Yin","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jiaotong University , , ,","place":["Xi\u2019an, China, 710049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2528-6423","authenticated-orcid":true,"given":"Yonghong","family":"Cheng","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jiaotong University , , ,","place":["Xi\u2019an, China, 710049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3982-4763","authenticated-orcid":true,"given":"Xiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jiaotong University , , ,","place":["Xi\u2019an, China, 710049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5336-9854","authenticated-orcid":true,"given":"Hong","family":"Zheng","sequence":"additional","affiliation":[{"name":"Xi\u2019an Jiaotong University , , ,","place":["Xi\u2019an, China, 710049"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,31]]},"reference":[{"key":"2026091408072232700_cit1","doi-asserted-by":"publisher","first-page":"94908552","DOI":"10.26599\/NR.2026.94908552","article-title":"Single-molecule spin\ndevices: Fundamentals, advances, and prospects","volume":"19","author":"Yuzhe","year":"2026","journal-title":"Nano Res."},{"key":"2026091408072232700_cit2","doi-asserted-by":"publisher","first-page":"12919","DOI":"10.1021\/acs.inorgchem.2c00859","article-title":"Molecular Compounds in Spintronic\nDevices: An Intricate Marriage of Chemistry and Physics","volume":"61","author":"Zlobin","year":"2022","journal-title":"Inorg. Chem."},{"key":"2026091408072232700_cit3","doi-asserted-by":"publisher","first-page":"107","DOI":"10.3390\/magnetochemistry10120107","article-title":"Exploring Spin-Crossover\nCobalt(II) Single-Ion Magnets as Multifunctional\nand Multiresponsive Magnetic Devices: Advancements and Prospects in\nMolecular Spintronics and Quantum Computing Technologies","volume":"10","author":"Rabelo","year":"2024","journal-title":"Magnetochemistry"},{"key":"2026091408072232700_cit4","doi-asserted-by":"publisher","first-page":"2105663","DOI":"10.1002\/adma.202105663","article-title":"Spin-Crossover Molecules\non Surfaces: From Isolated Molecules to Ultrathin Films","volume":"33","author":"Kipgen","year":"2021","journal-title":"Adv. Mater."},{"key":"2026091408072232700_cit5","doi-asserted-by":"publisher","first-page":"3531","DOI":"10.1021\/acsaelm.3c00472","article-title":"Toward Molecular\nSpin Qubit Devices: Integration of\nMagnetic Molecules into Solid-State Devices","volume":"5","author":"Fursina","year":"2023","journal-title":"ACS Appl. Electron. Mater."},{"key":"2026091408072232700_cit6","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1038\/s41578-019-0146-8","article-title":"Molecular\nMagnetism: From Chemical Design to Spin Control in Molecules, Materials\nand Devices","volume":"5","author":"Coronado","year":"2020","journal-title":"Nat. Rev. Mater."},{"key":"2026091408072232700_cit7","doi-asserted-by":"publisher","first-page":"2401302","DOI":"10.1002\/smtd.202401302","article-title":"Understanding\nthe Spin\nof Metal Complexes from a Single-Molecule Perspective","volume":"9","author":"Guo","year":"2025","journal-title":"Small Methods"},{"key":"2026091408072232700_cit8","doi-asserted-by":"publisher","first-page":"2470","DOI":"10.1039\/C5SC03224E","article-title":"The Rise of\n3-d Single-Ion Magnets\nin Molecular Magnetism: Towards Materials from Molecules?","volume":"7","author":"Frost","year":"2016","journal-title":"Chem. Sci."},{"key":"2026091408072232700_cit9","doi-asserted-by":"publisher","first-page":"2381","DOI":"10.1021\/acs.accounts.6b00222","article-title":"Understanding the Magnetic\nAnisotropy toward Single-Ion Magnets","volume":"49","author":"Meng","year":"2016","journal-title":"Acc. Chem.\nRes."},{"issue":"39","key":"2026091408072232700_cit10","doi-asserted-by":"publisher","first-page":"12992","DOI":"10.1021\/ja802417d","article-title":"M2@C79N (M=\nY, Tb): isolation and characterization of stable endohedral metallofullerenes\nexhibiting M M bonding interactions inside Aza [80] fullerene cages","volume":"130","author":"Zuo","year":"2008","journal-title":"J. Am. Chem. Soc."},{"issue":"25","key":"2026091408072232700_cit11","doi-asserted-by":"publisher","first-page":"9741","DOI":"10.1021\/ja202011u","article-title":"Gd2@C79N: isolation, characterization,\nand monoadduct formation of a very stable heterofullerene with a magnetic\nspin state of S= 15\/2","volume":"133","author":"Fu","year":"2011","journal-title":"J. Am. Chem. Soc."},{"issue":"20","key":"2026091408072232700_cit12","doi-asserted-by":"publisher","first-page":"11130","DOI":"10.1039\/d0nr02519d","article-title":"Dy2@C79N: a new member of dimetalloazafullerenes\nwith strong single molecular magnetism","volume":"12","author":"Wang","year":"2020","journal-title":"Nanoscale"},{"issue":"39","key":"2026091408072232700_cit13","doi-asserted-by":"publisher","first-page":"20513","DOI":"10.1039\/D0NR06114J","article-title":"Unusually large hyperfine\nstructure of the electron spin levels in an endohedral dimetallofullerene\nand its spin coherent properties","volume":"12","author":"Zaripov","year":"2020","journal-title":"Nanoscale"},{"issue":"1","key":"2026091408072232700_cit14","doi-asserted-by":"publisher","first-page":"16098","DOI":"10.1038\/ncomms16098","article-title":"Single molecule magnet with an unpaired electron trapped between\ntwo lanthanide ions inside a fullerene","volume":"8","author":"Liu","year":"2017","journal-title":"Nat.\nCommun."},{"issue":"1","key":"2026091408072232700_cit15","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1038\/s41467-019-08513-6","article-title":"Air-stable redox-active nanomagnets\nwith lanthanide spins radical-bridged by a metal-metal bond","volume":"10","author":"Liu","year":"2019","journal-title":"Nat. Commun."},{"issue":"13","key":"2026091408072232700_cit16","doi-asserted-by":"publisher","first-page":"4242","DOI":"10.1002\/anie.201511930","article-title":"Crystallographic Evidence for Direct\nMetal\u2013Metal Bonding in\na Stable Open-Shell La2@Ih-C80 Derivative","volume":"55","author":"Bao","year":"2016","journal-title":"Angew. Chem., Int. Ed."},{"issue":"25","key":"2026091408072232700_cit17","doi-asserted-by":"publisher","first-page":"13953","DOI":"10.1021\/jp5028492","article-title":"Metal-Dependent\nStability of Pristine\nand Functionalized Unconventional Dimetallofullerene M2@Ih-C80","volume":"118","author":"Wang","year":"2014","journal-title":"J. Phys. Chem. C"},{"issue":"1","key":"2026091408072232700_cit18","doi-asserted-by":"publisher","first-page":"2305190","DOI":"10.1002\/advs.202305190","article-title":"Nd\u2013 Nd Bond in Ih and D5h Cage Isomers of Nd2@C80 Stabilized by Electrophilic\nCF3 Addition","volume":"11","author":"Yang","year":"2024","journal-title":"Adv. Sci."},{"issue":"7","key":"2026091408072232700_cit19","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1007\/s11172-008-0192-7","article-title":"Endohedral\ngadolinium-containing\nmetallofullerenes in the trifluoromethylation reaction","volume":"57","author":"Kareev","year":"2008","journal-title":"Russ. Chem. Bull."},{"issue":"1","key":"2026091408072232700_cit20","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1021\/ja509956y","article-title":"Hiding and recovering\nelectrons in a dimetallic\nendohedral fullerene: air-stable products from radical additions","volume":"137","author":"Yamada","year":"2015","journal-title":"J. Am. Chem. Soc."},{"issue":"19","key":"2026091408072232700_cit21","doi-asserted-by":"publisher","first-page":"10730","DOI":"10.1021\/jacs.3c01405","article-title":"Synthesis and Crystallographic\nCharacterization of a Reduced Bimetallic Yttrium ansa-Metallocene\nHydride Complex, [K(crypt)][(\u03bc-CpAn)Y(\u03bc-H)]2 (CpAn= Me2Si[C5H3(SiMe3)-3]2), with a 3.4 \u00c5 Yttrium\u2013Yttrium Distance","volume":"145","author":"Wedal","year":"2023","journal-title":"J. Am. Chem. 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Commun."},{"issue":"41","key":"2026091408072232700_cit24","doi-asserted-by":"publisher","first-page":"22599","DOI":"10.1021\/jacs.3c07686","article-title":"Steering Single-Electron\nMetal\u2013Metal Bonds and Hyperfine Coupling between a Transition\nMetal-Lanthanide Heteronuclear Bimetal Confined in Carbon Cages","volume":"145","author":"Xiang","year":"2023","journal-title":"J. Am. Chem. Soc."},{"issue":"35","key":"2026091408072232700_cit25","doi-asserted-by":"publisher","first-page":"24310","DOI":"10.1021\/jacs.4c04720","article-title":"CaY@C2n:\nExploring Molecular Qubits with Ca\u2013Y Metal\u2013Metal Bonds","volume":"146","author":"Qiu","year":"2024","journal-title":"J. Am. Chem. Soc."},{"issue":"1","key":"2026091408072232700_cit26","doi-asserted-by":"publisher","first-page":"7170","DOI":"10.1038\/s41467-025-62649-2","article-title":"Molecular spin sensor for in-situ monitoring of crystallization behavior\nand phase transition in aromatic materials","volume":"16","author":"Liu","year":"2025","journal-title":"Nat. Commun."},{"issue":"3","key":"2026091408072232700_cit27","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1021\/jacs.7b12170","article-title":"Endohedral\nMetallofullerene as Molecular High Spin Qubit: Diverse Rabi Cycles\nin Gd2@C79N","volume":"140","author":"Hu","year":"2018","journal-title":"J. Am. Chem.\nSoc."},{"issue":"10","key":"2026091408072232700_cit28","doi-asserted-by":"publisher","first-page":"2981","DOI":"10.1021\/acs.accounts.9b00373","article-title":"Single-Electron Lanthanide-Lanthanide Bonds Inside\nFullerenes toward Robust Redox-Active Molecular Magnets","volume":"52","author":"Liu","year":"2019","journal-title":"Acc. Chem. Res."},{"issue":"47","key":"2026091408072232700_cit29","doi-asserted-by":"publisher","first-page":"15055","DOI":"10.1021\/jacs.5b10796","article-title":"Steering metallofullerene\nelectron\nspin in porous metal\u2013organic framework","volume":"137","author":"Feng","year":"2015","journal-title":"J. Am. Chem. Soc."},{"issue":"8","key":"2026091408072232700_cit30","doi-asserted-by":"publisher","first-page":"4635","DOI":"10.1021\/acs.jpcc.7b11353","article-title":"Anisotropic paramagnetic properties of metallofullerene confined\nin a metal\u2013organic framework","volume":"122","author":"Zhao","year":"2018","journal-title":"J. Phys.\nChem. C"},{"issue":"77","key":"2026091408072232700_cit31","doi-asserted-by":"publisher","first-page":"11511","DOI":"10.1039\/C9CC05220H","article-title":"Construction of a short metallofullerene-peapod\nwith a spin probe","volume":"55","author":"Zhao","year":"2019","journal-title":"Chem. Commun."},{"issue":"9","key":"2026091408072232700_cit32","doi-asserted-by":"publisher","first-page":"4660","DOI":"10.1021\/acs.jpcc.3c00158","article-title":"Enhanced spin-nuclei\ncouplings of paramagnetic azametallofullerene hooped in cycloparaphenylene","volume":"127","author":"Lu","year":"2023","journal-title":"J. Phys. Chem. C"},{"issue":"42","key":"2026091408072232700_cit33","doi-asserted-by":"publisher","first-page":"17305","DOI":"10.1021\/jacs.1c04605","article-title":"The impact of ligand\nfield symmetry\non molecular qubit coherence","volume":"143","author":"Kazmierczak","year":"2021","journal-title":"J. Am. Chem. Soc."},{"key":"2026091408072232700_cit34","volume-title":"Electron\nParamagnetic Resonance Spectroscopy:\nPrinciples and Applications","author":"Su","year":"2022"},{"issue":"3","key":"2026091408072232700_cit35","doi-asserted-by":"publisher","first-page":"2131","DOI":"10.1021\/acs.jpcc.9b08340","article-title":"Endohedral Metallofullerene M2@C80: A New Class\nof Magnetic Superhalogen","volume":"124","author":"Jiang","year":"2020","journal-title":"J. Phys. Chem. C"},{"issue":"5","key":"2026091408072232700_cit36","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1143\/JPSJ.11.612","article-title":"Note on the\nElectron Spin Resonance\nof the V1-center\u2500Calculation of the Electronic g-value","volume":"11","author":"Inui","year":"1956","journal-title":"J. Phys. Soc. Jpn."},{"issue":"13","key":"2026091408072232700_cit37","doi-asserted-by":"publisher","first-page":"6158","DOI":"10.1063\/1.478522","article-title":"Toward reliable density functional methods without\nadjustable parameters: The PBE0 model","volume":"110","author":"Adamo","year":"1999","journal-title":"J. Chem.\nPhys."},{"issue":"11","key":"2026091408072232700_cit38","doi-asserted-by":"publisher","first-page":"5029","DOI":"10.1063\/1.478401","article-title":"Assessment\nof the Perdew\u2013Burke\u2013Ernzerhof\nexchange-correlation functional","volume":"110","author":"Ernzerhof","year":"1999","journal-title":"J. Chem. Phys."},{"issue":"8","key":"2026091408072232700_cit39","doi-asserted-by":"publisher","first-page":"084106","DOI":"10.1063\/1.2834918","article-title":"Systematic\noptimization of long-range corrected hybrid\ndensity functionals","volume":"128","author":"Chai","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2026091408072232700_cit40","unstructured":"Frisch, M.; Trucks, G.; Schlegel, H.; Scuseria, G.; Robb, M.; Cheeseman, J.; Scalmani, G.; Barone, V.; Petersson, G.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A., Jr; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. 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Phys."},{"issue":"15","key":"2026091408072232700_cit43","doi-asserted-by":"publisher","first-page":"154101","DOI":"10.1063\/1.2065267","article-title":"A density-functional\nmodel of the dispersion interaction","volume":"123","author":"Becke","year":"2005","journal-title":"J. Chem.\nPhys."},{"issue":"2","key":"2026091408072232700_cit44","doi-asserted-by":"publisher","first-page":"024101","DOI":"10.1063\/1.1949201","article-title":"A post-Hartree\u2013Fock\nmodel of intermolecular\ninteractions","volume":"123","author":"Johnson","year":"2005","journal-title":"J. Chem. Phys."},{"issue":"17","key":"2026091408072232700_cit45","doi-asserted-by":"publisher","first-page":"174104","DOI":"10.1063\/1.2190220","article-title":"A post-Hartree-Fock model of intermolecular interactions:\nInclusion of higher-order corrections","volume":"124","author":"Johnson","year":"2006","journal-title":"J. Chem.\nPhys."},{"issue":"15","key":"2026091408072232700_cit46","doi-asserted-by":"publisher","first-page":"154104","DOI":"10.1063\/1.3382344","article-title":"A consistent and accurate\nab initio parametrization of density functional dispersion correction\n(DFT-D) for the 94 elements H-Pu","volume":"132","author":"Grimme","year":"2010","journal-title":"J. Chem. Phys."},{"issue":"22","key":"2026091408072232700_cit47","doi-asserted-by":"publisher","first-page":"224108","DOI":"10.1063\/5.0004608","article-title":"The ORCA quantum\nchemistry program package","volume":"152","author":"Neese","year":"2020","journal-title":"J. Chem. Phys."},{"issue":"14","key":"2026091408072232700_cit48","doi-asserted-by":"publisher","first-page":"3069","DOI":"10.1021\/jp3126126","article-title":"Excited States of Large Open-Shell Molecules: An Efficient, General,\nand Spin-Adapted Approach Based on a Restricted Open-Shell Ground\nState Wave function","volume":"117","author":"Roemelt","year":"2013","journal-title":"J. Phys. Chem. A"},{"issue":"50","key":"2026091408072232700_cit49","doi-asserted-by":"publisher","first-page":"10430","DOI":"10.1021\/jp983453n","article-title":"Effective\nnuclear charges for the\nfirst-through third-row transition metal elements in spin\u2013orbit\ncalculations","volume":"102","author":"Koseki","year":"1998","journal-title":"J. Phys. Chem. 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