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.