{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:44:54Z","timestamp":1792784694633,"version":"4.5.0"},"reference-count":92,"publisher":"American Chemical Society (ACS)","issue":"18","license":[{"start":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T00:00:00Z","timestamp":1788393600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T00:00:00Z","timestamp":1788393600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T00:00:00Z","timestamp":1788393600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"name":"Beijing Municipal Natural Science Foundation","award":["2252006"],"award-info":[{"award-number":["2252006"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["12234001"],"award-info":[{"award-number":["12234001"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Density matrix embedding theory (DMET) provides an elegant framework in quantum chemistry to describe local properties of chemical systems, which allows a high-level method to solve an embedded subsystem constructed based on a low-level treatment of the whole system and therefore achieves a balance between efficiency and accuracy. However, because the embedded subspace in DMET is typically constructed from the mean-field ground-state Slater determinant, the resulting bath orbitals inherently favor the ground state, leading to unbalanced descriptions of ground and excited states for local excitations. In this work, we first demonstrate the starting point dependence of DMET in excitation energy calculations and then generalize the original ground state-based DMET by extending the starting point from the single Slater determinant to the state-averaged (SA) complete active space self-consistent field (CASSCF), hence termed as SA-DMET. In calculations of magnetic anisotropy and excitation energies of transition metal and lanthanide complexes, SA-DMET shows significant improvement in accuracy compared to the single-state DMET. Configuration-averaged Hartree-Fock (CAHF), which is equivalent to SA-CASSCF when all states in the chosen active space are equally averaged, is found to give comparable accuracy as a DMET starting point, thus offering a more efficient choice for state-averaged embedding. Finally, the recently proposed nonorthogonal atomic orbital-based DMET (AO-DMET) is tested on various systems and gives very promising results in all cases. These results establish SA-DMET, especially in combination with AO-DMET and CAHF, as a robust and efficient embedding framework for local excited states in strongly correlated metal complexes.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01158","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T20:18:47Z","timestamp":1788466727000},"page":"9483-9495","source":"Crossref","is-referenced-by-count":0,"title":["State-Averaged\nDensity Matrix Embedding Theory for\nLocal Excitations"],"prefix":"10.1021","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6783-2631","authenticated-orcid":true,"given":"Zhebin","family":"Guan","sequence":"first","affiliation":[{"name":"Peking University , , ,","place":["Beijing, China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3187-2023","authenticated-orcid":true,"given":"Hong","family":"Jiang","sequence":"additional","affiliation":[{"name":"Peking University , , ,","place":["Beijing, China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,3]]},"reference":[{"key":"2026092209082438600_cit1","doi-asserted-by":"publisher","first-page":"2705","DOI":"10.1021\/acs.accounts.6b00356","article-title":"Quantum Embedding Theories","volume":"49","author":"Sun","year":"2016","journal-title":"Acc.\nChem. Res."},{"key":"2026092209082438600_cit2","doi-asserted-by":"publisher","first-page":"3281","DOI":"10.1021\/jacs.9b10780","article-title":"Embedding Methods\nfor Quantum Chemistry: Applications from Materials to Life Sciences","volume":"142","author":"Jones","year":"2020","journal-title":"J. Am. Chem. Soc."},{"key":"2026092209082438600_cit3","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1038\/s43588-022-00279-0","article-title":"Quantum Embedding\nTheories to Simulate Condensed Systems on Quantum Computers","volume":"2","author":"Vorwerk","year":"2022","journal-title":"Nat. Comput. Sci."},{"key":"2026092209082438600_cit4","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1021\/acs.chemrev.5c00486","article-title":"Multireference\nEmbedding and Fragmentation Methods for Classical and Quantum Computers:\nFrom Model Systems to Realistic Applications","volume":"126","author":"Verma","year":"2026","journal-title":"Chem. Rev."},{"key":"2026092209082438600_cit5","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1002\/wcms.1175","article-title":"Subsystem Density-Functional Theory","volume":"4","author":"Jacob","year":"2014","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026092209082438600_cit6","doi-asserted-by":"publisher","first-page":"2768","DOI":"10.1021\/ar500086h","article-title":"Embedded Correlated Wavefunction\nSchemes: Theory and Applications","volume":"47","author":"Libisch","year":"2014","journal-title":"Acc. Chem.\nRes."},{"key":"2026092209082438600_cit7","doi-asserted-by":"publisher","first-page":"5891","DOI":"10.1021\/cr500502v","article-title":"Frozen-Density\nEmbedding Strategy\nfor Multilevel Simulations of Electronic Structure","volume":"115","author":"Wesolowski","year":"2015","journal-title":"Chem. Rev."},{"key":"2026092209082438600_cit8","doi-asserted-by":"publisher","first-page":"e1700","DOI":"10.1002\/wcms.1700","article-title":"Subsystem Density-Functional Theory (Update)","volume":"14","author":"Jacob","year":"2024","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026092209082438600_cit9","doi-asserted-by":"publisher","first-page":"1428","DOI":"10.1021\/ct301044e","article-title":"Density Matrix\nEmbedding: A Strong-Coupling Quantum\nEmbedding Theory","volume":"9","author":"Knizia","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit10","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1021\/ct5011032","article-title":"Embedded Mean-Field\nTheory","volume":"11","author":"Fornace","year":"2015","journal-title":"J. Chem. Theory\nComput."},{"key":"2026092209082438600_cit11","doi-asserted-by":"publisher","first-page":"074102","DOI":"10.1063\/1.4960986","article-title":"Bootstrap Embedding: An Internally\nConsistent Fragment-Based Method","volume":"145","author":"Welborn","year":"2016","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit12","doi-asserted-by":"publisher","first-page":"E10861","DOI":"10.1073\/pnas.1712611114","article-title":"Extending Density Functional Embedding Theory for Covalently\nBonded Systems","volume":"114","author":"Yu","year":"2017","journal-title":"Proc. Natl. Acad. Sci. U. S.\nA."},{"key":"2026092209082438600_cit13","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1103\/RevModPhys.78.865","article-title":"Electronic\nStructure Calculations\nwith Dynamical Mean-Field Theory","volume":"78","author":"Kotliar","year":"2006","journal-title":"Rev. Mod.\nPhys."},{"key":"2026092209082438600_cit14","doi-asserted-by":"publisher","first-page":"023047","DOI":"10.1088\/1367-2630\/aa5d34","article-title":"Finite Temperature Quantum Embedding Theories for Correlated Systems","volume":"19","author":"Zgid","year":"2017","journal-title":"New J. Phys."},{"key":"2026092209082438600_cit15","doi-asserted-by":"publisher","first-page":"2116","DOI":"10.1021\/acs.jctc.0c01258","article-title":"Quantum Embedding Theory\nfor Strongly Correlated States in Materials","volume":"17","author":"Ma","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit16","doi-asserted-by":"publisher","first-page":"021006","DOI":"10.1103\/PhysRevX.11.021006","article-title":"Ab Initio Full Cell GW+DMFT for Correlated Materials","volume":"11","author":"Zhu","year":"2021","journal-title":"Phys. Rev. X"},{"key":"2026092209082438600_cit17","doi-asserted-by":"publisher","first-page":"186404","DOI":"10.1103\/PhysRevLett.109.186404","article-title":"Density Matrix Embedding: A Simple Alternative to Dynamical\nMean-Field Theory","volume":"109","author":"Knizia","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"2026092209082438600_cit18","doi-asserted-by":"publisher","first-page":"2706","DOI":"10.1021\/acs.jctc.6b00316","article-title":"A Practical\nGuide to Density Matrix Embedding Theory in Quantum Chemistry","volume":"12","author":"Wouters","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit19","doi-asserted-by":"publisher","first-page":"1192","DOI":"10.1126\/science.abm2295","article-title":"Systematic\nElectronic\nStructure in the Cuprate Parent State from Quantum Many-Body Simulations","volume":"377","author":"Cui","year":"2022","journal-title":"Science"},{"key":"2026092209082438600_cit20","doi-asserted-by":"publisher","first-page":"10627","DOI":"10.1021\/acs.jpclett.2c02890","article-title":"Efficient\nMulticonfigurational Quantum Chemistry Approach\nto Single-Ion Magnets Based on Density Matrix Embedding Theory","volume":"13","author":"Ai","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"2026092209082438600_cit21","doi-asserted-by":"publisher","first-page":"9631","DOI":"10.1021\/acs.jctc.5c01336","article-title":"Density Matrix Embedding\nTheory-Based Multiconfigurational Quantum Chemistry Approach to Lanthanide\nSingle-Ion Magnets","volume":"21","author":"Ai","year":"2025","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit22","doi-asserted-by":"publisher","first-page":"224111","DOI":"10.1063\/5.0269968","article-title":"Density-Matrix Embedding\nBased Multi-Reference Perturbation Theory\nApproach to Single-Ion Magnets","volume":"162","author":"Guan","year":"2025","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit23","doi-asserted-by":"publisher","first-page":"164115","DOI":"10.1063\/5.0297017","article-title":"Efficient Evaluation of Spin-Orbit Couplings in Single-Molecule Magnets\nUsing DMRG within the DMET Framework","volume":"163","author":"Sun","year":"2025","journal-title":"J. Chem.\nPhys."},{"key":"2026092209082438600_cit24","doi-asserted-by":"publisher","DOI":"10.1038\/s41524-023-01045-0","article-title":"Ab Initio\nQuantum Simulation of Strongly Correlated Materials with Quantum Embedding","volume":"9","author":"Cao","year":"2023","journal-title":"npj Comput. Mater."},{"key":"2026092209082438600_cit25","doi-asserted-by":"publisher","first-page":"6801","DOI":"10.1021\/acs.jctc.5c00114","article-title":"Toward Quantum-Centric\nSimulations of Extended Molecules: Sample-Based Quantum Diagonalization\nEnhanced with Density Matrix Embedding Theory","volume":"21","author":"Shajan","year":"2025","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit26","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1021\/acs.jctc.5c01435","article-title":"Large-Scale Efficient\nMolecule Geometry Optimization with Hybrid Quantum-Classical Computing","volume":"22","author":"Hao","year":"2026","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit27","doi-asserted-by":"publisher","DOI":"10.1038\/s41524-024-01406-3","article-title":"Quantum Embedding Method with Transformer\nNeural Network Quantum States for Strongly Correlated Materials","volume":"10","author":"Ma","year":"2024","journal-title":"npj Comput. Mater."},{"key":"2026092209082438600_cit28","doi-asserted-by":"publisher","first-page":"054113","DOI":"10.1063\/1.4891861","article-title":"Electron\nCorrelation in Solids via\nDensity Embedding Theory","volume":"141","author":"Bulik","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit29","doi-asserted-by":"publisher","first-page":"1960","DOI":"10.1021\/acs.jctc.7b01248","article-title":"Can Density Matrix Embedding Theory\nwith the Complete Activate Space Self-Consistent Field Solver Describe\nSingle and Double Bond Breaking in Molecular Systems?","volume":"14","author":"Pham","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit30","doi-asserted-by":"publisher","first-page":"7483","DOI":"10.1021\/acs.jpclett.2c01915","article-title":"Periodic Density\nMatrix Embedding for CO Adsorption on the MgO(001) Surface","volume":"13","author":"Mitra","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"2026092209082438600_cit31","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1021\/acs.jctc.9b00933","article-title":"Efficient Implementation\nof Ab Initio Quantum Embedding\nin Periodic Systems: Density Matrix Embedding Theory","volume":"16","author":"Cui","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit32","doi-asserted-by":"publisher","first-page":"4273","DOI":"10.1021\/acs.jpclett.3c00551","article-title":"Local Excitations\nof a Charged Nitrogen Vacancy in Diamond with Multireference Density\nMatrix Embedding Theory","volume":"14","author":"Haldar","year":"2023","journal-title":"J. Phys. Chem. Lett."},{"key":"2026092209082438600_cit33","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-64374-2","article-title":"A Multi-Resolution Systematically\nImprovable Quantum Embedding Scheme for Large-Scale Surface Chemistry\nCalculations","volume":"16","author":"Huang","year":"2025","journal-title":"Nat. Commun."},{"key":"2026092209082438600_cit34","doi-asserted-by":"publisher","first-page":"194108","DOI":"10.1063\/1.5053992","article-title":"Incremental\nEmbedding: A Density Matrix Embedding Scheme for Molecules","volume":"149","author":"Ye","year":"2018","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit35","doi-asserted-by":"publisher","first-page":"014115","DOI":"10.1063\/1.5100290","article-title":"Energy-Weighted\nDensity Matrix Embedding of Open Correlated\nChemical Fragments","volume":"151","author":"Fertitta","year":"2019","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit36","doi-asserted-by":"publisher","first-page":"124107","DOI":"10.1063\/5.0229787","article-title":"Fragment Quantum Embedding Using\nthe Householder Transformation: A Multi-State Extension Based on Ensembles","volume":"161","author":"Cernatic","year":"2024","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit37","doi-asserted-by":"publisher","first-page":"216402","DOI":"10.1103\/PhysRevLett.133.216402","article-title":"Interacting-Bath Dynamical\nEmbedding for Capturing Nonlocal Electron\nCorrelation in Solids","volume":"133","author":"Li","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"2026092209082438600_cit38","doi-asserted-by":"publisher","first-page":"026502","DOI":"10.1103\/kqx7-fr2m","article-title":"Exploring\nNovel Quantum Embedding\nMethods with Nonorthogonal Decomposition of Slater Determinants","volume":"135","author":"Ai","year":"2025","journal-title":"Phys. Rev. Lett."},{"key":"2026092209082438600_cit39","doi-asserted-by":"publisher","first-page":"3092","DOI":"10.1021\/acs.jpclett.5c00287","article-title":"Strongly Correlated\nStates of Transition Metal Spin Defects: The\nCase Of an Iron Impurity in Aluminum Nitride","volume":"16","author":"Otis","year":"2025","journal-title":"J. Phys. Chem. Lett."},{"key":"2026092209082438600_cit40","doi-asserted-by":"publisher","first-page":"5348","DOI":"10.1021\/acs.jpclett.5c00829","article-title":"Density Matrix\nEmbedding Pair-Density\nFunctional Theory for Molecules","volume":"16","author":"Verma","year":"2025","journal-title":"J. Phys. Chem.\nLett."},{"key":"2026092209082438600_cit41","doi-asserted-by":"publisher","first-page":"17097","DOI":"10.1039\/D1CP02640B","article-title":"Modern Multireference Methods and Their Application\nin Transition Metal Chemistry","volume":"23","author":"Khedkar","year":"2021","journal-title":"Phys. Chem. Chem.\nPhys."},{"key":"2026092209082438600_cit42","doi-asserted-by":"publisher","first-page":"e202200014","DOI":"10.1002\/ejic.202200014","article-title":"Ab Initio Methods\nin First-Row Transition Metal Chemistry","volume":"2022","author":"Feldt","year":"2022","journal-title":"Eur.\nJ. Inorg. Chem."},{"key":"2026092209082438600_cit43","first-page":"1","volume-title":"Computational Modelling\nof Molecular Nanomagnets","author":"Chibotaru","year":"2023"},{"key":"2026092209082438600_cit44","doi-asserted-by":"publisher","first-page":"20189","DOI":"10.1039\/D4SC05471G","article-title":"Performance\nof Quantum Chemistry\nMethods For a Benchmark Set of Spin-State Energetics Derived from\nExperimental Data of 17 Transition Metalcomplexes (SSE17)","volume":"15","author":"Radon\u0301","year":"2024","journal-title":"Chem. Sci."},{"key":"2026092209082438600_cit45","doi-asserted-by":"publisher","first-page":"2686","DOI":"10.1021\/acs.jpclett.2c00400","article-title":"Rare Earth Complexes\nwith 5d-4f Transition: New Emitters in Organic\nLight-Emitting Diodes","volume":"13","author":"Wang","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"2026092209082438600_cit46","doi-asserted-by":"publisher","first-page":"094107","DOI":"10.1063\/1.5142481","article-title":"A Zeroth-Order\nActive-Space Frozen-Orbital Embedding\nScheme for Multireference Calculations","volume":"152","author":"He","year":"2020","journal-title":"J. Chem.\nPhys."},{"key":"2026092209082438600_cit47","doi-asserted-by":"publisher","first-page":"1527","DOI":"10.1021\/acs.jctc.1c01099","article-title":"Second-Order Active-Space Embedding\nTheory","volume":"18","author":"He","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit48","doi-asserted-by":"publisher","first-page":"034112","DOI":"10.1063\/1.5096177","article-title":"Using SCF Metadynamics to Extend\nDensity Matrix Embedding Theory to Excited States","volume":"151","author":"Tran","year":"2019","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit49","doi-asserted-by":"publisher","first-page":"075131","DOI":"10.1103\/PhysRevB.101.075131","article-title":"Finite-Temperature\nDensity Matrix Embedding Theory","volume":"101","author":"Sun","year":"2020","journal-title":"Phys. Rev.\nB"},{"key":"2026092209082438600_cit50","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1002\/9781119129271.ch8","volume-title":"Fragmentation:\nToward Accurate Calculations on Complex Molecular Systems","author":"Wouters","year":"2017"},{"key":"2026092209082438600_cit51","doi-asserted-by":"publisher","first-page":"011046","DOI":"10.1103\/physrevx.12.011046","article-title":"Systematic Improvability in Quantum Embedding for Real\nMaterials","volume":"12","author":"Nusspickel","year":"2021","journal-title":"Phys. Rev. X"},{"key":"2026092209082438600_cit52","doi-asserted-by":"publisher","DOI":"10.1063\/5.0157746","article-title":"A Unified Density Matrix Functional\nConstruction of Quantum Baths in Density Matrix Embedding Theory beyond\nthe Mean-Field Approximation","volume":"159","author":"Sekaran","year":"2023","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit53","doi-asserted-by":"publisher","first-page":"035121","DOI":"10.1103\/PhysRevB.104.035121","article-title":"Householder-Transformed\nDensity Matrix Functional Embedding Theory","volume":"104","author":"Sekaran","year":"2021","journal-title":"Phys. Rev. B"},{"key":"2026092209082438600_cit54","doi-asserted-by":"publisher","first-page":"11688","DOI":"10.1021\/acs.jpclett.1c03229","article-title":"Excited States\nof Crystalline Point Defects with Multireference Density Matrix Embedding\nTheory","volume":"12","author":"Mitra","year":"2021","journal-title":"J. Phys. Chem. Lett."},{"key":"2026092209082438600_cit55","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1063\/1.462209","article-title":"Second-Order Perturbation Theory\nwith a Complete Active Space Self-Consistent Field Reference Function","volume":"96","author":"Andersson","year":"1992","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit56","doi-asserted-by":"publisher","first-page":"10252","DOI":"10.1063\/1.1361246","article-title":"Introduction of n-Electron Valence States for Multireference\nPerturbation Theory","volume":"114","author":"Angeli","year":"2001","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit57","doi-asserted-by":"publisher","first-page":"5794","DOI":"10.1063\/1.440892","article-title":"A Quadratically Convergent\nMCSCF Method for the Simultaneous Optimization\nof Several States","volume":"74","author":"Werner","year":"1981","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit58","volume-title":"Matrix Analysis","author":"Hom","year":"2013","edition":"2"},{"key":"2026092209082438600_cit59","doi-asserted-by":"publisher","first-page":"2533","DOI":"10.1021\/acs.jctc.6b01118","article-title":"Second-Order Self-Consistent-Field\nDensity-Matrix Renormalization Group","volume":"13","author":"Ma","year":"2017","journal-title":"J. Chem.\nTheory Comput."},{"key":"2026092209082438600_cit60","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.ccr.2017.03.018","article-title":"Covalency\nand Chemical Bonding in\nTransition Metal Complexes: An Ab Initio Based Ligand Field Perspective","volume":"344","author":"Singh","year":"2017","journal-title":"Coord. Chem. Rev."},{"key":"2026092209082438600_cit61","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1021\/acs.jpca.9b11227","article-title":"Improvement of Ab Initio\nLigand Field\nTheory by Means of Multistate Perturbation Theory","volume":"124","author":"Lang","year":"2020","journal-title":"J. Phys. Chem. A"},{"key":"2026092209082438600_cit62","doi-asserted-by":"publisher","first-page":"7460","DOI":"10.1021\/ic200196k","article-title":"Detailed Ab Initio First-Principles Study of the Magnetic Anisotropy\nin a Family of Trigonal Pyramidal Iron(II) Pyrrolide Complexes","volume":"50","author":"Atanasov","year":"2011","journal-title":"Inorg. Chem."},{"key":"2026092209082438600_cit63","doi-asserted-by":"publisher","first-page":"3102","DOI":"10.1021\/acs.inorgchem.7b00097","article-title":"Magneto-Structural\nCorrelations in Pseudotetrahedral Forms of the [Co(SPh)4]2- Complex Probed by Magnetometry, MCD Spectroscopy,\nAdvanced EPR Techniques, and Ab Initio Electronic Structure Calculations","volume":"56","author":"Suturina","year":"2017","journal-title":"Inorg. Chem."},{"key":"2026092209082438600_cit64","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.ccr.2014.10.015","article-title":"First Principles Approach to the\nElectronic Structure, Magnetic Anisotropy\nand Spin Relaxation in Mononuclear 3d-Transition Metal Single Molecule\nMagnets","volume":"289\u2013290","author":"Atanasov","year":"2015","journal-title":"Coord. Chem. Rev."},{"key":"2026092209082438600_cit65","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1038\/nature23447","article-title":"Molecular\nMagnetic Hysteresis at 60 K in Dysprosocenium","volume":"548","author":"Goodwin","year":"2017","journal-title":"Nature"},{"key":"2026092209082438600_cit66","doi-asserted-by":"publisher","first-page":"15807","DOI":"10.1039\/C6CP02325H","article-title":"Configuration-Averaged\n4f Orbitals in Ab Initio Calculations of Low-Lying Crystal Field Levels\nin Lanthanide(III) Complexes","volume":"18","author":"Van Den Heuvel","year":"2016","journal-title":"Phys. Chem. Chem.\nPhys."},{"key":"2026092209082438600_cit67","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1103\/RevModPhys.32.179","article-title":"Self-Consistent\nField Theory for Open Shells of Electronic Systems","volume":"32","author":"Roothaan","year":"1960","journal-title":"Rev. Mod. Phys."},{"key":"2026092209082438600_cit68","volume-title":"Methods of Molecular\nQuantum Mechanics","author":"McWeeny","year":"1989","edition":"2"},{"key":"2026092209082438600_cit69","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1002\/qua.560350409","article-title":"A Configuration-Averaged\nHartree-Fock Procedure","volume":"35","author":"Zerner","year":"1989","journal-title":"Int. J. Quantum Chem."},{"key":"2026092209082438600_cit70","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1610.08423","article-title":"Co-iterative Augmented\nHessian Method for Orbital Optimization","author":"Sun","year":"2016"},{"key":"2026092209082438600_cit71","doi-asserted-by":"publisher","first-page":"4063","DOI":"10.1021\/acs.jctc.7b00128","article-title":"Automated Construction of Molecular\nActive Spaces from Atomic Valence Orbitals","volume":"13","author":"Sayfutyarova","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit72","doi-asserted-by":"publisher","first-page":"214111","DOI":"10.1063\/5.0094292","article-title":"A Combined First- and Second-Order\nOptimization Method\nfor Improving Convergence of Hartree-Fock and Kohn-Sham Calculations","volume":"156","author":"Kreplin","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit73","doi-asserted-by":"publisher","first-page":"024109","DOI":"10.1063\/5.0006074","article-title":"Recent Developments in the PySCF Program Package","volume":"153","author":"Sun","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit74","doi-asserted-by":"publisher","first-page":"241102","DOI":"10.1063\/1.2137315","article-title":"Quasirelativistic Theory\nEquivalent to Fully Relativistic Theory","volume":"123","author":"Kutzelnigg","year":"2005","journal-title":"J.\nChem. Phys."},{"key":"2026092209082438600_cit75","doi-asserted-by":"publisher","first-page":"9136","DOI":"10.1063\/1.1413512","article-title":"Interfacing\nRelativistic and Nonrelativistic Methods. IV. One- and Two-Electron\nScalar Approximations","volume":"115","author":"Dyall","year":"2001","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit76","doi-asserted-by":"publisher","first-page":"031104","DOI":"10.1063\/1.3159445","article-title":"Exact Two-Component\nHamiltonians Revisited","volume":"131","author":"Liu","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit77","doi-asserted-by":"publisher","first-page":"034107","DOI":"10.1063\/1.1829047","article-title":"Efficient\nand Accurate Approximations to the Molecular Spin-Orbit Coupling Operator\nand Their Use in Molecular g-Tensor Calculations","volume":"122","author":"Neese","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2026092209082438600_cit78","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/0009-2614(96)00119-4","article-title":"A Mean-Field Spin-Orbit\nMethod Applicable to Correlated Wavefunctions","volume":"251","author":"He\u00df","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2026092209082438600_cit79","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1038\/s42254-021-00340-3","article-title":"Measuring Molecular Magnets for Quantum\nTechnologies","volume":"3","author":"Moreno-Pineda","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"2026092209082438600_cit80","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1146\/annurev-matsci-081420-042553","article-title":"Molecular\nMagnetism","volume":"52","author":"Chilton","year":"2022","journal-title":"Annu. Rev. Mater. Res."},{"key":"2026092209082438600_cit81","doi-asserted-by":"crossref","DOI":"10.1002\/9783527690541","volume-title":"Introduction to Molecular\nMagnetism: From Transition Metals to Lanthanides","author":"Benelli","year":"2015"},{"key":"2026092209082438600_cit82","article-title":"Magnetic Interactions in Molecules\nand Solids","volume-title":"Theoretical Chemistry and Computational\nModelling","author":"de Graaf","year":"2016"},{"key":"2026092209082438600_cit83","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/S0009-2614(02)00498-0","article-title":"The Restricted\nActive Space (RAS)\nState Interaction Approach with Spin-Orbit Coupling","volume":"357","author":"Malmqvist","year":"2002","journal-title":"Chem. Phys. Lett."},{"key":"2026092209082438600_cit84","doi-asserted-by":"publisher","first-page":"2977","DOI":"10.1021\/ct900326e","article-title":"Universal Theoretical Approach to\nExtract Anisotropic\nSpin Hamiltonians","volume":"5","author":"Maurice","year":"2009","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit85","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1002\/9781118571767.ch6","article-title":"Ab Initio\nMethodology for Pseudo-Spin Hamiltonians of Anisotropic Magnetic Complexes","volume":"153","author":"Chibotaru","year":"2013","journal-title":"Adv. Chem. Phys."},{"key":"2026092209082438600_cit86","doi-asserted-by":"publisher","first-page":"1400","DOI":"10.1126\/science.aav0652","article-title":"Magnetic Hysteresis up to 80 K in\na Dysprosium Metallocene\nSingle-Molecule Magnet","volume":"362","author":"Guo","year":"2018","journal-title":"Science"},{"key":"2026092209082438600_cit87","doi-asserted-by":"publisher","first-page":"14164","DOI":"10.1021\/acs.inorgchem.2c02353","article-title":"Complexes of Ce(III)\nand Bis(pyrazolyl)borate Ligands: Synthesis,\nStructures, and Luminescence Properties","volume":"61","author":"Guo","year":"2022","journal-title":"Inorg.\nChem."},{"key":"2026092209082438600_cit88","doi-asserted-by":"publisher","first-page":"30800","DOI":"10.1039\/D3CP03537A","article-title":"Benchmarks\nfor Transition Metal Spin-State Energetics: Why and How to Employ\nExperimental Reference Data?","volume":"25","author":"Radon\u0301","year":"2023","journal-title":"Phys. Chem. Chem.\nPhys."},{"key":"2026092209082438600_cit89","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1021\/acs.jctc.6b01005","article-title":"Spin State Energetics in First-Row\nTransition Metal Complexes: Contribution of (3s3p) Correlation and\nIts Description by Second-Order Perturbation Theory","volume":"13","author":"Pierloot","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"2026092209082438600_cit90","doi-asserted-by":"publisher","first-page":"7947","DOI":"10.1021\/jacs.0c02122","article-title":"A Vanadium(III) Complex with Blue and NIR-II Spin-Flip\nLuminescence in Solution","volume":"142","author":"Dorn","year":"2020","journal-title":"J. Am. Chem. Soc."},{"key":"2026092209082438600_cit91","doi-asserted-by":"publisher","first-page":"6478","DOI":"10.1039\/D0DT00993H","article-title":"Accurate\nComputed Spin-State Energetics\nfor Co(III) Complexes: Implications for Modelling Homogeneous Catalysis","volume":"49","author":"Neale","year":"2020","journal-title":"Dalton Trans."},{"key":"2026092209082438600_cit92","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1098\/rspa.1961.0175","article-title":"Single Determinant Wave Functions","volume":"263","author":"Amos","year":"1961","journal-title":"Proc. R. Soc. London, Ser. A"}],"container-title":["Journal of Chemical Theory\nand Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jctc.6c01158","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/18\/9483\/68277505\/acs.jctc.6c01158.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/18\/9483\/68277505\/acs.jctc.6c01158.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T13:50:11Z","timestamp":1790085011000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jctcce\/article\/22\/18\/9483\/5412409\/State-Averaged-Density-Matrix-Embedding-Theory-for"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,3]]},"references-count":92,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9,3]]},"published-print":{"date-parts":[[2026,9,22]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jctc.6c01158","relation":{},"ISSN":["1549-9618","1549-9626"],"issn-type":[{"value":"1549-9618","type":"print"},{"value":"1549-9626","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,3]]}}}