Can SCF and ROKS DFT methods predict inverted singlet-triplet gap?: Benchmarking and rationalization

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 lowest 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) and have benchmarked these results against wavefunction-based methods, such as EOM-CCSD, NEVTP2 and SCS-CC2. We herein demonstrated that ROKS always predicts a positive ΔEST and has been shown to be almost functional-independent. Besides, the ΔSCF usually gives a negative ΔEST, although it is functional-dependent. Our findings indicate that the ΔSCF method together with the PBE0 functional provides the lowest MSD and MAD with respect to EOM-CCSD reference method. However, a very poor Pearson correlation coefficient was computed for all functionals whatever a ROKS or a ΔSCF scheme was employed. We also demonstrated that orbital relaxation and the difference in orbital set in the singlet and the triplet states are the fundamental reasons to ex-plain why ΔSCF is able to predict a negative energy gap. Indeed, we showed that they naturally involve the inclusion of double and higher-order excitations and a difference in spatial localiza-tion of the and spins wavefunctions resulting in spin polarization, namely one of the two reasons for observing a negative ΔEST together with a minimized exchange energy.