(SOS1-)PBE-DH-INVEST double hybrid functionals for INVEST systems: Validation for azaphenalene compounds

INVEST systems (INVErted Singlet-Triplet excited-state energies) have attracted increasing interest due to their potential relevance in organic light-emitting diodes and photocatalytic applications. However, their accurate theoretical description remains challenging because the singlet-triplet energy gap, ΔEST, is strongly governed by electron-correlation effects and double-excitation contributions, which are not properly captured by conventional time-dependent density functional theory approaches. In this work, the recently developed double-hybrid density functional PBE-DH-INVEST, together with its spin-opposite-scaled variant SOS1-PBE-DH-INVEST, is assessed for the AP117 benchmark set of azaphenalene derivatives. Excitation energies for the S1 ← S0 and T1 ← S0 transitions, as well as the corresponding ΔEST values, were computed using the aug-cc-pVDZ basis set within the Tamm-Dancoff approximation and compared against CC2 reference data. The results show that PBE-DH-INVEST provides a robust description of both excitation energies and singlet-triplet gaps, with low deviations relative to the reference values and a marked improvement over the corresponding self-consistent hybrid treatment lacking double-excitation corrections. In particular, the inclusion of the Δ(D) contribution for double excitations is shown to be essential for reproducing the inverted energetic ordering characteristic of INVEST systems. The SOS1-PBE-DH-INVEST variant also yields competitive results at a reduced formal computational cost, although with slightly larger errors.