Valverde Danillo, Ricci Gaetano, Sancho-García Juan Carlos, Beljonne David, Olivier Yoann
Laboratory for Computational Modeling of Functional Materials, Namur Institute of Structured Matter, University of Namur, Rue de Bruxelles, 61, Namur B-5000, Belgium.
Laboratory for Chemistry of Novel Materials, University of Mons, Place du Parc, 20, Mons 7000, Belgium.
J Chem Theory Comput. 2025 Mar 11;21(5):2558-2568. doi: 10.1021/acs.jctc.4c01600. Epub 2025 Mar 1.
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 (Δ), i.e., an inversion of the lowest singlet (S) and triplet (T) excited states, that goes against Hund's rule. In this study, the Δ 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 Δ 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 Δ, 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 Δ. 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.
反向单重态 - 三重态能隙系统（INVEST）已成为一类一类有趣一类引人关注的材料，具有在有机发光二极管（OLED）中作为发光体的潜在应用。实际上，这类材料表现出负的单重态 - 三重态能隙（Δ），即最低单重态（S）和三重态（T）激发态发生反转，这与洪德规则相悖。在本研究中，在受限开壳层Kohn - Sham（ROKS）和Delta自洽场（ΔSCF）方法框架内计算了一组15个INVEST分子的Δ，并将结果与在EOM - CCSD、NEVPT2和SCS - CC2水平进行的基于波函数的计算进行基准对比。我们发现，ROKS使用全局杂化、meta - GGA和长程校正泛函时总是（且错误地）预测出正的Δ，并且这几乎与泛函无关。我们还表明，获得反向能隙的唯一方法是采用双杂化泛函。相比之下，使用上述泛函时，ΔSCF通常给出负的Δ，尽管结果在很大程度上依赖于泛函。总体而言，应用基于PBE0泛函的ΔSCF方法相对于EOM - CCSD结果具有最低的平均平方偏差（MSD）和平均绝对偏差（MAD）。我们进一步表明，单重态 - 三重态反转是由单重态与三重态状态下不同程度的轨道弛豫驱动的，并且这在ΔSCF计算中得到了很好的体现。事实上，ΔSCF中的这种轨道弛豫在某种程度上模拟了EOM - CCSD中双重和高阶激发的参与，这导致α和β自旋的空间局域化存在差异，从而引入了（局部）自旋极化效应，产生了负的Δ。然而，鉴于在此使用的分子数据基础上，ΔSCF方法与参考EOM - CCSD结果的定量相关性有限，在使用ΔSCF方法筛选具有潜在INVEST行为的材料时应谨慎。
