Spin-Adapted Spin-Flip Tamm-Dancoff Approximation (XSF-TDA) for Singlet-Triplet Gaps in MR-TADF and INVEST Emitters

In this work, we assess the recently introduced spin-adapted TDA for spin-flip-down excitations (XSF-TDA) [Mol. Phys. e2631735 (2026)] as a practical approach to this problem. Starting from a high-spin restricted open-shell Kohn–Sham reference, XSF-TDA generates spin-adapted low-spin roots arising from open–open (OO), core–open (CO), open–virtual (OV), and core–virtual (CV) types of spin-flip-down excitations. Across four application sets comprising 243 benchmark cases, XSF-TDA substantially reduces the systematic positive bias observed for TDA and unrestricted spin-flip TDA (USF-TDA). With the B3LYP functional, XSF-TDA reduces the equal-set-weighted macro-MAE relative to USF-TDA from 0.252 eV (0.158 eV) to 0.102~eV (0.056~eV) with the ALDA0 (multicollinear) kernel. Its accuracy is competitive with state-specific $\mathrm{\Delta }$DFT and quasiparticle-energy DFT (QE-DFT), while being able to provide deeper mechanistic insight through the response vector. In particular, spin-adapted CV configurations provide selected higher-excitation character that strengthens the OO–CV dynamical-spin-polarization channel, which preferentially stabilizes the singlet states. We also identify an INVEST emitter with appreciable OO–OV mixing, suggesting a possible additional contribution to singlet stabilization when the CV contribution is small. The XSF-TDA method therefore provides practical singlet–triplet gap predictions together with interpretable state analysis for the screening and mechanistic understanding of MR-TADF and INVEST emitters.