UTDA-xDH: Accurate Doublet–Doublet Excitation Energies via XYG3-Type Doubly Hybrid Density Functionals within the Unrestricted Tamm–Dancoff Approximation

We develop UTDA-xDH, an excited-state method that combines the XYG3-type doubly hybrid density functional (xDH) with the unrestricted Tamm-Dancoff approximation (UTDA). Three xDH methods, XYG3, XYGJ-OS, and xDH-PBE0, are assessed against a data set of doublet-doublet excitation energies of small radicals. All three xDHs exhibit excellent accuracy and robustness for both valence and Rydberg excitations, with mean absolute deviations of 0.07-0.13 eV. These results not only outperform conventional density functional theory methods but also rival the unrestricted equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method. Remarkably, the assessed xDHs show substantially reduced spin contamination compared to non-xDH counterparts, enabling highly accurate predictions even for challenging cases such as the ²Σ⁺ state of CNO. These results support (U)TDA-xDH as an efficient, broadly applicable excited-state approach for open- and closed-shell systems.