The important task of a TADF emitter is to convert triplet into singlet excitations. To do this, the reverse intersystem crossing rate, k rISC , should be high, which is only possible if the energy difference between the first singlet and the first triplet excited state is small, Δ E ST < 0.1   eV . A typical example of a TADF emitter is CzDBA (Wu et al., 2018), shown in Figure 1. CzDBA has a D- π -A- π -D architecture: two carbazole (Cz) fragments, two m-xylene bridges and a central 5,10-dihydroboranthrene (DBA) core. The methyl groups on the m-xylene bridge ensure that the core unit is nearly orthogonal to the π bridge, leading to a small overlap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) and hence nearly zero Δ E ST .

To ensure a broad recombination zone within the emission layer, the thin film of the TADF emitter should provide balanced and trap-free transport of holes and electrons. To realize this, one needs to select compounds with an ionization energy (IE) and electron affinity (EA) lying within the trap-free energy window (Kotadiya et al., 2019b), i.e., with ionization energy (IE) < 6.5 eV and electron affinity (EA) > 2.5 eV. These criteria ensure that contaminants such as oxygen or water do not serve as energetic traps for holes and electrons.

From a dipolar glass model, the energetic disorder present in a disordered molecular solid is proportional to the dipole moment of the composing molecule. Therefore, thin organic films with molecules with a small dipole moment (D) normally have a narrower density of states (Novikov and Vannikov, 2009; Lin et al., 2019; Mondal et al., 2021; Stankevych et al., 2021). This design criteria can be enforced by selecting centrosymmetric molecules only of the D- π -A- π -D or A- π -D- π -A type, similar to CzDBA. This molecular architecture ensures a small dipole moment and hence narrow density of states (Liu et al., 2021).

The combination of the core and the arm fragments gives in total 441 A- π -D- π -A and 504 D- π -A- π -D compounds. Due to convergence problems in geometry optimization, especially in the anionic state with implicit solvent, the final database contained 433 A- π -D- π -A and 481 D- π -A- π -D compounds.

The IE and EA of all compounds either lies within the “trap-free window” or close to the borderline of the window, showing that the effectiveness of prescreening of the building blocks. Therefore, we put our emphasis on the small Δ E ST criterion. The distributions of the E_S1 and ΔE_ST are shown in Figure 4 (A- π -D- π -A) and Supplementary Figure S2 (D- π -A- π -D). Around 50% of the compounds (206 out of 433 for A- π -D- π -A and 268 out of 481 for D- π -A- π -D) have very small singlet-triplet energy level splitting, Δ E ST < 0.1 eV, which illustrates the efficiency of the design strategy, that is the use of the m-xylene bridge. Moreover, the computed S 1 energy and Δ E ST of CzDBA is 2.487 and 0.016 eV, which is in excellent agreement with the experimental values of 2.48 and 0.033 eV (Wu et al., 2018; Kotadiya et al., 2019a).

Among these small- Δ E ST compounds, we observed a broad distribution in the S 1 energy, ranging from 0.2 to 2.9 eV. This indicates the opportunity to design single-layer emitting OLEDs of different colors, including the infrared region. The two branches in Figure 4 represent the rest (50%) of the emitters with Δ E ST > 0.1 eV, where a similar branch is also observed for D- π -A- π -D (Supplementary Figure S3). This is counterintuitive as the Δ E ST should be small if the HOMO and the LUMO are separated via the m-xylene bridges.

To better understand the origin of the large Δ E ST , we calculated the charge transfer (CT) number ranging from 0 to 1, using the fragment-based analysis (see Supplementary Note S2). We define the core as one fragment (f_C) and two bridge + arm pairs as the other fragment (f_A). If the hole is 100% located at one fragment and the electron is 100% located at the other one, the charge transfer number is 1, representing a 100% CT character. In contrast, if the hole and the electron are both localized on the same fragment, the CT number is 0, featuring a local-excitation (LE) character. In most cases, the CT number is a fraction between 0 and 1 since most adiabatic excited states exhibit a mixture of CT and LE characters. The larger the CT number of the excited state is, the higher the CT character it has.

Figure 5 depicts the 2D histogram based on the CT numbers of T₁ and S₁ states for the 227 A- π -D- π -A compounds with Δ E ST > 0.1 eV. Most of the scatter points are located at the upper left corner, meaning that these emitters possess a charge-transfer S₁ and locally-excited T₁ states. A similar result was observed in the D- π -A- π -D case (see Supplementary Figure S4).

The emergence of the LE states can be explained utilizing the frontier molecular orbital (FMO) energies of the constituent building blocks (Blaskovits et al., 2020), which is illustrated in Figure 6A. The competition between the CT excitation and LE excitation depends on the relative ordering of the FMOs. In this context, we can define two descriptors, R A = ( E LUMO A − E HOMO A ) / ( E LUMO A − E HOMO D ) , R D = ( E LUMO D − E HOMO D ) / ( E LUMO A − E HOMO D ) , where E LUMO / HOMO A / D are the LUMO/HOMO energies of the acceptor/donor. If the R A or the R D is much larger than 1, the CT excitation is more favorable than the LE for the low-lying excited states and vice versa. Figure 6B demonstrates that this simple approximation works quite well for our A- π -D- π -A database: For R A or R D smaller than ∼1.2, the CT number of T₁ becomes close to 0. The same behavior was also found in the D- π -A- π -D database, as shown in Supplementary Figure S5. This indicates that a prescreening step based on the individual building blocks saves the computational cost, similar to pre-screening of singlet fission donor-acceptor copolymers (Blaskovits et al., 2020).

The S₁ and T₁ states of most molecules that pass the first screening step ( Δ E ST < 0.1 eV) exhibit CT character. According to the El-Sayed rule, the k rISC is zero between two states having the same excited-state character, which implies that the rISC may not occur for these pre-screened compounds. However, the conformational disorder present in the solid state leads to a distribution of dihedral angles between the constituent donor and acceptor (Weissenseel et al., 2019). This disorder gives rise to different excited-state characters, that is different mixing of CT and LE diabatic states of the S₁ and T₁ states, (de Silva et al., 2019), resulting in non-zero k rISC . This explains why TADF could still be observed in the thin film of CzDBA, where CT_S1 and CT_T1 are both close to 1 in the gas phase (Kotadiya et al., 2019a).

In addition, higher triplet states (T _n with n > 1 ) with different excited-state character from that of S₁, can also assist in the rISC process via a two-step mechanism (Gibson et al., 2016). A large second order coupling can be achieved when the energies of S₁, T₁ and T _n are close to each other. Compounds with close-lying S₁ and T₁ that already show different excited-state characters would possess large first-order coupling and hence high k _rISC. Therefore, we applied additional screening criteria to the as-screened ∼500 molecules: 1) there should be at least one triplet state T_n that is close to S₁ (| E_S1 − E_{T n} | < 0.1 eV); 2) for the triplet states that are energetically close to S₁, the difference between the CT numbers of S₁ and T_n should be larger than 0.5 (CT_S1 −CT_{T n} > 0.5) to give reasonable spin-orbit coupling.

Overall, around 100 molecules pass the criteria (49 A- π -D- π -A and 46 D- π -A- π -D), where the molecular structures are summarized in Figure 7. All of these compounds, except for A- π -D- π -A molecules with non-centrosymmetric core boant4 ( D = 4 − 5 Debye), possess nearly zero molecular dipole moment. Therefore, they are considered promising candidates for single-layer OLED emitters. The position of the electroluminescence (EL) spectrum maximum of each compound, as shown in Figure 7, was estimated by subtracting the computed S₁ energy by a value δ, which is defined as δ = E S 1 − λ E L , m a x = 2.480 − 2.214 = 0.266   eV , where E_S1 and λ _EL,max is the experimental optical gap and the wavelength of the EL spectrum maximum of CzDBA (Kotadiya et al., 2019a). These values are listed in Supplementary Tables S1,S2. We obtained a series of potential TADF emitters with various EL spectrum maximum, ranging from infrared (0.716 eV) to blue color (2.660 eV), which paves the way for future development of single-layer OLED devices.

More sophisticated solid-state simulations can then be performed for the much smaller molecular dataset, which is now only ∼10% of the initial number of compounds. As a proof of concept, we computed the charge carrier density of states for the blue A- π -D- π -A emitter, 37bdt1-ant2 (as shown in Figure 8). The amorphous simulated morphology was generated using molecular dynamics, where the details can be found in Supplementary Note S4. The energetic disorder for electrons (0.11 eV) and holes (0.12 eV) is relatively small, which indicates a good hole/electron mobility. This also demonstrates the success of our design strategy regarding small molecular dipole moment. Since the simulated IE and EA of 37bdt1-ant2 lie at the border of the trap-free window, further experimental measurements are necessary to verify if it is really free from universal traps.