Can SCF and ROKS DFT-based methods predict the inversion of the singlet-triplet gap in organic molecules?

Inverted singlet-triplet gap materials (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 (ΔEST), i.e., an inversion of the low-est singlet (S1) and triplet (T1) excited states, that goes against Hund’s rule. In this study, the ΔEST 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 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 ΔEST 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 get an inverted gap was to resort to double hy-brid functionals. In contrast, using the above-mentioned functionals, ΔSCF usually gives a nega-tive ΔEST, although the results are largely functional-dependent. Overall, applying a ΔSCF meth-od based on the PBE0 functional provides the lowest MSD and MAD with respect to 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 calcula-tions. 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 locali-zation of the and spins, and accounts for spin polarization effects sourcing the negative ΔEST. 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.