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This approach employs the Breit\u2013Pauli Hamiltonian and Wigner\u2013Eckart\u2019s theorem applied to the reduced one-particle transition density matrices, together with the spin\u2013orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states. Benchmark calculations using several closed-shell organic molecules, diradicals, and a single-molecule magnet illustrate the efficiency of the SOC protocol. The results for organic molecules (described by standard TD-DFT) show that SOCs are insensitive to the choice of the functional or basis sets, as long as the states of the same characters are compared. In contrast, the SF-TD-DFT results for small diradicals (CH2, NH2+, SiH2, and PH2+) show strong functional dependence. The spin-reversal energy barrier in a Fe(III) single-molecule magnet computed using non-collinear SF-TD-DFT (PBE0, \u03c9PBEh\/cc-pVDZ) agrees well with the experimental estimate.<\/jats:p>","DOI":"10.1063\/5.0130868","type":"journal-article","created":{"date-parts":[[2022,11,28]],"date-time":"2022-11-28T10:36:10Z","timestamp":1669631770000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":27,"title":["Spin\u2013orbit couplings within spin-conserving and spin-flipping time-dependent density functional theory: Implementation and benchmark calculations"],"prefix":"10.1063","volume":"157","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0778-404X","authenticated-orcid":false,"given":"Saikiran","family":"Kotaru","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of Southern California , Los Angeles, California 90089-0482, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5754-9836","authenticated-orcid":false,"given":"Pavel","family":"Pokhilko","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Southern California , Los Angeles, California 90089-0482, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6788-5016","authenticated-orcid":false,"given":"Anna I.","family":"Krylov","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Southern California , Los Angeles, California 90089-0482, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2022,12,13]]},"reference":[{"key":"2023121301063049400_c1","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1039\/b614390c","article-title":"Understanding the kinetics of spin-forbidden chemical reactions","volume":"9","year":"2007","journal-title":"Phys. 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