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Spin-adapted RPA was developed using tensor equation-of-motion and applying the Wigner\u2013Eckart theorem with tensor decoupling. Casting the RPA Fock matrix and kernels as energy derivatives gives a TDDFT extension. To restore spin-component degeneracy and eliminate multicounting of spin correlation in pure exchange-correlation functionals, we use hybrids combining HF exchange with spin-unpolarized pure XC parts. Given that the mapping from spin-adapted RPA to spin-adapted TDDFT is ad hoc, we introduce a first-principles framework for evaluating the expectation value \u27e8S\u03022\u27e9 of excited states in order to rigorously prove their spin purification. In addition, we derive explicit working equations for the computation of the single-particle density matrix of excited states, thereby enabling a natural orbital analysis of their electronic structure. Benchmarks, diradicals\/triradicals, Cr2 dissociation, and phenol O\u2013H conical intersections demonstrate the method.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01068","type":"journal-article","created":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T06:53:27Z","timestamp":1788332007000},"page":"9437-9449","source":"Crossref","is-referenced-by-count":1,"title":["Translating Spin-Adapted\nRPA to Spin-Adapted TDDFT"],"prefix":"10.1021","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4178-3519","authenticated-orcid":true,"given":"Xiaoyu","family":"Zhang","sequence":"first","affiliation":[{"name":"Peking University , , ,","place":["Beijing, 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, China, 100871"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,28]]},"reference":[{"key":"2026092209072379200_cit1","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1142\/9789812830586_0005","article-title":"Time-dependent density functional response theory\nfor molecules","volume-title":"Recent Advances in Density\nFunctional Methods","author":"Casida","year":"1995"},{"key":"2026092209072379200_cit2","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.theochem.2009.07.036","article-title":"Excited-state spin-contamination\nin time-dependent density-functional theory for molecules with open-shell\nground states","volume":"914","author":"Ipatov","year":"2009","journal-title":"THEOCHEM"},{"key":"2026092209072379200_cit3","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1002\/qua.560560414","article-title":"Spin-unrestricted\ncharacter of kohn-sham\norbitals for open-shell systems","volume":"56","author":"Pople","year":"1995","journal-title":"Int. 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