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The electronically excited states are often hard to model due to the complex nature of the wave function. This especially holds true in the case of heavy-element systems, for which the treatment of spin\u2013orbit coupling (SOC) is crucial for a good description. To address this, we have modified the SOC-corrected restricted open-shell Kohn\u2013Sham (ROKS) time-dependent density functional theory approach within the Tamm\u2013Dancoff approximation (TDA). We have extended the ROKS-TDA-SOC method by including scalar relativistic spin-flip-down states (in addition to the spin-conserved and spin-flip-up ones) from ROKS-TDA, which participate in the SOC state interaction. Our assessment shows that ROKS-TDA-SOC is able to efficiently calculate the lowest-lying SOC-split excitation energies in molecular systems that contain heavy elements and two or more unpaired electrons.<\/jats:p>","DOI":"10.1063\/5.0305111","type":"journal-article","created":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T11:53:30Z","timestamp":1767873210000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Restricted open-shell time-dependent density functional theory with perturbative spin\u2013orbit coupling: Inclusion of spin-flip-down states"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3007-4808","authenticated-orcid":false,"given":"Chima S.","family":"Chibueze","sequence":"first","affiliation":[{"name":"Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit , De Boelelaan 1108, 1081 HZ Amsterdam,","place":["The Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7748-6243","authenticated-orcid":false,"given":"Lucas","family":"Visscher","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit , De Boelelaan 1108, 1081 HZ Amsterdam,","place":["The Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,1,8]]},"reference":[{"key":"2026010806532181100_c1","volume-title":"Time-Dependent Density-Functional Theory: Concepts and Applications","year":"2011"},{"key":"2026010806532181100_c2","first-page":"33","article-title":"TDDFT for excited states","volume-title":"Computational Methods in Catalysis and Materials Science","year":"2009"},{"key":"2026010806532181100_c3","doi-asserted-by":"publisher","first-page":"094111","DOI":"10.1063\/5.0275059","article-title":"Spin-adapted spin-flip-down time-dependent density functional theory","volume":"163","year":"2025","journal-title":"J.\u00a0Chem. 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