Can ΔSCF and ROKS DFT-Based Methods Predict the Inversion of the Singlet-Triplet Gap in Organic Molecules?

Inverted singlet-triplet gap systems (INVEST) have emerged as an intriguing class of materials with potential applications as emitters in Organic Light Emitting Diodes (OLEDs). Indeed, this type of material exhibits a negative singlet-triplet energy gap (ΔE_ST), i.e., an inversion of the lowest singlet (S₁) and triplet (T₁) excited states, that goes against Hund's rule. In this study, the ΔE_ST of a set of 15 INVEST molecules has been computed within the framework of Restricted Open-Shell Kohn-Sham (ROKS) and Delta Self-Consistent Field (ΔSCF) methods and the results were benchmarked against wavefunction-based calculations performed at the EOM-CCSD, NEVPT2, and SCS-CC2 levels. We find that ROKS always (and wrongly) predicts a positive ΔE_ST with global hybrid, meta-GGA, and long-range corrected functionals and that this is almost functional-independent. We also show that the only way to obtain an inverted gap was to resort to double hybrid functionals. In contrast, using the above-mentioned functionals, ΔSCF usually gives a negative ΔE_ST, although the results are largely functional-dependent. Overall, applying a ΔSCF method based on the PBE0 functional provides the lowest MSD and MAD with respect to the EOM-CCSD results. We further show that the singlet-triplet inversion is driven by different degrees of orbital relaxation in the singlet versus triplet state and that this is well captured by ΔSCF calculations. As a matter of fact, this orbital relaxation in ΔSCF somehow mimics the involvement of double and higher-order excitations in EOM-CCSD, which leads to a difference in spatial localization of the α and β spins, and thus introduces (local) spin polarization effects sourcing the negative ΔE_ST. However, care should be taken when using the ΔSCF method to screen materials with potential INVEST behavior in view of their limited quantitative correlation with reference EOM-CCSD results on the molecular data basis used here.