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MRSF-TDDFT improves the description of the spin-flip target states and the respective energy differences and eliminates the problem of spin-contamination that often spoils the description of higher-lying states in SF-TDDFT. This article presents the theoretical framework and details of a new implementation of MRSF-TDDFT in the Q-Chem software package. The implementation includes calculations of energies and properties, including transition dipole moments, oscillator strengths, spin\u2013orbit couplings, and density-matrix based analyses of the MRSF states and transitions. The capabilities of the theory are illustrated by applications to diradicals, butadiene, and a reduced retinal model, the penta-2,4-dieniminium cation, used to evaluate the performance of electronic structure methods in describing conical intersections.<\/jats:p>","DOI":"10.1063\/5.0340840","type":"journal-article","created":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T12:07:46Z","timestamp":1788869266000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["New implementation of mixed-reference spin-flip time-dependent density functional theory and application to molecules with variable diradical character and conical intersections"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7528-9943","authenticated-orcid":false,"given":"Arnab","family":"Chakraborty","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of Southern California 1 , Los Angeles, California 90089,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1230-4664","authenticated-orcid":false,"given":"Zheng","family":"Pei","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Brandeis University 2 , Waltham, Massachusetts 02453,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9337-341X","authenticated-orcid":false,"given":"Yihan","family":"Shao","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Brandeis University 2 , Waltham, Massachusetts 02453,","place":["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 1 , Los Angeles, California 90089,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,8]]},"reference":[{"key":"2026090808071838300_c1","doi-asserted-by":"publisher","first-page":"28700","DOI":"10.1039\/d2cp02827a","article-title":"DFT exchange: Sharing perspectives on the workhorse of quantum chemistry and materials science","volume":"24","year":"2022","journal-title":"Phys. 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