Noncollinear Mixed-Reference Spin-Flip TDDFT: Removing the Dependence on High Exact Exchange

Collinear mixed-reference spin-flip TDDFT (MRSF-TDDFT) omits the transverse exchange–correlation (xc) response from its spin-flip channel, making large fractions of exact exchange practically necessary. We remove this restriction by incorporating the multicollinear transverse xc kernel into MRSF-TDDFT without empirical rescaling. The U(1) spin-rotation selection rule confines the added response to the matrix blocks within each triplet reference and leaves the inter-reference spin-pairing coupling unchanged. The resulting noncollinear MRSF-TDDFT (nc-MRSF-TDDFT) reduces the offset between the spin-lowered MS = 0 response root and the bare MS = ±1 references by 86–99%, from 0.75–2.9 to 0.03–0.11 eV, and restores the diagonal spin-rotation condition without imposing an exact zero mode. Thiel and QUEST benchmarks show that B3LYP and PBE0 give the most balanced singlet, triplet, and singlet–triplet gap errors, whereas BH&HLYP tends to overcorrect the absolute excitation energies after the transverse response is restored. Ethylene torsion separates the complementary roles of the theory: the mixed-reference configuration space describes the continuous development of open-shell character, while the NC kernel corrects the relative spin-state energetics. The same correction improves diradical singlet–triplet gaps at published state-specific geometries. The transverse kernel increases the response-step cost, but the unchanged SCF and other shared steps make the relative overhead smaller for the total calculation. By restoring the missing xc response rather than compensating for it with high exact exchange, nc-MRSF-TDDFT extends the practical functional and chemical scope of MRSF-TDDFT while retaining its description of multiconfigurational and doubly excited states.