Negative Singlet–Triplet Excitation Energy Gap in Triangle-Shaped Molecular Emitters for Efficient Triplet Harvesting

Abstract

The full harvesting of both singlet and triplet excitons can pave the way towards more efficient molecular light-emission mechanisms (i.e., TADF or Thermally Activated Delayed Fluorescence) beyond the spin statistics limit. This TADF mechanism benefits from low (but typically positive) singlet-triplet energy gaps or ∆E ST . Recent research has suggested the possibility of inverting the order of the energy of lowest singlet and triplet excited-states, thus opening new pathways to foster light emission without any energy barrier through triplet to singlet conversion, which is systematically investigated here by means of theoretical methods. To this end, we have selected a set of heteroatom-substituted triangle-shaped molecules (or triangulenes) for which ∆E ST < 0 is predicted. We successfully rationalize the origin of that energy inversion, and the reasons for which theoretical methods might produce qualitatively inconsistent predictions depending on how they treat n-tuple excitations (e.g., the large contribution of double excitations for all the ground-and excited-states involved). Unfortunately, the TD-DFT method is unable to deal with the physical effects driving this behaviour, which prompted us to the use here of more sophisticated ab initio methods such as SA-CASSCF, SC-NEVPT2, SCS-CC2, and SCS-ADC(2).

Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT

“…Furthermore, we note how the S 1 ← S 0 excitation energies are overestimated (severely in the case of 7AP) by both methods with respect to experimental or SCS-CC2 reference results. Note that many previous publications [14][15][16][17][18][19][20][21] already demonstrated how this was the case for all exchange-correlation functionals assessed up to now, which is also confirmed here.…”

“…Therefore, theoretical methods based on one-electron excitations (i.e., Time-Dependent Density Functional Theory or TD-DFT) are questioned in its current implementation to recognize that excited-state energy inversion, due to the lack of inclusion of higher-thansingle excitations into their formulation. In contrast, wavefunction methods have been shown in recent studies [14][15][16][17][18][19][20][21] to provide reasonably accurate values for that ∆E ST energy difference, although at a cost certainly higher than TD-DFT.…”

“…The set of systems selected is exclusively motivated by the previous experimental and theoretical findings mentioned above. The set of azaphenalene molecules shown in Figure 1 is known to display negative ∆E ST values at various wavefunction levels, from pioneering studies [14][15][16] later extended to related and/or larger systems [17][18][19][20][21], which clearly constitutes a challenge for any theoretical method.…”

Narrowband Deep-Blue Multi-Resonance Induced Thermally Activated Delayed Fluorescence: Insights from the Theoretical Molecular Design

“…Furthermore, several strategies for designing MR-TADF molecules have been presented, such as boron-nitrogen (BN) type [18][19][20][21], boron-oxygen type [19,22,23], and boron-carbonyl type [21,24]. Moreover, heterodoped MR-TADF emitters with triangulene backbone of different sizes have been reported [25][26][27][28][29][30]; researchers also synthesized the graphene-like BN-MR-TADF blue molecules B2 and B3 (Figure 1c,d), which are also promising blue TADF materials with small ∆E ST (0.15-0.18 eV) and narrow FWHM (32-34 nm) [31]. The representative MR-TADF compounds are a new class of polycyclic aromatic compounds, designed with fused planar structures containing boron and nitrogen (or oxygen).…”

Origin of The Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps

“…11 Sancho-Garcia and co-workers have suggested that small chemical modifications of the triangle derivatives can produce good candidates for inverted singlet-triplet gap using several correlated wave function methods. 13,19 While many wave function-based electronic structure methods, such as configuration interaction singles with doubles correction (CIS(D)) 20 , EOM-CCSD 18 and similarity transformed equation-of-motion coupled-cluster singles and doubles (STEOM-CCSD) 21,22 , have predicted inverted singlet-triplet gaps qualitatively correctly, one of the most widely used excited-state electronic structure method, linear response time-dependent density functional theory (LR-TDDFT) 23 has failed to predict the inversion of singlet-triplet gaps.Computational studies, in the past, pointed towards the inability of LR-TDDFT to incorporate double excitations by going beyond adiabatic approximation 24 as the source of this error. 10…”