{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T18:48:41Z","timestamp":1791917321959,"version":"4.3.4"},"reference-count":71,"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\/501100018537","name":"National Science and Technology Major Project","doi-asserted-by":"publisher","award":["2025ZD0808600"],"award-info":[{"award-number":["2025ZD0808600"]}],"id":[{"id":"10.13039\/501100018537","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018537","name":"National Science and Technology Major Project","doi-asserted-by":"publisher","award":["2025ZD0808601"],"award-info":[{"award-number":["2025ZD0808601"]}],"id":[{"id":"10.13039\/501100018537","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>TDDFT for open-shell systems, whether spin-conserving or spin-flip, has long suffered from spin contamination. This problem arises because the single-excitation space built upon a single Kohn\u2013Sham determinant is not spin-complete. Adopting spin tensor reference states therefore offers an elegant and promising route to resolving this issue. In this work, we revisit the tensor TDDFT equations within the Tamm\u2013Dancoff approximation (TDA) from a noncollinear perspective. We show that, for S = 1\/2 reference states, the internal consistency of the spin tensor formulation can, with the aid of the zero-excitation-energy theorem, be recast as a set of constraints that the exchange\u2013correlation kernel must satisfy. Standard noncollinear functionals, however, generally fail to meet these constraints. To address this, we propose a kernel reconstruction scheme that is independent of the specific functional form and free of empirical parameters. This scheme enforces the required constraints, restoring internal consistency in the full spin tensor structure, with spin adaptation following as a natural consequence. Furthermore, when extended to tensor reference states with other values of S, such as S = 1 for the oxygen molecule, the scheme eliminates the so-called artifact states, namely solutions with severely underestimated excitation energies. In addition, the scheme allows the target states that ROKS reference states aim to describe to be expressed and computed, at the TDA level, within the same unified framework as other states, a capability that spin-adapted spin-conserving TDDFT has so far lacked.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01470","type":"journal-article","created":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T14:02:52Z","timestamp":1790344972000},"page":"10192-10202","source":"Crossref","is-referenced-by-count":0,"title":["Spin-Consistency\nConstraints in Noncollinear Tensor\nTDA"],"prefix":"10.1021","volume":"22","author":[{"given":"Wenxian","family":"Qin","sequence":"first","affiliation":[{"name":"Peking University , , ,","place":["Beijing, The People\u2019s Republic of China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-5775-5483","authenticated-orcid":true,"given":"Tai","family":"Wang","sequence":"additional","affiliation":[{"name":"Peking University , , ,","place":["Beijing, The People\u2019s Republic of China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Yu","sequence":"additional","affiliation":[{"name":"Peking University , , ,","place":["Beijing, The People\u2019s Republic of China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanyang","family":"Liu","sequence":"additional","affiliation":[{"name":"Peking University , , ,","place":["Beijing, The People\u2019s Republic of China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4309-9376","authenticated-orcid":true,"given":"Yi Qin","family":"Gao","sequence":"additional","affiliation":[{"name":"Peking University , , ,","place":["Beijing, The People\u2019s Republic of China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0770-1240","authenticated-orcid":true,"given":"Yunlong","family":"Xiao","sequence":"additional","affiliation":[{"name":"Peking University , , ,","place":["Beijing, The People\u2019s Republic of China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,25]]},"reference":[{"key":"2026101310075974600_cit1","doi-asserted-by":"publisher","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous Electron Gas","volume":"136","author":"Hohenberg","year":"1964","journal-title":"Phys. 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Phys."},{"key":"2026101310075974600_cit7","doi-asserted-by":"publisher","first-page":"4009","DOI":"10.1021\/cr0505627","article-title":"Single-Reference Ab Initio Methods for the Calculation\nof Excited States of Large Molecules","volume":"105","author":"Dreuw","year":"2005","journal-title":"Chem.\nRev."},{"key":"2026101310075974600_cit8","doi-asserted-by":"publisher","first-page":"2270","DOI":"10.1021\/acs.jctc.3c00059","article-title":"Noncollinear and Spin-Flip\nTDDFT in Multicollinear Approach","volume":"19","author":"Li","year":"2023","journal-title":"J. Chem. Theory\nComput."},{"key":"2026101310075974600_cit9","doi-asserted-by":"publisher","first-page":"3010","DOI":"10.1021\/acs.jctc.5c00115","article-title":"Analytic Gradient for Spin-Flip TDDFT\nUsing Noncollinear Functionals in the Multicollinear Approach","volume":"21","author":"Li","year":"2025","journal-title":"J. Chem. Theory Comput."},{"key":"2026101310075974600_cit10","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1021\/acs.jctc.5b01219","article-title":"Critical Assessment\nof Time-Dependent Density Functional Theory for\nExcited States of Open-Shell Systems: II. Doublet-Quartet Transitions","volume":"12","author":"Li","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"2026101310075974600_cit11","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1021\/acs.jctc.5b01158","article-title":"Critical Assessment\nof TD-DFT for Excited States of Open-Shell Systems:\nI. Doublet\u2013Doublet Transitions","volume":"12","author":"Li","year":"2016","journal-title":"J. Chem.\nTheory Comput."},{"key":"2026101310075974600_cit12","doi-asserted-by":"publisher","first-page":"11291","DOI":"10.1021\/acs.chemrev.9b00260","article-title":"Do Diradicals Behave\nLike Radicals?","volume":"119","author":"Stuyver","year":"2019","journal-title":"Chem. 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Phys."},{"key":"2026101310075974600_cit28","doi-asserted-by":"publisher","first-page":"9437","DOI":"10.1021\/acs.jctc.6c01068","article-title":"Translating Spin-Adapted RPA to Spin-Adapted TDDFT","volume":"22","author":"Zhang","year":"2026","journal-title":"J. Chem. Theory Comput."},{"key":"2026101310075974600_cit29","doi-asserted-by":"publisher","first-page":"134101","DOI":"10.1063\/1.3573374","article-title":"Spin-Adapted Open-Shell Time-Dependent\nDensity Functional Theory. II. Theory and Pilot Application","volume":"134","author":"Li","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2026101310075974600_cit30","doi-asserted-by":"publisher","first-page":"2091","DOI":"10.1002\/qua.22065","article-title":"Relativistic\nAdiabatic Time-Dependent\nDensity Functional Theory Using Hybrid Functionals and Noncollinear\nSpin Magnetization","volume":"109","author":"Bast","year":"2009","journal-title":"Int. J. Quantum Chem."},{"key":"2026101310075974600_cit31","doi-asserted-by":"publisher","first-page":"1457","DOI":"10.1063\/1.1680203","article-title":"General SCF Operator Satisfying Correct Variational\nCondition","volume":"59","author":"Hirao","year":"1973","journal-title":"J. Chem. Phys."},{"key":"2026101310075974600_cit32","unstructured":"NonDFT NEST (Noncollinear Electronic Structure Theory). GitHub Repository, 2026; https:\/\/github.com\/NonDFT\/NEST (accessed July 15, 2026)."},{"key":"2026101310075974600_cit33","doi-asserted-by":"publisher","DOI":"10.1002\/wcms.1340","article-title":"PySCF: The Python-Based\nSimulations of Chemistry Framework","volume":"8","author":"Sun","year":"2018","journal-title":"WIREs Comput.\nMol. 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