{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T09:18:45Z","timestamp":1788254325447,"version":"build-2803163510"},"reference-count":101,"publisher":"American Chemical Society (ACS)","issue":"33","license":[{"start":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T00:00:00Z","timestamp":1786665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-23-1-2333"],"award-info":[{"award-number":["N00014-23-1-2333"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000078","name":"Division of Materials Research","doi-asserted-by":"publisher","award":["2141754"],"award-info":[{"award-number":["2141754"]}],"id":[{"id":"10.13039\/100000078","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000078","name":"Division of Materials Research","doi-asserted-by":"publisher","award":["2308708"],"award-info":[{"award-number":["2308708"]}],"id":[{"id":"10.13039\/100000078","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000082","name":"Division of Graduate Education","doi-asserted-by":"publisher","award":["1650114"],"award-info":[{"award-number":["1650114"]}],"id":[{"id":"10.13039\/100000082","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006151","name":"Basic Energy Sciences","doi-asserted-by":"publisher","award":["DE-AC02-98CH10866"],"award-info":[{"award-number":["DE-AC02-98CH10866"]}],"id":[{"id":"10.13039\/100006151","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,8,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Solid-state nuclear magnetic resonance (NMR) spectroscopy is a powerful probe of local chemical environments in functional materials, many of which incorporate paramagnetic transition-metal or rare-earth ions. Unpaired electrons can induce strong electron\u2013nuclear hyperfine interactions, giving rise to large paramagnetic shifts that encode detailed information about the local atomic and electronic structure. These same interactions, however, often produce severe line broadening, complicating spectral assignment\u2500particularly in materials exhibiting mixed valence, magnetic and charge ordering, defects, or compositional disorder. Although first-principles calculations can aid in interpreting paramagnetic shifts, their computational cost becomes prohibitive for structurally and chemically complex systems. This limitation motivates the development of new approaches that retain first-principles accuracy while enabling tractable simulations across disordered, multicomponent materials. Here, we introduce an ab initio framework that combines cluster expansion techniques with Monte Carlo sampling to predict finite-temperature paramagnetic (Fermi contact) shifts. We demonstrate the approach for 7Li and 17O NMR shifts in the cathode material Li2MnO3. A magnetic cluster expansion reveals that nearest- and next-nearest-neighbor Mn\u2013O\u2013Li interactions dominate the 7Li Fermi contact shift. Extension to 17O further uncovers significant long-range contributions mediated by Mn\u2013O\u2013Mn\u2013O pathways, identified here for the first time. This methodology enables first-principles-level predictions of paramagnetic NMR shifts in complex materials containing open-shell species, providing a route to interpreting spectra in real-world systems, including those relevant to energy storage, catalysis, and solid-state lighting.<\/jats:p>","DOI":"10.1021\/jacs.6c07045","type":"journal-article","created":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T11:02:11Z","timestamp":1786705331000},"page":"35575-35593","source":"Crossref","is-referenced-by-count":0,"title":["A Statistical Mechanical\nFramework for Predicting\nFermi Contact NMR Shifts"],"prefix":"10.1021","volume":"148","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8827-7175","authenticated-orcid":true,"given":"Euan N.","family":"Bassey","sequence":"first","affiliation":[{"name":"University of California Santa Barbara , , , ,","place":["Santa Barbara, California, United States, 93106-5050"]},{"name":"University of California Santa Barbara , , , ,","place":["Santa Barbara, California, United States, 93106-5050"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2678-3536","authenticated-orcid":true,"given":"Elias","family":"Sebti","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara , , , ,","place":["Santa Barbara, California, United States, 93106-5050"]},{"name":"University of California Santa Barbara , , , ,","place":["Santa Barbara, California, United States, 93106-5050"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anton","family":"Van der Ven","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara , , , ,","place":["Santa Barbara, California, United States, 93106-5050"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3611-1162","authenticated-orcid":true,"given":"Raphae\u0308le J.","family":"Cle\u0301ment","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara , , , ,","place":["Santa Barbara, California, United States, 93106-5050"]},{"name":"University of California Santa Barbara , , , ,","place":["Santa Barbara, California, United States, 93106-5050"]},{"name":"Max Planck Institute for Solid State Research , ,","place":["Stuttgart, Germany, 70569"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,14]]},"reference":[{"key":"2026090104513474200_cit1","doi-asserted-by":"publisher","first-page":"1602888","DOI":"10.1002\/aenm.201602888","article-title":"Narrowing the Gap between Theoretical and Practical Capacities in\nLi-Ion Layered Oxide Cathode Materials","volume":"7","author":"Radin","year":"2017","journal-title":"Adv.\nEnergy Mater."},{"key":"2026090104513474200_cit2","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1021\/ja3091438","article-title":"The Li-Ion Rechargeable Battery:\nA Perspective","volume":"135","author":"Goodenough","year":"2013","journal-title":"J. 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Mater."},{"key":"2026090104513474200_cit6","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1038\/nature08917","article-title":"Spin liquids\nin frustrated magnets","volume":"464","author":"Balents","year":"2010","journal-title":"Nature"},{"key":"2026090104513474200_cit7","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.1126\/science.1212858","article-title":"A perovskite oxide optimized for\noxygen evolution catalysis\nfrom molecular orbital principles","volume":"334","author":"Suntivich","year":"2011","journal-title":"Science"},{"key":"2026090104513474200_cit8","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1038\/s41586-025-09068-x","article-title":"Coordination\nenvironments of Pt single-atom catalysts from NMR signatures","volume":"642","author":"Koppe","year":"2025","journal-title":"Nature"},{"key":"2026090104513474200_cit9","doi-asserted-by":"publisher","first-page":"1325","DOI":"10.1021\/acs.chemmater.5b04219","article-title":"Defect Physics and\nChemistry in Layered Mixed Transition\nMetal Oxide Cathode Materials: (Ni,Co,Mn) vs (Ni,Co,Al)","volume":"28","author":"Hoang","year":"2016","journal-title":"Chem. Mater."},{"key":"2026090104513474200_cit10","doi-asserted-by":"publisher","first-page":"723","DOI":"10.3390\/cryst12050723","article-title":"Ni\/Li Antisite\nDefects in the Li1.2Ni0.2Mn0.6O2 Li-Rich Layered Oxide: A DFT Study","volume":"12","author":"Tuccillo","year":"2022","journal-title":"Crystals"},{"key":"2026090104513474200_cit11","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1021\/acs.chemmater.1c04152","article-title":"Cation Diffusion\nFacilitated by Antiphase Boundaries\nin Layered Intercalation Compounds","volume":"34","author":"Kaufman","year":"2022","journal-title":"Chem. Mater."},{"key":"2026090104513474200_cit12","volume-title":"Electron Paramagnetic\nResonance of Transition Ions","author":"Abragam","year":"1970"},{"key":"2026090104513474200_cit13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.pnmrs.2018.05.001","article-title":"Paramagnetic NMR in solution and\nthe solid state","volume":"111","author":"Pell","year":"2019","journal-title":"Prog. Nucl. Magn. Reson. Spectrosc."},{"key":"2026090104513474200_cit14","volume-title":"Solution NMR of Paramagnetic\nMolecules: Applications to Metallobiomolecules and Models","author":"Bertini","year":"2001"},{"key":"2026090104513474200_cit15","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1016\/j.ccr.2010.09.001","article-title":"Moving the frontiers\nin solution\nand solid-state bioNMR","volume":"255","author":"Bertini","year":"2011","journal-title":"Coord. Chem. Rev."},{"key":"2026090104513474200_cit16","doi-asserted-by":"publisher","first-page":"7318","DOI":"10.1021\/ja00069a034","article-title":"Paramagnetic\nions as structural probes\nin solid-state NMR: distance measurements in crystalline lanthanide\nacetates","volume":"115","author":"Brough","year":"1993","journal-title":"J. Am. Chem. Soc."},{"key":"2026090104513474200_cit17","doi-asserted-by":"publisher","first-page":"2218","DOI":"10.1021\/ja068105a","article-title":"Paramagnetic\nIons Provide Structural Restraints in Solid-State NMR of Proteins","volume":"129","author":"Balayssac","year":"2007","journal-title":"J. Am. Chem. Soc."},{"key":"2026090104513474200_cit18","doi-asserted-by":"publisher","first-page":"245101","DOI":"10.1103\/physrevb.63.245101","article-title":"All-electron\nmagnetic response with pseudopotentials: NMR chemical\nshifts","volume":"63","author":"Pickard","year":"2001","journal-title":"Phys. Rev. B: Condens. 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Reson."},{"key":"2026090104513474200_cit25","doi-asserted-by":"publisher","first-page":"4493","DOI":"10.1021\/cr020734p","article-title":"NMR Studies\nof Cathode Materials for Lithium-Ion Rechargeable\nBatteries","volume":"104","author":"Grey","year":"2004","journal-title":"Chem. Rev."},{"key":"2026090104513474200_cit26","doi-asserted-by":"publisher","first-page":"174103","DOI":"10.1103\/PhysRevB.67.174103","article-title":"Understanding the NMR shifts in paramagnetic transition metal oxides\nusing density functional theory calculations","volume":"67","author":"Carlier","year":"2003","journal-title":"Phys. Rev. B: Condens. Matter Mater. 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Soc."},{"key":"2026090104513474200_cit28","doi-asserted-by":"publisher","first-page":"1723","DOI":"10.1021\/cm400201t","article-title":"Density Functional Theory-Based Bond\nPathway Decompositions\nof Hyperfine Shifts: Equipping Solid-State NMR to Characterize Atomic\nEnvironments in Paramagnetic Materials","volume":"25","author":"Middlemiss","year":"2013","journal-title":"Chem.\nMater."},{"key":"2026090104513474200_cit29","doi-asserted-by":"publisher","first-page":"8387","DOI":"10.1021\/acs.jpcc.8b09645","article-title":"Computation of NMR\nShifts for Paramagnetic Solids Including Zero-Field-Splitting\nand Beyond-DFT Approaches. Application to LiMPO 4 (M = Mn, Fe, Co,\nNi) and MPO 4 (M = Fe, Co)","volume":"123","author":"Mondal","year":"2019","journal-title":"J. Phys. Chem. C"},{"key":"2026090104513474200_cit30","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1021\/acs.jctc.7b00991","article-title":"Large-Scale Computation\nof Nuclear\nMagnetic Resonance Shifts for Paramagnetic Solids Using CP2K","volume":"14","author":"Mondal","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"2026090104513474200_cit31","doi-asserted-by":"publisher","first-page":"17178","DOI":"10.1021\/ja306876u","article-title":"Spin-Transfer\nPathways in Paramagnetic Lithium Transition-Metal\nPhosphates from Combined Broadband Isotropic Solid-State MAS NMR Spectroscopy\nand DFT Calculations","volume":"134","author":"Cle\u0301ment","year":"2012","journal-title":"J. Am. Chem. 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Mater."},{"key":"2026090104513474200_cit35","doi-asserted-by":"publisher","first-page":"054412","DOI":"10.1103\/PhysRevB.95.054412","article-title":"DFT investigation of\nthe effect of spin-orbit coupling on the NMR\nshifts in paramagnetic solids","volume":"95","author":"Pigliapochi","year":"2017","journal-title":"Phys. Rev. B"},{"key":"2026090104513474200_cit36","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1021\/acs.chemmater.7b04314","article-title":"Structural Characterization\nof the\nLi-Ion Battery Cathode Materials LiTixMn2\u2013xO4 (0.2 \u2264 x \u2264 1.5): A Combined Experimental 7Li NMR and First-Principles\nStudy","volume":"30","author":"Pigliapochi","year":"2018","journal-title":"Chem. Mater."},{"key":"2026090104513474200_cit37","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1021\/acsphyschemau.3c00019","article-title":"Structure Determination and Refinement\nof Paramagnetic\nMaterials by Solid-State NMR","volume":"3","author":"Koppe","year":"2023","journal-title":"ACS Phys. Chem.\nAu"},{"key":"2026090104513474200_cit38","doi-asserted-by":"publisher","first-page":"13089","DOI":"10.1021\/jacs.9b04674","article-title":"When Do Anisotropic Magnetic Susceptibilities\nLead to Large NMR Shifts? Exploring Particle Shape Effects in the\nBattery Electrode Material LiFePO4","volume":"141","author":"Pigliapochi","year":"2019","journal-title":"J. Am. Chem.\nSoc."},{"key":"2026090104513474200_cit39","volume-title":"Materials Modelling Using\nDensity Functional Theory: Properties and Predictions","author":"Giustino","year":"2014"},{"key":"2026090104513474200_cit40","doi-asserted-by":"publisher","DOI":"10.1002\/wcms.1360","article-title":"Quantum-mechanical\ncondensed matter simulations with CRYSTAL","volume":"8","author":"Dovesi","year":"2018","journal-title":"Wiley\nInterdiscip. Rev.:Comput. Mol. Sci."},{"key":"2026090104513474200_cit41","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1524\/zkri.220.5.571.65065","article-title":"CRYSTAL: A computational tool for the ab initio study\nof the electronic properties of crystals","volume":"220","author":"Dovesi","year":"2005","journal-title":"Z.\nKristallogr."},{"key":"2026090104513474200_cit42","doi-asserted-by":"publisher","first-page":"12601","DOI":"10.1021\/ja9817794","article-title":"6Li and\n7Li MAS NMR Studies of Lithium\nManganate Cathode Materials","volume":"120","author":"Lee","year":"1998","journal-title":"J. Am. Chem. 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Solid-State Lett."},{"key":"2026090104513474200_cit45","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0022-3697(58)90107-0","article-title":"An Interpretation\nof the magnetic properties of the Perovskite-type mixed crystals La(1-x)Sr(x)CoO(3-y)","volume":"6","author":"Goodenough","year":"1958","journal-title":"J. Phys. Chem. Solid."},{"key":"2026090104513474200_cit46","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1103\/PhysRev.79.350","article-title":"Antiferromagnetism.\nTheory of Superexchange Interaction","volume":"79","author":"Anderson","year":"1950","journal-title":"Phys. Rev."},{"key":"2026090104513474200_cit47","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1143\/PTP.17.177","article-title":"Theory of\nthe Magnetic Properties of Ferrous and Cobaltous Oxides, I","volume":"17","author":"Kanamori","year":"1957","journal-title":"Prog. Theor. Phys."},{"key":"2026090104513474200_cit48","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1143\/PTP.17.197","article-title":"Theory of\nthe Magnetic Properties of Ferrous and Cobaltous Oxides, II","volume":"17","author":"Kanamori","year":"1957","journal-title":"Prog. Theor. 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Mater."},{"key":"2026090104513474200_cit52","doi-asserted-by":"publisher","first-page":"8228","DOI":"10.1021\/acs.chemmater.6b03074","article-title":"Insights\ninto the Nature and Evolution upon Electrochemical Cycling of Planar\nDefects in the beta-NaMnO 2 Na-Ion Battery Cathode: An NMR and First-Principles\nDensity Functional Theory Approach","volume":"28","author":"Cle\u0301ment","year":"2016","journal-title":"Chem. Mater."},{"key":"2026090104513474200_cit53","doi-asserted-by":"publisher","first-page":"4226","DOI":"10.1021\/acs.chemmater.3c03103","article-title":"Probing\nJahn\u2013Teller Distortions and Antisite\nDefects in LiNiO2 with 7Li NMR Spectroscopy and Density Functional\nTheory","volume":"36","author":"Genreith-Schriever","year":"2024","journal-title":"Chem. Mater."},{"key":"2026090104513474200_cit54","doi-asserted-by":"publisher","first-page":"9493","DOI":"10.1021\/acs.chemmater.4c01320","article-title":"Strong Magnetic Exchange Interactions and Delocalized\nMn\u2013O States Enable High-Voltage Capacity in the Na-Ion Cathode\nP2\u2013Na0.67[Mg0.28Mn0.72]O2","volume":"36","author":"Bassey","year":"2024","journal-title":"Chem. Mater."},{"key":"2026090104513474200_cit55","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1016\/0378-4371(84)90096-7","article-title":"Generalized cluster description of\nmulticomponent systems","volume":"128","author":"Sanchez","year":"1984","journal-title":"Phys. A"},{"key":"2026090104513474200_cit56","first-page":"33","volume-title":"Solid State\nPhysics","author":"De Fontaine","year":"1994"},{"key":"2026090104513474200_cit57","doi-asserted-by":"publisher","first-page":"104404","DOI":"10.1103\/PhysRevB.69.104404","article-title":"Spin-cluster\nexpansion: Parametrization of the general\nadiabatic magnetic energy surface with ab initio accuracy","volume":"69","author":"Drautz","year":"2004","journal-title":"Phys. Rev. B: Condens. Matter Mater. Phys."},{"key":"2026090104513474200_cit58","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1146\/annurev-matsci-070317-124443","article-title":"First-Principles\nStatistical Mechanics of Multicomponent Crystals","volume":"48","author":"Van der Ven","year":"2018","journal-title":"Annu. Rev. Mater. 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