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.