{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T17:45:59Z","timestamp":1791913559647,"version":"4.3.4"},"reference-count":73,"publisher":"American Chemical Society (ACS)","issue":"19","license":[{"start":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T00:00:00Z","timestamp":1790294400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T00:00:00Z","timestamp":1790294400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T00:00:00Z","timestamp":1790294400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["RS-2023-NR119931"],"award-info":[{"award-number":["RS-2023-NR119931"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["RS-2024-00432113"],"award-info":[{"award-number":["RS-2024-00432113"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["RS-2025-23324056"],"award-info":[{"award-number":["RS-2025-23324056"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["RS-2026-25478965"],"award-info":[{"award-number":["RS-2026-25478965"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,13]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>When a chemical system of interest contains heavy elements, it is important to obtain a balanced description of relativistic effects and electron correlation. The exact two-component (X2C) Hamiltonian includes both scalar-relativistic and spin\u2013orbit effects with a reasonable computational cost. By using the spin\u2013orbit X2C Hamiltonian in state-averaged complete active space self-consistent field (SA-CASSCF) calculations, it is possible to obtain equivalent descriptions of the states with different spin characters. For molecular geometry optimizations within this framework, the nuclear gradients should be efficiently evaluated. In this work, we describe a state-specific analytical gradient algorithm for X2C-SA-CASSCF theory with the density-fitting approximation. To realize such calculations, we formulate and implement the response (Z-vector) equation for X2C-SA-CASSCF theory. Using the obtained state-specific nuclear gradients, we optimize the equilibrium geometries of metal porphyrins and the singlet\u2013singlet and singlet\u2013triplet minimum energy crossing points or minimum energy conical intersections of 2-thiouracil.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01549","type":"journal-article","created":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T07:02:55Z","timestamp":1790319775000},"page":"10203-10212","source":"Crossref","is-referenced-by-count":0,"title":["State-Specific\nAnalytical Nuclear Gradients for the\nDensity-Fitted Exact Two-Component State-Averaged Complete Active\nSpace Self-Consistent Field (X2C-SA-CASSCF) Theory"],"prefix":"10.1021","volume":"22","author":[{"given":"Saemee","family":"Song","sequence":"first","affiliation":[{"name":"Korea Research Institute of Chemical Technology (KRICT) , , ,","place":["Daejeon, Korea, 34114"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4701-8801","authenticated-orcid":true,"given":"Jae Woo","family":"Park","sequence":"additional","affiliation":[{"name":"Chungbuk National University (CBNU) , , ,","place":["Cheongju, Korea, 28644"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,25]]},"reference":[{"key":"2026101310071349600_cit1","doi-asserted-by":"publisher","first-page":"3470","DOI":"10.1021\/acs.jctc.9b00282","article-title":"The Influence\nof the Electronic Structure Method on Intersystem Crossing Dynamics.\nThe Case of Thioformaldehyde","volume":"15","author":"Mai","year":"2019","journal-title":"J. Chem. Theory\nComput"},{"key":"2026101310071349600_cit2","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1021\/acs.jctc.1c01048","article-title":"Nonadiabatic Molecular Dynamics by\nMulticonfiguration Pair-Density Functional Theory","volume":"18","author":"Calio","year":"2022","journal-title":"J. Chem. Theory Comput"},{"key":"2026101310071349600_cit3","doi-asserted-by":"publisher","first-page":"024104","DOI":"10.1063\/5.0203722","article-title":"Non-adiabatic\ndynamics of photoexcited\ncyclobutanone: Predicting structural measurements from trajectory\nsurface hopping with XMS-CASPT2 simulations","volume":"161","author":"Vindel-Zandbergen","year":"2024","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit4","doi-asserted-by":"publisher","first-page":"1978","DOI":"10.1021\/acs.jpclett.6b00616","article-title":"Intersystem Crossing Pathways in\nthe Noncanonical Nucleobase 2-Thiouracil: A Time-Dependent Picture","volume":"7","author":"Mai","year":"2016","journal-title":"J. Phys. Chem. Lett"},{"key":"2026101310071349600_cit5","doi-asserted-by":"publisher","first-page":"13077","DOI":"10.1038\/ncomms13077","article-title":"The origin of efficient triplet state population in\nsulfur-substituted nucleobases","volume":"7","author":"Mai","year":"2016","journal-title":"Nat. Commun"},{"key":"2026101310071349600_cit6","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1111\/php.12975","article-title":"Photochemical and\nPhotodynamical Properties of Sulfur-Substituted Nucleic Acid Bases","volume":"95","author":"Ashwood","year":"2019","journal-title":"Photochem. Photobiol"},{"key":"2026101310071349600_cit7","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S1011-1344(97)00116-4","article-title":"Thionucleobases\nas intrinsic photoaffinity probes of nucleic acid structure and nucleic\nacid-protein interactions","volume":"42","author":"Favre","year":"1998","journal-title":"J. Photochem. Photobiol.,\nB"},{"key":"2026101310071349600_cit8","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195140866.001.0001","volume-title":"Introduction to Relativistic Quantum Chemistry","author":"Dyall","year":"2007"},{"key":"2026101310071349600_cit9","volume-title":"Relativistic Quantum Chemistry: the\nFundamental Theory of Molecular Science","author":"Reiher","year":"2015","edition":"2nd"},{"key":"2026101310071349600_cit10","doi-asserted-by":"publisher","first-page":"241102","DOI":"10.1063\/1.2137315","article-title":"Quasirelativistic Theory Equivalent to Fully Relativistic Theory","volume":"123","author":"Kutzelnigg","year":"2005","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit11","doi-asserted-by":"publisher","first-page":"2225","DOI":"10.1080\/00268970600662481","article-title":"Quasirelativistic theory\nI. Theory in terms of a quasi-relativistic\noperator","volume":"104","author":"Kutzelnigg","year":"2006","journal-title":"Mol. Phys"},{"key":"2026101310071349600_cit12","doi-asserted-by":"publisher","first-page":"114107","DOI":"10.1063\/1.2710258","article-title":"Quasirelativistic Theory. II. Theory at Matrix Level","volume":"126","author":"Liu","year":"2007","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit13","doi-asserted-by":"publisher","first-page":"064102","DOI":"10.1063\/1.2436882","article-title":"An infinite-order two-component\nrelativistic Hamiltonian by a simple\none-step transformation","volume":"126","author":"Ilias\u030c","year":"2007","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit14","doi-asserted-by":"publisher","first-page":"104106","DOI":"10.1063\/1.2772856","article-title":"Making Four- and Two-Component Relativistic\nDensity Functional Methods Fully Equivalent Based on the Idea of \u201cFrom\nAtoms to Molecule\u201d","volume":"127","author":"Peng","year":"2007","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit15","doi-asserted-by":"publisher","first-page":"124116","DOI":"10.1063\/1.3239505","article-title":"The molecular\nmean-field approach for correlated relativistic calculations","volume":"131","author":"Sikkema","year":"2009","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit16","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":"2026101310071349600_cit17","doi-asserted-by":"publisher","first-page":"1679","DOI":"10.1080\/00268971003781571","article-title":"Ideas of Relativistic\nQuantum Chemistry","volume":"108","author":"Liu","year":"2010","journal-title":"Mol. Phys"},{"key":"2026101310071349600_cit18","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1007\/s00214-011-1081-y","article-title":"Exact Decoupling of\nthe Relativistic Fock Operator","volume":"131","author":"Peng","year":"2012","journal-title":"Theor. Chem.\nAcc"},{"key":"2026101310071349600_cit19","doi-asserted-by":"publisher","first-page":"4928","DOI":"10.1063\/1.1678164","article-title":"LiH Potential Curves\nand Wavefunctions for X1 \u03a3 +, A1 \u03a3+, B1 \u03a0, 3\u03a3+, and 3\u03a0","volume":"57","author":"Docken","year":"1972","journal-title":"J. Chem.\nPhys"},{"key":"2026101310071349600_cit20","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1002\/qua.560160511","article-title":"MCSCF Optimization through Combined\nUse of Natural Orbitals and the Brillouin\u2013Levy\u2013Berthier\nTheorem","volume":"16","author":"Ruedenberg","year":"1979","journal-title":"Int. J. Quantum Chem"},{"key":"2026101310071349600_cit21","doi-asserted-by":"publisher","first-page":"5802","DOI":"10.1063\/1.440893","article-title":"MCSCF study of the\navoided curve crossing of the two lowest 1 \u03a3+ states of LiF","volume":"74","author":"Werner","year":"1981","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit22","doi-asserted-by":"publisher","first-page":"4549","DOI":"10.1063\/1.447428","article-title":"On the Evaluation\nof Nonadiabatic Coupling Matrix Elements Using SA-MCSCF\/CI Wave Functions\nand Analytic Gradient Methods. I","volume":"81","author":"Lengsfield","year":"1984","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit23","doi-asserted-by":"crossref","DOI":"10.1002\/9781119019572","volume-title":"Molecular Electronic-Structure Theory","author":"Helgaker","year":"2000"},{"key":"2026101310071349600_cit24","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/S0009-2614(98)00252-8","article-title":"The Multi-State\nCASPT2Method","volume":"288","author":"Finley","year":"1998","journal-title":"Chem. Phys. Lett"},{"key":"2026101310071349600_cit25","doi-asserted-by":"publisher","first-page":"7983","DOI":"10.1063\/1.465674","article-title":"Quasidegenerate\nperturbation theory with multiconfigurational self-consistent-field\nreference functions","volume":"99","author":"Nakano","year":"1993","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit26","doi-asserted-by":"publisher","first-page":"4043","DOI":"10.1063\/1.1778711","article-title":"A Quasidegenerate\nFormulation of the Second Order N-Electron Valence\nState Perturbation Theory Approach","volume":"121","author":"Angeli","year":"2004","journal-title":"J. Chem.\nPhys"},{"key":"2026101310071349600_cit27","doi-asserted-by":"publisher","first-page":"3273","DOI":"10.1002\/qua.23052","article-title":"A Perspective\non the CASPT2Method","volume":"111","author":"Pulay","year":"2011","journal-title":"Int. J. Quantum Chem"},{"key":"2026101310071349600_cit28","doi-asserted-by":"publisher","first-page":"7293","DOI":"10.1021\/acs.chemrev.8b00244","article-title":"Multireference Approaches for Excited\nStates of Molecules","volume":"118","author":"Lischka","year":"2018","journal-title":"Chem. Rev"},{"key":"2026101310071349600_cit29","doi-asserted-by":"publisher","first-page":"5878","DOI":"10.1021\/acs.chemrev.9b00496","article-title":"Multireference\nElectron Correlation Methods: Journeys along Potential Energy Surfaces","volume":"120","author":"Park","year":"2020","journal-title":"Chem. Rev"},{"key":"2026101310071349600_cit30","doi-asserted-by":"publisher","DOI":"10.1002\/wcms.1370","article-title":"Nonadiabatic Dynamics: The SHARC\nApproach","volume":"8","author":"Mai","year":"2018","journal-title":"WIREs Comput. Mol. Sci"},{"key":"2026101310071349600_cit31","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1002\/wcms.1158","article-title":"Newton-X: A Surface-Hopping Program\nfor Nonadiabatic Molecular Dynamics","volume":"4","author":"Barbatti","year":"2014","journal-title":"WIREs Comput.\nMol. Sci"},{"key":"2026101310071349600_cit32","doi-asserted-by":"publisher","first-page":"13502","DOI":"10.1021\/acs.chemrev.7b00177","article-title":"Theory and Simulation\nof the Ultrafast Double-Bond Isomerization of Biological Chromophores","volume":"117","author":"Gozem","year":"2017","journal-title":"Chem. Rev"},{"key":"2026101310071349600_cit33","doi-asserted-by":"publisher","first-page":"3531","DOI":"10.1039\/D4CP03671A","article-title":"Analytical\nnuclear gradient and derivative coupling theories for multireference\nperturbation methods","volume":"27","author":"Park","year":"2025","journal-title":"Phys. Chem. Chem. Phys"},{"key":"2026101310071349600_cit34","doi-asserted-by":"publisher","first-page":"2974","DOI":"10.1021\/acs.jctc.9b00011","article-title":"Variational Relativistic\nTwo-Component Complete-Active-Space Self-Consistent Field Method","volume":"15","author":"Jenkins","year":"2019","journal-title":"J. Chem. Theory Comput"},{"key":"2026101310071349600_cit35","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1038\/s41557-018-0158-9","article-title":"Relativistic quantum\nchemical calculations\nshow that the uranium molecule U2 has a quadruple bond","volume":"11","author":"Knecht","year":"2019","journal-title":"Nat. Chem"},{"key":"2026101310071349600_cit36","doi-asserted-by":"publisher","first-page":"204104","DOI":"10.1063\/5.0004844","article-title":"The DIRAC Code for Relativistic\nMolecular Calculations","volume":"152","author":"Saue","year":"2020","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit37","doi-asserted-by":"publisher","first-page":"104113","DOI":"10.1063\/1.4793736","article-title":"A fully variational spin-orbit coupled complete active space self-consistent\nfield approach: Application to electron paramagnetic resonance g-tensors","volume":"138","author":"Ganyushin","year":"2013","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit38","doi-asserted-by":"publisher","first-page":"3988","DOI":"10.1021\/acs.jctc.6c00321","article-title":"Relativistic Complete\nActive Space Self-consistent-Field Method with a Hierarchy of Exact\nTwo-Component Hamiltonians","volume":"22","author":"Wang","year":"2026","journal-title":"J. Chem. Theory\nComput"},{"key":"2026101310071349600_cit39","doi-asserted-by":"publisher","first-page":"7154","DOI":"10.1021\/acs.jctc.6c00400","article-title":"A Perturbative\nSuper-CI Approach for Orbital Optimization\nin Two-Component Relativistic CASSCF","volume":"22","author":"Guo","year":"2026","journal-title":"J. Chem.\nTheory Comput"},{"key":"2026101310071349600_cit40","doi-asserted-by":"publisher","first-page":"2983","DOI":"10.1021\/acs.jctc.2c00171","article-title":"Exact-Two-Component Relativistic\nMultireference Second-Order Perturbation Theory","volume":"18","author":"Lu","year":"2022","journal-title":"J. Chem. Theory Comput"},{"key":"2026101310071349600_cit41","doi-asserted-by":"publisher","first-page":"5011","DOI":"10.1021\/acs.jpca.2c02150","article-title":"Relativistic Kramers-Unrestricted\nExact-Two-Component Density Matrix Renormalization Group","volume":"126","author":"Hoyer","year":"2022","journal-title":"J. Phys. Chem. A"},{"key":"2026101310071349600_cit42","doi-asserted-by":"publisher","first-page":"2947","DOI":"10.1021\/acs.jctc.2c00062","article-title":"Exact-Two-Component\nMulticonfiguration\nPair-Density Functional Theory","volume":"18","author":"Sharma","year":"2022","journal-title":"J. Chem. Theory\nComput"},{"key":"2026101310071349600_cit43","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1002\/wcms.1171","article-title":"Analytical\nderivatives, forces, force constants, molecular geometries, and related\nresponse properties in electronic structure theory","volume":"4","author":"Pulay","year":"2014","journal-title":"WIREs Comput. Mol. Sci"},{"key":"2026101310071349600_cit44","doi-asserted-by":"publisher","first-page":"084114","DOI":"10.1063\/1.3624397","article-title":"Analytic energy gradients for the spin-free exact two-component theory\nusing an exact block diagonalization for the one-electron Dirac Hamiltonian","volume":"135","author":"Cheng","year":"2011","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit45","doi-asserted-by":"publisher","first-page":"244104","DOI":"10.1063\/1.3667202","article-title":"Analytic second derivatives\nfor the spin-free exact two-component\ntheory","volume":"135","author":"Cheng","year":"2011","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit46","doi-asserted-by":"publisher","first-page":"214106","DOI":"10.1063\/1.4921915","article-title":"Analytical\nEnergy Gradient for the\nTwo-Component Normalized Elimination of the Small Component Method","volume":"142","author":"Zou","year":"2015","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit47","doi-asserted-by":"publisher","first-page":"2181","DOI":"10.1021\/acs.jctc.5b00928","article-title":"Implementation\nof Analytical Energy\nGradient of Spin-Dependent General Hartree-Fock Method Based on the\nInfinite-Order Douglas\u2013Kroll\u2013Hess Relativistic Hamiltonian\nwith Local Unitary Transformation","volume":"12","author":"Nakajima","year":"2016","journal-title":"J. Chem.\nTheory Comput"},{"key":"2026101310071349600_cit48","doi-asserted-by":"publisher","first-page":"104110","DOI":"10.1063\/1.5022153","article-title":"Efficient implementation of one-\nand two-component analytical energy gradients in exact two-component\ntheory","volume":"148","author":"Franzke","year":"2018","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit49","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.1021\/acs.jctc.9b01120","article-title":"Analytic Energy Gradients and Hessians\nof Exact Two-Component Relativistic Methods: Efficient Implementation\nand Extensive Applications","volume":"16","author":"Zou","year":"2020","journal-title":"J. Chem. Theory\nComput"},{"key":"2026101310071349600_cit50","doi-asserted-by":"publisher","first-page":"5523","DOI":"10.1021\/acs.jctc.5c00405","article-title":"Analytical\nGradient Theory for Density-Fitted Exact Two-Component (X2C) Generalized\nHartree\u2013Fock (X2C-GHF), State-Specific Complete Active Space\nSelf-Consistent Field (X2C-CASSCF), and Second-Order M\u00f8ller\u2013Plesset\nPerturbation (X2C-MP2) Theories","volume":"21","author":"Park","year":"2025","journal-title":"J. Chem. Theory\nComput"},{"key":"2026101310071349600_cit51","doi-asserted-by":"publisher","first-page":"151101","DOI":"10.1063\/5.0086281","article-title":"Geometry Optimizations\nwith Spinor-Based Relativistic Coupled-Cluster Theory","volume":"156","author":"Zheng","year":"2022","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit52","doi-asserted-by":"publisher","first-page":"244113","DOI":"10.1063\/5.0175041","article-title":"Analytic gradients\nfor relativistic exact-two-component equation-of-motion coupled-cluster\nsingles and doubles method","volume":"159","author":"Zhang","year":"2023","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit53","doi-asserted-by":"publisher","first-page":"12071","DOI":"10.1021\/acs.jctc.5c01543","article-title":"Approximate\nSpin\u2013Orbit Eigenstates with Static and Dynamical Correlations:\nX2CSO-DSRG-MRPT2 Prescription","volume":"21","author":"Park","year":"2025","journal-title":"J. Chem. Theory\nComput"},{"key":"2026101310071349600_cit54","doi-asserted-by":"publisher","first-page":"2097","DOI":"10.1021\/acs.jctc.5b00134","article-title":"Multireference\nDriven Similarity Renormalization Group:\nA Second-Order Perturbative Analysis","volume":"11","author":"Li","year":"2015","journal-title":"J. Chem.\nTheory Comput"},{"key":"2026101310071349600_cit55","doi-asserted-by":"publisher","first-page":"204111","DOI":"10.1063\/1.5019793","article-title":"Driven\nSimilarity Renormalization Group for Excited\nStates: A State-Averaged Perturbation Theory","volume":"146","author":"Li","year":"2018","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit56","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1146\/annurev-physchem-042018-052416","article-title":"Multireference\nTheories of Electron Correlation Based\non the Driven Similarity Renormalization Group","volume":"70","author":"Li","year":"2019","journal-title":"Annu. Rev. Phys. Chem"},{"key":"2026101310071349600_cit57","doi-asserted-by":"publisher","first-page":"7230","DOI":"10.1021\/acs.jctc.6c00935","article-title":"One-Step\nRelativistic Driven Similarity Renormalization\nGroup Multireference Perturbation Theory","volume":"22","author":"Zhao","year":"2026","journal-title":"J.\nChem. Theory Comput"},{"key":"2026101310071349600_cit58","doi-asserted-by":"publisher","first-page":"5031","DOI":"10.1063\/1.447489","article-title":"On the Evaluation\nof Analytic Energy Derivatives for\nCorrelated Wave Functions","volume":"81","author":"Handy","year":"1984","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit59","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0009-2614(84)85513-X","article-title":"A New Determinant-Based\nFull Configuration Interaction\nMethod","volume":"111","author":"Knowles","year":"1984","journal-title":"Chem. Phys. Lett"},{"key":"2026101310071349600_cit60","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/0009-2614(82)80024-9","article-title":"On the Energy\nVariation Method","volume":"90","author":"Hendekovic\u0301","year":"1982","journal-title":"Chem. Phys. Lett"},{"key":"2026101310071349600_cit61","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1088\/0031-8949\/21\/3-4\/014","article-title":"A Comparison of the\nSuper-CI and the Newton\u2013Raphson Scheme in the Complete Active\nSpace SCF Method","volume":"21","author":"Siegbahn","year":"1980","journal-title":"Phys. Scr"},{"key":"2026101310071349600_cit62","doi-asserted-by":"publisher","first-page":"2384","DOI":"10.1063\/1.441359","article-title":"The Complete\nActive Space SCF (CASSCF) Method in a Newton\u2013Raphson Formulation\nwith Application to the HNO Molecule","volume":"74","author":"Siegbahn","year":"1981","journal-title":"J. Chem.\nPhys"},{"key":"2026101310071349600_cit63","doi-asserted-by":"publisher","first-page":"2342","DOI":"10.1063\/1.440384","article-title":"A Quadratically Convergent\nMulticonfiguration\u2013Self-Consistent\nField Method with Simultaneous Optimization of Orbitals and CI Coefficients","volume":"73","author":"Werner","year":"1980","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit64","doi-asserted-by":"publisher","first-page":"5053","DOI":"10.1063\/1.448627","article-title":"A second order multiconfiguration SCF procedure with\noptimum convergence","volume":"82","author":"Werner","year":"1985","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit65","doi-asserted-by":"publisher","first-page":"014106","DOI":"10.1063\/1.5036594","article-title":"Large-Scale\nRelativistic Complete\nActive Space Self-Consistent Field with Robust Convergence","volume":"149","author":"Reynolds","year":"2018","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit66","doi-asserted-by":"publisher","first-page":"1560","DOI":"10.1021\/acs.jctc.8b00910","article-title":"Zero-Field Splitting\nParameters from Four-Component\nRelativistic Methods","volume":"15","author":"Reynolds","year":"2019","journal-title":"J. Chem. Theory Comput"},{"key":"2026101310071349600_cit67","doi-asserted-by":"publisher","first-page":"244117","DOI":"10.1063\/1.3603454","article-title":"Development\nand application of the\nanalytical energy gradient for the normalized elimination of the small\ncomponent method","volume":"134","author":"Zou","year":"2011","journal-title":"J. Chem. Phys"},{"key":"2026101310071349600_cit68","doi-asserted-by":"publisher","first-page":"7809","DOI":"10.1103\/PhysRevB.62.7809","article-title":"Approximate\nTwo-Electron Spin-Orbit Coupling Term for Density-Functional-Theory\nDFT Calculations using the Douglas\u2013Kroll\u2013Hess Hamiltonian","volume":"62","author":"Boettger","year":"2000","journal-title":"Phys. Rev. B"},{"key":"2026101310071349600_cit69","doi-asserted-by":"publisher","DOI":"10.1002\/wcms.1331","article-title":"BAGEL: Brilliantly\nAdvanced General Electronic-structure Library","volume":"8","author":"Shiozaki","year":"2018","journal-title":"WIREs Comput. Mol. Sci"},{"key":"2026101310071349600_cit70","doi-asserted-by":"publisher","first-page":"3696","DOI":"10.1021\/acs.jctc.7b00593","article-title":"Segmented Contracted\nError-Consistent Basis Sets of\nDouble- and Triple-\u03b6 Valence Quality for One-\nand Two-Component Relativistic All-Electron Calculations","volume":"13","author":"Pollak","year":"2017","journal-title":"J. Chem. Theory Comput"},{"key":"2026101310071349600_cit71","doi-asserted-by":"publisher","first-page":"10863","DOI":"10.1021\/acs.jctc.5c01219","article-title":"Physics-Driven Construction of Compact\nPrimitive Gaussian\nDensity Fitting Basis Sets","volume":"21","author":"Surjuse","year":"2025","journal-title":"J. Chem. Theory\nComput"},{"key":"2026101310071349600_cit72","doi-asserted-by":"publisher","first-page":"5518","DOI":"10.1002\/anie.201410637","article-title":"Electron Flow in Reaction Mechanisms\u2500Revealed\nFrom First Principles","volume":"54","author":"Knizia","year":"2015","journal-title":"Angew. Chem., Int. Ed"},{"key":"2026101310071349600_cit73","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1021\/jp0761618","article-title":"Optimizing\nConical Intersections\nwithout Derivative Coupling Vectors: Application to Multistate Multireference\nSecond-Order Perturbation Theory (MS-CASPT2)","volume":"112","author":"Levine","year":"2008","journal-title":"J. Phys. Chem. B"}],"container-title":["Journal of Chemical Theory\nand Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jctc.6c01549","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/doi\/10.1021\/acs.jctc.6c01549\/68647577\/acs.jctc.6c01549.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/doi\/10.1021\/acs.jctc.6c01549\/68647577\/acs.jctc.6c01549.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T16:54:18Z","timestamp":1791910458000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jctcce\/article\/22\/19\/10203\/5438192\/State-Specific-Analytical-Nuclear-Gradients-for"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,25]]},"references-count":73,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2026,9,25]]},"published-print":{"date-parts":[[2026,10,13]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jctc.6c01549","relation":{},"ISSN":["1549-9618","1549-9626"],"issn-type":[{"value":"1549-9618","type":"print"},{"value":"1549-9626","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,25]]}}}