It matters which double-hybrid is applied: On the sensitivity of singlet–triplet energy gaps in MR-TADF emitters to the ingredients of new models

In the quest for high-performance organic light-emitting diodes (OLEDs), the multiresonant thermally activated delayed fluorescence (MR-TADF) emitters are prominent choices owing to their narrowband emission profiles, high photoluminescence quantum yields, and remarkable chemical stability. As one of the greatest challenges governing the critical features of MR-TADF emitters, accurate modeling of the energy difference between the lowest singlet and triplet excited-states, known as the singlet-triplet energy gap, should be taken into consideration. To properly address this challenge from the theoretical viewpoint, balanced treatment of both electron correlation and double excitations is of paramount importance, where the double-hybrid (DH) functionals with a perturbative correlation taking doubly excited configurations into account can come into play. Hereby, in this work, we employ a series of MR-TADF emitters with experimentally measured singlet-triplet energy gaps as systems under study to systematically evaluate the performance of the DH functionals and propose new models, providing insight into their applicability for describing singlet-triplet energy gaps in MR-TADF emitters. Pragmatically, we first extend our earlier endeavors in the field by further developing several DH models free from any fitted parameter based on the spin-opposite-scaled (SOS) configuration interaction singles with perturbative doubles correction [CIS(D)]. Furthermore, through detailed comparisons, we have also assessed the performance of a variety of DHs, including parameterized, parameter-free, range-separated exchange, and the recently proposed spin-component-scaled (SCS) models, for the purpose. It is shown that many of the DHs cannot deliver reliable singlet-triplet energy gaps for the MR-TADF emitters, leading even incorrectly to inverted (negative) energy gaps. Furthermore, perusing the numerical data of the DHs discloses that neither the extreme fractions of nonlocal exchange and correlation nor the parameters in the direct and indirect terms alone suffice to ensure accurate results, but delivering reliable outcomes hinges on the balanced interplay among all the involved terms. In particular, from our presented DHs, the parameter-free models based on the regularized and restored strongly constrained and appropriately normed (r2SCAN) and Perdew-Burke-Ernzerhof (PBE) combined with a quadratic integrand (QI) paradigm, denominated as SOS0-CIS(D)-r2SCAN-QIDH and SOS0-CIS(D)-PBE-QIDH, respectively, demonstrate outstanding accuracy and computational efficiency for predicting the singlet-triplet energy gaps in MR-TADF emitters. On the other hand, from the already available functionals, there are also some methods that provide reasonable results, where the parameterized SOS-B2GP-PLYP21 model outperforms others. More importantly, in search of the qualified DHs that can simultaneously be applied not only to the MR-TADF emitters with positive singlet-triplet energy gaps but also to the inverted singlet-triplet (INVEST) emitters, another important message is uncovered, where our SOS0-CIS(D)-PBE-QIDH and SCS(SOS)-PBE-QIDH models emerged as promising candidates. We envisage that the recommended models in this study can be utilized as reliable computational tools to screening, rational design, and machine-learned applications in the field of OLED technology based on both MR-TADF and INVEST emitters, thus killing two birds with one stone.